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djyliett [7]
2 years ago
5

Gerry plans to place a 29 foot ladder against the side of his house to clean his gutters. The bottom of the ladder will be 3 fee

t from the house. How far up the side of the house will the ladder reach (in ft)?
Mathematics
1 answer:
tensa zangetsu [6.8K]2 years ago
5 0

Answer:

8\sqrt{13}

Step-by-step explanation:

Using the pythagorean theorem (Assuming the house's walls are perpindicular to the ground):

a^2+b^2=c^2

we can find that 3=a and 29=c

3^2+b^2=29^2

9+b^2=841

b^2=832

b=\sqrt{832}

b=\sqrt{64*13}

b=8\sqrt{13}

That is the height that the ladder will reach

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Maria, an experienced shipping clerk, can fill a certain order in 9 hours. Jim, a new clerk, needs 11 hours to do the same job.
tester [92]

Answer:

4 19/20 hours or 4 hours , 57 minutes

Step-by-step explanation:

Given

In 9 hours Maria can fill a certain order let Say X

In 9/9 hours Maria can fill   X/9 of the order

in 1 hour Maria can fill   X/9 of the order

__________________________________

In 11 hours Jim can fill a certain order let Say X

In 11/11 hours Maria can fill   X/11 of the order

in 1 hour Maria can fill   X/11 of the order

_____________________________________________

Therefore total order filled by them in one hour will sum of individual work done by them in one hour.

Mathematically,

total order filled by Jim and maria in one hour = work done by Jim in one + work done by Maria in one hour

total order filled by Jim and maria in one hour = 1/11 + 1/9

=> 1/11 + 1/9 \\=> (9 + 11)/11*9\\=> 20/99

=>20/99 of certain order is filled by both of them in one hour.

=>Total order is one. Hence, to get 1 from 20/99 we need to multiply it with its reciprocal (i.e 99/20) as 20/99 *99/20 = 1

now

=>20/99 of certain order is filled by both of them in 1 hour.

=>multiplying both order and hour with 99/20 we have

20/99 *99/20 of certain order is filled by both of them in 1* 99/20 hour

Thus total order is filled by them in 99/20 hours = 4 19/20 hours.

1 hour has 60 minutes

so 19/20 has 60*19/20 minutes = 57 minutes.

Working together, Jim and Maria   will  take 4 hours , 57 minutes  to fill the order.

3 0
3 years ago
Solve on the interval [0,2pi) 3cscx-1=2
aliya0001 [1]

Answer:

on APEX its d) pi/2

3 0
3 years ago
Find the indicated term of the given arithmetic sequence. a1=45, d= -3, n=10
klasskru [66]

In this sequence, we're given the first term, which is 45.

The difference between each term is -3, which means 3 will be subtracted in each term.

We're asked to find the value of the tenth term, and we can do so by using this formula:

a(n) = a(1) + d(n - 1)

Replace values.

a(10) = 45 + -3(9)

a(10) = 18

<h3>The value of the tenth term is 18.</h3>
3 0
3 years ago
Read 2 more answers
What is Chloe's speed in miles per hour show your work and explain your reasoning
Arlecino [84]
Divide distance with time
6 0
3 years ago
Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 3.6% interest per year. He will put some o
noname [10]

Answer: He should invest $44000 in fund A and $11000 in fund B.

Step-by-step explanation:

Let x represent the amount which he invested in fund A.

Let y represent the amount which he invested in fund B.

Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 3.6% interest per year. He will put some of the money into Fund A that earns 2% per year and the rest in Fund B that earns 10% per year.. This means that

x + y = 55000

The formula for determining simple interest is expressed as

I = PRT/100

Considering fund A,

P = $x

T = 1 year

R = 2℅

I = (x × 2 × 1)/100 = 0.02x

Considering fund B,

P = $y

T = 1 year

R = 10℅

I = (y × 10 × 1)/100 = 0.1y

The interest that he wants to earn on the total amount in a year is 3.6%. The interest would be

I = (55000 × 3.6 × 1)/100 = 1980

Therefore,

0.02x + 0.1y = 1980 - - - - - - - - - -1

Substituting x = 55000 - y into equation 1, it becomes

0.02(55000 - y) + 0.1y = 1980

1100 - 0.02y + 0.1y = 1980

- 0.02y + 0.1y = 1980 - 1100

0.08y = 880

y = 880/0.08

y = 11000

x = 55000 - y = 55000 - 11000

x = 44000

4 0
3 years ago
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