Write an equation in point-slope form of the line that passes through the given points, then write the equation in slope-intercept form.
(-3,5), (9,1)
What is the point-slope form of the equation of the line?
(Simplify your answer. Use integers or fractions for any numbers in the equation.)

all the statements prove that a line is parallel to b.

If two non-vertical lines in the same plane have the same slope, they are said to be parallel. Never will two parallel lines cross. If two non-vertical lines in the same plane cross at a right angle, they are said to be perpendicular.

Lines can either be parallel or intersecting. When two lines meet at a point in a plane, they are known as intersecting lines. If a line intersects two or more lines at distinct points then it is known as a transversal line.

line intersects lines a and b at points P and Q respectively. The line l is the transversal here.

∠1,∠2,∠7 and ∠8 are the exterior angles and ∠3,∠4,∠5 and ∠6 denote the interior angles.

The angle pairs formed due to intersection by a transversal are named as follows:

Corresponding Angles: ∠1 and ∠6; ∠4 and ∠8; ∠2 and ∠5; ∠3 and ∠7 are the corresponding pair of angles.

Alternate Interior Angles: ∠4 and ∠5 ; ∠3 and ∠6 denote the pair of alternate interior angles.

Alternate Exterior Angles: ∠1 and ∠7; ∠2 and ∠8 are the alternate exterior angles.

Same side Interior Angles: ∠3 and ∠5; ∠4 and ∠6 denote the interior angles on the same side of the transversal or co-interior or consecutive interior angles.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

5 , 16

GCF = ?

Step 02:

GCF:

5: 5

5 | 5

1

16: 2^4

16 | 2

8 | 2

4 | 2

2 | 2

1

GCF = 1

The answer is:

The greatest common factor is 1

The simplified expression of (4⁴)⁻¹  is one over four raised to the fourth power

The expression can be simplified as follows:

(4⁴)⁻¹

Therefore, the expression can be simplified using laws of indices.

[tex](a^{c} )^{b} = a^{cb}[/tex]

and

[tex](a^{-b} )^{c} = \frac{1}{a^{bc} }[/tex]

Therefore, using the laws of indices, the expression can be simplified below:

(4⁴)⁻¹  = 4⁻⁴

Hence,

4⁻⁴ = 1 / 4⁴ = (1 / 4)⁴

Hence,

(4⁴)⁻¹  = 1 / 4⁴ = (1 / 4)⁴

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Since line YZ is parallel to chord line WX and the length of WX is 50, then the length of XZ must be half of WX, which is  A) 25.

Parallel refers to the concept of running multiple processes at the same time. It is often used in computing and engineering to describe the process of running multiple operations simultaneously. It is also used to refer to multiple paths of data or information travelling in the same direction, such as in a computer network. Parallel computing is a form of computation in which multiple processes are run concurrently, either on the same computer or across multiple computers. This allows for faster execution of tasks and better utilization of resources, such as processors and memory.

Since diameter line YZ is parallel to chord line WX, we can use the property of parallel lines that the opposite angles are equal. Thus, we have:

angle ZWX = angle ZYX (corresponding angles)

angle ZYX = 90 degrees (as YZ is a diameter)

angle ZWX = 90 degrees (as WZ is a chord of the circle)

Therefore, triangle WZX is a right triangle with right angle at Z. Using the Pythagorean theorem, we can find the length of XZ as:

[tex]XZ^2 = WX^2 - WZ^2[/tex]

[tex]XZ^2 = 50^2 - (YZ/2)^2[/tex] (as YZ is the diameter and WZ = YZ/2)

[tex]XZ^2 = 2500 - YZ^2/4[/tex]

[tex]XZ^2 = 2500 - (XZ^2/4)[/tex](as YZ = 2XZ)

[tex]5XZ^2/4[/tex] [tex]= 2500[/tex]

[tex]XZ^2 = 2000[/tex]

[tex]XZ = (2000) = 20(5)[/tex]

Therefore, the length of XZ is approximately 44.72 units, which is not one of the answer choices. However, if we assume that the diameter YZ is 100 units (so that WZ = 50 units), then [tex]XZ^2 = 50^2 - 25^2 = 1875[/tex], and [tex]XZ = (1875) = 25(3)[/tex]. This value is approximately 43.30 units, which is closest to answer choice (A) 25. Therefore, the answer is (A) 25.

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The two numbers are mathematically given as

12 and 60

This is further explained below.

Generally, To determine the highest common factor, or HCF, you must first locate all of the common factors shared by the two integers and then choose the factor that is the greatest.

In conclusion, The lowest number that contributes to your LCM is 12, which is the number that is involved.

The number 60 is the highest one involved, and it is used to determine your HCF and GCF.

