Describe how to solve the following:
a. 2√25
b. √150

The value of x and y in the angles are 15.6 and 10.5 respectively.

When parallel lines are cut by a transversal lines, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.

Therefore, line XD, TZ, YF and LP are parallel to each other.

WC is the transversal line.

Hence,

m∠CNL = 6x - 17.6

m∠FBH = 12y - 22

m∠THR = 3x + 29.2

Hence,

180 - (12y - 22) = 6x - 17.6(corresponding angles)

Corresponding angles are congruent

180 - 12y + 22 = 6x - 17.6

6x + 12y = 180 + 22 + 17.6

6x + 12y = 219.6

Therefore,

180 - (3x + 29.2) = 12y - 22 (alternate angles)

Alternate angles are congruent .

180 - 3x - 29.2 = 12y - 22

180 + 22 - 29.2 = 12y + 3x

172.8 = 3x + 12y

combine the equation

6x + 12y = 219.6

3x + 12y = 172.8

subtract equation(ii) from equation(i)

3x = 46.8

x = 46.8 / 3

x = 15.6

12y = 219.6 - 6(15.6)

12y = 219.6 - 93.6

12y = 126

y = 126 / 12

y = 10.5

Therefore,

x = 15.6

y = 10.5

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Answer: (-5, 8)

Step-by-step explanation:

       The x-coordinate is responsible for left and right, and the y-coordinate is responsible for up and down translations. Coordinate points are written as (x, y).

(-8, 9) ➜ (-8 + 3, 9 - 1) ➜ (-5, 8)

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The area of a circle is changing at a rate of 576π cm²/sec when the radius of the circle is 32 cm.

For the given question;

Express the circle's area as a function of the its radius.

A = πr²

Determine the area's derivative with respect towards its radius.

dA/dr = 2πr

Using the chain rule, calculate the derivative of a area with respect to time.

dA/dt =  dA/dr . dr/dt

dA/dt = 2πr(9)

dA/dt = 18πr

When the radius is 32 cm, find the derivative of a area with respect to time.

dA/dt = 18π(32)

dA/dt = 576π

As a result, the area of a circle is changing at a rate of 576π cm²/sec when the radius of the circle is 32 cm.

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In the graph, which compares the snowfall for the same three months last year and this year, you can see that the total snowfall for last year was 36.4 inches. how much more snow fell over the course of three months this year than did so last year: 5.45

what is the explanation?

The first step is to calculate the amount of snowfall from the previous year, which are:

12.6+6+9.2

=27.8

The next stage is to calculate how much snow has fallen this year, which includes:

10+15.75+7.5

=33.25

Now let's compare the snowfall over the first three months of current year to that of last year.

33.25-27.8

=5.45

In conclusion Graph showing snowfall during the same three months last year and this year, if the total snowfall for last year was 36.4

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The single inequality:

y > |x + 2|

Can be rewritten into:

y > x + 2

y > -x - 2

So the second option is the correct one.

Remember that an absolute value equation like:

|x + a| = b

Can be rewritten as:

x + a = b

x + a = -b

So the inequality:

y > |x + 2|

Also can be rewritten into two equations, which are:

y > x + 2

-y < x + 2

The direction of the sign changes in the second one because the sign of the variable in the left changes.

Then if we multiply both sides by -1 of the second inequality, we get:

y > -x - 2

Then the two inequalities are:

y > x + 2

y > -x - 2

So the correct option is the second one.

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Applying logarithm properties, the solution of the highlighted question is given as follows:

x = 4.

The logarithmic equation is given as follows:

[tex]\log_{a}(x + 2) = \frac{1}{3}\log_{a}{8} + \log_{a}{3}[/tex]

First, we apply the power rule, meaning that the multiplying coefficient of the logarithm can be the power of the given term, hence:

[tex]\frac{1}{3}\log_{a}{8} = \log_{a}{8^{\frac{1}{3}}} = \log_{a}{\sqrt[3]{8}} = \log_{a}{2}[/tex]

Then the equivalent expression is:

[tex]\log_{a}(x + 2) = \log_{a}{2} + \log_{a}{3}[/tex]

Now we apply the product rule, as the sum of two logarithms of same base can be written as a single logarithm, keeping the base and multiplying the terms.

