what is the inverse function of f(x) = 4x - 1
Answer:
[tex]f(x) = \frac{x + 1}{4}[/tex]
Step-by-step explanation:
To inverse the function switch the places of x and y like this:
x = 4y - 1
Now, solve for y:
[tex]x + 1 = 4y\\\frac{x + 1}{4} = y[/tex]
It's that easy!
I hope this helps!!
- Kay :)
Multiply the following polynomials, then place the answer in the proper location on the grid. Write the answer in
descending powers of x.
(8x + 3)(4x + 7)
Answer:
32x^2+68x+21
Step-by-step explanation:
Answer:
32x^2+68x+21
Step-by-step explanation:
This is right just did this!!
Ms.Sarah makes 300 cupcakes.She gives 2 cupcakes to each student.How many students can she give cupcakes to if she wants at least 20 cupcakes left?
Answer:
140
Step-by-step explanation:
300-20=280
280 divided by 2
140
Answer:
140 is your answer
Step-by-step explanation:
Halp pls!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
This is finding exact values of sin theta/2 and tan theta/2. I’m really confused and now don’t have a clue on how to do this, please help
First,
tan(θ) = sin(θ) / cos(θ)
and given that 90° < θ < 180°, meaning θ lies in the second quadrant, we know that cos(θ) < 0. (We also then know the sign of sin(θ), but that won't be important.)
Dividing each part of the inequality by 2 tells us that 45° < θ/2 < 90°, so the half-angle falls in the first quadrant, which means both cos(θ/2) > 0 and sin(θ/2) > 0.
Now recall the half-angle identities,
cos²(θ/2) = (1 + cos(θ)) / 2
sin²(θ/2) = (1 - cos(θ)) / 2
and taking the positive square roots, we have
cos(θ/2) = √[(1 + cos(θ)) / 2]
sin(θ/2) = √[(1 - cos(θ)) / 2]
Then
tan(θ/2) = sin(θ/2) / cos(θ/2) = √[(1 - cos(θ)) / (1 + cos(θ))]
Notice how we don't need sin(θ) ?
Now, recall the Pythagorean identity:
cos²(θ) + sin²(θ) = 1
Dividing both sides by cos²(θ) gives
1 + tan²(θ) = 1/cos²(θ)
We know cos(θ) is negative, so solve for cos²(θ) and take the negative square root.
cos²(θ) = 1/(1 + tan²(θ))
cos(θ) = - 1/√[1 + tan²(θ)]
Plug in tan(θ) = - 12/5 and solve for cos(θ) :
cos(θ) = - 1/√[1 + (-12/5)²] = - 5/13
Finally, solve for sin(θ/2) and tan(θ/2) :
sin(θ/2) = √[(1 - (- 5/13)) / 2] = 3/√(13)
tan(θ/2) = √[(1 - (- 5/13)) / (1 + (- 5/13))] = 3/2
Simplefly the problem 1/2x/45>61
Answer:
x>5490
x
>61
x>61×90
x>5490
Solve each system of equations by elimination.
y= -x+1 y=4x-14
By ELIMINATION
Answer:
X=3, y=-2
Step-by-step explanation:
Solve the equation 3x^2+8=83
Answer:
x = 5
Step-by-step explanation:
3x² + 8 = 83
3x² = 83 - 8
3x² = 75
x² = 75/3
x² = 25
x = √25
x = 5
-TheUnknownScientist
Answer:
x =5
Step-by-step explanation:
3x²+8=83
3x²=83-8
3x²=75
x²=75
3
x²=25
x=√25
x=5
hope it help u.
One box has 16 apples another box has 24 lemons.
Answer:
Like the other person said there's 40 apples.
Step-by-step explanation:
but is there more to the question or..?
5x2= wat??? i really didnt get this in class and really need help
Answer:
10
Step-by-step explanation:
5 x 2 = 10
Let's put it this way. 5 two times. 5 and 5. 5 + 5
Add them. you get 10.
Answer:
10, bro if you in college like the question says i feel bad for you. other wise you in 2nd grade.
Step-by-step explanation:
What inequality symbol does "at least" correspond to?
A. less than
B. less than or equal to
C. greater than
D. greater than or equal to
Answer:
C, if someone else gets the same answer as me then its right
Step-by-step explanation:
A scuba diver descends 0.75 meters per second. What is her change in elevation after 25 seconds?
-25.75 meters
-50.00 meters
-18.75 meters
-100 meters
Answer:
-18.75 Meters
Step-by-step explanation:
0.75 x -25 = -18.75 Meters :D
Find the value of x in the triangle shown below.
X
5
6
Answer:
C. x = √61
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Trigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²Step-by-step explanation:
Step 1: Define
We are given a right triangle. We can use PT to solve for the missing length.
Step 2: Identify Variables
Leg a = 6
Leg b = 5
Hypotenuse c = x
Step 3: Solve for x
Substitute: 6² + 5² = x²Exponents: 36 + 25 = x²Add: 61 = x²Isolate x: √61 = xRewrite: x = √61Answer: 61
Step-by-step explanation:
25+36=x
61=x
x=61
I am an odd number that is less than 10 and is not the number of sides on a triangle.I can be divided by three what number am I?
Answer:
I think that it would be 9 because it is less than ten and can be divided equally by 3.
Step-by-step explanation:
3r + 6y - 2z = -6 2x + y + 4z = 19 -5x - 2y+8z = 62
solve each system of equations
please graph (-5,2) thank you
Answer:
I hope this helps!!!
Step-by-step explanation:
Divide 25000 in the ratio 2:3:5
Pls answer this question
It is reaaaallyy imp
Will mark as brainliest
Let the parts be 2x, 3x and 5x.
Sum= 25000
Therefore,2x+3x+5x=25000
10x=25000
x=25000/10
x=2500
Therefore, parts:-
1. 2×2500=5000
2. 3×2500=7500
3. 5×2500=12500
Answer:
5000, 7500, 12500
Step-by-step explanation:
[tex]2 + 3 + 5 = 10[/tex]
[tex]25000[/tex] ÷ [tex]10[/tex] = [tex]2500[/tex]
[tex]2500[/tex] × [tex]2 = 5000[/tex]
[tex]2500[/tex] × [tex]3 = 7500[/tex]
[tex]2500[/tex] × [tex]5 = 12500[/tex]
[tex]\therefore[/tex] [tex]25000[/tex] will split into [tex]5000[/tex], [tex]7500[/tex], and [tex]12500[/tex].
To check if the answer is correct, you can add the values up and see if they sum up to [tex]25000[/tex]:
[tex]5000 + 7500 + 12500 = 25000[/tex]
Hope this helps :)
Explain briefly why the vertical line test is used to determine if a graph represents a function.
Answer:
One x input cannot have two or more resulting y outputs
Step-by-step explanation:
That's why we use the vertical line test to see if there's two y vales for a corresponding x value, hope that helped
Need help, I’ll give brainliest if correct.
Hello,
2x+1=x(2+0)
True or false???????
Answer:
false right
Step-by-step explanation:
Type the correct answer in the box.
If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is
°.
Correct question is;
Type the correct answer in the box bellow: If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is ...........
Answer:
x = 35°
Step-by-step explanation:
We are told that;
cos x = sin(20 + x)°
and 0° < x < 90°
From trigonometric identities, we know that;
cos x = sin (90 - x)
Applying to our question gives;
sin (90 - x) = sin (20 + x)°
Comparing both sides, we have;
90 - x = 20 + x
Rearranging;
90 - 20 = x + x
70 = 2x
x = 70/2
x = 35°
Write numbers to make each line have the same sum
Answer:
There is nothing here?
Step-by-step explanation:
The price of a 7 -minute phone call is $1.75. What is the price of a 14 -minute phone call?
Answer:
$3.50
Step-by-step explanation:
14 is double 7
So the price should be double
1.75 x 2 = 3.5
(Assuming there's no base fee and the charge is purely for minutes)
On a coordinate grid, point P is at (1, 7) and point R is at (−2, −3). Points Q and S are a reflection of both points across the x-axis. What are the coordinates of Q and S? (1 point) Q(−1, 7), S(2, −3) Q(−1, −7), S(2, 3) Q(−1, 7), S(−2, 3) Q(1, −7), S(−2, 3)
9514 1404 393
Answer:
(d) Q(1, −7), S(−2, 3)
Step-by-step explanation:
Reflection across the x-axis negates the y-coordinate:
(x, y) ⇒ (x, -y) . . . . reflection across the x-axis
Then we have ...
P(1, 7) ⇒ Q(1, -7)
R(-2, -3) ⇒ S(-2, 3)
These coordinates match the last choice.
Give the domain and range.
-3 0 3 у -6 0 6.
a. domain: {-3, 0, 3), range: 2-6, 0, 6)
b. domain: {-6, 0, 6), range: {-3, 0, 3}
c. domain: {3, 0, 3), range: {6, 0, 6}
d. domain: {6,0, 6), range: {3, 0,3}
Answer:
The domain: {-3, 0, 3}
The range: {-6, 0, 6}
Therefore, option (a) is correct.
Step-by-step explanation:
Given the table
x -3 0 3
y -6 0 6
Determining the Domain:
We know that the domain of a relation is the set of all the x-values of the set X. In other words, the domain of relation consists of all the input values.Therefore, the domain: {-3, 0, 3}
Determining the Range:
We know that the range of a relation is the set of all the y-values of the set Y. In other words, the range of relation includes all the output values.Therefore, the range: {-6, 0, 6}
Therefore, we conclude that option (a) is correct.
For a study of adolescents' disclosure of their dating and romantic relationships, a sample of 224 high school students was surveyed. One of the variables of interest was the level of disclosure to an adolescent's mother (measured on a 5-point scale, where 1 = "never tell" and 5 ="always tell"). The sampled high school students had a mean disclosure score of 3.38 and a standard deviation of 0.98. The researchers hypothesize that the true mean disclosure score of all adolescents will exceed 3. Do you believe the researchers?
Conduct a formal test of hypothesis using α = 0.05. Set
Answer:
The decision rule is
Reject the null hypothesis
The conclusion is
There sufficient evidence that the true mean disclosure score of all adolescents will exceed 3
Step-by-step explanation:
From the question we are told that
The sample is n = 224
The sample mean is [tex]\= x = 3.38[/tex]
The standard deviation is [tex]s = 0.98[/tex]
The population mean is [tex]\mu = 3[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 3[/tex]
The alternative hypothesis is [tex]H_a : \mu > 3[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \= x - \mu }{ \frac{s}{ \sqrt{n} } }[/tex]
=> [tex]z = \frac{ 3.38 - 3 }{ \frac{0.98 }{ \sqrt{224} } }[/tex]
=> [tex]z = 5.80[/tex]
From the z table the area under the normal curve to the right corresponding to 5.80 is
[tex]p-value = 0[/tex]
From the value obtained we that [tex]p-value < \alpha[/tex] , hence
The decision rule is
Reject the null hypothesis
The conclusion is
There sufficient evidence that the true mean disclosure score of all adolescents will exceed 3
Divide four people into three rooms, in which only one room could host two people. How many ways are there to arrange them so that A, B are not in the same room
Step-by-step explanation:
AC B D
AD B C
A BC D
A BD C
hope it's right
the question is above in the picture
5) Express as a single logarithm. You do NOT need to expand the polynomials:
5 In(x - 2) + 8 In(x + 3) - 3 ln(x + 8)
5 ln(x - 2) + 8 ln(x + 3) - 3 ln(x + 8)
ln(x - 2)⁵ + ln(x + 3)⁸ - ln(x + 8)³
since [tex]a\log_cb=\log_cb^a[/tex] (for any base c)
ln((x - 2)⁵ (x + 3)⁸ / (x + 8)³)
since [tex]\log_c(a)+\log_c(b)=\log_c(ab)[/tex] and [tex]\log_c(a)-\log_c(b)=\log_c\frac ab[/tex] (also for any base c)
Watch help video
In an all boys school, the heights of the student body are normally distributed with a
mean of 69 inches and a standard deviation of 2.5 inches. Using the empirical rule,
what percentage of the boys are between 61.5 and 76.5 inches tall?
Answer:
99.7%
Step-by-step explanation:
99.7% of boys fall between 61.5 and 76.5
The percentage of the boys that are between 61.5 and 76.5 inches tall is 99.73%
How to determine the percentage between the range?The given parameters are:
Mean = 69Standard deviation = 2.5Start by calculating the z score for x = 61.5 and 76.5 using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So, we have:
[tex]z_1 = \frac{61.5 - 69}{2.5} = -3[/tex]
[tex]z_2 = \frac{76.5 - 69}{2.5} = 3[/tex]
The percentage is then represented as:
Percentage = P(-3 < x < 3)
Using the z table of probabilities, we have:
Percentage = 0.9973
Express as percentage
Percentage = 99.73%
Hence, 99.73% of the boys are between 61.5 and 76.5 inches tall
Read more about normal distribution at:
https://brainly.com/question/4079902
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