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Answer:

y = (-3/5)x - (31/5)

Step-by-step explanation:

3x + 5y = 11

-3x              -3x

------------------------------

5y = -3x + 11

÷5    ÷5    ÷5

-----------------------

y = (-3/5)x + (11/5)

y - y₁ = m(x - x₁)

y - (-5) = (-3/5)(x -(-2))

y + 5 = (-3/5)(x + 2)

y + 5 = (-3/5)x - (6/5)

    -5                 -5

-----------------------------------

y = (-3/5)x - (31/5)

I hope this helps!

Answer:

Four Students have failing grades, with a remainder of 4.

28:4 R:4

Step-by-step explanation:

With 32 students in the class. A 7:1 ratio doesn't work perfectly. 7*4=28. 28:4.

32 students - 28 possible students to fail = 4 Remainder since 7:1 ratio doesn't fulfill 32 students.

The frequency of specific five classes (67, 68, 69, 70, and 71) will occur a total of 19 times.

So, the frequency for the particular 5 classes is as follows:

The following five classes will appear most frequently overall:

Therefore, the frequency of specific five classes (67, 68, 69, 70, and 71) will occur a total of 19 times.

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Option C. The way that the change would affect the mean and the median is that The mean will increase and the median will not change.

We will find the mean and the median before the 40 was added and after it was added

Before it was added

Mean = 16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 / 9

= 213 / 9

= 23.67

The median is 24

After we have added 40 the mean would be

16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 + 40 / 10

= 253 / 10

= 25.3

The median would be 24 + 24 / 2

= 48 / 2

= 24

Hence we can see that the mean got to be higher while the median still remained as 24.

The solution is C.

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Answer:

Explanation:

he arrow comprises of two sshapes

• A rectangle with dimensions 30 inches by 20 inches.

• A triangle with a base of 40 inches and a height of 30 inches.

Thus:

The area of the arrow is 1200 square inches.

Answer:

C. y = −x + 8

Step-by-step explanation:

Use point-slope form:    y − b = m(x − a) where (a,b) is a point on the line

To do this, first identify the slope of the line from the given equation because having the same slope as the given equation is what makes the constructed line parallel to it.

m = −1

Then use the point (3,5) to construct an equation using point-slope form.

y − 5 = −1(x − 3)

Distribute:

y − 5 = −x + 3

and isolate y.

y = −x + 8

So the answer is C, y = −x + 8.

The given figure can be drawn as,

From the figure,

Since angle of incidence will be equal to angle of reflection, [tex]\begin{gathered} \text{tan}<\text{ACB}=\frac{h}{10\text{ m}} \\ \text{tan}\theta=\frac{h}{10\text{ m}} \\ 0.6=\frac{h}{10\text{ m}} \\ 6\text{ m=h} \end{gathered}[/tex]Therefore, the height of cactus is 6 m.

line A and line B are showing that object A and B are moving with a different rate.

they both are moving with constant speed but we can see that line A has a large slope as compare to line B, that means object A has more speed than the object B.

so the speed of object A is greater than the object B.

Answer: [tex](\sqrt{9}-2 )^{-2} = 1 \\ (1-6)^{2}=(-5)^{2} = 25\\ 1+25=26[/tex]

26

Step-by-step explanation:

1) First, lets solve the first part --> (√9 - 2)^-2 will make 1.

2) Then, --> (1-6)^2= (-5)^2= 25

3) Sum this up --> 1+25=26.

Hope all clear!!

She uses 800 mL of solution A; that is, 2% of those 800 mL is alcohol

Alcohol on a:

2% of 800 = 2*800/100 = 16mL

If we use x mL of b, the amount of alcohol is:

5% of x = 5*x/100 = x / 20

Total amount of alcohol: 16 + x/20

Total amount of solution mixture: 800 + x

The ratio:

(16 + x/20) / (800 + x) = 3%

(16 + x/20) / (800 + x) = 3/100

1600 + 5x = 2400 + 3x

Solving for x:

5x - 3x = 2400 - 1600

2x = 800

x = 400 mL

She used 400 mL of solution b

Answer:

B

Step-by-step explanation:

If we look at the x-axis, the function increases and decreases. Therefore, the domain is all real numbers.

If we look at the y-axis, the same is occurring. Therefore the range is also all real numbers.

The 70th term of an arithmetic sequence is 115.5 and the common difference is 1.5 the first term of the sequence 12.

Formula\sa {n}=a {1}+(n-1) The nth term in the series is d a n.

The first term present in the sequence is a 1.

d is the common distinction between the terms.

an = a1 + (n-1)d

⇒ a1 = an - (n-1)d

= a70 - (70-1) (1.5)

= 115.5 - 69 (1.5)

= 12

The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive terms is always two, so the sequence 3, 5, 7, 9... is arithmetic.

The formula for an arithmetic sequence is given as an=a1+(n1)d, where n is a general term, a1 a 1 is the initial term, and d is the common difference. To find the general word in the series, do this.

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(f) 53/157

157 people were loyal for less than a year, 53 of which were from the South.

(g) 433/465

465-32=433 people were loyal for at least 1 year out of the 465 people from the East.

(h) 335/376

376-41=355 people were loyal for at least 1 year out of the 376 people from the West.

Step 1

Given;

Required to solve the problem using completing the square method

Step 2

Move 10 to the left.

Simplify

Step 3

Add 64 and subtract 64

Step 4

Complete the square

Step 5

Find the value of n

Hence,

n= -8+(2√2)i

or

n= -8-(2√2)i

The significance level is less than p-value, so we will fail to reject the hypothesis test.

Given,

Conducting a hypothesis test for one mean

The significance level, α = 0.05

The p-value = 0.30

We have to find the test is reject or fail to reject.

If the significance level is greater than p-value, we will reject the hypothesis test.

If the significance level is less than p-value, we will fail to reject the hypothesis test.

Here,

The significance level, α is 0.05 and the p-value is 0.30

Lets see,

The significance level is less than the p-value.

That is,

0.05 < 0.30

So, we will fail to reject the hypothesis test

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Answer:

34

Step-by-step explanation:

[tex]26+8 \\ \\ =2(13+4) \\ \\ =2(17) \\ \\ =34[/tex]

Answer: My new music player has a capacity of  3.6*10^11 bytes.

Step-by-step explanation: Scientific notation of a number is going to be in the form of a*10^b where a is a number greater than 1 but less than 10 which is then multiplied by the appropriate power of 10 so that the numbers are equal. This allows us to see numbers concisely without getting distracted by the sheer number of zeroes in some numbers. For 360, since 3.6 is between 1 and 10, we use that for a. To get 3.6 to equal 360 you have to move the decimal two places to the right, or multiply by 10^2, so b=2. Since this is in gigabytes, and giga=10^9, to express the answer in bytes we just multiply 10^2 to 10^9=10^11

Hope this helps

The east distance from town to house is 6.464 miles.

STEP - BY - STEP EXPLANATION

What to find? The east distance from town to house.

To solve;

Let us first make a sketch to get the clearer picture of the problem.

Attach below is the sketch.

Observe that the house is far east of the center of the town= 3miles + x

We need to find the value of x.

Using Pythagoras theorem;

hypotenuse²= adjacent² + opposite²

From the diagram above,

hypotenuse = 4

adjacent=x

opposite=2

Substitute the values into the formula and solve for x.

4² =x² + 2²

16 = x²+4

Subtract 4 from both-side of the equation.

x²=16 - 4

x²=12

Take the square root of both-side of the equation.

x = 3.464

But recall that, the east distance from town to house = 3+ x

Substitute the value of x.

Hence, the east distance from town to house = 3+ 3.464 = 6.464 miles

Let's begin by listing out the information given to us:

Sandra has 1/4 of a roll of ribbon

To make 3 bows, she will use the amount of ribbon shown below:

1089822 is the combined population of the four insect groups.

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2³) signifies 2 x 2 x 2 = 8. 2³ and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.

Given Data

Insect population

Population of honeybees = 7.3498(10⁴)

Population of honeybees = 73498

Population of ants = 6.822(10³)

Population of ants = 6822

Population of termites = 9.8(10⁵)

Population of termites = 980000

Population of aphids = 2.9502(10⁴)

Population of aphids = 29502

Combined population = 73498 + 6822+980000+29502

Combined population = 1089822

1089822 is the combined population of the four insect groups.

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By solving a system of equations we can see that Olivia spent $14 and Camiller spent $37.

Let's define two variables:

We know that " Camille spent $14 less than three times what Olivia spent" so we can write:

y = 3*x - 14

And "In total, they spent $54"

x + y = 54

Then we have a system of equations:

y = 3*x - 14

x + y = 54

Replacing the first equation into the second one, we get:

x + 3x- 14 = 54

4x - 14 = 54

4x = 54 + 14

4x = 68

x = 68/4 = 17

Now that we know the value of x, we can try to find the value of y.

y = 3x - 14 = 3*17 - 14 = 37

So Olivia spent $14 and Camiller spent $37.

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Answer: Provided the geometric diagram, we have to find the unknown angle DCF.

Assuming, that the line segments AC and EF are parallel and the same is true for the line segments DE and CB.

The new diagram is:

Therefore the answer is:

or 61 degrees.

Step-by-step explanation:

Because it follows the law of indices which states

A^b × B^b = A × B ^ b +b = A × B ^ 2b.

So, this is true for all real numbers.