9514 1404 393
Answer:
57
Step-by-step explanation:
Apparently, you want to simplify ...
[tex]\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}[/tex]
so the denominator is rational. It looks like the form you want is ...
[tex]\dfrac{A\sqrt{2} + B\sqrt{3} + C\sqrt{7} + D\sqrt{E}}{F}[/tex]
And you want to know the sum A+B+C+D+E+F.
__
We can start by multiplying numerator and denominator by a conjugate of the denominator. Then we can multiply numerator and denominator by a conjugate of the resulting denominator.
[tex]\displaystyle =\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}\cdot\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{\sqrt{2} + \sqrt{3} - \sqrt{7}}=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\\\\=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\cdot\frac{\sqrt{6}+1}{\sqrt{6}+1}=\frac{(1+\sqrt{6})(\sqrt{2}+\sqrt{3}-\sqrt{7})}{10}\\\\=\frac{\sqrt{2}+\sqrt{3}-\sqrt{7}+2\sqrt{3}+3\sqrt{2}-\sqrt{42}}{10}=\frac{4\sqrt{2}+3\sqrt{3}-\sqrt{7}-\sqrt{42}}{10}[/tex]
Comparing this to the desired form we have ...
A = 4, B = 3, C = -1, D = -1, E = 42, F = 10
Then the sum is ...
A +B +C +D +E +F = 4 + 3 -1 -1 +42 +10 = 59 -2 = 57
The sum of interest is 57.
Which of the statements is true for the two division problems below? A: (x^2-3x-18)/(x-6) B. (x^3-x^2-5x-3)/(x^2+2x+1)
Answer:
B is the right statement
Answer:
add the answer choices
Step-by-step explanation:
Find the missing pieces of the triangle round to the nearest tenth
Answer:
8√3
Step-by-step explanation:
Missing side,
√(19²-13³)
= 8√3
Answered by GAUTHMATH
A town recently dismissed 8 employees in order to meet their new budget reductions. The town had 9 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that at least 7 employees were over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
The probability that at least 7 employees were over 50 is 0.0073%.
Step-by-step explanation:
Given that a town recently dismissed 8 employees in order to meet their new budget reductions, and the town had 9 employees over 50 years of age and 16 under 50, if the dismissed employees were selected at random, to determine what is the probability that at least 7 employees were over 50, the following calculation must be performed:
9/25 x 8/24 x 7/23 x 6/22 x 5/21 x 4/20 x 3/19 = X
0.36 x 0.33 x 0.304 x 0.272 x 0.238 x 0.2 x 0.157 = X
0.000073 = X
100X = 0.0073
Therefore, the probability that at least 7 employees were over 50 is 0.0073%.
In the figure, triangles ABC and DEF are congruent.
Find the measure of DF.
a. 13m
b. 12m
c. 7m
d. 13.928m
A department store mails a customer satisfaction survey to people who make credit card purchases at the store. This month, 3521 people made credit card purchases. Surveys are mailed to 278 of these people, chosen at random, and 172 people return the survey form. Identify the population and the sample.
Answer:
The population is the population of 3521 people who made credit card purchases.
The sample is the 172 people who returned the survey form.
Step-by-step explanation:
Department mails customers satisfactions forms to those who make credit cards purchase at the store, totaling 3521 people. Thus, the population is the population of 3521 people who made credit card purchases.
Surveys are mailed to 278 of these people, chosen at random, and 172 people return the survey form.
Thus the sample, that is, those from whom the data will be taken and expanded to the rest of the population, is the 172 people who returned the survey form.
The population is all 3521 people who made credit card purchases.
The sample is the 172 people who returned the survey form.
The following expression gives an approximate value of the total average credit card debt in a U.S. household (in dollars) t years after 1995.
400t + 5750
Use this expression to predict what the total average credit card debt will be in the year 2025.
Answer: In the year 2025, the total average credit card debt for a U.S. household will be ------------ dollars.
Answer:
In 2025, t=30. so D=418*30+6000 = 18540
what is the radius of a circle in it in if the area is 36m²?
A.0.339 m
B.3.39 m
C.78.5 m²
D.339 m
Answer:
B. 3.39 m
Step-by-step explanation:
r² = A/π
= 36/3.14
= 11.465
r = √11.465 = 3.39
what is the length of a rectangular solid with a volume of 180 cu ft, if it is 9 ft high and 4ft wide?
