Dorothy is 7 years older than her brother William. If the product of their ages is 78, how old is Dorothy?

The equivalent fractions shown on the fraction bar is 3/4 and 6/8.

The multiplier is 2.

The equivalent fractions shown on the fraction bar are 4/6 and 12/18.

The divisor is 3.

A fraction is a non whole number that is made up of a numerator and a denominator. The numerator is the number above the line and the denominator or divisor is the number below the line. An example of a fraction is 1/10. 1 is the numerator and 10 is the denominator.

Equivalent fractions are fractions that have different numerators and denominators but when expressed in its simplest form, they are the same fractions. For example, 1/2 and 3/6 are equivalent fractions because when 3/6 is expressed in its simplest form, it is 1/2.

In the first fraction bar given, there are 4 bars and 3 are shaded. Thus, the fraction it represents is 4/6. Likewise in the second fraction bar, 6 are shaded and there are 8 bars.

In the third fraction bar, 12 are shaded and there are a total of 18 bars. The fraction is 12/18. In the fourth fraction bar, 4 are shaded and there are 6 total bars. The fraction is 4/6.

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Answer:   2 x 4

Reason:

There are 2 rows and 4 columns. The order is important since 4x2 is different from 2x4.

Answer:

28

Step-by-step explanation:

J(x) = 3x^2 + 2x - 5

they have asked us to find J(3), therefore substitute x with 3 throughout the equation.

j(3) = 3*3^2 + 2*3 - 5

J(3) = 3*9 + 6 - 5

J(3) = 27 + 6 - 5
J(3) = 33 - 5 = 28

Considering the definition of parallel line, the statement "They are parallel" describes the graph of y= -x+3 and y=-x+6.

A linear equation o line can be expressed in the form y = mx + b

where:

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope or value of m and different y-intercepts or value of b.

In this case, you know:

Two lines are parallel if they have the same slope and different y-intercepts. Then, both lines are parallel.

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Answer:

Use the distributive property to solve this.

(3x²-5x+7)(2x²+x-2)

= 6x⁴+3x³-6x²-10x³-5x²+10x+14x²+7x-14

= 6x⁴-7x³+3x²+17x-14

Answer: 2.An element from the domain is paired with more than one element from the range.

Step-by-step explanation:

I did the quiz

Correct me if im wrong

Have a great day!

Answer:

B

Step-by-step explanation:

3 5/6 = 23/6

Reciprocal: 6/23 i hope you pass(ﾉ◕ヮ◕)ﾉ*:･ﾟ✧

Answer:

Step-by-step explanation:

hshshaahhs

Answer:

[tex]\textsf{Slope}: \quad \dfrac{1}{3}[/tex]

[tex]\textsf{Point-slope form}: \quad y-8=\dfrac{1}{3}(x-9)[/tex]

[tex]\textsf{Slope-intercept form}: \quad y=\dfrac{1}{3}x+5[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Slope formula}\\\\slope ($m$) $=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\end{minipage}}[/tex]

Define the given points:

Substitute the defined points into the slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-8}{-3-9}=\dfrac{-4}{-12}=\dfrac{1}{3}[/tex]

[tex]\boxed{\begin{minipage}{4.6 cm}\underline{Point-slope formula}\\\\$y-y_1=m(x-x_1)$\\\\where $m$ is the slope and\\ $(x_1,y_1)$ is a point on the line.\end{minipage}}[/tex]

Substitute point (9, 8) and the found slope into the point-slope formula:

[tex]\implies y-8=\dfrac{1}{3}(x-9)[/tex]

[tex]\boxed{\begin{minipage}{3.8 cm}\underline{Slope-intercept formula}\\\\$y=mx+b$\\\\where $m$ is the slope\\ and $b$ is the $y$-intercept.\end{minipage}}[/tex]

To write the equation of the line in slope-intercept form, rearrange the point-slope formula:

[tex]\implies y-8=\dfrac{1}{3}(x-9)[/tex]

[tex]\implies y-8=\dfrac{1}{3}x-3[/tex]

[tex]\implies y-8+8=\dfrac{1}{3}x-3+8[/tex]

[tex]\implies y=\dfrac{1}{3}x+5[/tex]

The percentage change is 16%

The initial value is 125.99

It changed to 150

The percentage change can be calculated  as follows

= 150 - 125.99/150 × 100

= 24.01/150 × 100

= 0.16 × 100

= 16%

Hence the percentage change is 16%

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[tex]-(5)^{2*4} \\-(5)^{8} \\\\=-390,625[/tex]

Answer: Option D is correct.

y = -4x + 4

Answer:

y = -4x + 4

Step-by-step explanation:

D. is your answer ^^

The measure of the triangle for the value of x is x = 11.

A triangle is a 2-dimensional closed shape with three sides, three angles, and three vertices. A triangle is a type of polygon.

For the given value of triangle;

The three angles are given as;

By the sum of all angles of triangle property.

The sum of all three angles of the triangle is 180°

Thus,

3x + 8 + 4x + 11 + 84 = 180

Simplifying;

7x = 180 - 103

7x = 77

x = 11

Thus, the solution of x of the given triangle is found as x = 11.

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Answer:

(-5, -3)

Step-by-step explanation:

We can use the fact that the diagonals of a parallelogram bisect each other

Let me classify the points as

A (-4, 7)

B (2, -5)

C (3, 5)

Let us assume the 4th vertex is D(x, y) where x and y have to be determined

We will assume that AB is the diagonal of the parallelogram ABCD

The midpoint of a line segment from (x1, y1) to (x2, y2) is given by
(1/2)(x1 + x2, y1 + y2) ie the average of their x and coordinates

If we let O be the midpoint of AB, coordinates of O are
1/2 x (-4 + 2, 7 -5) = 1/2 x ( -2, 2) = (-1, 1)

We know the other diagonal CD must pass through point O and O is also the midpoint of CD

Therefore if coordinates of D are (x, y)

then  x-coordinate of O which is -1 should be the average of x coordinate of C and x coordinate of D
==>  - 1 = (3 + x)/2

=> -2 = 3 + x

=>  -2 - 3 = x

=> -5 = x

=> x = -5

Similarly
1 = (5 + y)/2

=> 2 = 5 + y

=> 2 - 5 = y

=> -3 = y

y = -3

So the coordinate of the fourth vertex D are (-3, -5)

Check the attached graphs for a clearer understanding

The appropriate choice of ratio  will be given by

She will need 6 cups of orange juice to keep the ratio in a full punch bowl the same.

What is ratio?

Ratio determines the comparision among many quantities with the same unit.

Here,

Let the number of cups of Cranberry juice be 4x,

Number of cups of lemon lime soda be x

Number of cups of orange juice be 2x,

Number of cups of pineapple juice be 2x

Total = 4x + x  + 2x + 2x = 9x cups

By the problem,

                          9x = 27

                            x = [tex]\frac{27}{9}[/tex]

                            x = 3

Number of cups of orange juice = 2 * 3 = 6 cups

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Answer:

6 out of 24

Step-by-step explanation:

5+5+6+8 = 24

there are 6 peanut butter cookies

In all there are 24 cookies

Since there are 6 peanut butter cookies since there are 24 cookies there is a chance of 6 and 24 of getting a peanut butter cookie.

Answer: Let's be honest, no one knows the answer. Unless you want to pay coursehero $9.95/mo for an answer and step-by-step explanation, you're toast.

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Simply put, your grade is toast.

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The next fraction in the given sequence is 13/18

In this question, we have been given a sequence of fractions.

17/ 18 , 8 /9 , 5/ 6 , 7/ 9 , . . .

We need to determine the next fraction in the given sequence.

We rewrite the fraction 8/9 as,

8/9 = 8 × 2 / 9 × 2

      = 16/18

We rewrite the fraction 5/6 as,

5/6 = 5 × 3 / 6 × 3

      = 15/18

We rewrite the fraction 7/9 as,

7/9 = 7 × 2 / 9 × 2

      = 14/18

This means, the given sequence of fractions is 17/18, 16/18, 15/18, 14/18, ...

From this sequence, the next fraction would be 13/18

Therefore, the next fraction in the given sequence is 13/18

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Answer:

y = (5/2)x + 2

Step-by-step explanation:

(2, 7)

(x₁, y₁)

m = (5/2)

y - y₁ = m(x - x₁)

y - 7 = (5/2)(x - 2)

y - 7 = (5/2)x - 5

   +7              +7

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

y = (5/2)x + 2

I hope this helps!

Answer:

70°

Step-by-step explanation:

The sum of the interior angles is 180.  Subtract the 40 that you know about and you have 140.  Since the two sides are equal, the angles opposite them are equal.  140/2 = 70

Answer:

3x^2-2x+3 with a remainder of 1/x+2

Step-by-step explanation:

The values of interior angle is 63°,  46°,  71°

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three interior angles. Interior angles are sometimes defined as "angles enclosed in the interior region of two parallel lines when they are intersected by a transversal."

Put all the values equal to 180°,

=> (2x+5) + (x+17) + (3x-16) = 180°

Now, solve this equation and find x,

=> 6x + 22 - 16 = 180

=> 6x = 180 - 6

=> x = 174 / 6

=> x = 29°

Put x = 29° in the 2x + 5, x + 17, 3x - 16

2x + 15                |   x + 17          |   3x - 16      

2 * 29 + 15          |  29 + 17        |   3 * 29 - 16

63°                      |   46°             |   71°

Therefore, the  values of interior angle is 63°,  46°,  71°

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Angle #1 = 90 Reason:  Every angle of a rectangle measures 90°. Opposite sides are equal and parallel. It has 2 diagonals of equal length.

# 22= 90. Reason:  Every angle of a rectangle measures 90°. Opposite sides are equal and parallel. It has 2 diagonals of equal length.

# 8 = 90 . Reason:  Every angle of a rectangle measures 90°. Opposite sides are equal and parallel. It has 2 diagonals of equal length.

# 2 =  90. Reason: A right triangle is a type of triangle that has one angle that measures 90°.

#17 = 60. Reason:  We have the sum of all interior angles at 180.

180 degrees  = 30+ 90+ #17

so # 17 = 180 - ( 30+90) = 60.

#23= 90. Reason: A right triangle is a type of triangle that has one angle that measures 90°.

# 19= 90. Reason:  Opposite sides are equal and parallel. It has 2 diagonals of equal length.

#26 = 90. Reason: Opposite sides are equal and parallel. It has 2 diagonals of equal length.

#21 = 90.  Reason: Opposite sides are equal and parallel. It has 2 diagonals of equal length.

# 16 = 60  Reason:  We have the sum of all interior angles at 180. And Opposite sides are equal and parallel. So # 16 + 90 + # 27 = 180

so # 16 + #27 = 180-90 = 90.

#3= 30. We have # 16 +# 3 = 90. So 60 +# 3 = 90. Hence, # 3 = 30.

#27 = 30.

The average rate of change from week 1 to week 4 is 3 animals per week.

It should be noted that a mean simply refers to the average set of numbers that are given.

This will be illustrated as thus:

The total number of rate of change animals from week 1 to week 4 will be:

= (73 - 62) + (78 - 73) + (86 - 78)

= 11 + 5 + 8.

= 24

Therefore, the average will be:

= Total changes / Number of weeks

= 24 / 8.

= 3

Therefore, there's an average of 3 animals added every week.

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Answer:

0.5 entrances per minute

Step-by-step explanation:

9 customers entered a store over the course of 18 minutes. At what rate were the customers entering the store in minutes per customer?

9/18 = 0.5 entrances per minute

Answer: 2 minutes/Customer

Step-by-step explanation:

Total time passed: 18 minutes

Total customers entered: 9 nos.

using unitary method, number of minutes requires for one customer to enter or minutes per customer is:

18/9 that is , 2 minutes/customer.

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Missing value of the table is 9.

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent. If two or more ratios have the same value when reduced to their most basic form, they are said to be equal. For instance, the ratios 1:2, 2:4, and 4:8 are identical. When reduced to their most basic form, all three ratios have the same value, or 1:2. We can multiply or divide the words by a natural number to get analogous ratios to a given ratio. When two words are co-prime (have just one other common factor), we multiply them by any natural number instead of performing the division procedure.

Given Data

Violins

Cellos

8  24

3

Let missing number be x

[tex]\frac{8}{24}[/tex] = [tex]\frac{3}{x}[/tex]

When we compare two ratios, they are said to be equivalent.

If two or more ratios have the same value when reduced to their most basic form, they are said to be equal

simplifying, [tex]\frac{8}{24}[/tex]

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

[tex]\frac{3}{x}[/tex] =[tex]\frac{3}{9}[/tex]

Missing value of the table is 9.

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