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3 years ago

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Which of the following are solutions to | x-1|= 5x + 2 ? Check all that apply.

1 answer:

agasfer [191]3 years ago

4 0

By definition of absolute value, if $x-1\ge0$ , then $|x-1|=x-1$ , so

$|x-1|=5x+2\implies x-1=5x+2\implies4x=-3\implies x=-\dfrac34$

On the other hand, if $x-1$ , then $|x-1|=-(x-1)=1-x$ , and

$|x-1|=5x+2\implies1-x=5x+2\implies6x=-1\implies x=-\dfrac16$

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Factor using a GCF:<br> 16xy2+28xy+8y

Lorico [155]

Answer:

4y( 4xy + 7x +2)

Step-by-step explanation:

16xy^2+28xy+8y

16xy^2 =2*2*2*2*x*y*y

28xy = 2*2*7 *x*y

8y = 2*2*2*y

The common factors are 2*2*y = 4y

2*2*2*2*x*y*y + 2*2*7 *x*y+2*2*2*y

2*2*y( 2*2*x*y + 7 *x+2)

4y( 4xy + 7x +2)

7 0

3 years ago

a box holds nine smaller boxes. each of the smaller boxes holds nine plastic containers. each plastic contai.er holds nine bags.

svp [43]

So, basically ..you just multiply
9*9*9*9
6561

4 0

4 years ago

In a trivia game, you lose points for incorrect answer. You answer the first 3 questions wrongs. Your score after the 3 question

Ksivusya [100]

Each incorrect answer is 25 points

5 0

3 years ago

What is the perimeter of the triangle shown on the coordinate plane,to the nearest tenth of a unit ?

ollegr [7]

Answer:

25.6 units

Step-by-step explanation:

From the figure we can infer that our triangle has vertices A = (-5, 4), B = (1, 4), and C = (3, -4).

First thing we are doing is find the lengths of AB, BC, and AC using the distance formula:

$d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}}$

where

$(x_1,y_1)$ are the coordinates of the first point

$(x_2,y_2)$ are the coordinates of the second point

- For AB:

$d=\sqrt{[1-(-5)]^{2}+(4-4)^2}$

$d=\sqrt{(1+5)^{2}+(0)^2}$

$d=\sqrt{(6)^{2}}$

$d=6$

- For BC:

$d=\sqrt{(3-1)^{2} +(-4-4)^{2}}$

$d=\sqrt{(2)^{2} +(-8)^{2}}$

$d=\sqrt{4+64}$

$d=\sqrt{68}$

$d=8.24$

- For AC:

$d=\sqrt{[3-(-5)]^{2} +(-4-4)^{2}}$

$d=\sqrt{(3+5)^{2} +(-8)^{2}}$

$d=\sqrt{(8)^{2} +64}$

$d=\sqrt{64+64}$

$d=\sqrt{128}$

$d=11.31$

Next, now that we have our lengths, we can add them to find the perimeter of our triangle:

$p=AB+BC+AC$

$p=6+8.24+11.31$

$p=25.55$

$p=25.6$

We can conclude that the perimeter of the triangle shown in the figure is 25.6 units.

6 0

3 years ago

Vince has a rectangular rug in his room with an area of 10 ft the length of the rug is 18 inches longer than the width what coul

aev [14]

The length of the rug is 4 ft.

The width of the rug is 2.5 ft.

Explanation:

The area of the rug is 10 ft.

The length of the rug be l.

Let us convert the inches to feet.

Thus, $18 inches = 1.5 ft$

Thus, the length of the rug is $l=1.5+w$

Let the width of the rug be w.

Substituting these values in the formula of area of the rectangle, we get,

$A=length\times width$

$10=(1.5+w)(w)\\10=1.5w+w^2\\w^2+1.5w-10=0$

Solving the expression using the quadratic formula,

$w=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Substituting the values, we have,

$$w=\frac{-15 \pm \sqrt{15^{2}-4 \cdot 10(-100)}}{2 \cdot 10}\\$

$w=\frac{-15 \pm \sqrt{4225}}{20}$

$w=\frac{-15 \pm 65}{2 0}$

Thus,

$w=\frac{-15 + 65}{2 0}\\w=\frac{50}{20} \\w=2.5$ and $w=\frac{-15 - 65}{2 0}\\w=\frac{-80}{20} \\w=-4$

Since, the value of w cannot be negative, the value of w is 2.5ft

Thus, the width of the rug is 2.5ft

Substituting $w=2.5$ in $l=1.5+w$ , we get,

$l=1.5+2.5\\l=4$

Thus, the length of the rug is 4 ft.

4 0

3 years ago