40 POINTS !! 40 POINTS !!

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Answer:

X^2-8x+16

X^2-4x-4x+16

Factorise by gouping terms

X(x-4)-4(x-4)

=(x-4)(x-4)

There are a couple of formulas that we should know about quadratic functions, and this one utilizes this one:

(x - a)^2 = x^2 -2ax + a^2

Notice how x^2 - 8x + 16 fits into the formula:

x^2 - 8x + 16

x^2 - 2*x*4 + 4^2

(x - 4)^2

(x - 4)(x - 4)

Of course, not all expanded quadratic expressions fit into that formula, so there is a universal method to factor quadratic expressions:

x^2 + x(a + b) + ab —> (x + a)(x + b)

Basically, the middle term is the sum of an and b times x, and the last term is the product of an and b. So, if we are using the expression given in the problem, notice how -4 * -4 is 16, and the sum of -4 and -4 is -8. Thus, a and b are both -4 and the factored form is (x - 4)(x - 4)

Answer: 26 - 6

Step-by-step explanation: i think sorry if rong

Formula for sine: Opposite/Hypotenuse

Answer:

427,000...

Step-by-step explanation:

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Given:

[tex]x=\log_{10}31,500[/tex]

To find:

Select the true statements from the given options about the given value.

Solution:

We have,

[tex]x=\log_{10}31,500[/tex]

It can be written as

[tex]x=\log_{10}(2^23^25^37)[/tex]

[tex]x=\log_{10}(2^2)+\log_{10}(3^2)+\log_{10}(5^3)+\log_{10}(7)[/tex]     [tex][\because \log(ab)=\log a+\log b][/tex]

[tex]x=2\log_{10}2+2\log_{10}3+3\log_{10}5+\log_{10}(7)[/tex]

[tex]x=2\left(0.30105\right)+2\left(0.47712\right)+3\left(0.69897\right)+0.8451[/tex]

[tex]x=4.49835[/tex]

Clearly, the value of x lies between 4 and 5. So, [tex]x>4[/tex] and [tex]x<5[/tex].

Therefore, the correct options are C and D.

The true statements are: (c) x > 4 and (d). x < 5

The logarithmic expression is given as:

[tex]x = \log_{10}(31500)[/tex]

Express 31500 as a product of 100

[tex]x = \log_{10}(315 * 100)[/tex]

Apply the law of logarithm

[tex]x = \log_{10}(315) + \log_{10}(100)[/tex]

Evaluate log 100 base 10

[tex]x = \log_{10}(315) + 2[/tex]

Evaluate log 315 base 10

[tex]x = 2.50 + 2[/tex]

Add the expressions

[tex]x \approx 4.50[/tex]

4.5 is greater than 4 and less than 5

Hence, the true statements are: (c) x > 4 and (d). x < 5

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Answer:

i think the anwser is 2

Step-by-step explanation:

Answer: 24 cubes

Step-by-step explanation:

Step-by-step explanation:

[tex]4x + 2 = 22 \\ 4x = 20 \\ x = 5[/tex]

Answer:

9 & 27

Step-by-step explanation:

since all prime numbers above 5 end in 1,3,7 and 9then to find a prime number between say 70 and 80 the only possibilities are 71,73,77,79

Answer:

9 & 27

Step-by-step explanation:

Plz mark as Brainliest...

Answer:

$22.5.

Step-by-step explanation:

The total revenue that is gained from the sales of the cakes is determined by multiplying the number of cakes by the price. If we let x be the number of $1 that should be deducted from the price and y be the total revenue,

                              y = (25 - x)(100 + 5x)

Simplifying,

                             y = 2500 + 25x - 5x²

We get the value of x that will give us the maximum revenue by differentiating the equation and equating the differential to zero.

                            dy/dx = 0 = 25 - 10x

Answer:

area equals 36 and 3 fourths because if you cut the triangle off of one of the sides and add it to the other side it makes a rectangle then you do length times width to find regular area of a rectangle.

Answer:

8 triangles

Step-by-step explanation:

1 Triangle = 2 needed to be solve. 4 triangle × 2 =8.

Answer:

The 95% confidence interval for the mean remaining sentence of all people in the jail is between 628.5 days and 661.5 days.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 16 - 1 = 15

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1315

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.1315\frac{31}{\sqrt{16}} = 16.5[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 645 - 16.5 = 628.5 days

The upper end of the interval is the sample mean added to M. So it is 645 + 16.5 = 661.5 days

The 95% confidence interval for the mean remaining sentence of all people in the jail is between 628.5 days and 661.5 days.

