Write the equation of the line passing through the points (0, -4) and (-2, 2).

Given:

The vertices of a parallelogram GHJK are K(1,2), J(5,2), G(0,8).

To find:

The coordinate of the vertex H.

Solution:

We know that the diagonals of a parallelogram bisects each other. It means the midpoint of the diagonals are same.

Let the coordinate of the vertex H are (a,b).

Midpoint formula:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

In parallelogram GHJK ,

Midpoint of diagonal GJ = Midpoint of diagonal HK

[tex]\left(\dfrac{0+5}{2},\dfrac{8+2}{2}\right)=\left(\dfrac{a+1}{2},\dfrac{b+2}{2}\right)[/tex]

[tex]\left(\dfrac{5}{2},\dfrac{10}{2}\right)=\left(\dfrac{a+1}{2},\dfrac{b+2}{2}\right)[/tex]

On comparing both sides, we get

[tex]\dfrac{5}{2}=\dfrac{a+1}{2}[/tex]

[tex]5=a+1[/tex]

[tex]5-1=a[/tex]

[tex]4=a[/tex]

And,

[tex]\dfrac{10}{2}=\dfrac{b+2}{2}[/tex]

[tex]10=b+2[/tex]

[tex]10-2=b[/tex]

[tex]8=b[/tex]

Therefore, the coordinates of the vertex H are (4,8). Hence, option B is correct.

Answer: 8

Step-by-step explanation:

Given

Money deposited [tex]P=200[/tex]

Interest rate [tex]R=4\%[/tex]

Time period [tex]T=1\ yr[/tex]

For a year simple and compound interest is the same

[tex]\therefore \text{Interest}=\dfrac{P\times R\times T}{100}\\\\\Rightarrow \text{Interest}=\dfrac{200\times 4\times 1}{100}\\\\\Rightarrow 8[/tex]

Thus, interest earned is 8 units

Answer:

27.82

Step-by-step explanation:

make a proportion

31.99/115 = x/100

Answer:

0, -2

Step-by-step explanation:

Can I have brainliest? I hope this helped and have a nice day!

Answer:

(-1, -5)

Step-by-step explanation:

The function that represents the number of patients she sees is; y = 9/4x + 5 and number of patients after 2 hours is 9 patients

We are given;

Number of patients the dental hygeinist cleans before lunch = 5

Average number that she cleans after lunch = 9 patients in 4 hours

Thus, number of patients per hour is 9/4

The formula for slope intercept form is;

y = mx + c

Thus, equation to represent the situation in the question is;

y = 9/4x + 5

At 2 hours after lunch, number of patients is;

y = 9/4(2) + 5

y = 9.5

Approximately 9 patients

Read more about Functions at;

https://brainly.com/question/1415456

#SPJ2

Answer:

in 5 weeks i think

Step-by-step explanation

I added 300+20 5 times. Same with the 250

Answer:

5

Step-by-step explanation:

to vick = W1 = 300 + 20 x    (  1 )

to anya = W2 = 250 + 30 x    ( 2)           Both 1 and 2 ( simulataneous )

When W1 =  W2

300 + 20 x = 250 + 30 x

          10 x   = 5

  so they need 5 months

Answer:

Pages                Time(hours)

 [tex]\frac{85}{2}[/tex]                       [tex]\frac{5}{3}[/tex]

 [tex]x[/tex]                        [tex]1[/tex]

[tex]x*\frac{5}{3} = \frac{85}{2} *1\\\\x = \frac{85*3}{5} = 17*3 = 51 \ pages[/tex]

Answer:

Not accomplishable.

Step-by-step explanation:

Could you please stucture this question more simply. This partly doesn't make sense, unless I am wrong.

See attachement for the diagram of the triangle

Answer/Step-by-step explanation:

To find the length of HJ, we can use different equations as follows:

✔️Recall: SOHCAHTOA

Let's take <G as the reference angle = 28°

Opposite side to reference angle = HJ

Hypotenuse = 20

Apply SOH.

Thus:

Sin 28° = opp/hyp

Sin 28° = HJ/20 (Alex's equation is correct).

Solving further, we would have:

HJ = Sin 28 * 20 ≈ 9.4

✔️Another way is by using <H as the reference angle.

m<H = 180° - (90° + 28°) (sum of triangle)

m<H = 62°

Adjacent side to reference angle (<H) = HJ

Hypotenuse = 20

Apply CAH:

Cos 62° = Adj/Hyp

Cos 62° = HJ/20 (Marlene's equation is correct)

Solving further, we would have,

HJ = Cos 62° * 20 ≈ 9.4

As you can see, the equation of both students are correct. Both would arrive at the same answer using any of the two equations.

Answer:

7 4 9

5 6 1

3 2 8

Step-by-step explanation:

..........................

Answer:

7 4 9

5 6 1

3 2 8

Hope this helps!

Answer:

=1/2 (2) (1/3)

Step-by-step explanation:You have to find the size of the sides using the intersecting lines and then multiply L*W

Answer:

1/2 (2) 1/3

Step-by-step explanation:

trust me broo

Answer:

so the answer could either be

Yes. as elevation increases, the temp decreases

but..

there is also no trend coz the points are scattered i.e the temp

as the elevation is increasing the temp does vary.

so My final answer would be no, there is not a trend

Answer: $700

Step-by-step explanation:

The store is selling at 30% off.

If a mattress is $1,000, first find out what 30% of $1,000 is:

= 1,000 * 30%

= $300

The store is selling 30% off, this means that they are reducing the price by 30%:

= 1,000 - 300

= $700

Answer:

13

Step-by-step explanation:

Answer:

Adriana is correct

Step-by-step explanation:

if you get rid of E, it is a 90 degree angle. so:

90-20=70

which is Adriana's answer

Answer:

-28c+144

Step-by-step explanation:

if you simplify -16(c-4)-12c+80

it equals -28c+144

Explanations:

Distribute

-16(c-4)-12c + 80 ---> -16c + 64 - 12c +80

Add the numbers

-16c+64-12c+80 ---> -16c+144-12c

Combine like terms

-16c+144-12c

-28c+144

Answer:

55 degrees

Step-by-step explanation:

Angle ACE and BDE are congruent so segments AC and BD are parallel.  That makes angles CAE and DBE congruent.

6x - 15 = 5x - 1

x - 15 = -1

x = 14

So, the measure of angle BDE = 4x = 56 degrees.  The measure of angle DBE = 5x - 1 = 69 degrees.

The total of all angles in triangle BDE is 180 degrees, so the measure of angle E = 180 - 56 - 69 = 55

Answer:

where is the graph????

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rewrite in slope-intercept form.

Tap for more steps...

y

=

4

5

x

−

5

Use the slope-intercept form to find the slope and y-intercept.

Tap for more steps...

Slope:  

4

5

y-intercept:  

(

0

,

−

5

)

Any line can be graphed using two points. Select two  

x

values, and plug them into the equation to find the corresponding  

y

values.

Tap for more steps...

x

y

0

−

5

25

4

0

Graph the line using the slope and the y-intercept, or the points.

Slope:  

4

5

y-intercept:  

(

0

,

−

5

)

Answer:

The correct answer is: D Conditional Statement. Explanation: A conditional statement is a statement in "if, then" form. This statement is "If A, then B." This makes it a conditional statement

Step-by-step explanation:

Answer:

i think the second answer??

Step-by-step explanation:

Answer:

Look at the image.

Step-by-step explanation:

C = 2πr

2 · π · 5

≈ 31.42

31.42 ÷ 4 = 7.855

Answer:

hope this helps

Step-by-step explanation:

If a variable with an exponent has an even exponent then it is a perfect square. To get the square root, we simply divide the exponent by 2. For example x8 is a perfect square, its square root is x4

Answer:

25%

Step-by-step explanation:

so out of 32 marbles, 8 of them are red. This means the rest are blue which is 24 blue. To make a percentage, all you do is make a fraction. out of 32, 8 were red so 8/32. Fractions are basically division so 8/32 is 0.25. This means 25%.

Answer:

4.09

Step-by-step explanation:

Circumference=

[tex]2\pi \times r[/tex]

The circumference of the circular base of the object is 4.082 in

The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center.

Given that, we need to find the circumference of the circular base of the object, whose radius is 0.5 in

The circular object is referred as circle, the circle's circumference is its boundary length measured in unit whose power is always 1, like m, cm, km etc.

Here, if we calculate the circumference of the object, we will get,

The circumference of any circular object given by :-

C = 2π×radius

C = 2×3.14×0.65 = 4.082 in

Hence, the circumference of the circular base of the object is 4.082 in

Learn more about circumference, click;

https://brainly.com/question/28757341

#SPJ6