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3 years ago

A triangle has side lengths of 5 inches, 8 inches, and 9 inches. What are possible side lengths of a similar triangle?

1 answer:

3 0

The answer is A: 30 in, 48 in, and 54 in.

Explanation:
If you multiply all of the sides by 6 you get answer. 5 * 6 = 30, 8 * 6 = 48, and
9 * 6 = 54.

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According to the properties of inequality, when should the inequality symbol be reversed when solving a two-step any quality in

Marina86 [1]

According to the properties of inequality, we reverse the inequality symbol when we add or multiply by any negative number

Given inequality is Ax + B > C

In the first step, we subtract B from both sides

Ax + B > C

Ax + B - B > C - B

Ax > C - B

Now to remove A we divide by A on both sides

If A is negative then the reverse the inequality sign

When A is negative then > symbol becomes < symbol

so the inequality symbol be reversed when the value of A is negative

3 0

3 years ago

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A mother has two children whose ages differ by 5 years. The sum of the squares of their ages is 97. The square of the mother's

svetoff [14.1K]

Answer:

41 years old.

Step-by-step explanation:

Let x represent age of younger child.

We have been given that a mother has two children whose ages differ by 5 years. So the age of older child would be $x+5$ .

The sum of the squares of their ages is 97. We can represent this information in an equation as:

$x^2+(x+5)^2=97$

Let us solve for x.

$x^2+x^2+10x+25=97$

$2x^2+10x+25-97=0$

$2x^2+10x-72=0$

Divide both sides by 2:

$x^2+5x-36=0$

$x^2+9x-4x-36=0$

$x(x+9)-4(x+9)=0$

$(x+9)(x-4)=0$

$(x+9)=0 ; (x-4)=0$

$x=-9 ; x=4$

Since age cannot be negative, therefore, age of younger child is 4 years.

Age of older child would be $x+5\Rightarrow4+5=9$

Therefore, the age of older child would be 9 years.

We have been given that the square of the mother's age can be found by writing the squares of the children's ages one after the other as a four-digit number.

Square of 4: $4^2=16$

Square of 9: $9^2=81$ .

Square of mother's age: $1681$

To find mother's age, we need to take positive square root of 1681 as:

$\sqrt{1681}=41$

Therefore, the mother is 41 years old.

4 0

3 years ago

What is the simplest form of the expression? 3sqrt(24a^10b^6)?

Anastasy [175]

Answer:

$\text{The simplest form is }6\sqrt6a^5b^3$

Step-by-step explanation:

Given the expression $3sqrt(24a^{10}b^6)$ .

we have to find the simplest form of the expression.

$3sqrt(24a^{10}b^6)$

= $3(24^{\frac{1}{2}}a^{\frac{10}{2}}b^{\frac{6}{2}})$

= $3(24^{\frac{1}{2}}a^5b^3)$

= $6\sqrt6a^5b^3$

which is the simplest form of the given expression.

8 0

3 years ago

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a square flower garden in Samantha's backyard has an area of 100 square feet how much fencing will she need to enclose the flowe

Arlecino [84]

If Samantha's backyard has an area of 100 square feet, and you need to know how much fencing to enclose the garden, you know you are looking for the parameter of the garden. To fine the parameter you have to know the length of the sides. Area of a square is length times width and length and width are the same value. So what you know the square-root of 100 is the value of each side. So each side of the garden is 10 feet long. To find parameter all you do is add up all four sides. 10+10+10+10 = 40 feet need to enclose the flower garden.<span />

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3 years ago

A farmer takes 8 days to cultivate a plot of land i ha in area. What area

Kaylis [27]

More information is needed

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3 years ago

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