If 7 liters of petrol cost $14.70, calculate the cost of 15 liters of petrol.​

Answer:

3(x + 4)

Step-by-step explanation:

Factor out a 3 from both terms, since 3 and 12 are both divisible by 3.

3x + 12

3(x + 4)

So, the factored expression is 3(x + 4)

Answer: 3(x+4)

Step-by-step explanation:

Hii! Do you need to factor the expression 3x+12? No problem! :)

Note that, both 3x and 12 have something in common. This "something" is known as the greatest common factor, or g.c.f.

The g.c.f. of 3x and 12 is 3, so we divide both 3x and 12 by 3

x+4; next we put parentheses around x+4.

(x+4)

Now  we put 3 outside the parentheses.

3(x+4)

Voila! There's our solution, cheers!

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Hope that this helped! Best wishes.

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Answer:

Answers in the pic

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask =)

Answer:

For every  7  small prizes won, there were  3  large prizes won.

ratio : 42:18 or 7:3

As 42/18  is the same as 7/3  For every 7 small prizes won, there were 3 large prizes won.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, At a certain game at a school carnival, people won 42 small prizes and 18 large prizes.

Now, 42/18 = 21/9 = 7/3.

∴  For every 7 small prizes won, there were 3 large prizes won.

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Complete Question:

A ball is kicked with an initial height of 0.75 meters and initial upward velocity of 22 meters/second. This inequality represents the time, t in

seconds, when the ball's height is greater than 10 meters.

-4.9t² + 22t + 0.75 > 10

The ball's height is greater than 10 meters when t is approximately between __ and __ seconds

Answer:

The ball's height is greater than 10 meters when t is approximately between 0.47 and 4.02 seconds

Step-by-step explanation:

Given

[tex]-4.9t\² + 22t + 0.75 > 10[/tex]

Required

Solve the inequality

[tex]-4.9t\² + 22t + 0.75 > 10[/tex]

Subtract 10 from both sides

[tex]-4.9t\² + 22t + 0.75 - 10> 10 - 10[/tex]

[tex]-4.9t\² + 22t + -9.25> 0[/tex]

Solve using quadratic formula

[tex]t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

In this case;

a = -4.9; b = 22; c = -9.25

[tex]t = \frac{-22 \± \sqrt{22^2 - 4 * (-4.9) * (-9.25)}}{2 * -4.9}[/tex]

[tex]t = \frac{-22 \± \sqrt{484 - 181.3}}{-9.8}[/tex]

[tex]t = \frac{22 \± \sqrt{484 - 181.3}}{9.8}[/tex]

[tex]t = \frac{22 \± \sqrt{302.7}}{9.8}[/tex]

[tex]t = \frac{22 \± 17.398}{9.8}[/tex]

Split

[tex]t = \frac{22 + 17.398}{9.8}[/tex]    or      [tex]t = \frac{22 - 17.398}{9.8}[/tex]

[tex]t = \frac{39.398}{9.8}[/tex]   or     [tex]t = \frac{4.602}{9.8}[/tex]

[tex]t = 4.02[/tex] or  [tex]t = 0.47[/tex]

Convert to inequality;

[tex]0.47 < t < 4.02[/tex]

Hence;

The ball's height is greater than 10 meters when t is approximately between 0.47 and 4.02 seconds

Answer:

0.47 and 4.02

Step-by-step explanation:

Edmentum/Plato

Answer:

x=6

Step-by-step explanation:

Answer: x=6

Explanation:

1. Add:     15+25=40

2.Subtract 4 from each side:   40=4+6x

3.Divide by 6:   36=6x

4. x=6

Answer:

A single sheet of paper should weigh: 0.00645 pound or  [tex]6.45*10^{-3}[/tex] (in scientific notation)

Step-by-step explanation:

Divide 3.225 (the weight of the ream of paper) by 500 (the amount of paper in a ream).

If you need the scientific notation form, simply move the decimal point/place right or left until you end up with a whole number that is between 1 and 10 (in this case, 3 times to the right), then determine what power of 10 it should be, depending on the number of times you moved the decimal place (in this case, the power is -3).

The power/exponent is determined by the direction you have to move your decimal point, right=negative and left=positive. For example, if you started off with the number 6450, you would move the decimal point 3 times to the left and your power would be positive 3, which results in [tex]6.45*10^{3}[/tex].

Hope this helps!

Answer:

(-6,7) (2,8) (-4,3)

Step-by-step explanation:

Answer:

The first one

Step-by-step explanation:

According to definition of proportion, the correct statement is,

⇒ AC / BC = DF / EF

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

⇒ Δ ABC ≅ Δ EFD

Now,

Since, We have;

⇒ Δ ABC ≅ Δ EFD,

Hence, By definition of congruency, the ratio of there corresponding sides are equal.

So, We get;

⇒ AC / BC = DF / EF

Thus, ''Option 3'' is true.

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Answer:

4u - 24

Step-by-step explanation:

(u-6)*4

Distribute

4*u - 4*6

4u - 24

Answer:

408 quarts

Step-by-step explanation:

Answer:

Its irrational because pi is a repeating number with no pattern.

UwU hope this helps

Slope formula: y2-y1/x2-x1

Part one:

-7-4/-7-(-7)

-11/0

Since the denominator is 0, the slope is undefined.

Part two:

-9-(-9)/2-(-5)

0/7

Since the numerator is 0, the slope is 0.

Best of Luck!

Problem 1

Use the slope formula to get

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

m = (-7 - 4)/(-7 - (-7))

m = (-7 - 4)/(-7 + 7)

m = -11/0

The result is undefined as we cannot divide by zero.

This line is vertical and all vertical lines have undefined slopes. This happens when both points have the same x coordinate.

=========================================================

Problem 2

Use the slope formula again, just with different values of course

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

m = (-9 - (-9))/(2 - (-5))

m = (-9 + 9)/(2 + 5)

m = 0/7

m = 0

In contrast to the previous problem, we can have 0 in the numerator. Dividing 0 over any nonzero value leads to 0.

This line is horizontal as both y coordinates are the same value. All horizontal lines have a slope of 0. You can think of it like

slope = rise/run = 0/1

rise = 0 means we don't move up or down

run = 1 means we move to the right 1 unit

Answer:

The answer is 573 this is correct

Answer:

wHOLE number

Step-by-step explanation:

IT is a whole number

Answer:

23/99

Step-by-step explanation:

0.23 is x.

Because x is recurring in two decimal places, we will multiply it by 100.

100x=23.23

Then we subtract.

100x-x=23.23-0.23

99x=23

x=23/99

Answer:

the answer is 27

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

when you add 5.1 and 7.7 together it would be 12.8 but you have to move the decimal to the left again since it has more than one number to the left then the ^5 would turn into ^6 and 1.28x10^6 is 1,280,000 and the other is only 1,000,000

Answer:

D

Step-by-step explanation:

Answer:

a) on the way there, the speed = 50 m/hr

b) on the way back home, speed = 30 m/hr

Step-by-step explanation:

[tex]speed (s) = \frac{distance(d)}{time(t)} \\distance = speed\ \times\ time[/tex]

on the way to Disney land:

distance = d

speed = s

time = t = 6 hours

d = s × t

d = s × 6

d = 6s - - - - - (1)

On the way back:

speed decreased by 20m/hr

This means that s₂ = (s - 20)m/hr

time = t₂ = 10 hours

∴ d = s₂ × t₂

d = (s - 20) × 10

d = 10s - 200  - - - - (2)

Note that the distance is the same to and from disney land, therefore, equation (1) equals equation (2)

∴ 6s = 10s - 200

collecting like terms:

10s - 6s = 200

4s = 200

∴ s = 200 ÷ 4

s = 50 m/hr

Therefore on the way there, the car was moving at a apeed of 50m/hr

speed on the way back home (s₂) = (s - 20) m/hr

∴ s₂ = 50 - 20

s₂ = 30 m/hr

Therefore on the way back home the speed was 30 m/hr

Answer:

Step-by-step explanation:

Answer:

it is x=-4

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Step-by-step explanation:

Given the expression sec²34°−tan²34°, to get the exact value using the fundamental identities​ and/or the complementary angle theorem, we will apply the trigonometry identity

From sin²θ+cos²θ = 1

Divide both sides of the expression by cos²θ

sin²θ/cos²θ+cos²θ/cos²θ = 1/cos²θ

tan²θ+1 =sec²θ

Since sec²θ= tan²θ+1, hence  sec²34°= tan²34°+1... 1

Substituting equation 1 into the expression given in question we will have;

sec²34°−tan²34°

=  (tan²34°+1)-tan²34°

collect like terms

= tan²34°-tan²34°+1

= 1

Hence the exact value of the expression sec²34°−tan²34° is 1

Answer:

We use negative values for the money Arleen spends.

a) We determine the change to the value on her gift card:

4(-35)+(-9)= -140+(-9)=-149

b) We determine the amount on money she has left on the gift card after renting the tiller and buying the rake:

200+(-149)=51

Since she has got $51 on her gift card and a wheelbarrow is $50 she is able to buy it:

51>50

RESULT

a) -$149 less b) yes

Step-by-step explanation:

Answer: 7

Step-by-step explanation:

2−(−4)+3+(−6)−(−2)2

solution:

– x – = +

– x + = –

= 2−(−4)+3+(−6)−(−2)2

= 6 + 3 + ( – 6) – ( 2 ) 2

= 9 + ( –6 ) – ( –2 ) 2

= 3 – (–2)2

= 3 – ( –4 )

= 7

To solve any expression the BODMAS priority rule is applicable. Thus, the solution of the expression is 7.

The given expression is [tex]2-(-4)+3+(-6)-(-2)2[/tex]

Apply the BODMAS priority rule to the above expression.

To set the priorities of mathematical operations, the BODMAS is applied. BODMAS rule can be explained below:

  B stands for brackets.

  O stands for of, and or terms.

  D stands for divide.

  M for multiply.

  A for addition.

  S for subtraction.

Therefore, apply the BODMAS and solve the expression further.

[tex]\begin{aligned}2-(-4)+3+(-6)-(-2)2&=2-(-4)+3+(-6)-(-4)\\&=2+4+3-6+4\\&=7\end{aligned}[/tex]

Thus, the solution of the expression is 7.

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Answer:

(9+2)d

Step-by-step explanation:

The sum of 9+2

Times the variable, d

Answer: Approximately 1336.50301206033 square cm

=======================================================

Explanation:

If we know the three side lengths of a triangle, then we can use Heron's formula to get the area

Heron's formula is

[tex]A = \sqrt{S(S-a)(S-b)(S-c)[/tex]

with S being the semiperimeter, or half the perimeter, so [tex]S = \frac{a+b+c}{2}[/tex]. We add up all three sides and divide by 2.

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

The smaller triangle has side lengths of a = 19, b = 40, c = 41. So we get a semiperimeter of S = (a+b+c)/2 = (19+40+41)/2 = 50

Plug this along with the a,b,c values to get an area of...

[tex]A = \sqrt{S(S-a)(S-b)(S-c)}\\\\A = \sqrt{50(50-19)(50-40)(50-41)}\\\\A = \sqrt{139500}\\\\A \approx 373.496987939661\\\\[/tex]

which is approximate

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

Do the same for the larger triangle as well

S = (a+b+c)/2 = (19+180+181)/2 = 190

[tex]A = \sqrt{S(S-a)(S-b)(S-c)}\\\\A = \sqrt{190(190-19)(190-180)(190-181)}\\\\A = \sqrt{2924100}\\\\A = 1710\\\\[/tex]

Interestingly enough, we get an exact area value this time as opposed to some approximation.

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

The difference between the two results is the area of the shaded region

1710 - 373.496987939661 = 1336.50301206033

This is approximate since the first result was approximate.

Answer:

K = 1710 cm^2  - K = 373.497 cm^2  = 1337 cm^2

Step-by-step explanation:

Why don't you just look for the whole area and deduct the non-shaded area?

Total

Sides:

a = 180 cm

b = 181 cm

c = 19 cm

Angles:

A = 83.9744 °

B = 90 °

C = 6.02558 °

Other:

P = 380 cm

s = 190 cm

K = 1710 cm^2

r = 9 cm

R = 90.5 cm

________________________

Non shaded area:

Answer:

Sides:

a = 40 cm

b = 41 cm

c = 19 cm

Angles:

A = 73.519 °

B = 79.3849 °

C = 27.0961 °

Other:

P = 100 cm

s = 50 cm

K = 373.497 cm^2

r = 7.46994 cm

R = 20.8569 cm

where:

A = angle A

B = angle B

C = angle C

a = side a

b = side b

c = side c

P = perimeter

s = semi-perimeter

K = area

r = radius of inscribed circle

R = radius of circumscribed circle

Answer:

inductive

Step-by-step explanation:

Inductive reasoning is based on generalization, and making conclusions without hard evidence. If Micheal has red hair and is from Chicago, inductive reasoning draws the conclusion that everyone in Chicago has red hair. Deductive reasoning would be predicting that everyone in Chicago has red hair, and then testing it to see if you are right.

Answer:

(-6,14)

Step-by-step explanation:

We are given one endpoint and the midpoint, so we have to figure out how far apart these two points are:

(4,12) and (-1,13)

First, we take the x values because these two points are using the (x,y) pattern.

How far away are 4 and -1? The answer is 5.

How far away are 12 and 13? Only 1

If we start at the endpoint (4,12) and go to the midpoint at (-1,13), we go 5 to the left. That means we need to go 5 more spaces to the left to get to the other endpoint. The first part of our answer is -6, which is 5 to the left of -1.

Doing the same thing for the y values now, to get from 12 to 13 we go up 1. So we have to go up one more to find the y value of the other endpoint. If you are at 13 and you go up one, you are at 14.

Answer:

3·2 - 3·b = 6 - 3b

Step-by-step explanation:

You "distribute" the 3 over the 2 and the -b.