MAT
8. The development budget, C, for a computer game company is described by the equation
C = $50,000t + $10,000, where t is the number of years since the company's creation.
Which statement is true?
A. Each year development expenses increase by $50,000.
B. Each year development expenses increase by $60,000.
C. Each year development expenses are $50,000.X
D. Each year development expenses are $60,000.

Answer:

The solution is the ordered pair (3,2)

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=\frac{1}{3}x+1[/tex] -----> equation A

[tex]x+y=5[/tex] ----> equation B

Solve by graphing

Remember that

The solution of the system of equations is the intersection point both lines

using a graphing tool

The intersection point is (3,2)

see the attached figure

therefore

The solution is the ordered pair (3,2)

A system of equation can be solved in several ways, which includes the use of graphs

The solution to the system of linear equations is (3,2)

The system of equations is given as:

[tex]y=\frac 13x+1[/tex]

[tex]x+y=5[/tex]

See attachment for the graphs of  [tex]y=\frac 13x+1[/tex]  and [tex]x+y=5[/tex].

From the attachment, the point of intersection of the lines of both equations is (3,2)

Hence, the solution to the system of linear equations is (3,2)

Read more about system of equations at:

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Answer:

The area at time t is given  by [tex]A(t) =\pi (4t^2+2t+0.25).[/tex]

Step-by-step explanation:

We know the radius [tex]r(t)[/tex] of the oil spill as a function of time, and we know the area [tex]A(r)[/tex] as a function of radius, and we want the area at time t. In other words we are looking for area as a function of time [tex]A(t)[/tex]

We find [tex]A(t)[/tex] by putting [tex]r(t)[/tex]  into [tex]A(r)[/tex] as a substitute to r:

[tex]A(t) = A(r(t))= \pi r(t)^2 =\pi (0.5 + 2t)^2={\pi (4t^2+2t+0.25).}[/tex]

[tex]\boxed{A(t) =\pi (4t^2+2t+0.25).}[/tex]

Which is our answer.

To find the composite function for the area of the oil spill over time, replace 'r' in A(r) = πr2 with the function r(t). The function becomes A(t) = π(0.5 + 2t)2.

In order to find the function that represents the area of the oil spill over time, we need to write a composite function. This means we plug the function r(t) into A(r). Since r(t) = 0.5 + 2t, you can replace every instance of 'r' in A(r) = πr2 with (0.5 + 2t) to get the area as a function of time 't'. So, the composite function becomes A(t) = π(0.5 + 2t)2. Now we have a composite function that represents the area of the oil spill, denoted by A(t), as a function of time. The function is: A(t) = π(0.5 + 2t)2.

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Answer:

20. 3

Step-by-step explanation:

23.6 - 2 × 3 ÷ 2 = 23.6 - 3

                         = 20.3

Answer:

Hence after solving the given equation we get x = 13/20.

Step-by-step explanation:

Given:

-3 x + 0.1 + 10 x = x + 4

-3 x + 10 x - x = 4 - 0.1

6 x = 3.9

x = [tex]\frac{3.9}{6}[/tex]

x = [tex]\frac{1.3}{2}[/tex]

x = [tex]\frac{13}{20}[/tex]

The number of unripe apples in a sack, given that there are N total apples and 3 are ripe, is calculated by subtracting 3 from N (N - 3).

The question posed is asking for a basic subtraction calculation within the context of ripe and unripe apples.

Given that there are N apples in total and 3 of them are ripe, we need to find out how many are not ripe.

The number of not ripe apples is N - 3, where N is the total number of apples in the sack.

To solve this, we subtract the number of ripe apples from the total number of apples:

For example, if a sack has 10 apples and 3 are ripe, then there would be 10 - 3 = 7 unripe apples.

Answer:

see below

Step-by-step explanation:

The given statement written in symbolic language is x = 3y + 4 and x + y = 72 where "x" is the cost of one book and "y" is the cost of another book

Solution:

Given that Bruce bought two books

One book costs $ 4.00 more than three times the other

Let the two books be denoted as Book A and book B

Let "x" be the cost of book A

Let "y" be the cost of Book B

From given,

One book costs $ 4.00 more than three times the other

Let Cost of book A = $ 4.00 more than three times the other book B

x = 4 + 3 times cost of Book B

x = 4 + 3y

x = 3y + 4 --- (i)

Also given that Together, the two books cost him $72

cost of book A + cost of Book B = 72

x + y = 72 ------- (ii)

Therefore the given statement written in symbolic language is:

x = 3y + 4 and x + y = 72

George shovels at a rate of 8.33 square yards per hour. In 5 1/2 hours, he will shovel approximately 45.815 square yards of his driveway.

The student asked about how many square yards of driveway George would shovel in 5 1/2 hours after shoveling 12 2/4 square yards in 1 1/2 hours. To find this, we first need to calculate the rate at which George is shoveling.

George shovels 12 2/4 square yards in 1 1/2 hours. Simplifying these fractions, we have 12.5 square yards in 1.5 hours. The rate is therefore 12.5 ÷ 1.5 yards per hour = 8.33 square yards per hour.

Next, we multiply this rate by the total time George will be shoveling to find how much he would shovel in 5 1/2 hours:

8.33 yards/hour × 5.5 hours = 45.815 square yards

So, George will shovel approximately 45.815 square yards of his driveway in 5 1/2 hours.

Final answer:

To find out how many square yards of driveway George would shovel in 5 1/2 hours, we can set up a ratio using the given information and multiply the rate by the time.

Explanation:

To find out how many square yards of driveway George would shovel in 5 1/2 hours, we can set up a ratio using the given information. In 1 1/2 hours, he shovels 12 2/4 square yards of snow. We can write this as a fraction: 12 2/4 / 1 1/2. To simplify this fraction, we can convert the mixed numbers to improper fractions: 50/4 / 3/2.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (50/4) × (2/3). Multiplying the numerators and denominators, we get (50 × 2) / (4 × 3) = 100/12.

So, in 1 1/2 hours, George shovels 100/12 square yards of snow. To find out how many square yards he would shovel in 5 1/2 hours, we can multiply this rate by 5 1/2: (100/12) × (5 1/2). Multiplying the numerators and denominators, we get (100 × 11) / (12 × 2) = 1100/24. Simplifying this fraction, we get 275/6.

Therefore, George would shovel approximately 275/6 square yards of driveway in 5 1/2 hours.

Answer:

Step-by-step explanation:

Set this up as a proportion with granola on the top and chocolate chips on the bottom:

[tex]\frac{g}{cc}:\frac{1.75}{\frac{1}{3} }=\frac{x}{1}[/tex] and cross multiply to solve for x:

1/3x = 1.75 Multiply both sides by 3 to get

x = 5.25

This means for every 1 cup of chocolate chips, he needs 5 1/4 cups of granola.

Answer:

$240

Step-by-step explanation:

i = prt

i = $2,000 x 0.03 x 4

i = $240

The amount of interest Antonia will earn in 4 years is $240.

Answer:

x=-3, y=-6. (-3, -6).

Step-by-step explanation:

-4x+y=6

-5x-y=21

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

-9x=27

x=27/-9

x=-3

-5(-3)-y=21

15-y=21

y=15-21

y=-6

Answer:

The only correct statement is the first one

because the product of a number greater than 1 and another positive number always makes the second number greater than its original value

:)

Answer:

Yes, both equations should be true.

*I'm not sure what you mean when to add and subtract but I hope this helps!

Answer:

Triangle1: 13

Triangle2: 25

Triangle3: 17

Step-by-step explanation:

*Pythagorean Theorem Formula: a²+b²=c² where c is the hypotenuse (the side opposite of the right angle)

Triangle1:

1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.

  5²+12²=c²

  25+144=c²

  169=c²

  c=√169

  c=13

Triangle2:

1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.

  15²+20²=c²

  225+400=c²

  625=c²

  c=√625

  c=25

Triangle3:

1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.

  8²+15²=c²

  64+225=c²

  289=c²

  c=√289

  c=17

Final answer:

The area of Triangle B is two times greater than the area of Triangle A, due to the height of Triangle B being twice that of Triangle A with the base remaining constant.

Explanation:

The question pertains to the comparison of the areas of two triangles that share the same base. The height of Triangle B is twice the height of Triangle A. To find the area of a triangle, we use the formula 1/2 × base × height. Given that both triangles have the same base, if we call the height of Triangle A 'h', then the height of Triangle B is '2h'.

