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3 years ago

4x + 16 ≤ 74 solve the inequality and show your work

Mathematics

2 answers:

marshall27 [118]3 years ago

7 0

Answer:

x ≤14.5

Step-by-step explanation:

4x+16≤74

Subtract 16 from the 74 and that gives you 58

Then divide each side by 4. 58/4=14.5

Hope this helps! sry if I get it wrong! :(

Gnoma [55]3 years ago

4 0

Answer: x ≤ 29/2

Explanation:

Subtract 16 from both sides

4x + 16 - 16 ≤ 74 -16

Simplify

4x ≤ 58

Divide both sides by 4

4x/4 ≤ 58/4

Simplify

x ≤ 29/2

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If Rib-eye steaks are on sale for $8.52 per pound. Ms. Markum bought a 0.9-pound steak. How much did the steak cost?

Pepsi [2]

Answer: The steak costs $ 7.67.

Step-by-step explanation:

Given: Cost per pound of Rib-eye steaks = $8.52

Ms. Markum bought a 0.9-pound steak.

To find : cost of 0.9 pound steak =

Then cost of 0.9 pound steak = 0.9 x (Cost per pound of Rib-eye steaks )

= $ (0.9 x 8.52)

= $7.668 ≈ $ 7.67

Hence, the steak costs $ 7.67.

7 0

3 years ago

From deltamath.com Help me please i really don't get it.

Brums [2.3K]

Answer:

cos = adjacent/hypotenuse

3/square root13

now you do square root 13 x3 divided by square root 13^2

= 3square root13/13

hope that answers your question

3 0

3 years ago

What is the square root of 902?

ad-work [718]

the square root is 30.0333148

4 0

3 years ago

Read 2 more answers

How to solve this trig

n200080 [17]

Hi there!

To find the Trigonometric Equation, we have to isolate sin, cos, tan, etc. We are also given the interval [0,2π).

First Question

What we have to do is to isolate cos first.

$\displaystyle \large{ cos \theta = - \frac{1}{2} }$

Then find the reference angle. As we know cos(π/3) equals 1/2. Therefore π/3 is our reference angle.

Since we know that cos is negative in Q2 and Q3. We will be using π + (ref. angle) for Q3. and π - (ref. angle) for Q2.

Find Q2

$\displaystyle \large{ \pi - \frac{ \pi}{3} = \frac{3 \pi}{3} - \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{2 \pi}{3} }$

Find Q3

$\displaystyle \large{ \pi + \frac{ \pi}{3} = \frac{3 \pi}{3} + \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{4 \pi}{3} }$

Both values are apart of the interval. Hence,

$\displaystyle \large \boxed{ \theta = \frac{2 \pi}{3} , \frac{4 \pi}{3} }$

Second Question

Isolate sin(4 theta).

$\displaystyle \large{sin 4 \theta = - \frac{1}{ \sqrt{2} } }$

Rationalize the denominator.

$\displaystyle \large{sin4 \theta = - \frac{ \sqrt{2} }{2} }$

The problem here is 4 beside theta. What we are going to do is to expand the interval.

$\displaystyle \large{0 \leqslant \theta < 2 \pi}$

Multiply whole by 4.

$\displaystyle \large{0 \times 4 \leqslant \theta \times 4 < 2 \pi \times 4} \\ \displaystyle \large \boxed{0 \leqslant 4 \theta < 8 \pi}$

Then find the reference angle.

We know that sin(π/4) = √2/2. Hence π/4 is our reference angle.

sin is negative in Q3 and Q4. We use π + (ref. angle) for Q3 and 2π - (ref. angle for Q4.)

Find Q3

$\displaystyle \large{ \pi + \frac{ \pi}{4} = \frac{ 4 \pi}{4} + \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{5 \pi}{4} }$

Find Q4

$\displaystyle \large{2 \pi - \frac{ \pi}{4} = \frac{8 \pi}{4} - \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{7 \pi}{4} }$

Both values are in [0,2π). However, we exceed our interval to < 8π.

We will be using these following:-

$\displaystyle \large{ \theta + 2 \pi k = \theta \: \: \: \: \: \sf{(k \: \: is \: \: integer)}}$

Hence:-

For Q3

$\displaystyle \large{ \frac{5 \pi}{4} + 2 \pi = \frac{13 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 4\pi = \frac{21 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 6\pi = \frac{29 \pi}{4} }$

We cannot use any further k-values (or k cannot be 4 or higher) because it'd be +8π and not in the interval.

For Q4

$\displaystyle \large{ \frac{ 7 \pi}{4} + 2 \pi = \frac{15 \pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 4 \pi = \frac{23\pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 6 \pi = \frac{31 \pi}{4} }$

Therefore:-

$\displaystyle \large{4 \theta = \frac{5 \pi}{4} , \frac{7 \pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} , \frac{29\pi}{4}, \frac{15 \pi}{4} , \frac{23\pi}{4} , \frac{31\pi}{4} }$

Then we divide all these values by 4.

$\displaystyle \large \boxed{\theta = \frac{5 \pi}{16} , \frac{7 \pi}{16} , \frac{13\pi}{16} , \frac{21\pi}{16} , \frac{29\pi}{16}, \frac{15 \pi}{16} , \frac{23\pi}{16} , \frac{31\pi}{16} }$

Let me know if you have any questions!

3 0

3 years ago

F(x)=2x^2 find f(-3)

vekshin1

Answer:

f(- 3) = 18

Step-by-step explanation:

Substitute x = - 3 into f(x) , that is

f(- 3) = 2(- 3)² = 2(9) = 18

8 0

4 years ago

Read 2 more answers