Given f of x is equal to 2 divided by the quantity x squared plus 3x minus 10 end quantity, which of the following is true?
f(x) is positive for all x < –5

f(x) is negative for all x < –5

f(x) is positive for all x < 2

f(x) is negative for all x > 2

The function of the area of the figure is M(x) = (x + 2)(3/2x - 2)

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

The composite figure

The total area of the composite figure is the sum of the areas of the individual shapes

So, we have

Area = Rectangle + Triangle

Using the area formula, we have

M(x) = (x + 2)(x - 2) * 1/2 * x * (x + 2)

Factorize

M(x) = (x + 2)(x - 2 + x/2)

So, we have

M(x) = (x + 2)(3/2x - 2)

Hence, the function of the area of the figure is M(x) = (x + 2)(3/2x - 2)

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\(\textit{internal division of a line segment using ratios} \\\\\\ A(-4,-2)\qquad B(6,3)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(-4,-2)=3(6,3)\)

\((\stackrel{x}{-8}~~,~~ \stackrel{y}{-4})=(\stackrel{x}{18}~~,~~ \stackrel{y}{9})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-8+18}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-4+9}}{3+2} \right)} \\\\\\ P=\left( \cfrac{10}{5}~~,~~\cfrac{5}{5} \right)\implies P=(2~~,~~1)\)

The volume of the triangular pyramid is 150 cubic units.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

We have to find the volume of triangular pyramid

Volume = 1/3×B×h

B is the area of base

B=1/2×10×6

B=30 units

Height = 10 units

Volume = 1/2×30×10

=150 cubic units

Hence, the volume of the triangular pyramid is 150 cubic units.

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The main answer is that without specific values or elements for sets A and B, we cannot determine the result of A - B and B - A.

To find A - B, we need to subtract the elements in set B from set A. Similarly, to find B - A, we need to subtract the elements in set A from set B.

However, I need the specific values or elements of sets A and B to perform the calculations. Could you please provide the values or elements of the sets?In order to perform set subtraction, we need the specific elements or values of sets A and B. Set subtraction involves removing the common elements between the sets.

Let's say set A is {1, 2, 3} and set B is {2, 3, 4}. To find A - B, we remove the elements in set B from set A. Thus, A - B would be {1}.

To find B - A, we remove the elements in set A from set B. Therefore, B - A would be {4}.

Please provide the values or elements of sets A and B, and I will be able to calculate A - B and B - A accordingly.

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Step-by-step explanation:

Set up f(x).

\( \sqrt[3]{11x - 3} = f(x)\)

Replace f(x) with y

\( \sqrt[3]{11x - 3} = y\)

Swap x and y

\( \sqrt[3]{11y - 3} = x\)

Solve for y

Cube both sides

\(11y - 3 = {x}^{3} \)

Add 3 to both sides

\(11y = {x}^{3} + 3\)

Divide both sides by 11

\(y = \frac{x {}^{3} + 3 }{11} \)

so

\(f {}^{ - 1} (x )= \frac{ {x}^{3} + 3}{11} \)

The value of a must be equal to (k + 2), and then the equation is only true if k = 6, then a = 8.

We want the equation:

(k + 2)x + 3k = ax + 18

To be true for all values of x, then we must have the same thing in both sides of our equation.

Now we wod want the dependence on x to dissapear, then:

(k + 2)x = ax

(k + 2) = a

That must be value of a, and then the equation becomes:

k*x + 2x + 3k = (k+ 2)x + 18

3k = 18

This is only true if k = 6, then:

k + 2 = a

6 + 2 = a

a = 8

That must the value of a.

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Answer:

4778.4

Step-by-step explanation:

The volume of a cone is given by:

(π•r²•h)/3

(π•13²•27)/3

(π•169•27)/3

(4,563•π)/3

14,334.66/3=4778.4

Answer: 5 1/2 (5.5)

Step-by-step explanation:

550/100

Answer:

\(5 { \times 54}^{2} \)

Answer:

The p-value falls between 0.005 and 0.01.

Step-by-step explanation:

Random sample of 30 observations, you obtain t = 2.35

This means that the pvalue is 1 subtracted by the pvalue of Z = 2.35, as we are testing that the mean is more than a value.

Looking at the z-table, z = 2.35 has a pvalue of 0.9906

1 - 0.9906 = 0.0094

So, between 0.005 and 0.01.

Answer: The p-value falls between 0.01 and 0.02.

Step-by-step explanation: I took the FLVS test.

frequency of the function is 0.95 per sec.

frequency is the number of waves that pass a fixed point in a unit of time as well as the number of cycles or vibrations that a body in periodic motion experiences in a unit of time. After moving through a sequence of situations or locations and then returning to its initial position, a body in periodic motion is said to have experienced one cycle or one vibration. See also basic harmonic motion and angular velocity.

               The frequency is 2 per second if the period, or time interval, needed to complete one cycle or vibration is 1/2 second; it is 100 per hour if the duration is 1/100 of an hour. In most cases, the frequency is equal to the period, or time interval, reciprocally, therefore frequency = 1/time period = 1/ (time interval). A little bit more than 12 cycles per year are how frequently the Moon rotates around Earth. A violin's A string has a frequency of 440 vibrations or cycles per second.

frequency = 1/T        (T is equal to time period of function)

so, from the figure,

there are 3 intervals from 0 to π .

since,π = 3T

  T = π/3

therefore, frequency(f) is 1/T

so, f = 3/π

f= 0.95 per second

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Frequency of the function is 0.95 per sec.

In addition to the number of cycles or vibrations a body in periodic motion experiences in a unit of time, frequency is the number of waves that pass a fixed point in a unit of time. A body in periodic motion is considered to have experienced one cycle or one vibration after passing through a series of conditions or locations and then returning to its starting position. See also angular velocity and fundamental harmonic motion.

If one cycle or vibration takes half a second to complete, the frequency is two per second; if it takes one hundredth of an hour, it is one hundred per hour. The frequency and the period, or time interval, are often reciprocally equal, therefore frequency = 1/time period = 1/ (time interval). The Moon spins around Earth about a little bit more than 12 times a year. The A string on a violin vibrates at a frequency of 440 cycles per second.

frequency = 1/T        (T is equal to time period of function)

so, from the figure,

there are 3 intervals from 0 to π .

since,π = 3T

 T = π/3

therefore, frequency(f) is 1/T

so, f = 3/π

f= 0.95 per second

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Answer:

( 0 , 8)

Step-by-step explanation:

The y-intercept is when the graph intersects the y axis, in other words, when x is zero. Hence substitute 0 in for x

f ( x ) = 8 \(( 0.25 )^{x}\)

f ( 0 ) = 8 \((0.25)^{0}\)

Any number to the power zero is one;

f ( 0 ) = 8 * 1

f(0) = 8

The y-intercept is 8.

Answer:

I think b

Step-by-step explanation:

Answer:

(7,5)

Step-by-step explanation:

You could understand it better if you made the line more visible.

Another equation for line C is y = 6.

Any point with a y-coordinate less than 6 will be plotted under the line.

So we have two chords intersecting each other. One of the angles in this intersection is equal to 86°. It's also important to note there are another two chords of equal measure that define a and c respectively. This means that arcs a and c have the same measure. What's more, these two arcs are related since they are also defined by the chords that made the 86° angle and the relation between them and this angle is:

If we use the fact that a=c we get:

Then the value of a is 86° and the answer is option B.

Answer:

Since the two angles, A and C are given to be 48° ang 46.7°, respectively, the value of angle B may be calculated by difference. Note that for a triangle, the sum of the angles is 180°. This makes the angle B equal to 85.3°. By the Sine Law,

                             b / sin B = a / sin A

Substituting,

                             b / sin 85.3° = 44 / sin 48°

The value of b from the equation is approximately equal to 59.01.

Answer:

35

Step-by-step explanation:

is correct for ape x

Answer:

slope = - \(\frac{1}{4}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, - 5) and (x₂, y₂ ) = (7, - 6)

m = \(\frac{-6-(-5)}{7-3}\) = \(\frac{-6+5}{4}\) = - \(\frac{1}{4}\)

As a result, option two (3.50) is correct.

Step-by-step explanation:                                                    
                                   
The code chunk that allows you to filter the data frame for chocolate bars with at least 70% cocoa and a rating of at least 3.5 pounds is as follows

∴ filter(Cocoa, percent>='70%'&Rating>=3.5)


Therefore, the code you write is facet wrap(Cocoa. Percent). Facet wrap() is a function in this code chunk that allows you to wrap a variable's facets. All of the ingredients are derived from cocoa beans. Cacao solids (the "brown" part, which contains health benefits and the unmistakable chocolatey flavor) and cacao butter (the "white" part, which contains the chocolate's fatty component) are split in proportion.


As a result, 3.5 appears in row 1 of your Tibble.

Other options I (iii), and (iv) are incorrect because the question states that any rating greater than or equal to 3.5 points can be considered a
high rating, and the rating here should be 3.5, not 3.75, 4.25, or 4

So, option (ii) is correct.  


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Answer:

a. The fare for a 9-mile journey =  £ 10.6

Step-by-step explanation:

Fare = £2.50 + £0.90 x miles

Fare(9) = £2.50 + £0.90 x ( 9 miles) = £2.50 +  £ 8.1 =  £ 10.6

a. The fare for a 9-mile journey =  £ 10.6

The area of the segment is 9( π-2) units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.

Area of segment = area of sector - area of triangle

area of sector = 90/360 × πr²

= 1/4 × π × 36

= 9π

area of triangle = 1/2bh

= 1/2 × 6²

= 18

area of segment = 9π -18

= 9( π -2) units²

therefore the area of the segment is 9(π-2) units²

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The equation of a line perpendicular to line y = 1/5x-2 in slope-intercept form that contains point (-3, 1) is y = -5x - 14.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the information provided, an equation of the first line WX is given by;

y = x/5 - 2

Therefore, slope (m) = 1/5

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/5 × m₂ = -1

m₂ = -5.

At point (-3, 1), an equation of the line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -5(x - (-3))

y - 1 = -5(x + 3)

y = -5x - 15 + 1

y = -5x - 14

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Answer:

B(6, 5), C(1, -7)

Step-by-step explanation:

A(2, 5)

From A to B, there is translation x, (4, 0).

Add 4 to A's x-coordinate, and add 0 to A's y-coordinate.

B(2 + 4, 5 + 0) = B(6, 5)

From C to B there is the translation y, (5, 12).

Since we are going from B to C, we undo translation y.

The translation from B to C is (-5, -12).

C(6 - 5, 5 - 12) = C(1, -7)

Answer:

Start with the original equation.

k + a = 500

Subtract a from both sides of the equation.

k + a – a = 500 – a

           k = 500 – a

Step-by-step explanation: this was my edmentum answer

part a.

There is  a 49.1% chance that HRC finds a sample mean between $477 and $527.

part b.

There is a 20.9% chance that the sample mean falls between $492 and $512.

The standard error (SE) of the sample mean.

SE = σ / √(n)

σ = $80 and n = 68.

SE = 80 / √(68)

z1 = (X1 - μ) / SE

z2 = (X2 - μ) / SE

for first scenario:

X1 = $477, X2 = $527, and μ = $499.

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

For the range $477 to $527:

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

z1 = -0.275

z2 = 0.35

Probability 1 =  0.4909 = 49.1%

We have a 49.1% chance that HRC finds a sample mean between $477 and $527.

For the second scenario

X1 = $492, X2 = $512, and μ = $499.

z1 = (492 - 499) / Standard Error

z2 = (512 - 499) / SE

We have a 20.9% chance that the sample mean falls between $492 and $512.

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$2010.458 is her new balance after she makes one new transaction for $51.

What does a credit balance mean?

The amount that the credit card company owes you is shown as a credit balance on your billing statement. Each payment you make results in credits being added to your account.

                                   When you return something you purchased with your credit card, you can receive an additional credit.

Credit balance  = $1,603

   APR = 28.6%

        = 28.6%  * $1,603

         =   458.458

Credit balance  = $1,603 + 458.458

                        = $2061.458

  net balance =  $2061.458 - 51

                      = $2010.458

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The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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The three transformations—rotations, reflections, and translations—can be combined to produce congruent shapes. The truth is that any pair of congruent shapes can be matched to one another by combining one or more of these three transformations.

Explain transformations.

A point, line, or geometric figure has four different transformations that can be applied to alter its appearance. While the term "Image" refers to the position and final shape of the object, "Pre-Image" refers to the object's shape before transformation.

Given Information

The size and shape of the figures are preserved during stiff transformations, as we already know (reflections, translations, and rotations). Always in harmony with one another is the pre-image.

These transformational skills are all possessed by Matt:

Reflection

The reason a reflection maintains its original form Comparable locations between the pre-image and the picture remain apart from the line of reflection.

Rotations as a Transformation of Congruence

When a figure rotates, it twists. Despite being the same size and shape, the figurine appears to have toppled over. A clock is an excellent example of how the globe rotates in reality. Every hour or every day, the connecting arms of a clock revolve around its axis. The degree of a rotation determines what kind of rotation it is; popular rotations include 90, 180, and 270 degrees. Before spinning around completely and going back to where it started, the figure rotates 360 degrees. the clockwise or counterclockwise direction in which a rotation is made. This data can be used to determine the degree, amount, a revolution's speed and direction.

Congruence translational transformation

When an object or shape is transferred from one location to another without altering its size, shape, or orientation, we refer to the transfer as a movement. A translation, often known as a slide, involves moving every point on an object or shape uniformly and in one direction.

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Answer:

$144

Step-by-step explanation:

2 shirts/$16 = 18 shirts/$x

Multiply 16 by 9 to get 144 (because 18/2 is 9)

Answer:

$144

Step-by-step explanation:

$16 / 2 = $8

$8 per shirt

$8 x 18 = $144

Hope that helps!

Answer:

The distance would be a little over four feet

Step-by-step explanation: