Factor completely.

4p²+36p+81
Question 3 options:

(2p−9)2

(2p+9)2

(4p+6)2

The volume of a square pyramid is a^2 * h/3, assuming a is the base edge and h is the height. Plug the numbers in and you get your answer.

The volume of the square pyramid with base edges of 4 m and height 3 m is [tex]16 \, \text{m}^3[/tex]

To find the volume of a square pyramid, you can use the formula:

[tex]\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]

For a square pyramid, the base area is the area of the square base. The formula for the area of a square is \( \text{Area} = \text{side}^2 \).[tex]\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]

Given:

- Base edges = 4 m

- Height = 3 m

1. Calculate the Base Area:

  The base of the square pyramid is a square, so its area is:

Base Area = [tex]\text{side}^2[/tex]

Base Area = [tex]4^2[/tex]

Base Area = [tex]16 \, \text{m}^2[/tex]

2. Plug the Values into the Volume Formula:

  Now, we can plug the values into the volume formula:

Volume  = [tex]\frac{1}{3} \times \text{Base Area} \times \text{Height}[/tex]

Volume = [tex]\frac{1}{3} \times 16 \, \text{m}^2 \times 3 \, \text{m}[/tex]

Volume  = [tex]\frac{1}{3} \times 48 \, \text{m}^3[/tex]

Volume  = [tex]16 \, \text{m}^3[/tex]

So, the volume of the square pyramid with base edges 4 m and height 3 m is [tex]16 \, \text{m}^3[/tex]

Answer:

The next step is to put all terms into the left side of the equation and group the like trems

Step-by-step explanation:

The first step in determining the solution to the system of equations, [tex]y =-x^2-4x-3[/tex] and [tex]y = 2x + 5[/tex], algebraically is to set the two equations equal as [tex]-x^2-4x-3 = 2x + 5.[/tex]

The next step is to put all terms into the left side of the equation and group the like trems:

[tex]-x^2-4x-3-2x-5=0,\\ \\-x^2+(-4x-2x)+(-3-5)=0,\\ \\-x^2-6x-8=0.[/tex]

Now you can multiply this equation by -1:

[tex]x^2+6x+8=0[/tex]

and solve it using quadratic formula:

[tex]x_{1,2}=\dfrac{-6\pm \sqrt{6^2-4\cdot 8\cdot 1}}{2\cdot 1}=\dfrac{-6\pm\sqrt{4}}{2}=\dfrac{-6\pm 2}{2}=-4,\ -2.[/tex]

Answer:

Step-by-step explanation:

There are 4 quarts in a gallon.

So, that is $32 a gallon.

2 gallons is $64

Answer: Angles 1 and 5

Step-by-step explanation: Corresponding angles are angles that have the same measures.

Since angle 1 and 5 have the same measure on these lines, that means that the answer must be angle 1 and 5.

Answer:

15+c-d

Step-by-step explanation:

4(3+1/4c-1/2d) or in decimals 4(3+0.25c-0.5d)

distribute the 4 (in other words use the distributive property)

4 · 3 = 12

4 · 0.25 = 1

4 · 0.5 = 2

12 + 1 + 2 = 15

15 + c-d is your answer

hope I helped <3

Answer: Objects have the same velocity only if they are moving at the same speed and in the same direction. Objects moving at different speeds, in different directions, or both have different velocities.

Step-by-step explanation:

Divide the circumference by pi to get diameter, which is 14. Divide 14 by 2 for the radius, which is 7. Now square the radius to get 49, and multiply by pi for the area.

Area is 49pi.

The area of the circle in terms of π with a circumference of 14π is 49π units².

Given a circle.

Also, given that:

Circumference of the circle = 14π

It is required to find the area of the circle.

It is known that:

Circumference of a circle is:

C = 2πr, where r is the radius.

So, here,

2πr = 14π

2r = 14

r = 7

So, the radius of the circle is 7.

So, the area of the circle is:

A = πr²

  = π(7)²

  = 49π

Hence, the area is 49π.

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Answer:

B and D

Step-by-step explanation:

The surface area is the area of each face of the cube. The volume is the amount that will fill the cube. These are two separate processes which cannot give you the same measurement by calculating one part of the surface area. B is false.

Doubling the sides of the cube will not double the surface area. It will quadruple it. D is false too.

Answer:

if you want to find a percent first you have to find the fraction. for an example for other, if 75 people out of 300 people are working you would divide 75 by 300. that would give you .25. then you multipluy by a hundred. that would give you 25 percent

Step-by-step explanation:

Answer:

the answer for this is 57 I believe

Step-by-step explanation:

I cue the shape into a small rectangle with sides of 3, 3, and 1 which comes out to 9 cubic feet, and then I took the rest of the shape which became a bigger rectangle with sides of 2, 6, and 4 which comes out to 48 cubic feet. 48+9=57. Sorry if I am wrong, I tried my best. Hope this helps!

Answer: 36

Step-by-step explanation:

1) Chop the image like a hamburger, leaving the top part sticking out. You can draw a line.

2) Find the length, width, and height. 2*3*4=24

3) Find the top part that was separated from the bottom part with the line that you drew. The height of the bottom prism was 2 and the height on the other side of the prism was 3. 3-2=1

4) So, you got the height of the piece that is cut out like a small square on the top left corner of the shape. That height will be used as the height for the top part now.

5) You found the height, which was 1. Now the length is shown at the bottom of the bottom prism, which is 3. All that's left is to find the width. The width is the same as the bottom prism, which is 4. 1*3*4=12

6) Add the two volumes together to find the whole volume. 24+12=36

1.50 waters 2.80 nachos

hope this helps :)

The cost of each nachos is $2.50 and the cost of each water bottle is $1.50.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let x be the cost of each water bottle and y be the cost of each nachos.

Two bottled water and an order of cheese nachos costs $5.50.

So, 2x+y=5.50 -------(I)

Three bottled water and two orders of cheese nachos costs $9.50​

3x+2y=9.50 -------(II)

Multiply equation (I) by 2, we get

4x+2y=11 -------(III)

Subtract equation (II) from equation (III), we get

4x+2y-(3x+2y)=11-9.50

x=$1.50

Substitute x=1.50 in equation (I), we get

2(1.50)+y=5.50

y=$2.50

Therefore, the cost of each nachos is $2.50.

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"Your question is incomplete, probably the complete question/missing part is:"

Two bottled waters and an order of cheese nachos costs $5.50. Three bottled waters and two orders of cheese nachos costs $9.50​. How much money does the nachos cost.

Answer:

[tex]\frac{2y+3}{7y-1}[/tex]

Step-by-step explanation:

The given expression is

[tex]\frac{10y^2+15y}{35y^2-5y}[/tex]

Factor both the numerator and the denominator.

[tex]=\frac{5y(2y+3)}{5y(7y-1)}[/tex]

Cancel out the common factors.

[tex]=\frac{2y+3}{7y-1}[/tex]

Answer:

The correct answer is,

(10y² + 15y)/(35y² - 5y) = (2y + 3 )/( 7y - 1)

Step-by-step explanation:

It is given an expression,

(10y² + 15y)/(35y² - 5y)

To simplify the given expression

Taking 5y as common from both numerator and denominator,

(10y² + 15y )/( 35y² - 5y) = 5y( 2y + 3)/5y( 7y - 1)

 = (2y + 3 )/( 7y - 1)

Therefore the simplified form of given expression is given by,

(10y² + 15y)/(35y² - 5y) = (2y + 3 )/( 7y - 1)

You would need 8 vans because:

48/6 = 8

16/2=8

Plus, if you add the number of students and teachers together it equals 64. Then divide it by the number of people who can fit into the van, which is 8.

64/8=8 vans

there will be needed 10 buses so other people can fit in

Answer:

A

Step-by-step explanation:

Each hour is 30 degrees. 11 to 6 is 7 hours so 30 * 7 = 210 degrees, which is greater than a semicircle, which is 180 degrees.

Answer:

A. The hands are at 11 and 6; arc measured clockwise

Step-by-step explanation:

A semicircle measures 180º and when you measure the distance from 11 to 6 the difference in the hands of the clock by each hour is given by the equation:

[tex]\frac{360}{12}[/tex]= 30

So there are 7 numbers between the 11 and the 6 if you measure it clockwise, that means that the angle formed by the two hands of the clock measured clockwise is:

7*30= 210

Wich is greater than 180º, which is why that is the correct answer.

The approximate values are:

c = 55.2°

r = 22.8°

x = 9.9 miles

- To find angle [tex]c[/tex], we are using the rule of sines: [tex]\frac{a}{sin(A)} =\frac{b}{sin(B)} =\frac{c}{sin(C)}[/tex]

For our triangle [tex]a=21,A=c,b=x,B=r,c=25[/tex] and [tex]C=102[/tex]

Replacing the values we get: [tex]\frac{21}{sin(c)} =\frac{x}{sin(r)} =\frac{25}{sin(102)}[/tex]

We can pick up two suited values to find [tex]c[/tex]:

[tex]\frac{21}{sin(c)} =\frac{25}{sin(102)}[/tex]

[tex]21=\frac{25sin(c)}{sin(102)}[/tex]

[tex]21sin(102)=25sin(c)[/tex]

[tex]sin(c)=\frac{21sin(102)}{25}[/tex]

[tex]c=sin^{-1}(\frac{21sin(102)}{25})[/tex]

[tex]c=55.2[/tex]

- Now that we have angle [tex]c[/tex], we can use the angle sum theorem to find angle [tex]r[/tex].

The angle sum theorem states the the interior angles of a triangle add up to 180°, so:

[tex]r+c+102=180[/tex]

[tex]r+55.2+102=180[/tex]

[tex]r+157.2=180[/tex]

[tex]r=22.8[/tex]

- Now that we have angle [tex]r[/tex], we can use the rule of sines, one more time, to find side [tex]x[/tex]

[tex]\frac{21}{sin(c)} =\frac{x}{sin(r)} =\frac{25}{sin(102)}[/tex]

[tex]\frac{x}{sin(r)} =\frac{25}{sin(102)}[/tex]

[tex]\frac{x}{sin(22.8)} =\frac{25}{sin(102)}[/tex]

[tex]x=\frac{25sin(22.8)}{sin(102)}[/tex]

[tex]x=9.9[/tex]

Answer: 1) r=23° , c=55° , x=10°

Step-by-step explanation:

correct on edge 2020

Answer:

The total surface area = 10956 m²

Step-by-step explanation:

∵ The pyramid is rectangular pyramid

∴ It has a rectangular base with dimensions of 50 m and 78 m

∴ It has four faces each two opposite are congruent

* to find the total surface area, we will find the area of

  each face and add them together

- Area base = L × W

∴  Area base = 50 × 78 = 3900 m² ⇒ (1)

- Area of triangular face of dimensions:

 base = 50 m and height = 60 m

∵ Area triangle = 1/2 × base × height

∴ Area triangle = 1/2 × 50 × 60 = 1500 m²

∵ We have another triangle congruent to this triangle (opposite faces)

∴ Area of the two congruent faces = 1500 × 2 = 3000 m² ⇒ (2)

- Area of triangular face of dimensions:

 base = 78 m and height = 52 m

∵ Area triangle = 1/2 × base × height

∴ Area triangle = 1/2 × 78 × 52 = 2028 m²

∵ We have another triangle congruent to this triangle (opposite faces)

∴ Area of the two congruent faces = 2028 × 2 = 4056 m² ⇒ (3)

∴ Add (1) , (2) and (3)

∴ The total surface area = 3900 + 3000 + 4056 = 10956 m²

Answer:

The total answer is : 10956 m²

Step-by-step explanation:

Answer: tithe area of figure b is 315.

Step-by-step explanation:

Answer:

80 is the volume

Step-by-step explanation:

l*b*h

5*2*8

80

L*W*H

8*5 = 40

40*2 = 80

The volume is 80 cm^3

Answer:

y = 1/2 x

Step-by-step explanation:

slope = 1/2 and y-intercept = 0

so equation

y = 1/2 x

The complete factorization of the given polynomial is (x² + 1)(x + 2).

To factorize the polynomial [tex]x^3 + 2x^2 + x + 2[/tex], we first look for any common factors. In this case, we don't have any common factors, so we move on to factoring by grouping.

Unfortunately, this cubic polynomial does not factorize nicely into simpler terms using rational numbers. It would involve using heavy algebra and complex numbers to factor. Usually, for a cubic polynomial of this nature, a numerical method will be employed to find its roots.

We can group the terms as [tex]x^3 + 2x^2 + x + 2[/tex]). Taking out the common factors from each group, we get:

[tex]x^2[/tex](x + 2) + 1(x + 2).

Now, notice that we have a common binomial term (x + 2), so we can factor that out as well:

([tex]x^2[/tex] + 1)(x + 2).

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9514 1404 393

Answer:

  A (and C)

Step-by-step explanation:

A relationship that is a direct proportion is described by the equation ...

  y = kx

for some constant k.

You can examine the tables to see what the value of k is by looking at ...

  k = y/x

__

In table A, the values of k are 125/5 = 250/10 = 500/20 = 25.

In table B, the values of k are 100/50 = 2, 250/20 = 125, 50/10 = 5. These are not constant, so the relation is not a proportional one.

In table C, the values of k are -125/5 = -250/10 = -500/20 = -25.

In table D, the values of k are 8/2 = 4, 10/4 = 2.5, 12/6 = 2. These values are not constant, so the relation is not a proportional one.

__

We see that the tables of A and C both represent proportional relationships. We usually expect the value of k to be positive, but there is nothing in the definition of a proportional relationship that demands that be the case.

If this is a single-answer question, choose A.

If this is an "all that apply" question, choose A and C.

Answer: Bonnie went to a meadow to pick flowers there was 20 flowers in one area and had decided to pick 18 of the flowers, how many flowers are left?

Step-by-step explanation: I don't know.... Just something random, hope I was able to help!

A Number story was written to describe the given mathematical equation.

Mercy had 20 balls, 6 were of green color, 6 were of blue color, 6

were of red color, 2 were of yellow colors. One day six of her friends came

to her home and each of them liked the balls Mercy had. All of them

requested Mercy to offer one ball of each color i.e. green, blue, and red. Since they were the best friends of Mercy so Mercy couldn't deny it.

She offered each friend 3 balls of green, blue, and red color each. Since She offered 3 balls to each of her friends i.e 18 balls, she was left with

20-(3*6) = 2 yellow color balls.

Thus, a number story was written to describe the given mathematical equation.

Answer:

HOPEFULLY THIS HELPS YOU

Arithmetic sequence: an = a1 + (n-1)d

In this case: an = 7 +(n-1)(-4)

Answer:

[tex]\large\boxed{g)\ 6xy^2=(3x)(2y^2)}\\\boxed{h)\ 25a^3b^2=(5a^2b^2)(5a)}\\\boxed{i)\ 6x+6y+6p=6(x+y+p)}[/tex]

Step-by-step explanation:

[tex]g)\ 6xy^2=3\cdot2\cdot x\cdot y\cdot y=(3\cdot x)(2\cdot y\cdot y)=(3x)(2y^2)\\\\h)\ 25a^3b^2=5\cdot5\cdot a\cdot a\cdot a\cdot b\cdot b=(5\cdot a\cdot a\cdot b\cdot b)(5\cdot a)=(5a^2b^2)(5a)\\\\i)\ 6x+6y+6p=6\cdot x+6\cdot y+6\cdot p=6(x+y+p)[/tex]

Other way for g) and h):

[tex]g)\ \dfrac{6xy^2}{3x}=\dfrac{6}{3}\cdot\dfrac{xy^2}{x}=2y^2\\\\6xy^2=(3x)(2y^2)\\\\h)\ \dfrac{25a^3b^2}{5a^2b^2}=\dfrac{25}{5}\cdot\dfrac{a^3}{a^2}\cdot\dfrac{b^2}{b^2}=5a\\\\25a^3b^2=(5a^2b^2)(5a)[/tex]

To factor by identifying a common factor in each term, divide out the greatest common factor of the terms.

To factor by identifying a common factor in each term, we look for a number or variable that can be divided out of each term. Let's go through the expressions one by one:

g) 6xy2 = (3x) ?

We can see that both terms have a common factor of 3x. Dividing each term by 3x gives us 2y2.

h) 25a3b2 = (5a2b2) ?

Again, both terms have a common factor, which is 5a2b2. Dividing each term by 5a2b2 gives us 5a.

i) 6x + 6y + 6p

Here, all three terms have a common factor of 6. Dividing each term by 6 gives us x + y + p.

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the statement is true

Answer: second option

Step-by-step explanation:

The standard form of a quadratic equation is:

[tex]ax^2+bx+c=0[/tex]

Then, to write the quadratic equation given in the problem in standard form, you must substract 1 from both sides of the equation. Then you have:

[tex]2x^2+5x-1=0[/tex]

Given the quadratic equation above, to find the value of [tex]b^2-4ac[/tex]  you must substitute:

a=2; b=5 and c=-1 into [tex]b^2-4ac[/tex]

Thenrefore, you obtain the following result:

[tex]5^2-4(2)(-1)=33[/tex]

Answer:

[tex]33[/tex]

Step-by-step explanation:

The given quadratic equation is

[tex]1=2x^2+5x[/tex]

We want to rewrite this equation in the form;

[tex]ax^2+bx+c=0[/tex]

We add [tex]-1[/tex] to both sides of the equation to obtain;

[tex]0=2x^2+5x-1[/tex]

This is the same as

[tex]2x^2+5x-1=0[/tex]

This implies that;

[tex]a=2,b=5,c=-1[/tex]

We substitute these values into the expression [tex]b^2-4ac[/tex]

[tex]\Rightarrow 5^{2}-4(2)(-1)[/tex]

[tex]=25+8[/tex]

[tex]=33[/tex]

Answer:

arc EAC = 280 degrees

Step-by-step explanation:

Given: the measure of arc AB is 55  and the measure of arc CD is 25

Vertical angles are equal so <AOB = <DOE = 55

In a circle, the degree measure of an arc is equal to the measure of the central angle.

so if <DOE = 55 then arc DE = 55

As you know, the arc angle to a full angle in a circle = 360

so

arc EAC = 360 - arc CD - arc DE

arc EAC = 360 - 55 - 25

arc EAC = 280

Answer:

arc EAC = 280 degrees

The measure of EAC = 280°

A circle is a round-shaped figure with all points lie in the same plane, the distance between all the points on the circle and the center of the circle is equal.

The line that passes through the center of the circle and has end point on the circumference is called the diameter, the radius is half the measure of the diameter.

The circumference is the perimeter of the circle, it is the distance that is covered by a man to take one round around the circle.

The area is defined as the space required by a two dimensional object in space.

The chord AD and BE is the diameter of the circle,

They intersect each other, the sector formed by the circle is of equal measure.

The measure of arc AB is 55 and,

The measure of arc CD is 25

The sector ED = AB = 55 degree.

The measure of EAC = 360 - measure of ED and DC

The measure of EAC = 360 - 55 - 25

The measure of EAC = 280°

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Answer:

Step-by-step explanation:

The formula of a circumference of a circle:

[tex]C=2\pi r[/tex]

r - radius

We have C = 21.99 ft. Substitute and solve for r:

[tex]21.99=2\pi r[/tex]             divide both sides by 2π

[tex]r=\dfrac{21.99}{2\pi}[/tex]

Use [tex]\pi\approx3.14[/tex]

[tex]r\approx\dfrac{21.99}{2(3.14)}=\dfrac{21.99}{6.28}\approx3.5[/tex]

The radius of a circle with a circumference of 21.99 feet is 3.50 ft

where

r = radius

Therefore,

circumference = 21.99 ft

circumference = 2πr

circumference = 2 × 3.14 × r

21.99 = 6.28r

divide both sides by 6.28

r = 21.99 / 6.28

r = 3.50159235669

r = 3.50 ft

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Answer:

The diagonal  is about 14 m

Step-by-step explanation:

A = s^2

98 = s^2

so

s = √98

diagonal c^2 = 98 + 98

c^2 = 196

c = √196

c  ≈ 14

Answer:

The diagonal  is about 14 m

Answer:

C= 14

Step-by-step explanation:

The side is the square root of the area

S × S = A

S = √98

The diagonal is the hypotenuse of a right triangle formed by the two sides so

a²  + b² = c²

Where C = the diagonal A = √98 , B = √98

so C²= (√98)² + (√98)²

This gives: C²= 98 + 98 or

C² = 196

√C² = √196

C= 14