What is the solution to the system of equations below?
(-1, 2)
(1, -2)
(2, -1
(-2, 1)

The statements are A. ∠x and ∠y are supplementary angles, B. ∠w and ∠z are a linear pair.

Angle is the void between two surfaces or lines that meet. The angle is also expressed in degrees. The angle is 360 degrees for a full rotation.

Supplementary angle: When two angles add up to 180 degrees, they are considered to be supplementary angles.

Corresponding angle: The third line if two lines are parallel. Equal angles are formed by the matching angles.

Angles that are vertically opposed to one another are equal when two lines intersect.

Alternate angle: When two lines are parallel, a third line forms a z-angle, which is an equal angle to the parallel lines.

Complementary angle - When two angles add up to 90 degrees, they are considered to be complementary angles.

Angle x and angle y are supplementary angles. True.

Angle w and angle z are a linear pair. True.

Angle w and angle y are adjacent angles. False.

Angle x and Angle z are vertical angles. False.

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The gradient of a function points in the direction in which the function increases the fastest because it represents the direction of greatest increase of the function.

The gradient of a function is a vector that points in the direction of the steepest increase of the function at a particular point. This means that if we move in the direction of the gradient, the value of the function increases the fastest.

To understand why this is true, let's consider the definition of the gradient. The gradient of a function f(x) is defined as a vector of partial derivatives:

∇f(x) = (∂f/∂x1, ∂f/∂x2, ..., ∂f/∂xn)

Each component of the gradient vector represents the rate of change of the function with respect to the corresponding variable. In other words, the gradient tells us how much the function changes as we move a small distance in each direction.

When we take the norm (or magnitude) of the gradient vector, we get the rate of change of the function in the direction of the gradient. This means that if we move in the direction of the gradient, the value of the function changes the fastest, because this is the direction in which the function is most sensitive to changes in the input variables.

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Answer:

51 minutes

Step-by-step explanation:

50+5(unlimited)=55

65.23-55=10.23

10.23/.20=51.15 rounded to nearest is 51.

We can represent "f(x)" as:

The derivate of a monomial we multiply the monomial by its expoent and subtract one on the expoent. We have:

The correct option is "a".

Answer:

30 dollars

Step-by-step explanation:

The y-intercept is 15 and the slope is 30

How?

slope = change in y/change in x

Answer:

what is the difference between 880 and 580

Yes , the given statement is true , after implying Pythagoras theorem we conclude that the sides can be 5 cm 12 cm 13 cm.

We can use Pythagoras theorem to check whether the sides of a triangle can measure 5 cm 12 cm 13 cm or not .

The sum of square of two smaller sides should be equal to the third side.

13²   = 12² + 5²

13²   = √144 + 25

13²   =√169

13²   = 13

Therefore, we can conclude that the sides of a triangle can be 5 cm 12 cm 13 cm.

Pythagoras theorem states that the sum of smaller sides could be equal to the larger side. AC²   = AB² + BC².

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Answer: The probability that no man will be selected is the number of ways that only women can be selected divided by the total number of combinations of candidates for the 2 data analyst positions. There are 2 ways to choose 2 women from the 2 available women, and there are C(4,2) = 6 ways to choose 2 candidates from the 3 men and 2 women, so the probability that no man will be selected is 2/6 = 1/3.

The probability that both men will get selected is the number of ways to choose 2 men from the 3 available men divided by the total number of combinations of candidates for the 2 data analyst positions. There are C(3,2) = 3 ways to choose 2 men from the 3 available men, and there are C(5,2) = 10 ways to choose 2 candidates from the 3 men and 2 women, so the probability that both men will get selected is 3/10 = 3/5.

If Jyothi gets one more resume of a woman, there will be a total of 3 men and 3 women. The probability that only one man gets selected is the number of ways to choose 1 man and 1 woman from the 3 men and 3 women divided by the total number of combinations of candidates for the 2 data analyst positions. There are C(3,1) * C(3,1) = 9 ways to choose 1 man and 1 woman, and there are C(6,2) = 15 ways to choose 2 candidates from the 3 men and 3 women, so the probability that only one man gets selected is 9/15 = 3/5.

Step-by-step explanation:

The equation of the line is: y = 0.05x + 0.1.

A linear equation written in slope-intercept form is y = mx + b, where slope or unit rate is m, and y-intercept or starting value is b.

From the information given, we can derive the two points (3, 0.25) and (13, 0.75) if:

x = year

y = price per pound of apples

Find the slope (m) of the equation:

Slope (m) = change in y / change in x = 0.75 - 0.25 / 13 - 3

Slope (m) = 0.5 / 10

m = 0.05

Find y-intercept (b) by substituting m = 0.05 and (x, y) = (3, 0.25) into y = mx + b:

0.25 = 0.05(3) + b

0.25 = 0.15 + b

0.25 - 0.15 = b

b = 0.1

To write the linear equation, substitute m = 0.05 and b = 0.1 into y = mx + b:

y = 0.05x + 0.1

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Answer:

15.26

Step-by-step explanation:

By using a^2+b^2=c^2, we can plot the numbers into the equation, 8^2+13^2=c^2. Then answering the exponents, it will equal 64+169=c^2. Add that together to get 233=c. Lastly, we have to square-root 233, which equals 15.26. Hope this helped!

Answer:

24420.5

Step-by-step explanation:

Multiply all the numbers together to get the length of the cubiod

221*8.5*13= 24420.5

Hope this helped!

Answer:

\(\Huge \boxed{\mathrm{2 \ cm }}\)

Step-by-step explanation:

\(\sf Volume \ of \ cuboid= length \cdot width \cdot height\)

The width is 8.5 cm.

The height is 13 cm.

The volume is 221 cm³.

\(221 = l \cdot 8.5 \cdot 13\)

Solving for \(l\)

\(221=l \cdot 110.5\)

Dividing both sides by 110.5

\(2=l\)

The length is 2 cm.

Answer: \(12\ ft\)

Step-by-step explanation:

Given

Total height of utility pole is 18 ft

After breakage, only 5 foot tall portion is standing

The fallen part is \(18-5=13\ ft\) in length

From the figure, apply the Pythagoras theorem

\(\Rightarrow 13^2=x^2+5^2\\\Rightarrow x^2=169-25\\\Rightarrow x=\sqrt{169-25}\\\Rightarrow x=\sqrt{144}\\\Rightarrow x=12\ ft\)

Thus, the fallen part is \(12\ ft\) away from the base of the pole.

Here, we've rewritten the original statement without using the words "necessary" or "sufficient" by applying the rules of negating a ∀ statement and an if-then statement.

To rewrite the given statement without using the words "necessary" or "sufficient", we'll apply the rules mentioned in the question.

Statement: Being a polynomial is not a sufficient condition for a function to have a real root.

1. Identify the sufficient condition: "Being a polynomial"
2. Identify the necessary condition: "A function having a real root"

Now, we'll use the fact that the negation of an if-then statement is an and statement. The given statement can be written as:

If a function is a polynomial, then it has a real root.

The negation of this if-then statement would be:

A function is a polynomial and it does not have a real root.

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a) The negation of "Being divisible by 8 is a necessary condition for being divisible by 4" is:

"There exists a number that is divisible by 4 but not by 8." Using the negation of a universal quantifier, we can rewrite this as "Not all numbers divisible by 4 are also divisible by 8."

b) The negation of "Having a large income is a necessary condition for a person to be happy" is:

"There exists a person who is happy but does not have a large income." Using the negation of a universal quantifier, we can rewrite this as "Not all happy people have a large income."

c) The negation of "Having a large income is a sufficient condition for a person to be happy" is:

"There exists a person who does not have a large income but is still happy." Using the negation of an if-then statement, we can rewrite this as "Having a large income and being happy are not always true together."

d) The negation of "Being a polynomial is a sufficient condition for a function to have a real root" is:

"There exists a function that is a polynomial but does not have a real root." Using the negation of an if-then statement, we can rewrite this as "Being a polynomial and having a real root are not always true together."

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Answer:  

Here we answer the question: "What two numbers multiply to -36 and add up to -16?"

The answer to your question is:

2 and -18

Step-by-step explanation:     2 x -18 = -36

2 + (-18) = -16

Are you asking because you are trying to figure out how to factor the following quadratic equation?

x2 - 16x - 36 = 0

If so, the solution to factor the quadratic equation above is:

(X + 2 ) (X - 18)

To summarize, since 2 and -18 multiply to -36 and add up -16, you know that the following is true:

x2 - 16x - 36 = (X + 2 ) (X - 18)

The two numbers are -4 and -9.

A number is a count or measurement.

We are asked to find two numbers that multiply to 36 and add to -13,

Let the two numbers be x and y,

x+y = -13.............(i)

xy = 36

x = 36/y...............(ii)

Put eq(ii) in eq(i)

36/y + y = -13

Multiply the whole equation by y,

36 + y² = -13y

y²+13y+36 = 0

Solving for y,

y²+9y+4y+36 = 0

y(y+9)+4(y+9) = 0

(y+4)(y+9) = 0

y = -4 or y = -9

If we put y = -4 then we will get x = -9 similarly if y = -9 then x = -4

Hence the two numbers are -4 and -9.

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The volume of the rectangular prism given the length, width and height is 6 14/27 cubic feet.

The correct answer choice is option B

Volume of a rectangular prism= length × width × height

Length= 1 5/6 ft

Width = 1 1/3 ft

Height = 2 2/3 ft

Volume of a rectangular prism= length × width × height

= 1 5/6 × 1 1/3 × 2 2/3

= 11/6 × 4/3 × 8/3

= (11 × 4 × 8) / (6 × 3 × 3)

= 352 / 54

= 6 28/54

= 6 14/27 cubic feet

In conclusion, the volume of the rectangular prism is 6 14/27 cubic feet

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Answer:

4•(2+5)^2 -5^2 = 171

Step-by-step explanation:

Do BIDMAS
(brackets, indices, division, multipy, add, sub)

so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps

Answer: Brackets => 4 x (7)^2 - 5^2
               Indices/Orders => 4 x 49 - 25

               Multiplication => 196 - 25

               Subtraction => 171

Answer:

The bearing of B from A is 335 Degrees

Step-by-step explanation:

Measure bearings clockwise.

Bearings are measured from the North line.

There are 25 degrees between B and North.

360 Degrees in a circle.

360 - 25 = 335

Answer:

x=23.5

Step-by-step explanation:

\(cos59.3=\frac{12}{x}\\x(cos59.3)=12\\x=\frac{12}{cos59.3}\\x=23.5\)

Answer:  The amount of grain it can hold can also be called it's volume. 423.9

The formula for volume is PI × Raduis² × Height

And for the radius we divide the diameter by 2.

Answer:

Option A.

V = π × r(9)² × 15 ≈ 3,817.04

Which rounds closest to

3,815.10 inches

Check the picture below.

now, the Range and Domain are both assuming the lines goes no further, keeping in mind that most lines go to infinity.

the x-intercepts are just where the graph intersects or touches the x-axis.

the y-intercepts are just where the graph intersects or touches the y-axis.

vertex is simply where it makes the U-turn, and axis of symmetry is simply most of the time the x-coordinate of the vertex, of namely the line where the graph begins making a mirror image.

Answer:

5x+x=132

Step-by-step explanation:

132/6=22

22*5=110

Charlie weighs 110 pounds and Tali weighs 22 pounds.

Answer:

26

Step-by-step explanation:

w = 5 so 7w is 7 x 5 = 35 and x = 9 so it’s 35 - 9 which is 26

Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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The two buses are initially 515 miles apart and are moving toward each other. They will pass each other around 2:30 P.M.

To solve this problem, we can use the concept of relative speed. The combined speed of the two buses is the sum of their individual speeds, which is 48 + 55 = 103 miles per hour.

We can calculate the time it takes for the buses to meet by dividing the initial distance between them (515 miles) by their combined speed (103 miles per hour):

Time = Distance / Speed

Time = 515 miles / 103 miles per hour

Time ≈ 5 hours

Therefore, the two buses will pass each other approximately 5 hours after they start traveling toward each other. To determine the exact time, we need to consider the starting time (9:30 A.M.) and add 5 hours to it. So, they will pass each other around 2:30 P.M.

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Answer: 17,482

Step-by-step explanation:

Just move the decimal 4 times to the right

The scientific notation 1.7482 x 10^4 is equivalent to the ordinary number 17482. You convert it by moving the decimal point 4 places to the right.

The number 1.7482 x 10^4 is written in scientific notation. Scientific notation is a method used to simplify computations with very large or very small numbers. To convert this to a standard, or ordinary, number, you simply move the decimal point 4 places to the right (because 10^4 means we're multiplying by 10 four times).

When we do this, the number becomes "17482." This is the equivalent ordinary number for 1.7482x10^4.

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Answer:

i think ur answer is f in my mind

The solution to the equation 0.2(10 - 5c) = 5c - 16 is c = 3.

To solve the equation 0.2(10 - 5c) = 5c - 16, we will first distribute the 0.2 on the left side of the equation:

0.2 * 10 - 0.2 * 5c = 5c - 16

Simplifying further:

2 - 1c = 5c - 16

Next, we will group the variables on one side and the constants on the other side by adding c to both sides:

2 - 1c + c = 5c + c - 16

Simplifying:

2 = 6c - 16

To isolate the variable term, we will add 16 to both sides:

2 + 16 = 6c - 16 + 16

Simplifying:

18 = 6c

Finally, we will divide both sides by 6 to solve for c:

18/6 = 6c/6

Simplifying:

3 = c

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When we use a confidence interval to reach a conclusion about the population mean, we are applying a type of reasoning or logic called inferential statistics.

Inferential statistics involves using sample data to make inferences about a larger population. In the case of a confidence interval for the population mean, we use a sample mean and standard deviation to estimate the true population mean, and then we use the confidence interval to quantify our uncertainty about this estimate.

The confidence interval gives us a range of values within which we can be confident that the true population mean lies. The level of confidence chosen for the interval determines the width of the interval and the probability that the true population mean lies within it.

Inferential statistics plays a crucial role in making decisions based on sample data when it is not feasible or practical to collect data from the entire population.

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The probability of pulling two consecutive blue marbles is 0.1622

In this question we have been given  a bag with 20 red marbles, and 14 blue marbles.

we need to find the probability of pulling two consecutive blue marbles.

Total number of marbles = 20 red marbles + 14 blue marbles

                                       = 34 marbles

The probability of pulling a blue marble is:

p1 = 14/34

After pulling 1 blue marble there would be 13 blue ,arbles and 33 total marbles in a bag.

So, the probability of pulling next blue marble would be,

p2 = 13/33

So, he probability of pulling two consecutive blue marbles would be,

p = p1 * p2

p = 14/34 * 13/33

p = 0.1622

Therefore, the required probability is 0.1622

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