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2 years ago

Can the area of a trapezoid be exactly twice the area of the triangle?

Mathematics

1 answer:

Dafna11 [192]2 years ago

5 0

Answer:

No. It has 2 congruent triangles, but they do not encompass the whole area.

Step-by-step explanation:

I would say no, because then it would be a rectangle, because there would be no angle on the sides.

A=1/2(b1+b2)*h

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Jenny and Kath hire the canal boat for 14 days. They share the hire cost of £1785.00 in the ratio 2:3. Work out the smaller shar

Dafna1 [17]

Answer:

£714.00

Step-by-step explanation:

The first step is to set up expresssions for the two shares:

Let x = the amount of one share. The other share is 1785 - x. You don't have to worry about which is smaller--that part will work out automatically!

The two shares are in the ratio of 2:3, so set up the proportion

$\frac{x}{1785-x}=\frac{2}{3}$

Again, you don't have to worry--you could set up the proportion "upside down" and everything will work out in the end.

Solve the proportion for x by "cross multiplying" -- use the Means-Extremes Property of proportions.

$(3)(x)=(2)(1785-x)\\3x=3570-2x\\5x=3570\\x=714$

So one share is £714£ and the other is £1785 - £714 = £1071.

The smaller share is £714.

5 0

2 years ago

What is the Y intercept pls help

Ad libitum [116K]

Answer:

y- intercept = 1

Step-by-step explanation:

The y- intercept is the point on the y- axis where the graph crosses.

This occurs when the x- coordinate is 0

From the table the point (0, 1 ) is where the graph crosses the y- axis

Then y- intercept = 1

5 0

2 years ago

A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the

Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0

2 years ago

Mr. Voelz estimates that he will spend $10 on concessions at the basketball game. He actually spends $15. What is the percent er

irina [24]

Answer:

I am not sure but if you divide those 2 numbers such as dividing 10 by 15 you will get 0.666666666667 but if you round it you will have 67%

Step-by-step explanation:

Plz mark Brainliest

5 0

2 years ago

What is the slope of the line represented by the equation y=- 5x? 0-5 or w/N wind 5

Alexandra [31]

Answer:

the slope would be -5

Step-by-step explanation:

in linear equations, the slope of the line is the coefficient of x

so in this case, it is -5

5 0

3 years ago