Mathematics High School

What is the completely factored form of 2x2 – 32?
A) (2x2 + 16)(x – 16) '
B) 2(x + 4)(x – 4)
C) 2(x + 8)(x – 4)
D) 2(x – 8)(x – 4)

Answers

Answer 1
2x^2 - 32
2(x^2 - 16)
2(x + 4)(x - 4) <==
Answer 2

The completely factored form of [tex]2x^2 - 32[/tex] is 2(x + 4)(x - 4).

Given that,

The equation is [tex]2x^2 - 32[/tex].We have to determine the factors of the above equation.

Based on the above information, the calculation is as follows:

[tex]= 2x^2 - 32\\\\= 2(x^2 - 16)[/tex]

= 2(x + 4)(x - 4)

Therefore we can conclude that option B is correct.

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Related Questions

If m<1 = 7x + 6 and m<2 = 8x - 6, find the value of x so that p is perpendicular to q

Answers

Answer:

x = 12

Step-by-step explanation:

Given: [tex]\angle 1=7x+6[/tex]

[tex]\angle 2=8x-6[/tex]

∠1 and ∠2 form by two intersection line p and q.

p is perpendicular to q.

Therefore, ∠1 = ∠2 = 90°

So, 7x + 6 = 90°

7x = 84

x = 12

8x - 6 = 90°

8x = 96

x = 12

7x + 6 = 8x - 6

x = 6 + 6

x = 12

So, we get x=12 from all three equations.

hence, The value of x is 12

help me ............

Answers

3 1/2 x 2 = 7

4 2/3 x 2 = 9 1/3

7 + 9 1/3 = 16 1/3 yards

How to solve equations

Answers

Here are some things you should know when solving algebraic equations.

If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.

You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.

To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.

The distributive property is another important rule you will need to understand.

The distributive property is used mostly for simplifying parentheses in expressions/equations. 

For example, how would you get rid of the parentheses here?

6(x + 1)

If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves.
The distributive property states that a(b + c) = ab + ac
So, now we can simplify our expression.

6(x + 1) = 6x + 6

What are the solutions to the equations |x-10|-4=2x

Answers

x is going to equal two in this equation.

0. 135 written as a fraction

Answers

0.135 is the same as 135/1000 so change it to that

Find the GCF of 135 and 1000 and that would be 5.

Divide both the numerator and denominator by the GCF

Simplify

Answer: 27/200.

Explains how to write 0.135 as a fraction.

0.135 written as a fraction is 135/1000.

Kwamee bought kona beans that cost 11.00 and bought fuji beans that cost 7.50.he bought a total of 23 pounds of coffee and it cost 197.00 write a system of equations to solve how many pounds of kona and fuji beans kwamee bought

Answers

k= kona beans. f= fugi beans

k + f= 23. ==> -75k - 75f= -1725
11k + 7.5f= 197 ==> 110k + 75f= 1970

35k = 245
k= 7 lb of kona beans

7 + f = 23
f= 16 lb of fugi beans

Tonya is twice Kevin's age. In three years, Tonya will be 17. And in another three years, Uncle Rob will be three times Tonya’s age.
How old is Kevin and Uncle Bob

Answers

Kevin is 7 1/2 and Uncle Rob is 54

17-3 = 14 ( Tonya's age now)

14/2 = 7 ( Kevin's age)

14*3 = 42 ( Uncle Bob's age)

number 4 I have absolutely no idea how to do. I generally understand finding distance on the coordinate plane but this has really confused me. Please help.

Answers

For Part A, in creating the square, you did it correctly.

Now for Part B, you can create a right triangle by adding a point at -4, -3, and we'll call it, say, T.

Then you can use the Pythagorean's Theorem to find the length of one side of the square.

The Pythagorean's Theorem is [tex] a^{2} + b^{2} = c^{2} [/tex]

A would be the distance between P and T, and B would be the distance between Q and T. So then, a would be 7, and B would be 2. 

To fill it in, it would be [tex]7^{2} + 2^{2} = c^{2} [/tex]

or 49 + 4 = [tex] c^{2} [/tex]

or 53 = [tex]c^{2} [/tex]

or [tex] \sqrt{53} [/tex] = x

Which is equal to about 7.28

Now multiply that by 4 to get the perimeter, or 29.12

So the perimeter would be about 29.12


Calculate the area of the figure below using the following information:

Area of triangle ABC = 23.85 square units

Area of triangle ACD = 29.4 square units

Area of triangle AED = 26.25 square units


The area of the Figure ABCDE is ______ square units.

Answers

The area of ​​the figure ABCDE  is equal to the sum of the areas of the triangles ABC, ACD and AED

Area = 23.85 + 29.4 + 26.25 = 79.5 square units 

Answer:

Area of pentagon ABCDE =  23.85  + 29.4 + 26.25 = 79.5 unit²    

Step-by-step explanation:

Area of pentagon ABCDE is sum of area of triangles ABC, ACD and ADE

Area of pentagon ABCDE = Area of ΔABC +Area of ΔACD + Area of ΔADE

Area of ΔABC = 23.85 unit²

Area of ΔACD = 29.4 unit²

Area of ΔAED = 26.25 unit²

Area of pentagon ABCDE = Area of ΔABC +Area of ΔACD + Area of ΔADE

Area of pentagon ABCDE =  23.85  + 29.4 + 26.25 = 79.5 unit²          

The perimeter of a square garden is to be at least 20 ft but no more than 32 ft. find all possible values for the lengths of its sides using a compound inequality

Answers

20 < = 4a < = 32
20/4 < = (4/4)a < = 32/4
5 < = a < = 8

so the squares perimeter can be at least 5 ft but no more then 8 ft

Answer:

Answer in pic

Step-by-step explanation:

What's the parabola in vertex for for (-5,0) and has a vertex (-2,1)

Answers


hello :
the parabola's equation is : f(x) = a(x+2)²+1

but ; f(-5) = 0
0 = a(- 5+2)²+1
9a+1=0.....a= -1/9
f(x) = (-1/9)(x+2)²+1

What is the slope of the equation y = -x + 4

Answers

This is in slope-intercept form which is:

y = mx + b

In this equation, m is the slope, so the slope in this equation is -1

Hope this helps!

The length of a rectangle is five times its width. if the perimeter of the rectangle is 96 ft , find its area.

Answers

So the perimeter is 2 * length + 2 * width.

So we can assign the width a variable, x, and then for length, 5x, because it's five times the width, or x.

So, 2 * 5x + 2 * x

Or 10x + 2x

12x

Since that equals 96,

12x = 96

/12     /12

x = 8

Area is length times width.

Length is 5x, and width is x.

So basically, 5x * x = area

Or, if you substitute the variable in:

5 * 8 * 8 

320 square feet
Final answer:

The width of the rectangle is 8 ft and the length is 40 ft. Therefore, the area of the rectangle is 320 square feet.

Explanation:

To find the dimensions of the rectangle, let's use variables. Let the width of the rectangle be x. Since the length is five times the width, the length would be 5x. The perimeter of a rectangle is equal to twice the sum of its length and width. Therefore, we can set up the equation 2(5x + x) = 96 to find the width.

Simplifying the equation, we have 12x = 96. Dividing both sides by 12, we get x = 8. So the width of the rectangle is 8 ft.

Now, we can calculate the length by multiplying the width by 5. The length would be 5(8) = 40 ft. The area of a rectangle is equal to its length multiplied by its width. Therefore, the area of this rectangle is 8 ft * 40 ft = 320 square feet.

The area of a rectangle is 72 cm². The length of the rectangle is 6 cm longer than the width.

What is the width of the rectangle?



2 cm

6 cm

8 cm

10 cm

Answers

Area =72 sq. cm

length = x+6

Width = x

l×b = Area
(x+6)x =72
x2 +6x=72
x2+6x-72=0
x2+12x-6x-72=0
x (x+12) -6 (x+12)=0
(x+12) ( x-6) =0
x=-12, x=6

since width can't be negative , the answer is x=6.

therefore, the width is 6cm

Answer:

6cm

step-by-step explanation

just dived each number bye 72 to find 12 witch we would get 6cm

Find the value of x for which l is parallel to m. The diagram is not to scale.
a. 31
b. 62
c. 93
d. 149

Answers

If we continue the  line which comes from line segment  I till we reach line n  then the angle formed will be 31 degrees ( interior alternate to 31 degrees)

x + 31 = 62 ( external angle of a triangle theorem).

Therfore x = 31 degrees answer

When is it necessary to use three points to name an angle? If CP bisects and DPB , what is the measure of angle CPB?

Answers

Angle CP = 45 degrees, because it's bisecting a right angle (90 degrees) and half of 90 degrees is 45.
Final answer:

In geometry, three points are used to name an angle when there are multiple angles that share the same vertex. If CP bisects angle DPB, angle CPB is divided into two equal angles, and the measure of angle CPB is half of the measure of angle DPB.

Explanation:

In geometry, it is necessary to use three points to name an angle when there are multiple angles that share the same vertex. By using three points, we can clearly identify which angle we are referring to. In this case, if CP bisects angle DPB, it means that angle CPB is divided into two equal angles, and CP is one of the dividing lines. Therefore, the measure of angle CPB is half of the measure of angle DPB.

Learn more about Geometry here:

https://brainly.com/question/31408211

#SPJ2

Summer paints a room that has 400 square feet of wall space in 2.5 hours. at this rate, how long will it take her to paint a room with 720 square feet of wall space?

Answers

400/2.5 = 160 sq feet every hour

720 sq ft/160 sq ft = 4.5 hours

Which transformation will be equivalent to rotating a figure 180° counterclockwise?

A) reflecting over the line y = x.
B) reflecting over the line y = -x.
C) reflecting over the x-axis and the y-axis.
D) translating left 3 units and down 5 units.

Answers

If we have given coordinates of the image are in form (h,k).

The resulting coordinates of image rotation of 180° around the origin would be (-h,-k).

We have rule (h,k) ---> (-h,-k).

We can see that x-coordinate is being multiplied by -1 and then y-coordinate is also being multiplied by -1.

Above rule could be break into two parts.

(h,k) ---> (-h,k) ---->  (-h,-k).

We can see in first step, (h,k) ---> (-h,k) is being reflecting over the x-axis and

in second step (-h,k) ---->  (-h,-k) is being reflecting over the y-axis.

Therefore, correct option is C) reflecting over the x-axis and the y-axis.

The transformation which is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise is reflecting over the [tex]x[/tex]-axis and [tex]y[/tex]-axis. Therefore, the [tex]\fbox{\begin\\\ \bf option (C)\\\end{minispace}}[/tex] is correct.

Further explanation:

Consider a coordinate in the form [tex](a,b)[/tex] where [tex]a[/tex] and [tex]b[/tex] are real numbers.

If [tex]a[/tex] and [tex]b[/tex] are positive then the point [tex](a,b)[/tex] lies in the first quadrant.

If we rotate the coordinate [tex](a,b)[/tex] [tex]180^{\circ}[/tex] counterclockwise then the coordinates become [tex](-a,-b)[/tex].

The coordinate [tex](-a,-b)[/tex] lies in the third quadrant.

If we reflect the coordinate [tex](a,b)[/tex] about the [tex]x[/tex]-axis then the coordinates become [tex](a,-b)[/tex].

The coordinate [tex](a,-b)[/tex] lies in the fourth quadrant.

If we reflect the coordinate [tex](a,-b)[/tex] about the [tex]y[/tex]-axis then the coordinates become [tex](-a,-b)[/tex].

The coordinate [tex](-a,-b)[/tex] lies in the third quadrant.

This implies that rotating a figure [tex]180^{\circ}[/tex] counterclockwise is equivalent to transformation of reflecting over [tex]x[/tex]-axis and reflecting over [tex]y[/tex]-axis.

Option (A)

In option (A) it is given that reflection about the line [tex]y=x[/tex] is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.

If we reflect the coordinate [tex](a,b)[/tex] about the line [tex]y=x[/tex] then the coordinates become [tex](b,a)[/tex].

This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.

Therefore, the option (A) is incorrect.

Option (B)

In option (B) it is given that reflection about [tex]y=-x[/tex] is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.

If we reflect the coordinate [tex](a,b)[/tex] about the line [tex]y=-x[/tex] then the coordinates become [tex](-b,-a)[/tex].

This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.

Therefore, the option (B) is incorrect.

Option (C)

In option (C) it is given that reflection about [tex]x[/tex]-axis and [tex]y[/tex]-axis is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.

If we reflect the coordinate [tex](a,b)[/tex] about [tex]x[/tex]-axis and [tex]y[/tex]-axis then the coordinates become [tex](-a,-b)[/tex].

This is same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.

Therefore, the option (C) is correct.

Option (D)

In option (D) it is given that shifting a point [tex]3[/tex] units left and [tex]5[/tex] units down is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.

If we shift the point [tex](a,b)[/tex], [tex]3[/tex] units left and [tex]5[/tex] units down the coordinate is [tex](a+3,b-5)[/tex].

This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.

Therefore, the option (D) is incorrect.

Therefore, the [tex]\fbox{\begin\\\ \bf option (C)\\\end{minispace}}[/tex] is correct.

Learn more

1. Learn more about the rotation of the triangle   about the origin https://brainly.com/question/7437053.

2. Learn more about when a triangle is rotated  about the origin https://brainly.com/question/2992432.

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Geometry

Keywords: Transformation, rotation, reflection, clockwise, geometry, counterclockwise,  -axis,  - axis, coordinates, graph, origin, line, degrees, translation, symmetry.

Which two expressions could be used to solve this problem?



Roberto ordered 4 pepperoni pizzas, 2 mushroom pizzas, and 3 cheese pizzas for his party. He paid the same price for each pizza. The total cost was $90. How much did each pizza cost?



Choose exactly two answers that are correct.



A.


4 × 2 × 3


B.


90 – 24


C.


90 ÷ 9


D.


90 obelus divided by(4 + 2 + 3)

Answers

I think the answer would most likely be C.

Find the value of x in the equation 2√ x
a. –5
b. 1
c. 16
d. 25 11. simplify the expression .
a.
b.
c.
d. + 20 = 15 + 3√ x

Answers

the answer to that question would be a c d

6=x+2/3

Please help ASAP!!! 10 Points!!! :)

Answers

x=18 you multiply 2/3 by its reciprocal 3/2 which cancels it and then multiply 6 by 3 which gives you 18
The answer is x= 16/3. I hope this helps love! :)

Including a 8 %8% sales​ tax, an inn charges $ 135$135 per night. Find the​ inn's nightly cost before the tax is added.

Answers

that would be $135 / 1.08  =   $125

Find the amount (future value) of the ordinary annuity. (round your answer to the nearest cent.) $1500/semiannual period for 8 years at 2.5%/year compounded semiannually

Answers

The formula of the future value of an annuity ordinary is
Fv=pmt [((1+r/k)^(kn)-1)÷(r/k)]
Fv future value?
PMT semiannual payment 1500
R interest rate 0.025
K compounded semiannual 2
N time 8 years
Fv=1,500×(((1+0.025÷2)^(2×8)
−1)÷(0.025÷2))
=26,386.75

Hope it helps!

Completely factor the expression.

w^2 - 15w + 54

Answers

It would be (w-6)(w-9) and so the solutions would be 6 and 9.

If a(x)=3x+1 and b(x)=

Answers

b°a means that we plug a into the x value of b and go from there. In this case, we get [tex] \sqrt{(3x+1)-4} = \sqrt{3x-3} = \sqrt{3(x-1)} [/tex] (using the distributive property) and we have to figure out what the domain is. The domain is what x can equal, and since you can't have a square root of a negative number, 3(x-1) has to be greater than or equal to 0. Solving for that, we get 3(x-1)≥0. Dividing both sides by 3, we get x-1≥0. Next, we can add 1 to both sides to get x≥1. In interval notation, [1 encompasses 1 while (1 is everything above 1. In addition, it doesn't have to be less than anything, so we have ∞) at the end, making it [1, ∞). We have the parenthesis at the end because it doesn't include infinity, but everything less than it

The answer is C. [1, ∞] on edge

The following list shows the items and prices for a restaurant order. Calculate the total amount if there is a 7% tax and the customer leaves a 20% gratuity. 1 appetizer: $7.39 2 entrees: $16.99 each 1 dessert: $5.29 2 drinks: $2.30 each a. $65.82 b. $65.10 c. $54.85 d. $40.60

Answers

The answer is B. $65.10
7% of $51.26 is $3.59, which adds up to $54.85
20% of $51.26 is $10.25, which, with the tax included here, adds up to $65.10. Hope this helped.
the answer is b $65.10 . took the  test got it right

Which of the following shows the numbers ordered from least to greatest?

A)0.004, 0.07, 0.6, 0.32
B)0.004, 0.6 0.07, 0.32
C)0.004, 0.07, 0.32, 0.6
D)0.004, 0.32, 0.07, 0.6

Answers

I'm gonna say C cause 0.004 is less than 0.07 and 0.32 is less than 0.6 cause 0.6 = 0.60....so ya the answer is C

Solve the quadratic equation by taking square roots. Allow for imaginary solutions. Enter your answer in simplest form. Equation: 5x (squared) - 5 = -17

Answers

5x^2 - 5 = -17

First add 5 to both sides:

5x^2 = -12

Now, divide by 5

x^2 = -12/5

Take the square root of both sides

x = sqrt -12/5

Because there can't be a square root of a negative number, your answer is:

x = sqrt -12/5 * i

Hope this helps!

What is 19.2×108 minutes in hours? 1.152×1011 ​h​ 3.200×109 ​h​ 1.152×107 ​h 3.200×107 ​h​

Answers

The answer to this question would be: 3.2 x 10^7 hours

To answer this question, you need to know how many minutes in an hour is, then convert the minutes into hours. To do this, you just need to divide the number with 60 minutes/hour. The calculation would be:

19.2×10^8 minutes / (60 minutes/hour) = 0.32 x 10^8= 3.2 x 10^7 hours

4.5/17 - x = 3/8 solve

Answers

First, you move the x to the other side by adding x on both sides, getting
4.5/17 = 3/8 + x.
Then, you subtract 3/8 from both sides, getting 4.5/17 + 3/8 = x, and then you simplify the fraction.
The final answer would be x = 87/136, or 0.64.

Answer:

The value of the equation is [tex]x=\frac{-15}{136}[/tex] Or [tex]x=-0.1102[/tex].  

Step-by-step explanation:

Consider the provided equation.

[tex]\frac{4.5}{17}- x =\frac{3}{8}[/tex]

We need to solve the provided equation for x.

Add x to both side.  

[tex]\frac{4.5}{17}- x+x=\frac{3}{8}+x[/tex]

[tex]\frac{4.5}{17}=\frac{3}{8}+x[/tex]

Subtract 3/8 from both sides.

[tex]\frac{4.5}{17}-\frac{3}{8}=x[/tex]

[tex]x=\frac{4.5}{17}-\frac{3}{8}[/tex]

[tex]x=\frac{36-51}{136}[/tex]

[tex]x=\frac{-15}{136}[/tex]

Or

[tex]x=-0.1102[/tex]

Hence, the value of the equation is [tex]x=\frac{-15}{136}[/tex] Or [tex]x=-0.1102[/tex].  

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