I need help with geometry

Based on the information provided, we have:

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

Given the following functions:

f(x) = 5x

g(x) = x - 3.

Next, we would determine the value of composite function f(g(x)) as follows:

f(g(x)) = f(x - 3)

f(g(x)) = 5(x - 3)

f(g(x)) = 5x - 15.

Also, we would determine the value of composite function g(f(x)) as follows:

g(f(x)) = g(5x)

g(f(x)) = (5x) - 3

g(f(x)) = 5x - 3.

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[tex] x + 5 = 12 \\ x = 12 - 5 \\ x = 7[/tex]

she brought 7 bananas

Given statement 'My bank raised its interest rate on savings accounts from 2% to 2.8%, which was a 40% increase.' is True.

The correct answer is an option (E) The statement is true. To determine how much a value increased by, the relative change should be computed. In this case, the relative change is 40%

In this question, we have been given a statement 'My bank raised its interest rate on savings accounts from 2% to 2.8%, which was a 40% increase.'

We need to check whether given statement is true or false.

The bank raised its interest rate on savings accounts from 2% to 2.8%

We find the percent increase.

Here the absolute increase is: |2.8 - 2| = 0.8

The relative increase is: absolute increase / original value

= 0.8 / 2

= 0.4

The percent increase is: relative increase × 100

= 0.4 × 100

= 40%

Therefore, given statement 'My bank raised its interest rate on savings accounts from 2% to 2.8%, which was a 40% increase.' is True.

The correct answer is an option (E) The statement is true. To determine how much a value increased by, the relative change should be computed. In this case, the relative change is 40%

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The lenght of the side b is 5 units

According to the given information the triangle is an right angled triangle with sides a,b, c where a and b are the two legs of the triangle and c is the hypotenuse the measurments of the side a and c are given 12 and 13 respectively . For finding the value of  b we need to use pythagoras theorem that is (Hypotenuse)² = (base)² + (height)²

Here we are going to use the same theorem for finding the value of the side b

According to the question:

hypotenuse = c = 13 units

height = a = 12 units

base = b = ?

As per  the theorem : hypotenuse ² = base ² + height²

∴ (13)² = b² + (12)²

=> 169 = b² + 144

=> b² = 169 - 144

=> b² = 25

=>b = √√25 = ±5

b = 5 [∵ lenght cannot be negative ]

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By using algebra and trigonometry properties, the expression (cot² t + 1) · (sin² t + 1) is equivalent to the expression cot² t + 2.

In this problem we find an equivalence between two trigonometric expressions. This can be done by transforming the expression at one side by using algebra and trigonometry properties until the expression of the other side is found. The procedure is now presented and explained:

(cot² t + 1) · (sin² t + 1)                              Given

(cot² t + 1) · sin² t + (cot² t + 1)                 Distributive property

cot² t · sin² t + sin² t + cot² t + 1              Distributive property

cos² t + sin² t + cot² t + 1                         cot t = cos t / sin t / Associative and commutative properties / Existence of multiplicative inverse / Modulative property

1 + cot² t + 1                                              cos² t + sin² t = 1

cot² t + 2                                                  Commutative and associative properties / Definition of addition

Thus, the expression (cot² t + 1) · (sin² t + 1) is equivalent to the expression cot² t + 2.

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Ths meaning of the slope based on the information is that the model predicts that cereals will have approximately 26 more milligrams of potassium for every additional gram of fiber.

It should be noted that the analysis of the amount of fiber (in grams) and the potassium content(in milligrams) in servings of 77 breakfast cereals produced the regression model.

The model used was:

Potassium = 35 + 26 Fiber

Therefore, the meaning of the slope based on the information is that the model predicts that cereals will have approximately 26 more milligrams of potassium for every additional gram of fiber.

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The distance of the running is 15 miles and the distance of the bicycling is 27 miles.

According to the statement,We have to find that the distance of the run and the bicycle race.

So, For this purpose, we know that the

The distance between two points is that the length of the trail connecting them.

From the given information:

you have entered a 42-mile biathlon that consists of a run and a race. During your run, your average velocity is 5 miles per hour, and through your race, your average velocity is 27 miles per hour. You finish the race in 4 hours.

Then

Total distance of the race = 42 miles

The average velocity of the running = 5 miles per hour

The average velocity of the bicycling = 27 miles per hour

Then

If let he covers 27 miles with the cycles then

The distance he runs = 42-27

The distance he runs = 15.

Then it means he runs for a 3 hours.

So, The distance of the running is 15 miles and the distance of the bicycling is 27 miles.

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Ms. Cody needs 45.05 yards of fabric to make 17 pillow.

For the given question;

Ms. Cody needs 2.65 yards of fabric to make one pillow.

For finding yards for 17 pillows, simply multiply the given yards by 17.

For 17 pillows = 17×2.65

For 17 pillows = 45.05

Thus, 45.05 yards of fabric is required to Ms.Cody to make 17 pillows.

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The scale rectangular of the pool must be 3 x 8 inches.

According to the question,

Given that,

a rectangular pool yard is 150 ft. × 400 ft,

create a scale drawing with a scale factor of 1 to 600, the following calculation must be followed :

[tex]\frac{150}{600} = \frac{1}{4} = 0.25[/tex]

[tex]\frac{400}{600} = \frac{2}{3} = 0.6667[/tex]

1 foot = 12 inches

12 x 0.25 = 3

12 x 0.666 = 8

Then, the scale drawing of the pool must be 3 x 8 inches.

we understand better with the help of some example

“If you are going to build a model, you have to use a scale. You shrink down the real dimensions so that you can actually build a model that everyone will be able to see, think about it, Everest is 29,035 feet high, you can’t build that using the real dimensions,

First, let’s think about our unit scale.

1 inch = 3 feet

If we have a building 24 feet long, that is the actual dimensions. We need to represent the dimensions using our unit scale.

We can say that 8 inches = 24 feet. This is our answer.

First, let’s make a note of the unit scale.

1 inch = 8 feet

We have been given the scale dimension and not the actual dimension. We are going to need to solve for the actual dimension. Let’s write a proportion to do this.

scale dimension actual dimension=1 in8 ft=5 inches

We can see that one times five is equal to five. We can do this to the actual dimension as well. Eight times five is equal to forty.

The actual length of the building is 40 feet.

Popular for ships, especially liners and capital ships. This is the traditional scale for comparative drawings of ships, used by the Royal Navy as it is about one-tenth of a nautical mile to the foot. Warship models produced by  produces airliner models in this scale.

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Answer:

[tex]56e \geqslant 53 \geqslant [/tex]

Hi

Tristan's forecast for income next year is $3,876.

The forecast income can be determined using the mathematical operation of multiplication.

First, the total number of hours worked next year is determined as 204.  This is a product of 17 weeks and a 12-hour week.

Lastly, the above product multiplies the hourly pay rate at $9.50 by two semesters, to determine the expected income for next year.

The average hours of work by Tristan per week = 12 hours

Hourly pay rate = $9.50

The total number of weeks to work = 17 weeks

The total number of hours to be worked = 204 hours (17 x 12)

Expected earnings for each semester = $1,938 ($9.50 x 204)

Expected earnings for two semester = $3,876 ($1,938 x 2)

Thus, Tristan should expect to earn $3,876 for next year.

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The constant of proportionality is 190.

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality.

To find proportionality constant we will find difference of weights of the baby whale after 2 days and at birth.

5710 - 5520 = 190

Now we will find difference of weights of the whale after 14 days and at birth.

We will divide the difference by 14.

(8180-5520) ÷ 14 = 190

Weights are rising at a consistent rate of 190 pounds every day, as can be seen. As a result, 190 is our proportionality constant.

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Answer:

301

Step-by-step explanation:

If we want the two ratios to be equivalent, then we need to use x = 15 and y = 33.

Let's say that we have a simple ratio between two amounts, it is A:B

If we multiply both of these amounts by the same scalar, k, we will get:

k*A and k*B

And the ratio between the new amounts k*A: k*B is equivalent to the first ratio, A:B

So we will use this to solve the problem, here we have two ratios:

5:2:11 = x:6:y

Note that in the first ratio the first value is 2, and in the second case it is 6 so let's find the value of k such that:

2*k = 6

k = 6/2 = 3

Then if we multiply the correspondent values in the first ratio by 3, we will get:

x = 5*3 = 15

y = 11*3 = 33

Then we can see that the ratios:

5:2:11 and 15:6:33 are equivalent.

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Answer:

A) B 20.5 -A s-2.5=-3 is (0.5x)-(-2.5x) = -3x

B) A and B = 2 skydiver's distance each from x = -2.5 and 0.5 inequality shows us when x = 0 then A < -2.5 The second inequality shows us when x = 0 then B2 0.5 here on number line we an keep closed circles and shaded lines in opposite direction each from O showing domain is x domain = -2.5 to O and x domain= 0 to 5 (using commas instead of to) The actual expression then goes B≥0.5-A≤ -2.5=-3 so we an just use (0.5x)-(-2.5x)=-3x

Nadia's solution is incorrect because she should have squared each leg length and then found the sum.

