use interval notation to express the set of real numbers $x$ that satisfies the inequality $(x 2)(x-5) < 0$.

The length of the two segments, written as radicals, are:

AB = √117

PQ = √244

Remember that for a segment whose endpoints are (x₁, y₁) and (x₂, y₂), the length of the segment is:

L = √( (x₂ - x₁)² + (y₂ - y₁)²)

First, for the segment AB the endpoints are:

A = (-4,  -4)

B = (2, 5)

Then the length is:

L =  √( (-4 - 2)² + (-4 - 5)²)

L = √117

For the segment PQ the endpoints are:

P = (-6, 8)

Q = (6, -2)

The length is:

L =  √( (-6 - 6)² + (8 + 2)²)

L = √244

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The equivalent expression to the expression (a⁻⁷ × b⁻²)⁻⁹ is (a⁷ × b²)⁹.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

The given expression is (a⁻⁷ × b⁻²)⁻⁹.

= a⁻⁷ˣ⁻⁹ × b⁻²ˣ⁻⁹.

= a⁶³ × b¹⁸.

= (a⁷ × b²)⁹.

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Answer:

oranges €0·2б     apples€0·32

Step-by-step explanation:

Answer:

apple $0.32 , orange $0.26

Step-by-step explanation:

let o and a represent the cost of an orange and apple, respectively , then

12o + 7a = 5.36 → (1)

8o + 5a = 3.68 → (2)

multiplying (1) by 8 and (2) by - 12 and adding will eliminate o

96o + 56a = 42.88 → (3)

- 96o - 60a = - 44.16 → (4)

add (3) and (4) term by term to eliminate o

0 - 4a = - 1.28

- 4a = - 1.28 ( divide both sides by - 4 )

a = 0.32

substitute a = 0.32 into either of the 2 equations and solve for o

substituting into (1)

12o + 7(0.32) = 5.36

12o + 2.24 = 5.36 ( subtract 2.24 from both sides )

12o = 3.12 ( divide both sides by 12 )

o = 0.26

the cost of an apple is $0.32 and the cost of an orange is $0.26

An infinite number of solutions is generated with a multiple of the first function, hence, the correct option is:

\(y = -\frac{1}{4}(4x - 8)\)

The graph given is:

\(y = -x + 2\)

When two equations are multiple, the system involving these two equations has infinite solutions.

Among the options, the multiple of the original function is:

\(y = -\frac{1}{4}(4x - 8)\)

\(y = -x + 2\)

Hence, \(y = -\frac{1}{4}(4x - 8)\) is the correct option.

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The correct answer is C

-Banana

The y intercept is 0 and the slope of the graph of the equation is 1/2. As the value of y increase by 1, the value of x increases by 2

An equation is an expression that shows the relationship between two or more numbers and variables. Types of equation are linear, quadratic, cubic and so on.

The standard equation of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

where m is the rate of change and b is the y intercept

Given the equation:

y = (1/2)x

The y intercept is 0 and the slope of the graph of the equation is 1/2.

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Answer:

  20 ft

Step-by-step explanation:

The formula for the surface area of a pyramid is often written in terms of the base dimensions and the slant height. We can solve that formula for the slant height.

  SA = base area + lateral area

  SA = b² + 2bs . . . . . where b is the base dimension, and s is the slant height

  SA -b² = 2bs . . . . . subtract the base area

  s = (SA -b²)/(2b) . . . . divide by the coefficient of s

Using the given values for surface area and base length, we find ...

  s = (896 -16²)/(2·16) = 640/32 = 20 . . . feet

The slant height of the pyramid is 20 feet.

We can claim that after answering the above question, the So, logarithm \(log4 (0.5^(1/2)) =-0.0752\)

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

Using the following property of logarithms:

\(log_a (b^c) = c * log_a (b)\\log4 (0.5^(1/2))\\(1/2) * log4 (0.5)\\log4 (0.5) = log (0.5) / log (4)\\log (0.5) ≈ -0.3010\\log (4) = 2\)

Therefore,

\(log4 (0.5) ≈ -0.3010 / 2 ≈ -0.1505\\(1/2) * log4 (0.5) ≈ (1/2) * (-0.1505) ≈ -0.0752\\\)

So, \(log4 (0.5^(1/2)) =-0.0752\)

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\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

The volume of the cylinder would be 2120.6\(units^3.\)

To find the volume of a cylinder, you need to use the formula:

Volume = π x \(radius^2\) x height

Where π (pi) is a mathematical constant approximately equal to 3.14159, radius is the distance from the center of the cylinder to its edge, and height is the distance from one end of the cylinder to the other.

To apply this formula, you need to know the values of the radius and height of the cylinder. Once you have these values, simply substitute them into the formula and solve for the volume.

For example, if the radius of a cylinder is 5 units and the height is 27 units, the volume of the cylinder would be:

Volume = π x \(radius^2\)x height

Volume = 3.14159 x\(5^2\)x 27

Volume = 2120.6 \(units^3\)

Therefore, the volume of the cylinder would be 2120.6\(units^3.\)

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Answer:

6 feet per minute.

Step-by-step explanation:

The turtle and snail are moving towards each other, so their speeds add up. Therefore, the combined speed at which they approach each other is:

5 feet/min (turtle's speed) + 1 feet/min (snail's speed) = 6 feet/min

Therefore, the turtle and snail are approaching each other at a speed of 6 feet per minute.

Answer:

6 feet per minute.

Answer:

\(XY : WX = 1.39\)

Step-by-step explanation:

Given

\(RS = 18; ST = 25; TR = 11\)

Required

Which is closest to \(XY : WX\)

From the question, we understand that: \(\triangle RST\) and \(\triangle WXY\) are similar.

This means that, the following sides are similar:

\(RS \to WX\)

\(ST \to XY\)

\(TR \to YW\)

So:

\(XY : WX = ST : RS\)

This gives:

\(XY : WX = 25 : 18\)

Express as fraction

\(XY : WX = \frac{25 }{ 18}\)

\(XY : WX = 1.39\) --- approximated

Answer:

An exponential function is written in the form of f(x) = a (b)x. When we want to find an initial value of 500, it means that when x = 0, then y must equal 500. So, you plug in 0 to x in the exponential function, which leaves you with f(0) = a. Then, since f(0) = 500, that means a = 500

Hope this will help! =)

Step-by-step explanation:

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer:

Faye has $3,000 that she is going to deposit into each of the two accounts as shown:

•Account A: 5% simple interest for 5 years

•Account B: will earn $828.84 over 5 years

Assuming Faye does not make any additional deposits nor withdrawals, find t combined amount of her two accounts after 5 years.

Step-by-step explanation:

sub to sir sir bmgo ΔΔ

The sets A and B are equivalent but they are not equal.

We know that a set is a collection of elements. The elements that we can find in a set are arranged in order such that we can easily see what is composed of the set.

Now two sets are said to be equivalent if they have the same cardinality. We can see that the set of the sets A and B are equal but not equivalent because they contain the same elements and also have the same cardinality since the cities must all have mayors.

Thus, the number of cities is equivalent to the number of mayors thus the two sets could have the same cardinality (equivalent) but not the same elements thus they are not equal.

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Answer:

16%

Step-by-step explanation:

First we start by solving for the z score

We have the following information

x = 3.25

Standard deviation = sd = 2.25

Mean = 5.50

Z = (x - mean)/sd

z = 3.25 - 5.50/2 25

z = -1.00

If we look this up in the standard normal distribution table,

P(z<-1.00) = 0.1587

Which when approximated gives us

16%

Therefore approximately 16% of lobsters will have to be returned back to the sea.

The required value of the sum of the decimal values is 0.5536. Option c is correct.

Given that,
0.4 + 0.143 + 0.3706 =

It is defined as a decimal number that only consists of repeating digits after a certain interval after the decimal. For example, 94.642642642..., 213.569569... etc.

Here,
To simplify 0.4 + 0.143 + 0. 3706 we transform it into
= 0.0400 + 0.1430 + 0.3706
= 0.1830 + 0.3706
= 0.5536

Thus, the required value of the sum of the decimal values is 0.5536. Option c is correct.

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Evaluating the function in x = -1, we get:

H(-1) = 7

When we have a function:

y = f(x)

Evaluating the function in a value, like x = a gives:

y = f(a).

This means that we need to replace all the "x" in the equation by the number "a".

In this case:

H(x) = 6 - x

And we want to get:

H(-1)

So we need to replace the x by -1.

H(-1) = 6 - (-1) = 7

H(-1) = 7

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Answer:

  rhombus

Step-by-step explanation:

It is helpful to plot the points on a graph. There, you can see that the rise and run of each segment are 1 and 4 (or vice versa). This tells you they are the same length, but not perpendicular.

A quadrilateral with all sides the same length, but not perpendicular, is a rhombus.

Answer: Rhombus

Step-by-step explanation: I got it right on pearson

In statistics, a residual is defined as the difference between the predicted value of an outcome variable and the observed value of that variable. Residuals are used to evaluate how well a regression model fits the data.In order to calculate the residuals for a scatterplot, follow these steps:

Step 1: Plot the data on a scatterplot.

Step 2: Perform a regression analysis on the data to find the equation of the regression line. This equation should take the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

Step 3: Using the equation of the regression line, calculate the predicted value of y for each data point in the scatterplot.

Step 4: Subtract each predicted value of y from the actual value of y for each data point in the scatterplot. This difference is the residual for that data point.

Step 5: Plot the residuals on a new scatterplot. The x-axis of this scatterplot should be the independent variable, and the y-axis should be the residual values.

Step6: This scatterplot is called a residual plot.Residuals are useful for identifying patterns in data that the regression model fails to capture. If the residuals are randomly scattered around the horizontal axis, then the regression model is a good fit for the data. If there are clear patterns in the residual plot, then the regression model may not be a good fit for the data and further analysis is required.

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The Function  f(g(x)) = g(f(x)) = x + 8.

The functions are: f(x) = x + 4 and g(x) = x + 4. We can find f(g(x)) by substituting g(x) in place of x in f(x).

f(g(x)) = f(x + 4) = (x + 4) + 4 = x + 8

Similarly, we can find g(f(x)) by substituting f(x) in place of x in g(x).g(f(x)) = g(x + 4) = (x + 4) + 4 = x + 8

Thus, we can see that f(g(x)) and g(f(x)) are equal to each other,

which is x + 8.

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HI MATE

Answer:

im a curious cat lolololol

Step-by-step explanation:

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

Answer:

ACD

Step-by-step explanation:

All statements are correct for two congruent trianglesStep-by-step explanation:If two triangles are congruent than the rules states thatTriangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other.As the fig shows two triangleΔ PQRΔ LMNAll three corresponding sides of triangle are congruentall three corresponding angles are congruentBoth triangle are of same sizeBoth are of same shapehence all the statements are CORRECT Keywords:Geometry

The probability of selecting any Heart from the deck and then tossing a tail using the coin is 0.125

From the question, we have the following parameters that can be used in our computation:

To find the probability of selecting a Heart and then tossing a tail,

We need to multiply the probability of selecting a Heart by the probability of tossing a tail.

So:

P(selecting Heart and tossing tail) = P(selecting Heart) x P(tossing tail)

= 1/4 x 1/2

Evaluate

= 0.125

Hence, the probability is 0.125

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