Answers
Answer:
[tex]\huge\boxed{\bf\:2}[/tex]
Step-by-step explanation:
[tex]\frac{4}{3 + \sqrt{7}}[/tex]
Rationalise the denominator by multiplying the numerator & denominator of the fraction with [tex](3 - \sqrt{7})[/tex].
[tex]\frac{4\left(3-\sqrt{7}\right)}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}[/tex]
Now, we an see that the denominator is in the form of the algebraic identity: (x + y) (x - y) = x² - y². So,
[tex]\frac{4\left(3-\sqrt{7}\right)}{3^{2}-\left(\sqrt{7}\right)^{2}} \\= \frac{4\left(3-\sqrt{7}\right)}{9-7} \\= \frac{4\left(3-\sqrt{7}\right)}{2} \\[/tex]
The new denominator is 2.
[tex]\rule{150pt}{2pt}[/tex]
Answer:
Option D. 2
Step-by-step explanation:
Hello!
To rationalize the denominator, we should multiply the numerator and the denominator by the conjugate of the denominator. The conjugate simply means the same terms but with the opposite operation.
Rationalize[tex]\frac4{3+\sqrt7}[/tex][tex]\frac4{3+\sqrt7} * \frac{3 - \sqrt7}{3 - \sqrt7}[/tex][tex]\frac{12 - 4\sqrt7}{9 - 7}[/tex][tex]\frac{12 - 4\sqrt7}{2}[/tex]The new denominator is 2.
Related Questions
Solve the following equation algebraically:
x^2 = 192
A. 13.86
B. -13.86, 13.86
C. -14.36, 14.36
Emergency!!
Answers
PLEASE PLESE HELP ME WITH THIS!!!!
Answers
The new center is 5 units away from the original, hence we added 5 to the x-value.
If you notice the sides of the new triangle are twice the size of the original one, meaning that it was dilated by a scale factor of 2.
PLEASE HELP IM STUCK ON THIS!!
Draw the dilation image A’B’C’D’ of the trapezoid ABCD with the center of the dilation at the origin and the scale factor -2. include the original trapezoid ABCD in your drawing.
Answers
Answer:
Im stuck on this one as well lol
Step-by-step explanation:
Good luck
You find out the answer for this one? I'm stuck on it
rudy has punch cards for his favorite tea house abs his favorite coffee shop. he currently has 1 punch on the tea punch card and 2 punches on the coffee punch card. given his regular routine he consistently earns 7 new punch cards per week on the tea punch card and 6 on the coffee punch card. before too long rudy will have the same number of punches on each card. how long will it take? how many punches will rudy have on each card?
Answers
The time it would take for Rudy to have the same number of each punch card is 1 week.
The number of punches on each card Rudy would have is 8 punches.
How long will it take to have the same number of punches on each card?The equation that represents the number of punches on the tea punch card is: 1 + 7t
The equation that represents the number of punches on the coffee punch card is: 2 + 6t
Where t represents the number of weeks
When both cards would have the same amount of punches, the two above equations would be equal:
1 + 7t = 2 + 6t
To find the value of t, take the following steps:
Combine similar terms
7t - 6t = 2 - 1
t = 1 week
What will be the number of punches on each card?
Number of punches on each card = 1 + 7(1) = 8 punches
To learn more about when the two different variables would have the same amount, please check: https://brainly.com/question/25711114
Write 19% as a fraction.
Answers
Answer:
19/100
Step-by-step explanation:
Answer:
19/100
Step-by-step explanation:
The answer is 19/100 because the percentage should be out of 100. Therefore, the fraction is 19/100.
What is the area of the shaded sector of Point B below?
Answers
Answer:
A) 175π / 9 squared inches,
Step-by-step explanation:
Radius = 10 inches
AB = BD = 10 = radius
Triangle ABD is isosceles
Angle DAB = Angle BDA = 35 degrees,
Base angles theroem
35 + 35 + x = 180, angles in triangle
x = 180 - 70
x = 110 degrees
Angle DBC is supplementary with ABD
110 + x = 180
x = 70
70 degrees is angle for the sector
70 is 70/360, 7/36 of the circle
The area will also be 7/36 of the circle area
Area of circle = πr^2
Area = 100π
Area of sector = (100π * 7) / 36
Area of sector = 700π / 36
Simplified area = 175π / 9 squared inches
Let x represent the paper 1 score (out of 40) and y
represent the predicted paper 2 score (out of 100).
