For the following exercises, find functions
f(x) and g(x) so the given functions can be expressed as h(x)=f(g(x)). There are multiple possible answers. If the answers require exponents, enter the answer with an exponent in f(x) but not in g(x).
h(x)= 8/(x+4)^2

Answer:

39.3°, 140.7°

Step-by-step explanation:

supplementary angles means that together they have 180°.

so, when we have 2 angles, x and y.

x + y = 180

x = y - 101.4

using the second equation in the first

y - 101.4 + y = 180

2y - 101.4 = 180

2y = 281.4

y = 281.4/2 = 140.7°

x = y - 101.4 = 140.7 - 101.4 = 39.3°

so, the starting angle is 39.3°, and every supplementary angle is then 140.7°.

The length of the major arc QSR is 39.77 inches

The given parameters are:

m∠QPR = 170 degree

Radius, r = 6 inches

The length of the major arc QSR is calculated as:

Arc length = (360 - Angle/360) * 2πr

Substitute the known values in the above equation

Arc length = (360 - 170/360) * 2 * 3.14 * 6

Evaluate the difference

Arc length = (190/180) * 2 * 3.14 * 6

Evaluate the product

Arc length = 39.77

Hence, the length of the major arc QSR is 39.77 inches

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Y equals f(x) is written on the first line, The second line, marked y = g(x). When the input is for either of the two functions, the result is x=0 and return the output is same value.

Given that,

Y equals f(x) is written on the first line, which also passes through (-1, 2), (0, 2), and (2, 2). The second line, marked y = g(x), points at (0, -1), passes through (-0.5, -2), and (1, 1). The lines come together at (1.5, 2).

We have to find the input value for which f(x) = g(x) is true using the graph. x = 0.5, x = 1, x = 1.5, x = 2.

The final two actions:

f(x)=-2/3(x+1)

g(x)=1/3(x-2)

The output are equation

f(x)=g(x)

-2/3(x+1)=1/3(x-2)

-2(x+1)=1(x-2)

-2x-2=x-2

-2x-x=-2+2

-x=0

x=0

When x = 0 is used as an input, the first two functions always return the same results.

f(x) traverses (-1,2), (0,2), and (2,2)

The paths that g(x) takes are (-0.5,-2), (0,-1), (1,1)

Therefore, When the input is for either of the two functions, the result is x=0 and return the output is same value.

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make it simple its x=1.5

The sinusoidal function for the given conditions can be written as h(t) = 9cos(1.67π(x - 2.1)) + 39.

The term sinusoidal refers to a curve, also known as a sine wave or a sinusoidal, that shows smooth, periodic oscillation. It is named after the function y=sin (x). Sinusoidal appear often in mathematics, physics, engineering, signal processing, and many other fields.

A general form of a cosine function is given as shown below,

g(x) = a cos(bx+c) + d

Where the values of the given constant is,

a = amplitude

b = The period is of 2pi/B

c = phase shift

d = vertical shift

Since for the given condition the greatest value is 48 and the smallest value is 30 (a difference of 18), therefore, the amplitude is of the function can be written as,

2a = 18

a = 9

Further, a conventional cosine function with amplitude 9 would fluctuate between -9 and 9, while this one ranges between 30 and 48, resulting in d = 39 vertical shift.

Also, The minimum and maximum values form half the period, therefore, we can write,

π/B = 2.7 - 2.1

B = π/0.6

B = 1.67π.

Furthermore, The maximum value in the normal function is at x = 0, but the greatest value in this function is at x = 2.1, thus, the phase shift is 2.1 units to the right, or c = -2.1.

Hence, the sinusoidal function for the given conditions can be written as h(t) = 9cos(1.67π(x - 2.1)) + 39.

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The patient consumed 935 milliliters of fluids in 24 hours.

Restrictions of fluid per day = 1000 milliliters

Consumption of fluid by patient in past 24 hours are :

    Milk = 3 ounces

IV fluid = 725 Milliliters

  Juice = 4 ounces

As we know that,

One fluid ounce = 30 milliliters

Then,     Milk = 3 × 30  = 90 milliliters

               Juice = 4 × 30 = 120 milliliters

To determine the total amount of fluids we will add the total amount of Milk, IV fluids and Juice.

Fluids consume by patient = 90 + 725 + 120

                                          = 935 milliliters

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Hence , the construction of the triangle is given below.

 AB = 10 cm           BC = 6 cm           AC = 11 cm

We have to find ∠A, ∠B, and ∠C.

