Answer:
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
the question asks us to rationalise the given term ! thus , we'll just have to remove the √3 from th denominator anyhow !
let's start ~
[tex] \frac{2 \sqrt{5} }{7 - \sqrt{3} } \\ \\ \implies \: \frac{2 \sqrt{5} }{7 - \sqrt{3} } \: \times \: \frac{7 + \sqrt{3} }{7 + \sqrt{3} } = \frac{14 \sqrt{5} + 2 \sqrt{15} }{(7) {}^{2} - ( \sqrt{3) {}^{2} } } \\ \\ \implies \frac{14 \sqrt{5} + 2 \sqrt{15} }{49 - 3} \\ \\ \implies \frac{14 \sqrt{5} + 2 \sqrt{15} }{46} \\ \\ \implies \: \frac{\cancel{2}(7 \sqrt{5{} } \: + \sqrt{15} )}{\cancel{46} } \\ \\\bold\red{ \implies \: \frac{7 \sqrt{5} + \sqrt{15} }{23}}[/tex]
hope helpful :D
A 2-yard piece of linen costs $18.54. What is the price per foot?
Answer:
3.09 per ft
Step-by-step explanation:
1 yd = 3ft
so 2 yd = 6ft
6ft = 18.54
18.54 /6ft
3.09 per ft
An isosceles triangle MNP has one angle, N, with a measure of 20". The
angles M and Pare congruent. Which is the measure of angle P?
P=80º
Start by doing 180-20 since N=20
M and P are congruent, so P = 160/2
P=80
Select all pairs of complementary angles in the diagram.
Answer:
Step-by-step explanation:
Complementary angles sum to 90 degrees.
< BAF and < BFA
<CDE and < CED.
Supplementary ( sum to 360):
< FBC and <BFE
<BCE and < FEC.
y= 45(1.6)^2
I need help with this, thanks!
Which weight occurs most often? Which weight occurs least often? How can you tell from the line plot?
A bank surveyed all of its 60 employees to determine the proportion who participate in volunteer activities. Which of the following statements is true?
The bank should not use the data from this survey because this is an observational study.
The bank can use the result of this survey to prove that working for the bank causes employees to participate in volunteer activities,
The bank did not select a random sample of employees, so the survey will not provide the bank with useful information
D
The bank would have to use the survey data to construct a confidence interval in order to estimate the proportion of employees who participate in volunteer activities.
The bank does not need to use an inference procedure to determine the proportion of employees who participate in volunteer activities because the survey was a census of all
employees
DELL
The true statement about the bank survey is (e) The bank does not need to use an inference procedure to determine the participant proportion
How to determine the true statement?The population and the sample size are given as:
N = 60
This is so because the bank surveyed all her staff.
Since all the bank staffs participated in the survey, it means that the proportion of the study is 1 or 100%.
So, the bank do not need to determine the proportion that participates
Hence, the true statement is (e)
Read more about surveys at:
https://brainly.com/question/15713806
A small cube has a volume of 64 cubic feet. A larger cube has sides that are three times as long as the small cube. How long are the sides of each cube?
The side of a larger cube is equal to 12 ft meanwhile the side of a small cube is equal to 4 ft.
Volume of a CubeA cube is a 3D- form of a square and its volume is found in the formula:
V=s³, where: s is the length of each side of a cube.
If the small cube has a volume ([tex]V_s[/tex]) of 64 ft³, you can apply the formula V=s³ for finding its the length of its sides. Thus
[tex]V_s[/tex]=64 ft³
[tex]s_v^3[/tex]=64
[tex]s_v=\sqrt[3]{64}\\ \\ s_v=4 ft[/tex]
A larger cube has sides ([tex]s_l[/tex]) that are three times as long as the small cube. Therefore, [tex]s_l=3s_v[/tex]. If [tex]s_v[/tex]=4 ft, the [tex]s_l[/tex] will be:
[tex]s_l=3s_v\\ \\ s_l=3*4\\ \\ s_l=12 ft[/tex]
Read more about the volume of a cube here:
https://brainly.com/question/3390425
Helppppp!!! What is the area of the trapezoid shown below?
Answer:
The area of T is equal to sum of area of R and Triangle
Step-by-step explanation:
[tex]area = 12 \times 2[/tex]
Area)= 24
[tex]area = \frac{1}{2} \times 12 \times 15[/tex]
Area= 90
Area of T = 90 PLUS 24
AREA == 114
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASEI know the answer I just need to know how to solve it. The highlighted is the answer.
[tex]x^2+4x+4 = 8\\\\\implies x^2+2\cdot 2 \cdot x+2^2 = 8\\ \\\implies (x+2)^2 = 8\\\\\implies x+2 =\pm\sqrt 8\\\\\implies x +2 = \pm\sqrt{4 \times 2}\\\\\implies x +2 = \pm2\sqrt 2\\\\\implies x =-2 \pm2\sqrt2[/tex]
what is the answer to this problem
Answer:
∠1 = 130°
∠2 = 50°
∠3 = 130°
Step-by-step explanation:
As we can see Angles 1 and 50° are on a straight line. As :
Angles on a straight line add up to 180. So :
50 + ∠1 = 180
∠1 = 180-50
∠1 = 130
As we can angles 1 and 2 are on a straight line. As :
Angles on a straight line add up to 180. So :
∠1 + ∠2 = 180
As we worked out ∠1 we can substitute that in to work out ∠2 :
130 + ∠2 = 180
∠2 = 180-130
∠2 = 50
As we can angles 2 and 3 are on a straight line. As :
Angles on a straight line add up to 180. So :
∠2 + ∠3 = 180
As we worked out ∠2 we can substitute that in to work out ∠3 :
50 + ∠3 = 180
∠3 = 180-50
∠3 = 130
Hope this helped and brainliest please.
What is the fifth term of the sequence?
a = m
an = 2an-1
=
0 2m
O 4m
O 8m
O 16m
Answer:
8m
Step-by-step explanation:
an = 2 an-1 means that each term in the sequence( except the first) is obtained by multiplying the last term by 2, so the first 4 terms are m, 2m, 4m, 8m.
jacob poured 5/6 cup of orange juice and a cup 5/8 of cranberry juice into a pitcher . He drank 1/2 cup of the juice in the pitcher. How many cups of juice are left in the pitcher?
Which of the following is equal to ? (In the picture)
Answer:
2^1/6
Step-by-step explanation:
either find the result of all equations or
times square root(2) by cube root (3) and put it over 1
... 1/6 and put this as the power to the number in the question
Please Help!!! 100 Points!!! Will Mark Brainliest If Correct!!!
Make sure everything is spaced out and easy to understand. Please show all of your work(if needed).
Task 1
Nonlinear Systems of Equations
Create a system of equations that includes one linear equation and one quadratic equation.
Part 1. Show all work in solving your system of equations algebraically.
Part 2. Graph your system of equations and show the solution graphically to verify your solution.
Task 2
Polynomial Identities
Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.
Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a3 + b3 = (a + b)(a2 − ab + b2) to calculate the sum of the cubes of your numbers without using a calculator.
Answer:
Step-by-step explanation:
Part A, the system of equation is, presented here as follows;
(1) 2·y = 3·x + 2
(2) y = 2·x² - 3·x + 2
Part B; The graph of the system of equation is attached
The reason for the above answers is as follows;
Part A
A system of equations are a given number of equations from which a common solution of the system can be found
A linear equation is an algebraic equation in which the maximum exponent of the variables is one and the graph of the equation is a straight line which is of the form y = m·x + c
A maximum value of the exponents of the variable quadratic equation is 2, and the general form of the quadratic equation is y = a·x² + b·x + c, where a, b, and c are real numbers
Therefore, the system of equation that can be created is as follows;
(1) 2·y = 3·x + 2
(2) y = 2·x² - 3·x + 2
Method for solving;
Divide equation (1) by 2, and equate both values of y to find the common solution as follows;
2·y/2 = (3·x + 2)/2 = 1.5·x + 1
∴ y = 1.5·x + 1
Equating both values of y gives;
y = 1.5·x + 1
y = 2·x² - 3·x + 2
Therefore;
1.5·x + 1 = 2·x² - 3·x + 2
2·x² - 3·x - 1.5·x + 2 - 1 = 0
2·x² - 4.5·x + 1 = 0
Using the quadratic formula, we get;
x = (4.5 ± √((-4.5)² - 4×2×1))/(2 × 2)
x = 2, or x = 0.25
From which we get;
y = 1.5 × 2 + 1 = 4, or y = 1.5 × 0.25 + 1 = 1.375
The points where the line graph and the quadratic graph intersect are;
(2, 4), and (0.25, 1.375)
Part 2
The area of a triangle is found by multiplying half of the measure of its base by its height. The area of the following right triangle is 18 square centimeters.
A. Write and solve an equation to find the value of h. Include all of your work in your answer.
B. In two or more complete sentences, verify your answer using mental math.
50 points
Answer:
[tex]\sf Area\:of\:a\:triangle=\dfrac12 \times base \times height[/tex]
Given:
area = 18 cm²base = 6 cmheight = (h + 1) cmSubstitute the given values into the equation and solve for h:
[tex]\sf \implies 18 = \sf \dfrac12 \times 6 \times (h+1)[/tex]
[tex]\sf \implies 18 = \sf \dfrac62 (h+1)[/tex]
[tex]\sf \implies 18 =3(h+1)[/tex]
expand using distributive property of addition [tex]a(b+c)=ab+ac[/tex]:
[tex]\sf \implies 18=3h+3[/tex]
subtract 3 from both sides:
[tex]\sf \implies 3h=15[/tex]
divide both sides by 3:
[tex]\sf \implies h=5[/tex]
To verify:
Half of the base is 3 cm.
If h=5, then the height of the triangle is 6 cm.
Multiplying 3 by 6 is 18.
This matches the given area, so we can verify that h = 5.
Answer:
Below!
Step-by-step explanation (a):Given:
Area of Triangle = 18 cm²Base of Triangle = 6 cmHeight of (Triangle = (h + 1) cmFormula:
[tex]\text{Area of triangle} = \dfrac{1}{2} \times \text{Base} \times \text{Height}[/tex]
Substitute the measures into the formula:
[tex]:\implies 18 \ \text{cm}^{2} = \dfrac{1}{2} \times 6 \times \text{(h} + 1\text{)}[/tex]
SImplify the R.H.S:
[tex]:\implies18 \ \text{cm}^{2} = 3 \times \text{(h} + 1\text{)}[/tex]
Divide both sides by 3:
[tex]:\implies \dfrac{18}{3} = \dfrac{3 \times \text{(h} + 1\text{)}}{3}[/tex]
Simplify both sides:
[tex]:\implies 6 = \text{(h} + 1\text{)}[/tex]
Subtract 1 both sides:
[tex]:\implies 6 - 1 = \text{h} + 1- 1[/tex]
Simplify both sides:
[tex]:\implies 5= \text{h}[/tex]
Step-by-step explanation (b):Reviewing on how to verify our answer:
We can verify our answer by substituting the value of "h" in (h + 1) to determine the height of the triangle. Then we can substitute the height and the base in the "area of triangle" formula (1/2 x Base x Height).
Note: Keep in mind that the evaluated area should be 18 cm², as said in the question. If the area evaluated is different from 18 cm², then the value of "h" is incorrect.Verifying our answer through mental math:
Clearly, the height of the triangle is 6 cm, as when "h" is substituted in the expression (h + 1), we get 5 + 1.As said above, the formula for determining the area of a triangle is 1/2 x Base x Height. Clearly, half of 6 is 3. Lastly, when 6 (Base) and 3 (Half of the height) are multiplied, we get 18 cm², which is the area stated in the question.Thus, the value of "h" is verified through mental math.
What are the solutions to log subscript 6 baseline (x squared 8) = 1 log subscript 6 baseline (x)
The solution of the logarithmic equation is given by the antilog. Then the value of x is 2 and 4.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The logarithmic equation is given below.
[tex]\log _6(x^{2} +8)= 1+ \log _6x\\\\\log _6(x^{2} +8)= \log_66+ \log _6x\\\\\log _6(x^{2} +8)= \log _66x\\[/tex]
Take antilog, then we have
[tex]\begin{aligned} x^{2} +8 &= 6x\\\\x^2 -6x + 8 &= 0\\\\x^2 -4x - 2x +8 &=0\\\\(x-4)(x-2) &= 0\\\\x&= 2, 4\end{aligned}[/tex]
Then the value of the x is 2 and 4.
More about the factorization link is given below.
https://brainly.com/question/6810544
Answer:
D. 2 and 4
Step-by-step explanation:
Answer and you get brainliest
Answer:
m = 30w
Step-by-step explanation:
Answer:
The answer that looks the best is m=30w
Step-by-step explanation:
I asked my teacher and he said it was right
Use the picture I provided to help me answer the question.
Answer:
both answer is wrong because in this expression
4g+12-g+5
3g+17 is the answer
Cindy's apartment complex is offering renters insurance through their insurance company. the insurance company charges an annual premium of $565.00 which can be paid in equal payments throughout the year with her monthly rent. cindy's monthly rent is currently $789.00. what will cindy's new rent be if she includes the renters insurance? a. $47.08 b. $630.75 c. $836.08 d. $1,354.00
Cindy's new rent when she includes the renter's insurance will be C. $836.08.
What is renters insurance?As an insurance policy, renters insurance offers the policyholder insurance coverage over personal belongings, liabilities, and living expenses.
Data and Calculations
Annual insurance premium = $565.00
Monthly insurance premium = $47.08 ($565/12)
Current monthly rent = $789.00
Cindy's new rent with the renters insurance included = $836.08 ($789.00 + $47.08).
Thus, Cindy's new rent when she includes the renter's insurance will be C. $836.08.
To learn more return insurance visit:
https://brainly.com/question/24441770
The other person is correct!
The answer is C: $836.08
------------------------------------------------------------
Have a great day and God bless! :D
You have $5,000 to invest for ten years. The Bank pays simple interest at an annual rate of 5%. Calculate your balance after 10 years.
Answer: $7,500
Step-by-step explanation:
Use the formula: SI = P(1 + rt)
SI = 5000(1 + 0.05[10])
SI = 5000 + 2500
SI = $7,500
After 10 years, your balance should be $7,500
Amir has $50 in a bank account. Every month, he pays $3.99 from his account for a game app. After 6 months, Amir wants to spend$25.00 on a school T-shirt. Does he have enough money in his bank account to buy the shirt?
yes and you also have $1.06 as a remainder.
hope it helps..!!!
please help me solve this!!!!!!
Answer:
C. 9
Step-by-step explanation:
y = -4x^2 + 2kx
subtitute 3:
y = -4(9)^2 + 2k(9)
y = -4(81) + 18k
let y = 0
=> 0 = -324 + 18k
=> k = 324/18 = 9
this is my calculations hope it helps
Please help me please please I need it so bad
Answer:
A i= 44. B i= 44. C i= 40.
solve this correctly to become the love of my life
Answer:
It is B.
Step-by-step explanation:
explanation is in the pic.
What is the perimeter of this rectangle? a. 2(x2 − x1) 2(y2 − y1) b. (x2 − x1)(y2 − y1) c. d. e. 4(y2 − x1)(x2 − y1)
The perimeter of the rectangle of length (x₂ - x₁) and width (y₂ - y₁) will be 2(x₂ - x₁) + 2(y₂ - y₁). Then the correct option is A.
What is a rectangle?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.
The length of the rectangle will be (x₂ - x₁) and the width of the rectangle will be (y₂ - y₁).
Then the perimeter of the rectangle will be
Perimeter = 2(x₂ - x₁) + 2(y₂ - y₁)
More about the rectangle link is given below.
https://brainly.com/question/10046743
A quadratic equation of the form 0=ax2 bx c has a discriminant value of -16. how many real number solutions does the equation have? -1 0 1 2
The provided quadratic equation, which has a negative discriminant value of -16, has no real number solutions.
What is the discriminant value in a quadratic equation?The standard form of the quadratic equation is,
[tex]ax^2+bx+c=0[/tex]
Here,(a,b, c) is the real numbers and (x) is the variable.
For this equation, the discriminant value can be given as,
[tex]D=b^2-4ac[/tex]
In this equation,
If the discriminant value is positive (D>0), then the equation has 2 real solution.If the discriminant value is equal to zero (D=0), then the equation has 1 real solution.When the discriminant value is negative (D<0), then the equation has 2 imaginary solution.The quadratic equation given as,
[tex]0=ax^2 +bx +c[/tex]
This quadratic equation has a discriminant value of -16. As the value of discriminant is negative, thus it has no real solution.
Hence, the provided quadratic equation, which has a negative discriminant value of -16, has no real number solutions.
Learn more about the discriminant value here;
https://brainly.com/question/24730520
Suppose you pull a card from a standard 52-card deck. Find Place or black). Express your answer as a fraction in simplest form.
Answer:
32/52 = 16/26 = 8/13
Step-by-step explanation:
If only Black cards = 26 this includes all black face cards
Face cards = 3 in each suit, 2 red suits so 3 × 2=6
26 + 6 = 32
Find the center and radius of the circle defined by the equation given below.
22 + 2x + y2 + 10y = 15
A:center (-1, – 5), radius: 15
B:center. (1, 5), radius: 15
C:center. (-1, – 5), radius: 141
D: center. (1, 5), radius: 41
Answer:
your question seem off but if its x² + 2x + y² +10y=15
Step-by-step explanation:
the answer will be
center = (-1,-5)
radius = square root 41
which will be C:center (-1,-5), radius square root 41
Chang bought a pad of paper for $1.50, a pen for $.80, and a ruler for $0.90 at the school store.
How much did Chang spend?
O A. $2.70
B. $3.20
C. $10.40
D. $18.50
Add the prices together:
1.50 + 0.80 + 0.90 = 3.20
Answer: B. $3.20
Answer:
$ 3.20 (Answer B)
Step-by-step explanation:
Add up the three prices given:
$1.50
0.80
0.90
-------------
$ 3.20 (Answer B)
what is the value of 2x to the 3rd power + x to the 2nd power -x when x+3?
Answer:
I am unsure of the wording of this question, so I will answer both ways I see it.
When x = x + 3, the value of 2x³ + x² - x is 2x³ + 19x² + 59x + 66.
When x = 3, the value of 2x³ + x² - x is 60.
Step-by-step explanation:
x = x + 3 solution:
It is given that:
f(x) = 2x³ + x² - x
We are trying to find this when x = x+3. Substitute this value in for every x in the function.
f(x + 3) = 2(x + 3)³ + (x + 3)² - (x + 3)
Expand the first part.
f(x + 3) = 2(x + 3)(x + 3)(x + 3) + (x + 3)² - (x + 3)
Multiply pairs together.
f(x + 3) = 2(x + 3)(x² + 6x + 9) + (x + 3)² - (x + 3)
Multiply the remaining pairs together.
f(x + 3) = 2(x³ + 9x² + 27x + 27) + (x + 3)² - (x + 3)
Distribute the two inside the parenthesis.
f(x + 3) = 2x³ + 18x² + 54x + 54 + (x + 3)² - (x + 3)
Evaluate (x + 3)².
f(x + 3) = 2x³ + 18x² + 54x + 54 + (x² + 6x + 9) - (x + 3)
Remove all parenthesis and start simplifying.
f(x + 3) = 2x³ + 18x² + 54x + 54 + x² + 6x + 9 - x - 3
Combine all terms ending in x².
f(x + 3) = 2x³ + (18x² + x²) + 54x + 54 + 6x + 9 - x - 3
f(x + 3) = 2x³ + 19x² + 54x + 54 + 6x + 9 - x - 3
Combine all terms ending in x.
f(x + 3) = 2x³ + 19x² + (54x + 6x - x) + 54 + 9 - 3
f(x + 3) = 2x³ + 19x² + 59x + 54 + 9 - 3
Last, combine the final numbers to get:
f(x + 3) = 2x³ + 19x² + 59x + 60
x = 3 solution:
It is given that:
f(x) = 2x³ + x² - x
Substitute 3 in for every value of the function.
f(3) = 2(3)³ + (3)² - 3
Evaluate 3 cubed and then multiply it by 2.
f(3) = 2(27) + 3² - 3
f(3) = 54 + 3² - 3
Evalute 3 squared.
f(3) = 54 + 9 - 3
Add 54 and 9.
f(3) = 63 - 3
Subtract 3 from 63 to get:
f(3) = 60