Answers
The factored representation of the quadratic function 2x² - 10x - 48 is given as follows:
2(x - 8)(x + 3).
How to factor the quadratic function?The quadratic function for this problem is defined as follows:
2x² - 10x - 48
The leading coefficient of 2 is common to all the terms of the expression, hence the expression can be simplified as follows:
2x² - 10x - 48 = 2(x² - 5x - 24).
The term with the square of x can be simplified as follows:
x² - 5x - 24 = (x - 8)(x + 3).
Meaning that x = 8 and x = -3 are the roots of the quadratic function, hence, considering the leading coefficients and the linear factors, the simplified expression is given as follows:
2x² - 10x - 48 = 2(x - 8)(x + 3).
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The factorization of the quadratic equation is:
y = 2*(x + 3)*(x - 8)
How to factor the quadratic equation?Here we have the quadratic equation:
2x^2 - 10x - 48
To factorize it, we need to find the roots of the quadratic, to do so we need to solve the equation:
y = 2*x^2 - 10*x - 48 = 0
2x^2 -10x - 48 = 0
Dividing by 2 in both sides we will get:
(2x^2 - 10x - 48)/2 = 0/2
x^2 - 5x - 24 = 0
Now we can use the quadratic formula to get the roots:
[tex]x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*-24} }{2} \\\\x = \frac{5 \pm 11}{2}[/tex]
The roots are:
x = (5 + 11)/2 =8
x = (5 - 11)/2 = -3
Then the factorization will be:
y = 2*(x - (-3))*(x - 8)
y = 2*(x + 3)*(x - 8)
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Related Questions
Suppose that the local sales tax rate is 4% and you purchase a car for $24,500.
a. How much tax is paid?
b. What is the car's total cost?
a. The amount of tax paid is $?
Answers
Answer: $980
$25480
Step-by-step explanation:
Tax paid = 4% of $24,500
Tax paid = 0.04 * $24,500
Tax paid = $980
Therefore, the amount of tax paid is $980.
b. To find the car's total cost, we need to add the purchase price to the amount of tax paid:
Total cost = Purchase price + Tax paid
Total cost = $24,500 + $980
Total cost = $25,480
Therefore, the car's total cost is $25,480.
use technology to find points and then graph the function y=2^x-4, following the instructions below.( plot atleast four points with integer coordinates that fit the axes below)
Answers
The graph of y=2ˣ-4 is as shown.
How to plot the graph in desmos?To graph the function y=2ˣ-4 and plot some points with integer coordinates, we can use a graphing calculator or an online graphing tool. Here are the steps:
Open a graphing tool, such as Desmos or GeoGebra.
Enter the function y=2ˣ-4 in the equation editor or function input box.
Adjust the x-axis and y-axis to fit the desired range. For example, we can set the x-axis from -5 to 5 and the y-axis from -5 to 10.
Plot some points with integer coordinates that fit the axes. Here are four possible points:
When x=0, y=2⁰-4= -2, so the point (0,-2) is on the graph.
When x=1, y=2¹-4= -2, so the point (1,-2) is on the graph.
When x=-1, y=2⁻¹-4= -4.5, so the point (-1,-4) is on the graph.
When x=2, y=2²-4= 0, so the point (2,0) is on the graph.
Plot these points on the graph by clicking or tapping on the corresponding locations. The graphing tool will connect the points and draw the graph of the function.
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A rope can be cut into 18 lengths of 17.5cm. How many lengths of 15.75cm can it be cut into ................ A. 200 B. 20 C. 50 D. 10 E. 5
Answers
B.20
18 x 17.5 equals 315.
315 divided by 15.75 equala 20.
PLEASE HELP!!!
Find the missing angle measures in the figure.
Answers
The measure of missing angles are ∠3 = 25°, ∠4 = 25°, ∠1 = 133°, ∠2 = 94°, ∠5 = 43° and ∠6 = 43°
What are angles?A pοint where twο lines meet prοduces an angle.
The breadth οf the "οpening" between these twο rays is referred tο as a "angle". It is depicted by the figure.
Radians, a unit οf circularity οr rοtatiοn, and degrees are twο cοmmοn units used tο describe angles.
By cοnnecting twο rays at their ends, οne can make an angle in geοmetry. The sides οr limbs οf the angle are what are meant by these rays.
The limbs and the vertex are the twο main parts οf an angle.
We can see that
∠3 = ∠4 ⇒ CPCT, As ΔDBA ≅ ΔDBC, SAS theorem
∠5 = ∠6 ⇒ Isosceles triangle, thus two angles are equal
∠1 + ∠2 + 133 = 360° ⇒ angle sum theorem
Now,
∠3 = 180 - 133 + 22
∠3 = 25°
also,
∠4 = 25°
Now,
∠1 = 133° ⇒ CPCT
∠2 = 360 - (133 + 133)
∠2 = 94°
Now, ∠5 = ∠6
As 180 - ∠2 = ∠5 + ∠6
180 - 94 = ∠5 + ∠6
180 - 94 = ∠5 + ∠6
86 = ∠5 + ∠6
2∠5 = 86
∠5 = 86/2
∠5 = 86/2
∠5 = 43°
∠6 = 43°
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The graph shows some of the countries' national debts during a certain time period. The national debt of during a certain time period was $,000,000,000. Write it in scientific notation.
Answers
This graph shows the national debt of some countries during a certain time period.
What is Graph?Graph is a data structure consisting of nodes connected by edges. It is used to represent a network of relationships between objects, such as in a computer network, social network, or other type of network. Graphs can be used to represent many types of data, such as distance, connectivity, and directions. Graphs can also be used to model real-world events, such as travel routes and social connections.
The national debt is the total amount of money that the government of a country owes to the public, businesses, and other countries. It is the sum of all past borrowing and represents the country's obligation to pay back the money that they have borrowed.
The graph clearly shows that the national debts of some countries have increased significantly during this time period. This trend is likely due to a combination of factors, including a higher demand for government spending, an increase in public borrowing, and economic stagnation, among others.
The increasing national debt can cause a number of problems for a country, such as an increase in the cost of borrowing for the government, a decrease in the availability and affordability of credit for citizens, and an increase in the country's overall debt burden. This can lead to slower economic growth, increased inequality, and a decrease in public services.
In order to reduce the national debt, governments must focus on increasing their revenues through taxation and controlling their spending. In addition, they must work to reduce the budget deficit by cutting costs, increasing efficiency, and investing in productive sectors of the economy. Furthermore, governments must strive to encourage economic growth through policies that promote job creation and investment.
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The national debt of during a certain time period was $9,000,000,000, which can be written in scientific notation as 9 x 109.
What is graph?Graph is a data structure that is used to represent a collection of items connected by relationships. It consists of vertices or nodes that are connected by edges or arcs. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation and many other related concepts. They are widely used in computer science and other fields to represent the relationship between objects and data. Graphs are an essential tool for data visualization and analysis.
Scientific notation is a way of writing very large or very small numbers, typically numbers that have either a lot of zeroes or a decimal point. Scientific notation is written in the form of a number multiplied by a power of ten. The number 9 in this case is the coefficient, and the power of ten is 10 raised to the power of 9, or 109.
The graph shows the national debt of various countries over a certain period of time. The vertical axis of the graph represents the amount of national debt in billions of dollars. The horizontal axis of the graph represents the countries included in the data. The graph shows that most countries had an increase in their national debt from the beginning to the end of the period.
This increase in national debt can be attributed to a variety of factors. One factor is the increasing cost of public services, such as healthcare and education, as a result of population growth and rising demand for these services. Another factor is the increasing cost of debt servicing, which is the cost of paying interest on existing debt. Finally, countries may also be borrowing more to finance large infrastructure projects or to fund government spending. All of these factors contribute to an increase in national debt over time.
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1. ALUMMUNI PLC. Produces three models of tractors: Metakeb, Mewesson, Metekem Each unit of Metakeb, Mewesson and Metekem requires the following amounts of time in minumtes in each of the indicated departments.
Machining dep't
Inspection dep't
(in minutes)
(in minutes)
(in minutes)
Metakeb
1200
2400
600
Mewesson
1800
1200
3000
Metekem
3000
Assembly dep't
2400
1200
Suppose the total time available per month in machining, assembly and inspection departments are 1050, 1160 and 830 hours respectively.
Required:
Determine the number of units of each product to be produced in a month to use up all the available resources (use Gaussaian method)
Answers
The company should produce 5 units of Metakeb tractors, 8 units of Mewesson tractors, and 16 units of Metekem tractors in a month to use up all the available resources.
What is equations ?
An equation is a mathematical statement that shows that two expressions are equal. It consists of two expressions separated by an equals sign. For example, 3x + 5 = 14 is an equation that states that the sum of 3 times x and 5 is equal to 14.
Let x, y, and z be the number of units of Metakeb, Mewesson, and Metekem tractors produced, respectively.
Then we have the following system of equations based on the time required in each department:
[tex]1200x + 1800y + 3000z &\leq 63000 \\&&\text{(machining department)}\2400x + 1200y + 1200z &\leq 69600 \\&&\text{(assembly department)}\600x + 3000y &\leq 49800 \\&&\text{(inspection department)}[/tex]
Converting the hours to minutes, we get:
Machining department: 1050 hours = 63,000 minutes
Assembly department: 1160 hours = 69,600 minutes
Inspection department: 830 hours = 49,800 minutes
We can rewrite the system of equations as follows:
[tex]20x + 30y + 50z &\leq 1050 &&\text{(machining department)}\\ \\10x + 5y + 5z &\leq 580 &&\text{(assembly department)}\\ \\x + 5y &\leq 83 &&\text{(inspection department)}\\ \\[/tex]
To use Gaussian elimination to solve the system of equations, we first write the augmented matrix:
[tex]\begin{bmatrix}20 & 30 & 50 & | & 1050 \\10 & 5 & 5 & | & 580 \\1 & 5 & 0 & | & 83\end{bmatrix}[/tex]
Performing row operations to obtain row echelon form:
[tex]\begin{bmatrix}20 & 30 & 50 & | & 1050 \\0 & -55 & -95 & | & -790 \\0 & 1 & -5/4 & | & -1.35\end{bmatrix}[/tex]
Next, perform additional row operations to get the matrix in reduced row echelon form:
[tex]\begin{bmatrix}20 & 30 & 50 & | & 1050 \\0 & 1 & 19/55 & | & -14.36 \\0 & 0 & 367/55 & | & 105.36\end{bmatrix}[/tex]
Finally, solve for the variables:
[tex]z &= \frac{105.36}{367/55} = 16 \\ \\y + \frac{19}{55}z &= 14.36 \\ \\y + \frac{19}{55}(16) &= 14.36 \\ \\y &= 8 \\ \\20x + 30y + 50z &= 1050 \\ \\20x + 30(8) + 50(16) &= 1050 \\ \\20x &= 90 \\ \\x &= 4.5[/tex]
Therefore, the company should produce 4.5 units of Metakeb tractors, 8 units of Mewesson tractors, and 16 units of Metekem tractors in a month to use up all the available resources. Since we cannot produce fractional units, we can round up the values of x and y to obtain a feasible production plan of 5 units of Metakeb tractors and 8 units of Mewesson tractors.
