Which of the equations below describes a circle with radius 7? A. x2 - y2 = 7 B. x2 + y2 = 49 C. x2 + y2 = 77 D. x2 + y2 = 7​

The factorization of the given expression [tex]\rm x^2+10x+21[/tex] is (x+3)(x+7) the option first is correct.

It is given that the expression [tex]\rm x^2+10x+21[/tex]

It is required to find which expression is the factorization of the given expression, the options are:

a) (x + 3)(x + 7)

b) (x + 4)(x + 6)

c) (x + 6)(x + 15)

d) (x + 7)(x + 14)

Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.

We have an expression:

[tex]\rm x^2+10x+21[/tex]

[tex]\rm x^2+7x+3x+21[/tex]  

Breaking 10x into 7x and 3x because the multiplication of 7x and 3x is [tex]\rm 21x^2[/tex] and the addition is 10x.

[tex]\rm x^2+7x+3x+21\\\\\rm x(x+7)+3(x+7)\\\\\rm (x+7)(x+3)[/tex]or

[tex]\rm (x+3)(x+7)[/tex]

Thus, the factorization of the given expression [tex]\rm x^2+10x+21[/tex] is (x+3)(x+7) the option first is correct.

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Step-by-step explanation:

there are in total 21 marbles.

5 black, 6 blue = 11 black or blue marbles.

so, the probability of pulling a black or blue marbles is as always desired possible outcomes / total possible outcomes = 11/21

Answer:

[tex]\frac{5}{6}:1[/tex]

Step-by-step explanation:

[tex]10:12[/tex] divide both sides of this ratio by 12 to give a ratio in the form [tex]n:1[/tex]

[tex]\frac{10}{12}:1[/tex] which simplifies to [tex]\frac{5}{6}:1[/tex]

The number of rectangular prism container that would be set on the shelf is: 4.

Volume of rectangular prism = length × width ×height

Given the following:

Find the length of one rectangular prism using the volume formula since volume for one prism = 45 in.³

45 = length × 9

length = 5 in.

Each rectangular prism container is 5 in. long, therefore, the number of the containers that can be set on the shelf that is 24 in. long, if the 4.5 in by 2 in. face touches each other = 24/5 = 4.8.

The fifth container won't fit in. Therefore, the number of rectangular prism container that would be set on the shelf is: 4.

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Based on the speed Alyssa used to get to London and the speed back to Boston, the average speed was 540 mph.

The average speed that Alyssa was going can be found by the formula:

= (Initial speed + Final speed) / 2

Solving gives:

= (480 + 600) / 2

= 1,080 / 2

= 540 mph

In conclusion, Alyssa's average speed was 540 mph.

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Eigenvalues are the special set of scalar values which is associated with the set of linear equations in matrix equations.

Your information is incomplete. Therefore, an overview will be given. An eigenvector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it.

The eigenvectors of matrix A are those vectors X for which multiplication by A will result in a vector in thesame direction or opposite direction to X.

Since the zero vector 0 has no direction, 0 is never allowed to be an eigenvector.

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An eigenvector of a linear transformation and eigenvectors of a system

Ax = Bx can be determined where B is an eigenvalue of A.

An eigenvector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it.

The eigenvectors of matrix A are those vectors X for which multiplication by A will result in a vector in the same direction or opposite direction to X.

The basic equation is

Ax = Bx

here B is an eigenvalue of A.

Since the zero vector has no direction, zero is never allowed to be an eigenvector.

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Answer:

The slope is 5/7.

Step-by-step explanation:

Use a slope formula.

Slope:

[tex]\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]

y₂ = (17)

y₁ = (7)

x₂ = (18)

x₁ = (4)

Rewrite the problem down.

[tex]\sf{\dfrac{17-7}{18-4}=\dfrac{10}{14}={\dfrac{10\div2}{14\div2}=\boxed{\sf{\dfrac{5}{7}}}[/tex]

Therefore, the slope is 5/7.

I hope this helps! Let me know if my answer is wrong or not.

Answer:

5/7

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(17-7)/(18-4)

m=10/14

simplify

m=5/7

Answer:

This question is asking for you to determine if the tables represent linear functions, functions in y=mx+b form, and to find the equation for the line.

If something is a linear function, each of the input values will have it's own corresponding y value, therefore c cannot be linear, as -1 and 1 both have 10 as the output.

I hope this helps, but if you need more clarification, please tell me in the comments!

Answer:

Circumference = 7.68 cm

Area = 113.04 cm²

Step-by-step explanation:

First, let us find the radius of the given circle.

d = 2r

r = d / 2

r = 12 / 2

r = 6 cm

And now, let us find the circumference of the circle using the below formula.

C = 2 π r

C = 2 × 3.14 × 6

C = 37.68 cm

And now let us find the area of the circle using the below formula.

A = π r²

A = 3.14 × 6 × 6

A = 113.04 cm²

Answer:

Matt used diameter of the ball instead of Radius

Step-by-step explanation:

The volume of a sphere is given as:

⇒ Matt made an error in his calculation by failing to covert the value of the diameter given to Radius.

⇒ By dividing the diameter by 2 = 15 / 2 = 7.5, we obtain the Radius, which is what Billy did in her own calculation.

Answer:

X = 6

Step-by-step explanation:

Hope this helped!!

maybe mark brainiest

The difference in the volume of bedroom door in the house taken the length and width into consideration will be 120 inches³.

It should be noted that the volume of a door is simply gotten by multiplying the length by width.

Let's assume that the width is 20 inches. Therefore, the difference will be:

= (36 × 20) - (30 × 20)

= 720 - 600

= 120 inches³

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Answer:

MAYBE

Step-by-step explanation:

Answer:

SORRY

Step-by-step explanation:

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SORRY

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SORRY

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SORRY

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SORRY

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SORRY

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SORRY

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SORRY

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SORRY

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SORRY

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SORRY

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SORRY

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SORRY

Step-by-step explanation:

ANSWER

SOORY

The new length of the enlarged figure will 18 cm.

A scale factor is a number which scales, or multiplies, the original figure by some quantity.

We have the equation for the scale factor.

Y=Cx

C is a scale factor for x. It is called the constant of proportionality or scale factor of y to x.

As the given length is 4.5 cm, so with a scale factor of 4, the length of the enlarged figure will be

[tex]Y=4.5\times4=18\ cm[/tex]

Therefore, the new length of the enlarged figure will 18 cm.

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The sales receipt for the purchase includes the sales tax

The sales tax is calculated as:

Percentage sales tax * (Sum of Items subjected to tax) =  Sales tax.

So, we have:

T * (3 + 0.5) =  0.21

Evaluate the sum

T * (3.5) =  0.21

Divide both sides by 3.5

T =  6%

Hence, the sales tax is 6%

The price (p) at the top is calculated using:

p = 13 - 3 - 2 - 0.5

Evaluate the difference

p = 7.5

Hence, the price at the top is $7.50

60% of the original price (P) is p.

So, we have:

60% * P = p

Substitute 7.5 for p

60% * P = 7.5

Divide both sides by 60%

P = 12.5

Hence, the original price at the top is $12.50

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Answer:

t=-\frac{20}{11}

Step-by-step explanation:

Answer:

yeh

Step-by-step explanation:

1 gallons = 4 quarts

4,8,20,28

quarts= 2 pints

1,3,6,16

1 pint= 2 cups

2,6,5,18

Answer:

For example, 16/21

Step-by-step explanation:

Are there choices?

There is an infinite number of numbers between any two numbers.

2/3 = 14/21

6/7 = 18/21

One example of a fraction between 2/3 and 6/7 is 16/21

16/21 is between 2/3 and 6/7.

Answer:

Step-by-step explanation:

emma really smells bad do not answer this question

Answer:

x = -1.33333333333

Step-by-step explanation:

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}[/tex]

[tex]-2x+1-1=4x+9-1[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-2x=4x+8[/tex]

[tex]\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}[/tex]

[tex]-2x-4x=4x+8-4x[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-6x=8[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-6[/tex]

[tex]\frac{-6x}{-6}=\frac{8}{-6}[/tex]

[tex]x=-\frac{4}{3}[/tex]

[tex]x=-1.33333333333[/tex]

~Lenvy~

Answer:

m = 41/6

Step-by-step explanation:

Convert everything into improper fractions with a denominator of 6.

The probability that a worker chosen at random works at least 8 hours is Option C: 0.84 approx.

Suppose the random variable in consideration be X, and it is discrete.

Then, the probability of X attaining at least 'a' is written as:

[tex]P(X \geq a)[/tex]

It is evaluated as:

[tex]P(X \geq a) = \sum_{\forall \: x_i \geq a} P(X = x_i)[/tex]

The probability distribution of X is:

        x                      f(x) = P(X = x)

        6                               0.02
        7                               0.11

        8                               0.61

        9                               0.15

        10                              0.09

Worker working at least 8 hours means X attaining at least 8 as its values.

