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2 years ago

7x+39≥53 AND 16x+15>31 {solve for x}

Mathematics

1 answer:

ira [324]2 years ago

5 0

Answer:

A. $7x+39 \geq 53$

=> $7x \geq 53-39$

=> $7x \geq 14$

=> $x\geq 2$

The solution is the interval is [2,∞)

B. $16x+15>31$

=> $16x>31-15$

=> $16x>16$

=> x >1

The solution is (1,∞)

Now, the solution of the inequality A AND B is equal to

[2,∞) ∩ (1,∞)=[2,∞)

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The graph shows the speed of a ball in free fall for 10 seconds. Which is the constant of proportionality shown in the graph?

Marizza181 [45]

<u>Given</u>:

The graph shows the speed of a ball in free fall for 10 seconds.

We need to determine the constant of proportionality for the given graph.

<u>Constant of proportionality:</u>

The constant of proportionality can be determined using the formula,

$\frac{y}{x}=k$

Where k is the constant of proportionality.

Let us consider any of the coordinate from the graph and substitute in the formula.

Consider the coordinate (4,40) and substitute in the above formula.

Thus, we have;

$\frac{40}{4}=k$

$10=k$

Thus, the constant of proportionality is 10 meters per second squared.

3 0

2 years ago

The combined average weight of an okapi and a llama is 450450450 kilograms. The average weight of 333 llamas is 190190190 kilogr

Kisachek [45]

I'm going to assume that you meant 450kg for the combined weight, 190kg more and 3 Llamas. I'm pretty sure Llamas and Okapis don't weigh 450450450kg (that's 993,073,252 pounds). :)

x= Okapi weight
y= Llama weight

EQUATIONS:
There are 2 equations to be written:

1) 450kg is equal to the weight of one Okapi and one Llama

450kg= x + y

2) The weight of 3 llamas is equal to the weight of one Okapi plus 190kg.

3y=190kg + x

STEP 1:
Solve for one variable in one equation and substitute the answer in the other equation.

450kg= x + y
Subtract y from both sides
450-y =x

STEP 2:
Substitute (450-y) in second equation in place of x to solve for y.

3y=190kg + x
3y=190 + (450-y)
3y=640 -y
add y to both sides

4y=640
divide both sides by 4

y=160kg Llama weight

STEP 3:
Substitute 160kg in either equation to solve for x.

3y=190kg + x
3(160)=190 + x
480=190 + x
Subtract both sides by 190

290= x
x= 290kg Okapi weight

CHECK:
3y=190kg + x
3(160)=190 + 290
480=480

Hope this helps! :)

8 0

2 years ago

PLEASE HELP TO SOLVE QUESTION with full process c) Mr. Thapa bought a motorbike for Rs 1,25,000 and fixed its price 20 % above t

klasskru [66]

Answer: Rs. 1,52,550

Step-by-step explanation:

CP of motorcycle = 125000

Selling Price fixed = 125000 + 20% = 150000

10% discount = 150000*10% = 15000

SP after 10% discount

= 150000-15000= 135000

VAT at 13% = 135000 * .13 = 17550

Mr Gurung paid total

135000 + 17550 = 152550

8 0

2 years ago

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It is known that a cable with a cross-sectional area of 0.300.30 sq in. has a capacity to hold 2500 lb. If the capacity of the

vesna_86 [32]

Answer:

0.84 square in

Step-by-step explanation:

Since the capacity of the cable is proportional to its cross-sectional area. If a cable that is 0.3 sq in can hold 2500 lb then per square inch it can hold

2500 / 0.3 = 8333.33 lb/in

To old 7000 lb it the cross-sectional area would need to be

7000 / 8333.33 = 0.84 square in

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2 years ago

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Beatrice threw a stone one and seven fourteenths yards. Tilly threw a stone nine fourteenths of a yard. What is a reasonable est

scoundrel [369]

Answer:

1 yard

Step-by-step explanation:

7/14 is 1/2 while 9/14 is greater than 1/2 but a lot less than a whole. So a strong estimate would assume that it is (1 1/2)-(1/2) for the approximate difference in their throws were

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2 years ago

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