Solve: 16n + 28 = -20

The coordinates of points A, B, C, D, E, and F are as follows:

A: (-2, 0, 0)

B: (-2, 0, -7)

C: (0, 4, -7)

D: (0, 4, 0)

E: (0, 0, -7)

F: (0, 0, 0)

What is the equation of the plane that contains points B, C, E, and P?

The equation of the plane containing points B, C, E, and P can be determined using the formula for the equation of a plane. We can select any three non-collinear points from the four given points (B, C, E, and P) and use them to find the equation. Let's choose points B, C, and E. We first find two vectors on the plane: BC → (0, 4, -7) - (-2, 0, -7) = (2, 4, 0) and BE → (0, 0, -7) - (-2, 0, -7) = (2, 0, 0). Taking the cross product of BC and BE, we get the normal vector N → (0, 14, 8). Now, using the coordinates of point B and the normal vector N →, we can write the equation of the plane as 0x + 14y + 8z + d = 0. Substituting the coordinates of point B into the equation, we find that d = -56. Therefore, the equation of the plane containing points B, C, E, and P is 14y + 8z - 56 = 0.

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The values of the function table for the equations f(x) = 2x + 13, f(x) = x² + 15, f(x) = -x²  + 9x + 11 are represented below

A function table is a table that shows which coordinates should be plotted in the coordinate system, so that you can draw the graph of the function.

In the first equation;

f(x) = 2x + 13

x = -1

f(-1) = 2(-1) + 13

f(-1) = -2 + 13

f(-1) = 11

x = 0

f(0) = 2(0) + 13

f(0) = 13

when x = 1

f(1) = 2(1) + 13

f(1) = 15

x = 2

f(2) = 2(2) + 13

f(2) = 19

In the second equation;

f(x) = x² + 15

when x = (-2)²  + 15

f(-2) = 19

when x = 0

f(0) = 15

When x = 1

f(1) = (1)² + 15

f(1) = 16

When x = 3

f(3) = (3)² + 15

f(3) = 24

In the third equation;

f(x) = -x²  + 9x + 11

when x = -4

f(-4) = -(-4)² + 9(-4) + 11

f-4) = -41

when x = -2

f(-2) = -11

When x = 0

f(0)  = 11

When x = 2

f(2) = 25

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Answer: It will take 10 weeks! :)

Step-by-step explanation:

So let's look at this together.

The question states that they raise 90$ per week.

There's two ways you can do this

You can multiply,

Think, what times 90 will equal 900? The answer is 10!

90 x 10= 900!

(if you need help with multiplication, let me know)

Or you can divide.

900/90=10!

(if you need help with division, let me know)

So it would take, in total, 10 weeks to raise 900 dollars.

Answer:

Step-by-step explanation:

y=−3x+12

when x=0 then y=12 , the y intercept is (0,12)

when y=0 then -3x+12=0, -3x=-12, x=12/3=4

x intercept =(4,0)

The x and y intercepts of the line are (4, 0) and (0, 12).

In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

When y=0, we get

x=4

So, x-intercept is (4, 0)

When x=0, we get

y=12

So, y-intercept is (0, 12)

Therefore, the x and y intercepts of the line are (4, 0) and (0, 12).

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Answer:

10

Step-by-step explanation:

the square root of 100 is 10

√100=10

Answer:  10 + i

thats answer

The number of waffles can be made from 15 eggs are, 20 waffles.

the waffles can be calculates as follows

4 cups of fluor + 6 eggs +2 tbsp oil = 8 waffles

we need 6 eggs to make 8 waffles

So, the waffles can we make from 15 eggs = \(\frac{8}{6} X 15 = 20\) waffles

Hence, the number of waffles can be made from 15 eggs are 20 waffles.

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Answer:

0.142

Step-by-step explanation:

From the question, we identify the following parameters;

n = 49

p = 82% = 82/100 = 0.82

alpha, α = 1-0.99 = 0.01

Zα/2 = Z_0.005 = 2.575

margin of error = Zα/2 * √( p(1-p)/n)

Margin of error = 2.575 * √(0.82)(1-0.82)/49

Margin of error =0.1416005 which is approximately 0.142

The total area of the colored rectangles is 62 square feet

Given that: the room is  12 x 16 with an 8 x 10 piece of linoleum centered in the room

The shape will be treated as a composite rectangle. Thus, the room can be divided into smaller rectangles as shown in the image attached.

