Jane ran 8 fewer miles this week than last week. This week, she ran 10 times
as far as John. John ran 3 miles. How many miles did Jane run last week?

Step-by-step explanation:

I know that

[tex] \cot {}^{2} (x) + 1 = \csc {}^{2} (x) [/tex]

So These the steps I need to do:

First Apply Reciprocal Identies to find Cot x.

[tex] \frac{1}{ \tan(x) } = \cot(x) [/tex]

So cot x is

[tex] \frac{24}{7} [/tex]

Now, I can squared that result and add 1 to get csc^2(x).

[tex] \frac{576}{49} + 1 = \frac{576}{49} + \frac{49}{49} = \frac{625}{49} [/tex]

Now, I take the principal square root since csc is positve when theta is in the 1st quadrant.

[tex] \frac{ \sqrt{625} }{ \sqrt{49} } = \frac{25}{7} [/tex]

So

[tex] \csc(x) = \frac{25}{7} [/tex]

[tex]cosec{\theta=\frac{25}{7}is\ the\ answer.}[/tex]

[tex]If\ tan\ \theta=\frac{7}{24},0\ degrees < \theta < 90\ degrees[/tex]

[tex]sec\ \theta=\sqrt{1+\tan^2\theta}=\sqrt{1+\frac{49}{576}}=\sqrt{\frac{625}{576}}=\frac{25}{24}[/tex]

[tex]cos\ \theta=\frac{1}{sec\ \theta}=\frac{24}{25}[/tex]

[tex]sin\ \theta=\sqrt{1-\cos^2\theta}=\sqrt{1-(\frac{24}{25})^2}=\sqrt{\frac{49}{625}}=\frac{7}{25}[/tex]

[tex]cosec\ \theta=\frac{1}{sin\ \theta}=\frac{25}{7}[/tex]

[tex]Hence,\ cosec\ \theta=\frac{25}{7}is\ the\ answer.[/tex]

I hope this helps you

:)

Answer:

31/2

Step-by-step explanation:

Answer:

60 1/8

Step-by-step explanation:

6 1/2 * 9 1/4 =

= 13/2 * 37/4

= (13 * 37)/(2 * 4)

= 481/8

= 60 1/8

Answer:

1. a = 0 and 5

2. no solutions

Step-by-step explanation:

For absolute value, it's the distance from that number on the number line to 0, so it has to be positive. We define absolute value as when |a| = b, a = b and a = -b.

1. |a - 5| = 5 - a

a - 5 = 5 - a

2a = 10

a = 5

AND

a - 5 = -(5 - a)

a - 5 = -5 + a

-5 = -5

a = 0 (a could work as 0 in this scenario)

Thus our solutions are a = 0 and 5.

2. |a| = -1

Now we have to catch ourselves here. Since absolute value is always positive, nothing works. There is no negative distance to 0 (at least in real numbers).  Hence, we can say that there are no solutions.

Answer:

I am not sure your is correct

Answer:

Answer:

[tex]z = - 3[/tex]

[tex]y - z = 1[/tex]

[tex]y + ( - 3) = 1[/tex]

[tex]y = 4[/tex]

[tex]x + 4 +3 = 17[/tex]

[tex]x = 10[/tex]

Answer: 34

Step-by-step explanation:

Answer:

YZ=34

Step-by-step explanation:

[tex]xy(xz)=xw(xv)\\\\6(2x+12+6)=10(x+3+10)\\\\6(2x+18)=10(x+13)\\\\12x+708=10x+130\\\\12x-10x=130-108\\\\\cfrac{2x}{2} =\cfrac{22}{2} \\\\x=11[/tex]

[tex]yz=2x+12\\\\2(11)+12\\\\22+12\\\\yz=34[/tex]

~

Answer:

Step-by-step explanation:

if n is a positive integer then 4^n has last digit 4 or 6

we choose any number having 4 digits whose sum is divisible by 3 and last digit is 4 or 6.

1014,1026,1104 etc.

The distance the club head is from the pivot point is about 5.2 feet.

A circle is the locus of a point such that its distance from a fixed point known as the center is always constant.

Let r represent the radius of the circle, that is the distance the club head is from the pivot point. Hence:

Length of arc = angle in radians * radius

26 = 5r

r = 5.2 feet

The distance the club head is from the pivot point is about 5.2 feet.

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Answer:

(-3, 2)

Step-by-step explanation:

If we are dealing with vertical movement up/down, we manipulate the x-axis.

If we are dealing with horizontal movement left/right, we manipulate the y-axis.

We are trying to move the point right 4 units (horizontal movement) and down 4 units (vertical movement).

(1, -2) → (1 - 4, -2 + 4) → (-3, 2)

Answer:

(270+150)/(2020-2000)= 21 - average rate of change in the height per year

Answer:

I think to get the average rate you subtract 150 from 270 centimetres you'll get 120 centimetres then subtract 2000 from 2020 to get 20 now to get the rate divide 120cm by 20 and you will get six so the rate is 6 cm per year

Answer:

F=3-53-5=-12-t-2-54-

Step-by-step explanation:

Answer:

a. -6

b. -12

c. -30

Step-by-step explanation:

a. f(-1)                                b. f(0)                              c. f(3)

f(-1)=- 2|3× -1 +5| -2          f(0)= -2|3× 0 +5| -2          f(3)= -2|3× 3 +5| -2

f= -2|-3+5|-2                     f= -2|0+5| -2                    f= -2|9 +5| -2

f= -2|2|-2                          f= -2|5| -2                         f= -2|14| -2          

f= -4-2                              f= -10-2                             f= -28 -2

f= -6                                 f= -12                                 f= -30

If radius, r = 5in., then we can compute that the area of the circle = 78.55in² or approximately 79in².

Using the formula, Area of Circle = πr²

It is given in the question, r = 5in and as we know that the value of π = 3.142 

Now, putting the values from above in the formula of area of circle, we will get:

A = π × 5² = 3.142 × 25 = 78.55

= 79in² (to the nearest whole number).

The space a circle takes up in a two-dimensional plane is known as its area. Alternately, the area of a circle is the area contained within the circumference or boundary of the circle. The sum of the square units inside that circle is another name for it.

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Answer:

(0, 4)

Step-by-step explanation:

The y-intercept is defined as the point where the line intersects the y-axis. All we need to do is find where the line intersects the y-axis.

(0, 4) is the answer.

Answer:

[tex]15cm^2[/tex]

Step-by-step explanation:

Split the shape

Find the area of smaller shapes

Add two smaller shapes' area together

Answer:

Axis of symmetry:

1. x=2

2. x=3/4

3. x=-1

Vertex:

1. (2,-1)

2. (3/4, -31/8)

3. (-1,-7)

Vertex min/max:

1. Minimum

2. Maximum

3. Minimum

Answer: 10

Step-by-step explanation:

Since -2 is in between -5 and 0, we will use the part of the function that says f(x)=x^2 + 3x.

Substituting x=-2, we get (-2)^2 -3(-2)=4+6=10

Answer:

0.052

Step-by-step explanation:

0.52 divided by 10

Answer:

Simple. It’s 0.052.

Step-by-step explanation:

0.052•10=.52

Answer:

insane, fanatical, deranged, etc.

Step-by-step explanation:

Answer:

4/16 cm

Step-by-step explanation:

I just did the test and i got it right yourwelcome bye

The % decrease in the number of scheduled passenger flights from February of 1999 to last February was 12.97%.

Given that last February there were 617,624 scheduled passenger flights in a certain country, and in February of 1999 there were 709,639, to determine the % decrease in the number of scheduled passenger flights from February of 1999 to last February, the following calculation must be made:

Therefore, the % decrease in the number of scheduled passenger flights from February of 1999 to last February was 12.97%.

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Answer:

all x are the solution

Step-by-step explanation:

x - 4×3 - 4×(-2x) = 3×3x + 3×4

x - 12 + 8x = 9x +12

9x + 12 = 9x + 12

9x = 9x

(0 = 0)

no matter which number we take for x the equation will always be correct

ex. x = 3 : left : 9×3 = 27

right : 9×3 = 27

Answer:

24:40

Step-by-step explanation:

To find the radio for red dye to total drops of dye, just add the red and blue dye.

The ratio of drops of red dye to total drops of dye is 3:2.

When a number is divisible by another number, then it can be written in the form of a:b, this is called Ratio.

Priya is making frosting.

The number of drops of blue dye is 16.

The number of drops of red dye is 24.

Ratio ( Red dye : Blue dye) = 24 : 16

Ratio ( Red dye : Blue dye) = 3:2

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Answer:

Yards

Step-by-step explanation: Yards make the most since because the average car is about 3 to 5 yards.

Answer:

The nth term of an arithmetic sequence is given by. an = a + (n – 1)

Answer:

The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.

Step-by-step explanation:

Answer:

Anna owes $3600 to the bank

Step-by-step explanation:

12/100 * 6000 = 720 * 5 years

= $3600

Hence Anna owes $3600 to the bank