Simplify using the distributive property.
8(y + 12)
8y=12
20y
20 - y
8y + 96​

Answer:

1.  6x

2. -3x + 2

3. -4x - 4

4. 4x + 11

5. -8x + 9

6. -14x - 18

Step-by-step explanation:

1. Finding sum of -3x+9x

As both the terms have different signs, the terms will be subtracted and the sign in the answer will be of the larger terms (the term with greater coefficient)

So the answer of -3x+9x is 6x

2. Finding the sum of -7x and 4x + 2

For sum,

-7x + (4x+2)

= -7x + 4x + 2

= -3x + 2

3. Finding the difference when 6x is subtracted from 2x - 4

= 2x - 4 - (6x)

= 2x - 4 - 6x

= 2x - 6x - 4

= -4x - 4

4. Finding the difference when -3x - 7 is subtracted from x + 4

= (x+4) - (-3x-7)

= x + 4 + 3x + 7

= x + 3x + 4 + 7

= 4x + 11

5. Finding the result when 13x + 2 is subtracted from 11 + 5x

= (11 + 5x) - (13x + 2)

= 11 + 5x - 13x - 2

= 5x - 13x + 11 - 2

= -8x + 9

6. Finding the result when -18x - 4 is added to 4x - 14

= (4x - 14) + (-18x - 4)

= 4x - 14 - 18x -4

= 4x - 18x - 14 - 4

= -14x - 18

..

A random variable can be either discrete or continuous. It is discrete it can assume only a finite number of values, or a countable infinity of values at most.

It is continuous if it can assume values in an interval, or in general, an uncountable infinity of values.

That being said, we have:

Option A is a discrete random variable, because the number of heads in 5 throws can be 0, 1, 2, 3, 4 or 5. So, we have finitely many possible values.

Option B is a discrete random variable, because the number you roll on a die is either1, 2, 3, 4, 5 or 6. So, we have finitely many possible values.

Option C is a discrete random variable, because if there are n students in a class, the number of boys is an integer between 0 and n. So, we have finitely many possible values.

Option D is finally a continuous random variable, because the height of a 10-year-old can be any number (in a suitable range of course).

Final answer:

The example of a continuous random variable is D. Height of 10-year-olds, as height is a measured quantity that can have various values on a continuous scale.

Explanation:

When considering which of these is an example of a continuous random variable, it is important to understand the difference between discrete and continuous random variables. A discrete random variable consists of countable values, such as the number of heads when flipping a coin, whereas a continuous random variable includes values that are measured on a continuous scale, such as weight or height. Therefore, the correct answer to the student's question is D. Height of 10-year-olds because height is measured rather than counted, and it can take on a theoretically infinite number of values within a range.

[tex]s = \frac{a + b}{2} \times h[/tex]

S = (19+23)/2×14

S = 42/2×14

S = 21×14

S = 294 cm^2

Answer294

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]|4r-2|>8\iff4r-2>8\ \vee\ 4r-2<-8\qquad\text{add 2 to both sides}\\\\4r>10\ \vee\ 4r<-6\qquad\text{divide both sides by 4}\\\\r>\dfrac{10}{4}\ \vee\ r<\dfrac{-6}{4}\\\\r>\dfrac{5}{2}\ \vee\ r<-\dfrac{3}{2}\\\\r>2.5\ \vee\ r<-1.5[/tex]

<, > - open circle

≤, ≥ - closed circle

<, ≤ - line to the left

>, ≥ - line to the right

Answer:

C. $199.84

Step-by-step explanation:

The price of an upholstery fabric is $ 12.49 per yard.

This means that 1 yard costs $ 12.49

Now we want to find the cost of 16 yards of the upholstery fabric.

We just have to multiply $12.49 by 16.

We multiply to obtain:

[tex]12.49\times 16=199.84[/tex]

Therefore 16 yards will cost $ 199.84

The correct answer is C.

The answers are:

Question 7:

154.29°

Question 8:

Yes, because the opposite sides are congruent.

For question 7:

We know that the sum of all interior angles of any polygon is determined by the following formula:

[tex]Angles=180*(sides-2)[/tex]

Therefore the sum of all interior angles of a 14-gon is equal to 2160°, so, the measure of each interior angle is given by the following calculation:

[tex]14-gon=(14-2)*180\°=2160\°[/tex]

Each interior angle is equal to:

[tex]\frac{2160\°}{12}=154.29\°[/tex]

For question 8:

We know that a quadrilateral is a parallelogram when the opposite sides are parallel or congruent.

From the statement we know that:

BE≅ED

and

AE≅EC

So, we can assume that the triangles formed by the sides BE and AE, and the sides EC and ED, are also congruent, meaning that the opposite sides BA and CD are congruent, so, the quadrilateral is a parallelogram.

Have a nice day!

Answer:

[tex] g ( x ) * f ( x ) = ( x + 9 ) ^ 2 [/tex]

Step-by-step explanation:

We are given the following two functions and we are to find [tex]g(x) * f(x)[/tex]:

[tex]f(x)=x2-81[/tex]

[tex]g(x)=(x - 9)^{-1} ( x + 9)[/tex]

[tex]g(x)*f(x)=x^{-81} * \frac{x+9}{x-9}[/tex]

[tex]g ( x ) * f ( x ) =\frac{(x+9)(x-9)(x+9)}{x-9}[/tex]

[tex] g ( x ) * f ( x ) = ( x + 9 ) ( x + 9 ) [/tex]

[tex]  g ( x ) * f ( x ) =( x + 9 ) ^ 2 [/tex]

For this case we have the following fusions:

[tex]f (x) = x ^ 2-81\\g (x) = (x-9) ^ {- 1} * (x + 9)[/tex]

We can rewrite g (x) as:

According to the following power property:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Also:

If we factor f (x) we have:

[tex]f (x) = (x + 9) (x-9)[/tex]

We must find:

[tex]f (x) * g (x) = (x + 9) (x-9) * \frac {(x + 9)} {(x-9)}[/tex]

We simplify common terms in numerator and denominator:

[tex]f (x) * g (x) = (x + 9) ^ 2[/tex]

ANswer:

[tex]f (x) * g (x) = (x + 9) ^ 2[/tex]

AC would be the sum of ab plus bc.

AC = 9 + 12 = 21

Answer:

A.

9 centimeters

B.

12 centimeters

C.

15 centimeters

D.

18 centimeters

heres the answer choices, i need this too!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

From first piece -6 < x ≤ 0.

From second piece 0 < x ≤ 4.

Therefore -6 < x ≤ 4 → x ∈ (-6, 4]

-7 ∉ (-6, 4]

-6 ∉ (-6, 4]

4 ∈ (-6, 4]

5 ∉ (-6, 4]

Answer:

3 -1 > 1/4

Step-by-step explanation:

On the left hand side we have the expression;

3 - 1

3- 1 = 2

On the right hand side we have the value;

1/4

Therefore we are comparing 2 and 1/4

Since 2 is greater than 1/4 we have;

2 > 1/4

3 -1 > 1/4

Answer:

18x + 27

Step-by-step explanation:

Distribute

-9(-2x-3)

18x + 27

Solution

18x + 27

Answer:

18x + 27

Step-by-step explanation:

- (8) * - (5 ) is = + 40

-----------------------------

-9( - 2x -3)

(-9*-2) + (-9*-3)

(18x )+(27)

18x + 27

Answer:

DATA GATHERING

Step-by-step explanation:

Answer:

x>-3 is the answer hope it helps

Answer:

4 or up

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 sides of the top cube is exposed.

so we get 1*1*5 = 5 in ^2

the second cube has 4 sides exposed also, so 2^2 * 4 = 16 in ^2, but also it has one side with the cube on top, so we have 4-1 = 3 on that side, so the overall is 19 in ^2

Then we have for the 3rd cube 5 sides exposed, so we have 3^2 * 5 = 45. We also have the area of the 2 in cube on it, so we get 3^2 - 2^2 = 9-4 =5.

So the overall is 45+5+19+5 = 55+19 =74

I hope im right sorry if im not!

The surface area of the three cube tower is 71 square inches.

Calculating the Surface Area of a Three Cube Tower

To find the surface area of the three cube tower, we need to carefully consider how the cubes are stacked and which faces are exposed.

Calculate the surface area of each individual cube:

Each face is 3x3 = 9 sq. inches. Since a cube has six faces, the total surface area is 6 x 9 = 54 sq. inches.

    2. For the 2-inch cube:

       Each face is 2x2 = 4 sq. inches. The surface area is 6 x 4 = 24 sq. inches.

    3. For the 1-inch cube:

        Each face is 1x1 = 1 sq. inch. The surface area is 6 x 1 = 6 sq. inches.

Consider overlapping faces between stacked cubes:

Combine the visible surface areas:

Therefore, the surface area of the three cube tower is 71 square inches.

Answer:

c. 28 liters

Step-by-step explanation:

Given tha tJanet is mixing a 15% glucose solution with a 35% glucose solution. This mixture produces 35 liters of a 19% glucose solution. Now we need to find about how many liters of the 15% solution is Januet using in the mixture.

Let the number of liters of the 15% solution is Januet using in the mixture = x

Let the number of liters of the 35% solution is Januet using in the mixture = y

Then we get equations:

x+y=35...(i)

and

(15% of x) + (35% of y) = 19% of 35.

or

0.15x+0.35y=0.19(35)

15x+35y=19(35)

3x+7y=19(7)

3x+7y=133 ...(ii)

solve (i) for x

x+y=35

x=35-y...(iii)

Plug (iii) into (ii)

3x+7y=133

3(35-y)+7y=133

105-3y+7y=133

105+4y=133

4y=133-105

4y=28

y=28/4

y=7

plug y=7 into (iii)

x=35-y=35-7=28

Hence final answer is c. 28 liters

Answer: C on edge:)

Step-by-step explanation:

Answer:

60√5

Step-by-step explanation:

(5√5)(6√4)

= (5√5)(12)

= 60√5

Answer:

$101.99

Step-by-step explanation:

She doesn't go over her 200 free miles.

If she drives 155 miles, then the amount she need to pay for the rental is:

                          $ 101.99

She got a special weekend rental deal for $101.99, with 200 free miles.

and $0.32 per mile after.

This means that for any mile covered less than or equal to 200 she just need to pay $ 101.99.

If she drives 155 miles, which is less than 200 miles then the amount she need to pay as a rent is:

             $ 101.99

Answer:

p = 80- 64 = 16

p = 16

Step-by-step explanation:

That's is the answer

Nandini needs to score at least 17 points to win.

To represent the number of points Nandini needs to win the game, we can use the inequality:

[tex]\( p > 80 - 64 \)[/tex]

Now, let's solve this:

[tex]\( p > 16 \)[/tex]

Therefore, Nandini needs more than 16 points to win the game.

Explanation:

1. Nandini needs more than 80 points to win the game, which means her total score should exceed 80 points.

2. She currently has 64 points, so to find out how many more points she needs, we subtract her current score from the total required points: \( 80 - 64 = 16 \).

3. Hence, the inequality representing the number of points she needs, denoted by \( p \), is \( p > 16 \), indicating that she needs more than 16 points to win the game.

This means Nandini needs to score at least 17 points to win.

Complete question:

Nandini needs more than 80 points to win a game. She has 64 points so far. which inequality represents p, the number of points she needs to win the game

Calculate half the base by multiplying the length of a side ( 60 cm) by the fraction of the ratio from the base to the vertex ( 5/12).

Then multiply that by 2 for the width of the base.

60 x 5/12 = 300/12 = 25 cm.

Full width = 25 x 2 = 50 cm.

Answer:

Full width = 25 x 2 = 50

Answer:

The sum is [tex]S=\frac{16}{5}=3.2[/tex]

Step-by-step explanation:

To find the sum of the infinite geometric series we must first find the common ratio r.

The series is:

4-1 + 1 / 4-1 / 16 +

[tex]r =\frac{a_{n+1}}{a_n}[/tex]

[tex]r=\frac{-1}{4}=-\frac{1}{4}\\\\r=\frac{\frac{1}{4}}{-1}=-\frac{1}{4}[/tex]

Then the common ratio r is

[tex]r=-\frac{1}{4}[/tex]

The first term is: [tex]a_1=4[/tex]

By definition when [tex]0 <| r | <1[/tex] then the sum of the infinite sequence is:

[tex]S=\frac{a_1}{1-r}\\\\S=\frac{4}{1-(-\frac{1}{4})}\\\\S=\frac{4}{\frac{5}{4}}\\\\S=\frac{16}{5}[/tex]

Answer:

The answer is 32.45

Step-by-step explanation:

d ≅ 272ft. A car that is traveling at 70mph it will stop 272ft after the brakes are applied.

The key to solve this problem is using the equation d = k(r²), where d is the distance after the brakes are applied, k is the desaceleration constant and r is the speed of the car.

In order to maintain the consistency of the units, we have to convert mph to ft/s using the equation ft/s = mph x 1.467.

30mph x 1.467 ≅ 44ft/s

We know the speed of the car and the distance travelled after brakes are applied. The, clear k for the equation d = k(r²)

k = d/(r²)

Solving with d = 50ft and r = 44 ft/s

k = 50ft/(44ft/s)²= 0.0258 s²/ft

Then, is the same car now is traveling at 70mph, how many feet will it take to stop?

Convert 70mph to ft/s

70mph x 1.467 = 102.69ft/s

Using the equation d = k(r²), where k = 0.0258 s²/ft and r = 102.69ft/s

d = 0.0258s²/ft[(102.69ft/s)²] = 272.06ft

Answer:

(x - 3), (x + 2), (x + 1) and (x + 3)

Step-by-step explanation:

Using synthetic division, I'd begin by testing various factors of -18 to determine whether any of them will divide into f(x)=x^4+3x^3-7x^2-27x-18 with no remainder.  Note that possible factors of -18 are ±1, ±2, ±3, ±6, ±18.

Let's arbitrarily start with -3.  In synthetic division, will the divisor yield a zero remainder ( which would tell us that -3 is a root of f(x)=x^4+3x^3-7x^2-27x-18 and that (x + 3) is a factor)?

-3   )   1    3    -7    -27    -18

              -3    0      21    +18

     ------------------------------------

         1      0    -7     -6      0  

Since the remainder is zero, -3 is a root and (x + 3) is a factor.  The coefficients of the quotient are shown above:  1  0  -7  -6.  Possible factors of 6 include ±1, ±2, ±3, ±6.  Arbitrarily choose 2.  Is this a root or not?

2    )    1     0     -7    -6

                 2     4     -6

      --------------------------

          1       2     -3    -12    

Here the remainder is not zero, so +2 is not a root and (x - 2) is not a factor.

Continuing to use synthetic division, I find that -1 is a root and (x + 1) is a factor, because the remainder of synth. div. is zero.  The coefficients of the quotient are 1, -1 and -6, which represents the quadratic y = x^2 - x - 6, whose factors are (x - 3)(x + 2).

Thus, the four factors of the original polynomial are (x - 3), (x + 2), (x + 1) and (x + 3).

The Volume is approximately 226

To find the volume of the cylindrical barrel with a height of 8 feet and a diameter of 6 feet, use the formula V = πr²h where r is the radius and h is the height. The approximate volume is approximately 226.08 cubic feet.

The approximate volume of the cylindrical barrel can be calculated using the formula V = πr²h.

Given that the diameter is 6 feet, the radius (r) would be half of the diameter, which is 3 feet. The height (h) is 8 feet.

Substitute the values into the formula to find the volume: V ≈ 3.14 × (3)² × 8 ≈ 226.08 cubic feet.

Answer:

12

Step-by-step explanation:

Hi

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Equation A is linear and equation B is nonlinear

Answer:

Equation A is linear and equaiton B is nonlinear

Step-by-step explanation:

Equation A respresents a straight line with a x-intercept of x=-3/2 and a y-intercept of y = -2. This equation is linear because it is a first degree polynomical equation with x^1 = x

Equation A is not a linear equation and is written as :

[tex]y=3/(x+5)[/tex]  

This is a rational function but it is not linear because x is in the denominator and not numerator.

Answer:

[tex]-\frac{7}{3}[/tex]

Step-by-step explanation:

To solve this, we are using the average rate of change formula:

[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]

where

[tex]m[/tex] is the average rate of change

[tex]a[/tex] is the first point

[tex]b[/tex] is the second point

[tex]f(a)[/tex] is the function evaluated at the first point

[tex]f(b)[/tex] is the function evaluated at the second point

We want to know the average rate of change of the function [tex]f(x)=0.5^x-6[/tex] form x = -3 to x = 0, so our first point is -3 and our second point is 0. In other words, [tex]a=-3[/tex] and [tex]b=0[/tex].

Replacing values

[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]

[tex]m=\frac{0.5^0-6-(0.5^{-3}-6)}{0-(-3)}[/tex]

[tex]m=\frac{1-6-(8-6)}{3}[/tex]

[tex]m=\frac{-5-(2)}{3}[/tex]

[tex]m=\frac{-5-2}{3}[/tex]

[tex]m=\frac{-7}{3}[/tex]

[tex]m=-\frac{7}{3}[/tex]

We can conclude that the average rate of change of the exponential equation form x = -3 to x = 0 is [tex]-\frac{7}{3}[/tex]

Answer:

38.46%

Step-by-step explanation:

There are 91 students and 35 of them received a score of 90 or above.

So, there are 35/91 students with an A grade.

The probability to pick a random student that would be the same proportion that those who got the right score, so 35 / 91 = 0.3846 or 38.46%

38.46% of chances to pick someone who got an A (90 score or above), and, the opposite, 61.54% of chances to pick someone who didn't get an A.  That's a strong class!

Answer:

38.46% of the class received an "A"

Step-by-step explanation:

The Class has a total student count of 91 students. Out of those 91 students 35 of them received an "A" (90 or above). Meaning the percentage of students in the whole class who received a 90 or above is calculated by dividing the amount of students who received an "A" by the total amount of students in the class, as shown below.

[tex]\frac{35}{91} = 0.3846[/tex]

0.3846 * 100 = 38.46% ...... we multiply the decimal by 100 to get the percent

So 38.46% of the class received an "A"

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

The answer is the fourth choice , I think

The symbol for congruent in mathematics is ≅. It signals that two figures have the same shape and size, and is vital in ensuring dimensional consistency in equations, analogous to ensuring that measurements are directly comparable.

The mathematical symbol for congruent is ≅. This symbol is used to denote that two figures are of the same size and shape. When dealing with equations, it is important that both sides of the equation have the same dimensions, meaning they can be directly compared or equated. For instance, you cannot sensibly add two quantities of different dimensions, similar to the saying "You can't add apples and oranges". In geometry, congruent figures are identical in form and dimension, just as measurements must be commensurate within equations to maintain dimensional consistency.

Another important concept in mathematics and physics is dimensional analysis, where different physical quantities are expressed with respect to their basic unit dimensions, such as length (L), mass (M), and time (T). Comparing measurements of different units also falls under this analysis. To indicate two measurements are related but not necessarily the same, we can use inequality symbols or symbols like ≈ (approximately) when numbers are close in value but not exactly equal.

The correct option is C.

In an isosceles triangle ABC with base angles A and the sides b and c equal, you can use the Law of Cosines to find the length of the other side (a) in terms of b and c. The Law of Cosines is given by:

[tex]\[a^2 = b^2 + c^2 - 2bc \cos(A)\][/tex]

Given that A = π/4, b = c = 4, you can substitute these values into the equation:

[tex]\[a^2 = 4^2 + 4^2 - 2 \cdot 4 \cdot 4 \cos\left(\frac{\pi}{4}\right)\][/tex]

Simplify the expression:

[tex]\[a^2 = 16 + 16 - 32 \cos\left(\frac{\pi}{4}\right)\][/tex]

Now, you know that [tex]\(\cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}\)[/tex], so substitute that in:

[tex]\[a^2 = 16 + 16 - 32 \cdot \frac{\sqrt{2}}{2}\][/tex]

[tex]\[a^2 = 32 - 16\sqrt{2}\][/tex]

Now, factor out 16 from the expression:

[tex]\[a^2 = 16(2 - \sqrt{2})\][/tex]

So, the correct answer is:

[tex]\[a^2 = 4^2(2 - \sqrt{2})\][/tex]

Complete the question:

Suppose an isosceles triangle ABC has A= π /4 and b=c=4. What is the length of a^2 ？ A. 4^2sqrt(2) B. 4^2(sqrt(2)-2) C. 4^2(2-sqrt(2)) D. 4^2(2+sqrt(2))

Final answer:

By applying the Pythagorean theorem to the 45-45-90 isosceles triangle, we find that since both the sides a and b are 4, the square of side a is a² = 16.

Explanation:

In the context of an isosceles triangle with sides labeled a, b, and c, where side a is opposite angle A and side b equals side c, we can utilize the Pythagorean theorem to find the length of side a given that it's a right triangle. The Pythagorean theorem states:

a² + b² = c².

Given that angle A = π/4 radians (45 degrees), it implies that triangle ABC is a 45-45-90 right triangle, which tells us that sides a and b are equivalent in length. Under these conditions, the Pythagorean theorem simplifies to:

2a² = c².

We're given that b = 4, accordingly a would also be 4 (since a=b in an isosceles right triangle), and we're asked to find the length of a². Squaring side a, we get:

a² = 4² = 16.

Therefore, the length of a² is 16.