Find the slope of the line represented by the table of values.
A) 1/2
B) 2
C) −1/2
D) −2

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:

$22.30

Step-by-step explanation:

To determine how much money Chapman saved from purchasing a gift for his mother, calculate 2/5 of $55.75, which equals $22.30.

To find how much money Chapman saved:

Calculate 2/5 of $55.75: (2/5) x $55.75 = $22.30

Therefore, Chapman saved $22.30

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:

$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

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

The number you are looking for is 89.

The number you are looking for is 89.

Here is how we can find it:

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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.

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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:

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]

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:

9/25

Step-by-step explanation:

The answer is 9/25

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:

72 is 8 times as many as 9

Step-by-step explanation:

72 is the product of 8 groups of nine

72 is 9 times as many as 8 is the answer that completes the statement.

To solve the equation 72 = q × 8, we need to find the value of q.

By dividing both sides by 8, we get:

72/8 = q × 8/8

q = 72/8

q = 9.

This means that 72 is 9 times greater than 8 and to correctly complete the statement, we write: 72 is 9 times as many as 8.

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]

Answer:

-10

Step-by-step explanation:

Write out the equation

5n-8=n-48

move like terms to the same side

4n=-40

divide 4n and 4 by 4 to get n by itself.

n=-10

The number is -10.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given,

Eight less than 5 times a number is 48 less than the number

Let the number be x

then statement can be written as

5x - 8 = x - 48

5x - x = - 48 + 8

4x = -40

x = 40/4

x = -10

Hence, -10 is the number.

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Answer:   The answer is C

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

Hope this helps :)

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:

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

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:

[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:

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.

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]

[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]

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

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:

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:

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:

n=2

Step-by-step explanation:

I am assuming that you want to solve this algebraic equation

4n+3 =11

Subtract 3 from both sides

4n+3-3=11-3

4n =8

Divide each side by 4

4n/4 = 8/4

n =2