Find the area of the shaded region . RQ= 71.5 inches and PO=93.4 inches . Use 3.14 as necessary

Answer:

y = 3x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate the slope using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (- 1, 0) ← 2 points on the line

m = [tex]\frac{0-3}{-1-0}[/tex] = [tex]\frac{-3}{-1}[/tex] = 3

The line crosses the y- axis at (0, 3) ⇒ c = 3

y = 3x + 3 ← equation of line

Answer:

grade point average​ (GPA) as a weighted mean = 3.14

Yes, student makes the Dean's list.

Step-by-step explanation:

Since the data is not given I will explain the question with a relevant example:

For example

Data:

Students grades are:  A, C, B, A, D

The corresponding number of credit hours: 3, 3, 3, 4, 1

The grading system assigns quality points to letter grades as​:

A = 4

B = 3

C = 2

D = 1

F = 0

To find:

grade point average​ (GPA) as a weighted mean

If the​ Dean's list requires a GPA of 3.00 or​ greater, did this student make the​ Dean's list?

Solution:

Weighted Mean =   Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] / Σw[tex]_{i}[/tex]

Here

Using the earned grades of A, C, B, A, D and corresponding quality points to these letter grades we get:

A = 4

C = 2

B = 3

A = 4

D = 1

So the values in x[tex]_{i}[/tex] are:

x

4

2

3

4

1

Now the number of credit hours are represented as weights w[tex]_{i}[/tex] :

w

3

3

3

4

1

In order to calculate weighted mean first multiply x[tex]_{i}[/tex] with w[tex]_{i}[/tex]

x[tex]_{i}[/tex] w[tex]_{i}[/tex]

4 * 3 = 12

2 * 3 = 6

3 * 3 = 9

4 * 4 = 16

1 * 1 = 1

The sum of x[tex]_{i}[/tex] w[tex]_{i}[/tex] is :

Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] = 12 + 6 + 9 + 16 + 1 = 44

Σx[tex]_{i}[/tex] w[tex]_{i}[/tex]  =  44

Now compute the sum of w[tex]_{i}[/tex]

Σw[tex]_{i}[/tex] = 3 + 3 + 3 + 4 + 1 = 14

Σw[tex]_{i}[/tex] = 14

Putting the values in the weighted mean formula:

Weighted Mean =   Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] / Σw[tex]_{i}[/tex]

                           =  44 / 14

                           = 3.1429

Weighted Mean =   Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] / Σw[tex]_{i}[/tex] = 3.14

Since the​ Dean's list requires a GPA of 3.00 or​ greater and the grade point average​ (GPA) as a weighted mean of the student is 3.14 so the student makes the​ Dean's list because his/her GPA is higher than 3.00

Answer:

318

Step-by-step explanation:

Bob=x

Marc=x+30

Donny=3(x+30)

x+x+30+3x+90=500

5x=500-120

5x=380

x=76

Bob has x = 76

Marc has x+30=106

Donny has 3*112=318

318+106+76=500

Answer:

2

Step-by-step explanation:

3x^2

The coefficient is 3

The variable is x

The exponent is 2

Answer:

Correct option is

b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.

Step-by-step explanation:

Here, we are given the line RQ, which is divided in two equal parts by a line PS which is perpendicular to RQ.

The foot S of PS is on the line RQ.

First of all, let us do a construction here.

Join the point R with P and P with Q.

Please refer to the attached image.

Now, let us consider the triangles  PQS and PRS:

Now, Two sides and the angle included between the two triangles are equal.

So by SAS congruence we can say that [tex]\triangle PRS \cong \triangle PQS[/tex]

Therefore, the corresponding sides will also be equal.

RP = QP

RP is the distance between R and P.

QP is the distance between Q and P.

Hence, to prove that P is equidistant from R and Q, we have proved that:

b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.

Answer:

N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg

therefore, N(t)=130∗.545/24=35.44mg

Step-by-step explanation:

N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg

therefore, N(t)=130∗.545/24=35.44mg

Answer:

≈ 130 mg

Step-by-step explanation:

This is about the half-life of the substance.

There is a formula for this kind of calculations:

N(t)= N₀*(0.5)^(t/T), where

In our case, we have:

And the calculation:

Answer: about 130 mg of substance remains after 20 hours

Answer:

The cousins have 4 bags of white marbles and 4 bags of pink marbles.

Step-by-step explanation:

If x is the number of bags with white marbles and y is the number of bags with pink marbles, we can write the following system:

x + y = 8 -- Equation 1

5x + 7y = 48 -- Equation 2

5x + 5y = 40 -- Equation 3 (Multiply Equation 1 by 5)

2y = 8 -- (Subtract Equation 3 from 2)

y = 4 -- (Divide both sides by 2)

x + 4 = 8 -- (Substitute y = 4 into Equation 1)

x = 4 -- (Subtract 4 from both sides)

Answer:

see explanation

Step-by-step explanation:

sum the parts of the ratio, 2 + 1 = 3 parts , thus

81 cm² ÷ 3 = 27 cm² ← value of 1 part of the ratio

2 parts = 2 × 27 = 54 cm²

Area of A = 54 cm² and area of B = 27 cm²

The side of the original square = [tex]\sqrt{81}[/tex] = 9 cm

The width of both rectangles is 9 cm ( width remains unchanged after cut )

Thus

Rectangle A

9 × length = 54 ( divide both sides by 9 )

length = 6 cm

Rectangle B

9 × length = 27 ( divide both sides by 9 )

length = 3 cm

Rectangle A → length = 6 cm, width = 9 cm

Rectangle B → length = 3 cm , width = 9 cm

Answer:

Rectangle A                 Rectangle B

length = 9 cm                length = 9 cm

width = 6 cm                  width = 3 cm

Step-by-step explanation:

Area of square At = 81 cm²

Square is cut into two pieces = A + B

The ration of area A to B = 2:1

Find

Rect A        Rect B

length         length

width           width

---------------------------------

first, get the side of the square = A = s²

81 = s²,      

s = √81      

s = 9 cm

since the ratio is 2:1, therefore the side can be divided into 3

9 ÷ 3 = 3 cm ----- take note of this to get the Width

Rectangle A

L = 9 cm (which is the s = 9 cm)

W = 3 cm (2 ratio) = 6 cm

Rectangle B

L = 9 cm  (which is the s = 9 cm)

W = 3 cm (1 ratio) = 3 cm

Proof:

At = A + B

81 = (9x6) + (9x3)

81 = 54 + 27

81 = 81  ----- OK

Answer:

160

Step-by-step explanation:

x = original price

x+ 25% x = 200

Change to decimal form

x + .25x = 200

1.25x = 200

Divide each side by 1.25

x = 200/1.25

x =160

The original price was 160

Answer:

A.

Step-by-step explanation:

All of those graphs represent functions. You are able to tell because they all pass the vertical line test. The vertical line test is conducted by drawing a line that goes vertically and intercepts any point of the line in question. If the function crosses the vertical line twice, it is not a function. If it only intercepts once, it is a function. In this case, every graph is a function because they would intercept a vertical line once.  

Answer:

See explanation below.

Step-by-step explanation:

A bullet shot at you will definitely hit you because of the direction it is travelling.

Your fight and flight response won't be activated either because of the speed of the event (bullet) or if you don't know how harmful a gun is (you'll remain calm/ignorant in this case)?

Try to post academic problems.

Best Regards!

Answer:

The expression that could help calculate the price of the TV is;

$P - 20% of $P

Step-by-step explanation:

Here, we want to write an expression that corresponds to the price of a television set that is on sale at a price which is 20% off the regular price.

From the question, we can see that the regular price is $P

So now we are having 20% off;

This corresponds to;

20/100 * p = p/5 = 0.2p

So in the expression form, we can have;

$P - 20% of $P

Answer:

20°

Step-by-step explanation:

The measure of the inscribed angle is equal to the half of the arc it sees

Since AC is the diameter the measure of arc ABC is 180°

and since A sees arc BC and C sees the arc AB

A< + C< = 90° so angle C = 20°

Answer:

Ques 1: 7.85

Ques 2: both [tex]\sqrt{0.25}[/tex] and [tex]-\sqrt{16}[/tex] are rational.

Ques 3: 0.9

Step-by-step explanation:

Ques 1:

Solving the [tex]\sqrt{61.6}[/tex], we get 7.8485.

Rounding off to nearest hundredth, we see that next digit is 8, so we increase the previous digit by 1.

So, the answer to nearest hundredth is 7.85.

Ques 2:

[tex]\sqrt{0.25}[/tex] and [tex]-\sqrt{16}[/tex]to be checked  whether they are rational or irrational.

We know that [tex]\sqrt{16}[/tex] is equal to 4.

[tex]-\sqrt{16}[/tex] = -4 which is a rational value.

Let us solve [tex]\sqrt{0.25}[/tex] now.

[tex]\sqrt{0.25} = \sqrt{\dfrac{25}{100}}\\\Rightarrow \dfrac{5}{10}[/tex]

Which is a rational value.

So, both are rational.

Ques 3:

Simplify [tex]\sqrt{0.81}[/tex]

0.81 can be written as [tex]\frac{81}{100}[/tex] in rational form.

Now, taking the square root, we need to take the square root for both Numerator and Denominator and then we can divide to get the desired square root.

[tex]\sqrt{0.81} = \sqrt{\dfrac{81}{100}}\\\Rightarrow \dfrac{9}{10} = \bold{0.9}[/tex]

So, the answers are:

Ques 1: 7.85

Ques 2: both [tex]\sqrt{0.25}[/tex] and [tex]-\sqrt{16}[/tex] are rational.

Ques 3: 0.9

Answer:

A: 2:30

B: 13:15.

C: 4:05 A.M

D: 3:25 P.M

Step-by-step explanation:

Answer:

a) 0230 hours

b) 1315 hours

c) 4:05 am

d) 3:25 pm

Step-by-step explanation:

To change a 12 hour clock to a 24 hour clock, note that when it hits p.m., anything over 12 p.m. will have the number added to it.

a) 2:30 am

2:30 am is earlier than 12 pm, therefore, 0230 is your answer. Remember, you must place the 0 in the front to not confuse a user that the 2 is in the tens place value.* *Essentially, use military time:

b) 1:15 pm

1:15 pm is later than 12 pm, therefore, add 12 to the 1 in the hours. Use military time:

0115 + 1200 = 1315

1315 hours is your answer.

To change a 24 hour clock to a 12 hour clock, note the time frame in which the time is given. if over 1200, then subtract by 12, and add the p.m.

0405 = 4:05 am.

1525 = 12 pm + 3:25 = 3:25 pm.

~

Answer:

[tex]15\sqrt{2}[/tex]      or       21.2132

Step-by-step explanation:

[tex]\sqrt{450}[/tex]

[tex]\sqrt{15^{2} }[/tex]   (root of a product is equal to the product of the roots of each factor)

[tex]\sqrt{15^{2} } \sqrt{2}[/tex]                (simplify)

[tex]15\sqrt{2}[/tex]    or   ≈ 21.2132

Answer:

[tex]15\sqrt{2}[/tex] or 21.213

Step-by-step explanation:

For radical form: think of multiples of 450. Think of a pair that contains one perfect square, particularly the higher, the better . These 2 numbers are 25 and 18. 25 is the perfect square number since the two numbers that multiply to be 25 is 5 and 5.

Now take the perfect square of 25 and put it outside of the radical. The 18 remains inside: [tex]5\sqrt{18}[/tex]

Now, since 18 is a high number that needs to get reduced, do the same for 18 as we did for 450--find two numbers, one of which is a perfect square. These two numbers are 9 and 2.

Now take the perfect square of 9. This is 3. Take it out of the radical so that only the two remains inside. The 3 will now multiply with the 5: [tex]5*3\sqrt{2}[/tex]

Multiply 5 and 3 to get 15. The 15 stays outside the radical. Your answer is:

[tex]15\sqrt{2}[/tex]

Answer:

2/3

Step-by-step explanation:

I am not sure

Answer:

Step-by-step explanation:

[tex]Let \:the \: unknown \: fraction \: be \: x\\\\\frac{5}{3} -x = 1\\\\\frac{5}{3}-x=1\\\\\mathrm{Subtract\:}\frac{5}{3}\mathrm{\:from\:both\:sides}\\\\\frac{5}{3}-x-\frac{5}{3}=1-\frac{5}{3}\\\\\frac{5}{3}-x-\frac{5}{3}=-x\\\\1-\frac{5}{3}=-\frac{2}{3}\\-x=-\frac{2}{3}\\\\x=\frac{2}{3}\\[/tex]

Answer:

16%

Step-by-step explanation:

rental charge per year = $80

rental charge at the rate $8 per year = 8 * 12 = 96

the increased amount = 96 - 80 = 16

% = 16 / 100 = 16%

Answer:

Yes

Step-by-step explanation:

Because 12/18 = 2/3..(cancel 12 and 18 by 6)

Answer:

yes

Step-by-step explanation:

2x6=12

3x6=18

6 is the multiplying number

( the 2 equations are the same amount )

Answer:

Area= 97.9 km²

Step-by-step explanation:

Angle at w = 180-119-34

Angle at w = 27°

Side XV= x

x/sin27= 26/sin119

x= sin27(26/sin119)

x= 0.454(26/0.8746)

x= 13.5 km

Side WX = y

y/sin 34= 26/sin119

y= sin34(26/sin119)

y= 0.559(26/0.8746)

y= 16.6 km

S= (16.6+13.5+26)/2

S= 56.1/2

S=28.05

Area = √(28.05(28.05-26)(28.05-13.5)(28.05-16.6))

Area=√(28.05(2.05)(14.55)(11.45))

Area=√(9579.772744)

Area=97.8763

Area= 97.9 km²

Answer:

Step-by-step explanation:

[tex]\frac{1}{4}[/tex] of 600 is 150

hope this helps

plz mark as brainliest!!!!!!

Answer:

Step-by-step explanation:

400 km  =       x    

  6 min         9 min  

cross multiply:

6x = 400 ( 9)

x = 3600 / 6

x = 600 km

Answer:

[tex]\Large \boxed{\mathrm{Option \ D}}[/tex]

Step-by-step explanation:

(6, 4)

x = 6 and y = 4

y > -1/2x + 7

Plug in the values to check if it is true.

4 > -1/2(6) + 7

4 > -3 + 7

4 > 4

This statement is false.

(6, 4) lies on the line.

Answer:

The answer is B)

[tex]y = - \frac{1}{2}x + 8[/tex]

Answer:

B.  y = -[tex]\frac{1}{2}[/tex]x + 8

Step-by-step explanation:

The line is perpendicular to line whose equation is:

y = 2x + 4 and;

passes through point (4,6) .

The product slopes of two perpendicular lines is -1.

The slope of the line whose equation is y = 2x + 4 is; 2

Let the slope of the perpendicular line (l2) be [tex]m_{l2}[/tex]

[tex]m_{l2} * 2 = -1[/tex]

[tex]m_{l2}[/tex] = [tex]-\frac{1}{2}[/tex]

Taking another point xy on line l2;

[tex]\frac{y - 6}{x - 4} = -\frac{1}{2}[/tex]

Cross multiplying this gives;

y = -[tex]\frac{1}{2}[/tex]x + 8 which is the equation of the perpendicular line!

Answer:

B, because that's the side that wasn't given

Step-by-step explanation:

The statement AB ≅ PQ is required to be congruent.

Option B is the correct answer.

There are ways to prove that two triangles are congruent.

- Side-Side-Side (SSS) Congruence.

The three sides of one triangle are equal to the corresponding three sides of another triangle.

- Side-Angle-Side (SAS) Congruence.

The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.

- Angle-Side-Angle (ASA) Congruence.

The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.

- Angle-Angle-Side (AAS) Congruence.

We have,

Side-Side-Side (SSS) Congruence.

The three sides of one triangle are equal to the corresponding three sides of another triangle.

Now,

ΔABC and ΔPQR

AC ≅ PR  (given) (side)

BC ≅ QR (given ) (side)

AB ≅ PQ (side)

ΔABC ≅ ΔPQR (SSS)

Thus,

AB ≅ PQ is required to be congruent.

Learn more about triangle congruency here:

https://brainly.com/question/12413243

#SPJ7

Answer:

818.8333333 *pi

or

Using the pi button on the calculator

2572.440785

Using 3.14 for pi

2571.13666666

Step-by-step explanation:

We need the radius

r = d/2

r = 17/2 = 8.5

We can find the volume using

V = 4/3 pi r^3

V = 4/3 pi ( 8.5)^3

V =818.8333333 *pi

  Using the pi button on the calculator

2572.440785

Using 3.14 for pi

2571.13666666

Answer:

x = -67/15 = -4-46667

Step-by-step explanation:

4(-3x+1) - 3x = 71

4*-3x + 4*1 - 3x = 71

-12x + 4 - 3x = 71

-15x = 71-4

-15x = 67

x = 67/-15

x = -4.46667

check:

4(-3*-4.46667 + 1) - 3*-4.4666= 71

4(13.4+1) + 13.4 = 71

4*14.4 + 13.4 = 71

57.6 + 13.4 = 71

Answer:

$26 for each child

Step-by-step explanation:

35 * 3 = 105 / 4 = 26.25

Answer:

Step-by-step explanation:

[tex]Selling \:price = 3000gh Cedis\\Profit \% = 25\%\\Cost\:price =?\\\\CP =\frac{ ( Selling\:price \times 100 )}{ ( 100 + percentage profit)} \\\\C.P = \frac{3000\times 100 }{100+25}\\\\ C.P = \frac{300000}{125} \\\\Cost\: Price = 2400gh Cedis[/tex]