which expressions represent rational numbers? Check all that apply A.√6 + √9 B. √64+(6/11) C. √36+√21 D.√16+√169 E. 17.43 (43 is repeated)+√49 F. √44+√25

Answer:

Hey there!

Your answer would be x/2 - 9

Answer:

2 ÷ x - 9

Step-by-step explanation:

Quotient of two is written as = 2 ÷ x

Nine less is written as = -9

Final answer = 2 ÷ x - 9

Hope this helped! :)

Answer:

AB=8 BC=17 AC=9 BD=18

Step-by-step explanation:

Okay, so A is -3 and B is 5, so the distance would be 8, because the difference between -3 and 5 is 8. The same goes for all the rest. The distance on the number line is the difference between the two numbers they represent.

Answer:

320 people

Step-by-step explanation:

[tex]\frac{2 people}{5 people}[/tex]=[tex]\frac{x}{800 people}[/tex]

solve for x by using cross multiplication

     -multiply 2 by 800 to get 1,600

     -divide 1,600 by 5 people to get 320

your answer is 320 people

Answer:

(x-5)(x-8)(x+2)=0

Step-by-step explanation:

first look at the x intercept to find the factor

x:-2,5,8

x=-2 then x+2=0

x=5 then x-5=0

x=8 then x-8=0

(x-5)(x-8)(x+2)=0

check for y in the polynomial when x=0

x^3-11x^2+14x+80

x=0 y=80 ( correct according to the graph

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

[tex]\sqrt{x-1} =2-\sqrt{x+3}[/tex]

Square both sides.

[tex]\left(\sqrt{x-1}\right)^2=\left(2-\sqrt{x+3}\right)^2[/tex]

[tex]x-1=x+7-4\sqrt{x+3}[/tex]

Subtract x on both sides.

[tex]x-1-x=x+7-4\sqrt{x+3}-x[/tex]

[tex]-1=-4\sqrt{x+3}+7[/tex]

Subtract 7 on both sides.

[tex]-1-7=-4\sqrt{x+3}+7-7[/tex]

[tex]-8=-4\sqrt{x+3}[/tex]

Square both sides.

[tex]\left(-8\right)^2=\left(-4\sqrt{x+3}\right)^2[/tex]

[tex]64=16x+48[/tex]

Subtract 48 on both sides.

[tex]64-48=16x+48-48[/tex]

[tex]16=16x[/tex]

Divide both sides by 16.

[tex]\frac{16}{16} =\frac{16x}{16}[/tex]

[tex]1=x[/tex]

Switch sides.

[tex]x=1[/tex]

Answer:

  z = 1.58n

Step-by-step explanation:

To find the total amount (z), the cost of a bag (1.58) must be multiplied by the number of bags (n).

  z = 1.58n

Answer:

1.58 times the number of bags you're buying will give you how much money it all is: z=1.58n

Answer:

The answer is option A.

[tex] \frac{3}{ {n}^{5} } [/tex]

Hope this helps you

The expression for " 3 divided by n to the fifth" is given by

[tex]\frac{3}{n^{5} }[/tex].

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

According to the given question.

We have a statement

" 3 divided by n to the fifth"

Since, n to the fifth can be written as [tex]n^{5}[/tex].

Therefore,

the expression for " 3 divided by n to the fifth" is given by

[tex]\frac{3}{n^{5} }[/tex].

Thus, option A is the correct.

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Answer:

sister and brother

Answer:

D.

Step-by-step explanation:

As long as the function's largest power is two, it is a quadratic function.

a. (3x - 2)(4x + 7)

= 12x^2 - 8x + 21x - 14

The largest power is 2. This is a quadratic function.

b. 7x^2 + 8x

The largest power is 2. Quadratic function.

c. (2x - 1)^2

= 4x^2 - 4x + 1

Largest power is 2. Quadratic function.

d. 8x^4- 3x^3 + 5x^2

Largest power is 4. Non-quadratic function.

Hope this helps!

Answer:

A. 12 for every 7

Step-by-step explanation:

There are 12 peas in her bowl.

There are 7 peas in her hair.

