A line passes through (2,-1) and (4,5). Which answer is the equation of the line?

Answer:

x = [tex]5\sqrt{2}[/tex].

Step-by-step explanation:

The question says that the hypotenuse is 10, while the other two sides are both x. That means that the triangle is a 45-45-90 angle.

Because this is a 45-45-90 triangle, the proportions of the side lengths are 1-1-sqrt(2).

Since the hypotenuse is 10, and the side length is x, we can make a proportion.

[tex]\frac{10}{\sqrt{2}} =\frac{x}{1}[/tex]

[tex]x\sqrt{2}[/tex] = 10

x = [tex]\frac{10}{\sqrt{2} }[/tex]

x = [tex]\frac{10 * (\sqrt{2} )}{(\sqrt{2})(\sqrt{2} ) }[/tex]

x = [tex]\frac{10\sqrt{2} }{2}[/tex]

x = [tex]5\sqrt{2}[/tex]

Hope this helps!

Answer:

Number common to both sides=6

Step-by-step explanation:

Average of first four numbers=5

4*5=20

Average of the last four numbers=8

4*8=32

Average of all seven numbers=6 4/7

7*6 4/7

Find the number common to both sets of four numbers

Solution

4*5=20

4*8=32

32+20=52

7 * 6 4/7

=7*46/7

=46

Number common to both sides=52-46

=6

Answer:

y = 13

Step-by-step explanation:

Step 1: Distribute

3/2y - 3/2 = y + 5

Step 2: Subtract y on both sides

1/2y - 3/2 = 5

Step 3: add 3/2 on both sides

1/2y = 13/2

Step 4: Divide both sides by 1/2

y = 13

Answer:

y = 13.

Step-by-step explanation:

3/2(y-1) = y+5

3/2y - 3/2 = y + 5

3/2y - y = 5 + 3/2

1/2y = 6 and 1/2; 6.5; 13/2

y = 13.

To check out work...

3/2(13 - 1) = 13 + 5

3/2(12) = 18

3 * 6 = 18

18 = 18

On a number line, all you need to do is plot a point where it says 13. On a cartesian plane, you would have a horizontal line that expands infinitely in each direction, where y = 13.

Hope this helps!

Answer:

∠ BDG = 148°

Step-by-step explanation:

The tangent- chord angle BDG is half the measure of its intercepted arc DCG

The 2 arcs in the circle sum to 360°, thus

arc DCG = 360° - arc DG = 360° - 64° = 296° , thus

∠ BDG = 0.5 × 296° = 148°

Answer: x≈3.7

Step-by-step explanation:

7x+4=30

-4 on both sides

30-4=26

7x=26

divide 7 on both sides

x=3.7142...

Answer:

3.7

Step-by-step explanation:

7x+4=30

7x=30-4

7x=26

26/7

3.7

Answer:

i. weight of wastage(kg) = 179.775 kg

ii. weight of rice cultivated = 765 kg - 179. 775 kg = 585.225 kg

percentage of rice cultivated = 100 - 23.5 = 76.5%

Step-by-step explanation:

A land of 1000 sq. meter  is used to cultivate 765 kg of rice with wastage of 23.5%.

i. The wastage in percentage is 23.5% but the weight of the wastage in weight is  23.5% of 765 kg

weight of wastage = 23.5/100 × 765

weight of wastage = 17977.5/100

weight of wastage(kg) = 179.775 kg

ii. weight and percentage of rice cultivated.

weight of rice cultivated = 765 kg - 179. 775 kg = 585.225 kg

percentage of rice cultivated = 100 - 23.5 = 76.5%

Answer: [tex]\frac{5a^2}{-10a^4b^9}[/tex]

Step-by-step explanation:

Any negative exponent can be moved to the other side of the fraction as a positive exponent.

Thus, simply move the negative exponents to get: 5a^2/b*b^8*-10a^4.  Then, use the exponent rule to get 5a^2/-10a^4b^9

Hope it helps <3

Answer:

Number of lawns mow in 49 hours = 31.5 lawns

Step-by-step explanation:

Given:

Number of lawns mow = 9

Time taken = 14 hours

Find:

Number of lawns mow in 49 hours

Computation:

Time taken for 1 lawn = 14 / 9

Number of lawns mow in 49 hours = 49 / Time taken for 1 lawn

Number of lawns mow in 49 hours = 49 / (14/9)

Number of lawns mow in 49 hours = 31.5 lawns

Answer:

$959.69 per oz

Step-by-step explanation:

A gold alloy is produced from pure gold and alloy.

10 oz of pure gold costs $1,288 per ounce

55 oz of alloy costs $900 per ounce

The first step is to add the cost of both the pure gold and alloy together

= (10 oz × $1288)+(55 oz × $900)

= $12,880+$49,500

= $62,380

Therefore the cost per ounce can be calculated as follows

= $62,380/10 oz + 55 oz

= $62,380/65 oz

= $959.69 per oz.

Hence the cost per ounce of the gold alloy is $959.69 per ounce

Answer:

D

Step-by-step explanation:

So that you can have an equation equal to zero to solve for x

Answer:

(f-g) (x) is

[tex] {4}^{x} - 5x - 14[/tex]

Step-by-step explanation:

f(x)=4ˣ - 8

g(x)=5x+6

(f-g) (x) is

[tex] {4}^{x} - 8 \: - (5x + 6) \\ {4}^{x} - 8 - 5x - 6[/tex]

The final answer is

[tex] {4}^{x} - 5x - 14[/tex]

Hope this helps you.

Answer:

BF=16

Step-by-step explanation:

To find BF, (I will be calling it x) you need to use the equation

CF/FB=CE/EA Substitute

FB=x

24/x=18/12 cross multiply

18x=288 divide both sides by 18

x=16

FB=16

Hope this helps, if it does, please consider giving me brainliest, it will help me a lot.

Have a good day! :)

Replace f with 190, replace P with 4148 and solve for  s:

4148 = 1.85s + 4.2(190)

Simplify:

4148 = 1.85 + 798

Subtract 798 from both sides:

3350 = 1.85s

Divide both sides by 1.85:

s = 1,810.81

Rounded to nearest square foot = 1811 square feet.

Answer:

The length of the arc is 89 yards

Step-by-step explanation:

Mathematically, to find the length of an arc, we use the formula below;

Length of an arc = Theta/360 * 2 * pi * r

In this case, Theta = 300 and r = 17 yards

Length of the arc = 300/360 * 2 * 22/7 * 17 = 89.047619047583 which is 89 yards to the nearest yard

Answer:

(i) 1/21

(ii) 1/10

(iii) Take a look at the explanation: Try this one yourself. I have given you some hints.

Step-by-step explanation:

(i) Two red balls:

To do this, we need to find the total amount of possible choices first. To do this, we multiply 15 by 14. This is our denominator:

15(14) = 210

Now, we need to find the total combinations of red balls. We solve 5 choose 2 for this one.

5 choose 2 = 5(4)/2! = 10

Our numerator is 10. Therefore, our probability is 10/210 = 1/21.

(ii) Two blue balls or two black balls:

To do this, we need to add the probabilities of getting a blue ball with a black ball. (Since there is an "or" sitting there. If there is an "and", we multiply)

So, let's calculate the probability of getting a blue ball first:

Blue:

We use the same denominator as before: 210.

Our numerator is now 6 choose 2, which is:

6 choose 2 = 6(5)/2! = 15.

Now, our fraction is 15/210, BUT, dont simplify, as we will need to add.

Black:

Same steps: denominator is 210, but the numerator is 4 choose 2.

Solving 4 choose 2:

4 choose 2 = 4(3)/2! = 6.

Our numberator is 6.

But, we cant forget to add them!

(15 + 6)/210 is 21/210, which is 1/10.

(iii) I'll let you try this one by yourself. Here is a hint:

Solve for the probability of chooseing a black ball and a red ball. Then, multiply.

Enjoy the process, and I hoped this helped you! (If you have any questions, feel free to ask)

Answer:

y = x/3 + 10

Step-by-step explanation:

Let y be the number of minutes the flight takes

She can take off 10 minutes later than expected. She will be able to travel at  a speed three times than expected.

Let her expected speed be s, therefore, she can travel at 3s.

x = number of minutes the flight was expected to take.

In terms of distance and speed:

x = d / s ______(1)

where d = total distance traveled

The time for the flight (minus waiting time) is now the division of the distance she traveled and her speed, i.e.:

t = d / 3s

From (1):

=> t = x / 3

The time she spent waiting is 10 minutes.

Therefore, the total time that the flight takes (plus waiting time) is:

y = t + 10

=> y = x/3 + 10

Answer:

(0,0)

Step-by-step explanation:

x = -⅛y²

The equation exchanges x and y, so this is a sideways parabola.

It opens to the left because the coefficient of y² is negative.

The vertex form of a sideways parabola with its vertex at (h, k) is:

x =  a(y – k)² + h

Your equation is

x = -⅛(y - 0)² + 0

By comparing the two equations, we find that

h = 0; k = 0.

The vertex is at (0, 0).  

The Figure shows your parabola with its vertex at (0,0).

Answer:

(0,0)

Step-by-step explanation:

Answer:

Option D is the right option.

solution,

[tex] \frac{ac}{bc} = \frac{bc}{dc} \\ or \: \frac{18}{ m} = \frac{m}{7} \\ or \: m \times \: m = 18 \times 7(cross \: multiplication) \\ or \: {m}^{2} = 126 \\ m = \sqrt{126} [/tex]

Hope this helps..

Good luck on your assignment.

Hope

Answer:

Step-by-step explanation:

Answer:

In the graph attached there is a sample generated with a correlation coefficient r=-0.5.

Step-by-step explanation:

A value of r that is -0.5 shows that there is a certain correlation and that this correlation is negative.

As there are no examples in this question, I searched for a generator of random samples with a user-input correlation coefficient between the two variables.

In the graph attached there is a sample generated with a correlation coefficient r=-0.5.

Answer:

In the graph attached there is a sample generated with a correlation coefficient r=-0.5.

Step-by-step explanation:

Answer: Option A

Step-by-step explanation:

Answer:

The answer is option A.

∆BDC is a right angled triangle

Angles in a triangle add up to 180°

That's

z + 35 + 90 = 180°

z = 180 - 35 - 90

z = 55°

Alternate angles are equal

Angle DBC = Angle BDA

That's

35 = 7y

Divide both sides by 7

y = 5

y = 5 z = 55

Hope this helps you

Answer:

  2x -3y = 19

Step-by-step explanation:

For the two points (8, -1) and (2, -5), the two-point form of the equation of a line is ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (-5-(-1))/(2 -8)(x -8) +(-1)

  y = -4/-6(x -8) -1

  3y = 2x -16 -3 . . . . multiply by 3

  2x -3y = 19 . . . . . . rearrange to standard form

__

The point-slope form is y +1 = 2/3(x -8). It helps to have all the numbers.

Answer:

2x + -3y = 19

Step-by-step explanation:

I promise

Answer:

x= -4

Step-by-step explanation:

2x+4=6x+20

so 2x-6x=20-4

divide both sides by -4

-4x/-4 = 16/4

=-4

Answer:

a. 1/12 (hope it help)

Step-by-step explanation:

5sec/60sec=1/12

Answer:

√3 * 5 = 5√3 cm

Step-by-step explanation:

→ ABCDEFGH is a cube.

→ CF = Diagonal of cube.

→ CH = Diagonal of Base Face BCDH.

→ Let the side of Each cube = a.

Than,

in Right ∆CFH, By Pythagoras Theoram, we have,

→ CH² + FH² = CF² --------- Equation (1)

and, Similarly, in Right ∆CDH ,

→ CD² + DH² = CH² ------- Equation (2).

Putting Value of Equation (2) in Equation (1), we get,

→ (CD² + DH²) + FH² = CF²

→ a² + a² + a² = CF²

→ CF² = 3a²

→ CF = √3a .

Hence, we can say That Diagonal of a cube is √3 times of its sides.

__________________

Given:-

Side of cube = 5cm.

So,

→ Diagonal of cube = √3 * 5 = 5√3 cm. (Ans.)

Answer:

y = 40.5 cm

Step-by-step explanation:

The total area of the shape is 792 cm²

let's find the area of the four parallelograms

To do that we should calculate the area of the rhombus inside and then substract it from the total area

The area of a rhombus is given by the formula:

Let A be the area of the shape , A' the area of the rhombus and A" the area of the four parallelograms

Let a be the area of the single parallelogram

the area of a parallelogram is fiven by the formula :

let's find y

Answer:

Starting with the smallest, we will have; D , C, A, B

Step-by-step explanation:

Given;

A = 3/4

B  = 5/6

C = 16/25

D = 9/15

Convert the fractions to decimal, to determine their sizes;

A = 3/4 = 0.75

B  = 5/6 = 0.833

C = 16/25 = 0.64

D = 9/15 = 0.6

From the decimal form of the fractions, it be observed that,

B > A > C > D

Starting with the smallest, we will have; D , C, A, B

Answer:

32

Step-by-step explanation:

Lets work it out.

First we combine the two equations to get 5x-10. That is equal to 70 so we get out x = 16 we put that into the equation 3x-10 and get 32

Answer:

C

Step-by-step explanation:

Equation A

16x - 7 = 11x - 32

(16x - 7) - 11x = (11x - 32) -11x

5x - 7 = -32

(5x - 7) + 7 = (-32) + 7

5x = -25

(5x)/5 = (-25)/5

x = -5

Equation B

-4x - 10 = 2x + 20

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

-6x - 10 = 20

(-6x - 10) + 10 = (20) + 10

-6x = 30

(-6x)/-6 = (30)/-6

x = -5

Both Equation A and Equation B have a solution of -5.