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The Equation of bisector 5x-7y+3=0 which is a straight line.

A straight line that divides an angle of a triangle in equal value.

The line that lies perpendicular to a side and goes through the midpoint of its length.

Given, coordinate H (-7,2), K (3, -4) and L (5,4)

we plot a triangle HKL with this point.

midpoint of side HK is found by (-7+3)/2 and (2-4)/2

hence, midpoint of HK is (-2,-1) is denoted by P

the perpendicular bisector of side HK means a straight line from the midpoint of HK to the point L(5,4). The bisector line PL divide the angle HLK.

so, the equation of bisector is y-y₁ = (y₂-y₁)/(x₂-x₁)[x-x₁] because the bisector line passes through the point P(-2,-1) and L(5,4)

  y-(-1) = [4-(-1)]/[5-(-2)]× [x-(-2)]

y+1 = 5/7×(x+2)

7y+7= 5x+10

5x-7y+3=0

hence, the equation of bisector is 5x-7y+3=0

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Answer:

A. 12.6 ft

Step-by-step explanation:

Using sin because of opposite over hypotenuse, you can find x.

sin(52) = x/16

16sin(52) = x

Plug it into your calc.

x = 12.6082

And you have your final answer.

Answer:

12.6 ft

Step-by-step explanation:

Did the quiz and I got it right

Answer: The value of x is 49.

Step-by-step explanation:

To find the value of x, you will first need to cross multiply the fractional variables together.

5x - 80 = 3x + 18

Then, move the numerical term 80 to the right side of this equation and add it to 18.

5x - 80 = 3x + 98

Move 3x to the left side of the equation and subtract it this time to the variable 5x.

2x = 98

Finally, you divide both of the equation's sides by 2 and you will get 49.

x = 49

When you actually add x to this problem, you would get 33/55.

49 - 16/49 +6 = 33/55

You can then simplify 33/55 and get the same answer 3/5.

3/5

Therefore, the value of x for this variable equation with the fractions would be equal to x = 49. Hope this helps!

-From 5th Grader Honors Student

Answer:

B

Step-by-step explanation:

B is the best example where substitution is the best method since you already have one where y = something and you can plug -2/7x + 11 into the bottom equation for y and solve it that way. A and C make you get x or y by itself first first substitution would work and D already gives you the answers. B is the best since its already set in that format.

I’m sorry but I could not find a pdf version of the Envision volume 2 book for 5th grade online. However, I found some websites that have answer keys and lesson plans for the book. You can check them out by searching for the following queries:

I hope this helps you with your homework.

Blank 1: 3

Blank 2: 27

Blank 3: 21

you have to distribute the three to everything inside the parenthesis, and because it's directly in front of the parenthesis it's being multiplied.

3(x - 9) = 3x - 27

Now you need to isolate the y, in this e ample you need to add 6 to both sides

the final equation should be:

y = 3x - 21

Without using a calculator, the only solution to the equation    \((x^3 - 1000)^{1/2} = (x^2 + 100)^{1/3}\) is 10.1136.

To solve this equation without using a calculator, we need to simplify both sides of the equation and then use algebraic techniques to isolate x.

\((x^3 - 1000)^{1/2} = (x^2 + 100)^{1/3}\)

square both sides of the equation and cube both sides of the equation, we will have;

(x³ - 1000)³ = (x² + 100)²

We can simplify the left-hand side of the equation by applying the cube of a binomial formula, which states that:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Let's apply this formula with a = x³ and b = -1000:

(x³ - 1000)³ = x⁹ - 3x⁶(1000) + 3x³(1000)² - 1000³

Next, let's simplify the right-hand side of the equation:

(x² + 100)² = x⁴ + 200x² + 10000

Now we can substitute these expressions back into the original equation:

x⁹ - 3x⁶(1000) + 3x³(1000)² - 1000³ = x⁴ + 200x² + 10000

We can then rearrange the terms to get a polynomial equation in x:

x⁹ - 3x⁶(1000) + 3x³(1000)² - x⁴ - 200x² - 10000 - 1000³ = 0

This equation is difficult to solve exactly, but we can make an educated guess that x is close to 10. If we substitute x = 10, we get:

(10³ - 1000)³ ≠ (10² + 100)²

Increase the value of x a little, say 10.1136

(10.1136³ - 1000)³ ≈ (10.1136² + 100)²

This is true, so x = 10.1136 is a solution to the equation. We can check that there are no other integer solutions by noting that the left-hand side of the equation is always larger than the right-hand side for x > 10, and smaller than the right-hand side for x < 10.

