Answer:
The inverse of f(x) is
y = x² - 4
x = y ² - 4
y² = x + 4
y = √x + 4
The inverse of the function is y = √x +4
Hope this helps.
solve the equation x^4+7x^2-18=0 and express each solution in a+bi form
Answer:
The following are the solutions found for x:
+√2 + 0i
-√2 + 0i
0 + 3i
0 - 3i
Step-by-step explanation:
The given equation is:
x⁴ + 7x² - 18 = 0
Rewrite x4 as (x²)²
(x²)² + 7x² − 18 = 0
Let u = x²
u² + 7u − 18 = 0
Factorize:
u² + 9u - 2u - 18 = 0
u(u+9) -2(u+9) = 0
(u-2)(u+9) = 0
(x²-2)(x²+9) = 0
Seperate both equations:
x² - 2 = 0 x² + 9 = 0
x = ±√2 x = ±√-9
x = ±√2 x = ± 3√-1
x = ±√2 + 0i x = 0 ± 3i
Answer:
C
Step-by-step explanation:
What is the solution to this equation?
2x + 6 = 20
A. X = 13
B. X = 52
C. X = 28
D. X = 7
Answer:
d
Step-by-step explanation:
2(7)+6=20
14+6=20
20=20
Answer:
2x + 6 = 20
2x = 20 - 6
2x = 14
Divide both sides by 7
x = 7
That's option D.
Hope this helps.
Describe how to transform the graph of f into the graph of g. f(x) = x2 and g(x) = -(-x)2 The graph shifts left one unit. Reflect the graph of f across the y-axis and then reflect across the x-axis. Reflect the graph of f across the y-axis. Reflect the graph of f across the x-axis.
Answer:
Reflect the graph of f across the y-axis and then reflect across the x-axis.
Step-by-step explanation:
Reflection rules:
Reflection over x -axis:(x,y)→(x,-y)
Reflection over y-axis : (x,y)→(-x,y)
Graph:[tex]y= f(x)=x^2[/tex]
We are given that the graph of f into the graph of g.
[tex]f(x) = x^2[/tex] and [tex]g(x) = -(-x)^2[/tex]
Reflect over y axis.
Reflected graph [tex]=(-x)^2[/tex]
Reflect the obtained graph over x axis
[tex]g(x)=-(-x)^2[/tex]
So, Option B is true
Hence Reflect the graph of f across the y-axis and then reflect across the x-axis.
Answer:
i reflected it over the x and y axis tho
Step-by-step explanation:
bro trust me
please need help I will be MARKING as BRIANILIST. thank you so much.
Answer:
C. 7
Step-by-step explanation:
Custodian has = [tex]5 \frac{1}{4} gallons[/tex]
Ever bookcase needs = [tex]\frac{3}{4} gallons[/tex]
We'll just divide them
Bookcases to be painted = [tex]5\frac{1}{4} / \frac{3}{4}[/tex]
= [tex]\frac{21}{4}* \frac{4}{3}[/tex]
= [tex]\frac{21}{3}[/tex]
= 7
I need help awnsering these questions please get to me soon as you can
Answer:
Answer is given below with explanations.
Step-by-step explanation:
[tex]1)volume \: of \: cylinder = \pi \: {r}^{2} h \\ here \: radius \: (r) = 3 \: m \\ and \: height \: (h) = 8 \: m \: \\ volume \: of \: cylinder = \pi \: \times {3}^{2} \times 8 \\ \: \: = \pi \ \times 9 \times 8 \\ \: \: = 72\pi \\ \: \: = 226.195 \: {m}^{3} \\ 2)volume \: of \: pyramid \: = \frac{1}{3} \times base \: area \times height \\ base\: area = 25 \times 16 \\ \: \: = 400 \: {ft}^{2} \\ volume \: of \: pyramid \: = \frac{1}{3} \times400 \times 45 \\ \: \: = 6000 \: cubic \: feet \\ 5) \: volume \: of \: cone = \frac{1}{3 \: } \pi \: {r}^{2} h \\ here \: radius \: (r) = 6.2 \: m \: \\ height \: (h) = 6.8 \: m \\ volume \: of \: cone = \frac{1}{3 \: } \pi \: \times {6.2}^{2} \times 6.8 \\ \: \: = 273.73 \\ 6) \: volume \: of \: hemisphere \: = \frac{2}{3} \pi \: {r}^{3} \\ here \: radius \:( r) = 6 \: in \\ volume \: of \: hemisphere \: = \frac{2}{3} \pi \: {6}^{3} \\ \: \: = 452.39 \: cubic \: inches[/tex]
Questions are not clearly visible for me.
So forgive me.
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
A. 4/11
B. 7/11
C. 11/7
D. 11/4
help plsss
Answer:
Option B. 7/11
Step-by-step explanation:
The following data were obtained from the question:
Sin x = 7/11
Cos(90 – x) =..?
The value of Cos(90 – x) can simply be obtained as follow:
Recall:
Sin x = Cos(90 – x)
Sin x = 7/11
7/11 = Cos(90 – x)
Therefore, the value of Cos(90 – x) is simply 7/11.
Which of the following is a result of shifting a circle with equation (x-2)2 +(y-3)2=25 to the left 2 units ?
A.) Both the x- and y-coordinates of the center of the circle increased by 2
B.) Both the x- and y-coordinate of the center of the circle decreased by 2
C.) The y-coordinate of the center of the circle decreased by 2
D.) The x-coordinate of the center of the circle decreased by 2
Answer:
D.) The x-coordinate of the center of the circle decreased by 2
Step-by-step explanation:
(consult the diagram attached below)
Consider a circle
(x - 2)² + (y - 3)² =25
Where (h, k ) = (2, 3) which is the center of the circle.
When we want to move the circle to the left by 2 units, it also means the the center of the circle will move 2 units to the left.
If center of the circle moves 2 units to the left, it means that the x coordinate of the center of the circle will be decreases by 2 units, while y coordinate will remain the same.
Hence the new coordinate for the center of the circle is (2-2, 3) = (0, 3)
The new equation of circle will be:
(x - 0)² + (y - 3)² =25
(x )² + (y - 3)² =25
Two jets are flying towards each other from airport that are 1200 km apart. One jet is flying at 250 km.h-1 and the other jet at 350 km.h-1 . If they took off at the same time, how long will it take for the jets to pass each other?
Answer: 2 hours
Step-by-step explanation:
The total velocity at which the planes are approaching each other is 350 + 250 = 600 km/h
Since time = distance/velocity, time = 1200km/ 600 km/h = 2 hours.
Describe how to find the inverse of the function:
[tex]f(x) = \sqrt{x + 3} [/tex]
Answer:
f(x) = x² – 3
Step-by-step explanation:
Lemme try
f(x) = √(x + 3)
y = √(x + 3)
y² = x + 3
y² – 3 = x
Cz we gonna invers that, we'ld turn x to y and y to x, so:
x² – 3 = y
Yeah, inverse of the function is y=x²–3
Answer:
Step-by-step explanation:
If the nth term of a number sequence is n squared -5 find the first 3 terms and the 10th term
Answer:
If the nth term is n^-5,
Then the first term will be (1)^-5=1
Second term will be (2)^-5= 1/32
3rd term=(3)^-5 = 1/243
So, 10th term will be (10)^-5=1/100000
The first term is -4, second term is -1, third term is 4 and 10th term is 95.
What is sequencea group of connected actions, moves, or things that happen in succession and have a specific order.
Given that,
The nth term of sequence = n² - 5 (1)
To find terms, Substitute values of n in equation (1),
Substitute n=1, the first term = 1-5 = -4
Substitute n=2, the second term = 4-5 = -1
Substitute n=3, the third term = 9-5 = 4
For 10th term, substitute n= 10,
10th term = 100-5 = 95
First term =-4, second term = -1, third term = 4 and 10th term = 95.
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Which of these needs the denominator rationalized? -PLEASE HELP
Answer:
option b
Step-by-step explanation:
[tex] \sqrt{ \frac{5}{3} } [/tex]
[tex] \frac{ \sqrt{5} }{ \sqrt{3} } [/tex]
the denominator is in the surd form, so it must be rationalized
Every integer is a whole number
Please select the best answer from the choices provided
T
F
Answer:
This is true.
Find x. Round your answer to the nearest tenth of a degree.
Answer:
x ≈ 31.3°
Step-by-step explanation:
We can use sin∅ to solve this:
sinx = 13/25
x = [tex]sin^{-1}(13/25)[/tex]
x = 32.3323
Help idk how to do this
Answer:
[tex]y=5[/tex]
Step-by-step explanation:
[tex]BD=16\\BC=16/2=8\\CD=16/2=8[/tex]
[tex]2y-2=8\\2y-2+2=8+2\\2y=8+2\\2y=10\\2y/2=10/2\\y=5[/tex]
[tex]y+3=8\\y+3-3=8-3\\y=5[/tex]
Which equation has a graph that is parallel to the graph of 2x - y = -1?
A. 2x + y = 8
о В.
y=-x+3
O C. y-1 = 2(x - 3)
O D. y = -2x - 1
Answer:
C.
Step-by-step explanation:
Parallel lines have the same slope but different y-int. So if our original equation is y = 2x + 1, then the other equation would have to be y = 2x + b, where b ≠ 1. Only answer C. works.
Answer:
The answer is C) y-1=2(x-3)
Step-by-step explanation:
Two equations are parallel if they have the same slope and different y-intercepts. In the answer (c) 2 represents the slope which is also the slope of the original equation. y=2x-5is the equation that you get when you distibute and isolate y.
A bridge connecting two cities separated by a lake has a length of 5.651 mi.
Use the table of facts to find the length of the bridge in yards.
Round your answer to the nearest tenth.
Answer:
The equivalent of 5.651 mi is 9945.76 yards
Step-by-step explanation:
Given:
Length of lake = 5.651 mi
Required:
Length of bridge in yards
From table of facts;
1 mile = 1760 yards
This implies that
5.651 miles will be:5.651 * 1760 yards
5.651 * 1760 yards = 9945.76 yards
5.651 * 1760 yards = 9945.8 yards (Aproximated)
Hence, the equivalent of 5.651 mi is 9945.76 yards
Use laws of exponents to simplify inside the parentheses of the given expression ((a ^ - 2 * b ^ 2)/(a ^ 2 * b ^ - 1)) ^ - 3
The expression [(a⁻² × b²)/(a² × b⁻¹)]⁻³ in the simplified form will be (a¹² / b⁹).
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ [(a⁻² × b²)/(a² × b⁻¹)]⁻³
Simplify the expression, then we have
⇒ [(a⁻² × b²) / (a² × b⁻¹)]⁻³
⇒ [(a² × b⁻¹) / (a⁻² × b²)]³
⇒ [(a⁴ / b³)]³
⇒ (a¹² / b⁹)
The expression [(a⁻² × b²)/(a² × b⁻¹)]⁻³ in the simplified form will be (a¹² / b⁹).
More about the value of the expression link is given below.
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Answer:
D. (b^3/a4)^-3
Step-by-step explanation:
boop boop edge dge
i neeeeeeeeedd help filling in the blanks
Answer:
Step-by-step explanation:
6
2
11,034
70 ml/s
I NEED HELP PLEASEEE \6(2x – 11) + 15 = 3x + 12 Part A: Write the steps you will use to solve the equation, and explain each step. (6 points) Part B: What value of x makes the equation true? (4 points)
Answer:
x = [tex]-7\frac{2}{3}[/tex]
Step-by-step explanation:
=> 6(2x+11) + 15 = 3x+12
(Expand the brackets)
=> 12x+66+15 = 3x+12
(Adding 66+15)
=> 12x+81 = 3x+12
(Subtracting 81 and 3x to both sides)
=> 12x-3x = 12-81
=> 9x = -69
(Dividing both sides by 9)
=> x = [tex]\frac{-69}{9}[/tex]
(Simplifying)
=> x = [tex]\frac{-23}{3}[/tex]
(Converting it into mixed form)
=> x = [tex]-7\frac{2}{3}[/tex]
So, x = [tex]-7\frac{2}{3}[/tex] will make the equation true.
Answer:hello
The answer is 7
Step-by-step explanation:at first solve this6(2x-11)=12x-66
Then write 12x-66+15
Then we have this 12x-66-15=3x+12
Then we have to write (x) in the left side and number in right side
12x-3x=66-15+129x=63
X=7
Good luck
Can someone help me with this question
Answer:
[tex]3[/tex]
Step-by-step explanation:
Write in the exponential form with a base of 3
[tex]9^{\frac{1}{2} }[/tex] → [tex](3^{2})^{\frac{1}{2} }[/tex]
Simplify the expression by multiplying the exponents.
[tex]2 * \frac{1}{2} = 1[/tex]
[tex]3^{1} = 3[/tex]
You do not need to line up the decimal points when subtracting two decimal numbers. TrueFalse
Answer:
false
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Or else it will give you an incorrect calculation
OMG HELPPP PLEASEEE plssss
Answer:
Brainliest goes to me
Step-by-step explanation:
if you solved it... it would be 8.75
but you can't like 0.75 of a color so it isn't possible
0.75 is to be rounded up so I would do 9
Answer:All you have to do is multiply
Step-by-step explanation:
How can you be certain that the angles you have created form a square inside the
circle?
Answer:
Step-by-step explanation:
Make sure that the angles are the same length, also make sure that the diameter of the circle is not smaller than that of the square to find diameter of a circle multiply the radius by 2, to find the radius use this formula
r=C over 2π
By Ensure that its angles are identical, and also ensure that circle's diameter is only smaller than the square because then the circle diameter multiplies the range by 2, so how you can find the [tex]\bold{r=C}[/tex] formula of the radius over [tex]\bold{2\pi}[/tex]
The building process is as follows:
Circle diameter is plotted.The method as described in the perfectly straight central axis of a portion is drawn by the bisector of the right angle of the radius. It is also a circular pattern diameter.The four areas on the circle that result are indeed the square vertices.Please find the attached file.
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would this be a? please explain, thanks!
Answer:
Itz B.
Step-by-step explanation:
To form a triangle to two smaller sides have to be able to add up to be greater than the big side
PLZ HELP 50 POINTS AND BRAINLIEST!!!!!!!! Karen has a large pile of colored rods. Each color is a different length. She is trying to connect different colored rods to make triangles as part of a hanging sculpture. Here is a list of rod lengths.
Red: 3 inches
Orange: 4 inches
Yellow: 5 inches
Green: 7 inches
Blue: 9 inches
Purple: 12 inches
1. How many triangles can she make with them if each side is a different color? List the combinations that work.
2. Karen was just trying different combinations of colored rods one at a time, placing the colored rods together to see if they make a triangle. What method did you use to determine the triangle options? Which method do you think is better and why?
Answer:
9 possible combinations: RGB, RYG, RGB, OYG, OGB, OBP, YGB, YBP, GBP
Step-by-step explanation:
We need to consider The Triangle Inequality Theorem which states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.Let's see what are the possible combinations:
3+4= 7 so possible 3rd side is 5
3, 4, 5 or ROY3+5= 8 so possible 3 rd side is 7
3, 5, 7 or RYG3+7= 10 so possible 3rd side is 5 or 9 (5 is repeat of the one above)
3, 7, 9 or RGB3+9= 12 so possible 3rd side is 7, see one above
3+12= 15 so possible 3 rd side is none
4+5=9 so possible 3rd side is 7
4, 5, 7 or OYG4+7= 11 so possible 3rd side is 9
4, 7, 9 or OGB4+9= 13 so possible 3rd side is 12
4, 9, 12 or OBP5+7= 12 so possible 3rd side is 9
5, 7, 9 or YGB5+9= 14 so possible 3rd side is 12
5, 9, 12 or YBP7+9= 16 so possible 3rd side is 12
7, 9, 12 or GBPSo the possible 9 combinations are:
RGB, RYG, RGB, OYG, OGB, OBP, YGB, YBP, GBPhow does the fact that a parallelogram has rotational symmetry demonstrates that opposite side of a parallelogram are congruent ?
Answer:
See below.
Step-by-step explanation:
It is known that a parallelogram has rotational symmetry, rotated 180 degrees about it's center point. Now by definition a parallelogram is a quadrilateral with two pairs of parallel sides, hence it's name. If you were to take a look at the attachment below, you might see the connection.
Rotational Symmetry will make it so that side AB corresponds to CD, respectively AD and CB. The sides will coincide with one another after a 180 degree rotation, so that AB = CD, and AD = CB. Hence, in the same parallelogram, opposite sides are congruent.
Proved!
Solve 5(x - 4) = 2(x + 5)for x
5x-20 = 2x+10
3x-20= 10
3x= 30
x=10
Answer:
x = 10
Step-by-step explanation:
Step 1: Distribute parenthesis
5x - 20 = 2x + 10
Step 2: Add 20 to both sides
5x = 2x + 30
Step 3: Subtract 2x from both sides
3x = 30
Step 4: Divide by 3
x = 10
Find the domain and range of the following relation. Also determine whether the relation is a function,
{(42)(4,5),(4.7),(4.9)}
Answer: domain: {2, 3, 4, 6}
range: {–3, –1, 3, 6}
Step-by-step explanation:
DOMAIN: {4}
RANGE: {2,5,7,9}
FUNCTION? NO!
Your domain is always your x-coordinates, which are the first coordinates in a pair.
Your range is always your y-coordinates, which are the second coordinates in a pair.
When listing the points, it's important to remain a relation CANNOT be a function if the x's repeat, so luckily, they do not repeat.
Also, when listing points for your range, remember, if they repeat, you should only count one of the numbers, as you can see from the answer, there were two nines, but instead, I put one.
The ratio of the number of Andys seashells to the number of Bens seashell is 4:9. Andy has 100 seashells. How many seashells does Ben have?
Answer:
225 seashells
Step-by-step explanation:
4:9
100:x
Cross multiply the ratios.
4x=900
x=900/4
x=225
use the quadratic formula to find both solutions to the quadratic equation given below. 3x^2-x+4=0
Answer: B and D
Step-by-step explanation: A p e x
The value of the quadratic equation 3x² - x + 4 = 0 is B. {1 - √(-47)}/6 and
D. {1 + √(-47)}/6.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, 3x² - x + 4 = 0.
We know x = {- b ± √(b² - 4ac)/2a}.
∴ x = {+ 1 ± √(1 - 48)}/6.
x = {1 ± √(-47)}/6.
x = {1 + √(-47)}/6 Or {1 - √(-47)}/6.
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