Write the equations after translating the graph of y=|1/2x-2|+3. One unit to the left

Answers

Answer 1

Answer:

[tex]g(x) = |\frac{1}{2}x - \frac{3}{2} | + 3[/tex]

Step-by-step explanation:

Given

[tex]y = |\frac{1}{2}x - 2| + 3[/tex]

Required

Translate the above one unit to the left

Replace y with f(x)

[tex]y = |\frac{1}{2}x - 2| + 3[/tex]

[tex]f(x) = |\frac{1}{2}x - 2| + 3[/tex]

When an absolute function is translated to the left, the resulting function is

[tex]g(x) = f(x - h)[/tex]

Because it is been translated 1 unit to the left, h = -1

[tex]g(x) = f(x - (-1))[/tex]

[tex]g(x) = f(x + 1)[/tex]

Calculating [tex]f(x+1)[/tex]

[tex]f(x+1) = |\frac{1}{2}(x+1) - 2| + 3[/tex]

Open bracket

[tex]f(x+1) = |\frac{1}{2}x + \frac{1}{2} - 2| + 3[/tex]

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

[tex]f(x+1) = |\frac{1}{2}x + \frac{-3}{2} | + 3[/tex]

[tex]f(x+1) = |\frac{1}{2}x - \frac{3}{2} | + 3[/tex]

Recall that

[tex]g(x) = f(x + 1)[/tex]

Hence;

[tex]g(x) = |\frac{1}{2}x - \frac{3}{2} | + 3[/tex]

Answer 2

Answer:

y=l1/2x-3/2l+3

Step-by-step explanation:

cause im him


Related Questions

There are 20 cars in my building’s parking lot. All of the cars are red or white. 12 of them are red, 15 of them are 4-door, and 4 of them are 2-door and white. How many of the cars are 4-door and red?

Answers

Answer:

11 cars

Step-by-step explanation:

There are 20 cars in my building's parking lot, 15 cars are 4-door, then

20 - 15 = 5 cars are 2-door.

5 cars are 2-door, 4 of them are 2-door and white, then

5 - 4 = 1 car is 2-door and red.

12 cars are red, 1 car is 2-door and red, then

12 - 1 = 11 cars are 4-door and red.

plz give me brianlist

f(x) = x2. What is g(x)?

Answers

Answer:

A

Step-by-step explanation:

consider the form g(x) = aX^2, where a is negative, means the curve is flip upside down.

-3, shifted down for 3 units.

5) The solution of (2x - 1)2 = 9 is equal to
d) 21
a) - 1
b) 2
c) - 1,2
d) None of these
6) The GCD of x2 - 2xy + y2​

Answers

Answer:

Q5 d

Step-by-step explanation:

(2x-1)2=9

4x-2=9

4x=9+2

4x=11

x=2.75

ans: none of these

Nancy needs at least 1000 gigabytes of storage to take pictures and videos on her upcoming vacation. She
checks and finds that she has 105 GB available on her phone. She plans on buying additional memory
cards to get the rest of the storage she needs.
The cheapest memory cards she can find each hold 256 GB and cost $10. She wants spend as little
money as possible and still get the storage she needs.
Let C represent the number of memory cards that Nancy buys. 2)what is the least amount of money Nancy can spend to get the storage she needs?

Answers

Answer:

The answer to this question can be defined as follows:

In option 1, She buys 4 memory cards.

In option 2, The cost of memory is $40  

Step-by-step explanation:

Given:

Available space is = 105 GB

required space = 1000 GB

256 GB memory cost $10.

Find needed memory:

=  1000 GB - 105 GB

= 895 GB

∴ the available memory is 256 GB.

∵ 256 × 4 = 1024  GB

The total memory she have = 1024 + 105 = 1129 GB

And  she needs to buy 4 memory cards.

The cost of the four memory cards is= 4 ×10 =  $40.

Using proportions, it is found that the least  amount of money Nancy can spend to get the storage she needs is of $40.

------------------------------

This question is solved by proportions, using a rule of three.Nancy needs at least 1000 GB, but she only has 105 GB available. Thus, she needs to buy 1000 - 105 = 895 GB.The cheapest cards she can buy have 256 GB. How many of these cards she has to buy?

The rule of three is of:

1 card - 256 GB

x cards - 895 GB

Applying cross multiplication:

[tex]256x = 895[/tex]

[tex]x = \frac{895}{256}[/tex]

[tex]x = 3.5[/tex]

Rounding, she has to buy 4 cards.

Each card costs $10, thus, she has to spend $10 x 4 = $40.

A similar problem is given at https://brainly.com/question/17594062

Two cars are traveling north along a highway. The first drives at 40 mph, and the second, which leaves 3 hours later, travels at 60 mph. How long after the second car leaves will it take for the second car to catch the first?

Answers

Answer:

Step-by-step explanation:

We will make a table and fill it in according to the information provided. What this question is asking us to find, in the end, is how long did it take the cars to travel the same distance. In other words, how long, t, til car 1's distance = car 2's distance. The table looks like this:

              d     =      r     *     t

car1

car2

We can fill in the rates right away:

             d       =      r     *     t

car1                       40

car2                       60

Now it tells us that car 2 leaves 3 hours after car 1, so logically that means that car 1 has been driving 3 hours longer than car 2:

            d     =      r      *      t

car1                     40         t + 3

car2                     60           t

Because distance = rate * time, the distances fill in like this:

                   d      =      r      *      t

car1    40(t + 3)    =      40        t+3

car2          60t     =       60         t

Going back to the interpretation of the original question, I am looking to solve for t when the distance of car 1 = the distance of car 2. Therefore,

40(t+3) = 60t and

40t + 120 = 60t and

120 = 20t so

t = 6 hours.

Given: r || s, and t is a transversal that cuts both r and s. Prove: <1 = <5, <2 = <6, <3 = <7, and <4 = <8 Write a paragraph proof to prove that the corresponding angles shown are congruent.

Answers

Answer:

Lines r and s are parallel as Corresponding Angles given. There are four pairs of corresponding angles: angle 1 and angle 5, angle 2 and angle 6, angle 3 and angle 7, and angle 4 and angle 8. Since r and s are parallel, the slope of r is equal to the slope of s. Since t is a straight line, the slope of t is the same at both intersections, by the definition of a straight line. Thus, the corresponding angles created at both intersections must have the same measure, since the difference of the slopes at each intersection is the same, and the intersections share a common line. So, corresponding angles must have equal measure. Therefore, by definition of congruent angles, corresponding angles are congruent: angle 1 is congruent to angle 5, angle 2 is congruent to angle 6, angle 3 is congruent to angle 7, and angle 4 is congruent to angle 8.

Step-by-step explanation

answer from haven

Which ordered pair is a solution of this equation?
Please and thank you

Answers

Answer:

Hey there!

-9x-y=-15

9x+y=15

A solution with integer values would be 9(1)+6=15

Thus, x=1 and y=6

(1, 6)

Hope this helps :)

Answer:

(6,1)

Step-by-step explanation:

Help is appreicated! (10 points!)

Answers

Answer:

5

Step-by-step explanation:

5


Please answer this question now

Answers

Answer:

7.8

Step-by-step explanation:

To do this problem you need to know Pythagorean Theorem which is also known as [tex]a^{2} +b^{2} =c^{2}[/tex].

In this problem 6 would be a, 5 would be b, and d would be c. So to do this we would do 5 squared (which is 25)+ 6 squared which is 36) and you would get 61 and when you do that you will just take the square root of that which is 7.81 and round it to the nearest tenth which is 7.8 and that would be the final answer

What degree of rotation about the origin will cause the triangle below to map onto itself?

Answers

Answer:

=360

explanation:

When you’re talking about rotation you go counterclockwise and each quadrant is another 90 degrees.

Answer:

360

Step-by-step explanation:

Can anyone help me with this plz Which pair of triangles can be proved congruent by the SAS Postulate?

Answers

Answer: Second choice. Triangle ABX and triangle EDX.

Check out the diagram below. I have color coded the segments that are the same length. The congruent angles are due to the fact we have a pair of vertical angles, which are always the same measure. The green angles are between the red and blue sides for each triangle.

Answer:

Congruent Triangles

Step-by-step explanation:

From the available information, let's concentrate on the fact that lines AX≅EX and lines BX≅DX. This simply means that line AX is equal to line EX and line BX equals DX. since the two lines cross each other to make the vertically opposite angles AXB and DXE equal (AXB≅DXE), then the opposite triangles are congruently sharing two pairs of equal sides and the same.

The congruent triangles are ΔABX and ΔEDX

Please help me with this. I am really struggling...

Answers

The correct answer is option A

Step by step is in the picture


Hopefully this help you :)

Plz ans with steps... Thx!!

Answers

Answer:

16

Step-by-step explanation:

Let the 1st part of your answer be x , so the 2nd part will be 40-x . From the given information, we can write the equation: (1/4)x = (3/8) × (40-x) . We can simplify this into (1/4)x = (120-3x)/8 ; 8x = 480-12x ; 8x+12x = 480 ; 20x = 480 ; x = 480/20; x = 24

Therefore, the 1st part = 24

Plug this into your 40-x equation to get: 40 - 24 = 16

In the figure, m∠CED = m∠A. Complete the following proportions: ED/ A F= CE/? = CD/?

Answers

Answer:

The completed proportions are;

ED/A_F = CE/CA = CF/CD

Step-by-step explanation:

The given m∠CED = m∠A

∴ Angle ∠CDE = Angle ∠A_FC, (corresponding angles)

Angle ∠ECD = Angle ∠ACF (reflexive property)

Triangle ΔDCE is similar to triangle ΔACF (Angle Angle Angle (AAA) similarity)

In triangle ΔDCE and triangle ΔACF

m∠A is bounded by CA and A_F

m∠CED is bounded by CE and ED

∠DCE is bounded by CE and DE

∠C is bounded by CA and CF

Based on the orientation of the two triangles, we have

ED is the corresponding side to A_F, CD is the  corresponding side to CF, CE is the corresponding side to CA

Therefore, we have;

ED/A_F = CE/CA = CF/CD.

evaluate the following using suitable identities : (102)^2​

Answers

You answer is 10404 to get this answer multiply the 102 double time

find the point of intersection between 2x - 6y = 12 and the line x = -2.

slope intercept: y = 1/3x - 2​

Answers

Answer:

(-2, -8/3)

Step-by-step explanation:

2(-2) - 6y = 12

-4 -6y = 12

-6y = 16

y = -16/6 = -8/3

please help!!!!! idk how to do this

Answers

Answer:

30 seconds.

Step-by-step explanation:

So, we have the equation:

[tex]h(t)=-16t^2+h[/tex]

Where t is the time in seconds and h is the initial height.

A barometer falls from a weather balloon at a height of 14,400 feet. In other words, the initial height is 14,400. Substitute for h:

[tex]h(t)=-16t^2+14400[/tex]

We need to find when the barometer hits the ground. Ground level is 0 feet. Therefore, we can substitute h(t) for 0 and solve for the equation (solve for t) in order to find how long (in seconds) it took for the barometer to fall:

[tex]0=-16t^2+14400\\-14400=-16t^2\\900=t^2\\t=\pm\sqrt{900} \\\text{Time cannot be negative.}\\t=\sqrt{900}\\ t=30 \text{ seconds}[/tex]

Therefore, it took 30 seconds for the barometer to hit the ground when it fell at a height of 14,400 feet.

Edit: Spelling.

If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 0), (negative 1, 2). (–2, 0) (0, –2) (5, –7) (5, –2)

Answers

Answer:

(0, –2)

Step-by-step explanation:

I am assuming that point 'B' is (-5 , 0).

The translation rule is: [tex](x,y)\rightarrow(x+5,y-2)[/tex].

Apply the rule to point 'B':

[tex]\frac{(-5,0)\rightarrow(-5+5,0-2)}{(x,y)\rightarrow(x+5,y-2)}\rightarrow\boxed{(0,-2)}[/tex]

B' should be (0, -2).

Answer:

Guy above me might be right but Im not sure. Im on the cumulative exam on edge.

Step-by-step explanation:

A certain server works four 6-hour shifts a week at a restaurant and has a base salary of $9.75/ℎ. An average server sells $1400 in a single shift. If the server makes an average of 14% tip of a bill, what is the annual gross income of the server?

Answers

Answer:

The annual gross income of the server is $52936

Step-by-step explanation:

The server works four 6-hour shift a week.

the server earns $9.75/h

An average seller sells $1400 in a single shift, and makes 14% tip of a bill.

For the 6-hour shift, the server earns

6 x $9.75 = $58.5 a shift

in a week, the total money made for the four shifts in a week will be

4 x $58.5 = $234

The server makes an average of 14% of a bill, and makes about  $1400 in a single shift.

