The rectangle has an area of 128 square inches and a width of 8 inches. Find the perimeter of the rectangle.

The solution of the given equation is (i) x = 3 ,(iii) x=-1/2 .

Quadratic equation's roots The roots of a quadratic equation are the values of the variables that satisfy the equation. In other words, if f() = 0, therefore x = is a root of the quadratic equation f(x). The x-coordinates of the points where the curve y = f(x) intersects the x-axis are the real solutions of an equation f(x) = 0.

So we can find the root of 2[tex]x^2[/tex]— 5x —3 = 0 by factorising them.

=> 2x² - 5x - 3 = 0

=> 2x² - 6x + x - 3 = 0

=> 2x(x - 3) + (x - 3) = 0

=> (x-3)(2x+1) = 0

so the value of x = 3 , - 1/2

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Complete question :

For 2[tex]x^2[/tex]— 5x —3 = 0, determine which of the following are solutions?

(i) x = 3 (ii) x= –2

(iii) x=-1/2 (iv) x=-1/3

Answer:

Translation, then Rotation

Step-by-step explanation:

It is first moved(translation), then rotated(rotation) around the left meeting point of the graph by about 90 degrees to the right.

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:

[tex]\huge\boxed{\sf x = -100}[/tex]

Step-by-step explanation:

[tex]\displaystyle -\frac{x}{5} -8=12\\\\Add \ 8 \ to \ both \ sides\\\\-\frac{x}{5} = 12+ 8\\\\-\frac{x}{5} = 20\\\\Multiply \ both\ sides \ by \ 5\\\\-x = 20 \times 5\\\\-x = 100\\\\Multiply\ both \ sides \ by\ -1\\\\x = -100\\\\\rule[225]{225}{2}[/tex]

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 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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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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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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Answer:

5 _12 5947272950381_8294

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 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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Answer:

(x+3) and (5x-2)

Step-by-step explanation:

first get everything onto one side

5x^2+13x-6=0

then multiply 5 by 6 to get 30 and 15 times 2 is thirty and 15-2=13

5x^2+15x-2x-6=0

then split in half and factor both sides

5x^2+15x factored is 5x(x+3)

-2x-6 factored is -2(x+3)

so the answer is (x+3) and (5x-2)

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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Colleen's velocity increased from the first section to the second section, while it remained constant from the second section to the third section.

The measures in this problem are obtained considering the relation between velocity, distance and time.

The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:

v = d/t.

In which:

For session 1, considering decimal numbers, the parameters are given as follows:

Hence the velocity is of:

v = 9.9/2.2 = 4.5 miles per hour.

For session 2, the parameters are given as follows:

Hence the velocity is of:

v = 11.875/2.5 = 4.75 miles per hour.

For session 3, the parameters are given as follows:

Hence the velocity is of:

v = 15.4375/3.25 = 4.75 miles per hour.

The table is given by the image presented at the end of the answer.

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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 equation of the line with given slope and passing through the given point is y = -5x - 6.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.

General form of slope intercept form of line is,

y = mx + d

Here d is the y intercept, which is the value of y coordinate when x coordinate is 0. And m is the slope.

Given that slope, m = -5

Also we have a point on the line (-2, 4)

Substituting these,

4 = (-5 × -2) + d

4 = 10 + d

d = -6

So the equation is y = -5x - 6.

Hence the equation of the line is y = -5x - 6.

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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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So the sin(z) is approximately 0.4866.

In a right triangle, the two non-right angles are complementary, meaning that their measures add up to 90 degrees.

So, if ∠x is complementary to ∠z, then we can write the equation ∠x + ∠z = 90°

We also know that in a right triangle, the cosine of one angle is equal to the ratio of the adjacent side to the hypotenuse.

And the sine of one angle is equal to the ratio of the opposite side to the hypotenuse.

Given that cos(x) = 0.6.

We can find sin(z) by using the trigonometric identity, sin²(z) + cos²(z) = 1

sin²(z) = 1 - cos²(x)

sin²(z) = 1 - 0.6²

sin²(z) = 0.24

sin(z) = √0.24

sin(z) = 0.4866

So the sin(z) is approximately 0.4866.

It's important to note that the result is an approximation since the value of cos(x) is given as 0.6, which is not exact.

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Answer: OK IM HURRYING LOL

its y = -3x+2

Step-by-step explanation:

NO TIME

Answer:

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

Given system:

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

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

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.

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.

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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why, it's clearly D stoopid

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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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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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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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: