All categories

3 years ago

Solve the inequality

Mathematics

1 answer:

worty [1.4K]3 years ago

6 0

Treat it just like and equation at first. Multiply the 10 on both sides to get rid of it, leaving you with 50 $\leq$ x. Then on the number line, since there is a line under it, you would make a filled in circle and an arrow pointing towards 51 and beyond

You might be interested in

The height of a football is given by the function h of t equals negative16 t squared plus 56 t plus 3, where h of t is the heigh

kykrilka [37]

Answer:

27 feet.

Step-by-step explanation:

Graph the quadratic equation, then find the point on the graph which aligns with x=3. Y would equal 27.

8 0

2 years ago

Please help me i don’t understand this question at all.

Maru [420]

9514 1404 393

Answer:

Step-by-step explanation:

The wording "when x is an appropriate value" is irrelevant to this question. That phrase should be ignored. (You may want to report this to your teacher.)

When you look at the answer choices, you see that all of them are negative except the last one (D). When you look at the problem fraction, you see that it is positive.

The only reasonable choice is D.

Your calculator can check this for you.

√12/(√3 +3) ≈ 3.4641/(1.7321 +3)

= 3.4641/4.7321 ≈ 0.7321 = -1 +√3

If you want to "rationalize the denominator", then multiply numerator and denominator by the conjugate of the denominator. The conjugate is formed by switching the sign between terms.

$\displaystyle\frac{\sqrt{12}}{\sqrt{3}+3}=\frac{\sqrt{12}}{(\sqrt{3}+3)}\cdot\frac{(\sqrt{3}-3)}{(\sqrt{3}-3)}=\frac{\sqrt{36}-3\sqrt{12}}{3-9}\\\\=\frac{6-3\cdot2\sqrt{3}}{-6}=\boxed{-1+\sqrt{3}}$

_____

<em>Additional comment</em>

We "rationalize the denominator" in this way to take advantage of the relation ...

(a -b)(a +b) = a² -b²

Using this gets rid of the irrational root in the denominator, hence "rationalizes" the denominator.

We could also have multiplied by (3 -√3)/(3 -√3). This would have made the denominator positive, instead of negative. However, I chose to use (√3 -3) so you could see that all we did was change the sign from (√3 +3).

3 0

3 years ago

Abc bookstore sells new books, n, for $12, used books, u, for $8, and magazines, m, for $5 each. The store earned $340 revenue l

poizon [28]

Answer:

The number of new books sold = 10

The number of used books sold (u) = 15

The number of magazines sold (m) = 20

Step-by-step explanation:

Let us assume the number of new books = n

So, the number of used books sold (u) = New books sold + 5 = n + 5

Also, the number of magazines sold (m) = 2 x ( Number of new books sold)

= 2 n

⇒ u = n + 5, m = 2 n

Here, the cost of each new book n- = $12

So, the cost of n new books = n x ($12) = 12 n

the cost of each used book u = $8

So, the cost of u = (n+ 5) used books = n+5 x ($8) = 8 n + 40

the cost of each magazine m = $5

So, the cost of m = (2n ) magazines = 2n x ($5) = 10 n

Also, total earnings = $340

⇒ 12 n + 8n +40 + 10 n = 340

or, 30 n = 300

or,n = 300/30 = 10

Hence the number of new books sold = n = 10

The number of used books sold (u) = n + 5 = 15

The number of magazines sold = m = 2 n = 20

4 0

3 years ago

Label the slope and y intercept

klasskru [66]

Slope is 2 and the y intercept is 4

7 0

3 years ago

Read 2 more answers

A restaurant owner installed a new automated drink machine. The machine is designed to dispense 530 mLof liquid on the medium si

lidiya [134]

Answer:

a.H0: μ =530mL vs. Ha: μ > 530mL

Step-by-step explanation:

-A hypothesis test will be used to provide evidence that the median is more or equal to the stated median value.

#In a normally distributed population, the mean=mode=median:

$Mean=Mode=Median=\mu$

-The null hypothesis states that the median is equal to the stated value:

$H_o:\mu=530 \ mL$

-The alternative hypothesis provides evidence that the median value is greater than the stated value:

$H_a:\mu>530\ mL$

Hence, the correct hypotheses are H0: μ =530mL vs. Ha: μ > 530mL

6 0

3 years ago