A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch. How much does it cost to fund 4.5 inches of the construction?

Question 1

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

Explanation:

To compute f(g(2)), we'll first need to find g(2).

Locate 2 in the x row. Then read straight down until you get to the g(x) row. You should find that g(2) = 4

This means f(g(2)) becomes f(4). We then repeat the same process as before. Locate 4 in the x row, read straight down til you get to the f(x) row to find that f(4) =  -9

Overall, we can say f(g(2)) = -9

We do the same set of steps to compute g(f(-1)). You should find that f(-1) = -1 and g(f(-1)) = g(-1) = -2

Lastly, we subtract the results we got:  

f(g(2)) - g(f(-1)) = -9 - (-2) = -9+2 = -7

==============================================

Question 2

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

Explanation:

If you were to graph each equation, you should get what you see below.

The red and blue curves do not intersect in any way. We need an intersection point to have a solution. Because there are no intersections, we don't have any solutions. The system is considered inconsistent.

==============================================

Question 3

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

Explanation:

x = number of scooters made and sold

Each scooter costs $150 to make. If you made x of them, then it costs 150x dollars. Then tack on the fixed cost of $2000 to get the expression [tex]150x+2000[/tex]

The cost function is [tex]C(x) = 150x+2000[/tex]. We'll subtract this from the revenue function R(x) to get the profit P(x)

[tex]\text{Profit} = \text{Revenue} - \text{Cost}\\\\P(x) = R(x) - C(x)\\\\P(x) = (400x-2x^2) - (150x+2000)\\\\P(x) = 400x-2x^2-150x-2000\\\\P(x) = -2x^2+250x-2000\\\\[/tex]

==============================================

Question 4

[tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]

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

Explanation:

[tex]g(x) = \frac{1}{x+1}\\\\g(f(x)) = \frac{1}{f(x)+1}\\\\g(f(x)) = \frac{1}{x^2+x-3+1}\\\\g(f(x)) = \frac{1}{x^2+x-2}\\\\g(f(x)) = \frac{1}{(x+2)(x-1)}\\\\(g\circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\[/tex]

I started with the outer function g(x) and replaced each x with f(x) in the second step. Then I plugged in f(x) = x^2+x-3 and simplified. Factoring the denominator is helpful to determine where the denominator becomes zero. Specifically, it happens when x = -2 and x = 1. These x values must be kicked out of the domain to avoid a division by zero error.

So we start off with the real number line, and poke holes at x = -2 and x = 1.

The notation [tex]x \in \mathbb{R}[/tex] means x is a real number. Then we tack on [tex]x \ne -2, x \ne 1[/tex]

Overall, the domain is [tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]

Let's see what happens if we tried plugging x = -1 into this composite function:

[tex](g \circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\(g \circ f)(-1) = \frac{1}{(-1+2)(-1-1)}\\\\(g \circ f)(-1) = \frac{1}{(1)(-2)}\\\\(g \circ f)(-1) = \frac{1}{-2}\\\\(g \circ f)(-1) = -0.5\\\\[/tex]

We don't get a division by zero error, so x = -1 is allowed. The same can be said about any other x value as long as it's not -2 and not 1 either.

Answer:

Step-by-step explanation:

power = work / time

work = force x distance

force = newtons

w = fd

w = 40N(8m)

w = 320J

p = w/t

p = 320J/3s

            __

p = 106.66

(sixes repeat)

Answer: 61 haircuts

Step-by-step explanation:

If tall is completely dominant over short, then the mother's genotype is either TT or Tt. The father is short so his genotype is tt.

Crossing TT with tt produces only heterzygous offspring with genotype Tt. Then the genotypic and phenotypic ratios are 0 TT : 1 Tt : 0 tt and 1 tall : 0 short, respectively. As percentages, these would

• geno:   0% TT : 100% Tt : 0% tt

• pheno:   100% tall : 0% short

Crossing Tt with tt on the other hand produces offspring with genotype either Tt or tt with equal probability, so that the geno and pheno ratios are 0 TT : 1 Tt : 1 tt and 1 tall : 1 short. As percentages,

• geno:    0% TT : 50% Tt : 50% tt

• pheno:   50% tall : 50% short

Answer:

Step-by-step explanation:

As BA = BC, this is an isosceles triangle and the angles adjacent the equal length legs are also identical.

∠C = ∠A = 56°

B = 180 - 2(56) = 68°

Answer:

56°

Step-by-step explanation:

It is because Angle A = Angle C,since triangle ABC is isosceles triangle are equal

i think the answer is 4 hope it helps

Answer:

102 degrees below horizontal

Step-by-step explanation:

if the first angle is 78 degrees, the angle on the other side of the line is 102 degrees because a straight line is 180 degrees, and a box would have a total of 360 degrees in it

because the same line passes through both horizontal lines, the angle 3 is equal to the opposite angle to the 78

180-78 = 102

another way to look at it is that the 78 degrees is the same angle directly above angle 3 because the horizontal lines are parallel, and if it is 78 degrees, that makes the angle below it (angle 3) 102 degrees since a straight line must add to 180 degrees

Answer:

102

Step-by-step explanation:

Answer:

132

Step-by-step explanation:

corresponding angles are the same

Answer:

