please help me with this

Answer:

55°

Step-by-step explanation:

In circle with center O, OA and OB are radii and PA and PB are tangents drawn from external point P.

Since, tangent is perpendicular to the radius of the circle.

[tex] \therefore m\angle PAO = m\angle PBO = 90°\\

m\angle APB = 70°....(GIVEN) \\[/tex]

In quadrilateral PAOB,

[tex] m\angle PAO + m\angle PBO+ m\angle APB \\+m\angle AOB = 360°\\

\therefore 90° + 90° + 70° +m\angle AOB = 360°\\

\therefore 250° +m\angle AOB = 360°\\

\therefore m\angle AOB = 360°- 250°\\

\huge \purple {\boxed {\therefore m\angle AOB = 110°}} \\[/tex]

Since, angle subtended at the circumference of the circle is half of the angle subtended at the centre of the circle.

[tex] \therefore m\angle ACB = \frac {1}{2} \times m\angle AOB\\\\

\therefore m\angle ACB = \frac {1}{2} \times 110°\\\\

\huge \orange {\boxed {\therefore m\angle ACB = 55°}} [/tex]

Answer:

The rate of each train is 74 miles per hour and 90 miles per hour respectively.

Step-by-step explanation:

Given;

distance between the two trains, d = 492 miles

total time traveled by each train before meeting the other, t = 3 hours

Let the speed for the first train = p

Let the speed for the second train = q

Assuming the first train is 16 mph slower than the second train, then;

q = p + 16

Distance = speed x time

492 miles = (p + q) x 3

492 = 3p + 3q

but, q = p + 16

492 = 3p + 3(p + 16)

492 = 3p + 3p + 48

492 - 48 = 6p

444 = 6p

p = 444 / 6

p = 74 miles per hour

q = 74 + 16

q = 90 miles per hour

Therefore, the rate of each train is 74 miles per hour and 90 miles per hour respectively.

Answer:

N/2 + 7 = 2N - 5

N + 14 = 4N - 10

24 = 3N

N = 8

Answer:

1/2n + 7 = 2n - 5

2 · 1/2n + 7 · 2 = 2n · 2 - 5 · 2

n + 14 = 4n - 10

n - n + 14 = 4n - n - 10

14 = 3n - 10

14 + 10 = 3n - 10 + 10

24 = 3n

24 / 3 = 3n / 3

n = 8

Step-by-step explanation:

Answer:

12+(t÷7)=V is the answer

Step-by-step explanation:

Answer

Answer:

Triangle C and Triangle D

Step-by-step explanation:

If you look closely at all of the different triangles, you can see that there are two pairs of congruent triangles.

Triangle A and Triangle E are congruent, both being right triangles and approximately the same size.

Triangle B and Triangle F are congruent, as both of them are isosceles triangles, and again, the same size.

The two that remain, Triangles C and D, are both scalene triangles, but they are not congruent to one another. Triangle C clearly has a smaller obtuse angle than Triangle D.

Hope this helps!

Answer:

independent is the y value or the value that changes at a steady rate no matter what, the dependent variable or x is the variable that is subject to change and is dependent on the y value to find a pattern

Step-by-step explanation:

Answer:

Variables are given a special name that only applies to experimental investigations. One is called the dependent variable and the other the independent variable. The independent variable is the variable the experimenter changes or controls and is assumed to have a direct effect on the dependent variable.

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Here in this question, we are to estimate the experimental probability.

Now, to estimate the experimental probability, we shall be looking at previous attempts.

Thus, the probability that he would hit his next target would be; number of previous hits/number of total trials

From the question, number of previous hits were 10 and the number of total trials = 30

The probability he is hitting the next ball is thus 10/30 = 1/3

Answer:

  7.  ∠CBD = 100°

  8.  ∠CBD = ∠BCE = 100°; ∠CED = ∠BDE = 80°

Step-by-step explanation:

7. We presume the angles at A are congruent, so that each is 180°/9 = 20°.

Then the congruent base angles of isosceles triangle ABC will be ...

