What is the area of rectangle PQRS? ​

Answer:

Step-by-step explanation:

(x₁, y₁) = (-3 , 6)   &

(x₂ , y₂) = ( 5 , -9)

[tex]Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         [tex]=\dfrac{-9-6}{5-[-3]}\\\\\\=\dfrac{-15}{5+3}\\\\\\=\dfrac{-15}{8}[/tex]

I assume your question was to simplify the following fraction ;

[tex]{:\implies \quad \sf \dfrac{4a+3}{5}-\dfrac{2a+3}{3}}[/tex]

Taking LCM will yield ;

[tex]{:\implies \quad \sf \dfrac{3(4a+3)-5(2a+3)}{15}}[/tex]

[tex]{:\implies \quad \sf \dfrac{12a+9-10a-15}{15}}[/tex]

[tex]{:\implies \quad \boxed{\bf \dfrac{2a-6}{15}}}[/tex]

This is the required answer

Answer:

See below.

Step-by-step explanation:

7,824/10=782.4

782.4

 |

The 8 is in the tens place. It represents 80.

-hope it helps

Answer:

80

Step-by-step explanation:

7824÷10=782.4

Therfore the 8 is in the tens place meaning that the 8 in this is 80

The scatterplot is an illustration of a linear regression.

The equation that best models the scatter plot is y = 4x+ 35

The equation of a linear regression is represented as:

y = mx + b

Where:

m represents the slope

b represents the y-intercept

From the graph, we have the following points on the line of best fit (see attachment)

(x,y) = (10,75) and (20,105)

The equation is then calculated as:

[tex]y = (\frac{y_2 - y_1}{x_2 - x_1})(x -x_1) + y_1[/tex]

This gives

[tex]y = (\frac{105 - 75}{20- 10})(x -10) + 75[/tex]

Evaluate

[tex]y = 4(x -10) + 75[/tex]

Open the bracket

[tex]y = 4x -40 + 75[/tex]

Simplify

[tex]y = 4x+ 35[/tex]

Hence, the equation that best models the scatter plot is y = 4x+ 35

Read more about scatter plots at:

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Answer:

The population of 75 hours from now would be 40,000.

Step-by-step explanation:

The reason for this is because your initial number is 10,000 and when 25 hours pass by, your population would be 20,000. Another 25 hours pass by, and then your population would be 40,000. If you multiply 25 by 3, you will notice 75 hours have just passed, so your answer would be 40,000.

Answer:

$13,082.60 more

Step-by-step explanation:

Melanie:

[tex]A=P(1+\frac{r}{n})^(20)\\ A=9800(1+\frac{.045}{4})^(20)\\A=$12,257.36[/tex]

Amelia:

[tex]A=Pe^(rt)\\A=9800e^(.0475*20)\\A=$25,339.95[/tex]

Amelia-Melanie= $13,082.60

Step-by-step explanation:

the total surface area is the sum of the 5 individual areas in the surface :

2 triangle sides (left and right).

1 back rectangle side

1 rectangle floor

1 inclined rectangle front side

to get the length of the baseline (Hypotenuse) of the right-angled triangles on the side. we use Pythagoras

c² = a² + b²

where c is the Hypotenuse (the side opposite of the 90° angle).

c² = 3² + 4² = 9 + 16 = 25

c = 5

so, now, we have everything we need.

the area of a triangle side (since it is right-angled) :

4×3/2 = 6

2 sides, that makes 12

the area of the back side

6×3 = 18

the area of the floor

6×4 = 24

the area of the inclined front side

6×5 = 30

so, the total surface area is

12+18+24+30 = 84

Answer:

1207

Step-by-step explanation:

Total number of customers last week: 92 + 5 + 25 = 122

Number of customers who paid cash: 92

Percent of customers who paid cash last week: 92/122 × 100% = 75.4%

Next week:

Total number of customers: 1600

Expected number of customers paying cash:

75.4% of 1600 = 0.754 × 1600 = 1207

Answer:

App. 83.33 kg

Step-by-step explanation:

10/60=0.167 kg/minute

0.167/3=0.056 kg/minute/person

0.056 x 25 x 60= 83.33...6

Answer:

8.57

Step-by-step explanation:

Hope it helps.......

Answer:

x = 8.57

Step-by-step explanation:

Hi! So first of all, I attached an image that has my best visual explanation of how the 2 triangles overlap but are indeed two separate triangles!

Since the question states that the triangles are similar, that basically means in simple terms that their sides are proportional or, are all based on the same fraction (proportion)! (An example of this is the triangles with the sides that correlate [in this problem, 11 to 7] would be 1 to 2, 3 to 6, and 4 to 8)

Now, we have to figure out which of our sides correspond, the first one being 11 to 7, and the second one being x + 15 (which I got by adding the small portion I have from the big triangle, and the portion I have from the smaller triangle together because the small triangle is inside of the big one!) to 15.

Next, I have to find out what x is based on the fraction (proportion) I already have which is 11 to 7 or [tex]\frac{11}{7}[/tex]. Then, I compare this by setting this proportion equal to are other proportion with x in it!

[tex]\frac{11}{7} = \frac{x+15}{15}[/tex]

Finally, I have to get x by itself to find what it is equal to, which you can see in the image! (If you have a number in the denominator and a variable in the numerator, and a regular number or fraction without a variable on the other side, you can just multiply both sides by the number in the denominator to cancel out the bottom of said variable fraction!)

So! X is equal to 8.57!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

7 feet

Step-by-step explanation:

60 inches is 5 feet add the 2 feet

Answer:

1. (a. 8 b. 3 d. 6,6,12 e. 3,3,9) 2. (a. 2,3 b. 4,5 c. 6,6,2,3 d. 5,3,5) 3. (a.2/3 b.1/3 c.2/3 f.1/2 g.7/8 h.4/5)

Step-by-step explanation:

OK this is quite simple. Just multiply the top and bottom, otherwise known as the numerators and denominators, by whatever is next to it. In this case, 1a is [tex]\frac{2*4}{5*4}[/tex].

That would result in [tex]\frac{8}{20}[/tex]

Hey there!

In order to multiply fractions, we should multiply the numerator of the 1st fraction by the numerator of the 2nd fraction.

Same with denominators.

Let's multiply these fractions.

2/5=2*4/5*4=8/20

2/3=2*6/3*6=12/18

1/4=1*3/4*3=3/12

3/4=3*3/4*3=9/12

now divide:

10/15=10:5/15:5=2/3

12/18=12:6/18:6=2/3

12/15=12:3/15:3=4/5

15/25=15:5/25:5=3/5

Now, simplify the following fractions:

4/6

divide the top & bottom by 2:

2/3

next:

5/10

divide the top & bottom by 5:

1/2

next

5/15

divide the top & bottom by 5:

1/3

next:

12/18

divide the top & bottom. by 6

2/3

next

5/10

divide the top & bottom by 5

1/2

next

14/16

divide the top & bottom by 2

7/8

and then last but not least

28/35

divide the top & bottom by 7

4/5

And we're done!

Hope everything is clear.

Let me know if you have any questions!

#LearningDoesn'tEnd

:-)

Answer:

Step-by-step explanation:

Formulae

Area of a triangle = 1/2 x base x height

Area of a rectangle = width x length

Question 1

Surface area of square based pyramid = area of base + 4 × area of triangle

⇒ SA = (6 × 6) + 4(1/2 × 6 × 14)

         = 36 + 168

         = 204 yd²

Question 2

Surface area of a cuboid = 2 × base area + 2 × end area + 2 × side area

⇒ SA = 2(10 × 6) + 2(6 × 3) + 2(10 × 3)

         = 120 + 36 + 60

         = 216 mm²

Extra credit question

Surface area of a triangular based prism = base area + 2 × triangle area + 2 × side areas

base area = 3 × 10 = 30 mm²

triangle area = 1/2 × 3 × 2 = 3 mm²

side area = 10 × 2.5 = 25 mm²

⇒ total SA = 30 + (2 × 3) + (2 × 25)

                 = 30 + 6 + 50

                 = 86 mm²

❍ Concept :-

We can solve these questions by using the formulas of area of triangle and rectangle, which will make our work easier. So, we know that,

⠀

[tex] \blue{ \underline{ \boxed{ \begin{array}{cc} \sf1. ~Area_{Triangle} = \dfrac{1} {2} \times b \times h \qquad \: \: \: \: \: \: \: \\ \\ \\ \sf2. \: Area_{Rectangle} = Length \times Breadth \end{array}}}} \\ \\ [/tex]

Using these formulas and figuring out the number of triangles and rectangles in each shape, we will solve this question.

⠀

✰ Solution :-

⠀

1. In this square pyramid, if we closely observe, we will get to know that there are 1 rectangle and 4 triangular faces. Thus,

⠀

[tex]\sf \hookrightarrow Area=6 \times 6 + 4( \dfrac{1}{2} \times 6 \times 14) \\ \\ \\ \sf \hookrightarrow Area=36 + 168 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {204 \: yd}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ [/tex]

⠀

2. Now, here, we can use the formula of total surface area for cuboid, i.e.

⠀

TSA = 2( lb + bh + hl )

⠀

[tex]\sf \hookrightarrow Area=2(10 \times 6 + 6 \times 3 + 10 \times 3) \\ \\ \\ \sf \hookrightarrow Area=2(60 + 18 + 30) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=2 \times 108 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {216 \: mm}^{2} \: \: \qquad \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

⠀

Extra Credit Question.

⠀

Here, we can find out the total surface area by finding,

⠀

Base area i.e. length x breadth ( B.A. )

Side area i.e. length x breadth ( S.A. )

triangular area = 1/2 x b x h ( T.A. )

⠀

Now,

⠀

TSA = BA + 2 x S.A. + 2 x T.A.

⠀

[tex]\sf \hookrightarrow Area=(10 \times 3) + 2(10 \times 2.5) + 2(\dfrac{1}{2} \times 3 \times 2) \\ \\ \\ \sf \hookrightarrow Area= 30 + 2 \times 25 + 2 \times 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=30 + 50 + 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {86 \: mm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

Answer: Answer in picture

Step-by-step explanation:

Math

Answer:

5:6

Step-by-step explanation:

To find the ratio of side lengths you need to cube root of the ratio of the volumes. The reason you use the cube root is because you are multiplying 3 things together when you find volume.

[tex]\sqrt[3]{\frac{125}{216} } =\frac{5}{6}[/tex]

5 : 6

Answer:

hello

g (x)= x² - 5

g (3) = 3² - 5 =  9 - 5 =  4

Step-by-step explanation:

After converting yards to miles:

2640 yards =  1.5 miles

Given,

2640 yards= ________ miles

Now,

To convert to yard to miles the conversion factor is 0.000568182.

So,

1 yard ⇒ 0.000568182 miles

Multiply 2640 on both sides,

2640 yards ⇒ 1.5 miles.

Therefore 2640 yards is equivalent to 1.5 miles.

Know more about unit conversion,

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Answer:

Left 2, up 1

Step-by-step explanation:

If you use slope, remember rise/run. You go up then left.

Answer: left 2 up 1

Step-by-step explanation: I did it by using the rule rise over run so it goes up then left . Hope it helps

The amount of orange that Manny and Josh have leftover after eating lunch is 1.

A fraction is a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below

Oranges Manny has left = 1 - 4/9 = 5/9

Oranges Josh has left = 1 - 5/9 = 4/9

Oranges they both have left = 5/9 + 4/9 = 1

To learn more about subtraction of fractions, please check: https://brainly.com/question/915789

Answer:

Step-by-step explanation:

This is a logical question that can be d=solved thus;

To decide which decision to make,one has to calculate the amount for both methods to detrmine which is higher.

1. Using simple interest formula of ( P X R X T)/ 100

Since p  = 1500, r  = 2.5%,  T = 3

1500 x 2.5% x 3  / 100  =  1500 x 0.025 x 3 / 100

112.5 / 100 = 1.125

to find amount  = 1.125 + 1500 = 1501.25 for the three 3years.

2. Using compound interest formula of ( P ( 1 + r/n)∧nt

1 + (2%/3) ∧3(3)

1500( 0.02/3) ∧ 9

1500  x 0.006 ∧9

1500 x 2.60 = 3900

A = 3900 + 1500 = 5400

SO FROM THE ABOVE I WILL G FOR THE HIGH YIELD SAVINGS AS IT IS HIGHER THAN THE INTEREST SAVINGS

Given the data from the question, the best account to use is:

A high interest savings account, with 2.5% simple interest annually (Option 1)

I = PRT / 100

A = I + P

Where

A = P(1 + r/n)ⁿᵗ

Where

I = PRT / 100

I = (1500 × 2.5 × 3) / 100

I = $ 112.5

Thus

A = I + P

A = 112.5 + 1500

A = $ 1612.5

A = P(1 + r/n)ⁿᵗ

Since n = 1,

A = P(1 + r)ᵗ

A = 1500(1 + 0.02)³

A = $ 1591.8

SUMMARY

The amount at the end of 3 years using:

Thus, the best account to use is a high interest savings account, with 2.5% simple interest annually (option 2)

Learn more about simple interest:

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Answer:

A.

Step-by-step explanation:

hope its help^^

Answer:

105

Step-by-step explanation:

nth term=a+(n-1)d (a=first term,d=difference)

a=6,d=9-6=3

34th term=6+(34-1)3

=6+(33×3)

=6+99=105

For the first question it's 52.99 cm^3 because the formula for volume of a cylinder is V=πr^2h.

The second question is 722.57 or 722 cm^2 because the formula for surface area is A=2πrh+2πr^2.

hope it helps!

Answer:

For question 3: 52.9875 cm^3 or 52.99 cm^3.

For question 4: 1,413 cm^3.

Step-by-step explanation: To find the volume of a cylinder, you need the area of the base times the height.  We don't have the area of the base, but we can find out by using the formula 3.14 x r^2 where r is the radius, which is 1.5 for question 3 and 5 for question 4.  It should look like this:

For question 3: 3.14 x 1.5^2 = 7.065.

For question 4: 3.14 x 5^2 = 78.5.

When you find the area of the base, you multiply it by the height, which is 7.5 for question 3 and 18 for question 4.  It should look like this:

For question 3: 7.065 x 7.5 = 52.9875 or 52.99.

For question 4: 78.5 x 18 = 1,413.

Therefore, 52.9875 cm^3 or 52.99 cm^3 is your answer for question 3 and 1,413 cm^3 is your answer for question 4.

Let me know if this is right! :)

Answer: y = 12.5x

Step-by-step explanation:

Because 250 bottles are filled every 20 minutes:

250/20=12.5

So, x=1, y=12.5

Hence, x=2 y=25

Because the number of bottles is directly proportional to the operation of the machine so:

12.5=a+b, 25.2a+b

a=12.5, b=0

Therefore, the equation is y = 12.5x

The Desmos graph of y = 12.5x is attached below

Answer:

8/(x + 2) - 4/(x + 6)

Step-by-step explanation:

4x + 40 = Ax + 6A + Bx + 2B

Equating coefficients of x

4 = A + B      (1)

Equating constant terms:

40 = 6A + 2B    (2)

Multiply  equation (1) by -2:

-8 = -2A - 2B   .. (3)

Add (2) and (3):

32 = 4A

A = 32/4

A = 8.

4 = 8 + B

B = 4 - 8

B = -4.

The decomposition of the given partial fraction in terms of x is [tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex].

The partial fraction is the result of writing a rational expression as the sum of two or more fractions.

According to the given question.

We have a partial fraction

[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{A}{(x+2)} +\frac{B}{(x+6)}[/tex]

We have to decompose the above partial fraction in terms of x.

The above partial fraction can be written as

[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{A(x+6)+B(x+2)}{(x+2)(x+6)}[/tex]

⇒[tex]4x+40 = A(x+6)+B(x+2)[/tex]

⇒[tex]4x + 40 = Ax + 6A + Bx + 2B[/tex]

⇒[tex]4x + 40 = x(A+B) +6A + 2B...(i)[/tex]

On comparing the coefficient of x and the constant terms.

[tex]A+B = 4..(ii)[/tex]

⇒[tex]A = 4 - B[/tex]

and, [tex]6A+2B = 40..(iii)[/tex]

⇒[tex]2(3A+B) = 40[/tex]

Substitute the value of A in (iii)

⇒[tex]2(3A+B) = 40[/tex]

⇒[tex]3A+B = 20[/tex]

⇒[tex]3(4-B)+B = 20[/tex]

⇒[tex]12 - 3B +B = 20[/tex]

⇒[tex]12 - 2B = 20[/tex]

⇒[tex]-2B = 8[/tex]

⇒[tex]B = -4[/tex]

So, [tex]A = 4-(-4) = 8[/tex]

Substitute the value of A and B in the given partial fraction.

⇒[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex]

Hence, the decomposition of the given partial fraction in terms of x is [tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex].

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Usando proporciones, hay que:

Una proporción es una fracción de la cantidad total.

En este problema, dos automovis, en sentidos opostos, salen al mismo tiempo. Por eso, su velocidad relativa es de 90 km/h + 80 km/h = 170 km/h.

La distancia es de 255 km, por eso, el tiempo en que se encontraran, en horas, es dado por:

t = 255/170 = 1.5h

La distancia recorrida por cada auto es dada por:

dA = 90 x 1.5 = 135 km.

dB = 80 x 1.5 = 120 km.

Puede-se aprender mas a cerca de proporciones en brainly.com/question/26425852

Answer:

51.24 mg

Step-by-step explanation:

400 x (0.71^6) = 51.24

Answer:

51.24 mg

Step-by-step explanation:

400 x (0.71^6) = 51.24

Answer: A, C, F

Step-by-step explanation: