The table below gives the dimensions of a statue and a scale drawing of the statue.
Find the scale factor of the drawing to the real statue.
Write your answer as a fraction in simplest form.

Answer:

slope = 2.5 and the y intercept is 3

Step-by-step explanation:

To find the slope we can use the formula

m = (y2-y1)/(x2-x1)

I will use the point (2,8) (6,18)  We can pick any 2 point we want.

 = (18-8)/(6-2)

  = (10/4)

  = 2.5

To find the y intercept we need to find the equation of the line.

We will use the point slope form

y-y1= m(x-x1)

y-8 = 2.5(x-2)

Distribute the 2.5

y-8 = 2.5x-5

Add 8 to each side

y-8+8 = 2.5x-5+8

y = 2.5x+3

This equation is in slope intercept form  y = mx+b

where the slope is 2.5 and the y intercept is 3

Hi There!

-----------------------------------

Find The Slope:

[tex]m = \frac{13 - 8}{4 - 2} = \frac{5}{2} or 2.5[/tex]

-----------------------------------

Find The Y-Intercept:

Substitute using x = 2 and y = 8

Use y = mx + b

Substitute: 8 = 2.5(2) + b

Simplify: 8 = 5 + b

Subtract 5 too both sides: 8 - 5 = 5 + b - 5

Simplify: 3 = b

Y-Intercept = 3

-----------------------------------

Point Slope Form: y - 8 = 2.5(x - 2)

Slope Intercept Form: y = 2.5x + 3

-----------------------------------

Hope This Helps :)

Answer:

angle A and angle D equals 100 degrees, angle B and angle E equals 30 degrees, and angle C and angle F equal 50 degrees.

Step-by-step explanation:

a triangle has to equal 180 degrees, and since they are similar, it should equal the same. Hope this helped you. :))

The angles of triangles △ABC and △DEF, which are similar, are 100°, 30°, and 50°. This is calculated using the properties of similar geometry and the fact that the sum of all angles in a triangle equals 180°.

In Triangle Similarity, the corresponding angles are equal due to the property of similarity in geometry.

Since we know that △ABC and △DEF are similar and we have m∠A=100° and m∠B=30°, we can determine that angles A and B in triangle △DEF are also 100° and 30°, respectively.

The third angle in both triangles can be calculated using the property that the sum of all angles in a triangle equals 180°.

Hence, in △DEF and △ABC we can calculate the measure of the third angle by 180° - (100°+30°) = 50°.

So for triangles △ABC and △DEF, the angles are 100°, 30° and 50° respectively.

Learn more about Triangle Similarity here:

https://brainly.com/question/14926756

#SPJ6

The number you are looking for is 89.

The number you are looking for is 89.

Here is how we can find it:

https://brainly.com/question/35915729

#SPJ2

The concept of solving a problem by elimination is to solve for one variable, by getting rid of the other.

Let's solve [2y = x + 2, x - 3y = -5] in terms of y.

Start by transforming the second equation into one of the same form as the first (y = x + c).

x-3y = -5

x = -5 + 3y

3y = x+5

Now we have two equations that are in the same form:

3y = x+5

2y = x+2

To solve in terms of y, we need to get rid of x -- so subtract the first equation from the second equation - this will yield the following:

y = 3 [[ 3y - 2y = y, x - x = 0, 5 - 2 = 3 ]]

Now take this information and solve for x:

2(3) = x+2

6 = x+2

x = 4

Now we have the solution, just make it a coordinate point:

(4, 3)

Answer:

Apex Answer (4,3)

Step-by-step explanation:

Just did the apex quiz yall add me julius_rob

Answer:

The system of linear equations are

y = 15 + 2x  

y = 3x

Step-by-step explanation:

Let us assume that the number of new release movies be x.

Let us assume that the total cost  be y.

As given

Members of a movie rental club pays a minimum of $15 annual membership fee and $2 for new release movies.

Than the equation becomes

y = 15 + 2x

As given

Nonmembers pay $3 for new release movies.

y = 3x

Therefore the system of linear equations are

y = 15 + 2x  

y = 3x

Answer: Let x=length of the longest side of the smaller triangle.

x/20=3/12

x=60/12

x=5

Final answer:

To find the longest side of the similar triangle, multiply the longest side of the original triangle (20) by the scale factor, which is the ratio of the shortest sides (3/12 = 0.25). This results in a longest side of 5 units for the similar triangle.

Explanation:

The question pertains to finding the longest side of a similar triangle given that the shortest side is 3 and the original triangle has sides 12, 15, and 20. To find the answer, we need to calculate the scale factor between the similar triangles. The scale factor is obtained by dividing the shortest side of the new triangle (3) by the shortest side of the original triangle (12), which is ¼ or 0.25.

We then multiply the longest side of the original triangle (20) by the scale factor (0.25) to get the longest side of the similar triangle. Calculating, 20 * 0.25 = 5. Therefore, the longest side of the triangle with the shortest side 3 is 5 units long.

Answer:

7 buses are needed.

Step-by-step explanation:

There are 325 students and adults.

Each bus holds 48 people.

The number of buses needed = [tex]\frac{325}{48}[/tex] = 6.770833333

Since we cant have 0.770833333 buses, we accept that only 7 buses are needed here and that;

325 - (48 × 6) = 37 people will not fill the last bus.

Answer:

Total charge per month = $ 16 + (0.08) * x

equation for having same charge

0.08 x - 0.12 y = 8

Step-by-step explanation:

Part 1:

Monthly fee = $ 16

Per check fee = $ 0.08

Checks signed in month = x

Total Charge monthly = Monthly fee + Checks fee

Putting the values

Total charge per month = 16 + (0.08) * x             ...........(i)

Part 2: Let she signs y checks for account B

Monthly fee of B = $ 14

per check fee = @ 0.12

Total Charge = monthly fee + checks fee

                     =  $ 14 + y *(0.12)                         ..................(ii)

For having same value in the bank then equation (i) and  (ii) shuld be equal to each other

i.e.

16 + 0.08x = 24 + 0.12y

0.08 x - 0.12 y = 24-16

0.08 x - 0.12 y = 8

this will be the equation

Answer:

We will need 27/31 of an ounce of red

Step-by-step explanation:

3 /10 red + 11 /15 blue  makes 1 1/30 purple

Get a common denominator of 30

3/10 * 3/3 = 9/30  red

11/15 *2/2 = 22/ 30  blue

1  1/30 = 31/30   purple

So the ratio of red to purple is

9/30

--------  =   9/ 31

31/30

Keeping this ratio, we want 3 ounces purple

9 red                      x red

--------           =  --------------

31 purple             3   purple

Using cross products,

9*3 = 31 *x

27 = 31x

Divide each side by 31

27/31 = x

We will need 27/31 of an ounce of red

Answer:

f(x) = -8 x + 34

Step-by-step explanation:

First, normalize the equation 8y = x-16 into y = ... form (divide by 8):

y = 1/8 x - 2

So the slope of this line is 1/8. The slope of a perpendicular line is the negative reciprocal, which means you swap numerator and denominator and add a minus sign. So the slope of our line is -8 and our function will look like f(x) = -8x + b

Now all we have to do is find b such that f(x) goes through (5,-6).

So f(5) = -8*5 + b = -6, and solve it for b:

-40 + b = -6 =>

b = 34.

So f(x) = -8x + 34

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}.\\\\\text{We have}\ 8y=x-16\qquad\text{divide both sides by 8}\\\\y=\dfrac{1}{8}x-2\to m_1=\dfrac{1}{8}.\\\\\text{Let}\ y=mx+b.\ \text{It's perpendicular to given line. Therefore}\ m=-\dfrac{1}{\frac{1}{8}}=-8.\\\\y=-8x+b.\\\\\text{The line passes through point (5, -6)}.\ \text{Put the coordinates of the point}\\\text{to the equation of a line:}[/tex]

[tex]-6=-8(5)+b\\-6=-40+b\qquad\text{add 40 to both sides}\\34=b\to b=34\\\\Answer:\ \boxed{f(x)=-8x+34}[/tex]

Answer:

System has only one solution. x= 4 and y = 2.

Step-by-step explanation:

We have given two equations :

2x + y = 10    ----------(1)

x - 3y = -2   ----------(2)

From equation (2), we can write:

x - 3y = -2

or x = -2 + 3y  , substitute this in equation (1).

We get,  2x + y = 10

2*(-2 + 3y) + y = 10

-4 + 6y + y = 10

7y = 10 + 4

y = 14/7 = 2

And x = -2 + 3*2 = -2 + 6 = 4

Hence we get x= 4 and y = 2. System has only one solution

The system of equations 2x+y=10 and x-3y=-2 has one solution, which is found by solving for y in terms of x using the first equation, substituting into the second equation, and solving for x, then solving for y. The solution is (4, 2).

To solve the system by substitution, we can express one variable in terms of the other using one of the equations and then substitute this into the second equation. Starting with the system:

2x + y = 10

x - 3y = -2

We can solve the first equation for y:

y = 10 - 2x

Next, we substitute this expression for y into the second equation:

x - 3(10 - 2x) = -2

Solving this equation for x:

x - 30 + 6x = -2

7x = 28

x = 4

Now we substitute x = 4 back into the equation y = 10 - 2x to find y:

y = 10 - 2(4)

y = 2

So the one solution to the system is (4, 2).

Since we found a unique solution, the system of equations has exactly one solution and is therefore consistent and independent.

[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\dfrac{4}{-3\sqrt{64}}=\dfrac{\not4^1}{-3(\not8_2)}=-\dfrac{1}{6}[/tex]

The answer you are looking for is 9/11.

When dividing fractions, you multiply the first value by the inverse of the second value. The inverse is found by simply flipping the numbers of the last fraction. So, the inverse is 9/4. Then, multiply 4/11 and 9/4 to get 36/44. 36/44 simplified (divided by 4/4) is 9/11. Thus making 9/11 the answer.

I hope this helps.

Answer:

9/11

Step-by-step explanation:

Answer:

Ricky = 1201

Pedro = 1476

Step-by-step explanation:

Assign variables

let p be the number of Pedro's base hits

let r be the number of Ricky's base hits

Create a system of equations

p + r = 2677            <= Pedro and Ricky got 2677 base hits

p = r + 275              <= Pedro had 275 more hits than Ricky

Solve using the substitution method (replace a variable with an expression)

p + r = 2677

Substitute "p" with "r + 275"

r + 275 + r = 2677

Combine like terms to simplify

2r + 275 = 2677

Isolate "r" by moving everything else to the right side.

2r = 2677 - 275                  Subtract 275 from both sides

2r = 2402

2r/2 = 2402/2                     Divide both sides by 2

r = 1201                              Ricky's base hits

To find Pedro's hits, substitute "r" into any equation.

p = r + 275

p = 1201 + 275                    Substitute r = 1201, then add

p = 1476                             Pedro's base hits

∴ Ricky had 1201 base hits and Pedro had 1476 base hits.

Final answer:

By setting up an equation where R represents Ricky's hits, and calculating R + 275 for Pedro's hits, we can solve for R and then find the number of hits for each player. Ricky had 1201 hits, while Pedro had 1476 hits.

Explanation:

To solve the problem of determining how many base hits Pedro and Ricky each had last season, we can use algebra. Let's let the variable R represent the number of hits Ricky had. Since Pedro had 275 more hits than Ricky, we can express Pedro's number of hits as R + 275. According to the question, the sum of their hits is 2677, so the equation will be R + (R + 275) = 2677.

Now, let's solve the equation:

R + R + 275 = 2677

2R + 275 = 2677

2R = 2677 - 275

2R = 2402

R = 2402 / 2

R = 1201

So, Ricky had 1201 hits. To find Pedro's hits, we substitute R into the expression R + 275:

Pedro's hits = R + 275 = 1201 + 275 = 1476

Therefore, Ricky had 1201 hits and Pedro had 1476 hits.

Answer:

1/12 of the watermelon in each piece

Step-by-step explanation:

The final answer is 1/12.

I hope this helped!

Answer:

The fraction of the watermelon that corresponds to each piece is [tex]\frac{1}{12}[/tex]

Step-by-step explanation:

Caleb has [tex]\frac{1}{3}[/tex] of a watermelon. To know what fraction each portion of watermelon represents after cutting it into 4 equal parts, just divide the portion that Caleb owns ([tex]\frac{1}{3}[/tex]) by the amount of sliced ​​portions (4):

[tex]\frac{\frac{1}{3} }{4}[/tex]

Given that 4 can also be represented by the fraction [tex]\frac{4}{1}[/tex], then:

[tex]\frac{\frac{1}{3} }{\frac{4}{1} }[/tex]

To divide two fractions, the SECOND FRACTION must be reversed, that is, change the denominator to the numerator and change the numerator to the denominator. Then, the two fractions are multiplied.

[tex]\frac{\frac{1}{3} }{\frac{4}{1} } =\frac{1}{3} *\frac{1}{4} =\frac{1}{12}[/tex]

The fraction of the watermelon that corresponds to each piece is [tex]\frac{1}{12}[/tex]

The coefficient of q in the sum of (23q - 34) and (-16q - r) is 7.

In mathematics, a coefficient is a numerical factor or constant that multiplies a variable or term in an algebraic expression. It determines the scale or magnitude of the term and is often used in equations, polynomials, and linear expressions.

The sum of the two expressions is (23q - 34) + (-16q - r).

To find the coefficient of q in this sum, we need to combine the like terms.

Combining the q terms, we have 23q - 16q = 7q.

Therefore, the coefficient of q in the sum of the two expressions is 7.

Answer:

SA = 201 in^2

Step-by-step explanation:

The formula for surface area of a sphere is

SA = 4pi r^2

We know that the diameter is 8

To find the radius we cut the diameter in half.

r = d/2

r = 8/2 =4

Substitute in what we know.

SA = 4 *pi *4^2

    = 4*pi*16

   = 64*pi

Letting pi = 3.14

  = 200.96 in^2

We want to round to the nearest whole number

SA = 201 in^2

Answer:   The answer is C

Step-by-step explanation:  15 - 2 = 13     13+5=18

Hope this helps :)

Answer:

9R30  

Step-by-step explanation:

         9

36)354

    324

      30

The volume of a larger cone:

[tex]V_l=\dfrac{1}{3}\pi\cdot4.5^2\cdot(3+6)=\dfrac{1}{\not3_1}\pi\cdot20.25\cdot\not9^3=(20.25)(3)\pi=60.25\pi\ cm^3[/tex]

The volume of a smaller cone:

[tex]V_s=\dfrac{1}{3}\pi\cdot3^2\cdot6=\dfrac{1}{\not3_1}\pi\cdot\not3^1\cdot3\cdot6=18\pi\ cm^3[/tex]

The volume of the frustum:

[tex]V=V_l-V_s\\\\V=60.25\pi-18\pi=42.75\pi\ cm^3[/tex]

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (1, 3) and (3, 1). Substitute:

[tex]d=\sqrt{(3-1)^2+(1-3)^2}=\sqrt{2^2+(-2)^2}=\sqrt{4+4}=\sqrt8\approx2.8[/tex]

Answer:

9/25

Step-by-step explanation:

The answer is 9/25

Answer:

Option B.

Step-by-step explanation:

Dr. Peterson works about 178 hours each month.

There are 12 months in one year.

So Dr. Peterson works in a year = 178 × 12 = 2,136 hours

We will go through all the options to find which is the closest to the answer.

Option A : 200 × 20 = 4,000 hours

Option B : 180 × 10 = 1,800 hours

Option C : 100 × 12 = 1,200 hours

Option D : 100 × 10 = 1,000 hours

Therefore, Option B is the best estimate of the number of the hours she works in a year.

Answer:2x−3y=6

Step-by-step explanation:Standard form: Ax + By = C

Just take 2/3x to the other side.

So the answer would be

−23x+y=−2

In standard form

x

can't be negative and A, B and C need to be an integers (whole numbers)

(I multiplied the whole equation by -3)

2x−3y=6

So the final answer would be: 2x−3y=6

Answer:

-3

Step-by-step explanation:

6-4 (x+3)

2(x+3)

2x+6=0

2x=-6

2x/2= -6/2

x=-3

Answer:

First, you have to get all of the variables on one side of the equation.

x15 on both sides

8 + a = 15+15a/6

x6 on both sides

48 + 6a=15+15a

Subtract 15 on both sides and Subtract 6a on both sides

33=11a

a=3

Step-by-step explanation:

Answer:

[tex]\frac{19}{12}[/tex] feet

Step-by-step explanation:

First, we need to find the height after one year:

2.25 + 1 1/6 = [tex]\frac{41}{12}[/tex]

Now to find the amount in the second year, we can subtract the above amount from 5:

5 - [tex]\frac{41}{12}[/tex] = [tex]\frac{19}{12}[/tex]

So in the second year it grew [tex]\frac{19}{12}[/tex] feet

Answer:

$60

Step-by-step explanation:

Each payment was 10% of $600.

You need to find what 10% of $600 is.

To find a percent of a number, multiply the percent by the number. Change the percent to a decimal by moving the decimal point of the percent two places to the left.

10% of $600 =

= 10% * $600

= 0.10 * $600

= $60

Answer:

60

Step-by-step explanation:

600 * .10= 60

To find out how much longer the record alligator is than the one Taylor saw, we subtract the length of the alligator Taylor saw from the record length. The record alligator is 6 feet and 3/4 feet longer than the alligator Taylor saw.

To find out how much longer the record alligator is than the one Taylor saw, we need to subtract the length of the alligator Taylor saw from the record length.

To do this, we need to convert the mixed numbers to improper fractions. 12 11/12 is equal to 155/12 and 19 1/6 is equal to 115/6.

Subtracting 155/12 from 115/6 gives us (115/6) - (155/12) = (230/12) - (155/12) = 75/12 = 6 3/4.

Therefore, the record alligator is 6 feet and 3/4 feet longer than the alligator Taylor saw.

Answer:

y = 3(x + 3)² - 31

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h. k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

take out a common factor of 3 from the first 2 terms

y = 3(x² + 6x) - 4

add/subtract ( half the coefficient of the x-term)² to x² + 6x

y = 3(x² + 2(3)x + 9 - 9 ) - 4

y = 3(x + 3)² - 27 - 4

y = 3(x + 3)² - 31 ← in vertex form