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2 years ago

Solve for x. 4x−4<8 AND9x+5>23

Mathematics

2 answers:

djyliett [7]2 years ago

6 0

I think the first one is
x<3

And the second one is
x<2

Stella [2.4K]2 years ago

6 0

Answer:

x < 3 and x > 2

Step-by-step explanation:

We are to solve for 4x - 4 < 8 and 9x + 5 > 23

So 4x - 4 < 8,

4x < 8 + 4

4x < 12

x < 12/4

x < 3

And for

9x + 5 > 23

9x > 23 - 5

9x > 18

x > 18/9

x > 2

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Rectangle ABCD with coordinates A(1,1), B(4,1), C(4,2) and D(1,2) dilates with respect to the origin to give rectangle A’B’C’D’.

Delvig [45]

Answer: Option C.

Step-by-step explanation:

You need to find the distance AB with the formula for calculate the distance between two points:

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

Then, substituting the coordinates of the points A(1,1) and B(4,1), you get:

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

You know that A'B'=6, then the scale factor of dilation can be calculated with:

$k=\frac{A'B'}{AB}$

Substituting values, you get:

$k=\frac{6}{3}\\\\k=2$

This matches with the option C.

8 0

2 years ago

Read 2 more answers

Which expression is equivalent to Negative 2 and one-fourth divided by negative two-thirds? StartFraction 9 over 4 EndFraction d

Tanzania [10]

Answer:

The correct answer is:

Negative StartFraction 9 over 4 EndFraction divided by two-thirds

i.e.

$-\dfrac{9}{4} \div \dfrac{2}{3}$

Step-by-step explanation:

We have to find equivalent expression to :

Negative 2 and one-fourth divided by negative two-thirds

i.e.

$-2\dfrac{1}{4} \div \dfrac{2}{3} = ?$

We have to convert the the mixed fraction form $-2\frac{1}{4}$ to simpler $\frac{p}{q}$ fraction form.

Let us learn the concept first.

Mixed fraction is combination of a whole number and a fraction.

Expression of the form $a\frac{b}{c}$ have the following understanding:

c is the divider

b is the remainder and

a is the quotient.

To convert mixed fraction to fraction we can use the following:

$a\dfrac{b}{c} = \dfrac{a \times c+b}{c}$

$\therefore -2\dfrac{1}{4} = -\dfrac{(2 \times 4+1)}{4} = -\dfrac{9}{4}$

Hence

$-2\dfrac{1}{4} \div \dfrac{2}{3} = -\dfrac{9}{4} \div \dfrac{2}{3}$

i.e. the given expression is equivalent to :

Negative StartFraction 9 over 4 EndFraction divided by two-thirds

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2 years ago

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Ax+16=b−3x what is a= and what does b= ?

Vlad1618 [11]

Answer:

Slope=4

x−intercept=−

=−4

b−intercept=

=16.0000

Step-by-step explanation:

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2 years ago

Which expression is equivalent to StartFraction (5 a b) cubed Over 30 a Superscript negative 6 Baseline b Superscript negative 7

lorasvet [3.4K]

Answer: $\frac{25}{6} a^{9} b^{10}$

Step-by-step explanation:

Assuming the described expression is:

$\frac{(5ab)^{3}}{30 a^{-6} b^{-7}}$

And knowing the condition $a \neq 0$ and $b \neq 0$

We cansimplify it following the rules related to the exponents with the same base:

$\frac{25}{6} a^{3} b^{3} a^{6} b^{7}$

Finally:

$\frac{25}{6} a^{9} b^{10}$

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2 years ago

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A rectangular solid with a square base has a volume of 5832 cubic inches. (Let x represent the length of the sides of the square

Aleks04 [339]

Answer:

a) 18 in x 18 in x 18 in

b) $S = 1944\ in2$

Step-by-step explanation:

a) Let's call 's' the side of the square base and 'h' the height of the solid.

The surface area is given by the equation:

$S = 2s^2 + 4sh$

The volume of the solid is given by the equation:

$V = s^2h = 5832$

From the volume equation, we have that:

$h = 5832/s^2$

Then, using this value of h in the surface area equation, we have:

$S = 2s^2 + 4s(5832/s^2)$

$S = 2s^2 + 23328/s$

To find the side length that gives the minimum surface area, we can find where the derivative of S in relation to s is zero:

$dS/ds = 4s - 23328/s^2 = 0$

$4s = 23328/s^2$

$4s^3 = 23328$

$s^3 = 23328/4 = 5832$

$s = 18\ inches$

The height of the solid is:

$h = 5832/(18)^2 = 18\ inches$

b) The minimum surface area is:

$S = 2(18)^2 + 4(18)(18)$

$S = 1944\ in2$

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2 years ago