Given: AB= 4
AD= 6
What is the length of BD?
2
4
6

Answer:

4x^4

Hope this helps

For this case we must find an expression equivalent to:

[tex](256x^{16}) ^ {\frac {1} {4}[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Then, rewriting the expression:

[tex](256 ^ {\frac {1} {4}} * x ^ {\frac {16} {4}}) =[/tex]

We have by definition:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]\sqrt [4] {256} * x ^ 4 =\\\sqrt [4] {4 ^ 4} * x ^ 4 =\\4x ^ 4[/tex]

ANswer:

Option B

Answer:

She can read 180 pages in 4 hours

45*4=180

Carol can read 180 pages in four hours.

Simply multiply the rate (45 pages/hour) by the time (4 hours) to get 180 pages/4 hours.

Answer:

Step-by-step explanation:

[tex]4^x=\left(\dfrac{1}{8}\right)^{x+5}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\4^x=(8^{-1})^{x+5}\\\\(2^2)^x=\bigg((2^3)^{-1}\bigg)^{x+5}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2x}=2^{-3(x+5)}\iff2x=-3(x+5)\qquad\text{use the distributive property}\\\\2x=-3x-15\qquad\text{add}\ 3x\ \text{to both sides}\\\\5x=-15\qquad\text{divide both sides by 5}\\\\x=-3[/tex]

Answer:

B, -3

Step-by-step explanation:

[tex](x-1)(x-3)=x^2-3x-x+3=x^2-4x+3[/tex]

Answer:

50

Step-by-step explanation:

Hello There!

There are 50 states in the United States

Alabama

Alaska

Arizona

Arkansas

California

Colorado

Connecticut

Delaware

Florida

Georgia

Hawaii

Idaho

Illinois Indiana

Iowa

Kansas

Kentucky

Louisiana

Maine

Maryland

Massachusetts

Michigan

Minnesota

Mississippi

Missouri

Montana Nebraska

Nevada

New Hampshire

New Jersey

New Mexico

New York

North Carolina

North Dakota

Ohio

Oklahoma

Oregon

Pennsylvania Rhode Island

South Carolina

South Dakota

Tennessee

Texas

Utah

Vermont

Virginia

Washington

West Virginia

Wisconsin

Wyoming

Final answer:

To find the garden's width, factor the area trinomial to match the given length of the garden. The width is represented by the other factor, which in this case is g - 6.

Explanation:

The area of a garden is given by the trinomial [tex]g^2[/tex] - 2g - 24, and the garden's length is g + 4. To find the garden's width, we need to factor the trinomial such that it is the product of two expressions, one of which must be the length (g + 4).

Factoring [tex]g^2[/tex] - 2g - 24, we look for two numbers that multiply to -24 and add up to -2. These numbers are -6 and +4. So, we can factor the area trinomial as:

(g - 6)(g + 4) = [tex]g^2[/tex] - 2g - 24.

Since the length of the garden is g + 4, the other factor, g - 6, must represent the width of the garden. Thus, the garden's width is g - 6.

Answer:

Filling in the blanks: (rectangular prism) (cylinder) (rectangular prism)

The cylinder has the greater volume because the cylinder fits within the rectangular prism with extra space between the two figures.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

We can see this by comparing the formulas for the volumes of the two shapes.

The volume V of a rectangular prism with length L, width W, and height H is given by:

V = L x W x H

The volume V of a cylinder with radius r and height H is given by:

V = πr²H

Now,

We are told that the length of each side of the prism base is equal to the diameter of the cylinder.

Since the diameter is twice the radius, this means that the width and length of the prism base are both equal to twice the radius of the cylinder.

So we can write:

L = 2r

W = 2r

Substituting these values into the formula for the volume of the rectangular prism, we get:

V prism = L x W x H

V prism = 2r x 2r x H

V prism = 4r²H

Substituting the radius and height of the cylinder into the formula for its volume, we get:

V cylinder = πr^2H

To compare the volumes,

We can divide the volume of the cylinder by the volume of the prism:

V cylinder / V prism = (πr²H) / (4r²H)

V cylinder / V prism = π/4

π/4 is greater than 1/1,

Thus,

The cylinder has a greater volume.

The cylinder fits within the rectangular prism with extra space between the two figures because the cylinder is inscribed within the prism, meaning that it is enclosed within the prism but does not fill it completely.

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Answer:

34,560

Step-by-step explanation:

Started of with 20 and earned 12%  each year.

12% is just 12 as a whole number

so from that 20  12x12x12=1,728

1,728x20=

34.560

Answer:

Measure of central tendency (center)

it is called median

Answer:

The value of CD is 2√5

Step-by-step explanation:

* Lets describe the figure to know its name

- ABCD is a quadrilateral

∵ BC parallel to AD

∵ BC = 6 units and AD = 8 units

- The quadrilateral which has two parallel sides not equal in length is a

 trapezoid

∴ ABCD is a trapezoid, where BC and AD are its bases

∵ BA perpendicular to AD

∴ BA is the height of the trapezoid

- The area of the trapezoid = 1/2 (base 1 + base 2) × its height

∵ The bases of the trapezoid are BC and AD

∵ BC = 6 and AD = 8

∵ Its area = 28 units²

∴ 1/2 (6 + 8) × height = 28

∴ 1/2 (14) × height = 28

∴ 7 × height = 28 ⇒ divide both sides by 7

∴ height = 4

∵ The height is BA

∴ BA = 4 unit

- To find the length of CD draw a perpendicular line from C to AD and

 meet it at E

∵ BA and CE are perpendicular to AD

∴ BA // CE

∵ BC // AD

- Perpendicular lines between parallel lines are equal in lengths

∴ BA = CE and BC = AE

∵ BA = 4 and BC = 6

∴ CE = 4 and AE = 6

∵ AD = 8 units

∵ AD = AE + ED

∴ 8 = 6 + ED ⇒ subtract 6 from both sides

∴ ED = 2 units

- In ΔCED

∵ m∠CED = 90°

∴ CD = √[(CE)² + (ED)²] ⇒ Pythagoras theorem

∵ CE = 4 and ED = 2

∴ CD = √[(4)² + (2)²] = √[16 + 4] = √20 = 2√5

* The value of CD is 2√5

Final answer:

The value of the unknown side CD in quadrilateral ABCD can be found using the area of a trapezoid formula and the Pythagorean theorem. Given the area, and the lengths of BC and AD, we calculated that CD equals 8 units.

Explanation:

The student has asked to find the value of CD in a quadrilateral ABCD, where BC is parallel to AD, BA is perpendicular to AD, the area of quadrilateral ABCD is 28 square units, BC is 6 units, and AD is 8 units.

Since BA is perpendicular to AD and BC is parallel to AD, we can determine that ABCD is a trapezoid with AB and CD as the non-parallel sides. The area of a trapezoid is given by the formula Area = ½ × (sum of parallel sides) × height. So we have:

½ × (AD + BC) × height = 28
½ × (8 + 6) × height = 28
½ × 14 × height = 28
7 × height = 28
height = 4 units

Since BA is perpendicular to AD, and given BA is the height of the trapezoid, this means that AB = 4 units. Now, because ABCD has right angles at A and B, triangles ABD and ABC are right triangles and we can use the Pythagorean theorem to calculate CD.

In triangle ABD:

Since CD is the hypotenuse of triangle ABD:

Therefore, the correct answer is CD = 8 units.

22.7

They are opposites because they are both the same distance from 0 and are on different sides of 0 on a number line.

They are also opposites because when either of them is multiplied by -1, you get the other one.

[tex]22.7*-1=-22.7[/tex]

[tex]-22.7*-1=22.7[/tex]

Answer:

22.7 because it's the same number but different

Answer:

Step-by-step explanation:

Before we can determine which measure of central tendency is the best we need to determined whether data set is skewed or not.

We can determine the skewness, if we know at least the median and the mean.

