Solve for x. Enter the solutions from least to greatest.
6x² - 6x - 72 = 0

The measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation if the triangle ABC implies it is bigger than the triangle A'B'C' with a scale factor 1/2 since AC = 10 and A'C' = 5

side A'B' = 8 × 1/2

side A'B' = 4

Therefore, the measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

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Answer:

the answer is B, 4. :)

Answer:

195m^3

Step-by-step explanation:

Volume of a rectangle = Length x Width x Height

L = 5m

W = 3m

H = 13m

V = 5m x 3m x 13m

V = 195m^3

The simplified forms of the fractions are 3 and -5 repectively

To simplify a fraction, you divide both the numerator (top number) and denominator (bottom number) by their greatest common factor (GCF) until there are no more common factors. The result will be the simplified form of the fraction.

We have to note that;

1 ) 1 + 1/2 = 3/2

Then we have;

3/2 * 2/1 = 6/2 = 3

2) 3/4 - 2 = -5/4

Then we have;

-5/4 * 4/1 = -5

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The volume of the conical hole will be 154 cubic feet.

The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.

Given that a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 feet,

The volume of the cone will be calculated as:-

Volume = (1/3)πr²h

The circumference of the cone is,

2πr = 44

2 x ( 22 / 7 ) x r =  44

r = 7 feet

The volume of the cone will be calculated as:-

Volume = (1/3)πr²h

Volume = ( 1 / 3 )  x ( 22 / 7 ) x 7 x 7 x 3

Volume = 22 x 7

Volume = 154 cubic feet

Therefore, the volume will be 154 cubic feet.

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Answer:

1 harmful

Step-by-step explanation:

2 they will be not use if you not use

Answer:

Let's first calculate the amount of interest that would be earned if the interest were compounded annually. The formula for the future value of a single sum is:

F = P * (1 + r/n)^(nt)

Where:

F is the future value

P is the principal (the initial deposit)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For our calculation, we have:

P = $10,000

r = 1.8% = 0.018

n = 1 (annual compounding)

t = 30

So, the future value of the account with annual compounding is:

F = $10,000 * (1 + 0.018/1)^(1 * 30) = $10,000 * (1.018)^30 = $21,784.08

Now, let's calculate the amount of interest that would be earned if the interest were compounded monthly. The formula for the future value of a single sum is the same, but we need to use the monthly compounding rate (r/12) instead of the annual rate and the number of months (12t) instead of the number of years:

F = P * (1 + r/n)^(nt)

Where:

F is the future value

P is the principal (the initial deposit)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For our calculation, we have:

P = $10,000

r = 1.8% = 0.018

n = 12 (monthly compounding)

t = 30

So, the future value of the account with monthly compounding is:

F = $10,000 * (1 + 0.018/12)^(12 * 30) = $10,000 * (1.0015)^360 = $22,254.51

The difference in the two future values is $22,254.51 - $21,784.08 = $470.43.

So, the account would be worth $470.43 more if interest were compounded monthly rather than annually over a period of 30 years. Round to the nearest dollar, the answer is $470.

Step-by-step explanation:

D. $128.94. is the total amount of money Nate will earn after taxes when he buys a CD for $1000  The formula for compound interest is:

A = P * (1 + r/n)^(nt), where A is the amount after t years, P is the principal amount, r is the interest rate as a decimal, n is the number of times interest is compounded per year, and t is the number of years.

We can use this formula to calculate the amount of money Nate will have after 5 years:

A = 1000 * (1 + 0.03/4)^(4 * 5) = 1000 * (1 + 0.0075)^20 = 1000 * 1.1629 = 1162.9

The interest earned is 1162.9 - 1000 = $162.9.

And the amount of interest taxed is 20% of $162.9, which is 20% * $162.9 = $32.58.

So, the total amount of interest earned after taxes is $162.9 - $32.58 = $130.32.

Therefore, the correct answer is D. $128.94.

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Using simultaneous equations, the child ticket costs $18.

Simultaneous equations are two or more equations solved concurrently or at the same time.

Simultaneous equations are also known as a system of equations.

                Family A     Family B      Total Cost

Adults            2                  2                $62

Children         1                  4                 $70

Let the ticket cost per child = x

Let the ticket cost per adult = y

2x + 2y = 62 ... Equation 1

x + 4y = 70 ... Equation 2

Multiply Equation 1 by 2

4x + 4y = 124 ... Equation 3

Subtract Equation 2 from Equation 3:

4x + 4y = 124

-

x + 4y = 70

3x = 54

x = 18

= $18

From Equation 2, Substitute x = 18:

x + 4y = 70

18 + 4y = 70

4y = 52

y = 13

= $13

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Another family of one adult and four children pays $70.

Vοlume οf the cylinder in will be 226.28 yd³, Vοlume οf Slanted cylinder is 141.37 in³ and Vοlume οf οblique cubοid is 1224 cm³.

What exactly is a cylinder?

In geοmetry, a cylinder is οne οf the fundamental 3d fοrms with twο parallel circular bases at a distance. The curving surface cοnnects the twο circular bases at a predetermined distance frοm the centre. The axis οf the cylinder is the line cοnnecting the centres οf twο circular bases. The height οf the cylinder is the distance between the twο circular bases.

A. Nοw,given that diameter οf base = 6 yd then radius=6/2=3 yd

and height will be =√10²-6²  (By Pythagοras theοrem )

= √64

= 8 yd

then vοlume οf cylinder is=πr²h

= 22/7*3*3*8

= 1584/7

= 226.28 yd³

Hence, Vοlume οf the cylinder  will be 226.28 yd³.

B. Vοlume οf Slanted cylinder is V = πr²h

V = π3²5

V = π × 3 × 3 ×5

V = 141.37 in³

Hence, Vοlume οf Slanted cylinder is 141.37 in³

C. Vοlume οf οblique cubοid is V = lwh

V = 17 × 18 × 4

V = 1224 cm³

Therefore ,Vοlume οf οblique cubοid is 1224 cm³.

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On solving the provided question, we can say that the equation we have here is[tex]X_(n+1)= (x-n)^{3} - \frac{2}{10}[/tex] at [tex]x_1 = -1[/tex] n = 0 , [tex]x_1 = \frac{-3}{10}[/tex]

Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality.

A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14.

The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol.

A simple equation is a mathematical formula that, on both sides of the "equal to" sign, expresses the relationship between two expressions. Equations in this category include a variable, which is typically expressed as x or y. Simple equations often need to be rearranged in order to be solved.

the equation we have here is

[tex]X_(n+1)= (x-n)^{3} - \frac{2}{10}[/tex] , at [tex]x_1 = -1[/tex]

n = 0

[tex]x_1 = \frac{-3}{10}[/tex]

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The price of one citron is 5 units and the price of one fragrant wood apple is 3.5 units." Let's call the price of one citron "c" and the price of one fragrant wood apple "w".

Using the information from the first equation:

4c + 3w = 34

Using the information from the second equation:

3c + 4w = 29

We can now solve the system of equations to find the value of "c" and "w".

Subtracting the second equation from the first:

4c + 3w - (3c + 4w) = 34 - 29

c = 5

Substituting the value of c back into one of the original equations:

3c + 4w = 29

3 * 5 + 4w = 29

15 + 4w = 29

4w = 14

w = 3.5

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The probability of drawing a green ball in one draw is 8/14 = 4/7. Since the balls are replaced after each draw, each draw is independent of the others. Therefore, the probability of getting 6 green balls in a row is (4/7)^6 ≈ 0.066.

Rounding to three decimal places, the probability is approximately 0.066.

Answer:

the answer of the equation is b

E. This polynomial could be factored by using grouping or the perfect squares methods.

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

x^2 + 2x + 1

Expand

x^2 + x + x + 1

Factorize the expression

(x + 1)(x + 1)

This gives

(x + 1)^2

Hence, the solution is (e)

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Answer:

Step-by-step explanation:

Substitute for r.

1/5(1/4) + 9/20  ->  1/20 + 9/20 = 10/20.

Simplify the final answer.

10/20 = 1/2

Answer:

-60, +1180

Step-by-step explanation:

The value of P(Greater than 2) is 0.75

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

Spinner = 6 5 7 2

Using the above as a guide, we have the following:

Greater than 2 = 3

Total = 4

The probability is

P = Greater than 2/Total

Substitute the known values in the above equation, so, we have the following representation

P(Greater than 2) = 3/4

Evaluate

P(Greater than 2) = 0.75

Hence, the solution is 0.75

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Answer:

10 hours would've gone by, and they have collected 190 signatures.

Step-by-step explanation:

1.511; 1.512 ;1.5113

Step-by-step explanation:

we know that there are infinite numbers.

and every decimal number is a rational number

now, extend the number upto 3 decimal or 2 decimal .

then it will become 1.500

there are numbers upto 1.599

like this we can extend upto infinite values

you can write infinite numbers, but question is asked for only 3

Answer: Let's denote the original number of pages Mark planned to read as "P".

From the first statement, we know that P - 18 pages will take 5 more days, which means P pages will take 5 days less, or 5 - 5 = 0 days.

From the second statement, we know that P - 24 pages will take 8 more days, which means P pages will take 8 days less, or 8 - 8 = 0 days.

So, we have two equations:

P - 18 = 5 * X

P - 24 = 8 * Y

Where X and Y are the number of pages Mark reads per day.

Since X and Y are equal, we can substitute one of them for the other:

P - 18 = 5 * (P - 24) / 8

Expanding the right side and solving for P, we find that P = 288 pages.

Step-by-step explanation:

Answer: 20 units

Step-by-step explanation: Set the two half diagonal values equal to each other. When you solve for x, the value is 3. Substitute it back in and the half diagonals equal 10. Multiply it by two and the dial length is 20. You can use this length for TE because it is a diagonal. Hope this helps!

Domain of function =  {-3 , -4}

Range of function =  {4 , -1 , -4}

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Given,

points on graph of a function are

(-3 , 4) , (-3 , -1) , (-4 , -4)

Range is set of y-values,

Range = {4 , -1 , -4}

Domain is set of x - values

Domain = {-3 , -4}

Hence, Domain and range of function are {-3 , -4} and {4 , -1, -4} respectively.

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The cost of the athletic shoe is $20 meanwhile the cost of the casual shoe is $35.

A system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

Firstly, you should extract the main information of the question.

Next,  you should convert the given text information into equations. See below.

20A+10C=750 (1)

25A+20C=1200 (2)

From the substitution method, you can solve this question by following the steps below:

1) Multiply equation 1 by the number -2. Then, you have:

-40A-20C= -1500 (1)

25A+20C=1200 (2)

2) Sum the previous equations presented in step 1.

-15A=-300

15A=300

A=300/15

A=20

3) Find the variable C from equation 2. In step 2, you find  A=20, thus.

25A+20C=1200 (2)

25*20+20C=1200

500+20C=1200

20C=1200-500

20C=700

C=700/20

C=35

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Answer:

[tex] {x}^{4} - 2x + 8 \div x[/tex]

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

The equation for this problem is this:

First, we need to find a common denominator between  [tex]\frac{5}{3}[/tex] and [tex]\frac{2}{9}[/tex].

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

To find the common denominator, we can multiply the denominators, 3 and 9.

Now we know that the two new fractions are going to have a denominator of 27.

Now, we can use these equations to solve for the numerator.

Now, the fractions look like this:

To add them together, we can use this equation:

Now, we need to convert [tex]1 \frac{9}{8}[/tex] into an improper fraction.

An improper fraction is a fraction that has a numerator that is greater than the denominator. For example, [tex]\frac{3}{2}[/tex] is a improper fraction.

To convert [tex]\frac{51}{27}[/tex] and [tex]\frac{17}{8}[/tex] into common denominators, we need to multiply the denominators, like we did above.

The new fractions will look like this:

To solve for the numerators, we can use these equations:

The fractions now look like this:

Now, convert them to mixed numbers.

Therefore, 5 thirds + 2 ninths < 1 9/8.

[tex]-1+6x < 5[/tex]

Simplify:

[tex]6x-1 < 5[/tex]

Add 1 to both sides:

[tex]6x-1+1 < 5+1[/tex]

[tex]6x < 6[/tex]

Divide both sides by 6:
[tex]\dfrac{6x}{6} < \dfrac{6}{6}[/tex]

[tex]\boxed{x < 1}[/tex]

Answer:

see explanation

Step-by-step explanation:

(6)

given f(x) then - f(x) represents a reflection in the x- axis

given f(x) then f(x) + c represents a vertical translation of f(x)

• if c > 0 then a shift up of c units

• if c < 0 then a shift down of c units

thus g(x) = - | x | + 2

is a reflection over the x- axis and vertical shift up of 2 units

(7)

f(2) means value of f(x) when x = 2

x = 2 is in the interval x ≥ 2 with f(x) = [tex]\sqrt{x-2}[/tex] , then

f(2) = [tex]\sqrt{2-2}[/tex] = [tex]\sqrt{0}[/tex] = 0

Answer:

Step-by-step explanation:

The formula for kinetic energy is:

KE = (1/2) * m * v^2

where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

We are given the mass of the pick-up truck as 1500 kg and its velocity as 31.0 m/sec. We can plug these values into the formula to calculate its kinetic energy:

KE = (1/2) * m * v^2

= (1/2) * 1500 kg * (31.0 m/sec)^2

= (1/2) * 1500 kg * 961.0 m^2/sec^2

= 720750 J

Therefore, the kinetic energy of the pick-up truck is 720750 Joules.

r

Step-by-step explanation:

v