The ordered pairs (6,8), (9, 12), (x, 20), (18, y) represent a proportional relationship. Find the value of X and the value of Y. Select the two correct answers.

First we find the slope of the line 2x−3y+8=0 by placing it into slope intercept form:

2x−3y+8=0

⇒−3y=−2x−8

⇒3y=2x+8

⇒y=  

3

2

​

x+  

3

8

​

Therefore, the slope of the line is m=  

3

2

​

.

Now since the equation of the line with slope m passing through a point (x  

1

​

,y  

1

​

) is

y−y  

1

​

=m(x−x  

1

​

)

Here the point is (2,3) and slope is m=  

3

2

​

, therefore, the equation of the line is:

y−3=  

3

2

​

(x−2)

⇒3(y−3)=2(x−2)

⇒3y−9=2x−4

⇒2x−3y=−9+4

⇒2x−3y=−5

Hence, the equation of the line is 2x−3y=−5.

Answer:

y=2/3x-11/3

Step-by-step explanation:

Hi there!

We are given the equation 2x-3y=9 and we want to write an equation that is parallel to it and that passes through (4,-1)

Parallel lines have the same slopes

So we need to first find the slope of 2x-3y=9

We can do this by converting the equation of the line from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

To do this, we need to isolate y on one side

2x-3y=9

subtract 2x from both sides

-3y=-2x+9

divide both sides by -3

y=2/3x-3

as 2/3 is in the place where m is, 2/3 is the slope of the line

It's also the slope of the line parallel to it that passes through (4,-1).

Here's the equation of that line so far:

y=2/3x+b

now we need to find b

as the line will pass through the point (4,-1), we can  4 as x and -1 as y in order to solve for b

-1=2/3(4)+b

multiply

-1=8/3+b

subtract 8/3 to both sides

-11/3=b

Substitute -11/3 as b into the equation

y=2/3x-11/3

There's the equation

Hope this helps!

Answer:

[tex]4.2025\pi\:\mathrm{m^2}[/tex]

Step-by-step explanation:

The area of a circle with radius [tex]r[/tex] is given by [tex]A=r^2\pi[/tex]. In the figure, we're given a diameter of 4.1. All diameters of a circle are exactly 2 times the length of all radii of the circle. Therefore, the radius of the circle is [tex]4.1\cdot \frac{1}{2}=2.05[/tex].

Thus, the area of the circle is [tex]2.05^2\pi=\boxed{4.2025\pi\:\mathrm{m^2}}[/tex]

Answer:

3 positive tiles hope.helps

Step-by-step explanation:

[tex](1) \: \: \sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } \times \frac{ \sqrt[3]{64} }{ \sqrt[3]{3} } \times \frac{ \sqrt[6]{9} }{ \sqrt[3]{2} } [/tex]

Note that the 1st two factors can be combined:

[tex] \sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } = \sqrt[3]{5 \times \frac{2}{5} } = \sqrt[3]{2} [/tex]

We also know that the numerator in the 3rd factor can be rewritten as

[tex] \sqrt[3]{64} = 4[/tex]

And the numerator in the 4th term can be rewritten as

[tex] \sqrt[6]{9} =({( {3})^{2} })^{ \frac{1}{6} } = \sqrt[3]{3} [/tex]

So let's rewrite expression #1

[tex] \sqrt[3]{2} \times \frac{4}{ \sqrt[3]{3} } \times \frac{ \sqrt[3]{3} }{ \sqrt[3]{2} } [/tex]

Notice that all the radical terms cancel out except for 4 therefore,

[tex]\sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } \times \frac{ \sqrt[3]{64} }{ \sqrt[3]{3} } \times \frac{ \sqrt[6]{9} }{ \sqrt[3]{2} } = 4[/tex]

Answer:

B

Step-by-step explanation:

When x=1, we will use the second equation

-(1)+1 = 0

Answer:

Step-by-step explanation:

22 = 21 [tex]e^{7k\\}[/tex]

(22/21) = [tex]e^{7k}[/tex]

ln(22/21) = 7k ln(e)

ln(22/21) = 7k  

0.046520016 = 7k

k=0.006645717

~~~~~~~~~~~~~~~~

P = 21 [tex]e^{0.006645717*17\\}[/tex]

P = 23.51  

Answer:

49.87%

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 70%

σ is the population standard deviation = 8%

a) For x = 70%

z = 70% - 70%/8%

z = 0

Probability value from Z-Table:

P(x = 70) = 0.5

b) For x = 70%

z = 94% - 70%/8%

z = 3

Probability value from Z-Table:

P(x = 94) = 0.99865

The probability of students that receive between a 70% and 94%

P(x = 94) - P(x = 70)

0.99865 - 0.5

0.49865

Therefore, the percentage of students that receive between a 70% and 94% is

0.49865 × 100

= 49.865%

Approximately = 49.87%

Answer:

b. 8 inches wide and 25 inches long

Step-by-step explanation:

Here are the options

5 inches wide and 25 inches long

b. 8 inches wide and 25 inches long

c. 15 inches wide and 15 inches long

d 15 inches wide and 25 inches long

Area of a rectangle = length x width

10 x 20 = 200

first option

5 x 25 = 125 does not have the same area as the one lanu drew

second option

8 x 25 = 200 has  the same area as the one lanu drew

third option

15 x 15 = 225 does not have the same area as the one lanu drew

fourth option

15 x 25 = 375 does not have the same area as the one lanu drew

Answer:

904.78

Step-by-step explanation:

I hope this is correct, if it isn't please feel free to let me know and I can fix it. I'm sorry in advance if it is incorrect.

Answer:

6h + 5b = a

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

By using geometric mean theorem in the given right triangle ABC,

[tex]\frac{AD}{BD}= \frac{BD}{DC}[/tex]

BD² = AD × DC

h² = (AC - CD) × DC

h² = (25 - 16) × 16

h² = 9 × 16

h = [tex]\sqrt{144}[/tex]

h = 12

Therefore, measure of side h = 12 units.

Option D will be the correct option.

Answer:

12 is correct via a p e x

1. Alternate angle

2. Alternate exterior angle

3. Corresponding angle

4. Vertical angle

5. Consecutive angle

6. Alternate exterior angle

7. x = 110°

8. x = 70°

9. x = 60°

10. x = 130°

11. x = 53°

12. x = 60°

13. x = 30°

14. x = 65°

15. x = 24°

16. x = 174°

hope this helps....

Answer:

A

Step-by-step explanation:

The scale factor k is the ratio of corresponding sides, image to original.

k = [tex]\frac{CP'}{CP}[/tex] = [tex]\frac{15}{75}[/tex] = 0.2

Since k < 1 this represents a reduction.

Answer:

G is smaller than P. Visually comparing G to P you are doing a rough comparison to a 90° (or right) angle. Angle G is a little bit tilted to the right making it just under 90°

The statement which correctly compares the angles is Angle G is smaller than angle P.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

Given are two triangles.

Given that,

GK is congruent to PN.

HG is congruent to MP.

Also, given that,

HK = 32 cm and MN = 40 cm

Angle G is opposite to the side HK.

Angle P is opposite to the side MN.

Angles opposite to the greater side will be greater.

So angle P is greater than angle G

Or, angle G is smaller than angle P.

Hence, Angle G is smaller than angle P.

Learn more about Angles here :

https://brainly.com/question/11846909

#SPJ7

Answer:

Swag actually means stylish and confident

Answer:

8

Step-by-step explanation:

In order to find the range you need to subtract maximum card number from the minimum card number. We know that the range is 5 and that the minimum card is 6 so we can set up the equation like this to find the maximum shown as x.

[tex]5=x-6[/tex]

Add 6 to both sides

[tex]11=x[/tex]

Now we know all the the numbers of the three cards Anthony has since we were given the minimum = 6, 7, and solved for the last card which was the maximum = 11. In order to find the mean we have to add all of the numbers then divide by how many numbers there are (in this case it will be 3):

[tex]mean=\frac{6+7+11}{3}[/tex]

Add 6+7+11

[tex]mean=\frac{24}{3}[/tex]

Divide by 3

[tex]mean=8[/tex]

Answer/Step-by-step explanation:

✔️10x - 4y = -8

-5x + 6y = 10

Multiply the first equation by ½ to eliminate the x-term

Thus:

½ × 10x - 4y = -8 (eqn 1)

5x - 2y = -4

✔️-2x + 6y = 3 (eqn 1)

4x + 3y = 9

To eliminate the x-terms when adding to the second equation, multiply the first equation by 2

Thus:

2 × -2x + 6y = 3

-4x + 12y = 6

✔️3x - 8y = 1 (eqn 1)

6x + 5y = 12

To eliminate the x-terms when adding to the second equation, multiply the first equation by -2

Thus:

-2 × 3x - 8y = 1 (eqn 1)

-6x + 16y = -2

✔️-8x + 10y = 16 (eqn 1)

-4x - 5y = 13

To eliminate the x-terms when adding to the second equation, multiply the first equation by -½

Thus:

-½ × -8x + 10y = 16 (eqn 1)

4x - 5y = -8

Answer:

Match each system to the number the first equation can be multiplied by to eliminate the x-terms when adding to the second equation.

8x + 10y = 16

-2

4x-5y = 13

2× + бу = 3

4x + 3у = 9

3x - 8y = 1

6x + 5y = 12

10x - 4y =-8

-5x + бу = 10

1/2

2

-1/2Step-by-step explanation:

Answer:

5 hours

divide 25 by 5 you get 5

Answer: m∠x = 40°

Step-by-step explanation:

This works the exact same way as the other one

Being adjacent angles in a parallelogram, the two angles would be supplementary (add up to 180°).

140° + x° = 180°

x = 40°

Answer:

The area will be 2 times the old area.

Step-by-step explanation:

When you double something, that means you multiply it by 2, therefor it will be 2 times the old area.

Answer:

option 3

Step-by-step explanation:

Length = 5 m, Base = 3 m

Area = Length x Base

       = 5 x 3

       = 15 m²

Base is double = 2 x 3 = 6 m

Length remains same = 5m

New Area = Length x Base

               = 5 x 6

               = 30 m²

The new Area is increase by 2 times the old Area .

answer:

ans:

Step-by-step explanation:

1000 m = 1 km

1000 mL = 1 L

100 cg = 1 g

Answer:

The base is 19.5.

Step-by-step explanation:

The given question is, "The perimeter of a rectangle is 58 and its base exceeds its width by 10, how long is the base?"

Perimeter = 58

Base, l = 10+b

The perimeter of a rectangle is :

P = 2(l+b)

58 = 2(10+b+b)

29 = (10+2b)

29-10 = 2b

19 = 2b

b = 9.5

Base, l = 10 + 9.5

= 19.5

Hence, the base is 19.5.

Answer:

15

Step-by-step explanation:

50 * .30=15

Answer:

24

Step-by-step explanation:

x + (1/4)x + (1/3)x = 38

multiply both sides by 12 to clear the fractions

12x + 3x + 4x = 456

19x = 456

Divide both sides by 19

x = 24

Answer:

24

Step-by-step explanation:

x+1/4x+1/3x=38

x+7/12x=38

19/12x=38

x=38*12/19=24

Answer:

B

Step-by-step explanation:

the area of the triangle is  18 square units