Simplify:

2(d + 3) + 3(d – 3)
A. –5d – 1
B. 5d – 3
C. 5d + 15
D. 6d – 3

Answer:

[tex]1.\ 8n+4\\\\2.\ 5x+13\\\\3.\ x+3\\\\4.\ x-6\\\\5.\ 4x+1[/tex]

Step-by-step explanation:

1.

[tex]Sum=2n+6+6n-2\\\\Sum=2n+6n+6-2\ \ \ \ \ \ \ \ (using\ commutative\ property\ of\ addition\ a+b=b+a)\\\\Sum=8n+4[/tex]

2.

[tex]Sum=3x+9+2x+4\\\\Sum=3x+2x+9+4\ \ \ \ \ \ \ \ (using\ commutative\ property\ of\ addition\ a+b=b+a)\\\\Sum=5x+13[/tex]

3.

[tex]Difference=(3x+5)-(2x+2)\\\\Difference=3x+5-2x-2\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=3x-2x+5-2\ \ \ [commutative\ property]\\\\Difference=x+3[/tex]

4.

[tex]Difference=(4x+3)-(3x+9)\\\\Difference=4x+3-3x-9\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=4x-3x+3-9\ \ \ [commutative\ property]\\\\Difference=x-6[/tex]

5.

[tex]Difference=(6x+2)-(2x+1)\\\\Difference=6x+2-2x-1\ \ \ \ \ \ \ [using\ distributive\ property\ -(a+b)=-a-b]\\\\Difference=6x-2x+2-1\ \ \ [commutative\ property]\\\\Difference=4x+1[/tex]

The solution to the system of equations is x = -2 and y = 4

How to solve the equation

To solve this system of equations using Cramer's rule, we need to first express the equations in standard form: Ax + By = C

According to the problem, we have the equations

4x + 3y - 4 = 0

6x = 8 - 5y.

This is the same as

4x + 3y = 4

6x + 5y = 8

The determinants required for Cramer's rule:

Coefficient matrix (D)

[tex]\[D = \begin{vmatrix} 4 & 3 \\ 6 & 5 \end{vmatrix} = (4 \times 5) - (3 \times 6) = 20 - 18 = 2\][/tex]

For Dₓ

[tex]\[D_x = \begin{vmatrix} 4 & 3 \\ 8 & 5 \end{vmatrix} = (4 \times 5) - (3 \times 8) = 20 - 24 = -4\][/tex]

For D y

[tex]\[D_y = \begin{vmatrix} 4 & 4 \\ 6 & 8 \end{vmatrix} = (4 \times 8) - (4 \times 6) = 32 - 24 = 8\][/tex]

Using Cramer's rule:

[tex]\[x = \frac{D_x}{D} = \frac{-4}{2} = -2\][/tex]

[tex]\[y = \frac{D_y}{D} = \frac{8}{2} = 4\][/tex]

complete question

Solve the following simultaneous equations using Cramer's rule.

4x + 3y - 4 = 0

6x = 8 - 5y

Answer:

The stage directions describe how characters react to Helen.

Step-by-step explanation:

In the given scene, the different characteristics of Helen as well as how other characters react when they see Helen is depicted in the scene. Other characters in the scene react differently to Helen when they come in contact with her. This is the main objective of the stage direction. It shows the interaction between Helen and others.

The stage directions represent the additions of the meaning to the play in terms of the stage directions describe how characters react to Helen.

The following information should be considered:

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It costs $ 30240 to stain floor of the entire room

Solution:

Given that,

Sgt. Merritt has bought a house now that his tour of duty is up

He wants to stain the wood floors of the living room, which measure 18 x 14

Therefore,

length = 18 yards

Width = 14 yards

[tex]Area = length \times width\\\\Area = 18 \times 14\\\\Area = 252[/tex]

Thus area of wood floors is 252 square yards

The stain costs $120 per square yard

[tex]Cost = 252 \times 120\\\\Cost = 30240[/tex]

Thus it costs $ 30240 to stain floor of the entire room

To stain Sgt. Merritt's living room floors, which measure 18x14 feet, first calculate the area in square feet, convert to square yards, and then multiply by the cost per square yard. The total cost will be $3,360.

To determine the cost to stain the wood floors in the living room, first we need to calculate the total area in square yards since the stain is sold by square yard. The room measures 18 feet by 14 feet.

Step 1: Calculate Square Footage

Multiply the length and width in feet to get the square footage:

18 feet × 14 feet = 252 square feet

Step 2: Convert Square Feet to Square Yards

There are 9 square feet in 1 square yard. Therefore, we divide the total square footage by 9 to convert to square yards:

252 square feet / 9 square feet per square yard = 28 square yards

Step 3: Calculate the Cost

The cost to stain one square yard is $120. So, we multiply the total square yards by $120 to get the total cost:

28 square yards × $120 per square yard = $3,360

Therefore, the cost to stain the entire living room floor will be $3,360.

Answer:

30 people.

Step-by-step explanation:

In a survey it is found that 20% of the people preferred umpt juice to all other juices.

Now, if 6 of the surveyed people are being preferred umpt juice, then we have to find the total number of people that were surveyed altogether.

So, 20% of the people being surveyed is equal to 6 people.

Therefore, 100% of the people is equal to [tex]6 \times \frac{100}{20} = 30[/tex] people. (Answer)

Answer:

5

Step-by-step explanation:

the answer would be 819

Answer: 5

Step-by-step explanation:

Answer:

0.3859

Step-by-step explanation:

Assuming on the average, a jar of peanut butter contains 452 grams, with a standard deviation of 10.4 grams.

Then we have

[tex] \mu = 452 \: and \: \sigma = 10.4[/tex]

We want to find the probability that a jar contains less than 449 grams.

We first determine the z-score of x=449 grams using:

[tex]z = \frac{x - \mu}{ \sigma} [/tex]

We plug in these values to get:

[tex]z = \frac{449 - 452}{10.4} [/tex]

[tex]z = \frac{ - 3}{10.4} = - 0.29[/tex]

Now we read from the standard normal distribution table the area that corresponds to a z-score of -0.29

P(X<449)=0.3859

To find the probability that a jar contains less than 449 grams, calculate the z-score and use a standard normal distribution table or calculator.

To find the probability that a jar contains less than 449 grams, we can use the standard normal distribution and the z-score formula. The z-score is calculated as (X - mean) / standard deviation. In this case, X = 449, mean = 452, and standard deviation = 10.4. By substituting these values into the formula, we can find the z-score, and then use a standard normal distribution table or calculator to find the probability.

1. Calculate the z-score: (449 - 452) / 10.4 = -0.2885

2. Use a standard normal distribution table or calculator to find the probability associated with a z-score of -0.2885. The probability is approximately 0.3830, or 38.30%.

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The wavelength of an electromagnetic wave with a frequency of 135,000 Hz is approximately 2,222 meters. This can be calculated using the equation λ = c / f, with c being the speed of light and f the frequency of the wave.

The wavelength of an electromagnetic wave can be calculated from the frequency when we understand their relationship through the wave's speed. In the case of an electromagnetic wave, this speed is the speed of light (denoted by c), which is approximately 3.00 x 108 m/s. This relationship is expressed by the equation c = fλ, where f is the frequency and λ is the wavelength.

To calculate the wavelength (λ) from the frequency (f), we rearrange the equation to λ = c / f. Substituting 3.00 x 108 m/s for c and 135,000 Hz for f, gives λ = 3.00 x 108 m/s / 135,000 Hz. After performing the calculation, we find the wavelength to be approximately 2,222 meters.

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The wavelength of an electromagnetic wave with a frequency of 135,000 Hz is approximately 2,222 meters, based on the relationship provided by the equation c = fλ.

The wavelength of an electromagnetic wave is directly related to its frequency by the equation c = fλ, where 'c' is the speed of light in vacuum, 'f' is the frequency and 'λ' is the wavelength. In this equation, the speed of light 'c' is typically 3.00 × 108 m/s. Therefore, if we want to figure out the wavelength of an electromagnetic wave with a frequency of 135,000 Hz, we can rearrange the equation to solve for the wavelength: λ = c/f. Substituting the given values, we have λ = (3.00 × 108 m/s)/(135,000 s-1), which simplifies to λ = 2,222 m.

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Answer:

39 percent is increase in mileage.

Thus, the correct option is B. 39%.

Step-by-step explanation:

Given:

A runner increased her distance from 9 miles to 12.5 miles a week.

Now, to find percent increase in mileage.

Previous mileage = 9 miles.

Present mileage = 12.5 miles.

Mileage increase = 12.5 - 9 = 3.5 miles.

Now, to get the percent increase in mileage:

[tex]\frac{Mileage\ increased}{previous\ mileage} \times 100[/tex]

[tex]=\frac{3.5}{9} \times 100[/tex]

[tex]=\frac{350}{9}[/tex]

[tex]=38.88\%.[/tex]

Approximately the percent increase = 39%.

Therefore, 39% is increase in mileage.

Thus, the correct option is B. 39%.

Answer:

5

Step-by-step explanation:

7 + (5 - 9)2 +3(16/8)

7 + (-4)2 +3(2)

7+(-8) +6

7 -8 +6

7 -2

5

Answer:

40(x-10)

Step-by-step explanation:

x = 0,1

y = 0,-5

hope this helped  ___~ ~___

                                      0

\

Answer:

16

Step-by-step explanation:

Using the Remainder theorem

f(x) divided by (x + h) then the remainder is the value of f(- h)

here the divisor is (x + 3), thus remainder is f(- 3)

remainder = 5(- 3)² + 9(- 3) - 2 = 5(9) - 27 - 2 = 45 - 29 = 16

Answer:

Step-by-step explanation: Area =length × width

7050m^2 = X× 75m

7050 =75X

Divide both sides by 75

7050÷75 =75÷75

74m= X

Answer:

The probability that Jenny picked a gray tile with her second pick given that she picked a blue tile with her first pick = 0.25

Step-by-step explanation:

i.) there are 6 gray tiles and 3 blue tiles

ii) the probability that Jenny picked a blue tile first is given by

[tex]\frac{number\hspace{0.1cm} of \hspace{0.1cm} blue\hspace{0.1cm} tiles }{total \hspace{0.1cm}number\hspace{0.1cm} of \hspace{0.1cm}tiles\hspace{0.1cm} } = \frac{3}{9} = \frac{1}{3}[/tex]

iii) the probability that Jenny picked a gray tile with her second pick without replacing the first tile[tex]\frac{number\hspace{0.1cm} of \hspace{0.1cm} blue\hspace{0.1cm} tiles }{total \hspace{0.1cm}number\hspace{0.1cm} of \hspace{0.1cm}tiles\hspace{0.1cm} } \times \frac{number\hspace{0.1cm} of \hspace{0.1cm} gray\hspace{0.1cm} tiles }{total \hspace{0.1cm}number\hspace{0.1cm } of \hspace{0.1cm}tiles\hspace{0.1cm} - 1 } = \frac{3}{9} \times \frac{6}{8} = \frac{1}{3} \times \frac{3}{4} = \frac{1}{4} = 0.25[/tex]

The probability that Jenny picked a gray tile with her second pick given that she picked a blue tile with her first pick = 0.25

P = perimeter

L = length

W = width

Formula for the perimeter of a rectangle = L + L + W + W  or  P = 2L + 2W

You know:

P = 110ft

L = W + 5  [length is 5ft greater than the width]

So plug this into the formula:

P = 2L + 2W             Substitute/plug in (W + 5) for L

110 = 2(W + 5) + 2W           Distribute/multiply 2 into (W + 5)

110 = (2)W + (2)5 + 2W

110 = 2W + 10 + 2W       Combine like terms (2W + 2W)

110 = 4W + 10       Subtract 10 on both sides

110 - 10 = 4W + 10 - 10

100 = 4W     Divide 4 on both sides to get "W" by itself

[tex]\frac{100}{4}=\frac{4W}{4}[/tex]

25 = W        Now that you know the width, plug it into the equation for length

L = W + 5       Plug in 25 for W

L = 25 + 5

L = 30

L = 30 ft

W = 25 ft

PROOF

P = 2L + 2W

110 = 2(30) + 2(25)

110 = 60 + 50

110 = 110

Answer:

False

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

The 5 in 458,039 is 100 times greater than the 5 in 271,145 because it represents 50,000 while the 5 in 271,145 represents 500. This can be determined by understanding place values, as each digit's value depends on its position in the number.

The 5 in 458,039 is in the ten thousands place, meaning it represents 50,000. The 5 in 271,145 is in the hundreds place, meaning it represents 500. To understand how many times greater one is than the other, we would divide 50,000 by 500. The result is 100, therefore, the 5 in 458,039 is 100 times greater than the 5 in 271,145. So, the answer is B. 100.

This problem involves place values in numbers, where each digit in a number has a different value depending on its position.

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Answer:

3)  x = 15; 95 and 85      4)  x = 12; 98 for both angles

Step-by-step explanation:

2x + 65 + 3x + 40 = 180       Set the equations equal to 180

5x + 105 = 180                      Combine like terms

     - 105  - 105                      Subtract 105 from both sides

5x = 75                                  Divide both sides by 5

x = 15

Plug 15 into both equations

2(15) + 65 = 95

3(15) + 40 = 85

4)  5x + 38 = 9x - 10             Set the equations equal to each other

  - 5x          - 5x                    Subtract 5x from both sides

 38 = 4x - 10

+ 10       + 10                         Add 10 to both sides

48 = 4x                                  Divide both sides by 4

12 = x

Plug 12 into both equations

5(12) + 38 = 98

9(12) - 10 = 98

1 million is 1*10^6

300 thousand is 3*10^5

Since 300,000 is one power of ten below 1 million, it's either A or B.

The correct choice is A, however, because of 1 million being 10^6. We choose the biggest value we get.

Hope this helped!

The options that  can be angle measures of a triangle is

2. Set: 25°, 130°, 25°

How to find measure of triangle

To determine whether a set of three angle measures can be the angle measures of a triangle, you can use the sum of internal angles of a triangle which is 180 degrees

Let's analyze each set of three angle measures:

1. Set: 41°, 112°, 52°

41 + 112 + 52 = 205

This cannot be a triangle

2. Set: 25°, 130°, 25°

25 + 130 + 25 = 180

This can be a triangle

3. Set: 30°, 40°, 90°

30 + 40 + 90 = 160

This cannot be a triangle

4. Set: 132°, 141°, 31°

132 + 141 + 31 = 304

This cannot be a triangle

Step-by-step explanation:

Hope it helps you in your learning process.

Answer:

C

Step-by-step explanation:

(4√6)/(5√6)

= 6^(¼) ÷ 6^(1/5)

= 6^(1/4 - 1/5)

= 6^[(5-4)/20]

= 6^(1/20

When dividing roots, multiply them together: 4 x 5 = 20

Invert the product: 1/20

Raise the number under the root by that

Answer = 6 ^ 1/20

Answer:

75 sides when the interior angle is 175.2

Step-by-step explanation:

these problems are all done the same way. Subtract the interior angle from 180 and divide the result into 360

360/(180 - 175.2)

360 / 4.8

75 sides

Final answer:

The algebraic expression for half the quantity of X plus Y is (1/2) × (X + Y) or (X + Y) / 2.

Explanation:

To write an algebraic expression for half the quantity of X plus Y, you start by adding X and Y together. This can be represented as (X + Y). To find half of this quantity, you multiply the sum by 1/2 or divide by 2. Therefore, the algebraic expression that represents half the quantity of X plus Y is (1/2) × (X + Y) or (X + Y) / 2.

Answer:

10+20=30

10 is what percent of 30?

10 is 1/3 of 30

Step-by-step explanation:

10 is 33.33% of 30

so 33% of the shirts sold were blue

33.33% of the shirts sold were blue.

Given that, Friday, a store sold 10 blue shirts and 20 white shirts.

We need to find out what percentage of the shirts sold were blue.

The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Now, 10+20=30

We need to calculate 10 is what per cent of 30.

Let the percentage be x.

So, x% of 30=10

⇒x/100 × 30=10

⇒3x/10=10

⇒3x=100

⇒x=33.33%

Therefore, 33.33% of the shirts sold were blue.

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Answer:

2/3x = 10.....multiply both sides by 3/2 giving u :

x = 10 * 3/2  

x = 30/2 which equals 15

Step-by-step explanation:

So your answer is 3/2 or 32

Answer:

[tex]\frac{23}{32}\ hours[/tex]

Step-by-step explanation:

step 1

Find out the number of hours worked by April on her math project

Multiply 1 1/8 by 5 3/4

so

[tex]1\frac{1}{8} (5\frac{3}{4})[/tex]

Convert mixed number to an improper fraction

[tex]1\frac{1}{8}=1+\frac{1}{8}=\frac{1*8+1}{8}=\frac{9}{8}[/tex]

[tex]5\frac{3}{4}=5+\frac{3}{4}=\frac{5*4+3}{4}=\frac{23}{4}[/tex]

substitute

[tex]\frac{9}{8} (\frac{23}{4})=\frac{207}{32}\ hours[/tex]

Convert to mixed number

[tex]\frac{207}{32}=\frac{192}{32} +\frac{15}{32} =6\frac{15}{32}\ hours[/tex]

step 2

How many more hours did April work?

Subtract the hours worked by Carl from the hours worked by April

[tex]\frac{207}{32}-\frac{23}{4}=\frac{207-8*23}{32}=\frac{23}{32}\ h[/tex]

Answer:

83 Hours

Step-by-step explanation:

First do 13x6=78

then add 5 hours to 78 hours and you get 83