The measures of two supplementary angles total 180 degrees. The measure of angle y is 65 degrees less than the measure of angle x. What are the measures of the angles?
The measure of angle x is 122.5 degrees. The measure of angle y is 57.5 degrees.
The measure of angle x is 115 degrees. The measure of angle y is 65 degrees.
The measure of angle x is 57.5 degrees. The measure of angle y is 122.5 degrees.
The measure of angle x is 65 degrees. The measure of angle y is 115 degrees.

A quadratic equation x² = 16 has two solutions, x = 4 and x = -4.

A quadratic equation has standard form:

ax² + bx + c = 0

There are several methods to solve a quadratic equation:

- using factorization

- by completing the square

The given quadratic equation is: x² = 16

Method 1: Using factorization

x² = 16

x² - 16 = 0

(x + 4) (x - 4) = 0

Hence, the solution is x = 4 and x = -4

Method 2: By completing the square

x² = 16

This is already a perfect square. Hence,

x = ±√16

x = ±4

Hence, the solution is x = 4 and x = -4

Conclusion: there are two solutions of  x² = 16,  x = 4 and x = -4

There was typos in your question, most likely your question was:

How many solutions does x² = 16 have?

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For the given mean and other values the value of data point will be 131.6.

What is mean?

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

The formula for the z-score is

z = (x - μ)/σ

x = data point

μ = mean

σ = standard deviation

Now

Given

Mean=102.8

standard deviation=15.4

z-value=1.87

putting the values in the formula

z = (x-μ)/σ

where x is the data point , μ is the population mean, and σ is the population standard deviation

1.87=(x-102.8)/15.4

Hence,

x=131.6

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Answer:

9 students

Step-by-step explanation:

24×3/8 to get 9 students

Answer:

Step-by-step explanation:

out of 24 students, the amount riding the bus is 192/3  but can be simplified to 64/1. Hope this helps you !

The prior amount is $600.00, the finance charge is $7.50, the new purchases are $90.00, and the payments and credits are each worth $100.00. 597.5 is the new balance.

By doing the identical action on both sides of the =-sign, you can solve equations by using the balance approach. The name is derived from the idea behind it: An (ancient) weighing device known as a balance has a scale, dish, or weighing pan on each side. You place a piece of the equation on each side of the balance.

Even if we change the amounts on either side of the equation by the same number, the balance will remain the same. In order to balance an addition equation, add the side that has no missing numbers first. The opposite side must match this amount. The number that is present on the side with the missing value is then taken, and it is subtracted from your total.

= Purchase - Payments

= 90 - 100

= - 10

New balance   = Previous balance  + Finance charge - Purchase

                         = 600 + 7.50 -10

New balance   = 597.5

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The definite integral by u-substitution: [tex]$$\int_0^2 x^3 \sqrt{x^4+1} dx$$[/tex] will be 11.515

The region beneath a curve between two set limits is a definite integral. For a function f(x), defined with reference to the x-axis, the definite integral is written as baf(x)dx a b f (x) d x, where an is the lower limit and b is the upper limit.

The upper limit and lower limit are the two stated limits that make up the definite integral.

As per the question,

We have the value: [tex]$$\int_0^2 x^3 \sqrt{x^4+1} dx$$[/tex]

Given:-

[tex]I=\int_0^2 x^3 \sqrt{x^4+1} dx[/tex]

Let [tex]x^4+1=t[/tex]

[tex]\\& 4 x^3 d x=d t \\& x^3 d x=\frac{d t}{4}[/tex]

x=0, t=0^4+1=1

x=2,

t=2^4+1

t=16+1=17

Now evaluating the value of integration:

[tex]$$\begin{aligned}I & =\int_{t=1}^{17} \sqrt{t} \frac{d t}{4} \\I & =\frac{1}{4} \int_1^{17} t^{1 / 2} d t \\& =\frac{1}{4}\left[\frac{t^{1 / 2+1}}{\frac{1}{2}+1}\right]_q^{17} \\& \left.=\frac{1}{4}\left[\frac{17^{3 / 2}-1^{3 / 2}}{\frac{3}{2}}\right]^{17 \sqrt{17}-1}\right] \\& =\frac{1}{4} \times \frac{2}{3} \times[120]\end{aligned}$$[/tex]

[tex]I=\frac{1}{6}[17 \sqrt{17}-1]=11.51546594[/tex]

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The correct questions should be:

Evaluate the definite integral by u-substitution: [tex]$$\int_0^2 x^3 \sqrt{x^4+1} dx$$[/tex]

The correct answer is D. The station's faulty prediction is a result of bias. Only people watching the news will respond, and their preference may differ from that of other voters. The sampling method may systematically produce samples that do not represent the population of interest.

The TV station's "Pulse-Poll" method of collecting data is not a random sample of the population of interest, which is the entire voter population. Instead, it only captures the opinions of people who are watching the evening news and choose to text in their vote. This group of people may not be representative of the entire voter population, as it only includes viewers of that specific TV station and those who are motivated enough to text in their vote. The sample is not representative of the population of interest, and therefore the results are biased and should not be used to make predictions about the election outcome.

This self-selected group of people may have different characteristics and opinions than the general voter population. For example, viewers of the specific TV station may have different political leanings than the general population, and those who are motivated enough to text in their vote may have different levels of political engagement. As a result, the sample is not representative of the population of interest, and therefore the results are likely to be biased.

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The exponential equation y = 2500 * 0.76^t models the relationship between the value of a laptop computer (y) and the number of years since it was purchased (t). It shows that each year the value decreases by 24%.

y = 2500 * 0.76^t

Given:

In 2005, a laptop computer was purchased for $2500.

Each year since then, the real value has decreased by 24%.

Let t be the number of years since 2005.

Let y be the value of the laptop computer, in dollars.

We can model this relationship using an exponential function.

Since the real value has decreased by 24% each year, we can use the equation 1 - 0.24 = 0.76 to represent this.

We can then use this to write the exponential function.

y = 2500 * 0.76^t

This equation shows the relationship between y (the value of the laptop computer) and t (the number of years since 2005). The exponential equation y = 2500 * 0.76^t models the relationship between the value of a laptop computer (y) and the number of years since it was purchased (t). It shows that each year the value decreases by 24%.

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An exponent of a number appears how many times we are multiplying a number by itself. For example, 3³ means we are multiplying 3 four times. Its expanded form is 3×3×3. An exponent is defined as the power of a number.

The exponent of a number defines how many times the number is multiplied by itself. For example, 2×2×2 can be written as 2³, as 2 is multiplied by itself three times. Here, 2 is said to be the "base" and 3 is said to be the "exponent" or "power." In general, [tex]x^{n}[/tex] this means that x is multiplied by itself by n times.

Example :  5*5 = 5²

An expression that means repeated multiplication of the same factor is called a power.

The number 5 is said to the base and the number 2 is said to the exponent.

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The scale factor can alter an object's size, either making it bigger or smaller.

By multiplying the x and y coordinates of the original figure by the scale factor, you may locate locations on the dilated image when a dilation in the coordinate plane has the origin as the centre of dilation. (X, Y) is how the dilation is expressed algebraically for scale factor k.

An object's size can be changed by the scale factor, either making it larger or smaller. To determine a dilated figure's scale factor, use the following simple formula: Scale factor is the product of the old shape's dimension and the new shape's dimension.

By constructing the new function f (x) → f (x), it is possible to dilate a function f (x) in the vertical direction by a scale factor of a. The function's roots and the x-coordinates of any turning points remain unaltered when a function is dilated vertically.

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Answer:

  d = 8.24

Step-by-step explanation:

You want the measure of d, the side opposite the 31° angle in the right triangle shown as having a hypotenuse of length 16.

The mnemonic SOH CAH TOA was invented to remind you of the relations between sides and trig functions in a right triangle. In the triangle shown, you have an angle, the side opposite (O), and the hypotenuse (H). The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

Filling in the values shown, this tells you ...

  sin(31°) = d/16

Multiplying by 16 gives the value of d:

  d = 16·sin(31°)

Your calculator can tell you what this value is, rounding it if you want.

The value of d is 8.24.

__

Additional comment

The other parts of the mnemonic tell you ...

You will notice the flag in the lower left corner of the calculator display tells you the mode is set to Degrees (DEG), rather than radians (RAD) or grads (GRA). This is required in order for sin(31) to be properly interpreted.

Answer:

Yes

Step-by-step explanation:

Pythagoras' theorem states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.

Function A have a greater initial value compared to function B

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the initial value

For function A, from the table, using the point (0, 4) and (2, 0):

y - 4 = [(0 - 4)/(2 - 0)](x - 0)

y - 4 = -2x

y = -2x + 4

Function A have an initial value of 4

Function B have an initial value of 3

Function A have a greater initial value.

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The Simplification of the rational expression n[1/x - 1/(x + 2) / 2] gives 1/[x(x+2)] or 1/(x²+2x)

Simplification of a rational expression as a way of writing an expression in the most efficient and compact form without affecting the value of the original expression

[1/x - 1/(x+2)] /2

The LCM of x and (x+2) is x(x+2). Thus, we have:

[1/x - 1/(x+2)] /2 = [(x+2 - x) / x(x+2)] /2

                        = [ 2 / x(x+2)] /2

                        = 1 / [x(x+2)]

                        = 1/(x²+2x)

Thus, the expression simplifies to 1/[x(x+2)] or 1/(x²+2x)

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Answer:

a 4 by 4 square

a 5 by 5 square

Step-by-step explanation:

The three shapes are

1) a square 1 unit by 1 unit

2) a square 2 units by 2 units

3) a square 3 units by 3 units

The next two shapes are

4) a square 4 units by 4 units

5) a square 5 units by 5 units

Establish,Set a condition and Include an iteration are the three action.

Looping math is a part of lion that starts and end at the same point. It can refer to a continuous curve like Circle or a or to a sequence of discrete Point like a polygonal line.

1. Establish a loop control variable - This is a variable that will be used to control the loop. It is typically assigned an initial value before the loop starts, and is then modified each time the loop runs.

2. Set a condition - The loop should include a condition that will be evaluated each time the loop runs. If the condition is true, the loop will continue, and if the condition is false, the loop will end.

3. Include an iteration - The loop should include an instruction that will be executed each time the loop is run. This instruction can modify the loop control variable, or it can perform some other action.

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Answer:

The probability that a student has an A given that the student is female is 8/9.

Step-by-step explanation:

We know that:

P(B) = 9/20 (the probability that a student is female)

P(A and B) = 8/20 (the probability that a student is female and has an A in the class)

We can use the formula:

P(A|B) = P(A and B) / P(B)

So, P(A|B) = 8/20 / 9/20 = 8/9

The area of the wall is 80.7293 square feet. The number of cans that Asher needs is 4.

What is a pentagon?

A pentagon is a five-sided polygon with five angles. The term "pentagon" is made up of two terms, Penta and Gonia, both of which mean five angles. All of the sides of a pentagon meet end to end to form a shape.

Given the wall on a storage shed is a pentagonal shape.

The area of a pentagon can be divided into two shapes. The shapes are one is a rectangle and another is a triangle.

The length of the rectangular shape is (1+1+1) = 3 meters.

The width is (1+1) = 2 meters.

The area of the rectangular shape is 3 × 2 = 6 square meters.

The length of the base of the triangle is 3 meters.

The height of the triangle is 1 meter.

The area of the triangle is 1/2× base× height = 1/2 × 3×1 = 3/2 square meter.

Total area of the pentagon is  6 + 3/2 = 7.5 square meters.

1 square meter = 10.7639 square feet

7.5 square meters = (7.5×10.7639) square feet

                              = 80.7293 square feet

1 can of paint covers an area of 24 square feet.

Therefore to cover 80.7293 square feet, he needs 80.7293/24 = 3.36.

Thus he needs a minimum 4 cans of paint.

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The 53rd term of the arithmetic sequence is 584

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2

The nth term of an arithmetic sequence is given as : a(n) = a+(n-1) d

where a is the first term and d is the common difference.

The first term in the sequence is -12 and the common difference is -1-(-12) = 11

a(53) = -12+( 53-1) 11

= -12+ 52×11

= 12+ 572

a(53) = 584

Therefore the 53rd term is 584

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The length of the third side of the triangle which is the hypotenuse is 17 with other sides being 8 and 12.

This is referred to as a three-sided polygon that consists of three edges and three vertices and the longest side is referred to as the hypotenuse.

In other to get the length of the sides of a triangle, we have to apply pythagoras theorem which is seen below:

a² + b² = c²

To get the hypotenuse , we can use c=√a²+b²

c = √8² + 12²

c = √64 + 144

c = √289 = 17.

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Answer:

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

Given system:

Plot each line and find the intersection, this is the solution.

The solution is (2, - 2) as per attached graph.

Answer:

Here is your answer

((3 * 6) ^ 8) ^ 7 =

(18 ^ 8) ^ 7 =

11019960576 ^ 7 = 19736052228807988194997231645899399052500495522364054175325333567307776

Step-by-step explanation:

Answer:

5 _12 5947272950381_8294

Answer:

2980.95799

Step-by-step explanation:

The cost of each t-shirt is $20 and cost of each pair of pant is $12.

In the given question a shopper purchased 8 t shirts and 5 pairs of pants for $220

The next day he purchased 5 t shirts and 1 pair of pants for $112. We have to find the cost of each pair of t-shirts and pants.

Suppose that t is the price of a T-shirt and p is the price of a pair of pants.

For $220, a customer bought 5 pairs of pants and 8 T-shirts:

8t + 5p = 220...…..(1)

He spent $112 on 5 T-Shirts and 1 pair of slacks the following day:

Now the equation should be

5t + p = 112...…..(2)

From the equation 2, p = 112 - 5t

Now putting the value of p in equation (1)

8t + 5(112 - 5t) = 220

8t + 560 - 25t = 220

Subtract 560 on both side, we get

-17t = -340

Divide by -17 on both side, we get

t = 20

Now putting the value of t in p = 112 - 5t

p = 112 - 5(20)

p = 112 - 100

p = 12

Hence, the cost of each t-shirt is $20 and cost of each pair of pant is $12.

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Step-by-step explanation:

what did your teacher want to achieve by the 2 questions that have the same answer ? or is sea level different from the surface of that body of water ? that information would be missing.

the driver descends 15.2 ft per second =

= 15.2/1 ft/s = 15.2 ft/s

after 4.1 seconds the diver descends 15.2 × 4.1 = 62.32 ft.

so, the diver is at that time 62.32 ft under the surface of that body of water.

if sea level is different to the surface of that body of water, then that difference has to be added (when sea level is higher that the water surface) or subtracted (when sea level is below the water surface) to get the the position below or above sea level.

Answer: If 20% of a farmer's harvest had to be given to Pharaoh, and the farmer had to give 40 bushels, we can set up the equation:

(x * 0.2) = 40 bushels

where x represents the number of bushels the farmer harvested. To find the value of x, we can divide both sides of the equation by 0.2:

x = 40 bushels / 0.2

x = 200 bushels

Therefore, the farmer harvested 200 bushels of grain that year.

Step-by-step explanation:

why, it's clearly D stoopid

Answer: OK IM HURRYING LOL

its y = -3x+2

Step-by-step explanation:

NO TIME