We have the following:
[tex]10\div\frac{2}{9}[/tex]solving:
[tex]\frac{10}{\frac{2}{9}}=\frac{\frac{10}{1}}{\frac{2}{9}}=\frac{10\cdot9}{2\cdot1}=\frac{90}{2}=45[/tex]The answer is 45
How many solutions does this equation have?-4k + 4k = 0
Let's try so solve this equation:
[tex]\begin{gathered} -4k+4k=0 \\ 0=0 \end{gathered}[/tex]When you have a result of 0 = 0, that means the equation has infinite solutions, that is, any value of k we use would satisfy the equation.
So the equation has infinitely many solutions.
Find the value of k so that x-1 is a factor of x^2 - 2x^2 + 3x + k
The value of k so that x - 1 is a factor of the polynomial, x² - 2x² + 3x + k is -2.
How to find the factor of a polynomial?The polynomial given is x² - 2x² + 3x + k.
Let's find the value of k so that x - 1 is a factor of the polynomial x² - 2x² + 3x + k.
Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.
Therefore, the value of k that will make x - 1 a factor is when the polynomial is equals to zero when we input the root of x - 1 in the polynomial.
Hence,
x - 1 = 0
x = 1
let's substitute the value of x in the polynomial. The polynomial must be equals to 0 for x - 1 to be a factor of the polynomial.
0 = x² - 2x² + 3x + k
0 = (1)² - 2(1)² + 3(1) + k
0 = 1 - 2 + 3 + k
0 = - 1 + 3 + k
0 = 2 + k
k = - 2
Therefore, the value of k is -2.
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Three different transformation are performed on the shaded triangle. Each transformation results in on of three images. Match each image to the transformation applied on the shaded triangle
We are given a triangle and three possible transformations performed on it. The first transformation shows that the triangle has no change in orientation, therefore, this transformation is a translation only.
For image 2 we notice that the orientation of the triangle changes. If we draw a horizontal line in the middle of the shaded triangle and image 2 we notice that these two images are related by a reflection, also after this reflection the image was translated therefore, for image two we have reflection across a horizontal line followed by a translation.
For image 3 we can draw a vertical line in the middle of the shaded triangle and image 3 and we do a reflection across this vertical line since there is a change in the orientation of the figure.
6.724x
Melinda went for a run. She was doing a great job until she got to a hill. She was so tired
running up the hill that she tripped over a rock at the top of the hill. She rolled all the way
down the hill. It took her 90 seconds to reach the bottom of the hill. She rolled for 225
feet. What is Melinda's rate of decent?
The Melinda's rate of decent from the top of the hill is 3.75 ft/sec.
What is termed as the rate of decent/speed?Speed is defined as the proportion of distance traveled to time spent traveling. Because it has only one direction and no magnitude, speed is a scalar quantity. When an object travels the same distance in equal time intervals, it is said to be moving at a uniform speed.For the given question;
The distance covered by the Melinda after she tripped over a rock at the top of the hill is 225 feet.
The time taken by Melinda to reach the bottom of the hill is 90 seconds.
Then, the rate of decent will be the speed at which she will fall.
Speed = distance/ time
Speed = 225/60
Speed = 3.75
Thus, the Melinda's rate of decent from the top of the hill is 3.75 ft/sec.
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The adult skeleton consist of 206 Bones in the school and 30 bones in the arm and legs. Out of the 28th skull bones, 14 are facial bones. Six or ear bones and eight are cardinal bones. How many more bones are there in the arm and legs than in the faceA) 2B) 6C) 14D) 16
We need to compare the number of bones in the arms and legs with the number of bones in the face.
The question says that there are 30 bones in the arms and legs.
The question also says that there are 14 bones on the face.
So, the difference between these will be how many more bones there are in the arms and legs than in the face:
[tex]30-14=16[/tex]A construction worker dropped a hammer while building the Grand Canyon skywalk, 8100 feetabove the Colorado River. Use the formula t=(square root of h)/4 to find how many seconds it took for thehammer to reach the river.
Given:
[tex]t=\frac{\sqrt[]{h}}{4}[/tex]To find the time when the height h=8100 feet:
Substitute h=8100 in the given function.
[tex]\begin{gathered} t=\frac{\sqrt[]{8100}}{4} \\ t=\frac{90}{4} \\ t=22.5\text{ seconds} \end{gathered}[/tex]Thus, the time required for the hammer to reach the river is 22.5 seconds.
4x + x + 4 = 8x -3x + 4
x can take any real value
Explanation
[tex]4x+x+4=8x-3x+4[/tex]
Step 1
add similar terms in both sides
[tex]\begin{gathered} 4x+x+4=8x-3x+4 \\ 5x+4=5x+4 \end{gathered}[/tex]Step 2
subtract 5x+4 in both sides
[tex]\begin{gathered} 5x+4=5x+4 \\ 5x+4-(5x+4)=5x+4-(5x+4) \\ 0=0 \end{gathered}[/tex]0=00 means that as an equation, its solution is that x can take any real value .
I hope this helps you
3. Which of the following points would produce a negative slope? (A) (B) (C) (D) (-1,2) and (4,2) (-2,-2) and (0,4) (1,3) and (-1,4) (2,4) and (-2,-1)
The sequation to calculate the slope is,
[tex]m=\frac{y2-y1}{x2-x1}[/tex]The solpe of line joining (-1,2) and (4,2) is,
[tex]\begin{gathered} m=\frac{2-2}{4+1} \\ m=0 \end{gathered}[/tex]The slope of the line joining (-2,-2) and (0,4) is,
[tex]\begin{gathered} m=\frac{4+2}{0+2} \\ m=3 \end{gathered}[/tex]The slope of the line joining (1,3) and (-1,4) is,
[tex]\begin{gathered} m=\frac{4-3}{-1-1} \\ m=-\frac{1}{2} \end{gathered}[/tex]Negative slope.
The slope of the line joining (2,4) and (-2,-1) is,
[tex]\begin{gathered} m=\frac{-1-4}{-2-2} \\ m=\frac{5}{4} \end{gathered}[/tex]Positive slope.
Please help me and tell me the process I have a test in an hour.Value of x.
Vertical angles are congruent.
From the figure, angle 3 and angle (7x + 3) are vertical angles, therefore angle 3 is (7x + 3)
Angle 1 and 127 degrees are supplementary angles and have a sum of 180 degrees.
That will be :
[tex]\begin{gathered} \angle1+127=180 \\ \angle1=180-127 \\ \angle1=53 \end{gathered}[/tex]Angle 2 and 133 degrees are also supplementary angles and have a sum of 180 degrees.
That will be :
[tex]\begin{gathered} \angle2+133=180 \\ \angle2=180-133 \\ \angle2=47 \end{gathered}[/tex]Now we have angles 1, 2 and 3 which are angles in a triangle, and the sum of interior angles in a triangle is 180 degrees.
[tex]\begin{gathered} \angle1+\angle2+\angle3=180 \\ 53+47+(7x+3)=180 \\ \text{Solve for x :} \\ 100+7x+3=180 \\ 7x+103=180 \\ 7x=180-103 \\ 7x=77 \\ x=\frac{77}{7} \\ x=11 \end{gathered}[/tex]ANSWER :
x = 11
Which of the following values have 3 significant figures? Check all that apply.A. 10.1B. 100.05C. 120D. 129
The number of significant figures in 10.1 is 3 as there are two digits before the decimal and one digit after the decimal.
The number of significant digit in 100.05 is 5 as there are 3 digits before the decimal and two digits after the decimal.
The number of significant digits in 120 is 2.
The number of significant digits in 129 is 3.
Hence, the correct answers are (A) and (D)digit
The number line below shows the values of x that make the inequality x > 1 true. Select all the values of x from this list that make the inequality x> 1 true. a. 3 b. -3c. 1 d. 700 e. 1.052. Name two more values of x that are solutions to the inequality.
Answer:
(a)3, 1, 700 and 1.05
(b)6 and 9
Explanation:
(a)The values of x from the list that make the inequality x> 1 true are:
3, 1, 700 and 1.05
(b)Two more values of x that are solutions to the inequality x>1 are:
6 and 9.
need help with excerise step by step been 20 year's
Given:
Standard deviation
[tex]\sigma=5.18[/tex]Mean
[tex]\mu=129[/tex]Required:
Find the longest braking distance one of these cars could have and still in the bottom.
Explanation:
The z-score formula is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the given values and find the value of z.
[tex]z=\frac{x-129}{5.18}[/tex]This is the first percentile which is X when Z has a p-value of 0.01, so z = -2.327.
[tex]\begin{gathered} -2.327=\frac{x-129}{5.18} \\ x-129=-2.327(5.18) \\ x-129=-12.054 \\ x=129+12.054 \\ x=116.946\text{ ft} \end{gathered}[/tex]Final answer:
The longest braking distance one of these cars could have and still in the bottom 1% is 116.946 ft.
The Jones family took a 12-mile canoe ride down the Indian River in 2 hours. After lunch, the return trip back up the river took 3 hours. Find the rate of the canoe in still water and the rate of the current.
Answer:
Step-by-step explanation:
As per the distance formula, the rate of the canoe in still water is 5 mph; the rate of the current is 1 mph.
Distance formula:
Distance is defined as the total movement of an object without any regard to direction. So, it is defined as the distance that covers how much ground an object despite its starting or ending point.
Distance = Speed x time
Given,
The Jones family took a 12-mile canoe ride down the Indian River in 2 hours. After lunch, the return trip back up the river took 3 hours.
Here we need to find the rate of the canoe in still water and the rate of the current.
According to the given question we know that,
Speed downriver = (12 mi)/(2 h) = 6 mph.
Speed upriver = (12 mi)/(3 h) = 4 mph.
Now, we need to find the canoe's rate in still water is the average of these speeds:
=> (6+4)/2 = 5 miles per hour.
Then the current's rate is calculated as the difference between the actual rate and the canoe's rate:
=> 6 - 5 = 1 miles per hour.
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the top ten medal- winning nations in a tournament in a particular year are shown in the table. use the given information and calculate the mean number of gold medals for all nations
You have 1/5 of a box of erasers and you need to share them with 3 total people, including yourself. What fraction of the box should each person get?
You have 1/5 of a box of erasers
Number of box of erasers = 1/5.
you need to share them with 3 total people, including yourself
Total number of people = 3 + 1( yourself)
Total number of people = 4
Since, we have to distribute the box of erasers to 4 people
So, divide 1/5 by 4:
[tex]\begin{gathered} \frac{1}{5}\text{ }\div4=\frac{\frac{1}{5}}{4} \\ \frac{1}{5}\text{ }\div4=\frac{1}{5}\times\frac{1}{4} \\ \frac{1}{5}\text{ }\div4=\frac{1}{5\times4} \\ \frac{1}{5}\text{ }\div4=\frac{1}{20} \end{gathered}[/tex]The fraction of the box that each person will get is 1/20
Answer: 1/20
Given rectangle BCDE below. If BF = 22, find EF.
Okay, here we have this:
Considering the provided graph, we are going to find the requested measure, so we obtain the following:
Let us remember that a rectangle besides having the properties of a parallelogram also stands out because it has congruent diagonals. So considering this we have:
BD=EC
EF=BF
EF=22
Finally we obtain that EF is equal to 22 units.
Can someone please help me on this question, I'm a little stuck? The question should be down below!
We have a right triangle with a missing side.
When we have two sides given sides on the right triangle and we need to find the missing side, we use the Pythagoras theorem:
The formula is given by:
[tex]a^2=b^2+c^2[/tex]Where:
a = Hypotenuse
b= Opposite side
c= Adjacent side
Now, we need to label the sides of the given triangle:
The largest side, represents the hypotenuse, in this case, a=15m.
The adjacent side is between the 90 degrees angle and the hypotenuse, in this case, c = 9m
Therefore, the missing side is the opposite side, let set b for this side:
Replacing these values:
[tex](15m)^2=b^2+(9m)^2[/tex][tex]225=b^2+81[/tex]Solve the equation for b:
[tex]225-81=b^2[/tex][tex]144=b^2[/tex][tex]\sqrt[]{144}=\sqrt[]{b^2}[/tex]Therefore, the missing side:
[tex]12=b[/tex]
Hugo averages 42 words per minute on a typing test with a standard deviation of 5.5 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(42,5.5). Suppose Hugo types 60 words per minute in a typing test on Wednesday. The z-score when x=60 is ________. This z-score tells you that x=60 is ________ standard deviations to the ________ (right/left) of the mean, ________. Correctly fill in the blanks in the statement above.
The z score when x = 60 is 3.27.
This z score tells you that x = 60 is 3.27 standard deviations to the right of the mean.
Given,
Consider as a normal distribution:
The mean should be equals to 42 (μ)
The standard deviation (σ) = 5.5
We have to find the z score when x = 60.
That is,
z = (x - μ) / σ = (60 - 42) / 5.5 = 18/5.5 = 3.27
Therefore,
The z score when x = 60 is 3.27.
This z score tells you that x = 60 is 3.27 standard deviations to the right of the mean.
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uhh im stuck and im stressed .. and i dont understand area model math..
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(5x + 6)(2x² + 3x + 8) = ?
Step 02:
Area Model
First, you must multiply the values in the rows by each of the values in the columns.
Then, you must add all the values resulting from the multiplications.
10x³
2x²
+ 12x²
15x²
18x
3x
40x
48
8
--------------------------------------------
10x³ + 29x² + 61x + 56
The answer is:
(5x + 6)(2x² + 3x + 8) = 10x³ + 29x² + 61x + 56
help meeeeeeeeeeeeeeeee
For the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
As given in the question,
Given function :
f(x) = x³ +x +1
g(x) =-x
Composition of the given function is equal to :
(fog)(x) = f(g(x))
= f(-x)
= (-x)³ +(-x) +1
= -x³ -x +1
(g of)(x) = g(f(x))
=g(x³ +x+1)
= -(x³ +x+1)
Therefore, for the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
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Andre drew a plan of a courtyard at a scale of 1 to 60. On his drawing, one side of the courtyard is 2.75 inches. What is the actual measurement of that side of the courtyard? Show your work.
Okay, here we have this:
Considering that the scale is of 1 to 60, we obtain the following:
2.75 inches * 60 =165.
What is the area of the circle to the nearest 10th unit?
First, lets find the radius of the circle.
For a circle inscribed in a square, the diameter of this circle is equal to the side lenght.
D = 4.4
Since the radius (r) is D/2
r = 4.4/2 = 2.2
Now, we can calcule the area of the circle (A), using the following equation:
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A=\pi\cdot2.2^2 \\ A=4.8\pi units^2 \\ Or,\text{ since }\pi=3.14 \\ A=4.8\cdot3.14 \\ A=15.2\text{ }units^2 \end{gathered}[/tex]I tried it and got imaginary numbers in the answer.
Given the following equation:
[tex]\frac{x}{x-4}-\frac{4}{x}=\frac{3}{x-4}[/tex]First, we will identify the zeros of the denominator
So, the zeros are: x = {0,4}
Second, multiply the equation by x(x-4) to eliminate the denominators
[tex]x(x-4)*(\frac{x}{x-4}-\frac{4}{x})=x(x-4)*\frac{3}{x-4}[/tex]Simplify the equation:
[tex]x^2-4(x-4)=3x[/tex]Expand the equation and combine the like terms:
[tex]\begin{gathered} x^2-4x+16=3x \\ x^2-7x+16=0 \end{gathered}[/tex]The last quadratic equation will be solved using the quadratic rule:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Substitute a = 1, b = -7, c = 16
[tex]\begin{gathered} x=\frac{7\pm\sqrt{(-7)^2-4(1)(16)}}{2(1)} \\ \\ x=\frac{7\pm\sqrt{-15}}{2}=\frac{7\pm i\sqrt{15}}{2} \\ \\ x=\lbrace\frac{7+i\sqrt{15}}{2};\frac{7-i\sqrt{15}}{2}\rbrace \end{gathered}[/tex]So, the answer will be:
[tex]x=\lbrace\frac{7+i\sqrt{15}}{2};\frac{7-i\sqrt{15}}{2}\rbrace[/tex]I need help with this practice problem solving The subject is trigonometry It asks to graph the functionIf you can, use Desmos to graph… it is recommend
In order to determine the graph of the given function, cosider:
The function f(x) is indetermined when the argument of the cot is 0.
[tex]\begin{gathered} x+\frac{\pi}{6}=0 \\ x=-\frac{\pi}{6} \end{gathered}[/tex]In this case, the period is 2pi. Then, not only for x=-pi/6, but for x=5pi/6 the function is indeterminate.
Then, the graph is:
Question 5 Multiple Choice Worth 1 points)(05.02 MC)A nurse collected data about the average birth weight of babies in the hospital that month. Her data is shown using the dot plot. Create a box plot to represent the data.Monthly Birth Weight:8.28.3 8.4 8.5 8.6Birth Weight (in pounds)82 83 8.4 85 86 87 8.882 8384 8.5 86 87 60 6.982 83 84 8.5 8.6 8.7 8.0 8.9 98283 84 85 86 87 88 8.998.1816.181$F
Given:
Here we have data about the average birth weight of babies in the hospital that month.
Required:
We need to create a box plot to represent the data.
Explanation:
Here we have monthly birth weight in pounds as
8.2 , 8.2 , 8.3 , 8.3 , 8.4 , 8.4 , 8.5 , 8.5 , 8.5 , 8.7 , 8.9
now by data we get Q2 is 8.4
now for this data
8.2 , 8.2 , 8.3 , 8.3 , 8.4
we get Q1 is 8.3
by this data
8.5 , 8.5 , 8.5 , 8.7 , 8.9
we get Q3 is 8.5
and we have maximum 8.9 and minimum 8.2
now make a box plot
Final answer:
Bobby was making a road trip to visit his parents. He stopped for gas and bought x number of gallons for $2.25 per gallon and a soda for $1.75. How much did he spend at the gas station if her purchased 15 gallons of gas?
Answer:
$35.5
Explanation:
If Bobby purchased 15 gallons of gas and each gallon cost $2.25, the total cost of the gallons of gas is:
15 x $2.25 = $33.75
Adittionally, Bobby bought a soda for $1.75, so he spend a total of:
$33.75 + $1.75 = $35.5
So, he spends $35.5
The triangles below are congruent by SSS, so we can say that < E is congruent to ______ by CPCTC.
The triangles are given to be congruent by the side-side-side (SSS) congruence property.
Hence, the congruent statement is:
[tex]\triangle DEF\cong\triangle HIJ[/tex]It is required to complete the given statement.
Recall that CPCTC means Corresponding Parts of Congruent Triangles are Congruent.
The corresponding part to ∠ E is ∠I. Hence, by CPCTC, the angle congruent to ∠E is ∠I.
The answer is option b.
A triangular banner has an area 2000 square yards. Find the measures of the base and height of the triangle if the base is five-eighths of the height. What are the units of measurement.
ANSWER:
Height = 80 yds
Base = 50 yds
STEP-BY-STEP EXPLANATION:
Given:
Area = 2000 square yards
Height = h
Base = 5/8h
We can calculate the value of the height using the triangle area formula, just like this:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ \text{ We replacing} \\ 2000=\frac{h\cdot \frac{5}{8}h}{2} \\ h^2=\frac{2000\cdot2\cdot8}{5} \\ h=\sqrt{6400} \\ h=80\text{ yd} \\ \text{ therefore, the base is:} \\ b=\frac{5}{8}\cdot80 \\ b=50\text{ yd} \end{gathered}[/tex]Height = 80 yds
Base = 50 yds
through: (5,-4), slope = -9/5
The slope intersept form of a line is ,
[tex]y-y_1=m(x-x_1)[/tex]Given the point (x1,y1) is (5,-4) and slope is -9/5 implies,
[tex]undefined[/tex]which numbers are all divisible by 5
Answer:
numbers that end with 0 or 5.
Answer: 5 35 790 55
Step-by-step explanation:
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