Find the distance between the two points in simplest radical form.
(-5,8) and (-3, 1)

Answer:

When point A with coordinates (0, -1) is reflected across the x-axis and mapped onto point A', the coordinates of A' will be (0, 1).

i.e A'(0, 1) is the image of point A after a reflection.

Hence, point A is reflected across the x-axis.

Step-by-step explanation:

When we reflect a point A across the x-axis, the value of 'y' gets negated, but the value of 'x' remains unchanged.

In other words, when point P with coordinates (x, y) is reflected across the x-axis and mapped onto point P', the coordinates of P' will be (x, -y).

Thus, the rule is:

P(x, y) → P'(x, -y)

Thus, when point A with coordinates (0, -1) is reflected across the x-axis and mapped onto point A', the coordinates of A' will be (0, 1).

i.e A'(0, 1) is the image of point A after a reflection.

Hence, point A is reflected across the x-axis.

[tex]a_n[/tex] is the n-th term in the sequence. So

• the first term (n = 1) is a₁ = 3 + 6•(1 - 1) = 3

• the second term (n = 2) is a₂ = 3 + 6•(2 - 1) = 9

• the third term (n = 3) is a₃ = 3 + 6•(3 - 1) = 15

• the fourth term (n = 4) is a₄ = 3 + 6•(4 - 1) = 21

• the fifth term (n = 5) is a₅ = 3 + 6•(5 - 1) = 27

The common difference between terms is what you get from subtracting consecutive terms in the sequence, or the number [tex]a_n-a_{n-1}[/tex]. Just by taking any two consecutive numbers from above, you have d = 6, since

9 - 3 = 6

15 - 9 = 6

and so on. More generally,

[tex]a_n-a_{n-1}=(3+6\cdot(n-1)) - (3+6\cdot(n-2))=6\cdot((n-1)-(n-2))=6[/tex]

if he started working in 45 min he can make time for it

movie started at 2.55 pm

As per the question

Movie start at -2.55 pm

time take to drive the theatre - 10 min

So the time taking is

2.55-0.10=2.45 pm

(Let's take 10 min =0.10)

Marcus start the yard work at -2.00 pm

So the time take - start time

2.45-2.00 pm

= 45 minutes

If Marcus take the yard work for 45 minutes he can make it on time for movie

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The possible number of person is 5.

Linear equation: an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution

Let,

The total amount of coffee= c

The total amount of milk = m

Total number of person = p

according to the question, c and m can't be .

Given,

Total amount of milk and coffee is 8 oz.

so,

[tex]\frac{c}{4} +\frac{m}{6} =8\\[/tex]

[tex]\frac{3c+2m}{12} =8[/tex]

So, this is linear equation.

3c+2m=8×12

[tex]$$ \\$3 \mathrm{c}+2 \mathrm{~m}=96$[/tex]

and

[tex]\eq[/tex][tex]c+m=8p[/tex]

2(c+m) = 8p×2

[tex]2c+2m=24p[/tex] ...(2)

By equation 1 and 2

[tex]3c+2m=96\\ 2m=96-3c\\ 2c+2m=16p\\ 2c+96-3c=16p\\96-c=16p\\96=16p+c\\[/tex]

16p and 96 both are divisible by 16

So, let c =16k

Now 3c+2m =96

3(16k) +2m= 96

48k =2m= 96

k can't be 0, otherwise c is 0 and k cannot be 2, otherwise m is 0. Therefore k must be 1,

[tex]48+2m=96\\2m=96-48\\2m=48\\m=\frac{48}{2} \\m=24[/tex]

BY putting m=24 in equation (1)

[tex]3c+2m=96\\3c+2(24)=96\\3c+48=96\\3c=96-48\\3c=48\\c=\frac{48}{3} \\c=16[/tex]

Therefor, the number of person is 5

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Answer:

D. y = 2x + 3

Step-by-step explanation:

[tex]y - 5 = 2(x - 1) \\ \\ y - 5 = 2x - 2 \\ \\ y = 2x - 2 + 5 \\ \\ y = 2x + 3[/tex]

Answer:

400

Step-by-step explanation:

EE

Sports its in the game

Answer:

1/2

Step-by-step explanation:

The formula for slope is (y2 - y1)/(x2-x1)

In this case, it is (2 - 1/2)/(4-1) which is 1.5 over 3. The slope is 1/2

Answer:

quadrant I

Step-by-step explanation:

after the rotation will be in quadrant ll, then reflected back into  quadrant I

Answer:

2x-3/y-5/37=0

Step-by-step explanation:

here, given equation of line is

y=3/2x+3

or,y(2x+3)=3

or,2x+3=3/y

or,2x-3/y+3=0...eqn(i)

equation of any line parallel to line (i) is

2x-3/y+k=0.. eqn(ii)

since, the line passes through (4,5)[replacing x=4 and y=5 in eqn(ii), we get]

2*4-3/5+k=0

or,8-3/5+k=0

or,40-3/5+k=0

or,k=-5/37

substituting the value of k=-5/37 in eqn(ii)

2x-3/y-5/37=0 is the required equation of line.

Answer:

1x-7.875 *is les than symbol* 0.375

Step-by-step explanation:

If the store sold 52 apples total and 20 of the  apples they sold were red, then the ratio of green apples sold to red apples sold is 8:5

Given,

The total number of apples sold in the morning= 52 apples

Number of red apples sold = 20 apples

Number of green apples sold = Total number of apples sold -  Number or red apples sold

Then,

Number of green apples sold = 52-20=32

The ratio of green apples sold to red apples sold = 32:20

We have find the simplest form

[tex]32:20= \frac{32}{20}[/tex]

Then, divide both numerator and denominator by 4

[tex]\frac{32}{20}=\frac{8}{5}[/tex]

The ratio = 8:5

Hence, if the store sold 52 apples total and 20 of the  apples they sold were red, then the ratio of green apples sold to red apples sold is 8:5

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Answer:

π 3.142?

Step-by-step explanation:

The 38th term of the Arithmetic Progression (355, 348, 341, ...) will be 36.

As per the question statement, we are provided with a series of numbers such as (355, 348, 341, ...)

We are required to calculate the 38th term of the above mentioned series.

To solve this question, first we are required to identify the nature of the series. We can see that, the consecutive terms have a common difference between them, i.e.,

[tex](355-348)=7\\(348-341)=7[/tex]

Therefore, the given series is an Arithmetic Progression (A.P.). Thus, we need to know the formula to calculate a certain nth term of an A.P. which goes as

[tex]T_{n}=[a+(n-1)d][/tex],

Where, "Tₙ" is the nth term required,

"a" is  the first term of the A.P.,

And, "d" is the common difference between every pair of consecutive terms of the A.P.

In this case, (a = 355), (n = 38) and {d = (-7)}. Then, using these values in the above mentioned formula, we get,

[tex]T_{38}=[355+(38-1)(-7)]\\ or, T_{38}=355+[37*(-7)]\\or,T_{38}=355+(-259)\\or, T_{38}=(355-259)\\or,T_{38}=96[/tex]

Hence, the 38th term of the Arithmetic Progression (355, 348, 341, ...) will be 36.

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Answer:

A)3(2x²-x+4)

Step-by-step explanation:

Answer: wow thats a lot of questions

Step-by-step explanation:

Answer:

I'll try to do my best man, with all of my warnings

Step-by-step explanation:

Answer:

690 miles

Step-by-step explanation:

Step one:

given data

For the first plane

the velocity is 300km/h

from noon (12:00) to 2pm is= 2 hours

the distance covered is expressed using the formula

velocity= distance/time

distance= velocity*time

distance= 300*2

distance= 600 miles

For the second plane

the velocity is 45km/h

from noon (12:00) to 2pm is= 2 hours

the distance covered is expressed using the formula

velocity= distance/time

distance= velocity*time

distance= 45*2

distance= 90 miles

Step two:

the total distance apart is the sum of the individual distances covered by the planes

= 600+90

=690 miles

Answer:

7 minutes per mile

Step-by-step explanation:

42/6=7

Answer:

the cosine of x is 60

Step-by-step explanation:

Answer:

y = (-13/11)x - 5/11

Step-by-step explanation:

Where's the list of equations from which you're to choose?

The line that connects points (-8 ,9) and (3, -4) has the following slope:

          9 - (-4)

m = ----------------- = -13/11

          -8 - 3

Then the new line with this slope is y = (-13/11)x + c

and because (-8, 9) satisfies this equation, 9 = (-13/11)(-8) + c, and we need to calculate c from this.                                 9 = 104/11 + c, or

                                                                        -c = 104/11 - 99/11, or - 5/11

Then the desired equation is y = (-13/11)x - 5/11

Multiply commission percentage by sales and add to the salary.

1200 x 0.045 = 54

325 + 54 = 379

Total made = $379

9514 1404 393

Answer:

  x = -5/2

Step-by-step explanation:

The equation ...

  [tex]\dfrac{1}{4}x=-\dfrac{5}{8}[/tex]

is a "one-step" linear equation. It has a variable term on one side of the equal sign and a constant term on the other sided of the equal sign. It is solved by multiplying both sides of the equation by the reciprocal of the coefficient of the variable. The variable coefficient is 1/4, so you multiply by the reciprocal of that, 4. Multiplying by this value causes the coefficient of the variable to become the multiplicative identity element, 1. Both sides of the equation are multiplied by this value in accordance with the multiplication property of equality. That way, the variable value is not changed. Then the equation becomes ...

  [tex]\dfrac{4}{4}x=-\dfrac{5\cdot4}{2\cdot4}\\\\x=-\dfrac{5}{2} \qquad\text{simplified}[/tex]

After simplifying the coefficient and the constant, the solution is found to be x = -5/2, or x = -2 1/2.

Your goal is to isolate the x. This is a multiplication problem, so use the inverse operation, which is division. Divide both sides of the equation by

1

4 by multiplying by the reciprocal, 4. (−

5

8)(4) is −

5

2. Use substitution to check the answer. x = −

5

2

Answer: five is < than 5.4

The amount of 10% alcohol solution in 50 ml alcohol solution is 30ml and amount 15% alcohol solution is 20ml.

In the given question

Bruce wants to make 50ml solution with 12 % concentration.

and he has 10% and 15% alcohol solution for that .

Let the amount of 10% alcohol solution = x

Let the amount of 15% alcohol solution = y

Given that x+y=50    ...(i)

According to the question the equation to find the 10% solution will be

0.10x + 0.15(50 – x) = 0.12(50)

Solving further we get

0.10x + 7.5 - 0.15x = 6

-0.05x + 7.5 = 6

-0.05x = 6 - 7.5

-0.05x = -1.5

x = -1.5/-0.05

x=30

So , 10% solution is 30 ml

Substituting the value of x=30 in equation (i)  we get

30 + y = 50

y = 20

So , 15% solution is 20 ml

Therefore , the amount of 10% alcohol solution in 50 ml solution is 30ml and amount 15% alcohol solution is 20ml.

The given question is incomplete , the complete question is

Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use.

How much of the 10% alcohol solution should Bruce use?

How much of the 15% alcohol solution should Bruce use?

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Answer: x ≈ 44

because ΔHIJ is a right triangle at J

=> sin x = 47/68

=> x ≈ 44°

Step-by-step explanation:

Answer:

0.14

Step-by-step explanation:

0.02 * 7 = 0.14

Answer:

-4/5

Step-by-step explanation:

Since theta is in quadrant II, we can visualize a triangle with two acute angles at (0,0) and (-x, 3). The distance between the two acute angles is 5 (hypotenuse), so using the Pythagorean Theorem, x = sqrt(5^2 - 3^2) = sqrt(16) = 4. Therefore the hypotenuse is 5, opposite is 3, and adjacent is -4.

COS = ADJ/HYP = -4/5

Answer:

[tex]\cos \theta =-\frac{4}{5}[/tex]

Step-by-step explanation:

We are given:

[tex]\sin \theta =\frac{3}{5}[/tex]

Then

[tex]\cos^{2} \theta =1-\sin^{2} \theta[/tex]

         [tex]= 1 - (\frac{3}{5} )^2[/tex]

         [tex]= 1 -\frac{9}{25}[/tex]

Then

[tex]\cos^{2} \theta =\frac{16}{25}[/tex]

Then

[tex]\cos \theta =\sqrt{\frac{16}{25} }\ \ \text{or}\ \ \cos \theta =-\sqrt{\frac{16}{25} }[/tex]

We know that θ is in Quadrant 2.

Then  cos θ < 0.

Therefore

[tex]\cos \theta =-\sqrt{\frac{16}{25} }[/tex]

        [tex]= -\frac{4}{5}[/tex]

Answer:

more details

Step-by-step explanation: