Solve the system of equations.

x + 14y = 38

1

7

x + 2y = 5

What is the solution to the system of equations?

The first, second, third, and fifth statements are true, but the fourth and sixth statements are false. The responses are based on evaluating the square root calculations.

The statements we are analyzing are related to the square root of 1.8 (√1.8). Let's work through them:

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Answer:

37 1/3

Step-by-step explanation:

14 divided by 3/8=

14*8/3=

37 1/3

the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].

To find the average rate of change of the function over the interval (10 < x < 15), we use the formula:

[tex]\[ \text{Average Rate of Change} = \frac{\text{Change in } f(x)}{\text{Change in } x} \][/tex]

We can calculate the change in [tex]\(f(x)\)[/tex] by subtracting the function values at the end and start of the interval, and the change in x by subtracting the end and start values of x.

Given the function values:

- [tex]\(f(10) = 30\)[/tex]

- [tex]\(f(15) = 24\)[/tex]

And the interval [tex]\(10 < x < 15\)[/tex], the change in [tex]\(f(x)\) is \(f(15) - f(10) = 24 - 30 = -6\)[/tex].

The change in x is [tex]\(15 - 10 = 5\)[/tex].

Now, we plug these values into the formula for the average rate of change:

[tex]\[ \text{Average Rate of Change} = \frac{-6}{5} \][/tex]

So, the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].

The complete Question is given below:

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10 < x < 15

x       |   f(0)

0       |   42

5       |   36

10      |   30

15      |   24

20     |   18

25     |   12

Answer:

a parabola, sort of like a u shape

Step-by-step explanation:

Answer:8

Step-by-step explanation:

There are 12 months in a year if you divide by 3 you get 4 and whatever you do to the numerator you have to do the denominator vice versa so you would multiply by four and get eight so it would be eight months

Answer:

2/3 of a year is 8 months

Step-by-step explanation:

Answer:look

Step-by-step explanation:

The diagonals of a rectangle exist congruent the necessary conditions are

A. Opposite sides are congruent.

C. Opposite sides are perpendicular.

A quadrilateral exists named a rectangle if the opposite sides exist congruent and parallel to each other. All interior angles exist as right angles and are congruent.

To verify that the diagonals of a rectangle exist congruent the necessary conditions are:

1. Opposite sides of a rectangle exist congruent.

2. All right angles exist congruent.

Therefore, the correct answer is options A and C.

A. Opposite sides are congruent.

C. Opposite sides are perpendicular.

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Answer:

he drinks 56oz of water

Step-by-step explanation:

divide 21 by 3 that would equal seven than multiply it by 8 which is 56

Answer:

57 ounces

Step-by-step explanation:

[tex]\frac{3 miles}{8oz water}[/tex] × 7 = [tex]\frac{21miles}{56ozwater}[/tex]

Answer:3/2

Step-by-step explanation:

Answer: 198 pencils per class

Explanation:

22 boxes * 45 pencils = 990 pencils

990 pencils / 5 classes = 198 pencils per class

Answer: 198 pencils per class

Explanation:

22 boxes * 45 pencils = 990 pencils

990 pencils / 5 classes = 198 pencils per class

.

Answer:

Step-by-step explanation:

[tex]\frac{6}{\frac{2}{6} } =6*\frac{6}{2} =6*3=18[/tex]

Answer:

18

Step-by-step explanation:

6/(2/3)

Turn 6 into a fraction first.

(6/1) / (2/6)

(6/1) x (6/2)

36/2

18

Answer:

4x² - 20x + 16

Step-by-step explanation:

Given

(4x - 4)(x - 4)

Each term in the second factor is multiplied by each term in the first factor, that is

4x(x - 4) - 4(x - 4) ← distribute both parenthesis

= 4x² - 16x - 4x + 16 ← collect like terms

= 4x² - 20x + 16

Answer:

9120

Step-by-step explanation:

Answer:

I just know that for number 9.)It's C because it has a greater number, meaning it has a greater chance of containing Adam's house number.

Measures of the angles are 24°, 48° and 108°

Step-by-step explanation:

Let angles be 2x, 4x and 9x.

