The line AB is shown on the grid.
a) Find the gradient of a line
perpendicular to AB.
b) Find the equation of the line
perpendicular to AB and passing
through the midpoint of AB.
X

Answer:  x = -5/2 and x = -3/2

Step-by-step explanation:

(2x + 5)2 = 4x (x + 5) +25

   4x + 10 = 4x² + 20x + 25

   [minus 4x on both sides.]

            10 = 4x² + 16x + 25

   [minus 10 on both sides.]

            0 = 4x² + 16x + 15

ac = 4(15) = 60,then find the factors that add up to 16, which is 6 and 10.

            0 = 4x² + 6x + 10x + 15

            0 = 2x(2x + 3) + 5(2x + 3)

            0 = (2x + 5)(2x + 3)

2x + 5 = 0                                 2x + 3 = 0

       2x = -5                                    2x = -3

         x = -5/2                                    x = -3/2

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

[tex]\textbf{Assuming you meant: }\mathsf{(2x + 5)^2 = 4x(x + 5) + 25}[/tex]

[tex]\textbf{If so, simplify both sides of your equation you're working with}[/tex]

[tex]\mathsf{ 4x^2 + 20x + 25 = 4x^2 + 20x + 25}[/tex]

[tex]\textbf{SUBTRACT }\rm{\bf 4x^2}\text{ \bf to BOTH of the SIDES}[/tex]

[tex]\mathsf{4x^2 + 20x + 25 - 4x^2 = 4x^2 + 20x + 25 - 4x^2}[/tex]

[tex]\textbf{Simplify it!}[/tex]

[tex]\mathsf{20x + 25 = 20x + 25}[/tex]

[tex]\textbf{SUBTRACT 20x to BOTH of the SIDES}[/tex]

[tex]\mathsf{20x + 25 - 20x = 20x + 25 - 20x}[/tex]

[tex]\large\textbf{SIMPLIFY IT! (as well)}[/tex]

[tex]\mathsf{25 = 25}[/tex]

[tex]\textbf{SUBTRACT 25 to BOTH of the SIDES}[/tex]

[tex]\mathsf{25 - 25 = 25 - 25}[/tex]

[tex]\textbf{Lastly, SIMPLIFY THAT!}[/tex]

[tex]\textbf{We get: }\mathsf{0 = 0}[/tex]

[tex]\large\textsf{This means that your \boxed{\textsf{solutions}} are \bf REAL NUMBERS.}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: }\\\boxed{\mathsf{All\ \underline{\underline{REAL\ NUMBERS}}\ are\ solutions.}}}\huge\checkmark[/tex]

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

Answer: A

Step-by-step explanation:

The angle opposite the shortest side in a triangle has the smallest measure.

Answer:

C

Step-by-step explanation:

Solution

There are 8 apples in the bowl

There are 8 + 14 = 22 total fruits in the bowl.

Ratio apples / total = 8 / 22. But that is not the answer. You can divide top and bottom of the ratio by 2.

When you do that, you get 4/11 which is C

Answer: 4/11 or C

The total amount you have paid from May 2014 to July 2022 is $75,319.86

= 96 + 2

= 98 months

Total amount paid from May 2014 to July 2022 = $768.57 × 98 months

= $75,319.86

The total amount paid so far from May 2014 to July 2022 is $75,319.86

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Answer:

x=58

Step-by-step explanation:

Exterior angle of one interior angle in a triangle is equal to the sum of the other two remote interior angles. (Ext. Angle Th.) So, 3x-32=84+x

2x=116

x=58

The component form of the vectors shown is (-6, -5)

In order to determine the component of the vectors shown, we will subtract the coordinate points from both each other.

Given the vector coordinates on the line. as (-5, -3) and (1, 2). Take the difference;

Difference = [(-5-1), (-3-2])

Difference = (-6, -5)

Hence the  component form of the vectors shown is (-6, -5)

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Answer:

D

Step-by-step explanation:

the answer is D because the range is the lowest possible value up to the highest possible value and when listed it doesn't repeat

Puja Limbu had the better performance than Raju Limbu.

Such question are generally solved using percentages.

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.

Percentage of Raju limba = [tex]\frac{11}{15}[/tex] X 100 = 73.3%

Percentage of Puja Limba = [tex]\frac{8}{10}[/tex] x 100 = 80%

As percentage of Puja Limba is greater than that of Raju Limba .

Hence performance of Puja Limba is better

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Answer: h>0 and k>0

Step-by-step explanation:

If the circle is centered in Quadrant I, then both the x and y coordinates of the center are positive.

This means that h>0 and k>0.

Answer:

The graph of g(x) is wider.

Step-by-step explanation:

Parent function:

[tex]f(x)=x^2[/tex]

New function:

[tex]g(x)=\left(\dfrac{1}{2}x\right)^2=\dfrac{1}{4}x^2[/tex]

Transformations:

For a > 0

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of}\:a\\ & \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a\\\end{aligned}[/tex]

[tex]\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a\\& \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a\\\end{aligned}[/tex]

If the parent function is shifted ¹/₄ unit up:

[tex]\implies g(x)=x^2+\dfrac{1}{4}[/tex]

If the parent function is shifted ¹/₄ unit down:

[tex]\implies g(x)=x^2-\dfrac{1}{4}[/tex]

If the parent function is compressed vertically by a factor of ¹/₄:

[tex]\implies g(x)=\dfrac{1}{4}x^2[/tex]

If the parent function is stretched horizontally by a factor of ¹/₂:

[tex]\implies g(x)=\left(\dfrac{1}{2}x\right)^2[/tex]

Therefore, a vertical compression and a horizontal stretch mean that the graph of g(x) is wider.

Answer:

No. The correct equation is

y= 1/2 x - 2

Step-by-step explanation:

See picture

The estimation goal is to estimate a population parameter. The estimation process uses sample statistics.

The goal of hypothesis testing is testing to claim whether it is right or wrong.

The hypothesis testing also uses statistics to determine whether or not a treatment has an effect.

The estimation goal is to estimate a population parameter. The estimation is used to determine how much effect a treatment has.

To estimate a parameter, a sample statistics of the parameter is used.

Thus, the estimation is to estimate a population parameter.

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The probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

цр = р

The standard deviation of this sampling distribution of sample proportion is:

бр = √ρ(1-ρ)÷n

The information provided is:

ρ = 0.22

ⁿ = 276

As the sample size is large, i.e. n = 276 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion.

Compute the value of P(р-p<0.06) as follows:

P(р-p<0.06) = P(р-p ÷ бp<0.06 ÷√0.22(1 - 0.22) ÷ 276

= P ( Z < 2.41 )

= 0.99202

≈ 0.992

Thus, the probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.

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C. Between E and F and between G and H the elevator could be travelling from a higher floor to a lower floor.

We have to justify all the options with respect to the graph :-

Option A : Between A and B, the elevator would be travelling from a lower floor to a higher floor. Also between C and D, the elevator would be travelling from a lower floor to a slightly higher floor.

So, this option is not correct.

Option B : Between B and C, the elevator wouldn't go higher. And also the same would happen in between D and E.

So, this option is not correct.

Option C : Between E and F, the elevator would be travelling from higher floor to lower and also between G and H.

So, this option is correct.

Option 4 : Between F and G, there would not have much changes. So it will be omitted.

So, this option is not correct.

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The polar form of any complex number can be written as

[tex]z = |z| e^{i\arg(z)}[/tex]

where [tex]\arg(z)[/tex] is the argument of [tex]z[/tex], i.e. the angle it makes with the positive real axis in the complex plane.

If [tex]z=\sqrt3+i[/tex], then [tex]z[/tex] has modulus

[tex]|z| = \sqrt{\left(\sqrt3\right)^2 + 1^2} = \sqrt4 = 2[/tex]

and argument

[tex]\arg(z) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6[/tex]

Then

[tex]\sqrt3 + i = 2e^{i\frac\pi6} = 2 \left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)[/tex]

Answer:

Point-slope form of equation of a line that passes from (-1,3) and (0,0) is given as y-3=-3(x+1).

Slope-intercept form of equation is given as y=-3x.

Step-by-step explanation:

In the question, it is given that the line passes from (-1,3) and (0,0).

It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.

Step 1 of 2

Passing point of line is (-1,3).

Hence, [tex]$x_{1}=-1$[/tex] and

[tex]$$y_{1}=3 \text {. }$$[/tex]

Also, Passing point of line is (0,0).

Hence, [tex]$x_{2}=0$[/tex] and

[tex]$$y_{2}=0 \text {. }$$[/tex]

Substitute the above values to find the slope of line which is given by [tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{0-3}{0-(-1)} \\m &=\frac{-3}{1} \\m &=-3\end{aligned}$$[/tex]

Hence, slope of the line is -3

Step 2 of 3

It is obtained that m=-3

[tex]$y_{1}=3$[/tex]

and [tex]$x_{1}=-1$[/tex]

Substitute the above values in point-slope form of equation given by [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]

[tex]$y-y_{1}=m\left(x-x_{1}\right)$\\ $y-3=-3(x-(-1)$\\ $y-3=-3(x+1)$[/tex]

Hence, point-slope form of equation given as y-3=-3(x+1).

Step 3 of 3

Solve y-3=-3(x+1) to write it as slope-intercept form given by y=mx+c

[tex]$y-3=-3(x+1)$\\ $y-3=-3 x-3$\\ $y=-3 x-3+3$\\ $y=-3 x$[/tex]

Hence, slope-intercept form of equation is given as y=-3x.

