[tex] \tt \huge \leadsto \frac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} + \sqrt{3} } [/tex]
[tex] \tt \huge \leadsto \frac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} + \sqrt{3}} \times \frac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} - \sqrt{3} } [/tex]
[tex] \tt \huge \leadsto \frac{7 - 3}{ (\sqrt{7 })^{2} - ( \sqrt{3})^{2} } [/tex]
[tex] \tt \huge \leadsto \frac{4}{7 - 3} [/tex]
[tex] \tt \huge \leadsto\frac{4}{4} [/tex]
[tex]\tt\huge\leadsto{1}[/tex]
Answer:
Step-by-step explanation:
To rationalize the denominator multiply the numerator and denominator by the conjugate of √7 + √3 = √7- √3
[tex]\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}=\frac{(\sqrt{7}-\sqrt{3})(\sqrt{7}-\sqrt{3})}{(\sqrt{7}+\sqrt{3})(\sqrt{7}-\sqrt{3})}\\\\\\= \frac{(\sqrt{7}-\sqrt{3})^{2}}{(\sqrt{7})^{2}-(\sqrt{3})^{2}}\\\\\\= \frac{(\sqrt{7})^{2}-2*(\sqrt{7})*(\sqrt{3})+(\sqrt{3})^{2})}{7-3}\\\\=\frac{7-2\sqrt{21}+3}{4}\\\\=\frac{10-2\sqrt{21}}{4}\\\\=\frac{2(5-\sqrt{21})}{4}\\\\=\frac{5-\sqrt{21}}{2}[/tex]
7x+8/2 = 9x+1
Give your answer as a fraction in its simplest form
Answer:
3/2
Step-by-step explanation:
the LCM is 2Thanks Hope It HelpA jar is filled with 74 different colored marbles, 10 of which are red, 38 of which are blue, and 26 of which are green. A player is asked to draw a single marble from the jar and if they draw a red marble they will win $20, if they draw a blue marble they will lose $10, and if they draw a green marble they will lose $5. You may round your answer to the nearest cent
Solution :
Colored marble Prize
Red ---- 10 20
Blue --- 38 10
Green --- 26 5
P(red) = 10/74 = 5/37
P(blue) = 38/74 = 19/37
P( green) = 26/74 = 13/37
Therefore,
X → Red Blue Green
P(X) 5/37 19/37 13/37
The expected values are :
[tex]$20 \times \frac{5}{37} - 10 \times \frac{19}{37} - 5 \times \frac{13}{37}[/tex]
= -4.189
Thus it is not profitable to play the game.
A chocolate chip cookie recipe requires three and one third cups of flour to one cup of chocolate chips. If one and one quarter cups of flour is used what quantity of chocolate chips will be needed according to the recipe?
Answer:
3/40 cup
Step-by-step explanation:
3 1/3 =10/3
10/3 to 1 is 1/4 to x
i then proceeded to use the butterfly method to find the answer
find the coordinates of the points which divide the join X(-1,7) and Y(4,-3) in the ratio of 7:2.
Answer:
(26/9 , -7/9)
Step-by-step explanation:
Here,
let the points be
X(-1,7) = (x1, y1)
Y(4,-3) = (x2,y2)
and let the ratio be...
m:n = 7:2
and.. let the point that divides the line be
P(x,y)
now using the section formula for internal division..
P(x,y) = ( m.x2 + nx.1 / m+ n , my2+ny2/m+n )
= ( 7.4+2.-1 / 7+2 , 7.-3 + 2.7/7+2 )
= ( 26/9 , -7/9 )
find the smallest number by which 252 must be multiplied to get a perfect square . also find the square root of the perfect square so obtained.
We shall proceed in hit and trial method
Find some nearest multiples of 252
252(2)=504252(3)=756252(4)=1008252(5)=1260252(6)=1512252(7)=1764Yes last one is square of 42
So smallest no is 7
Solve for x. Round to the nearest tenth.
Answer:
D. 14.1
Step-by-step explanation:
Use sin, opposite over hypotenuse.
sin67 = 13/X
solve for X
using the inverse trig functions, find the measure of angle X to the nearest degree
1. 64°
2. 16°
3. 90°
4. 74°
Answer:
Option 4.
Step-by-step explanation:
Tan(X)=perpendicular/base
Tan(X)=48/14
X=arctan(48/14)=74
Which of the following accurately describes the median of a set of data? Multiple choice question. The midpoint of the data when it is arranged in order. The difference in the largest and smallest values. The most numerous observation in a set of data. The arithmetic average of the values in the set.
Answer:
The midpoint of the data when it is arranged in order.
Step-by-step explanation:
Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order
For example, the median of the following set of numbers is 5
1, 2, 5, 10, 20
Range is the difference between the highest and lowest values of a set of observations
Range = highest value - lowest value
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
Which graph represents the following piecewise defined function? g(x) = 1/2 x +3 , x< -2 g(x) = 2, -2<_ x <_3 g(x) = 2x-3 , x>3
In this question, a piece-wise function is asked to be graphed.
Piece-wise function:
A piece-wise function is a function that has different definitions, depending on the input.
In this question, the function has three different definitions:
When x is less than -2, the definition is:
[tex]g(x) = \frac{x}{2} + 3[/tex]
When x is between -2 and 3, inclusive, the function is:
[tex]g(x) = 2[/tex]
When x is greater than 3, the definition is:
[tex]g(x) = 2x - 3[/tex]
The graphic is given by the image at the end here, with the closed circle indicating the inclusive on the intervals.
For another example of a piece-wise graphic, you can check https://brainly.com/question/24324639.
Answer:
D
Step-by-step explanation:
edge!
What sum of money amount to Rs 6000 in two years at the rate of 10% per annum find it
Answer: Rs 5000 sum of money amount to Rs 6000 in two years at the rate of 10% per annum.
Step-by-step explanation:
Amount = Rs 6000
T = 2 year
R = 10%
So
I = A-P
so
I = PTR/100
or, A-P = (P*2*10)/100
or, 6000-P = 20P/100
or, 600000-100P = 20P
or, 600000 = 120P
or, P = 600000/120
so, P = Rs 5000
Solve for b.
- 3b-5> - 8 or b - 4 < 0
Answer:
b<4
Step-by-step explanation:
- 3b-5> - 8 or b - 4 < 0
Solve the first inequality
- 3b-5> - 8
Add 5 to each side
- 3b-5+5> - 8 +5
-3b> -3
Divide by 3, flipping the inequality
-3b/-3 < -3/-3
b <1
Then solve the second inequality
b-4<0
Add 4 to each side
b<4
Put them back together
b<1 or <4
Merge them since they overlap
b<4
Solve x^2−4x−12=0 by completing the square. PLEASE HELP QUICK WILL GIVE BRAINLIEST
Answer:
The answer is B
Step-by-step explanation:
If u use calculator,u will get the ans as x¹=6 and x²= -2 but u have to change it to the opposite which means negatif to positive(-2=2) and positive to negative(6= -6).Hope u can understand...sorry,English isn't my first language
Answer:
x= 6 and x=-2
Step-by-step explanation:
find the two factors that when multiplied will get -12 and when summed up will get -4.
so -6 and 3
(xsquare-6) +(2x -12)=0
x(x-6)+2(x-6)=0
(x-6)=0 (x+2)=0
group like terms
x=6. x=-2
Can someone help me with this math problem please?
Answer:
C
Step-by-step explanation:
g(x) is larger than f(x) and not the same size so B and D are out of question because those are translation not dilation.
f(x) is stretched in the vertical direction to get g(x). So this means the scale factor has to be greater than 1. so A is wrong.
The answer is c
Find the measure of FG
Answer:
D. 7
Step-by-step explanation:
I guessed on it because i had the same problem and then i checked and it was right!
Solve x4 – 2x2 – 24 = 0.
Answer: 7
Step-by-step explanation:
La sombra que proyecta un edificio es de 16 m si el coseno del ángulo que se forma entre la punta de la sombra y el techo del edificio es 16/20 cual es la altura del edificio
Answer:
dont understand clearly
Step-by-step explanation:
dont understand clearly
y Given: 6x + 7 = 8x - 17; Prove: x = 12
On the left aide is the equation solved step by step and on the right side is where you have to explain what you did to do that equation..(in each column just say what property you used to solve it..Distributive Property, Subtraction Property, Addition Property, Division Property, Multiplication Property etc..)
REASONS:-
1ST STEP
[tex]6x + 7 = 8x - 17 [/tex]
GIVEN LHS = RHS
2ND STEP
[tex]7 = 2x - 17[/tex]
Bez +ve 6x when move to another side will change to -ve so it reduces 8x to 2x
3RD STEP
[tex]24 = 2x [/tex]
Bez -ve 17 when move to another side will change to +ve so it increases 7 to 24
4TH STEP
[tex]12 = x[/tex]
Bez 2 in multiplication when move to another side will change to division so it reduces 24 to 12
5TH STEP
[tex]x = 12[/tex]
it the answer we obtained after solving
Find the sum that amounts to Rs 9,144 in 3 years at 9% per year simple interest.
Given:
Amount = Rs. 9,144
Time = 3 years.
Rate of simple interest = 9%
To find:
The principal value.
Solution:
The formula for simple interest is:
[tex]I=\dfrac{P\times r\times t}{100}[/tex]
Where, P is principal, r is the simple rate of interest, and t is the number of years.
Putting [tex]r=9,t=3[/tex] in the above formula, we get
[tex]I=\dfrac{P\times 9\times 3}{100}[/tex]
[tex]I=\dfrac{27P}{100}[/tex]
[tex]I=0.27P[/tex]
We know that,
[tex]\text{Amount}=\text{Principal + Interest}[/tex]
[tex]9144=P+0.27P[/tex]
[tex]9144=1.27P[/tex]
Divide both sides by 1.27, we get
[tex]\dfrac{9144}{1.27}=P[/tex]
[tex]7200=P[/tex]
Therefore, the principal value is Rs. 7200.
One more, again I aplolgize!
Identify the solid.
A.
pentagonal prism
B.
dodecahedron
C.
hexahedron
D.
hexagonal prism
Answer:
I would say it is D
Step-by-step explanation:
Given that line AD is the angle bisector of
Step-by-step explanation:
3x+1 = 5x-1
3x+2= 5x
2x= 2
x= 1
3.)The lateral surface area of a right circular cylinder is 120cm² and the circumference of the bases is 12cm.Find the altitude of the cylinder
Answer:
Lateral surface area= circumference*height
120=12*h
h=10cm
Answer:
h=10 cm
Step-by-step explanation:
cicumference of a circle C=2πr=12
lateral surface area of cylinder=2πrh
120=12h
h=120/12=10 cm
A truck was carrying 10 bags of sugar. Each bag weighed 50kg. Calculate the total mass of sugar on the truck. Write your answer in grams.
Answer:
1beg-------------50kg
10beg------------x
x=500kg to grames 500×1000=500000grams
Answer:
500000g
Step-by-step explanation:
first of you multiply the 50kg with the 10 bags
which gives 500kg
then you convert 500kg to grams
which is 500kg/1×1000g/1kg
when you cancel out the kg what is left is to multiply both sides and then you get 50000g.
What is 125x^9+64y^12 written as sum of cubes
Answer:
33
45
ety
fyjfb
fgnf
ffjn
34
Find UT given the base?
Answer:
19
Step-by-step explanation:
[tex] In \:\triangle HGI[/tex]
HU = UG & HT = TI (Given)
Therefore, U and T are the midpoints of sides HG and HI respectively.
So, by mid point formula:
[tex] UT = \frac{1}{2} GI \\ \\ UT = \frac{1}{2} \times 38 \\ \\ UT = 19 [/tex]
Can someone help me with this math homework please!
Answer:
Step-by-step explanation:
1) (-2, 0)
2) (2 , 0)
3) (0, -4)
Ajmal has filled 5 boxes with marbles. He claims that at least 60% of the marbles in each box are red marbles. The table below shows the number of red marbles and the total number of marbles in all boxes.
Answer:
There is no table below, so how to figure it out? Huh???
Step-by-step explanation:
Can someone help me with this math homework please!
Answer:
Step-by-step explanation:
Answer:
1: (D)
2: (A)
3: (D)
4: (B)
5: (A)
Step-by-step explanation:
Question 1:
The local minimum is the lowest point in an area/interval of the function. That means the y-value will be the lowest, so it's either (-2, -15) or (2, -15). However, only (2, -15) is listed as an answer choice, so that's your answer.
Question 2:
The graph starts at the x-value of 0 and continues forever as x increases positively. The answer is x >= 0.
Question 3:
The first term of the sequence if -1.5, so replace n with 1:
f(1 + 1) = -2f(1)
Then replace f(1) with -1.5:
f(2) = -2 * -1.5
f(2) = 3
The next term of the sequence is 3.
Question 4:
On the graph, there are two different outputs (y-values of 3 & -2) for one input (x-value of 1). You can either remove (1, 3) or (1, -2), but since only (1, 3) is listed as an answer choice, that's your answer.
Question 5:
The formula represents the conversion from Fahrenheit to Celsius, so C(76.1) would be the temperature of 76.1 degrees Fahrenheit being converted to degrees Celsius since Kareem stated in the question that 76.1 was degrees Fahrenheit.
Hope this helps (●'◡'●)
simplify the expression and choose the best choice
Answer:
D
Step-by-step explanation:
[tex]\sqrt{3^{15} }[/tex]
[tex]\sqrt{3*3*3*3*3*3*3*3*3*3*3*3*3*3*3}[/tex]
[tex]\sqrt{3^{14} * 3}[/tex]
[tex]\sqrt{((3^7)^2)*3}[/tex]
[tex]3^{7}[/tex][tex]\sqrt{3}[/tex]
[tex]\boxed{\text{Solve for 'x'.}}\\\\\frac{x+3}{6}=\frac{2}{3}[/tex]
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x = 1[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the answer...}}\\\\\frac{x+3}{6}=\frac{2}{3}\\\----------\\\rightarrow (\frac{x+3}{6})6=(\frac{2}{3})6\\\\\rightarrow x + 3 = 4\\\\\rightarrow x + 3 - 3 = 4 - 3\\\\\rightarrow \boxed{x=1}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x = 1
Step-by-step explanation:
( x + 3 ) / 6 = 2 / 3
Step 1 Cross multiply
( x + 3 ) * 3 = 3x + 9
2 * 6 = 12
We now have 3x + 9 = 12
Step 2 Subtract 9 from both sides
3x + 9 - 9 = 12 - 9
9 - 9 cancels out
12 - 9 = 3
We now have 3x = 3
Final step; divide both sides by 3
3x/3 = x
3/3 = 1
We're left with x = 1
To check our answer we can plug in 1 for x in the expression
( x + 3 ) / 6 = 2 / 3
Substitute 1 for x
1 + 3 / 6 = 2 / 3
Simplify addition
4/6 = 2/3
Simplify fraction
2/3 = 2/3 ✓
Three fourths of the offspring of two fruit flies have short wings, while the rest have wild-type wings . In a batch of offspring from those two flies, 100 have wild-type wings. How many of the flies have short wings?
Answer:
300
Step-by-step explanation:
If three-fourths of the offspring of two fruit flies have short wings and the rest have wild-type wings, then [tex]1-\frac{3}{4}=\frac{1}{4}[/tex] of the offspring must have wild-type wings. This means that the number of offspring that have short wings must be [tex]\frac{3/4}{1/4}=\frac{3}{4}\cdot \frac{4}{1}=3[/tex] times larger than the number of offspring that have wild-type wings. Since there are 100 offspring who have wild-type wings, there must be [tex]100\cdot 3=\boxed{300}[/tex] that have short wings.
Alternative:
If three-fourths of the offspring of two fruit flies have short wings and the rest have wild-type wings, then [tex]1-\frac{3}{4}=\frac{1}{4}[/tex] of the offspring must have wild-type wings. Therefore, 100 represents one-fourth of the total number of offspring, meaning there must be [tex]100\cdot 4=400[/tex] offspring total. Thus, there are [tex]400-100=\boxed{300}[/tex] offspring with short wings.