To construct a triangle,

Firstly draw a line segment AB = 10 cm

From A we need a point C at a distance of 6 cm. So with A as the center, draw an arc of 6cm in length from point A.

From B we need a point C at a distance of 11 cm. So with B as the center, draw an arc of 11cm in length from point B.

Mark the point of intersection of the arcs as C.

Meet points C to A and B respectively.

By using a protractor measure the angles of A, B, and C.

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Answer:

f(7) = 92

Step-by-step explanation:

f(7) means what is the value of f(x) when x = 7

substitute x = 7 into f(x)

f(7) = 2(7)² - 6 = 2(49) - 6 = 98 - 6 = 92

A decimal point is used when working with dollars but the decimal point is not necessary when working with cent for each dollar amount, the equivalent amount expressed as cents of $5.74 is 574 cents and $0.16 is 16 cents

We know that 1 dollar is equal to 100 cents

So, x dollar = x(100) cents

For $5.74 = 5.74(100) cents

                 = 574 cents

For $0.16 = 0.16(100) cents

                 = 16 cents

Integer and non-integer numbers are represented using the decimal numeral system, also known as the base-ten positional numeral system, denary, or decanary. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the term used to describe how numbers are represented using the decimal system.

It is indicated by a '.', for instance, 3.14

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A statement that best describes the area of the triangle is It is one-half the area of a square of side length 4 units.

The area of a triangle can be found by the formula:
= 1/2 x base x height

The base is 4 units and the height if 4 units.

Area of the triangle is:

= 1/2 x 4 x 4

= 8 units²

The area of a square of side length 4 units. is:

= 4 x 4

= 16 units²

In conclusion, option B is correct.

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Answer:

3.5

Step-by-step explanation:

21x+6

21/21    6/21

x=3.5

The average rate of change of f(x)=[tex]8x^{2} -5[/tex] on the interval [4,b] is [tex]\frac{128-8b^{2} }{4-b}[/tex]

Given,

The function f(x) =[tex]8x^{2} -5[/tex]

The intervals = [4,b]

The average rate of change = [tex]\frac{f(a)-f(b)}{a-b}[/tex]

Where a and b are the interval

f(4)= [tex]8(4)^{2}-5[/tex]

=123

f(b)= [tex]8b^{2}-5[/tex]

The average rate of change = [tex]\frac{123-(8b^{2}-5) }{4-b}[/tex]

[tex]=\frac{123-8b^{2}+5 }{4-b} \\=\frac{128-8b^{2} }{4-b}[/tex]

Hence, The average rate of change of f(x)=[tex]8x^{2} -5[/tex] on the interval [4,b] is [tex]\frac{128-8b^{2} }{4-b}[/tex]

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Answer:

[tex]p(x) = -5x^3 -6x^2 + 3x + 1[/tex]

Step-by-step explanation:

Given cubic function:

[tex]p(x) = ax^3 + bx^2 + cx + d[/tex]

As point (0, 1) is on the curve, substitute x = 0 into the function, set it to 1, and solve for d:

[tex]\begin{aligned} p(0) & = 1\\ \implies a(0)^3 + b(0)^2 + c(0) + d & = 1\\ \implies d & = 1 \end{aligned}[/tex]

Differentiate the function:

[tex]\begin{aligned} p(x)& = ax^3 + bx^2 + cx + d\\\implies p'(x)&=3 \cdot ax^{3-1}+2 \cdot bx^{2-1}+1 \cdot cx^{1-1}+0 \\p'(x)&=3ax^2+2bx+c\end{aligned}[/tex]

The tangent equation at the point (0, 1) is y = 3x + 1.  

Therefore, the gradient of the tangent equation when x = 0 is 3.

To find the gradient of the function at a given point, substitute the x-value of that point into the differentiated function.  Therefore, substitute x = 0 into the differentiated function, set it to 3, and solve for c:

[tex]\begin{aligned}p'(0) & =3 \\ \implies 3a(0)^2+2b(0)+c & =3\\ \implies c & = 3\end{aligned}[/tex]

Substitute the found values of c and d into the function:

[tex]p(x) = ax^3 + bx^2 + 3x + 1[/tex]

Substitute point (-1, -3) into the function and solve for b:

[tex]\begin{aligned}p(-1) & = -3\\\implies a(-1)^3 + b(-1)^2 + 3(-1) + 1 & = -3\\-a+b-3+1&=-3\\-a+b&=-1\\b&=a-1\end{aligned}[/tex]

To find the turning points of a function, set the differentiated function to zero and solve for x.  