The array of the above data set is,

16,18,28,29,35,36,37,38,40,41,44,66,68,72

The Median of the above array is  

\frac{37 + 38}{2} = \frac{75}{2} = 37.5  

The mean is

\frac{16 + 18 + 28 + 29 + 35 + 36 + 37 + 38 + 40 + 41 + 44 + 66 + 68 + 72}{14} = \frac{532}{14} = 38

Since the mean and the median are not the same, the distribution is skewed.

<b>For a skewed distribution, the best measure of central tendency is the median.</b>

To one decimal place, the median is;

37.5

NB: If the distribution is not skewed then it is normal. In a normal distribution the median is equal to the mean. The mode is considered the best measure of center in this case.

Step-by-step explanation:

The median of a data set is the measure of center that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude

Answer:

6 miles

Step-by-step explanation:

4+2.75m=20.50

-4              -4

2.75m=16.50/2.75

m=6

Answer:

6 miles

Step-by-step explanation:

So the total charge is $20.50, what I personally did was

Subtract $4 from $20.50

You get $16.50

Now divide $16.50 by $2.75

There's your miles

Answer:

A. 236

B. 164

Step-by-step explanation:

18% of 200= 36

200+36=236

200-36=164

Answer:

A. 236

B. 164

Step-by-step explanation:

To solve it first you need to find what 18% of 200 is. To do that take the 18% and make it a decimal % is out of 100, so 18/100 = .18. Then to find how much 18% out of 200 is, multiply .18 * 200. You should get 36. Then you can add and subtract that from 200 to get 18% more and 18% less.

Answer:

y + 8 = 6(x + 1)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 6 and (a, b) = (- 1, - 8), hence

y - (- 8) = 6(x - (- 1)), that is

y + 8 = 6(x + 1)

ANSWER

[tex]y + 8=6(x + 1)[/tex]

EXPLANATION

The point-slope form of an equation is given by the formula:

[tex]y-y_1=m(x-x_1)[/tex]

Where

[tex](x_1,y_1)[/tex]

is a point on this line and

[tex]m[/tex]

is the slope of the line.

From the question, the line has slope 6 and passes through (-1,-8).

This means that

[tex]x_1=-1[/tex]

[tex]y_1=-8[/tex]

and

[tex]m = 6[/tex]

We substitute these values into the point-slope formula to get:

[tex]y- - 8=6(x- - 1)[/tex]

We simplify to get:

[tex]y + 8=6(x + 1)[/tex]

Answer:

B + 281d

Step-by-step explanation:

I think that's the answer the "is" is throwing me off "is" is either = or (x)

Hope my answer has helped you and if not i'm sorry.

Answer:

My mom drives about 120 miles, grandpa: 160, and dad: 200

Step-by-step explanation:

Answer:

My dad drives about 80

Step-by-step explanation:

He only goes shopping and takes me to school.

The factorized form of the given polynomial is (3x + 4)(3x - 4). Using one of the factorization methods of polynomial, the result is obtained.

Writing a polynomial as the product of its factors (monomial, binomial or and so on) is called the factorization of the polynomial.

There are different methods of factorization. Some of them are the grouping method, GCF method, the difference of squares method, etc.

The given polynomial is  [tex]9x^2-16[/tex]

Using the difference of squares method we can write the given polynomial as

[tex]9x^2-16 = (3x)^2-(4)^2[/tex]

We know that difference between any two squares is

[tex]a^2-b^2=(a+b)(a-b)[/tex]

So,

[tex]9x^2-16[/tex] = (3x + 4) (3x - 4)

Therefore, the factors of the given polynomial are (3x + 4) and (3x - 4).

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Answer:

x= 1, -2/3

Step-by-step explanation:

Answer:

G(2+h)=3(2+h)^3

Step-by-step explanation:

We need to put the value of the required digit , we have to find the value of . So go on solving and you will get your answer.

Answer:

b.  (3, 0.5).

