Answers
In order to determine the coordinates of A, use the following formula for the area of a triangle:
A = b·h/2
where b is the base of the triangle, and it is equal to the length of the segment CB = 8 units. h is the height of the triangle and it is equal to the length of segment AC.
Due to you know what is the area of the triangle (A = 28 units²), solve the formula for h, and replace the rest of the parameters, as follow:
h = 2A/b
h = 2(28 units²)/(8 units)
h = 7 units
Then, segment AC = 7 units. Due to the point A is on the y-axis, it is necessary that the coordinates of A are A(0,7)
Related Questions
Calculate the value of x on the diagram (a) 9m2 (b) 16m2 (c) 5m (d) 3m (e) 4mpls check the attachment for the diagram
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Given: A right triangle ABC with sides AB=3M and BC=4M.
Required: To determine the side length of AC.
Explanation: The side AC=X can be determined by joining B to C and considering the triangle ABC as a right-angled triangle.
Now using the Pythagoras Theorem, we can write-
[tex]AC^2=AB^2+BC^2[/tex]Substituting the values-
[tex]\begin{gathered} X^2=(3M)^2+(4M)^2 \\ X^2=9M^2+16M^2 \\ X=\sqrt{25M^2} \\ X=5M \end{gathered}[/tex]Final Answer: Option C is correct.
Select three measures that could be the threeside lengths of a right triangle.17 cm20 cm21 cm29 cm
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To know if the three side length of a triangle makes a right angle or not, the three sides must be a Pythagoras triple.
This means the sum of the squares of the two shortest sides (a and b) must be equal to the square of the longest side (c).
[tex]a^2+b^2=c^2[/tex]When we find the squares of all the sides,
[tex]\begin{gathered} 17^2=289 \\ 20^2=400 \\ 21^2=441 \\ 29^2=841 \end{gathered}[/tex]From the squares above, the one that will give a right triangle from Pythagoras theorem will be,
[tex]\begin{gathered} 20^2+21^2=29^2 \\ 400+441=841 \\ 841=841 \\ \\ S\text{ ince,} \\ a^2+b^2=c^2,\text{ then 20,21 and 29 are Pythagoras triples } \\ \text{They will be the thr}e\text{ sides of a right triangle} \\ S\text{ ince they obey the Pythagoras theorem.} \end{gathered}[/tex]Therefore, 20cm, 21cm and 29cm are the side lengths of a right triangle.
From the squares above, the one that will give a right triangle from Pythagoras theorem will be,
[tex]\begin{gathered} 20^2+21^2=29^2 \\ 400+441=841 \\ 841=841 \\ \\ S\text{ ince,} \\ a^2+b^2=c^2,\text{ then 20,21 and 29 are Pythagoras triples } \\ \text{They will be the thr}e\text{ sides of a right triangle} \\ S\text{ ince they obey the Pythagoras theorem.} \end{gathered}[/tex]Therefore, 20cm, 21cm and 29cm are the side lengths of a right triangle.
You are saving to buy a car, and you deposit $200 at the end of each month for two years at an APR of 2.4% compounded monthly. What is the future value for this savings arrangement? That is, how much money will you have for the purchase of the car after two years? (Round your answer to the nearest cent.)
Answers
You are saving to buy a car
You save $200 at the end of each month
The present, P = $200
At the rate of 2.4% compounded monthly,
Rate of return, r, will be
[tex]r=\frac{\frac{2.4}{100}}{12}=\frac{0.024}{12}=0.002[/tex]Rate of return, r = 0.002
The deposit is made at the end of every month for 2 years,
Number of periods, n, will be
[tex]n=2\text{ }\times12=24[/tex]The formula to find the present value is
[tex]FV=P\lbrack\frac{(1+r)^n-1}{r}\rbrack[/tex]Substiute the values into the formula
[tex]\begin{gathered} FV=200\lbrack\frac{(1+0.002)^{24}-1}{0.002}\rbrack \\ FV=200\lbrack\frac{(1.002)^{24}-1}{0.002}\rbrack \\ FV=200\lbrack\frac{0.049120363}{0.002}\rbrack \\ FV=200(24.56) \\ FV=\text{ \$4912} \end{gathered}[/tex]Hence, the future value is $4,912
What is the equation for the line in slope intercept formEnter your answer in the box
Answers
Hello!
First, let's write two points that this line passes through:
• A = (-4, 4)
,• B = (-2, 0)
Now, we will have to use the formula below to calculate the slope:
[tex]\text{Slope}=\frac{y_B-y_A}{x_B-x_A}[/tex]So, let's replace the values in the formula:
[tex]\text{Slope}=\frac{0_{}-4_{}}{-2-(-4)}=\frac{-4}{-2+4}=\frac{-4}{2}=-2[/tex]As we know the slope, we have to calculate the y-intercept.
We can use the slope-intercept form to obtain it:
[tex]\begin{gathered} y=mx+b \\ -2=-2\cdot0+b \\ -2=b \\ b=-2 \end{gathered}[/tex]So, we know that:
• Slope: -2
,• Y-intercept: -2
Let's write the equation of the line in slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ y=-2x-2 \end{gathered}[/tex]Answer:y = -2x -2
Ingrid walked her dog and washed her car. The time she spent walking her dog was one-half the time it took her to wash her car. It took Ingrid 23 minutes to walk the dog. How long did it take Ingrid to wash her car? Use the variable w to represent how long it took Ingrid to wash her car.
Answers
Let w be the time Ingrid took to wash her car.
We know that she spent half that time walking her dog, this means that:
[tex]\frac{1}{2}w[/tex]is the time she spent walking her dog. We also know that she spent 23 minutes doing that, then we have the equation:
[tex]\frac{1}{2}w=23[/tex]Solving for w we have:
[tex]\begin{gathered} \frac{1}{2}w=23 \\ w=2\cdot23 \\ w=46 \end{gathered}[/tex]Therefore she spent 46 minutes whashing the car.
A car on the highway is getting 13 kilometers per liter of gas. How many meters pe milliliter would this be? 1.3 meters per milliliter 13 meters per milliliter 26 meters per milliliter 39 meters per milliliter 24 points)
Answers
We assume that we have to convert from 13 km/lt to m/ml.
To do this conversion, we need to remember that:
1 km = 1000 m
1 lt = 1000 ml
Then, we can proceed as follows to convert those quantities:
[tex]13\cdot\frac{\operatorname{km}}{lt}\cdot\frac{1000m}{\operatorname{km}}\cdot\frac{1lt}{1000ml}=13\frac{m}{ml}[/tex]Then, the answer is 13 m/ml.
A rectangular auditorium seats 3300 people. The number of seats in each row exceeds the number of rows by 16. Find the number of seats in eachrow.
Answers
Take x as the number of rows and y as the number of seats in each row.
There are 3300 seats in the auditorium, which means that the product of x and y is 3300:
[tex]x\cdot y=3300[/tex]We also know that y exceeds x by 16, this is:
[tex]y=x+16[/tex]Use these equations to find the number of seats and rows.
[tex]\begin{gathered} x\cdot(x+16)=3300 \\ x^2+16x=3300 \\ x^2+16x-3300=0 \end{gathered}[/tex]Use the quadratic equation to find x:
[tex]\begin{gathered} x=\frac{-16\pm\sqrt[]{16^2-4(1\cdot-3300)}}{2\cdot1} \\ x=\frac{-16\pm116}{2} \\ x1=\frac{-16+116}{2}=\frac{100}{2}=50 \\ x2=\frac{-16-116}{2}=\frac{-132}{2}=-66 \end{gathered}[/tex]As x is the number of rows, it can take negative values, so take the value of 50.
Use this values to find y:
[tex]\begin{gathered} x\cdot y=3300 \\ y=\frac{3300}{x} \\ y=\frac{3300}{50} \\ y=66 \end{gathered}[/tex]There are 50 seats in each row and there are 66 rows.
Johnny your friend claims that the green trail is 10 Mi longer than the pink Trail what calculation error might Bonnie and have made what is the correct comparison of the length of the pink trail to the length of the Green trial
Answers
Johnny forgot that each little square is 1/2 of a mile. SO the correct comparison is that the green trial is 5 miles longer than the pink one
Latex paint sells for $28 per gallon and will cost you $224 to paint your room. If each gallon will cover 340 square feet, how many square feet of wall space do you have in your room?
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Latex paint sells for $28 per gallon and will cost you $224 to paint your room. If each gallon will cover 340 square feet, how many square feet of wall space do you have in your room?
How many gallons did you buy?
224/28 = 8 gallons
How many square feet of wall space do you have in your room?
8*340 = 2,720 sq ft
Jamal's deck is in the shape of a polygon and is shown on the grid below.(-8,6)(6,6)o[(-8, 4),(6,4)What is the area of Jamal's deck?square units
Answers
Answer:
The area of a rectangle is the product of its width and length.
[tex]A=w\times L[/tex]Now, in our case, the width is the vertical distance of the rectangle and it is found by counting the boxes from (-8, -4) to (-8,6). There are 10 boxes from the given points; therefore the width of the rectangle is w = 10.
Now the length is the distance between (-8,-4) and (6, -4). Counting the boxes we find that there are 14 boxes; therefore, L = 14.
With the value of width and length in hand, we now calculate the area
[tex]A=10\times14=140[/tex]Hence, the area of Jamal's deck is 140 square units.
A birdhouse is constructed of a rectangular prism with a square base and a square pyramid at the top of the house. If a student wanted to put a fence around the entire birdhouse to see all of the animals, determine how square feet of fence would be required to make the fence.
Answers
Solution:
The area of fence needed is the area of the upper pyramid plus the area of the square prism. That is:
[tex]A\text{ = Pyramid area + rectangular prism area}[/tex]the area of a Pyramid is given by the following formula:
and the area of the rectangular prism is:
A = 2lw +2lh+2wh
where
l is the lenght, h is the height and w is the width
Thus, using the data from the problem and the equations above, we can conclude that:
[tex]A\text{ = Pyramid area + rectangular prism area}=340+3200=3540[/tex]so that, the correct answer is:
[tex]3540[/tex]y = x + 124x + 2y = 27Solve each system of equations algebraically
Answers
ANSWER
x = 1/2
y = 12 1/2
EXPLANATION
We have to solve the system of equations algebraically:
y = x + 12
4x + 2y = 27
We can solve this using substitution method. Substitute the first equation into the second equation:
4x + 2(x + 12) = 27
4x + 2x + 24 = 27
6x = 27 - 24
6x = 3
Divide through by 6:
x = 3 / 6
x = 1/2
Recall that:
y = x + 12
=> y = 1/2 + 12
y = 12 1/2
That is the solution of the system of equations.
For a normal distribution with a mean of μ = 100 and a standard deviation of o= 15, find each of thefollowing probabilities:a. p(X>108)p=b. p(X<80)p=c. p(X<125)p=d. p(90
Answers
ANSWER:
a. 0.2981
b. 0.0918
c. 0.9525
d. 0.4972
STEP-BY-STEP EXPLANATION:
Given:
μ = 100
σ = 15
We must calculate the z-score using the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Then determine the probability with the normal table.
We calculate in each case:
a. p(X > 108)
[tex]\begin{gathered} z=\frac{108-100}{15}=0.53 \\ \\ p(z>0.53)=1-p(z<0.53) \end{gathered}[/tex]We look for the value of the normal table:
Therefore:
[tex]\begin{gathered} p(z\gt0.53)=1-p(z\lt0.53) \\ \\ p\left(X>108\right)=1-0.7019=0.2981 \end{gathered}[/tex]b. p(X < 80)
[tex]\begin{gathered} z=\frac{80-100}{15}=-1.33 \\ \\ p(z<-1.33) \end{gathered}[/tex]We look for the value of the normal table:
Therefore:
[tex]p\left(X<80\right)=0.0918[/tex]c. p (X < 125)
[tex]\begin{gathered} z=\frac{125-100}{15}=1.67 \\ \\ p(z<1.67) \end{gathered}[/tex]We look for the value of the normal table:
Therefore:
[tex]p(X<125)=0.9525[/tex]d. p (90 < X <110)
[tex]\begin{gathered} z=\frac{90-100}{15}=-0.67 \\ \\ z=\frac{110-100}{15}=0.67 \\ \\ p(-0.67We look for the value of the normal table:Therefore:
[tex]\begin{gathered} p(-0.67Is 3,600 an non repeating decimal ?
Answers
3,600 is not a non-repeating decimal. A non-repeating decimal is a number like
π or the √2, which are numbers with a lot of decimals without a pattern.
Answer: 3,600 is not a non-repeating decimal
is √24 rational or irrational
Answers
Answer:
it is irrational
Step-by-step explanation:
√24=4.898979486
Home work thanks need help with this problem multi part question
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b) $2273.47
c) The expected salary with 13 years of experience is $78879.59
Explanation:a) To write a linear model, we will use the linear equation formula:
y = mx + b
m = slope, b = y-intercept
First we need to find the slope using the formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]Picking any two points on the table, we use in the formula:
[tex]\begin{gathered} (0,\text{ 49900) and (2, 52400)} \\ x_1=0,y_1=49900,x_2=2,y_2\text{ = }52400 \\ \text{slope = }\frac{52400\text{ - 49900}}{2-0} \\ \text{slope = 2500/2} \\ \text{slope = 12}50 \\ \end{gathered}[/tex]There is something wrong with the values in the table. The slope is supposed to be constant for any two points in the table but that is not so here.
I will be using a linear regression instead:
[tex]\begin{gathered} Regression\text{ }Equation\colonŷ=bX+a \\ X\text{ = years of experience} \\ ŷ\text{ = salary in dollars} \end{gathered}[/tex]Graphing the values, we have:
[tex]ŷ=2273.46939X+49324.4898[/tex]b) The slope of the model we got is 2273.47
It means the rate of salary per year of experience is $2273.47
c) for 13 years of experience, x = 13
[tex]\begin{gathered} we\text{ replace X with 13:} \\ ŷ=2273.46939(13)+49324.4898 \\ ŷ\text{ = 78879.59} \end{gathered}[/tex]The expected salary with 13 years of experience is $78879.59
s = square root of 18d can be used to find the speed s of a car in miles per hour when the car needs d feet to come to a complete stop after slamming on the brakes. If it took a car 12 feet to come to a complete stop after slamming on the brakes, estimate the speed of the car
Answers
ANSWER:
14.7 miles per hour
STEP-BY-STEP EXPLANATION:
We have that the speed is given by the following function:
[tex]s=\sqrt[]{18d}[/tex]where s is calculated in miles per hour and d is given in feet, therefore, we substitute and calculate the value of the speed:
[tex]\begin{gathered} s=\sqrt{18\cdot12} \\ s=14.7\text{ miles per hour} \end{gathered}[/tex]The speed of car is 14.7 miles per hour
what values of x make inequality 1 + 5x < -9
Answers
Dividing both sides by 5, we have
[tex]\begin{gathered} \frac{5x}{5}<\frac{-10}{5} \\ x<-2 \end{gathered}[/tex]What is the x-value in the solution to the system of equations below?x = y - 52x + y = 11
Answers
x = 2
Explanation:The system of equations is:
x = y - 5............................(1)
2x + y = 11........................(2)
Substitute equation (1) into equation (2)
2(y - 5) + y = 11
2y - 10 + y = 11
Collect like terms
2y + y = 11 + 10
3y = 21
y = 21/3
y = 7
Substitute y = 7 into equation (1)
x = y - 5
x = 7 - 5
x = 2
Solve the following system by graphing. Whichfigure shows the graphic solution to the equationsbelow?
Answers
To solve this question, we need to find the x-intercepts and the y-intercepts for each of the equations. After having these values, we will have a pair of points for one equation, and another pair of points for the other equation.
We can proceed as follows:
First case:
We can find the y-intercept if we have x = 0. Then, the y-intercept is:
[tex]y=-\frac{1}{4}x+3,x=0\Rightarrow y=3[/tex]Similarly, the x-intercept is (for y = 0, we then have x):
[tex]0=-\frac{1}{4}x+3\Rightarrow-3=-\frac{1}{4}x\Rightarrow-4\cdot(-3)=-4\cdot(-\frac{1}{4}x)\Rightarrow12=x\Rightarrow x=12[/tex]Then, for the first equation, we have that the y-intercept is (0, 3), and the x-intercept is (12,0). These two points are important to graph this equation.
Second Case:
We can proceed in the same way to find the y-intercept and the x-intercept.
[tex]y=\frac{3}{4}x-1,x=0\Rightarrow y=-1[/tex]Then, the y-intercept is (0, -1).
The x-intercept is
[tex]0=\frac{3}{4}x-1\Rightarrow\frac{3}{4}x=1\Rightarrow\frac{4}{3}\cdot\frac{3}{4}x=\frac{4}{3}\cdot1\Rightarrow x=\frac{4}{3}[/tex]Hence, the x-intercept is (4/3, 0).
Having all of this information, we can graph the first line using the points:
The y-intercept is (0, 3)
The x-intercept is (12,0)
And then, we can graph the second line using the points:
The y-intercept is (0, -1)
The x-intercept is (4/3, 0).
The graph is
And the solution is the point where both lines intercept each other, that is the point x = 4, and y = 2.
If we see the answer choices we have that the answer is the second graph.
The volume of the aquarium is V = pi (2h - 3)2h cubic inches.Which statement about the volume is true?A. The volume does not depend on area of the base, π (2h - 3)².B. The volume is a product of the area of the base, n (2h - 3)², and the height, h.C. The volume is a product of the radius, (2 h - 3), and the height, h.D. The volume is the sum of the area of the base, n (2h - 3)², and the height, h.
Answers
Given:
It is given that the volume of an aquarium is V = pi ((2h - 3)^2)h cubic inches.
where h is height and 2h-3 is radius as shown in the given figure,
Find:
we have to find the correct sentence about the volume of the aquarium.
Explanation:
we know the area of the base of the aquarium = pi(ra
Alex went to Sam's club and Bar a Halloween costume and several bags of candy she has $30 to spend the costume cost her $12 and each bag of candy cost her $3. write the equation of the representation of this situation.
Answers
hello
let the number of bags of candy be represented by x
[tex]30=12+3x[/tex]so x represents the total number of bags of candy she bought
total amount she spent = 30
she bought costume = $12
and bought x bags of candy
if a spacecraft is descending at a rate of 13.81 per minute. what its change in height after 5 1/2 min.
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using the formula A=bh, if the base if a rectangle is 5 feet and the height of the rectangle is 10 feet,what units would represent the area?
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Area of the rectangle = Base * height
A = bh, where
A is the area of the rectangle
b is its base
h is its height
In the question the base of the rectangle is 5 feet
b = 5 ft
The height of the rectangle is 10 feet
h = 10 ft
Let us substitute b and h in the formula of A
[tex]A=5\times10=50ft^2[/tex]The area of the rectangle is 50 square feet
D. 52 3. Which statement is not true of the function? A. The independent variable is x. B. The dependent variable is y. C. When the input is 1, the output is -2. D. When the input is 8, the output is 32.