The guitarist makes 70$ a performance

Step-by-step explanation:

To find how much he makes per performance we need to make an equation where how much he makes per performance is x

The equation would be:

6×x=420

Then we would divide both sides by 6

6÷6×x=420÷6

which would make the equation

x=70

meaning that the guitarist makes 70$ per performance

Let performances be x

[tex]\\ \sf{:}\dashrightarrow 6x(2)=420[/tex]

[tex]\\ \sf{:}\dashrightarrow 12x=420[/tex]

[tex]\\ \sf{:}\dashrightarrow x=420/12[/tex]

[tex]\\ \sf{:}\dashrightarrow x=35[/tex]

Answer:

A=15 inches. B=h=5+2.5w inches

Step-by-step explanation:

Our starting height is 5 inches.

It grew at a constant rate of 2.5 inches per week.

A. How tall after 4 weeks?

Well, we can solve by making an equation.

height=5inches+2.5(x)

In this situation, x is 4.

Height will be 15 inches.

B. This is just asking for the equation.

We already did that in part a!

We just need to switch x out with w.

h=5+2.5w

Step-by-step explanation:

Least to greatest

= 0.919, 0.99, 1.09

Answer:.919,099,1.09

Step-by-step explanation:

Answer:

1/9 —> 11 1/9%, 1/3 —> 33 1/3%, 5/9 —> 55 5/9%, and 8/9 —> 88 8/9%

Step-by-step explanation:

Answer:

its easy. just match numbers that look close to each other

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=0

Answer:

8

Step-by-step explanation:

18×4 = 72

And 72 ÷ 9 = 8

So 9×8 would be 72

Answer:

$100

Step-by-step explanation:

12x5=60

+40= $100

Answer:

$100

Step-by-step explanation:

This is easy

12x5=60

+40=$100

Answer:

Surface area = 6l^2

Volume = l^3

If total surface area increased by 2, then the length increased by [tex]\sqrt{2}[/tex]

Volume then is increased by ([tex]\sqrt{2}[/tex]l)^3 = 2[tex]\sqrt{2}[/tex]l^3

1 :2 [tex]\sqrt{2}[/tex]

Which is not an option in the question so this question clearly has a problem.

First of all It's supposed to be "then" not "than," so I'm not sure who teaches math without even knowing this basic grammar.

Second of all, if the answer is 8:1 the question should be "If each sides of a cube is doubled" not "the lateral surface area." Come to think of it what even is lateral surface area of a cube if all sides of the cube is supposed to be same.

Or, if the answer is 2:1 then, it should be If height lateral surface area of a cube is doubled by doubling the height and without changing the length and width"  But, then the the shape would no longer be a cube.

Who even wrote this garbage question what.

Answer:

Agree

Step-by-step explanation:

Just copy and paste (without quotations): "I agree because r < -5 is just a flipped inequality of -5 > r. In other words, 'r is less than -5' is the same as '-5 is greater than r'."

Answer:

last one

Step-by-step explanation:

Answer:

A) X≥4

B) Can't see question

C)x<8

D) x>40

E)x≥5

F) Can't see question

G)x ≥43

H) x ≤75

Step-by-step explanation:

Answer:

that is so hard sorry

The value of x in the given triangle is 25

The triangle shown is a right triangle.

Each side of the triangle can be found by using the Pythagora's theorem

The Pythagora's theorem states that the "square of the hypotenuse equals the sum of the squares of the other two sides"

Applying the Pythagora's theorem:

[tex]x^2=24^2+7^2\\\\x^2=576+49\\\\x^2=625\\\\x=\sqrt{625}\\\\ x=25[/tex]

Learn more on missing sides of right triangle here: https://brainly.com/question/23987176

Answer: $54.66

Step-by-step explanation:

The 18% turns into 0.18, they mean the same thing.

46.32 * 0.18 = 8.34 (Unsimplified answer: 8.3376)

Add tip to the cost.

46.32 + 8.34 = 54.66

Correct me if it is incorrect.

Answer:

Step-by-step explanation:

20 cm³ of pure alcohol is added to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution.

Let x represent the volume of pure alcohol (100%) in cm³ needed to be added. Hence:

x * 100% + 10 cm³ * 10% = 70% * (x + 10 cm³)

x * 1 + 10 * 0.1 = 0.7 * (x + 10)

x + 1 = 0.7x + 7

x - 0.7x = 7 - 1

0.3x = 6

x = 20 cm³

Therefore 20 cm³ of pure alcohol is added to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution.

Find out more on equation at: https://brainly.com/question/13763238

Answer:

20 cm³

Step-by-step explanation:

Answer:

$100

Step-by-step explanation:

sum the parts of the ratio, 2 + 5 = 7 parts , then

$350 ÷ 7 = $50 ← value of 1 part of the ratio , then

2 parts = 2 × $50 = $100 ← smaller share

Answer:

where are you from me

Step-by-step explanation:

:philipines

btw ty sayo

Answer:

Samantha wants a simple, starter car, or the extra accessories have a higher price than the one's without it.

Answer:

rectangle= 22*9 = 198ft

triangle=11*10 = 110 ft

110+ 198 = 308 polygon