Hence the equivalent expression is:

[tex]\log_{a}(x + 2) = \log_{a}{(2 \times 3)}[/tex]

[tex]\log_{a}(x + 2) = \log_{a}{6}[/tex]

The logarithm function is one-to-one, meaning that if they have the same input, they will have the same output, hence we can solve for x as follows:

x + 2 = 6

x = 6 - 2

x = 4.

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The equation for the purchase of n number of notebooks by Caitlin is

4n = c , where c is representing the cost that Caitlin paid.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Finding the value of a single unit using the unitary technique allows us to determine the value of the necessary number of units based on this value.

the price for one notebook was = $4 each

n number of notebooks were purchased by caitlin

therefore the cost price of 4 notebooks will be = 4 * n

as per given in the question cost price = c

therefore the equation formed will be

4n = c

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Answer:

39.

Step-by-step explanation:

50779 divided by 590 is 86, with a remainder of 39.

By the concept of basic arithmetic solo acts are 5 minutes long and ensemble acts are 15 minutes long

Mathematics' fundamentals are arithmetic operations. Addition, subtraction, multiplication, and division are the main operations that make up this concept. The phrase "mathematical operations" also refers to these.

The math operation of subtracting two integers reveals the difference between them. The '-' sign is used to indicate it. In math, subtraction is the process of taking one number away from another to determine what is left over after something has been taken away. Rational number operations are equivalent to those performed on whole numbers. The main distinction is that rational numbers take the form p/q, where p and q are integers and q is not equal to 0. It is necessary to take the LCM of the numerators when adding or subtracting two rational integers.

Here we are discussing the four basic rules of arithmetic operations for all real numbers.

12 × x + 2 × y = 90

6 × x + 2 × y = 60

To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.

B.  Here we can multiply second equation with negative 1 and add it to first equation.

6x = 30

x = 5

Now we replace x in any of 2 equations to get y.

30 + 2y = 60

2y = 30

y=15

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Answer:

86

Step-by-step explanation:

I'll assume the expression is meant to be 10^2 - 5a +6

4a- 3 =13

4a = 16

a = 4

10^2 - 5a +6

10^2 - 5(4) +6

10^2 - 20 +6

100 - 14 = 86

Answer:

[tex]\textsf{Gradient\;$=-\dfrac{1}{3}$}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope (gradient). \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]x+3y=13[/tex]

Rearrange the equation to make y the subject.

Subtract x from both sides of the equation:

[tex]\implies x+3y-x=13-x[/tex]

[tex]\implies 3y=-x+13[/tex]

Divide both sides of the equation by 3:

[tex]\implies \dfrac{3y}{3}=\dfrac{-x}{3}+\dfrac{13}{3}[/tex]

[tex]\implies y=-\dfrac{1}{3}x+\dfrac{13}{3}[/tex]

Compare the rearranged equation with the slope-intercept form.

Therefore, the gradient (slope) of the given equation is -¹/₃.

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Answer:

Step-by-step explanation:

y = mx + b

The gradient is slope "m" (coefficient by "x")

~~~~~~~~~~~~~~~~~

x + 3y = 13

Solve for "y" :

3y = - x + 13

[tex]\frac{3y}{3}[/tex] = - [tex]\frac{x}{3}[/tex] + [tex]\frac{13}{3}[/tex]

y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{13}{3}[/tex]

The gradient is ( - [tex]\frac{1}{3}[/tex] )

Reason:

We look for two values that

Using trial and error, you should find those two values are 2 and 6

This is how we arrive at (x+2)(x+6)

Use the FOIL rule to expand that out and you should get x^2+8x+12 to confirm the answer.

The equation of the graph of g is represented by y  - 6 =  (x-2)²

The very first step in balancing a variable equation is to correctly identify the specific values of the variables that lead to equality.

The graph of the function is f is y = x²

Now we can see that the graph of g is translated to 2 units to the right and 6 units up.

We know from the properties of translation that when the graph moves 2 units to the right we get the equation as y = (x-2)²

Again when the graph moves 6 units up wards the graph changes by

y  - 6 =  (x-2)²

Therefore the equation of g is  y  - 6 =  (x-2)²

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The formula for getting the volume of a sphere is:

where r = radius of the sphere.

Let's plug into the formula the given radius of the sphere in the question.

Then solve.

Multiply 10 cm by itself three times.

Multiply 1000 by 4, then divide by 3.

Rounding the calculated volume to the nearest whole number, the volume of the sphere is 1,333π cm³ (Option D or 4)

Answer:

The volume of the sphere is 1,333π cm³ (Option D or 4)

Answer:9 days

Step-by-step explanation:A lot of division is required, but because 8.75 probably isn't an answer, I rounded up to 9.

Answer:

Assuming that this is referring to simple interest, your answer is C) 1,750.

Step-by-step explanation:

[tex]5000[/tex] x [tex]0.05[/tex] = [tex]250[/tex]

[tex]250[/tex] x [tex]7[/tex] = [tex]1750[/tex]

Answer: Width = 8/20 ÷ 7/8  = 8/20 x 8/7   = 16/35 Therefore, the width will be 16/35 miles. Hope you do great :) !

If a circle has a circumference of 320 cm, then its radius can be calculated as 50.92 cm according to the formula of circumference of a circle.

In geometry, the circumference can be defined as the perimeter of a circle or an ellipse. It can also be said as the linear distance present around it.

To better describe it, you can imagine that if a circle is opened out and placed as a straight line, then the total length of that straight line can be described as the circumference of the circle.

It is synonymous to perimeter, but the terminology can only be used with circled and ellipses. It is the curved length of the object. In this case, the object is mostly 2 dimensional but sometimes 3 dimensional objects can also be placed to take out their circumference with other methods.

In this particular question,

2[tex]\pi[/tex]r = 320

⇒ r = 320/2[tex]\pi[/tex]

⇒ r = 50.92

⇒ r ≈ 51 cm

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The graph of the quadratic equation:

y = x^2 -8x + 16

Can be seen in the image at the end.

First, we have a quadratic function:

y = x^2 -8x + 16

To graph this we need to find some points on the parabola, to do that, we will evaluate it in some values of x.

if x = 0

y = 0^2 - 8*0 + 16 = 16

So we have the point (0, 16)

if x = 1

y = 1^2 - 8*1 + 16 = 9

So we have the point (1, 9)

if x = -1 we have:

y = (-1)^2 - 8*-1 + 16 = 23

So we have the point (-1, 23)

And so on, once you have enough points, you can graph them in a coordinate axis and then draw a parabola that connects them, the graph of the quadratic equation can be seen in the image below.

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The weight of the plane with 20 gallons of fuel in its tank 2218 pounds. using a linear function.

what is linear function?
A straight line makes up the graph of a linear function. The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one.

Let y be the weight of the airplane and x be the amount of fuel

And we know that the general form of a linear

function is

(1) And given that the slope of the line is

y = mx + c

m = 5.9

Then (1) becomes

y = 5.9x + c

And given that for x = 53 , y = 2212.7

Then from (2), we have

2212.7 = 5.9 (53) + c

⇒ 2212.7 = 312.7 + c

c = 2212.7 - 312.7

c = 1900

Thus, (2) becomes

y = 5.9x + 1900

Then for x=22, from (3) y = 118 + 2100

= w = 2218

The weight of the plane with 20 gallons in its fuel tank is 2218 pounds

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Answer:

x = 130°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 50° + 80° = 130°

Answer: 130

Step-by-step explanation:

180 = y + 50 + 80

y = 50

180 - y = x

x = 130

Answer: 4x-9y=27 is this equation in standard form.

Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.

The alternative hypothesis states that political beliefs and marijuana use depend on one another within the population, contrary to the null hypothesis that asserts these two variables are independent.

H₀ : Pij = Pi · Pj ; i = 1, 2, 3 ; j = 1, 2, 3

Ha : at least one Pij ≠ Pi · Pj

We want to test whether there is a relationship between political views and marijuana usage levels. The results of a random sample of size n = 1353 are derived from the following formula;

e = (Row total) x (Column total) /Total sample size

We are told to use the 0.01 level of significance to test the null hypothesis. Thus, α = 0.01. The table has r = 3 rows and c = 3 columns. An r × c table has degrees of freedom df = (r - 1) x (c - 1). So, a 3×3 table has degrees of freedom df = (3 - 1) x (3 - 1) = 4. From formula the df = 4 and α = 0.01, χ²₀.₀₁ = 13.277. Reject the null hypothesis if X² ≥ 13.277 where

x² =Σ(a - e)²/e

Substituting the observed and expected frequencies summarized in the table above into the formula for x², we get

X² = 68.732

Rejection Region → X² ≥ 13.277

Test statistic → X² = 68.732

Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.

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The correct option or equation that applies to the given situation is 7*6 = (4*6) + (3*6).

According to the question,

We have the following information:

Akela drew smaller arrays to find the product of a larger array.

Now, we have two figures where one has 6*3 boxes (6 horizontal boxes and 3 horizontal boxes) and in the second figure we have 6*4 boxes (6 horizontal boxes and 4 vertical boxes).

Now, to find the correct option, we will look for these two in options:

So, the option that has both of them is  7*6 = (4*6) + (3*6).

Now, we can verify whether the sides of the equation given are correct or not.

We have:

7*6 = 42

On right hand side, we have:

(4*6) + (3*6)

24+18

42

Hence, the correct option is 4th one.

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Hellow what grade of math is this?

Answer:

its A

Step-by-step explanation:

:)

The customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).

We are given with the cost of ham is $2.49 per pound and

Cost of swiss cheese is $3.79 per pound.

So, the cost of 2 pounds of ham will be given as-

= 2× $2.49

= $4.98

Since, the customer has a total of  $9.50 to spend on 2 pounds of ham and some cheese,

∴ Let the number of pounds of cheese she can purchase be x.

Then the equation will be this:

2.49*2 + 3.79*x = 9.50

4.98 + 3.79x = 9.50

Subtracting 4.98 from each side we get-

4.98 -4.98 + 3.79x = 9.50-4.98

3.79x = 4.54

x  [tex]=\frac{4.54}{3.79}[/tex]

x = 1.19788 pounds of cheese (approximately 1.2 pounds).

Hence, the customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).

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x = milliliters of 40% alcohol

y = milliliters of 20% alcohol

so just alcohol alone in each quantity will just be "x" * (40/100) = 0.4x and "y" * (20/100) = 0.2y, whilst trying to get 1000 mL of 36% alcohol only.

[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{mL of }}{amount}\\ \cline{2-4}&\\ \textit{40\% solution}&x&0.4&0.4x\\ \textit{20\% solution}&y&0.2&0.2y\\ \cline{2-4}&\\ mixture&1000&0.36&360 \end{array}~\hfill \begin{cases} x+y=1000\\\\ 0.4x+0.2y=360 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=1000\implies }x=1000-y ~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.4(1000-y)+0.2y=360} \\\\\\ 400-0.4y+0.2y=360\implies 40-0.4y+0.2y=0\implies 40-0.2y=0 \\\\\\ 40=0.2y\implies \cfrac{40}{0.2}=y\implies \boxed{\stackrel{mL}{200}=y} ~\hfill \boxed{\underset{mL}{\stackrel{1000~~ - ~~200}{x=800}}}[/tex]

Explanation

We are given the measure of arc PR = 118°.

We are required to find m∠PQR.

We know that an arc measure is an angle the arc makes at the center of a circle. Therefore, we have:

Hence, the answer is:

But since Q is the measure of the angle, then the final answer is 118°.