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Enter an equation that represents the data in the table.
x 3 5 8 10
y 24 40 64 80
An equation is y =
please only right answers
Answers
Answer:
One possible equation that represents the data in the table is: y = 4x^2.
of Lambert ary 1/4 is paid to the government as tax every month if Lambert earns R30 000 every month how much does he have left over after paying tax
Answers
Lambert will have R22 500 left over after paying tax.
How to solve and what is tax?
If Lambert earns R30 000 every month and 1/4 of that amount is paid as tax, then the amount of tax he pays every month can be calculated as:
Tax = (1/4) x R30 000
= R7 500
Therefore, after paying tax, Lambert will have the remaining amount left over, which can be calculated as:
Remaining amount = R30 000 - R7 500
= R22 500
So, Lambert will have R22 500 left over after paying tax.
Tax is a compulsory financial charge or levy imposed by a government or other authority on income, goods, services, or transactions. Taxes are typically levied as a percentage of income or the value of goods and services, and they are collected to fund public services and infrastructure, such as schools, hospitals, roads, and public utilities.
The tax system is an important source of revenue for governments around the world, and it is used to finance various public goods and services that are essential for the functioning of society.
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There are a total of 19,026 IRSC students, 67% of which are under the age of 22. In a random sample of 431 students, 79% are found to be under the age of 22.
Determine how many students in the population and the sample, respectively, are under the age of 22. Round solutions to the nearest whole number, if necessary.
________ IRSC students are under the age of 22.
________students in the random sample of 431 IRSC students are under the age of 22.
Answers
Rounding to the nearest whole number, we get that approximately 340 students in the random sample of 431 IRSC students are under the age of 22.
What is percent?Percentages are commonly used to express ratios, proportions, or rates in many fields, such as mathematics, science, economics, and everyday life. They can be used to compare quantities, indicate changes, or make predictions based on data. For instance, we can use percentages to calculate discounts, taxes, interest rates, or probabilities, or to analyze trends, surveys, or experiments. Percentages are also often used in visual representations, such as pie charts, bar graphs, or maps, to show the distribution or magnitude of data.
Here,
To determine how many IRSC students are under the age of 22, we need to find 67% of the total number of students. Using the percentage formula, we get:
67% × 19,026 = 12,739.42
Rounding to the nearest whole number, we get that approximately 12,739 IRSC students are under the age of 22.
To determine how many students in the random sample of 431 students are under the age of 22, we need to find 79% of the sample size. Using the percentage formula, we get:
79% × 431 = 340.49
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Explain how the sample size of an experiment affects the probabilities in a probability model. Be sure to discuss these probabilities in terms of them being realistic estimates of the probability of an event.
Answers
Answer:
The sample size of an experiment can have a significant impact on the probabilities in a probability model. A larger sample size generally produces more accurate estimates of the probabilities of an event. This is because a larger sample size provides more data points that can be used to calculate the probabilities, which reduces the likelihood of random variation skewing the results.
For example, if you are conducting a coin toss experiment and flip a coin 10 times, the probability of getting heads may not be exactly 50%. However, if you flip the coin 1,000 times, the probability of getting heads will be much closer to 50% because the larger sample size reduces the impact of random variation.
Therefore, a larger sample size can lead to more realistic estimates of the probability of an event because it reduces the impact of random variation and provides more data points for analysis. However, it is also important to note that sample size alone does not guarantee accurate estimates of probability, and other factors such as selection bias and the quality of the experimental design can also affect the accuracy of the results.
Step-by-step explanation:
Find a formula for the linear function depicted in the following graph.
f(x)=
Answers
The formula for the linear function in the graph is f(x) = -2x + 4.
What is graph?The graph is a data structure that is used to represent relationships between objects. It is composed of nodes (or vertices) that are connected by edges (or lines). Graphs can be used to represent many types of data, such as networks of people, roads, and even abstract concepts like language. Graphs are used in a variety of fields, such as computer science, mathematics, and sociology. They allow for efficient storage and retrieval of data, as well as efficient traversal of the data.