The ratio of peas in her bowl to peas in her hair is 12 for every 7.

Answer:

C. Negative three-fourths

Step-by-step explanation:

Given two fractions -1 1/4 and 1/2, the sum of the fractions is expressed as shown below:

-1 1/4 + 1/2

Converting the improper fraction -1 1/4 to mixed fraction will give -5/4. The expression will now become:

-5/4 + 1/2

Taking the LCM of the expression

= (-5+2)/4

= -3/4

Hence the sum of fraction Negative 1 and one-fourth and one-half is negative three-fourths

Answer:

-3/4

Step-by-step explanation:

-1 1/4 +1/2

-5/4    +    2/4

-3/4

Answer:

[tex]\frac{(a-b)^2+b^2}{a^2}[/tex]

which agrees with the first choice (A) in your list of possible answers

Step-by-step explanation:

Notice that the area of the outer square is given by the square of it side [tex](a)[/tex].Then the outer area is given by: [tex]a^2[/tex]

Now, the inner square's area we calculate by subtracting from the outer area four equal right angle triangles (those shaded in grey in the figure provided). Each of such right angle triangles have an area given by the general formula of a triangle's area:

[tex]Area_{triangle}= \frac{base\,*\,height}{2} =\frac{(a-b)\,b}{2} =\frac{ab-b^2}{2}[/tex]

Therefore the internal square's area is:

[tex]a^2-4\frac{ab-b^2}{2} =a^2-2ab+2b^2[/tex]

And then the quotient of this are over the larger square area becomes:

[tex]\frac{a^2-2ab+2b^2}{a^2} =\frac{a^2-2ab+b^2+b^2}{a^2}=\frac{(a-b)^2+b^2}{a^2}[/tex]

Answer:

Step-by-step explanation:

a=10   (4,0,2,4,3,1,2,3,1,4)

b=4    (7,5,6,9)

c=6    (13,13,13,10,13,12)

d= 5   (17,16,17,17,16)

e=6    (21,23,20,20,21,23)

I hope this helps you

Sphere Surface Area Formula is

4.pi.r^2

4.pi.13^2

4.pi.169

676.pi

The surface area of the sphere with radius 13 units is S = 676π units²

A sphere is a three-dimensional geometrical object that is perfectly round in shape. A sphere is a fully spherical, three-dimensional geometrical object. Every point on its closed surface is equally spaced from the centre, which is the only point on the surface.The distance from the center to any point on the surface of the sphere is known as the radius of the sphere..

Surface Area of a Sphere = 4πr²

Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

They are used to represent many natural and man-made objects such as planets, basketballs, and molecules.

Let the data be ,

Let r = 13 units be the sphere's radius.

Let S be the sphere's surface area.

And , Surface Area of a Sphere = 4πr²

On simplifying , we get

S = 4π ( 13 )²

S = 4π ( 169 )

S = 676π units²

Thus, the sphere's surface area is S = 676 units2.

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Answer:

(3) =  119

(4) =  119

Step-by-step explanation:

Given isosceles triangle with vertex angle 58.

Need exterior angles of base angles 1 & 2.

Solution:

Vertex angle = 58.

Base angle = x

Sum of triangles = 180 =>

x + x + 58 = 180

Solve for x

x = (180-58)/2 = 122/2 = 61

Exterior angles are supplementary to interior (base) angles, so

(3) = 180-(1) = 180 - 61 = 119

(4) = 180-(2) = 180 - 61 = 119

* note: supplementary means sum of two angles = 180.

The measurements of angle 3 and angle 4 are​ 119degrees and 119degrees respectively.

The sum of the interior angle of the triangle is 180degrees.

According to the diagram shown:

m<1 + m<2 + 58 = 180

Since <1 = <2, hencce:

m<1 + m<1 + 58 = 180

2m<1 = 180 - 58

2m<1 = 122

m<1 = 122/2

m<1 = 61 degrees

Since <1 = <2, thereofore m<3 = m<4

Get the measure of m<3

m<1 + m<3 = 180 (supplementary angles)

61 + m<3 = 180

m<3 = 180 - 61

m<3 = 119 degrees

Recall that m<3 = m<4, hence m<4 = 119degrees

The measurements of angle 3 and angle 4 are​ 119degrees and 119degrees respectively.

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Answer:

The formula for perimeter is 2l+2w, where l is the length and w is the width.

The formula for area is lw, where l is the length and w is the width.

Answer:

Tim needs to finish 59/90

Step-by-step explanation:

Add together what Evan Claire and Jaya ran  

9/10 + 7/9+ 2/3

The common denominator is 90

9/10 (9/9) +7/9 *10/10  + 2/3 *30/30

81/90 + 70/90 + 60/90

211/90

We need 3 km = 3 *90/90 = 270 /90

270/90 - 211/90 = 59/90

Answer:

.44444444

Step-by-step explanation:

πr²=full circumference

18/π(9)²=x/2π

Answer:

29

Step-by-step explanation:

Let the smaller integer be x.

The other integer is 1 greater than 3 times x, or 3x + 1.

The product is 154.

x(3x + 1) = 154

3x^2 + x - 154 = 0

157 = 2 * 7 * 11

14 * 11 = 154

22 * 7 = 154

(3x + 22)(x - 7) = 0

3x + 22 = 0 or x - 7 = 0

3x = -22 or x = 7

x = -22/3 or x = 7

-22/3 is not a positive integer, so we discard that solution.

The smaller integer is 7.

3x + 1 = 3(7) + 1 = 22

The greater integer is 22.

The sum of the integers is 7 + 22 = 29

Answer: 29

Step-by-step explanation:

Answer:

[tex]2xy\sqrt[3]{2x^2z}[/tex] and [tex]2xy(2x^2z)^{\frac{1}{3}}[/tex].

Step-by-step explanation:

The given radical expression is

[tex]\sqrt[3]{16x^5y^3z}[/tex]

We have to simplify the above expression.

The above expression can be written as

[tex]\sqrt[3]{(2\times 8)(x^{3+2})y^3z}[/tex]

[tex]\sqrt[3]{(2\times 2^3)(x^3\times x^2)y^3z}[/tex]    [tex][\because a^{m+n}=a^ma^n][/tex]

[tex]\sqrt[3]{(2^3x^3y^3)(2x^2z)}[/tex]

[tex]\sqrt[3]{(2xy)^3}\sqrt[3]{2x^2z}[/tex]    [tex][\because (ab)^m=a^mb^m][/tex]

[tex]2xy\sqrt[3]{2x^2z}[/tex]    [tex][\because \sqrt[n]{x^n}=x][/tex]

It can be written as exponent form.

[tex]2xy(2x^2z)^{\frac{1}{3}}[/tex]    [tex][\because \sqrt[n]{a}=a^{\frac{1}{n}}][/tex]

Therefore, the required expressions are [tex]2xy\sqrt[3]{2x^2z}[/tex] and [tex]2xy(2x^2z)^{\frac{1}{3}}[/tex].

Answer:

D. The data are discrete because the data can only take on specific values.

Step-by-step explanation:

Continuous variables are variables that can take on any value in an interval. Examples of continuous variables are length, time, etc.

Discrete variables on the other hand are variables that can only take on specific values.

The durations of movies in minutes can only take on integer values from 0 to 60. Therefore, it is a discrete data.

The correct option is D.

Answer:

The cup holds 26.2 in3 more ice cream than the cone.

Step-by-step explanation:

1. Let's find the volume of ice cream that the cone holds, this way:

Volume = π * r² * h/3

Replacing with the real values, we have:

Volume = 3.14 * 2.5² * 5/3

Volume =32.7 inches³

2. Let's find the volume of ice cream that the cup holds, this way:

Volume = π * r² * h

Diameter = 5 inches ⇒ Radius = 2.5 inches

Replacing with the real values, we have:

Volume = 3.14 * 2.5² * 3

Volume =58.9 inches³

3. Let's find the difference, this way:

Volume of the cup - volume of the cone = 58.9 - 32.7 = 26.2 inches³

The cup holds 26.2 in³  more ice cream than the cone.

Answer:

Annual Interest Rate, r  = 5.69%

Step-by-step explanation:

Amount of loan taken = 220,000

Closing fee is 5% of the loan value

Closing fee = 5% of 222,000 = 0.05 * 220000 = 11000

Therefore, Principal, P = Loan amount + closing fee

P = 220000 + 11000

P = 231, 000

Annual rate, r= 5.25% = 0.0525

Monthly rate, i = 0.0525/12 = 0.004375

Time, n = 30 years = 30*12 = 360 months

The monthly payment will be calculated by:

[tex]PMT = \frac{P*i}{1 - (1 + i)^{-n}} \\\\PMT = \frac{231000 * 0.004375}{1 - (1 + 0.004375)^{-360}} \\\\PMT = 1275.59[/tex]

Assuming payments are made based on 220,000, let us calculate the monthly interest rate.

[tex]PMT = \frac{P*i}{1 - (1 + i)^{-n}} \\\\1275.59 = \frac{220000 * i}{1 - (1 + i)^{-360}} \\\\i = 0.00474229[/tex]

Annual rate, r = 12 * 0.0047429

r = 0.0569 = 5.69%

Answer:

The two x-intercepts are (-1, 0) and (3, 0).

Step-by-step explanation:

Set each factor = to 0 and solve for x:

x + 1 = 0 => x = -1.  One x-intercept is thus (-1, 0).

x - 3 = 0 => x = 3.  The other x-intercept is (3, 0).

Answer:

42

Step-by-step explanation:

When calculating the greatest common divisor, you must look for the smallest divisors that can divide the no. s given simultaneously.

So in this case the smallest divisor will be 2.

378 =189. 420 =210

2. 2

The next divisor that 189 and 210 can both be divided with is 3

189 =63. 210 =70

3. 3

The third smallest divisor that can 63 and 70 can be divided with is 7

63 =9. 70 =10

7. 7

9 and 10 have no common divisors that can divide them fully without leaving a remainder

So to get the greatest common divisor, multiply all the divisors you have used

In this case we've used 2,3,7

2x3x7= 42

Answer:

y = 2/3x + 1/3

Answer:

y = 2/3x + 1/3

Step-by-step explanation:

Answer:

D)

Step-by-step explanation:

Use desmos in the future to help you determine if all of those coordinate make a straight line.

Answer:

6 granite, 3 marble, 14 sandstone, 1 slate

ratio of sandstone to marble

how many sandstone does she have .....14

how many marble does she have......3

so the ratio would be 14:3

Answer:

C. 14:3

Step-by-step explanation:

Dana has 14 pieces of sandstone.

Dana has 3 pieces of marble.

The ratio of pieces of sandstone to pieces of marble is 14:3.

The ratio cannot be simplified further.

Answer:

The graph g(x) is vertically shrunk by a factor of 1/9.

Step-by-step explanation:

Parent Graph: f(x) = a√(bx - c) + d

Since we are only modifying a, we are dealing with vertical shrink (a < 1) and stretch (a > 1). Since 1/9 < 1, we have a vertical shrink by a factor of 1/9.

The correct description is:

"The graph of g(x) is shrunk vertically by a factor of 1/9"

There are two types of dilations.

Vertical dilation:

For a function f(x), a vertical dilation of scale factor k is written as:

g(x) = k*f(x).

Where if k > 1, we have a dilation, if 0 < k < 1, we have a contraction.

Horizontal dilation:

For a function f(x), a horizontal dilation of scale factor k is wrtten as:

g(x) = f(x/k).

Where if k > 1, we have a dilation, if 0 < k < 1, we have a contraction.

Here we have:

So we can see that g(x) is a vertical contraction of scale factor 1/9.

Then the correct option is:

"The graph of g(x) is shrunk vertically by a factor of 1/9"

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Answer:

1

Step-by-step explanation:

The number of terms in the polynomial;

7b^7

The number of terms in this polynomial is simply 1

Since the two are together, they are treated as a single term in the polynomial.

Take for example a quadratic polynomial;

3x^2 + 2x + 1

This is a polynomial with 3 terms.

All multiplications are treated as a single unit.

This is the case in terms of what we have too