The enrollment for a school in 2010 was 1510 students. In 2020, the enrollment was 860 students. Find and interpret the rate of change in enrollment from 2010 to 2020.

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_3(y)=11.03\hspace{5em}\log_3(z)=7.74\hspace{5em}\log_3(t)=5.44 \\\\[-0.35em] ~\dotfill[/tex]

[tex]12\log_3\left( \cfrac{z^7}{y^5 t^2} \right)\qquad \textit{let's nevermind the 12 for now} \\\\\\ \log_3\left( \cfrac{z^7}{y^5 t^2} \right)\implies \log_3(z^7)-\log_3(y^5 t^2)\implies \log_3(z^7)-[\log_3(y^5)+\log_3(t^2)] \\\\\\ \log_3(z^7)-\log_3(y^5)-\log_3(t^2)\implies 7\log_3(z)-5\log_3(y)-2\log_3(t) \\\\\\ 7(7.74)-5(11.03)-2(5.44)\implies \stackrel{\textit{let's put back the 12}}{12 ~~ [7(7.74)-5(11.03)-2(5.44)]} \\\\\\ ~\hfill \text{\LARGE -142.2}~\hfill[/tex]

Answer:

ANS:- = -25/18

Step-by-step explanation:

= (5/6)/(-3/5)

=5*5/6*(-3)

=25/-18

= -25/18

Applying the definition of supplementary angles, the reasons that complete the two-column proof that proves x = 15 are:

a. Substitution property

b. Combine like terms

c. Division property of equality.

Two angles are supplementary angles if their sum is equal to 180 degrees when they are added together.

Given that m∠RST = 5x° and m∠UVW = 7x°, and both angles are supplementary angles, the two-column proof that proves x = 15 is shown below.

Statement                                  Reason                                            

m∠RST = 5x°; m∠UVW = 7x°    Given

∠RST and ∠UVW are

supplementary angles.

m∠RST + m∠UVW = 180          Definition of supplementary angles

5x + 7x = 180                             Substitution property

12x = 180                                   Combine like terms

x = 15                                         Division property of equality

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x = 9 or -7 is the solution of the quadratic equation

Given: the quadratic equation (x−1)²−20 = 44

(x−1)²−20 = 44

Add 20 to both sides:

(x−1)² = 44+20

(x−1)² = 64

Take the square root of both sides:

(x−1)² = 64

x-1 = ±√64

x = 1±√64

x = 1±8

x = 1+8 or 1-8

x = 9 or -7

Therefore, the solution of the equation is x = 9 or -7

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The zeroes of the polynomial in discuss whose factors are; ( 3x - 2), ( x² - 1 ), and ( x + 4 ) are; 2 / 3, +1, -1 and -4.

To determine the zeroes of a polynomial, the factors of the polynomial must be equated to zero.

On this note, since the given factors of the polynomial are; (3x-2), (x^2-1), and (x+4).

The zeroes are determined as follows;

3x - 2 = 0; 3x = 2; Therefore; x = 2 /3.

x² - 1 = 0; x² = 1; Therefore, x = ±1.

x + 4 = 0; Therefore; x = -4.

Consequently, it can be concluded that the zeroes of the polynomial as determined from its factors are; 2 / 3, -1, +1, -4.

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The rearranged equation for V is V = E - F

From the question, we have the following parameters that can be used in our computation:

E=F+V

Rewrite the above equation properly

So, we have the following representation

E = F + V

The variable expense is V

So, we have

E = F + V

Subtract F from both sides

V = E - F

hence, the equation is V = E - F

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Answer:

Yes, the runners number of strides will fit evenly into the length of the race.

Step-by-step explanation:

The bridge is 138,435 feet. You would divide this to get 46,145 as a whole number.

Answer:

Step-by-step explanation:

You are dividing 138435 by 3.

The quotient would be 46145 with no remainder. So the answer would be yes.

A 2nd way to do this is to see if 183435 is a multiple of 3.

Hope this helps!

Have a great day!

If Kareem has 3.5 cups of sugar then the amount of flour that Kareem need to make the muffins is 7 cups  .

In the question ,

it is given that ,

the ratio that Kareem uses to make the muffin is 3.5 cups of flour for every 1.75 cups of sugar .

let the number of cups of flour be "y" and

the number of cups of sugar be "x" .

So , y ∝ x ,

y = k*x , where k is the constant of proportionality .

From the given data ,

3.5 = k*1.75

k = 3.5/1.75

k = 2 .

we have to find the cups of flour that Kareem needs , if he has 3.5 cups of sugar .

the equation becomes ,

y = 2*3.5

y = 7

Therefore , Kareem needs 7 cups of flour .

The given question is incomplete , the complete question is

Kareem makes muffins using a ratio of 3. 5 cups of flour for every 1. 75  cups of sugar. If he has 3. 5 cups of sugar, how much flour does he need to make the muffins ?

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The original price of the T.V is 350 dollars

a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

le the original price of T.V be x.

so if the t.v was sold 40% off, I means that the sale price of T.V  = 60x/100

0.6x.

if the original price is 140 more than sale price, it means sale price is 140 less = x - 140

Equating both expressions we have

x - 140 = 0.6x

x - 0.6x = 140

0.4x = 140

x = 140/0.4

x = 350 dollars

In conclusion, the original price of tv is 350 dollars

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The values of sin2x, cos2x and tan2x is  [tex]-\frac{3\sqrt{13}}{11}[/tex], 2/11 and  [tex]-\frac{3\sqrt{13}}{2}[/tex] respectively.

What is tan function?

The tan function, one of the primary six trigonometric functions, is typically expressed as tan x. It is the ratio of the angle's opposite and adjacent sides when a right-angled triangle is being considered.

Tangent is a verb that means "to touch" in Latin, from the root tangere. A circle is precisely the point at which a line tan to it intersects. In trigonometry, the tan function, a periodic function, is crucial. Utilizing the unit circle will make understanding the tangent function the simplest possible.

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Answer:

x=64/39

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Subtract 2/13 from both sides.

Step 3: Multiply both sides by 2/(-1).

Answer:

1 25/39

Step-by-step explanation:

on my test

Answer:

y + 9 = 2(x + 5): slope is 2

y - 4 = -3(x - 3): slope is -3

(12/5, 29/5)

Step-by-step explanation:

y + 9 = 2(x + 5)

y + 9 - 9 = 2(x + 5) - 9   ==> subtract both sides by 9 to isolate y

y = 2(x + 5) - 9 ==> simplify

y = 2x + 2*5 - 9  ==> distribute x and 5 by multiplying them by 2

y = 2x + 10 - 9

y = 2x + 1  ==> slope is 2

y - 4 = -3(x - 3)

y - 4 + 4 = -3(x - 3) + 4  ==> add both sides by 4 to isolate y

y = -3(x - 3) + 4

y = -3x - 3(-3) + 4  ==> multiply x and -3 by -3 by distributive property

y = -3x - (-9) + 4

y = -3x + 9 + 4  ==> simplify

y = -3x + 13  ==> slope is -3

Since y = -3x + 13 and y = 2x + 1:

2x + 1 = -3x + 13  ==> solve for x

2x + 3x + 1 = -3x + 3x + 13

5x + 1 = 13

5x + 1 - 1 = 13 - 1

5x = 12

x = 12/5

y = 2x + 1

y = 2(12/5) + 1  ==> plug in 12/5 for x

y = 24/5 + 1  ==> solve for y

y = 24/5 + 5/5

y = (24+5)/5  ==> y = 29/5   ==> (x, y) = (12/5, 29/5)

Khadija has 8 nickels and 2 quarters

From the question, we have the following parameters that can be used in our computation:

Worth of coins = $0.90

Type of coins = Dimes and quarters

Represent the nickels with n and the quarters with q

So, we have the following representation

n + q = 10

0.05n + 0.25q = 0.9

Make n the subject

n = 10 - q

So, we have

0.05(10 - q) + 0.25q = 0.9

Evaluate the products

0.5 - 0.05q + 0.25q = 0.9

This gives

0.2q = 0.4

Divide both sides by 0.2

q = 2

Recall that

n = 10 - q

So, we have

n = 10 - 2

Evaluate

n = 8

Hence, the number of nickels is 8

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0.0227 is the probability that a randomly selected bolt will have a diameter greater than 0.604 inches.