In a single shift he makes a tip of

14% of $1400 = 0.14 x $1400 = $196

in a week he makes 4 x $196 = $784

Total money the server makes in a week is

==> $234 + $784 = $1018

There are 52 weeks in a year.

The server's annual gross income will be

52 x $1018 = $52936

i will give brainliest.On every sale of goods worth N10,000.00, there is a commission of N550.00. If

an agent delivers N150,000.00, find his commission. pls helllp​

Answers

Answer:

8250

Step-by-step explanation:

I think

The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5 . find the original number

Answers

Answer:

5/8

Step-by-step explanation:

Let the numerator = n.

Let the denominator = d.

The fraction is

n/d

"The denominator of a rational number is greater than its numerator by 3."

d = n + 3

The fraction is

n/(n + 3)

"If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5."

(n - 3)/(n + 3 + 2) = 1/5

(n - 3)/(n + 5) = 1/5

Cross multiply.

5(n - 3) = 1(n + 5)

5n - 15 = n + 5

4n = 20

n = 5

d = n + 3 = 5 + 3 = 8

n/d = 5/8

The original number is 5/8.

Find the slope of the line passing through the points D(10, 8) and E(-4, 4).

Answers

Answer:

[tex]\frac{2}{7} x[/tex]

Step-by-step explanation:

To find the slope of a line with 2 points we use the following formula.

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

So with the following points,

E(-4,4)

D(10,8)

So 8 is y2 and 4 is y1 8-4 = 4

10 - -4 = 14

Slope: 2/7x

Thus,

the slope of the line is 2/7x.

Hope this helps :)

Angle ABC is a straight angle. MAngleDBC = 130° and Ray B E bisects AngleABD. The center of line A C is point B. Two lines extend from point B. One line extends to the left and contains point E. Another line extends up and to the left and contains point D. What is mEBA? °

Answers

Answer:

25°

Step-by-step explanation:

Since ∠DBC = 130°, ∠DBC + ∠ABD = 180° (sum of angles on a straight line is 180°). Solving for ∠ABD:

∠DBC + ∠ABD = 180°

130 + ∠ABD  = 180°

∠ABD = 180° - 130°

∠ABD = 50°

∠ABD  is bisected by line BE, therefore ∠ABD = ∠EBA + ∠DBE (angle addition postulate).

The angle addition postulate states that if w is the interior of xyz then ∠XYZ = ∠XYW + ∠ZYW

Since E is the interior of ∠ABD, then:

∠ABD = ∠EBA + ∠DBE

But ∠EBA = ∠DBE

∠ABD = 2∠EBA

50 = 2∠EBA

∠EBA = 25°

Answer:

The answer is 25 degrees

PLEASE help me with this question! No nonsense answers and answer with full solutions please!

Answers

Answer:  b) {-3, 0.5}

Step-by-step explanation:

The new equation is the original equation plus 6.  Move the original graph UP 6 units.  The solutions are where it crosses the x-axis.

[tex]\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6[/tex]

+6 means it is a transformation UP 6 units.  

Solutions are where it crosses the x-axis.

The curve now crosses the x-axis at x = -3 and x = 0.5.

what are three different whole numbers whose sum and product are equal

Answers

Three different whole numbers whose sum and product are equal are 1, 2, and 3.

1 + 2 + 3 = 6

1 x 2 x 3 = 6

As demonstrated above, the sum and product of 1, 2, and 3 is the same.

Hope this helps!! :)

Answer:

1 2 and 3

Step-by-step explanation:

NEED HELP ASAP!! FIRST ONE TO GET THE ANSWER RIGHT GETS THE MOST BRAINLIEST

Answers

Answer:

125

Step-by-step explanation:

Add all the angles then subtract by 360.

Answer:

Vp-by-step explanation:

What is the domain of the function shown on the graph? A. -10

Answers

Answer:

Option (C)

Step-by-step explanation:

Domain of any graph is defined by the x-values or the input values of a function.

Similarly, y-values on the graph of a function define the Range.

In the graph attached, x-values varies from (-∞) to (+∞).

Therefore, Domain of the graphed function will be (-∞, ∞)

Or -∞ < x < ∞

Similarly, y-values of the graph varies from (-∞) to (1)

Therefore, range of the graphed function will be (-∞, 1).

Or -∞ < y < 1

Option (C) will be the answer.

How many real solutions In this problem

Answers

Answer:

D

Step-by-step explanation:

Given

y = x² + 1

y = x

Equating gives

x² + 1 = x ( subtract x from both sides )

x² - x + 1 = 0

Consider the discriminant Δ = b² - 4ac

with a = 1, b = - 1 and c = 1

b² - 4ac = (- 1)² - (4 × 1 × 1) = 1 - 4 = - 3

Since b² - 4ac < 0 then there are no real solutions

help me answer this question.

The midpoint of the diagonal of a square is 2 units from the vertex of the square. Calculate the area of the square

I will mark u as the brainliest. ​

Answers

Answer:

8 units²

Step-by-step explanation:

Let side of the square = a

The , Area of square = a²

Now, Midpoint of Diagonal DB is E

And DE = 2 units

So, DB = 2 DE = 2 × 2 = 4 units

Now, using Pythagoras theorem in BCD

DB² = DC² + BC²

plug the values

[tex] {4}^{2} = {a}^{2} + {a}^{2} [/tex]

Collect like terms

[tex] {4}^{2} = 2 {a}^{2} [/tex]

Evaluate the power

[tex]16 = 2 {a}^{2} [/tex]

Swipe the side of the equation

[tex]2 {a}^{2} = 16[/tex]

Divide both sides of the equation by 2

[tex] \frac{2 {a}^{2} }{ 2 } = \frac{16}{2} [/tex]

Calculate

[tex] {a}^{2} = 8[/tex]

Therefore, The area of the square is 8 sq.units.

Hope this helps..

Best regards!!

The area of the square is 8 square units.

Let's assume that the side length of the square is "s". Since the midpoint of the diagonal is 2 units from the vertex of the square, the diagonal of the square is 4 units (twice the distance from the vertex to the midpoint).

We can use the Pythagorean theorem to find the side length "s" of the square:

[tex]s^2 + s^2 = 4^2\\2s^2 = 16[/tex]

Divide both sides by 2:

[tex]s^2 = 8[/tex]

Now, to find the area of the square, we use the formula:

[tex]Area = side length^2\\Area = s^2 = 8[/tex]

So, the area of the square is 8 square units.

To know more about area:

https://brainly.com/question/33403734

#SPJ2

Question 1
Solve the equation that models the volume of the shipping box, 8(n + 2)(n + 4) = 1,144. If
you get two solutions, are they both reasonable?​

Answers

Answer:

n = -15 and n = 9. n = -15 is not reasonable because you can't have negative boxes or negative units of measurement.

Step-by-step explanation:

8(n + 2)(n + 4) = 1,144

(n + 2)(n + 4) = 143

n^2 + 2n + 4n + 8 = 143

n^2 + 6n - 135 = 0

(n + 15)(n - 9) = 0

n + 15 = 0

n = -15

n - 9 = 0

n = 9

I got two solutions: n = -15 and n = 9. Only one is reasonable because you cannot have a negative number of boxes or negative weight.

Hope this helps!

Simplify the equation, and set it equal to zero to prepare for factoring.

Multiply the two factors in parentheses using the distributive property:

8(n2 + 2n + 4n + 8) = 1,144

Combine like terms inside the parentheses:

8(n2 + 6n + 8) = 1,144

Multiply the terms inside the parentheses by 8 using the distributive property:

8n2 + 48n + 64 = 1,144

Set the equation equal to zero by subtracting 1,144 from each side:

8n2 + 48n − 1,080 = 0

Factor out the GCF, which is 8:

8n2 + 48n − 1,080 = 0

8(n2 + 6n − 135) = 0

Divide both sides of the equation by 8:

n2 + 6n − 135 = 0

Compare the equation with the standard form ax2 + bx + c = 0, and get a, b, and c:

a = 1, b = 6, c = -135

The leading coefficient of the equation is 1. So, find two numbers that have a sum of 6 and a product of -135:

6 = -9 + 15

-135 = -9 • 15

The two numbers are -9 and 15. Use the two numbers to write the factors of the quadratic expression:

(n − 9)(n + 15) = 0

Use the zero product property, and solve for n:

n − 9 = 0 or n + 15 = 0

n = 9 or n = -15

There are two solutions for n. But since n represents the width of the helmet box, it can’t be negative. Therefore, the only reasonable solution is n = 9

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