The graphs of f(x) and g(x) are shown below.

On a coordinate plane, a straight line with negative a slope represents f (x) = negative x. The line goes through points (0, 0), (negative 6, 6) and (6, negative 6). On a coordinate plane, a straight line with a positive slope represents g (x) = 2 x. The line goes through points (negative 3, negative 6), (0, 0) and (3, 6).

Which of the following is the graph of (g – f)(x)?
On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6)
On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 6, negative 6), (0, 0), and (6, 6).

Answer:

option 2: (-1,170, -23,400) and (170, 3,400)

Step-by-step explanation:

correct answer for e2020

Answer:

B. (-1,170, -23,400) and (170, 3,400)

Step-by-step explanation:

Eileen was 600 feet away from the finish line before the race began.

Step-by-step explanation:

Step 1; Eileen rode at a speed of 20 feet per second whereas Andrew rode at a speed of 15 feet per second. So for every second that passes the distance in between decreases by 5 seconds. Assume x is the number of seconds at which the distance in between is 0. The distance in between at the beginning of the race is 150 feet due to the headstart.

Distance between them = Decreasing distance every second × x

150 feet = 5 feet/ second × x

x = 150 feet / 5 feet/second = 30 seconds.

So it takes Eileen 30 seconds to cover the distance between her and Andrew and cross the finishing line at the same time.

Step 2; The race lasted for 30 seconds so we can find the distance Andrew and Eileen traveled by multiplying their speed per second with the total number of seconds.

Distance Andrew traveled = speed per second × total number of seconds

= 15 feet per second × 30 seconds = 450 feet

Distance Eileen traveled = speed per second × total number of seconds

= 20 feet per second × 30 seconds = 600 feet

Graph plot;

The X-axis is time with 5 seconds for each cm

the y-axis is distance with 100 feet for each cm.

Eileen's plot (0,0), (5,100), (10,200), (15,300), (20,400), (25,500), (30,600).

Andrew's plot (0,150), (5,225), (10,300), (15,375), (20,450), (25,525), (30,600).

Answer:0.5

Step-by-step explanation:

Supplementary angles add up to 180 degrees. If one angle measures 56 degrees, the other supplementary angle equals 180-56 which equals 124 degrees. So, the second angle measures 124 degrees.

Supplementary angles are two angles that add up to 180 degrees. Therefore, if one of these angles measures 56 degrees, the other one must be the value that when added to 56 completes 180. We can find it by using the formula for supplementary angles: angle B = 180 - angle A.

So, to find the measure of the second angle, we subtract the measure of the first angle (56 degrees) from 180 degrees.

Angle B = 180° - 56° = 124°.

Therefore, the second angle measures 124 degrees (Choice D).

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Answer:

Multiplication

Step-by-step explanation:

PEMDAS

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

-Since there are parentheses you do that first, so multiplication.

Final answer:

The first operation to perform when simplifying the expression is D: Multiplication, specifically within the brackets where it states 54 × 6. The answer is option D.

Explanation:

When simplifying the expression 63 − (2 + 54 × 6) ÷ 5, according to the order of operations, commonly known as PEMDAS or BEDMAS, we must first perform the operation in the Brackets (in American English, Parentheses are used instead of Brackets).

Within the brackets, the correct sequence of operations is Exponentiation, Multiplication/Division (from left to right), and then Addition/Subtraction (from left to right). Since there is no exponentiation in the brackets, we start with multiplication (54 × 6), which will affect the result within the brackets before performing the addition (2 + ...) and then division ÷ 5. Therefore, the first operation to perform is D: Multiplication.

Answer:

x = 5

Step-by-step explanation:

Start by distributing the 5 to remove parentheses.  To do this multiply the numbers and variable in the parentheses by 5.

10x - 20 - 11 = 4 + 3x

Next. you want to get the variables to one side.  This is done by subtracting 3x from both sides.

7x - 20 - 11 = 4

Now solve the -20 - 11.

7x - 31 = 4

You need to have the variable all by itself.  To do this, first add -31 to both sides.

7x = 35

Finally divide by 7.

x = 5

Hope this helped.  

Answer:

17.78 meters

Step-by-step explanation:

Let

x ----> the horizontal distance, in meters, to home plate

[tex]\theta[/tex] ----> the angle of vision

we know that

[tex]tan(\theta)=\frac{40}{x}[/tex] ----> by TOA (opposite side divided by the adjacent side)

we have

[tex]tan(\theta)=\frac{9}{4}[/tex]

substitute

[tex]\frac{9}{4}=\frac{40}{x}[/tex]

solve for x

[tex]x=40(4)/9\\x=17.78\ m[/tex]

Answer:

15 units²

Step-by-step explanation:

The figure is composed of 2 rectangles.

The rectangle on the left has

A = 4 × 3 = 12 units²

The rectangle on the right has

A = (3 - 2) × (7 - 4) = 1 × 3 = 3 units²

Thus area of figure = 12 + 3 = 15 units²

To find the area of an irregular polygon, divide it into regular shapes and sum their areas. The area of a square is simple: side length squared. When scaling, areas of similar shapes increase by the square of the scaling factor.

To calculate the area of an irregular polygon, we often need to divide it into regular shapes such as triangles, rectangles, or squares. Once we do that, we can calculate the area of each shape and then sum all the areas to find the total area of the irregular polygon. For instance, if an irregular shape fits within a square of side a, its area is less than a² based on the premise that the area of a circle inscribed in a square is smaller than the square's area yet larger than half. For a square, the calculation is relatively straightforward with the formula for area being side length squared (a²).

Calculating the area becomes even more important when applied to real-life examples, such as surveying land parcels which can have highly irregular outlines. The concept is similar to understanding the relationship between the area of a square and its side length when measuring larger plots of land like a state or a carpet on a house's blueprint. We use scales or conversion factors to translate a drawn measurement to actual size.

The comparison of areas can also be seen in the example where Marta's larger square's area is four times that of the smaller one because areas of similar shapes scale by the square of the scaling factor (in this case, 2).

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Answer:

Explanation:

The student used convenience sampling.

The population of the study is the entire population of students of the school.

Since it is time consuming to survey all the students, the high school volunteer student needs to survey a sample.

A systematic random sample would have used a procedure, algorithm,  method (a system) to select a random sample. This is not what the student did, thus the first option is incorrect.

A voluntary sampling consits of volunteer people who agree to take part in the study and answer the survey. This isn't either how the sample was choosen, thus the second option is also incorrect.

A convenience sample is when the sample is chosen for the researcher's ease, i.e. convenience. In this case, the student decided to survey only members of his class instead of selecting a representative sample of all the classes. This sample is not random, since not every member of the population has equal chances to be chosen, but it is easy for the student to survey a group that is very close to him. Hence, the third statement is correct.

The was not an statrified sampling (fourth choice), since statrified sampling consists in creating different groups and chosing some members from every group. This is not what the researcher did.

Answer:

Step-by-step explanation:

C! hopes this helps

Answer:

d. 5

Step-by-step explanation:

Answer:

PRIME

Step-by-step explanation:

the GCF of 64 and 27 is 1

>therefore the polynomial is already factored and can’t be factored further.

Answer:10x+9

Step-by-step explanation:

First you have to multipy the 3 into the parenthesis using distributive property.

After that you get 3x+9+7x.

Then you get 10x+9 because you can only combine like terms

See the graphs below

FOR GRAPH 1:

Let's take:

[tex]f(x)=sin(x)[/tex]

Let's transform this function as follows:

Step 1. Horizontal compression by 1/2:

[tex]f(x)=sin(2x)[/tex]

Step 2. Vertical stretch:

[tex]f_{1}(x)=2sin(2x)[/tex]

Step 3. Vertical shifting 3 units down

[tex]f_{2}(x)=2sin(2x)-3[/tex]

Finally:

[tex]h(x)=f_{2}(x)=2sin(2x)−3[/tex]

The graph is shown in the First Figure below.

FOR GRAPH 2:

Applying a similar method we get:

The graph is shown in the Second Figure below.

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To graph h(x) = 2sin(2x) - 3 and g(x) = 4cos(2x) - 2, multiply the sine and cosine functions by 2 and 4 for amplitude, adjust the period by halving it due to the 2x factor, and shift vertically by -3 and -2 respectively.

To graph h(x) = 2sin(2x) - 3 and g(x) = 4cos(2x) - 2, you can follow these steps:

The resulting graphs will show sine and cosine waves with adjusted amplitudes, periods, and vertical shifts. Remember to use 3.14 as an approximation for π to determine the x-values where key points like maxima, minima, and intercepts occur.

Answer:

4 years

Step-by-step explanation:

9% of the population is 1800. subtract that to get 18200. thats 1 year. subtract again to get 16400. thats 2 years. again to get 14600. 3 years. and then again to get 12800 which is less than 13000. so its 4 years.

Final answer:

Using the exponential decay formula, it takes approximately 8 years for a town's population of 20,000 to decrease to fewer than 13,000 at a yearly decrease rate of 9%.

Explanation:

The question involves calculating the number of years it takes for a town's population to decrease to fewer than 13,000 given an initial population of 20,000 and a yearly decrease rate of 9%. To solve this, we use the formula for exponential decay, which is P(t) = P₀[tex]e^{rt}[/tex], where P(t) is the population at time t, P0 is the initial population, r is the rate of decrease, and t is the time in years.

Substituting the given values, we have 13,000 = 20,000[tex]e^{-0.09t}[/tex]. Solving for t, we take natural logarithms on both sides, which gives ln(13,000/20,000) = -0.09t, leading to t = ln(13,000/20,000) / -0.09. This calculation yields t ≈ 8.04 years, meaning the population will be fewer than 13,000 in about 8 years.

This is a practical application of exponential decay in analyzing population dynamics, highlighting how populations decrease over time under consistent negative growth rates.

Answer:

4-12X

Step-by-step explanation:

Expression: (x+2)-(1x-2)-12x

First step: x+2-1x+2-12x

Second step: (2+2)+(x-1x-12x)

Third step: 4-12X

Answer:

9

Step-by-step explanation:

Answer:

x-int: (2, 0)

y-int: (0,8)

(8-0)/(0-2)= 8/-2=  -4

y - 0 = -4(x - 2)

y = -4x + 8

Step-by-step explanation:

Answer:

7 and 1/4 or 7.25

Step-by-step explanation:

28/4 = 7

1/4 = 0.25

7 + 0.25 = 7.25

Answer:

[tex]\frac{29}{4}[/tex] or [tex]7\frac{1}{4}[/tex]

Step-by-step explanation:

29/4 is the most simplified it can get, if you want it as a mixed fraction then it is 7 1/4.

Answer:

-9 is correct

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

<3

Answer:It  equals -7/20 because Here's how to convert 0.35 to a fraction... There is not much that can be done to figure out how to write 0.35 as a fraction, except to literally use what the decimal portion of your number, the .35, means. Since there are 2 digits in 35, the very last digit is the "100th" decimal place. So we can just say that .35 is the same as -35/100. The fraction -35/100 is not reduced to lowest terms. We can reduce this fraction to lowest terms by dividing both the numerator and denominator by 5. Why divide by 5? 5 is the Greatest Common Divisor (GCD) or Greatest Common Factor (GCF) of the numbers 35 and 100.

So, this fraction reduced to lowest terms is -7/20.

So your final answer is: 0.35 can be written as the fraction -7/20

Hope this helps... Plz mark me brainliest if the answer is correct... Stay safe and have a great weekend!!! :D

Final answer:

The average speed of the second car is calculated by subtracting the distance traveled by the first car from the total distance apart, and then dividing by the time elapsed. The second car has an average speed of 50 mph.

Explanation:

The student is asking for help to find the average speed of the second car when two cars, starting at the same point and traveling in opposite directions, end up being 520 miles apart after 4 hours. The first car travels at an average speed of 80 mph.

To solve this, we need to calculate the total distance covered by both cars in the time frame given. We already know the total distance apart is 520 miles.

The first car travels at 80 mph for 4 hours, covering 80 mph * 4 h = 320 miles. To find out how far the second car traveled, subtract the distance covered by the first car from the total distance apart: 520 miles - 320 miles = 200 miles.

Finally, to find the average speed of the second car, divide the distance traveled by the time. Thus, the second car's average speed is 200 miles / 4 h = 50 mph.

Final answer:

To find the average speed in mph of the other car, divide the total distance traveled by the time. Subtract the first car's average speed from the total speed to find the other car's average speed.

Explanation:

To find the average speed in mph of the other car, we need to determine the total distance traveled. Since the two cars are 520 miles apart at the end of 4 hours, we can divide the total distance by the time to find the average speed.

The first car has an average speed of 80 mph, so the total distance traveled by both cars is 80 mph * 4 hours = 320 miles.

