Simplify: -2(3x – 2) -5(7 – x)

The dimensions of the region which enclose the maximum area is a side of 162 feet and vertical segment of 108 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the side parallel to the vertical segment and y represent the other side. If the farmer has 648 feet of fencing, hence:

x + x + y + y + x = 648

3x + 2y = 648

y = 324 - 1.5x

Area (A) = xy

A = xy

A = x(324 - 1.5x)

A = 324x - 1.5x²

The maximum area is at A' = 0, hence:

A' = 324 - 3x

324 - 3x = 0

3x = 324

x = 108 feet

y = 324 - 1.5(108) = 162 feet

x = 108 feet, y = 162 feet

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Answer:

Step-by-step explanation:

To find the unit rate, we divide the price by the number of items bought.

In this question:

Price: $99

Items: 9 books

Unit rate: $99/9 = $11

The unit rate is of $11 per book.

Answer:

1/3

Step-by-step explanation:

0.3333...=1/3

The coordinates of the image of polygon A'B'C'D' would be A' (-1, 1), B' (-1, -2), C' (3, -2), D' (3, 2).

A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

Since the pre-image of polygon ABCD is translated (shifted) vertically downward by 4 units and right 5 units, the coordinates of the image of polygon A'B'C'D' would be given by:

(x, y)                    →            (x + 5, y - 4)

Coordinate A = (-6, 5)   →    Coordinate A' (-6 + 5, 5 - 4) = (-1, 1)

Coordinate B = (-6, 2)   →    Coordinate B' = (-6 + 5, 2 - 4) = (-1, -2)

Coordinate C = (-2, 2)   →     Coordinate C' = (-2 + 5, 2 - 4) = (3, -2)

Coordinate D = (-2, 6)   →     Coordinate D' = (-2 + 5, 6 - 4) = (3, 2)

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Answer: c

Step-by-step explanation:

The solution set for the inequality is p > -9.4. See attachment below for the graph.

An open circle is used when the inequality sign involved is ">" or "<". That is, it is used for numbers that are less than or greater than.

An arrow shaded to the right means the solution set is greater than a given value, while an arrow shaded to the left means the solution set includes all values that are less than a given value.

Given the inequality, p + 3.6 > −5.8, solve for p:

p + 3.6 > −5.8

Subtract 3.6 from both sides

p + 3.6 - 3.6 > -5.8 - 3.6

p > -9.4

Thus, the solution set would be all the values that are greater than -9.4. The graph is shown below.

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Answer: x < 9

Step-by-step explanation:

Move all terms not containing x to the right side of the inequality.

Answer:

2000

Step-by-step explanation:

Number of shares after split is 5/2 times the pre split value =800*5/2 = 2000

The fraction of straight section of motor racing circuit is 3/14 miles.

To find the fraction of circuit which is straight, we will perform division. The fraction will be found as - Fraction = length of straight section ÷ total length of motor racing circuit

Keep the values in mentioned relation to find the fraction of circuit which is straight.

Converting the mentioned lengths from mixed fraction to fraction.

Length of motor racing circuit = (6×5 + 5)/6

Length of motor racing circuit = 35/6

Length of straight section of circuit = (4×1 + 1)/4

Length of straight section of circuit = 5/4

Fraction of straight circuit = (5/4)/(35/6)

Simplifying the fraction

Fraction of straight circuit = (5×6)/(35×4)

Performing multiplication in numerator and denominator

Fraction of straight circuit = 30/140

Performing division

Fraction of straight circuit = 3/14 miles

Thus, the straight section is 3/14 miles.

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The measurement deviates from the mean by more than 100 standard deviations.

It's a way to gauge how widely apart each data point is from the mean. The standard deviation formula comes in two different forms: Standard deviation for the population When you can measure the entire population or the entire collection of data, you use the population version of the formula. Experts in statistics have determined that measurements that fall within a 2 SD range of the true value are more accurate than those that do not..

based on the facts provided;

the average population, =100

The standard deviation for the population

σ=10

Z score:

Z=X−μσ

X:The measurement.

The number of standard deviations the measurement is from the mean:

We are not given the measurement. So, assuming the measurement is equal to 139.

When

X=139

Z=139−100/10

=3.9

It implies that the measurement of

139 is 3.9

standard deviation above the mean of 100;

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The equation for the given function passing through (0,5) and (4,0) is equal to y = (-5 /4)x +5.

As given in the question,

As shown in the graph drawn we have

( x₁ , y₁ )=(0, 5)

( x₂ , y₂ )=( 4, 0)

Equation for the given function passing through ( x₁ , y₁ ) = (0, 5) and

( x₂ , y₂ )=( 4, 0) is given by :

( y - y₁ )/ (x -x₁ )=( y₂ - y₁ )/( x₂ - x₁ )

⇒( y -5) / (x -0)=( 0 -5)/( 4 -0)

⇒( y - 5) /x=-5/4

⇒y -5=(-5/4)x

⇒y=(-5/4)x + 5

Therefore, the equation for the given function passing through (0,5) and (4,0) is equal to y=(-5 /4)x +5.

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The result of the function n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex] when x = -2,0 and 5

n(-2) = 4/3

n(0) = 2/3

n(5)  = -1

The function is n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex]

The function is an equation which expression the relationship between one variable and another variable. If one variable is independent variable then another variable will be dependent variable.

The function is n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex]  when x= -2,0 and 5

Here we have to substitute the value of x in the given function

n(-2) = -1-(1/3)(-2)+5/3

= -1+(2/3)+5/3

= 4/3

n(0) = -1-(1/3)(0)+5/3

= -1+(5/3)

= 2/3

n(5) = -1-(1/3)(5)+5/3

=  -1-(5/3)+(5/3)

= -1

Hence, the result of the function n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex] when x = -2,0 and 5

n(-2) = 4/3

n(0) = 2/3

n(5)  = -1

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Grayce has 0.825 g of diamonds and Morgan has 0.824 g of diamonds. Grayce has more grams of diamonds

From the question, we are to determine the person that has more grams of diamonds

From the given information,

"Grayce has three diamonds that weigh 0.275 g each"

and

"Morgan has two diamonds that weigh 0.412 g each"

Thus,

The total mass of Grayce's diamonds is 3 × 0.275 g

3 × 0.275 g = 0.825 g

Also,

The total mass of Morgan's diamonds is 2 × 0.412 g

2 × 0.412 g = 0.824 g

Since 0.825 is greater than 0.824,

Then,

Grayce has more grams of diamonds.

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Answer:

x = 22° (alternate angles, M//N)

Answer69

Step-by-step explanation:

Answer

Step 1:         6,3

Step 2:       x1  -1                     y2- 2

Step 3:           1, 7

Step-by-step explanation:

a) fractions; 15.3/3

b) yes, it is a rational number

Answer:

x = 3y

y + x = 4y = 180

y = 45

x = 135

99th term of the given arithmetic sequence 7, 3, -1, -5, ... is -385.

We are provided with the arithmetic sequence mentioned below;

7, 3, -1, -5, ................. -385

[tex]a_{n}[/tex] =  [tex]a_{1}[/tex] + (n−1)d

where [tex]a_{1}[/tex] is the first term, [tex]a_{n}[/tex] is the nth term and d is the difference between a term and its previous term.

With the help of provided arithmetic sequence we can write;

[tex]a_{n}[/tex] = -385

[tex]a_{1}[/tex] = 7

d = difference between a term and its previous term = 3 - 7 = -4

Put these values in equation 1 , we will get

-385 = 7 + (n-1) (-4)

392 = 4n -4

4n = 396

n = 99

So we can conclude that the 99th term of the arithmetic sequence 7, 3, -1, -5, ... is -385.

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250 word in 5 minutea

Step-by-step explanation:

1. 25×2 (Because 25 is half of a minute so I need to multiplie by two)

2. It gives you 50 u multiplie by 5 because u need to find the answer for 5 minutes

3. 50×5= 250!!

Answer:

250

Step-by-step explanation:

25x2 (wpm) * 5 (minutes) = 250
words per minute means words typed every minute. if ben types 50 words per minute, this means he can type 250 words in 5 minutes.

(sorry for edit, i misread words in half minute as words per minute, credit to lina6561 for making me realize)

Answer:

I think C. Correct me if I am wrong.

Step-by-step explanation:

Hope it helps! =D

Answer: The answer is C.

Step-by-step explanation: Because I use a graphing calculator

The y intercept of the function f(x) = 2^2−4 is 0

The x intercept of the function f(x) = 2^2−4 is 0 or 2

The zeros of the function f(x) = 2^2−4 is 0 or 2

When f(x) = f(-4) then the function f(-4) = 48

When f(x) = 2 then x = -0.4142 or 2.142

given data

f(x) = 2^2 − 4

The y intercept

f(x) = 2^2−4

y = 2^2−4

at x = 0

y = 2 ( 0 ) ^2 - 4 ( 0 )

y = 0 - 0

y = 0

The x intercept

f(x) = 2^2 − 4

y = 2^2− 4

at y = 0

0 = 2^2− 4

0 = 2x( x - 2 )

2x = 0    OR     x - 2 = 0

x = 0      OR     x = 2

The zeros

This same as the x intercept

f(-4)

f(x) = 2^2− 4

f(-4) = 2 (-4)^2 - 4 * -4

f(-4) = 2 * 16 + 16

f(-4) = 48

f(x) = 2 when x =

f(x) = 2^2− 4

2 = 2x( x - 2 )

1 = x^2 - 2x

0 = x^2 - 2x - 1

x = -0.4142 or 2.142

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Answer:2x^2+3x-2

Step-by-step explanation:

2x-1*x+2=2x^2+3x-2

Answer:

2x+3

Step-by-step explanation:

so first you plug in g(x) in for x in f(x). this is how it will look like

2(x+2)-1

then you distribute the 2 in both terms in the parenthesis.

2(x)+2(2)-1

after that, you multiply them and you will get this

2x+4-1

subtract 4 and 1 and this is your answer

2x+3

a.

[tex] {3}^{2} \times {3}^{x} = {3}^{7 \\ } \\ \\ {3}^{2 + x} = {3}^{7} \\ 2 + x = 7 \\ x = 7 - 2 \\ x = 5[/tex]

b.

[tex] {7}^{8} \div {7}^{y} = {7}^{6} \\ {7}^{8 - y} = {7}^{6} \\ 8 - y = 6 \\ y = 8 - 6 \\ y = 2[/tex]

c.

[tex]( {q}^{4} )^{z} = q ^{12} \\ q^{4 \times z} = q^{12} \\4 z = 12 \\ \frac{4z}{4} = \frac{12}{4} \\ z = 3[/tex]

I used the laws of exponents.

The range for the given domain D = {2, -3, 0} of the function f(x) = 2x² + 7 is; R = {7, 15, 25}

We are given the function as;

f(x) = 2x² + 7

We are given the domain set as;

D = {2, -3, 0}

Now, the range will simply be gotten by plugging in each domain value into the given function to get the output. Thus;

Range when x = 0 is;

y = 2(0)² + 7

y = 7

Range when x = 2 is;

y = 2(2)² + 7

y = 15

Range when x = -3 is;

y = 2(-3)² + 7

y = 25

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We need to calculate the 10% of 20. By definition, a% is:

Where a can be any positive number. In this case a = 10, then:

In mathematics, the word "of" is reserved for the product. Then 10% of 20 is just:

Solving this leads to 2.

Answer:

50 percent.

Step-by-step explanation:

10 of 20 as a fraction is

10/20

- divide top and bottom by 10 and this simplifies to

1/2.

To convert to a percentage we multiply by 100:

= 1/2 * 100

= 50%.

The angles that are supplementary angles are: ∠SRT and ∠SRO

Angles that are supplementary will give us a sum of 180 degrees when we add the two angles together. One is the supplement of the other.

Some examples of angles that are supplementary angles that are formed when two parallel lines are intersected by a transversal include:

Angle SRT and angle SRO are angles that are adjacent to each other because they share a common side SR and a common vertex R. They line on the straight line OT.

Therefore, angle SRT and angle SRO are two angles that are supplementary angles as shown in the diagram attached below where lines NP and QS are parallel lines. The supplementary angles are therefore angle SRT and angle SRO.

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Using vertical angles, Maggie made her mistake when combining the like terms of x, which has a result of -3x and not 3x, hence the correct result is of x = 9.

Vertical angles are two angles that are opposite by the same vertex when two lines cross each other, and they are congruent, that is, they have the same measure.

For this problem, the vertical angles are given as follows:

Since they are congruent, we can solve for the variable x as follows:

4x + 2 = 7x - 25.

Moving all the terms with x to the left side of the equality and all the constant terms to the right side, with opposite signal, we have that:

4x - 7x = -25 - 2

Combining the like terms, it is found that:

-3x = -27.

Here happened Maggie's mistake, as 4x - 7x = -3x, hence the correct solution is given by:

3x = 27

x = 27/3

x = 9.

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Answer:

x=mp-n

so that leaves us with the answer

Step-by-step explanation:

m=n+x/p

first you want to move the P over to the left side by x P

so:

mp=n+x

the P on the right side cancels out

now you want to move the n to the left side by subtracting it form both sides

Answer:|2.5|

Step-by-step explanation:

En este caso el valor absoluto de 0 a |2.5| es 2.5. Esto se debe a que ya sea que cambies la ecuación o no para que sea igual a otro número, la respuesta SIEMPRE será 2.5. ¡Espero que esto haya ayudado! :D