solve the following simultaneous linear equations by the substitution method.
2p + 3q = 10
p - 2q = -2​

Answer:

60

Step-by-step explanation:

Subsitute the number if large vehicles

5x + 10(50) = 800

5x + 500 = 800

5x =300

X =60

Answer:

60

Step-by-step explanation:

Substitute y = 50 into the equation and solve for x

5x + 10(50) = 800 , that is

5x + 500 = 800 ( subtract 500 from both sides )

5x = 300 ( divide both sides by 5 )

x = 60

That is 60 small vehicles were washed in total

Answer:

w = 12 cm  and l = 20 cm

Step-by-step explanation:

[tex] \frac{3}{8} \div \frac{4}{9} \\ = \frac{3}{8} \times \frac{9}{4} \\ = \frac{27}{32} [/tex]

Hope it helps!!!

Thanks!!!

Answer:

0.5miles

Step-by-step explanation:

800meters is 0.497097miles

Round 0.497097miles to the nearest hundredth which would be 0.5 miles.

Answer:

57.3 minutes

Step-by-step explanation:

We know that the temperature as a function of time of an object is described by the equation:

[tex]T(t) = T_a + (T_0 - Ta)*e^{-k*t}[/tex]

Where:

k is a constant

Tₐ =  room temperature = 68°F

T₀ =  initial temperature of the object = 375°F

Replacing these in our equation we will get

T(t) = 68°F + (375°F - 68°F)*e^{-k*t} = 68°F + (307°F)*e^{-k*t}

And we know that after 25 minutes, at t = 25min, the temperature of the casserole is 190°F

then:

T(25min) = 190°F = 68°F + (307°F)*e^{-k*25 min}

Now we can solve this for k:

190°F = 68°F + (307°F)*e^{-k*25 min}

190°F - 68°F = (307°F)*e^{-k*25 min}

(122°F)/(307°F) = e^{-k*25 min}

Now we can apply the natural logarithm in both sides:

Ln( 122/307) = Ln(e^{-k*25 min}) = -k*25min

Ln( 122/307)/(-25 min) = k = 0.0369 min^-1

Then the temperature equation is:

T(t) = 68°F + (307°F)*e^{-0.0369 min^-1*t}

Now we want to find the value of t such that:

T(t) = 105°F = 68°F + (307°F)*e^{-0.0369 min^-1*t}

We can solve this in the same way:

105°F - 68°F =  (307°F)*e^{-0.0369 min^-1*t}

37°F =  (307°F)*e^{-0.0369 min^-1*t}

(37°F)/(307°F) = e^{-0.0369 min^-1*t}

Ln( 37/307) = -0.0369 min^-1*t

Ln( 37/307)/( -0.0369 min^-1 ) = 57.3 min

So after 57.3 minutes, the temperature of the casserrole will be 105°F

Answer:

Yeah, so that is right, just put it into a formula.

[tex]9.07*10x^{-2}[/tex]

Answer:

A = 58

B = 112

Step-by-step explanation:

A + B = 180                           Supplementary angles

B = 2A - 24                           Given

Substitute for B in the first equation

A + 2A - 24  = 180

3A - 24 = 180                         Add 24 to both sides

3A = 180 + 24                        Combine the right

3A = 204                               Divide both sides by 3

A = 204/3

A = 68

B = 2A - 24

B = 2*68 - 24

B = 136 - 24

B = 112

Answer:

Moses ran 8 Luis ran 12.

Step-by-step explanation:

.

Number of laps to Louis run is 12 when Moses ran 8 laps.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

The ratio of the number of laps Moses ran to the number of laps Louis ran = 2 : 3

Now,

Since,  The ratio of the number of laps Moses ran to the number of laps Louis ran = 2 : 3

So, Number of laps Moses ran = 2x

And, Number of laps Louis ran = 3x

If Moses ran 8 laps.

Then, we get;

2x = 8

x = 4

Then, Number of laps Louis ran = 3x

                                                 = 3 × 4

                                                 = 12

Thus, Number of laps to Louis run is 12 when Moses ran 8 laps.

Learn more about the ratio visit:

https://brainly.com/question/25927869

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Answer:

8.373

Step-by-step explanation:

Cone

Find the volume of the cone

V = 1/3 pi r^2 h

r = d/2

r = 4/2

r = 2 inches

h = 6 inches

pi = 3.14

V = 1/3 * 3.14 * 2^2 *  6

V = 25.12

Half sphere

V = 1/2 (4/3) pi r^3

r = 2 from above calculation

pi = 3.14

V = 2/3 * 3.14 * 2^3

V = 2/3 * 3.14 * 8

V = 16.74

Nothing spills out so I scoop must be a whole sphere. The sphere is 2 times what I calculated it to be or

V = (4/3) * 3.14 * 2^3

V = 33.49 cubic inches

The difference in volume is 33.49 - 25.12 = 8.373

Answer:

x=6

Step-by-step explanation:

First, we combine like terms.

6x=2x+24

6x-2x=24

4x=24

Then we divide both sides by 4.

x=6

Answer:

x=6

Step-by-step explanation:

6x=2x+24

Transpose 2x to the other side

6x-2x=24

4x=24

x=24/4=6

x=6

Hope this helps

Please mark me as brainliest

Hello,

[tex]sin(45^o)=\dfrac{\sqrt{2} }{2} \\\\sin(45^o)=\dfrac{a}{c} \\\\\dfrac{\sqrt{2} }{2}=\dfrac{a}{6} \\\\a=6*\dfrac{\sqrt{2} }{2}=3\sqrt{2}\\[/tex]

Answer A

Answer:

A. 25,000 (1 minus 0.15) Superscript 5, or approximately $11,093

Step-by-step explanation:

A. 25,000 (1 minus 0.15) Superscript 5, or approximately $11,093

B. 25,000 minus 1500 (5), or approximately $17,500

C. 25,000 (0.15) Superscript 5, or approximately $18,984

D. 25,000 minus left-bracket (100 minus 15) (5) Right-bracket, or approximately $24,575

Value of the car = $25,000

Percentage decrease per year = 15%

Value after 5 years

Total percentage value of the car = 100%

Percentage value remaining each year = (100% - 15%)

= (1 - 0.15)

Decrease of the car in the next 5 years = $25,000(1 - 0.15)^5

= $25,000(0.85)^5

= $25,000(0.4437053125)

= $11,092.6328125

Approximately = $11.093

Value of the car in the next 5 years = $25,000 - $11,093

= $13,907

Answer:

It's A, $11,093

Step-by-step explanation:

Took the test on Edge

Answer:

it is not possible result is not given so it is not possible

Answer:

the first row in the table has x = -2 and f(x) = 1

therefore,

f(-2) = 1

f(x) = -2

when x = 4 as in 3rd row.

Answer:

slope is undefined

Step-by-step explanation:

Calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (6, 2) and (x₂, y₂ ) = (6, - 3)

m = [tex]\frac{-3-2}{6-6}[/tex] = [tex]\frac{-5}{0}[/tex]

Division by zero is undefined , then slope is undefined

Answer:

57%

Step-by-step explanation:

200+245+125 = 570

570/1000 = .57

Answer:

57%

Step-by-step explanation:

First find the total number of families in the sample.

Total = 350 + 200 + 245 + 125 + 66 + 10 + 4

Total = 1000

Next find the number of families that have 3, 4 or 5 people.

Total(3,4 or 5) = 200 + 245 + 125

Total(3,4 or 5) = 570

Now the % = (Total 3,4 or 5) / Total ) * 100

% = 570 / 1000 * 100

% = 57%

Answer:

Check your question one time

Answer:

(S-2πr^2)/ 2πr = h

Step-by-step explanation:

S = 2πrh + 2πr^2

Subtract 2 pi r^2 from each side

S-2πr^2  = 2πrh + 2πr^2 -2πr^2

S-2πr^2  = 2πrh

Divide each side by 2 pi r

(S-2πr^2)/ 2πr = 2πrh/2πr

(S-2πr^2)/ 2πr = h

It is given that,

→ S = 2πrh + 2πr²

Now subtract 2πr² from the both sides,

→ S - 2πr² = 2πrh + 2πr² - 2πr²

→ S - 2πr² = 2πrh

Then divide both sides by 2πr,

→ (S-2πr²)/2πr = 2πrh/2πr

→ (S-2πr²)/2πr = h

Hence, (S-2πr²)/2πr = h is the result.

Answer:

paper clips = $1.85

index cards = $3.95

Step-by-step explanation:

Mark

12 paper clips = x

10 index cards = y

$61.70 total

Janice

15 paper clips = x

7 index cards = y

$55.40 total

12x + 10y = 61.70

15x + 7y   = 55.40

*** you want to cancel out one of the letters

(12x + 10y = 61.70) * -7

(15x + 7y   = 55.40) * 10

-84x -70y = -431.9

150x + 70y = 554.0

150x + 70y = 554.0

-84x -70y = -431.9

66x + 0 = 122.1

66x = 122.1

x = 122.1 ÷ 66

x = 1.85

plug it back in

15(1.85) + 7y   = 55.40

27.75 + 7y   = 55.40

7y   = 55.40 - 27.75

7y = 27.65

y = 27.65 ÷ 7

y = 3.95

Answer:

let the number be a

product of a number and six = 6 times a=6a

three less than the product of a number= 6a-3

then the full equation will be 6a-3=27

Step-by-step explanation:

a, 1/4+2/5=13/20

b,-1/8+1=7/8

c, 4/25×-1/8=-1/50

d, 2×1/9-1/2=2/9-1/2=-5/18

e, 1+2/5-1/4=7/5-1/4=23/20

Answer:

5:6 lol

Step-by-step explanation:

Answer:

p = 11           q = 3

Step-by-step explanation:

      2p - 3q = 13

-      p - 3q = 2

p = 11

p - 3q = 2​

(11) - 3q = 2

-3q = -9

q = 3

Answer:

p=11 q=3

Step-by-step explanation:

subtract second from first

2p-3q=13

-p+3q=-2

p=11

plug in

11-3q=2

-3q=-9

q=3

Answer:

AG = 18

Step-by-step explanation:

The relationship of the segments created is one is 1/3 (shorter) and the other (longer) is 2/3 of the total length.

Lets make x represent AG.

So, 2/3 of x is 12

or

[tex]\frac{2}{3}[/tex]x = 12

Multiply both sides by the reciprocal of [tex]\frac{2}{3}[/tex] , which is [tex]\frac{3}{2}[/tex].

( [tex]\frac{3}{2}[/tex]) [tex]\frac{2}{3}[/tex]x = 12 ([tex]\frac{3}{2}[/tex])  (x is left alone, the fractions = 1 when multiplied)

x = 12 ([tex]\frac{3}{2}[/tex])         ( 12 times 3 = 36, divided by 2 = 18)    

x = 18

Perpendicular lines have negative reciprocal slopes.

This is just a fancy way of saying flip the fraction and change the sign.

So the slope of line c is 7/2.

Answer:

3% = 0.03 = [tex]\frac{3}{100}[/tex]

Answer: 3/100

Step-by-step explanation:

3%=0.03=3/100

Have a great day!!

Answer:

Step-by-step explanation:

Given:

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[tex]\sf{log_{5}}(\tt{10x-1})=\sf{log_{5}}(\tt{9x+7})\\\\10x-1=9x+7\\\\10x-9x=7+1\\\\\pmb{\green{\underline{\sf{x=\frak{8}}}}}[/tex] 

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