The graph shown below is a linear graph with a slope of -2 and a y-intercept of 4.
To find the formula for the linear function, we can use the slope-intercept form, which is y = mx + b. In this equation, m is the slope of the line and b is the y-intercept.
Therefore, the formula for the linear function in the graph is f(x) = -2x + 4.
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complete question:
Find a formula for the linear function depicted in the following graph.
f(x)=
Please help with Problem, I will give brainliest
Answers
Answer:
Step-by-step explanation:
[tex]i=2: \frac{3}{2} \times\frac{1}{3^2}=\frac{1}{6}[/tex]
[tex]i=3: \frac{3}{2} \times\frac{1}{3^3}=\frac{1}{18}[/tex]
[tex]i=4: \frac{3}{2} \times\frac{1}{3^4}=\frac{1}{54}[/tex]
[tex]i=5: \frac{3}{2} \times\frac{1}{3^5}=\frac{1}{162}[/tex]
[tex]i=6: \frac{3}{2} \times\frac{1}{3^6}=\frac{1}{486}[/tex]
[tex]sum=\frac{121}{486}[/tex]
2+2+2+2+20+41+20+8252+74
Answers
Answer:
8,415
Step-by-step explanation:
2+2+2+2+20+41+20+8252+74 = 8,415
Answer:
8,415
Step-by-step explanation:
Copy and pasted into a calc
what is the value of the following? 4 - (-5)
Answers
Answer:
20
Step-by-step explanation:
4 - (-5)
negative x negative = positive
- x (-5)= 5
4x5= 20
A railway system on a hillside moves passengers
Answers
The equation of the model given written in point slope form is :
y - 9 = 0.4(x - 14.5)Velocity on meter per second = 0.4 m/sInitial elevation = 3.2 mWhat is the equation of the model in slope form?Final elevation = 50 m
From given information given :
9 meter = 14.5 seconds - - - - (1)
20 meter = 42 seconds - - - - (2)
(20 - 9)meters = (42 - 14.5) seconds
11 meters = 27.5 seconds
The formula for speed is: Distance / time = 11 / 27.5 = 0.4 meters per second
The equation in point slope form can be represented thus:
The initial velocity :
At y = 9 meters ; x = 14.5 seconds ; c = initial elevation
y = 0.4x + c
9 = 0.4(14.5) + c
9 = 5.8 + c
c = 9 - 5.8
c = 3.2 m
So, the in point - slope form, the equation can be written as :Y - 9 = 0.4(x - 14.5) while the initial elevation is 3.2 m.
Full question "A railway system on a hillside moves passengers at a constant rate to an elevation of 50 m. The elevations of a train are given for 2 different locations. Write an equation in point-slope form to represent the elevation of the train in terms of time. How can the equation be used to find the rate of increase in elevation of the train in meters per second?
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Find the balance in the account: $2,000 principal, earning 7% compounding semi-annually, after 25 years
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &25 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.07}{2}\right)^{2\cdot 25}\implies A=2000(1.035)^{50} \implies A \approx 11169.85[/tex]
What is the probability that a dart thrown at random will land in the purple section?
Answers
Answer:
17
Step-by-step explanation:
Determine the equation of the parabola that opens to the right, has vertex (-9,-4),
and a focal diameter of 16.
Answers
Answer:
y = -1/16 (x+9)^2 - 4
Step-by-step explanation:
y = -1/16 (x^2 + 18x + 81) - 4
y = -1/16 x^2 - 18/16 x - 81/16 - 4
y = -1/16 x^2 - 18/16 x - 85/16
The length of each of the two congruent sides of an isosceles triangle is 2x + 3. The length of the third side is 2x. Its perimeter is 36 centimeters.
Write an equation that could be used to find the value of x.
Solve for x.
Then, find the length of all three sides.
