What are the domain and range of g of x equals the square root of the quantity x plus 4?
D: [4, ∞) and R: [0, ∞)
D: (–4, ∞) and R: (–∞, 0)
D: [–4, ∞) and R: [0, ∞)
D: (4, ∞) and R: (–∞, 0)
Using it's concept, it is found that the domain and range of the function are given by:
D: [–4, ∞) and R: [0, ∞)
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In this problem, the function is:
[tex]g(x) = \sqrt{x + 4}[/tex]
The square root function does not exist for negative values, hence the domain is represented by:
[tex]x + 4 \geq 0 \rightarrow x \geq -4[/tex]
The range of the square root function is [tex]x \geq 0[/tex], which remains the same as there are no vertical translations.
Hence the correct option is given by:
D: [–4, ∞) and R: [0, ∞)
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Answer: C) D: [–4, ∞) and R: [0, ∞)
Step-by-step explanation:
Which of the following quadratics will have a maximum value at x = 3?
(1) y = x² - 6x +19
(3) y=-2x² + 20x - 49
(2) y=-4x² +24x-21
(4) y = 2x² – 3x+7
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{y = x^2 - 6x + 19}\\\mathsf{y = 6^2 - 6(3) + 19}\\\mathsf{y = 36 - 18 + 19}\\\mathsf{y = 18 + 19}\\\mathsf{y = 37}[/tex]
~~~~~~~~~~~~~~~~~
[tex]\mathsf{y = -2x^2 + 20x - 49}\\\mathsf{y = -2(3)^2 + 20(3) - 49}\\\mathsf{y = -2(9) + 60 - 49}\\\mathsf{y = -18 + 60 - 49}\\\mathsf{y = 42 - 49}\\\mathsf{y = -7}[/tex]
~~~~~~~~~~~~~~~~~~~~~
[tex]\mathsf{y = -4x^2 + 24x - 21}\\\mathsf{y = -4(3)^2 + 24(3) - 21}\\\mathsf{y = -4(9) + 72 - 21}\\\mathsf{y = -36 + 72 - 21}\\\mathsf{y = 36 - 21}\\\mathsf{y = 15}[/tex]
~~~~~~~~~~~~~~~~~~~~~
[tex]\mathsf{y = 2x^2 - 3x + 7}\\\mathsf{y = 2(3)^2 - 3(3) + 7}\\\mathsf{y = 2(9) - 9 + 7}\\\mathsf{y = 18 - 9 + 7}\\\mathsf{y = 9 + 7}\\\mathsf{y = 16}[/tex]
~~~~~~~~~~~~~~~~~~~~
[tex]\large\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
hello please help me with this
Answer:
physical contact needed
Step-by-step explanation:
need to see you
How can I write a model of a function in a linear relationship? No links or I will report you! The best explanation and answer gets Brainliest!
Answer:
build linear model
When modeling scenarios with linear functions and solving problems involving quantities with a constant rate of change, we typically follow the same problem solving strategies that we would use for any type of function.
fitting linear models to data
A professor is attempting to identify trends among final exam scores. His class has a mixture of students, so he wonders if there is any relationship between age and final exam scores. One way for him to analyze the scores is by creating a diagram that relates the age of each student to the exam score received.
distinguish between linear and nonlinear relations
As we saw in the cricket-chirp example, some data exhibit strong linear trends, but other data, like the final exam scores plotted by age, are clearly nonlinear. Most calculators and computer software can also provide us with the correlation coefficient, which is a measure of how closely the line fits the data.
use a linear model to make predictions
Once we determine that a set of data is linear using the correlation coefficient, we can use the regression line to make predictions. As we learned previously, a regression line is a line that is closest to the data in the scatter plot, which means that only one such line is a best fit for the data.
key concepts
1. Scatter plots show the relationship between two sets of data.
2. Scatter plots may represent linear or non-linear models.
3. The line of best fit may be estimated or calculated using a calculator or statistical software.
4. Interpolation can be used to predict values inside the domain and range of the data, whereas extrapolation can be used to predict values outside the domain and range of the data.
glossary
correlation coefficient
1. a value, r, between –1 and 1 that indicates the degree of linear correlation of variables or how closely a regression line fits a data set.
extrapolation
1. predicting a value outside the domain and range of the data
Step-by-step explanation:
A triangle has side lengths of (5h – 4k) centimeters, (10h + 7m) centimeters, and
(5m – 2k) centimeters. which expression represents the perimeter, in centimeters,
of the triangle?
A mathematical expression which best represents the perimeter of this triangle is (15h - 6k + 12m) centimeters.
Given the following data:
Length A = (5h – 4k) centimeters
Length B = (10h + 7m) centimeters
Length C = (5m – 2k) centimeters.
What is a triangle?A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
How to calculate the perimeter of a triangle.Mathematically, the perimeter of a triangle is given by this formula:
[tex]P=A+B+C[/tex]
Where:
A, B, and C are length of sides.Substituting the given parameters into the formula, we have;
[tex]P=(5h - 4k) +(10h + 7m) +(5m - 2k)\\\\P=5h+10h-4k-2k+7m+5m\\\\P=(15h-6k+12m)\;centimeters[/tex]
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At which point would the graphs of the equations below intersect?
{
3
x
−
4
y
=
−
2
−
6
x
+
5
y
=
7
3x-4y = -2 -6x+5y = 7
A.
(
−
2
,
−
1
)
(
-
2
,
-
1
)
B.
(
2
,
−
1
)
(
2
,
-
1
)
C.
(
−
1
,
2
)
(
-
1
,
2
)
D.
(
−
1
,
−
2
)
Answer:
can't explain without you arranging your mathematical expression
Dillon buys a hand bag priced at $33. Shipping and handling are an additional 30% of the price. How much shipping and handling will Dillon pay?
Answer:
$10.89 should be your answer
Given that lines b and c are parallel, select all that apply.
Which angles are congruent to 3?
4
7
2
6
Answer:
Angles 7, 2, and 6
Step-by-step explanation:
Angle 7 is congruent by corresponding angles to angle 3.
Angle 2 is congruent by vertical angles to angle 3.
Angle 6 is congruent by vertical angles to angle 7, which is congruent to angle 3, so angle 3 and angle 6 must also be congruent.
Answer:
7,2,6
Step-by-step explanation:
Suppose the demand d, in units sold, for a company's jeans at price x, in dollars, is d(x)=800−4x.
A. If revenue=price×demand, write the rule for the function r(x), which represents the company's expected revenue in jean sales. Then state the domain of this function.
B. If the price is $30, how much revenue will the company earn?
A. The rule for the function r(x) is r(x)=
Answer:
Sorry let me try to understand the question
Step-by-step explanation:
The domain of the function r(x) is (0, 200).
The revenue earned when the price is $30 is $20400.
The rule for the function r(x) is x(800 - 4x).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Demand:
d(x) = 800 - 4x
Price = x
Revenue = Price x demand
Revenue = r(x)
A)
The rule for r(x).
r(x) = x d(x) = x(800 - 4x)
The domain of r(x) is 0 < x < 200 i.e (0, 200).
B)
x = 30
r(x) = 30(800 - 4 x 30)
r(x) = 30(800 - 120) = 30 x 680 = 20400
C)
r(x) = x(800 - 4x)
Thus,
The answers are given above.
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The top-grossing movies last year were Movie A with $700 million, Movie B with $680 million, Movie C with $610
million, and Movie D with $420 million. Suppose we randomly selected 2 of the movies. Fill in all of the means that
are not already provided in the table?
The maximum and the least grossing movies are the combinations of movies A & B and movies C & D, respectively
How to determine the maximum and the least amounts?The grossing amounts are given as:
Movie A = $700 millionMovie B = $680 millionMovie C = $610 millionMovie D = $420 millionThe selection of two movies could be any of the following selections
Selection = AB, AC, AD, BC, BD, and CD
The gross of each selection is:
AB = $700 million + $680 million = $1.38 billion
AC = $700 million + $610 million = $1.31 billion
AB = $700 million + $420 million = $1.12 billion
BC = $680 million + $610 million = $1.29 billion
BD = $680 million + $420 million = $1.10 billion
CD = $610 million + $420 million = $1.03 billion
In the above computation, the maximum and the least gross amounts are:
AB = $1.38 billion
CD = $1.03 billion
Hence, the maximum and the least grossing movies are the combinations of movies A & B and movies C & D, respectively
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Answer:
mean of A, C = 655
mean of B, C = 645
mean of C, D = 515
Step-by-step explanation:
you just take whatever the 2 numbers are (for A, B, C, D) and find the mean between them both,, also correct on edge
Find the geometric mean of 3 and 13. Show work
Answer:
b
Step-by-step explanation:
a/b=c/d
ad=bc
3/x=x/13
3*13=x*x
√39=√x2
6.244997998398=x
A triangle has sides that measure 2 units, 5 units, and 5. 39 units. What is the area of a circle with a circumference that equals the perimeter of the triangle? Use 3. 14 for π, and round your answer to the nearest whole number. 39 units2 25 units2 49 units2 12 units2.
The circumference of the circle is equal to the perimeter of the triangle, then the area of the circle is 12 square units. Option D is correct.
What is a circle?It is a locus of a point drawn equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
A triangle has sides that measure 2 units, 5 units, and 5.39 units.
The circumference of the circle is equal to the perimeter of the triangle. Then the radius of the circle will be
[tex]2 \pi r = 5 + 2 +5.39\\\\r = 1.97[/tex]
Then the area of the circle will be
[tex]\rm Area \ of \ circle = \pi r^2\\\\Area \ of \ circle = \pi 1.97^2\\\\Area \ of \ circle = 12.21 \approx 12[/tex]
The area of the circle is 12 square units.
More about the circle link is given below.
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What is another way to write 3x+9y=-8 to get exactly one solution
Answer:
Step-by-step explanation:
Slope = -0.667/2.000 = -0.333
x-intercept = 8/3 = 2.66667
y-intercept = 8/9 = 0.88889
Answer:
Step-by-step explanation:
Nasrin invested $6000 in a bond at a yearly rate of 3%. She earned $450 in interest. How long was the money invested?
someone help please
Steps to finding the line in the diagram with the format 'ax + by = c
1. Find the slope
To find the slope, we need any two points on the line --> (0,4) and (3,0)[tex]Slope = \frac{y2-y1}{x2-x1} =\frac{4-0}{0-3} =-\frac{4}{3}[/tex]
2. Set up, with any one point on the line and the slope, in point-slope form
[tex](y-y0)=m(x-x0)\\(y-4)=-\frac{4}{3} (x-0)\\y-4 = -\frac{4}{3} x\\\frac{4}{3}x+y = 4[/tex]
Answer: [tex]\frac{4}{3}x+y = 4[/tex]
Hope that helps!
Answer:
[tex]\sf 4x+3y=12[/tex]
Step-by-step explanation:
Choose two points on the line:
Let [tex]\sf (x_1,y_1)=(0,4)[/tex]
Let [tex]\sf (x_2,y_2)=(3,0)[/tex]
Use the slope formula to find the slope of the line:
[tex]\sf slope(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-4}{3-0}=-\dfrac43[/tex]
Use the point-slope formula to find the equation of the line:
[tex]\sf y-y_1=m(x-x_1)[/tex]
Substitute values into the formula:
[tex]\sf y-4=-\dfrac43(x-0)[/tex]
Expand the brackets:
[tex]\sf y-4=-\dfrac43x[/tex]
Add 4 to both sides:
[tex]\sf y=-\dfrac43x+4[/tex]
Rearrange into the form [tex]ax+by=c[/tex]
Multiply both sides by 3
[tex]\sf 3y=-4x+12[/tex]
Add 4x to both sides:
[tex]\sf 4x+3y=12[/tex]
Find the solution of the system of equations.
8x – 2y = -30
–9x + 4y = 18
Step-by-step explanation:
8x – 2y = -30 } ×2
16x - 4y = -60
–9x + 4y = 18
___________
7x=-42
x=-6
8(-6)-2y=-30
-2y=-18
y=9
Answer:
(-6,-9)
Step-by-step explanation:
The quickest way is to solve with elimination. Multiply the top equation by 2.
2(8x – 2y = -30)
16x-4y=-60
16x-4y=-60
–9x + 4y = 18
7x=-42
x=-6
8x – 2y = -30
8(-6) – 2y = -30
-48-2y=-30
-2y=18
y=-9
y- 1) The value, y, of a car x years after it is purchased is modeled by the function exponential function y = f(x), whose graph is shown above Which statement about the car's value is true? A) Its initial value is B + A, and it will fall to a value of B B) its initial value is A, and it will fall to a value of B C) Its initial value is A and it will fall to a value of A-B
Given the exponential function y = f(x), a is the initial value and it will fall to a value of B
What is an exponential function?
An exponential function is given by:
y = abˣ
Where a is the initial value of y and b is the multiplication factor.
The value, y, of a car x years after it is purchased is modeled by the exponential function y = f(x), a is the initial value and it will fall to a value of B
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40.quadrilateral efgh was translated 3 units to the left and 8 units up to create quadrilateral e' f'g'h'. which
rule describes this transformation
Answer:
translation
Step-by-step explanation:
What is the volume of this figure? Enter your answer in the box. ft³
Answer:
75 ft³ for K12
mia draws a cone with a height of 9 inchess and a radius of 4 inches
The volume of the cone that was drawn by Mia is equal to 150.816 cubic inches.
How to calculate the volume of a cone.
Mathematically, the volume of a cone is given by this formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Where:
h is the height.r is the radius.Given the following data:
Radius of cone = 4 inches.
Height of cone = 9 inches.
Substituting the given parameters into the formula, we have;
Volume = 1/3 × 3.142 × 4² × 9
Volume = 3.142 × 16 × 3
Volume = 150.816 in³
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Select all the ways below that correctly describe the ratio of bananas to monkeys in this picture: There’s 4 monkeys and 5 bananas.
1. 4 to 5
2. 5 to 4
3. 4:5
4. 5:4
5. 4/5
6. 5/4
7. 4.5
8. 5.4
(I seriously need help with this, I don’t know how to use Brainly but I hope this works.)
The center of the sphere is C and its circumference is 7pi centimeters.
Find the radius of the sphere. Find the diameter of the sphere.
Answer:
384800 square centimeters (cm²); 3.848 × 107 square millimeters (mm²); 1.48572E-5 square miles (mi²); 46.0217 square yards (yd²)
Step-by-step explanation:
is this correct if not whats the answer
Answer:
That answer is correct, when you do a survey, you pick people at random! So your answer is correct. :) If you have any more questions feel free to ask me. ^-^
The blue dot is at what value on the number line?
Answer:
17
Step-by-step explanation:
✌
What value of c makes the polynomial below a perfect square?
Answer:
B
Step-by-step explanation:
x² + 9x
to complete the square
add ( half the coefficient of the x- term )² to x² + 9x
= x² + 2([tex]\frac{9}{2}[/tex] )x + ([tex]\frac{9}{2}[/tex] )²
= x² + 9x + [tex]\frac{81}{4}[/tex] ← the value of c
= (x + [tex]\frac{9}{2}[/tex] )² ← a perfect square
Find the domain over which the function y = x^2 +6x is mono tonic increasing. Please help
Answer:
x > -3
Step-by-step explanation:
The function will be increasing where its derivative is positive.
__
y = x^2 +6x . . . . . given function
y' = 2x +6 . . . . . . . derivative
The derivative is positive for ...
2x +6 > 0
2x > -6
x > -3 . . . . . domain where the function is increasing
If we want to know if diagonals or sides are congruent we would use the
formula.
distance
midpoint
slope
When we want to know if the diagonals or sides are congruent we would use the D. Slope.
What is congruent?It should be noted that congruent in geometry simply means when two objects have same shapes and size.
In this case, when we want to know if the diagonals or sides are congruent we would use the slope. This can show the equality in the shape.
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A scale drawing of a house is 2:9. If the length of the actual kitchen is 18 feet, how long was it in the drawing?
Answer: 4:18
Work:
2:9
2 inch:9 feet
2 · 9 = 18
2 · 2 = 4
4 inch:18 feet
Examine this right triangle. A right triangle has a side length of 16 meters and hypotenuse of 20 meters. Which equation can be used to find the missing leg in the triangle? a2 202 = 162 202 162 = a2 a2 162 =202 16 a2 = 20.
The equation can be used to find the missing leg in the triangle [tex]20^{2} = 16^{2} +a^{2}[/tex].
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.
It is given that a right triangle has a side length of 16 meters and a hypotenuse of 20 meters.
From a Pythagoras theorem
[tex]b^{2} = c^{2} +a^{2} \\20^{2} = 16^{2} +a^{2}\\20^{2}-16^{2} =a^{2}\\a^{2} = 20^{2}-16^{2} \\[/tex]
Thus, the equation can be used to find the missing leg in the triangle [tex]20^{2}-16^{2} =a^{2}[/tex].
Learn more about the right-angle triangle;
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Answer:
Its C
a2 + 162 =202
Step-by-step explanation:
Solve the equation and enter the value of x below.
6x + 7 = 43
X =
6x + 7 = 43
6x + 7 - 7 = 43 - 7
6x = 36
x = 36/6
x = 6
check
6 * 6 + 7 = 36 + 7 = 43
Answer:
x=6
Step-by-step explanation:
6x+7=43
6x=43-7
6x=36
6x/6=36/6
x=6
hope dis helps!!!!!