As there is a turning point of function p(x) when x = -1, substitute x = -1 into the differentiated function and set it to zero (remembering to substitute the found value of c = 3 into the differentiated function):

[tex]\begin{aligned} p'(-1) & =0\\\implies 3a(-1)^2+2b(-1)+3 & = 0\\3a-2b+3&=0\end{aligned}[/tex]

Substitute the found expression for b into the equation and solve for a:

[tex]\begin{aligned}3a-2b+3&=0\\\implies 3a-2(a-1)+3&=0\\3a-2a+2+3&=0\\a+5&=0\\a&=-5\end{aligned}[/tex]

Finally, substitute the found value of a into the found expression for b and solve for b:

[tex]\begin{aligned}b & = a-1\\\implies b & = -5-1\\b & = -6\end{aligned}[/tex]

Therefore:

Differentiation Rules

[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4cm}\underline{Differentiating a constant}\\\\If $y=a$, then $\dfrac{\text{d}y}{\text{d}x}=0$\\\end{minipage}}[/tex]

The height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground

From the graph, we have the y-intercept to be

y-intercept = (0, y), where y > 0

This means that the graph starts above the origin

This in other words mean that the initial height of the cannonball is above the ground (e.g. it could be on a building)

Hence, the height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground

In this case, the domain is from t = 0 till the ball lands on the floor, while the range is from the initial height of the cannonball till the maximum height

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The lengths of the other two sides of the triangle is 8√6 units.

Given that,

AD is the angle bisector of ∠A .

BD = 2 units .

DC = 4 units .

AE ⟂ BC and √15 units .

So, AB / AC = BD / DC { By angle bisector theorem }

AB / AC = 2/4

AB / AC = 1/2  ......... Eqn.(1)

Also, BC = BD + DC = 2 + 4 = 6 units .

Now let BE = x units .

So, in right-angled ∆AEB ,

AB = √(15 + x²) { By pythagoras theorem }

In right angled ∆AEC ,

AC = √{15 + (x - 6)²} { By pythagoras theorem }

Putting both values in Eqn.(1),

AB/AC = 1/2

√(15 + x²)/√(15 + x² + 36 - 12x) = 1/2

Squaring both sides,

(15 + x²) / (x² - 12x + 51) = 1/4.

4(15 + x²) = x² - 12x + 51.

60 + 4x² = x² - 12x + 51.

4x² - x² + 12x + 60 - 51 = 0.

3x² + 12x + 9 = 0.

3x² + 3x + 9x + 9 = 0.

3x(x + 1) + 9(x + 1) = 0.

(3x + 9)(x + 1) = 0.

x = (-3) and (-1) .

Taking x = (-1),

AB = √(15 + x²) = √(15 + 1) = 4 units .

So, AC = 4 * 2 = 8 units .

Taking x = (-3),

AB = √(15 + 9) = √24 = 4√6 units.

So, AC = 2 * 4√6

= 8√6 units .

Hence, the lengths of the other two sides of the triangle is  8√6 units.

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Based on the probability of rain in Nevada, the probability that it will not rain is 0.7.

The probability that if it does not rain, the school bus will be on time is 0.85.

The probability that it will rain and the school bus will still be on time is 0.6.

The probability that it will not rain in Nevada can be found by the formula:

= 1 - probability of rain in Nevada

= 1 - 0.3

= 0.7

The probability that if it does not rain, the school bus will be on time is:

= 1 - probability of the school bus being late if it does not rain

= 1 - 0.15

= 0.85

The probability that it will rain and the school bus will still be on time is:

= 1 - probability of the school bus being late if it rains

= 1 - 0.4

= 0.6

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Answer: 21x^3 + 3 + 12x^2 + x

Step-by-step explanation:

Step-by-step explanation:

2 . (6² + 2²) ÷ 4 - 10

= 2 . (36 + 4) ÷ 4 - 10

= 2 . 40 ÷ 4 - 10

= 80 ÷ 4 - 10

= 20 - 10

= 10

Answer: y = -1/5x -3

Step-by-step explanation:

Answer:

Answer given by bryc31 is correct: [tex]y = -\frac{1}{5}x -3[/tex] is correct

I am simply providing an explanation in case you need it

Step-by-step explanation:

