The graphs of f(x) = 5x and its translation, g(x), are shown on the graph.

On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 1) and goes through (1, 5) and (2, 25). g (x) approaches y = negative 10 in quadrant 2 and increases into quadrant 1. It goes through (0, negative 9), (1, negative 5), (2, 15).

What is the equation of g(x)?

g(x) = 5x – 9
g(x) = 5x – 10
g(x) = 5x – 9
g(x) = 5x – 10

Answers

Answer 1

According to the function transformations, the equation of function g(x) is [tex]g(x) = 5^x - 10[/tex]

How to determine the equation of g(x)?

The complete question is in the attachment

The function f(x) is given as:

[tex]f(x) = 5^x[/tex]

From the attached graph, we can see that the function f(x) is 10 units down to get g(x).

This is so because the y values of g(x) are 10 less than the corresponding y values of f(x)

This transformation is represented by:

(x, y) => (x, y - 10)

So, we have:

g(x) = f(x) - 10

Substitute [tex]f(x) = 5^x[/tex]

[tex]g(x) = 5^x - 10[/tex]

Hence, the equation of function g(x) is [tex]g(x) = 5^x - 10[/tex]

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The Graphs Of F(x) = 5x And Its Translation, G(x), Are Shown On The Graph.On A Coordinate Plane, 2 Exponential

Related Questions

The set of all numbers greater than or equal to −5 and less than 5.

Answers

Answer:

No. greater than of equal to (-5) = -4,-3,-2,-1,0,1,2,3,4,5,6...........

No. less than 5 = 4,3,2,1 ,0,-1......

{ -4,-3,-2,-1,0,1,2,3,4}


Reuben rented a truck for one day. There was a base fee of $14.95, and there was an additional charge of 80 cents for each mile driven. Reuben had to pay
$135.75 when he returned the truck. For how many miles did he drive the truck?

Answers

Answer:

hczgdjatulsfulsitsfisfula7tl7roa7pts

Challenge time! Isn't time to give your brains a break? Its a fun challenge! EARN 20 POINTS NOW

Answers

Answer:

The answer is 64

Step-by-step explanation:

If you find this answer helpful pls mark it the brainliest answer

it's easy 64 the key is in the pic.

The cost of renting a car is $47 /week plus $0.25 /mile traveled during that week. An equation to represent the cost would be y=47+0.25x , where x is the number of miles traveled.

Answers

Answer:

a. 61.25

b. 70

c. 212

Step-by-step explanation:

a. What is your cost if you travel 57 miles?

The cost is $ .

y=47+0.25x

y=47+0.25(57)

y=47+14.25

answer: 61.25

b. If your cost was $64.50, how many miles were you charged for traveling?

You were charged for traveling miles.

64.50-47=0.25x

17.50=1/4x

17.50*4

answer 70=x

c. Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?

The maximum number of miles you could travel is miles.

100-47

53=1/4x

answer : x= 212

if the third place value of a number is 64 , What base is the number in ?

A) 2
B) 4
C) 8
D) 16

Answers

Answer:

B

Step-by-step explanation:

4, 16, 64 should be the correct order

Find the area.
help pls

Answers

Answer:

30 square feet

Step-by-step explanation:

The area of a trapezoid is equal to (a+b)/2 * h
In this case, the value of a is 5, b is 10, and h is 4. You can substitute those numbers into the formula and get the answer of 30.

30 square feet I’m guessing

Question 7 of 10 Which system of inequalities is graphed below? 10 -10 -8- 8 10 OA. y > X - 4 y < x +6 OB. VS X - 4 y < x +6 O c. y2 x -4 y > x + E OD. VS X - 4 y > x2 + 6

Answers

Because in both graphs the shaded region is above the curve, the correct option is C.

Which pair of inequalities is graphed?

On the graph we can see two parabolas, such that the y-intercepts of these are:

y = 6

y = -4

So we just need to find the pair of options with these y-intercepts, and noticing that for both cases, we must have:

y > parabola.

Because both shaded regions are above the parabolas.

