Show you work for full credit Use the SUBSITUTION method or ELIMINATION method to solve this system of equations. y = 4x and 8x + y = 18

The volume of the rectangular prism is 27/2 square units

The volume is calculated as:

Volume = Base area * Height

This gives

Volume = 27/5 * 5/2

Evaluate the product

Volume = 27/2

Hence, the volume of the rectangular prism is 27/2 square units

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Answer:

[tex]\frac{31}{8} or 3\frac{7}{8}[/tex]

Step-by-step explanation:

First, these 2 fractions are proper fractions, we will convert them into improper ones.

[tex]5\frac{2}{8} = \frac{42}{8}[/tex]

[tex]1\frac{3}{8} =\frac{11}{8}[/tex]

Now to subtract fractions, we must ensure the denominators are the same, which in this case is already the same, so we can subtract straightaway.

[tex]\frac{42}{8} - \frac{11}{8} \\=\frac{31}{8} or 3\frac{7}{8}[/tex]

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{5 \dfrac{2}{8} - 1 \dfrac{3}{8}}[/tex]

[tex]\mathsf{= \dfrac{5 \times 8 + 2}{8} - \dfrac{1 \times 8 + 3}{8}}[/tex]

[tex]\mathsf{= \dfrac{40 + 2}{8} - \dfrac{8 + 3}{8}}[/tex]

[tex]\mathsf{= \dfrac{42}{8} - \dfrac{11}{8}}[/tex]

[tex]\mathsf{= \dfrac{42 - 11}{8 - 0}}[/tex]

[tex]\mathsf{= \dfrac{42 - 11}{8}}[/tex]

[tex]\mathsf{= \dfrac{31}{8}}[/tex]

[tex]\mathsf{\approx 3 \dfrac{7}{8}}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{3 \dfrac{7}{8}}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040}[/tex]

Answer:

1. 8.8 gallons per hour

2. 9:20 am

3. 8:04 am

Step-by-step explanation:

The tank lost 22 gallons of water in 150 minutes (2.5 hours)

This is a rate of 0.14666 gallons per minute or 8.8 gallons per hour

The function: 200 - 0.147(x)

So at 4:30 pm, the tank lost 63 gallons. So at a rate of 8.8 gallons per hour, that means it has been leaking for 7.16 (.16 hours = 9.6 minutes) hours.

So it has been leaking since 9:20 am.

In order for it to completely empty, it needs to drain 115 gallons of water.

At a rate of 8.8 gallons per hour, that means it needs 13.068 hours or 13 hours and 4 minutes.

So it will be empty at 8:04 am.

Answer:

Step-by-step explanation:

2n + 1.6 = 17.6 what is the value of n?​

2n + 1.6 = 17.6

2n = 17.6 - 1.6

2n = 16

n = 16 : 2

n = 8

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

check

2n + 1.6 = 17.6

2*8+1.6=17.6

16+1.6=17.6

17.6=17.6

the answer is good

[tex] \frac{z + 12}{5} = \frac{3z + 3}{4} [/tex]

[tex]4(z + 12) = 5(3z + 3)[/tex]

[tex]4z + 48 = 15z + 15[/tex]

[tex]48 - 15 = 15z - 4z[/tex]

[tex]33= 11z[/tex]

[tex]z = \frac{33}{11} \\ z = 3[/tex]

Answer:

x = 4

Step-by-step explanation:

co interior angles add up to 180.

this means that: 48 + 34x - 4 = 180

thus 48 + 34x = 184

therefore, 34x = 136

so, x = 4.

The two angles labeled in the given diagram are interior angles on the same side of the transversal. They can also be called interior supplementary angles.

These angles have a sum of 180 degrees.

The two angles given have measures of 48 degrees and (34x-4) degrees.

They have a sum of 180 degrees.

Form an equation:

[tex]48+(34x-4)=180\\48+34x-4=180\\44+34x=180\\34x=180-44\\34x=136\\x=4[/tex]

[tex]x=4[/tex]

Answer:

Function 2

Step-by-step explanation:

An initial value of a function, aka y-intercept, is obtained by using x=0 and evaluating the function at that point. Evaluating the two functions given:

Function1: y = 2x(1/3)^x|x=0 = 2*0*1=0

with the chart

xy

03

16

2 12

3 24

Function2 has value 3 for x=0

So, Function 2 has a greater initial value

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Answer:

70

Step-by-step explanation:

10tickets x 8students = 80tickets

150tickets-80tickets=70tickets

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the absolute value of -6.2? It's _____________.

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

No matter what the number is, its absolute value is always positive.

The number -6.2 is not an exception, there's nothing special about that number. Its absolute value is also positive.

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

              [tex]\bf{=6.2}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]

The absolute value of -6.2 is 6.2 (option 1).

The absolute value of a number represents its distance from zero on the number line, regardless of its sign. For the value -6.2, the distance from zero is 6.2 units. Therefore, the correct answer is 1. 6.2. Option 1 accurately reflects that the absolute value of -6.2 is indeed 6.2.

The other options (2. 6, 3. 7, and 4. -6) do not accurately represent the absolute value of -6.2. The absolute value operation ensures that the result is always a positive value, showing how far a number is from zero. In this case, the absolute value of -6.2 is 6.2.

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Answer:

it will be a rectangle mostly...

Answer:

c)102 degrees

Step-by-step explanation:

[tex]\angle EHF=90^{\circ}[/tex] (an angle inscribed in a semicircle is a right angle)

[tex]\angle HEF=38^{\circ}[/tex] (alternate segment theorem)

[tex]a=52^{\circ}[/tex] (angles in a triangle add to 180 degrees)

[tex] \frac{36 - 40}{2 - 1} = 4[/tex]

Answer:

A) 384

B) 576

Step-by-step explanation:

the area of a rhombus is

pq/2

First Rhombus

we have p but to find q we can cut the triangle in half to form a right triangle, that allows us to use the Pythagorean theorem

20² = 12² + b²

400 - 144 = b²

b² = 256

b = 16

since the height (b) is half the rhombus, we double it to get q

p = 24

q = 32

a = [tex]\frac{24*32}{2}[/tex]

a = 384

Second Rhombus

Since rhombuses are parallelograms, we can use its area formula  (b)(h)

a = (24)(24)

a = 576

A function assigns the value of each element of one set to the other specific element of another set. The correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8.

1.) g(1) = -2

Since the range is from 0 to 18. Therefore, this is not the correct option.

2.) g(5) = 12

Since the domain is from -1 to 4. Therefore, this is not the correct option.

3.) g(3) = 18

This is the only option that is feasible. Thus, this is the correct option.

4.) g(2) = 4

Since the value of g(2) is 8. Therefore, this is not the correct option.

Hence, the correct option is C.

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R, which is the rate is 20%.

Simple interest is the interest on a sum of money invested or borrowed for a specific period of time.

The sum invested is called the principal.

Analysis:

simple interest (I) = PRT/100 = 300

P = principal = 3000

R = rate = ?

T = 0.5 year

300 = 3000 x R x 0.5/100

R = 20%

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Answer: [tex]\angle BCA \cong \angle ACD[/tex]

Step-by-step explanation:

By the reflexive property, [tex]\overline{AC} \cong \overline{AC}[/tex]. So, we just need the pair of angles between these corresponding sides to be congruent.

Richard’s account balance at the end of the week is $ 132.45

The amount of money in a person's bank account is called the account balance of that person

It is given that

Account balance of Richard’s at the beginning of the week = $57.34

Deposits in the week  : $ 163.75

Expenses in the week : Groceries + Credit card bill + Gas

Total Expenses in the week = 25.37 + 50 + 13.27

                                               = $ 88.64

The Richard’s account balance at the end of the week = Account Balance +Total Deposits - Total Withdrawals

= 57.34 + 163.75 - 88.64

Therefore , Richard’s account balance at the end of the week is $ 132.45.

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Answer:

Rate of change: 4/3

Step-by-step explanation:

Number of sodas/Total cost

pick a number

24/18 = 4/3

Answer:

4/3

Step-by-step explanation:

Rate of change is also known as slope.

To find slope, you have to find the change in y divided by the change in x.

y2-y1 / x2-x1

The variable y in this situation is the number of sodas.

The variable x in this situation is the total cost.

28 - 24 / 21 - 18

= 4 / 3

The rate of change in this problem is 4/3.

Answer: (1, 18)

Step-by-step explanation:

Test each x, y pair.

Getting to the last one, plug in 1 for the x value.

y = 3 * (6 ^ x)

y = 3 * (6 ^ 1)

y = 3 * 6

y = 18

This matches with (1, 18) so it must lie on the graph.

The required solution to the equation is [tex]0.3y+\frac{y}{z}[/tex] at y=10, z=5 is 5.

As we have the equation [tex]0.3y+\frac{y}{z}[/tex] and find solution At y =10 and z=5

What is equation?

The equation is the relationship between dependent and independent variables through some mathematical operators.

Now,
      putting the value of  y=10, z=5 in [tex]0.3y+\frac{y}{z}[/tex]
  ⇒[tex]0.3*10+\frac{10}{5}[/tex]
   =  5

Thus the required value of the equation at y=10 and z =5 is 3.

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The price of the car after 10 years is $7524.25 if the new car costs $34,000 and its value depreciates at 14% of its value each year.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let y represent the value of the car after x years. A new car costs $34,000 and its value depreciates at 14% of its value each year. Hence:

y = 34000(0.86)ˣ

After 10 years:

y = 34000(0.86)¹⁰ = 7524.25

The price of the car after 10 years is $7524.25 if the new car costs $34,000 and its value depreciates at 14% of its value each year.

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The percentage of the survey respondents that do not like both hamburgers and burritos is 16.09%.

The percentage of the survey respondents that do not like both hamburgers and burritos will be:

= 33/205 × 100

= 16.09%

The marginal relative frequency of all customers that like hamburgers will be:

= 134/205

= 0.65

The data point that has strongest association of its two factors will be:

Those who like hamburger and burrito = 39/134 = 0.29

Those who like hamburger and not burrito = 95/134 = 0.71

Those who like burrito but not hamburger = 38/71 = 0.53

Those who do not like hamburger or burrito = 33/71 = 0.47.

Therefore, the data point that has strongest association of its two factors will be those who like hamburgers but not burritos.

A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:

Likes hamburgers Does not like hamburgers Total

Likes burritos 38 77

Does not like burritos 95 128

Total 134 71

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Answer:

1

Step-by-step explanation:

Knowing that the entire number line equals 7, and that the second line segment RS equals 6, we can subtract the two values to find QR.

[tex]7-6=1[/tex]

Therefore, QR equals 1.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:QR = 1 \:\: unit [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \qquad \tt \rightarrow \: QR + RS = QS[/tex]

Let QR = x

[tex]\qquad \tt \rightarrow \: x + 6 = 7[/tex]

[tex]\qquad \tt \rightarrow \: x = 7 - 6[/tex]

[tex]\qquad \tt \rightarrow \: x = 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The required linear equation is given by y=10x + 15

The data collected by Harvard Business School plots the linear relationship of business startup success vs. Time.

The statistic is the study of mathematics which deal with relations between comprehensive data.

As clearly, points represents on graph startup success vs Time
part of a straight line
so we take two points on graph at (1,25), (2,35)
now equation of line

 [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
= [tex]y-25=\frac{35-25}{2-1} (x-1)[/tex]
[tex]y=10x+15[/tex]

Thus, The required expression is given by y=10x + 15 which show the relation ship between startup success Vs time

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The intervals that represent the number line are given as follows:

b. [tex](-\infty, -5] \cup [8, \infty)[/tex]

The first painted interval is of numbers to the left of x = -5(inclusive due to closed circle), hence:

[tex](-\infty, -5][/tex]

The second interval is of numbers to the right of x = 8, also inclusive, hence:

[tex][8, \infty)[/tex]

Hence the union is given by:

[tex](-\infty, -5] \cup [8, \infty)[/tex]

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Answer:

B

Step-by-step explanation:

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Answer:

2x +3y -3

Step-by-step explanation:

The perimeter of a rectangle is the sum of the lengths of all its sides.

Perimeter of a rectangle= 2 length +2 width

16x -4y -4= 2(6x -5y +1) +2(width)

Expand:

16x -4y -4= 12x -10y +2 +2(width)

2(width)

= 16x -4y -4 -(12x -10y +2)

= 16x -4y -4 -12x +10y -2

= 4x +6y -6

2(width)= 2(2x +3y -3)

Divide both sides by 2:

width= 2x +3y -3