Worth 60 points

Consider the following system of equations:
y = -x + 2
y = 3x + 1
Which description best describes the solution to the system of equations?
Line y = -x + 2 intersects line y = 3x + 1
Lines y = -x + 2 and y = 3x + 1 intersect the x-axis.
Lines y = -x + 2 and y = 3x + 1 intersect the Y-axis
Line y = -x + 2 intersects the origin

The cosine and the sine of the angle are the x and y coordinates of P, respectively

Assume that the coordinate of a point P is:

P = (x,y)

The trigonometry ratios are represented using:

(cos(t), sin(t))= (x,y)

Where t represents the angle formed between the initial and terminal arm.

Hence, the cosine and the sine of the angle are the x and y coordinates of P, respectively

Read more about Cartesian planes at:

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Answer:

X = 80

Step-by-step explanation:

A flat line is equal to 180 degrees, meaning that if you use linear, you can find out that if you subtract 100 from it, it becomes 80, which resembles the X.

Answer:

D

Step-by-step explanation:

Add 10:45 by 3

Answer:

n²+n+2

Step-by-step explanation:

1)Find the difference between the numbers.

Difference= +1,+2,+3,+4,+5

2)Find the second difference between the first differences.

Difference= +1 each time

2 differences=Quadratic sequence

3)Quadratic Sequence Equation= an²+bn+c

Find the values of a, b and c by using these terms:

a (bottom)

2a+b (middle)

a+b+c (top)

4)Substitute values into equation

a=1    b=1    c=2

n²+n+2

Answer:

2xy²/9

Step-by-step explanation:

Answer:

the fiftieth term is 76

Step-by-step explanation:

first subtract 15 by 6

15-6= 9

22+ 6 (9)

6 x 9= 54

22 + 54= 76

Answer: 76

Answer:

  (a)  Grade 6

Step-by-step explanation:

You want to know which grade (6 or 7) has the higher mean score, based on the given dot plots.

The scores of Grade 6 range from 70 to 100. Those of grade 7 range from 50 to 80.

Both distributions are approximately symmetrical, but have slightly more scores farther below the middle of the range than above. This means the mean in each case will be slightly below the middle of the range.

Even so, the mean of Grade 6 scores will be substantially above the mean of Grade 7 scores. Grade 6 has the higher mean score.

__

Additional comment

Assume the mean of Grade 6 is 85, the middle of the range of scores. Subtract the fewest number of dots (4) from each column, and we have 2 scores 15 units below that assumed mean, and 2 scores at 5 units above that assumed mean. The total of these is 2(-15) +2(+5) = -20. This tells us the actual mean of Grade 6 scores is -20/20 = -1 from the assumed mean of 85. The Grade 6 mean is 84. This is higher than any Grade 7 score, so Grade 6 must have the higher mean.

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Answer: 113.04 in^2

Step-by-step explanation:

area of a circle = pir^2

R = 12/2 = 6

A= 3.14 * 6^2

= 113.04

Answer:

3.25×10^15

Step-by-step explanation:

(8.69×10)^8_(9.6×10)^6. (3.25)×10^15_(7.83)×10^11=3.25×10^15

Answer:

73.3 cm

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

Dana takes a survey of 60 students out of 900 total to see how many will attend the dance.

Based on whatever result she gets out of the 60 students, she can take that number and multiply it by 15 to get a closer prediction to the actual result.

Answer:

yes , if you substitute X (1) in both the equations you will get y=9 and if you substitute y(9) in both the equations you will get X=1

Answer: 13

Step-by-step explanation:

[tex]$$Let $x$ be the number of \$5 bills \& let $y$ be the $10 \$$ bills.\\Then $x+y=27 \quad(\because$ total 27 bills $)$ - (1) \\ And $5 x+10 y=205 $\Rightarrow x+2 y=41 - (2)$$[/tex]

[tex]$$Now, (1) - (2) gives us.$$-y=14 \Rightarrow y=14$$Hence, $\quad x=13$\\So there were 13 \$5 bills.[/tex]

Answer:

blurry

Step-by-step explanation:

Answer:

y-intercept: 4
slope: 2

Step-by-step explanation:

Using an exponential function, it is found that it's annual growth rate is of 4%.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, the card appreciates exponentially in value by 50% over 10 years, hence:

A(10) = 1.5A(0).

Thus:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]1.5A(0) = A(0)(1 + r)^{10}[/tex]

[tex](1 + r)^{10} = 1.5[/tex]

[tex]\sqrt[10]{(1 + r)^{10}} = \sqrt[10]{1.5}[/tex]

1 + r = 1.04.

r = 0.04.

0.04 x 100% = 4%.

It's annual growth rate is of 4%.

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Answer:

24 boxes in 4 packs.

36 boxes in 6 packs.

60 boxes in 10 packs.

600 boxes in 100 packs.

Step-by-step explanation:

If 6 boxes are in 1 pack and 12 in 2, you can use a ratio, which is 1:6 meaning for every 1 pack are 6 boxes.

There are two ways you can get an answer

Multiplication:

For however many packs there are you multiply it by 6 boxes.

For 4 packs, you multiply it by 6 boxes. You would get 24 boxes.

For 6 packs, you multiply it by 6 boxes again getting 36 boxes.

Below is a table I made for an example.

P | B

1  | 6

2 | 12

3 | 18

4 | 24

5 | #

6 | 36

10 x 6 is 60

100 x 6 is 600.

whenever the multiplier starts with 1 and ends in 0, just add the number of zeros behind that number. Example: 7 x 1,000,000 = 7,000,000

Answer:

[tex]6^{6}[/tex]

Step-by-step explanation:

When the coefficient is the same (in this case it is 6), you can subtract the exponents when it's being divided.

So in this case, the exponents are 9 and 3. The 9 is being divided by the 3, So:

[tex]6^{9-3}[/tex]

[tex]6^{6}[/tex]

Jada's claim as a conjecture would be:
"All the segments in Δ ABC are parallel to the corresponding segments in Δ A'B'C' because both triangles are dilated from center P".

Whenever a shape is a dilation of another, we agree that the current shape and the dilated image's corresponding side lengths are in the same proportion and are all associated by the same scale factor, k.

Attached are the images showing the parallelity of the segments and their corresponding lines.

Hence, from the above, we can confirm that the above conjecture is true.

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Answer:

The name of this term is a quartile.

Answer:

No. Only 1 to 100, logically.

Let's make a scenario to solve this.

So let's say I have an all yellow, 9 quarter spinner board and I spin. It will always land on yellow, so it has a 9/9 or 100% chance of landing on yellow.

Now we must create another scenario.

For instance, I have one bottle, its starting direction was North, and I spin it. It will have a 1/4 chance of landing on North, East, South, or West because it will land in a random direction. For the 4 diagonal directions southeast, southwest, northeast, northwest it will be the same because there are only 4 directions, therefore giving the probability a 1 in 4 chance of landing on either one. :)

No. Only 1 to 100, logically.Let's make a scenario to solve this.So let's say I have an all yellow, 9 quarter spinner board and I spin. It will always land on yellow, so it has a 9/9 or 100% chance of landing on yellow.Now we must create another scenario.For instance, I have one bottle, its starting direction was North, and I spin it. It will have a 1/4 chance of landing on North, East, South, or West because it will land in a random direction. For the 4 diagonal directions southeast, southwest, northeast, northwest it will be the same because there are only 4 directions, therefore giving the probability a 1 in 4 chance of landing on either one. :)

Step-by-step explanation:

Answer:

Please check the question.  As written, the value is 1, which is not amoung the answers

Step-by-step explanation:

(-3 + 3) + (-2 + 3)

(-3 + 3) = 0

(-2 + 3) = 1

0 + 1 = 1

Answer:

$20.9

Step-by-step explanation:

First you find what 45% of the cost is:

0.45 x 38 = 17.1

Then, because this is a special/decrease in original price, you subtract:

38 - 17.1 = 20.9

$20.9

The area of the regular heptagon which has a radius of approximately 27.87 cm and the length of each side is 24.18 cm is 2125 cm².

Heptagon is the closed shape polygon which has 7 sides and 7 interior angles.

The area of the regular heptagon is found out using the following formula.

[tex]A=\dfrac{7a}{4}\cot \left(\dfrac{180}{7}\right)[/tex]

Here, (a) is the length of the heptagon.

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. Put the value of side in the above formula,

[tex]A=\dfrac{7\times24.18}{4}\cot \left(\dfrac{180}{7}\right)\\A\approx 2125\rm\; cm^2[/tex]

Hence, the area of the regular heptagon which has a radius of approximately 27.87 cm and the length of each side is 24.18 cm is 2125 cm².

Learn more about the area of a heptagon here;

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Answer: b

Step-by-step explanation:

Answer:

C: Speed of the waves in meters per second

Step-by-step explanation:

on edge

The frequency is inversely proportional to the time. Then the correct option is D.

The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.

The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.

The table is given below.

The constant variation of 340 represents this situation will be

The frequency is inversely proportional to the time. Then it represents time in seconds.

More about the wavelength link is given below.

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As here we are given with an equilateral triangle, whose side is 3 cm, and we need to find the height and area of the equilateral triangle. So, for this let's recall that, the area of any equilateral triangle with side a is given by ;

So, if we substitute a = 3, in our Formula, it will yield to

[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(3)^{2}}[/tex]

[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(9)}[/tex]

[tex]{:\implies \quad \boxed{\bf{Area_{(Equilateral\:\:Triangle)}=\dfrac{9\sqrt{3}}{4}\:\:cm^{2}}}}[/tex]

Now, as we know that, for any triangle we also have a formula that is ;

Now, Here as the triangle is equilateral, so it's base will just be same 3, and if we let height be H, so we will be having

[tex]{:\implies \quad \sf \dfrac{1}{2}\times 3\times H=\dfrac{9\sqrt{3}}{4}}[/tex]

[tex]{:\implies \quad \sf H=\dfrac{9\sqrt{3}}{4}\times \dfrac23}[/tex]

[tex]{:\implies \quad \boxed{\bf{Height=\dfrac{3\sqrt{3}}{2}\:\:cm}}}[/tex]

Answer:

OC

Step-by-step explanation:

I got it right on my test!