12. Solve for x. (6x-21) P Q T S R​

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:

13

Step-by-step explanation:

Answer:

Ok this time sense you want explanation i give you it your welcome. -7 1/2 reduces to -15/2 and -15/2 + 2 = -5 1/2 or -11/2

Answer:

-Exact form: 11/2

Answer:

immma send you the link friend me on hereStep-by-step explanation:

Answer:

17

Step-by-step explanation:

25 + = 42

42 - 25

= 17

Answer:

y = 4/5x + 32/5

Step-by-step explanation:

(-3,4) and (2, 8)

Slope:

m=(y2-y1)/(x2-x1)

m=(8-4)/(2+3)

m= 4/5

Slope-intercept:

y - y1 = m(x - x1)

y - 4 = 4/5(x + 3)

y - 4 = 4/5x + 12/5

y = 4/5x + 32/5

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:

755887578787-∵°

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The average rate of change for f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 1, 3 ] , then

f(b) = f(3) = 27 ← value of y from table for x = 3

f(a) = f(1) = 3 ← value of y from table for x = 1

average rate of change = [tex]\frac{27-3}{3-1}[/tex] = [tex]\frac{24}{2}[/tex] = 12

Answer:

This is hard

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

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Answer:

3(7-g)=90

You multiply the expression by 3. The difference means to subtract two values. The whole equation equals 90.

Answer:

See Explanation

Step-by-step explanation:

Required

The meter reading in ccf

The question is incomplete, as the  meter readings is not given. So, I will solve using an assumed value for the meter readings.

Let

[tex]x\ m^3 \to meter\ readings[/tex]

The readings in ccf is:

[tex]Reading = \frac{x}{2.832}[/tex]

Now, assume the value of x is 25; The readings will be:

[tex]Reading = \frac{25}{2.832}ccf[/tex]

[tex]Reading = 8.83\ ccf[/tex]

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:

a

Step-by-step explanation:

First convert 3/5 to a percentage.

3/5 is 60% and 20% of the students chose Hulk. That leaves 20% who chose Iron Man. The simplest form of 60:20:20 is 6:2:2.

Answer:

i solved for t and got

t= -3, -12

Step-by-step explanation:

Answer:

t = - 12, t = - 3

Step-by-step explanation:

Given

t² + 15t = - 36 ( add 36 to both sides )

t² + 15t + 36 = 0 ← in standard form

(t + 12)(t + 3) = 0 ← in factored form

Equate each factor to zero and solve for t

t + 12 = 0 ⇒ t = - 12

t + 3 = 0 ⇒ t = - 3

Answer:

4 [tex]1/2[/tex] cups are needed for 3 batches.

Step-by-step explanation:

1 1/2 = 1.5

3*1.5 = 4.5

4.5 = 4 1/2

Have a nice day!

Answer:

[tex]\frac{11\sqrt{2}}{2}}[/tex] or 5.5√2

Step-by-step explanation:

We can see that this is a 45-45-90 triangle

refer to the image below to see what that means

we can see that (in the image) 11=x√2

which means that x= 11/√2

to rationalize this fraction we mulitply both sides by √2 to get

[tex]\frac{11\sqrt{2}}{2}}[/tex] or 5.5√2

Answer:

Step-by-step explanation:

x = [tex]\frac{11\sqrt{2} }{2}[/tex]

Answer:2.77*10^-8

Step-by-step explanation:

8.89*10^-7/32.0

The capacitance of the capacitor is approximately 2.78 x 10⁻⁹ Farads (F).

The capacitance of a capacitor can be calculated using the formula:

C = Q / V

Where C represents the capacitance, Q represents the charge stored in the capacitor, and V represents the voltage applied to the capacitor.

In this case, we are given that the charge stored in the capacitor is 8.89 x 10⁻⁷ C and the voltage applied is 32.0 V. Plugging these values into the formula, we get:

C = (8.89 x 10⁻⁷ C) / (32.0 V)

Simplifying the expression, we find:

C ≈ 2.78 x 10⁻⁹ F

The Farad is the SI unit of capacitance, representing the ability of a capacitor to store charge per unit voltage.

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Answer:

the equation is y=80-x

hope it helps

Answer:

25,120 sq. metres

Step-by-step explanation:

Find the diagram attached

Lateral surface area = πrl

r is the radius

l is the slant height

Given

r = 160/2 = 80m

l = √r²+h²

l = √80²+60²

l  = √6400+3600

l = √10,000

l = 100cm

Lateral surface area = 3.14 * 80 * 100

Lateral surface area = 25,120 sq. metres

Answer: 18) the degree is 45.57 20) 25.01 degree (I am not sure if you need to round up the degree but if you do round it up you will get 46 degree for 18 and 25 degree for 20

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:

the answer is 6x+16y+8

Answer:

y = 1/4x + 1/2 and x = -2 +4y

Step-by-step explanation:

Solving it in a way that x/4 is a fraction and not division so you would make that 1/4x. y = x/4 +1/2 x/4 is 1/4x so then you subtract 1/2 from both sides to get y - 1/2 = 1/4x. You can then divide 1/4 on both sides. -1/2 divided by 1/4 is -2 and 1/4y. This will get your answer of x = 1/4y -2 for x. Y is just 1/4x + 1/2