a. You ride your bike to a store, 4 mi away, to pick up things for dinner. When there is no wind, you ride at 10 mi/h. Today your trip to the store and back took 1 hour. What was the speed of the wind today?

The measure of ∠C in ΔABC is 35°.

Angle Sum Property of a triangle states that sum of all the interior angle of a triangle is 180°.

In the given Question

∠B=90° , ∠A=∠C+20°...(1)

By angle sum property of triangle for ΔABC

we get

∠A+∠B+∠C=180°

Substituting the values of ∠B and ∠C from equation (1) we get

∠C+20°+90°+∠C=180°

2∠C+110°=180°

2∠C=180°-110°

2∠C=70°

∠C=35°

Therefore  , the value of ∠C in ΔABC is 35°.

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Answer:

[tex]10 { }^{ - 5} [/tex]

Step-by-step explanation:

that is the answer above

4 cups of pasta are used per cup of sauce.

Given,

Greta uses 3 cups of pasta for every 3/4 cup of sauce.

We need to find how much pasta she uses per cup of sauce.

Example:

12 apples = 2 basket ____(1)

For 5 baskets:

We need to make 2 baskets = 5 baskets.

We can divide by 2 and multiply 5 on both sides on (1).

5/2 x 12 apples = 5/2 x 2 baskets

30 apples = 5 baskets.

We have,

3 cups of pasta = 3/4 cup of sauce

We need to make 3/4 cup of sauce as 1 cup of sauce.

Multiply 4/3 on both sides.

4/3 x 3 cups of pasta = 4/3 x 3/4 cup of sauce

4 cups of pasta = 1 cup of sauce

Thus 4 cups of pasta are used per cup of sauce.

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The simplied form of the given fraction will be -3 11/40.

There is a fraction, containing numerator(upper value) and denominator(lower value).  When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction. A proper fraction is also called fraction which is less than 1 an improper fraction is ≥ 1. A mixed fraction contains a sum of whole number and a proper fraction.

WE have been given an expression as;

−3/8+(−2 9/10)

Then first we will solve the mixed fraction;

−2 9/10 = -29/10

Now solve the fraction;

−3/8+-29/10

-131/40

In mixed number form:

-3 11/40

Hence, The simplied form of the given fraction will be -3 11/40.

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The sequence 1,1,2,3,5,8, ........... doesn't form an AP as they have the varying common difference.

In Arithmetic Progression, the difference between these two numerical orders is a fixed number (AP). Arithmetic Sequence is another name for it.

We'd come across a few specific keywords in AP that had been labeled as:

As shown below, the AP can also be explained in expressed in the form of common differences.

Now, the sequence given is; 1,1,2,3,5,8, ...........

The series contains of given 6 terms.

Let the initial term be 'a₁' = 1.

The second term be 'a₂' = 1.

The third term be 'a₃' = 2.

And, the fourth term is 'a₄' = 3.

For the sequence to form the AP, they must have the equal common difference. So,

d = a₃ - a₂

Substitute the values.

d₁ = 2 - 1

d₁ = 1

Thus, the calculated common difference is 1.

or d = a₅ - a₄  (Put the values)

d₂ = 5 - 3

d₂ = 2

Since, d₁ ≠ d₂

Thus, we can say that the given sequence is not forming an AP.

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A parabola with a vertical axis of symmetry is graphed at the end of the answer.

The equation of a quadratic function, of vertex (h,k), with a vertical axis of symmetry, is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

The most simple example of this is the parabola y = x², which is graphed at the end of the answer.

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The angles that has C as a vertex are:

13. ∠HVJ, ∠HVI, ∠JVI

14. ∠DVF, ∠DVE, ∠FVE

Angles that have letter V at their vertex can be named as an angle contain V as a point.

13. The angles that have V as vertex are:

∠HVJ

∠HVI

∠JVI

They all contain vertex V.

14. The angles that have V as vertex are:

∠DVF

∠DVE

∠FVE

They all contain vertex V.

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Answer:

112.5miles

Step-by-step explanation:

4hrs=8 half hours

And 1hr30min=3 half hours

If a car travels 300miles in 8 half hours with the mathematical expression of

300miles-8hh

Then for the 3 half hour we have

X-3hh

Comparing the two

300miles-8hh

Xmiles-3hh

By cross multiplying

8×X=3×300

8X=900

X=900/8

X=112.5miles

   The value of the volume of the other rectangular prism is V = 101.25 yd³.

  A numerical ratio is a constant value that relates a system of two or more variables, it allows us to know how their variations will be as the values change.

   First we must find the ratio between the heights of the rectangular prisms, for this we determine the height in the same unit:

 We express the following:

For volume

1/2³ = 1/8 = V/810

V = 101.25 yd³

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Answer:

Step-by-step explanation:

A rectangle as the only parallelogram that can be inscribed in a circle.

Every circle has an inscribed triangle with any three given angle measurements (summing to 180°, of course), and every triangle can be inscribed in any circle (which is called its circumscribed circle or circumcircle). Every triangle has an incircle, which is a circle that has been inscribed.

The only parallelogram that can be inscribed in a circle is a rectangle. Because every rectangle can be inscribed in a (unique circle), the important point is that the radius of the circle is R. (I think). One of the properties of a rectangle is that the diagonals bisect in the 'center,' which is also the center of the circumscribing circle.

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Answer:

is it -180?

I don't remember most of this stuff!

sorry if its wrong

Step-by-step explanation:

Answer:

650 Rupees

Step-by-step explanation:

Add all together

The slope is 1/2 and the y-intercept is 3/4 in the equation  - [ (1/2)x - y ] = 3/4.

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope

We know that the equation for slope(m) and y - intercept(c) of a line is given by :

y = mx + c

Here given the equation - [ (1/2)x - y ] = 3/4, lets simplify

⇒ - [ (1/2)x - y ] = 3/4

⇒ -(1/2)x + y  = 3/4

⇒ y =  (1/2)x + 3/4

Hence, the slope is 1/2 and the y-intercept is 3/4 in the equation  - [ (1/2)x - y ] = 3/4

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Answer:

C

Step-by-step explanation:

Just the spread of normally distributed data tells us nothing about the mean, mode or median, so answers A, B, and E are out of question.

The range is based on the difference between the highest and lowest elements. As there can be big outliers, we have no idea if D is true, although we expect distributions with bigger spread to generally exhibit bigger ranges.

We're left with answer C. Standard deviation is a measure of "how much the data can deviate from the mean". It's also one of the measures of spread. We expect data that's more spread out (higher spread) to have a higher standard deviation.

Answer:

From the Soldier's point of view, the American Civil War was not a continuous battle. Instead, it was long monotonous marches and long residency in camps punctuated by the terror and chaos of combat. When winter set in and the campaigning season came to a close, most Soldiers counted on a long, cold stay in a winter camp. The four log cabins at the center of the Army Heritage Trail represent the types of buildings which Soldiers in both the Union and the Confederate Armies spent the long dreary months of winter. The cabins are modeled after images from the USAHEC collection, including the Army of the Potomac's winter camp at Brandy Station and the Confederate camp at Centerville

  The given function  y = 2x - y - 13² , is a linear function

 where:

A function is the definition of a mathematical expression or equation that helps us to give a visual representation, through graphs to analyze the behavior of the same, a function is not real when it cuts the vertical axis at a same point of x.

 The function we have is particular because it has two variables, and these two are "x" and "y", but the y is the image so we do not consider it a variable.

y + y = 2x - 13

2y = 2x - 13

y = (2x - 13)/2

y = x - 13/2

y = x - 6.5

  Here we notice that we have a linear function

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Answer:

3 option

Step-by-step explanation:

To find the missing side (c) you need to do a^2 and b^2

Formula a^2 + a^2 = c^2

Given an arithmetic sequence -2,-13,-24, . . . , the recursive formula is: a(n) = a(n-1) -11 and the explicit formula is a(n) = 9 - 11n

Suppose we are given an arithmetic sequence:

  a(1), a(2), a(3), a(4), ....

Then, in an arithmetic sequence, the next term is obtained by adding a constant to the previous term. This constant is called a common difference.

Let d = common difference, then
a(2) = a(1) + d

a(3) = a(2) + d

and so on, until

a(n) = a(n-1) + d

This is a recursive formula. Here a(n) = nth term, and a(n-1) = (n-1)th term.

The sequence in the problem:

       -2,-13,-24, . .

Notice that:

-13 = -2 + (-11)

-24 = -13 + ( -11)

Hence, d = -11, and therefore, the recursive formula for the nth term is:

a(n) = a(n-1) -11

To find the nth term, we can also use the explicit formula:

a(n) = a(1) + (n-1).d

In the given sequence, a(1) = -2, and d = -11. Substitute these parameters:

a(n) = -2 + (n-1) . (-11)

      = -2 - 11n + 11

      = 9 - 11n

Thus, the explicit formula is a(n) = 9 - 11n.

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There are a couple ways we can get the equation of a line, depending on what we're given.

Most linear equations are organized in slope-intercept form:

[tex]y=mx+b[/tex]

The slope of a line can be calculated algebraically when we know two points that fall on the line:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The y-intercept is the value of y when the line crosses the y-axis, or when x = 0. When given a graph, you can sometimes read the y-intercept directly from the graph.

For instance, if the line passes through the point (0,5), then the y-intercept is 5.

You can also find the y-intercept algebraically if you know the slope and one point that falls on the line. You plug in that point as (x,y) and isolate b.

For most cases, you can use the following method to find the equation of a line:

Answer:

y = 2016 - 112x

Step-by-step explanation:

because he is paying 112 dollars each month for 18 months

y= 2016 -112x

for instance, he paid it for 6 months we would say

y = 2016 - 112(6)

y = 2016 - 672

y = 1334

so, y = 2016 - 112x

Answer:

7

Step-by-step explanation:

Hope this helps!!

Answer:

well done .... keep practicing....

Answer:

30 inches

Step-by-step explanation:

We know that the total length of the board is 90 inches and we know that the shorter piece is two times smaller than the other so we have two pieces divided into three sections 90 divided by three is 30 and since we realize that 30x2=60 and 60+30=90 it means the longer board is 60 inches and smaller one is 30 I hope this helps.

Answer: The answer is 25/3.

Step-by-step explanation: 8 1/3 = 8 x 3 + 1/3 = 24 + 1    =   25/3

                                                      --------           -----------                                                      

                                                         3                    3

Answer:

0, -7 or Slope is Undefined

Step-by-step explanation:

y2 - y1 / x2 - x1

(x2 - y2) (x1 - y1)