Step-by-step explanation:

x + 2y = 4

2x - 2y = 5

Adding the 2 equations eliminates the y:

3x = 9

x = 3

Substitute fro x in the first equation:

3 + 2y = 4

2y = 1

y = 0.5.

Option B is correct, (3, 0.5) is the solution of the  system of equations.

Two or more expressions with an Equal sign is called as Equation.

The two equations are

x+2y=4...(1)

2x-2y=5...(2)

Add equation 1 and 2

x+2y+2x-2y=4+5

3x=9

Divide both sides by 3

x=3

3+2y=4

Subtract 3 from both sides

2y=1

y=1/2

y=0.5

Hence, option B is correct, (3, 0.5) is the solution of the  system of equations.

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Answer:

y=68(1.5)^(x-1)

Step-by-step explanation:

Answer:

The function is:

[tex]y = 68 (1.5) ^ x[/tex]

Step-by-step explanation:

Note that the number of people increases by a factor of 1.5 per hour, and the initial number of people is 68.

So:

 After an hour the number of people is:

[tex]y = 68 (1.5)[/tex]

After two hours the number of people is:

[tex]y = 68 (1.5) (1.5) = 68 (1.5) ^ 2[/tex]

After x hours the number of people is:

[tex]y = 68 (1.5) ^ x[/tex]

Therefore, the exponential growth function that models the number of people y at the fair after x hours is:

[tex]y = 68 (1.5) ^ x[/tex]

Answer:

The equation y = 1 - 2x is represented by this table.

The correct answer is A.

Answer:

Step-by-step explanation:

y=6x-2

y=6x-4

6x - 2 = 6x - 4

6x -6x = -4+2

0 = -2  ....false

no solutions

Answer:

y = -5 (x+2)

Step-by-step explanation:

We can use the point slope form of a line

y-y1 = m(x-x1) where (x1,y1) is the point and m is the slope

y-0 = -5(x--2)

y = -5 (x+2)

Answer:

The answer is [4,3] Hope this helps.

Step-by-step explanation:

The solution to the both system of equations A and B are (3.875, 2.375) for system A and (4.133, 2.289) for system B.

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

Consider system A.

x + 3y = 11

15x − 3y = 51

Adding both equations,

16x = 62

x = 3.875

3y = 7.125

y = 2.375

Consider system B.

x + 3y = 11

15x = 62 ⇒ x = 4.133

3y = 6.867

y = 2.289

Hence the solutions are (3.875, 2.375) for system A and (4.133, 2.289) for system B.

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Answer:

option D) (x,y,z)

Step-by-step explanation:

we know that

The three-dimensional Cartesian coordinate is defined by three axes at right angles to each other, forming a three dimensional space.

The three axes are labeled x ,y and z.

The x-axis is called abscissa

The  y-axis is called ordinate

The z-axis is called applicate

therefore

A point in a three-dimensional Cartesian coordinate is represented by (x,y,z)

Answer:

A. 3x - 1 + [3x - 1]⁻¹

Step-by-step explanation:

Use Polynomial Long Division to arrive at this answer.

**[3x - 1]⁻¹ = 1\[3x - 1]

Answer:

2/3

Step-by-step explanation:

Y varies directly as x

Y =kx

Y=6 when x = 72

First find the relationship between y and x.

i.e find the value of k

Substitute the value of x and y

6 = k *72

Make k the subject of the formula

K = 6/72

K= 1/12

:. The rlationship between x and y is

Y = 1/12x

When x is 8

Y = 1/12 * 8

Y = 8/12

Y = 2/3 and that is the answer

Hope it helped you

Answer:

The answer is : 2/3

Step-by-step explanation:

Given is that y varies directly as x.

Means as y increases or decreases, x also increases or decreases.

When y is 6 when x is 72,

So, when x = 8, we have to find y.

We can write the relation as follows:

[tex]\frac{6}{y}= \frac{72}{8}[/tex]

[tex]72y=48[/tex]

[tex]y=\frac{48}{72}[/tex] = [tex]\frac{2}{3}[/tex]