The inverse of a quadratic parent function with a limited domain is a
function.
A. negative
B. cubed
C. square root
D. hyperbolic
The inverse of a quadratic parent function with a limited domain is given by the square root function, hence option C is correct.
How to find the inverse of a function?Supposing we have a function y = f(x), to find the inverse, we exchange x and y, and isolate y.
The quadratic function is:
[tex]y = x²[/tex]
Exchanging and isolating y:
[tex]x = y^2[/tex]
[tex]y^2 = x[/tex]
[tex]y = \sqrt{x}[/tex]
[tex]f^{-1}(x) = \sqrt{x}[/tex]
Hence option C is correct.
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Find the inverse equations for f and g.f(x)=3x+5g(x)=x2−6Explain your process. Then write about the relationship between the functions and their inverses. Does the domain and range of all functions and inverses follow a pattern?View keyboard shortcuts
[tex]g = \frac{x}{5} - \frac{6}{5x} - \frac{3}{5} [/tex]
Step-by-step explanation:
[tex]3 + 5g = \frac{ {x}^{2} - 6 }{x} \\ 5g = x - \frac{6}{x} - 3 \\ g = x - \frac{ \frac{6}{x} - 3}{5} \\ g = \frac{x}{5} - \frac{ \frac{6}{x} }{5} - \frac{3}{5} [/tex]
When a die is rolled, what is the theoretical probability that number five will be rolled?
Answer: 1/6
Step-by-step explanation: there is 6 faces on a standard die, one of them is 5.
Find the area of each triangle. Round to the nearest tenth.
Answer:
A ≈ 9.6 units²
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = product of 2 sides × sin (angle between them ) , that is
A = 3 × 5 × sin40° = 15 × sin40° ≈ 9.6 units² ( to the nearest tenth )
Aleka earns her regular pay or $14 per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week, Aleka earns 14 times her regular pay. How much does Aleka earn in a week in which she works 48 hours?
a. $576
b. $672
c. $728
d. $744
e. 1008
If Aleka earns her regular pay or $14 per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week, Aleka earns 14 times her regular pay. Then $728 she earns in a week in which she works 48 hours
What is equation?Two or more expressions with an equal sign is called as Equation.
Given that Aleka earns her regular pay or $14 per hour for up to 40 hours of work per week.
14x40=560
For each hour over 40 hours of work per week, Aleka earns 14 times her regular pay.
Fourteen plus seven equal to twenty one
14+7=21
Twenty one times of eight is equal to one hundred sixty eight
21x8=168
Now let us add five hundred sixty and one hundred sixty eight
560+168=728
Hence she earns $728 in a week in which she works 48 hours.
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Solve for x: 2 over 3 (x − 4) = 2x.
[tex] \frac{2}{3} (x - 4) = 2x \\ \frac{2}{3} x - \frac{8}{3} = 2x \\ \frac{2}{3} x - 2x = \frac{8}{3} \\ \frac{2}{3} x - \frac{6}{3} x = \frac{8}{3} \\ \frac{ - 4}{3} x = \frac{8}{3} \\ - 12x = 24 \\ x = \frac{24}{ - 12} \\ x = - 2[/tex]
What is the value of x?
Answer:
46 degrees
Step-by-step explanation:
Solve: log8 (x - 4) = 2
Answer:
x = 68
Explanation:
⇒ log₈(x - 4) = 2
apply log rules: logₐN = x then N = aˣ
⇒ (x - 4) = 8²
simplify
⇒ x - 4 = 64
add 4 on both sides
⇒ x = 64 + 4
add the integers
⇒ x = 68
Answer:
x = 68
Step-by-step explanation:
Given equation:
[tex] \rm log_{8}(x - 4) = 2[/tex]
To Find:
Value of x
Solution:
Rewrite the equation in exponential form which is equivalent to b^y = x.
[tex] \implies {8}^{2} = x - 4[/tex]
Now find the value of x.
[tex] \implies \:64 = x - 4[/tex]
Transpose 4 from RHS to LHS, make sure to change its sign from (-) to (+) .
[tex] \implies \: 64 + 4 = x[/tex]
Overturn the equation
[tex] \implies \: x = 68[/tex]
Thus, value of x is 68.
~30 PTS, BRAINLIEST, AND 5 STARS TO BEST ANSWER!~
1.) Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8).
2.)Find point Z that partitions the directed line segment XY in the ratio of 2:1 where X(1, 2) and Y(7, 5).
(PLS PROVIDE A DETAILED RESPONSE, ALONG WITH AN EASY
STEP BY STEP PROCESS. TY!)
For both problems, we can use the section formula.
1) [tex]P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}[/tex]
2) [tex]Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}[/tex]
What Fraction shows the product of 2×3/5
Answer:
Improper fraction
Step-by-step explanation:
2×3/5
=6/5 i.e Improper fraction
can you help me figure of the value of y?and possible x (I think I got it)
The values of x and y from the figure are 22.5 and 10 respectively
Vertical anglesThe angles that meet at a point X are equal and vertically opposite
From the diagram shown
6x - 5 = 8x - 50
6x - 8x = -50 + 5
-2x = -45
x = 22.5
Similarly
2y + 30 = 3y + 20
2y - 3y = 20 - 30
-y = -10
y = 10
Hence the values of x and y from the figure are 22.5 and 10 respectively
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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Since the two lines intersects each other we can conclude that :
6x - 5 = 8x - 50and
2y + 30 = 3y + 20[ That's because they form vertical opposite angle pair ]
So, let's solve for x and y ~
[tex]\qquad \sf \dashrightarrow \:6x - 5 = 8x - 50[/tex]
[tex]\qquad \sf \dashrightarrow \:8x - 6x = - 5 + 50[/tex]
[tex]\qquad \sf \dashrightarrow \:2x = 45[/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{45}{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = 22.5[/tex]
And
[tex]\qquad \sf \dashrightarrow \:2y + 30 = 3y + 20[/tex]
[tex]\qquad \sf \dashrightarrow \:3y - 2y = 30 - 20[/tex]
[tex]\qquad \sf \dashrightarrow \:y = 10[/tex]
I hope the steps are clear ~ let me know if you have doubts ~
Which type of data would be best displayed in a dot plot. (Help fast)
The type of data that would be best displayed in a dot plot is the correspondent to the third option.
Which type of data would be best displayed in a dot plot?
A dot plot is a plot where in the horizontal axis different numbers or properties (discrete set, usually we want smaller ranges, just so the graph are easier to read.) are marked, and above these, we mark dots, that represents how many times these are repeated on the data set.
We don't want large ranges (like in the first option 725 to 2450) because it means that we need to mark 725 points, or we need to find a common factor so each point represents more than one unit.
So, we need to have discrete data and with ranges not to large. The only option that meets both conditions is the third one, where on the horizontal axis we would have each of the 15 school dental clinics, and the dots would represent the number of dentist volunteering on each of them.
Then the correct option is the third one.
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Answer:
3rd option
Step-by-step explanation:
Solve for x. Round to nearest tenth
SOMEONE PLEASE HELP ME WITH THIS ILL GIVE YOU BRAINLIST ANSWER
Image above
Answer: the answer to your question is 42.2
Step-by-step explanation:25 x 25 + 34 X 34 = c^2
Answer:
20
Step-by-step explanation:
34 + 90 = 124
180-124 = 56 degrees
c = 56 degrees
to find x we need to use sin
sin = SOH (Sin = opposite/hypotenuse
sin 56 = x/25
sin 56 x 25 = x
x = 20.72593931
x = 20 (rounded to the nearest 10th)
hope this helped :)
A patch of farmland is currently worth $78,125. The expected increase in its market value can be modeled by the function below, where t is the time in years. How many years will it take for the farmland's market value to reach $125,000?
The number of the years to take for the farmland's market value to reach $125,000 will be 19 years.
The missing function will be given below.
[tex]\rm p(t) = 78,125\ e^{0.025t}[/tex]
What is an exponent?Let a is the base and x is the power of the exponent function and b is the y-intercept. The exponent is given as
y = aˣ
A patch of farmland is currently worth $78,125. The expected increase in its market value can be modeled by the function below.
[tex]\rm p(t) = 78,125\ e^{0.025t}[/tex]
Then the number of the years to take for the farmland's market value to reach $125,000 will be
[tex]\rm 78,125 \ e^{0.025t} = 125,000\\\\e^{0.025t} = 1.6[/tex]
Then take log on both sides, then we have
0.025t lne = ln 1.6
0.025t = 0.47
t = 18.8
t = 19 years
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Brian usually brushes his teeth in the morning, but 10% of the time he forgets. What is the probability that he will forget to brush his teeth three days in a row (Assume that forgetting one day does not influence any other day.)
Using it's concept, it is found that there is a 0.001 = 0.1% probability that he will forget to brush his teeth three days in a row.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, for each day, there is a 0.1 probability that he forgers to brush his teeth, and days are independent, hence for 3 consecutive days the probability is given by:
p = (0.1)³ = 0.001.
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The rectangle is 93 m long and 70 m wide what is the area if you use 3.14 for pie
Answer:
i might just be mind numb right now but you don't use pie on rectangles for area
Area = 6510
Step-by-step explanation:
A = L x W
A = 93 x 70
A = 6510
the product of two numbers is 16/9. if one of the numbers is 5/2, find the other number
Answer:
[tex] \frac{32}{45} [/tex]
Step-by-step explanation:
if the multiplication of two numbers is 16)9, and one of the numbers is 5/2. then the other number can be found by dividing the number from the product to get the other number.
Q38: Rearrange g=2hm to make m
the subject
The expression g = 2hm can be written as in terms of g and h when m is the subject is m = g/2h.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
g = 2hm
To make m as the subject and solve it:
Divide the above expression by 2h on both sides:
g/2h = m or
m = g/2h
Thus, the expression g = 2hm can be written as in terms of g and h when m is the subject is m = g/2h.
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What is the scale factor if a 8 in. by 10 in. photograph is enlarged to a poster that is 6 ft. by 7.5 ft.?
9
1/9
1.33
1/1.33
What is the factored form of 4x2 23x – 72? (4x 8)(x – 9) (4x – 8)(x 9) (4x 9)(x – 8) (4x – 9)(x 8)
Answer:
(x+8)(4x-9)
Step-by-step explanation:
Rewrite expression 4x^2 + 32x - 9x - 72
Factor out 4x 4x(x+8) - 9x - 72
Factor out x+8 4x(x+8) - 9(x+8)
Simplify (x+8)(4x-9)
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The shaded region in the graph represents the solutions of this system of linear inequalities:
y ___
4x + ___
y ≤ ___
x + ___
Note: Use the symbols <, >, <=, and >= for inequality signs.
Based on the calculations, the solutions of this system of linear inequalities are equal to:
y < 4x + 5y ≤ 2x + 3 What is an inequality?An inequality simply refers to a mathematical relation that's used to compare two (2) or more integers (variables) in an equation based on any of the following:
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).In order to determine the solutions of this system of linear inequalities, we would find the slope of each line.
For line A, we have:
Slope, m = (11 - 3)/(4 - 0) = 8/4
Slope, m = 2.
Mathematically, the standard equation of a line is given by y = mx + b.
y = 2x + 3
y ≤ 2x + 3.
For line B, the slope is equal to 4. Also, the y-intercept from the graph is equal to 5.
Therefore, the standard equation of a line is given by:
y = 4x + 5
y < 4x + 5
In conclusion, the solutions of this system of linear inequalities are equal to:
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Consider the equation -5\cdot e^{10t}=-30−5⋅e
10t
=−30minus, 5, dot, e, start superscript, 10, t, end superscript, equals, minus, 30.
Solve the equation for ttt. Express the solution as a logarithm in base-eee.
t=
Approximate the value of ttt. Round your answer to the nearest thousandth.
t=
The approximate equation is n = (ln 6)/10 and approximate value is n = 0.179.
What is Exponential equation?In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Here, given equation; (we are using n in place of t)
-5.e¹⁰ⁿ = -30
On dividing -5 both sides, we get
-5.e¹⁰ⁿ/-5 = -30/-5
e¹⁰ⁿ = 6
Taking 'ln' on both side, we get
10n = ln 6
n = (ln 6)/10
n = 1.791759/10
n = 0.179
Thus, the approximate equation is n = (ln 6)/10 and approximate value is n = 0.179.
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3x=3(x-1)
Step by step ( 20 pts )
Answer:
No solution.
Step-by-step explanation:
[tex]\textbf{Given that,}\\\\~~~~~~~~3x = 3(x-1)\\\\\\\implies \dfrac{3x}3 = \dfrac{3(x-1)}{3}~~~~~~~~~~~~~~~~~;\textbf{Dividing both sides by 3}\\\\\\\implies x = x-1\\\\\\\implies x-x = x-1-x~~~~~~~~~~~~~;\textbf{Subtracting}~ x ~ \textbf{from both sides} \\\\\\\implies 0 = -1\\\\\\\textbf{Which is not true, so there are no solutions.}[/tex]
I need help on this 1 question. Thank you.
Answer: 5/6, 3/4, 4/12
Step-by-step explanation:
Convert them all into a common denominator, 12.
5/6=10/12, 3/4=9/12, and 4/12 stays the same. 10>9, and 9>4
work out the value of T using the formula T=3x^{2]p-2p when p= -1?
The solution of the equation when p = -1 is [tex]T=3x^{-2}[/tex]
How to determine the value of the equation?The equation is given as:
[tex]T=3x^{2p}[/tex]
The value of p is -1.
So, we have:
[tex]T=3x^{2*-1}[/tex]
Evaluate the product
[tex]T=3x^{-2}[/tex]
Hence, the solution of the equation when p = -1 is [tex]T=3x^{-2}[/tex]
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Solve for x. Each figure is a trapezoid. # 18 has a midsegment.
13)
Question 13
[tex]{12x+2}=\frac{18+34}{2}\\\\12x+2=26\\\\12x=24\\\\x=\boxed{2}[/tex]
Question 14
Base angles of an isosceles trapezoid are congruent, so:
[tex]73x+1=74\\73x=73\\x=\boxed{1}[/tex]
Graph the function f(x)= 2x -4
Find the range.
3 -9 7 -1 5 -4 2
Answer:
16
Step-by-step explanation:
The range is the distance between the largest number and the smallest number. To find the range, you take the smallest number and subtract it from the largest number. In this case, the smallest number is -9 and the largest number is 7. 7 minus -9 is a double negative, so you can also do 7+9=16. 16 is the range.
What is the volume, in cubic centimeters, of a right square pyramid
with base edges that are 64 cm long and a slant height of 40 cm
The volume of the right squared pyramid with the given base edges and slant height is 32768 cubic centimeters.
What is the volume of right square pyramid?The volume of a square pyramid is expressed as;
V = (1/3)a²h
Where a is the base length and h is the height of the pyramid
Given that;
Base edges of the square base a = 64cmSlant height s = 40cmHeight of the pyramid h = ?Volume = ?First, we determine the height of the pyramid using Pythagorean theorem.
c² = a² + b²
c = s = 40cma = half of the base length = a/2 = 64cm/2 = 32cmb = h(40cm) = (32cm)² + h²
1600cm² = 1024cm² + h²
h² = 1600cm² - 1024cm²
h² = 576cm²
h = √576cm²
h = 24cm
Now, we calculate the volume of the right square pyramid;
V = (1/3)a²h
V = (1/3) × (64cm)² × 24cm
V = (1/3) × 409664cm² × 24cm
V = 32768cm³
Therefore, the volume of the right squared pyramid with the given base edges and slant height is 32768 cubic centimeters.
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which sequence of transformations could be used to move triangle RST so it completely covers triangle R”S”T?
Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"
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