Weekly math review-Q1.6

Answer:

A. [tex]f(x)=-4|x+2|+3[/tex]

Step-by-step explanation:

We have been given an image of an absolute function. We are asked to find the formula for our given absolute function.

The formula of parent absolute function is [tex]f(x)=|x|[/tex] with vertex at (0,0)

We can see that the vertex of our given function is at [tex](-2,3)[/tex]. This means that our function is shifted to left by 2 units. We can represent this information as: [tex]f(x)=|x--2|=|x+2|[/tex]

We can also see that our graph is reflected across x-axis, so after reflection our function would be [tex]f(x)=-|x+2|[/tex]

We can see that our graph is shifted upwards by 3 units, so graph after shifting would be [tex]f(x)=-|x+2|+3[/tex].

Our graph is stretched vertically by a scale factor of 4, so after stretching our function would be [tex]f(x)=-4|x+2|+3[/tex].

Therefore, option A is the correct choice.

Answer:

[tex]\sqrt{\frac{7}{11} }[/tex]

Step-by-step explanation:

The right expression of the question is

[tex]\frac{\sqrt{7} }{\sqrt{11} }[/tex]

The simplest radical form of this expression is obtained by applying the right property, which is about the quotient between radicals. According to this property, the quotient of radical is equal to the radical of the quotient, that is

[tex]\frac{\sqrt{7} }{\sqrt{11} }=\sqrt{\frac{7}{11} }[/tex]

The value of b in the equation of the trend line is 21

The equation of the trend line of the scatter plot is given as:

y = 15x + b

The points are given as: (6.4, 117) and (6.6, 120).

Using (6.4, 117), we have:

117 = 15 * 6.4 + b

Evaluate the products

117 = 96 + b

Subtract 96 from both sides

21 = b

Rewrite as:

b =21

Hence, the value of b in the equation of the trend line is 21

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Answer:

Remaining amount of jeans after x sales = 688 - 2x

In this expression

2x = The number of jeans purchased.

-2 = The number of jeans the stock is reduced by from each sale.

2 = The number of jeans sold with each purchase.

Step-by-step explanation:

Given information:

Total number of jeans = 688

He decides to reduce the stock by having a buy one get one free sale.  It means that every purchase will reduce this inventory by 2 pairs of jeans.

Average rate of change = -2

Let x be the number of purchase.

So, the total amount of jeans in stock after each sale is

Remaining amount of jeans after x sales = 688 - 2x

In this expression

2x = The number of jeans purchased

-2 = The number of jeans the stock is reduced by from each sale.

2 = The number of jeans sold with each purchase

Answer:

-250

Step-by-step explanation:

Answer: yeah it's -250

Step-by-step explanation: just submitted the test

It would be 7 units because when you put down the points and you draw a diaganal line between the two points and it crosses 7 intersections.

Hope you stay safe and this answer helps you.

The simplified expression is -202.2, which can be expressed as a decimal as -202.2.

To simplify the expression, we need to perform the operations in order of operations (PEMDAS/BODMAS). First, we simplify the expressions inside the parentheses:

2.7 + 5 = 7.7

Next, we can rewrite the expression:

3(7.7) - 23(7.7) - 2

Now, we can multiply each term:

3 * 7.7 = 23.1

23 * 7.7 = 177.1

-23.1 - 177.1 - 2

Finally, we can combine like terms:

-202.2

The simplified expression is -202.2, which can be expressed as a decimal as -202.2.

Final answer:

To simplify the expression 3(2.7+5)−23(2.7+5)−2, we first evaluate the addition inside the parentheses and then perform the multiplication and subtraction step by step to get the final simplified answer as -156.

Explanation:

To simplify the expression 3(2.7+5)−23(2.7+5)−2, we first evaluate the addition inside the parentheses: 2.7+5 = 7.7.

Substituting this value back into the expression, we get 3(7.7) - 23(7.7) - 2.

Next, we perform the multiplication: 3(7.7) = 23.1 and 23(7.7) = 177.1.

Substituting these values back into the expression, we have 23.1 - 177.1 - 2.

