Factor the GCF:
-4y^2 + 12y - 16
A.) -1(4y^2-12y+16)
B.) -4y(y^2-3y+4)
C.) -(y^2-3y+4)
D.) -4(y^2+3y-4)

Answer:

[tex]\large\boxed{y=\dfrac{7}{2}x-18}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

Convert the equation of a line 3x + 4x = 2y - 9 to the slope-intercept form:

[tex]3x+4x=2y-9[/tex]

[tex]7x=2y-9[/tex]             add 9 to both sides

[tex]7x+9=2y[/tex]       divide both sides by 2

[tex]\dfrac{7}{2}x+\dfrac{9}{2}=y\to y=\dfrac{7}{2}x+\dfrac{9}{2}[/tex]

Parallel lines have the same slope. Therefore we have the equation:

[tex]y=\dfrac{7}{2}x+b[/tex]

Put the coordinates of the point (4, -4) to the equation:

[tex]-4=\dfrac{7}{2}(4)+b[/tex]

[tex]-4=7(2)+b[/tex]

[tex]-4=14+b[/tex]       subtract 14 from both sides

[tex]-18=b\to b=-18[/tex]

Finally we have the equation:

[tex]y=\dfrac{7}{2}x-18[/tex]

b. Any two negative numbers when multiplying gives positive answers which are never between negative numbers. -9*-3=27

c. same logic, positive answer so never less than either negative number.

The product of two negative numbers will always be positive, so both cases described in the question are not possible. This is due to the property of real numbers which states that the product of two negative numbers results in a positive number.

b. The product of two negative numbers will always be positive, so the case where the product of two negative numbers falls between the two numbers is not possible.

c. The product of two negative numbers is always positive, which is larger than their negatives. Therefore, the scenario of two negative numbers having a product that is less than both numbers cannot occur.

These conclusions are based on the property of real numbers which specifies that the product of two negative numbers is a positive number. For example, if you multiply -3 by -2, the result is 6, which is a positive number and larger than both -3 and -2.

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Answer:

The volume is [tex]904,320\ mm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=120/2=60\ mm[/tex] ----> the radius is half the diameter

[tex]\pi=3.14[/tex]

substitute the values

[tex]V=\frac{4}{3}(3.14)(60)^{3}=904,320\ mm^{3}[/tex]

Final answer:

The volume of a sphere-shaped beanbag with a diameter of 120 millimeters is calculated using the formula V = (4/3)πr³, resulting in a volume of approximately 904.32 cubic centimeters.

Explanation:

To calculate the volume of a beanbag in the shape of a sphere, we use the formula for the volume of a sphere, which is V = (4/3)πr³. Given that the diameter of the beanbag is 120 millimeters, we first need to find the radius, which is half of the diameter, so r = 60 millimeters or 6 centimeters. Plugging the values into the formula, we get:

V = (4/3) × 3.14 × (6 cm)³

V = (4/3) × 3.14 × 216 cm³

V = (4/3) × 3.14 × 216

V = (4) × 3.14 × 72

V = 904.32 cm³

Therefore, the volume of the beanbag is approximately 904.32 cubic centimeters (cm³).

Answer:

There is not enough information

Step-by-step explanation:

In Circle 1

Minor Arc : [tex]\widehat{AB}=140^{\circ}[/tex]

Radius = AO=OB

In Circle 2

Minor Arc : [tex]\widehat{GH}=140^{\circ}[/tex]

Radius =OG =OH

We need to show that the arcs are congruent .

Since the length of the radii are not given .

So, There is not enough information to prove that the arcs are congruent.

Hence Option D is true.

Answer: d/ there is not enough information to determine

Step-by-step explanation:

I just did this on a p e x

Answer:

Option b

[tex]p = -6[/tex] or [tex]p = 12[/tex]

Step-by-step explanation:

The absolute value is a function that transforms any value x into a positive number.

Therefore, for the function [tex]f(x) = |x|[/tex]  x> 0 for all real numbers.

Then the equation:

[tex]|p-3| = 9[/tex] has two cases

[tex](p-3) = 9[/tex]    if [tex]h > 3[/tex]  (i)

[tex]-(p-3) = 9[/tex]    if [tex]h < 3[/tex] (ii)

We solve the case (i)

[tex]p = 9 + 3\\p = 12[/tex]

We solve the case (ii)

[tex]-p +3 = 9\\p = 3-9\\p = -6[/tex]

Then the solution is:

[tex]p = -6[/tex] or [tex]p = 12[/tex]

Answer:

b

Step-by-step explanation:

Answer: 45 DVDs

Step-by-step explanation:

45 is the least common multiple of 3, 5, and 9.

45 can be equally divided by 3, 5, and 9:

45 ÷ 3 = 15

45 ÷ 5 = 9

45 ÷ 9 = 5

recall that the reference angle, is the angle made by the terminal point with the x-axis.

Check the picture below.

Answer:

[tex]5x^7(16x^2+9)(16x^2-9)[/tex]

Step-by-step explanation:

we have

[tex]1,280x^{11}-405x^{7}[/tex]

we know that

[tex]1,280=(2^8)(5)[/tex]

[tex]405=(3^4)(5)[/tex]

substitute

[tex](2^8)(5)x^{11}-(3^4)(5)x^{7}[/tex]

Factor 5x^7

[tex]5x^7[(2^8)x^{4}-(3^4)][/tex]

[tex]5x^7[256x^{4}-81][/tex]

Applying difference of square

[tex][256x^{4}-81]=(16x^2+9)(16x^2-9)[/tex]

substitute

[tex]5x^7(16x^2+9)(16x^2-9)[/tex]

Answer:

5x^7(4x-a 3)(4x+3)(16x^2+9)

Step-by-step explanation:

[tex]4) \: {x}^{2} + 11x + 28 = 0 \\ \Leftrightarrow {x}^{2} + 7x + 4x + 28 = 0 \\ \Leftrightarrow x(x + 7) + 4(x + 7) = 0 \\ \Leftrightarrow (x + 4)(x + 7) = 0 \\\Leftrightarrow x = - 4 \: \vee \: x = - 7 \\ \\ 5) \: (3a + 8)(3 {a}^{2} - a - 7) \\ = 9 {a}^{3} - 3 {a}^{2} - 21a + 24 {a}^{2} - 8a - 56 \\ = 9 {a}^{3} + 21 {a}^{2} - 29a - 56[/tex]

Answer: 0.29

Step-by-step explanation: The first thing that you need to know is that a ton equals 2,000 pounds. Therefore, 6,000 pounds of rocks cost $1,740. In order to solve the problem you need to divide $1,740 by 6,000. 1,740 / 6,000 = .29

Each pound cost $ 0.29. (29 cents)

Answer:  $0.29 per pound

Step-by-step explanation:

[tex]\dfrac{price}{pound}:\ \dfrac{\$1,740}{3\ tons}\times \dfrac{1\ ton}{2,000\ pounds}=\dfrac{\$1,740}{6,000\ pounds}=\large \boxed{\dfrac{\$0.29}{1\ pound}}[/tex]

Answer:

c

Step-by-step explanation:

Note there is a difference of 1 between consecutive integers.

let an integer be n then then the next one is n + 1 followed by n + 2

Hence

n + (n + 1) + (n + 2) = 36 → C

The median is the moddle number of a data set. If the number of numbers is even add the 2 middle numbers and divide by 2.

Median = (7+7)÷2 = 7

The mean is the averagw value in a data set. You find it be adding all the numbers and then divide the answer by the number of numbers.

Mean: (6+6+6+7+7+7+8+8+8+9) ÷ 10

= 72 ÷ 10 = 7.2

Happy to help! Marking my answer as the Brainliest would really be aprreciated.

Answer:

C.) Rectangular prism

Step-by-step explanation:

Answer:

[tex]\Large \boxed{\mathrm{Rectangular \ prism}}[/tex]

Step-by-step explanation:

The net represents a three-dimensional shape.

The figure that the net represents is a rectangular prism.

Answer:

7

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

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

here [ a, b ] = [ 4, 6 ]

f(b) = f(6) = 6² - 3(6) - 10 = 36 - 18 - 10 = 8

f(a) = f(4) = 4² - 3(4) - 10 = 16 - 12 - 10 = - 6, hence

average rate of change = [tex]\frac{8-(-6)}{6-4}[/tex] = [tex]\frac{14}{2}[/tex] = 7

The dimensions of the box are = 4 feet (length); 3 feet(width); 2 feet(height)

So, volume of the box is = [tex]4\times3\times2=24[/tex] cubic feet

The dimensions of the storage locker are = 12 feet(length); 6 feet(width) ; 9 feet(height)

So, volume of the storage locker is = [tex]12\times6\times9=648[/tex]

So, the greatest number of boxes that can be stored are =

[tex]\frac{648}{24}= 27[/tex] boxes

Hence, a maximum of 27 boxes are stored.

Jayden's storage locker has a volume of 648 cubic feet, and each of his boxes has a volume of 24 cubic feet. By dividing the locker's volume by the volume of a single box, we find that Jayden can store a maximum of 27 boxes in the locker.

