Gabe charges $30 to mow a lawn. Nate
charges $25 to mow a lawn. Their total
combined revenue one summer was $2020.
Nate mowed 6 more lawns than Gabe.
Write a system of equations to represent
this situation. Then solve the system of
equations by substitution. Explain what the
solution means.

The solution to the given inequality is [tex]b\leq 1.7[/tex]

From the question, we to determine the solution to the inequality.

To determine the solution of the inequality, we will determine the value of the variable. The variable in the given question is b.

The inequality can be solved as shown below.

[tex]\frac{7}{2} \geq b + \frac{9}{5}[/tex]

Multiply through by 10

That is,

[tex]10 \times \frac{7}{2} \geq 10\times b + 10\times \frac{9}{5}[/tex]

This becomes

[tex]5 \times 7 \geq 10b + 2 \times 9[/tex]

[tex]35 \geq 10b + 18[/tex]

Now, subtract 18 from both sides

[tex]35 - 18\geq 10b + 18-18[/tex]

[tex]17 \geq 10b[/tex]

This becomes,

[tex]10b \leq 17[/tex]

Divide both sides by 10

[tex]\frac{10b}{10} \leq \frac{17}{10}[/tex]

[tex]b\leq 1\frac{7}{10}[/tex]

OR

[tex]b\leq 1.7[/tex]

Hence, the solution to the given inequality is [tex]b\leq 1.7[/tex]

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Answer:

false

Step-by-step explanation:

because it doesn’t have the three complete angles

Answer:

False

Step-by-step explanation:

The area of the L-shaped figure formed is 225 square inches.

To find the area of the L-shaped figure formed after cutting corners, start by calculating the area of the square from which the corners were removed.

The larger square has sides of length 15 inches, so its area is 15 x 15 = 225

When you cut corners of 9 inches by 9 inches from each corner of the larger square, you effectively create a smaller square. Since each side of the smaller square is 9 inches shorter than the larger square, its side length is -

15 - 2 x 9

= - 3

However, a negative side length is not possible, so we adjust it to zero. This implies that there's no square left after cutting off such large corners.

The area of the L-shaped figure is the difference between the area of the larger square and the area of the smaller square:

Area of L-shaped figure=Area of larger square−Area of smaller square

= 225 - 0

= 225

Thus, the area of the L-shaped figure formed is 225 square inches.

Answer:

[tex]V=12\ ft^{3}[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

In this problem

[tex]P*V=k[/tex]

step 1

Find the value of K

For [tex]P=24\ psi ,V=15\ ft^{3}[/tex]

substitute

[tex]24*15=k[/tex]

[tex]k=360[/tex]

the equation is [tex]P*V=360[/tex]

step 2

For [tex]P=30\ psi ,V=\ ft^{3}[/tex]

substitute in the equation

[tex](30)*V=360[/tex]

[tex]V=360/30=12\ ft^{3}[/tex]

Using Boyle's law, which states volume and pressure of a gas at constant temperature are inversely proportional, we find that at a pressure of 30 pounds per square inch, the volume will be 12 cubic feet.

The concept behind your question involves Boyle's law, which states the volume of a given amount of gas held at constant temperature is inversely proportional to the pressure under which it is measured. This means as pressure increases, volume decreases and vice versa while maintaining the same temperature.

To solve this, we can use the mathematical expression for Boyle's law: P₁V₁ = P₂V₂.

Where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume. Applying these values: 24 pounds per square inch * 15 cubic feet = 30 pounds per square inch * V₂. By rearranging the equation and solving for V₂, we get: V₂ = (24 pounds per square inch * 15 cubic feet) / 30 pounds per square inch = 12 cubic feet.

Therefore, when the pressure is 30 pounds per square inch, the volume will be 12 cubic feet.

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Answer:

each section will equal 2.5 miles

Step-by-step explanation:

if you divide 10 from 4 you get 2.5

To divide a 10-mile bike race into four equal sections, we calculate the length of one section by dividing 10 miles by 4, resulting in each section being 2.5 miles long.

The question pertains to the division of a 10-mile bike race into four equal sections. To find the length of each section, we divide the total distance of the race (10 miles) by the number of sections (4). This calculation will give us the length of one section.

10 miles \ 4 sections = 2.5 miles per section.

Thus, each section of the bike race would be 2.5 miles long. This application of division in real-world situations like races and marathons is a fundamental concept in mathematics, allowing participants and organizers to understand and manage distances more effectively.

Answer:

1,760

Step-by-step explanation:

A mile is 5280 feet

3 feet in a yard

so     5280/3=1760

your answer is A) 1,760 yards

Answer:  y = x

Step-by-step explanation:

First, find the point where 5x - 2y + 3 and 4x - 3y + 1 intersect using the Elimination Method.

5x - 2y + 3 = 0  →  3(5x - 2y + 3 = 0)  →  15x - 6y + 9 = 0

4x - 3y + 1 = 0   → -2(4x - 3y + 1 = 0)  →   -8x + 6y - 2 = 0

                                                                 7x         + 7 = 0

                                                                 7x               = -7

                                                                   x               = -1

5x - 2y + 3 = 0

5(-1) - 2y + 3 = 0

-5 - 2y + 3 = 0

    -2y  - 2 = 0

    -2y        = 2

        y        = -1

(-1, -1)

Next, find the point where x = y and x = 3y + 4 intersect using the Substitution Method.

x = y

x = 3y + 4    →    y = 3y + 4

                      -2y = 4

                         y = -2

x = y

x = -2

(-2, -2)

Now, find the line that passes through (-1, -1) and (-2, -2) using the Point-Slope formula.  (x₁, y₁) = (-1, -1)  and m = 1

y - y₁ = m(x - x₁)

y + 1 = 1(x + 1)

    y = x

Answer:

Number 7 is 40

Step-by-step explanation:

set up a proportion 5/1 = x/8 cross multiply a divide and you get 40

B is the answer hope this helps!

B) is the answer, my reasoning is that A) is 2n - 15 and four tenths which is the wrong way around , C) is just nonsense and D) is n multiplied by 15 and four tenths take away 2 which is also wrong , as that would be n x 13 and four tenths , hope this helps :)

the carpet is rectangular, thus its area is simply the product of its two dimensions, namely 8*6 = 48 m².

how much is the shaded area?  well, since it's also rectangular, its area is also that product of 2*2 = 4, recal is a square so length = width = 2.

[tex]\bf \stackrel{\textit{how many times does 48 go into 4?}}{\cfrac{shaded}{total~area}\qquad \cfrac{4}{48}\implies \stackrel{simplified}{\cfrac{1}{12}}}[/tex]

Answer:

N = 3

Step-by-step explanation:

I don't know what the whole thing above is, but just disregard that.

All it is here is cross multiplication.

So 28N = 21 * 4

Multiply...

28N = 84

And divide each side by 28

N = 3

Answer:

(C)$62.00

Step-by-step explanation:

$200 x .31 = $62.00

the answer is C it is $62.00

Answer:

1/6

Step-by-step explanation:

If we're assuming that this is a six-sided die, then we can find that the results can be 1,2,3,4,5,6. Only 1 of those 6 numbers are 5, so the probability of the cube landing on 5 would be 1/6.

Answer:

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

Step-by-step explanation:

Probability is measured as

[tex]\frac{favourableoutcome}{count}[/tex]

The favourable outcome is obtaining roll > 4, that is a 5 or 6

P( > 4 ) = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

Answer:   There are two points of intersection (2, 4) and (-4, -2)

Step-by-step explanation:

x - y + 2 = 0     →       x = y - 2

Use Substitution Method:

x² + y² = 20

(y - 2)² + y² = 20              replaced x with (y - 2)

y² - 4y + 4 + y² = 20        expanded (y - 2)²

2y² - 4y + 4 = 20             added like terms

2y² - 4y - 16 = 0               subtracted 20 from both sides

y² - 2y - 8 = 0                  divided both sides by 2

(y - 4)(y + 2) = 0               factored

y - 4 = 0    and      y + 2 = 0       applied Zero Product Property

y = 4        and       y = -2

Input the y-values into x = y - 2 to solve for x.

y = 4;   x = 4 - 2                      y = -2;    x = -2 - 2

           x = 2                                         x = -4

      (2, 4)                                         (-4, -2)

Answer:

A=54in²

Step-by-step explanation:

Answer:

A = 75°

B = 90°

C = 15°

Step-by-step explanation:

The diagram tells us that C = 15°.

The diagram places a square in the angle of B, showing you the angle is a 90° right angle.

You can solve for A because all angles of a triangle must equal 180°. 180° - 90° (B) = 90°. 90° - 15° (C) = 75°, the measure of A.

The volume of a hemisphere with a radius of 5 inches is calculated by first determining the volume of a full sphere using the formula V = (4/3)πr³, and then dividing that by 2. The final volume of the hemisphere is 261.7994 cubic inches.

Volume of a Hemisphere

The question involves finding the volume of a hemisphere, which is half of a sphere, with a given radius of 5 inches. First, we would calculate the volume of a full sphere using the formula V = (4/3)πr³, and then divide that by 2 to get the hemisphere volume. Therefore, for a sphere with a radius of 5 inches:

Volume of the sphere, V = (4/3)π × 5³.

Volume of the hemisphere = V/2.

After performing the calculations:

Volume of the sphere, V = (4/3)π × 125 = 523.5988 cubic inches.

Volume of the hemisphere = 261.7994 cubic inches.

Answer:

g(f(0)) = 6

Step-by-step explanation:

Evaluate f(0 ) and substitute this value into g(x)

f(0) = 0² = 0 and

g(0) = 0 + 6 = 6

⇒ g(f(0)) = 6

The value of g(f(0)) is 6.

If two functions f(x), g(x) are present , then (f o g) of x is also known as a composite function and it is mathematically denoted as f(g(x)) or (f ∘ g)(x). It means that x = g(x) should be substituted in f(x). It is an operation that combines two functions to form another new function.

Given , f(x) = [tex]x^{2}[/tex]  and  g(x) = x + 6

We have to find g(f(0)).

To get the value of this composite function g(f(x)), we first have to find the value of f(x) at the given value x = 0 and then substitute the value of f(x) into g(x).

⇒ f(0) = 0.

∴ g(f(0)) = g(0) = 0 + 6 = 6.

Therefore we have the value of g(f(0)) as 6.

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Answer:

b=4

Step-by-step explanation:

-14+2b= -2b+2​

Add 2b to each side

-14+2b+2b= -2b+2b+2

-14+4b =2

Add 14 to each side

-14+4b+14= 14+2​​

4b = 16

Divide each side by 4

4b/4 = 16/4

b =4

Answer:

#6.  36    #30. 24

Step-by-step explanation:

6. You add 7+29=36 so 36 is the missing number

Answer:

428,820,000 pounds

Step-by-step explanation:

The amount of garbage is number of person times the amount produced by each person. Thus, we have:

Amount of Garbage (in pounds) = 2.61 × 10^5 * 1.643 × 10^3

Note: We multiply 2.61 and 1.643, which is 4.28823 & multiplying 10^5 and 10^3 is 10^(5+3) = 10^8

Thus, we have 4.28823 * 10^8 = 428,823,000 pounds

This is approximately 428,820,000 pounds, last answer choice.

Answer:

Other answer is correct, confirmed on E2020

Step-by-step explanation:

Final answer:

Ms. Gordon will need 1 1/3 cups of melted butter, 16 cups of marshmallows, and 8 2/3 cups of cereal.

Explanation:

To find how much of each ingredient Ms. Gordon needs, we need to use the information provided in the recipe and the fact that she is only using 2/3 of the recipe.

For each ingredient, multiply the original amount by 2/3.

So, Ms. Gordon will need:

Answer:

(x - 7)² + (y - 2)² = 130

Step-by-step explanation:

The first step is finding the length of the radius.

r² = (2 - -5)² + (7 - -2)²

    = 7² + 9²

    = 49 + 81

   = 130

The general equation of a circle is:

(x - a)² + (y - b)² = r²

Where (a, b) is the coordinate of the center and r is the radius.

∴ The equation of the required circle is;

 (x - 7)² + (y - 2)² = 130

To find the probability of not rolling factors of 6 on both six-sided dice, multiply the individual probabilities of rolling a 4 or 5 on each die. The probability is 1/9.

The factors of 6 are 1, 2, 3, and 6. Therefore, the outcomes that are not factors of 6 are 4 and 5.

Since each die has six faces, the total number of possible outcomes when rolling two dice is 6 x 6 = 36.

Of these 36 possible outcomes, we need to count how many do not involve factors of 6. For each die rolled independently, we have 2 outcomes that are not factors of 6: {4, 5}.

So, we need to calculate the product of these individual probabilities to find the probability of both dice showing a non-factor of 6.

For a single die, the probability of rolling a non-factor of 6 (either a 4 or a 5) is 2/6 or 1/3, since we have 2 favorable outcomes out of 6 possible ones.

To find the probability for both dice, we multiply these individual probabilities:

Probability of not rolling a factor of 6 on both dice = (1/3) x (1/3) = 1/9.

This is the product rule in probability, which tells us that the probability of two independent events both happening is the product of their individual probabilities.

Therefore, the probability of not rolling a factor of 6 on both dice is 1/9.

True

A linear recurrence relation involving a sequence of numbers [tex]a_n[/tex] is one of the form

[tex]\displaystyle\sum_{k=0}^nc_{n-k}a_{n-k}=c_na_n+c_{n-1}a_{n-1}+\cdots+c_2a_2+c_1a_1=c[/tex]

where [tex]c_1,c_2,\ldots,c_n[/tex] and [tex]c[/tex] are any fixed numbers.

The given recurrence can be rearranged as

[tex]a_n=a_{n-1}+2\implies 1\cdot a_n+(-1)\cdot a_{n-1}=2[/tex]

A nonlinear recurrence would have a more "exotic" form that cannot be written in the form above. Some example:

[tex]a_n+\dfrac1{a_{n-1}}=1[/tex]

[tex]a_na_{n-1}=\pi[/tex]

[tex]{a_n}^2+\sqrt{a_{n-1}}-\left(\dfrac{a_{n-2}}{\sqrt{a_n}}\right)^{a_{n-3}}=0[/tex]

The query pertains to 'linear recurrence relations' in Mathematics, particularly concerning high school algebra and series expansions, such as the binomial theorem, and plotting data on a logarithmic scale.

The term linear recurrence relation refers to a sequence of numbers where each term is a linear combination of previous terms. The relationship is defined by two aspects: the number of terms that go into the combination (order of the relation), and the coefficients of each of those terms. A classic example of a linear recurrence relation is the Fibonacci sequence, where each term is the sum of the two preceding terms.

When addressing series expansions like the binomial theorem, it is an expression that allows us to expand polynomials raised to a power in a series format. The theorem is a key concept in algebra and is particularly useful for calculating powers of binomials and deriving coefficients of individual terms within expanded polynomials.

To plot data like the recurrence interval on a logarithmic scale, it is essential to understand that each increment on the axis represents a multiplication by a certain factor, rather than a linear addition. This type of representation is particularly useful when dealing with data that varies by orders of magnitude.

Answer:

F

Step-by-step explanation:

Answer:

639

Step-by-step explanation:

put the 71 on the top then the 9 on the bottom then 9x1=9 then 9x7=63

639!

Answer:

The profit function would be p(x) = 7x - 20

Step-by-step explanation:

In order to find this, start by listing just as asked.

p(x) = r(x) - c(x)

Now input the functions where indicated

p(x) = 12x - (5x + 20)

p(x) = 12x - 5x - 20

p(x) = 7x - 20

Answer:

The value of [tex]p(x)=-5x-8[/tex]

Step-by-step explanation:

Given : The revenue from selling x shirts is [tex]r(x)=12[/tex]. The cost of buying x shirts is [tex]c(x)=5x+20[/tex]. The profit from selling x shirts is [tex]p(x)=r(x) - c(x)[/tex].

To find : What is p(x)?

Solution :

The revenue from selling x shirts is [tex]r(x)=12[/tex].

The cost of buying x shirts is [tex]c(x)=5x+20[/tex].

The profit from selling x shirts is [tex]p(x)=r(x) -c(x)[/tex]

Substitute the values in the formula,

[tex]p(x)=12 -(5x+20)[/tex]

[tex]p(x)=12 -5x-20[/tex]

[tex]p(x)=-5x-8[/tex]

Therefore, The value of [tex]p(x)=-5x-8[/tex]