Which correctly states the equation for the least-
squares regression line and the interpretation of its
slope?
Answers
Answer:
A
Step-by-step explanation:
18/2x-6
step by step please
Answers
Answer:
[tex]\frac{9}{x-3}[/tex]
Convert the problem into split up expressions.
[tex]\frac{18}{2}(x - 6)[/tex]
Take both 6 and 18's most common factor here, 2, and divide by 2 to simplify.
[tex]\frac{18}{2} = 9\\\\\frac{6}{2} = 3[/tex]
Cancel.
18 becomes 9
6 becomes 3
The equation turns into:
[tex]\frac{9}{x - 3}[/tex]
note that because we, "canceled" 2, that also means it does not appear in the simplified form since it was a factor.
The reference angle for (5pi)/4 is pi/4 , which has a terminal point of (sqrt2/2), (sqrt2/2). What is the terminal point of 5pi/4?
Answers
Using the unit circle, it is found that the terminal point of the angle 5pi/4 is given by:
A. [tex]\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)[/tex]
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
The angle 5pi/4 is in the third quadrant, as it is greater than pi and less than 1.5pi, in which both the sine and the cosine are negative. Hence, considering the reference angle, we have that:
[tex](\cos{(\left(\frac{5\pi}{4}\right)}, \sin{(\left(\frac{5\pi}{4}\right)}) = (-\cos{(\left(\frac{\pi}{4}\right)}, -\sin{(\left(\frac{\pi}{4}\right)}) = \left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)[/tex]
Hence option A is correct.
More can be learned about the unit circle at https://brainly.com/question/16852127
#SPJ1
A line passes through the points (1, 4) and (-4, -2)
2). Which of the following is an equation of the line?
Answers
Answer:
slope intercept
y=6/5x+14/5
point slope=
y-4=6/5 (x-1)
therefore y-4/x-1=6/5 is the answer
Need help with this
Answers
If f is a one-to-one continuous function defined on an interval, then its inverse f−1 is also one-to-one and continuous.
solve:
-7=12x-16
If you help me with this I will be your best friend!!!
Answers
Answer:
x = 0.75
Step-by-step explanation:
first make the x term the subject
-7 = 12x - 16
-7 + 16 = 12x
add the like terms
9 = 12x
solve for x
9÷ 12 = 12x ÷ 12
0.75 = x
One root of the equation "[tex]x^{2} -m^{2}x -m + 1 = 0[/tex]" (with unknown x) is the number "x1 = 1". Determine the other root "x2".
Answers
Answer:
0; 3.
Step-by-step explanation:
1) if to substitute x=1 into the given equation, it is possible to calculate the value of 'm':
1-m²-m+1=0; ⇔ m²+m-2=0; ⇒ m₁=-2; m₂=1;
2) if m=-2 and m=1, then the initial equation is:
x²-4x+3=0 or x²-x=0;
3) according to the item 3), the 2d root is:
x₂=3 or x₂=0.
NO LINKS!! Please help me with this problem
Answers
#1
[tex]\\ \rm\Rrightarrow \dfrac{WX}{GH}=\dfrac{UY}{JI}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{8}{14}=\dfrac{UY}{28}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{8(28)}{14}=UY[/tex]
[tex]\\ \rm\Rrightarrow UY=8(2)=16[/tex]
#2
[tex]\\ \rm\Rrightarrow \dfrac{UV}{UY}=\dfrac{FJ}{JI}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{UV}{16}=\dfrac{21}{28}[/tex]
[tex]\\ \rm\Rrightarrow UV=\dfrac{3}{4}\times 16[/tex]
[tex]\\ \rm\Rrightarrow UV=3(4)=12[/tex]
#3
[tex]\\ \rm\Rrightarrow \dfrac{WX}{XY}=\dfrac{GH}{HI}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{8}{XY}=\dfrac{14}{35}=\dfrac{2}{5}[/tex]
[tex]\\ \rm\Rrightarrow 2XY=40[/tex]
[tex]\\ \rm\Rrightarrow XY=20[/tex]
Answer:
UY = 16
UV = 12
XY = 20
Step-by-step explanation:
If UVWXY ~ JFGHI
then:
UV~JF
VW~FG
WX~GH
XY~HI
UY~JI
The only pair of sides that both have measures is WX and GH:
WX = 8
GH = 14
⇒ GH/WX = 14/8 = 1.75
Therefore, JFGHI is and enlargement of UVWXY by scale factor 1.75
As IJ = 28
⇒ UY = 28 ÷ 1.75 = 16
As JF = 21
⇒ UV = 21 ÷ 1.75 = 12
As HI = 35
⇒ XY = 35 ÷ 1.75 = 20
Evaluate a=81 and b=3.
a/9 -b=
Answers
Answer:
6
Step-by-step explanation:
once you replace the letters with numbers you get, 81/9-3 and 81/9 is equal to 9 and 9-3=6
HELP PLEASEE ITS EASY!!!!!!!!!
Answers
Answer:
4 inches
Step-by-step explanation:
The scale is 1:3 based on that info, x:12
There is a 4-factor increase, meaning x=4
The Zoo is 16 Inches from the school
A researcher is studying the growth of bacteria. He starts eith 280 of the bacteria. It grows continuously at a rate of 6% per hour. How many bacteria will there be in 16 hours?
Answers
711
[tex]\bold{EXPLANATIONS:}[/tex]
What is the estimate for 54×31
Answers
Answer:
50 * 30 = 1500
Answer:
Actual Product =54*31= 1,674
Estimated Product = 50*30=1,500
Step-by-step explanation:
PLS HELP ASAP DUE TODAY
Answers
1. 135° × π/180 = 2.356rad
Sorry if I get it wrong
What’s the inverse of the function?
f(x)=3^x+1
Answers
[tex]y= f(x) = 3^x+1\\\\\text{Replace x with y and solve for y}\\ \\~~~~~~x=3^y+1\\\\\implies 3^y = x-1\\ \\\implies \ln(3^y) = \ln(x-1)\\\\\implies y \ln 3= \ln(x-1)\\\\\implies y= \dfrac{\ln(x-1)}{\ln 3}\\\\\implies f^{-1}(x) = \dfrac{\ln(x-1)}{\ln 3}[/tex]
Find the slope of the line if it exists
Answers
Answer:
m = 7/6
Step-by-step explanation:
Find coordinates of two points:
(-2,3)
(-8,-4)
Slope formula =
y1 - y2 / x1 - x2
So...
-4-3 / -8 -- 2
-7 / -6
7/6
remember brainliest and have a great day!
Joey makes an hourly wage of $12. For hours over 40, he earns 1.5 times his regular pay. Last week joe worked 46 hours. Fill out the table below.
Answers
Answer:
Step-by-step explanation:
Find the area of the parallelogram.
A. 35 cm2
B. 42 cm2
C. 12 cm2
D. 24 cm2
Answers
Answer:
35 cm²
Step-by-step explanation:
This is because the formula of the area of a parallelogram is;
area = (base) x (height)
since the base is 5, and the height is 7;
area = (5) x (7)
area = 35
Hope this helps!
Answer:
[tex]\boxed{\sf{A. \quad 35cm^2}}[/tex]Step-by-step explanation:
The formula of area of the parallelogram is used to find the area of the parallelogram.
Area of the parallelogram formula:
[tex]\Longrightarrow: \sf{A=B*H}[/tex]
B stands for "base".
H stands for "height".
The base is 5.The height is 7.Multiply.
Solve.
5*7=35
= 35cm²
Therefore, the area of the parallelogram is 35cm², which is our answer.I hope this helps! Let me know if you have any questions.
The endpoints of AB are A(4,3) and B(1,1). What are the coordinates of A’’ after the image has been translated (x,y)—> (x-5,y-1) and rotated 180 degrees about the origin?
Answers
Answer:
A"(1, -2)
Step-by-step explanation:
In addition to the translation transformation given, you are asked to transform the figure further by rotating it 180° about the origin. The translation for that is ...
(x, y) ⇒ (-x, -y)
Then the composition of the two transformations is ...
(x, y) ⇒ (-(x -5), -(y -1)) = (-x +5, -y +1)
__
Applied to the given point(s), we have ...
(x, y) ⇒ (-x +5, -y +1)
A(4, 3) ⇒ (-4 +5, -3 +1) = A"(1, -2)
B(1, 1) ⇒ (-1 +5, -1 +1) = B"(4, 0)
The coordinates of A" after translation and rotation are (1, -2).
Mrs. Reynolds has $153. She buys a bicycle for $105.
Then, she finds $20 at the bottom of her purse.
How much money does she have now? Use the bar diagrams to help you.
Step 1:
Step 1: a bar diagram shows 105 and m, the money left after buying a bike. Together 105 and m is equal to 153.
Step 2:
Step 2: a bar diagram shows that 20 and m is equal to s, the money now.
Enter your answer in the box.
Mrs. Reynolds has $
now.
Answers
Answer:
$68
Step-by-step explanation:
Mrs. reynolds now has 68 dollars. 153-105=48. 48+20=68
Answer:
She has $68 dollars remaining
Step-by-step explanation:
(no bar diagram needed, lol jk.)
anyways she started off with 153, right?
She then buys a bike worth $105; thats -$105 which leaves here with $48 dollars
Then ooo its her lucky day, she finds a $20 dollar bill, you add it to $48 (+$20) , now she has $68 dollars in total.
<3
help an someone help
Answers
O parte din traseul Bușteni-Babele a fost parcurs de mai multi turiști astfel: in prima ora 1/3 din distanta, a doua ora 1/4 din distanta. Dupa cele doua ore le-au mai ramas de parcurs 5km. Care este distanta parcursa de turiști?
Answers
Answer:
7km
Step-by-step explanation:
[tex] \frac{1}{3} x + \frac{1}{4} x = \frac{4}{12} x + \frac{3}{12} x = \frac{7}{12} x \\ \\ \\ x - \frac{7}{12} x = \frac{12}{12} x - \frac{7}{12} x = \frac{5}{12} x \\ \\ \frac{5}{12} x = 5 - - - > x = 12[/tex]
[tex]12 \times \frac{7}{12} = 7[/tex]
what is 3/4 of 1/3
Reduce your answer to simplest form.
Answers
Answer:
1/4.
Step-by-step explanation:
3/4 of 1/3
= 1/3 * 3/4
= 3/12
= 1/4
Solve the equation. Write your answer as an integer or simplified fraction.
8n−7 n−2 =18
n=______
Answers
Corrected question :
Solve the equation. Write your answer as an integer or simplified fraction.
8n - 7 (n - 2) = 18Required Solution :
The given equation,
8n - 7 (n - 2) = 18★ Multiplying -7 into (n - 2),
>> 8n - 7 × (n - 2) = 18
>> 8n - 7n + 14 = 18
★ On substracting 7n from 8n we gets,
>> n + 14 = 18
★ Now transposing 14 which is in L.H.S. into R.H.S. (Remember that sign would be . So 14 would be -14),
>> n = 18 - 14
>> n = 14
★ Therefore,
Value of n is 14.Learn more from brainly.com :
https://brainly.com/question/27432186
https://brainly.com/question/22661149
https://brainly.com/question/26727230
xy=10
4x+2y=30
I need help asap
Answers
Answer:
x = 25/3; y = -5/3
Step-by-step explanation:
You did well so far by multiplying both sides of the first equation by 2.
Now notice that you have -2y in the new first equation and 2y in the second equation. -2y and 2y add to 0.
Now add the equations to eliminate y.
2x - 2y = 20
(+) 4x + 2y = 30
-------------------------
6x = 50
6x/6 = 50/6
x = 50/6 = 25/3
2x - 2y = 20
2(25/3) - 2y = 20
50/3 - 2y = 60/3
-2y = 60/3 - 50/3
-2y = 10/3
-2y/2 = (10/3)/(-2)
y = -5/3
Solution: x = 25/3; y = -5/3