What are the factors of 4x2 - 4x - 15?
Select TWO correct answers.
2x-5
4x + 5
2x + 3
2x-3
x-3
2x + 5

Answer:

The correct answer is D

Step-by-step explanation:

the negative power shows that on the exponent shows that the value is small and is being simplified.

When ever there is a negative power we increase zeros with respect to the exponent value.

By using the concept of proportionality, it can be concluded that

y = 5x is the proportional relation

Third option is correct

What is proportionality?

Suppose there are two quantities. Proportionality indicates that if there's a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio

Proportionality are often direct or inverse

Direct proportion

Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.

For example cost of an article and quantity of an article are in direct proportion

Inverse proportion

Two quantities are said to be in inverse proportion if on increasing the value of one quantity,  the value of other quantity decreases and vice versa.

For example Number of men and number of days taken by those men to complete a work are in inverse proportion

For the first option

7x - 2 = y

y = 7x - 2

Here a non zero constant (-2) is added after the term with variable x

So this relation is not proportional

For the second option

y = 2x + 4

Here a non zero constant (4) is added after the term with variable x

So this relation is not proportional

For the third option

y = 5x

Here, no non zero constant is added after the term with variable x

So this relation is proportional.

For the fourth option

y + 1 = 3x

y = 3x - 1

Here a non zero constant (-1) is added after the term with variable x

So this relation is not proportional

So the correct option is the third option

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The terms which are equivalent to the slope in a proportional relationship include:

Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."

The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope formula is the rise over run formula, where the fraction consists of a rise, whether the line is going up or down, divided by the run.

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Complete question

Select all the terms which are equivalent to the slope in a proportional relationship.

Constant of proportionality

Origin

Inverse

Rise over run

Unit rate

Answer:

Option D: 8.19 inches

Step-by-step explanation:

i hope this helps..have a great day! :)

The equation 4y = -x is a direct variation and k = - 1 / 4.

The equation  3x = 2y - 7 is neither a direct variation nor a inverse variation.

Direct variation describes a simple relationship between two variables . We say y varies directly to x when it is represented as follows:

y = kx

where

Therefore,

4y =  - x

divide both sides of the equation by 4

4y / 4 = -x / 4

[tex]y =- \frac{x}{4}[/tex]

Therefore, the equation is direct variation and the value of k is - 1 / 4.

For two quantities with inverse variation, as one quantity increases, the other quantity decreases. Inverse variation is represented as follows:

y = k / x

Therefore, 3x = 2y - 7 is neither an inverse  nor a direct variation.

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Answer:

$93.75

Step-by-step explanation:

$125 × 0.75 = $93.75

Answer:

$93.75

Step-by-step explanation:

125x0.25

31.25

125-31.25

$93.75

Hopes this helps

With a manufacturing cost of $80 per phone, the selling price of $292.5 would result in the largest annual profit.

Profit is the amount of gain realized from a transaction. The profit formula is useful for figuring out the profit from selling a specific product, typically in a business, or for figuring out the gain in any financial transaction. If the selling price is more than the cost price, a profit can be determined.

Given,

q = -6p+3030

p = 505 - q/6

R(q) = 505q - q²/6

C(q) = 80q

Now, the profit function,

P(q) = R(q) - C(q)

      = (505q - (q²/6)) - 80q

P(q) = 425q - q²/6

P(q) = 425 - q/3

q = 1275 units

Now, put it in the demand function,

p = 505 - q/6

  = 505 - 212.5

  = 292.5

Therefore, the selling price is $292.5.

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Answer:

5 coffees will cost $9.25

Step-by-step explanation:

If you divide $5.55 by the 3 coffees, you get $1.85 which is the price per coffee. Multiply $1.85 by 5 to get $9.25 which is the cost for 5 coffees

Answer: (7/x) + 10

A quotient is a result you get after dividing two numbers, for example, 10 divided by 2 is 5. 5 is the quotient because it's the result of 10/2. Hence, the quotient of seven and a number is simply (7/x), x being any number. And that value is added to 10, leaving us with the expression (7/x) + 10.

The complete table of values of the function is

x | f(x)

0 | 1

1 | 2

2 | 4

3 | 8

The ordered pairs are (x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)

The equation of the function is given as

f(x) = 2ˣ

On the incomplete table of values, we have the following x values

x = 0, 1, 2, 3

Next, we substitute x = 0, 1, 2, 3 in the equation f(x) = 2ˣ

So, we have:

f(0) = 2⁰ = 1

f(1) = 2¹ = 2

f(2) = 2² = 4

f(2) = 2³ = 8

So, the complete table is

x | f(x)

0 | 1

1 | 2

2 | 4

3 | 8

When represented as ordered pairs, we have

(x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)

See attachment for the graph

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Answer:

Step-by-step explanation: First since the cookies are 36.44 dollars and the total spent is 102.44, use 102.44-36.44= 66 dollars

66/11=6 cupcake boxes

6 cupcake boxes + 1 cookie box = 7 boxes in total

Answer: x=16

Step-by-step explanation: 18=2x-14

32=2x

x= 16

Answer:

need more information to answer

The equation of the transformed graph is y = -2|x| + 2

(graph attached)

Transformation is a term used in mathematics to refer to the movements made by objects.

information from the question

equation of the preimage f(x) = |x|

A graph showing the transformed image

The image show a reflection over x axis, the transformation rule for this is

Transformation rule (x, y) → (x, -y)

applying the rule to f(x) = |x| gives -f(x) = -|x|

followed by translation 2 units up, this achieved by Transformation rule

-f(x) → -f(x) + 2

Then a vertical stretch of 2 units,  transformation rule for vertical stretch is

-2f(x) → -2|x| + 2

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Answer:

Step-by-step explanation:

domain: 1,2,3,4

Range: 8,6,4,2

D=-2

[tex]a_{n}=a_{1}+(n-1)-2[/tex] formula

The length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

According to the question,

We have the following information:

Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters.

We know that the following formula is used to find the area of rectangle:

Length*width = 18

Length*3 = 18

Length = 18/3

Length of the rectangular garden = 6 meters

Now, perimeter of the rectangular garden:

2(length+width)

2(6+3)

2*9

18 meters

Hence, the length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

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The equation of the line is y = (-2/3)x + 8/3

What is a perpendicular line?

Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular line can be used to graphically depict the condition of perpendicularity. It can be defined between any pair of lines, any pair of planes, or any pair of lines and planes.

The slope-intercept form of a line is written in the form:

y = mx + b

where:

y = y-coordinate

m = slope

x = x-coordinate

b = y-intercept

Here, We have

y= 3/2x + 1/2 that passes through the point (-2,4)​

But we do not know the value of b.

We can do this by substituting the point(-2,4), into the equation and we get

y = mx + b

4 = (-2/3)(-2) + b

b = 8/3

Now that you know all your values, rewrite the equation in slope-intercept form:

y = (-2/3)x + 8/3

Hence, the equation of the line is y = (-2/3)x + 8/3

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The formula for the perimeter of the rectangle is:

P(x) = 14x - 16

We know that for a rectangle of length L and width W the perimeter is given by the formula:

P = 2*(W + L)

In this case we know that:

W = 2x - 1

L = 5x - 7

Replacing that in the perimeter formula we get:

P(x) = 2*(2x - 1 + 5x - 7)

Now we can simplify this so we get:

P(x) = 2*(2x + 5x - 1 - 7)

P(x) = 2*(7x - 8)

P(x) = 14x - 16

That is the perimeter of the rectangle in terms of x.

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The quantity of sugar required to make 78 cookies is 8.1 cups.

Given that, you need 1.25 cups of sugar to make 1 dozen cookies.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,

The quantity of sugar to make 1 cookie

= 1.25/12

= 0.10417

The quantity of sugar to make 78 cookies

= 78×0.10417

= 8.1 cups

Therefore, the quantity of sugar required to make 78 cookies is 8.1 cups.

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For the given right angled triangle, the base of the triangle is 10 units and perpendicular side is 9 units then its side length x is equal to 13.45 units (nearest hundredth).

As given in the question,

Given right angled triangle,

Base of the triangle is equal to 10 units

Perpendicular side of a triangle is equal to 9 units

Side length 'x' is the hypotenuse of the right angled triangle.

Using Pythagoras theorem we get,

(Hypotenuse)² = ( Base)² + ( Perpendicular side)²

⇒ x² = (10)² + (9)²

⇒ x² = 100 + 81

⇒ x² = 181

⇒ x = √181

⇒ x = 13.4536...

⇒ x = 13.45 units ( nearest hundredth)  

Therefore, for the given right angled triangle, the base of the triangle is 10 units and perpendicular side is 9 units then its side length x is equal to 13.45 units (nearest hundredth).

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The value of each term is

The length of the line ED = 45 units

The length of the line DF = 27 units

The length of the line EF = 36 units

Here we have to use the trigonometric function

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

Substitute the value in the equation

sin D = Opposite side / Hypotenuse

= 36/45

= 4/5

sin E = Opposite side / Hypotenuse  

= 27/45

= 3/5

cos D = Adjacent side / Hypotenuse

= 27/45

= 3/5

cos E = Adjacent side / Hypotenuse

= 36/45

= 4/5

Hence, the value of each term is  

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Answer:

-4

Step-by-step explanation:

When answering questions like these first, combine like terms you get 3x+5 =3x+8, Subtract 5 from both of the sides you get 3x=3x+3 remove 3x from both sides and you got 0=3 this is a contradicting statement meaning no solution ∅

B) Distribute first, 3x + 2 -x  = x + 3 + 3x +4

2, Combine the like terms 2x - 1 = 7 + 4x

3, Isolate variable and constants 2x = 8 + 4x

3(1) Cont- Isolation -2x = 8

Thus divide both side by -2 giving us -4

William needs to detail his parents at least 12 times to buy the golf club.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.

The symbols we use in Inequality Expressions are

Not equal ' ≠ '  

Greater than  ' > '

Less than ' < '

Less than or equal  ' ≤ '

Greater than or equal ' ≥'

Here we have

William plans to buy the new Callaway Rogue for at least $ 550

The amount that William saved = $ 325

The amount he earns each time he details his parents = $ 20

Here we don't know how many times he detailed his parents,

So represent it with a variable x

After detailing x times the amount he earned will equal $ 20x

The total amount that William will have = $ 325 + $ 20x

William wants at least $550

Therefore,

The inequality that will represent the above situation is

=> 325 + 20x ≥ 550 ------(1)

Now solve the above inequality to get the value of x

=> 65 + 4x ≥ 110

=> 4x ≥ 45

=> x ≥ 11.25

Here we can say 11.25 times so x = 12 times

Therefore,

William needs to detail his parents at least 12 times to buy the golf club.

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Answer:

yes if b is odd then b+6 is odd

Step-by-step explanation:

example

consider a odd number 1,3,5,7,and 9

1+6=7

3+6=9

5+6=11

7+6=13

9+6=15

all answers are odd number

Answer:

y = 1.2·x

x = 1;  y = 1.2·1 = 1.2

x = 2;  y = 1.2·2 = 2.4

x = 3;  y = 1.2·3 = 3.6

Regarding the given matrix, it is found that:

1. a. The matrix has three rows.

1. b. The matrix has five columns.

1. c. The matrix has two dimensions.

2. The entry is 2.

3. The entry is 7.

4. The entry is -2.

5. The entry is 0.

6. The entries are: m21 and m33.

The matrix is composed by three lines of elements, and each line has five elements, hence:

The number of dimensions of the matrix are:

2, which are the rows and the columns.

The entries are symbolized as follows:

mrc.

In which:

Hence the entry m11, for example, is the element at the first row and at the first column, which is of 2.

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Using the percentage, Rapunzel participated in 9581/100 matches.

In the given question we have to find the fraction of the wrestling matches did Rapunzel participate in.

Rapunzel's team participated in a total of 143 wrestling matches.

Rapunzel participated in 67 percent of the wrestling matches.

Total matches = 143

Participated in = 67%

Total number of matches in which Rapunzel participated is

= 143*67%

= 143* 67/100

= 9581/100

Rapunzel participated in 9581/100 matches.

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Answer:

Step-by-step explanation:

2x(x + 7)(x²+49) = 0

(apply the zero product)

x=0 or x+7 =0 or x² + 49 = 0

x+7 =0

x=-7

x² + 49 = 0

no real solution for this i think

Answer = x=0 or x=-7

The equations that can be used are y(y - 5) = 750, y² - 5y = 750, and (y + 25)(y – 30) = 0.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Length = y

Width = y - 5

Area = 750

The area of a rectangle is written as,

Length x Width = Area

y x (y - 5) = 750

y² - 5y = 750

y² - 5y - 750 = 0

(y + 25)(y – 30) = 0

The equations that can be used are y(y - 5) = 750, y² - 5y = 750, and (y + 25)(y – 30) = 0.

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Answer:

(4)

Step-by-step explanation:

Let's make the smaller number equal to x. Since they are consecutive odd numbers, the larger number is x+2.

Twice the smaller number is 2x. Three times the larger number is 3(x+2). If twice the smaller is subtracted from three times the larger, then the expression should be: 3(x+2) - 2x

Then, since the result of this is four more than the smaller, this expression is x+4.

Finally, we put it all together, so we get: 3(x+2) - 2x = x + 4. Option 4 is our correct answer.

Hence, the option (4) is correct.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger, the result is four more than the smaller.

Let us assume the smaller number is [tex]x[/tex].

The larger number is  [tex](x+2)[/tex].

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger than it is

[tex]3(x+2)-2x[/tex]

So, the result is four more than the smaller.

i.e., [tex]3(x+2)-2x=x+4[/tex]

Hence, the option (4) is correct.

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