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The system of equations has

Answer:

6

Step-by-step explanation:

Answer:

Step-by-step explanation:

a = 0

So that AOB makes a right triangle with sides 3-4-5

Answer:

a = 8

Step-by-step explanation:

Calculate AB using the distance formula and equate to 5

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (0, 4 ) and (x₂, y₂ ) = B (3, a )

d = [tex]\sqrt{(3-0)^2+(a-4)^2}[/tex]

  = [tex]\sqrt{3^2+(a-4)^2}[/tex]

  = [tex]\sqrt{9+(a-4)^2}[/tex] , then

[tex]\sqrt{9+(a-4)^2}[/tex] = 5 ( square both sides )

9 + (a - 4)² = 5² = 25 ( subtract 9 from both sides )

(a - 4)² = 16 ( take square root of both sides )

a - 4 = 4 ( add 4 to both sides )

a = 8

Answer:

Because square root is essentially the same thing as the power to a half

sqrt(x) is the same as (x)^1/2

Answer:  [tex]3 \times 10^{13}[/tex]

Explanation:

Highlight the first digit on the very left (2). The 7 right next to it means we'll round that 2 up to a 3. Every other digit becomes a zero.

The number 27,895,168,401,112 rounds to 30,000,000,000,000 which is the number 30 trillion.

It converts to the scientific notation [tex]3 \times 10^{13}[/tex] because we basically start with 3.0 and move the decimal point 13 spots to the right to arrive at 30 trillion as shown above.

Answer:

Step-by-step explanation:

x = 3y

x + y = 180°

3y + y = 180° ⇒ y = 45° = a

x = 3( 45° ) ⇒ x = 135° = b

The sizes of angles represented by a and b​ are 45 and 135 degrees.

An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.

The point of their joint is called vertex of that angle.

Those two line segments forming it are called arms of that angle.

The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on.

We are given that

x = 3y

Since we know that the linear pair is

x + y = 180°

Therefore, 3y + y = 180°

y = 45° = a

x = 3( 45° )

x = 135° = b

Learn more about angles here:

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Answer:

The difference between the maximum and the minimum temperature on that day is [tex]18^0C[/tex]

Step-by-step explanation:

The maximum temperature of an island was recorded [tex]15.5^0C[/tex]

The minimum temperature was recorded [tex]-2.5^0C[/tex]

Difference in temperature

[tex]=15.5--2.5\\\\=18^0C[/tex]

Answer:

the difference between 15.5 and -2.5 is 18

Step-by-step explanation:

14. Slope (m) of PQ = -4

Slope (m) of RS = 1/4

The lines are perpendicular.

15. mPQ = -3

mRS = 3

They are neither perpendicular nor parallel lines.

16. mPQ = 0

mRS = 0

The lines are parallel.

17. x = -6

18. x = -2

If two lines have the same slope (m), then both lines are parallel to one another. On the other hand, if the slopes of two lines are negative reciprocals to each other, then both lines are regarded as perpendicular lines because the product of their slopes is equal to -1.

Slope (m) = change in y / change in x

14. Slope (m) of PQ = (-3 - 17) / (1 -(-4))

Slope (m) of PQ = -20/5 = -4

Slope (m) of RS = (4 - 3) / (-5 -(-9))

Slope (m) of RS = 1/4

(1/4)(-4) = -1, therefore, the lines are perpendicular.

15. Slope (m) of PQ = (-1 - 14) / (2 -(-3))

Slope (m) of PQ = -15/5 = -3

Slope (m) of RS = (-10 - 8) / (-2 - 4)

Slope (m) of RS = -18/-6 = 3

They are neither perpendicular nor parallel lines.

16. Slope (m) of PQ = (-1 - (-1)) / (-3 - 2)

Slope (m) of PQ = -0/-5 = 0

Slope (m) of RS = (9 - 9) / (-7 -(-11))

Slope (m) of RS = 0/4 = 0

The lines are parallel.

17. If CD║EF, their slope will be equal. Therefore:

Slope of CD = slope of EF

(-4 - 16)/(2 - x) = (4 - 14)/(-2 -(-6))

-20/(2 - x) = -10/4

-20/(2 - x) = -5/2

Cross multiply

-20(2) = -5(2 - x)

-40 = -10 + 5x

-40 + 10 = 5x

-30 = 5x

-30/5 = x

-6 = x

x = -6

18. Slope of JK = slope of l

(-5 -(-8))/(-1 - x) = 6/2

3/(-1 - x) = 3

3(-1 - x) = 3

-3 - 3x = 3

-3x = 3 + 3

-3x = 6

-3x/-3 = 6/-3

x = -2

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Step-by-step explanation:

remember the priorities of the different mathematical operations

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

so,

14 + 14/7 = 14 + 2 = 16

Hey there!

14 + 14 ÷ 7

14 ÷ 7 = 2

= 14 + 2

= 16

Therefore, your answer is: 16

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

Let the first term is a and common difference is d.

The nth term is:

We have:

The difference of these terms is:

Then the first term is:

The nth term equation is:

If the nth term is 22, find n:

Answer:

AAS

Step-by-step explanation:

Answer:

AAS

Step-by-step explanation:

Answer:

[tex](5z + 5) \: + \: (7z + 4)[/tex]

[tex]5z + 5 - 7z - 4[/tex]

[tex]5z - 7z + 5 - 4[/tex]

[tex]2z + 1[/tex]

Answer:

x=-2

Step-by-step explanation:

7x - 4 = -18

+ 4. +4

7x = -14

÷7. ÷7

x=-2

Answer:

Step-by-step explanation:

7x - 4 = -18?

7x - 4 = -18

7x = -18 + 4

7x = -14

x = -14 : 7

x = -2

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

check

7 * (-2) - 4 = -18

-14 - 4 = -18

-18 = -18

the answer is good

Her monthly average would have decreased by $19.57 and it can be determined by using taking the average value of every month.

Katie works as a waitress and records her monthly tips in the table shown below.

June, July, August, September, October, November

$133.45, $235.31, $239.45, $258.87, $298.45, $115.67

If Katie decided not to work the month of November,

How would her five-month average compare to her six-month average for monthly tips?

Katie works as a waitress and records her monthly tips in the table below.

June, July, August, September, October, November

$133.45, $235.31, $239.45, $258.87, $298.45, $115.67

To find out how not working in November would affect the average of Katie's tips.

The average of her working June until October only.

[tex]\rm Average = \dfrac{133.45 + 235.31 +239.45 + 258.87 + 298.45}{5}\\\\Average =\dfrac{ 1165.53 }{ 5}\\\\Average = 233.10[/tex]

Then, The average is with the month of November is,

[tex]\rm Average = \dfrac{133.45 + 235.31 +239.45 + 258.87 + 298.45 + 115.67}{6}\\\\Average =\dfrac{ 1281.2 }{ 6}\\\\Average = 213.53[/tex]

Therefore,

On comparing the average of her five-month average to her six-month average for monthly tips is,

[tex]233.10 - 213.53 = 19.57[/tex]

The average will decrease because 213.53 is less than 233.10.

Therefore, Her average will decrease by $19.57.

Hence, Her monthly average would have decreased by $19.57.

For more details about the Average value refer to the link given below.

https://brainly.com/question/8916264

Answer:

b

Step-by-step explanation:

Answer:

answer is x=15

AM=18

AB=4

1=2

2=10

3=20

The number of pennies is an illustration of pattern and sequence.

The number of pennies in the nth square is [tex]2^{n-1[/tex]

From the complete question, we have the following parameters

[tex]f(1) =1[/tex]

[tex]f(2) =2[/tex]

[tex]f(3) =4[/tex]

[tex]f(4) =8[/tex]

Rewrite the functions as follows:

[tex]f(1) = 2^0[/tex]

[tex]f(2) = 2^1[/tex]

[tex]f(3) = 2^2[/tex]

[tex]f(4) = 2^3[/tex]

Express 3 as 4 - 1

[tex]f(4) = 2^{4-1[/tex]

Replace 4 with n

[tex]f(n) = 2^{n-1[/tex]

Hence, the number of pennies in the nth square is [tex]2^{n-1[/tex]

Read more about pattern and sequence at:

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The first one (when simplify) is

5.6>8.91

Which is not true if you plot it on a number line

The second one (when simplify) is

5.6<-8.91

which is not true because it is the same thing as number 1

The third one (when simplify) is

-5.6>8.91

which is obviously not true since negatives are way smaller than positives

So that leaves us the last one

Thefore the answer is OD.

I hope this helped!!

Answer:

Step-by-step explanation:

You can use a fill in the blank formula called "point-slope" formula because you were given a point and the slope. But there's an even easier way because they gave you a special point. The point (0, -2) is on the y-axis. So it actually IS the y-intercept. So just in this case, you can use the slope-intercept formula as a fill-in-the-blank formula bc you were actually given the slope (we always use m for slope) and the y-intercept.

This is y = mx + b... fill in the given slope for the m, fill in the y-intercept for the b, then you're done!

y = 2x -2

Answer:

I don't understand the question. Write it again & briefly.

Answer:

$113.94

18.99 multiplied by 6 is 113.94

Answer: D) 0.78

Step-by-step explanation:

Add all the given probabilities to find the answer:

45/100 + 18/100 + 15/100 = 78/100 = 78% or 0.78

Explanation:

Let's say this school has 1000 seniors.

25% of this count is 0.25*1000 = 250 to indicate there are 250 seniors with blue eyes. Of this smaller count, 60% of them are girls with blue eyes. So there are 0.60*250 = 150 female seniors with blue eyes.

Divide that last number over the original value: 150/1000 = 0.15 = 15%

The probability that the senior selected randomly is a blue-eyed female is 15%.

It is given that 25% of the seniors class has blue eyes of the blue student 60% are females.

Probability refers to the occurrence of random events. Basically, it is the possibility to predict how likely events are to happen.

Probability of event = Number of favorable outcomes / Total number of outcomes.

Let's consider this school has 1000 seniors.

25% of this count

0.25 × 1000 = 250

Which shows that there are 250 seniors with blue eyes.

Similarly, 60% of them are girls with blue eyes.

So, there are 0.60 × 250 = 150

there are 150 female seniors with blue eyes.

Here, the probability that seniors selected randomly is a blue-eyed female

150/1000 = 0.15

                = 15%

Therefore, the probability that the senior selected randomly is a blue-eyed female is 15%.

Learn more about the probability here;

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Answer:

Step-by-step explanation:

50/100 = 1/2 or 0.5

25/100 = 1/4 or 0.25

Answer:

Original Price = $23

Step-by-step explanation:

$5.75 is the price after a discount of 75%

Let the original price be x and x is 100% of the price

5.75 = 100%x - 75%x

5.75 = 25%x

The new price is 25% of the original because you are subtracting 75%

25% is also written as 0.25

5.75 = 0.25x

x = 5.75/0.25

x = 23

The original price is 23

-Chetan K

Answer: is not congruent

To be congruent, it has to be same size and shape. It can face in any directions. Both the shapes have to be equal in all side lengths and equal angles.

Looking at the triangle you can understand that it is not congruent as the triangles have a size difference of being big and small. But if you still desire detailed explanation then here:

There is four rules for a triangle to be congruent. If one of these rule matches then you can say the triangle is congruent.

1. The three sides are equal

2. Two angles are the same and a corresponding side is the same

3. Two sides are equal and the angle between the two sides is equal

4. Two angles are equal and the side between them is equal

There are no angles, so find if all the three sides are equal. Even if one side is not equal, you can say it is not congruent. So if you just measure any side length of the smaller and big triangle, the length is not equal. None of the side lengths in either of the triangle is equal.

loss%=loss/CP×100%

=Rs.360/Rs.900×100%

=Rs. 360/9

loss% =40% ans