Finally, we perform the subtraction: 23.1 - 177.1 = -154 and -154 - 2 = -156.

Therefore, the simplified answer as a decimal is -156.

-5(-2f-6)

 distribute by multiplying -5 by everything inside the parenthesis

-5 * -2f = 10f

-5 *-6 = 30

so you get 10f+30

The coordinates for the points of intersection of the line y=-1.5x + 3 with the coordinate axes are (0,3) for y-axis and (2,0) for the x-axis.

To find the points of intersection of the line with the coordinate axes, we will set the values of y and x to zero separately. So, let's start from the intersection of the line with the y-axis. For this, we set x=0 in the equation y = -1.5x + 3. Thus, y = 0*(-1.5) + 3 which gives us y = 3. So one point of intersection is (0,3). Next, finding the x-intercept requires setting y=0, which gives 0 = -1.5x + 3. Solving this equation, we get x = 3 / 1.5 or x=2. Hence, the other point of intersection is (2,0). Therefore, the coordinates for the points of intersections are (0,3) and (2,0).

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To convert 175% to a fraction, write it as 175/100 and then simplify by dividing both numerator and denominator by their greatest common divisor, 25, which gives a simplified fraction of 7/4.

One hundred seventy five percent as a fraction can be converted by writing the value of the percent as a fraction with a denominator of 100. To convert the percent to a fraction, we write 175% as 175/100. This fraction can then be simplified. To simplify, we can divide both the numerator and the denominator by their greatest common divisor, which is 25.

Here is the step-by-step simplification process:

Write 175% as a fraction: 175/100

Divide both the numerator and the denominator by 25: (175 ÷ 25) / (100 ÷ 25) = 7/4

The simplified fraction for 175% is therefore 7/4.

complete question given below:

What is one hundred seventy five percent as a fraction?

To find the missing rate and new balance, we used the simple interest formula. The rate was calculated to be 5% and the new balance after 3 years, including interest earned, was determined to be $517.50.

The subject in question here is simple interest calculation, which is a fundamental concept in finance and mathematic subjects. To solve for the missing rate and new balance, we can use the formula Interest = Principal x rate x time.

First, we rearrange the interest formula to solve for the rate:

Rate = Interest / (Principal x Time)

Plugging in the provided numbers:

Rate = $67.50 / ($450 x 3)

Rate = $67.50 / $1350

Rate = 0.05 or 5%

Now, we find the new balance using the formula:

New Balance = Principal + Interest

New Balance = $450 + $67.50

New Balance = $517.50

Therefore, the interest rate is 5% and the new balance after 3 years is $517.50.

Answer:

Correct option is:

C. (f + g)(x) = 3x² – 2x – 1

Step-by-step explanation:

f(x) = –4x + 3 and g(x) = 3x² + 2x – 4

We have to find (f + g)(x).

We know that (f+g)(x)=f(x)+g(x)

⇒ (f+g)(x)=-4x+3+3x²+2x-4

⇒ (f+g)(x)=3x²-2x-1

Hence, Correct option is:

C. (f + g)(x) = 3x² – 2x – 1

Final answer:

By adding the distance from A to M to A's coordinate, we find that M's coordinate is 1.

Explanation:

The question asks to find the coordinate of point M on a number line where point A has a coordinate of −1.5, point B has a coordinate of 6, and the ratio of the distances AM to MB is 1:2. To solve this, we first identify that AM and MB are segments on the number line with point M somewhere between A and B. Since AM:MB = 1:2, we know that for every unit distance from A to M, there are 2 unit distances from M to B.

The total distance between A and B is 6 - (−1.5) = 7.5 units. Dividing this distance in the ratio 1:2, implies that AM takes up one-third of the total distance and MB takes up two-thirds of the total distance. Therefore, AM = ¼ * 7.5 = 2.5 units. Adding this distance to the coordinate of A gives us the coordinate for M: −1.5 + 2.5 = 1. So, the coordinate of point M is 1.

Answer:

5n = 30 + 3(n - 4)

Step-by-step explanation: