Kate and Nora each have a sum of money. The ratio of the amount of money Kate has to that of Nora is 3 : 5. After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9. Find the sum of money Kate had initially.

Answer:

x = 3

4^2 + x^2 = 5^2

solve for x

16 + x^2 = 25

x^2 = 25-16

x^2 = 9

sqrt of x^2 = 3

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Hope this helps! If so, please mark my answer as brainliest!

Answer: D I think?

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

How do I know?

Well first you have to see where it is going with this. It is negative no? so cross out the postive numbers. Then you are left with infinite and (-4,-8). Now do you see the pattern. -4, -4, -8. It will not go to infinite so cross out that. Now what are you left with? That's right (-4,-8)

 Please don't forget to mark me brainliest.

Answer:

$9.55

Step-by-step explanation:

152.80/8=19.10-what he makes per hour

19.10/2=9.55 what he makes for half an hour

Answer:

19.1 I think is the answer I am not sure

Step-by-step explanation:

Step-by-step explanation:

area of rectangle= x ( x +2 ) = 24

X2 + 2X = 24

X 2 +2X _24 = 0

(X +6 ) ( X _4 ) = 0

X= 4

X= - 6.......refused

side length of rectangle is 4 , 6

perimeter= 2( 4+6) = 20 Cm

The side lengths are 4cm , 6cm and perimeter of rectangle is 20cm.

The perimeter of a rectangle is the sum of its four sides. Hence,

Perimeter of Rectangle = 2 (Length + Width) units.

The area of the space occupied within the perimeter of a rectangle is called the area of a rectangle. It is calculated by finding the product of the length and breadth of the rectangle.

Area of rectangle = Length * Breath

According to the question

Area of a rectangle =  24 square centimeters

Side length  = x+ 2

Side Breath  = x  

Now,

a>  using Formula of Area of rectangle

Area of rectangle = Length * Breath

substituting the value

24 = x * (x+2 )

24 = [tex]x^{2} +2x[/tex]

[tex]x^{2} +2x[/tex] - 24 = 0

[tex]x^{2} + (6-4)x -24 =0[/tex]

(x +6 ) (x-4) = 0

x = -6 , +4

side cannot be negative

Therefore

Breath  of rectangle (x) = 4 cm

Length of rectangle (x+2) = 6 cm

b> Perimeter of the rectangle  = 2 (Length + Breath) units.

substituting the value

Perimeter of the rectangle  = 2 ( 4 + 6 )  

                                               = 20 cm

Hence, The side lengths are 4cm , 6cm and perimeter of rectangle is 20cm.

To know more about perimeter and area of rectangle here:

https://brainly.com/question/16572231

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Answer:

it has 2 lines of symmetry 1 going across it diagonally and 1 going straight through the middle.

Step-by-step explanation:

Explanation:

Despite there only being one line shown, there are actually two lines here. One just happens to be directly on top of the other.

We can see this by noting that 2y = 3x-1 turns into 4y = 6x-2 when we multiply both sides by 2. Multiplying both sides by the same number keeps the same equation, so that's why we have identical graphs.

The two identical graphs intersect each other infinitely many times, leading to infinitely many solutions. All solutions are (x,y) points on the blue line. Two such solutions are (1,1) and (3,4). All solutions are of the form [tex]\left(x, \frac{3x-1}{2}\right)[/tex]

Answer:

-7n - 3

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define Expression

5n - 3(4n + 1)

Step 2: Simplify

Answer:

y=1/2x+1/2

m=1/2

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(5,3) and (-3,-1).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (5,3), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=5 and y1=3.

Also, let's call the second point you gave, (-3,-1), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-3 and y2=-1.

Now, just plug the numbers into the formula for m above, like this:

m=

-1 - 3 over

-3 - 5

or...

m=

-4 over

-8

or...

m=1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(5,3). When x of the line is 5, y of the line must be 3.

(-3,-1). When x of the line is -3, y of the line must be -1.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (5,3) and (-3,-1).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(5,3). y=mx+b or 3=1/2 × 5+b, or solving for b: b=3-(1/2)(5). b=1/2.

(-3,-1). y=mx+b or -1=1/2 × -3+b, or solving for b: b=-1-(1/2)(-3). b=1/2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(5,3) and (-3,-1)

is

y=1/2x+1/2

Answer:

Total boxes= 75

Step-by-step explanation:

Giving the following information:

A baseball bat factory produces 24,000 bats per day and uses 50 boxes for packing the bats.

First, we need to determine the number of bats that fits into a box:

Bats per box= 24,000 / 50

Barts per box= 480

Now, the number of boxes for 36,000 bats:

Total boxes= total bats / bats per box

Total boxes= 36,000/480

Total boxes= 75

Answer:75

Step-by-step explanation:

Bats 24000/50

Box 480

Answer:

Eq 1) x^2 + x - 6

Factors are : x-2(x+3)

Eq 2) 2x^2 + 4x + 0

Factor out 2x

Factors are: 2x(x+2)

Answer: 2x(to the fourth power) + 6x (to the third power) - 8x (to the second power) - 24x

Step-by-step explanation:

Answer:

I hope this helps:)

Step-by-step explanation:

Given that,

An oil company fills 1 over 10 of a tank in 1 over 5 hour.

To find,

How long it will take for the tank to fill completely.

Solution,

Let it takes t time to fill the tank completely. It can be calculated as follows :

[tex]t=\dfrac{\dfrac{1}{10}}{\dfrac{1}{5}}\ \text{hours}\\\\=\dfrac{1}{10}\times 5\ \text{hours}[/tex]

Hence, the rate is "1 over 10 • 5 hours ". The correct option is (b).

Answer:

$40

Step-by-step explanation:

Answer:

G

Step-by-step explanation:

I think its G because i counted the numbers...and i pretty sure its not a Negative so yah

Answer:

47

Step-by-step explanation:

Answer:

x = 63

Step-by-step explanation:

180 = 47 + 70 + x

180 = 117 + x

180 - 117 = x

63 = x

Answer : 2.5 cups per dollar

Step-by-step explanation:

You need to find to unit rate 4 cups divided by 10$ is 0.40$. Then you need to divided 0.40 into a dollar (which would be 1.00) so 1.00 divided by 0.40 is 2.5 cups

Answer:

Step-by-step explanation:

54

Answer:

I believe because everything adds to 180

Answer:

domain is x = 3

Thus domain means that for every fruit cup costs $3

Range is f(20) = 60

Step-by-step explanation:

We are given;

Total students for the fruit cup party = 18

Total teachers for the fruit cup party = 2

Cost of each fruit cup =$ 3

Delivery charge = $ 10

Now, the total number of people attending the party = Total number of students + Total number of teachers

Thus;

Total number of people attending party = 18 + 2 = 20

Since cost of each fruit cup is $3.

Thus, for 20 fruit cups, the function is;

f(x) = 20x where x is cost of each fruit cup.

It means the cost of 20 fruit cups = $3 × 20 = $60

Thus, domain is x = 3

Thus domain means that for every fruit cup costs $3

Range is f(20) = 60

Answer:

1,184.00

Step-by-step explanation:

used a calculator

Answer:

10

Step-by-step explanation:

½ x + 5 = 10

½ x = 10 – 5

x = 5 x 2

x = 10

follow my account ^^

Answer: 2/3x + 15

Step-by-step explanation:

(⅚x + 10) - (⅙x -5)

The first thing to do here is to open the bracket. This will be:

= ⅚x + 10 - ⅙x + 5

= ⅚x - ⅙x + 10 + 5

= 4/6x + 15

= 2/3x + 15

Answer:

Domain → x > 0

Solution → x = 100

Step-by-step explanation:

Given equation is,

[tex]x^{0.5\text{logx}}=0.01x^2[/tex]

Since, log of any number 'x' is defined when x > 0

Therefore, domain of the equation → x > 0

By taking log on both the sides of the equation,

[tex]\text{log}(x^{0.5\text{logx}})=\text{log}(0.01x^2)[/tex]

0.5(logx)(logx) = log(0.01) + log(x²)

0.5(logx)²= -2 + 2log(x)

Let log(x) = a

Then the equation becomes as,

0.5a² = -2 + 2a

0.5a² - 2a + 2 = 0

a² - 4a + 4 = 0

(a - 2)² = 0

a = 2

Since, a = log(x)

log(x) = 2

x = 10²

x = 100

Therefore, solution of the given equation is x = 100.

[tex]\boxed{\boxed{\pink{\tt \leadsto The \ domain \ of \ x \ is \ (0,\infty ). }}}[/tex]

A equation is given to us and need to find the domain of the equation . So , given equation is ,

[tex]\bf\implies x^{0.5\:log\ x } = 0.01x^2 [/tex]

Now , let's simplify this equation to find the domain of x .

[tex]\bf\implies x^{0.5\:log\ x } = 0.01x^2 \\\\\bf\implies x^{0.5\:log\ x } -0.01x^2 =0 \\\\\bf \implies x^{log \:x^{\frac{1}{2}}} - 0.01x^2=0 \\\\\bf\implies x^{log \ \sqrt{x}} - 0.01x^2=0 [/tex]

Now set the argument in log( √x) Greater than or equal to zero to see where the expression is defined. Since the value of log is non - negative.

[tex]\bf\implies \sqrt{x} > 0 \\\\\bf\implies (\sqrt{x})^2>0^2 \\\\\bf\implies x>0\\\\\bf\implies \boxed{\red{\bf x \in ( 0, \infty ) }}[/tex]

In set builder Notation we can write as ,

[tex]\boxed{\red{\bf \{ x | x > 0 \} }}[/tex]