Drag each tile to the correct box. Not all tiles will be used.
Consider function f.
Place the steps for finding in the correct order.
Answers
If the function is f(x) = √(7x – 21). Then the inverse function of the function will be f⁻¹(x) = (1/7) x² + 3.
What is inverse of a function?Let the function will be
f: X → Y
Then the inverse function will be
f⁻¹: Y → X
The function is given below.
f(x) = √(7x – 21)
Then the inverse function will be
x = √[7{f⁻¹(x)} – 21]
x² = 7f⁻¹(x) – 21
7f⁻¹(x) = x² + 21
f⁻¹(x) = (1/7) x² + 3
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Related Questions
Add.
(3+x3+3x2)+(2x3−2−4x2)
Express the answer in standard form.
Enter your answer in the box.
Answers
Step-by-step explanation:
(3+3+3*2)+(2*3-2-4*2)
The value of the addition of the two polynomials is 3x³ - x² + 1.
What is addition of polynomial?The addition of polynomials involves combining like terms of two or more polynomials to create a new polynomial. A polynomial is an expression consisting of variables, coefficients, and exponents, connected by addition and subtraction operations.
To add the given polynomials:
(3 + x³ + 3x²) + (2x³ - 2 - 4x²)
First, let's group the like terms:
(x³ + 2x³) + (3x² - 4x²) + (3 - 2)
Combine the coefficients of the like terms:
3x³ + 3x² - 4x² + 3 - 2
Simplify the expression:
3x³ - x² + 1
Therefore, the sum of the given polynomials is: 3x³ - x² + 1.
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PLEASE ANSWER ASAP!!!!!! WILL GIVE BRAINLIEST!!!
Answers
Answer ya so 1 is the answer
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Given expression:
[tex]\sf \left(\dfrac{3a^{-2}b^6}{2a^{-1}b^5} \right)^2[/tex]
To find the value of the expression when a = 3 and b = -2, substitute these values into the expression:
[tex]\implies \sf \left(\dfrac{3(3)^{-2}(-2)^6}{2(3)^{-1}(-2)^5} \right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}[/tex]
[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{3^2}\right)(-2)^6}{2\left(\dfrac{1}{3^1} \right)(-2)^5} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{9}\right)(-2)^6}{2\left(\dfrac{1}{3} \right)(-2)^5} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{3}{9}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (2^6)}{\left(\dfrac{2}{3} \right) (-(2^5))} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (64)}{\left(\dfrac{2}{3} \right) (-32)} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1 \times 64}{3}\right)}{\left(\dfrac{2 \times -32}{3} \right)} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\dfrac{64}{3}}{\dfrac{-64}{3}} \right)^2[/tex]
When dividing fractions, flip the second fraction and multiply it by the first:
[tex]\implies \sf \left( \dfrac{64}{3} \times \dfrac {3}{-64} \right)^2[/tex]
[tex]\implies \sf \left( \dfrac{64 \times 3}{3 \times (-64)}\right)^2[/tex]
[tex]\implies \sf \left( \dfrac{192}{-192}\right)^2[/tex]
[tex]\implies \sf \left(-1\right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]
[tex]\sf \implies 1^2=1[/tex]
Mai bought a wedge with a central angle of 45 degrees and radius 10 centimeters. what is the area of the top surface of this wedge? , 1 of 2. select choice square centimeters
Answers
Using the area of a sector formula, we get the area to be:
[tex]\pi (10)^{2} \left(\frac{45}{360} \right)=\boxed{12.5\pi \text{ cm}^{2}}[/tex]
f(X)= 4X^2 + 7X -3 g(X) = 6X^3 - 7X^2-5 Find (f + g) (x).
Answers
By using the binary operator of addition, the result of summing f(x) = 4 · x² + 7 · x - 3 and g(x) = 6 · x³ - 7 · x² - 5 is equal to (f + g)(x) = 6 · x³ - 3 · x² + 7 · x - 8.
How to apply operations between functions
Binary operators is a operator that connects two functions. There are five binary operators between two functions: (i) Addition, (ii) Subtraction, (iii) Multiplication, (iv) Division, (v) Composition.
In this question we must apply the addition between two quadratic functions. In addition, we know by algebra that the sum of a quadratic function and a cubic function is equal to a cubic function. Hence, the resulting expression is:
(f + g)(x) = f(x) + g(x)
(f + g)(x) = (4 · x² + 7 · x - 3) + (6 · x³ - 7 · x² - 5)
(f + g)(x) = 6 · x³ - 3 · x² + 7 · x - 8
By using the binary operator of addition, the result of summing f(x) = 4 · x² + 7 · x - 3 and g(x) = 6 · x³ - 7 · x² - 5 is equal to (f + g)(x) = 6 · x³ - 3 · x² + 7 · x - 8.
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The vertex of this parabola is at (3-2). When the value is 4 the
y-value is 3. What is the coefficient of the squared expression in the
parabola's equation?
A. 7
B. 1
C. -1
D. 5
Answers
Answer:
D
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (3, - 2 ) , then
y = a(x - 3)² - 2
to find a substitute the point (4, 3 ) into the equation
3 = a(4 - 3)² - 2 ( add 2 to both sides )
5 = a × 1² = a
the coefficient of the squared expression is 5
Give ur answer in standard form.
3 x 10^4 ÷6 x 10^-4
Answers
Answer:
5.0×10⁷
Step-by-step explanation:
(3÷6)×(10⁴÷10^-4)
(0.5)×(10⁸)
5.0×10^-1×10⁸
5.0×10⁷
[tex] \frac{3 \times {10}^{4} }{6 \times {10}^{ - 4} } \\ \\ \frac{1 \times {10}^{4 - ( - 4)} }{2 } \\ \\ \frac{ 1 \times {10}^{4 + 4} }{2} \\ \\ \frac{1 \times {10}^{8} }{2} \\ \\ 0.5 \times {10}^{8} .[/tex]
What is a 10% margin increase on 1,810.69?
Answers
Answer:
1991.759
Step-by-step explanation:
1810.69×%10=181.069
1810.69+181.069=1991.759
URGENT PLEASE DUE TONIGHT ;(( functions
Answers
The value of (f/g)(-1) is 0, value of (g . f) (2) is -3√3, the value of (g - f)(-1) is √15, and the value of (g + f) (2) is √3 - 3
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have two functions:
f(x) = 1 - x²
g(x) = √(11 - 4x)
f(-1) = 0
g(-1) = √15
f(2) = -3
g(2) = √3
(f/g)(-1) = f(-1)/g(-1) = 0/√15 = 0
(g . f) (2) = g(2)f(2) = (√3)(-3) = -3√3
(g - f)(-1) = g(-1) - f(-1) = √15 - 0 = √15
(g + f) (2) = g(2) + f(2) = √3 + (-3) = √3 - 3
Thus, the value of (f/g)(-1) is 0, value of (g . f) (2) is -3√3, the value of (g - f)(-1) is √15, and the value of (g + f) (2) is √3 - 3
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Help please answer this point an brainlist
Answers
i'm confused
Find the value of x.
A. 5
B. 31
C. 25
D. 11
Answers
Answer:
D. 11
Step-by-step explanation:
Take the two horizontal line measurements and subtract them.
13-9=4
That is how much it changed between these two numbers. Since x is exactly halfway between, simply divide 4 and 2.
4/2=2
Now, add that to 9 or subtract it from 13.
9+2=11
or
13-2=11.
Hope this helps!
If not, I am sorry.
Answer:
D. 11
Step-by-step explanation:
Since segment AC bisects segments ED and BF, the length of AC is the average of the lengths of EB and DF.
AC = x = (EB + DF)/2 = (9 + 13)/2 = 22/2 = 11
Answer: D. 11
solution.
5(4x + 7)-2x = ________+ 21
Answers
Answer:
18x + 14
Step-by-step explanation:
First, we need to distribute the 5:
5(4x + 7) - 2x = __ + 21
20x + 35 - 2x = __ + 21
Now, we can combine like terms:
20x + 35 - 2x = ___ + 21
18x + 35 = ___ + 21
> subtract 21 from both sides to isolate "___"
18x + 35 = __ + 21
-21 -21
18x + 14 = ___
now that we have a solution, we should check that it works:
5(4x + 7) - 2x = ____ + 21
5(4x + 7) - 2x = 18x + 14 + 21
{simplify both sides:}
20x + 35 -2x = 18x + 35
18x + 35 = 18x + 35
(TRUE)
So, we know our solution is 18x + 14
hope this helps!!
f(x)=x^2. which of these is g(x) ?
a. g(x)=(1/5x)^2
b. g(x)=5x^2
c.g(x)=(1/4x)^2
d.g(x)=1/5x^2
Answers
Answer:
a
Step-by-step explanation:
we know that g(x) means y therefore in this case let's suppose we have the coordinate (5;y) so we must find the corresponding y value
*DO THE TRIAL AND ERROR METHOD*
take any equation above and substitute the value of x of which is 5 and the corresponding value should be 1.
[tex]g(x) = (\frac{1}{5} x) {}^{2} [/tex]
What is the equation of the line that passes through the point (5,-2) and has a
slope of -2/5
Answers
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -2/5x}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Passes through (5, -2) and slope of -2/5}[/tex]
Find: [tex]\textsf{The equation that follows the details provided}[/tex]
Solution: We first need to plug into the point-slope form and after simplifying, distributing, and solving for y we will complete our equation.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-2) = -2/5(x - 5)}[/tex]Distribute and simplify
[tex]\textsf{y + 2 = -2/5(x - 5)}[/tex][tex]\textsf{y + 2 = (-2/5 * x) + (-2/5 * (-5))}[/tex][tex]\textsf{y + 2 = -2/5x + 2}[/tex]Subtract 2 from both sides
[tex]\textsf{y + 2 - 2 = -2/5x + 2 - 2}[/tex][tex]\textsf{y = -2/5x + 2 - 2}[/tex][tex]\textsf{y = -2/5x}[/tex]Therefore, the final equation that follows the information that was provided is y = -2/5x.
The correlation in error terms that arises when the error terms at successive points in time are related is termed _____.
Answers
Answer:
auto correlation is the answer to the question
4. Write the function of a linear equation that includes the
points (1,3) and (2,9).
Answers
Answer:
y = 6x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form ( linear function ) is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 3 ) and (x₂, y₂ ) = (2, 9 )
m = [tex]\frac{9-3}{2-1}[/tex] = [tex]\frac{6}{1}[/tex] = 6 , then
y = 6x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (1, 3 ) , then
3 = 6 + c ⇒ c = 3 - 6 = - 3
y = 6x - 3 ← equation of linear function
The sin (0) = - and lies in Quadrant III. Find the exact values of the sine
6'
and cosine of 20.
Answers
Answer:
Can you give exanation
I don't understand
Given: l || m; ∠1 ∠3
Prove: p || q
Horizontal and parallel lines l and m are intersected by parallel lines p and q. At the intersection of lines l and p, the uppercase left angle is angle 1. At the intersection of lines q and l, the bottom right angle is angle 2. At the intersection of lines q and m, the uppercase left angle is angle 3.
Complete the missing parts of the paragraph proof.
We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because
. We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the
.
Answers
The parts that are missing in the proof are:
It is given
∠2 ≅ ∠3
converse alternate exterior angles theorem
What is the Converse of Alternate Exterior Angles Theorem?The theorem states that, if two exterior alternate angles are congruent, then the lines cut by the transversal are parallel.
∠1 ≅ ∠3 and l║m because we are: given
By the transitive property,
∠2 and ∠3 are alternate interior angles, therefore, they are congruent to each other by the alternate interior angles theorem.
Based on the converse alternate exterior angles theorem, lines p and q are proven to be parallel.
Therefore, the missing parts pf the paragraph proof are:
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Answer:
it is given
angle 2
angle 3
converse alternate exterior angles theorem
Step-by-step explanation:
The expression 55 + 14m - 2n + 3p has _________ terms.
1. 3
2. 4
3. 2
4. 5
Answers
A basketball coach recorded how many shots each of the 30 players at tryouts made in a set of 6 attempts.
Answers
Answer:
Step-by-step explanation:
what is the question?
Answer:
Median = A
Mean = B
Step-by-step explanation:
Khan Academy
f(x)=(2x−3)(x+6)(5x+6)f, left parenthesis, x, right parenthesis, equals, left parenthesis, 2, x, minus, 3, right parenthesis, left parenthesis, x, plus, 6, right parenthesis, left parenthesis, 5, x, plus, 6, right parenthesis has zeros at x=-6x=−6x, equals, minus, 6, x=-\dfrac{6}{5}x=− 5 6 x, equals, minus, start fraction, 6, divided by, 5, end fraction, and x=\dfrac{3}{2}x= 2 3 x, equals, start fraction, 3, divided by, 2, end fraction. What is the sign of fff on the interval -6
Answers
Answer:
566
Step-by-step explanation:
I got it right..................
hat is the total surface area of the square pyramid below? A square pyramid. The square base has side lengths of 10 centimeters. The triangular sides have a height of 14 centimeters. 100 cm2 200 cm2 280 cm2 380 cm2
Answers
Answer:
Step-by-step explanation:
area of square + 1/2 area of 1 triangle * 4
Lillian went shopping for a new phone because of a sale. The price on the tag was $20, but Lillian paid $16 before tax. Find the percent discount.pls help
Answers
Answer:
20 % discount
Step-by-step explanation:
Lilian got 4 dollars off of the original price (20 - 16 = 4 )
4 / 20 * 100% = 20% off
The percentage of discount that Lillian gets because of sale is 20%.
What is percentage?Percentage is a measurement to find value of given number out of hundred.
Given that,
The price of phone on tag = $20.
Lillian paid for phone = $16.
To find the percent discount on phone,
First find amount of discount = 20 - 16 = $4.
The percentage of discount = (4 / 20) x 100 = 20 %
Lillian gets 20% discount on new mobile.
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An architect is designing new housing structures for the primate section at the zoo. Her plan is shown below. Which animals will live in a building that is similar to the main primate house? A orangutans B chimpanzees C gibbons D gorillas
Answers
Answer:
A
Step-by-step explanation:
:p
What is the sum of the arithmetic sequence 3, 9, 15..., if there are 24 terms? (5 points)
Answers
There's a fixed difference of 6 between terms (9 - 3 = 6, 15 - 9 = 6, and so on). The first term of the sequence is 3, so the [tex]n[/tex]-th term is
[tex]3 + 6(n-1) = 6n - 3[/tex]
If there are 24 terms in the sum, then the last term is 6×23 - 3 = 135.
Let [tex]S[/tex] be the sum,
[tex]S = 3 + 9 + 15 + \cdots + 123 + 129 + 135[/tex]
Reverse the order of terms:
[tex]S = 135 + 129 + 123 + \cdots + 15 + 9 + 3[/tex]
If we add up the terms in the same positions, we get twice [tex]S[/tex] on the left side, while on the right side we observe that each pair of terms will sum to 138.
[tex]S + S = (3 + 135) + (9 + 129) + (15 + 123) + \cdots + (135 + 3)[/tex]
[tex]2S = 138 + 138 + 138 + \cdots + 138[/tex]
and since there are 24 terms in the sum, the right side is the sum of 24 copies of 138. In other words,
[tex]2S = 24 \times 138[/tex]
and solving for [tex]S[/tex] gives
[tex]S = \dfrac{24\times138}2 = \boxed{1656}[/tex]
neeeed helppp asapp
Answers
Answer:
y=3x-1
Step-by-step explanation:
you use the equation y=mx + b. b is your y intercept. in this question, -1 is your y intercept, because the graph passes the y axis at the point (0, -1).
m is also the slope, which is rise over run. so you go up 3 units and 1 unit to the right, which is 3/1 as your m .
overall, your equation of the line is:
y = 3x - 1
if x + 3y = 25 write y in terms of x and also find the two solutions of this equation
Answers
Answer:
y= 25/3 - x/3
Step-by-step explanation:
y= 25/3 - x/3
The quadrilateral below is formed from a parallelogram and an
isosceles triangle.
Calculate the size of angle VQU.
Answers
Answer:
VQU =58°
Step-by-step explanation:
angle QUV is 61 because of F angles (I don't know what they call them in ur country)
triangle QUV is an isosceles triangles so base angles are the same
61+61=122
180-122=58
Triangle AA'B'C' is the image of AABC under a dilation.
Answers
A sequence is defined by the recursive function f(n + 1) = one-half(n). If f(3) = 9 , what is f(1) ?
Answers
The value of f(1) is 81
What is Recursive function?Recursive Function is a function that repeats or uses its own previous term to calculate subsequent terms and thus forms a sequence of terms
Given:
f(n + 1) = 1/3* f(n)
f(3) = 9
let n=0
f(0+1) = 1/3 * f(0)
f(1) = 1/3 * f(0)
Let n=1
f(1+1) = 1/3 * 1/3*f(0)
f(2) = 1/9 * f(0)
let n=2
f(2+1) = 1/3 * 1/9* f(0)
f(3) = 1/27 * f(0)
Also, f(3) =9
So,
9 = 1/27 * f(0)
f(0) = 27 * 9
f(0) = 243
Now,
f(1) = 1/3 * f(0)
f(1) = 1/3/ 243
f(1) = 81
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1 in = 2.54 cm
how many millimeters are in 10.5 feet?
A.266.7 mm
B. 1,260 mm
C. 320.04 mm
D. 3,200.4 mm
Answers
Answer:
[tex]\fbox {D. 3,200.4 mm}[/tex]
Step-by-step explanation:
Given :
[ 1 inch = 2.54 centimeters ]
Unit conversions to keep in mind :
1 feet = 12 inches1 cm = 10 mmSolving
10.5 feet10.5 x 12 inches126 inches126 x 2.54 cm320.04 cm320.04 x 10 mm3200.4 mm