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3 years ago

Translate the English phrase into an algebraic expression, then evaluate the expression. Eight less than negative nineteen

Mathematics

1 answer:

bixtya [17]3 years ago

6 0

Translate:

“Eight less than negative nineteen.”

-19-8

Evaluate:

-19-8 = -27

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The length of a rectangular floor is twice its width. The floor is partially covered by a rectangular carpet whose length is the

r-ruslan [8.4K]

Answer:

Option C is correct.

Step-by-step explanation:

Let the length be L

Let the width be W

The length of a rectangular floor is twice its width.

So, we get $L=2W$

The length of the carpet is L

Carpet width is 2 feet less than the room, so $W=W-2$

Area of the carpet = 160 sq feet

We get :

$L(W-2)=160$

As L=2W, we get

$2W(W-2)=160$

=> $2W^{2} -4W=160$

Equating to zero, we have

$2W^{2} -4W-160=0$

Taking out 2 common

$W^{2} -2W-80=0$

=> $W^{2} -10W+8W-80=0$

=> $W(W-10)+8(W-10)=0$

We get roots as : (W-10) and (W+8)

Hence, W = 10 and W = -8(neglect this negative value)

Now, the width = 10 feet

Length = $2(10)=20$ feet

Hence, option C is the answer.

7 0

3 years ago

PLEASE HELP Identify the radius and center x^2 +y^2 -6x -2y + 1 = 0

Trava [24]

Answer:

The center is the point (3,1) and the radius is 3 units

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

$(x-h)^{2}+(y-k)^{2}=r^{2}$

we have

$x^{2}+y^{2}-6x-2y+1=0$

Convert to standard form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$(x^{2}-6x)+(y^{2}-2y)=-1$

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

$(x^{2}-6x+9)+(y^{2}-2y+1)=-1+9+1$

$(x^{2}-6x+9)+(y^{2}-2y+1)=9$

Rewrite as perfect squares

$(x-3)^{2}+(y-1)^{2}=9$

The center is the point (3,1) and the radius is 3 units

4 0

4 years ago

What the missing term is

arlik [135]

Answer:

10x . . . . . (Note the sign of the middle term is negative. 10x goes in the box.)

Step-by-step explanation:

The sum of the two roots is ...

... (5 -3i) +(5 +3i) = 10

In a quadratic with leading coefficient 1, the coefficient of the 1st-degree term is the opposite of the sum of the roots. Here, that means the middle term is -10x. The minus sign is given, so the answer is 10x.

_____

How Do We Know?

When "a" and "b" are roots of a quadratic in x, it has factors (x -a)(x -b). The product of those two factors is ...

... (x -a)(x -b) = x² -(a+b)x +ab

Here, that means the product of the factors (5 -3i)(5 +3i) is ab = 34, which it is. Their sum is (a+b) = 10, so the x-term is -(a+b)x = -10x.

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3 years ago

Find the value of x. (6x+8) (7x-7)

dimaraw [331]

Answer:95

Step-by-step explanation:

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3 years ago

Reduce the fraction to lowest terms m^2/m^2-n^2

Softa [21]

Answer:

$\boxed{\bold{\frac{m^2}{\left(m+n\right)\left(m-n\right)}}}$

Step-by-step explanation:

Factor $\bold{m^2-n^2}$

$\bold{\left(m+n\right)\left(m-n\right)}$

Rewrite Equation

$\bold{\frac{m^2}{\left(m+n\right)\left(m-n\right)}}$

4 0

4 years ago

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