∠ABC is a 40∘ angle. Point A is at (7, 1) Point B is at (3, 2) Point C is at (8, -1) If ∠ABC is rotated 180∘ about the origin, what are the new points on the image and what is the new angle degree measurement?

Over this 10-minute interval, the car's average acceleration is

[tex]\dfrac{30\,\mathrm{mph}-20\,\mathrm{mph}}{10\,\mathrm{min}}=\dfrac{10\,\mathrm{mph}}{\frac16\,\mathrm h}=60\dfrac{\rm mi}{\mathrm h^2}[/tex]

The MVT says that at some point during this 10-minute interval, the car must have had an acceleration of 60 mi/h^2.

The acceleration in this lapse of time is 60 miles per hour squared.

To get this, we need to use the formula:

A = (difference in velocity)/time

The change in velocity is:

30mph - 20mph = 10mph

The time is from 2:00pm to 2:10 pm, so 10 minutes, but we need this in hours so:

10 min = (10/60) hours = 1/6 hours

Then the acceleration is given by:

A = 10mph/(1/6) = 60 m/h²

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1/3

7/12

9/12

1/4

and more

The fraction that is not equivalent to [tex]\( \frac{8}{12} \) is \( \frac{6}{10} \), option D, as it simplifies to \( \frac{3}{5} \), while the others simplify to \( \frac{2}{3} \), which is equivalent to \( \frac{8}{12} \).[/tex]

To find the fraction that is not equivalent to [tex]\( \frac{8}{12} \), we need to simplify each option and compare it with \( \frac{8}{12} \).[/tex]

We simplify each option:

A) [tex]\( \frac{2}{3} \)[/tex]

B) [tex]\( \frac{24}{36} = \frac{2}{3} \) (Equivalent to \( \frac{8}{12} \))[/tex]

C) [tex]\( \frac{4}{6} = \frac{2}{3} \) (Equivalent to \( \frac{8}{12} \))[/tex]

D)[tex]\( \frac{6}{10} = \frac{3}{5} \)[/tex]

So, the fraction that is not equivalent to [tex]\( \frac{8}{12} \) is \( \frac{6}{10} \),[/tex]option D.

Answer:

1,080 Pennies

Step-by-step explanation:

This question is fairly simple, you just have to simplify it. You are starting at already half-full, so you can keep that 1/2 in mind. Then, she adds 360 pennies to get 5/6. If you convert 1/2 into 3/6, you can see that 360 pennies fills 2/6 of the piggy bank. So now you can solve two different ways. The first, you can take 360 and multiply it by 3 to get the amount that can fit in the piggy bank, because 2 * 3 = 6 and that would make it 6/6, or 1. The other way would be to divide 360 by 2 to get 1/6 of the piggy bank, or 180. Then you can multiply 180 by 6 to get the entire amount.

Hope this helped ^-^

By setting up a proportion, we can find that the total capacity of Amy's penny bank is 1440 pennies.

The subject of this problem is mathematics. We know that after adding 360 pennies, Amy's penny bank was 5/6 full. Before she added those pennies, it was 1/2 full. So, those 360 pennies represent the difference between 5/6 and 1/2 of the capacity of the penny bank.

To find the total capacity of the penny bank, we can set up a proportion as follows:

360 pennies / (5/6 - 1/2) = x pennies / 1

Therefore, x = 360 * (1 / (5/6 - 1/2))

By simplifying this, we find that the total capacity of Amy's penny bank is 1440 pennies.

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Answer:

  4.  maximum: 22; minimum: 1

  5.  maximum: 24; minimum: -6.25

  6.  maximum: 49.7; minimum: 39.625

Step-by-step explanation:

I find a graphing calculator to be "appropriate technology" for answering questions of this sort. For the first and last questions, the extremes are the values of the function at the ends of the intervals specified.

For the second question, the parabola opens upward and the vertex is in the given interval, so the vertex is the minimum. The maximum is found at the end of the interval that is farthest from the vertex.

(x + 3) divided by 2

third option

Answer:

(x + 3) divided by 2

third optionStep-by-step explanation:

Answer:

  A.) 0.9cm, 1.2cm, 1.5cm

Step-by-step explanation:

The side ratios of the offered answers are ...

  A — 3:4:5 . . . . . . obviously a right triangle

  B — 3:5:5 . . . . . . isosceles, but not a right triangle

  C — 3:4:6 . . . . . . an obtuse triangle

  D — 3:2:5 . . . . . . not even a triangle (just a line segment)

_____

Comment on 3:4:5

This set of small integers appears often in problems involving right triangles. It is the smallest "Pythagorean triple" — a set of integers that satisfies the relationship of the Pythagorean theorem — and it is the only Pythagorean triple that is an arithmetic sequence (differences between the numbers are the same).

When you see a triangle with sides in these ratios, you know it is a right triangle. When you see a right triangle with two of the sides having a ratio of 3:4, 3:5, or 4:5 (where "5" is the hypotenuse), then you know the length of the remaining side.

Answer:

Step-by-step explanation:

The graph a.) is the best draw that represents a line with positive rate of change.

Best regards

Answer:

  25 in

Step-by-step explanation:

The diameter is shown to be 10/4 times the height, so the diameter of the smaller solid is ...

  (10/4)×(10 in) = (100/4) in = 25 in

Answer:

25 in.

Step-by-step explanation:

Answer:

60 m/h

Step-by-step explanation:

1. the basic formula is Time=Distance/Speed;

2. total time is time1 (for 84 miles)+time2 (for 130 miles)=time (4 hours);

3. the time for the first 84 mi. is time1=84/S;

4. the time for the rest 130 mi. is time2=130/(S-10);

5. using all the data of items 2-4, it is possible to substitute into the basic formula and resolve an equation:

[tex]\frac{84}{s} +\frac{130}{s-10} =4; \ => \ 2s^2-127s+420=0;[/tex]

[tex]\left[\begin{array}{ccc}s=60\\s=3.5\end{array}[/tex]

note, that the value of speed has one condition: s>10. It means, the only value is true: 60 miles per hour.

Answer:

Step-by-step explanation:

If we take 1 candy bar and split it between 8 people, each person will get 1/8 of a candy bar. 1/8 for each of those 12 candy bars will give each person 12 × 1/8 = 12/8, or 3/2 = 1 1/2 bars.

You are trying to share 12 candy bars between 8 friends.

Therefore,

12 candy bars ÷ 8 friends = 1.5 bars per person

12 ÷ 8 = 1.5 candy bars

I already did this question once so I'm just gonna include the answer

Answer: The value of KP = 12 units.

Step-by-step explanation:

Since we have given that

KE is a tangent with KE = 18

KPL is a secant with PL = 15

Let KP = x

Since we know that The product of segments of secants is square of the tangents.

Mathematically, it is expressed as ,

[tex]KE^2=KP.KL\\\\18^2=x(x+15)\\\\324=x^2+15x\\\\x^2+15x-324=0\\\\x^2+27x-12x-324=0\\\\x(x+27)-12(x+27)=0\\\\(x+27)(x-12)=0\\\\x=-27,x=12[/tex]

Measure of secant can't be negative.

So, KP = 12

Answer:

This is the simplified number for Pi, which is 3.14

Step-by-step explanation:

Answer:

• 2/3|2 -x| = 1/15

• |2 -x| = 1/10

• 1/5 +|4/3 -2/3x| = 4/15

Step-by-step explanation:

Starting with the given equation, subtract 1/5 = 3/15.

(2/3)|2 -x| = 4/15 - 3/15

(2/3)|2 -x| = 1/15 . . . . . . . . matches the first choice

Now, multiply by 3/2.

|2 -x| = 3/30

|2 -x| = 1/10 . . . . . . . . . . . . matches the third choice

___

If you decide to distribute the coefficient 2/3 instead, you have

1/5 + |2·2/3 -x·2/3| = 4/15

1/5 + |4/3 -2/3x| = 4/15 . . . . matches the selected choice

Answer:

The answer is A and C

Step-by-step explanation:

I just did the work

Good luck

Answer:  [tex]\bold{\dfrac{7w^2y^3}{32}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3w^9y^4}{8w^5}\cdot \dfrac{7y^4}{12w^2y^5}\\\\\\\text{Multiply across. ADD exponents when like bases are being multiplied}\\=\dfrac{21w^9y^8}{96w^7y^5}\\\\\\\text{Cancel out common factors. SUBTRACT exponents when dividing}\\=\dfrac{7w^2y^3}{32}[/tex]

See the image for solution

Answer:

Parallel line = Same m value (same slope)

Perpendicular line = The reciprocal m value (x/y = y/x).

Going through a point = First, find the slope of the line (perpendicular or parallel), then plug in the point (4,10) to find the y intercept.

Answer:

See below.

Step-by-step explanation:

Parallel

y = -1/2x + b

The slope is the same for any set of parallel lines. The point determines the y intercept.

x = 4

y = 10

Solve for b

10 = -1/2(4) + b

10 = - 2 + b

b = 10 + 2

b = 12

Equation: y = - 1/2 x + 12

Perpendicular

Here you actually have to solve for the slope.

Equation

m1 * m2 = - 1

m1 is the given slope of - 1/2 which I will chance to -0.5. Substitute for m1.

-0.5 * m2 = - 1                          Divide by -0.5

m2 = -1/-0.5

m2 = 2

Now what you have is

y = 2x + b

x = 4

y = 10

10 = 2*4 + b

10 = 8 + b

10 - 8 = b

b = 2

Equation: y = 2x + 2

Answer:

200 Boxes of Popcorn

Step-by-step explanation:

To find the total amount of popcorn boxes there are in the store, we need to consider the amount of boxes displayed at the front of the store.

We have:

60 boxes = Cinnamon + Cheese

60 boxes = 15% + 15%

60 = 30% of the total boxes in the store.

Now we know that 60 boxes is equivalent to 30%, we can use this to find the number of kettle corn.

60 + 60 = 120

30% + 30% = 60%

This means that we have 120 Kettle Korn boxes.

We can also use the amount of 60 boxes to find what 10% will be equivalent to.

60 boxes = 30%

So if we divide the number of boxes by 3, we'll get the 10% of the total number of boxes.

60/3 = 30%/3

20 = 10%

So all in all we have:

120 Kettle Korn

60 Cinnamon + Cheese

20 Caramel

120 + 60 + 20 = 200

There are 200 popcorn boxes in the store.

The answer is D. 45%

The answer would be 45%

To solve this pretend that 370 is 100

Then put (x) as the value you are looking for

So 100%=370

(x)%=166.5

Then set it up like this:

100%. 370

=

x%. 166.5

Then divide or do cross multiplication and you find out that x is 45%

Hope this helps! :3

Answer:

The area is multiplied by 0.84 (decreased 16%)

Step-by-step explanation:

The length is multiplied by (1 +0.40) = 1.4.

The width is multiplied by (1 -0.40) = 0.6

So, the new area is ...

A = (L·1.4)·(W·0.6) = LW·0.84

The original area was the product of the original length and width, so was LW. This means the new area is 0.84 times the original area.

0.84 = 1 - 0.16

so, another way to describe the change is to say the area decreased 16%.

We want to see how some changes in the measures of a rectangle affect the area of the given rectangle.

We will see that the new area is 0.84 times the original area (meaning that the area decreases by 16%).

We will have.

First, we know that for a rectangle of length L and width W the area is given by:

A = L*W

Now, if we increase the length bt 40%, the new length will be:

L' = L +  (40%/100%)*L = L*1.4

And if the width is decreased by 40%, the new width will be:

W' = W - (40%/100%)*W = W*0.6

The new area is given by:

A' = L'*W' = (L*1.4)*(W*0.6) = (L*W)*(1.4*0.6) = 0.84*(L*W)

Where L*W is the area of the original rectangle, so we can write:

A' = 0.84*A

Meaning that the area decreased, the new area is 0.84 times the original area (we can actually see that the area decreased by 16%).

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Answer:

The base = 4 units and the height = 3 units

Step-by-step explanation:

* Lets remember the rule of the distance between 2 points

- The two points are (x1 , y1) and (x2 , y2)

∴ The distance = √[(x2 - x1)²+(y2 - y1)²]

* The vertices of the triangles are (-3 , 4) , (1 , 4) , (1 , 1)

- If two points have the same y-coordinate

∴ The line joining the to point is horizontal

∴ Its length = x2 - x1

- Because √[(x2 - x1)²+(y2 - y1)²] and y2 = y1

∴ d = √(x2 - x1)² ⇒ cancel power 2 with the radical sign

∴ d = x2 - x1

* Similar you can find the vertical distance

- If two points have the same x-coordinate

∴ The line joining the to point is vertical

- Its length = y2 - y1

∵ The points (-3 , 4) , (1 , 4) have same y-coordinate

∴ This side of the triangle is horizontal

∴ Its length = 1 - -3 = 4

∵ The points (1 , 4) , (1 , 1) have same x-coordinate

∴ This side of the triangle is vertical line

∴ Its length = 4 - 1 = 3

* The two sides of the triangle are ⊥

∴ One of them is the base of the triangle and the other is the height

* The base = 4 units and the height = 3 units

A kite is a quadrilateral.

So the correct answer is A.

Hope this helps,

Davinia.

Final answer:

A kite is a quadrilateral, which is a shape with four sides, but with unique properties that differentiate it from parallelograms, rectangles, and trapezoids.

Explanation:

A kite in geometry is a quadrilateral. A quadrilateral is a kind of shape with four sides, which might not be as commonly discussed in early education as shapes like squares and triangles. A kite is defined by two pairs of adjacent sides that are equal in length, with one pair longer than the other. Unlike a parallelogram, the sides of a kite do not always have to be parallel to each other. In addition, a kite does not necessarily have right angles as a rectangle does, nor does it have only one pair of parallel sides as a trapezoid does. Therefore, when characterizing a kite, the correct answer is A. quadrilateral.

Answer:

It depends on the max amount you can have.

Step-by-step explanation:

For example, if 100 points was the max you'd have 97.6%.

Hope this helps!

Answer:

  -2 < x < 4/3

Step-by-step explanation:

A graphing calculator can show you the solution. I like to recast the equation as a comparison to zero, since a graphing calculator often can display zeros of a function easily. Here that means ...

  |6x +2| -10 < 0

___

If you want to solve this by hand, you can "unfold" the absolute value to get ...

  -10 < 6x +2 < 10

  -12 < 6x < 8 . . . . . . subtract 2

  -12/6 < x < 8/6 . . . . divide by 6

  -2 < x < 4/3 . . . . . . simplify

This graphs on the number line as a solid line between open circles at -2 and 4/3. On the attached graph, the boundary values are shown as dotted blue lines, and the solution space is shown in blue.

Answer:

either of Step 3 or Step 4

Step-by-step explanation:

At Step 3, -1 is added to both sides of the equation. Technically, this is correct (not an error), but it does not lead to a solution to the equation (so, could be considered to be an error). Adding +1 to both sides of the equation would lead more directly to a solution.

__

At Step 4, x -1 -1 is simplified to x. This is an error, as the correct simplification is x-2, so the equation after this step should read x-2 = 5. If Step 3 had been executed by adding +1 to both sides of the equation, then the simplification here would be x=7.

_____

Answering "why" someone does something is always tricky. One can project one's own interpretation onto the actions of others, but one never really knows whether that is accurate or not.

The "why" in this case could go back to the motivation of the problem's author, which may be to see if the student can recognize that the opposite of -1 is +1, or that the sum -1-1 is not zero.

___

My guess is that Step 3 is considered to be the erroneous step, and that choosing Step 4 will get you into a losing argument with your grader.

Answer:

8. (10/7)x^(0.7) +C

10. (x^-2)/2 -x^-1 +C

Step-by-step explanation:

The integral of x^a is x^(a+1)/(a+1).

8. a = -.3, so the integral is x^0.7/0.7

___

10. This is the difference of two integrals, one with a=-2; the other with a=-3, so ...

the integral is (x^-1)/(-1) -(x^-2)/(-2)

_____

Of course, an arbitrary constant is added to each result to complete the indefinite integral.

Answer:

2.  22/35

3a. 0.24

3b. 0.84

3c. 0.54

3d. 0.73

Step-by-step explanation:

2. There are 22 songs on albums 1 and 2, and 35 total songs. Thus the probability of randomly choosing a song from albums 1 or 2 is 22/35.

__

3. The sum of the probabilities of all possible mutually exclusive events is 1, so ...

a. p(blue) = 1 - p(any other color) = 1 - 0.76 = 0.24

b. p(not green) = 1 - p(green) = 1 - 0.16 = 0.84

c. p(green+yellow+blue) = p(green) +p(yellow) +p(blue) = 0.16 +0.14 +0.24 = 0.54

d. p(not(yellow+red)) = 1 - p(yellow+red) = 1 - 0.27 = 0.73

Answer:

  [550, 1250] miles ([minimum, maximum] miles)

  700 miles (difference between minimum and maximum)

Step-by-step explanation:

"Range" has different meanings in different contexts with respect to a list of numbers and/or ordered pairs.

For a function, characterized by ordered pairs, the range is often specified by the interval between the minimum and the maximum. That is, the range of the function ...

  (Jan, 914), (Feb, 740), (Mar, 815), (Apr, 550), (May, 815), (Jun, 1250), (Jul, 740)

can be specified either as the list of dependent variable values:

  {550, 740, 815, 914, 1250}

or as the interval between the minimum and the maximum:

  [550, 1250]

___

If you're plotting these values or creating a histogram, the "range" you're interested in is often the difference between the minimum and maximum:

  1250 -550 = 700

The widths of bins of a histogram are defined by dividing this range into a suitable number of smaller intervals.

Answer:

Equation:  (1 2/3)(2 1/3) = x

Answer:  3 8/9 cups

Step-by-step explanation:

x represents the amount of flour she will need in cups.

To solve, convert the mixed numbers to improper fractions and multiply...

1 2/3 becomes 5/3

2 1/3 becomes 7/3

Now we have

(5/3)(7/3) = x

  35/9 = x

35/9 is 3 8/9 as a mixed number

An equation that represents the number of cups of flour Genise will need​ is (1 2/3 ) × (2 1/3) which gives the value 3 8/9 cups.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Number of cups of flour needed to make 1 batch of cookies = 1 2/3 cups

                                                                                                    = 5/3 cups

We have to calculate the number of cups of flour for 2 1/3 batches.

Number of cups of flour needed to make 2 1/3 batches of cookies is,

(5/3) × (2 1/3)

= (5/3) × (7/3)

= (35/9)

= 3 8/9

Hence the number of cups of flour needed is 3 8/9 cups.

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Answer:

Fiona has 6 quarters

Step-by-step explanation:

If Fiona were to have 1 quarter and 1+6 dimes she would have 8 coins

If she were to have 2 quarters and 2+6 dimes she would have 10 coins

If she were to have 3 quarters and 3+6 dimes she would have 12 coins

If she were to have 4 quarters and 4+6 dimes she would have 14 coins

If she were to have 5 quarters and 5+6 dimes she would have 16 coins

If she were to have 6 quarters and 6+6 dimes she would have 18 coins

Therefore, she has to have 6 quarters in order to have 6 more dimes and a total of 18 coins

I hope this helps, and I'm sorry it took so long for me to write this out