Olivia, Charles, and Reese had a challenge to see who could run the farthest in a week. Olivia ran 13 miles, Charles ran 18 times as many miles as Olivia and Reese ran 1/2 as many miles as Charles. What equation could you use to find how many miles Reese ran?

[tex]~~~~~5\sin 2x +4 =10 \sin^2 x\\\\\implies 5\cdot 2\sin x \cos x+4 =10 \sin^2 x\\\\\implies 10 \sin x \cos x +4 = 10\sin^2 x\\\\\implies 10\tan x + 4\sec^2 x = 10\tan^2 x~~~~~;[\text{Divide both sides by}~ \cos^2 x]\\\\\implies 10\tan^2 x -10 \tan x -4(1+ \tan^2 x)=0\\\\\implies 10\tan^2 x -10 \tan x -4 -4\tan^2 x =0\\\\\implies 6 \tan^2 x -10 \tan x -4 =0\\\\\implies 3 \tan^2 x -5 \tan x -2 =0~~~~~;[\text{Divide both sides by 2}]\\\\\implies 3\tan^2 x - 6\tan x +\tan x -2 =0\\\\[/tex]

The geometric series will be D. 2 + 14 + 98 + 686 because it is having a common ratio 7.

In mathematics, a geometric series is the sum of an infinite number of terms that have a constant or common ratio between successive terms

A. 6 + 13 + 20 + 27 .

the difference between two terms are 13-6 = 7 , 20-13= 7

The terms are increasing by 7. So it is not geometric

B. 7 + 21 + 35 + 45

the difference between two terms are 21-6 = 14 , 35-21= 14

The terms are increasing by 14. So it is not geometric

C. 14 + 21 + 28 + 35

the difference between two terms are 21-14 = 7 , 28-21= 7

The terms are increasing by 7. So it is not geometric

D. 2 + 14 + 98 + 686

Here the difference is not same, so we find the ratio

14/2= 7

98/14= 7

686/98= 7

So common ratio is 7

When the common ratio is same then it is Geometric series

Hence the geometric series will be D. 2 + 14 + 98 + 686 because it is having a common ratio 7.

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Answer:

D

Step-by-step explanation:

multiplied by 7 each time

Arithmetic sqaure: a + (n-1) * d

              where "a" is the first term, "d" is the common difference

Here given:

a = 10 gallons

d = 5.5 gallons

Solve for first 5 terms:

10 + (1-1) * 5.5 = 10

10 + (2-1) * 5.5 = 15.5

10 + (3-1) * 5.5 = 21

10 + (4-1) * 5.5 = 26.5

10 + (5-1) * 5.5 = 32

first five terms: 10, 15.5, 21, 26.5, 32

General formula

So

Answer:

10

Step-by-step explanation:

My guy just plug in the number for x it's not that hard

Answer:

7 with a remainder of 2

Step-by-step explanation:

i just did the math rn

Answer:

9.411

Step-by-step explanation:

Answer:9.144

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

1)

[tex]\longrightarrow (-\dfrac{1}{2} +2)[/tex]

[tex]\longrightarrow (-\dfrac{1}{2} +\dfrac{4}{2} )[/tex]

[tex]\longrightarrow \dfrac{-1+4}{2}[/tex]

[tex]\longrightarrow \dfrac{3}{2}[/tex]

[tex]\sf \bold{\longrightarrow 1\dfrac{1}{2}}[/tex]         (final answer)

2)

[tex]\longrightarrow \sf 4(\dfrac{1}{2} +\dfrac{5}{4} ) + (-5)[/tex]

[tex]\longrightarrow \sf 4(\dfrac{2}{4} +\dfrac{5}{4} ) + (-5)[/tex]

[tex]\longrightarrow \sf 4(\dfrac{7}{4} ) + (-5)[/tex]

[tex]\longrightarrow \sf 7-5[/tex]

[tex]\longrightarrow \bold{\sf 2}[/tex]        (final answer)

Answer:

they played 20 games together

Step-by-step explanation:

use percentages

Let x be the number of total games.

If 60% is won games then 40% is lost games.

(8/x)*100 = 40

8/x = 4/10

80 = 4x

X = 80/4

Therefore the number of games is 20

Your answer is 53

Yw :D

Answer:

x = -1

Step-by-step explanation:

First we expand both sides :

Let's start with the right side:

6(x-1) = 6x-6

Now we do the left side:

4(x-2) = 4x-8

Now we add 6 to both sides:

(6x-6)+6 = (4x-8)+6

Simplify:

6x = 4x -2

Subtract 4x from both sides:

6x - 4x = (4x-2) - 4x

Simplify:

2x = -2

Divide both sides by 2:

2x÷2 = -2÷2

Simplify:

x = -1

I dont see a box so can't do the second part.

Hope this helps and brainliest please

Answer:

D) It is discontinuous because there is a value for a such that [tex]\lim_{x \to \\a } f(x)[/tex] does not exist.

Step-by-step explanation:

Just did the practice.

Answer:

- sign indicates the fact that it's Below sea level

Answer:

24

Step-by-step explanation:

The way you calculate the volume of a shape is length x width x height. 4 x 3 x 2 = 24.

the slope is m= -1/5.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

y_2 - y₁ = m(x₂ - x₁).

here, we have,

the slope of the line that passes through the points (-1, 6) and (14, 3)

Slope: m=  y_2 - y₁/(x₂ - x₁).

              = 3-6/14+1

              = -1/5.

hence, the slope is m= -1/5.

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Answer:

It's B

Step-by-step explanation:

All you're doing is adding 1.5 each time

Hope this helps :)

Answer:

a = 39.2650873379cm

b = 11.5529459767cm

Step-by-step explanation:

a - Use the area of a triangle equation -  1/2 * a * b * Sin(C)

1/2 * 8 * 10 * Sin(79) = 39.2650873379cm

b - Use the cosine rule - c^2 = a^2 + b^2 - (2 * a * b * Sin(C)

64 + 100 - (2 * 8 * 10 * Cos(79)) = 133.4705607398

c = square root of 6.9396506484 = 11.5529459767cm

Put to however many significant figures / decimal places required.

:)

Answer:

8

Step-by-step explanation:

From 5 to get to 20 it would be (X4), so we would do the same for the 2, and 2 times 4 would be 8. The answer is 8.

Answer:

45 im not to shur

Step-by-step explanation:

10 + 7 + 9 + 11 + 8 = ?

? = 45

1The two equivalent equations will be

1. [tex]y=\dfrac{-6}{4}x+10[/tex]

2. [tex]3x+2y=5[/tex]

An equation between two variables that gives a straight line when plotted on a graph.

The required two equivalent equations are

[tex]y=\dfrac{-6}{4}x+10[/tex]

[tex]3x+2y=5[/tex]

The above equation has no repeating numbers and fulfill the criteria.

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Factor out the numerator first

The hole is at x-3=0 i.e x=3

And

The hole is at (3,6)

Answer:

The First problem is empty

The second is (-oo,3) U [6,oo)

Step-by-step explanation:

Set C is defined for all reals less than or equal to. 3.

Set D is defined for all reals greater than or equal to 6.

The First cardinal want us to find when the two Set intersects. They never intersect so that the Set is empty.

The next cardinal want us to find when the Set contains both of their subsets.

Set C can be from any negative number up to 3 inclusive.

Set D start at 6, exclusively and continues forever to thr positve. So

the Set C And Set D will be

(-oo, 3) U [6,oo)

Answer:

Slope < 0  : 1     slope between 0 and1 :3

slope greater than 1 : 2     #4 has 'undefined' slope

Step-by-step explanation:

Answer:

48%

Step-by-step explanation:

First, we need to add the amounts together to be able to see what percent of all the cups are dirty. (228 + 247 = 475). Now we can find one percent of 475 we can do this by moving the decimal point two to the left. (4.75). so If 4.75 is 1% we can multiply 4.75 until we get 228.

4.75 x 20 = 95.

4.75 x 40 = 190

4.75 x 45 = 213.75

4.75 x 50 = 237.5

4.75 x 48 = 228

Since every time we multiplied by 1 more we went up 1%. We multiplied by 48 so 48%.

Answer: Alex 28

Frank 22

Step-by-step explanation: Age difference is 6. Addition is 50

base= 25 mm

height= 28 mm

the volume of the square pyramid.

[tex]volume = {a}^{2} \frac{h}{3} [/tex]

[tex]v = {25}^{2} \frac{28}{3} [/tex]

[tex]v = 5833.33333 {mm}^{3} [/tex]

[tex]v = 5833.3 {mm}^{3} [/tex]

A circle is a curve sketched out by a point moving in a plane. The point that lies on the circle is (-4, 12), (-6, 6), and (4, 16).

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The simple way to do such questions is to make the given circle and plot the points on the graph. As shown below.

The other way to do the question is to find the distance between the centre point of the circle and the point if it is equal to the radius of the circle, the point will lie on the circle, otherwise not.

The formula to find the distance between the two points on a graph is,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Hence, the point that lies on the circle is (-4, 12), (-6, 6), and (4, 16).

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