Find the length of the side x in this right triangle (image)

Answer:

1.

Original square side: s

Area = s^2

Modified square:

Length = 1.3s

Width = 0.82s

Area = 1.3s * 0.82s = 1.066s^2

(1.066 - 1)/1 * 100% = 6.6%

The area increases by 6.6%

2.

[tex] \dfrac{1}{x} + \dfrac{1}{y} = \dfrac{2}{15} [/tex]

[tex] \dfrac{y}{xy} + \dfrac{x}{xy} = \dfrac{2}{15} [/tex]

[tex] \dfrac{x + y}{xy} = \dfrac{2}{15} [/tex]

[tex] x + y = \dfrac{2xy}{15} [/tex]

[tex] \dfrac{7y + 5xy + 7x}{y + x + 2xy} = [/tex]

[tex] = \dfrac{7x + 7y + 5xy}{x + y + 2xy} [/tex]

[tex] = \dfrac{7(x + y) + 5xy}{x + y + 2xy} [/tex]

[tex] = \dfrac{7(\frac{2xy}{15}) + 5xy}{\dfrac{2xy}{15} + 2xy} [/tex]

[tex] = \dfrac{15}{15} \times \dfrac{7(\frac{2xy}{15}) + 5xy}{\dfrac{2xy}{15} + 2xy} [/tex]

[tex] =  \dfrac{14xy + 75xy}{2xy + 30xy} [/tex]

[tex] =  \dfrac{89xy}{32xy} [/tex]

[tex] =  \dfrac{89}{32} [/tex]

3.

[tex] \dfrac{x - 3}{x^3 + 3x} = \dfrac{A}{x} + \dfrac{Bx + C}{x^2 + 3} [/tex]

[tex] = \dfrac{A(x^2 + 3)}{x(x^2 + 3)} + \dfrac{(Bx + C)x}{(x^2 + 3)x} [/tex]

[tex] = \dfrac{Ax^2 + 3A}{x(x^2 + 3)} + \dfrac{Bx^2 + Cx}{(x^2 + 3)x} [/tex]

[tex] = \dfrac{Ax^2 + 3A + Bx^2 + Cx}{x(x^2 + 3)} [/tex]

[tex] \dfrac{x - 3}{x^3 + 3x} =\dfrac{(A + B)x^2 + Cx + 3A}{x(x^2 + 3)} [/tex]

[tex] A + B = 0 [/tex]

[tex] C = 1 [/tex]

[tex] 3A = -3 [/tex]

[tex] A = -1 [/tex]

[tex] -1 + B = 0 [/tex]

[tex] B = 1 [/tex]

[tex] A + B + C = -1 + 1 + 1 = 1 [/tex]

Answer:

let people=x

and shoes=y

now,as per the question

2x-4=y

Answer:

Step-by-step explanation:

15 x^2 - 9 + 4 x - 5 x^2 - 11

by grouping the like terms,

15 x^2 - 5 x^2 + 4x - 9 - 11

10 x^2 + 4x - 20

Hope this helps

plz mark as brainliest!!!!!!

Answer:

10x^2+4x-20

Step-by-step explanation:

Subtarct 5x^2 from 15x^2

Subtract 11 from -9

Answer:

Hey there!

10(5t+5)-10(10t+6)

50t+50-100t-60

-50t-10

Let me know if this helps :)

Answer:

[tex]Number\ of\ bags = 3{\frac{3}{8}[/tex]

Step-by-step explanation:

Given

Size of Flower Pot = 9 cubic-inch

Size of filling bag = [tex]2\frac{2}{3}[/tex] cubic-inch

Required

Determine the number of bags needed to fill the pot

To solve this, we simply divide the volume of the flower pot by the volume of the filling bags;

This is shown as follows:

[tex]Number\ of\ bags = \frac{Volume\ of\ Pot}{Volume\ of\ filling\ bags}[/tex]

Substitute 9 for Volume of Pot and [tex]2\frac{2}{3}[/tex] for Volume of filling bags

[tex]Number\ of\ bags = \frac{9}{2\frac{2}{3}}[/tex]

Convert denominator to improper fraction

[tex]Number\ of\ bags = \frac{9}{\frac{8}{3}}[/tex]

Rewrite Expression

[tex]Number\ of\ bags = 9 / {\frac{8}{3}[/tex]

[tex]Number\ of\ bags = 9 * {\frac{3}{8}[/tex]

[tex]Number\ of\ bags = {\frac{9 * 3}{8}[/tex]

[tex]Number\ of\ bags = {\frac{27}{8}[/tex]

Convert to Mixed Fraction

[tex]Number\ of\ bags = 3{\frac{3}{8}[/tex]

Hence, the number of bags needed to fill the flower pot is [tex]3{\frac{3}{8}[/tex]

Answer:

The answer is

Step-by-step explanation:

Volume of a cylinder = πr²h

where

h is the height

r is the radius

From the question

h = 7 in

To calculate the radius from the diameter we use the formula

radius = diameter/2

From the question

diameter = 6

radius = 6/2 = 3 in

Volume of the cylinder is

(3)²(7)π

= 9(7)π

= 63π

= 197.9203

We have the final answer as

Hope this helps you

Answer:

5.385 Units

Step-by-step explanation:

5²+2²=c²

25+4=c²

29=c²

c=√29

c=5.385

Answer:8

Step-by-step explanation:

Answer:

because the square root of 10 is an irrational number, and only rational numbers are integers. integers are whole numbers and have no fractions or decimels... hope it helps

Answer:

[tex]2\sqrt{71}[/tex]

Step-by-step explanation:

[tex]a^{2} + b^{2}=c^{2}[/tex]

[tex]59+225=284[/tex]

[tex]\sqrt{284}= 2\sqrt{71}[/tex]

Answer:

c=[tex]2\sqrt{71}[/tex]

Step-by-step explanation:

[tex]a^{2} +b^{2} =c^{2} \\15^{2} +(\sqrt{59} )^{2}=c^{2}\\225+59=c^{2}\\284=c^{2} \\2\sqrt{71} =c[/tex]

Step-by-step explanation:

We are given 4x+y=6x-1 to graph. The easiest way to graph is to turn this equation into slope-intercept form, which is y=mx+b.

First, we are going to subtract 4x from both sides to isolate the y variable which gets us y=2x-1, and now we have slope-intercept form. Now we're going to use what we know about the form to graph.

In such form, m is the slope and b is the y-intercept. Our b in our equation is -1, so you're going to put a dot at (0,-1) on the y-axis. Then for our slope, it is 2, but it's easier to envision as rise over run where 2 is how much we rise and 1 is how much we run (or move to the right). So from our starting point from the y-axis, we're going to move up 2 units and then to the right one unit. And with two dots on the graph, we can run a line through it which will give us our graphed line.

For safe measures, you can continue the pattern of rising 2 and running 1, or you can go down 2 and left 1, which is the opposite and yet still confines to the line.

If you don't understand this explanation, I also recommend checking out desmos! It's a graphing calculator online in which you can plug this equation in and it graphs it for you! The file I have attached to this is from desmos to help you see the graph, I hope you do well!

To solve this problem we will have to convert 4x + y = 6x - 1 to point - slope form, for simplicity --- ( 1 )

4x + y = 6x - 1,

- 2x + y = - 1,

Point - Slope Form : y = 2x - 1

Now let's graph this equation. Consider the x - intercept and y - intercept of this graph --- ( 2 )

0 = 2x - 1

2x = 1

x = 1 / 2 = 0.5 ( x - intercept ),

y = 2(0) - 1 = 0 - 1 = - 1 ( y - intercept )

We know that the x - intercept is 0.5, so we can plot the point (0, 0.5). Similarly we can plot the point ( - 1,0 ) given the y - intercept is - 1. After plotting these points we can run a line through them, creating our graph.

Answer:

1.) 20 dollars

2.) (2t + 10) dollars

Step-by-step explanation:

Given that There is an automatic fee of $10 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot.

1.) How much total money would London have to pay for parking if she left her car in the lot for 5 hours?

5 × 2 = 10 dollars

Then add the automatic price which is $10

Therefore, London will pay a total of

10 + 10 = 20 dollars

2.) How much would London have to pay if she left her car in the lot for tt t hours?

(2 × t) + 10

2t + 10

Answer:

Step-by-step explanation:

The rate of change in this case is 50 pounds per box. The fixed amount that the elevator must carry is 210 pounds, which is how much he weighs. The amount that varies with additional boxes is 50 pounds per box, making it the rate of change. If this situation was graphed, George's weight would be the y-intercept and the rate of change would be the slope.

Answer: x=7

Step-by-step explanation: 4(7+4)=44. 7(7)-5=44.

Answer:

x=7

Step-by-step explanation:

4(x + 4) = 7x - 5

Distribute

4x+16 = 7x-5

Subtract 4x from each side

4x+16 -4x = 7x-5-4x

16 = 3x -5

Add 5 to each side

16+5 = 3x-5+5

21 = 3x

Divide by 3

21/3 = 3x/3

7 =x

Answer:#2 is D and #3 is false

Step-by-step explanation:

Answer:

f(x) down 5 units

and shifted to the left 9 units

Step-by-step explanation:

Transforming f(x) = |x| into g(x) = |x+9| - 5

involves:

1) shifting the graph horizontally 9 units to the left (with the subtraction of -9 from the variable "x", getting x+9 inside the absolute value symbols, and

2) shifting its graph 5 units down by subtracting 5 from the full expression

Answer:

Step-by-step explanation:

10 (x + 50) = 90

The question is incomplete. Here is the complete question.

The football team needed to buy Gatorade for Saturday's big game. They have two options. The first option is they can buy it pre-made in 48 ounces bottles for $3.84 for each bottle. Or they can buy packets and mix with water. Each packet makes 64 ounces and will cost $4.80.

a) Find the cost per ounce of each.

b) Which size costs less?

c) The team will need to buy 192 ounces of Gatorade. How much do you save using the choice from answer b?

Answer: a) Pre-made: $0.08 cost per ounce; Packet: $0.075 cost per ounce

              b) Packets

              c) Save $0.96.

Step-by-step explanation:

a) Cost per ounce:

Pre-made:

[tex]\frac{3.84}{48}[/tex] = 0.08

Packet:

[tex]\frac{4.8}{64}[/tex] = 0.075

b) Comparing costs per ounce, packets costs less than pre-made.

c) Buying packets, the cost will be:

0.075*192 = $14.4

Buying pre-made:

0.08*192 = $15.36

Comparing costs, pre-made is 0.96 more than packets, so they will save 96 cents.

Answer:

See explanation below

Step-by-step explanation:

Using the exponent rule for products:

[tex]x^a\,*\,x^b = x^{(a+b)}[/tex]

we can write:

[tex]20^{12}\,*\,20^8=20^{(12+8)}=20^{20}[/tex]

Answer:

a = 7

Step-by-step explanation:

a - 17 = -10

Add 17 to each side

a - 17+17 = -10+17

a = 7

Answer:

a = 7

Step-by-step explanation:

I hope this helps!

Answer:

{2, 6}

Step-by-step explanation:

Subset: A subset is a set of which all the element are contained or can be find in the universal set.

From the question above,

μ = {1,2,4,5,6}

* The first option {0,1,2} is wrong because  0 is not contained in the universal set.

* The second option {3,4} is wrong because, 3 is not contained in the universal set.

* The third option {5,6,7} is wrong because 7 is not contained in the universal set.

* The last option {2,6} is correct because all of the element of the set are contained in the universal set, and as such makes it a subset.

Hence the subset of {1,2,4,5,6} is {2, 6}

Answer:

24 bouquet

Step-by-step explanation:

300 divide by 12.50

Answer:

B = 48

Step-by-step explanation:

You are given that the two vertical lines are parallel. That means that the alternate interior angles are  equal (they form a Z shape).

So the given is that A = B

A = 5x - 12

B = 2x + 24

Solution

5x - 12 = 2x + 24

5x - 12 = 2x + 24 + 12

5x = 2x + 36

5x - 2x = 36

3x = 36

x = 36/3

x = 12

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

B is

B = 2x + 24

B = 2*12 + 24

B = 24 + 24

B = 48

Answer:

B=48

Step-by-step explanation:

so angle A and B are on what I call the z-angles which are normally equal in that if you view the parallel lines horizontally you will see the form of a z and the corners of it are equal that said you equate both of them to get x

5x-12=2x+24

join like terms

5x-2x=12+24

3x=36

x=12

so to find angle B substitute x with 12

Answer:

Step-by-step explanation:

Answer:

a. Assuming we are starting out with the same mass or number of both cells, definitely there would be more cells of sample 2 after three hours

b. If there are equal number of both cells initially, there would be 8 times more of cell 2 than cell 1

Step-by-step explanation:

a.The first part of the question asks if there would be more cells of sample 1 or 2 after three hours.

Now, the first assumption we shall be making is that we have equal numbers or let’s say mass of both cells initially.

Okay, let’s say we have x g of both cells initially.

Now sample 1 cell divides every 20 minutes.

How many times will have divided in 3 hours? The correct way to tackle this is by knowing the number of two minutes in 3 hours.

In an hour, we have 3 20 minutes. So in 3 hours, we will have 9 20 minutes

Let’s take a look at the sample 2 cell.

it divides every 30 minutes.

Now, in an hour, we have 2 30 minutes. In 3 hours, we will be having 6 30 minutes

Since cell 2 underwent 6 divisions while cell 1 underwent 9 divisions within the same 3 hours and they both have the same mass initially, then we will have more of cell 2 after three hours.

b. We want to know by how many more.

Now, for cell 1 since the division is 9 times, and it is definitely an exponential division, the mass or amount of the original left after 9 half divisions would be;

(1/2)^9 = 1/512

So 1/512 of x would be left and that would be x/512 left

For cell 2, we have the same approach. There are six divisions.

The amount left after the 6th division would be;

(1/2)^6 = 1/64

So the amount left after the sixth division would be x * 1/64 = x/64

Now, we want to know by which amount is the division of cell 2 greater.

That would be x/64 divided by x/512 = x/64 * 512/x = 8

Answer:

A car travels 20km in 15 minutes, what is the average speed that the car travelled at?

the average speed that the car travelled at is 80km per hour

Step-by-step explanation:

Answer:

1. A bus travels 16km in 4 mins. The total time is 4 minutes.

2. A speeding car traveling at 40 km/hr decides to slow down to 30 km/hr after covering half the distance. The total distance the car travels is 34.29 km/h.

3.  A truck goes from Haryana to Bangalore with an average speed of 60 km/hr. The journey takes 30 hours. It returns from Bangalore to Haryana on the same road with an average speed of 40 km/hr. The average speed of the truck during the road trip is 48 km/hr.

Answer:

3x³ - 3y - 3   or     3(x³ - y - 1)

Step-by-step explanation:

3 - 3 + x³ + 6x³ - 3y - 3 - 4x³

group like terms

= x³ + 6x³ - 4x³ - 3y + 3 - 3 - 3

add similar terms

= 3x³ - 3y - 3   or     3(x³ - y - 1)

Answer:

I don’t know this one sorry

Step-by-step explanation:

I think it's -3

[tex]2x - 5 = \frac{1}{2} (3x - 13)[/tex]

[tex]4x - 10 = 3x - 13[/tex]

[tex]x = - 3[/tex]

First box has 15 packets and every packet has 20 toys in it.

Second box has 20 packets and every packet has 15 toys in it.

For the first box, 15 x 20 = 300

For the second box, 20 x 15 = 300 again.

So these two box equal to each other.

Answer:

i think it is the control group sorry if i am wrong

Step-by-step explanation: