GRAPH each triangle and CLASSIFY the triangle according to its sides and angles.
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Answer:
[tex]\Delta CAT\text{ is an ISOSCELES triangle}[/tex]Explanation:
To properly classify the traingle, we need to get the length of the sides
To get the length of the sides, we need to get the distance between each two points using the distance between two points formula
Mathematically,we have the formula as:
[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where (x1,y1) refers to the coordiantes of the first point while (x2,y2) refers to the coordinates of the second point
let us get the coordinates of the individual points as seen from the plot shown
C (1,8)
A (5,10)
T (7,6)
So, let us find the distance between each two points
For AC, we have:
[tex]D\text{ = }\sqrt[]{(5-1)^2+(10-8)^2}\text{ = }\sqrt[]{20}[/tex]For AT, we have:
[tex]D=\sqrt[]{(7-5)^2+(6-10)^2\text{ }}\text{ = }\sqrt[]{20}[/tex]Lastly, for CT, we have:
[tex]D\text{ = }\sqrt[]{(7-1)^2+(6-8)^2\text{ }}\text{ = }\sqrt[]{40}[/tex]From our calculations, we can see that AC = AT
If we have a triangle which has two of its sides equal in length (the angle facing these sides would be same too), we call this an isosceles triangle
So, the class of triangle CAT is isosceles triangle
Related Questions
1. A train moves at a constant speed and travels 6 miles in 4 minutes. What is its speed in miles per minute? d/t = r time distance t d 4 mins. 6 miles
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Answer: 1.5 miles / minute
Given that:
Distance travelled = 6
Time = 4 minutes
Speed = Distance / time
Speed = 6 / 4
1.5 mile / minute
In certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth of dfeet below the surface, is given by the following equation:4dP = 14 +11If a scientific team uses special equipment to measures the pressure under water and finds it to be 318pounds per square foot, at what depth is the team making their measurements?Answer: The team is measuring atfeet below the surface.
Answers
1) Given this equation for Pressure, we need to plug into p the pressure of 318 lbs/ft² to get the depth according to the model described by this equation.
2) So, we can write out:
[tex]\begin{gathered} P=14+\frac{4d}{11} \\ 318=14+\frac{4d}{11} \\ 11\times318=11\times(14+\frac{4d}{11}) \\ 3498=154+4d \\ 3498-154=4d \\ 3344=4d \\ 4d=3344 \\ \frac{4d}{4}=\frac{3344}{4} \\ d=836ft \end{gathered}[/tex]Note that we multiplied both sides by 11 to get rid of the fraction.
Thus this is the depth below the surface that generates such pressure
write each percent as a decimal 1%
Answers
You have the following percentage:
24.1%
In order to determine the associated decimal to this fraction you proceed as follow:
A building worth $829,000 is depreciated for tax purposes by its owner using the straight-line depreciation method.
The value of the building, y, after x months of use, is given by y=829,000-2700x dollars. After how many years will
the value of the building be $699,400?
Answers
The value of the building would be $699,400 in 4 years.
What will be the value of the building?Depreciation is the when the value of an asset reduces as a result of wear and tear. Straight line depreciation is a method used in depreciating the value of an asset linearly with the passage of time.
The equation that can be used to determine the value of the building with a straight line depreciation is:
Value of the asset = initial value of the asset - (number of months x deprecation rate)
y = 829,000 - 2700x
The first step is to determine the number of months it would take for the building to have a value of $699,400.
$699,400 = 829,000 - 2700x
829,000 - 699,400 = 2,700x
129,600 = 2,700x
x = 129,600 / 2,700
x = 48 months
Now convert, months to years
1 year = 12 months
48 / 12 = 4 years
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an alloy contains copper and zinc in the ratio 3:7. find the mass of the metal in 750g of alloy
Answers
Given:
An alloy contains copper and zinc in a ratio of 3:7. The total mass of the alloy is 750g.
Required:
Find the mass of the metal in 750g of alloy.
Explanation:
Let the mass of the metal is x gm.
The weight of copper = 3x
The weight of zinc= 7x
Total weight
[tex]\begin{gathered} 3x+7x=750 \\ 10x=750 \\ x=\frac{750}{10} \\ x=75\text{ gm} \end{gathered}[/tex]
3 Drag each equation to the correct location on the table. Determine the number of solutions to each equation. Then place each equation in the box that corresponds to its number of solutions. 35 = 2+ +1 2 – 1 = 45 + 3 31 – 2 35 + 1 2x + 3 = 35 – 1 1 2x + 1 = 21 No Solutions 1 Solution 2 Solutions Reset Next All rights reserved. i NE
Answers
Then, it has just 1 solution, and it should be placed in the second column.
[tex]\begin{gathered} 2^x-1=4^x+3. \\ \text{This has no solution} \end{gathered}[/tex][tex]\begin{gathered} 3x-2=3^x+1 \\ \text{This has no solution.} \end{gathered}[/tex]Next;
[tex]\begin{gathered} \frac{1}{2}x+3=3^x-1 \\ \text{This has no solution. It should be in the first column} \end{gathered}[/tex][tex]\begin{gathered} 2x+1=2^x \\ \text{Let x=0,} \\ 2(0)+1=2^0=1 \end{gathered}[/tex]This has one solution, and it should be placed in the second column.
I I need help solving problem number 8 please :)
Answers
Answer:
(8, -1)
Explanation:
Given the below system of equations;
[tex]\begin{gathered} y^2+x^2=65\ldots\ldots\ldots\text{.Equation 1} \\ y+x=7\ldots\ldots\ldots\ldots\text{.Equation 2} \end{gathered}[/tex]Let's go ahead and test each of the given solutions and see which of them is the correct one;
For (8, -1), we have x = 8 and y = -1;
Substituting the above values in Equation 1, we have;
[tex]\begin{gathered} (-1)^2+(8)^2=65 \\ 1+64=65 \\ 65=65 \end{gathered}[/tex]Substituting the values into Equation 2;
[tex]\begin{gathered} (-1)+8=7 \\ -1+8=7 \\ 7=7 \end{gathered}[/tex]We can see that (8, -1) is a solution to the given system of equations
Not everyone pays the same price for the same model of a car that the figure is the streets a normal distribution for the price paid for the particular model of a new car the meanest $24,000 and a standard deviation is $1000 user 68–95-99.7 Raw to find a percentage of buyers who paid more than $27,000
Answers
The Solution:
The correct answer is 0.15%
Given the data in the given question,
We are required to find the percentage of buyers who paid more than $27,000.
The percentage of the total buyers is 100%
The percentage of buyers that paid between $21,000 and $27,000 is given to be 99.7%
This means that the total percentage of buyers who paid less than $21,000 and the buyers who paid more than $27,000 is
[tex]100-99.7=0.3\text{ \%}[/tex]Since the distribution is a normal distribution, it follows that half of 0.3% is the percentage of buyers who paid more than $27,000.
[tex]\frac{0.3}{2}=0.15\text{ \%}[/tex]Thus, the percentage of buyers who paid more than $27,000 is 0.15%
The top of the hill rises 243 feet above checkpoint 2, which is -162. What is the altitude of the top of the hill?
Answers
The altitude of the top of the hill or the difference in elevation point is 406 feet.
Difference in Elevation PointThe vertical distance between two points is called the difference in elevation. The process of measuring differences in elevation is called levelling , and is a basic operation in topographical surveys.
To determine the difference in elevation between two points, determine the elevation at each point and then calculate the difference.
Point A = 243 feetPoint B = -162 feetThe difference in elevation between the two points is
Point A - Point B = 243 - (-162) = 243 + 162 = 406
The difference in the elevation point is 406 feet.
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2625÷32 long division way
Answers
Answer: 82 R1 or decimal form 82.031
Step-by-step explanation:
0082
. --------
-0
26
. - 0
. 262
. -256
65
-64
. 1
What kind of transformation converts the graph of f(x)=(5x+6)^2 into the graph of g(x)=-(5x+6)^2
Answers
In order to get from
[tex]f(x)=(5x+6)^2[/tex]To
[tex]f(x)=-(5x+6)^2[/tex]You have to reflect across the x-axis.
Remember that the x-axis is the line with equation
[tex]y=0[/tex]Answer: Option A
y= 3(x-3)^2-12E) Find two more points on The Graph. You can choose what x-values to use. Write your points as coordinates x y
Answers
Given:
[tex]y=3(x-3)^2-12[/tex]The quadractic equation above is written in vertex form:
[tex]y=a(x-h)^2+k[/tex]Where:
(h, k) is the coordinate of the vertex of the parabola
We have
a = 3
h = 3
k = -12
Let's find the following:
A.) Identify the coefficients, a, h, and k
Comparing the equation with the vertex form, we have:
a = 3
h = 3
k = -12
B.) Identify whether the graph opens up or opens down.
If a is greater than zero, then the graph opens up
If a is less than zero, then the graph opens downwards
Here, a = 3
Since a is greater than zero, the graph opens up.
The graph of the equation opens up
C.) Find the vertex.
The coordinates of the vertex is = (h, k)
Given:
h = 3
k = -12
Therefore, the vertex is: (3, -12)
D.) Find the axis of symmetry.
The axis of symmetry is the line that passes through the vertex and the focus.
To find the axis of symmetry we have:
x = h
where h = 3
Thus, the axis of symmetry is:
x = 3
E.) Let's find two more points.
Point 1 ==> (x, y)
Let's take x = 1
Substitute 1 for x and solve for y:
[tex]\begin{gathered} y=3\mleft(x-3\mright)^2-12 \\ \\ y=3(1-3)^2-12 \\ \\ y=3(-2)^2-12 \\ \\ y=3(4)-12 \\ \\ y=12-12 \\ \\ y=0 \end{gathered}[/tex]When x is 1, y is 0.
Therefore, we have the point:
(x, y) ==> (1, 0)
Point 2:
Let's take x = 2
Substitute 2 for x and solve for y:
[tex]\begin{gathered} y=3\mleft(x-3\mright)^2-12 \\ \\ y=3(2-3)^2-12 \\ \\ y=3(-1)^2-12 \\ \\ y=3(1)-12 \\ \\ y=3-12 \\ \\ y=-9 \end{gathered}[/tex]When x is 2, y is -9.
Therefore, we have the points:
(x, y) ==> (2, -9)
ANSWER:
A.) a = 3
h = 3
k = -12
B.) The graph opens up
C.) (3, -12)
D.) x= 3
E.) (1, 0), (2, -9)
Which of the following shapes is the cross-section for a cylinder?A. SquareB. TriangleC. CircleD. Pentagon
Answers
Solution:
Concept:
The vertical cross-section of a cylinder is a rectangle, and the horizontal cross-section is a circle.
From the explanation above,
The final answer is CIRCLE
OPTION C is the right answer
which is the new equation written in the slope-intercept form
Answers
he slope-intercept form is
y = mx + c
here, m = slope of the line and C is intercept on y axis.
Graph the inequality. Then write the solution set in interval notation.
Answers
Representing intervals as we are doing for your question means we will represent all the possible values of x. To do that we will colour in blue all possible values of x but there is a detail we must to consider. The limits of the interval. for that we have two symbols, [ that means "closed on the value" and ( that means "opened on the value". So if there is a [ on a number it means that number makes part of the interval, but if there is a ( it means that number is not in the interval.
Now, for our inequality we have
Once x can be equal or superior to 2 it means 2 is part of the interval because x can be this value, but x is inferior to 8 but it can not be 8 so 8 is not on the interval. Once we know that, know we can represent our interval as follows:
And that is our final answer.
For an interval notation we can write [2,8).
write the linear equation that passes through the two given points (2,-2) and (0,-1)
Answers
Given the points:
(x1, y1) ==> (2, -2)
(x2, y2) ==> (0, -1)
To find the linear equation, use the form:
y = mx + b
where m is the slope.
To find the slope, use the formula below:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Thus, we have the slope as:
[tex]m=\frac{-1-(-2)}{0-2}=\frac{-1+2}{0-2}=\frac{1}{-2}=-\frac{1}{2}[/tex]Input 2 for x, -2 for y, and -1/2 for b to find b.
[tex]\begin{gathered} -2=-\frac{1}{2}(2)+b \\ \\ -2=-1+b \\ \\ -2+1=b \\ \\ -1=b \end{gathered}[/tex]Therefore, the linear equation is:
[tex]y=-\frac{1}{2}x-1[/tex]ANSWER:
[tex]y=-\frac{1}{2}x-1[/tex]Finding a time to reach the limit in a word problem on exponential growth or decay
Answers
We are told that each year the value of the laptop is 75% of the value of the value of the previous year. This means that every year the current value of the laptop is multiplied by 0.75. Then if v is the original value of the laptop its value after t years is given by:
[tex]V(t)=v0.75^t[/tex]We need to find after which year V(t) is equal to 500 or less then we have V(t)≤500 and since the original value of the laptop was 4200 we have v=4200:
[tex]4200*0.75^t\leq500[/tex]We divide both sides by 4200:
[tex]\begin{gathered} \frac{4200\times0.75^t}{4200}\leqslant\frac{500}{4200} \\ 0.75^t\leq\frac{5}{42} \end{gathered}[/tex]Then we apply the logarithm to both sides:
[tex]\log_{10}(0.75^t)\leqslant\log_{10}(\frac{5}{42})[/tex]Then we use the property of logarithm regarding exponents:
[tex]\begin{gathered} \operatorname{\log}_{10}(0.75^{t})\leqslant\operatorname{\log}_{10}(\frac{5}{42}) \\ t\log_{10}(0.75)\leq\operatorname{\log}_{10}(\frac{5}{42}) \end{gathered}[/tex]And we divide both sides by the logarithm of 0.75 (we change the inequality symbol because log(0.75) is negative):
[tex]\begin{gathered} \frac{t\operatorname{\log}_{10}(0.75)}{\operatorname{\log}_{10}(0.75)}\ge\frac{\log_{10}(\frac{5}{42})}{\operatorname{\log}_{10}(0.75)} \\ t\ge\frac{\log_{10}(\frac{5}{42})}{\operatorname{\log}_{10}(0.75)} \end{gathered}[/tex]Then we get:
[tex]t\ge7.398[/tex]So the laptop's value is less than $500 after 7.398 years.
AnswerSince we are requested to write a whole number as the answer and the smallest whole number that is bigger than 7.398 is 8 we have that the answer is 8 years.
Find the slope of the line that goes through the given points.
(-3,-2) and (– 15,13)
Answers
(13 - -2)/(-15 - -3) = (13 + 2)/(-15 + 3) = 15/-12 = -5/4 (after simplifying by dividing by 3).
So your answer is -5/4
Answer:
Answer:
Slope m= [tex]-\frac{5}{4}[/tex]
As a decimal:
m = -1.25
Step-by-step explanation:
[tex]m=\frac{Rise}{Run} =\frac{y}{x} \\m=\frac{y2-y1}{x2-x1} \\m=\frac{13--2}{-15--3} \\m=\frac{15}{-12} \\m=-\frac{5}{4}[/tex]
I am not good at word problems this is a project so need extra help
Answers
M = $6,400
C = $3,600
CD interest = $180
Money market interest = $256
Here, we want to start by completing the chart
We proceed as follows;
Let us take it line by line
a) The rate for the CD account is 5%
Writing this as decimal is 5/100 = 0.05
b) The time for the CD account is 1 year
Next line;
a) Principal invested in money market is $M
b) The time is also 1 year
Next line;
The interest earned on investment is the sum of both
That will be;
0.05c + 0.04m
So, let us write the equations to solve simultaneously;
[tex]\begin{gathered} c\text{ + m = 10,000} \\ 0.05c\text{ + 0.04m = 436} \\ \text{second equation multiplied through by 100;} \\ 5c\text{ + 4m = 43,600} \\ \text{From i;} \\ c\text{ = 10,000-m} \\ \text{put this into the multiplied equation} \\ 5(10,000-m)\text{ + 4m = 43600} \\ 50,000\text{ - 5m + 4m = 43600} \\ m\text{ = 50,000-43600} \\ m\text{ = 6400} \\ c\text{ = 10,000-6400} \\ c\text{ = 3,600} \end{gathered}[/tex]So, let us fill the last parts;
a) $3,600 + $6,400 = Total $10,000 invested
b) CD interest is 0.05 c = 0.05 (3,600) = $180
Money market interest = 0.04M = 0.04 (6,400) =$256
$180 + $256 = $436 total interest
A pair of bikes cost $89.99 and the sales tax is 8%.What is the total cost of the shoes including tax?
Answers
Answer
Total Cost of the bike including tax = $97.1892
Explanation
Cost of the bike = $89.99
Sales Tax = 8% of Cost of bike = 8% (89.99) = 0.08 (89.99) = $7.1992
Total Cost of the bike = (Cost of the bike) + (Sales Tax)
= 89.99 + 7.1992
= $97.1892
Hope this Helps!!!
Simplify.1,5m^7(-4m^50^2A. -6m^14B. 24m^17C. 24m^14D. 12m^17There is a picture too if you need it.
Answers
The expression can be simplified as,
[tex]\begin{gathered} 1.5m^7(-4m^5)^2 \\ =1.5m^7(16m^{10}) \\ =24m^{17} \end{gathered}[/tex]Thus, option (b) is the correct solution.
I need help with this Tyler’s mom purchased a saving bond for Tyler. The value of the savings bond increases by 4% each year one year after it was purchased, the value of the savings bond was $156.00 find the value of the bond when Tyler’s mom purchased it. Explain your reason
Answers
Let x = value of the bond when Tyler’s mom purchased it.
After one year, this value increased by 4%. This new value is calculated as follows:
[tex]\text{new value = }x\cdot1.04[/tex]The new value is $156.00, then
[tex]\begin{gathered} 156.00=x\cdot1.04 \\ \frac{156.00}{1.04}=x \\ 150.00=x \end{gathered}[/tex]The value of the bond was $150.00 when Tyler’s mom purchased
Of the twenty-two students in a classroom, ten are transfer students, seven are nursing students, four are AAS students and one student is undecided.If three students are chose randomly, without replacement, find the probability that all three students are nursing students.
Answers
Given that:
• There are a total number of 22 students in the classroom.
,• 10 of them are transfer students.
,• 7 are nursing students.
,• 4 are AAS students.
,• 1 student is undecided.
,• Three students are chosen randomly.
Since you need to find the probability that all three students that are chosen randomly are nursing students, you need to set up that this is:
[tex]P(A)[/tex]Where Event A is that one of the students is a nursing student.
Therefore, the probability that three of the chosen students are nursing students can be set up as:
[tex]\begin{gathered} P=P(A)\cdot P(A)\cdot P(A)=P(A)^3 \\ \\ P=P(A)^3 \end{gathered}[/tex]Knowing that the total number of students is 22 and 7 of them are nursing students, you know that:
[tex]P(A)=\frac{7}{22}[/tex]Therefore:
[tex]P=(\frac{7}{22})^3[/tex][tex]P=0.0322[/tex]Hence, the answer is:
[tex]P=0.0322[/tex]16 - 2t = 5t +9 Can you help me solve this?
Answers
1=t
add 2t to the second side, so that it is going to be 16=7t+9
now, subtract 9 from the right side: 16-9=7t
7t=7
t=1
These figures are similar. Thearea of one is given. Find thearea of the other.area=32 in?9 in12 in[ ? Jina
Answers
To find the area of similar figures whe you know the area of one of the figures and the length of corresponding sides:
1. Find the scale factor: in this case as you have the area of the largest figure find the scale factor for a reduction:
[tex]SF=\frac{small}{\text{big}}=\frac{9}{12}=\frac{3}{4}[/tex]2. Find the missing area: the area in similar figures is equal to the scale factor squared multiplied by the given area.
[tex]\begin{gathered} A=(\frac{3}{4})^2\cdot32in^2 \\ \\ A=(\frac{9}{16})\cdot32in^2 \\ \\ A=\frac{288}{16}in^2 \\ \\ A=18in^2 \end{gathered}[/tex]Then, the missing area is 18 square inchesFind all numbers whose absolute value is .4]
Answers
The numbers 4 and - 4 have an absolute value equal to 4.
What numbers are associated to a given absolute value?
In this question we need to find all the numbers such that absolute value is equal to 4. This can be found by using the definition of absolute value:
|x| = x for x ≥ 0.|x| = - x for x < 0.Absolute values are functions that contains only the magnitudes of the numbers, that is, their distances with respect to zero. Then, if the absolute value is 4, then, the number may be 4 or - 4.
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The absolute value is 4, then, the number may be 4 or - 4.
What are Absolute values?Absolute value describes the distance from zero that a number is on the number line, without considering direction
To find all the numbers such that absolute value is equal to 4.
By definition of absolute value we have
|x| = x for x ≥ 0.
|x| = - x for x < 0.
Absolute values contains magnitude which does not have direction.
|4|=4 for 4≥ 0.
|4| = -4 for x < 0.
Then, if the absolute value is 4, then, the number may be 4 or - 4.
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the product of 4 and the diference of 9 and 2 find the value of your expression
Answers
Answer:
28
Step-by-step explanation:
4(9-2)
4(7)
28
Please find the coordinates and graph the points on the graph and rotate the image.Please demonstrate the pre image and the rotated image on the graph after finding the coordinates.
Answers
We have that the general rule for a counterclockwise rotation of 270 degrees is given by the following expression:
[tex]R_{270}(x,y)=(y,-x)[/tex]then, in this case,we have the following:
[tex]\begin{gathered} R_{270}(4,5)=(5,-4)=D^{\prime} \\ R_{270}(6,-2)=(-2,-6)=E^{\prime} \\ R_{270}(1,-2)=(-2,-1)=F^{\prime} \end{gathered}[/tex]and the graph would look like this:
which function has an inverse that is also a function horizontal line test
Answers
If the graph of a function y = f(x) is such that no horizontal line intersects the graph at more than one point, then f has an inverse function.
A. The absolute value function f(x) = | x | is intersected twice by any horizontal line at y > 0. Thus this function does not have an inverse
B. The quadratic function f(x) = x^2 has a graph called parabola. If we plot any horizontal line at y>0, that line will intersect the function twice. This function has no inverse function
kenny has red marbles, 3 blue marbles,and 4 black marbes. Which ration compares a part to the whole? Please help me
Answers
A ratio comparing a part to the whole must then have 9 as the second number.
In this question, we have been given Kenny has red marbles, 3 blue marbles, and 4 black marbles.
We need to find the ratio that compares a part to the whole.
Here, the total number of marbles are:
2 red + 3 blue + 4 black = 9 marbles.
Let x be either number of marbles (either red marbles or blue marbles or black marbles)
Then the ratio that compares a part to the whole would be,
x : 9
Therefore, a ratio comparing a part to the whole must then have 9 as the second number.
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