Answer:

1) 18 inches

Step-by-step explanation:

By the Midsegment Theorem: A midsegment connecting two sides of a triangle is parallel to the third side and is half as long the third side.

ans: 36/2 = 18

Answer:

Volume of the figure = 10π cubic meters

Step-by-step explanation:

Volume of the right prism like figure = Area of the base × Height

Area of the base of the prism = [tex]\frac{1}{4}(\pi r^{2})[/tex]

                                                 = [tex]\frac{1}{4}(\pi)(2)^2[/tex]

                                                 = π m²

Height of the prism = 10 m

Volume of the prism given in picture = π × 10

                                                              = 10π cubic meters

Answer: 10π

Step-by-step explanation:

Answer:

95%

Step-by-step explanation:

Just answer it

Answer:

27gallons

Step-by-step explanation:

First we need to convert 16pints to gallons

Since;

1 pint = 0.125gallons

16 pints = x

Cross multiply

1 * x = 16 * 0.125

x = 2gallons

Since Holbrooks ordered 25 gallons of orange juice and 16 pints of cranberry juice for their resturant, the total juice he has is 25gallons + 2 gallons = 27gallons

Answer: The value of x from the equation is 64 ft. Thus, they will be needing approximately 64 ft of rope.

Step-by-step explanation: The concept that is useful in order to answer this item is the concept of ratio and proportion. Let x be the height of the rock from the ground. We use the equation below to answer.

                                   5.5 ft / 18 ft = x ft / 209.5 ft

Answer:

x = -3

Step-by-step explanation:

There are 175 cubic unit initially in the tank

The table of values is given as:

Time (minutes)     Amount of Water

1                              150

3                             100

6                             25

Calculate the slope (m) of the table using:

m = (y2 - y1)/(x2 - x1)

This gives

m = (100 - 150)/(3 -1)

Evaluate

m = -25

This means that as the time increases by 1, the amount of the water reduces by 25 cubic unit

When x = 1, y = 150

So, we have:

x = 1 - 1 when y = 150 - (-25)

This gives

x = 0 when y = 175

Hence, there are 175 cubic unit initially in the tank

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Answer:

1. $670

2.$920

3.$1500

4.$2100

Step-by-step explanation:

Hope it was fast enough & helpful .

Good luck ^^

Answer:

13,000 i think

Step-by-step explanation:

Answer:

64.8 and 1.8

Step-by-step explanation:

The banner measure inches in yards are 64.8 and 1.8.

We have given that,

We have to determine the length does the banner measure in inches and yards.

An inch is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to 136 yard or 112 of a foot.

Therefore we get the banner measure inches in yards are 64.8 and 1.8.

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Answer: 7.0 because you add 10 to - 3 it makes7.0

Step-by-step explanation:

Answer:

lol dababy ur my idol

Step-by-step explanation:

84b /32b

3b

Answer:

3b^2

Step-by-step explanation:

12b^7 / 4b^5  

=12b^7/ 4b^5

=12b^2/4

=3b^2

Answer:

x= 32

w=74

Step-by-step explanation:

my explanation is in the picture

The value of w and x in circle M below  mathematically given as

w = 74 , x = 32

Generally, the equation for the sum of angle of a triangle  is mathematically given as

w+x+c = 180

w+a = 106

w+x = 106

therefore,

106 +c = 180

c = 180-106

c = 74

w = 74

thus,

w+x+c = 180

74 + x + 74 = 180

x = 180 -148

x = 32

In conclusion, the value of w and x in circle M below is

w = 74 , x = 32

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A maze game can be constructed successfully by abiding by the specified guidelines in a systematic manner. Here is a comprehensive guide consisting of multiple steps to create it:

1. Initially, plot the initiation point and conclusion point across different quadrants.

2. Commence the game: Participants must start from the starting point and locate the ending spot through the shortest possible route.

3. Illustrate two sample games through drawing colored paths utilizing pencils or markers which should then be described using coordinates for each route.

4. Compute the overall distance travelled by extracting geographical details available from the used path's coordinates via the distance formula.

5. Finally, determine the most concise path course among all other alternatives.

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Answer:2yu

Step-by-step explanation:if you see this hi

Answer:

c

Step-by-step explanation:

ka

The area of the school is about 827 m² less than the area of the museum.

Area is the amount of area occupied by an object's flat (2-D) surface or shape.

Given:

Sammy finds satellite images of a school and a museum. They put the images on a coordinate grid (shown below).

School coordinate values are in meters.

To find the area of the school:

The school is rectangular.

Area of the rectangle = length x width

To find the length,

use distance formula.

We interpreted coordinates,

Fort length (-20, 20) and (-40, 80)

For width (-50, 10) and (80, -20)

Distance of length = √(60)²+(-20)² = 20√10

Distance of width = √(30)²+(10)² = 10√10

Area of the rectangle = length x width

Area of the rectangle = 20√10 x 10√10 = 2000 m²

The area of the museum is πr².

And r = 30

The area of the museum  =  π(30)². ≈ 2827 m².

Subtracting the area's = 827 m².

Therefore, the area of the school is about 827 m² less than the area of the museum.

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Answer:

Step-by-step explanation:

2x 4 =- 8

2 x + 4 = 8 2x+4=8 2x+4=8. Subtract 4 from both sides. Simplify 8 − 4 8-4 8−4 to 4. Divide both sides by 2.