4. Solve the polynomial.
7x³ + 21x² - 63x = 0

Answer:

x² - (5 + √7)x + 5√7

Explanation:

A polynomial with zeros at x = a and x = b can be written as:

(x - a)(x - b)

So, if the roots are x = √7 and x = 5, we can write the equation for the polynomial as follows:

(x - √7)(x - 5)

Then, to write it in standard form, we need to apply the distributive property, so:

Therefore, the answer is:

x² - (5 + √7)x + 5√7

The sum of 3 and r can be represented by "3 + r"

If this sum is less than 7, we can use the symbol "lesser than" (<) to compare the sum with the number 7, so our number sentence is:

An example of situation involving quantitative comparison is:

The game-plan of an offensive coach for a NFL game.

Quantitative variables are variable that assume numbers as results, instead of labels such as yes/no or good/bad.

When an NFL offensive coordinator is game-planning, he has to consider numeric stats of the opponent defense, such as these ones:

These stats are also compared to the NFL average to verify if the weak point of the opponent defense is the run or the pass, hence the game-plan is adjusted accordingly as follows:

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In order to simplify the expression, we would multiply the terms inside the bracket by the term outside. It becomes

2 * m + 2 * 10

= 2m + 20

7.18° the angle which the road makes with the horizontal.

Define Trigonometric functions

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given,

Height of hill = 250 feet

Length of the slope = 2000 feet

find the angle,

we know, sin(x) = perpendicular / hypotenuse

sin(x) = 250 / 2000

x = sin^-1 (0.125)

x = 7.18°

Hence, 7.18° the angle which the road makes with the horizontal.

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To draw a triangle, you cannot take three random line segments, they have to satisfy the triangle inequality theorems.

0. Triangle Inequality Theorem One: the lengths of any two sides of a triangle must add up to more than the length of the third side.

Procedure:

• Evaluating the first values given: (adding the two smallest values)

Now, we have to compare this addition with the bigger value. As 13.4 > 12.8, these can be side lengths of a triangle.

• Evaluating the second values given: (adding the two smallest values)

Comparing this addition with the bigger value, we can see that 6 < 10, meaning that these values cannot be side lengths of a triangle.

• Evaluating the third values given: (adding the two smallest values)

Comparing, we can see that 6 < 15. Therefore, these cannot be side lengths of a triangle.

• Evaluating the final values given:

We can see that 12 < 13, so these cannot be side lengths of a triangle.

Answer:

• 12.8, 5.2, 8.2: ,can be side lengths of a triangle.

• 5, 10, 1: ,cannot be side lengths of a triangle.

• 3, 3, 15: ,cannot be side lengths of a triangle.

• 7, 13, 5: ,cannot be side lengths of a triangle.

From the graph of f(x), it can be obseved that function f(x) value at x = 0 is -3, which means that f(0) = -3.

From the graph of g(x), it can be observed that g(0) = 0.

As value 0 is greater than -3. So f(0) is lesser than g(0).

Answer: f(0) < g(0)

Let us write out our expressions:

The trick here is to get rid of the minus, then solve the sum as usual, and add a minus to the result. Let us do that for each of them:

-29+(-7)] Step one gives us:

Step two gives us:

Step three gives us:

Then, -29+(-7) should be linked to -36.

-34+(-94)] Step one gives us:

Step two gives us:

Step three gives us:

Thus, -34+(-94) should be linked to -128.

-8+(-14)] Step one gives us:

Step two gives us:

And step three gives us:

This implies that -2+(-14) should be linked to -22.

-12+(-48)] Step one gives us:

Step two gives us:

And step three gives us:

Then, -12+(-48) should be linked to -60.

Conversion factors are the numbers for which we need to multiply a certain variable to convert it to another unit. In this case we need to convert gallons to cups, which have a conversion factor of 16 and minutes to seconds, which has a conversion rate of 60. Doing this we have:

The rate is:

Consider that the total number of fruits are 10. The probability to get some fruit is given by the quotient in between the number of suc a fruit and the total number of fruits.

Then, at the first time, the probability of getting a kiwi is:

p1 = 1/10 = 0.1 (becasue there is one kiwi)

After the kiwi is taken out, the number of fruits are 9. In this case, the probability of getting one orange is:

p2 = 3/9 = 0.33 (because there are three oranges)

THe probability of the two previous events, that is, to obtain one kwi and then one orange is the product of the probabilities p1 and p2:

P = p1*p2 = (0.1)(0.33) = 0.03

Hence, the probabilty is approximately 0.03

The value of the expression 10 to the 2 power + (3 +5 to the power 2) -5 is 159.

An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The expression will be illustrated thus:

10² + (3 + 5)² - 5

= 100 + 8² - 5

= 100 + 64 - 5

= 164 - 5

= 159

The value is 159.

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The ways in which the graph of f(x) = (x + 7)^3 − 8 compare to the parent function g(x) = x^3 are as follows:

In Mathematics, the translation a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Geometry, g(x + 7) simply means shifting a graph 7 units to the left while subtracting 8 from the function simply means moving the graph down.

In this context, we can reasonably infer and logically deduce that the parent function g(x) was shifted 7 units to the left and 8 units down.

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Let:

Using elimination method:

Replace the value of y into (1):

The system has unique solution:

Step 1

Michael spends $18 at store A

He buys x pounds of turkey and y pounds of ham.

But turkey costs $3 in-store A and ham costs $4 in-store A

Therefore, we will have the following equation for Michael

Step 2

Ashley spends $27 in-store B

She buys x pounds of turkey and y pounds of ham.

But turkey costs $4.50 in-store B and ham costs $6 in-store B.

Therefore, we will have the following equation for Ashley

Step 3

Solve the equations graphically

If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. Since the graphs are the same, then there are infinitely many solutions true for both equations.

For instance, the points if we test for the points on the graph, we will conclude if both Michael and Ashley bought the same amount of turkey and ham.

Therefore yes, Michael and Ashley could have bought the same amount of turkey and ham.

The figure formed will be hexagonal

Given:

Required:

We want to find the area of given

Explanation:

As we can see that measurement of given figure is 5 by 5 so it is square and the area of square is

Final answer:

25 sq unit

Let's solve for each and see which gives 8

For A

5/2 x + 7/2 = 3/4 x + 14

collect like term aand solve for x

5/2 x - 3/4 x = 14 - 7/2

For B

5/4 x - 9 = 3/2 x -12

collect like term and solve for x

For C

5/4 x - 2 = 3/2 x - 4

collect like term and then solve for x

For D

5/4 x - 7 = 3/4 x + 14

collect like term and solve for x

Therefore, the correct option is C

Option A: The same line

The slope-intercept form of the equation of a line can be written as:

y = mx + c

Where m is the slope

and c is the intercept

Let us express the two equations given in the slope-intercept form

For the first equation:

y - 3 = 2(x - 3)

y - 3 = 2x - 6

y = 2x - 6 + 3

y = 2x - 3

The slope, m = 2

The intercept, c = -3

For the second equation:

y + 5 = 2(x + 1)

y + 5 = 2x + 2

y = 2x + 2 - 5

y = 2x - 3

We can see that both equations simplify to y = 2x - 3, this means the both equations represent the same line

ANSWER

The first number is 3 and the second number is 7

EXPLANATION

Let the first number be x.

Let the second number be y.

The first line of the word problem is:

One number added to three times another number is 24.

This means that:

x + 3(y) = 24

=> x + 3y = 24 ______(1)

The second line of the word problem is:

Five times the first number added to three times the other number is 36.

5(x) + 3(y) = 36

5x + 3y = 36 ______(2)

Now, we have a system of equations:

x + 3y = 24 ____(1)

5x + 3y = 36 ___(2)

From the first equation, we have that:

x = 24 - 3y

Substitute that into the second equation:

5(24 - 3y) + 3y = 36

120 - 15y + 3y = 36

Collect like terms:

-15y + 3y = 36 - 120

-12y = -84

Divide through by -12:

y = -84 / -12

y = 7

Recall that:

x = 24 - 3y

=> x = 24 - 3(7) = 24 - 21

x = 3

Therefore, the first number is 3 and the second number is 7.

She used 1/4 of the blue cloth to make her mother a apron:

She used 5/8 yd or 0.625yd of blue coth to make the apron

The discount price of the sweater will be, the original price minus the percentage of discount of the original price.

First, express the percentage of discount as a decimal:

60% = 60/100 = 0.6

so:

The discount price of the sweater is $200

ANSWER:

Dilation and translation

EXPLANATION:

Looking at the figures, the two moves used to get the first figure to the second figure is dilation and translation.

The figure was translated 6 units right and 7 units down.

The translation rule that occured here is==> (x+6, y-7)

Also, a dilation with a scale factor of 2 occured here.

Therefore, a dilation and translation occured in order to get the first figure to the second figure.

the given expression is,

thus, the answer is x = 6

We have the following:

solving:

Therefore, the answer is [B] 12

Given two equations,

Comapring both equations,

Therefore, x = 1/3.

Answer:

See graph

Step-by-step explanation:

When we divide a number by a power of 10, the decimal point changes its position. Specifically, the decimal points will move to the left according to the exponent of the power. For example, let's say we have the following division.

As we said before, we just have to move the decimal point to the left. In this case, we have to move it to 3 spots.

Hence, the division is equivalent to 0.542.

That's how the division works when you divide by a power of 10.

Hello there. To solve this question, we have to remember some properties about income and taxes.

The following table shows the progressive tax rate for calculating individual income tax:

We want to calculate the state income tax owed on a $50,000 per year salary.

For this, notice this value is contained in the interval 17,001 and up, hence the progressive tax rate for this value is 5.75%.

In this case, the tax is simply given by the product between the value and the rate:

Don't forget to divide the percentage value by 100% before multiplying.

This is the state income tax owed by one whose salary is $50,000 per year.

ANSWER

Monomial

EXPLANATION

A polynomial is a expression that contains variables, coefficients and sometimes constants.

These terms relate with one another by the use of mathematical signs like addition, subtraction, multiplication, etc

A polynomial with just one term is called monomial.

An example of a polynomial is:

An example of a monomial is:

Answer:

monomial

Step-by-step explanation:

Horizontal Asymptote

Observing the graph with the red dashed line, the horizontal asymptote of the function is at y = 6

Vertical asymptote

If we draw a line the graph we have the following

This indicates that the vertical asymptote is at x = 2.