5+2√3 / 7+4√3 = a-6√3
please answer this
[tex]~~~~\dfrac{5+2\sqrt 3}{7+4\sqrt 3} = a- 6\sqrt 3\\\\\\\implies a= \dfrac{5+2\sqrt 3}{7+4\sqrt 3}+6\sqrt3 \\\\\\\implies a=\dfrac{\left(5+2\sqrt 3 \right) \left( 7-4\sqrt 3\right)}{\left(7+4\sqrt 3 \right) \left(7-4\sqrt 3 \right)}+6\sqrt 3\\\\\\\implies a = \dfrac{35-20\sqrt 3+14\sqrt 3-24}{7^2 - \left(4\sqrt 3 \right)^2}+6\sqrt 3\\\\\\\implies a=\dfrac{11-6\sqrt 3}{49-48}+6\sqrt 3\\\\\\\implies a=11-6\sqrt 3+6\sqrt 3\\\\\\\implies a = 11[/tex]
cual es la inversa de la funcion f(x) = -1/2 (x + 3 )
Answer:
-2x - 3
Step-by-step explanation:
f(x) = -1/2(x + 3) is the same as y = -1/2(x + 3)
change all y terms to x terms and all x terms to y terms
So change y = -1/2(x + 3) to x = -1/2(y + 3)
Now use the new equation and slove for y
x = -1/2(y + 3)
-2x = -2· -1/2 (y + 3)
-2x = y + 3
-2x - 3 = y
Rewrite your answer y = -2x - 3
Write the equation in the inverse
Question 5 of 5
Roshaun kept track of the number of hours that he spent
playing his saxophone each week for several weeks. He
spent 8 25 10 and 5 hours.
What is the range of the data set?
O A 10 hours
B. Shours
C. 5 hours
OD 6 hours
SUBMIT
PREVIOUS
Maggie made 3 withdrawals of $30 each from her bank account. She also wrote a check for $50. What change did these transactions have on her bank account balance? F $80 g-$80 H $140 j-$140
A cylindrical piece of iron pipe is shown below. the wall of the pipe is 0.75 inch thick, and the pipe is open at both ends: the figure shows a cylinder of height 16 inches and diameter 6 inches. what is the approximate inside volume of the pipe? 113 cubic inches 452 cubic inches 410 cubic inches 254 cubic inches
Answer:
254.4
Step-by-step explanation:
if its 0.75 inch thick, then to get the radius you just times to thickness by 2 which gets 1.5.
6-1.5= 4.5
to get the radius you divide 4.5 by 2 which gets 2.25
and then put this in the formula you get=
V=πr2h=π·2.252·16≈254.469
so the answer is 254
edit:i might be wrong feel free to correct me
Answer: 254
Step-by-step explanation:
There is a bag filled with 4 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 that are different in colour?
Answer:
50% chance
Step-by-step explanation:
obviously
can some help me with this one question pls
Answer:
turn it
Step-by-step explanation:
A medical center conducted a study to investigate cholesterol levels in people who have had heart
attacks. A random sample of 16 people was obtained from the names of all patients of the medical
center who had a heart attack in the previous year. Of the people in the sample, the mean cholesterol level was 264.70 milligrams per deciliter (mg/dL) with standard deviation . Assuming all conditions for inference were met, which of the following is a 90 percent confidence interval for the mean cholesterol level, in, of all patients of the medical center who had a
heart attack in the previous year?
Using the t-distribution, as we have the standard deviation for the sample, it is found that the 90% confidence interval is (246.6, 282.8).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 16 - 1 = 15 df, is t = 1.7531.
Researching the problem on the internet, the standard deviation was of 42.1 mg/dL, hence the parameters are as follows:
[tex]\overline{x} = 264.7, s = 41.2, n = 16[/tex]
Thus, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 264.7 - 1.7531\frac{41.2}{\sqrt{16}} = 246.6[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 264.7 + 1.7531\frac{41.2}{\sqrt{16}} = 282.8[/tex]
The 90% confidence interval is (246.6, 282.8).
More can be learned about the t-distribution at https://brainly.com/question/16162795
Please show the figure in a piece of paper
Step-by-step explanation:
If you have any dout you can ask me.
Slope of line that passes through (3,6) and (8,2
Answer:
-4/5
Step-by-step explanation:
To find the slope of a line with two points, we do y2-y1/x2-x1.
y2 is 2. y1 is 6.
2-6 = -4
x2 is 8. x1 is 3
8-3 = 5
-4/5 is the answer meaning it is the slope.
Answer:
Slope of this line = -4/5.
Step-by-step explanation:
The formula is
Slope = (y2-y1)/(x2-x1) where (x1, y1) and (x2, y2) are the 2 points.
So here we have:
(6-2)/(3-8)
= -4/5.
solve and check
x=2x-4/3
Answer:
it = -1
Step-by-step explanation:
-1
help w this !!!!!!!!!!
Answer:
1. BC = 24
Perimeter of ABCD = 96
3. PT = 9
ST = 7
Step-by-step explanation:
Question 1
All the side lengths of a rhombus are equal.
Therefore, BC = AB = 24
So the perimeter of ABCD = 24 × 4 = 96
Question 3
The diagonals of a rhombus bisect each other at right angles.
Bisect means to divide into two equal parts.
Therefore, PT = TR so PT = PR ÷ 2
As PR = 18 then PT = 18 ÷ 2 = 9
QT = ST so ST = QS ÷ 2
As QS = 14 then ST = 14 ÷ 2 = 7
Bradley owns 2 surfboards and 4 wet suits. If he takes one surfboard and one wet suit to the beach, how many different combinations can he choose?
Answer:
The answer is eight
Step-by-step explanation:
4*2=8
What is the completely factored form of f(x) = x3 – 2x2 – 5x 6? f(x) = (x 2)(x – 3)(x 6) f(x) = (x 2)(x – 3)(x – 6) f(x) = (x – 2)(x 3)(x – 1) f(x) = (x 2)(x – 3)(x – 1)
[tex]x^3-2x^2-5x +6\\\\=x^3-x^2-x^2+x-6x+6\\\\=x^2(x-1)-x(x-1)-6(x-1)\\\\=(x-1)(x^2 -x -6)\\\\=(x-1)(x^2 -3x +2x -6)\\\\=(x-1)\textbf{[} x(x-3) +2(x-3)\textbf{]}\\\\=(x-1)(x-3)(x+2)[/tex]
The requried, factored form of the given expression is (x - 1)(x - 3)(x + 2).
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
To factor the polynomial f(x) = x³ – 2x² – 5x + 6 completely, we can use a combination of the rational root theorem and synthetic division.
We can use synthetic division to test each possible root and see if it is a factor of the polynomial. Starting with x = 2, we have:
2 | 1 -2 -5 6
| 2 0 -10
|_____________
1 0 -5 -4
Since the remainder is not zero, x = 2 is not a factor of the polynomial. Continuing with the other possible roots, we find that x = 1 and x = 3 are roots, but x = -1, x = -2, x = -3, and x = -6 are not roots.
Therefore, we can factor the polynomial as follows:
f(x) = x² – 2x² – 5x + 6
= (x - 1)(x - 3)(x + 2)
So the completely factored form of f(x) is f(x) = (x - 1)(x - 3)(x + 2).
Learn more about Factors here:
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Quick help please it will mean a lot if you help me :)
Answer:
Green heart is 2 and blue shape is 8.
Step-by-step explanation:
We know 1 purple drop equals 3.
So 3+3 = 6
The total weight is 16 so we can do 16-6 = 10
We have 10 left. Since we need the weight to be balanced the green heart must be 2.
Because then it would be 8 on 1 side (2 purples equals 6 and 1 heart equals 2, so 6+2=8) and 8 on the other side (8+8=16).
I need help with #1 & #2
Answer:
2. Letter B, see the attachment?
and also, I can't answer the #1 because I can't read it. I'm sorry
Already done #1 in your other question.
#2
2x-y=4y=2x-4Comapre to slope intercept form
slope=m=2Parallel lines have equal slope
Equation in point slope form
y+11=2(x+3)y+11=2x+6y=2x-5Which table contains only the points that lie on the line represented by y=5/4x-3
Answer:
A table that represents a linear equation should be your answer. This means your slope should be constant/straight not like a parabola or absolute function.
Step-by-step explanation:
When you're trying to solve something using slope-intercept you can graph it or plug numbers for (x,y).
Graph:
Start at (0,-3)
Then plot the point since that is your Y-Intercept
Then go 5 up and 4 over to find your next point.
Once done, you should connect the dots to form a slope or a linear equation.
In order to better decide how to market a new line of clothing, mary is researching the demographics of the customers of a certain clothing store. she counted the number of customers who visited the store over the course of a month, and found out how many of the customers were high school students. her collected data is in the table below. week 1 2 3 4 customers 2,848 3,141 3,861 3,911 students 2,033 1,937 2,076 1,721 mary predicts that the store will see 4,238 customers next week. approximately how many high school students should the store expect next week? a. 1,865 b. 2,392 c. 2,446 d. 3,025
Number of high school students which should the store expect next week, Mary predicts that the store will see 4,238 customers next week is 2392.
What is expected value?The expected value is the long term average of the data or the mean of the data.
In order to better decide how to market a new line of clothing, Mary is researching the demographics of the customers of a certain clothing store.
She counted the number of customers who visited the store over the course of a month, and found out how many of the customers were high school students.
Her collected data is in the table below.
Week 1 2 3 4 Customers 2,848 3,141 3,861 3,911 Students 2,033 1,937 2,076 1,721Mary predicts that the store will see 4,238 customers next week.
From using the long term mean value calculator for the provided data, the predicted value of the next week we get as 2392.
Hence, the number of high school students which should the store expect next week, Mary predicts that the store will see 4,238 customers next week is 2392.
Learn more about the expected value here;
https://brainly.com/question/15858152
Answer:
B
Step-by-step explanation:
B because the of the is the cool make of giga chad braincells :)
A university decides to accept only the top 15% of
the applicants applying. Their acceptance is based on
performance on an entrance exam. If the mean was 70 and
the standard deviation was 8, then what is the minimum
score needed to be accepted to the university?
The minimum score needed to be accepted in the university when it takes only top 15% performers where performace had mean 70 score and standard deviation of 8 is found being 78.32 approx.
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
For this case, suppose that:
X = the score a student gets in the considered university's entrance exam.
Then, we have:
[tex]X \sim N(\mu = 70, \sigma = 8)[/tex]
Let X = x be the score such that scores bigger than x is 15% of all the scores applicants get.
That means, P(X > x) = 15% of the total area the distribution of X have under its normal distribution. Or, we can say that there is 15% chance of getting scores above X = x
Now, we can rewrite this statement as:
[tex]1 - P(X \leq x) = 0.15[/tex]
Converting X to Z (standard normal variate), we get:
[tex]1 - P(X \leq x ) = 0.15\\\\1 - P\left(Z \leq z = \dfrac{x - 70}{8} \right) =0.15\\\\P(Z \leq z = (x-70)/8) = 0.85[/tex]
The value Z = z for which the p-value is approx 0.85 is found from the z-tables as:
Thus, we get:
[tex]z = \dfrac{x-70}{8}\\x = 8z + 70\\x \approx 8 \times 1.04 + 70 = 78.32[/tex]
Thus, the minimum score needed to be accepted in the university when it takes only top 15% performers where performace had mean 70 score and standard deviation of 8 is found being 78.32 approx.
Learn more about z-score here:
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URGENT URGENT URGENT URGENT URGENT URGENT URGENT URGENT URGENT!!!!!!!
Plans for a new apartment complex call for buildings directly across the fence from each other to be congruent. This computer printout shows Building A.
if the vertices of Building B are located at (2x1,2y1),(2x2,2y2),(2x3,2y3), and (2x4,2y4), will building B be congruent to Building A?
Because the transformation is a dilation, we conclude that the buildings are not congruent.
Is building B congruent to building A?
You need to remember that if the transformation applied to A is a dilation or a contraction, then the figures will not be congruent.
Where for a point (x, y), a dilation of scale factor k is written as:
(kx, ky).
The vertices of building A are:
(x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄).
And the vertices of building B are a dilation of the above ones, such that the dilation has a scale factor k = 2.
(2x₁, 2y₁), (2x₂, 2y₂), (2x₃, 2y₃), and (2x₄, 2y₄).
So, because there is a dilation, building B is not congruent to building A.
If you want to learn more about transformations, you can read:
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I DONT DO MATHHHHH?????
Need help asap
6. Choose a number that will produce an irrational answer when added to 7/8
Answer:
√7
Step-by-step explanation:
√7 is the only irrational number because it has the radical sign
√
https://brainly.com/question/19242625
Find the volume of the shaded region of the figure. Round answer to the nearest hundredths place.
Answer:
Step-by-step explanation:
Cylinder
Start by finding the volume of the cylinder as though the spheres were not there.
Volume of a cylinder = pi r^2 h
r = 6 inches
h = 25 inches. Put the givens in the formula
Volume = pi 6^2 * 25
Volume = pi * 36 * 25
Volume = 900 pi
One sphere
Don't try and find the volume of both spheres. Just do one and double it.
V = pi * (4/3) * r^3
r = 6 inches
V = pi * (4/3) * 6^3
V = pi * 288 Cubic inches
Two spheres
Total volume spheres = 2 * 288 pi
Total Volume of spheres = 576 pi
Volume of the shaded region.
The following will act as a formula for the answer to the question
V_shade = Volume of the cylinder - volume of the 2 spheres
Substitute values into formula
Volume shade = 900 * pi - 576* pi Take out common factor (pi)
Volume shade = pi * (900 - 576 )
Volume of the shaded area
Volumne shade = pi *324
pi = 3.14
Volume shade = 1017.36
Answer:
volume of the shaded region = 1018
Step-by-step explanation:
What is the value of K?
Answer:
k = 2.31
Step-by-step explanation:
You will use the Law of Cosine to determine the unknown angles, then you will use the Sine Rule to determine the unknown side.
The bowling team at Lincoln High School must choose a president, vice president, and secretary. If the team has 20 members, how many ways could the officers be chosen?
Using the permutation formula, as the order is important, it is found that the officers can be chosen in 6840 ways.
Each "position" is a different role(president, vice president and secretary), hence the order is important.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 3 people will be chosen from a set of 20, hence:
[tex]P_{20,3} = \frac{20!}{17!} = 6840[/tex]
The officers can be chosen in 6840 ways.
More can be learned about the permutation formula at https://brainly.com/question/25925367
There are 20 machines at the gym and Manuel wants to perform exercises on 5 different machines while he is there. How many different ways can he select the machines to use?
31008
1860480
100
15504
Selection of machines is persons choice and not arranged specifically, thus we will use Combination.
⇒ 20C5
⇒ 20!/5!(20-5)!
⇒ 15504
Use combination
total ways
[tex]\\ \rm\dashrightarrow ^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
[tex]\\ \rm\dashrightarrow ^{20}C_5[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{20!}{5!15!}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{20(19)(18)(17)(16)(15!)}{5(4)(3)(2)(15!}[/tex]
[tex]\\ \rm\dashrightarrow 15504[/tex]
kate has the following scores on her math test this quarter 89,79,83, and 94.if she want an average of 85 ,what musther score be on the 5th test
9=(1/27)^a+3 find a
-11/3
-7/3
7/3
11/3
Step-by-step explanation:
I think you made some mistakes in the problem definition.
I guess you mean
9 = (1/27)^(a+3)
let's think about how to create 9 out of 1/27 just by using exponents.
we note that 27 is 3³. and therefore the cubic root of 27 is 3.
so,
(1/27)^(1/3) = 1/3
because the exponent 1/3 means "cubic root". an exponent 1/2 means square root. and so on.
making the exponent negative means 1/...
so,
(1/27)^(-1/3) = 3
and now, with what exponent operation can we turn 3 into 9 ?
by squaring it.
so,
((1/27)^(-1/3))² = 9
putting an exponent on an exponent means to multiply the exponents during simplification.
therefore,
((1/27)^(-1/3))² = (1/27)^(-2/3) = 9
that means
a + 3 = -2/3
a = -2/3 - 3 = -2/3 - 9/3 = -11/3
so, the first answer option is correct.
I need help with is question please.
Who’s in 10th grade and who’s in 9th? I’m doing a poll for math?
Answer:
I'm in 10th
hope that would help, lol