Use the difference of two squares to find the values of the following.
a. 72² - 28²
b. 85² - 25​

Answer:

131.25 feet.

Step-by-step explanation:

We can use the concept of similar triangles to find the length of the monument's shadow.

Since the pole and the monument are casting the shadows, we can assume that the ratio of the height of the pole to the length of its shadow is equal to the ratio of the height of the monument to the length of its shadow.

12/5 = 315/x

Where x is the length of the monument's shadow.

We can cross-multiply and solve for x:

12x = 5315

x = 5*315/12

x = 131.25

So, the length of the monument's shadow is approximately 131.25 feet.

The measures, using the Law of Sines, are given as follows:

The law of sines states that the ratio between the sine of each angle and the side length opposite to this angle has to be equal for all the angles in the problem.

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle B is given as follows:

m < B + 25 + 36 = 180

m < B = 180 - (25 + 36)

m < B = 119º.

Then the length BC is obtained as follows:

sin(25º)/BC = sin(36º)/28

BC = 28 x sin(25º)/sin(36º)

BC = 20.13.

The length AC is obtained as follows:

sin(119º)/AC = sin(36º)/28

AC = 28 x sin(119º)/sin(36º)

AC = 41.62.

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Answer:

Step-by-step explanation:

Firstly, lets just add the fractions we got.

2/5 + 1/3 = 6/15 + 5/15 = 11/15

So, 11/15 of the total students bought stuff other than drinks.

Number of people who bought drinks will be the people left

So, 1 - 11/15, or 4/15

a) 4/15

b) Fraction of people who bought beef burger is 2/5.

2/5 x 3/4 = 3/10

So the fraction is 3/10.

Address the root of both issues radius  is  3 √ 6 v π ^2 / 2 π.

r is radius and v is volume.

Write the equation as follows:

4/3 ⋅ ( π r 3 ) = v . 4 /3 ⋅ ( π r 3 ) = v

Divide the two sides of the equation by 1 4 3.

1 / 4 . 3 π ( 4 / 3 ⋅ ( π r 3 ) ) = 1 /4 . 3π v

Simplify the issue from both perspectives.

For more steps, tap.

r 3 = 3 v 4 \sπ

To get rid of the exponent on the left side, take the required root from both sides of the equation.

To get rid of the exponent on the left side, take the required root from both sides of the equation. = 3 √ 3 v /4 π

3 3 v 4 should be made simpler.

For more steps, tap.

r = 3 √ 6 v π ^2 / 2π.

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Step-by-step explanation:

The floor of a round hut has a diameter of 4 yards. What is the floor's area?

Answer:

12.56637 or 4 pi hope this helps

Answer:

yes parallel is when two lines directly line up together like this ----

----

The period and the midline of this function is 8 and y = 6 respectively.

The horizontal line that exactly straddles the maximum and minimum points of the graph is known as the midline.

The vertical separation between the midline and one of the extremum points is known as the amplitude. The time interval between two consecutive maximum points or two consecutive minimum points is known as the period (these distances must be equal).

A periodic function's midline is the horizontal line that lies halfway between its maximum and minimum output values. The distance between a periodic function's maximum (or minimum) output value and the midline is known as the amplitude of the function.

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The quadratic equation for the given roots is x²-2x-1=0. Therefore, option 4 is the correct answer.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The roots of the quadratic equation are 1±√2.

Here, x=1+√2 and x=1-√2

x-1-√2=0 and x-1+√2=0

Now, (x-1-√2)(x-1+√2)=0

= x(x-1+√2)-1(x-1+√2)-√2(x-1+√2)=0

= x²-x+√2x-x+1-√2-√2x+√2-2=0

= x²-2x-1=0

Therefore, option 4 is the correct answer.

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Answer:

Step-by-step explanation:

The value of y is pi over 6. To solve for y, we use the fact that the sine of a sum is equal to the sum of the sines of each individual angle multiplied by the cosine of the other angle. This can be expressed mathematically as sin(x+y) = sin(x)cos(y) + cos(x)sin(y).

Substituting the given values into the equation, we have:

sin(x+y) = (√2/2)sin(x) + (√2/2)cos(x)

Rearranging, we can solve for y:

y = arcsin((√2/2)sin(x) + (√2/2)cos(x)) - x

Since x is equal to pi over 2, we can calculate y as follows:

y = arcsin((√2/2)sin(pi/2) + (√2/2)cos(pi/2)) - (pi/2)

= arcsin((√2/2)(1) + (√2/2)(0)) - (pi/2)

= arcsin(√2/2) - (pi/2)

= pi/6

Therefore, the value of y is pi over 6.

Answer:

21 and 18.48 respectively

Step-by-step explanation:

to solve this question,first we need to identify the quotients by dividing the numbers and multiply each by 21/5

The quotient of the [tex]\frac{55}{11}[/tex]=5

[tex]\frac{21}{5}[/tex]  of 5 = [tex]\frac{21}{5}[/tex]×5=21

The quotient of the [tex]\frac{22}{5}[/tex]=4.4

[tex]\frac{21}{5}[/tex] of 4.4 = [tex]\frac{21}{5}[/tex]×4.4=18.4

 so, the answer is 21 and 4.4 respectively.

The nearest person is 235620 populations away in the following year.

The country, territory, or geographic area's yearly average rate of change in population size over a certain time period.

From the given question, we have the following:

Total population this year = 238,000 population

If the  population of a city decreases by 1% per year, the population next year will be 99% of the current population to have:

Population this year = 99% of 238,000 population

Population this year = 0.99 *  238,000

Population this year = 235620 populations

Hence the next year's population to the nearest individual is 235620 populations

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If D and R are independent, then P(D or R) = 0.8412

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)

P(D) = 0.26 and P( R) = 0.26 , if D and R are independent, then,

P(D or R) = P(D) + P(R) - P(DnR)

then P(DnR) = P(D) × P(R) = 0.26×0.38 = 0.0988

P(D or R) = 0.26+0.38-0.0988

= 0.8412

Therefore the probability of P(D or R) if D and R are independent is 0.8412

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The solution for the given inequality is, (-∞, -5] ∪ [-1, ∞).

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Consider, the given inequality

|x + 3| - 2 ≥ 0

⇒ |x + 3| ≥ 2

Using: If |u| ≥ a,  a > 0 then u ≤ -a, u ≥ a

⇒  x + 3 ≤ -2,    x + 3 ≥ 2

x ≤ -5,      x ≥ -1

Hence, the solution for the given inequality is, (-∞, -5] ∪ [-1, ∞).

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Victor spent $1 on a pencil. Additionally, he spent $3 on some notebooks. Buying pencils and notebooks cost Victor no more than $13. 4 <= 13 equals the inequality.

[tex]$$1+3 \leq 13:\left[\begin{array}{cc}\text { Solution: } & \text { True } \\\text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$$[/tex]

Steps

[tex]$$1+3 \leq 13$$[/tex]

Simplify 1+3: 4

[tex]$4 \leq 13$[/tex]

The attribute of being unequal or uneven, such as social disparity, disparity of distribution or opportunity, or lack of evenness A key idea in social justice theories is inequality, which is the state of not being equal, particularly in terms of status, rights, and opportunities1. Due to the fact that it frequently has diverse meanings to different people, it can become confusing in public discourse. However, some differences are typical.

Related concepts include lifetime inequality (inequality in incomes over a person's lifetime), inequality of wealth (distribution of wealth across households or individuals at a particular point in time), and inequality of opportunity (impact on income of circumstances over which an individual has no control). According to experts, inequality hinders economic growth and promotes political dysfunction.

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The BODMAS acronym is for:

Addition and Subtraction

The final step is to calculate any addition or subtraction. Again, subtraction and addition rank equally, and you simply work from left to right.

Example:

⇒4 + 6 − 7 + 3 = ?

You start on the left and work your way across.

⇒4 + 6 = 10

⇒10 − 7 = 3

⇒3 + 3 = 6

The answer is 6.

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We can simplify the expression to get:

2³ + 3*(2) + 14/2 = 21

The correct option is E.

Here we want to simplify the expression below:

2³ + 3*(2) + 14/2

The additions are the last thing we need to do, we can replace:

2³ = 8

3*(2) = 6

14/2 = 7

Replacing that in the expression we will get:

2³ + 3*(2) + 14/2 = 8 + 6 + 7

8 + 6 + 7 = 21

So the correct option is E.

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Answer:

The inequality that can be used to solve for how many x paintings can be displayed is 22x + 9 <= 315

Step-by-step explanation:

This inequality states that the total square footage of the paintings and the sign must be less than or equal to 315 square feet. Each painting takes up 22 square feet, and the sign takes up 9 square feet, so the total square footage is represented by the expression 22x + 9.

The inequality states that 22x + 9 <= 315 which means for any number of paintings she displays it should be less than or equal to 315 sq.ft.

The other options:

22x + 9 315: the inequality is less than instead of less than or equal to, which means that the total cost should be less than 315 sq.ft which is not always the case.

22x + 92 315: the coefficient of x is 22 instead of 22 and the 92 is placed in a wrong position.

9x+22 315: the coefficient of x is 9 instead of 22 and the 22 is placed in a wrong position.

22z + 9 315: the variable used is z instead of x

Answer:

y = 5x - 4

Step-by-step explanation:

1. Parallel have the same slope (equation)

- Standard form of an equation of a line: y=mx + b

m = slope

x = x-coordinate

b = y-intercept

y = y-coordinate

SLOPE = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1}}[/tex]

Given that x-2y = 5

and the line has the point:

(-3,-1)

We need to find another point to find the slope

x - 2y = 5

Let's say x = 7 and y = 1

(7, 1)

Now plug it into the slope equation

[tex]\frac{-3-7}{-1-1} = \frac{-10}{-2} = 5[/tex]

Plug the slope into the standard form of an equation of a line

y = 5x + b

Plug in (7,1)

1 = 5 + b

b = -4

The answer is: y = 5x - 4

Hope this helps :)

Have a great day!

