Answers
Answer:
You're correct the answer is B) [tex]-5 \leq y \leq -1[/tex]
Step-by-step explanation:
The key behind this problem is think about the function [tex]\sqrt[3]{x}[/tex] and think what happen when you plug in values in it.
So we're going to try with some simply values for evaluate
[tex]\sqrt[3]{-8} = -2[/tex]
[tex]\sqrt[3]-1} = -1[/tex]
[tex]\sqrt[3]{0} = 0[/tex]
[tex]\sqrt[3]{1} = 1[/tex]
[tex]\sqrt[3]{8} = 2[/tex]
How you can see when plug in a negative number the function return a negative number, but when you plug in a positive number the function return a positive number (this isn't a proof of this happen in each value of the given interval, but is a good way of demonstrate the relation). This means that when you plug in a value this value is greater than the value of before, so the function is increasing it's outputs.
Now this is good because that's mean that the limits of the range are the limits of the domain evaluates in the function (because the smaller input give us the smaller output and the same with the greater). But the given function have different operation in it, so you have to interpret this operations of this way:
When you have a negative value in the [tex]x[/tex] like in this occasion ([tex]\sqrt[3]{-x}[/tex]) the function reflex it's values with respect to the y axis (image put the functions in a mirror a draw the given image in the same cartesian plane).And you have a -3 this is move each value of the function 3 units down.So with this information you evaluate each limit of the domain [tex]\{-8, 8\}[/tex] in the function and get the limits for the range.
[tex]f(-8) = \sqrt[3]{-(-8)} -3= \sqrt[3]{8} -3 = 2 -3 = -1[/tex]
[tex]f(8) = \sqrt[3]{-8} -3= -2 -3 = -5[/tex]
So the range of the function in the given interval is equal to [tex]\{-1, -5\}[/tex] in the interval notation is equal to [tex]-5 \leq y \leq -1[/tex]
Related Questions
The Cougars, a football team, must gain 10 yards in the next four plays to keep possession of
the ball. The Cougars gain 5 yards, lose 12 yards, gain 14 yards, and finally lose 8 yards. Do
the Cougars keep possession of the ball?
Answers
Answer:
No
Step-by-step explanation:
Gain 5= 5 to go
Lose 12= 7 to go
Gain 14= 7 to go
Lose 8=15 to go
What is the equation of the circle in center - radius form: x² + y2 + 12x - 10y
- 7 = 0?
Answers
Answer:
Radius: √ 61
Step-by-step explanation:
Complete the square for x^ 2 + 12 x = ( x + 6 ) ^2 − 36
Substitute ( x + 6 ) 2 − 36 for x 2 + 12 x in the equation x 2 + y 2 + 12 x − 10 y = 0
= ( x + 6 ) 2 − 36 + y 2 − 10 y = 0
Move − 36 to the right side of the equation by adding 36 to both sides
= ( x + 6 ) 2 + y 2 − 10 y = 0 + 36
Then you know the rest: radius will be √ 61
The center coordinate of the circle is (6,5) with a radius = 7.34
What is the equation of the circle?The equation of the circle is: [tex](x-a)^{2} + (y-b)^{2} = r^{2} x^{2}[/tex]
Substituting the values in the equation:
[tex](x-a)^{2} + (y-b)^{2} = r^{2} x^{2} - 2ax + a^{2} + y^{2} - 2by +b^{2} - r^{2} = 0[/tex]
⇒ -2ax = -12x
⇒ a = 6.
-2by = -10y
b= 5.
⇒ a² + b² - r² = -7
⇒ 6² + 5² + r² = -7
⇒ 36 + 25 + r² = -7
⇒ r² = 54
⇒ r = 7.34
Center coordinate (6,5) with r = 7.34
Learn more about the equation of the circle here: brainly.com/question/1471134
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10 x 9= what is it help
Answers
Answer:
10
[tex]10 \times 9 \\ 90[/tex]
Answer:
90 :)
Step-by-step explanation:
10 x 9 = 90
= 90 is correct answer
(Hope this helps can I pls have brainlist (crown)☺️)
Urgent! At a baseball game, a vender sold a combined total of 241 sodas and hot dogs. The number of sodas sold was 55 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Answers
Answer:
Sodas = 148
Hot dogs = 93
Step-by-step explanation:
Let S and H stand for the number of Sodas and Hot dogs, respectively.
We are told that:
H + S = 241
We are also told that:
S = H + 55
Use the second expression for S (H+55) in the first equation:
H + S = 241
H + (H+55) = 241
2H + 55 = 241
2H = 186
H = 93
Since H = 93,
S = 93+55, or 148
148 + 93 = 241 [Checks]
Sodas = 148
Hot dogs = 93
What’s 568 divided by 7
Answers
568 divided by 7 = 81.14
How many of the following statements are true?
19)
a
d Any set of ordered pairs is a function.
d The domain of a relation is the set containing the first
member of its ordered pairs.
d The independent variable in a relation is the variable
used for the range.
d A function is a relation in which each domain value is
paired with exactly one range value.
A) 1
B) 2
C) 3
D) 4
Answers
Answer:
A) 1
Step-by-step explanation:
yeah-ya,.................. right?
Step by step explanation:yeah…….right
(x + 1)(x + 2)(x + 1)(3x + 2)
Answers
Answer:
Is it the full question I mean what does it want next anyway?
But here's your answer :
3x^4 + 14x^3 + 23x^2 + 16x + 4
Describe and correct the error in rewriting the expression.
6(y+8) = 6y+8
Describe the error:
Correct the error:
Answers
Answer:
error: forgot to distribute 6 to the 8
correction: 6(y+8) = 6y+48
Step-by-step explanation:
in distributive property: you must multiply the number on the outside to both of the numbers in the inside
Can someone please solve question 8
Answers
Answer:
22.84
Step-by-step explanation:
[ASAP] Which graph represents a direct variation?
Answers
(ASAP) helpp i need to get this done 3m
Answers
3(a-4) + 1= 9 - a
3(a-4) = 8 - a
3a-12 = 8 - a
4a = 20
a=5
I hope this helps! :)
Answer:
a=5
Step-by-step explanation:
3(a-4)+1=9-a
3a-12+1=9-a
3a-11=9-a
3a+a=9+11
4a=20
a=20÷4
=5
3. Sally invested $5,000.00 in a savings account earning 3.49% simple interest. At the same time
Jon invested $3,000.00 in a money market account at a simple interest rate of 7.5%. How many
years will it take for the two to have the same amount of money in their accounts? How much
money do they have after that time period?
Answers
Answer:
ic hch7y8gygdr6dr6d7twwt7tfx7yuc yc i
help me with this problem thank youuup.
Answers
Step-by-step explanation:
it is a linear function, if the change in y is constant in relation to the changes of x.
in other words, if the slope y change/x change is the same for every point.
when we look at the table, we see x changes constantly by +2.
and y changes constantly by -6.
so, the change rate/slope is constantly -6/2 = -3.
and therefore it is a linear function.
the equation looks like (the slope is always the factor of x)
y = -3x + b
b we get by using one of the x,y pairs like 1,4
4 = -3×1 + b = -3 + b
b = 7
so, the full equation is
y = -3x + 7
Step-by-step explanation:
Given the table of values, {(-3, 16), (-1, 10), (1, 4), (3, -2), (5, -8)}:
We must determine whether the given relation or data can be modeled by a linear equation. It is necessary to analyze the pattern that exists between changes in y-values, along with the changes in x-values.
X-coordinates:Subtracting the x-coordinates provides a constant difference of 2:
Starting with the first two rows, given by the ordered pairs, (-3, 16) and (-1, 10): Subtract the two x-coordinates: -1 - (-3) = -1 + 3 = 2.For the second and third rows, given by the ordered pairs, (-1, 10) and (1, 4): Subtract the two x-coordinates: 1 - (-1) = 1 + 1 = 2.If you perform these same steps throught the remaining rows, then you'll get the same difference of 2.
Y-coordinates:We can perform the same steps for the y-coordinates. Subtracting the y-coordinates provides a constant difference of -6.
Starting with the first two rows, given by the ordered pairs, (-3, 16) and (-1, 10): Subtract the two y-coordinates: 10 - 16 = -6.For the second and third rows, given by the ordered pairs, (-1, 10) and (1, 4): Subtract the two y-coordinates: 4 - 10 = -6.If you perform these same steps throught the remaining rows, then you'll get the same difference of -6.
SlopeSince the constant change in y = -6, and the constant change in x = 2, then we can calculate for the slope as: Δy/Δx = -6/2 = - 3. Hence, the constant rate of change = -3.
As demonstrated throughout this post, we can infer that there is a linear pattern that exists between the x- and y-values.
Therefore, the data can be modeled by a linear equation because the rate of change is constant.
Linear Equation:In order to establish the linear equation that represents y as a function of x, we can use the slope, m = -3, and one of the given ordered pairs, (1, 4), to solve for the value of the y-intercept, b. Substitute these values into the slope-intercept form, y = mx + b:
y = mx + b
4 = (-3)1 + b
4 = -3 + b
Add 3 to both sides to isolate b:
4 + 3 = -3 + 3 + b
7 = b
Therefore, the linear equation that represents the given data is: y = -3x + 7.
The 66-mm-diameter solid shaft is made of 2014-t6 aluminum and is subjected to the distributed and concentrated torsional loadings shown where t=1. 7 kn⋅m.
Answers
Answer:
bbc
Step-by-step explanation:
Which graph best represents a function with zeros of -2, -1 and 2
Answers
Answer:
D
Step-by-step explanation:
Because if you see the x-intercept you will see function with zeros of -2, -1 and 2
wuts x uwu plssss 10 points
−2/9x+2.7=4
Answers
Answer:
x = -5.85
Step-by-step explanation:
Solve the equation
1) [tex]-\frac{2}{9} x + 2.7 = 4[/tex]
Subtract -2.7 on both sides by doing the inverse operation.
2) [tex]-\frac{2}{9}x = 1.3\\[/tex]
Multiply both sides by -9/2 to cancel out -2/9x, so that you can isolate "x" by itself.
3)[tex]x = -5.85[/tex]
7x+20=7x+20
help asap
step by step please
Answers
Answer:
The given equation is true for all x.
Step-by-step explanation:
6x-7y=7andx-7y=-8 find valve of x and y
Answers
Answer:
x = 3, y = 11/7.
Step-by-step explanation:
6x - 7y = 7
x - 7y = -8 Subtract:
5x = 15
x = 3
3 - 7y = -8
-7y = -11
y = 11/7.
Answer: x = 3 and y = 11/7
Step-by-step explanation: 6x-7y+(-6x) = 7+(-6x) -7y/-7 = -6x+7/-7 y = 6/7x-1 x-7 (6/7 (x) -1) = -8 -5x+7+(-7) = -8+(-7) -5x/-5 = -15/-5 x = 3 y = 6/7x-1 y = (6/7) (3) -1 y = 18/7-1 18/7-1/1 18/7-7/7 y= 11/7 x = 3 and y = 11/7
A 9-ounce can of peaches sells for $1.26. Find the unit price.
Answers
Answer:
0.14 per ounce
Step-by-step explanation:
1.26 ÷ 9= 0.14
Hope this helps! :)
The unit price of peach would be $0.14.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a 9-ounce can of peaches sells for $1.26.
9-ounce can of peaches sells for $1.26.
Then -
1 ounce of peach will cost = (1.26/9) = $0.14
Therefore, the unit price of peach would be $0.14.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
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taxi Cab Company B: $6.50 per ride and $0.50 per mile
Express in the table the cost of the cab ride given the number of miles. Hint: Fill in the table above using cost for company B.
Write an equation in slope-intercept form to represent the cost of a taxi ride using company B. Hint: use y= mx+b
Y = __________________
What does the slope mean in the context of this problem?
Hint: What changes the further you ride?
Answers
Using the slope - intercept relation, the equation which represents the cost of cab ride is y = 0.5x + 6.50
Cost per ride = $6.50Cost per mile = $0.50Using the slope - intercept relation :
y = bx + cb = change in cost per mile
c = constant price added for every taxi ride
Hence, the expression can be written thus :
y = 0.5x + 6.50Learn more : https://brainly.com/question/17225268
Help me with math!!!!
Answers
Answer:
-4
Step-by-step explanation:
so t is greater than -5, and for negatives, you need to get nearer zero.
pls help me out
4x - 10 = -6
Answers
Answer: x = 1
Step-by-step explanation:
Answer:
The value of x is 1
Step-by-step explanation:
4x - 10 = -6
Use APE or Additive Property of Equality
4x = 10 - 6
4x = 4
Use DPE or Division Property of Equality
4x/4 = 4/4
x = 1
Substitute it to the equation to check
4x - 10 = -6
4(1) - 10 = -6
4 - 10 = -6
-6 = -6
If a triangle has a base of 6 feet and a height of 5 feet, what is the area?
Answers
Answer:
15 square feet
Step-by-step explanation:
a = (1/2)bh
a = (1/2) * 6 * 5
a = 3 * 5
a = 15
15 square feet
how long is the Yangtze river
Answers
Answer:
3,915 mi
Step-by-step explanation:
You are 5 feet tall and cast an 8-foot shadow. A lamppost nearby casts a shadow that is 20 feet. Which equation can you use to solve for the height (ℎ) of the lamppost?
Answers
6 weeks to 12 days answer?
Answers
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answers
Answer:
x2 + (y + 8)2 = 36
Step-by-step explanation:
:) took the test
The equations which represent circles that have a diameter of 12 units and a center that lies on the y-axis are x² + (y – 3)² = 36 and x² + (y + 8)² = 36.
What is the Standard form of a Circle?Standard form of a circle is given by the equation,
(x - h)² + (y - k)² = r²
where, (h, k) is the center of the circle and r is the radius of the circle.
Given that,
A circle has a diameter of 12 units.
So radius = 12 / 2 = 6 units
Center of the circle lies on the Y axis.
So the x coordinate of the center of the circle will be 0.
So, in (h, k), h = 0
So the equation will be of the form,
(x - 0)² + (y - k)² = 6²
x² + (y - k)² = 36
Hence the options are x² + (y – 3)² = 36 and x² + (y + 8)² = 36.
Learn more about Equations of Circles here :
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One number is 3 times another. If the difference between the numbers is 14, what is the larger number?
Answers
Answer:
21
Step-by-step explanation:
One number is 3 times another
x and 3x
difference between the numbers is 14,
3x - x = 14
simplify
2x = 14
Divide both sides by 2
x = 7
3x = 21
Answer:
The larger number is 21.
Step-by-step explanation:
let, the smaller number be x.
the larger number be 3*x =3x.
Now,
3x-x=14
or, 2x=14
or, x=14/2
x=7
here,
3x=3*x=3*7=21
Please help me I need help with solving this equation worth 30 points
Answers
Answer:
1. -20
2. 27
3. 36
4. -200
Use long division to divide x3 + x2 - 2x + 14 by x + 3. Choose the correct quotient.
Answers
Answer:
x2 - 2x + 4 (remainder 2).
or we could write it as
x2 - 2x + 4 + 2/(x+3)
Step-by-step explanation:
x2 - 2x + 4 <------ quotient.
x + 3 ) x3 + x2 - 2x + 14
x3 + 3x2
-2x^2 - 2x
-2x2 - 6x
4x + 14
4x + 12
2 <--------- remainder
Step-by-step explanation: