if you draw two right triangles using the line as the hypotenuse, do the triangles have to be similar? Why or why not?

Answer:

The function is y = 2x + 1.

And mike graphed the function correctly.

Menna took the point where the function touches x-axis incorrectly.

Instead of (-1/2,0), Menna took it as (-2,0)

Step-by-step explanation:

The equation y = mx +c indicates a straight line whose slope is m

And y-intercept is c.

y-intercept is nothing but the distance between origin and point where the graph crosses the y-axis (0,c).

Now, this graph crosses x-axis when y = 0.

⇒ mx + c = 0;       ⇒ x = [tex]\frac{-c}{m}[/tex].

Now, by comparing y = 2x + 1 with y = mx + c.

m=2 and c=1

⇒ the graph should crosses y-axis at (0,c) = (0,1)

And touch x-axis at ([tex]\frac{-c}{m}[/tex] , 0) = ([tex]\frac{-1}{2}[/tex],0)

⇒ mike graphed the function correctly.

Menna took the point where the function touches x-axis incorrectly.

Instead of (-1/2,0), Menna took it as (-2,0)

Answer:

Step-by-step explanation:

y = 2x + 1.

Answer:

Use distributive property, add 3z to both sides, divide by -8 on both sides

Step-by-step explanation:

You have to do parenthesis first, then equal both sides, then divide

The x-coordinate of the point that divides the  directed line segment from K to J into a ratio of 1:3 is 7

Step-by-step explanation:

The formula for x-cooridnate of a point that divides a line in ratio m:n is given by:

[tex]x = \frac{nx_1+mx_2}{m+n}[/tex]

Given

K(9,2) = (x1,y1)

J(1,-10) = (x2,y2)

m = 1

n = 3

Putting the values in the formula

[tex]x = \frac{(3)(9)+(1)(1)}{1+3}\\x = \frac{27+1}{4}\\x = \frac{28}{4}\\x = 7[/tex]

Hence,

The x-coordinate of the point that divides the  directed line segment from K to J into a ratio of 1:3 is 7

Keywords: Ratio, fraction

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Find base and height of the triangle to find area.

Base=Perimeter/3

Base=36/3=12 cm

Height²=12²-6²

Height²=108

Height=(6√3) cm

area=base×height

area=1/2×12×6√3=62 cm² approx.

answer: 3rd choice

Answer:

Find base and height of the triangle to find area.

Base=Perimeter/3

Base=36/3=12 cm

Height²=12²-6²

Height²=108

Height=(6√3) cm

area=base×height

area=1/2×12×6√3=62 cm² approx.

answer: 3rd choice

Step-by-step explanation:

Answer:

Step-by-step explanation:

So the first step is to simply set up the problem based on what we are given. So here have two numbers, we are going to call the first number x and the second one y. With that now addressed, we can now proceed with the setup.

So the difference between the squares of the numbers is 24. So we have:

[tex]x^{2} -y^{2} = 24[/tex]

Then it says that three times the square of the first number (which we said was x) increased by the square of the second number is 76. So:

[tex]3x^{2} + y^{2} = 76[/tex]

Now we can see that this is simply a system of equations and we can use elimination to solve this! We even have the setup already as the coefficients in front of our y are opposite in sign and are equal. So:

[tex]x^{2} -y^{2} = 24\\3x^{2} +y^{2} = 76[/tex]

We can cancel our y squared terms out and that leaves, when we add the equations together:

[tex]4x^{2} = 100[/tex]

We can then solve for x by diving by four and taking the square root of the result.

[tex]x^{2} = 25\\[/tex]

Therefore, x = ±5

We have both negative and positive answers because if we squared -5 or +5 they would both give us 25. So we cant rule a negative answer out yet.

So now we can plug in x = -5 or +5 to either equation to solve for y as so:

[tex]5^{2} - y^{2} = 24\\25 - y^{2} = 24\\-y^{2} = -1 \\y^{2} = 1[/tex]

So y = ±1

In this case both negative and positive versions of our answer work (you can also double check), so we are left with:

x = ±5 and y = ±1

We can solve the problem by expressing one variable through another from one equation and substituting it into the second equation. Then solve for the first variable and substitute the found value in one of the equations to find the corresponding other variable.

The subject of this question is algebra, specifically equations involving squares of numbers and systems of equations. Let's denote the unknown numbers as 'x' and 'y'. From the problem, we know two equations:

One possible approach to finding the values of x and y would be to use the substitution method. From equation (1), we can express y² as x² - 24 and substitute this into equation (2):

3x² + (x² - 24) = 76

If we simplify and solve for x, we find that x = 4, -4.

Then, substituting 'x' into the first equation will yield corresponding 'y' values. That's how you can solve this kind of problems by using squares of numbers and method of substitution.

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Answer:

9

Step-by-step explanation:

9 times 5 =45

Answer:

9

Step-by-step explanation:

When you do the math, 9 multiplied by 5 will get you 45

Answer:

6 bicycles and 3 tricycles

Step-by-step explanation:

bicycles have two wheels therefore 6*2=12 total wheels

tricycles have three wheels therefore 3*3=9 total wheels

add the totals up and you have 21 total wheels

Final answer:

The shop can build 6 bicycles and 3 tricycles with the 21 wheels available.

Explanation:

To solve the problem of figuring out how many tricycles and bicycles can be built with 21 wheels, under the condition that there will be half as many tricycles as bicycles, we use algebraic methods.

Let's denote the number of bicycles as B and the number of tricycles as T.

Since each bicycle needs 2 wheels and each tricycle needs 3, we can establish the following equations based on these facts and the condition given:

Substituting T from the second equation into the first gives:

2B + 3(0.5B) = 21

2B + 1.5B = 21

3.5B = 21

B = 21 / 3.5 = 6

So, there are 6 bicycles. To find T, plug B back into the equation T = 0.5B:

T = 0.5×6 = 3

Therefore, the shop can build 6 bicycles and 3 tricycles with the 21 wheels available.

Answer:

Yes, △ABC ∼ △FED by AA postulate.

Step-by-step explanation:

Given:

Two triangles ABC and FED.

m∠A = m∠B

m∠C = m∠A + 30°

m∠E = m∠F = [tex]x[/tex]

m∠D = [tex]2x-20[/tex]°.

Now, let m∠A = m∠B = [tex]y[/tex]

So, m∠C = m∠A + 30° = [tex]y+30[/tex]

Now, sum of all interior angles of a triangle is 180°. Therefore,

m∠A + m∠B +  m∠C = 180

[tex]y+y+y+30=180\\3y=180-30\\3y=150\\y=\frac{150}{3}=50[/tex]

Therefore, m∠A = 50°, m∠B = 50° and m∠C =  m∠A + 30° = 50 + 30 = 80°.

Now, consider triangle FED,

m∠D+ m∠E + m∠F = 180

[tex]2x-20+x+x=180\\4x=180+20\\4x=200\\x=\frac{200}{4}=50[/tex]

Therefore,  m∠F = 50°  

m∠E = 50° and  

m∠D =  [tex]2x-20=2(50)-20=100-20=80\°[/tex]

So, both the triangles have congruent corresponding angle measures.

m∠A = m∠F = 50°

m∠B = m∠E = 50°

m∠C = m∠D = 80°

Therefore, the two triangles are similar by AA postulate.

Abdul drove the truck for 177 miles.

To find the number of miles driven by Abdul, we need to subtract the base fee from the total amount he paid and then divide the result by the additional charge per mile. Let's represent the number of miles driven by x.

Total amount paid - Base fee = Additional charge per mile * Number of miles driven

$146.16 - $16.95 = $0.73 * x

Simplifying the equation: $129.21 = $0.73x

Dividing both sides by $0.73, we get: x = 177

Therefore, Abdul drove the truck for 177 miles.

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Answer:

square root of 72 is approximately 8.49

i hope that right!

Step-by-step explanation:

Answer:

190.02

Step-by-step explanation:

Trust

The ending balance of the account after 8 years is approximately $184.16.

To find the ending balance of the account after 8 years, we can use the equation t=log1.03(E/150), where t is the time in years and E is the ending balance. Since the account was open for 8 years, we can substitute t=8 into the equation.

8=log1.03(E/150)

To solve for E, we can isolate it by first multiplying both sides of the equation by 150 and then raising both sides to the power of 1.03.

E/150=1.03⁸

E=150*1.03⁸

Using a calculator, we can find that E is approximately $184.16.

Answer:

[tex](2x+5)(4x^{2} -10x+25)=0[/tex]

Step-by-step explanation:

Given:

The given equation is.

[tex]8x^{3} +125=0[/tex]

Find the some of cube.

Solution:

[tex]8x^{3} +125=0[/tex]

[tex]2^{3}x^{3} +5^{3}=0[/tex]

[tex](2x)^{3} +5^{3}=0[/tex]----------(1)

The sum of the cube formula is given below.

[tex](a^{3} +b^{3})=(a+b)(a^{2} -ab+b^{2} )[/tex]-----------(2)

By comparing equation 1 and equation 2

[tex]a=2x, b=5[/tex]

substitute a and b value in equation 2

[tex]((2x)^{3} +5^{3})=(2x+5)((2x)^{2} -(2x)(5)+5^{2})[/tex]

[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -(10x)+25)[/tex]

[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -10x+25)[/tex]

Therefore the sum of the cube [tex](2x+5)(4x^{2} -10x+25)=0[/tex]

Answer:

The equation of the required line is: 2x + y = 8

Step-by-step explanation:

When a point on the line and the slope of the line are given, we use the slope - one - point form to determine the equation of the line.

Say, [tex]$ (x_1, y_1) $[/tex] is the point passing through the line and the slope of the line is say, [tex]m[/tex]. Then the equation would be:

                      [tex]$ (y - y_1) = m(x - x_1) $[/tex]

Here [tex]$ (x_1, y_1) = (7, -6) $[/tex] and slope, [tex]$ m = - 2 $[/tex].

Therefore, the equation of the line becomes:

[tex]$ y - (-6) = -2(x - 7) $[/tex]

[tex]$ \implies y + 6 = -2x + 14 $[/tex]

Rearranging we get:

[tex]$ 2x + y - 8 = 0 $[/tex] which is the required equation of the line.

By dividing 452 pictures of dogs by 4, we find that each of the 4 equal groups has 113 pictures. The division process involves using place value and the standard algorithm for long division.

To find out how many pictures of dogs are in each group, we need to divide the total number of pictures by the number of groups. The question states there are 452 pictures of dogs and these are divided into 4 equal groups. We can use long division to solve this.

Step-by-Step Solution:

Write down the division: 452 ÷ 4.

Start by looking at the hundreds place in 452. There are 4 hundreds in 452. Since 4 divided by 4 is 1, we put 1 in the hundreds place of the quotient.

Multiply the divisor (4) by the quotient (100) to get 400.

Subtract 400 from 452 to get 52.

Now, look at the tens place in 52. There are 5 tens in 52, and since 5 divided by 4 is 1 with a remainder, we put 1 in the tens place of the quotient and have a remainder of 12 after subtracting 40 (1 x 4 tens) from 52.

Next, look at the ones place in 12. There are 12 ones, and since 12 divided by 4 is 3, we put 3 in the ones place of the quotient.

After placing 3 in the ones place, we have no remainder, which means the division is complete and the quotient is 113.

Therefore, each group has 113 pictures of dogs.

Answer:

25.6

Step-by-step explanation:

Convert the percentage to decimal form by dividing by 100.

4% of 640

= 0.04(640)

= 25.6

Answer:

the number is X=2

Step-by-step explanation:

Suppose number is X

8X-1 =X+13

8X-X= 13+1

7X=14

X=2

Answer:

8n-1= 13+n is the equation, n=2 is the answer for the variable.

Step-by-step explanation:

8n-1= 13+n

Move the variable to one side.

8n-1= 13+n

-1n         -1n

7n-1= 13

Now, add to both sides, since that is the opposite of subtracting.

7n-1= 13

   +1  +1

Then, divide to both sides by 7 to leave the variable by itself.

