The graph of g(x) is shifted vertically by 5 units below the graph of f(x). The graph of g(x) is shifted horizontally by 5 units to the left of the graph of f(x)
What can be concluded about the graph of g(x)?Given: f(x) = 2x and g(x) = f(x + k). If k = -5
Subtituting k = -5, we have:
g(x) = f(x -5) = 2(x-5)
The graph of g(x) is shifted vertically by 5 units below the graph of f(x)
The graph of g(x) is shifted horizontally by 5 units to the left of the graph of f(x)
To see this, we can consider the value of x = 0 for both functions. For f(x), f(0) = 20 = 0. For g(x), g(0) = f(-5) = 2(-5) = -10. Thus, the value of g(0) is 5 units below the value of f(0).
Similarly, the value of x = 5 for f(x) is f(5) = 25 = 10, while the value of x = 0 for g(x) is g(0) = f(-5) = 2(-5) = -10. Thus, the value of x = 5 for f(x) is 5 units to the right of the value of x = 0 for g(x).
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Fatimah ate f cookies. Satvinder ate six fewer than two times the number that Fatimah ate. If Satvinder ate 4 cookies, write and solve an equation to find f, the number of cookies Fatimah ate.
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Fatimah ate f treats. Satvinder ate six less than twice the number that Fatimah ate.
Let 's' be the number of cookies eaten by Satvinder. Then the equation is given as,
s = 2f - 6
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be given as,
4 = 2f - 6
2f = 10
f = 5
On the off chance that Satvinder ate 4 treats, the number of treats that Fatimah ate will be 5.
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21. Is the following ordered pair (3, 6) a solution of the linear inequality y < -5x + 1?
The pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
What is linear inequality?
A linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
y < -5x + 1
Substitute the points and see if they are true
(3, 6)
6 < -5*(3) + 1
6 < -15 + 1
6 < -14
Not true not a solution
Hence, the pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
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Given the Trapezoid, BATS, where B (-4, 2), A (-2, 6), T (6, 6), S (8, 2). Graph and find the approximate area of BATS.
The graph of the trapezoid is shown below. The area is calculated as: D. 40 square units.
How to Find the Area of a Trapezoid?To find the area of a trapezoid, the formula used is given below:
Area of a trapezoid = 1/2 * (a + b) * h, where,
a = length of one of the basesb = length of one baseh = height of the trapezoid.The trapezoid BATS with the following vertices, B (-4, 2), A (-2, 6), T (6, 6), S (8, 2), ahs been plotted in the graph shown in the image attached below.
1 unit = 1 box, therefore, we have the following:
a = length of AT = 8 units.
b = length of BS = 12 units
h = 4 units
Plug in the values:
Area of trapezoid BATS = 1/2 * (8 + 12) * 4
Area of trapezoid BATS = 1/2 * (20) * 4
= 10 * 4
Area of trapezoid BATS = 40 square units.
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1. Simplify the following expressions:
10
a. 2¹⁰.2
-4
Answer:1020.2
Step-by-step explanation:
2) the labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. the bls reported in february 2012 that the labor force participation rate in the united states was 66.9% (calculatedrisk). a marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. what are the expected value and the standard error for a labor participation rate in the company's sample?
The expected value and the standard error for a labor participation rate in the company's sample is 0.0043
In the given question, the labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.
The BLS reported in February 2012 that the labor force participation rate in the united states was 66.9% (calculate risk).
A marketing company asks 120 working-age people if they either have a job or are looking for a job, or the labor force.
We have to find the expected value and the standard error for a labor participation rate in the company's sample.
Working age people sample n = 120
The labor force participation rate in the United States was 66.9% = 0.669
The Expected value is μ = p = 0.669
The standard error:
SE = √p(1-p)/n
SE = √0.669(1-0.669)/120
SE = √0.669*0.331/120
SE = √0.2214/120
SE = √0.001845
SE = 0.043
Hence, the expected value and the standard error for a labor participation rate in the company's sample is 0.0043.
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Find the y intercept y = – 17 x + 12.
Answer: 12
Step-by-step explanation:
The y-intercept in the equation that is in slope-intercept form is the constant.
What is the radius of the circumscribed circle of ABC?
Answer:
Given: △ABC, m∠A=120°, AB=AC=1 Find: The radius of circumscribed circle
Step-by-step explanation:
:]
The temperature cooled by 4° on the firt day of the year together on the 1t 2 day of the year the temperature heated up 7°
Answer:
If the temperature cooled by 4° on the first day of the year, and then heated up 7° on the second day, the net change in temperature would be a 3° increase. This means that the temperature increased by a total of 3° over the two days.
Step-by-step explanation:
On the first day of the year, the temperature starts at a certain degree (let's call it X).
On the same day, the temperature cools by 4°. This means that the temperature becomes X - 4°.
On the second day of the year, the temperature starts at X - 4° (the temperature from the previous day).
On the second day, the temperature heats up by 7°. This means that the temperature becomes (X - 4°) + 7° = X + 3°.
The net change in temperature over the two days is X + 3° - X = 3°.
I hope this helps to clarify the example! Let me know if you have any further questions.
2x+3forx=3
show work
Answer:
9
just sub value of x into the equation
(2x3)+3
6+3
9
When Lisa increased her speed in letter c,
the increase took two seconds. What was her acceleration?
Lisa's change in speed is 4 miles per hour.Lisa's acceleration is 2 miles per hour.
What was her acceleration?According to the question,
The speed of Lisa is = 3 miles per hour
A dog starts to chase her, and she speeds up to seven miles per hour.
The change in speed after dog chase her is,
= 7 miles per hour - 3 miles per hour
= 4 miles per hour
Lisa's change in speed is 4 miles per hour.
When Lisa increased her speed in letter c, the increase took two seconds.
Then,
The Lisa acceleration is,
Acceleration = Change in speed/Change in time
Acceleration = 4/2
Acceleration = 2 per mail.
Hence, Lisa's acceleration is 2 miles per hour.
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Explain how to solve 2^(x + 1) = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth
The solution of the given expression is equal to 2.17.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is [tex]2^{x+1} = 9[/tex]. The expression will be solved by using the logarithmic property below,
[tex]2^{x+1}=9[/tex]
Take logs on both sides,
(x+1) ln(2) = ln(9)
(x+1) = ln(9) / ln(2)
x + 1 = 3.17
x = 2.17
Hence, the expression will be solved by taking log on both sides.
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a study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. one hundred participants are recruited to participate, and half are randomly assigned to participate in the intervention while the others serve as a control group. what study design is being used?
A study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. The study design being used is a randomized controlled trial (RCT).
What is a randomized controlled trial?Generally, In an RCT, the study participants are randomly assigned to either the intervention group or the control group. This helps to ensure that any differences between the two groups are not due to preexisting differences between them, but rather are due to the intervention being tested.
In this case, the intervention is a daily exercise intervention, and the outcome being measured is blood pressure among people with pre-hypertension.
The control group serves as a comparison group, and any changes in blood pressure observed in the intervention group can be attributed to the intervention rather than other factors.
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Which polynomial is prime?
O x² +7
Ox²-25
O3x²-27
O 2x²-8
Explanation:
All of the polynomials listed are quadratic polynomials, which have the general form ax^2 + bx + c, where a, b, and c are constants and x is a variable. A polynomial is considered prime if it cannot be factored into the product of two or more polynomials with integer coefficients.It is not possible to determine whether any of the given polynomials are prime without further information, such as the values of the constants a, b, and c. For example, the polynomial x^2 + 7 could be prime, but it could also be factored into the product of two linear polynomials (x + 3)(x + 3), which would make it composite. Similarly, the polynomial x^2 - 25 could be prime, but it could also be factored into the product of two polynomials of the form (x + 5)(x - 5), which would make it composite. Without more information, it is not possible to determine whether any of the given polynomials are prime.
Which equation, when paired with y = 2x 5, creates an inconsistent system? 2x y = 5 y = 2x 5 2x – 4y = 10 2y – 4x = –10
The equation that creases an inconsistent system when paired with y = 2x + 5 is given as follows:
2y - 4x = -10.
What is an inconsistent system?A system of equations is called inconsistent when the number of equations of the system is of zero.
The system in this problem is composed by linear equations, which have the following format:
y = mx + b.
In which:
m is the slope.b is the y-intercept.For inconsistent system, we have that the equations:
Have the same slope.Have different intercepts.The function in this problem is given as follows:
y = 2x + 5.
Hence the inconsistent system is formed with:
2y - 4x = -10.
Which is simplified by 2 as follows:
y - 2x = -5.
y = 2x - 5.
Having the same slope of 2, but a different intercept.
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Answer: 2y – 4x = –10
Step-by-step explanation: trust.
please help almost done with this thing. also, will mark brainliest for the best answer
The functions for this problem are classified as follows:
Land: Linear function.Car: Linear function.How to classify a function as exponential or linear?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
For the land function, the rates are given as follows:
36.9/30 = 1.23.44.1/36.9 = 1.20.51.1/44.1 = 1.16.58.1/51.1 = 1.14.The differences are given as follows:
36.9 - 30 = 6.9.44.1 - 36.9 = 7.2.51.1 - 44.1 = 7.58.1 - 51.1 = 7.Neither are exactly the same, however the variations for the differences are less, meaning that it can be classified as a linear function.
For the car, the rates are given as follows:
12.1/9 = 1.344.15/12.1 = 1.24.17.9/15 = 1.19.20.9/17.9 = 1.17.The differences are given as follows:
12.1 - 9 = 3.1.15 - 12.1 = 2.9.17.9 - 15 = 2.9.20.9 - 17.9 = 3.Again less change on the differences, hence also linear.
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If f(x) = x2, g(x) = 5x, and h(x) = x + 4, find each value. 17. f[g(–2)]
a. 7 b. 10 c. 30 d. 100
Answer:
d.) 100
Step-by-step explanation:
To solve, first find the value of g(-2):
[tex]g(-2)=5(-2)\\g(-2)=-10[/tex]
Next, use this value to find f(-10):
[tex]f(-10)=(-10)^2\\f(-10)=100[/tex]
find the slope of the line that passes Through the points (2.5, 1) and (1,-3.5)
Answer:
3
Step-by-step explanation:
slope m = (y - y1)/(x - x1)
m = (-3.5 - 1)/(1 - 2.5) = (-4.5)/(-1.5) = 3
A study shows that 70% of the population of a city have brown eyes and 30% do not. The study also shows that 10% of the people who do not have brown eyes do
not have brown hair, while 80% of the people who have brown eyes have brown hair. A relative frequency table was constructed for this data. What is the largest
marginal relative frequency and its interpretation?
A. 0.56; Individuals with brown eyes
B. 0.70; Individuals with brown eyes
C. 0.80; Individuals with brown hair
D. 0.83; Individuals with brown hair
A study shows that 70% of the population of a city have brown eyes and 30% do not. The study also shows that 10% of the people who do not have brown eyes do not have brown hair, while 80% of the people who have brown eyes have brown hair. 0.80; Individuals with brown hair. Option C
What is the marginal relative frequency?Generally, The largest marginal relative frequency is 0.80, which corresponds to individuals with brown hair. This means that out of all the individuals in the city, 80% of them have brown hair.
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7x+14y=21,-7x+7y=7 using elimation
Answer:(x,y)=(1/3 , 4/3)
Step-by-step explanation:
The formula for the volume of a cylinder is V=\pi r^2 h,V=πr
2
h, where rr is the radius of the cylinder and hh is the height of the cylinder. Rewrite the formula to solve for hh in terms of rr and V.V.
The formula to solve for height(h) is given as, if the volume of the cylinder is, V = π r² h, is h = V / π r².
What is volume?An object's volume is a measurement of the amount of space it occupies in three dimensions. This indicates that an elephant's volume is more than a mosquito's volume.
Given:
V = π r² h
Here, r is the radius of the cylinder, V is the volume, and h is the height of the cylinder. The value of π is 3.14.
Take the remaining term of the right side to the left as shown below,
V / π r² = h
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for what values of x and y are the triangles congruent by HL?
For the given congruent triangles, the values of x = -1 and y = 3.
What do you mean by congruence of triangle?Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.
The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.
3y + x = y + 5 ...........(1)
y - x = x + 5 ..............(2)
Equation
1:3y + x = y + 5
3y - y = 5 - x
2y = 5 - x
x = 5 - 2y ..............(3)
Substitute this value of x in equation (2)
y - x = x + 5 y = x + x + 5y
= 2x + 5 y = 2(5 - 2y) + 5y
= 10 - 4y + 54y + y = 15
5y = 15 y = 15/ 5
y = 3
Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1
Therefore, x = -1 and y = 3
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suppose a juice box contains 30% juice with the remaining portion of the drink composed of water. what is the solute in this type of juice box?
Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.
Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.
Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.
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Kim and her friends watched the server making smoothies. The table shows the number of mango's that were used for each of the different sizes of smoothies that the friends ordered.
Mango Used Smoothie Size
Kim 1 8 oz
Bri 3 24 oz
Angela 4 32 oz
Which statement is correct based on the data?
The statement that is correct based on the data is that the table shows a proportional relationship
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Mango Used Smoothie Size
Kim 1 8 oz
Bri 3 24 oz
Angela 4 32 oz
Express properly
So, we have
Mango Used Smoothie Size
Kim 1 8 oz
Bri 3 24 oz
Angela 4 32 oz
Start by checking if the table has a constant rate
This is represented as
Constant rate = Smoothie Size/Mango Used
So, we have
Constant rate = 8/1 = 8
Constant rate = 24/3 = 8
Constant rate = 32/4 = 8
See that the constant rate is the same for all values
Hence, the table shows a proportional relationship
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Please help with this
Answer:
1. x = {-3, 3}
2. a = {-12, -2}
3. v = {-7, 10}
4. m = {-8, 8}
5. k = {-11, 1}
6. y = {-13, 19}
Step-by-step explanation:
|-2x| = 6
means that
-2x = 6 or -2x = -6
x = -3 or x = 3
|a + 7| = 5
means that
a + 7 = 5 or a + 7 = -5
a = -2 or a = -12
|8v-12| = 68
means that
8v-12 = 68 or 8v-12 = -68
8v = 80 or 8v = -56
v = 10 or v = -7
| m / -4 | + 1 = 3
| m / -4 | = 2
means that
m/-4 = 2 or m/-4 = -2
m = -8 or m = 8
3|k + 5| = 18
|k+5| = 6
means that
k + 5 = 6 or k + 5 = -6
k = 1 or k = -11
|2y - 6| / 4 = 8
|2y - 6| = 32
means that
2y - 6 = 32 or 2y - 6 = -32
y = 19 or m = -13
Justin is going to invest $90,000 and leave it in an account for 19 years. Assuming
the interest is compounded quarterly, what interest rate, to the nearest hundredth of
a percent, would be required in order for Justin to end up with $216,000?
Answer:
4.63%
Step-by-step explanation:
You want the interest rate that, compounded quarterly, will result in a balance of $216,000 for an investment of $90,000 after 19 years.
Compound interestThe formula for the balance of an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.
ApplicationFilling in the given values, we can solve for r:
216000 = 90000(1 +r/4)^(4·19)
2.4 = (1 + r/4)^76 . . . . . divide by 90,000
2.4^(1/76) = 1 +r/4 . . . . . . take the 76th root
(2.4^(1/76) -1) = r/4 . . . . . . subtract 1
r = 4(2.4^(1/76) -1) ≈ 0.0463437 ≈ 4.63%
The required interest rate is about 4.63%.
A sporting goods manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set $327. Find the original selling price of the ski set.
The original selling price of the ski is $385.
How to calculate the price?From the information, the sporting goods manager was selling a ski set for a certain price. The manager offered the markdowns as 15% making the one-day sale price of the ski set $327.
Let the original selling price of the ski be x.
This will be:
x - (15% × x) = 327
0.85x = 327
Divide
x = 327 / 0.85
x = 385
The original price is $385.
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Complete question
A sporting goods manager was selling a ski set for a certain price. The manager offered the markdowns as 15% making the one-day sale price of the ski set $327. Find the original selling price of the ski set.
solve the system by graphing y=-x+10 y=x+8
Answer:
Step-by-step explanation:
I graphed this system on Desmos because it's easier. The solution they have (the intersection- the point where they both touch at the same time-) is at point (1,9) ...
Can you help me please???
Which expressions are equivalent to (3w - 4x)4? Select TWO correct responses.
A. 4(-1wx)
B. 12 w -16 x
C. 7w -8x
D. -16 x +12w
Pick 2
Calculate the area of a cylinder with a diameter of 14 and a height of 20.
Answer:
The answer is 2990.8
Step-by-step explanation:
Answer:
volume = 980π = 3078.790801
Step-by-step explanation:
14 ÷ 2 = 7 = radius
π x [tex]r^{2}[/tex]= = 49π = area
area x 20 = volume
volume = 980π = 3078.790801
Deposited (dollars)
12,500
10,000
7,500
$5,000
rate of change=
2,500 initial value=
Time (years)
y
dollars per year
dollars
The rate of change is $2500 per year.
The initial amount is $5000.
What is slope?The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.
The formula for slope between two points (x₁, y₁) and (x₂, y₂) is,
m = (y₂ - y₁)/(x₂ - x₁)
In the given graph,
The initial value that deposited at x = 0 is $5000.
To find the rate of change in amount per year,
Find slope of the line, because rate of change will be equal to slope.
Let two points are (0, 5000) and (1, 7500)
The slope = (7500 - 5000 / 1 - 0) = 2500
The rate of change is $2500 per year.
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