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In rectangle ABCD below, AC = 15x+2 and BD = 9x+14.  

What is the length of diagonal AC?

15x +2 = 9x + 14

x = 2

AC = 9*2 + 14 = 32 

[ADSP] = [CB'P]

[SRP] = [PRQ] = [B'CQ]

Pavlov earns $4 and $3 for 1 load of laundry and 1 load of dishes respectively

Solution:

Given, Pavlov gets paid at home for doing extra chores.

We have to find How much does pavlov earn for completing each type of chore?

Let the amount for 1 load of laundry be m and amount for 1 load of dish be n.

Now, last week, he did 6 loads of laundry and 1 load of dishes, and his parents paid him $27.

Then, 6  amount for 1 load of laundry + 1  amount for 1 load of dish = 27

The week before, he finished 1 load of laundry and 9 loads of dishes, earning a total of $31

Then, 1  amount for 1 load of laundry + 9  amount for 1 load of laundry = 31  ⇒m + 9n = 31 ⇒ (2)

Now let us solve equations (1) and (2)

0 – 53n = - 159

-53n  = -159  

53n = 159

n = 3

Now, substitute n value in (1) ⇒ 6m + 3 = 27 ⇒ 6m = 24 ⇒ m = 4

Hence, pavlov earns $4 and $3 for 1 load of laundry and 1 load of dishes respectively.

Hey there, Guest!

So we have two equations:

8l+10d=28 and 3l+10d=23 (l is laundry and d is dishes)

We can then rewrite the equations:

10d+8l=28 and 10d+3l=23

Then we can solve and then find that d= $2 and that l= $1.

Hope this helped! :)

( ﾟдﾟ)つ Bye

Hey there, Caydog!

So let's solve this.

Step 1: Simplify both sides of the equation.

\(5−2(4a+1)+3a=13\)

\(5+(−2)(4a)+(−2)(1)+3a=13\) (Distribute)

\(5+−8a+−2+3a=13\)

\((−8a+3a)+(5+−2)=13\) (Combine Like Terms)

\(−5a+3=13\)

Step 2: Subtract 3 from both sides.

\(−5a+3−3=13−3\)

\(−5a=10\)

Step 3: Divide both sides by -5.

\(\frac{-5a}{-5}=\frac{10}{-5}\)

Therefore a=-2.

Hope this helped! :)

( ﾟдﾟ)つ Bye

Hey there, Guest!

So, the answer is 40%, and I explained the answer on that link.

Hope this helepd! :)

( ﾟдﾟ)つ Bye

Hey there, Guest!

I know that I'm super late, but here's a walk-through:

\(\frac{2}{5}*100=\) 40%

Hope this helped! :)

( ﾟдﾟ)つ Bye

nevermind i figured it out

the answer is 160 for anybody wondering 

your anwer is.........

𝑎=−2     

See image below

d ( tan 2 + tan4 ) = 400

d = 3815 ft

8/11 x = t        3/11 x = c

(8/11 x - 14) = 3/5 (x-14)

(40-33)/55  x = 14 - 3/5 ( 14)

7/55  x = 28/5

x = 44 pounds initially       8/11 (44 ) = turkey = 32 pounds initially     3/11 (42) = chicken = 12 pounds

Let $X$ be the position of the be.

Let $A$ be the highest point of the building.

Let $B$ be the lowest point of the building.

Let $C$ be the point that has the same altitude to $X$ (aka the shortest distance, which is what we are trying to find.)

We are given $AB = 400.$

Since we are given two angles and $AB$, we will try to relate $AB$ to $XC.$

Note $AB = AC + BC.$

We have that $AC = XC \tan 4^{\circ} \cong 0.070 XC.$

We also have that $BC = XC \tan 2^{\circ} \cong 0.035 XC.$

Thus we have $AB \cong 0.105 XC.$

And since we also have $AB = 400,$ we have that $0.105 XC \cong 400.$

$XC \cong \frac{200}{21} \cdot 400 \cong \boxed{3800 \text{ feet.}}$

What do you mean? 

Paul has 2/3 as many postcards as Shawn . The number of postcards Shawn has is 3/5 of the number of postcards Tim has. If the three boys have 280 postcards altogether,how many more postcards does Tim have than Paul ?

$p = \frac{2}{3}s$

$s = \frac{3}{5}t$

$p+s+t=280$

$p=\frac{2}{5}t$

$2t=280$

$t=140$

$(1-\frac{2}{5})t = \frac{3}{5} \cdot 140 = 3 \cdot 28 = \boxed{84}$

x 

z

I don't think anyone did! 

There are 38 different menu choices.

$5-2(4a+1)+3a=13$

$5-(8a+2)+3a=13$

$(-8a+3a)+(5-2)=13$

$(-8+3)a+3=13$

$-5a=10$

$a=\frac{10}{-5}=-\frac{10}{5}=\boxed{-2}$

The possible lengths are 8, 9, 10, 11, 12.

I think you meant 54, but good job! 

I didn't know your name was jimmy

Where's the equation?

James used 4/7 of his screws and 3/5 of his nails to construct a wooden cupboard. In the end, he had an equal number of screws and nails left. Given that James had a total of 145 screws and nails at first, how many nails did he use to construct the wooden cupboard?

Let s = the number of screws

Let n = the number of nails

We have: $(1-\frac{4}{7})s = (1-\frac{3}{5})n$

This is equal to $\frac{3}{7}s = \frac{2}{5}n.$

We also have $n+s = 145.$

If we multiply the first equation by its common denominator namely $7 \cdot 5 = 35,$ we have that $15s = 14n.$

Multiplying the second equation by 15 we have $15n + 15s = 145 \cdot 15.$

Let’s substitute $14n$ into $15s$: $15n + 14n = 145 \cdot 15 \Rightarrow 29n = 145 \cdot 15.$

Divide both sides by $29:$ $n = 5 \cdot 15 = \boxed{75}$

 - Jimmy

On the day after Halloween, Kabir had 5 times as much candy as Sam. If Kabir gives 18 pieces of candy to Sam, they will each have the same amount. How many pieces of candy do they have in all?

Let k = number of candies Kabir has.

Let s = number of candies Sam has.

We have $k = 5s \qquad$ (1)

We also have $k-18=s+18 \qquad$ (2)

(1) * (2) => $5s - 18 = s + 18$

$4s = 36$

$s = 9 \qquad$ (3)

(3) & (1) => $k = 45 \qquad$ (4)

(3) + (4) => $9 + 45 = \boxed{54}$