Find the coefficient of third term of (x + 2)³. A. 40 OB. 10 OC. 20 D. 80 Reset Selection A

In order to complete the square remember that

first, equal the expression divide all the expressions by 2,

then, we can find "a" using the second portion of the definition

then,

add 1 on both sides

rewrite as a square expression on the left,

multiply both sides by 2

bring all to the left side and equal to f(x)

Given:

Required:

We need to find the probability that the mean height of this sample will be greater than 57 inches,

Explanation:

Consider the formula to find the z-score.

From the z table, we get

Final answer:

The probability that the mean height of this sample will be greater than 57 inches is 0.703.

The integers are 71 and 72 respectively

An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, factors and constants.

They are also known to be composed of mathematical operations such as;

From the information given , we have;

x + 1 + x + 2 = 143

collect like terms

2x = 143 - 3

Subtract like terms

2x = 140

Make 'x' the subject

x = 140/2

x = 70

The numbers are;

x + 1  = 70 + 1  = 71

x + 2 = 70 + 2 = 72

Hence, the numbers are 71 and 72

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The probability that Dave will select a gray T-shirt is 13 / 25.

The odds in favor of picking a gray T-shirt is 13 : 25

Probability is used to calculate the odds that are in favor or against a random event happening. The odds in favor or against a random event happening has a probability value that lies between 0 and 1. The higher the odds that are in favor of the event happening, the closer the probability value would be to 1.

The probability that Dave will select a gray T-shirt = number of gray T-shirts / total number of T-shirts

13 / 25

Ratio is used to compare two or more numbers together.

The odds in favor of picking a gray T-shirt = number of gray T-shirt : total number of T-shirts = 13 : 25

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Answer:

  18.7 miles

Step-by-step explanation:

You want to know how far Kendall can ride her bike in 2 hours if she rides at the speed of 7 miles in 45 minutes.

The question assumes that distance is proportional to time, so the distance (d) of interest can be written in the proportion ...

   miles/minutes = 7/45 = d/120 . . . . . . 120 minutes is 2 hours

Multiplying by 120, we have ...

  d = 120(7/45) = 7(8/3) = 18 2/3 ≈ 18.7

Kendall can ride about 18.7 miles in 2 hours.

Answer:

[tex]\textsf{Vertex form}: \quad y=\dfrac{1}{36}(x+3)^2+1[/tex]

[tex]\textsf{Standard form}: \quad y=\dfrac{1}{36}x^2+\dfrac{1}{6}x+\dfrac{5}{4}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

Given:

Substitute the given vertex and point into the formula and solve for a:

[tex]\begin{aligned}y&=a(x-h)^2+k\\\\\implies 2&=a(-9-(-3))^2+1\\2&=a(-6)^2+1\\2&=36a+1\\36a&=1\\a&=\dfrac{1}{36}\end{aligned}[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]\boxed{y=\dfrac{1}{36}(x+3)^2+1}[/tex]

In standard form:

[tex]\implies y=\dfrac{1}{36}(x+3)(x+3)+1[/tex]

[tex]\implies y=\dfrac{1}{36}(x^2+6x+9)+1[/tex]

[tex]\implies y=\dfrac{1}{36}x^2+\dfrac{6}{36}x+\dfrac{9}{36}+1[/tex]

[tex]\implies y=\dfrac{1}{36}x^2+\dfrac{1}{6}x+\dfrac{5}{4}[/tex]

Given:

• Length of side adjacent the indicated angle = 48

• Length of hypotenuse = 56

Let's find the measure of the indicated angle.

To find the measure of the indicated angle, apply the trigonometric ratio formula for cosine:

Thus, we have:

Therefore, the measure of the indicated angle is 31 degrees.

ANSWER

Step-by-step explanation:

[tex] \sqrt{99} = 3 \sqrt{11} \\ \sqrt{44} = 2 \sqrt{11} \\ 3 \sqrt{11} + 2 \sqrt{11} = 5 \sqrt{11} [/tex]

Answer:

[tex]3 \sqrt{11} [/tex]

[tex]4 \sqrt{11} [/tex]

because we rewrite it as integer statements

Explanation:

Equation A

Let:

Given the polynomial:

The x-intercepts are the points in which the polynomial crosses the x-axis. That is, are the points (x, 0).

To find these points, use the quadratic formula according to the steps below.

Step 01: Substitute the values in the quadratic formula.

For a equation y = ax² + bx + c, the x-intercepts are:

In this question,

a = 1

b = 16

c = 64

Substituting the values:

Step 02: Solve the equation above.

Begin by solving the square and the multiplications:

Now, subtract the values inside the root.

Solve the root:

And find the values of x:

Answer: The x-intercepts are: (-8, 0), (-8, 0).

Answer:

Your answer is [tex]y = 2x - 2[/tex]

Step-by-step explanation:

Just test it out on all of them, it fits.

The exponent multiplies the logarithm of the base

So:

The answer is option C

When we want to determine the midpoint of two points on a line segment, we must first determine the coordinates of the two points. Then we divide the sum of the abscissa [tex](x)[/tex] by [tex]2[/tex] to find the abscissa of the midpoint and divide the sum of the ordinates [tex](y)[/tex] by [tex]2[/tex] to find the ordinate of the midpoint.

Let the coordinates of our midpoint be [tex]F(a,b)[/tex].

We found our midpoint.

the zeros of the graph tell us the time needed for the tank to be drain.

(2t-7)(2t-9)

We have that one simply way to write that equation is

Because we have that

The sales tax rate of an item which cost $430 and tax of $8.60 is 2%

Sales tax refers to local or state tax imposed as a percentage of the selling price of goods or services payable by the customer. The tax is not recognized as the seller's earnings as the seller only collects the tax and transmits it to local or state authorities.

Sales tax rate = Sales tax / Cost of item before tax × 100

= $8.60 / $430 × 100

= 0.02 × 100

= 2%

In conclusion, the sales tax rate of the item is given by 2%.

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SOLUTION:

Step 1:

In this question, we are given the following:

Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s.

For example, the value of a particular rocking chair is well approximated by:

where V is in dollars and t is the number of years since 1975.

Find the rate, in dollars per year, at which the price is increasing.

Step 2:

Next,

Now, we need to evaluate:

Hence, the rate, in dollars per year since 1975, at which the price is increasing is:





This is the correct answer, this is because it only function that the inverse is correctly represented

Answer:

(-5, 2)

Explanation:

If a point (x,y) is reflected in the line y=x, the x-coordinate and y-coordinate change places.

That is:

Therefore, the image of (2, -5) when reflected in the line y=x is:

Answer: y-1=3(x-3)

this in the correct answer.  you take one point on the line and substitues x and y of the point into the equation.  M is your slope.  y-y1=m(x-x1)

Answer: If you are simplifying the expression, 8m-1 is your answer.

If you are finding the roots of this polynomial, 1/8 is your answer. (Can also be written as 0.125, 2^-3)

After simplifying and using the Distributive Property, the final solution would be [tex]72-12k[/tex].

Hope this helps!

Using proportions, it is found that the number of people that each asked is given as follows:

a) Rasheed: 571 people.

b) Kamal: 667 people.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations, especially multiplication and division, with the unit rates or percentages of the problem.

For Rasheed, since he was counting people with silver cars, we have that 21% of the n people is equivalent to 120 people, hence the number of people n is calculated as follows:

0.21n = 120

n = 120/0.21

n = 571 people. (rounding)

For Kamal, since he was counting people with blue cars, we have that 18% of the n people is equivalent to 120 people, hence the number of people n is calculated as follows:

0.18n = 120

n = 120/0.18

n = 667 people. (rounding)

The percentages of car colors in the UK are mussing and are given as follows:

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B) The mean will increase by $5

1) The first scenario has the following mean, adding all the spendings and savings:

2) Since for the following week there's an increase of $10 for her savings and a decrease of $ 5 we can write:

3) We can see that the mean changes, and examining the options we can state that:

the answer is B, the mean will increase by $5

Answer:

3.7%

Explanation:

Given

Original value = 9,620,000

New values = 9,980,000.

Increment = New - Original

Increment = 9,980,000 - 9,620,000

Increment = 360,000

%increae = 360,000/9,620,000 * 100

%increase = 3.7%

Hence the percentage increase is 3.7%

Recall the definitions of the magnitude and direction of a vector:

The distributive property to write an equivalent expression.

8(4n+ 3) = 32n  + 24

12x-6=  1/2

5x+20= 4

3(x+6)= 3x + 18

7x-35= 5

20p + 16 = 4/5

The distributive property states that multiplying the sum of two or more addends by a number yields the same result as multiplying each addend separately by the number and combining the resulting products.

One of the most common properties in arithmetic is the distributive property. The multiplier is applied to each integer inside the parentheses, and the results are added to obtain the answer. This technique is used to simplify and solve multiplication problems.

the distributive property to write an equivalent  .

8(4n+ 3)

= 8 * 4n + 3* 8

= 32n  + 24

for 12x-6

12x-6  = 0

x = 6/12

x = 1/2

For 5x+20

5x+20 =

x = -4

For 3(x+6)

= 3 * x + 3 * 6

= 3x + 18

For 7x-35

= 35/7

= 5

For 20p + 16

= 20/16

= 5/4

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Answer:

x²-2

Explanation:

Let the number be x.

The square of the number = x²

If 2 is subtracted from the square of the number, we have:

Therefore, an algebraic expression for the statement "2 is subtracted from the square of a number" is x²-2.

1) Gathering the data

3 pencils ----------- $0.45