For the Yellow part:

Length(L) = 8 + 2 = 10 feet

width(W) = 3 feet

Area(A) = L × W

A = 10 × 3 = 30 square feet

For the Blue part:

Length(L) = 2 feet

Width(W) = 3 + 10 = 13feet

Area(A) = L × W

A = 13 × 2 = 26 square feet

For the Green part:

Length(L) = 2 feet

width(W) = 3 feet

Area(A) = L × W

A =  2 × 3 = 6 square feet

Total colored area = Area of Yellow +  Area of Blue +  Area of Green

Total colored area = 30 + 26 + 6 = 62 square feet

Therefore, the total colored area is 62 square feet

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The cost of one apple is $0.70.

Let's assume that the cost of one apple is "a" dollars and the cost of one banana is "b" dollars. We can create two equations based on the information given:

4a + 9b = 12.70 ...(1)

8a + 11b = 17.70 ...(2)

To solve for "a", we can use elimination method by multiplying equation (1) by 8 and equation (2) by -4, so that the coefficients of "a" in both equations will be equal and opposite:

32a + 72b = 101.60

-32a - 44b = -70.80

Adding these two equations, we get:

28b = 30.80

Simplifying and solving for "b", we get:

b = 1.10

Now, we can substitute the value of "b" in equation (1) and solve for "a":

4a + 9(1.10) = 12.70

4a + 9.90 = 12.70

4a = 2.80

a = 0.70

Therefore, the cost of one apple is $0.70.

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The given equations are as follows

\(\begin{aligned} A.&&\dfrac x4+1&=-3 \\\\ B.&&x+4&=-12 \end{aligned}\)

(1) First, multiply both sides of equation A by 4, we have

\(4\times\left(\frac{x}{4} +1\right)=4\times(-3)\)

Then, rewrite the left-hand side of the above equation by using the distributive property, we have

\(4\times\frac{x}{4}+4\times1=4(-3)\)

\(\Rightarrow x+4=-12\)

This is the required equation B.

In this way, first use choice D: Multiply both sides by the same non-zero constant, i.e 4.

Then, apply choice A to solve the equation, i.e using the distributive property to solve the left-hand side of the equation.

(2) In the previous answer, equation B has been derived from equation A, hence, both the equations are equivalent.

As both the equations are the same, so both will have the same solution.

Yes, they have the same solution.

\(\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\begin{array}{llll} \textit{"y" varies}\\ \textit{directly with "x"}\\ \textit{inversely with "z"} \end{array}\qquad y=\cfrac{kx}{z}\hspace{5em}\textit{we also know that} \begin{cases} x=10\\ z=4\\ y=15 \end{cases} \\\\\\ 15=\cfrac{k(10)}{4}\implies \cfrac{4}{10}\cdot 15=k\implies 6=k\hspace{8em}\boxed{y=\cfrac{6x}{z}} \\\\\\ \textit{when x = 20 and z = 6, what's "y"?}\qquad y=\cfrac{6(20)}{6}\implies y=20\)

Answer:

I think is 500 hope it helps

Answer:

y = -\(\frac{1}{2}\)x - 4

Step-by-step explanation:

If a line is parallel then it has the same slope as your original line, so solve your equation for y, 2y = -x +14, divide both sides by 2 so y = - 1/2 x + 7

So your new parallel line has a slope of -1/2, since it passes through (-8,0) now find your y-intercept, so y = -1/2 x + 7 is 0 = -1/2(-8) + b so 0 = 4 + b

so b = -4, so put it all together

y = -\(\frac{1}{2}\)x - 4

The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.

The given function is f(x) = e^x near x = 0.

To find the best linear approximation, L(x), we use the formula:

L(x) = f(a) + f'(a)(x-a),

where a is the point near which we are approximating.

Let a = 0, so that a is near the point x = 0.

f(a) = f(0) = e^0 = 1

f'(x) = d/dx (e^x) = e^x;

so f'(a) = f'(0) = e^0 = 1

Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1

Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.

For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.

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In the given scenario, the cable company decides to conduct a survey in the rural town of Podunk to determine the proportion of households that would buy their internet service. 50% of the households surveyed would buy internet service from a cable company

To calculate the proportion of households, we use the following formula:

The proportion of households = (Number of households who would buy the service) / (Total number of households surveyed)

The subdivision has 24 blocks, and each block has exactly 10 households, for a total of 240 households.

Therefore, the proportion of households = (Number of households who would buy the service) / (Total number of households surveyed)

Let's say that after conducting the survey, the company finds out that 120 households would buy their internet service. Then, the proportion of households who would buy their internet service can be calculated as follows:

The proportion of households = 120/240

The proportion of households = 0.5

Therefore, 50% of the households surveyed would buy internet service from a cable company. This information can help the company decide whether it is cost-effective to lay fiber-optic cable for high-speed internet in the subdivision. If the proportion of households willing to buy their service is high enough, the cable company will consider extending its line out to the area. However, if the proportion is too low, it may not be worth the expense to lay fiber-optic cable.

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Answer:

A=80 , B=65, C=35

Step-by-step explanation:

A-B=15 ⇒A=B+15

B-C=30⇒-C=30-B ⇒C=B-30

the sum of angle of a triangle = 180

A+B+C=180 ( substitute A and C)

B+15+B+B-30=180

3B-15=180

3B=180+15

B=195/3=65

C=B-30 ⇒ C=65-30=35

A=B+15=65+15=80

check : A+B+C=180

             80+65+35=180 ( correct)

Answer:

96

Step-by-step explanation:

Total area = area of cube + area of triangle

A = 8² + \(\frac{8*8}{2}\) = 64 + 32 = 96 in²

Answer:

96 square feet

to find the area of a triangle the formula is

A=1/2×b×h

8×8=64

1/2×8×8=32

32+64= 96

Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility test for three.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

add all number

9+9+0 = 18

and 18/3 = 6

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On solving the provided question, we can say that in this triangle 2x-6 = 3 => 2x = 9 => x = 9/2 and 2z = 4 => z = 2

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

in this triangle

2x-6 = 3

2x = 9

x = 9/2

2z = 4

z = 2

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If the GCF of a term and 12x²y is 4xy , then (a) The term is 8xy , The expression is 4xy(2 + 3x) .

The Greatest Common Factor of the two terms is 4xy ,

where , the first term is 12x²y , we have to find the second  term ,

Consider Option(a) : where the second term is 8xy ,

So , GCF of 8xy and 12x²y is

= 2(4xy) and  3x(4xy)

= 4xy(2 + 3x )      ....taking 4xy common from both the terms ,

Therefore , Yes , the second term is 8xy and the expression is 4xy(2+3x) .

The given question is incomplete , the complete question is

What term and 12x²y have a GCF of 4xy? Write an expression that shows the monomial factored out of the polynomial , choose the correct answer below :

(a) The term is 8xy , The expression is 4xy(2 + 3x)

(b) The term is 16xy , The expression is 4xy(4xy + 3x)

(c) The term is 3x , The expression is 12x²y(3x + 4xy)

(d) The term is 4x²y , the expression is 4xy(1 + 3x) .

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Answer: The tree has to be 60 feet tall

Step-by-step explanation: Jerry’s shadow is a third of Jerry, that means the Tree’s shadow is only a third of the tree. To find the tree’s height you have to multiply the shadow by 3, 20 multiplied by 3 is 60.

Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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Answer:-2.1,-0.5,5/100,0.5

Step-by-step explanation:

The test has average  80 true/false questions, 24 fill in the blank questions, and 28 multiple choice questions, with 7, 9 and 13 points respectively, totaling 1172 points.

The college entrance test consists of 112 questions in total, with different types of questions having different point values. There are 80 true/false questions, each worth 7 points, with a total of 560 points from these questions. There are also 24 fill in the blank questions, each worth 9 points, giving a total of 216 points from these questions. Finally, there are 28 multiple choice questions, each worth 13 points, for a total of 364 points from these questions. All together, the test has 1172 points available. The number of fill in the blank questions is 34 less than the number of true/false questions, meaning that there are more true/false questions than fill in the blank questions. The test is designed to assess a student's knowledge and comprehension of the subject they are taking the test for, and is made up of the three different types of questions to give a comprehensive assessment of their understanding.

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"The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9 and the range is -6 ≤ y ≤ 7" is correct.

What is the Domain and Range of the function?

The domain of a function is the set of all input values (x-values) for which the function is defined. It is the set of all values of x for which the function is defined.

The range of a function is the set of all output values (y-values) that the function can produce. It is the set of all possible values that the function can take on.

The domain of a function is the set of all input values (x-values) for which the function is defined. The range of a function is the set of all output values (y-values) that the function can produce.

When we shift a function horizontally, the domain remains unchanged, but the range will change. In the case of a shift of -2, the domain of f(x) is still -3≤x≤9

For 9(x) = f(x-2) - 8, it means that we are taking the output of f(x-2) and subtracting 8 from it. So, the range of 9(x) will be (2-8) ≤ y ≤ (15-8) = -6 ≤ y ≤ 7.

In summary,

The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9

The range of 9(x) = f(x-2) - 8 is -6 ≤ y ≤ 7

Hence, statement "The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9 and the range is -6 ≤ y ≤ 7" is correct.

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If x equals 3 then y must equal 1.2

Answer: y=6

-4(3)+5y=18

-12+5y=18

add 12 to both sides

-12+5y+12=18+12

5y=18+12

5y=30

divide both sides by 5

5y÷5=30÷5

y=30÷5

y=6

I hope this is good enough:

Answer:

Option (3)

Step-by-step explanation:

From the given figure,

\(a_n=a_1+(n-1)d\)

where \(a_n\) = nth term of an arithmetic sequence

\(a_1\) = first term of the sequence

n = number of term

d = common difference

When n = 1 : \(a_1=-1\)

When n = 2 : \(a_2=-6\)

common difference 'd' = -6 - (-1) = -5

Formula for the nth term for the given sequence will be,

\(a_n=-1+(n-1)(-5)\)

    = -1 - 5n + 5

\(a_n\) = 4 - 5n

Now the 12th term of this sequence will be,

\(a_{12}=4-5(12)\)

     = 4 - 60

     = -56

Therefore, Option (3) will be the answer.

The completely factored form of the provided polynomial is  (p -2) (p+ 2) (p² +4). The option 4 is the correct option.

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is a real number).

The polynomial equation given in the problem is,

\(p^4 - 16\)

Let the factor form of the polynomial is f(p). Thus,

\(f(p)=p^4 - 16\\f(p)=p^4 - 2^4\\f(p)=(p^2)^2- (2^2)^2\)

Using the formula of difference of squares, we get,

\(f(p)=(p^2-4)(p^2+4)\\f(p)=(p^2-2^2)(p^2+4)\\f(p)=(p-2)(p+2)(p^2+4)\)

Thus, the completely factored form of the provided polynomial is  (p -2) (p+ 2) (p² +4). The option 4 is the correct option.

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Answer:

D Edge 2022

Step-by-step explanation:

Answer:

These should be right hopefully! Hope it helps!

Answer:

C

Step-by-step explanation:

using

x × y = \(\sqrt{x^2+y^2}\) , then

2 × 4\(\sqrt{2}\)

= \(\sqrt{2^2+(4\sqrt{2})^2 }\)

= \(\sqrt{4+32}\)

= \(\sqrt{36}\)

= 6

\(\textsf {Applying this formula :}\)

\(\mathsf {(x) \times (y) =\sqrt{x^{2} + y^{2}}}\)

\(\textsf {Now take :}\)

\(\mathsf {x = 2}\\\mathsf {y = 4\sqrt{2}}\)

\(\mathsf {Solving :}\)

\(\implies \mathsf {\sqrt{(2)^{2} + (4\sqrt{2})^{2}}}\)

\(\implies \mathsf {\sqrt{4 + 32}}\)

\(\implies \mathsf {6}\)