Answers
Given function
y = 5x - 8
From the function
x is an independent variable. Option A is true
y is a dependent variable. Option B is true
when the input x = 1 , y = 5x - 8
y = 5(1) - 8
y = 5 - 8
y = -3
Option C is not true
when the input x = 8 , y = 5x - 8
y = 5(8) - 8
y = 5 - 8
y = -3
For the following function, determine whether the function is one-to-one.{(2,6) , (3,9) , (-7,11) , (6, -8)}Is the function one-to-one?yes or no
Answers
Consider that one-to-one function is a relation in which to each element of the domain corresponds only one element of range. The domain are the first elements of the pairs of numbers in the given data and the range are the second elements.
Based on the previous description, you can conclude that the given function is one-to-one.
which set of Integers is represents the length of the sides of an a isosceles triangle
Answers
Consider that atriangle is said to be an isosceles triangle if its two sides are equal.
Since the set of integers represent the length of sides, two values must be identical for an isosceles triangle.
Therefore, options C and D are ruled out, as all three integers are different in both sets.
Now,consider that any three side measures can form a triangle if the following condition is satisfied,
[tex]\text{Largest Side}<\text{ Sum of the remaining two sides}[/tex]Consider option A,
[tex]\begin{gathered} 6<6+5 \\ 6<11 \end{gathered}[/tex]As the statement holds true, the given set of integers (6,6,5) can form a triangle.
Consider option B,
[tex]\begin{gathered} 3<1+1 \\ 3<2 \end{gathered}[/tex]As the statement is false, the given set of integers (1,1,3) cannot form a triangle.
Thus, option A contains the set of values that will form a triangle whose two sides are equal, that is, an isosceles triangle.
Therefore, option A is the correct choice.
what is 35 divided into 2800 show your work
Answers
0.0125
Explanation:[tex]\begin{gathered} 35\text{ divided into 2800} \\ \\ We\text{ n}eed\text{ to find the number that divides 35 into 2800 places} \\ \text{This becomes:} \\ \frac{35}{2800} \end{gathered}[/tex][tex]\begin{gathered} 7\text{ divides the numerator and denominator:} \\ \frac{35}{2800}=\frac{5}{400} \\ \text{divide both numerator and denominator by 5:} \\ \frac{5}{400}\text{ = }\frac{1}{80}\text{ =0.0125} \\ \\ \text{Hence, }35\text{ into 2800 is 0.0125} \end{gathered}[/tex]If 3 computer disks and 5 notebooks cost $7.50 and 4 computer disks and 2 notebooks cost $6.50, how much does 1 computer disk cost?Group of answer choices$0.75
Answers
let x be the price of the computer disc and let y be the price of the notebooks.
Given the information on the problem, we can write the following equations:
[tex]\begin{gathered} 3x+5y=7.50 \\ 4x+2y=6.50 \end{gathered}[/tex]we can solve for y on the second equation to get the following:
[tex]\begin{gathered} 4x+2y=6.50 \\ \Rightarrow2y=6.50-4x \\ \Rightarrow y=\frac{6.50}{2}-\frac{4x}{2}=3.25-2x \\ y=3.25-2x \end{gathered}[/tex]then, we can substitute this expression on the first equation to get the following:
[tex]\begin{gathered} 3x+5(3.25-2x)=7.50 \\ \Rightarrow3x+16.25-10x=7.50 \\ \Rightarrow-7x=7.50-16.25=-8.75 \\ \Rightarrow x=\frac{-8.75}{-7}=1.25 \\ x=1.25 \end{gathered}[/tex]therefore, the cost of 1 computer disk is $1.25
Evaluate the expression when a = 3/10 and x = -3/20 4x-a write your answer in simplest form