The area of a rectangle is x²-4x-21
Write down an expression for the width and the length of
the rectangle.​

Answer:

82%

Step-by-step explanation:

4237-742 = 3495

3495/4237=0.824876

0.824876*100= 82%

Answer:

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.

Step-by-step explanation:

The volume of the prism whose length, breadth, and height are 10 inches, 4 inches, and 3 inches respectively is 120 inches².

A prism is a 3-D geometric shape that has two identical and parallel polygonal bases connected by a series of rectangular or parallelogram-shaped faces (also known as lateral faces).

As it is known that the volume of a prism is obtained by multiplying the area of the base and the height, i.e.,

Volume = area of the base × height

Also,

Area of the base = length × breadth

So,

Volume = length × breadth × height

             = 10 × 4 × 3

             = 120 square inches.

Therefore, the volume of the rectangular prism is 120 inches².

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The complete question is as follows:

Find the volume of the rectangular prism whose length, breadth, and height are 10 inches, 4 inches, and 3 inches respectively.

-2 dollars

0 + 8 = 8

8 - 10 = -2

In a case whereby In 1950, a U.S. population model was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be 288 million in the year 2000.

Population models are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).

The model was given as y=151x(1.013)^t-1950

where the future time t = 2000

Then we can substitute the given year 2000 as the value of 't'

then we will have y=[151x(1.013)^(2000-1950)] = 288 million

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To complete 2ab of (a+b)²

196 must be added on both sides to get complete square as (x+14)²

Answer:

196

Step-by-step explanation:

Given equation:

\(x^2+28x=11\)

Step 1

When completing the square for an equation in the form ax²+bx+c=0, the first step is to move the constant to the right side of the equation.

This has already been done in the given equation:

\(x^2+28x=11\)

Step 2  

Add the square of half the coefficient of x to both sides.  

This forms a perfect square trinomial on the left side:

\(\implies x^2+28x+\left(\dfrac{28}{2}\right)^2=11+\left(\dfrac{28}{2}\right)^2\)

Simplify:

\(\implies x^2+28x+14^2=11+14^2\)

\(\implies x^2+28x+196=11+196\)

\(\implies x^2+28x+196=207\)

Step 3

Factor the perfect square trinomial on the left side:

\(\implies (x+14)^2=207\)

We have now completed the square and can go onto solving the equation.

Therefore, 196 must be added to both sides of the equation to complete the square.

Answer:

firstly

we all know that the angles of a triangle they all add up to 180° meaning when you add them all they must give you 180°

88°+33°+L = 180° ( sum of angle in a ∆)

121° + L = 180°

L = 180° - 121°

L = 59°

Step-by-step explanation:

first you you must add all your angles and all equal to 180°

that you add the like terms

than you transpose 121° to the right hand side

The general equation of line passing through two points (x_1,y_1) and (x_2,y_2) is,

Determine the equation of line passing through two points.

So equation of line is y = 5.

Answer:

One ticket cost $10.90.

Step-by-step explanation:

The total spent was $98.50--food, drinks, admission--everything.

$44.00 was for food and drinks.

We can take the 44 away from the total.

98.50 - 44.00

= 54.50

They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.

54.50 ÷ 5 = 10.90



The price of one ticket was $10.90

To make this look like algebra class...

let x = the price of one ticket

5x = the price of 5 tickets

5x + 44 = 98.50

subtract 44

5x = 54.50

divide by 5

x = 10.90

The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.

     *look at the image I attached for a better explanation

By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation

    \(?^2+5^2 = 13^2\\?^2 + 25 = 169\\?^2 = 144\\? = 12\)

Thus the missing side length is 12 cm

Hope that helps!

Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

\(\sf{18x+5-3=65}\)

\(\sf{18x+2=65}\)

Subtract 2 from each side:

\(\sf{18x=63}\)

Now, divide each side by 18:

\(\sf{x=\dfrac{63}{18}\)

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

\(\sf{x=\dfrac{7}{2}}\)

\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)

Answer:

4 times

Step-by-step explanation:

If the smaller container only holds 2 liters, you would have to divide 8 by 2 which is 4.

Answer:

4 times

Step-by-step explanation:

Its 4 times cause 8/2=4

Answer:

4-(2n)= 30

Step-by-step explanation:

N is 17

Answer:

true

Step-by-step explanation:

the factors are simply what is being multiplied together. We can see there are 3 because we have 5,3,and 2. 30 is not a factor because that is the answer. I hope this helps!

Answer:

27

Step-by-step explanation:

FE is tangent to the circle with center D at point E and DE is radius.

\( \therefore FE \perp DE \implies m\angle FED = 90\degree \)

DE = x

DF = x + 18

FE = 36

By Pythagoras theorem:

\( DF^2 = DE^2 + FE^2 \)

\( (x+18)^2 = x^2 + 36^2 \)

\( x^2 + 36x + 324= x^2 + 1296\)

\( 36x + 324= 1296\)

\( 36x = 1296-324\)

\( 36x = 972\)

\( x = \frac{972}{36}\)

\( x =27\)

The value of x from the given figure, which is radius of a circle is 27 units.

From the given figure, FE=36 units, DE=x units and FD=x+18 units.

Tangent and radius of a circle meet at 90°. If we draw a radius that meets the circumference at the same point, the angle between the radius and the tangent will always be exactly 90°.

Using Pythagoras theorem, we have

FD²=FE²+DE²

⇒ (x+18)²=36²+x²

⇒ x²+36x+324=1296+x²

⇒ 36x=1296-324

⇒ 36x=972

⇒ x=972/36

⇒ x=27 units

Hence, the value of x from the given figure, which is radius of a circle is 27 units.

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Answer:

43) 79 years and 6 months

44)  17 years and 6 months

Step-by-step explanation:

As the account increases by a constant percentage bi-monthly, we can use the compound interest formula to write a function to model the situation.

\(\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

The interest is compounded bi-monthly, which means every 2 months.

Therefore, the interest is applied 6 times per year.

Given values:

Substitute the given values into the formula, and solve for t:

\(\begin{aligned}A&=P\left(1+\dfrac{r}{n}\right)^{nt}\\\\\implies 10000&=2400\left(1+\dfrac{0.018}{6}\right)^{6t}\\\\\implies 10000&=2400\left(1+0.003\right)^{6t}\\\\\dfrac{25}{6}&=\left(1.003\right)^{6t}\\\\\textsf{Take natural logs:} \quad \ln \left(\dfrac{25}{6}\right)&=\ln\left(1.003\right)^{6t}\\\\\ln \left(\dfrac{25}{6}\right)&=6t\ln\left(1.003\right)\\t&=\dfrac{\ln \left(\dfrac{25}{6}\right)}{6\ln\left(1.003\right)}\\\\t&=79.4031089...\end{aligned}\)

The account balance will reach $10,000 during the 79th year (after 79 years and 4.84 months).

As the interest is applied bi-monthly (every 2 months) we need to round up to the nearest 2 month interval. Therefore, the account balance will reach $10,000 after 79 years and 6 months.

Note: After 79 years and 4 months, the account balance will be $9,987.47, and after 79 years and 6 months it will be $10,017.43.

\(\hrulefill\)

As the account increases by a constant percentage quarterly, we can use the compound interest formula to write a function to model the situation.

\(\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

The interest is compounded quarterly, which means every 3 months.

Therefore, the interest is applied 4 times per year.

Given values:

Substitute the given values into the formula, and solve for t:

\(\begin{aligned}A&=P\left(1+\dfrac{r}{n}\right)^{nt}\\\\\implies 60000&=30000\left(1+\dfrac{0.04}{4}\right)^{4t}\\\\\implies 60000&=30000\left(1+0.01\right)^{4t}\\\\2&=\left(1.01\right)^{4t}\\\\\textsf{Take natural logs:} \quad \ln \left(2\right)&=\ln\left(1.01\right)^{4t}\\\\\ln \left(2\right)&=4t\ln\left(1.01\right)\\\\t&=\dfrac{\ln \left(2\right)}{4\ln\left(1.01\right)}\\\\t&=17.4151792...\end{aligned}\)

The value of the investment account will double during the 17th year (after 17 years and 4.98 months).

As the interest is applied quarterly (every 3 months) we need to round up to the nearest 3 month interval. Therefore, the investment account will double by 17 years and 6 months.

Note: After 17 years and 3 months, the account balance will be $59,606.83, and after 17 years and 6 months it will be $60,202.90.

Answer: Andre should buy Car 2. Brainliest?

Step-by-step explanation:

To compare the gas mileage of the two cars, we need to find out how many miles each car can travel per gallon of gas.

For Car 1: y = 25x

This means that for every gallon of gas used (x), the car can travel 25 times that amount in miles (y). So, the gas mileage for Car 1 is 25 miles per gallon (mpg).

For Car 2: we can calculate the miles per gallon by dividing the total miles traveled by the number of gallons of gas used:

For 2 gallons of gas, the car can travel 60 miles. So, the gas mileage is 30 mpg (60 miles ÷ 2 gallons).

For 5 gallons of gas, the car can travel 150 miles. So, the gas mileage is 30 mpg (150 miles ÷ 5 gallons).

For 7 gallons of gas, the car can travel 210 miles. So, the gas mileage is 30 mpg (210 miles ÷ 7 gallons).

For 8 gallons of gas, the car can travel 240 miles. So, the gas mileage is 30 mpg (240 miles ÷ 8 gallons).

For 11 gallons of gas, the car can travel 330 miles. So, the gas mileage is 30 mpg (330 miles ÷ 11 gallons).

Therefore, Car 2 has a consistent gas mileage of 30 mpg.

From the above calculations, we can see that Car 2 has a better gas mileage compared to Car 1. Car 2 can travel 30 miles on a gallon of gas, while Car 1 can only travel 25 miles on a gallon of gas.

Therefore, Andre should buy Car 2 if he wants to get the best gas mileage. Car 2 can travel 5 more miles per gallon than Car 1.

The inequality represented by the graph is given as follows:

y > 3x - 4.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -4, hence the intercept b is given as follows:

b = -4.

When x increases by 1, y increases by 3, hence the slope m is given as follows:

m = 3.

Hence the equation of the line is:

y = 3x - 4.

The inequality is composed by the values to the right (greater) of the line, and has an open interval due to the dashed line, hence:

y > 3x - 4.

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Answer:

10^oF

Step-by-step explanation:

Huda's error in evaluating (3) squared incorrectly led to the incorrect final result.

The correct answer should be -20, not 34.

Huda's error was that she evaluated (3) squared incorrectly.

Instead of calculating 3 squared as 9, she mistakenly considered it as 3. This error led to incorrect subsequent calculations and the final result of 34, which is not the correct answer.

To evaluate the expression correctly, let's go through the steps:

Negative 3 (8 minus 5) squared minus (negative 7) \(= -3(3)^2 - (-7)\)

First, we simplify the expression within the parentheses:

\(-3(3)^2 - (-7) = -3(9) - (-7)\)

Next, we evaluate the exponent:

-3(9) - (-7) = -3(9) + 7

Now, we perform the multiplication and addition/subtraction:

-3(9) + 7 = -27 + 7 = -20

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Answer:

22.7°

Step-by-step explanation:

Preliminaries:

SOH CAH TOA

Explanation:

Since we have the Opposite side and Adjacent side (OA) we will use the trigonometric function of Tangent.

The tangent equation is:

tan(x) = (O/A)

Substituting in our values we get tan(x) = (18/43)

To solve for x, we take the inverse tangent and get the equation:

x = tan⁻¹(18/43)

Use a calculator and you will get that x ≈ 22.7°

The value of LO if RU is 6 inches is solved to be 30 inches

This is a term used in geometry to mean that the respective sides of the polygons are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the polygon are congruent then the side should be in proportions

Examining the figure when LM is 45 inches, and RS is 9 inches

the constant of proportionality from quadrilateral RSTU to quadrilateral LMNO is 5

9 * 5 = 45

when RU = 6 inches

6 * 5 = 30 inches

hence LO is 30 inches

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Answer: 49,000

48805 is greater than 48500, so it rounds to 49,000

Step-by-step explanation:

\((a-b)^2=a^2-2ab+b^2\\\\2x^2-4x-9=0\qquad|\text{add 9 to both sides}\\\\2x^2-4x-9+9=0+9\\\\2x^2-4x=9\qquad|\text{divide both sides by 2}\\\\\dfrac{2x^2}{2}-\dfrac{4x}{2}=\dfrac{9}{2}\\\\x^2-2x=4.5\\\\x^2-2\cdot x\cdot1=4.5\qquad|\text{add}\ 1^2\ \text{to both sides}\\\\x^2-2\cdot x\cdot1+1^2=4.5+1^2\\\\(x-1)^2=5.5\iff x-1=\pm\sqrt{5.5}\qquad|\text{add 1 to both sides}\\\\x=1-\sqrt{5.5}\ \vee\ x=1+\sqrt{5.5}\)

hence we can use similarity of triangle to find out the slopes, and it will be same.

We can use the graph given to draw two similar triangles and then use ten to find the slope.

the Pythagorean theorem.

if ABC is a triangle with AC as the hypotenuse and angle B is 90 degree then we have

\((AC)^2=(AB)^2+(BC)^2\)

Refer to the diagram, we have

AD=44 UNIT

BD=1 UNIT (on graph)

and from Pythagorean theorem.

\(AB=\sqrt{(AD)^2+(BD)^2} \\\\AB=\sqrt{44^2+1}\\ \\AB=44.01 UNIT\)

Now for triangle

FA=44+44=88

CF=2BD

\(AC=\sqrt{88^2+4} \\\\AC=88.02\)

AC= 2AB

thus, all sides of ACF is twice of each corresponding sides of ADB. THUS BY SSS similarity

we have ΔADB ~ ΔAFC.

slope of hypotenuse of a right-angled triangle is the ratio of base and its height.

As base of AFC is twice of base of ADB and height of ADB.

thus, both triangles have same slope.

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Answer:

24

Step-by-step explanation:

I did the math

Answer:

X=9

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

For an expression to be undefined,. the denominator must be equal to 0

Therefore, in order to make that expression undefined, we must equate the denominator to 0

6 + 2v = 0

2v = 0 - 6

2v = -6

v = -6/2

v = -3

So in order to make the expression to be equal to 0, v must be -3