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3 years ago

Sally's cat is 3 years older than Helen's dog. The product of their ages is 54. How old is Helen's dog?

1 answer:

7 0

The first thing that we have to do is to assign variables to the cat's and the dog's ages. Let us use c to represent the age of the cat and d for the dog's age. So, let's translate the word problem into a mathematical one.

c = d + 3

This is the first equation while the second equation is

(d+3)*d = 54

which becomes

d^2 +3d -54 = 0

which can be factored into (d-6)(d+9). This gives us two roots which are 6 and -9. However, age is a non-negative number so we will take 6 as the age of Helen's dog. Thus, making Sally's cat 9 years old.

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A farmer has one square mile land . If he divides his land into square fields that are 1/4 mile long and 1/4 mile wide,how many

White raven [17]

A square field that is 1/4 mile long and 1/4 mile wide has area

$\dfrac{1}{4} \cdot \dfrac{1}{4} = \dfrac{1}{16}$

So, to know how many of these fields fit in the biggest field, you have to divide their areas:

$\dfrac{1}{\frac{1}{16}} = 16$

So, if the farmer divides his land into square fields that are 1/4 mile long and 1/4 mile wide, he will have 16 of these smaller fields.

8 0

3 years ago

Is this right pls...

Dmitry [639]

Yuppp, it is correct!

6 0

3 years ago

Read 2 more answers

Ughh i suck at dilation

Ivenika [448]

Look at!!:
Pre image A(3,4), B(1,5) C(6,6);
If you multiply these coordinates by 3/2, you get its images:

A(3,4) ⇒ A`(3*3/2, 4*3/2)=(4.5, 6)
B(1,5) ⇒B`(1.*3/2, 5*3/2)=(1.5, 7.5)
C(6,6) ⇒C`(6*3/2, 6*3/2)=(9,9)

Therefore the scale factor is 3/2.
When the scale factor of a dilation is >1, then we have an enlargement, an expansion.
In this case 3/2=1.5>1

Answer:

The dilation is expansion.
The scale factor is 3/2.

7 0

3 years ago

What is the value of minus 6 x cubed minus y squared minus 3 x y if if x = -2 and y = 4

Oksi-84 [34.3K]

Well, "minus 6 x cubed minus y squared minus 3 x y" translates to:

$-6x^{2} -y^{2} -3xy$

Then, if we insert the values for x and y, we get:

$-6(-2)^{2} -(4)^{2} -3(-2)(4)$

When we distribute and multiply:

$144-16-24$

And once we combine like terms:

104 is the answer

8 0

3 years ago

Read 2 more answers

1. If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter o

tester [92]

Answer:

Part 1) The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor (see the explanation)

Part 2) The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) The new figure and the original figure are not similar figures (see the explanation)

Step-by-step explanation:

Part 1) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its perimeters is equal to the scale factor

The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor

Part 2) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the area of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its areas is equal to the scale factor squared

The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) What would happen to the perimeter and area of a figure if the dimensions were changed NON-proportionally? For example, if the length of a rectangle was tripled, but the width did not change? Or if the length was tripled and the width was decreased by a factor of 1/4?

we know that

If the dimensions were changed NON-proportionally, then the ratio of the corresponding sides of the new figure and the original figure are not proportional

That means

The new figure and the original figure are not similar figures

therefore

Corresponding sides are not proportional and corresponding angles are not congruent

A) If the length of a rectangle was tripled, but the width did not change?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2W ----> P=6L+2W

The perimeter of the new figure is greater than the perimeter of the original figure but are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W) ----> A=3LW

The area of the new figure is three times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

B) If the length was tripled and the width was decreased by a factor of 1/4?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2(W/4) ----> P=6L+W/2

The perimeter of the new figure and the perimeter of the original figure are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W/4) ----> A=(3/4)LW

The area of the new figure is three-fourth times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

5 0

3 years ago