show that
[tex] \frac{2}{3 + \sqrt{7} } = 3 - \sqrt{7} [/tex]
I don't know what to do
please help with the steps.
for brainliest
Answer:
multiply by (3-√7)/(3 -√7) and simplify
Step-by-step explanation:
When there are radicals or complex numbers in the denominator, you can rewrite the expression so it has a real, rational denominator. You do this by multiplying numerator and denominator by the conjugate of the denominator. That value is the denominator with its sign changed.
This takes advantage of the factoring of the difference of squares.
(a -b)(a +b) = a² -b²
__
[tex]\dfrac{2}{3+\sqrt{7}}=\dfrac{2}{3+\sqrt{7}}\times\dfrac{3-\sqrt{7}}{3-\sqrt{7}}=\dfrac{2(3-\sqrt{7})}{3^2-(\sqrt{7})^2}=\dfrac{2}{9-7}\times(3-\sqrt{7})\\\\=\boxed{3-\sqrt{7}}[/tex]
what is 65% more of 140
65% more than 140 is 231
Through the successful study of personal finance, an individual will be better prepared to calculate financial risks able to spend available assets. faced with long-term challenges. more likely to avoid high opportunity costs.
Answer:
A. better prepared to calculate financial risks
Step-by-step explanation:
Through the successful study of personal finance, an individual will be better prepared to calculate financial risks.
What is Personal Finance?Personal finance is a broad word that encompasses money management, as well as saving for the future. Personal finance also includes some of the following:
Budgeting, Banking,Insurance, andEstate preparation etcA successful study of personal finance can help in various ways such as:
Assisting in increasing our income stream and cash flows. Keeping track of our expenses and spending habits.Tax preparation and careful budgeting guarantee that our hard-earned money is not wasted on needless purchases.Learn more about personal finance here:
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simplify the expression.
Answer:
-6m^2 *n^2
Step-by-step explanation:
formula: (m^x)/(m^y)= m^(x-y)
apply formula for (4m^2)/(2m^-3)
=(4m^(2--3)/(2)
=4m^5/2
divide 4/2
=2m^5
next part 3n^5/(-mn)^3
3n^5/(-mn)^3
expand
=3n^5/ (-m^3*n^3)
=3n^(5-3)/ -m^3
=3n^2/ -m^3
both parts:
(2m^5* 3n^2)/ -m^3
= -(2m^5* 3n^2)/ m^3
= -(2m^(5-3)* 3n^2)/ 1
= -(2m^2* 3n^2)
= -(6m^2*n^2)
= -6m^2 *n^2
What are the domain and range of the function below? Domain[0, ∞). range (-∞, ∞). Domain[0, ∞). Range (-∞,4). Domain(0,4). Range (-∞, ∞). Domain(-∞,4]. Range[0, ∞).
HELP IMMEDIATELY PLEASE
Answer:
Domain[0, ∞). Range (-∞,4).
Step-by-step explanation:
domain is your lowest x (zero) to your highest x (infinity)
range is the lowest y (negative infinity) to your highest y (four)
Answer:
its b
Step-by-step explanation:
how to evaluate in math?
HELP PLEASE
if f(x)=-x+2 find f(6)
Answer:
Answer: -4
Step-by-step explanation:
[tex]{ \rm{f(x) = - x + 2}} \\ \\ { \rm{f(6) = - (6) + 2}} \\ \\ { \rm{f(6) = - 4}}[/tex]
The value for f(6) = -4
What is the function of f(x)?The function of f(x) is set to a term such that for every value of x, there is a unique value for it on the graph.
From the given information, we are given a function
f(x) = -x + 2To find f(6), we replace x with 6.
f(6) = -6 + 2f(6) = -4Learn more about function of f(x) here:
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If you walked for 5 minutes, what would the ratio of feet to minutes be? Use your steps to minutes ratio from Task 1 to determine a ratio of feet to minutes. Show your calculation.
Answer:
2:1 RATIO
Step-by-step explanation:
If you walked for 5 minutes, the ratio of feet to minutes would be approximately 2.1665 feet per minute.
How did we get the value?To determine the ratio of feet to minutes, we can use the steps to minutes ratio from Task 1. Let's find the steps-to-feet ratio first:
Steps:Feet
4:10
6:15
12:30
30:40
Now, let's calculate the steps-to-feet ratio by finding the average of the steps-to-feet ratio from all the given data points:
Average Steps-to-Feet Ratio = [(10/4) + (15/6) + (30/12) + (40/30)] / 4
Average Steps-to-Feet Ratio = (2.5 + 2.5 + 2.5 + 1.333) / 4
Average Steps-to-Feet Ratio = 2.1665
Now, for the question at hand, if you walked for 5 minutes, the ratio of feet to minutes would be approximately 2.1665 feet per minute.
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Can someone help me plsssssssssssss
Answer:
The lines will cross at (-5,1)
Step-by-step explanation:
I graphed it
why you copy my profile picture hello.....
will mark brainleist pls hep
Answer: 242
Brainliest plsssssss
Kile’s weight is 30 pounds less than the product of Mindy’s weight and 3. Let m represent Mindy’s weight. Write an expression that represents Kile’s weight.
Answer:
3m - 30
Hope you could get an idea from here.
Doubt clarification - use comment section.
So the expression till now
[tex]\\ \sf{:}\Rrightarrow m(3)[/tex]
[tex]\\ \sf{:}\Rrightarrow 3m[/tex]
But the required weight is 30pounds less than it
[tex]\\ \sf{:}\Rrightarrow 3m-30[/tex]
Concrete tiles are made using buckets of cement, sand and gravel mixed in the ratio 1:4:6. If 20 buckets of sand are used, how many buckets of EACH of the following will be
needed?
a)
Cement:
T
b) Gravel:
The perimeter of the figure below is 140 ft.
Find the length of the missing side.
Answer:
9.2 ft
Step-by-step explanation:
140 - 9.6 - 10.2*8 - 19.8*2 = 9.2
mark me as brainliest PLEASE
Please help, I don’t understand this and I did this from a while ago but I’m still confused on how to do it now.
Answer:
A.) -3p +8
b.) (10/p) -3
3.)
a.) -3(5)+8= -7
b.) (10/5)-3= -1
Step-by-step explanation:
For A and B you just have to read it over and over until you understand what is happening. A tip is when it says "fewer than" then that number usually goes after the second part of the statement.
For 3 it is asking you to plug 5 in for the value of p and solve.
Hope this helps:) Have a good day!
Rhombus FGHI with vertices F(6, -1), G(11, -3), H(13, -8), and I(8, -6) is dilated using scale factor = 2, centered at (12, -1)
The final coordinate of the vertices after the transformation is F"(0, -1), G"(10, 5), H"(14, 15) and I"(4, -11)
If the coordinate vertice (x,y) is dilated by a factor k, the resulting coordinate of the image will be (kx, ky). Note that each of the coordinates was multiplied with the factor to get the resulting coordinate.For the coordinates of the rhombus FGHI with vertices F(6, -1), G(11, -3), H(13, -8), and I(8, -6), if dilated by a factor of 2, the resulting coordinates will be at F'(12, -2), G'(22, -6), H'(26, -16), and I'(16, -12)If the resulting coordinate is centered at (12, -1), we will simply subtract the center from the resulting coordinate to get the final position of the rhombus. The final coordinates will be as shown:
F'' = (12-12, -2+1) = (0, -1)
G'' = (22-12, -6+1) = (10, -5)
H'' = (26-12, -16+1) = (14, -15)
I" = (16-12, -12+1) = (4, -11)
Therefore final coordinate of the vertices after the transformation is F"(0, -1), G"(10, 5), H"(14, 15) and I"(4, -11)
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You have a total of 21 pens and pencils on your desk. You have 3 more pens than pencils. Write a system linear equations that represent this situation. How many of each do you have?
Answer:
x + y = 21x - y = 3
Step-by-step explanation:
Examine Kaitlyn’s steps for solving the system of equations. â€"3x 2y = 8 3x 2y = â€"6 Step 1: 4y = 2 Step 2: y = 2 Step 3: â€"3x 2(2) = 8 Step 4: â€"3x = 4 Step 5: x = â€"1. 333 Kaitlyn found the solution to be (1. 3, 2). Is her solution correct? Explain. Yes, she correctly solved the system of equations. No, she made an error in step 1. The y variable should have been eliminated when adding the system of equations. No, she made an error in step 2. She should have found y = 0. 5. No, she substituted y into the wrong equation to solve for x in step 3.
The error made by Kaitlyn when solving the system of equations is in step 2. Her solution will be incorrect.
The right option will be: No, she made an error in step 2. She should have found y = 0. 5.
Given the system of linear equations:
-3x + 2y = 8 ---> eqn. 1
3x + 2y = -6 ---> eqn. 1
First add both equations together:
Step 1: 4y = 2
Next, divide both sides by 4:
Step 2: y = 2/4
y = 0.5
Kaitlyn got y = 2 instead of 0.5 in this second step. The solution she would get will be incorrect since an error has occurred here.Therefore, the error made by Kaitlyn when solving the system of equations is in step 2. Her solution will be incorrect.
The right option will be: No, she made an error in step 2. She should have found y = 0. 5.
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10) $48,000 at 16% for 6 years
Answer:
No solution
Step-by-step explanation:
idek
34x+24x^2=35+57y
Solve for x
1) Move all terms to one side.
[tex]34x+24x^{2} -35-57y=0[/tex]
2) Use Quadratic Formula.
[tex]x=\frac{-34+2\sqrt{1368y+1129} }{48} ,\frac{-34-2\sqrt{1368y+1129} }{48}[/tex]
3) Simplify solutions.
[tex]x=-\frac{17-\sqrt{1368y+1129} }{24} ,-\frac{17+\sqrt{1368y+1129} }{24}[/tex]
The length of a metal rod is 9 3/4 feet. What is the length of 1/4 of the rod?
Answer:
2 [tex]\frac{5}{16}[/tex]
Step-by-step explanation:
2 [tex]\frac{5}{16}[/tex] × 4 = 9 3/4
9 3/4 × 1/4 = 2 5/16
I hope this helps!
Answer:
3 1/4 feet
Step-by-step explanation:
1/4 of 9 3/4
change 9 3/4 into an improper fraction → 39/3
1/4 x 39/3 = 39/12
convert back to a mixed number by dividing 12 into 39
which goes in three times with a remainder of 3 → 3 3/12
however, 3/12 can be simplified to equal 1/4
2616.95 rounded to the nearest tenth
a) A triangular plot is being constructed having its base twice to its altitude. What will be the base and altitude of the plot if the cost of levelling it at the rate of ₹25 per square meter is ₹11,025.
b)If the same plot from above question is being reconstructed into a square field, having the same area, then find the perimeter of square
THE BEST ANSWER WILL BE MARKED BRAINLIEST PLEASE GIVE PROPER ANSWER
THANK U
The base and altitude of the triangular plot are [tex]42m[/tex] and [tex]21m[/tex] respectively.
The perimeter of the square plot having the same area as the triangular plot is [tex]84m[/tex]
a) Calculate the base and altitude of the triangular plot
The relationship between the Total cost of leveling the triangular plot, the cost per unit area, and the area of the triangular plot is
[tex]\text{unit cost}=\frac{\text{total cost}}{\text{area}}\\\\\text{area}=\frac{\text{total cost}}{\text{unit cost}}\\\\=\frac{\text{11025Rs.}\rupee}{25Rs./m^2}=441m^2[/tex]
The formula for calculating the area of a triangle, given the base and altitude is
[tex]\text{area of triangle}=\frac{1}{2}\text{base}\times\text{altitude}[/tex]
From the question
[tex]\text{base}=2\times\text{altitude}[/tex]
so
[tex]\text{area of triangle}=\frac{1}{2}\times 2\times\text{altitude}\times\text{altitude}\\\\\text{area of triangle}=\text{altitude}^2\\441=\text{altitude}^2\\\text{altitude}=\sqrt{441}=21m[/tex]
from this we can get the base
[tex]\text{base}=2\times\text{altitude}\\=2\times21m=42m[/tex]
b) Calculate the perimeter of a square plot having the same area
Since we found the area of the triangular plot to be [tex]441m^2[/tex], we will use this value for the area of the square plot, so that we can obtain the side
[tex]\text{area of square plot}=side^2\\441=side^2\\\sqrt{441}=side=21m[/tex]
Hence, the perimeter is equal to
[tex]perimeter=4\times side\\=4\times21=84m[/tex]
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Transversal cuts parallel lines and as shown in the diagram, and m∠4 = 55.1°. What are m∠5 and m∠7? A. m∠5 = 34.9°, and m∠7 = 145.1°. B. m∠5 = 55.1°, and m∠7 = 34.9°. C. m∠5 = 124.9°, and m∠7 = 55.1°. D. m∠5 = 55.1°, and m∠7 = 124.9°. E. m∠5 = 34.9°, and m∠7 = 55.1°.
Answer:
m < 5 = 55.1 i think im not forsure
Step-by-step explanation:
Whenever the Transversal EF intersects parallel line AB and CD, the values of m∠5 and m∠7 are 55.1° and 124.9°, respectively.
What is an angle?An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol.
Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.
As per the information provided in the question,
Since the transverse line, EF, intersects the line segment AB and CD, it creates equivalent, alternate, and other angles.
As a result, the m∠5 and m∠7 are as follows:
First, supplementary angles ∠5 and ∠7 are present. Since they add up to 180 degrees, they are equal.
Since alternate angles are equivalent, ∠5 is an alternative angle to ∠4. Therefore,
m∠5 ≅ m∠4
m∠5 = 55.1°
So,
m∠5 + m∠7 = 180°
55.1 + ∠7 = 180
∠7 = 180 - 55.1
m∠7 = 124.9°
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Make y the subject of the formula
12m + 24y = 20
Answer: m=5/3-2y or if your solving for y y=-m/2+5/6
Step-by-step explanation:
Answer:
y = 5/6 - m/2
Step-by-step explanation:
4(3m + 6y) = 20
3m + 6y = 5
6y = 5 - 3m
y = 5/6 - 3m/6
y = 5/6 - m/2
Part A: Find the LCM of 7 and 8. Show your work. (3 points)
Part B: Find the GCF of 54 and 81. Show your work. (3 points)
Part C: Using the GCF you found in Part B, rewrite 54 + 81 as an expression of two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor. Show and explain your work.
Answer:
Part A:
LCM of 7 and 8 is 56.
7*8 = 56
-------------------------------------
Part B:
GCF of 54 and 81 is 27.
54: 1, 2, 3, 6, 9, 18, 27, 54.
81: 1, 3, 9, 27, 81.
-------------------------------------
Part C:
GCF of 54 and 81 is 27.
54 / 27 = 2
81 / 27 = 3
Final expression: 27(2 + 3)
Answer:
Part A: 56
Work:
7: 7, 14, 21, 28, 35, 42, 49, 56
8: 8, 16, 24, 32, 40, 48, 56, 64
Part B: 27
Work:
54: 54, 27, 9, 3, 1
81: 81, 27, 9, 3, 1
Part C: 27(2+3)
Work:
27×2 = 54
27×3 = 81
(27×2)+(27×3) = 54+81
(27×2)+(27×3)=27(2+3)
Explaining work:
First you find the numbers that multiply the GCF by to get the product (for 54 it is 2 and for 81 it is 3). Then you replace the the products with the equations (27×2) for 54 and (27×3) for 81 to get (27×2)+(27×3). Then simplify to get 27(2+3).
Here is a free 100 points annnnd brainliest
This question is about strategy
Skill
Precision
Alr here it is:
Problem one: Molly bought and infinite amount of bottles of dish soap. She had an infinite amount of money. When she bought the dish soap, she lost all of it.
How is this possible?
Problem one (part two): Molly then called her friend Blitzo over. Blitzo then gave Molly and infinite amount of money without losing all of his money.
How is this possible
If you have questions or want hints, ask in comments below this question
1. She bought the infinite dish soap with her money
2. you can't lose anything infinite
3. remeber our deal? brainliest pls.
9. In the figure below, Angle 1 is congruent to Angle 2.
What reason can be used to prove that mis parallel to n?
A. if a pair of verticals angles is congruent, then the lines forming them are parallel
B. If a pair of angles formed by a transversal is corresponding and supplementary, then two lines are parallel
C. If a pair of angles is congruent and the sum of their measures 180 degrees, then the line forming the angles are parallel
D. If two line are intersected by a transversal, and a pair of corresponding angles is congruent, then the two lines are parallel
Answer:
D
Step-by-step explanation:
When 2 angles are congruent and corresponding, the lines are parallel
solve the following x2-2x-24=0
Answer:
[tex]x=6[/tex] and [tex]x=-4[/tex]
Step-by-step explanation:
[tex]x^2-2x-24=0[/tex]
[tex](x-6)(x+4)=0[/tex]
[tex]x=6[/tex] and [tex]x=-4[/tex]
Jason was given a triangle that had a side length of 10m and a hypotenuse of
15m. When he substituted these values into the Pythagorean Theorem, he got 102 + 152 = c2
.
Part A. Find Jason’s mistake and explain it.
Part B. Solve for the missing length, show your mathematical thinking, and justify your answer.
Answer:
The pythagorean theorem is:
H = [tex]\sqrt{s_1^2 + s_2^2}[/tex]
With H being the hypotenuse, s1 one side, s2 the other one. He already has a side and the hypotenuse so he has to calculate the inverse formula:
s2 = [tex]\sqrt{H^2 - s_1^2}[/tex]
So the real side will be:
square root of (15^2 - 10^2) = square root of (225 - 100) = 125 m
Jason made a mistake calculating the squares of the hypotenuse and the side, he didn't subtract and didn't take the root of the result.
A plane flies at x miles per hour in still air. Flying with a tailwind, its speed is 35 miles per hour. Against the wind, its air speed is only 445 miles per hour. hat is the speed of the wind?
Answer:
Step-by-step exklamatorisks:
Tank you