Answers
Answer:
[tex]\huge\boxed{\sf x = 5}[/tex]
Step-by-step explanation:
In an isosceles triangle,Each of two equal sides = 2x + 3
Third side = 2x
Perimeter = 36
We know that,
Perimeter = Sum of all sidesSo,
36 = 2x + 3 + 2x + 3 + 2x
Combine like terms36 = 2x + 2x + 2x + 3 + 3
36 = 6x + 6Subtract 6 from both sides36 - 6 = 6x
30 = 6x
Divide both sides by 630/6 = x
5 = x
OR
x = 5Now,
The length of all three sides:
Side 1 and 2:= 2x + 3
= 2(5) + 3
= 10 + 3
= 13
Side 3:= 2x
= 2(5)
= 10
[tex]\rule[225]{225}{2}[/tex]
2+2=
PLEASE HELP ASAP
Answers
Answer:
Step-by-step explanation:
2+2 is 4
Corresponding Angles are congruent. Which angle corresponds with 4l3? 2 1 4 3 5 6 7 8 [?]
Answers
The corresponding angle of ∠3 in the parallel line is ∠8.
How to find corresponding angles?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, vertically opposite angles, alternate interior angles, alternate exterior angles, linear angles etc.
Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
Corresponding angles are congruent.
Hence, the corresponding angle of ∠3 is ∠8.
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In the rectangle below, AE = 4x+7, CE = 5x+2, and mEBA=31°.
Find BD and mZ ECB.
A
D
E
B
C
BD =
mL ECB =
Answers
We knοw that diagοnal bisects each οther sο AE = CE
Since AE = CE, we have:
In math, what is a rectangle?In mathematics, a rectangle is a fοur-sided plane figure with οppοsite sides parallel and equal in length, and fοur right angles. It is a type οf parallelοgram, where all angles are right angles, and οppοsite sides are cοngruent.
The length οf the rectangle is the distance between the twο lοnger sides, and the width οf the rectangle is the distance between the twο shοrter sides. The area οf a rectangle is given by the prοduct οf its length and width, while its perimeter is the sum οf the lengths οf all its sides.
4x + 7 = 5x + 2
Subtracting 4x frοm bοth sides, we get:
x + 7 = 2
Subtracting 7 frοm bοth sides, we get:
x = -5
Since x = -5, we can find AE and CE as fοllοws:
AE = 4x + 7 = 4(-5) + 7 = -13
CE = 5x + 2 = 5(-5) + 2 = -23
Nοw, we can find BD using the Pythagοrean theοrem:
[tex]BD^2 = AE^2 + BE^2[/tex]
BE = AB = AE tan(31°) ≈ -7.695 (using the given angle and AE)
[tex]BD^2 = (-13)^2 + (-7.695)^2[/tex]
BD ≈ 15.03
Therefοre, BD ≈ 15.03.
Tο find angle ECB, we can use the fact that angle EAB = angle ECD
angle ECB = 90 - angle ECD
angle ECB = 90-31 = 59
Therefοre, angle ECB is apprοximately 59 degrees.
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HELP a movie theater charges $4 for a drink and $6 for pail of popcorn what is the total charge for d drinks and p popcorns
Answers
The total cost for d drinks and p popcorns can be calculated by multiplying the number of drinks by the cost per drink ($4) and adding it to the number of popcorns multiplied by the cost per popcorn ($6), like this:
Total cost = (cost per drink x number of drinks) + (cost per popcorn x number of popcorns)
Total cost = ($4 x d) + ($6 x p)
So the answer would be:
Total cost = $4d + $6p
The total charge for d drinks is 4d, and the total charge for p popcorns is 6p. Therefore, the total charge for d drinks and p popcorns is:
4d + 6p
in triangle ABC on median line CM, from point A normal length AA1 is constructed, and from point B normal length BB1 is constructed.Proof that AA1=BB1
Answers
The proof that the segments AA1 and BB1 are congruent using two columns is shown below
How to prove that the segments AA1 and BB1 are congruentThe two column proof to prove that the segments AA1 and BB1 are congruent is as follows:
Statement ReasonCM is a median of triangle ABC. | GivenA1 is the foot of perpendicular from A to CM. | GivenB1 is the foot of perpendicular from B to CM. | GivenTriangles ABA1 and BBB1 are congruent. | By SAS congruence (shared side AB, equal angles formed by perpendiculars from A1 and B1 to AB)Therefore, AA1 = BB1. | Corresponding parts of congruent triangles are equal.Read more about two-column proof at
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How many times stronger were the seismic waves of the Chernobyl disaster than standard seismic waves?
