What is the result of subtracting the second equation from the first?
2
x
+
7
y
=
−
8
2
x
−
5
y
=
−
1
2x

Ms. Mundo can fill 5 full glasses with 40 ounces of tropical punch, with 5 ounces remaining. This remaining amount fills 2/3 of the last glass.

Ms. Mundo made 40 ounces of tropical punch to pour into glasses that each holds 7 1/2 ounces. To find out what fraction of the last glass is full of punch, we first need to determine how many full glasses can be poured from the 40 ounces.

Since each glass holds 7.5 ounces (which is the same as 7 1/2 ounces), we divide 40 by 7.5 to find the number of full glasses:

 40 ÷ 7.5 = 5 remainder 5

This means that 5 full glasses can be filled, with 5 ounces of punch remaining. Now, to find out what fraction of the last glass the remaining punch fills, we divide the leftover ounces by the capacity of one glass:

 5 ÷ 7.5 = 2/3

The fraction of the last glass that is full of punch is 2/3.

Answer:

2/3

Step-by-step explanation:

Cancel the common factor 2 = 2/3

Answer:

A = 10⁰

Step-by-step explanation:

We have 2.247 and this to represented as [tex]$ 2 \times A + 2 \times B + 4 \times C + 7 \times D $[/tex]

[tex]$ 2.247 = \frac{2247}{1000} $[/tex]

[tex]$ 2.247 = 2 \times 10^0 + 2 \times \frac{1}{10} + 4 \times \frac{1}{10^2} + 7 \times \frac{1}{10^3} $[/tex]

Comparing with the given data, we have:

A = 10⁰

B = [tex]$ \frac{1}{10} $[/tex]

C = [tex]$ \frac{1}{10^2} $[/tex]

D = [tex]$ \frac{1}{10^3} $[/tex]

Hence the answer A = 10⁰.

Answer: 11

Step-by-step explanation:

plug in 4 any instance you see "x"

f(x) = 3x - 1​

f(4) = 3(4) - 1 = 11

Functions are mappings who map inputs to at max one corresponding outputs. The value of function at x=4 is: [tex]f(4) = 11[/tex]

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

For given case, we have:

[tex]f(x) = 3x - 1[/tex]

Taking x = 4, we get:

[tex]f(4) = 3(4) - 1 = 3 \times 4 - 1 = 12 - 1\\f(4) = 11[/tex]

Thus, The value of function at x=4 is: f(4) = 11

Learn more about evaluating functions here:

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Answer:

6x^3

Step-by-step explanation:

2160x^8/ 60x^2

2160/60=36

x^8-2 because your dividing

x^6

36x^6 (you're not done)

after you've got the square root

6x^3 because

36=6*6

and the square root of 6 is 2.45 which rounds to 3

(I'm pretty sure this is the answer).

The simplified form of [tex]\rm \sqrt{\dfrac{2160 x^8}{60x^2}[/tex] is 6x³ , Option C is the right answer.

Square root of a positive square number is the number itself.

[tex]\rm \sqrt{y^8} = y^4[/tex]

In the given question the expression given is

[tex]\rm \sqrt{\dfrac{2160 x^8}{60x^2}[/tex]

To simplify this

the numerator and the denominator has to be simplified first

[tex]\rm \dfrac{2160x^8}{60x^2}\\[/tex]

[tex]\rm \dfrac{2160}{60}\\ \\\\\ \dfrac{1080}{30}\\\\\\ \dfrac{540}{15} \\\\\\ \dfrac{108}{3}\\\\= 36[/tex]

[tex]\rm \dfrac{x^8}{x^2} \\\\= x^{8-2}\\\\= x^6[/tex]

Therefore

[tex]\rm \sqrt{36x^6}[/tex]

6x³

The simplified form of [tex]\rm \sqrt{\dfrac{2160 x^8}{60x^2}[/tex] is 6x³ , Option C is the right answer.

To know more about Square root

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Answer:

what' you should do to stay healthy is eat vegetables and fruits grains and anything else you know is good for you and you should also drink water everyday. what you shouldn't do to stay healthy is basically eat junk food and drink soda also eat lots of candy but eating healthy is much better

Answer:

Staying healthy physically can help you stay healthy emotionally too. If you're eating the right food and keeping fit, your body will be strong and help you to cope with stress and also fight illness. Eating well and exercising often when you're a teenager will also help you stay in good health later in life.

Step-by-step explanation:

In the equation y=40+6x, 40 represents the initial number of comic books in Joylin's collection, given to her by her uncle. Over time, she gains additional comic books from monthly subscriptions.

In the provided equation, y=40+6x, the number 40 represents the initial amount of comic books Joylin has before the monthly subscriptions start. This is essentially the number of comic books Joylin's uncle gave her to start her collection. The number 6 represents the number of books she receives monthly from the subscriptions. Therefore, 'x' months after receiving the initial batch of comic books, Joylin has 40 + 6x comic books in her collection.

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Answer:

The number of sides of the polygon with 135° interior angle is 8  

Step-by-step explanation:

Given as :

The measure of each interior angle of regular polygon = 135°

Let The total number of sides = n

So, each internal angle of a regular polygon with n sides = [tex]180^{\circ}- \frac{360^{\circ}}{n}[/tex]

or,   135°  = [tex]180^{\circ}- \frac{360^{\circ}}{n}[/tex]

or, [tex]\frac{360^{\circ}}{n}[/tex] = 180° - 135°

or,   [tex]\frac{360^{\circ}}{n}[/tex] = 45°

∴   n = [tex]\frac{360^{\circ}}{45^{\circ}}[/tex]

I.e  n = 8

Hence the number of sides of the polygon with 135° interior angle is 8  Answer

Answer:

$7,500.00

Step-by-step explanation:

The Realtor commission will be 5% of $150,000.00

(5% * $150,000)/100% = $7,500.00

The realtor makes a 5% commission on a $150,000 house, which equates to a commission of $7,500 by multiplying the sale price by the commission rate (0.05).

To calculate the amount of commission a realtor earns on a house sale, you simply multiply the sale price of the house by the commission rate. In this case, the realtor makes a 5% commission on a $150,000 house sale. We calculate the commission as follows:

Therefore, the realtor will earn a commission of $7,500 for selling the $150,000 house.

Answer:

24

Step-by-step explanation:

in this, the blank is 'y'. I filled the x with -8

)(−8)−(−8−40)=(2)(−8)−(y−8)

Step 1: Simplify both sides of the equation.

(10)(−8)−(−8−40)=(2)(−8)−(y−8)

(10)(−8)+−1(−8−40)=(2)(−8)+−1(y−8)(Distribute the Negative Sign)

(10)(−8)+(−1)(−8)+(−1)(−40)=(2)(−8)+−1y+(−1)(−8)

(10)(−8)+8+40=(2)(−8)+−y+8

−80+8+40=−16+−y+8

(−80+8+40)=(−y)+(−16+8)(Combine Like Terms)

−32=−y+−8

−32=−y−8

Step 2: Flip the equation.

−y−8=−32

Step 3: Add 8 to both sides.

−y−8+8=−32+8

−y=−24

Step 4: Divide both sides by -1.

−y

−1

=

−24

−1

y=24

Answer:

y=24

Answer:

A'(-16,4), B'(16,-12), C'(8,12), D'(-4,16)

Step-by-step explanation:

The dilation with a center of dilation at (0,0) and scale factor of [tex]\frac{1}{4}[/tex] has the rule

[tex](x,y)\rightarrow \left(4x,4y\right)[/tex]

Quadrilateral ABCD has vertices at points A(-4,1), B(4,-3), C(2,3) and (-1,4).

Therefore, the image vertices are

Answer: x=-5

(^._.^)ﾉ

Step-by-step explanation:

4x-3=2x-13

Subtract

4x−3−2x=−13

Simplify

2x−3=−13

Add 3 to both sides

2x=−13+3

Simplify again

2x=-10

Divide both sides by 2

x=[tex]-\frac{10}{2}[/tex]

Simplify one last time

x=-5

You're finished! Not only that but you found the answer :3

Hope this helps, have a BLESSED and wonderful day! :-)

Part A

h(d) = (-1/5)d^2 + 2d is the same as h(d) = -0.2d^2 + 2d because -1/5 = -0.2

I'll use x in place of d, and y in place of h(d) to get this equivalent equation: y = -0.2x^2 + 2x

Let's find the vertex of y = -0.2x^2 + 2x

Note how y = -0.2x^2 + 2x is in the form y = ax^2+bx+c with

a = -0.2

b = 2

c = 0

So the x coordinate of the vertex is

h = -b/(2a)

h = -2/(2(-0.2))

h = 5

Plug this value into the h(d) function to compute the corresponding y coordinate

h(d) = -0.2d^2 + 2d

h(5) = -0.2(5)^2 + 2(5)

h(5) = 5

Coincidentally, the x and y coordinates of the vertex are both the same. This wont be the case in general.

-----------------

Answers:

The vertex is located at (5,5)

The interpretation is that the highest the dolphin can get is 5 feet off the surface of the water and this occurs 5 horizontal feet away from the starting point. Imagine a parabola that opens downward to have a highest point at the vertex mentioned.

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

Part B

From part A above, we found x = 5 to be the x coordinate of the vertex. Simply double this value to get 10 as the answer. The reason why this works is because x = 0 is the starting x intercept, or the starting point which the dolphin jumps from. Also, its because of the hint given how the vertex is between each x intercept.

If the dolphin started from any other point on the x axis, then this trick of "double the result from part A" wouldn't apply.

Part C below shows that x = 0 and x = 10 are the two x intercepts. This helps confirm the proper range.

-----------------

Answer: 10 feet

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

Part C

h(d) = y = height of dolphin

we want to find the two x values that make y = 0, which help us figure out when the dolphin jumps out of the water and when it lands back in the water

--------

Plug y = 0 into the equation y = -0.2x^2 + 2x and solve for x

y = -0.2x^2 + 2x

-0.2x^2 + 2x = y

-0.2x^2 + 2x = 0

x(-0.2x + 2) = 0 .... factor out x

x = 0 or -0.2x + 2 = 0 .... zero product property

x = 0 or -0.2x = -2

x = 0 or x = -2/(-0.2)

x = 0 or x = 10

-----------------

Answer:

The two x intercepts are x = 0 and x = 10

This means the parabola crosses the x axis at the locations (0,0) and (10,0).

Answer:

[tex]y=4\sqrt{3}\ units[/tex]

Step-by-step explanation:

Triangle MRN is created by folding an equilateral triangle by half. Since triangle MRN is right triangle, the equilateral triangle must be folded along the height drawn to one side.

In equilateral triangle with side length of a units, the height is [tex]\dfrac{a\sqrt{3}}{2}\ units[/tex] and the height is greater than half the side because

[tex]\dfrac{a\sqrt{3}}{2}>\dfrac{a}{2}.[/tex]

The leg with length x units has the smaller projection (2 units long) than the leg with length y units has (6 units long).

This means the leg with length y units is the height of the equilateral triangle. If the leg with length y units is the height of the equilateral triangle, then the hypotenuse MN = 8 units is the side of the equilateral triangle and lex with length x units is half the side, so x = 4 units.

By the Pythagorean theorem,

[tex]y^2=8^2-4^2\\ \\y^2=64-16\\ \\y^2=48\\ \\y=4\sqrt{3}\ units[/tex]

The value of y is 4*sqrt(3) units.

The problem states that triangle MRN is created by folding an equilateral triangle in half. Since triangle MRN is a right triangle, the equilateral triangle must have been folded along its height. We are given that the side length of the equilateral triangle is 8 units. We are asked to find the value of y, which is the length of the leg of triangle MRN that is opposite the right angle.

Here's how we can solve the problem:

1. Identify the relevant information:

   - Triangle MRN is a right triangle.

   - The original equilateral triangle has side length 8 units.

   - We want to find the value of y, which is the length of the leg of triangle MRN opposite the right angle.

2. Use the properties of equilateral triangles:

   - In an equilateral triangle, all sides are equal and all angles measure 60 degrees.

   - The height of an equilateral triangle divides the triangle into two 30-60-90 triangles.

   - The height of an equilateral triangle with side length a is sqrt(3)*a / 2.

3. **Relate the information to find y:**

   - Since the equilateral triangle was folded along its height, the height of the equilateral triangle is also the hypotenuse of triangle MRN (side MN).

   - Therefore, MN = sqrt(3)*8 / 2 = 4*sqrt(3).

   - We are given that MN = 8, so 4*sqrt(3) = 8.

   - Solving for sqrt(3), we get sqrt(3) = 2.

   - Now we can use the Pythagorean theorem in triangle MRN: y^2 + (4)^2 = (8)^2.

   - Substituting sqrt(3) = 2, we get y^2 + 16 = 64.

   - Solving for y, we get y = sqrt(48) = 4*sqrt(3).

Therefore, the value of y is 4*sqrt(3) units.

Answer:

675 ft 2

Step-by-step explanation:

just did it in a test

Answer:

40 games

Step-by-step explanation:

Here we need to find a number, x, such as 32 is the 80% of x. In this case x is our 100%.

So, if our x number is the correct it must be that the following ratios are equivalent:

100%/80% = x/32 if 32 is the 80% of x

Lets drop the % sign for simplicity:

100/80 = x/32

Now, multiply both sides by 32 to eliminate the 32 on the right side:

(100/80)*32 = (x/32)*32

100*32/80 = x

3200/80 =x

320/8 = x

40 = x

So 32 is the 80% of 40.

32 games is the 80% of 40 games.

Answer: 40

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

No - because the length of any one side must not be equal or greater than the sum of the other 2 sides.

Here 7 = 3 + 4 so they can't form a triangle.

Answer:

no

Step-by-step explanation:

as 3+4 = 7 and the sum of the first 2 sides is supposed to be greater than the third side and 7 is the sum of the first 2 side and the third side is also 7

Answer:

(3 + 4x)(9 - 12x + 16x²) = 0

(4m - 1)(16m² + 4m + 1) = 0

Step-by-step explanation:

Here we have to solve the sum of two cubes which is [tex]27 + 64x^{3}[/tex]

Now, the equation is [tex]27 + 64x^{3} = 0[/tex]

⇒ 3³ + (4x)³ = 0

⇒ (3 + 4x)[3² - 3(4x) + (4x)²] = 0

⇒ (3 + 4x)(9 - 12x + 16x²) = 0

So, (3 + 4x) = 0 or (9 - 12x + 16x²) = 0

Therefore, from the above two relation we can solve for x.

One root will be [tex]- \frac{3}{4}[/tex] and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.  

Again, we have to solve the difference of two cubes which is [tex]64m^{3} - 1[/tex]

Now, the equation is [tex]64m^{3} - 1 = 0[/tex]

⇒ (4m)³ - 1³ = 0

⇒ (4m - 1)[(4m)² + 4m(1) + 1²] = 0

⇒ (4m - 1)(16m² + 4m + 1) = 0

So, (4m - 1) = 0 or (16m² + 4m + 1) = 0

Therefore, from the above two relation we can solve for m.

One root will be [tex] \frac{1}{4}[/tex] and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.  (Answer)

Answer: –1.8x – 4.5

Step-by-step explanation:

The guy above me obviously doesn’t know how to do this so here this is the correct answer

Answer:

–1.8x – 4.5

Step-by-step explanation:

Answer:

equation- 4÷x=-7

x= -4/7

Step-by-step explanation:

I think the answer is -4/7 i tried my best :)

so x=-4/7

Answer:

x=-3, y=5. (-3, 5).

Step-by-step explanation:

y=x+8

x+y=2

----------

x+x+8=2

2x+8=2

2x=2-8

2x=-6

x=-6/2

x=-3

y=-3+8=5

Answer:

(-3,5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

(y-y)=m(x-x)

(y--3)=2(x-7)

y+3=2x-14

y+3+14=2x

Answer:

1. C

2. A

The drawings will help

Remember: Keep, Change, Flip

Answer: 10 free throws made, 9 two-point shots made

Step-by-step explanation:

x=number of free throws

y=number of two-point shots

x+y=19

x+2y=28

solve by elimination

x+2y=28

-(x+y=19)

--------------

y=9

x=10

Answer: 10 free throws made, 9 two-point shots made

Step-by-step explanation:

x=number of free throws

y=number of two-point shots

x+y=19

x+2y=28

solve by elimination

x+2y=28

-(x+y=19)

(Y=9

X=10)

Answer:

Step-by-step explanation:

c

Answer:

$18

Step-by-step explanation:

12*4=48

48-30=18

Answer:

x=15

Step-by-step explanation:

Answer:

x=15

Step-by-step explanation:

4x+10=x+5+50

4x+10=x+55

4x-x+10=55

3x+10=55

3x=55-10

3x=45

x=45/3

x=15

Answer:take 193 and subtract 35. you should get 158 then divide 158 bby 2 you should get 79 add 35 to 79 you should get 114. therefore kelly will have 114 and rachel will have 79

Step-by-step explanation:

Answer:

Kelly collected 114 pounds of newspaper. Rachel collected 79 pounds of newspaper.

Step-by-step explanation:

Write an expression for each girl to figure out how many pounds of newspapers they each collected:

(x represents pounds of newspapers)   Rachel = x     Kelly = x + 35

To solve, combine the two expressions into one equation: 2x + 35 = 193

Then, subtract 35 from both sides of the equation. Make sure you subtract from both sides of the equation to keep it equal: 2x + 35 - 35 = 193  - 35

The equation left is: 2x = 158

Divide both sides by two in order to get the x by itself: 2x ÷ 2 = 158 ÷ 2

The answer will be: x = 79

Then, substitute 79 for x in the first equations:

Rachel = 79    Kelly = 79 + 35

Solve for the final answer: Rachel = 79    Kelly = 114

To calculate the change in water amount after 1/3 hour, the draining rate of -3.75 gallons per hour is multiplied by 1/3, resulting in a total change of -1.25 gallons of water.

The student has asked about the change in the amount of water in a bathtub after a certain period, given a constant rate of draining. The bathtub drains at a rate of -3.75 gallons per hour. To find the total change in the amount of water after 1/3 hour (20 minutes), we multiply the rate by the time.

First, we convert 1/3 of an hour to minutes:

1/3 hour = 60 minutes / 3 = 20 minutes.

Next, we calculate the change in water:

Change in water = Rate  imes Time

Change in water = -3.75 gallons/hour  imes 1/3 hour

Change in water = -3.75 gallons/hour  imes 0.3333... (repeating)

Change in water = -1.25 gallons.

Therefore, the bathtub will drain 1.25 gallons of water in 1/3 of an hour.

Answer:

that's your answer...