  ∠B = ∠C = (180° -20°)/2 = 80°

The angle of interest, ∠CBD is the supplement of ∠ABC, so is ...

  ∠CBD = 180° -80°

  ∠CBD = 100°

__

8. In the isosceles trapezoid, base angles are congruent, and angles on the same end are supplementary:

  ∠CBD = ∠BCE = 100°

  ∠CED = ∠BDE = 80°

Answer:

x = 8.5

Step-by-step explanation:

In this question, we are to calculate the value of x.

To calculate this, we shall be utilizing one of the important properties of parallelogram.

This property is that opposite angles of a parallelogram are equal.

This means that mQSR = mSPQ = 4x + 90

Now to finally calculate x, we make use of another important parallelogram property which is that angles of parallelogram which faces each other are supplementary.

This means that they add up to be 180

Since mQSR faces mQRS

This means that;

4x + 90 + 9x -20 = 180

13x + 70 = 180

13x = 110

x = 110/13 which is approximately 8.5

Answer:

12000 x 0.015 = 180

12000 + 180 = 12180

12180 x 0.015 = 182.7

12180 + 182.7 = 12362.7

$12,362.7

Hope this helps

Step-by-step explanation:

Answer:

2.195%

Step-by-step explanation:

Assuming that both planets are a sphere, we have to:

26590 * 28% = 7445.2

7445.2 miles would be the diameter of the moon, now to calculate the volume, we know that the radius is half the diameter, so:

r2 = d2 / 2 = 7445.2 / 2 = 3722.6

and the radius of the planet would be:

r1 = d1 / 2 = 26590/2 = 13295

now the volume of the planet we know is equal to:

v1 = 4/3 * pi * r1 ^ 3

and the volume of the moon would be:

v2 = 4/3 * pi * r2 ^ 3

We want to calculate the percentage by volume, therefore:

v2 / v1 = 4/3 * pi * r2 ^ 3 / 4/3 * pi * r1 ^ 3

v2 / v1 = 3722.6 ^ 3/13295 ^ 3

v2 / v1 = 0.021952

that is, the volume of the moon represents 2.195%

Answer:

1)

c.

18,700

2)

a.

46,900

3)

a.

84,500

4)

a.

12,000

Step-by-step explanation:

1) 1 mile = 5280 ft.

Area of both sides = 5280 ft × 8 ft × 2 sides = 84480 ft²

Since 1 person for each 4.5 square feet, the ratio of one person to 1 square feet = [tex]\frac{1}{4.5}[/tex]

the size of a crowd = [tex]\frac{1}{4.5} *84480=18773.33[/tex] ≈ 18700

2) 1 mile = 5280 ft, therefore 2 mile = 10560 ft (5280 × 2)

Area of both sides = 10560 ft × 10 ft × 2 sides = 211200 ft²

Since 1 person for each 4.5 square feet, the ratio of one person to 1 square feet = [tex]\frac{1}{4.5}[/tex]

the size of a crowd = [tex]\frac{1}{4.5} *211200=46933.33[/tex] ≈ 46900

3) 1 mile = 5280 ft, therefore 2 mile = 10560 ft (5280 × 2)

Area of both sides = 10560 ft × 10 ft × 2 sides = 211200 ft²

Since 1 person for each 2.5 square feet, the ratio of one person to 1 square feet = [tex]\frac{1}{2.5}[/tex]

the size of a crowd = [tex]\frac{1}{2.5} *211200=84400[/tex] ≈ 84500

4) 1 yard = 3 ft, therefore 100 yard = 300 ft (100 × 3)

Area of both sides = 300 ft × 50 ft × 2 sides = 30000 ft²

Since 1 person for each 2.5 square feet, the ratio of one person to 1 square feet = [tex]\frac{1}{2.5}[/tex]

the size of a crowd = [tex]\frac{1}{2.5} *30000=12000[/tex]

Answer:

(5s + 8) is the missing factor.

Step-by-step explanation:

The given expression is 5s² + 23s + 24

We have to convert the given expression into the factored form.

One factor of the expression has been given as (x + 3)

5s² + 23s + 24 = 5s²+ 15s + 8s + 24

                        = 5s(s + 3) + 8(s + 3)

                        = (5s + 8)(s + 3)

So the factors of the expression will be (s + 3) and (5s + 8)

Therefore, the missing factor of the given expression is (5s + 8).

Answer:

d. Summarized account information

Step-by-step explanation:

Answer:

  it would miss the point

Step-by-step explanation:

If the compass point were placed randomly on the line and arcs drawn, you might get a perpendicular by connecting the points where the arcs intersect, but it is not guaranteed to go through the desired point.

Answer:

(1,3) maximum

Step-by-step explanation:

As you can see from the graph the tip of the parabola is the vertex which is at the point (1,3) which is a maximum because it is the tallest point on the graph.

Answer:

96 sq yards

Step-by-step explanation:

40-24 is 16, and 16/2 is 8. 8 is the second length, so 8 times 12 is 96 which is the area

Answer:

180 ml oil

240 g onions

1.35 kg potatoes

1.8 l milk

Step-by-step explanation:

The recipe makes 6 portions and you need 18 portions. Since 6 is 3 times smaller than what you need, just times everything you've been given by 3.

*you can choose to convert into the correct units of measurement before or after dividing. I converted after dividing. Either way works fine though.

1) 60 x 3 = 180 ml

2) 80 x 3 = 240 g

3) 450 x 3 = 1350 g

They want it in kilograms, so divide it by 1,000 to convert. this gives you 1.35 kg.

4) 600 x 3 = 1800 ml

They want it in l, so divide it by 1,000 to convert. this gives you 1.8 l.

Hope this helped : )

Answer:

7/10

Step-by-step explanation:

10 marbles in a bag 7 of them are blue and the (10-7)=3 green

P( blue) = blue / total

            = 7/10

Answer:on the circle

Step-by-step explanation:

Point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a center of the circle at D(-1, 3)

And point G(-10, 1) is on the circle.

We know the standard equation of the circle when a center is given:

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]

Where r is the radius of the circle and (h, k) is the center of the circle.

Here (h, k) ⇒ (-1, 3)

The circle equation becomes:

[tex]\rm (x+1)^2+(y-3)^2=r^2[/tex]

Put the point on the circle equation to get the radius of the circle:

[tex]\rm (-10+1)^2+(1-3)^2=r^2[/tex]

[tex]\rm (-9)^2+(-2)^2= r^2\\\\\rm 81+4 = r^2\\\\ \rm r = \sqrt{85} \ units[/tex]

Equation of circle is:

[tex]\rm (x+1)^2+(y-3)^2=85[/tex]

Now put the point J(-3, 12 ) in the circle equation:

[tex]\rm (-3+1)^2+(12-3)^2=85[/tex]

4+ 81 ⇒ 85

It means point J is lying on the circle.

Thus, point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

Learn more about circle here:

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Answer:

a. 2(^3 sqrt 3) - ^3 sqrt 18

Step-by-step explanation:

got it right on edge

[tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex][tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex][tex]2(\sqrt[3]{3})-\sqrt[3]{18}[/tex] option (A)  is Correct.

The problem can be solved by following steps.

The expression given is [tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex]

So , The first step we will do is Rationalize the figure

= [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }}{\sqrt[3]{9}*\sqrt[3]{9} }[/tex]

The product of radicals with the same index equals the radical of the product:[tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9*9^2} }[/tex]

Simplify using exponent with same base

[tex]a^{n}*a^{m} = a^{a+m}[/tex]

= [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^1+^2} }[/tex]

Calculate the sum or difference: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^3} }[/tex]

Simplify the radical expression: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {{9} }[/tex]

Calculate the power : [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{9} }[/tex]

Cross out the common factor: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{3} }[/tex]

Factor Greatest Common Factors : [tex]\frac{3*2\sqrt[3]{3}-\sqrt[3]{18} }{3}[/tex][tex]3*2\sqrt[3]{3}-\sqrt[3]{18}}[/tex]

Reduce the fraction : [tex]2\sqrt[3]{3}-\sqrt[3]{18}}[/tex]

Hence the First option is correct

Learn more about Quotient here

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Answer:

33% or with 10th place decimal 33.3%

Step-by-step explanation:

1/3 has a continuous decimal form of .333333...

So, it is usually rounded to .33

Hope this helps!

Answer: 33.33%

Step-by-step explanation:

Answer:

The answer is 7n3 + 6.

Step-by-step explanation:

To simplify, remove the parentheses and combine like terms.

The standard form of the given expression is 7n³+6.

The given expression is (4+2n³)+(5n³+2).

To add any two expressions group the like terms.

Here, 4+2n³+5n³+2

= (2n³+5n³)+4+2

= 7n³+6

Therefore, the standard form of the given expression is 7n³+6.

To learn more about an expression visit:

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Answer:

$10579.49

Step-by-step explanation:

The formula for amount gotten after a period of time (in years) on a principal which is compounded continuously is given as:

[tex]A = P(1 + r)^t[/tex]

where P = principal (amount borrowed)

r = interest rate

t = number of years

Peter accumulated $7,500 in credit card debt with interest rate as 3.5% per year and he does not make any payments for 10 years.

Therefore, his debt is:

[tex]A = 7500(1 + \frac{3.5}{100})^{10}\\ \\A = 7500 (1 + 0.035)^{10}\\\\A = 7500(1.035)^{10}\\[/tex]

A = $10579.49

He will owe $10579.49 after 10 years

Answer:

A= $10,643.01

Step-by-step explanation:

if you are rounded to the nearest cent

Identify the values of each variable in the formula. Remember to express the percent as a decimal.

A=?

P= $7,500

r= 0.035

t= 10 years

For compounding continuously, use the formula A=Pert.

Substitute the values in the formula and compute the amount to find

A= 7,500e [tex]x^0.035.10[/tex][tex]x^{0.035.10}[/tex]

A= $10,643.01

Answer:

  b.  b = 15.0, A = 113.2°, C = 300°

Step-by-step explanation:

The given sides are either side of the given angle, so the Law of Cosines can be used to find the unknown side.

  b² = a² +c² -2ac·cos(B)

  b² = 23² +12.5² -2(23)(12.5)cos(36.8°) = 224.829

  b = √224.829 = 14.99 ≈ 15.0 . . . . . matches choice B

__

For the purpose of selecting the correct multiple-choice answer, this is sufficient working.

__

If you want to find the remaining angles, you can use the law of sines to find one of them. The smallest angle* will be ...

  sin(C)/c = sin(B)/b

  C = arcsin(c/b·sin(B)) = arcsin(12.5/14.9942·sin(36.8°)) ≈ 30.0°

Then angle A can be found from the sum of angles in a triangle:

  A = 180° -36.8° -30° = 113.2° . . . . . also matches choice B

_____

* We choose to find the smallest angle because the largest one may be more than 90°. The Law of Sines is ambiguous in that case. Finding the smaller angle first resolves the ambiguity immediately.

Answer:

Choice C

Step-by-step explanation:

f: initial value of 200 decreasing at a rate of 4%

g: initial value of 40 increasing at a rate of 8%

f is decreasing so it must go down starting at 200

That eliminates a and d

g is increasing and starts at 40  That eliminates a

We must look at b and c

g is increasing faster than f is decreasing

Choice C

Answer:

The cube root for 216 is 6

Step-by-step explanation:

Answer:

the cube root of 216 is 6

Step-by-step explanation: