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nirvana33 [79]
3 years ago
11

One number is five times another number. Their sum is 42. What are the two numbers? Answer ASAP

Mathematics
1 answer:
vekshin13 years ago
3 0

Answer:

the numbers are 7 and 35

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A tangent line and its normal line have a point of tangency to the function f(x) at (x,y). If the slop of the normal line is m=(
alekssr [168]

Answer:

\displaystyle \\\left(\frac{49}{900},\frac{3761}{900}\right) or approximately (0.544, 4.179)

Step-by-step explanation:

A function and its tangent lines intersect when their slopes are the same. Find the x-coordinate when the slope of f(x) is equal to 8/7 by taking the derivative of f(x):

\displaystyle\\f(x)=\sqrt{x}-x+4\\f'(x)=\frac{1}{2}\cdot\frac{1}{\sqrt{x}}-1=\frac{1}{2\sqrt{x}}-1

Set f'(x) equal to 8/7 and solve for x:

\displaystyle \\\frac{1}{2\sqrt{x}}-1=\frac{8}{7},\\x=\frac{49}{900}

Therefore, f(x) will intersect at a point of tangency with a line of slope 8/7 at x=49/900. Plug in x=49/900 into f(x) to get the y-coordinate:

\displaystyle\\y=\sqrt{x}-x+4 \vert_{x=49/900}=\frac{3761}{900}

⇒Answer: (49/900, 3761/900) or approximately (0.544, 4.179)

5 0
3 years ago
Aaron participates in a walkathon for charity. He has a sponsor who has pledged a base donation of $2 for the first mile he walk
tino4ka555 [31]

Answer:

total amount donated when aaron walks n miles = $2 + $3(n-1)

Step-by-step explanation:

Aaron participates in a walkathon for charity. He has a sponsor who has pledged a base donation of $2 for the first mile he walks and then a certain dollar amount for each additional mile he walks. Based on this pledge, if Aaron walks 8 miles, the sponsor will donate a total of $23 to the charity.

Write a formula that can be used to determine the amount of money this sponsor donates when Aaron walks n miles.

total amount sponsor pays = base donations + (additional miles walked after first mile x amount paid)

when Aaron walks 8 miles

additional miles = 8 - 1 = 7

23 = 2 + 7x

23 - 2 = 7x

x = 3

additional amount paid is $3

total amount donated when aaron walks n miles = $2 + $3(n-1)

5 0
3 years ago
If an architect wants to draw a plan for a house that is 75 ft by 80 ft, and his paper is 10 in. by 17 in., what is the best sca
drek231 [11]
The best scale factor to make use of every inch of the paper would be that 1 inch represents 7.5 feet.
7 0
3 years ago
??????<br> What's this one
Soloha48 [4]
The closest distance is C. 12 feet
7 0
3 years ago
A spring has natural length 24 cm. Compare the work W1 done in stretching the spring from 24 cm to 34 cm with the work W2 done i
Scilla [17]

Answer:

From the analysis W1=W2.

they are directly related

Step-by-step explanation:

the work-done in stretching a spring can be expressed as

W=\frac{1}{2}kx^2

where k= spring constant

           x= change on length of spring

Hence for W1

Given data

x= 34-24= 10 cm

solving in terms of k we have

W=\frac{1}{2}k*10^2\\\W=\frac{1}{2}k*100\\\W=50k

Hence for W2

Given data

x= 44-34= 10 cm

solving in terms of k we have

W=\frac{1}{2}k*10^2\\\ W=\frac{1}{2}k*100\\\ W=50k

4 0
3 years ago
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