Line segment pr is a directed line segment beginning at p(-10,7) and ending at r(8,-5). find point q on the line segment pr that partitions it into the segments pq and qr in the ratio 4:5.

To solve the negative exponents , we have to apply the negative exponent rule or the fractional exponent rule.

To calculate the negative exponent we need to remember about the negative exponent that the base is on the opposite side of the fraction. Here , We need to flip the fraction so that the base will be on the other side.

Negative exponent Rule :-

[tex]a^{-n} = \frac{1}{a^{n} }[/tex]

Now , we will solve a fraction with negative exponent

For example ; Simplify the fraction [tex]\frac{3^{-2} }{9^{-2} }[/tex]

Solution : [tex]\frac{3^{-2} }{9^{-2} } = \frac{9^{2} }{3^{2} }= \frac{81}{9}[/tex]

= 9

Here, 9 is the answer of the above example.

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The expression that represents the width of the patio is (x+3) feet

From the question, we are to determine the width of the patio

The area of the patio = Length of the patio × Width of the patio

From the given information,

Length of the patio = (x+11) feet

Area of the patio = x^2+14x+33 = x²+14x+33

Putting the parameters into the formula,

x²+14x+33 = (x+11)  × Width of the patio

∴ Width of the patio = (x²+14x+33) / (x+11)

First, we will factor x²+14x+33

x²+14x+33

x²+11x+3x+33

x(x+11) +3(x+11)

(x+3)(x+11)

Thus,

Width of the patio = [(x+3)(x+11)] / (x+11)

∴ Width of the patio = (x+3) feet

Hence, the expression that represents the width of the patio is (x+3) feet

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Answer:

D. 2

Step-by-step explanation:

If you multiply any side from XYZ by 2 it will equal the same length of one of the sides of UVW.

Answer:

Step-by-step explanation:

16 - 4 = 12

16 + 4 = 20

then 20 ; 2 = 10

Half of 12 is 6, therefore the two numbers 10 - 6 = 4 and 10 + 6 = 16 will have a mean of 10 and a range of 12.

For both problems, we can use the section formula.

1) [tex]P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}[/tex]

2) [tex]Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}[/tex]

If the team can only send four divers to a competition. Then the number of the ways will be 330.

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

There are eleven divers on a swim team. If the team can only send four divers to a competition.

Then the number of the ways will be

Number of ways = ¹¹C₄

Number of ways = 11! / [(11 - 4)! x 4!]

Number of ways = 330

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Three points must be removed from this graph so that it will be a function

The points are given as:

(-3, 2), (-3, 3), (1, 4), (1, -4), (2, -4), (2, -2).

For a set of point to represent a function;

Each x coordinate must point to only one y coordinate

From the given points, we have the following highlights:

In the above highlights, one point each must be removed.

This means we have a total of 3 points

Hence, three points must be removed from this graph so that it will be a function

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Answer:

C. 3 points

Step-by-step explanation:

By counting the total number of outcomes, we conclude that the spinner has 4 sections.

Let's say that the spinner has N sections.

If we spin it twice, for the first outcome we have N possible outcomes and for the second spin there are N possible outcomes.

Then for the experiment of spinning the spinner twice, the number of outcomes is:

O = N*N

And we know that the number of possible outcomes for spinning the spinner twice is 16, then we have:

16 = N*N = N^2

Solving for N, we have:

N = √16 = 4

Then we conclude that the spinner has 4 sections.

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Answer + Step-by-step explanation:

GRASS method is an acronym for Given, Required, Analysis, Solution, and Statement.

Given:

Required:

Analysis:

50 (total) = x + 1/4 + 5/8 than solve for x

how much money leftover (x)

= total - spent on gif card - spent on new wallet

x = 50 - 1 / 4 - 5 / 8

Solution:

x = 50 - 1/4 - 5/8

x = 50 - 12.5 - 5/8

x = 50 - 12.5 - 31.25

x = 6.25

Statement:

We found that the leftover amount is $6.25.

Therefore, the leftover amount of money with a starting amount of $50.00 and purchasing a gift card and new wallet is in fact $6.25.

The ratio of the days it rained to number of days is 3 : 7

The proportion of the number of days it rained is given as:

Proportion = 3/7

This means that:

Proportion = Days it rained/Total number of days.

So, we have:

Days it rained/Total number of days = 3/7

Express as ratio

Days it rained : Total number of days = 3 : 7

Hence, the ratio is 3 : 7

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Step-by-step explanation:

width= x (let)

length= x+5

Area=50 cm

Now ,

area = l ×b

50 = (X×X+5)

50 = (2X + 5)

50÷ 2= X+5

25 -5 = X

X=20

LENGTH = X+5

20+5

=25

[tex]\left(- \dfrac 38 \right) \div \left(-\dfrac 13 \right)\\\\\\=-\dfrac 38 \times (-3)\\\\\\=\dfrac 98[/tex]

Given, a = 1

common difference = 3

Eighth term = a+(n-1)d = 1+(8-1)3

= 1 + 21 = 22

Hope this helps :)

Answer:

y=-2x+10

Step-by-step explanation:

i graphed it i graphed all of them

Answer:

y-2x-2

Step-by-step explanation:

The way I would do this is by first using the information given and making an equation in point-slope form, before bringing it to y=mx+b.

We know that the slope is -2, and we have a point, (2,-6). The formula for equations in point slope form is [tex]y-y_{1} =m(x-x_{1} )[/tex]. So, we can insert the given information into this formula to get [tex]y+6=-2(x-2)[/tex].

Next, we distribute the slope to the the parenthesis to get [tex]y+6=-2x+4[/tex]

Then, we subtract 6 from both sides to get [tex]y=-2x-2[/tex]

Since this equation is now in the form [tex]y=mx+b[/tex], the answer is [tex]y-2x-2[/tex]

Hope this helps! :)

f(x) = 4²ˣ, this is an exponential function. Then the correct option is E.

Let a is the base and x is the power of the exponent function and b is the y-intercept. The exponent is given as

y = aˣ + b

The exonentuial functions are given below.

a. f(x)=x³ + 2x²² -6, this is not an exponential function.

b. f(x) = 5/x, this is not an exponential function.

c. f(x) = 5x + 2, this is not an exponential function.

d. f(x) = 4x², this is not an exponential function.

e. f(x) = 4²ˣ, this is an exponential function.

Then the correct option is E.

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Given that

[tex]\displaystyle \lim_{x\to0} f(x) = 4[/tex]

we can use the properties of limits to show

[tex]\displaystyle \lim_{x\to0} \frac14 f(x)^4 = \frac14 \lim_{x\to0} f(x)^4 = \frac14 \left(\lim_{x\to0} f(x)\right)^4 = \frac14 \times 4^4 = 4^3 = \boxed{64}[/tex]

Let's see

[tex]\\ \rm\Rrightarrow \lim_{x\to 0}\dfrac{1}{4}f(x)^4[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\lim_{x\to 0}f(x)^4[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\times 4^4[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{256}{4}[/tex]

[tex]\\ \rm\Rrightarrow 64[/tex]

Step-by-step Explanation:

the volume of a pyramid is:

volume = (1/3) • base_area • height

(area = length • width)

(area) • (height) = (volume)³

Example:

area = 12cm² (12 cm squared)

height = 4cm

12 • 4 = 48cm³ (48 cm cubed)

Answer:

area: 6 • 8 = 48(1/2) = 24cm²

height: 12

volume: 24 • 12 = 288cm³(1/3) = 96cm³

The height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.

In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.

We have a square pyramid.

Length of the pyramid = 23.4 in

The slant height of the pyramid = 93.2 in

From the figure:

Base length CB  = DC = 23.4 in

In a right-angled triangle, BCD

Applying Pythagoras theorem:

DC² + CB² = DB²

23.4² + 23.4² = DB²

DB = 33.092 in

OB = (1/2)DB

OB = (1/2)33.092 = 16.546 in

In the right-angle triangle AOB, again applying Pythagoras theorem:

AO² + OB² = AB²

h² + 16.546² = 93.2²

AO = h (height of the square pyramid)

AB = slant height = 93.2 in

After calculating, we get:

h = 91.719 ≈ 91.72 in

Thus, the height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.

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Answer:3.46

Step-by-step explanation:i dont know the other one

Answer:

the answer is 40

Step-by-step explanation:

A = 10 x 8 over 2 which is 40

By graphing both equations, we see that the solutions of the system of equations are  (1.05, 4.05) and  (-4.97, - 1.97)

Here we have the system of equations:

y = x + 3

y = 13*(x + 5)*(x - 1).

To solve this system graphically, we need to graph both equations and see where the curves intercept.

The graph of the two equations can be seen below.

There are two solutions, one is (1.05, 4.05) and the other is (-4.97, - 1.97)

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Answer:

mean 38.22

median 34

mode 13 & 34

range 56

Step-by-step explanation:

mean- add all values together and divide by number of values

median- order from least to greatest find the middle value

mode- the value that appears most often, can be more than one value

range- smallest value subtracted from the largest

Answer:

Step-by-step explanation:

In this numbers:

14.63

85.62

The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.

To determine in which two numbers the digit 6 has a value of 0.6, we need to examine the place value of 6 in each number.

Let's go through each number:

1. 16.7: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).

2. 61.28: The digit 6 is in the ones place, so its value is 6 (not 0.6).

3. 14.63: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.

4. 28.16: The digit 6 is in the hundredths place, so its value is 6 * 0.01 = 0.06.

5. 96.77: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).

6. 85.62: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.

The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.

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