[tex] \sf \underline{ \red{Solution - }} \\ [/tex]
Given,
[tex] \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} }} \\ [/tex]
The denominator is √11 - √5.
We know that
Rationalising factor of √a-√b is √a+√b.
Therefore, the rationalising factor of √11-√5 is √11+√5.
On rationalising the denominator them
[tex] \longrightarrow \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} \times \dfrac{(\sqrt{11} + \sqrt{5})}{(\sqrt{11} + \sqrt{5})} }} \\ [/tex]
Multiplying (√11 + √5) with both the numerator of the fraction.
[tex] \longrightarrow \sf{\quad { \dfrac{-7(\sqrt{11} + \sqrt{5}) }{(\sqrt{11} - \sqrt{5})(\sqrt{11} + \sqrt{5})} }} \\ [/tex]
Performing multiplication in the numerator and by using identity (a + b)(a - b) = a² - b², solving further in the denominator.
[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{(\sqrt{11})^2 - (\sqrt{5})^2} }} \\ [/tex]
Writing the squares of the numbers in the denominator.
[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{11 -5} }} \\ [/tex]
Performing subtraction in the denominator.
[tex] \longrightarrow \quad \underline{ \boxed{ \dfrac{ \textbf{ \textsf{-7 }}\sqrt{ \textbf{ \textsf{11 }}} - \textbf{ \textsf{7}}\sqrt{ \textbf{ \textsf{5 }}}}{ \textbf{ \textsf{ 6}}}} } \\ [/tex]
Hence, the denominator is rationalised.
WILL MARK BRAINLIEST!
Simplify the term 3x - 2 (5x -3)
Answer:
No solution
Step-by-step explanation:
Combine like terms on the right hand side of equation
3x + 2 = 3x -1
This cannot be simplified so there are no solutions.
Answer:
the answer is − 7 + 6
Step-by-step explanation:
multiply -2 times 5 and -2 times -3
you should get 3x-10x+6
combine the terms, you should get -7x+6
-2r+3s
r=-8.2 s=-3.7
Answer:
5.3
Step-by-step explanation:
-2r+3s
Let r=-8.2 s=-3.7
-2(-8.2) +3(-3.7)
16.4-11.1
5.3
Answer:
5.3
Step-by-step explanation:
Substitute the variables.
-2(-8.2) + 3(-3.7) = 5.3
Which of the following best represents the solution to this system (3x+2y<2
Answer:
y < (2 - 3x)/2.
Step-by-step explanation:
(3x+2y)<2
2y < 2 - 3x
y < (2 - 3x)/2
APQR and ARST are shown.
What is m QPR?
QPR is 68 degrees
triangle=180 degrees
180-44=136
136/2=68 (R=68 and S=68)
R has two angles so both are 68 degrees
QPR=68 degrees
Which of the following represents an equation in standard form for the line that passes through (3, −1) and (−5, −3).
Answer:
y = ¼x + (-7/4)Step-by-step explanation:
find the gradient ( M)
M = y2- y1 ÷ x2-x1
M= -3 - (-1)÷(-5)-3 = ¼
thefind C in the equation (y=mx+c)
C = y-mx ( C = -1-¼(3)= -7/4(use in y and x values provided)
now replace the values you find in the equation (y=Mx+C)
final answer is
y = ¼x+(-7/4)y = ¼x + (-7/4) is the standard form for the line that passes through (3, −1) and (−5, −3)
What is Slope intercept form?y=mx=c is the slope intercept form of a line, m is the slope.
We need to find equation of line passing through (3, −1) and (−5, −3)
First we need to calculate slope 'm'.
slope m = y2- y1 / x2-x1
y2=-3, y1=-1, x2=-5, x1=3
m= -3 - (-1)/(-5)-3 = -2/-8=1/4
Equation of line, y=mx+c
find C in the equation (y=mx+c)
C = y-mx
C = -1-1/4(3)= -7/4
now replace the values you find in the equation (y=Mx+C)
y =1/4x-7/4
Hence y =1/4x-7/4 is the equation of line passes through (3, −1) and (−5, −3).
To learn more on slope intercept form click:
https://brainly.com/question/9682526
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Mental Math Using the slope formula, find the slope of the line through the points and . Use pencil and paper. Explain how you can use mental math to find the slope of the line. slope is 0,0 and 2,4
Answer:Slope is 2, assuming "0,0 and 2,4" is meant to read (0,0) and (2,4) for the 2 points.
Step-by-step explanation:
The slope is the Rise (change in y) over the Run (change in x). I can see the change in y is 4 (it goes from 0 to 4) and the change in x for this interval is 2 (goes from 0 to 2, or 2-0 = 2). Rise (4) over Run (2) is slope 2. 4/2 = 2 slope.
You want to purchase 7 Rubik’s cubes for a Rubik’s cube you are starting. A Rubik’s cube cost $7.99 How much does it cost to buy all seven to start your Rubik’s cube club
Answer:
just multiply 7.99 * 7. your tryna find how much 7 rubrics cubes cost so your answer should be 55.93 or 56
Step-by-step explanation:
help ME PLEASE FAILING GEOMETRY!
Evaluate the expression (ill give brainiest)
Answer:
2 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Substitute the given values into the expression
2 ( [tex]\frac{1}{16}[/tex] + ([tex]\frac{1}{4}[/tex] )² ) + 5([tex]\frac{1}{2}[/tex] )
= 2 ( [tex]\frac{1}{16}[/tex] + [tex]\frac{1}{16}[/tex] ) + [tex]\frac{5}{2}[/tex]
= 2 ([tex]\frac{2}{16}[/tex] ) + [tex]\frac{5}{2}[/tex]
= 2 ([tex]\frac{1}{8}[/tex] ) + [tex]\frac{5}{2}[/tex]
= [tex]\frac{1}{4}[/tex] + [tex]\frac{10}{4}[/tex]
= [tex]\frac{11}{4}[/tex]
= 2 [tex]\frac{3}{4}[/tex]
True or False?
VERY STUCK!!! PLEASE HELP!!!!
Answer:
I'm pretty sure it's True
Step-by-step explanation:
Congruent triangles are triangles that are the same shape and size. Each triangle has the numbers 71, 47, 62 so I'm assuming the answer is True
Hope that helped! Can I also get brainliest? I need a few more to advance, if not thank you anyways and have a nice day!!!
Solve for x: x - 10 = -12
Answer:
x = -2
Step-by-step explanation:
Step 1: Add 10 to both sides.
[tex]x - 10 + 10 = -12 + 10[/tex] [tex]x = -2[/tex]Step 2: Check if solution is correct.
[tex]-2 - 10 = -12[/tex] [tex]-12=-12[/tex]Therefore, x = -2.
h(x)=3x+3 g(x)=-4x+1 find (h+g)(10)
Answer:
-6
Step-by-step explanation:
h(x)=3x+3
g(x)=-4x+1
(h+g)(x) = 3x+3 -4x+1 = -x+4
(h+g)(10) = -(10)+4 =-6
Rittle - Mary didn't know how to pronounce the name but she knew that she had to go inside to impress her parents, where was she? (giving out the answer in 5 mins. SO HURRY)
four hundred five times seventy
Answer:
Step-by-step explanation:
28350, two thousand and eight, three hundred and fifty
Answer:
28350
Step-by-step explanation:
The ratio of men to women working for a company is 4 to 5. If there are 110 women working for the company, what is the total number of employees?
Answer:
198
Step-by-step explanation:
?/4 110/5
cross-multiply 4*110
440
divide 440/5
88 men
add total employees
110 women + 88 men = 198
free question
A certain shade of pink is created by adding 3 cups of red paint to 7 cups of white paint.
How many cups of red paint should be added to 1 cup of white paint?
Answer:
3/4 I think its that
Step-by-step explanation:
its a guess
please help I'm lost
Answer:
x=3
y=2
z=-3
Step-by-step explanation:
What is the value of x if the acute angles of a right triangle measure 3x and 17x
33556-"+";*((((:;"!"?"
Solve the equation by factoring.
x2 – 64 = 0
Answer:
x=32
Step-by-step explanation:
x2 -64 = 0
+64 = +64
x2=64
x2/2 = 64/2
x = 32
hope this helps.
An angle exceeds three times its complement by 10°, find it.
Answer:
30° angle it might be same
A car increased price by 3/4. after the increase it was priced at £84 what was the original price???
Answer: I think this is how we do it but i am not sure the answer is 48
Step-by-step explanation:
if the price increase by 3/4 then that mean it total will be 7/4 as 4/4 is it original price add so 7/4=84/x 84x4 is 336 336 divide by 7 is 48 to check 48 x 7/4 or 48 x 3/4 and add 48 if u math is correct than u should get 84
Omar can jog 3 2/5 miles in 2/3 of an hour. Find his average speed in miles per hour.
Answer:
9.6miles per hour
Step-by-step explanation:
2/3＝40min
32/5 /40＝0.16
0.16miles per min
0.16*60＝9.6
Step-by-step explanation:
he jogs 3 2/5 miles in 2/3 of an hour.
3 2/5 miles are 17/5 miles.
now, to get mph as speed unit, we need to bring the 2/3 hour to 1 hour.
we need to multiply 2/3 by a factor to get 1
2/3 × x = 1
2x = 3
x = 3/2
since we have to multiply the denominator of the ratio by 3/2, we also need to multiply the numerator by the same value to keep the overall value of the ratio/fraction the same.
17/5 / 2/3 × 3/2 / 3/2 = (17/5 × 3/2) / (2/3 × 3/2) =
= ((17×3)/(5×2)) / ((2×3)/(3×2)) =
= (51/10) / 1 = 51/10 = 5.1 mph
so, his jogging speed is 5.1 mph.
Chau rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 97 cents for each mile driven. Chau had to pay $306.13 when he returned the truck. For how many miles did he drive the truck?
Answer:
Chau drove 13.96 miles while he was using the truck
Step-by-step explanation:
Answer:
294 miles!!!!!!
Step-by-step explanation:
work out x when the area is root 4 2^2 and angle C is 45 and ab are (x+2)(2x-3)
Answer:
x = 3.08
Step-by-step explanation:
Area formula:
A = 1/2bhThe height is:
h = (x + 2)sin 45° = (x + 2) ×√2/2Substitute the value for area and set equation:
4√2 = 1/2 × (2x - 3) × √2(x + 2)/2(2x - 3)(x + 2) = 162x² + x - 6 = 162x² + x - 22 = 0D = 1 + 4*2*22 = 177x = (-1 + √177)/4 = 3.08 (rounded)Note the second root ignored as negative
Answer:
x = 3.08 (3 s.f.)
Step-by-step explanation:
Area of a Triangle (using sine)
[tex]\sf Area=\dfrac{1}{2}ac \sin B[/tex]
where:
a and c are adjacent sidesB is the included angleGiven:
Area = 4√2 m²a = (2x - 3) mc = (x + 2) mB = 45°Substitute the given values into the formula:
[tex]\implies 4\sqrt{2}=\dfrac{1}{2}(2x-3)(x+2) \sin 45^{\circ}[/tex]
[tex]\implies 8\sqrt{2}=(2x-3)(x+2) \sin 45^{\circ}[/tex]
[tex]\implies 8\sqrt{2}=(2x-3)(x+2) \left(\dfrac{\sqrt{2}}{2}\right)[/tex]
[tex]\implies 8\sqrt{2}\left(\dfrac{2}{\sqrt{2}}\right)=(2x-3)(x+2)[/tex]
[tex]\implies (2x-3)(x+2) =16[/tex]
[tex]\implies 2x^2+4x-3x-6=16[/tex]
[tex]\implies 2x^2+x-22=0[/tex]
Use the Quadratic Formula to solve for x:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies a=2, \quad b=1, \quad c=-22[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{1^2-4(2)(-22)} }{2(2)}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{177}}{4}[/tex]
[tex]\implies x=3.08, -3.58\:\: \sf (3 \:s.f.)[/tex]
As distance is positive:
[tex]\implies x=3.08 \:\:(3 \sf \:s.f.) \:\textsf{only}[/tex]
Which of the following equation represents the graph?
Answer:
y= -3/5x -3
Step-by-step explanation:
Find the y intercept for the equation of the line that passes through point (-1 , 5)if the slope is 5
Answer:
the y-intercept is 10
Step-by-step explanation:
What is 0.000000000325 in scientific notation?
Answer:
3.25*10^-10(is.3.25E−10)
3.25x10^-9
The coefficient must be between 1 and 10The negative exponent means the number is smallHope it helps!
~Just a joyful teen
[tex]GraceRosalia :)[/tex]
Can someone help me on this I’m struggling a lot
A) 2/16
B) 5/8
C) 6/8
D) 1/3
Answer:
B) 5/8
Step-by-step explanation:
Because we are working with fractions that have different denominators, we need to find the lowest common denominator, which would be 8, because 1/8 cannot be divided anymore in 2 or 4, but 1/2 can be multiplied in eighths.
So, to make 1/2 into eighths, we have to multiply both the numerator and denominator by 4 in order for 2 to become 8:
1/2 * 4 = 4/8
Now, we can add the amounts of the total granola bar that he consumed:
4/8 + 1/8 = 5/8
Because 5/8 cannot be simplified any further, that is our final answer.
Hope this helps :)
Can someone help me with this?
Answer:
they are correct
Step-by-step explanation:
Answer:
317m
Step-by-step explanation:
I am not sure its the perimeter (p) you need because thats what i understood.
p=2(109.7)+2(48.8)=317m
rewrite the equation in standard form y = - 3/4x - 6
Answer:
3x + 4y = - 24
Step-by-step explanation:
Brainliest?