The only option that meets these requirements is option C. Where there is a mistake, as you can see both curves have dashed lines, and always when we have dashed lines we should use the symbols > or <, while in that option we have a ≥ symbol

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Simplify this problem!!!

Answers

Answer:

C

Step-by-step explanation:

HOPE THAT HELPSBDNQBDB

The answer is c hope that helps you

in 1979 the Wincom river was 33 feet below the bridge. Because of silt build-up in the river bottom, the
river was only 12 feet below the bridge by 1986. Write an equation for the distance of the river from the
bridge, d, with t = 0 representing 1979. If the silt build-up continues at the same rate, what year will the
river reach the bridge?

Answers

Answer: d = 40 - 5/2t; 1995

Hope it helps :)

Calculate the length of the diagonal of the state of Wyoming.

Answers

The length of the diagonal of the state of Wyoming is 457 miles.

What is the length of the diagonal?

The length of the diagonal of the diagonal can be determined using Pythagoras theorem.

The Pythagoras theorem: a² + b² = c²

where:

a = lengthb = basec = hypotenuse

√365² + 275² = 457 miles

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Suppose we have already saved $55 towards the cost of a new television set.
We plan to save $6 more each week for the next several weeks.
i) Write an equation for the total amount T we will have after w weeks from now.
ii) Find the total amount that would be saved after 8 weeks.

Answers

Step-by-step explanation:

T = 55 + 6w

after 8 week $103

find the area dimensions are in centimeters. ​

Answers

Answer:

[tex]9600cm^{2}[/tex]

Step-by-step explanation:

Get the area of the triangle and the rectangle, then subtract the triangle's area for the rectangle's

What is x, the distance between points A and A'? D.15

Answers

The value of x that fills the coordinate are 7 or -5

Distance between two points

The formula for calculating the distance between two points is expressed as:

D = √(x2-x1)² +(y2-y1)²

Substitute the given coordinates

10 = √(15-7)² +(1-x)²

100 = 8²  +(1-x)²

(1-x)² = 100 - 64

(1-x)² = 36

1- x = -6

x = 7 or -5

Hence the value of x that fills the coordinate are 7 or -5

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Complete question

If the distance between two points (x, 7) and (1, 15) is 10, find the value of x.

Find the ratio of 18 inches to 2 yards B
A. 3/4 B. 1/4
C. 1/5 D. 2/5

Answers

Answer:

B. 1 / 4

Step-by-step explanation:

Step 1: We can turn 2 yards into 6 feet.

Step 2: Then we can turn 6 feet into 72 inches.

Step 3: We plug it into the ratio, getting 18 / 72.

Step 4: Simplify. We get 1 / 4 as the answer. Therefore, we choose B.

Need help with algebra homework

Answers

Answer:

the answer for this problem is A, big

what is 2 plus two.
please answer quickly

Answers

Answer:

2 + 2: 4

or 2 + 2: 5 from the dystopian novel 1984.

Two plus two is four (or 4 in written form). Why? Well, by beginning at the origin which is 0, we can count up to 5.

0, 1, 2, 3, 4, 5

Two plus two is a representative expression of the value initially being at 2, and adding two more values to the 2 that we already have. Since we are adding two to the quantity we already have, we can see that the answer is four (4) because we can simply count up two numbers from 2 to get what 2 + 2 equals. When counting up, we do not count the number that is already begun with because that would invalidate the equation. Since three (3) is after two (2), we can count starting at three. 3, 4! Those are the two values we get to when in the process of adding two. When we add one to two, we get three. When we add two to two, we get four. That is why 2 + 2 = 4. If you need help understanding better, let me know and I will gladly assist you!

Given positive integers $x$ and $y$ such that $2x^2y^3 + 4y^3 = 149 + 3x^2$, what is the value of $x + y$?

Answers

Answer:

5

Step-by-step explanation:

2x²y³ + 4y³ = 149 + 3x²

[tex] 2x^2y^3 - 3x^2 = 149 - 4y^3 [/tex]

[tex] x^2(2y^3 - 3) = 149 - 4y^3 [/tex]

[tex] x^2 = \dfrac{149 - 4y^3}{2y^3 - 3} [/tex]

[tex] x = \pm \sqrt{\dfrac{149 - 4y^3}{2y^3 - 3}} [/tex]

Try y = 1

[tex]x = \pm \sqrt{\dfrac{149 - 4(1)}{2(1)^3 - 3}} = \pm \sqrt{-145} = i\sqrt{145}[/tex]

For y = 1, x is imaginary.

Try y = 2

[tex] x = \pm \sqrt{\dfrac{149 - 4(2)^3}{2(2)^3 - 3}} = \pm \sqrt{9} = \pm 3[/tex]

Since x and y are positive integers, ignore x = -3.

When x = 3, y = 2.

x + y = 3 + 2 = 5

The value of x + y is 5.

What is Polynomial?

Polynomials are expressions which consist of variables, constants, coefficients and exponents.

We have the equation,

2x²y³ + 4y³ = 149 + 3x²

2x²y³ - 3x² = 149 - 4y³

x² (2y³ - 3) = 149 - 4y³

x² = (149 - 4y³) / (2y³ - 3)

x = √[(149 - 4y³) / (2y³ - 3)]

Now, we have to find two positive integers.

We can use trial and error method here.

Trial putting y = 1.

x = √[(149 - 4 × 1³) / (2 × 1³ - 3)]

  = √[145 / (-1)]

  = √(-145)

There is no real root for √(-145). So y = 1 is not applicable.

Trial putting y = 2.

x = √[(149 - 4 × 2³) / (2 × 2³ - 3)]

  = √[117 / 13]

  = √(9)

  = ± 3

But we need positive integers. So we ignore -3.

So x = 3 and y = 2 ⇒ x + y = 5

Hence x + y = 5.

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how many ways are there to make $3 with pennies, nickels, and dimes

Answers

Answer:

10

Step-by-step explanation:

You are given that cos(A)=−5/13, with A in Quadrant II, and sin(B)=7/25, with B in Quadrant II. Find cos(A+B). Give your answer as a fraction.

Answers

The value of cos(A+B) is 36/325.

What is Trigonometry?

The branch of mathematics concerned with specific functions of angles and their application to calculations.

Given:

cos(A)=−5/13

sin(B)=7/25

Now Using identity,

sin²A + cos² A= 1

sin A= √1 - cos² A

sin A = √1- 25/169

sin A= √144/169

sin A= 12/13

Again,

sin²B + cos² B= 1

cos B= √1 - sin² B

cos B = √1- 49/625

cos B= √576/625

cos B= -24/25

Now,

cos (A +B) = cos A cos B - sin A sin B.

= -5/13* (-24/25) - 12/13* 7/25

=  120/325 - 84/325

= 36/325

Hence, the value of cos (A + B) is 36/325.

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Is 3.5 greater than 3.39

Answers

Answer:

yes

Step-by-step explanation:

If you bought a stock last year for a price of $103, and it has risen 13.5% since then, how much is the stock worth now, to the nearest cent?

Answers

The stock worth now, to the nearest cent is  $90.75.

How to find the current worth of stock?

The current worth of stock = initial price of stock+increase in the price of stocks

If you bought stock last year for a price of $103, and it has risen 13.5% since then,

Let X be the worth of stock;

103 ×  100 = (13.5% + 100%) × X

10300 = 113.5X

X = 10300/113.5

X = 90.74889868

X = $90.75

Hence, The stock worth now, to the nearest cent is  $90.75.

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Lashawn makes scrambled eggs with 3 spoonfuls of salsa for every 2 eggs. Gilberta adds 7 spoonfuls of salsa for every 5 eggs.
Whose scrambled eggs have a stronger salsa taste?

A. Lashawn's eggs
B. Gilberta's eggs
C. The dishes of scrambled eggs have equal salsa tastes

Answers

Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs. Then the correct option is A.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Lashawn makes scrambled eggs with 3 spoonfuls of salsa for every 2 eggs.

Gilberta adds 7 spoonfuls of salsa for every 5 eggs.

Then the scrambled eggs have a stronger salsa taste will be

Lashawn's eggs = 3/2 = 1.5

Gilberta's eggs = 7/5 = 1.4

Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs.

Then the correct option is A.

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A tower on a college campus was built with a faulty foundation and is starting to lean. A student climbs to the tilted top and drops a rope down to the ground. The
end of the rope lands 3 feet from the base of the tower and measures 57 feet from
the top of the building to the ground. What is the angle that the tower is leaning?
Round your answer to the nearest degree, and enter the number only

Answers

Answer:

leaning at 3 degrees off of normal (to the nearest whole degree)

Step-by-step explanation:

To visualize, let's assume the tower is leaning to the right, (as viewed by us).

If the rope is dropped from the top to the ground, the tower, the rope and the ground (between the rope and the tower) form a right triangle.

The height and base of the triangle are given

Often we're looking for the angle near the ground, but here, we're looking for the angle between the rope and the tower because the angle is congruent to the angle that the tower forms with it's original vertical position (alternate interior angles).  If the tower was standing straight up and hadn't been leaning at all, we wouldn't say that the tower was leaning 90°... we would say it was leaning 0°.  Whereas if the tower fell over and was laying flat on the ground, we would say it was leaning at 90°.  So, we're not measuring the angle between the tower and the ground, but rather the angle between the tower where it should be, and where it is... which is the same angle as the rope forms with the tower.

Recall that [tex]tan(\theta)=\dfrac {opp}{hyp}[/tex]

Since we know the two legs of the right triangle, one can setup a tangent relationship with the two legs, but remember that the "opposite" side is going to be the ground, and the "adjacent side" will be the rope.

[tex]tan(\theta)=\dfrac {ground}{rope}\\tan(\theta)=\dfrac {3ft}{57ft}\\tan(\theta)=\frac {3}{57}\\\theta=tan^{-1}(\frac {3}{57})\\\theta=3.012787504^o\\\theta \approx 3^o\\[/tex]

Question 1
Kapoor Corporation uses the following activity rates from its activity-based costing to assign overhead costs to products.
Activity Cost Pools Activity Rate
Setting up batches $86.50 per batch
Assembling products $4.63 per assembly hour
Processing customer orders $52.16 per customer order

Data concerning two products appear below:

Product J00A Product S06U
Number of batches 34 43
Number of assembly hours 105 812
Number of customer orders 17 32

Required:
a. How much overhead cost would be assigned to Product J00A using the company's activity-based costing system?
b. How much overhead cost would be assigned to Product S06U using the company's activity-based costing system?

Overhead Cost:
There are some expenses incurred at the time of manufacturing of products and services that are not directly attributable to the finished products. These expenses are known as manufacturing overheads or indirect expenses.

Answers

The overhead cost would be assigned to Product J00A using the company's activity-based costing system is $4313.87.

How to calculate the cost?

The overhead cost that would be assigned to Product J00A using the company's activity-based costing system will be:

= ($86.50 × 34) + ($4.63 × 105) + ($52.16 × 17)

= $2941 + $486.15 + $886.72

= $4313.87

The overhead cost would be assigned to Product S06U using the company's activity-based costing system will be:

= ($86.50 × 43) + ($4.63 × 812) + ($52.16 × 32)

= $3719.50 + $3759.56 + $1669.12

= $9148.18

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You invest $1600 in an account paying 5.4% interest compounded daily. What is the account's effective annual yield? Write as a decimal.

Answers

Answer:

For a principle amount of $1600 and rate 5.4%, the effective annual yield is 5.55% if interest is compounded annually.

Step-by-step explanation:

Concept: The annual percentage yield (APY) or the effective annual yield is the real rate of return earned on an investment, taking into account the effect of compounding interest.

The principle amount is $1600, rate is 5.4% and period is 365 days. The formula to find yield is [tex]Y = (1+\frac{r}{n} )^{n} -1[/tex]. All the values are to be inserted in the formula. Here n = 365 and r = 5.4%.

[tex]Y=(1+\frac{0.054}{365} )^{365} -1\\Y=(1.000148)^{365} -1\\Y=5.55%[/tex]

The annual yield is 5.55%.

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find the slope of the line that passes through (3,10) and (1,17)​

Answers

Answer:

[tex]m=- \frac{7}{2}[/tex]

Step-by-step explanation:

The slope of a line passing through the two points [tex]\displaystyle{\large{{P}={\left({x}_{{1}},{y}_{{1}}\right)}}}[/tex] and[tex]\displaystyle{\large{{Q}={\left({x}_{{2}},{y}_{{2}}\right)}}}[/tex] is given by [tex]\displaystyle{\large{{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}}}[/tex].

We have that [tex]x_1=3[/tex], [tex]y_1=10[/tex], [tex]x_2=1[/tex], [tex]y_2=17[/tex].

Plug the given values into the formula for slope: [tex]m=\frac{\left(17\right)-\left(10\right)}{\left(1\right)-\left(3\right)}=\frac{7}{-2}=- \frac{7}{2}[/tex]

Answer: the slope of the line is [tex]m=- \frac{7}{2}[/tex].

Answer:

slope = - [tex]\frac{7}{2}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{x_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 10 ) and (x₂, y₂ ) = (1, 17 )

m = [tex]\frac{17-10}{1-3}[/tex] = [tex]\frac{7}{-2}[/tex] = - [tex]\frac{7}{2}[/tex]

PLEASE HELP ME WITH MY MATH

Answers

The definition for the graphed function is the one shown in option d:

y = -x + 2   if x < 1

y = -2x + 1   if x  ≥ 1.

Which piecewise function coincides with the graph?

Here we have a piecewise function, where for the first part we have a linear equation with a negative slope (for x < 1, we know that the symbol "<" must be used because of the open dot at the end of the line).

Then, we have another linear equation with a negative (and steeper) slope. This time there is a closed dot, so the domain for this second part is x ≥ 1.

With that we can conclude that the correct option is:

d:

y = -x + 2   if x < 1

y = -2x + 1   if x  ≥ 1.

Where you can see that the second part has a larger (in module) slope, and the domains are defined as we saw above.

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Instructions: Write the equation of the line in Point-Slope Form
given the information below. Use Point One.
Point One (-3, 3)
=
Point Two (-2,-1)
Point-Slope
=
Point-Slope Form:

Answers

Answer: [tex]y-3=-4(x+3)[/tex]

Step-by-step explanation:

The slope is

[tex]\frac{-1-3}{-2-(-3)}=\frac{-4}{1}=-4[/tex]

So, using the point (-3, 3) to substitute into point-slope form, the equation is [tex]\boxed{y-3=-4(x+3)}[/tex]

I need help question 4

Answers

Answer:

-51

Step-by-step explanation:

If the limits are reversed, then place a negative sign in front of the integral.

[tex]\int\limits^a_bf ({x}) \, dx =-\int\limits^b_a f({x}) \, dx[/tex]

[tex]\int\limits^a_3 f({x}) \, dx = 51\\[/tex] where [tex]\alpha =10\\[/tex]

[tex]\int\limits^3_\alpha f( {x}) \, dx =-51[/tex]  where[tex]\alpha =10[/tex]

The sum of a number and 3 is less than 10 if x denotes the number what would be the possible values of x
x>13
x<13
x>7
x<7

Answers

Answer:

x<7

Step-by-step explanation:

Consider the number x (as mentioned in the question). Now carefully pay attention to the given condition

⇒"The sum of a number and 3 is less than 10"

Remember the notation of  the term "less than" in mathematical context is indicated by "<" sign. Hence our inequality is

⇒ x+3<10

adding or subtracting any number from the both sides of an inequality DOESN'T change its direction. Thus, if we cancel out 3 from both sides it won't swap the inequality. Therefore

⇒ x+3-3<10-3

⇒ [tex]x<7[/tex]

In terms of  interval notation

[tex]\implies x\in( -\infty,7)[/tex]

In conclusion

The answer is D) [tex]x < 7[/tex]

Let the number be x

The sum of number and 3

x+3

Is less than 10

x+3<10

Lets solve it

x<10-3x<7

Hence

Option D is correct

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