Let f(x)= 4x +3 and g(x)=x²-7x+ 10. Perform the function operation and then find the domain.
f(x) g(x)

f(x) g(x)= (Simplify your answer.)


Please answer, I need help

The range for the given function, with x=1 is 10.

The given function is f(x)=10x.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

Here, put x=1 in the function y=10x, we get

y=10(1)

y=10

So, the range for the given x=1 is y=10.

Therefore, the range for the given function, with x=1 is 10.

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The solution to the logarithmic expression log²x + log²(x + 10) = log²11 is;

x = -11 and 1

We are given the logarithmic expression as;

log²x + log²(x + 10) = log²11

By the power rule of logarithm, we know that; log²x = 2log x

Thus;

log²x + log²(x + 10) = log²11 can be expressed as;

2log x + 2log (x + 10) = 2log 11

Divide through by 2 to get;

log x + log (x + 10) = log 11

We know from product rule of logarithm that log (ab) = log a + log b. Thus; log x + log (x + 10) = log 11 is;

log x(x + 10) = log 11

Log cancels out to get;

x² + 10x - 11 = 0

Using quadratic equation calculator gives;

x = -11 and 1

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In the given triangle, the angle between the two sides 5 and 6 is nearest 41°.

The term triangle means the polygon which has three sides and three angles and three vertices,

Here we have given that three  sides of a triangle have lengths 4, 5, and 6.

And here we need to find the angle between the two sides 5 and 6

According to the given values, let us consider a = 4, b = 5 and c = 6

So, the angle between 5 and 6 can be written as ∠b

And it can be calculated as the following is one way to perform the calculation and it may not be the best way.

∠B = arc cos(a² + c² - b²)/2ac

When we apply the values one the formula, then we get

=> 0.72273 rad

The approximate degree is written as

=> 41.41°

When we round off it then we get the resulting value,

=> 41°

Therefore, option (c) is correct.

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The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.

Given that,

We have a function f(x)=7sinx -4secx tanx.

We have to find the most general antiderivative of the function on the interval (-π/2, π/2).

We know that,

Take the function,

f(x)=7sinx -4secx tanx.

The antiderivative is

= [tex]\int {7sinx-4secxtanx} \, dx[/tex]

= [tex]7\int{sinx} \, dx -4\int {secxtanx} \, dx[/tex]

= 7(-cosx)-4[tex]\int {sinx/cos^{2}(x) } \, dx[/tex]

Take cosx =u

-sinxdx=du

= -7cosx-4[tex]\int {-1/u^{2} } \, du[/tex]

= -7cosx-4(1/u)+C

=-7cosx-4(1/cosx)+C      ( since we know u=cosx)

= -7cosx-4secx+C

Now for the interval (-π/2,π/2)

= -7(cosπ/2-cos(-π/2))-4(secπ/2-sec(-π/2))+C

= -7(0-0)-4(∞-∞)+C

=not defined

Therefore, The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.

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The vertex of the function is located at coordinates (119, 0).

[tex]f(z)= 2z^{2}+82+37\\ \\f(z)= 2z^{2}+119[/tex]

Check the attached image.

[tex]\frac{d}{dz} (2z^{2}+119)\\ \\f'(z)=2*2z^{2-1}\\ \\f'(z)=4z[/tex]

[tex]f'(z)=4z\\ \\4z=0\\ \\z=0[/tex]

[tex]f(0)= 2(0)^{2}+119\\ \\f(0)=119[/tex]

The vertex of the function is located at coordinates (0, 119).

Answer:

Step-by-step explanation:

1)11357*(105.7/100)^t

2)1 year 12000.121  2 year 12684  5 year 14979.1  10 years 19763.3

3)11357*(105.7/100)^t=22714 so t+12.5

Answer:

I believe it is A

Step-by-step explanation:

Just go backwards. translations on a graph are pretty simple once you understand left vs right and up vs down.

The required translation to move the image back to the original position is 3 units right and 3 units down. Option A is correct.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

The translation processes in geometry enable the shift of figures from one location to other.

Here,
The given translation is ,
a figure is translated 3 units left and 3 units up,
(x' , y') ⇒ (x - 3 , y + 3 )

To shift back the image,
x' = x - 3  ⇒ x = x' + 3
y' = y + 3 ⇒ y = y' -3

Thus, the required translation to move the image back to the original position is 3 units right and 3 units down. Option A is correct.

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The quantity that provides the best measure of the safety of drivers is A. the number of accidents per year.

Insurance is a risk management tool. When you purchase insurance, you are purchasing protection against unforeseen financial losses. If something bad happens to you, the insurance company will pay you or someone you choose. If you do not have insurance and an accident occurs, you may be held liable for all associated costs.

Insurance is a risk management tool. When you purchase insurance, you are purchasing protection against unforeseen financial losses. If something bad happens to you, the insurance company will pay you or someone you choose. If you do not have insurance and an accident occurs, you may be held liable for all associated costs.

In this case, the number of accidents will be a factor to illustrate the safety.

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Based on the provided information, Jerry's Z score will be negative, while Corey's Z score will be positive.

A Z-score refers to a numerical measurement that defines the raw value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it means that the data point's score is identical to the mean score. A negative z-score indicates that the data point is below average or mean and a positive z-score indicates that the data point is above average or mean. Consider the formula for z score which is given by:

z = (x - µ)/σ where x is the given data value, µ is the mean, and σ is the standard deviation.

Hence, if the x < µ, the z score will be negative while if x > µ, the z score will be positive. As Corey scored higher than the mean on his SAT, his z score will be positive, and Jerry scored lower than the mean on his SAT, his z score will be negative.

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The required probability for purchasing more than one costume is 0.03.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lies in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

The given problem can be solved as follows,

The number of visitors purchasing no costume, exactly one and more than one costumes are given as 81, 6 and 3 respectively.

Then, the total number is 81 + 6 + 3 = 90

Now, the probability of purchasing more than one costume is given as,

P(More than one costume) = 3/90

                                            =  1/30

                                            = 0.03

Hence, probability that the next person will purchase more than one costume is 0.03.

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Answer:

2

Step-by-step explanation:

2x-1 = __x-1

Make both sides match to make the statement true.

2x-1 = 2x-1

The account balance of Bob Rowinski if he kept the money on deposit for 6 months is $4,032.00.

The compound interest formula can be expressed as;

A = P(1 + r/n)^(n*t)

Where A is accrued amount, P is principal, r is interest rate, t is time elapsed.

Given the data in the question;

Plug the given values into the above formula and solve for A.

A = P(1 + r/n)^(n*t)

A = $4000( 1 + 0.016/2 )^(2*0.5)

A = $4000( 1 + 0.008 )^(1)

A = $4000( 1.008 )

A = $4,032.00

Therefore, the accrued amount after half a year is $4,032.00

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Answer:

okey baik dan sangat bagus

Answer:

there is no attached picture...

Step-by-step explanation:

Answer:

A represents the mesosphere

Length of diagonal WY is 13.03 units

What is Distance Formula?

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).

This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

According to the given question:

WXYZ is a rectangle and diagonals of a rectangle are equal in length

Coordinates of W = (-4,5) and Y = (3,-6)

To find the length of diagonal WY, we need to find distance between points W and Y.

Using distance formula to find WY

= √((3 – (-4))² + (-6 – 5)²)

= √170

= 13.03 units

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Chloe needs to cut 75 centimetres after the unit conversion piece of wood in order to use it for her desk.

What is unit conversion?

Unit conversion is a multi-step process that includes rounding, selecting the appropriate number of significant digits, and multiplying or dividing by a numerical factor.

Given, Chloe needs a 1.25-meter piece of wood

Total available 2-meter piece of wood

So, the extra piece of wood = 2-1.25 = 0.75 meter

Convert meter to centimetres

Then, 1 meter = 100 centimetres

0.75 meter = 0.75*100 centimetres = 75 centimetres

Hence, she needs to cut 75 centimetres piece of wood.

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The model's length 1.4.To do this, I'm going to put up a proportion. This time period is excessively long when compared to how long it takes to whip.

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We want to study the population formula of a given US state according to exponential equation.

a) 23.1 millions.

b) in 2013 - 2014

What is exponential equation?

The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable

Main body:

The population state is:

A = 23.1*e^(0.0153*t)

In millions.

Where t represents the number of years after 2000.

a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).

A(0) = 23.1*e^(0.0153*0) = 23.1

The population at year 2000 was 23.1 millions.

b) Now we want to solve:

A(t) = 28.3 = 23.1*e^(0.0153*t)

        28.3/23.1 = e^(0.0153*t)

       1.23 = e^(0.0153*t)

Now we can apply the natural logarithm to both sides:

ln(1.23) = ln( e^(0.0153*t) )

ln(1.23) = 0.0153*t

ln(1.23)/0.0153 = t = 13.5

Hence, 13.5 years after 2000 the population will be 28.3 million.

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The coordinates of triangle A'B'C' is A'(0, 4), B'(4, 0), C´(8, 8).

What are coordinates?

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Here, we have

Triangle ABC is dilated by a factor of 2 with the center of dilation at the origin to form triangle A'B'C'.

A = ( 0,2)

B = (2, 0)

C = (4,4)

After applying dilated by a factor of 2, we get

A' = (0,4)

B' = (4,0)

C' =(8,8)

Hence, the coordinates of triangle A'B'C' is A'(0, 4), B'(4, 0), C´(8, 8).

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Answer:

1/8, 1/8, 1/4, 1/4, 1/16, 1/16, 1/16, 1/16 = 1

1/2, 1/2 = 1

Step-by-step explanation:

from left to right

is this music class or math class lol?

Answer:

translation of 2 squares left and 1 square down

Step-by-step explanation:

consider the top vertex of both figures

S → T

then shape T is a translation of shape S

by moving 2 squares to the left and 1 square down

After 11.61 years the given principal amount of $ 900 will be double.

What is Compound interest?  

Compound interest is interest charged on a loan and is determined by both the principal amount and the rate of interest compounding per year.

The formula for the Amount when compound interest is calculated is given by

                  Amount, A = P(1+r/n)^nt  

P = Principal amount

r = Rate of interest

n = Number of compounds

t = Time period in years

Given:

Principal amount = $ 900

Rate of interest = 6% = 6/100 = 0.06

Number of compounds = 12    [ ∵ compounded monthly]

We need to find the time period

Assume that after 't' years the amount will be doubled

From the given data and formula,

Amount, A = 900(1+0.06/12)^12t        

                  = 900(1+0.06/12)^12t

                  = 900(1 + 0.005)^12t

                  = 900 (1.005)^12t  

As we assumed after 't' years the amount is double

=> 900 (1.005)^12t  = 2 × 900

=>         (1.005)^12t  = 2    

Applying log on both sides

=>  log (1.005)^12t  = log 2

=>    12t log(1.005) = log 2

=>                     12t = log 2/log(1.005)

=>                     12t = 0.30108/ 0.00216  

=>                     12t = 139.888

=>                         t =  11.61

Hence, after  11.61 years the given principal amount of $900 will be double.

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Answer:

the second

Step-by-step explanation:

the second is a linear graph

Answer:

The second Graph

Step-by-step explanation:

The question is asking what graph is linear.

The first graph is of an absolute value function which is not linear.

The second is of a line. This is linear.

The third looks to be either an exponential or a logarithmic function. Both of which are not linear.

The equation of the transformed graph will be y = -3(2ˣ) + 2.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

Suppose the equation of the given graph is y = A 2ˣ + k.

Substitute,(0,-1)

-1 = A 2⁰ + k

A + k = -1                (1)

Substitute, (1,-4)

-4 = A 2¹ + k

2A + k = -4            

A + k/2 = -2            (2)

Subtract 1 - 2 as

k - k/2 = -1 + 2

k/2 = 1

k = 2

And, A = -2 - 2/2

A = -3

Thus y = -3(2ˣ) + 2

Hence "The equation of the transformed graph will be y = -3(2ˣ) + 2 ".

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Answer:

(25,-5)

Step-by-step explanation:

Option 3 and 4 are the operations involving complex numbers have solutions represented by (-6, 7).

Find the attachment answer

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Answer:

1/2

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

If congruent then

x = y+5       and

x+3 = 3y          <======sub in the first equation for 'x'

y+5  +3 = 3y

8 = 2y    then   y = 4        x = y+5 = 9