Match the polar equations to their rectangular forms-

Answer:

x (y + 1)

Step-by-step explanation:

Simplify the following:

x y + x

Factor x out of x y + x:

Answer: x (y + 1)

An equation of the parabola that has the same shape as the graph of f(x) = 4x², but with the point (10,4) as the vertex is y = 4x² - 80x + 404.

             y = a(x - h)² + k  where (h, k) is the vertex.

Given:

f(x) = 4x²

Vertex =  (10,4)

a = 4

The value of a in the vertex form of the equation is taken to be 4 since the coefficients of x² must match for the parabola to have the same shape as the given parabola.

The equation can be written as,

y = a(x - h)² + k  where (h, k) is the vertex.

Replacing the value of the vertex, we get

y = 4(x - 10)² + 4

y = 4(x² - 20x + 100) + 4

y = 4x² - 80x + 400 + 4

y = 4x² - 80x + 404

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{8^3}{2^4}}[/tex]

[tex]\mathsf{= \dfrac{8\times8\times8}{2\times2\times2\times2}}[/tex]

[tex]\mathsf{= \dfrac{64\times8}{4\times4}}[/tex]

[tex]\mathsf{= \dfrac{512}{16}}[/tex]

[tex]\mathsf{= 512\div16}[/tex]

[tex]\mathsf{= 32}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{32}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Power of fractions, with numerator and denominator.

The power is composed of a base and an exponent, so the exponent indicates how many times the base is multiplied, then,

[tex]\boldsymbol{\dfrac{8^{3} }{3^{4} }=\dfrac{8\times8\times8}{2\times2\times2\times2} =\cfrac{512}{16}=32 }[/tex]

Answer:

b

Step-by-step explanation:

the square root of 9 is 3 because 3*3=9

3+6=9

[tex]d(f-4)=2(1-f)\\\\frac{d(f-4)}{d} =\frac{2(1-f)}{d} \\f-4=\frac{2(1-f)}{d} \\f=\frac{2(1-f)}{d} +4[/tex]

Attached is the solution

Answer:

Step-by-step explanation:

d= 2(1-f) / f-4

d = 2 - 2f / f-4

d = 1/2 - 2f - f

d = 1/2 - f

0=1/2-f-d

f = 1/2 - d

High school = 1446 students

Middle school = 1/6 as many as Highschool

Multiply 1/6 by the number of students enrolled at the high school.

m = 1/6 (1446) = 241

It is a multiplicative question

Answer:

  13,551,737

Step-by-step explanation:

You want the sum of the first 13 terms of the geometric sequence with first term 17, and successive terms 51, 153, ....

The common ratio is found by dividing a sequence term by the one before it:

  r = 51/17 = 3

The common ratio is 3.

The index of the 13th term of the sequence is n = 13.

The sum of n terms of a geometric sequence with first term a1 and common ratio r is ...

  Sn = a1·(r^n -1)/(r -1)

For a1 = 17, r = 3, and n = 13, the sum is ...

  [tex]S_{13}=17\cdot\dfrac{3^{13}-1}{3-1}=17\cdot\dfrac{1594322}{2}=\boxed{13,\!551,\!737}[/tex]

The last digits of multiplying 5s and 2s with at least one of each will be zero (0)

From the question, we are to determine what the last digit of the product could be

From the given information,

We are multiplying as many 5s and 2s as we want but we must have at least one of each

Since we must have at least one of each of 5 and 2, we will always have a 5 × 2

But, 5 × 2 = 10

NOTE: 10 multiplied by any number will always result in a number with a last digit of zero (0)

Example

2 × 5 × 2 × 2 × 2 × 2 = 160

5 × 2 × 5 × 5 × 5 × 5 = 6250

Thus, the last the digit of the product will be 0

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Explanation:

Think of -8.8 as -8.80

We're comparing -8.85 to -8.80, which means we're comparing the stuff after the decimal 85 and 80

Since 85 > 80, this places -8.85 to the left of -8.80

It's like saying how -85 is to the left of -80

I recommend drawing out a number line to see what's going on.

By solving both equations we get x =:

1. x = 12

2. x = 28/3

1. |x - 3| = 2x - 15

|x - 3| - 2x = 2x - 15 - 2x

by simplifying,

- 2x + |x - 3| = -15

- 2x + x -3 = -15  and -2x - (x - 3) = -15

by solving equation ,

= -x -3 = - 15

= -x = -12

x = 12

2. 8 - 2|6 - x|= 20

6 |6 - x| = 20

6 |-x + 6| = 20

dividing both side with 6,

(6 |-x + 6|)/6 = 20/6

| -x + 6| = 10/3

add 6 on both sides,

x - 6 + 6 = 10/3 +6

x = 28/3

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Congruent polygons are those that have equal measurements. Since we are given their graphs, we simply inspect each pair of polygons to determine which among them are congruent.

I have made an example using the first pair. I rotated the first polygon (the red one) to show that they are indeed congruent.

Following the same process, we can see that pairs 3 and 4 are also congruent.

Pair 2 are not congruent because the green rectangleis longer.

So the answer is pairs 1, 3, and 4.

Uniformly Varied Rectilinear Motion.

When we start to solve a physics exercise, we get the exercise data:

Initial Speed = 3.8m/s

Acceleration (a)= 3.7 m/s²

Time (t) = 3 sec.

He tells us that Carter treats at a speed of 3.8 m/s, this is the speed, since he asks us, at what speed does he treat now. Then we must calculate the final speed.

The formula to calculate the final velocity is:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=V_{o}+a*t} \end{gathered}$} }[/tex]

We substitute the data in the formula used and solve:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=3.8 \ \frac{m}{s}+3.7 \ \frac{m}{\not{s^{2}} }*3 \ s } \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=3.8 \ \frac{m}{s}+11.1 \ \frac{m}{s} } \end{gathered}$} }[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=14.9 \ m/s} \end{gathered}$} }}[/tex]

The resulting exponent form is, 1/9¹⁰

Exponent:

Exponent is used to show repeated multiplication of a number by itself. For example,

7 × 7 × 7 can be represented as 7³

Here, the exponent is ‘3’ which stands for the number of times the number 7 is multiplied.

Given,

Here we have the exponent form is,

9⁻⁸x9⁻²

Here we have to use the product property and then we have to get rid of negative exponents.

First step is to use the product property,

We know that, the product property states that,

for any non-zero term a,

yᵃ x yᵇ = yᵃ⁺ᵇ

where a and b are real numbers.

So, the given expression is written as,

=> 9⁻⁸⁺⁽⁻²⁾

=> 9⁻⁸⁻²

=> 9⁻¹⁰

Now the second step is to get rid of the negative components,

As per the rule, the exponent is negative, we can change the exponent into positive by writing the same value in the denominator and the numerator holds the value 1.

So, the value is,

=>  9⁻¹⁰ = 1/ 9¹⁰

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From the graph, the y-intercept is the point (0,40). We can calculate the slope of the line, given two points, using the following formula

In our case,

Therefore, the slope-intercept form of the equation of the line is

The answer is y=-20x+40

The binomial formula with the given parameters has a value of 0.0272

The given parameters are

N = 65

p = 0.5

X = 39

The interpretation of the above parameters are

Sample size, N = 65

Probability of success, p = 0.5

Number of success, X = 39

The binomial probability states that

P(x) = ⁿCₓ * pˣ * (1 - p)ⁿ⁻ˣ

Where n, p and x are the same as the parameters described above

When the values are substituted in the binomial probability formula, we have

P(39) = ⁶⁵C₃₉ * (0.5)³⁹ * (1 - 0.5)⁶⁵⁻³⁹

Evaluate the difference

P(39) = ⁶⁵C₃₉ * (0.5)³⁹ * (0.5)²⁶

Evaluate the products

P(39) = ⁶⁵C₃₉ * (0.5)⁶⁵

This gives

P(39) = 0.0272

Hence, the value of the binomial formula is 0.0272

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The types of funding sources that are available to businesses include:

A business can use a particular type of fund that meets its goals.

A reason why companies van use a mix of different funding is to improve a company's financial strength.

Providing resources to finance a need, a program, or a project is the act of funding. While usually in monetary form, this can also refer to an organization or company's time or effort.

Having adequate funding enables your firm to seize any possibilities that present themselves, such as investing in new goods and services that can advance your company. Working capital can act as a safety net when your company requires additional funding.

Although there are many diverse reasons why businesses want financing, there are certain frequent ones. Business grants and loans may be used for working capital, equipment purchases, staff expansion, or even the refinancing of existing debt to lower monthly payments.

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there are 4 properties we can use to prove if it is a parallelogram, in which 3 of them involve seeing if the sides are parallel or congruent, however for those we must know the value for the angles or sides, the other property is to prove that the diagonals bisect each other.

To prove the diagonals bisect each other is to see if the point of crossing divides into equal parts.

in this case since the division of the points gives the same values for both diagonals we can say that ABCD because the diagonals bisect each other.

Answer:

119

Step-by-step explanation:

substitute x = - 4 into the expression

8x² - 9

= 8(- 4)² - 9

= 8(16) - 9

= 128 - 9

= 119

Answer:

64 is the area!

- love bri <3

The slope of the linear equation that passes through the points (9,1) and (10,−1) is -2.

For a linear equation that goes through two points (x₁, y₁) and (x₂, y₂), the slope is given by the formula:

slope = (y₂ - y₁)/(x₂ - x₁)

In this case, we know that our line goes through the points (9,1) and (10, −1), so we can use these two values in the equation for the line, we will get:

slope = (-1 - 1)/(10 - 9) = -2/1 = -2

So the slope of the linear equation is -2.

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This is a Permutations of 4 people in a line

The answer is 24

The area is the entire amount of space occupied by a flat (2-D) surface or shape of an object.

The area of the face is 17 in²/17 inches2.

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area.

Draw a square on a piece of paper using a pencil. A 2-D figure, that is.

The term "Area" refers to the area that a shape occupies on paper.

By squaring the side's length, the area of each face may be calculated.

To determine the overall surface area of the cube, multiply the area of each face by the number of faces.

For big square,

a = 4 in

a*a = 4 * 4 inches

[tex]a^{2}[/tex] = 16 in²

For another small square,

a = 1 in

[tex]a^{2}[/tex] = 1*1 = 1 in²

In total,

[tex]a^{2}[/tex] = 16 + 1 = 17 in²

Therefore, the area of the face is 17 in²

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Answer:

Measure of angle B = 39

Step-by-step explanation:

(7x-20) + (2x-7) = 180 (combime like terms)

9x - 27 = 180 (move 27 to the other side)

9x = 207 (divide both sides by 9)

x = 23

2x - 7 (subsititute x with 23)

2 (23) - 7

46 - 7

39

measure of angle b = 39

The mean difference in game scores over the six​ games is 4.

The ratio of the overall sum of data to the total number of data sets is known as the mean. Mean is often computed by adding up all the data and dividing it by the total number of data.

Given that a basketball team played six games. In those​ games, the team won by 8 ​points, lost by 6​, won by 9​, won by 10​, lost by 4​, and won by 7.

The data's mean difference will be determined as follows:

Mean = ( 8 - 6 + 9 + 10 - 4 + 7 ) / 6

Mean = 4

Therefore, the mean difference in game scores over the six​ games is 4.

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The total number of lefties present in the class are 125.

For the given question;

The total students in the class are 50.

There are 10 out of 50 on an average students be left-handed.

Let the percentage of left handed be 'x'.

Then, x% of 50 = 10

x = 10×100 / 50

x = 20%.

Now the average number of left-handed students are 25.

The total students will be.

Let 'y' be the total number of students.

Then, 25 is the 20% of y.

20% of y = 25.

y = 25 ×100 / 20

y = 125

Thus, the total number of lefties present in the class are 125.

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Variable x would be easier to solve for.

Step - by - Step Explanation

What to find?

• The value of x.

• The value of y.

• The variable that was easier to solve.

Given:

5x+3y=22

4x-2y=16

Using elimination method,

First solve for x.

To solve for x, multiply through the first equation by 2 and then multiply through the second equation by 3.

10x + 6y = 44 _____________(3)

12x - 6y = 48 ______________(4)

Add (3) and (4)

22x = 92

Divide both-side of the equation by 22

x = 92/22

Reduce the fraction by 2.

x =46 / 11

To solve for y,

Multiply through the first equation by 4 and through the second equation by 5.

20x + 12y = 88 _________________ (5)

20x - 10y = 80 __________________(6)

Subtract equation 6 from 5.

22y= 8

Divide both-side of the equation by 22.

y = 8/22

We can reduce the fraction by 2.

y = 4 / 11

Judging from the steps above, we can deduce that the variable that was easier to solve is x.

Answer: x  of first equation

Step-by-step explanation:

Answer:

45 degrees

Step-by-step explanation:

The triangle is a 45, 45, 90 meaning that both angles other than the 90 are the same.

Another way to solve is you know that a triangle's angles = 180

Take the 180 and subtract 90 for the right angle

and then subtract 45 for the labeled angle and your answer is 45

The value of x is 52.5981

The given equation is:

In(x + 2) = 4

Taking log on the right hand side of the equation, we get

x + 2 = [tex]e^{4}[/tex]

The value of [tex]e^{4}[/tex] is 54.59815

⇒ x + 2 = 54.59815

Subtract 2 on both the sides of the equation

⇒ x = 54.59815 - 2

⇒ x = 52.59815

Rounding 52.59815 to 4 places, we get

⇒ x = 52.5981

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