7n= 14

7     7

n= 2

Answer:

The statement is false

Step-by-step explanation:

we have

[tex]4y=x[/tex]

Solve for y

That means ----> Isolate the variable y

Divide by 4 both sides

[tex]y=\frac{1}{4}x[/tex]

This is the equation of a proportional relationship between the variable x and the variable y

where the constant of proportionality k or slope m is equal to 1/4

therefore

The statement is false

Answer: none

Step-by-step explanation: since -6x+3y can't equal to -7−6x+3y

Answer:

8 or -4

Step-by-step explanation:

The error is they believed x2 meant x^2 OR they forgot that x could also equal to -4.

x^2 = 16 has two solutions. They are 4 and -4. So the value of x could also be -4.

Answer:

To answer X and Y, all you need is a little common sense and a little bit of algebraic thinking. -x can equal: -x = 0? -6?, etc. Y could equal: 3?, 6?, 12?, etc. But the answer will always no matter what number will be 6.

Answer:

[tex]AB=\dfrac{38}{3}\ units[/tex]

Step-by-step explanation:

ABCD is a rhombus, then

[tex]AB=BC=CD=DA[/tex]

Since

[tex]BC=2x+8\\ \\CD=5x+1,[/tex]

then

[tex]BC=CD\Rightarrow 2x+8=5x+1[/tex]

Solve this equation:

[tex]2x-5x=1-8\\ \\-3x=-7\\ \\3x=7\\ \\x=\dfrac{7}{3}[/tex]

Then

[tex]BC=2\cdot \dfrac{7}{3}+8=\dfrac{14}{3}+8=\dfrac{14+8\cdot 3}{3}=\dfrac{14+24}{3}=\dfrac{38}{3}\ units[/tex]

Therefore,

[tex]AB=\dfrac{38}{3}\ units[/tex]

Answer:

Number of movies that can be shown = 2

Step-by-step explanation:

Given:

Movie night duration = 4 hours

Duration of each movie = 1.75 hours

Time given for eating popcorn = 0.5 hours

Time alloted for movies (excluding popcorn time) = 4 - 0.5 = 3.5 hours.

Number of movies that can be shown = [tex]\frac{Total\ time\ alloted\ for\ movie}{Time\ for\ 1\ movie}=\frac{3.5}{1.75}= 2[/tex]

To determine the number of movies that can be watched, an equation M*X <= T can be formulated where M is the length of the movie, X is the number of movies, and T is the total time available. To find X, divide T by M. This works when the time for each movie is the same.

Without the actual graphic novel frame, it's hard to provide a specific equation. However, I can give you an example on how to approach this situation. Let's assume each movie is of length 'M' minutes and you have a total of 'T' minutes available for watching movies.

,

Let 'X' be the number of movies you can watch. You would write this as a mathematical equation like this: M*X <= T. This equation states that the total time spent watching movies should be less than or equal to the total time available.

,

To solve the equation, you would divide both sides of the equation by 'M'. The result will be X <= T/M. If you know the values of 'M' and 'T', you can plug them in here to get the maximum number of movies you can watch.

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(2/3)²+5×2-4

(4/9)+5×2-4

(4/9)+10-4

10 4/9 - 4

6 4/9

answer: second choice

Answer:

A = π/6 + kπ, or A = 2π/3 + kπ

Step-by-step explanation:

tan A / (1 − tan² A) = √3 / 2

Cross multiply and simplify:

√3 (1 − tan² A) = 2 tan A

√3 − √3 tan² A = 2 tan A

3 − 3 tan² A = 2√3 tan A

0 = 3 tan² A + 2√3 tan A − 3

Solve with quadratic formula:

tan A = [ -2√3 ± √((2√3)² − 4(3)(-3)) ] / 2(3)

tan A = [ -2√3 ± √(12 + 36) ] / 6

tan A = (-2√3 ± √48) / 6

tan A = (-2√3 ± 4√3) / 6

tan A = -√3 or √3/3

Solve for A:

A = 2π/3 + kπ, or A = π/6 + kπ

From Patrick's gains, tax rates, and the inflation rate, the following are true: $346.25, $1,731.25, $145.43 and $4,702.08.

State tax on initial profit can be calculated by;

= (17,000 - 10,000 - 25 - 25 - 25) x 5%

= $346.25

The federal tax is:

= 25% x (17,000 - 10,000 - 25 - 25 - 25) x 25%

= $1,731.25

Inflation after taxes is:

= (17,000 - 7,000 - 25 - 25 - 25 - 346.25 - 1,731.25) * (1% + 1% + 1%)

= $145.43

Real value in profit is:

= 17,000 - 7,000 - 25 - 25 - 25 - 346.25 - 1,731.25 - 145.43

= $4,702.08

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Patrick's initial profit is $7,000, and after state and federal taxes, he has $4,900. When adjusted for a 1% annual inflation rate over three years, the real value of his profit is approximately $4,805.03.

Patrick's profit from selling his stock is calculated by subtracting the initial investment from the current value, $17,000 - $10,000 = $7,000. The state tax he must pay on this profit is 5% of $7,000, which equals $350. Similarly, the federal tax on the profit is 25% of $7,000, equaling $1,750. After state and federal taxes, the remaining amount is $7,000 - $350 - $1,750 = $4,900. Lastly, the inflation effect over three years at 1% per year diminishes the purchasing power of the remaining amount. The cumulative effect of inflation can be calculated by the formula P = P0 * ((1 - r)^n), where P is the future value, P0 is the present value, r is the inflation rate, and n is the number of years. Thus, Patrick's remaining profit adjusted for inflation would be $4,900 * ((1 - 0.01)^3), which gives a result of approximately $4,805.03. This is the real value of Patrick’s profit after taxes and inflation adjustments.

Answer:

About $0.10 per ounce

Step-by-step explanation:

12 pound costs $18.75. Lets find the cost per pound first:

Cost Per Pound = [tex]\frac{18.75}{12}=1.5625[/tex]

We know, there are 16 ounces in 1 pound.

We know 1 pound costs 1.5625

To find cost per ounce, we have to divide this by 16.

So,

Cost Per Ounce = [tex]\frac{1.5625}{16}=0.097[/tex]

Rounded to nearest cent, that would be 10 cents per ounce

Answer: 44

Step-by-step explanation:

we will find RN and NQ, then add together to give us RQ.

To find RN;

RP= 17 PN = 15 and RN =?

using pythagoras theorem,

adj^2 = hyp^2 - opp^2

RN^2 = RP^2 - PN^2

?^2 = 17^2 - 15^2

?^2 = 17^2 - 15^2

?^2 = 289 - 225

?^2 = 64

? = √64

? = 8

RN=8

To find NQ,

PN = 15 PQ=39 and NQ=?

using pythagoras theorem

NQ^2 = PQ^2 - PN^2

?^2 = 39^2 - 15^2

?^2 = 1521 - 225

?^2 = 1296

? = √1296

? = 36

NQ= 36

RQ = RN + NQ

RQ= 8 + 36

RQ=44

Answer:

(x - 2)(x + 2).

Step-by-step explanation:

This is the difference of 2 squares:

a^2 - b^2 = (a - b)(a + b)

So

x^2 - 4 = (x - 2)(x + 2).

The slope of given coordinates (0,-2) and (2,-1) is [tex]\frac{1}{2}[/tex]

The slope intercept form is [tex]y = \frac{1}{2}x -2[/tex]

Given that the coordinates are (0,-2) and (2,-1)

To find: slope and slope intercept form

The slope of line is given as:

For a line containing two points [tex](x_1 , y_1)[/tex] and [tex](x_2, y_2)[/tex] , slope of line is given as:

[tex]{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Here in this problem,

coordinates are (0,-2) and (2,-1)

[tex]x_{1}=0 ; y_{1}=-2 ; x_{2}=2 ; y_{2}=-1[/tex]

Substituting the values in above formula,

[tex]m=\frac{-1-(-2)}{2-0}=\frac{-1+2}{2}=\frac{1}{2}[/tex]

Thus slope of line is [tex]\frac{1}{2}[/tex]

To find slope intercept form:

The slope intercept form is given as:

y = mx + b

Where "m" is the slope of line and "b" is the y-intercept

Substitute [tex]m = \frac{1}{2}[/tex] and (x, y) = (0, -2) in above slope intercept we get,

[tex]-2 = \frac{1}{2} \times 0 + b[/tex]

b = -2

Thus the required slope intercept is given as:

Substitute [tex]m = \frac{1}{2}[/tex] and b = -2 in slope intercept form,

[tex]y = \frac{1}{2}x -2[/tex]

Thus the slope intercept form is found