A right angled triangle is a three-sided polygon. The three sides are the length, base and the hypotenuse. The hypotenuse is the longest side of the triangle. The sum of angles in a right angled triangle is 180 degree.

The Pythagorean theorem can be used to determine the length of the hypotenuse given the lengths of the other sides of the triangle. According to this theorem, the sum of the square of the two sides is equal to the length of the hypotenuse.

The Pythagoras theorem: a² + b² = c²

where:

28²  + 45²

= 784 + 2025 = 2809

Hypotenuse = √2809= 53

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Answer:c

Step-by-step explanation:

I did the quiz

[tex] \bf \implies{f( - 4) \: = \: g( - 4) \: and \: f(0) = g(0)}[/tex]

We can observe from the given graph that the two functions intersect each other at (0,4) and (-4,4)

→ g(0) = f(0)

and g(-4) = f(-4)

Answer:

Hope This Helps

Step-by-step explanation:

S=450 + 30W

Plugging 14 into W, we get:  S= 450 +30(14)= $870.

Answer:

Step-by-step explanation:

2 is 0.00007

3 is 0.000875

1 i cant answer because it hurts my dyslexia

Assuming an hypergeometric distribution, the probability that both are red is equal to 33.99%

In an hypergeometric distribution, these three (3) conditions listed below must hold:

In Mathematics, probability from an hypergeometric distribution can be calculated by using this formula:

[tex]p(X = x) = \frac{^MC_x \;^{N-M}C_{n-x}}{^NC_n}[/tex]

N = 12 + 31 = 43

n = 2

M = 12

N - M = 43 - 12 = 31

Substituting the parameters into the formula, we have;

P (X = 2) = (¹²C₂ × ³¹C₂)/⁴³C₂

P (X = 2) = 30,690/903

P (X = 2) = 33.99%

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The greatest number of students that can attend the party is 16.

Given, the teacher has 48 juice boxes and

64 candies for a Halloween party.

Each student will be given an equal number of juice boxes or sweets, and each one must be consumed.

how many (greater) number of students can attend the party = ?

In order to determine the greatest students we need to calculate the greatest common divisor of the numbers.

To calculate the greatest common divisor, we need to find out the prime factors of each number.

Therefore, by the method of prime factorization.

Prime factors of 48 = 2 × 2 × 2 × 2 × 3

Prime factors of 64 = 2 × 2 × 2 × 2 × 2 × 2.

Now, HCF of (48,64) = 2 × 2 × 2 × 2 = 16

Therefore we get the gcd as 16.

Hence the greatest number of students who can attend the party is 16.

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Step-by-step explanation:

the slope of a line is always the factor of x, and it is defined as ratio (y coordinate change / x coordinate change) when going from one point to another on the line.

in that sense it is y/x.

the perpendicular slope turns that ratio upside-down and flips the overall sign.

so, in our case, the original slope is 3 = 3/1.

the perpendicular slope is then -1/3.

so, now, we have the slope and a point, and we can start with the point-slope form of the line equation :

y - y1 = a(x - x1)

"a" being the slope, (x1, y1) being the point.

y - 1 = -1/3 × (x - 9) = -x/3 + 3

y = -x/3 + 4

and that is the usual slope-intercept form

y = ax + b

"a" is again the slope, "b" is the y-intercept (the y value when x = 0).

Answer:

8/x

Step-by-step explanation:

Quotient means to divide the two numbers, in this case 8 and x.

Answer:

Step-by-step explanation:

1.63 meters = 163 centimeters. Formula

Answer: wdym

Step-by-step explanation:

Elise doesn't like sorbet.

(Assuming we fix the grammar???)

Answer: Rate of tree's height per year = 0.275 m per year.

Rate of tree's trunk per year = 0.025 m per year.

Step-by-step explanation:

Given data,

Exactly 120 years​ ago, students planted a tree in front of their school

Since​ then, the tree has grown 33 meters taller

The distance around the trunk has increased by 3 meters.

Define Unit rate :

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

So, we can write,

There are 2 various unit rates in this:

The increase of the tree's height per year

The increase of the tree's trunk per year

Let us assume,

The increase of the tree's height per year = x

The increase of the tree's trunk per year = y

we can solve it :

Rate of tree's height per year x = 33m / 120 years

                                                x = 0.275 m per year.

Rate of tree's trunk per year y = 3m / 120 years

                                              y = 0.025 m per year.

Therefore,

Rate of tree's height per year = 0.275 m per year.

Rate of tree's trunk per year = 0.025 m per year.

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Check the picture below.

yes, it doesn't have all whole numbers, is a so-called piece-wise function, whose behaviour can radically change per interval, notice the arrowheads, meaning the function continues indefinitely all the way up to ∞.