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2 years ago

Adding and subtracting unlike fractions in word functions

Mathematics

1 answer:

UkoKoshka [18]2 years ago

8 0

Answer:

3/8 tablespoons

Step-by-step explanation:

When we add fractions, we have to make each fraction a common denominator.

So we get 1/4 into 2/8 and we have 1/8

So we add and get 3/8

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A rectangle with an area of 4/7 m2 is dilated by a factor of 7. What is the area of the dilated rectangle

tatyana61 [14]

according to the picture we have:

x.y=4.7

(7)x(7)y=49xy=(49)(4.7)=230.3

6 0

3 years ago

How do you describe the solution set to a system of linear inequalities?

Tatiana [17]

Answer:

How do you describe the solution set to a system of linear inequalities?

Step-by-step explanation:

The solutions of a system of linear inequalities are all the ordered pairs that make all the inequalities in the system true.

6 0

1 year ago

Michael consumes a 16-ounce bag of potato chips and 12-ounce bag of pretzels every day after school. How many more ounces of pot

Paladinen [302]

Every day, Michael consumes 4 more ounces than the pretzels. Multiply 5 by 4 to recieve the answer:

4 x 5 = 20

So the answer is A.

7 0

1 year ago

Read 2 more answers

A container in the shape of this cuboid holds 2 litres of water.

zysi [14]

Given:

Volume of cuboid container = 2 litres

The container has a square base.

Its height is double the length of each edge on its base.

To find:

The height of the container.

Solution:

We know that,

1 litre = 1000 cubic cm

2 litre = 2000 cubic cm

Let x be the length of each edge on its base. Then the height of the container is:

$h=2x$

The volume of a cuboid is:

$V=l\times w\times h$

Where, l is length, w is width and h is height.

Putting $V=2000,\ l=x,\ w=x,\ h=2x$ , we get

$2000=x\times x\times 2x$

$2000=2x^3$

Divide both sides by 2.

$1000=x^3$

Taking cube root on both sides.

$\sqrt[3]{1000}=x$

$10=x$

Now, the height of the container is:

$h=2x$

$h=2(10)$

$h=20$

Therefore, the height of the container is 20 cm.

8 0

2 years ago

1.) Find the length of the arc of the graph x^4 = y^6 from x = 1 to x = 8.

xxTIMURxx [149]

First, rewrite the equation so that y is a function of x :

$x^4 = y^6 \implies \left(x^4\right)^{1/6} = \left(y^6\right)^{1/6} \implies x^{4/6} = y^{6/6} \implies y = x^{2/3}$

(If you were to plot the actual curve, you would have both $y=x^{2/3}$ and $y=-x^{2/3}$ , but one curve is a reflection of the other, so the arc length for 1 ≤ x ≤ 8 would be the same on both curves. It doesn't matter which "half-curve" you choose to work with.)

The arc length is then given by the definite integral,

$\displaystyle \int_1^8 \sqrt{1 + \left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx$

We have

$y = x^{2/3} \implies \dfrac{\mathrm dy}{\mathrm dx} = \dfrac23x^{-1/3} \implies \left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2 = \dfrac49x^{-2/3}$

Then in the integral,

$\displaystyle \int_1^8 \sqrt{1 + \frac49x^{-2/3}}\,\mathrm dx = \int_1^8 \sqrt{\frac49x^{-2/3}}\sqrt{\frac94x^{2/3}+1}\,\mathrm dx = \int_1^8 \frac23x^{-1/3} \sqrt{\frac94x^{2/3}+1}\,\mathrm dx$

Substitute

$u = \dfrac94x^{2/3}+1 \text{ and } \mathrm du = \dfrac{18}{12}x^{-1/3}\,\mathrm dx = \dfrac32x^{-1/3}\,\mathrm dx$

This transforms the integral to

$\displaystyle \frac49 \int_{13/4}^{10} \sqrt{u}\,\mathrm du$

and computing it is trivial:

$\displaystyle \frac49 \int_{13/4}^{10} u^{1/2} \,\mathrm du = \frac49\cdot\frac23 u^{3/2}\bigg|_{13/4}^{10} = \frac8{27} \left(10^{3/2} - \left(\frac{13}4\right)^{3/2}\right)$

We can simplify this further to

$\displaystyle \frac8{27} \left(10\sqrt{10} - \frac{13\sqrt{13}}8\right) = \boxed{\frac{80\sqrt{10}-13\sqrt{13}}{27}}$

7 0

2 years ago