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iogann1982 [59]
3 years ago
7

The sum of two numbers is 39, twice the first number plus three times the second number is 101 find the numbers

Mathematics
1 answer:
bezimeni [28]3 years ago
3 0
The two numbers are 23 and 16 and the method is shown algebraically using simultaneous equations in the photo

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Find 4 consecutive odd numbers such that twice the sum of the least 2 numbers is 40 less than three times the sum of the greates
ANTONII [103]
4 consecutive odd numbers....x, x + 2, x + 4, x + 6

2(x + x + 2) = 3(x + 4 + x + 6) - 40
2(2x + 2) = 3(2x + 10) - 40
4x + 4 = 6x + 30 - 40
4x + 4 = 6x - 10
4x - 6x = -10 - 4
-2x = - 14
x = -14/-2
x = 7

x + 2 = 7 + 2 = 9
x + 4 = 7 + 4 = 11
x + 6 = 7 + 6 = 13

ur numbers are : 7,9,11,13 <==
4 0
3 years ago
Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x.
Leni [432]

Answer:

a)

g(2.9) \approx -6.6

g(3.1) \approx -3.4

b)

The values are too small since g'' is positive for both values of x in. I'm speaking of the x values, 2.9 and 3.1.

Step-by-step explanation:

a)

The point-slope of a line is:

y-y_1=m(x-x_1)

where m is the slope and (x_1,y_1) is a point on that line.

We want to find the equation of the tangent line of the curve g at the point (3,-5) on g.

So we know (x_1,y_1)=(3,-5).

To find m, we must calculate the derivative of g at x=3:

m=g'(3)=(3)^2+7=9+7=16.

So the equation of the tangent line to curve g at (3,-5) is:

y-(-5)=16(x-3).

I'm going to solve this for y.

y-(-5)=16(x-3)

y+5=16(x-3)

Subtract 5 on both sides:

y=16(x-3)-5

What this means is for values x near x=3 is that:

g(x) \approx 16(x-3)-5.

Let's evaluate this approximation function for g(2.9).

g(2.9) \approx 16(2.9-3)-5

g(2.9) \approx 16(-.1)-5

g(2.9) \approx -1.6-5

g(2.9) \approx -6.6

Let's evaluate this approximation function for g(3.1).

g(3.1) \approx 16(3.1-3)-5

g(3.1) \approx 16(.1)-5

g(3.1) \approx 1.6-5

g(3.1) \approx -3.4

b) To determine if these are over approximations or under approximations I will require the second derivative.

If g'' is positive, then it leads to underestimation (since the curve is concave up at that number).

If g'' is negative, then it leads to overestimation (since the curve is concave down at that number).

g'(x)=x^2+7

g''(x)=2x+0

g''(x)=2x

2x is positive for x>0.

2x is negative for x.

That is, g''(2.9)>0 \text{ and } g''(3.1)>0.

So 2x is positive for both values of x which means that the values we found in part (a) are underestimations.

6 0
3 years ago
Witold says that 50% of a number will always be greater than 20% of any other number. Complete one inequality to support Witold'
Lelu [443]
.50 x 2 < .20 x 100
1 < 20

50% of 2 is not greater than 20% of 100.
4 0
3 years ago
Could you explain and answer the question?
podryga [215]

So F(6) means 6 on the x axis  then look to see where the graph is on the Y axis,

 in this case on x 6 y=4

7 0
3 years ago
Read 2 more answers
Find the length of a rectangle whose area=320²cm and breadth=16cm​
soldier1979 [14.2K]

Answer:

20

Step-by-step explanation:

area = length * breadth

320cm² = length * 16cm

divide both sides by 16cm to isolate length

20cm = length

6 0
3 years ago
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