So, the area of Triangle A is (1/2 × base × h), and the area of Triangle B is (1/2 × base × 2h). Simplifying the expression for the area of Triangle B, we find it is equal to 2 × (1/2 × base × h), which means it's exactly twice the area of Triangle A. Thus, the area of Triangle B is two times greater than the area of Triangle A.

If one triangle's height is double the other's, its area is four times greater, with same base.

let's break it down step by step.

1. Area of a Triangle Formula: The area of a triangle is calculated using the formula:

[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

2. Given Information:

  - Both Triangle A and Triangle B have the same base.

  - The height of Triangle B is twice the height of Triangle A.

3. Comparing the Areas:

  - Let's denote the base of both triangles as [tex]\( b \).[/tex]

  - Let the height of Triangle A be [tex]\( h_A \)[/tex] and the height of Triangle B be [tex]\( h_B \).[/tex]

4. Area of Triangle A [tex](A_A)[/tex]:

  - Using the area formula, the area of Triangle A is:

   [tex]\[ A_A = \frac{1}{2} \times b \times h_A \][/tex]

5. Area of Triangle B [tex](A_B)[/tex]:

  - Triangle B has double the height of Triangle A, so the height of Triangle B is [tex]\( 2h_A \).[/tex]

  - Using the area formula, the area of Triangle B is:

   [tex]\[ A_B = \frac{1}{2} \times b \times (2h_A) = b \times h_A \][/tex]

6. Comparing the Areas:

  - Since both triangles have the same base [tex](\( b \)),[/tex] and the height of Triangle B [tex](\( 2h_A \))[/tex] is twice the height of Triangle A [tex](\( h_A \)),[/tex] the area of Triangle B is [tex]\( b \times h_A \)[/tex] which is exactly the same as Triangle A.

7. Conclusion:

  - The area of Triangle B is not just greater, it's exactly the same as Triangle A.

So, if the base and one of the heights are doubled, the area of the triangle also doubles. This is because the area of a triangle is directly proportional to its height when the base is constant.

Answer:

56652.3 ft^3

Step-by-step explanation:

The formula for the volume of a right circular cone is V=13pi*r^2*h where r is the radius of the base.

So V=13pi*(15.6)^2*(5.7)=56652.3

Answer:

  9 loaves

Step-by-step explanation:

Judy get 3/4 of the bread, so ...

  (3/4) · 12 loaves = 9 loaves

Final answer:

In order to find out how much bread Kendra gives Judy, we can set up a system of equations.

Explanation:

In order to find out how much bread Kendra gives Judy, we can set up a system of equations based on the information given. Let's say Kendra gives Lynn x loaves of bread. According to the problem, Kendra gives Judy 3 times the amount she gives Lynn, so Judy receives 3x loaves of bread. Together, they receive 12 loaves of bread, so x + 3x = 12. Simplifying the equation, we get 4x = 12. Dividing both sides by 4, we find x = 3. Therefore, Kendra gives Judy 3x = 3(3) = 9 loaves of bread.

Answer:

238°

Step-by-step explanation:

In a cyclic quadrilateral, the pair of opposite angles add up to 180 degrees.

So, the angle "21x - 2" and the angle "38x + 5"  add up to 180.

So, we can write an equation and solve for x first:

[tex]21x-2+38x+5=180\\59x+3=180\\59x=180-3\\59x=177\\x=3[/tex]

x = 3

Now, Arc FGH is DOUBLE of Angle A. Angle A is "38x + 5". We know x, so angle A is:

Angle A = 38x + 5 = 38(3) + 5 = 119

Thus, Arc FGH = 2 * 119 = 238°

Answer: 50%

Step-by-step explanation:

12x1.5=18

Answer:

50% increase

Step-by-step explanation:

Percentage change = increase/original × 100

[tex]change = \frac{(18 - 12)}{12} \times 100[/tex]

[tex]change = \frac{6}{12} \times 100[/tex]

[tex]change = 0.5 \times 100[/tex]

[tex]change = 50\%[/tex]

Number of adult tickets sold is 100 and number of children tickets sold is 150

Solution:

Let "c" be the number of childrens ticket sold

Let "a" be the number of adult tickets sold

Cost of 1 children's musical ticket = $ 2.00

Cost of 1 adult musical ticket = $ 3.50

Given that 250 tickets were sold

number of childrens ticket sold + number of adult tickets sold = 250

c + a = 250 ---- eqn 1

250 tickets were sold for a total of 650

So we can frame a equation as:

number of childrens ticket sold x Cost of 1 children's musical ticket + number of adult tickets sold x Cost of 1 adult musical ticket = 650

[tex]c \times 2.00 + a \times 3.50 = 650[/tex]

2c + 3.50a = 650 ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "a" and "c"

From eqn 1,

c = 250 - a ----- eqn 3

Substitute eqn 3 in eqn 2

2(250 - a) + 3.50a = 650

500 - 2a + 3.50a = 650

1.5a = 150

From eqn 1,

c = 250 - 100

Thus number of adult tickets sold is 100 and number of children tickets sold is 150

Question is Incomplete, Complete question is given below.

Julia exercises at the gym. For every 3 minutes she spends running, she spends 5 minutes lifting weights.

Which of the following could be how Julia spends time at the gym?

A  Run for 10 mins and lifting weights for 12 mins.

B  Run for 15 minutes and lift weights for 25 mins.

C  Run for 20 mins and lift weights for 30 mins.

D  Run for 24 mins and lift weights for 48 mins.

E  Run for 30 mins and lift weights for 50 mins.

Answer:

B  Run for 15 minutes and lift weights for 25 mins.

E  Run for 30 mins and lift weights for 50 mins.

Step-by-step explanation:

Given:

Julia Spend s 3 minute for running and weight lifts for 5 mins.

We need to find which choices are correct match for the given data.

Hence we will check each.

A  Run for 10 mins and lifting weights for 12 mins.

Since given that she runs for 3 mins and in the above choice the given date is she is running for 10 mins it is neither 3 nor multiple of 3.

Hence this is Choice is Incorrect.

B  Run for 15 minutes and lift weights for 25 mins.

Now Given in choice is that she runs for 15 minutes and in given data she runs for 3 minutes hence 15 is multiple of 3 and is multiplied by 5 also given lift weights for 25 mins and in given data she lift weights for 5 mins since 25 is multiple of 5 and is multiplied by 5.

Hence the above Choice is Correct.

C  Run for 20 mins and lift weights for 30 mins.

Since given that she runs for 3 mins and in the above choice the given date is she is running for 20 mins it is neither 3 nor multiple of 3.

Hence this is Choice is Incorrect.

D  Run for 24 mins and lift weights for 48 mins.

Now Given in choice is that she runs for 24 minutes and in given data she runs for 3 minutes hence 24 is multiple of 3 and is multiplied by 8 also given lift weights for 48 mins and in given data she lift weights for 5 mins and 48 is not the multiple of 5.

Hence this is Choice is Incorrect.

E  Run for 30 mins and lift weights for 50 mins.

Now Given in choice is that she runs for 30 minutes and in given data she runs for 3 minutes hence 30 is multiple of 3 and is multiplied by 10 also given lift weights for 50 mins and in given data she lift weights for 5 mins since 50 is multiple of 5 and is multiplied by 10.

Hence the above Choice is Correct.

Answer:

  (-2, 3)

Step-by-step explanation:

f(x) +5 means 5 is added to the y-value that is output from the function. The given point indicates the function output is -2, so when 5 is added, the result is +3. The point (-2, 3) is on the graph of f(x)+5.

Answer:

The first answer is the correct choice.

Step-by-step explanation:

For this, there are two initial options. A cake or a shake. This means that there are two different trees that need to exist. One for Cakes and one for shakes.

Each of these trees needs to have the options of having vanilla and strawberry.

The first answer is the only one that follows this criteria

Answer:

1st one is correct.

Step-by-step explanation:

Answer:

$2.80 (rounded from 2.796)

Step-by-step explanation:

13.98*0.2

Answer:

$2.80

Step-by-step explanation:

Multiply $13.98 by 0.2 (0.2 = 20%):

[tex]13.98*0.2=2.796[/tex]

Since you can't tip less than a cent, round to the nearest cent (hundredth of a dollar):

[tex]2.80[/tex]

20% tip on a bill of $13.98 is $2.80.

Answer:

23 points

Step-by-step explanation:

If he shane scored 3 fewer points, then that means double of Jason's score is 56. divide 56 by two to get Jason's real score, which is 23.

Answer:

The smaller one measures 80 degrees.

Step-by-step explanation:

We are given:

[tex]a+b=180[/tex]

[tex]\frac{a}{b}=\frac{5}{4}[/tex]

So we have a system to solve.

I'm going to solve the bottom equation for [tex]a[/tex] by multiplying [tex]b[/tex] on both sides:

[tex]a=\frac{5}{4}b[/tex].

Let's plug this into the first equation: [tex]a+b=180[/tex]:

[tex]\frac{5}{4}b+b=180[/tex]

[tex]\frac{5}{4}b+\frac{4}{4}b=180[/tex]

[tex]\frac{9}{4}b=180[/tex]

Multiply both sides by 4/9:

[tex]b=\frac{4}{9} \cdot 180[/tex]

[tex]b=\4 \cdot \frac{180}{9}[/tex]

[tex]b=4 \cdot 20[/tex]

[texb=80[/tex].

This means [tex]a=\frac{5}{4} \cdot 80=5 \cdot \frac{80}{4}=5 \cdot 20=100[/tex].

We do have [tex]100+80=180 \text{ and } \frac{100}{80}=\frac{5}{4}[/tex].

So the smallest of the two angles is the one that measures 80 degrees.

The one that is the larger of the two is the one that measures 100 degrees.

Final answer:

The measure of the smaller angle, which is part of a pair of supplementary angles in a 5:4 ratio, is 80 degrees.

Explanation:

Supplementary angles are two angles that add up to 180 degrees. When two angles are in the ratio of 5:4, we can find the measure of the smaller angle by first adding the parts of the ratio together, which gives us 5+4=9 parts. Since the total is 180 degrees, each part is equal to 180 ÷ 9 = 20 degrees. Therefore, the smaller angle, which is 4 parts of the ratio, is 4 x 20 degrees = 80 degrees.

Firstly they are not numbers, they are ordered pairs or points with a form [tex](x,f(x))[/tex] yes they probably lie on a function graph but that would be rather impossible to find out. The function may be linear, exponential, logarithmic etc. we can't tell. All we can tell is that if these ordered pairs [tex]P_{1,2,3}[/tex] lie on a function graph [tex]P_{1,2,3}\in G_f[/tex] where [tex]G_f=\{(x,f(x)):\forall x\in D_f\wedge f(x)\in T_f\}[/tex] where D is definition set of function defined x's and T a transformation set of f(x)'s for this function. So yes they may lie on some lambda function but they themselves are nothing but an ordered pairs with no meaningful connection.

Hope this helps.

Answer:

no

Step-by-step explanation:

there are two coordinates with the same x value

Answer:

x = 1 , y = 2

Step-by-step explanation:

Solve the following system:

{5 x + 2 = 7 | (equation 1)

y = x + 1 | (equation 2)

Express the system in standard form:

{5 x+0 y = 5 | (equation 1)

-x + y = 1 | (equation 2)

Add 1/5 × (equation 1) to equation 2:

{5 x+0 y = 5 | (equation 1)

0 x+y = 2 | (equation 2)

Divide equation 1 by 5:

{x+0 y = 1 | (equation 1)

0 x+y = 2 | (equation 2)

Collect results:

Answer: {x = 1 , y = 2

Answer:

The required equation models the total profit, y, based on the number of hot dogs sold, x  is   y = 3 x - 30.

Step-by-step explanation:

Let x = total number of hot dogs sold

y = total profit from total sales of hot dogs

The given situation can be written as: y = m x +  C  ......[A]

Now, Profit for 40 hot dogs = $90 profit

So, here this can be written as:

90 = 40 m + C ......[1]

Profit for 80 hot dogs = $210 profit

So, here this can be written as:

210 = 80 m + C ......[2]

Now, solving both the equations, we get:

Subtracting  [1] and [2], we get

210  - 90  = 80 m + C  - (40 m + C)

or, 120 = 40 m

or, m = 120/40 = 3

or, m = 3

Solving for the value of C , we get: C = - 30

Putting the value of m back in the equation : y   = m x + C

y = 3 x -30

Hence, the required equation models the total profit, y, based on the number of hot dogs sold, x  is   y = 3 x - 30.