Prove: An odd number squared is
an odd number.
(2n + 1)² = [?]n² + [ ]n +
=
[](2n² + 2n) + [ ]
= an odd

The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66. Out of these factors, the greatest factor of 66. The next highest factor other than 66 is 33. A number which is three more than 33 is 33 + 3 = 36.

The options are not mentioned , but the correct graph is plotted and attached with the answer.

A function is a mathematical statement that relates a dependent variable with an independent variable .

It is given to find among the options which is the correct graph for

y = log₃ (x-1)

The options are not mentioned , but the correct graph is plotted and attached with the answer.

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The best buy is (d) a 9 oz box of rice $1.25

The best buy is the product that has the least unit rate.

The unit rate is calculated as:

Unit = Price/Weight

So, we have:

Box 1:

Unit rate = $0.90/6 oz = $0.150 per oz

Box 2:

Unit rate = $1.93/12 oz = $0.161 per oz

Box 3:

Unit rate = $2.42/16 oz = $0.151 per oz

Box 4:

Unit rate = $1.25/9 oz = $0.139 per oz

The least unit price is $0.139 per oz for box 4

Hence, the best buy is (d) a 9 oz box of rice $1.25

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The expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2

Given that the softball diamond is square in shape.

Let the side of the square i.e. distance between consecutive bases is x

The distance from the 1st base to the 3rd base creates the hypotenuse of a right triangle, where each side is equal to x i.e. x is the side length of the square formed by the baseball diamond.  

Using the Pythagorean theorem we have:

x² +x²= c²,

where c is the distance from the 1st base to the 3rd base.

Combining similar terms gives us

2x²=c²

Taking the square root of both sides we have

√2x²= √c²

⇒x√2=c

⇒c=x√2

This is the expression for the distance from the 1st base to the 3rd base in terms of side length.

Therefore the expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2.

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The margin error of the confidence interval 0.87<p<0.93 is 0.03.

Given confidence interval 0.87<p<0.93.

We have been given the confidence interval 0.87<p<0.93 and we have to find out the margin error E. The margin error is a statistic expressing the amount of random  sampling error in the results of a survey. The margin error depends on whether the problem is two tailed or half tailed but in this question we have not given whether it is two tailed or one tailed. The margin error is the half of the width of the confidence interval.

Confidence interval is 0.87<p<0.93.

Width of the interval= 0.93-0.87

=0.06

=0.03

Hence the margin of error is equal to 0.03.

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The measure of the acute angle is 60 degrees

Given the following trigonometry equation

tan x=2sinx

This can also be written as;

sinx/cosx=2sinx

Simplify to have:

1/cosx =2

2cosx = 1

cosx = 1/2

x = arccos(1/2)

x = 60 degrees

Hence the measure of the acute angle is 60 degrees

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Answer: D

Step-by-step explanation:  

6^4 = 6 x 6 x 6 x 6 = 1,296

6^4 = 1,296

The function is [tex]y = (x +2)^2 + 5.[/tex]

we use the vertex form of the quadratic equation

We have given a graph,

y = a(x - h)^2 + k.

Therefore the vertex of the given graph is

See the vertex at (-2, 5)

Since the general way to write the vertex is (h, k), we compare (h, k) to (-2, 5).

[tex]y = a(x - (-2))^2 + 5.\\y=a(x+2)^2+5......(1)[/tex]

Now we have given that (-4,1) use this value in the above equation so we get,

[tex](1)=a(-4+2)^2+5[/tex]

[tex]1=a(-2)^2+5[/tex]

[tex]1=4a+5[/tex]

[tex]1-5=4a[/tex]

[tex]-4=4a[/tex]

[tex]a=-4/4[/tex]

[tex]a=-1[/tex]

Using the value of an in equation (1) we get,

Therefore the function is [tex]y = (x +2)^2 + 5.[/tex]

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The population in the year 2023 is 120,780.

The growth is linear hence, the equation of the growth is
y=ax+b where b represents the initial population and a is the number of people growing yearly.

So, according to the question statement, we have that

y=280x+b where x is the number of years past and y is the population in the xth year.

According to the given problem population in 2022 will be 120,500.

Suppose that the initial population is taken at 2000.

Hence, 120,500=280×(2022-2000)+b

⇒b=120,500-280×22

⇒b=120,500-6,160

    =114,340

So, the Linear equation becomes

y=280x+114,340

⇒y=280×(2023-2000)+114,340

⇒y=120,780

Hence, the population in the year 2023 is 120,780.

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Answer:

A. 15

Step-by-step explanation:

Hypotenuse = 22

Since the two angles other than the 90° are both

45° , it means that the two legs of the right triangle are of equal length.

So, (x)²+ (x)² = 22²

2x² = 22²

x² = 484/2

x² = 242

x = √242

x = 15.55

x ≈ 15

The solution to the inequality d / 7 + 4 ≤ 0 will be (–∞, –28]. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality equation is given below.

d / 7 + 4 ≤ 0

By simplifying the equation, we have

d / 7 ≤ – 4

    d ≤ – 28

Then the value of d must be less than or equal to the negative 28.

Then the correct option is B.

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Answer: x = 130, y = 130

Step-by-step explanation:

By the corresponding angles theorem, x = 130

Thus, by the vertical angles theorem, y = 130

Answer: So you want to convert 5 cubic meters into cubic centimeters? If you're in a rush and just need the answer, the calculator below is all you need. The answer is 5000000 cubic centimeters.

Step-by-step explanation:

Answer:

= B

Step-by-step explanation:

Answer:

D

After graphing, you can analyze it accordingly.

Answer:

$57.60

Step-by-step explanation:

2/5 = 0.4

0.4*96 is 38.4

96-38.4 = 57.6

The gadget is discounted $38.40 off the original price of $96 and now costs $57.60

Answer:

1. 65

2. 52

3. 13

Step-by-step explanation:

For these answers, we can look at the graph:

Question 1:

For the helmet that costs 35 dollars, we look at the x-axis until we find the helmet that aligns with 35.

Then, we look at the y-axis and find the blue dot. The blue dot is the actual consumer rating that was recorded, NOT the red line. The red line is the predicted consumer rating in correlation to the price.

Hence, the consumer rating is 65.

Question 2:

For this, we can look back at the graph and apply the same concept as above. Notice how the 65 plot is 13 points away from the point predicted by the red line.

Therefore, 65 - 13 = 52

Question 3:

Just like the last two questions, we can look at the graph for this. The green line gives us this answer flat out, displaying the distance from the actual rating to the predicted rating.

Hence, the actual consumer rating was 13 above the predicted rating.

Answer:

60 on the first day and 80 on the second

Step-by-step explanation:

the first day was lesser than the second day by 20 minutes.

so the second day was more than the first day by 20 minutes.

Answer:

A, D, E

Explanation:

It's right on edge lol

The formula for the equation of y, the number of units sold as a function of x is y = 0.00625x + 250

From the information given, when the company spends no money on advertising, it sells 250 units and for each additional $4000 spent, an additional 25 units are sold.

The formula for y will be:

y = (25/4000)x + 250

y = 0.00625x + 250

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The quadratic form ax² + bx + c for the given set of factors is 5x² - 2x - 4.

The quadratic equation that takes the form ax^2+bx+c can be determined from a given set of factors by applying the rule:

Let us expand the eqaution: 2(x-1) (2x+3)

So, we have:

2(x - 1)(2x + 3) ⇒ 4x² + 2x - 6.

= 4x² + 2x - 6 + x² - 4x + 2

Now, let us group like terms, we have:

= 4x² + x² + 2x - 4x - 6 + 2

= 5x² - 2x - 4

Therefore, we can conclude that the quadratic form ax² + bx + c for the given set of factors is 5x² - 2x - 4.

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Blank 1: 3

Blank 2: 27

Blank 3: 21

you have to distribute the three to everything inside the parenthesis, and because it's directly in front of the parenthesis it's being multiplied.

3(x - 9) = 3x - 27

Now you need to isolate the y, in this e ample you need to add 6 to both sides

the final equation should be:

y = 3x - 21

Step-by-step explanation:

3x8=24

24x30=720

720÷18=40 cents

Answer: [tex]\left(\frac{1}{2}, 1 \right), (1, 2)[/tex]

Step-by-step explanation:

We have [tex]y=2x^{2}[/tex] and [tex]y=3x-1[/tex].

Since both of the equations are set equal to y, we can conclude that:

[tex]2x^2 = 3x-1\\\\2x^{2}-3x+1=0\\\\(2x-1)(x-1)=0\\\\x=\frac{1}{2}, 1[/tex]

If [tex]x=\frac{1}{2}[/tex], then [tex]y=3\left(\frac{1}{2} \right)-1=1[/tex]

If [tex]x=1[/tex], then [tex]y=3-1=2[/tex]

Therefore, the solutions are [tex]\left(\frac{1}{2}, 1 \right), (1, 2)[/tex]

The weight of the each pile yesterday would be 6 and 8 pounds.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given;

Yesterday the ratio of seeds in these piles was 3:4.

Let it be 3x and 4x.

If the 2 pounds of seeds is added in the bigger pile, then it become

4x + 2

He also ate 1/4 pound from the smaller pile, then

3x - 1/4

Now the quantities of seeds in those piles is in the ratio of 5:16.

So, 4x + 2 = 5x

3x - 1/4 = 16x

Solve;

So, 4x + 2 = 5x

2 = 5x - 4x

x = 2

The weight of the each pie would be

3x = 6 pound

4x = 8 pound

Hence, The weight of the each pile yesterday would be 6 and 8 pounds.

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Answer:

(x-1) and (x-5)

Answer:

1/2

Step-by-step explanation:

First parabola  f(x1)   =  a ( x+4)(x-6)    use point 0,-12 to find a = 1/2

                                = 1/2 (x+4)(x-6)

Second parabola    a ( x+4) (x-6)       using point  0, -24    shows a = 1

                       f(x2)       = (1)(x+4)(x-6)

Difference between the 'a' values =  1 - 1/2 = 1/2

Answer:

Step-by-step explanation:

she has 7 servings. Add 1/2 + 1/2 until you get 3 1/2 and it equals 7

The domain and the range of the function is (d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}

What are the domain and range of the function f(x) = x^2 + 8x + 7/x + 1

We have the function to be

[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]

Set the denominator to 0

x + 1 = 0

Solve for x

x = -1

This means that the domain of the function is the set of all real numbers except -1

Hence, the domain of the function is {x ∊ ℝ | x ≠ -1}

We have the function to be

[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]

Factorize the numerator

[tex]f(x) = \frac{(x + 1)(x + 7)}{x + 1}[/tex]

Simplify

f(x) = x + 7

The function is undefined at x= -1.

So, we have:

f(-1) = -1 + 7

f(-1) = 6

This means that the range of the function is the set of all real numbers except 6

Hence, the range of the function is {y ∊ ℝ | y ≠ 6}

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Answer:

It is d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}

Step-by-step explanation:

I took the test

The remaining area of the page will be 80 square inches.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.

The area of the remaining part will be calculated as;-

Area of the square page will be = 11 x 11 = 121 square inches.

Area of three pictures will be = 15 x 3 = 45 square inches.

So the remaining area will be = 121 - 45 = 80 square inches.

Therefore the remaining area of the page will be 80 square inches.

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