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2 years ago

What is the range and domain of: y= 4|x|-1

1 answer:

5 0

Function: y = 4|x| - 1.

Domain: R (all real numbers).

Range: As we know, the absolute value of x is always a non-negative number:

|x| >= 0

4|x| >= 4 * 0

4|x| >= 0

4|x| - 1 >= -1

y >= -1 <----- this is the range

I hope this helps. =)

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Describe 2 ways you could evaluate 37% of the sum of 27 3/5 and 15/9

miskamm [114]

First way is create an equation like this:
$0.37(27 \frac{3}{5}+ \frac{15}{9})$
and calculating it.
Second way is to find 37% of each number and then add it
$0.37*27 \frac{3}{5}$ + $0.37* \frac{15}{9}$
In both cases the result is 10.829

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3 years ago

3x - 5 = 1/2x + 2x solve the equation and please show your work im confused

Monica [59]

Answer:I searched it up on go

Step-by-step explanation:and I got 5x-5+ x/2

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2 years ago

D. Write a system of two linear equations that has more than one solution.

ddd [48]

D. y=5x+6 and 2y-12-10x=0 has infinitely many solutions and both lines are linear

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2 years ago

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:

$A=\sqrt{s(s-a)(s-b)(s-c)}$ , where $a$ , $b$ , and $c$ are three sides of the triangle and $s$ is the semi-perimeter ( $s=\frac{a+b+c}{2}$ ).

The semi-perimeter, $s$ , is:

$s=\frac{5+5+4}{2}=\frac{14}{2}=7$

Therefore, the area of the isosceles triangle is:

$A=\sqrt{7(7-5)(7-5)(7-4)},\\A=\sqrt{7\cdot 2\cdot 2\cdot 3},\\A=\sqrt{84}, \\A=2\sqrt{21}\:\mathrm{cm^2}$

Thus, the area of the quadrilateral is:

$6\:\mathrm{cm^2}+2\sqrt{21}\:\mathrm{cm^2}=\boxed{6+2\sqrt{21}\:\mathrm{cm^2}}$

4 0

2 years ago

Oscar has received a $4,000 gift and is looking for a bank to start a savings account. Which option

hoa [83]

Answer:

The best option for him would be a real interest rate of 5%.

Step-by-step explanation:

The nominal interest rate is the one that represents the percentage of increase of the money that is in a certain investment, without discounting the depreciation due to inflation or the payment of taxes.

On the other hand, the real interest rate is the one that represents the real increase in the money invested, after discounting inflation and any taxes to be paid.

Therefore, the best option for Oscar would be to invest his $ 4,000 in a savings account with a real interest rate of 5% per year.

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2 years ago