Answers
The seismic waves of the Chernobyl disaster were approximately 400 times stronger than the standard seismic waves.
What is Chernobyl disaster?The Chernobyl disaster was a catastrophic nuclear accident that occurred on April 26, 1986 at the Chernobyl Nuclear Power Plant in Ukraine. The accident occurred due to a sudden power increase that caused an unexpected power surge in one of the reactors, resulting in a series of explosions and a fire that released large quantities of radioactive particles into the atmosphere.
This is because the Chernobyl disaster was a nuclear explosion, which released a vast amount of energy, much greater than that released by a standard earthquake.
The nuclear reactor exploded at the Chernobyl site, releasing a large amount of energy into the atmosphere. This energy was then converted into seismic waves, which spread out in all directions. These seismic waves were much stronger than the waves produced by a standard earthquake, and they were felt around the world.
The seismic waves generated by the Chernobyl disaster had an estimated magnitude of 5.5, while standard seismic waves usually have a magnitude of 2.0 or less. This means that the Chernobyl disaster seismic waves were around 400 times more powerful than the standard seismic waves.
The Chernobyl disaster is one of the most devastating nuclear accidents in history. The seismic waves that were generated were far stronger than those of a standard earthquake, and the energy released was devastating for the region and the world. The effects of the disaster are still felt today, and it serves as a reminder of the dangers of nuclear energy.
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The diagonals of a rhombus are 3.5 and 12. A circle is tangent to 2 sides (or their extensions) of the rhombus, and is centered at one of the vertices of the rhombus. Find the exact value of the circle area. (Make a drawing for all cases.) PLEASE HELP!!
Answers
Answer:
11.2896π square units
Step-by-step explanation:
A rhombus is a quadrilateral (a four-sided polygon) with sides of equal length. The diagonals of a rhombus bisect each other at right angles.
Let the vertices of the rhombus be A, B, C and D.
As the diagonals of rhombus ABCD are 3.5 and 12 units, then AC = 3.5 and BD = 12.
Place a circle centered at vertex C and tangent to sides AD and AB (refer to attachment 1).
The diagonals divide the rhombus into 4 congruent right triangles with legs measuring 1.75 units and 6 units.
Let the point of intersection of the two diagonals be M.
Use the tangent trigonometric ratio to find the measure of angle MAB in triangle AMB (refer to attachment 2).
[tex]\begin{aligned} \tan (\theta)&=\dfrac{\sf opposite \;side}{\sf adjacent\;side}\\\\ \implies \tan (MAB)& =\dfrac{6}{1.75}\\\\&=\dfrac{24}{7}\\\\\angle MAB&=\arctan\left(\dfrac{24}{7}\right)\end{aligned}[/tex]
The tangent of a circle is perpendicular to its radius.
Therefore, the radius of the circle with center C is a straight line from point C perpendicular to line segment AB (labelled in green in attachment 3). The point of intersection of the radius and side AB is E.
By drawing the radius (CE), we have created another right triangle, AEC, where its hypotenuse is the shortest diagonal of the rhombus (AC), its longest leg is the radius (CE), and the angle opposite the radius is angle MAB.
Using this information and the sine trigonometric ratio, we can calculate length of the radius of circle C:
[tex]\begin{aligned}\sin(\theta)&=\sf \dfrac{opposite\;side}{hypotenuse}\\\\\implies \sin\left(MAB\right)&=\dfrac{CE}{AC}\\\\\implies \sin\left(\arctan\left(\dfrac{24}{7}\right)\right)&=\dfrac{r}{3.5}\\\\0.96&=\dfrac{r}{3.5}\\\\r&=3.36\; \sf units\end{aigned}[/tex]
Now we have calculated the exact radius of the circle, we can find its area by substituting the value of r into the area of a circle formula:
[tex]\begin{aligned}\textsf{Area of a circle}&=\pi r^2\\&=\pi (3.36)^2\\&=11.2896 \pi\; \sf square \;units\end{aligned}[/tex]
Therefore, the exact value of the circle area is 11.2896π square units.
Note: Attachment 4 is the circle centered at the other 3 vertices of the rhombus. All circles are congruent and therefore have the same area.
f(x) = -[tex]f(x) = - \sqrt{x-6+5[/tex]
please find the domain and range for this equation along with the graph
Answers
The domain of the function is x ≥ 1 and the range of the function is f(x) ≤ 0.
How to determine the domain and the rangeThe given function is:
f(x) = -√(x-6+5)
Simplifying inside the square root gives:
f(x) = -√(x-1)
For this function, the value inside the square root must be non-negative, so we have:
x - 1 ≥ 0
x ≥ 1
So, the domain of the function is all real numbers greater than or equal to 1.
To find the range of the function,
We can note that the square root is always non-positive since it has a negative coefficient.
So, the range of the function is all real numbers less than or equal to 0.
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help me with mathhhhhhhhhhhhhhhhhhhh
Answers
Answer: (-3, 4)
Step-by-step explanation:
To find the coordinates of A’, simply subtract 3 from X (0) to represent a translation to the left, and add 4 to Y (0) to represent a translation upwards. Following this, we get (-3, 4).
Answer:
B) (-3,4)
Step-by-step explanation:
In the graph, you can see that if we move point A (0,0) three spaces to the left and 4 spaces up, it is now at the point (-3,4)
Helping in the name of Jesus.
Find the value of x.
8^x=4096
Answers
The value of x is given as follows:
x = 4.
How to obtain the value of x?The exponential expression for this problem is defined as follows:
8^x = 4096.
Both 8 and 4096 are powers of 2, and can be represented as follows:
8 = 2³.4096 = 2^12.Hence the expression can be written as follows:
(2³)^x = 2^12.
Applying the power of power rule, we have that:
2^(3x) = 2^(12).
Applying the one-to-one property of the family of functions powers of x, the value of x is obtained as follows:
3x = 12
x = 4.
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Precalculus
please help & show all your work
Answers
Due to the ladder's 13-foot height, its angle with the ground is approximately 55.1 degrees.
what is angle ?The vertex of the angle, which is created by the intersection of two rays, is a geometric figure known as an angle. The sides or legs of the angle are often used terms to describe the rays. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (more than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), or reflex. Angles are measured in units of degrees or radians (greater than 180 degrees but less than 360 degrees).
given
In order to solve this puzzle, we must determine the angle that the ladder creates with the ground using the neighbouring side and hypotenuse of a right triangle. The trigonometric function cosine can be used to calculate the angle.
adjacent/hypotenuse = cos
cos θ = 7/13
θ = cos⁻¹(7/13) (using the inverse cosine of both sides) (taking the inverse cosine of both sides)
Calculating the answer, we obtain:
θ ≈ 55.1°
Due to the ladder's 13-foot height, its angle with the ground is approximately 55.1 degrees.
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The complete question is:- 1) A ladder that is 13 ft. tall has fallen against a house. If the top of the ladder touches the house 7 ft. above the ground, what is the angle that the ladder makes with the ground? Round your degrees to one decimal place.
Label the triangle and show all of your work! Circle your final answer.