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2 years ago

Two numbers are in the ratio 7:5 and their difference is 22.Find the numbers

Mathematics

1 answer:

omeli [17]2 years ago

4 0

Answer:

Let x and y be the two numbers. Then

yx=57 and x−y=20

Cross multiplying the proportion

5x=7y or y=75x

So, x−y=20

x−75x=20⇒77x−5x=72x=20

⇒x=2140=70

y=75x=75×70=50

So smaller number is 50.

Check :yx=5070=57 and 70−50=20

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Area of the triangle in cm2

love history [14]

Answer:

48cm².

Step-by-step explanation:

Area of a triangle = ½ × b × h.

½ × 12 × 8 = 48cm².

3 0

3 years ago

State true or false. If 9 is the solution of variable x in the equation fraction numerator 5 straight x space minus space 7 spac

Gekata [30.6K]

Answer:

False

Step-by-step explanation:

Based on what is stated in the question :

Expressing the worded equation Mathematically,

(5x - 7) / 2 = y

If y = 28

(5x - 7) / 2 = 28

Cross multiply

5x - 7 = 28 * 2

5x - 7 = 56

5x = 56 + 7

5x = 63

x = 63 / 5

x = 12.6

Hence, x ≠ 9

8 0

2 years ago

When this polynomial is divided by (x+3) , the remainder is 0. What is the value of the polynomial’s constant term.

saveliy_v [14]

Answer:

- 15

Step-by-step explanation:

Given f(x) divided by (x + h) then the remainder is the value of f(- h)

Here

f(x) = 3x³ - 5x² - 47x + k ← k is the constant term , then

f(- 3) = 3(- 3)³ - 5(- 3)² - 47(- 3) + k = 0 , that is

3(- 27) - 5(9) + 141 + k = 0

- 81 - 45 + 141 + k = 0

15 + k = 0 ( subtract 15 from both sides )

k = - 15

5 0

2 years ago

Read 2 more answers

Which of the following equations could be th equation to represent the given graph? Make sure you explain your answer thoroughly

Alex17521 [72]

Answer:

Option (C) is correct.

Step-by-step explanation:

The given options of the possible equation for the graph are as follows:

$(A) y=2\left(\frac{3}{2}\right)^x \\\\(B) y=-2\left(\frac{3}{2}\right)^{-x} \\\\(C) y=2\left(\frac{2}{3}\right)^x \\\\(D) y=-2\left(\frac{2}{3}\right)^{-x} \\\\$

The given graph is decreasing and at x=0, y=2.

So, first checking the value of the given options for x=0

$(A) y=2\left(\frac{3}{2}\right)^0=2\times 1= 2 \\\\(B) y=--2\left(\frac{3}{2}\right)^{-0}= -2\times 1= -2 \; (not\; possible) \\\\(C) y=2\left(\frac{2}{3}\right)^0= 2\times 1= 2 \\\\(D) y=2\left(\frac{2}{3}\right)^{-0} = -2\times 1= -2 \; (not\; possible)$

As, for x=0, y=2, so options (C) and (D) are not possible, so rejected.

Now, checking the nature (increasing or decreasing) of the given equation by differentiating it.

For option (A),

$\frac{dy}{dx}=2\left(\frac{3}{2}\right)^{x}\times \ln\left(\frac{3}{2}\right)$

As $\ln \left(\frac{3}{2}\right)=\ln(1.5)>0 \;and\; \left(\frac{3}{2}\right)^{x} >0$

So, $\frac{dy}{dx}>0$

Therefore, the function in option (A) is increasing function.

Similarly, for option (C),

$\frac{dy}{dx}=2\left(\frac{2}{3}\right)^{x}\times \ln\left(\frac{2}{3}\right)$

As $\ln \left(\frac{2}{3}\right)=\ln(0.67)0$

So, $\frac{dy}{dx}$

Therefore, the function in option (C) is decreasing function.

As the given graph is decreasing, so, (C) represents $y=2\left(\frac{2}{3}\right)^x$ the given graph.

Hence, option (C) is correct.

6 0

2 years ago

URGENT!!!!!!

Zinaida [17]

Answer: Choice B

a_n = 10(1/2)^(n-2) is the nth term

average rate of change = -35/3

=======================================================

Explanation:

Each time x increases by 1, y is cut in half. For instance, going from (2,10) to (3,5) shows this.

If we want to go in reverse, decreasing x by 1 will double the y value. So (1,20) is another point and (0,40) is another. We'll be using (0,40) and (3,5) because we want the average rate of change from x = 0 to x = 3. I'm using x in place of n here.

Use the slope formula to find the slope of the line through (0,40) and (3,5)

m = (y2-y1)/(x2-x1)

m = (5-40)/(3-0)

m = -35/3

The negative slope means the line goes downhill as you read it from left to right. The average rate of change from n = 0 to n = 3 is -35/3

The nth term of this geometric sequence is 20(1/2)^(n-1) since 20 is the first term (corresponds to n = 1) and 1/2 is the common ratio. Your teacher has done a bit of algebraic manipulation to change the n-1 into n-2. This means the 20 has to change to 10 to counterbalance.

In other words, 20(1/2)^(n-1) is equivalent to 10(1/2)^(n-2) when n starts at n = 1.

6 0

3 years ago

Two numbers are in the ratio 7:5 and their difference is 22.Find the numbers​

Two numbers are in the ratio 7:5 and their difference is 22.Find the numbers