Therefore, the only solution to the equation is x = 10.1136.

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"A school sports team sold candy bars to raise money for new uniforms.", The team sold the same amount of candy bars at

Week 3. 17/51 or 0.33 Option C.

This is further explained below.

Generally,  to give up something of worth in exchange for money or another commodity of value My brother bought the bicycle from him so that he could put it up for sale. The shop is a retailer of footwear. to be marketed or given a price The new product is doing quite well in the marketplace. Each one of them retails for one dollar.

In conclusion, The week with the highest percentage of sales is week three as

17/51>>8/25>>32%

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Answer:

-15

Step-by-step explanation:

Simplify the expression.

The gambler in a Las Vegas casino lost $150.

According to the question,

We have the following details:

The visitor lost $200 and $50 in a Las Vegas casino.

The visitor won $100.

So, in total, the visitor lost $250 overall.

Now, compare the amount the gambler lost and the gambler won in the casino. So, we notice that the gambler lost more amount.

Now, we will find the total amount lost:

Gambler's net worth = The amount lost - the amount won

Gambler's net worth = $(250-100)

Gambler's net worth = $150

Hence, the gambler lost $150 overall in the casino.

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The eigen vectors are :

\(\left[\begin{array}{ccc}-4&8\\-8&-4\end{array}\right]\) = 4\(\sqrt{5}\) \(\left[\begin{array}{ccc}cos(arctan(2)+π)&−sin(arctan(2)+π)\\sin(arctan(2)+π)&cos(arctan(2)+π)\end{array}\right]\)

given that

M = \(\left[\begin{array}{ccc}-4&8\\-8&-4\end{array}\right]\)

using the P\(D^{n}\)\(P^{-1}\) method

λ1=−4+8i  with the respective eigenvector which leads \(\left[\begin{array}{ccc}-i\\1\end{array}\right]\) factoring out the i out giving

\(\left[\begin{array}{ccc}0\\1\end{array}\right]\) + i \(\left[\begin{array}{ccc}-1\\0\end{array}\right]\)  which means P = \(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\) and \(P^{-1}\) = \(\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\)

D = 4\(\sqrt{5}\) \(\left[\begin{array}{ccc}cos(arctan(2)+π)&−sin(arctan(2)+π)\\sin(arctan(2)+π)&cos(arctan(2)+π)\end{array}\right]\)

I means \(\pi\)

\(\left[\begin{array}{ccc}-4&8\\-8&-4\end{array}\right]\) = 4\(\sqrt{5}\) \(\left[\begin{array}{ccc}cos(arctan(2)+π)&−sin(arctan(2)+π)\\sin(arctan(2)+π)&cos(arctan(2)+π)\end{array}\right]\)

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The graph which correct shows an image and pre-image after reflecting across the line; y = -x as required in the task content is; Option 1.

It follows from the task content that the answer choice which correctly represents an image ajd pre-image after reflecting across the line; y = -x.

First it is noteworthy to know that the line; y = -x is one which passes through the origin and has a negative slope of; -1.

On this note, by observation; when the line y = -x is drawn; the graph which represents the image and pre-image after reflecting across the line; y = -x is; Option 1.

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Answer:

54 cm^2.

Step-by-step explanation:

Area = 1/2 * altitude * base

= 1/2 * 6 * 18

= 54 cm^2.

3a. An equation in slope-point for this line is y + 2 = 1/2(x - 0).

3b. The equation in slope-intercept form is y = 1/2(x) - 2.

4a. An equation in slope-point form to represent this function is y - 3875 = -1/695(x - 19375).

4b. The cost of operating a car that has been driven 31250 km is $3892.086.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Part 3.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 + 2)/(4 - 0)

Slope (m) = 1/2

At data point (0, -2) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 1/2(x - 0)

y = 1/2(x) - 2

Part 4a.

Based on the information provided about Jay's business, we would determine the slope of the line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3900 - 3875)/(2000 - 19375)

Slope (m) = 25/-17375

Slope (m) = -1/695

At data point (19375, 3875) and a slope of -1/695, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3875 = -1/695(x - 19375)

Part 4b.

For the cost when x = 31250 km, we have:

y - 3875 = -1/695(31250 - 19375)

y = 17.086 + 3875

y = $3892.086.

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Answer + Step-by-step explanation:

\(\frac{5^{10}}{5^{5}} =5^{10-5} = 5^5\)

\(\text{used property :} \ \ \ \frac{a^{m}}{a^{n}} =a^{m-n}\)

_______________________

\((4^8)^3 = a^{8 \times 3}=a^{24}\)

\(\text{used property :} \ \ \ (a^n)^m = a^{n \times m}\)

_______________________

\(10^{-4}=\frac{1}{10^{4}} \ \text{not} \ \frac{1}{4^{10}}\)

_______________________

15⁶ × 15³ = 15⁶⁺³ = 15⁹

_______________________

Recall : If a ≠0  ⇒ a⁰ = 1

Then

Since 6⁸ ≠ 0  ⇒ (6⁸)⁰ = 1  

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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I hope that the attachment helps you..

Answer:

it is too blury to read

Step-by-step explanation:

Answer:

Yes, ∆PQR is a right triangle.

Step-by-step explanation:

A right triangle has one right angle, which is 90°. This triangle has one right angle, so it is a right triangle.

Answer:

15cm

Step-by-step explanation:

© the envelope is 15cm rall.

Answer:

15cm

Step-by-step explanation:

√289-64

√225

15cm

Answer:

30+6x ≤ 100 (inequality)

The maximum amount of rides is 11 rides

Step-by-step explanation:

So first the admission fee is 30

Each ride is 6

So since you can go on any amount of rides, its unknown so (x)

You only have a 100 dollars and you can’t go over but you can go lower

so 30+6x≤100

If you solve it

x≤11

So 11 rides

Answer:

8/3

Step-by-step explanation:

i put equations as this:

x+40 = y

where x is galllons of pure mixture and y is the gallons of the new mixture

the other equation i id was:

x+0.2(40) = 0.25y

x+8 = 0.25y

y = 4x+32

solve using substitution

(x+40) = 4x+32

x = 4x-8

-3x = -8

x = 8/3

\(7+3i-3+9i=\boxed{4+12i}\)

Answer:

A

Step-by-step explanation:

The way the flashback in these paragraphs advance the plot is C. It introduces Evan's motivation for working in the garden with Grandfather.

The technique of flashback in storytelling involves interrupting the chronological order of events to depict an earlier event or scene. It uses time travel to furnish the audience with necessary backstory, context, or a deeper understanding of the characters.

The technique of flashbacks is frequently employed as a means of divulging previous occurrences, recollections, or incidents that hold significance to the present narrative being conveyed.

Hence, it can be seen from the given text that the use of flashback helps show the motivation which Evans had for working in the garden with Grandfather

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A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The correct option is A.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.

The solid is described as a three-dimensional solid made from

two parallel and congruent discs, not in the same plane, and all the points

between them is a Cylinder.

Hence, the correct option is A.

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All of the points from Table D which shows a proportional relationship has been plotted in the graph shown in the image attached below.

The graph of any proportional relationship is represented by a straight line with the data points passing through the origin (0, 0) and it can be modeled by the following linear equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points contained in table D as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 1/2 = 3/6 = 4/8 = 2/10

Constant of proportionality, k = 1/2 or 0.5.

In conclusion, a linear equation for this proportional relationship can be correctly written and plotted using an online graphing calculator as follows:

y = kx

y = 0.5x

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