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3 years ago

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A catalog is discounting all sweaters 25%. How much will you pay for a sweater that is regularly $49.99? (A) $24.99 (B) $37.49 (

C) $124.98 (D) $49.74

1 answer:

rodikova [14]3 years ago

6 0

B becuase of 49.99 times .75

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I have 2 seperate pairs of = sides l. My equal sides are next to each other. My four sides cannot be equal. What am I?

coldgirl [10]

If by next to you mean across from, it could be a parallelogram.

8 0

3 years ago

Please help solve for x..

aalyn [17]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

$x^{100}-4^x \cdot x^{98}-x^2+4^x=0$

Factor out -1:

$\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0$

Divide both sides by -1:

$\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0$

Rearrange the terms:

$\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:$

$\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0$

Factor the first two terms and the last two terms separately:

$\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0$

Factor out the common term $(x^{98}-1)$ :

$\implies (4^x-x^2)(x^{98}-1)=0$

<u>Zero Product Property</u>: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the <u>Zero Product Property</u>, set each factor equal to zero and solve for x (if possible):

$\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}$

Therefore, the solutions to the given equation are: x = 1 or x = -1

Learn more here:

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3 0

1 year ago

Joe and grace are baking cookies.they need a total of 2 cups of sugar for the recipe. Joe has 11/10 cups of sugar and grace has3

labwork [276]

No, Joe and Grace don’t have enough together because 11/10 is only 1.1 and 3/4 is .75 and u add that together u get 1.85 which is less 2.

Grace needs 12 cups of sugar to make the cookies because 1 cups of sugar makes 6 cookies and each person is getting 3 that’s only enough for 2 people , so multiple every by 12 to get 24 people, 12 cups of sugar, and 72 cookies .

6 0

3 years ago

Solve the following system of equations for all three variables.

xz_007 [3.2K]

Answer:

Step-by-step explanation:

-2x + 3y – 4z = 8 ----------------(I)

5x – 3y + 5z = -8 -----------------(II)

7x – 3y + 3z = 8 ------------------(III)

Add equation (I) & (II) and thus y will be eliminated

(I) -2x + 3y – 4z = 8

(II) <u>5x – 3y + 5z = -8</u> {Add}

3x + z = 0 ------------------------(A)

Multiply equation (II) by (-1) and then add with equation (III). Thus y will be eliminated.

(II) * (-1) -5x + 3y - 5z = +8

<u>7x – 3y + 3z = 8</u> {Add}

2x -2z = 16 ---------------(B)

Multiply equation (A) by 2 and then add. Thus z will be eliminated and we will get the value of x

(A) * 2 6x + 2z = 0

(B) <u>2x - 2z = 16</u> {Add}

8x = 16

Divide both sides by 8

x = 16/8

x = 2

Plugin x = 2 in equation (A)

3x + z = 0

3*2 + z = 0

6 + z = 0

z = -6

Plug in x = 2 and z = - 6 in equation (I)

-2x +3y - 4z = 8

-2*2 + 3y - 4*(-6) = 8

-4 + 3y + 24 = 8

3y + 20 = 8

3y = 8 - 20

3y = -12

y = -12/3

y = -4

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7 0

3 years ago

Read 2 more answers

Simplify:2 1/3(4 1/4÷2)

kondor19780726 [428]

Answer:

$4\frac{23}{24}$

Step-by-step explanation:

We want to simplify:

$2\frac{1}{3}(4\frac{1}{4}\div 2)$

We convert to improper fraction to get:

$\frac{7}{3}(\frac{17}{4}\div 2)$

We now deal with the parenthesis by multiplying with the reciprocal of 2.

$\frac{7}{3}(\frac{17}{4}\times \frac{1}{2} )$

This gives:

$\frac{7}{3}(\frac{17}{8})$

We multiply to get:

$\frac{7}{3}(\frac{17}{8})$

This simplfies to:

$\frac{119}{24}$

We write as mixed number

$4\frac{23}{24}$

4 0

3 years ago