Mrs. Johnson conducted a survey in her Math class. The results of this survey showed that the ratio of Android phones to Apple phones was 2 to 5. There were a total of 10 Android phones. What is the total number of students in Mrs. Johnson's class

Answer:

RP/SP =3 , RP/RS = 3/4

Step-by-step explanation:

Here is the complete question

Three colinear points on the coordinate plane are R(x,y) S(x+8h, y+8k) and P(x+6h,y+6k) Determine value of RP/SP and RP/RS?

Solution

We first find the length of RS, SP and RP as follows

RS = S(x+8h, y+8k)  - R(x,y)

= √[((x + 8h) - x)² + ((y + 8k) - y)²]

= √[x - x + 8h)² + (y - y + 8k)²]

= √[(8h)² + (8k)²] = 8√(h² + k²)

SP = P(x + 6h,y + 6k) - S(x+8h, y+8k)  

= √[((x + 6h) - (x + 8h))² + ((y + 6h) - (y + 8k))²]

= √[x - x + 6h - 8h)² + (y - y + 6k - 8k)²]

= √[(-2h)² + (-2k)²] = 2√(h² + k²)

RP = P(x+6h, y+6k)  - R(x,y)

= √[((x + 6h) - x)² + ((y + 6k) - y)²]

= √[x - x + 6h)² + (y - y + 6k)²]

= √[(6h)² + (6k)²] = 6√(h² + k²)

So, RP/SP = 6√(h² + k²)/2√(h² + k²)

= 6/2

= 3

RP/RS = 6√(h² + k²)/8√(h² + k²)

= 6/8

= 3/4

Answer:

79.74

Step-by-step explanation:

Multiply 6 by 12 and that by 2:

(6 × 12) × 2 - (6 × 6) = 72 × 2 - 36= 144 - 36 = 108

That will be the equation for the shaded area besides the circle now lets calculate the circle and take it away from the equation. the circle's diameter is 6 so the radius should be 3, then use:

3 × 3 × 3.14 = 9 × 3.14 = 28.26

Then do this:

108 - 28.26 = 79.74

There you have it!

Answer:

64°

Step-by-step explanation:

So supplement angles are equal to 180, so first our two angles added together will be 180:

x + x = 180

Now one of these angles is 6 greater than half:

x + (x/2 + 6) = 180

Then we will solve for x:

x + (x/2 + 6) = 180

x + x/2 + 6 = 180

x + x/2 = 174

\(\frac{3}{2}\)x = 174

x = 116

Plug it back in:

x + (x/2 + 6) = 180

         /\

     x/2 + 6

   (116)/2 + 6

        64

To check:

116 + 64 = 180 ✓

Answer:

2 7/16

Step-by-step explanation:

1/2*13/4=13/8

13/8*3/2=39/16

39/16=2 7/16

Hope this helped!! :)

Stay safe and have a wonderful day/night!!!!!

Brainliest?!?!

Answer:

99-7a^2=36 when a =3

Step-by-step explanation:

99-7a²

99-7(3)²

99-7(9)

99-63

36

An isosceles acute triangle is a triangle with at least two equal angles and three angles that are all less than 90 degrees. 50°, 50°, and 80° are three examples of the angles that make up an isosceles acute triangle.

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles. Thus the vertex angle is 38 and the base angle is 71 and their sum is 109.

The triangles 45/45/90 are always isosceles. This indicates that two of the triangle's legs are congruent. Which two sides of the figure are congruent is shown. The Pythagorean Theorem can be used to determine the hypotenuse's length from this point.

This is an isosceles right triangle. The other triangle is named a 30-60-90 triangle, where the angles in the triangle are 30 degrees, 60 degrees, and 90 degrees.

Therefore,

An isosceles acute triangle is a triangle with at least two equal angles and three angles that are all less than 90 degrees. 50°, 50°, and 80° are three examples of the angles that make up an isosceles acute triangle.

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Answer:

It occurs 18 times.

Step-by-step explanation:

Notice that for the first altered function we have that:

Therefore the +7 would directly affect the x-values, so the graph would shift horizontally.

For the next function we have that:

Therefore the +7 would directly affect the y-values, so the graph would shift vertically.

The area of the surface obtained by rotating the circle \(x^2 + y^2 = r^2\) about the line y = r is π²r² square units.

To find the area of the surface obtained by rotating the circle

\(x^2 + y^2 = r^2\) about the line y = r, we can use the method of cylindrical shells.

The circle \(x^2 + y^2 = r^2\) is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.

When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.

Consider a small strip on the circle at a distance y from the line y = r.

This small strip is at a distance r - y from the y-axis.

The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).

The width of this strip is the change in x, which we can denote as dx.

The area of this small strip is then given by the product of its length and width, which is 2πy dx.

Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):

Total Surface Area = ∫[from -r to r] 2πy dx

Now, we need to express y in terms of x using the equation of the circle \(x^2 + y^2 = r^2:\\y^2 = r^2 - x^2\)

y = ±√(r² - x²)

Since we are considering the upper half of the circle, we take the positive square root:

y = √(r² - x²)

Now, we can rewrite the integral with respect to x:

Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx

To solve this integral, we can make a trigonometric substitution:

Let x = r sin(θ), then dx = r cos(θ) dθ.

When x = -r, θ = -π/2, and when x = r, θ = π/2.

Now the integral becomes:

Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ

Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ

Now, we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

√(1 - sin²(θ)) = cos(θ)

Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ

Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2

Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ

Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]

Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]

Since sin(π) = 0 and sin(-π) = 0:

Total Surface Area = 2πr² [(π/2 - (-π/2))/4]

Total Surface Area = 2πr² (π/2)

Total Surface Area = π²r²

So, the area of the surface obtained by rotating the circle \(x^2 + y^2 = r^2\) about the line y = r is π²r² square units.

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Answer:

20 and -20

20^2 = 400

(-20)^2=400 since two negative is positive

Because the p-value is less than 0.05, the null hypothesis should be rejected.

Given,

Null Hypothesis;-

The null hypothesis presupposes that any variation in the selected characteristics you observe in a set of data is the result of chance.

Alternative Hypothesis;-

The alternate response to your research question is the alternative hypothesis (Ha). It asserts that the populace is affected. Your research hypothesis and your alternate hypothesis are frequently identical. Alternatively said, it's the assertion that you anticipate or hope will be accurate.

Here,

Because the p-value is less than 0.05, the null hypothesis should be rejected. The allegation that the proportion of ball bearings with dimension values smaller than 2.20 cm in the current manufacturing process is the same as the proportion in the new process is sufficiently refuted by the evidence.

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Answer:x+10

Step-by-step explanation:just took the test

Answer:

-3

Step-by-step explanation:

Convert every fraction to an improper fraction just to make it easier.

43/10 - (12/5x + 11/2) = 1/2 (-18/5x + 6/10)

Distribute.

= 43/10 -12/5x - 11/2 = -18/10x + 6/10

Simplify using the common denominator, which is 10.

43/10 - 24/10x - 55/10 = -18/10 + 6/10

Isolate the x.

-24/10x + 18/10 = -43/10 + 55/10 + 6/10

Simplify.

-6/10x = 18/10

Multiply by the reciprocal (basically dividing fractions)

18/10 x -10/6

= -3

Answer:

x= -3

Step-by-step explanation:

43/10-12/5x-11/2=9/5x+3/5

-6/5=12/5x=-9/5x+3/5

-6-12x=-9x+3

-3x=9

x=-3

Answer:

draw a grid

Step-by-step explanation:

the slope is -4 by 3 which is usually put at y over x. you can draw a grid with -9 and 17  being put x by y then plot points on the graph which go down by 4 and go right by 3.

Answer:

To solve these questions , you need to plug in your numbers to y = mx + b

Step-by-step explanation

For A, 17 is your y, -4/3 is your m and -9 is your x

17 = -4/3(9) + b. Multiply -4/3 and 9, and subtract your answer from 17. that will give you the value of b.

Answer:

Step-by-step explanation:

If one bottle of perfume holds 5 millimeters and we only have two, we would only be able to fill the bottle 2/5 of the way.

Step-by-step explanation:

4th term =2(4)-1=7

10th term =2(10)-1=19

For the given fraction x^2-8x+16/x^2-16 if x≠4 and x≠-4 the simplified fraction is (x-4)/(x+4).

Simplified fraction refers to the fractions in their lowest form which has been reduced and simplified. The numerator and denominator in the fraction are reduced in simplified fraction to the extent that the only common factor between them is 1.

In order to simplify the fraction (x^2-8x+16)/(x^2-16), first, we must factor the numerator and denominator of the fraction:

Numerator: x^2-8x+16 = (x-4)(x-4) = (x-4)^2

Denominator: x^2-16 = (x-4)(x+4)

So the fraction becomes:

(x-4)^2/(x-4)(x+4)

Next, we can simplify the fraction by canceling out the (x-4) term in the numerator and denominator:

(x-4)/(x+4)

Therefore, the simplified fraction is (x-4)/(x+4) if x≠4 and x≠-4.

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Answer:

c = 9

Step-by-step explanation:

Since angle d and 59 are on a right angle (indicated by the small square)

We can equate the sum of these angles to 90:

d+59=90

Now we subtract 59 from both sides:

d+59-59=90-59

d=31

Since angles d,c and 140 are on a straight line we can equate the sum of these 3 to 180:

c+d+140=180

Substitute d with 31 from previous working out:

c+31+140=180

Simplify:

c+171=180

Subtract 171 from both sides:

c+171-171=180-171

Simplify:

c= 9

Answer: £67.875

Step-by-step explanation:

€90.50 x 3/4 = £67.875

The slope of the line perpendicular to the segment AB is 1/4

The slopes of perpendicular lines are negative reciprocals of each other.

Given the endpoints A(-8.1, 4.9) and B(-7.6, 2.9), the slope of this line is as follows:

(2.9 - 4.9)/[-7.6 - (-8.1)]

= (2.9 - 4.9)/(-7.6 + 8.1)

= -2/0.5

= -4

The negative reciprocal of -4 is 1/4

Therefore, the slope of the line perpendicular to the segment AB is 1/4

Answer:

32 units.

Step-by-step explanation:

look up a picture of a 306090 triangle, it will make sense :)

Answer:

32

Step-by-step explanation:

cos 30 = \(\frac{\sqrt{3} }{2}\)

\(\frac{\sqrt{3} }{2}\) = 16\(\sqrt{3}\) / n

n = 16\(\sqrt{3}\) * \(\frac{2}\sqrt{3} }\)

n = 32 units

Answer:

9

Step-by-step explanation:

3x+8 = 35

3x = 27

x = 9

Hope this helps :)

Step-by-step explanation:

Here, (3x + 8)° and 35° are vertically opposite angles which are equal, therefore,

3x + 8 = 35

3x = 35 - 8

3x = 27

x = 27/3

x = 9

Answer:

9/6

Step-by-step explanation:

Answer:

both cost $12

Step-by-step explanation:

Let's say the price of a senior citizen ticket is s dollars and the price of a child ticket is c dollars.

For, say, 7 senior citizen tickets, the cost would be s 7 times, or s * 7. Similarly, 6 child tickets would cost 6c. The total amount of (senior citizen ticket cost) + (child ticket cost) would equal the total sales.

Therefore,

first day:

7s + 6c = 156

second day:

7s + 3c = 120

7s + 6c = 156

7s + 3c = 120

we can solve this by solving for c in terms of s in one equation and plugging that into the other equation

7s + 6c = 156

subtract 7s from both sides to isolate the c and its coefficient

156 - 7s = 6c

divide both sides by 6 to isolate c

(156-7s)/6 = c

26-(7/6)s = c

plug that into the other equation

7s+3c = 120

7s + 3 (26-(7/6)s) = 120

7s + 78 - (21/6)s = 120

7s + 78 - (7/2)s = 120

(7/2)s + 78 = 120

subtract 78 from both sides to isolate s and its coefficient

(7/2)s = 42

multiply both sides by 2/7 to isolate s

12 = s

26 - (7/6)s = c

26 - 14 = c = 12

Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

Answer:

True, False

Step-by-step explanation:

Answer:

the first one is true

and the second one is false

Step-by-step explanation:

multiplication goes in any other however division does not

example: 4×2=8 and 2×4 is also = 8

but 4÷2 =2 but 2÷4 is not equal to 2

Answer:

A) d = \(\frac{C}{\pi}\)

B) d = \(\frac{8}{\pi}\) or 2.55 inches

C) r = 3 inches

Step-by-step explanation:

Given the formula for the circumference of a circle, C = πd, where d represents the diameter of a circle.

In order to solve for d, divide both sides of the equation by π:

\(\frac{C}{\pi} = \frac{\pi d }{\pi}\)

d = \(\frac{C}{\pi}\).

Given the circumference of the circle, C = 8 inches:

Use the formula for the diameter of the circle from part A of this post.

d = \(\frac{C}{\pi}\)

d = \(\frac{8}{\pi}\) or 2.55 inches.

Since the diameter of a circle is the same as twice the measure of the radius, r:  d = 2 × r

Then, we can rewrite the formula for the circumference of a circle as:

C = 2πr

Divide both sides by 2π to isolate r :

\(\frac{C}{2\pi } = \frac{2\pi r}{2\pi }\)

r = \(\frac{C}{2\pi }\)

Given the circumference of a circle, C = 6π:

\(r = \frac{6\pi }{2\pi } = 3\)

Therefore, the radius of the circle is 3 inches.

Answer:

Step-by-step explanation:

See attachment

Triangle ABD is congruent to triangle BCD

Congruent triangles are triangles with thesame corresponding sides and also with thesame corresponding angles.

To show that triangle ABD is congruent to triangle BCD

It has been shown that line AD is equal to line DC

i.e AD = DC

angle BMA = BMC = 90°

Therefore AB = BC

And line BD is common to both triangles

Therefore ;

AB = BC

AD = DC

Therefore we can say that triangles ABD is congruent to triangle BCD.

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