What is probability explained with an example?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

                           The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

The probability that randomly selected bolt will have a diameter grater than  

0.60x inches.

P(x > 0.604 ) = P( x - 0.600/0.002 > 0.604 - 0.600/0.002 )

                      = P( Z > 2 )

                       = 0.02275

     P(x > 0.604 ) = 0.0227

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The solution of the system of equations y = x + 2 and x - y = -2 is (c) infinite many solutions

From the question, we have the following parameters that can be used in our computation:

y = x + 2

x - y = -2

Substitute the equation y = x + 2 in the equation x - y = -2

So, we have the following representation

x - (x + 2) = -2

Open the bracket in the above equation

So, we have the following representation

x - x - 2 = -2

Evaluate the like terms in the above equation

So, we have the following representation

-2 = -2

Both sides of the above equation are the same

This means that the equation has a lot of solution

In other words, the equation has infinite many solutions

Hence, the solution is (c) infinite many solutions

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The polynomial x³ - 2x² - 13x - 10 divided by x + 2 will have quotient of x² - 4x - 5x and a remainder of zero.

The polynomial x³ - 2x² - 13x - 10 divided by x + 2 as follows;

We divide the first of the polynomial x³ by x to give x²

multiply x - 1 by x² to get x³ + 2x²,

then subtract x³ + 2x² from x³ - 2x² - 13x - 10 to get -4x² - 13x - 10

divide -4x² by x to get -4x

multiply x - 1 by -4x to get -4x² - 8x

then subtract -4x² - 8x from -4x² - 13x - 10 to get -5x - 10

divide -5x by x to get -5

multiply x - 1 by -5 to get -5x - 10,

then subtract -5x - 10 from -5x - 10 to get a remainder of zero.

Therefore, the division of the polynomial x³ - 2x² - 13x - 10 by x + 2 using long division give us the quotient x² - 4x - 5x and a remainder of zero.

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Answer:

  7.6

Step-by-step explanation:

You want to know the number of 360 ft football fields tall the 2722 ft Burj Khalifa building is.

The ratio of height to football field length is ...

  (2722 ft)/(360 ft/field) ≈ 7.6 fields

The height of the building is about 7.6 football field lengths.

Answer:

y = 4x + 2

Step-by-step explanation:

24 coins gained after 6 weeks

24 / 6 = 4 coins a week

y = 4x + 2

The answer to this Question based on Profits is No they cant make 5000$ profit

What is profit?

Profit is simply the extra money we earn on selling good etc things and there are tonnes of different ways of making money and profit

Solution:

Here Diego high school soccer team started a fundraiser selling treats at their games

Initial money spent = 1000$

They decided to make 0.3$ revenue on both candy and soda hence total 0.6$ revenue in one pack

one pack costs for 2$ where 0.6$ is revenue and actual cost is 1.4$

Total packs to sell = 1000/1.4

= 714 packs

hence total profit = 714 * 0.6 = 428$

hence maximum revenue they can make is 428$ and it is maximum

hence they cant make 5000$ profit

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Equation in slope intercept form and in standard form for (-2,6) and parallel to x3y=5 will be x + 3y = 10

Given equation =>  x + 3y = 5

3y = -x + 5 so, we have to write it in the equation form,

y = -(1/3)x + 5/3

slope = -1/3     Parallel lines have the same slope.

Now, you have a point and a slope, so use the Point-Slope form of the equation of a line.

y - y1 = m(x - x1) , by using the equation of line

y - 6 = (-1/3)(x - 2), then we get

y - 4 = (-1/3)x + 2/3

y = (-1/3)x + 3 1/3   Slope-intercept Form

(1/3)x + y = 10/3     Multiply both sides by 3.

x + 3y = 10    Standard form

So, the equation is x + 3y = 10

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Answer: x= 23/18

Step-by-step explanation:

4(3x-1) =-3(2x-6) + 1

12x - 4 = -6x + 18 + 1

12x -4 = -6x + 19

18x -4 = 19

18x = 23

x = 23/18

Answer: About 20.82 liters.

Step-by-step explanation:

         To go from gallons to liters, we will multiply by 3.785. Since we are in half gallons, we will multiply 11 by 0.5 for 5.5 full gallons. Now, we will multiply;

        5.5 gallons * 3.785 = 20.8198 ≈ 20.82 liters

The function y = (x + 2)^(1/2) + 3 belongs to the family of square root functions. A square root function is a type of function in which the independent variable (in this case, x) is under the radical sign.

In mathematics, a function is a relationship between a set of potential inputs and an equally likely set of outputs, with the condition that each input is associated to just one possible outcome. In other terms, a function is a category of mathematical action that accepts one or more parameters for input and generates a return result. Equations or graphs are frequently used to depict functions, which are useful for both modeling and solving mathematical issues.

In computer programming, a function is a block of code that completes a particular task and can be used repeatedly throughout a program. Programmers have the option of creating their own functions or using ones that are already included in the language.

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Answer:

Step-by-step explanation:

12

x=12y

2:3

3:14

nope-60/2=30

495/9=55

Answer: To solve the equation "-5/8x + 10" for x when x equals -8, we can first substitute -8 for x in the equation:

-5/8(-8) + 10

Next, we can simplify the expression by performing the calculations within the parentheses:

-5/8(-8) + 10 = 5/8(8) + 10 = 5(8)/8 + 10 = 40/8 + 10 = 5 + 10 = 15

Therefore, the value of "-5/8x + 10" when x equals -8 is 15.

The equation that is used to prove 1 + tan²(x) = sec²(x) is Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x)  , the correct option is (d) .

In the question ,

a trigonometric equation is given as 1 + tan²(x) = sec²(x) ,

we have to find the equation that will be used in proving .

the equation is 1 + tan²(x) = sec²(x)

rewriting the equation ,

we get ,

1+Sin²(x)/Cos²(x) = 1/Cos²(x)...because tan(x) = Sinx/Cosx and Secx = 1/cosx

taking the LCM as Cos²(x) , and solving further ,

we get ,

Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x)

that is option (d) .

Therefore , the equation is Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x) .

The given question is incomplete , the complete question is

Which equation can be used to prove 1 + tan²(x) = sec²(x) from the options given in the image below  ?

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The class intervals appropriate to use in creating a histogram of the data are 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130. The correct option is B.

A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.

The width of the intervals must be equal. This means that the difference between the lower bound and the upper bound must be equal. Also, the upper bound of the preceding interval must be the same as the lower bound of the next interval.

This means that the intervals must be overlapping. Of all the options, it is 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130 that satisfy both conditions.

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Answer:first option

Step-by-step explanation:

The simplified form of the given expression has a numerator of (x + 9)(2x + 1) and the denominator of (x + 7) and the expression does exist when (x = 9) and this can be determined by factorizing the given expression.

By identifying the biggest factors that the terms in the equation have in common, factoring is a technique used in mathematics to simplify algebraic expressions.

Given :

Expression - [tex]\frac{3x^2 - 27x}{2x^2+13x-7}[/tex] ÷ [tex]\frac{3x}{4x^2-1}[/tex]

First, factorize the expression, [tex]4x^2-1[/tex]

So, [tex]4x^2-1[/tex] = [tex](2x-1) (2x+1)[/tex]

Now, factorize the equation: [tex]2x^2+13x-7[/tex]

[tex]2x^2+13x-7[/tex] = [tex]2x^2+14x -x -7[/tex]

                     = [tex]2x(x+7) -1(x+7)[/tex]

                     = [tex](2x-1) (x+7)[/tex]

Now, factorize the equation: [tex]3x^2-27x[/tex]

So, [tex]3x^2-27x[/tex] = [tex]3x(x-9)[/tex]

Now, substitute the factorized terms in the given expression:

= [tex]\frac{3x(x-9)}{(2x-1) (x+7)}[/tex] ÷ [tex]\frac{3x}{(2x-1) (2x+1)}[/tex]

= [tex]\frac{(x+9) (2x+1)}{(x+7)}[/tex]

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The complete question is as follows:

Select the correct answer from each drop down menu. The simplest form of this quotient has a numerator of... and a denominator of.... The expression does exist when x=......