To determine the greatest number of boxes Jayden can store in the storage locker, we need to calculate the volume of the storage locker and the volume of one box. The storage locker is 12 feet long, 6 feet wide, and 9 feet high, so its volume is calculated as follows:

Storage Locker Volume = length × width × height = 12 ft × 6 ft × 9 ft = 648 cubic feet.

The box has dimensions of 4 feet long, 3 feet wide, and 2 feet high. Thus, its volume is:

Box Volume = length × width × height = 4 ft × 3 ft × 2 ft = 24 cubic feet.

Now, to find the greatest number of boxes that can fit into the locker, we divide the volume of the storage locker by the volume of one box:

Number of Boxes = Storage Locker Volume / Box Volume = 648 cubic feet / 24 cubic feet.

When we perform the division, we get:

Number of Boxes = 27.

Hence, Jayden can store a maximum of 27 boxes in the storage locker when placed upright with a 4-foot by 3-foot side on top.

Answer:

Step-by-step explanation:

A(-5, 1) → A'(-6, 0)

-5 - 1 = -6

1 - 1 = 0

B(-2, 7) → B'(-3, 6)

-2 - 1 = -3

7 - 1 = 6

C(0, 1) → C'(-1, 0)

0 - 1 = -1

1 - 1 = 0

The answer is: The first graphic representation.

We are given a quadratic equation, meaning that it could be two possible solutions for the exercise, however, we are talking about time, so we have to consider only the obtained positive values.

Let's make the equation equal to 0 in order to find the values of "t"

[tex]h(t)=-16.1t^2 + 150\\0=-16.1t^2 + 150\\16.1t^2=150\\t^2=\frac{150}{16.1}=9.32\\t=+-\sqrt{9.32}=+-3.05\\t1=3.05\\t2=-305[/tex]

So, discarding the negative value, we can use the possitive value to find the correct graphic representation.

To find the correct graphic representation we must take into consideration the following:

- We must remember that the sign of the coefficient of the quadratic term (t^2) will define if the parabola opens downward or upward.

From the given quadratic (or parabola) equation we have:

[tex]a=-1\\b=0\\c=150[/tex]

So, since the coefficient of the quadratic term is negative, the parabola opens downward.

- Since we are looking for a graphic that represents the change in height over time, we need to look for a graphic that shows only positive values for the x-axis (time)

- We are looking for a parabola which y-axis intercept is equal to 150.

Therefore, the graphic representation of the quadratic function that models a ball's height over time is the first graphic representation.

Have a nice day!

Answer: A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

*cough cough*

Answer:

Step-by-step explanation:

B

Among the following graph option (A) graph best represents y= -h(x)

The steps are as follow:

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Let x represent the unknown number.

7x - x = -48

Group like terms together.

6x = -48

Divide both sides by 6.

x = -8

Hence, the number is negative eight.

Answer:x=-8

Step-by-step explanation:

What I did was set up my equation and my equation was 7x-x=-48. My second step was to combine like terms and then I had 6x=-48 lastly I divided both sides by 6x then my final answer was x=-8.

Answer:

Perimeter of the shaded region is 268 m

Step-by-step explanation:

In this diagram a semi circle is drawn inside a rectangle of length 150m.

Length of diameter of a semicircle = 150 m

So radius of the semicircle = [tex]\frac{150}{2}=75 m[/tex]

We have to find the perimeter of the shaded region.

Perimeter of the shaded region = length of tangents drawn on the circle at A and B + m(arc AB)

Length of tangents = radius of the semi circle = 75 m

and m(arc AB) = [tex]\frac{\text{Perimeter of the circle}}{4}=\frac{2\pi r}{4}[/tex]

= [tex]\frac{2\pi (75)}{4}[/tex]

= [tex]\frac{2(3.14)(75)}{4}[/tex]\

= [tex]\frac{471}{4}[/tex]

= 117.75 m

Now Perimeter of the shaded region = 75 + 75 + 117.75

P = 267.75 ≈ 268 m

Given the image showing a rectangle that is 150 cm long with a semicircle inside of it, the perimeter of the shaded region is:  267.8 m

Recall:

Perimeter of a circle = [tex]2 \pi r[/tex]

Thus, given the semicircle in the diagram below, where:

Length of rectangle = 150 m

Radius of semi circle = half of 150 m = 75 m

Thus,

The width of the circle = 75 m

The shaded region is bounded by the circumference of a quarter circle (AB) and two sides measuring 75 m each.

Perimeter of Quarter circle = [tex]\frac{1}{4} \times 2 \pi r[/tex]

Perimeter of Quarter circle = [tex]\frac{1}{4} \times 2 \times \pi \times 75 = 117.8 m[/tex]

Perimeter of the shaded region = 117 + 75 + 75 = 267.8 m

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Answer:

2x^2- 8x

Step-by-step explanation:

2x(x-4)

distribute; multiply parenthesis by 2 x

2x * x-2x *4

calculate products

2x^2- 8x

Answer:  The required product is [tex]2x^2-8x.[/tex]

Step-by-step explanation:  We are given to find the following product :

[tex]P=2x(x-4).[/tex]

To find the above product, we need to multiply 2x to every term ithin the bracket.

The multiplication is as follows :

[tex]P\\\\=2x(x-4)\\\\=2x\times x-2x\times4\\\\=2x^2-8x.[/tex]

Thus, the required product is [tex]2x^2-8x.[/tex]

Answer:

option B

Elia multiply the dividend by 100 instead of 10.

Step-by-step explanation:

Given that,

divisor  = 0.6

dividend = 1.848

Elia decided to multiply each by 10 to get

but unfortunately she multiply the dividend by 100

As,

1.848 x 100 = 184.8

So,

Elia's error was that she multiply the dividend by 100 instead of 10.

Answer:

The measure of angle <RUS is 23°

Step-by-step explanation:

In this problem we know that

82°+24°+<RUS+51°=180°

solve for < RUS

157°+<RUS=180°

<RUS=180°-157°

<RUS=23°

Answer:

Step-by-step explanation:

23

The amount to which $500 will grow to is $881.17.

From the question, we have the following parameters that can be used in our computation:

Principal = 500

Rate = 12%

Time = 5 years

The future value is calclated as

FV = P * (1 + r)ⁿ

substitute the known values in the above equation, so, we have the following representation

FV = $500 * (1 + 0.12)⁵

Evaluate

FV = $881.17

Hence, the amount is $881.17

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Answer:

[tex]y=-222[/tex]

Step-by-step explanation:

When "y varies directly with x" this means that:

[tex]y=k\times x[/tex]

where k is a number we need to find out (called the constant of proportionality if you care about that).

We can figure out what k is because they tell us when y= -252, x=84. Substituting those values into our equation we get:

[tex]-252 = k \times 84[/tex]

and therefore:

[tex]k=-3[/tex].

So our equation or formula between y and x is:

[tex]y= -3x[/tex].

So when x = 74, then:

[tex]y=-3 \times 74 = -222[/tex]

Answer: Third option (In step 3 she needed to subtract c rather than divide)

Step-by-step explanation:

When she subtract b from both sides of the equation, she obtained:

[tex]3s-b=a+c[/tex]

Therefore, to leave the a alone at one member of the equation, she needs to subtract c from both sides of the equation.

Then, she would obtain the following:

[tex]3s-b-c=a+c-c\\3s-b-c=a\\a=3s-b-c[/tex]

Therefore the answer is the third option: In step 3 she needed to subtract c rather than divide.

Answer:

The true statement is: In step 3 she needed to subtract c rather than divide.

Step-by-step explanation:

Lets solve our equation [tex]s=\frac{a+b+c}{3}[/tex] step by step.

Step 1. Since 3 is the denominator of the right hand side, we need to multiply both sides of the equation by 3:

[tex]3s=\frac{3(a+b+c)}{3}[/tex]

Now we can cancel the 3 in the numerator and the 3 in the denominator to get

[tex]3s=a+b+c[/tex]

As you can see, the first statement is false

Step 2. Since we want to isolate the variable [tex]a[/tex], we need to subtract b from both sides of the equation:

[tex]3s=a+b+c[/tex]

[tex]3s-b=a+b+c-b[/tex]

[tex]3s-b=a+c[/tex]

The second statement is also false

Step 3. The last thing we to do to isolate [tex]a[/tex] (and solve for it) is subtract c from both sides of the equation:

[tex]3s-b-c=a+c-c[/tex]

[tex]3s-b-c=a[/tex]

[tex]a=3s-b-c[/tex]

Therefore, the third statement is true: In step 3 she needed to subtract c rather than divide.

Answer:

(-20)

Step-by-step explanation:

loss = a negative integer.

Answer:

13. x = 6

14. x = 3.5

Step-by-step explanation:

13. To find x when f(x) = -17, set the equation f(x) equal to -17 and solve.

-3x + 1 = -17                    Subtract 1 from both sides

-3x = -17 - 1

-3x = -18                          Divide by -3

x = 6

14. To find x when g(x) = 31, set the equation g(x) equal to 31 and solve.

10x - 4 = 31                    Add 4 to both sides

10x = 31 + 4

10x = 35                        Divide by 10

x = 3.5