A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yards as shown in the figure below. The flagpole will take up a square plot in the middle of the plaza and its base will have an area of x2−10x+25 yd2. Area of the flagpole plot: x2−10x+25 A plaza square with a small flagpole square in the middle. 100 yards100 yards Find the length of the base of the flagpole by factoring. (Hint: Because the area of the flagpole is an expression that involves the variable x, the length of the base will also involve the variable x.) The length of the base of the flagpole is

Answer: the answer is B or the second option /note b and the second option are the same thing

Step-by-step explanation:

n/a

Answer: The second one

Step-by-step explanation:

You have to go down 3 boxes, and go 6 boxes to the right in order to correlate with the same letter

a. The linear Equations :

3x + (x+42)= 90

⇒4x +42 =90

b. ∠ 1 = 36° and ∠2 =54°

Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the coordinate of this point.

here

4x+42 = 90 ⇒ x=12

∠1 =4 x 12=36 and ∠2 = 12+42=54

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In elimination method one equation is multiplied by the negative coefficient of the other

so then in this case y have coefficient 3, the other equation have coefficient y is 1 . Then divide 3/1 = 3 and change sign ,gives -3.

Then the final answer is -3, option c)

to find the slope of a line select the two points given.

in this case the point to the left will be (-4,-1) and the one to the right will be (3,1)

use the formula of the slope to calculate

replace the points into the formula

the slope of the line will be 2/7

Normally, by order of operations, we simplify what's in the parenthesis first. However, since we don't know the value of x, it is already simplified. So we use the distributive property to distribute -4 to the binomial.

-4(x - 2)
(-4 × x) + (-4 x -2)
-4x + 8

Answer:

-4x+8

Step-by-step explanation:

-4×(x)=-4x

-4×-2=8

Using equivalent angles, the correct options are given as follows:

Negative 25 degrees is on the fourth quadrant, with the positive angle measure being given by:

360 - 25 = 335º.

The equivalent angle on the first quadrant is of 360º - 335º = 25º, and the cosine on the first quadrant is positive, just like in the fourth, hence:

cos(-25°) = cos(25º).

The positive angle measure is given as follows:

360 - 136 = 224º.

Which is on the third quadrant, in which both the sine and the cosine are negative.

The equivalent angle on the first quadrant is given as follows:

224º - 180º = 44º.

Hence the expression is:

sin(-136º) = -sin(44º).

The positive angle measure is given as follows:

360 - 212 = 148º.

Which is on the second quadrant, in which the tangent is negative.

The equivalent angle on the first quadrant is given as follows:

180º - 148º = 32º.

Hence the expression is:

tan(-212º) = -tan(32º).

The positive angle is given as follows:

360 - 315 = 45º.

Which is already on the first quadrant, hence the expression is given as follows:

cot(-315º) = cot(45º).

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Given a table represents the number of eggs that hatched at 3 different temperature:

The total number of eggs = 14 + 11 = 25

There are just 25 eggs in each time to make the experiment

The number of eggs was not hatched at room temperature = 11

so, the percentage will be =

So, the answer will be = 44

h(t) = -16t^2+h^0

object falls untill height becomes 0, so h(t) =0, h^0 = 18.9feet

0 = -16t^2 + 18.9

-18.9= -16t^2

-18.9/-16 = -16t^2/-16

t^2=1.18125

ANSWER= OPTION B

The combined length is 9 feet 11 inches

What is length?

Distance is measured by length. Length is a quantity having the dimension distance in the International System of Quantities. Most measuring systems use a base unit for length from which all other units are derived. The metre is the basic unit of length in the International System of Units (SI). The greatest extended dimension of a stationary item is typically believed to be its length. This is not always the case, as it may depend on the location of the item. Height, sometimes known as vertical length or vertical extent, and width, breadth, or depth are all words used to describe the length of a stationary object. When length is the greatest dimension, width or breadth generally relate to a lesser dimension.

Given, length of a box = 3 feet 5 inches

length of another box = 2 feet 8 inches

length of microwave = 3 feet 10 inches

Total length = 3 feet 5 inches + 2 feet 8 inches + 3 feet 10 inches

                    = 9 feet 11 inches

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The money she will have after 4 months would be 31.50 dollars.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of the principal amount, rate, and period.

Simple Interest = (Principal × Rate × Time) / 100

If the initial amount (also called as principal amount) is given as 30, and the interest rate is 15% annually, and it is left for 4 months for that simple interest, then the interest amount earned is given by:

4 month = 0.333 year

Therefore,

Simple Interest = (Principal × Rate × Time) / 100

Simple Interest = (30 × 15× 0.333) / 100

Simple Interest = 31.50

Hence, the money she will have after 4 months would be 31.50 dollars.

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EXPLANATION

Let's see the facts:

Plan A --> $35 + $0.25/minute

Plan B --> $20 + $0.5/minute

Let's call "x" to the number of minutes that a person could talk.

Here we have two equations as follows:

(1) 35 + 0.25x

(2) 20 + 0.5x

Where x represents the number of minutes a person talks on the phone.

We need to equal both equations in order to obtain the same cost.

35 + 0.25x = 20 + 0.5x

Now, we need to solve this equality as shown as follows:

-Subtracting -35 to both sides:

35 + 0.25x -35 = 20 + 0.5x -35

-Adding similar terms:

0.25x = 0.5x - 15

-Subtracting -0.5x to both sides:

0.25x - 0.5x = -15

-Adding similar terms:

-0.25x = -15

-Dividing both sides by -0.25:

x = -15/-0.25

-Simplifying:

x= 60 minutes

So, when a person talks for 60 minutes the cost of both plans is the same.

To multiply them, we will multiply the coefficient 5 and 6

5 * 6 = 30

for x we will add their power to multiply them

We will multiply 6 by 1/2

6 * 1/2 = 3

Then add the power of x

Given:

The function is,

Explanation:

For x-intercept of the function f(x) = 0. So

Solve the equation for x.

So x-intercept of the function is x = -3.

Answer: x = -3

Option C is correct

2=-8-x Equation

x=-10

Explanation

Step 1

the scale is in balance, that indicates that the weights to the right and left are equal

Let

left side=2 squares of 1 each

then

left side=2

Step 2

rigth side=8 times (1) plus -x

rigth side=(8*-1)-x

rigth side=-8-x

Step 3

finally

Step 4

finally solve equation (1) for x

I hope this helps you

Answer:

242.

Step-by-step explanation:

Basically, you have to put the 2 numbers "1936" and "8" down. After you put the 2 numbers down, you have to figure out how many times 8 goes into 19 which is 2 times.

You put the 2 above the 1 in 1936. After you put the 2 up there, you have to figure out 2 x 8 which is 16. You have to put the 16 below the 19 and subtract 19 by 16 which is 3.

After you finish that equation, you must bring the 3 down next to the 3 you wrote down on 19 - 16. The number turns into 33 and you have to figure out how many times 8 goes into 33 which is 4 times. You put the 4 next to the 2 above and then do 4 x 8 which is 32. You do 33 - 32 which is 1.

You bring the 6 down in 1936. It turns into a 16. You now have to figure out how many times 8 goes into 16 which is 2 times. You put 2 next to the 2 and the 4 above and that turns the number into 242.

You then have to do 2 x 8 which is 16 and put 16 under the 16 from 33 - 32. That'll make an equation which is 16 - 16 which is 0. There is no remainder and all the numbers were added above so 242 is your answer.

Hopefully, this has helped, tried my best!

=================================

Long Division - Solution and Process    

=================================

We are given the Divisor 8 and the Dividend 1,936.

     242  ← Our Final Solution

8 | 1936

     16

     ___

       33

       32

      ____

          16

           16

            0

The quotient of the given problem would be 242 with a remainder of 0, or simply 242.

Hope this helps!

Using a system of equations, it is found that Sheldon's number is of 37.

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem.

For this problem, we have to consider that:

The sum of these numbers is given by:

x + x + 1 = 2x + 1 (combining the like terms).

The sum is equals to 75, hence we can solve for the natural number x as follows:

2x + 1 = 75

2x = 74

x =74/2

x = 37. (which is Sheldon's natural number).

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Answer:

18.25

Step-by-step explanation:

From the quadratic equation given, the time it will take till the arrow hits the ground is 22.75 seconds

To determine when the arrow hits the ground, we need to find the value of x when the height, f(x), is equal to 0. In other words, we need to solve the equation:

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation

In this case, a = -16, b = 24, and c = 16. Substituting these values into the quadratic formula:

x = (-(24) ± √((24)² - 4(-16)(16))) / (2(-16)).

Simplifying further:

x = (-24 ± √(576 + 1024)) / (-32),

x = (-24 ± √(1600)) / (-32),

x = (-24 ± 40) / (-32).

x = -101/4 or x = 101/4

Since x≠  negative;

x = 101/4 = 22.75 seconds

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Answer:

0.026, 8.062, 8.26, 8.6

Step-by-step explanation:

Hope this helps!

Btw, pls give brainliest, thanks!

Answer:

0.026, 8.062, 8.26, 8.6

The slope is 1

Choose the points (2, -3) and (4, -1)

The slope is:

To find the percent we are looking for we can use the rule of three:

then:

This means that 51 is 85% of 60.

Therefore 51 is 15% less than 60.

ANSWER

D 3/4 = 8/6

EXPLANATION

For the ratios to be proportional, the fraction on the left hand side must be equivalent to the one on the right hand side.

So, for each of them, we will check if the values are the same.

a) 3/4 = 6/8

Simplifying 6/8 by dividing numerator and denominator by 2 yields:

3/4 = 3/4

The ratio is proportional.

b) 3/6 = 4/8

Simplifying both sides yields:

1/2 = 1/2

The ratio is proportional.

c) 4/3 = 8/6

Simplifying 8/6 by dividing numerator and denominator by 2 yields:

4/3 = 4/3

The ratio is proportional.

d) 3/4 = 8/6

Simplifying 8/6 by dividing numerator and denominator by 2 yields:

3/4 = 4/3

Because the two fractions are not equal, the ratio is not proportional.

The answer is D.

Data

Starting hour = 2:50

Time = 3 h 30 min

Addition

1

2:50

+ 3:30

6:20 Use the hexadecimal system to solve this problem.

Given data:

Population Mean = 346

Standard Deviation = 72

Expected Value of e(x) = population mean = 346

Sample Size = 216

In this case, if many random samples of 216 are taken, then the mean of the sample mean numbers per week is 346. (Option C)

To solve for the variance of x or var(x), we follow the formula below:

In this case, the given standard deviation is 72 and the sample size is 216. Therefore, we have:

One of the properties of the Sampling Distribution of the Mean is that the sampling distribution of the mean is approximately normally distributed so long as the sample size is 30 or higher. Our sample mean here is 346 with a sample standard deviation of √24 or 4.899.

How likely is it to observe a sample mean number of sags per week that exceeds 390?

For this one, we have this formula to use:

Our bar "x" is 390. The "myu" symbol is our population mean which is 346. This σ symbol is the population standard deviation 72 and n is our sample size = 216.

Under a normal curve, the areas defined are between z = -3.5 to z = +3.5. Since our z should exceed > 8.98 and thus far greater than +3.5, then we can say that the probability of having a sample mean that exceeds 390 is zero.

Adding fractions

To add two fractions, you have to make sure that the numbers in the denominator are the same.

For the fractions

The denominators are different, you have to look for a common factor between 2 and 5, the quickest way is to multiply them, you know that 10 is both a multiple of 2 and of 5.

Multiply 1/2 by 5 to obtain the equivalent expressed in tenths and multiply 2/5 by 2 to obtain the equivalent fraction in tenths

Now that both fractions have the same denominator you can add them

Subtracting Fractions

You must apply the same procedure when subtracting two different fractions. First find a common factor so that the denominator is the same for both fractions:

As before, the common factor is 10, so the equivalent fractions will be:

Dividing fractions

To divide two fractions you have to do the following steps.

1- Invert the fraction that corresponds to the denominator of the division, i.e. the one you want to divide for (the second one).

This is called a reciprocal fraction.

2-Multiply the first fraction, the one you want to divide by the reciprocal fraction.

3-If possible, simplify the result.

1-Invert the denominator of the division

2-Multiply the denominator by the reciprocal fraction

1/2 divided by 2/5 equals 5/4

Answer:

the answer of the question is

y= 2x+6

Finding slope and y-intercept

for this equation.

-5x - y = 14

we know that

the equation of the line in slope intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

In this problem we have

-5x-y=14

Isolate the variable y

y=-5x-14

therefore

The Sam's rate is 10.35 miles per hours.

What is miles per hour?

In mathematics, miles per hour is the unit for the speed measurement. It is used for the calculation of the speed of the train or people or any another objects. It can be calculated by dividing the distance with time.

According to the question, the given data states that the Sam ran 63,756 feet in 70 minutes.

Distance = 63,756 feet and Time = 70 minutes

And the given conversion is: 5280 feet = 1 miles

Therefore, Sam's rate or speed in miles per hour is as written below:

Speed = Distance/Time

Speed = (63,756/70) x (1/5280) x 60 = 10.35 miles per hours

Hence, the Sam's rate is 10.35 miles per hours.

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For this case we have two points given:

(-4, -4) and (-4,4)

The third vertex for this case would be:

(4,-4)

And then the resulting base would be:

d= 4+4 = 8

correct answer:

8 units

Answer:

[tex]y < \frac{5}{3} x - 3 \\ [/tex]

Step-by-step explanation:

- General linear equation of a line passing through point (x, y) with a gradient m and y-intercept (0, c) is ;

[tex]{ \rm{y = mx + c}}[/tex]

- As finding gradient, m; consider points (0, -3) and (3, 2) from the graph;

[tex]{ \rm{slope \: m = \frac{2 - ( - 3)}{3 - 0} }} \\ \\ { \rm{m = \frac{5}{3} }}[/tex]

- Then our equation becomes y = 5/3x + c

- Consider point (0, -3), relate it with (0, c) hence c is -3;

[tex]{ \rm{y = \frac{5}{3}x - 3 }}[/tex]

- If you see the format of the coordinates, x coordinates are greater than y coordinates, hence y < x

[tex]{ \rm{y < \frac{5}{3}x - 3 }} \\ [/tex]

Answer:

[tex]y < \dfrac{5}{3}x-3[/tex]

Step-by-step explanation:

All given answer options have the same linear equation:

[tex]y=\dfrac{5}{3}x-3[/tex]

Therefore, there is no need to work out the equation of the line for this question as it is already given.

When graphing inequalities:

From inspection of the graph there is:

Therefore, the inequality that is represented by the graph is:

[tex]y < \dfrac{5}{3}x-3[/tex]

Explanation:

The total number of students in the algebra class is given below as

The number of girsl who won a graphing calculator is given below as

Concept:

To figure out the probabaility that a randomly chosen student will be a girl and own a graphing calculator, we will use the formula below

By substituting the values, we will have

Hence,

The final answer is

The FOUTH OPTION is the correct answer