⇒ 2x + 4x + 9x = 180

⇒ 15x = 180

⇒ x = 180/15 = 12

2x = 24°, 4x = 48° and 9x = 108°

Answer: four-fifteenths or [tex]\frac{4}{15}[/tex]

Step-by-step explanation:

What is written with words is mathematically expressed as:

[tex]\frac{9}{15}-\frac{2}{6}[/tex]

We can simplify both fractions, by dividing the numerator and denominator of the first by 3 and dividing the numerator and denominator of the second by 2:

[tex]\frac{9}{15}=\frac{3}{5}[/tex]

[tex]\frac{2}{6}=\frac{1}{3}[/tex]

Then:

[tex]\frac{3}{5}-\frac{1}{3}[/tex]

Calculating the least common multiple (l.c.m) in the denominator as [tex]15[/tex]:

[tex]\frac{9-5}{15}=\frac{4}{15}[/tex] This is the result: four-fifteenths

Answer:

42.06 ft²

Step-by-step explanation:

          2 sides = 2(2.7 ft × 3.2 ft) = 2 × 8.64 ft² =   17.28 ft²

 Front + back =  2(2.1 ft × 3.2 ft) = 2 × 6.72 ft² =   13.44 ft²

Top + bottom =   2(2.1 ft × 2.7 ft) = 2 × 5.67 ft² =   11.34 ft²

                                                         Total area = 42.06 ft²

Rachel bought six 20-cent stamps and eight 30-cent stamps.

Step-by-step explanation:

Given,

Amount spent on stamps = $3.60 = 3.60*100 = 360 cents

Let,

x = 20 cent stamps

y = 30 cent stamps

According to given statement;

20x+30y=360      Eqn 1

x = y-2                  Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex]20(y-2)+30y=360\\20y-40+30y=360\\50y=360+40\\50y=400[/tex]

Dividing both sides by 50

[tex]\frac{50y}{50}=\frac{400}{50}\\y=8[/tex]

Putting y=8 in Eqn 2

[tex]x=8-2\\x=6[/tex]

Rachel bought six 20-cent stamps and eight 30-cent stamps.

Keywords: linear equation, substitution method

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Final answer:

Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps. We solved a system of equations representing the cost of the stamps and their quantity relationship to determine the numbers.

Explanation:

Rachel spent $3.60 for stamps to mail packages, buying 30-cent stamps and 20-cent stamps. The number of 20-cent stamps was 2 less than the number of 30-cent stamps. To solve this, we can use a system of equations to represent the total cost and the relationship between the number of stamps:

Let x be the number of 30-cent stamps.

Let y be the number of 20-cent stamps.

Based on the information given:

0.30x + 0.20y = 3.60 (Total cost equation)

y = x - 2 (Relationship between the stamps)

We substitute the second equation into the first equation:

0.30x + 0.20(x - 2) = 3.60

0.30x + 0.20x - 0.40 = 3.60

0.50x = 4.00

x = 8

Now we solve for y using the second equation:

y = 8 - 2

y = 6

So Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps.

Answer:

Step-by-step explanation:

The absolute change is the difference between the earnings numbers:

  $15,556,113 -8,556,965 = $6,999,148

__

The relative change is the ratio of this difference to the original amount:

  $6,999,148/$8,556,965 × 100% ≈ 81.794748% ≈ 81.79%

The absolute change in opening weekend earnings from the original Footloose to its remake is $6,999,148, and the relative change is approximately 81.74%.

To calculate the absolute change in opening weekend earnings from the original Footloose movie to its 2011 remake, we subtract the earnings of the original movie from the earnings of the remake. Thus, the absolute change is $15,556,113 - $8,556,965 = $6,999,148.

To find the relative change, we divide the absolute change by the original amount and then multiply by 100 to get a percentage. This gives us ($6,999,148 / $8,556,965) * 100 ≈ 81.74%. Hence, the relative change is approximately 81.74%.

The absolute change represents the direct increase in dollar amount, while the relative change gives us the percentage increase from the original to the remake's opening weekend earnings, providing insight into the growth rate.

Answer:

10 Girls

Step-by-step explanation:

This shows that there is twice as many boys in the gym class than girls.

Step 1:  Determine what the ratio relates to the amount

1:2 -> 10:20

10 Girls

20 Boys

Answer:

The enswer is corect because is the biggest then girls to boys

Step-by-step explanation:

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Simplify the resulting fraction.

To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. So, the reciprocal of 7/6 is 6/7. Therefore, 49/50 ÷ 7/6 = 49/50 x 6/7. When we multiply the numerators (49 x 6) and the denominators (50 x 7), we get 294/350. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 14. Therefore, 294/350 simplifies to 21/25.

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Answer:

[tex]y=-2x-8[/tex]

Step-by-step explanation:

Let [tex]y=mx+c[/tex] be the equation of this line.

The points must satisfy this equation.

When x=-8, and y=8, we get:

[tex]8=-8m+c....(1)[/tex]

When x=1, and y=-10, we get:

[tex]-10=m+c...(2)[/tex]

Subtract equation (1) from equation (2) to get:

[tex]m--8m=-10-8[/tex]

9m=-18

m=-2

We put m=-2 in equation to get (2)

-10=-2+c

c=-10+2

c=-8

Therefore the equation is:

y=-2x-8

The system has one solution

Step-by-step explanation:

Let us revise the type of the solutions of a system of equations

The system of equations is:

y = 2x - 12 ⇒ (1)

y = 3x + 12 ⇒ (2)

∵ The equations are in its simplest form

∵ The coefficients of x in the two equations are different

- That is the 1st case above

∴ The system has one solution

Let us prove that by solving the system

To solve the system of equations equate (1) and (2) to find x

∵ 3x + 12 = 2x - 12

- Subtract 2x from both sides

∴ x + 12 = -12

- Subtract -12 from both sides

∴ x = -24

- Substitute the value of x in equation (1) or (2) to find y

∵ y = 3(-24) + 12

∴ y = -72 + 12

∴ y = -60

∴ The solution of the system is (-24 , -60)

The system has one solution

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Answer:

Step-by-step explanation:

Using this formula to find the length of the arc

Arc length = [tex]2\pi r (\frac{\theta}{360} )[/tex]

Here [tex]\theta = \frac{360}{60}\times 45[/tex]   [for 45 minutes]

            [tex]=270^\circ[/tex]

Radius(r) = length of the minute hand = 12 cm

The length of the arc is = [tex]2\pi \times 12\times \frac{270}{360}[/tex]

                                     = 56.57 cm

Therefore the tip of the minute hand on the clock moves 56.57 cm in 45 minutes.

Answer:

check the photo.

Step-by-step explanation:

The inverse of the function

f(x) = ax + b is g(x) = (x/a) - (b/a)

(learn it by heart)

Answer:

10 rows with the set of 100 blocks is what she will make

Step-by-step explanation:

Where

First row is 1

Second row is 3

Third row is 5

This shows that the blocks are set in an oddly fashion

Meaning each row has a odd number of blocks

Therefore from

1 block- row 1

3 blocks- row2

5 blocks- row 3

7 blocks - row 4

9 blocks- row 5

11 blocks - row 6

13 blocks- row 7

15 blocks - row 8

17 blocks- row 9

19 blocks - row 10

Add of the blocks it amounts to 100 blocks

Meaning the triangular will be at the 10th row when she has use 100 blocks

Answer:

Unit rate of people per book = 2.5

Step by step explanation:

Given:

Number of peoples =  [tex]10[/tex]

Number of books = [tex]4[/tex]

Their ratios = [tex]10 : 4[/tex]

We have to find the unit rate of people per book.

To find out the unit rate of people per book we have to divide the total number of peoples by the total number of books.

Or

For this we will follow the unitary method:

For [tex]4[/tex] book there are [tex]10[/tex] persons.

For [tex]1[/tex] book there will be [tex]\frac{10}{4}[/tex] persons.

So,

The numeric value = [tex]\frac{10}{4}[/tex]

                               = [tex]2.5[/tex]

There are 2.5 people per book and that it also the unit rate of people per book.

Answer:

∠ ABC = ∠ DBE = 65°

∠ ABD = ∠ CBE = 115°

Step-by-step explanation:

See the diagram attached to this question.

Now, ∠ ABC and ∠ DBE are two vertically opposite angles.

So, 3x + 38 = 5x + 20

⇒ 2x = 18

⇒ x = 9

So, ∠ ABC = ∠ DBE = 3(9) + 38 = 65° (Answer)

Again, ∠ ABC and ∠ ABD are supplementary angles.

Then, ∠ ABC + ∠ ABD = 180°

⇒ ∠ ABD = 180° - 65° = 115°

And ∠ ABD = ∠ CBE {Vertically opposite angles}

So, ∠ ABD = ∠ CBE = 115° (Answer)

Answer:

No the ratio 3:4 is not equal to 4:5

Step-by-step explanation:

3:4 = 3/4 and 4:5 = 4/5

3/4 is equal to 0.75 and 4/5 is equal to 0.8

0.75 [tex]\neq[/tex] 0.8

therefore, 3:4 [tex]\neq[/tex] 4:5

Hope this helps!

Answer:64

Step-by-step explanation:

Add 79 with 37 an you will get 116 you need to know the total angle for a triangle is 180 so 180 minus 116 is 64

The measure of the angle y for the triangle is 64°.

The triangle is a shape having three sides and the sum of the angles of the triangle is always equal to 180°.

Here in the given triangle, the two angles are 79° and 37°. The measure of the unknown angle y° will be calculated as:-

y + 79 + 37 = 180

Now solve for the value of angle y below,

y = ( 180 - 79 - 37 )

y = 64°

Therefore, the measure of the angle y for the triangle is 64°.

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