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EleoNora [17]
2 years ago
10

Teresa is maintaining a campfire.She has kept the fire steadily burning for 4 hours using 6 logs. The number of logs needed to k

eep the fire burning is proportional to the number of hours it burns. She wants to know how many logs she needs to keep the fire burning for 18 hours.
Select the equationis Teresa can use to determine the number of logs she needs, x, to maintain the fire for 18 hours.

A. x/6 = 4/18
B. x/6 = 18/4
C. x/18 = 6/4
D. x/4 = 18/6
E. 4/6 = 18/x
Mathematics
1 answer:
Alexeev081 [22]2 years ago
4 0

Answer:

E. 4/6 = 18/x

Step-by-step explanation:

4 hour using 6 logs

18 hours using x logs

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A health food store sells a mixture of raisins and roasted nuts.
murzikaleks [220]

Answer:

Raisins = 25 kg

Nuts = 15 kg

Step-by-step explanation:

Given that:

Kilograms of snack to be made = 40 kg

Price per kg would be $4.75kg.

Price of 40 kg would be = 4.75 * 40 = $190

Let,

x be the kilograms of raisins

y be the kilograms of nuts

According to given statement;

x+y=40        Eqn 1

4.00x+6.00y=190      Eqn 2

Multiplying Eqn 1 by 4

4(x+y=40)

4x+4y=160    Eqn 3

Subtracting Eqn 3 from Eqn 2

(4x+6y)-(4x+4y)=190-160

4x+6y-4x-4y=30

2y=30

Dividing both sides by 2

\frac{2y}{2}=\frac{30}{2}\\y=15

Putting y=15 in Eqn 1

x+15=40

x=40-15

x=25

Hence,

Raisins = 25 kg

Nuts = 15 kg

8 0
2 years ago
Read 2 more answers
I Really need help! I don’t understand this! Will give 100 points!
JulsSmile [24]

Answer:

All pair COMBINATION are supplementary (Opposite)

Step-by-step explanation:

According to theorem about inscribed quadrilateral

  • The opposite interior angles of an inscribed quadrilateral are supplementary .
  • I.e there sum is equal to 180°

<O+<Q=180

<P+<R=180

7 0
2 years ago
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Enter the trigonometric equation you would use to solve for x in the following right triangle. Do not solve the equation.
USPshnik [31]

Answer:

x = sine 70° / 8

Step-by-step explanation:

6 0
3 years ago
• a helicopter hovering at 10 m above the ground is shining a spotlight at a person 30 m away1 . if the person is 2 m tall how l
pshichka [43]

As shown in the figure

Height of helicopter above the ground=30 m

Distance from the base to the point where the person is standing=30 m

height of the person=2 m

Now the person cast the shadow of length x m.

Triangle ABC and triangle EDC are similar.

∵ ∠B= ∠D=90°

∠C is common.

So by AA similarity ΔABC and ΔEDC are similar.

As we know when triangles are similar their sides are proportional.

AB/AD =BC/DC

Let DC=x meter

⇒\frac{10}{x}=\frac{30+x}{x}

⇒5=\frac{30+x}{x}[/tex]

⇒5x=30+x

⇒4x = 30

⇒ x=30/4

⇒ x=7.5 meter

So length of shadow=7.5 meter

2. volume of a sphere of radius r is v (r) =\frac{4}{3}π r^{3}

\frac{\mathrm{d} }{\mathrm{d} r}V=4/3π×3r^2

       =4πr^2


surface area of a sphere of radius r is 4πr^2

b)  Ratio of derivative of volume of sphere to surface area of sphere=\frac{4\pi r^2}{4\pi r^2}

             =1  [ incomplete question but you have written few words ]

4 0
3 years ago
In 1-5, given: Two similar cylinders with heights of 8 and 5 respectively.
lana66690 [7]

Answer:

1. The ratio of their diameters is 8/5 = 8 : 5

2. The ratio of their surface area is (8/5)²

3. The ratio of their volume is (8/5)³

4.The area of the base of the larger cylinder is 128 cm²

Step-by-step explanation:

Given that the two cylinders are similar, we have;

Two cylinders are similar when the ratio of their heights is equal to the ratio of their radii

Therefore, we have;

1. The ratio of the height of the two cylinders = 8/5 = The radio of their radii = r₁/r₂

The ratio of their diameter = D₁/D₂ = 2·r₁/2·r₂ = r₁/r₂ = 8/5

The ratio of their diameters D₁/D₂ = 8/5 = 8 : 5

2. The surface area of the cylinders = 2·π·r·h + 2·π·r²

Therefore, we have;

(2·π·r₁·h₁ + 2·π·r₁²)/(2·π·r₂·h₂ + 2·π·r₂²) = (r₁·h₁ + r₁²)/(r₂·h₂ + r₂²)

h₁ = h₂ × 8/5

r₁ = r₂ × 8/5

= (8/5)²(r₂·h₂ + r₂²)/(r₂·h₂ + r₂²)  = (8/5)²

The ratio of their surface area = (8/5)²

3. The volume of the cylinder = π·r²·h

∴ The ratio of the volume = (π·r₁²·h₁)/(π·r₂²·h₂) = (8/5)³ × (π·r₂²·h₂)/(π·r₂²·h₂) = (8/5)³

The ratio of their volume = (8/5)³

4. The ratio of the area of the base of the larger cylinder to the area of the base of the smaller cylinder is (8/5)²

Therefore if the area of the base of the smaller cylinder is 50 cm², the area of the base of the larger cylinder = 50 cm² × (8/5)²  = 128 cm²

7 0
3 years ago
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