What is the factored form of the expression 35xy + 25x? 5(7xy + 5x) 5x(7y + 5) 25x(10y + 1) 10x(25y + 15)

Answer:

OPTION C

OPTION E

Step-by-step explanation:

Distributive property of Addition:

                            a(b + c) = ab + bc

In other words, 'a' is distributed over 'b' and 'c'.

Also, note that a mixed fraction, of the form [tex]$ \textbf{c} \frac{\textbf{x}}{\textbf{y}} = \textbf{c} + \frac{\textbf{x}}{\textbf{y}} $[/tex]

If a mixed fraction is of the type [tex]$ \textbf{-p}\frac{\textbf{q}}{\textbf{r}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{-(p + } \frac{\textbf{q}}{\textbf{r}}) \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{-p} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{q}}{\textbf{r}} $[/tex]

OPTION A:

[tex]\textbf{3} \bigg ( \textbf{-4} \frac{\textbf{1}}{\textbf{2}} \bigg )[/tex]

This can be written as: [tex]$ 3 \bigg ( - 4 - \frac{1}{2} \bigg ) $[/tex]

Now, we distribute 3 over -4 and [tex]$ -\frac{1}{2} $[/tex].

[tex]$ = 3(-4) + 3\bigg (-\frac{1}{2} \bigg ) $[/tex]

Therefore, OPTION A is incorrect.

OPTION B: [tex]$ \textbf{2} \frac{\textbf{1}}{\textbf{4}} \bigg ( \textbf{1} \frac{\textbf{3}}{\textbf{4}} \bigg ) $[/tex]

Now, this is written as: [tex]$ 2 + \frac{1}{2} \bigg ( 1 + \frac{3}{4} \bigg ) $[/tex]

We have distribute 2 and [tex]$ \frac{1}{2} $[/tex] separately over 1 and [tex]$ \frac{3}{4} $[/tex].

So, we should have [tex]$ 2 (1) + 2 \bigg ( \frac{3}{4} \bigg ) + \frac{1}{2} (1) + \frac{1}{2}. \frac{3}{4} $[/tex]

So, OPTION B is incorrect.

OPTION C: [tex]$ \textbf{-4} \bigg( - 5 \frac{\textbf{1}}{\textbf{3}} \bigg ) $[/tex]

[tex]$ = - 4 \bigg ( -5 - \frac{1}{3} \bigg) $[/tex]

[tex]$ = -4(-5) + (-4) \bigg (- \frac{1}{3} \bigg ) $[/tex]

Hence, OPTION C is correct.

Similar method will help us know that OPTION D has used the Distributive property incorrectly and OPTION E has.

So, the answers are:

OPTION A

OPTION C

OPTION E

Answer:

The probability distribution for which the value of the median is greater than the value of the mean is - negatively skewed probability distribution.

Step-by-step explanation:

The probability distribution for which the value of the median is greater than the value of the mean is - negatively skewed probability distribution.

Answer:

negative skewed  distribution

Step-by-step explanation:

As can be seen in the figure attached,

Answer:

4 units

Step-by-step explanation:

if f to g is 2 units and h to i is one unit you just add thoes together because that is what the outside of the f to i is. And 7-3 is 4

hope this helps luvs

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The distance between the points G and H  on the line that contains points F, G, H, I, and J is 4 units.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

Given that a line contains points F, G, H, I, J. The space between F and G is 2. The space between H and I is 1. The space between F and I is 7. Therefore, the distance between the two points G and H on the given line can be written as,

GH = FI - FG - Hi

= 7 units - 2 units - 1 unit

= 4 units

Hence, the distance between the points G and H  on the line that contains points F, G, H, I, and J is 4 units.

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Answer:

(0,-4)

Step-by-step explanation:

see the image for explanation.

Answer:

( [tex]\frac{4}{3}[/tex], 0 )

Step-by-step explanation:

The x- intercept is where the graph crosses the x- axis. At this point the y- coordinate is zero.

Substitute y = 0 into the equation and solve for x, that is

3x - 4 = 0 ( add 4 to both sides )

3x = 4 ( divide both sides by 3 )

x = [tex]\frac{4}{3}[/tex] ← x- intercept

Answer:  4 / -15

Step-by-step explanation:

Answer:

  350

Step-by-step explanation:

We have two points on the demand curve as (10, 450) and (15, 200). Using the two-point form of the equation for the line between them, we can find the "y" value for "x" = 12 as ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (200 -450)/(15 -10)(12 -10) +450

  = (-250/5)(2) +450

  = -100 +450 = 350

We predict the number of tickets sold at $12 will be 350.

_____

Check

The drop in sales of 50 tickets for each $1 increase in price is consistent with other table values.

Answer:

The other 2 angles combined measure 70

Step-by-step explanation:

all of a triangle's angles together measure 180.

If one angle is 110 the other 2 would be 70.

Answer:

True

Step-by-step explanation:

Yes, but not all angles in the triangle will be 90 degrees.

Final answer:

By using the elimination method to solve the given system of linear equations, we find that x = 18 and y = 15.

Explanation:

We are looking to solve the system of linear equations:

3x – 2y = 24

x + 2y = 48

To find the values of x and y, we can use substitution or elimination methods. In this case, the elimination method is very straightforward since the y coefficients in the two equations are additive inverses. If we add both equations together, the y terms will cancel out:

3x + x = 24 + 48

4x = 72

Dividing both sides by 4 gives us the value of x:

x = 18

To find y, we can substitute x back into either of the original equations. Let's use the second equation:

18 + 2y = 48

Subtracting 18 from both sides:

2y = 30

Dividing by 2:

y = 15

Thus, the solution to the system of equations is x = 18 and y = 15.

Using a calculator, 1200/180 = 6.67 approximately

If you use long division, then you'll get what you see in the diagram below

The 6's go on forever after the decimal point, but if you round to two decimal places, then you'll get that approximate value of 6.67

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

If you want a remainder, then 1200/180 = 6 remainder 120

You can think of it like you having 1200 cookies and 180 friends. Each friend will get 6 whole cookies and there will be 120 left over as the remainder.

Answer:

D

Step-by-step explanation:

3×16=48

4×12=48

Answer:

The relationship ⇒ 25x + 40y = 12,250

Step-by-step explanation:

The number of student memberships = x

The number of adult memberships = y

The monthly membership fee for a student = $25

The monthly membership fee for an adult = $40

The total fee = 25x + 40y

Al's Athletic Club receives $12,250 in membership fees for the month of January.

So, the relationship between x and y is:

25x + 40y = 12,250

For every 2 student memberships (2x$25=$50), there were 305 adult memberships.

To represent the relationship between the number of student memberships (2) and the number of adult memberships (y) at Al's Athletic Club for the month of January, we can use an equation based on the given information. Let's assume that there were 2 student memberships and y adult memberships in January. The monthly membership fees for students and adults are $25 and $40, respectively. The total membership fees collected for the month were $12,250.

The total fees can be represented as:

Total Fees = (Number of Student Memberships * Monthly Fee for Student) + (Number of Adult Memberships * Monthly Fee for Adult)

Using the given information, we can write the equation:

$12,250 = (2 * $25) + (y * $40)

Now, we can simplify this equation:

$12,250 = $50 + $40y

To isolate the variable y, we can subtract $50 from both sides of the equation:

$12,250 - $50 = $40y

$12,200 = $40y

Now, divide both sides by $40 to find the relationship:

y = $12,200 / $40

y = 305

So, the relationship between the number of student memberships (2) and the number of adult memberships (y) for the month of January is represented by the equation y = 305. This means there were 305 adult memberships in January for every 2 student memberships.

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Answer:

17.1

Step-by-step explanation:

The required round of number 17.0891 to the nearest tenth is 17.1.

Given that,
To round the number 17.0891 to the nearest tenth.

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,

Given number,
17.0891
Since the number on the tenth place after the decimal is 0 and the value next is 0.08 which is near to 0.1 so the number on the tenth place will increase by a unit and the whole number become,
= 17.1

Thus, the required round of number 17.0891 to the nearest tenth is 17.1.

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Answer:

20 - 4×(−6) = 20 + 4×6 = 20 + 24 = 44

Answer:

Step-by-step explanation:

a) increase

Increase = 200 -130 = 70

Percent increase = (70/130)*100 = 70*100/130 = 7*100/13

= 700/13

= 53.85%

Answer:

a) increase

Step-by-step explanation:

Answer:

The first operation performed when evaluating the given expression [tex]5+(\frac{9x-3}{2})[/tex]  for x=5 is given below :

Step 1: Put x=5 in the above given expression we get

[tex]5+(\frac{9(5)-3}{2})[/tex]

Step-by-step explanation:

Given equation is [tex]5+(\frac{9x-3}{2})[/tex] for x=5

To find the first operation performed when evaluating the given expression [tex]5+(\frac{9x-3}{2})[/tex]  for x=5

[tex]5+(\frac{9x-3}{2})[/tex]

Step 1: Put x=5 in the above expression we get

[tex]5+(\frac{9(5)-3}{2})[/tex]

[tex]=5+(\frac{45-3}{2})[/tex]

[tex]=5+(\frac{42}{2})[/tex]

[tex]=5+21[/tex]

[tex]=26[/tex]

Therefore [tex]5+(\frac{9x-3}{2})[/tex] for x=5 is 26

Therefore [tex]5+(\frac{9x-3}{2})=26[/tex] for x=5

- 2a = - 20 | x (-)

2a = 20

a = 20 : 2

a = 10

Answer:

a=10

Step-by-step explanation:

-2a=-20

Divide -2 on each side. You should get a=10

y is some number and it is equal to -4x+2

y being that same number is also equal to x-3

therefore, we can equate -4x+2 and x-3 to get x-3 = -4x+2

This is the same as starting with y = -4x+2 and replacing the y with x-3

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

Let's solve for x

x-3 = -4x+2

x-3+4x = -4x+2+4x .... add 4x to both sides

5x-3 = 2

5x-3+3 = 2+3 .... add 3 to both sides

5x = 5

5x/5 = 5/5 .... divide both sides by 5

x = 1

With this x value, you can now find the y value. Pick any equation that has x and y in it. If we picked the first equation, then

y = -4x+2

y = -4*1+2 ... plug in x = 1

y = -4+2

y = -2

Or we can pick the second equation

y = x-3

y = 1-3 .... plug in x = 1

y = -2

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

Graphing the two lines will have them intersect at this location.

Answer:

0.457 for all the apex students

Step-by-step explanation:

b

The expected number of bases for Ichiro Suzuki in a typical at-bat in 2001 is approximately 0.448, which rounds to 0.441 (Option D) to the nearest thousandth. Thus , the correct option is D.

To calculate the expected number of bases for Ichiro Suzuki in a typical at-bat in 2001, we can use the following formula:

E(X) = (0 ×P(Out)) + (1 × P(Single)) + (2 × P(Double)) + (3 × P(Triple)) + (4 ×P(Home Run))

First, we need to calculate the probabilities for each outcome:

P(Out) = (692 - 192 - 34 - 8 - 8) / 692 = 450 / 692 ≈ 0.651

P(Single) = 192 / 692 ≈ 0.278

P(Double) = 34 / 692 ≈ 0.049

P(Triple) = 8 / 692 ≈ 0.012

P(Home Run) = 8 / 692 ≈ 0.012

Now, plug these probabilities into the formula:

E(X) = (0 × 0.651) + (1 ×0.278) + (2 × 0.049) + (3 × 0.012) + (4 × 0.012)

E(X) ≈ 0.278 + 0.098 + 0.036 + 0.036 ≈ 0.448

Rounding to the nearest thousandth, E(X) is approximately 0.448.

So, the answer to the question is D. 0.441, which is the closest option provided.

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The expressions for the given questions are substituted and solved using the provided values of x and y. The solutions for the four questions respectively are 109, 15, 19, and 92.

To evaluate the expressions for questions 5-8, you will need to substitute the values of x and y into each given expression.

Through these steps, you can understand how to substitute and solve such expressions.

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To find the slope, use the slope(m) formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]        and plug in the two points

(0, 5) = (x₁, y₁)

(-9, -4) = (x₂, y₂)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-4-5}{-9-0}[/tex]

[tex]m=\frac{-9}{-9}[/tex]    [two negatives cancel each other out and become positive]

m = 1      The slope is 1

Answer:

half a meter long

Step-by-step explanation:

Answer: 5508

Step-by-step explanation:

all the numbers together equal 72 marbles in total.

(6x2)x (3x3)x (3x17)=

  12       9          51              first multiply the easy numbers 12x9 =108 then

108x51= 5508

Answer:

12

Step-by-step explanation:

This is an example of Addition property between two positive integers (i.e. whole value numbers), which means the result will be positive and larger than the two numbers.

The result of the addition would be:

[tex]5 + 7 = 12[/tex]

Another way to do it if you are struggling a bit you can write the value of [tex]7[/tex] as [tex]7 = 5 +2[/tex] so then you can say:

[tex]5 + (5 + 2) = 5 + 5 + 2 = 10 + 2 = 12[/tex]

Step-by-step explanation:

17.

Opposite angles of a parallelogram are equal.

So [tex]3y^{\circ}=123^{\circ}[/tex]

⇒ y= [tex](\frac{123}{3})^ {\circ}[/tex]

and sum of adjacent angle is = [tex]180^{\circ}[/tex]

Therefore, [tex](2x-5)^{\circ} + 123^ {\circ}=180^{\circ}[/tex]

⇒[tex](2x-5)^{\circ} =180^{\circ}-123^ {\circ}[/tex]

⇒[tex]2x^\circ=57^\circ+5^\circ[/tex]

⇒x=[tex]31^\circ[/tex]

Therefore x=[tex]31^\circ[/tex] and y= [tex](\frac{123}{3})^ {\circ}[/tex]

18.

The diagonals  of rectangle bisect each other.

so, 2x=x+9

⇔2x- x=9

⇔x = 9 units

Again opposite sides are congruent.

So,3y -9 =y+12

⇔3y - y =12+9

⇔y [tex]=\frac{21}{2}[/tex] units =10.5 units

Therefore x = 9 units and y = 10.5 units

19.

[tex]3x^\circ=45^\circ[/tex]         [∵ they are transversal angles]

⇔[tex]x=15^\circ[/tex]

And opposite sides are equal

7y = 4y + 21

⇔7y - 4y = 21

⇔3y = 21

⇔y = 7 units

Therefore [tex]x=15^\circ[/tex] and y = 7 units

Answer:

1. Basically, a ratio is a relation between two values, such that the change of one value will result in the same proportional change in the other (if one value increases 6 times, or decreases 4 times, for example, the same will happen with the other value too.

Since Mrs. Jollie will save $60 for every two panels, then the ratio is:

2 panels: $60

Every ratio can be written in a form of fraction, by simply dividing these values:

2/60  

or, as a reduced fraction:

1/30

2. Now we are given several ratios, which we need to use to find price for 9 panels.

First way:

we can set a proportion because we already said that if we change one value, others will change proportionally as well. So, we take any of these ratios and make a proportion:

2 : $3,000 = 9 : $ x

Solving for x, we get:

x = $3,000 • 9 / 2

x = $13,500

Second way:

From the ratio, we can find the price for a single panel. Then, we simply multiply that with 9 and find the price for nine panels:

one panel costs $3,000 / 2 = $1,500

nine panels cost $1,500 • 9 = $13,500

3. Now, we are again given several ratios and we need to find the price per hour for each company. We can do this by simply dividing:

- ABC Co. 5h : $128

so, price per hour is $128/5 = $25.6

- Solar R' Us 6h : $181

so, price per hour is $181/6 = $30.17

- Light in the Sky 8h: $195

so, price per hour is $195/8 = $24.4

So, the best deal means that the price per hour is the lowest, so the best deal is the Light in the Sky company.

Answer:

[tex] - \frac{53}{25} [/tex]

Step-by-step explanation:

Convert to a mixed number by placing the numbers to the right of the decimal over

100

. Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.

Answer:

13

Step-by-step explanation: