Solve the system of equations. What is the x-

What is 1.036 that add up to 4

Mamont248 [21]

Answer:

2.964

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The points (3, 2) and ( -2, -3) are solutions to a system of two linear equations. What must be true about the two linear equati

Gala2k [10]

Answer:

The two linear equations are the same line

Step-by-step explanation:

two different linear equations can only possibly intersect at one point. once the two lines intersect, they cannot curve back to intersect once again.

6 0

4 years ago

Devon made a box with length x+1, width x+3, and height x-3. What is the volume of Devon's box as a function of x?

erica [24]

Answer:

(a)

$V=x^3+x^2-9x-9$

(b)

$x=10$

(c)

$x=\frac{7}{2}$

Step-by-step explanation:

we are given

length is x+1

$L=x+1$

width is x+3

$W=x+3$

height is x-3

$H=x-3$

(a)

we can use volume formula

$V=L\times W\times H$

now, we can plug it

$V=(x+1)\times (x+3)\times (x-3)$

now, we can simplify it

$V=x^3+x^2-9x-9$

(b)

we are given volume =1001

so, we can set V=1001

and then we can solve for x

$V=x^3+x^2-9x-9=1001$

now, we can factor it

$\left(x-10\right)\left(x^2+11x+101\right)=0$

$x-10=0$

$x=10$

(b)

we are given volume

so, we can set

$V=14\frac{5}{8}=\frac{14\times 8+5}{8}$

$V=\frac{117}{8}$

and then we can solve for x

$V=x^3+x^2-9x-9=\frac{117}{8}$

now, we can factor it

$8x^3+8x^2-72x-189=0$

$\left(2x-7\right)\left(4x^2+18x+27\right)=0$

$2x-7=0$

$x=\frac{7}{2}$

8 0

4 years ago

Which expression is equivalent to the one in the picture?

Ne4ueva [31]

Answer:

d.

Step-by-step explanation:

To convert a root to a fraction in the exponent, remember this rule:

$\sqrt[n]{a^{m}}=a^{\frac{m}{n}}$

The index becomes the denominator in the fraction. (The index is the little number in front of the root, "n".) The original exponent remains in the numerator.

In this question, the index is 4.

The index is applied to every base in the equation under the root. The bases are 16, 'x' and 'y'.

$\sqrt[4]{16x^{15}y^{17}} = (\sqrt[4]{16})(\sqrt[4]{x^{15}})(\sqrt[4]{y^{17}}) = (2)(x^{\frac{15}{4}}})(y^{\frac{17}{4}}) = 2x^{\frac{15}{4}}}y^{\frac{17}{4}}$

To find the quad root of 16, input this into your calculator. Since 2⁴ = 16, $\sqrt[4]{16}$ = 2.

For the "x" and "y" bases, use the rule for converting roots to exponent fractions. The index, 4, becomes the denominator in each fraction.

$2x^{\frac{15}{4}}y^{\frac{17}{4}}$

5 0

4 years ago

Find the solution of 3 times the square root of the quantity of x plus 6 equals negative 12, and determine if it is an extraneou

Anna35 [415]

For this case we have the following equation:
$3 \sqrt{x+6}=-12$
Rewriting we have:
$\sqrt{x+6}= \frac{-12}{3}$
$\sqrt{x+6}=-4$
We raise both members of the equation to the square:
$(\sqrt{x+6})^2=(-4)^2$
Rewriting we have:
$x+6=16$
$x=16-6$
$x=10$
It's a extraneous solution because equality is not met by substituting x = 10 in the original equation:
$3 \sqrt{10+6}=-12$
$3 \sqrt{16}=-12$
$3(4)=-12$
$12=-12$
Answer:
The solution is:
$x=10$
It's a extraneous solution

6 0

4 years ago