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baherus [9]
3 years ago
10

16x − 7 ≤ − 71 Find the solution set of the inequality

Mathematics
1 answer:
natka813 [3]3 years ago
4 0

Answer:

x\leq -4\\

Step-by-step explanation:

Add 7 to other side making equation 16x\leq-71+7

16x\leq-64

16 goes into -64 -4 times.

Answer would give you x\leq-4

To check, you could substitute -4 into the inequality

16(-4)-7\leq-71

-71\leq-71 check

16(-10)-7\leq-71

-167\leq-71 check

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two trains leave stations 210 miles apart at the same time and travel tword each other. one train at 85 miles per hour while the
hodyreva [135]

recall your d = rt, distance = rate * time.


let's say we have two trains, A and B, A is going at 85 mph and B at 65 mph.


they are 210 miles apart and moving toward each other, at some point they will meet, when that happens, the faster train A has covered say d miles, and the slower B has covered then the slack from 210 and d, namely 210 - d.


When both trains meet, A has covered more miles than B because A is faster, however the time both have been moving, is the same, say t hours.


\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{Train A}&d&85&t\\ \textit{Train B}&210-d&65&t \end{array}\\\\ \dotfill\\\\ \begin{cases} \boxed{d}=85t\\ 210-d=65t\\[-0.5em] \hrulefill\\ 210-\boxed{85t}=65t \end{cases} \\\\\\ 210=150t\implies \cfrac{210}{150}=t\implies \cfrac{7}{5}=t\implies \stackrel{\textit{one hour and 24 minutes}}{1\frac{2}{5}=t}

3 0
3 years ago
What is the volume of this rectangular
Basile [38]
<h3>Given:</h3>
  • l= 5 m
  • b= 4 m
  • h= 3 m
<h3>Note that:</h3>
  • l= length
  • b= breadth
  • h= height
<h3>To find:</h3>

The volume of the given rectangular pyramid.

<h3>Solution:</h3>

\large\boxed{Formula:V=\frac{1}{3}lbh}

First, multiply the length (5), breadth (4) and height (3).

5×4×3

= 60 \: cm

Now, divide 60 by 3.

\frac{60}{3}

\large\boxed{V= 20 \: {m}^{3}}

<u>Therefore, the volume of the given rectangular pyramid is 20 cubic meters.</u>

8 0
2 years ago
(please help soon) Point Q is plotted on the coordinate grid. Point P is at (20, −30). Point R is vertically above point Q. It i
Triss [41]

Step-by-step explanation:

So, the distance between the points P and Q is 4 units.

8 0
3 years ago
What's the 2-step rules input 5,9,7,10 output 16 28 22 31
snow_tiger [21]

To solve this problem, we have to figure out a rule for the function. We are told that it is a two-step rule, so it is most likely the input multiplied by a coefficient plus a constant. Let’s let the input be represented by the variable x and the output be represented by the variable y. Using our knowledge, we can see that the outputs are close to triple the input, so we set up the preliminary equation:

y = 3x + b,

where b is a constant. If we want to solve for b, we must plug in one of our input/output pairs. If we plug in (5,16), we get the following:

16 = 3(5) + b

16 = 15 + b

1 = b

Then, we should substitute in this value into our equation and check our work.

y = 3x + 1

If we plug in the other points, this equation yields a true statement, so we know it is correct.

Hope this helps!

6 0
4 years ago
Kabul’s bookshop marks up all books by 40 percent of their cost. The overhead rate is 16 percent of the selling price. What is t
morpeh [17]

Answer:

The net profit rate on the book is 5.41

Step-by-step explanation:

Given as :

The marks up percentage of book = m = 40%

The overhead rate is 16% of selling price

The cost price of book = c.p = $18.10

Let The profit = $p

Let The selling price = s.p

<u>Now, According to question</u>

mark up percentage = \dfrac{s.p - c.p}{c.p}

I.e 40% =  \dfrac{s.p - 18.10}{18.10}

Or, \dfrac{40}{100} + 1 = \dfrac{s.p}{18.10}

Or, \dfrac{140}{100} =  \dfrac{s.p}{18.10}

Or, s. p = \dfrac{140\times 18.10}{100}

∴ s.p = $25.34

So, selling price of book = s.p = $25.34

Now, The overhead percentage = 16%

i.e overhead rate = \dfrac{\textrm estimated cost}{\textrm estimated total base unit}

Or, estimated cost = 16% × 25.34

I,e estimated cost = 0.16 × 25.34

∴ estimated cost = $4.05

Now,

Profit = selling price of book - estimated book cost

I.e p = $25.34 - $4.05

∴ p = $21.29

So, The profit rate% = \dfrac{\textrm profit}{\textrm estimated cost}

I.e The profit rate% = \dfrac{21.29}{4.05}

∴ profit rate %= 5.41

So, The profit rate = p = 5.41

Hence, The net profit rate on the book is 5.41  Answer

4 0
3 years ago
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