Which equation represents the line that passes through points (1, –5) and (3, –17)?​

Answer:

You are only given a Side, an Angle, and then a side.  So that is what I would choose.  It can't be AA because you weren't given two angles.  It can't be SSS because you weren't given 3 sides.

Step-by-step explanation:

ΔPQR and ΔXYZ are similar due to the SSS theorem.

Option B is the correct answer.

There are ways to prove that two triangles are congruent.

- Side-Side-Side (SSS) Congruence.

The three sides of one triangle are equal to the corresponding three sides of another triangle.

- Side-Angle-Side (SAS) Congruence.

The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.

- Angle-Side-Angle (ASA) Congruence.

The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.

- Angle-Angle-Side (AAS) Congruence.

We have,

Similar triangles are triangles that have the same shape but may have different sizes.

Two triangles are similar if their corresponding angles are equal, and their corresponding sides are proportional.

When two triangles are similar, they have the same shape, but one may be larger or smaller than the other.

Now,

ΔPQR and ΔXYZ

PQ/XY = 12/4 = 3

PR/XZ = 6/2 = 3

Since the two sides are proportional,

QR/YZ will be proportional.

Now,

PQ/XY = PR/XZ = QR/YZ

ΔPQR and ΔXYZ are similar due to the SSS theorem.

Thus,

ΔPQR and ΔXYZ are similar due to the SSS theorem.

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8:12 is 2/3 and so is 16:24, 2:3, and 20:30

Step-by-step explanation:

For example (includes simplified problem solving),

8 ÷ 4 = 2

12 ÷ 4 =3

You would want to divide the numerator and denominator by the greatest common factor (GCF)

The ratio 8:12 can be reduced to its lowest terms by dividing both terms by the GCF

Therefore 8:12 is 2:3

Answer:

  B. 3x¹¹ +9x⁷ +5x³ −x +4

Step-by-step explanation:

You want to identify the polynomial that has terms written in descending order of their degree.

The degree of a term is the exponent of x in that term. In the given polynomial, the term degrees are 3, 1, 7, 0, 11.

When these are put into descending order, that order is ...

  11, 7, 3, 1, 0

The answer to this question will be the polynomial with terms written in the order of their degree as shown above:

  3x¹¹ +9x⁷ +5x³ −x +4

__

Additional comment

When the exponent of x is 0, the value of the term x^0 is 1. That is why we can say the constant term is a term that has the variable to degree 0.

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Answer:

Step-by-step explanation:

Use below compound interest formula and the given data.

F- future amount, P- invested amount, r - interest rate, n - number of compounds, t- time

Given:

Find the amount after 3 years:

The requried probability that a randomly selected adult has an IQ between 85 and 115 is also 0.6827.

Standardize 85 and 115 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

For 85:

z = (85 - 100) / 15 = -1

For 115:

z = (115 - 100) / 15 = 1

So we want to find the probability that a standard normal random variable Z is between -1 and 1. Using a standard normal distribution table or a calculator, we can find that this probability is 0.6827.

Since IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, the probability that a randomly selected adult has an IQ between 85 and 115 is also 0.6827.

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Answer:

Image below

Step-by-step explanation:

Graph of a Line Given Two Points

We are given the points (1,5/2), (-1/2,-1/4).

A straight line is entirely defined by two points. We have to plot them and join them with a straight line ending in arrows.

The point (1,5/2) is converted to decimal as (1,2.5)

The point (-1/2,-1/4) is also converted to decimal: (-0.5,-0.25)

This helps to define the divisions of each axis and properly draw the line.

Please refer to the image below.

Answer:

14:46= 0.3

Step-by-step explanation:

Ratios can be expressed as a decimal, fraction or a math expression as above. (2 weeks is 14 days.)

Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

Answer:

10x³ - 7x² - 7x + 4

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

(10x³ - 3x - 5) - (7x² + 4x - 9)

Step 2: Simplify

Answer:

One solution

Step-by-step explanation:

I think its 1 solution but I could be wrong, I looked it up and it said one solution.

Answer:

one

Step-by-step explanation:

I am using substitution method:

2x+6=-x-3

subtract 6 from both sides

2x=-x-9

add x to both sides

3x=-9

divide by 3

x=-3

you can also graph this to see. I personally like using desmos.

Answer:

Area of circle = pie r²

= 3.14 × 2.25

=7.065

Answer: 7.07cm²

Step-by-step explanation: diameter=3

radius=d/2

          =3/2

          =1.5cm

area=πr²

       =22/7 x 1.5 x 1.5

       =22/7 x 2.25

       =99/2 ÷ 7

       =99/2 x 1/7

       =99/14

Answer:

40

Step-by-step explanation:

c= 5*(104-32)/9 =40

Answer:

1/4

Step-by-step explanation:

I could be wrong but that's what I would put

Answer:

Explanation:

in general when she picked 12 flowers, 3 were roses

3/12 = 1/4

(a) Verifying that y(x) = (x - c)^2 satisfies the differential equation y' = 2y:

To verify that the function y(x) = (x - c)^2 satisfies the differential equation y' = 2y, we can find the derivative y' and substitute it back into the equation:

y' = d/dx [(x - c)^2] = 2(x - c)

So, y' = 2y if and only if 2(x - c) = 2y, which can be simplified to x - c = y.

Therefore, y(x) = (x - c)^2 satisfies the differential equation y' = 2y for all x, including x = c.

(b) Values of b for which the initial value problem y' = 2/y, y(0) = b has no solution or a unique solution:

(i) No solution: If b = 0, the initial value y(0) = 0 and the denominator of the right-hand side of the differential equation y' = 2/y would be 0, making the equation undefined at that point. Therefore, the initial value problem y' = 2/y, y(0) = 0 has no solution.

(ii) Unique solution defined for all x: For all other values of b (b ≠ 0), the initial value problem y' = 2/y, y(0) = b has a unique solution that can be found using standard methods of solving initial value problems. This solution will be defined for all x.

The figure illustrating the fact that the initial value problem y' = 2/7, y(0) = 0 has infinitely many different solutions would show a family of curves that are all solutions to the differential equation y' = 2/7, with different starting values y(0) leading to different curves. This demonstrates that there are infinitely many different solutions to the initial value problem.

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Answer:

First, let's find where the lines:

x + 2y = 0

2x - y - 12 = 0

intersect.

First, let's isolate the variable y in one side of the equalities.

y = (-x/2)

y = 2x - 12

Now we have:

-(x/2) = 2x - 12

We can solve this for x.

12 = 2*x + x/2 = 2.5*x

12/2.5 = x = 4.8

Then, replacing that value in any of the lines, we can find the value of y.

y = 2*8 - 12 = 2*4.8 - 12 = -2.4

Then those lines intersect in the point (4.8, -2.4)

Now we want to find the line that passes through the points (-2, 3) and (4.8, -2.4)

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Then, the slope for our line is:

a = (3 - (-2.4))/(-2 - 4.8) = -0.79

And the

y-intercept will be:

y = -0.79*x + b

when x  = -2, y = 3.

3 = -2*-0.79 + b

3 - 2*0.79 = b = 1.42

The line is:

y = -0.79*x + 1.42

Answer:

If zero is added to any number, then the answer will always be equal to the initial number.

The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589

See table for sum of values.

The regression equation is:

y=α+βx

β = \(\frac{Sxx}{Syy}\)=6995-97799779\(\frac{6995-9\times\frac{779}{9}\times\frac{77}{9}}{68613-9(\frac{779}{9} )2}\)= 0.449

α=y-βx= 779-(0.449)7799 = =-30.27

The equation is y=-30.27+0.449x

Where y = predicted variable; x = independent variable = 0.449; - 30.27 = intercept/ slope

Constructing a 91% prediction interval for y:

x = 910

Inputting x = 91 into the regression equation : y = 0.449(91) - 30.27

y = 40.859 - 30.27 = 10.589

Prediction interval = y pm error margin

To save computing time, error margin (E) can be obtained using the online error margin calculator.

Obtained error margin (E) value = 2.3398

(10.589- 2.3398, 10.589+ 2.3398)

(8.2492, 12.9288)

(8, 13)

The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589

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There was 4 dollar of discount on the total amount.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that Adrian bought a jacket that costs 11 dollars and a scarf that costs 15 dollars.

At the counter, he received a discount. If he only paid 22 dollars total, then

Total cost 11 + 15 = 26

But 26 - 22 = 4

Therefore, the discount was 4 dollar.

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The numerical value of x in angle ABD is 9 as angle ABC is divided into two equal halves.

An angle bisector divided an angle into two equal halves.

From the diagram:

Line BD divides angle ABC into two equal halves.

Angle ABD = ( 3x - 7 ) degrees

Angle DBC = 20 degrees

Since angle ABD and DBC are equal haves;

Angle ABD = Angle DBC

Plug in the values:

( 3x - 7 ) = 20

Solve for x:

3x - 7 = 20

Add 7 to both sides:

3x - 7 + 7 = 20 + 7

3x = 27

x = 27/3

x = 9

Therefore, the value of x is 9.

Option A)9 is the correct answer.

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Answer:

1. 7:20hrs round to 7 hours (1 hour =60 minuite, and 20 is less than half of 60)

2. All numbers when divide by 1 is equal to itself (you can try with any number)

3. 9365<9635

the the second digit of 9635 is 6

the the second digit of 9365 is 3

Thus 9635 is greater

Brainliest please~

Given:

A diagram is given as

Find:

we have to find the measure of the angle formed by Explanation:

we know that PB (radius of the circle) is perpendicular to the tangent line AC.

Since, the angle between the radius of the circle and tangent line is 90 degree.

Therefore, the angle PBC is 90 degree.

Therefore, the correct option is D.

Answer:

x=2, y=2

Step-by-step explanation:

Put them on top of each other:

3x+2y=10

4x-2y=4

You add them together and then y cancels out, you now have 7x=14, divide by 7 on each sides and then you get x=2.

Substitute x in an equation and then solve. You get y=2

Answer:

\(x=2, y=2\)

(2,2)

Step-by-step explanation: Elimination just means canceling out a variable to solve for the value of the other. This equation has been set up easily to do so. All you need to do is combine both equations to get rid of the y-term.

\(3x+2y=10\\4x-2y=4\\7x=14\)

which means

\(x=2\)

plug it back in to get the y-value

\(3(2)+2y=10\\6+2y=10\\2y=4\\y=2\)

And there you go. Please mark brainliest.

Answer:

Step-by-step explanation:

1/3 m ^5 = 12                  Multiply both sides by 3

3(1/3) m^5 = 12 * 3

m^5 = 36

Now you have to be using a calculator capable of getting an answer that is a 1/5 power.

The key you need is either x^y or y^x or ^ All scientific calculators have one of these.

(m^5)^(1/5) = 36^(1/5)

m = 2.048 This has been rounded to the one thousandth place.

You should check this

2.048 * 2.048 * 2.048 * 2.048 * 2.048 = 36.029 which is very close considering how this was founded.

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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The image you described features a number line that goes from 0 to 6.5 in increments of 0.5.

On this number line, there is an arrow that starts at 0 and extends to 2.5, and then continues from 2.5 to 5.

This image can be visualized as follows:

0        1        2        3        4        5        6        6.5

|--------|--------|--------|--------|--------|--------|--------|

        |------------------------|------------------------|

             0 to 2.5                 2.5 to 5

The vertical lines represent the increments of 0.5 on the number line, and the arrow indicates the segments from 0 to 2.5 and from 2.5 to 5.

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The correct option : Both np and n(1 – p) are at least 10, for the a population with population proportion p.

A portion of a population that possesses a certain characteristic, given as a percentage, fraction, or decimal of the entire population.

For the stated data;

n = sample size of the population

p = population proportion

Then, for the sampling distribution of the sample proportion to be approximately normal both np and n(1 – p) are at least 10.

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