Answer:
5 ft
Step-by-step explanation:
The formula for Volume is V=lwh, or Volume = length x width x height.
The equation would be:
[tex]180=l(4)(9)[/tex]
or
[tex]180=36l[/tex]
To find the answer, divide by 36.
[tex]\frac{180}{36} =\frac{36l}{36}[/tex]
[tex]5=l[/tex]
Find the solution(s) of the system of equations. y = x2 + 4x y + x2 = –4x Question 7 options: A) (–4, 0) and (0, 0) B) (0, 0) C) (–4, 0) and (4, 0) D) (0, 0) and (4, 0)
Answer:
Hello,
Answer A (-4,0) and (0,0)
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y&=&x^2+4x\\y+x^2&=&-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\y&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\x^2+4x&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}2*x^2+8*x&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}x(x+4)&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\[/tex]
[tex]\left\{\begin{array}{ccc}x&=&0 \\y&=&0\\\end{array} \right. \ or\ \left\{\begin{array}{ccc}x&=&-4 \\y&=&0\\\end{array} \right.[/tex]
Our soccer team lost 9 games this season. That was 3/8 of all they played. How many games did they play this season?
Answer:
15
Step-by-step explanation:
3/8 = 9
9÷3= 3
the remainder of 3/8 is 5/8 so
5x3=15
Bobby wants to bring popsicles to a summer barbecue. He decides to try a new recipe for pineapple-orange popsicles, so he makes a small batch with 1 cup of pineapple juice and 3 cups of orange juice to taste. He likes the combination, so he uses 3 cups of pineapple juice and 7 cups of orange juice to make a larger batch for the barbecue. Which batch of popsicles tastes more like oranges?
Answer:The first would taste more like oranges
Step-by-step explanation:
How many spaces does it move over
Answer:
The point at the bottom has to move over 2 to the left to be aligned with the point at the top however they will have a 3 space in between the 2 same for the point at the top, the top point moves over 2 to the right to be aligned with the bottom point, then they will have a 3 square space between each other.
Answer:Around 3 spaces between?
Step-by-step explanation:
By which number should (2/5)^-3 be multiplied to get (1/2)^4 as a product ?
Answer:
[tex]\frac{2}{5}^{-3}[/tex]×[tex]x=\frac{1}{2}^{4}[/tex]
[tex]x=\frac{2}{5} ^{3} \\[/tex]×[tex]\frac{1}{2}^{4}[/tex]
(negative in the exponent means reciprocal of the fraction)
x= [tex]\frac{1}{250}[/tex]
Brainliest please
For a two-tailed test with a sample size of 20 and a .20 level of significance, the t value is _____. Selected Answer: d. 1.328
Answer:
1.328
Step-by-step explanation:
Given :
Sample size, n = 20.
Degree of freedom, df = n - 1
df = 20 - 1 = 19
α = 0.2
Using the T-distribution calculator :
Since it is two - tailed:
Tα/2 ; 19 = T0.2/2 ; 19 = T0.1, 19 = 1.3277 = 1.328
Using a t-distribution calculator, it is found that the t-value is of t = 1.328.
How to find the critical value of the t-distribution?In a calculator, these following inputs are needed:
The number of degrees of freedom, which is one less than the sample size.The level of significance.Whether the test is one-tailed or two-tailed.In this problem, inputting the data given in a calculator, it is found that the t-value is of t = 1.328.
More can be learned about the t-distribution at https://brainly.com/question/13873630
1+log2=log(x+1)
I know that x=19 but how do you get 19?
Step-by-step explanation:
Recall that [tex]\log 10 = 1[/tex] so we can rewrite the equation above as
[tex]\log 10 + \log 2 = \log (x + 1)[/tex]
Also recall that [tex]\log(ab) = \log a + \log b[/tex] so the left-hand side becomes
[tex]\log [(10)(2)] = \log (x + 1)[/tex]
or
[tex]20 = x + 1 \Rightarrow x = 19[/tex]
. In Habib High School 275 of 300 students received a grade of A, while in Public Hall 120 out of 150 students received a grade of A. Which of the two schools has a better record?
Match each set of vertices with the type of triangle they form.
