There are two numbers. One number is twice the other number. The difference of the smaller number and half the larger number is 20.

An equation created to find the smaller number will have

Answer:

The value of [tex]$(f \circ g)(x)$[/tex] is 17-18x and [tex]$(g \circ f)(x)$[/tex] is -7-18x.

Step-by-step explanation:

It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.

It is required to find [tex]$(f \circ g)(x)$[/tex] and [tex]$(g \circ f)(x)$[/tex].

To find [tex]$(f \circ g)(x)$[/tex], substitute g(x) for x in f(x) and simplify the expression.

To find [tex]$(g \circ f)(x)$[/tex], substitute f(x) for x in g(x) and simplify the expression.

Step 1 of 2

Substitute g(x) for x in f(x) and simplify the expression.

[tex]$$\begin{aligned}&(f \circ g)(x)=f(5-6 x) \\&(f \circ g)(x)=3(5-6 x)+2 \\&(f \circ g)(x)=15-18 x+2 \\&(f \circ g)(x)=17-18 x\end{aligned}$$[/tex]

Step 2 of 2

Substitute f(x) for x in g(x) and simplify the expression.

[tex]$$\begin{aligned}&(g \circ f)(x)=g(3 x+2) \\&(g \circ f)(x)=5-6(3 x+2) \\&(g \circ f)(x)=5-18 x-12 \\&(g \circ f)(x)=-7-18 x\end{aligned}$$[/tex]

The rule of reflection in the image shown is: (x, -y).

Reflection is a transformation which creates a new image by flipping over a line of reflection. The new image is congruent to the original image after reflection. The rule of reflection over an x-axis is given as, (x, -y).

In the image given we can see that rotating triangle LMN over the x-axis gave us:

M(-5, 4) → M'(-5, -4)

L(-4, 2) → L'(-4, -2)

N(-2, 3) → N'(-2, -3)

Therefore, the rule of reflection is: (x, -y).

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Step-by-step explanation:

180 250 300 H.C.F by division method

[tex]in \: pounds \\ 12 \times 288 = 3456 \: pounds[/tex]

[tex]1 \: kilo = 2.2046 \: pounds[/tex]

[tex]x \: kilos = 3456 \: pounds[/tex]

[tex]x = \frac{3456}{2.2046} = 1567.61 \: kilos[/tex]

Answer:

45units^2

Step-by-step explanation:

Break the polygon into two shapes. A rectangle and a triangle.

The area formula for a rectangle is A=L•W or

Area = Length x Width. Counting the units for length and width is 9 x 2. Which would equal 18units.

Now for the triangle, the formula is A=1/2 (b•h)

The base is 9 and Height is 6.

9 • 6 = 54

Since a triangle is half the area of a rectangle you divide 54 by 2. Area for triangle is 27.

Now add the rectangle area and triangle area.

18+27=45

Area=45 units ^2

Answer:

3π

Step-by-step explanation:

arc length = radius x central angle in radians

π = radius x π/3

radius = 3π

since OMN is an equilateral triangle, radius = MN

thus MN = 3π

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = -3 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: CD + DE = CE[/tex]

[tex]\qquad \tt \rightarrow \: x + 10 + x + 4 = 8[/tex]

[tex]\qquad \tt \rightarrow \: 2x + 14 = 8[/tex]

[tex]\qquad \tt \rightarrow \: 2x =8 - 14[/tex]

[tex]\qquad \tt \rightarrow \: 2x = - 6[/tex]

[tex]\qquad \tt \rightarrow \: x = - 3[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

[tex]\huge \boxed{\sf x=-3}\\\\\\\displaystyle \sf CD+DE=8 \\\\x+10+x+4=8\\\\2x+14=8\\\\Subtracting\ 14\ from\ each\ side\\\\ 2x+14-14=8-14\\\\2x=-6\\\\ Dividing\ each\ side\ by\ 2 \\\\ \frac{2x}{2} =\frac{-6}{2} \\\\x=-3[/tex]

Answer:

-14

Step-by-step explanation:

Given -x+5y=7

Now we substitute x+5y into -2(-x+5y)

-2(-x+5y) = (-2)(7)

= - 14

Okay so a 24hr clock is very simple. We usually turn to "PM" when its 12:00 (day time).
In the 24hr clock we do not, we don't use PM or AM but its crucial to know when converting a standard clock time to military time (aka. 24hr).

9:30 PM in 24hr clock is 12:00 + 9:30 because 9:30 is past that first 12 hours.

So in 24hr clock time it is 21:30. You can also count backwards from midnight to figure it out, for example 12:00 AM (midnight), minus 9:30 is 2:30. Therefore 24:00-2:30=21:30.

Hopefully it helps, heart will help me alot too!

Answer:

21:30

Step-by-step explanation:

The 24hour clock uses 0:00 for midnite. 1am through noon are just 1:00 - 12:00. But the pm hours continue counting up, 13 - 23.

For example, 1pm is 13:00 and 2pm is 14:00.

To change to 24 hour clock, for pm hours, ADD 12.

So for your problem, 9:30 is:

9:30 + 12

= 21:30

A number in a fraction implies the part of a number in another given number. While percentage relates a given number to 100%. Thus the answers to the given question are:

a. a fraction of penalty shots that the team missed = [tex]\frac{81}{100}[/tex]

b. percentage of penalty shots missed =  [tex]\frac{81}{100}[/tex] x 100%

                                                           = 81%

A fraction is a part of a given number stated in a quotient form. Generally, all numbers can be expressed in form of fractions, even whole numbers.

The percentage is an expression that shows the part of a number in a given number with respect to 100%. An example is 10%([tex]\frac{10}{100}[/tex]).

From the given question, let;

n, number of penalty shots made = 19

T, the total number of penalties taken = 100

Thus, the number of penalties missed = T - n

                                               = 100 - 19

                                               = 81

Thus,

i. a fraction of penalty shots that the team missed = [tex]\frac{81}{100}[/tex]

ii. percentage of penalty shots missed =  [tex]\frac{81}{100}[/tex] x 100%

                                                           = 81%

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The correct answer would be option(C) opposite angles of a parallelogram are congruent.

A parallelogram defined as a special type of quadrilateral which has both pairs of opposite sides parallel and equal.

Given that PQRS is a parallelogram.

PQ ≅ RS

QR ≅ PS

By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ.

Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.

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Answer:

"B"

Step-by-step explanation:

Based on the inscribed quadrilateral conjecture: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.

The inscribed quadrilateral conjecture states that the opposite angle of any inscribed quadrilateral are supplementary to each other. That is, they have a sum of 180 degrees.

From the diagram given, the opposite angles in the trapezoid, 115 + 65 = 180 degrees.

Therefore, we can conclude that: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.

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Answer:

Option A

Step-by-step explanation:

   [tex]\sf Slope=\dfrac{Change \ in \ y}{Change \ in \ x}=\dfrac{rise}{run}[/tex]

We can find the equation of line, by comparing the slope of line segment AC and slope of AE.

Slope of AC = Slope of AE

           [tex]\sf \dfrac{4}{3}=\dfrac{y +2}{x}[/tex]

Cross multiply

4*x = 3*(y +2)

4x   = 3y + 3*2

4x  = 3y + 6

Equation of the line in  standard form:

         4x - 3y - 6= 0

Transformation is a process that involves either increasing, or decreasing the size of a given object, or changing its orientation to produce an image.

The required transformations are:

i. For graph a - translation.

ii. For graph b - dilation.

Rigid transformation involves a change in the orientation of a given object or resizing of a given object to produce an image. The types of transformation are reflection, translation, rotation, and dilation.

i. Reflection is a type of transformation that requires flipping a given object about a reference point or line.

ii. Translation is a type of transformation that involves moving an object in a particular direction without a change in its size and orientation.

iii. Rotation is a type of transformation that involves turning an object at a given angle about a reference point.

iv. Dilation is a type of transformation that require increasing or decreasing the size of the object using a given factor.

Therefore the necessary transformation to transform the blue graph of f(x) into the red graph of g(x) is:

a. For graph a is translation.

b. For graph b is dilaton.

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Answer:

[tex]\frac{\sqrt{61} }{\sqrt{97} }[/tex]

Step-by-step explanation:

Sin(y) = opposite over hypotenuse

opposite side is [tex]\sqrt{61}[/tex]

hypotenuse is [tex]\sqrt{97}[/tex]

The ages of Lute,  Maya and Aran are respectively; 24, 8 and 6 years old.

Let Lute's age be x

Thus;

Maya's age = ¹/₃x

Aran's age = ¹/₄x

We are told the sum of their ages is 38. Thus;

x + ¹/₃x + ¹/₄x = 38

Multiply through by 12 to get;

12x + 4x + 3x = 456

19x = 456

x = 456/19

x = 24

Maya's age =  ¹/₃ * 24 = 8 years

Aran's age = ¹/₄ * 24 = 6 years

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The value of x from the given expression is 5/6

Given the expression to expand expressed as:

15 = 3/5(6x + 20)

We are to determine the value of x

15(5) = 3(6x + 20)

Expand

75 = 18x +60

Collect like terms

18x = 75 - 60

18x = 15

x = 15/18

x = 5/6

Hence the value of x from the given expression is 5/6

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The probability that a two-digit number selected at random has a tens digit less than its units digit is 0.2667 (4/15).

[tex]A=24B=90\\\\P=A/B\\\\P=24/90\\p=4/15[/tex]

There are 90 two-digit numbers (99-9). Of these, six numbers are divisible by 15 (15, 30, 45, 60, 75, 90). This is also divisible by 5. Therefore, the preferred case is 30-6 = 24. Therefore, the required probability is 24/90 = 4/15.

The probability of an event can be calculated by simply dividing the number of favorable results by the total number of possible results using a probabilistic expression. Whenever you are uncertain about the outcome of an event, you can talk about the probability of a particular outcome, that is, its potential.

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3 roots are exist, since the polynomial is of third degree.

According to statement

This follows immediately from the zero product property: if ab=0, then either a=0 or b=0. We have3 roots are exist, since the polynomial is of third degree.

(9x+ 7)(4x +1)(3x+ 4) = 0

from which it follows that each of which admits only one solution.

AND

using the fundamental theorem of algebra, expanding we have a polynomial that is of third degree:

(9x+ 7)(4x +1)(3x+ 4) = 0

108x^3 + 255 x^2 +169x + 28 =0

The theorem states that a polynomial will have up to n distinct roots. In this case, it follows that there are exactly 3, since the solutions to the system above are all distinct.

So, 3 roots are exist, since the polynomial is of third degree.

DISCLAIMER : The question was incomplete. Please find the full content below.

QUESTION

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0 1 root 3 roots 4 roots 9 roots

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The statements about the local maximums and minimums for the given function which are true include:

This is defined as the mathematical entities which assign unique outputs to given inputs and defines a relationship between the two variables.

According the the graph: over the interval [2, 4], the local minimum is –8 because the given minimum point is (3.4, -8) and over the interval [3, 5], the local minimum is –8.

Over the interval [1, 4], the local maximum is 0 and over the interval [3, 5], there is no maximum point hence why it is false.

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Look at the multiples of lcm(3, 8) = 24, each of which are divisible by both 3 and 8. Naturally, the number we're looking for must have at least two digits.

The last/ones digit of a number [tex]n[/tex] can be computed by evaluating [tex]n \pmod{10}[/tex]. Suppose the ones digit is 1. Then

[tex]n \equiv 24k \equiv 20k + 4k  \equiv 4k \equiv 1 \pmod{10}[/tex]

but this has no solution since no multiple of 4 ends in 1. So our number ends with a 2.

If our number has two digits, then in order for it to be divisible by 3, the first digit must be 1, since 1 + 2 = 3. But 12 is not divisible by 24.

If our number has three digits, then it's either 111 (with digital sum 1 + 1 + 1 = 3) or 222 (digital sum 2 + 2 + 2 = 6), since no other triplet of 1s and 2s sums to a multiple of 3. But 111 = 3×37 and 222 = 2×111, so neither are divisible by 24.

Now suppose [tex]n[/tex] has four digits. Also suppose that the tens digit is 2. Then our number must be 1122 to uphold divisibility by 3, but 1122 = 2×3×11×17 is not divisible by 8. So the tens digit must be 1. This in turn leaves two remaining candidates, 1212 and 2112. We have 1212 = 12×(100 + 1) not divisible by 8, so our number must be [tex]\boxed{n=2112}[/tex]. And it is, since 2112 = 24×88.

Answer: 6.8

Step-by-step explanation:

By the Law of Cosines,

[tex]c^2 = 5^2 + 9^2 - 2(5)(9)\cos 48^{\circ}\\\\c=\sqrt{5^2 + 9^2 - 2(5)(9)\cos 48^{\circ}}\\\\c \approx 6.8[/tex]

Answer:

8+16+2= 24 legs on ground

Step-by-step explanation:

Answer:

4(2x+7) which is equal to 8x+28

The lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.

Properties of a parallelogram include;

From the figure, we have that lines YZ and WZ are equivalent because the diagonal bisects the parallelogram to two four of which they are of equal lengths.

Thus, the lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.

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The appropriate hypothesis which is used to test the dropout rate are [tex]H_{0}:p > =0.081\\[/tex] and [tex]H_{1}: p < 0.081[/tex].

Given Drop out rate through 24 year old who are not enrolled is 8.1%, sample size=1000 and we have to find the hypothesis to test the drop out rate of the school.

The variable which needs to be studied is X=Number of individuals with age between 16 and 24 years old that are high school dropouts.

The parameter of interest is the proportion to high school drop outs is p.

Sample proportion=[tex]p^{1}[/tex]=0.065

The hypothesis can be formed as under:

[tex]H_{0}:p > =0.081[/tex]  (null hypothesis)

[tex]H_{1}:p < 0.081[/tex]      ( alternate hypothesis)

Null hypothesis is a hypothesis which is tested for its validity and alternate hypothesis is hypothesis which is opposite of null hypothesis means if null hypothesis is rejected then the alternate hypothesis will be true.

[tex]Z_{H_{0} }=(p^{1}-p)/\sqrt{p*(1-p)/n}[/tex]

=[tex]0.065-0.081/\sqrt{(0.081*0.0919)/1000}[/tex]

=-1.85

Hence the appropriate hypothesis  are [tex]H_{0}:p > =0.081[/tex] and [tex]H_{1}:p < 0.081[/tex].

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The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.

Given that the circumference of a sphere is 76cm and error is 0.5cm.

The formula of the surface area of a sphere is A=4πr².

Differentiate both sides with respect to r and get

dA÷dr=2×4πr

dA÷dr=8πr

dA=8πr×dr

The circumference of a sphere is C=2πr.

From above the find the value of r is

r=C÷(2π)

By using the error in circumference relation to error in radius by:

Differentiate both sides with respect to r as

dr÷dr=dC÷(2πdr)

1=dC÷(2πdr)

dr=dC÷(2π)

The maximum error in surface area is simplified as:

Substitute the value of dr in dA as

dA=8πr×(dC÷(2π))

Cancel π from both numerator and denominator and simplify it

dA=4rdC

Substitute the value of r=C÷(2π) in above and get

dA=4dC×(C÷2π)

dA=(2CdC)÷π

Here, C=76cm and dC=0.5cm.

Substitute this in above as

dA=(2×76×0.5)÷π

dA=76÷π

dA=24.19cm².

Find relative error as the relative error is between the value of the Area and the maximum error, therefore:

[tex]\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end[/tex]

As above its found that r=C÷(2π) and r=dC÷(2π).

Substitute this in the above

[tex]\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end[/tex]

Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.

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A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is 0.3 meters².

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is,

Area of rectangle = 6/8 meter × 4/10 meter

                              = 24 / 80 meters²

                              = 6 /20 meters²

                              = 0.3 meters²

Hence, The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is 0.3 meters².

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