The slope-intercept form equation of a straight line in 2D coordinates is given by y = mx + b

where m is the slope(rise/run) and b the y-intercept i.e. the y value where the line intersects the y axis

Given two points (x₁, y₁) and (x₂, y₂)  on the straight line, we can compute the slope as follows

m = [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex]

Two distinct points on the line are at (0, -3) and (5,-4)

[tex]m = \frac{-4 -(-3)}{5-0} = \frac{-4 + 3)}{5-0} = \frac{-1}{5} = - \frac{1}{5}[/tex]

So we know the equation to be

[tex]y = - \frac{1}{5}x + b[/tex]

To find b, take any point on the straight line, plug in y and x values in the above equation and solve for b

However, looking at the graph we see that the line crosses the y axis at

y = -3. So this is the value for the y intercept i.e. b

The equation of the line is therefore

[tex]y = - \frac{1}{5}x - 3[/tex]

Answer:

One litre of water has a mass of almost exactly one kilogram.kilograms = liters × density of a liquid.

Answer:

Look below

Step-by-step explanation:

The LCM of 25 and 100 is 100

The GCF of 25 and 100 are 25.

Answer:

x=-4

Step-by-step explanation:

this is if by roots, the problem is asking for the zeros of the equation

The location of a center of dilation in the figure is at the point where the corresponding vertex of the pre–image and image overlaps, which is point N, the correct option is therefore;

The given pre–image = Parallelogram LMNO

The image obtained from the pre–image = Parallelogram L'M'N'O'

Required: The location of the center of dilation

Solution:

The center of dilation is the point about which the figure or image is dilated.

It is the point that does not change following the dilation.

A vertex on the pre–image that gives an image vertex at the same point, is at the center of dilation which does not change in both the pre–image and image.

Therefore, given that point N and N' coincides, which indicates that the distance the pre–image point N is dilated to get the image point, N is 0. The center of dilation is at the vertex N.

The correct option is therefore;

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Answer:

On a vertex of figure LMNO

Step-by-step explanation:

The value invested in each security will be:

stock= $38000 ,

bonds= $46000

cds= $3000

Let the money invested in stocks be 'x', bonds be 'y' and CDs be 'z'.

Total money received as fund = x+y+z = $115000 -(Eqn 1)

$15000 more is invesed in bonds as compared to CDs i.e y = z + $15000 - (Eqn2)

Stocks pay 6.8%, bonds pay 3.6% and CDs pay 4% interest

Interest earned from stocks = 6.8% of x = 0.068x

Interest earned from bonds = 3.6% of x = 0.036x

Interest earned from CDs = 4% of x = 0.04x

Total interest earned = 0.068x + 0.036y + 0.04z = $5840 - (Eqn 3)

x + y + z =$115000 ----(1)

y = z + $15000 -----(2)

0.068x + 0.036y + 0.04z = $5840 ------(3)

Putting y = z+$15000 in Eqn 1 gives us:

x + (z+$15000) + z = $115000 ==> x = $100000 - 2z ----(Eqn 4)

Similarly,

Putting y = z+$15000 in Eqn 3 gives us:

0.068x + 0.036(z+$15000) + 0.04z = $5480 ==> 0.068x + 0.076z = $4940 ----(Eqn 5)

Putting Eqn 4 in Eqn 5,

0.068($100000 - 2z) + 0.076z = $4940

Hence, 0.06z = $1860

z = $31000

Put z = $31000 in Eqn 4 and get x = $100000 - 2z = $38000

Put z = $31000 in Eqn 2 and get y = z + $15000 = $46000

Hence final answer: x = $38000 , y = $46000, z = $31000

where x is the money invested in stocks, y in bonds and z in CDs.

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Answer:

-4

Step-by-step explanation:

keep value of x as 1 in 5x+1

g(1)=-5×1+1

=-4

Answer:Jorge and  Mike

Step-by-step explanation:

Nobody goes if Mike goes

Answer:

no

Step-by-step explanation:

89382

Answer: rises; your slope is positive

Every single time your slope is positive, your line goes upward.

Every time your slope is negative, however, your line goes downward.

Rearrange 9x - 27y = 81 to -27y = -9x + 81 because we want to put our equation into slope intercept so that we can eventually get our 'y' all by itself.

Divide by -27 for every variable.

Your slope intercept form should now look like this; y = 1/3x - 3

Now that we're completely done or that we have 'y' by itself, it's safe to say that our answer is 1/3, which is, also, positive.

Hope this helps, dawg.