A(2, 0), B(3, 2), C(5, 1)
obtuse scalene triangle
A(4, 2), B(6, 2), C(5, 3.73)
isosceles right triangle
A(-5, 2), B(-4, 4), C(-2, 2)
right triangle
A(-3, 1), B(-3, 4), C(-1, 1)
acute scalene triangle
A(-4, 2), B(-2, 4), C(-1, 4)
9514 1404 393
Answer:
rightacuteobtuserightobtuseStep-by-step explanation:
When the same problem is repeated, I like to solve it using a spreadsheet. That way, the formulas only need to be entered once, and the arithmetic is (almost) guaranteed to be done correctly.
A "form factor" computed from side lengths can be used to determine the type of triangle. Where 'c' is the long side, that factor can be computed as ...
f = a² +b² -c²
and interpreted as follows:
f = 0, right trianglef > 0, acute trianglef < 0, obtuse triangle(The sign of f matches the sign of the cosine of the largest angle computed using the law of cosines.)
Of course, a right triangle can also be identified by looking at the slopes of the sides of the triangle. If any pair of slopes has a product that is -1, or if any pair is 0 and "undefined", then the triangle will be a right triangle.
__
The attached spreadsheet is designed to accommodate a number of different problem requirements. It shows both side lengths and slopes, and it shows the "form factor" as described above. The final classification is shown at far right.
What are the zeroes of f(x) = x2 - X - 2?
x= -2,1
x = 2, -1
x= -2, -1
x = 2,1
Answer:
x=2 x=-1
Step-by-step explanation:
f(x) = x^2 - X - 2
0= x^2 -x-2
Factor
0 =(x-2)(x+1)
Using the zero product property
x-2 =0 x+1 =0
x=2 x=-1
Answer:
x=2, -1
Step-by-step explanation:
Hi there!
We want to find the zeros of this function: f(x)=x²-x-2
The zeros are the values of x that will make f(x)=0
So that means in order to find the zeros, set f(x) as 0
In that case,
x²-x-2=0
Now let's solve the quadratic equation
We can do it by factoring
-x is the sum of two numbers, while -2 is the product of those two same numbers
Now think: which two numbers add up to -1, but multiply to get -2?
Those numbers are -2 and 1
Now factor the polynomial by FOIL:
(x-2)(x+1)=0
Split and solve
x-2=0
x=2
x+1=0
x=-1
The zeros are x=2, -1
Hope this helps!
PLEASE HELP ANSWER THISS!!! I NEED THIS PLEASE!!! AND NO LINKS EITHER PLSS!!
It doesn't change because to add fractions, you need a common denominator. To find it, they multiplied 1/3 by 2 to make 2/6, to add to the 3/6.
Given the parabola below, find the endpoints of the latus rectum. (x-2)^2=-20(y+2)
Answer:
The endpoints of the latus rectum are [tex](12, -7)[/tex] and [tex](-8, -7)[/tex].
Step-by-step explanation:
A parabola with vertex at point [tex]C(x, y) = (h,k)[/tex] and whose axis of symmetry is parallel to the y-axis is defined by the following formula:
[tex](x-h)^{2} = 4\cdot p \cdot (y-k)[/tex] (1)
Where:
[tex]y[/tex] - Independent variable.
[tex]x[/tex] - Dependent variable.
[tex]p[/tex] - Distance from vertex to the focus.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex.
The coordinates of the focus are represented by:
[tex]F(x,y) = (h, k+p)[/tex] (2)
The latus rectum is a line segment parallel to the x-axis which contains the focus. If we know that [tex]h = 2[/tex], [tex]k = -2[/tex] and [tex]p = -5[/tex], then the latus rectum is between the following endpoints:
By (2):
[tex]F(x,y) = (2, -2-5)[/tex]
[tex]F(x,y) = (2,-7)[/tex]
By (1):
[tex](x-2)^{2} = -20\cdot (-7+2)[/tex]
[tex](x-2)^{2} = 100[/tex]
[tex]x - 2 = \pm 10[/tex]
There are two solutions:
[tex]x_{1} = 2 + 10[/tex]
[tex]x_{1} = 12[/tex]
[tex]x_{2} = 2-10[/tex]
[tex]x_{2} = -8[/tex]
Hence, the endpoints of the latus rectum are [tex](12, -7)[/tex] and [tex](-8, -7)[/tex].
Find RS. Can anyone help?
The segment XT splits the trapezoid exactly in half. The average of RS and Q will give us XT because of the properties of a trapezoid.
We find the area of a trapezoid by averaging the bases as well.
RS + Q / 2 = XT
RS + 26 / 2 = 22
RS + 26 = 44
RS = 18
Hope this helps!
Which of the binomials below is a factor of this trinomial?
x^2+8x+16
This is because the given expression factors to (x+4)(x+4), which condenses to (x+4)^2.
To factor, think of two numbers that A) multiply to 16, and B) add to 8. Those values would be 4 and 4
4+4 = 8
4*4 = 16
So that's how we end up with (x+4)(x+4). You can use the FOIL rule to expand that out and get x^2+8x+16 again to help verify you have the correct factorization.
Mr Gardner is making 6 treat bags. He has 185 chocolate-covered raisins to share evenly among the treat bags.
Answer:
✎There will be 30 Chocolate-Covered raisins in each bag.
✎ And 5 Remaining.
Step-by-step explanation:
Take 185 and divide it by 6 and you should get 30 per bag with a remainder of 5 :)
Which function is represented by the graph?
f(x) = −|x − 3| + 4
f(x) = −|x + 3| + 4
f(x) = −|x − 4| + 3
f(x) = −|x + 4| + 3
Linda leaves the school to go home. She walks 7 blocks south and then 9 blocks east. how far is Linda from her office?
A.8 blocks
B.11.5 blocks
C.20 blocks
D.14 blocks
Answer:
B. 11.5
Step-by-step explanation:
That missing length can be solved via the equation a^2+b^2=c^2, where the hypotenuse is c. We know A and B, which is 7 and 9.
7^2+9^2=130
sqrt 130 is 11.4017543
Here, you kinda have to break the rules of rounding to say that it is B.
There could be a more efficient route for resolving this answer, but this is the method that I was taught.
A map has a scale in which 1.25 inches represents 250 miles.
How many miles does 1 inch represent?
Answer: 200 miles
Work Shown:
(1.25 inches)/(250 miles) = (1 inch)/(x miles)
(1.25)/(250) = 1/x
1.25x = 250*1 ..... cross multiplication
1.25x = 250
x = 250/(1.25)
x = 200 miles
Kenji simplifies 3^5 x 4^ 5and gets the result 12^10, but Darlene is not sure. Is Kenji correct? Justify your answer.
That's a question about exponentiation.
Answer:
Kenji is wrong because he does not aply the porperty correctly.
Step-by-step explanation:
A exponetiation has this form:
[tex]\boxed{a^b}[/tex]
a is the base
b is the power or exponent
To understand that situation it's important to know a property about exponentiation. When we have a multiplication with the same exponent and diferent bases, the result is the multiplication of the bases with the same exponent. Let's see this above, in mathematical language:
[tex]\boxed{a^b \cdot c^b = (a\cdot c) ^b}[/tex]
Examples:
[tex]2^3 \cdot 8^3 = (2 \cdot 8) ^3 = 16^3[/tex][tex]10^9 \cdot 23^9 = (10 \cdot 23) ^9 = 230^9[/tex]Now, we can say why Kenji is wrong. It's easy simplify [tex]3^5 \cdot 4^5[/tex]! We know that the result is [tex](3 \cdot 4) ^5 = 12^5[/tex], but Kenji multiplied the bases and added the exponents, that's why he is wrong.
I hope I've helped. ^^
Enjoy your studies! \o/
Choose the correct solution for the given equation x^2-6x=40
Answer:
10,-4
Step-by-step explanation:
not sure where the options are but if you were to solve this equation first bring everything to one side.
x^2 - 6x - 40 = 0
factor it
(x-10)(x+4) = 0
set each part to 0
x-10 = 0 and x+4 = 0
solutions are 10 and -4
one month is what percentage of a year given that there are 7 days in a week, and 12 months in a year
Answer:
it should be 8.333333%
Step-by-step explanation:
T is the midpoint of pq where pt=3x-3 and tq=5x-7 find x
Answer: x = 2
Step-by-step explanation:
P-----------------------T----------------------Q
(3x-3) (5x-7)
Since T is the midpoint we know that PT and TQ are equal
Just solve the equation: 3x-3 = 5x-7
[tex]3x-3 = 5x-7[/tex]
now move the x to one side
[tex]-3 = 2x-7[/tex] (I subtracted the 3x)
then get the 2x by itself
[tex]4=2x[/tex]
lastly, divide by 2 to get x by itself
[tex]x=2\\[/tex]
