rationalize the denominator and simplify √6/ √5-√3​

Answer:65

Step-by-step explanation:

Length of first, second and third piece are 5, 15 ,25 inch

Given that;

Length of board = 45 inch

Second cut is 3 times as long as the first piece

Third cut is 5 times as long as the first piece

Find:

Length of all three piece

Computation:

Assume;

Length of first piece = a

So,

Length of second piece = 3a

Length of third piece = 5a

So,

Length of first piece + Length of second piece + Length of third piece = Total length

a + 3a + 5a = 45

9a = 45

a = 5

So,

Length of first piece = a

Length of first piece = 5 inch

Length of second piece = 3a = 3(5)

Length of second piece = 15 inch

Length of third piece = 5a = 5(5)

Length of third piece = 25 inch

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Answer:

A. 15

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

acc to ques ...total area=160=area of parallelogram + area of triangle

b×h +1/2×b×h=160

14×10+5x=160.....(let base of triangle =b=x)

5x=20

x=4......

Answer:

Slope of the line of best fit = -0.34868

Step-by-step explanation:

From the figure attached,

Coordinates of the points lying on the given line are (2, 3), (2, 5), (2, 6), (3, 5), (4, 3), (5, 4) and (7, 3)

By using the linear regression calculator,

Equation of the line of best fit → y = -0.34868x + 5.38816

Comparing this equation with, y = mx + b

Slope of the line of best fit → m = -0.34868

Answer:

-13

Step-by-step explanation:

Answer: 2(-4x+y)

Step-by-step explanation:

rewrite -8 as 4*2

4*2x+2y

factor out the common term (2)

2(-4x+y)

1/4

because not a lot of students have both gender as siblings!

Answer:

Step-by-step explanation:

28 students in total

21 - 7 = 14 students only has a brother

9 - 7 = 2 students only have a sister

7 students have both brothers and sisters

probability of a student having a brother and a sister:

[tex]\frac{7}{28} = \frac{1}{4}[/tex]

Answer:

7.362

Step-by-step explanation:

Given :

Mean = 35

Score, x value = 23

Zscore = - 1.63

Recall the Zscore formula :

Zscore = (X - mean) / standard deviation

-1.63 = (23 - 35) / standard deviation

-1.63 = - 12 / standard deviation

standard deviation * - 1.63 = - 12

Divide both sides by - 1.63

Standard deviation = - 12 / - 1.63

Standard deviation = 7.362

Answer:

4, 802 cans will be collected in two weeks

Step-by-step explanation:

343 aluminum cans = 1 day

? = 2 weeks

2 weeks = 14 days

So, 343 x 14 = 4, 802

Answer:

11.5

Step-by-step explanation:

-1*-11.5=11.5

uv= u times v

-1 times -11.5 equals 11.5

Answer:

32 siblings from the class theres a possibility that some students had more siblings and not everyone has one

Step-by-step explanation:

.

The probability that a student chosen randomly from the class has a brother and a sister is [tex]\frac{1}{15}[/tex].

The chance that something will happen, or how likely it is that an event will occur.

probability of an event = [tex]\frac{number of favorable outcomes}{Total number of outcomes}[/tex]

According to the given question

we have total 30 students.

6 have a brother

12 have a sister

and 14 who don't have any siblings

If we se the provided Venn diagram

the number of students who have only sister is 10

and the number of student who have only brother is 4.

because, 6+12+14 = 32

but we have only 30 students

⇒ 2 students has a brother and a sister.

therefore,

the probability that a student chosen randomly from the class has a brother and a sister = [tex]\frac{number of students as a brother and a sister}{total number of students}[/tex]= [tex]\frac{2}{30}[/tex] =[tex]\frac{1}{15}[/tex]

Hence, the probability that  the chosen student from the class has a brother and sister is [tex]\frac{1}{15}[/tex].

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Answer:

im pretty sure its 3 plz tell me if im wrong im new here but i think its right

Step-by-step explanation:

Answer:

2 and 2/3 mph

Step-by-step explanation:

The computation of the speed when he wants to keep the same distance is shown below:

Given that

Jenny left her house at 8:00AM

Went for a school at a speed of 2 and 2/3 mph

And, her brother left the house minutes later

So here the speed would be the same i.e.  2 and 2/3 mph

Answer:

Right triangles are congruent if both the hypotenuse and one leg are the same length. These triangles are congruent by HL, or hypotenuse-leg.

Step-by-step explanation:

Answer:

Yes, they are congruent

Step-by-step explanation:

Using Pythagorean theorem in ΔMNP,

Base² + altitude² = hypotenuse²

MP² + 28² = 35²

MP² + 784 = 1225

         MP² = 1125 - 784 = 441

         MP =√441

MP = 21

As per RH congruent rule,

Hypotenuse NP ≅ RS  and

Any one leg , here MP = RQ = 21'

Answer:

1. The ratio of their diameters is 8/5 = 8 : 5

2. The ratio of their surface area is (8/5)²

3. The ratio of their volume is (8/5)³

4.The area of the base of the larger cylinder is 128 cm²

Step-by-step explanation:

Given that the two cylinders are similar, we have;

Two cylinders are similar when the ratio of their heights is equal to the ratio of their radii

Therefore, we have;

1. The ratio of the height of the two cylinders = 8/5 = The radio of their radii = r₁/r₂

The ratio of their diameter = D₁/D₂ = 2·r₁/2·r₂ = r₁/r₂ = 8/5

The ratio of their diameters D₁/D₂ = 8/5 = 8 : 5

2. The surface area of the cylinders = 2·π·r·h + 2·π·r²

Therefore, we have;

(2·π·r₁·h₁ + 2·π·r₁²)/(2·π·r₂·h₂ + 2·π·r₂²) = (r₁·h₁ + r₁²)/(r₂·h₂ + r₂²)

h₁ = h₂ × 8/5

r₁ = r₂ × 8/5

= (8/5)²(r₂·h₂ + r₂²)/(r₂·h₂ + r₂²)  = (8/5)²

The ratio of their surface area = (8/5)²

3. The volume of the cylinder = π·r²·h

∴ The ratio of the volume = (π·r₁²·h₁)/(π·r₂²·h₂) = (8/5)³ × (π·r₂²·h₂)/(π·r₂²·h₂) = (8/5)³

The ratio of their volume = (8/5)³

4. The ratio of the area of the base of the larger cylinder to the area of the base of the smaller cylinder is (8/5)²

Therefore if the area of the base of the smaller cylinder is 50 cm², the area of the base of the larger cylinder = 50 cm² × (8/5)²  = 128 cm²

Answer:

#3= 8   #4=2   #5= 4,3   #6= 5  #7= 8   #8=9

Step-by-step explanation:

Answer:

The x graph

Step-by-step explanation:

The x graph

Answer: D

Step-by-step explanation:

Answer:

60 degrees

Step-by-step explanation:

set up like 240-120

240-120=120

120 divided by 2 equals 60

therefor, the angle is 60 degrees

Answer:

Step-by-step explanation:

Remark

The solution to this is to add the two vertically opposite arcs and take 1/2 of the result to get the intersecting angle of the chords.

Solution

<x = 1/2 (arc measure of 116 + 74)

<x = 1/2 (190)

<x = 95

answer:

haha my teacher saw my screen ( since im in-school ) and he said that you were a trapezoid

i would have answered this question in more detail but i didnt know how to, hope this help tho! :)

Answer:

the correct anwser is b b cause they both are positive y intercepts

Answer: I think its A

Step-by-step explanation:

The given function is  increasing from 1 to ∞. Therefore, option A is the correct answer.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

From the given graph, the vertex is (1, -2)

For a function y = f(x), if the value of y increases on increasing the value of x, then the function is an increasing function.

Here, the function is increasing from 1 to infinity.

Therefore, option A is the correct answer.

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Answer:

A)

Step-by-step explanation:

Answer:

Step-by-step explanation:

A negative number raised to an even exponent gives a positive result so it is the same as 3 raised to 6. That is 3 x 3 x 3 x 3 x 3 x 3 = 729

The (-3) to the sixth power, (-3)⁶, is equal to 729.

To express (-3) to the sixth power in exponential form, we write it as (-3)⁶.

Now, let's calculate (-3)⁶ properly:

(-3)⁶ = (-3) * (-3) * (-3) * (-3) * (-3) * (-3)

Multiplying -3 by itself six times:

(-3) * (-3) * (-3) * (-3) * (-3) * (-3) = 729

Therefore, (-3) to the sixth power, (-3)⁶, is equal to 729.

By raising -3 to the power of 6, we obtain the result of 729.

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Answer:

98 degrees

Step-by-step explanation:

278-82 over 2

196 divided by 2

This will lead to 98, therefor the angle is 98 degrees

Answer:

m= 9/8

Step-by-step explanation:

(5, 2) and (-3, -7)

Slope:

m=(y2-y1)/(x2-x1)

m=(-7-2)/(-3-5)

m=(-9)/(-8)

m=9/8

Answer:

[tex]8 .3 \times 2.10.5[/tex]

Step-by-step explanation:

Simplify 6 - 1 to 5.

[tex]8.3 \times 2.10 .5[/tex]

Therefor, the answer is 8.3 × 2.10.5