Answer:

Step-by-step explanation:

The population in the year 2020 is 4628

The given parameters are:

Initial, a = 12910

Rate, r = 5%

Since the population decreases, then we make use of an exponential decay function.

This is represented as:

f(n) = a * (1 - r)^n

So, we have:

f(n) = 12910 * (1 - 5%)^n

Evaluate the difference

f(n) = 12910 * 0.95^n

2020 is 20 years from 2000.

So, we have:

f(20) = 12910 * 0.95^20

Evaluate

f(20) = 4628

Hence, the population in the year 2020 is 4628

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The price of each taco is $10.5

What is unitary method?

We can solve this question by unitary method.
The unitary method is a method of finding the value of one unit and then finding the value of the required number of units. While solving a problem it is important to recognize the units and values.

In this question, 10 tacos cost $105.
Let's represent the cost of 1 taco as [tex]x[/tex]
10 tacos =$ 105
1 taco = [tex]x[/tex]
10[tex]x[/tex] = 105
[tex]x[/tex] = [tex]\frac{105}{10}[/tex]

[tex]x[/tex] = 10.5
Each taco cost $10,5
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The ordered pair is (-9, -25) and the word statement is if x is equal to -9, then the value of h(x) is -25

From the given table, f(x) = y means that the corresponding value of y given a value x.

For the function h(-9), we need to find the equivalent value of h(x) when x is -9. Hence h(-9) is -25

The ordered pair is (-9, -25) and the word statement is if x is equal to -9, then the value of h(x) is -25

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The percentiles are: P40 = 33, P70 = 45, and P89 = 54.1, while the quartiles are Q1 = 28.5 and Q3 = 47.5

The sorted dataset is:

22, 22, 24, 25, 26, 27, 27, 30, 30, 32,

33, 33, 35, 37, 38, 38, 40, 42, 44, 44,

45, 47, 48, 48, 49, 52, 55, 58, 62, 68

The number of data elements is:

N = 30

The 40th percentile (P40)

This is calculated using:

Element = (40% * N)th

So, we have:

Element = (40% * 30)th

Evaluate

Element = 12th

The 12th element is 33

Hence, the value of P40 is 33

The 70th percentile (P70)

This is calculated using:

Element = (70% * N)th

So, we have:

Element = (70% * 30)th

Evaluate

Element = 21st

The 21st element is 45

Hence, the value of P70 is 45

The 89th percentile (P89)

This is calculated using:

Element = (89% * N)th

So, we have:

Element = (89% * 30)th

Evaluate

Element = 26.7th

The element is calculated as:

Element = 26th + 0.7 * (27th - 26th)

So, we have:

Element = 52 + 0.7 * (55 - 52)

Element = 54.1

Hence, the value of P89 is 54.1

The 1st quartile (Q1)

This is calculated using:

Element = (1/4 * N)th

So, we have:

Element = (1/4 * 30)th

Evaluate

Element = 7.5th

The element is calculated as:

Element = 7th + 0.5 * (8th - 7th)

So, we have:

Element = 27 + 0.5 * (30- 27)

Element = 28.5

Hence, the value of Q1 is 28.5

The 3rd quartile (Q3)

This is calculated using:

Element = (3/4 * N)th

So, we have:

Element = (3/4 * 30)th

Evaluate

Element = 22.5th

The element is calculated as:

Element = 22nd + 0.5 * (23rd - 22nd)

So, we have:

Element = 47 + 0.5 * (48- 47)

Element = 47.5

Hence, the value of Q3 is 47.5

The 5th quartile (Q5)

There is no such thing as Q5 i.e. the 5th quartile

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The statement which is true about the given graph is  that f(x)<0 in the interval (-∞,3) which is option 3.

Given Graph of a function

We have to choose a statement which is correct about the function whose graph is given.

The graph of a function tells us about the domain and range of the function. The values on y axis are the codomain of the function and the values on x axis are the values of domain.

When we see the graph we can find that x=-∞ to x=3 the values are negative means when we put the values of x less than 0 we will get negative number. For example if we put the value of x=-1, we will get -20 which is a negative number.

Hence the third statement is true for the given graph which is that it has values less than zero in the interval (-∞,3).

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Answer:

AC = 6√3 in

Step-by-step explanation:

Join OC. Now ΔAOC is an isosceles triangle as OA = OC =radius.

 ∠A = ∠C = 30.

 ∠A + ∠C +  ∠AOC = 180 {angle sum property of traingle}

 30 + 30 + ∠AOC  = 180°

                 ∠AOC = 180 -60

                 ∠AOC = Ф = 120°

Find the length of radius using the bellow formula.

         [tex]\sf \boxed{\bf Arc \ length = \dfrac{\theta}{180}\pi r}[/tex]

            Ф = 120°

                Arc length = 4π

            [tex]\sf 4\pi =\dfrac{120}{180}*\pi *r\\\\ r =\dfrac{4\pi * 180}{120*\pi }\\\\ r = 6 \ in[/tex]

[tex]\sf \boxed{\bf chord \ length = 2rSin \ \dfrac{\theta}{2}}[/tex]

                         [tex]\sf b = 2*6*Sin \ \dfrac{120}{2}\\\\ b = 2 *6 * Sin \ 60^\circ\\\\ b = 2 * 6 * \dfrac{\sqrt{3}}{2}\\\\ \b = 6\sqrt{3}[/tex]

[tex]\sf \boxed{\bf AC = 6\sqrt{3} \ in}[/tex]

Deposit: $1,000

Annual interest: 4% = 0.04

Years: 3

For this type of question, when the question asks you to "continuously compound", you use this formula: [tex]Pe^{rt}[/tex]

Solving:

[tex]1000e^{(0.04)(3)} \\1000e^{0.12} \\=1127.50[/tex]

The value of Joaquin's investment after 3 years = 1,127.50$

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

An equation is shown. What is the value of n? [tex]\bf{n=1:17}[/tex] is shown

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\bf{n=1:17}[/tex] | divide

[tex]\bf{n=\dfrac{1}{17}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

          [tex]\bf{=n=\dfrac{1}{17}}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Step-by-step explanation for each question:

For Question 6, the range of a function is all the possible outputs of the function. Since the function can only take the inputs 0, 4, and 7, we can just plug in each into the formula and find their corresponding outputs.

g(0) = 0² - 9 = 0 - 9 = -9

g(4) = 4² - 9 = 16 - 9 = 7

g(7) = 7² - 9 = 49 - 9 = 40

Therefore the only possible outputs of function g, or the range, is {-9, 7, 40}.

For question 4, the input t is a given time, and h(t) is the height of the football at that time.

Hence, h(2.5) is the height of the football (in feet) at 2.5 seconds. The value 2.5 can be plugged into the function [tex]-16t^2+58t+2[/tex] to get the height. This gives us

[tex]-16(2.5)^2 + 58(2.5) + 2[/tex]

[tex]-16(6.25) + 58(2.5) + 2[/tex] [Squaring 2.5]

[tex]-100 + 145 + 2[/tex] [Multiplying]

[tex]47[/tex] [Combining all terms]

We find that the height of the football at 2.5 seconds is 47 feet.

For Question 5, the table of values show all the possible values x can be (or the domain), and what the output of the function f(x) would give for each.

A) f(-3) = 5, as the row with -3 for x has -5 for y.

B) f(0) = 0, as the row with 0 for x has 0 for y.

C) f(1) = -3, as the row with 1 for x has -3 for y.

The range of the function will be -9,7 and 40.

The domain denotes all potential x values, while the range denotes all possible y values.

Given equation;

g(x) = x²-9

The range of the given domain is found by putting the values one by one in the above equation as;

g(x) = x²-9

a)For x = 0

g(x) = 0²-9

g(x) =-9

b)For x =4

g(x) = 4²-9

g(x) =16-9

g(x) = 7

c)For x =7

g(x) = 7²-9

g(x) =49-9

g(x) = 40

Hence, the range of the function will be -9,7 and 40.

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Given

[tex]25x^{-4} - 99x^{-2} - 4 = 0[/tex]

consider substituting [tex]y=x^{-2}[/tex] to get a proper quadratic equation,

[tex]25y^2 - 99y - 4 = 0[/tex]

Solve for [tex]y[/tex] ; we can factorize to get

[tex](25y + 1) (y - 4) = 0[/tex]

[tex]25y+1 = 0 \text{ or } y - 4 = 0[/tex]

[tex]y = -\dfrac1{25} \text{ or }y = 4[/tex]

Solve for [tex]x[/tex] :

[tex]x^{-2} = -\dfrac1{25} \text{ or }x^{-2} = 4[/tex]

The first equation has no real solution, since [tex]x^{-2} = \frac1{x^2} > 0[/tex] for all non-zero [tex]x[/tex]. Proceeding with the second equation, we get

[tex]x^{-2} = 4 \implies x^2 = \dfrac14 \implies x = \pm\sqrt{\dfrac14} = \boxed{\pm \dfrac12}[/tex]

If we want to find all complex solutions, we take [tex]i=\sqrt{-1}[/tex] so that the first equation above would have led us to

[tex]x^{-2} = -\dfrac1{25} \implies x^2 = -25 \implies x = \pm\sqrt{-25} = \pm5i[/tex]

The interquartile range is 12.

The interquartile range is the difference between the third quartile and the first quartile. The first quartile is the first line on the box while the third quartile is the third line on the box.

First quartile = 11

Third quartile = 23

Interquartile range = 23 - 11  = 12

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