Answer:

Step-by-step explanation:

Answer: a. 7

Work Shown:

Given set = {6, 10, 7, 2, 9, 8, 7, 3, 5}

Sorted set = {2, 3, 5, 6, 7, 7, 8, 9, 10}

P = 15 = percentile value

n = 9 = sample size, i.e. number of values in the set

R = index rank

R = (P/100)*(n + 1)

R = (15/100)*(9+1)

R = 1.5

This rounds to R = 2 when rounding to the nearest integer.

This R value tells us to look at the 2nd slot of the sorted data set. The value "3" is in the 2nd slot.

This is why the answer is choice D

Answer:

The Milky Way is about 1,000,000,000,000,000,000 km

Step-by-step explanation:

about 100,000 light years or about 30 kpc) across.

Answer:

Step-by-step explanation:

Thandi's statement that 20% of Alaskan totem poles featured in the book have eagles carved in them is not accurate.

A two-way table, also known as a contingency table, is used to organize and display the relationship between two categorical variables. The table shows the frequency or count of observations for each combination of the two variables. In this case, the two variables are the animals carved in the totem poles and the regions where the totem poles are located.

To find the percentage of Alaskan totem poles that have eagles carved in them, we need to divide the number of Alaskan totem poles with eagles by the total number of Alaskan totem poles and multiply by 100. This can be calculated as:

(Number of Alaskan totem poles with eagles / Total number of Alaskan totem poles) * 100

Without the data for the two-way table it's impossible to check if the statement is correct or not. It's important to note that without the data it is also impossible to know the context of the statement and the information provided in the book.

Answer:

=Have Eagles

=50%

Step-by-step explanation:

If you select 5 samples starting from student number 8, the possible samples are student 8, 16, 24, 32, and 40.

A sample can be defined as small group taken from a population that can be used to study the whole population, and therefore to determine patterns, behaviors, preferences, etc. in the population.

Due to this, samples simplify the research process and make it feasible as in most cases the whole popualtion cannot be studied.

Although there are many methods for selecting a sample, one of the methods that is more commonly used is the random sampling in which participants are given a number and then the sample is chosen by using this numbers either by selecting the numbers randomly or as in this case by following a sequence.

Based on this principle, the possible samples are student 8, 16, 24, 32, and 40, if we start with student 8 and use this sequence.

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In the given question, the segments which are congruent are:-

RS and XP

Congruent refers to things that are exactly the same size and form. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another.

In the gievn figure

the length and size of RS and XP segments are equal

Hence they are congruent

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Answer:

We know that the ratio of female students to the total number of students is 4 to 9.

That means that for every 4 female students, there are 9 students in total.

So, we can set up the proportion:

4/9 = x/264

where x is the total number of students.

Solving for x, we get:

x = (4/9)*264 = 96

Since the ratio of teachers to students is 1 to 11, then for every 11 students there is 1 teacher, we can set up the proportion:

1/11 = y/96

where y is the total number of teachers.

Solving for y, we get:

y = (1/11)*96 = 8.72 ≈ 8

So, there are 8 teachers in the college.

Step-by-step explanation:

10 Km²  is the area of the triangular section that the forest managers plant with trees.

A sector is the area between any two circle radii and any arcs that connect them. Segment: A line segment in geometry is a section of a line that has two clearly defined end points and includes every point on the line in between them.

Firstly count how many cells are there

First line = 6

Second line = 1

Last line = 3

So the area of the section that the forest managers plant with tree is

6 + 1 + 3 = 10 Km²

( count more than half a grid or not count )

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Answer:

To find the value of x, we can substitute the value of y in the equation:

-2X + (-3) = 9

We can then solve for X by isolating it on one side of the equation:

-2X = 12

X = -6

So, the value of X is -6.

Step-by-step explanation:

Answer:

y + 13 = - [tex]\frac{2}{3}[/tex] (x + 11)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{2}{3}[/tex] and (a, b ) = ( - 11, - 13 ) , then

y - (- 13) = - [tex]\frac{2}{3}[/tex] (x - (- 11) ) , that is

y + 13 = - [tex]\frac{2}{3}[/tex] (x + 11)

The value of x = 4 makes the quadrilateral a parallelogram.

A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

Given:

The shape is a quadrilateral.

The opposite sides are parallel.

To show that the given quadrilateral is a parallelogram :

The opposite sides of the parallelogram are equal.

So,

2x + 3 = x + 7

2x - x = 7 - 3

x = 4

Therefore, the value of x is 4.

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The complete question is given in the attached image.