Thus, probability of a worker chosen at random working 8 hours is

P(X ≥ 8) = P(X = 8) + P(X = 9) +P(X = 10) = 0.85 ≈ 0.84 approx.

By the way, this probability distribution seems incorrect because sum of probabilities doesn't equal to 1.

The probability that a worker chosen at random works at least 8 hours is Option C: 0.84 approx.

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Given:

[tex]\\[/tex]

❍Let's assume, Length of rectangle x feet and width of the rectangle x - 5 feet respectively.

[tex]\\[/tex]

To calculate the dimensions of the rectangle we will use the formula of Area of rectangle:

[tex]\\[/tex]

[tex] \: \: \: \: \: \: \: { \underline{ \boxed{ \pmb{ \frak{ Area_{(rectangle)} = Length \times width }}}}} \\ \\ [/tex]

[tex]\\[/tex]

[tex] \underline {\sf{Substituting \: the \: values~ in~ above~formula: }} \\ [/tex]

[tex]\\[/tex]

[tex] : \implies \sf \:x \times (x - 5) = 126 \\ \\ \\ : \implies \sf \:x^2 - 5x = 126 \\ \\ \\ : \implies \sf \:x^2 - 5x - 126 = 0 \\ \\ \\ : \implies \sf \:x^2 - 14x - 9x - 126 = 0 \\ \\ \\ : \implies \sf \:x (x - 14) - 9 (x + 14) = 0 \\ \\ \\ : \implies \sf \:(x - 14)(x - 9) = 0 \\ \\ \\ : \implies { \boxed { \purple{\pmb { \: x = 14 \: \: or \: \: x = -9}}} } \\ \\ \\ [/tex]

Hence,

[tex]\\[/tex]

[tex] \\ { \underline{ \pmb{ \frak{\therefore Dimensions \: of \: rectangle \: are \: 9~ feet \: and \: 14 ~feet \: }}}}[/tex]

Given that, width of the rectangle is 5 feet less than the length and area of the rectangle is 126 sq. feet, and we are told to find the dimensions i.e the length and width of the rectangle.

As we know that the area of a rectangle is length times it's width, so if we assume our length to be x, so our width is just going to be (x - 5) , and putting it in the area formule we can thus obtain;

[tex]{:\implies \quad \sf x(x-5)=126}[/tex]

[tex]{:\implies \quad \sf x^{2}-5x-126=0}[/tex]

[tex]{:\implies \quad \sf x^{2}-14x+9x-126=0}[/tex]

[tex]{:\implies \quad \sf x(x-14)+9(x-14)=0}[/tex]

[tex]{:\implies \quad \sf (x-14)(x+9)=0}[/tex]

So, here either (x - 14) = 0 or (x + 9) = 0, when you equate both, you will get x = 14 or -9 but as x ≠ -9, so x = 14, and then x - 5 = 14 - 5 = 9

Hence, the required length and width are 14 feet and 9 feet respectively

The two inequalities that represents the constraints for the art studio classes per week are:

x + 1.5y = 40

35(x + y)  > 1,000

Here are inequalities signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

= means equal to

The inequality that represents the total hoursthe art studio is open would be an equal to sign. This is because the store is open for a maximum of 40 hours.

The inequality that represents the total earnings would be represented with a greater than sign because the studio earns more than $1000 weekly.

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The area of the sector that has a central angle of 120 degrees and radius of 8 units is 64π / 3 units²

The area of a sector is defined as follows:

area = ∅ / 360 × πr²

where

Therefore,

r = 8

∅ = 120°

Hence,

area of the sector = 120 / 360 × π × 8²

area of the sector = 1 / 3 × π × 64

area of the sector = 64π / 3 units²

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====================================================

let's evaluate this expression

[tex]\pmb{\displaystyle\frac{8-m}{n+p^2} }[/tex]

[tex]\pmb{\displaystyle\frac{8-8}{2+7^2}}[/tex] (step 1)

[tex]\pmb{\displaystyle\frac{0}{2+49}}[/tex] (step 2)

simplify:

[tex]\pmb{\displaystyle\frac{0}{51}}[/tex] (step 3)

[tex]\pmb{0}[/tex] (step 4)

=======================================

Hope everything is clear; if you need any more clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

6 1/4

Step-by-step explanation:

3+2=5

2+3

1/2+3/4= ----------------------------------------------------

4

=5/4

=1 1/4

5+ 1 1/4

=6 1/4