The other car's average speed can be found by subtracting the first car's average speed from the total speed: 320 miles - 80 mph = 240 mph.

Answer:

yessssssssssssssssssssssssss

Answer:Perimeter is the limit of any given geometric figure. Circumference is just the name given to a circle’s perimeter, in other words, the circle’s limit, its edge.

The reason for this is because the perimeter is, by definition, the sum of the lenghth of every side of any given geometric figure. A circle has either no sides, or number of sides, so its perimeter has to be treated differently.

Remember that π (Pi) equals 3.141592 approximately. This is a constant, meaning that no matter what circle you are studying, Pi will always have the same value. It is the relation between the diameter and the lenght of its circumference. A circle with diameter xwill travel 3.141592x before it completes a revolution. This is where Pi comes from.

So the difference would be that a “normal” perimeter is only the sum of the sides. A circumference is the perimeter of a circle, given a diameter and the constant value of Pi, that derives from other properties of the circle, and not by its sides (remember a circle has either none or nnumber of sides).

Answer:

12

Step-by-step explanation:

y = kx

2⅔ = k(¼)

8/3 = k/4

k = 4×8/3 = 32/3

y = (32/3)x

y = (32/3)(1⅛)

y = (32/3)(9/8)

y = 3×4 = 12

Number of pounds of macadamia nuts is 8 pounds and number of pounds of almonds is 4 pounds.

Step-by-step explanation:

Step 1:

Given total pounds of mixture = 12 pounds, cost of macadamia nuts per pound = $9, cost of almonds per pound = $5.25, total cost of mixture per pound = $7.75.

Let number of pounds of macadamia nuts be x and number of pounds of almonds be 12-x.

Step 2:

Form an equation using the above information.

⇒ 9x + 5.25 (12-x) = 12 × 7.75

⇒ 9x + 63 - 5.25x = 93

⇒ 9x - 5.25x = 30

⇒ 3.75x = 30

⇒ x = 8

Number of macadamia nuts is 8 pounds.

Step 3:

Calculate number pounds of almonds

⇒ Number of pounds of almonds = 12 - x = 4 pounds.

Answer:

20-2x=16

Divide all by 2

10-x=8

x=2,

Step-by-step explanation:

Answer: The answer is not 1 it's 2

Step-by-step explanation:

Multiply 4*1 to get 4

Multiply 1*2 to get 2

Your answer should be 4/2 which equals 2

Answer:

0.25

Step-by-step explanation:

Scale factor = ratio of the sides

Assuming the first rectangle is with shorter side 6,

Scale factor = 1.5/6 = 15/60 = 1/4 = 0.25

Divide the new length by the original length:

The arrow points from 6 to 1.5, so the new length is 1.5 and the original length was 6.

1.5 / 6 = 0.25. The scale factor was 0.25

Julie has 27 necklaces and 54 earrings.

Let's assume Julie has x necklaces. Since she has twice as many earrings as necklaces, she would have 2x earrings.

We know that Julie has a total of 81 pieces of jewelry, which includes both necklaces and earrings. Therefore, we can set up a system of equations to represent the given situation:

Equation 1: x + 2x = 81

In Equation 1, we add the number of necklaces (x) and the number of earrings (2x) together, resulting in 81, which is the total number of pieces of jewelry Julie has.

Now, we can solve Equation 1 to find the value of x:

3x = 81

x = 81 / 3

x = 27

So, Julie has 27 necklaces.

To find the number of earrings she has, we can substitute the value of x back into the equation:

2x = 2 * 27

2x = 54

Thus, Julie has 54 earrings.

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Complete Question:

julie has 81 pieces of jewelry. she has twice as many earrings as she has necklaces How many of each does julie have? Write a system of equations for the situation. (two seperate equations ). find the solution.

Final answer:

Using basic algebra, Julie has 27 necklaces and 54 earrings. We found this by setting up the equation 2N + N = 81, solving for N (number of necklaces), and then multiplying by 2 to get the number of earrings.

Explanation:

The student's question regarding Julie's 81 pieces of jewelry can be solved using basic algebra. We know that the number of earrings is twice the number of necklaces. Let's define the following:

We're given that T = 81, so we can substitute E with 2N to get the equation:

Hence, Julie has 27 necklaces. Now we can find the number of earrings:

Therefore, Julie has 54 earrings and 27 necklaces.