A lifeguard fills a pool with water at a constant rate. After 1/2 hour, 1/3 of the pool is filled.

At this rate, what fraction of the pool is filled per hour?

A. 1/6 of the pool
B. 1/3 of the pool
C. 1/2 of the pool
D. 2/3 of the pool

Answer: 1. [tex]x=-2[/tex]; 2. [tex]x=\frac{11}{9}[/tex]

Step-by-step explanation :

1.

[tex]6-5x=16\\6-5x-6=16-6\\-5x=10\\\frac{-5x}{-5}=\frac{10}{-5}\\x=-2[/tex]

2.

[tex]4-9x=-7\\4-9x-4=-7-4\\-9x=-11\\\frac{-9x}{-9}=\frac{-11}{-9}\\x=\frac{11}{9}[/tex]

Answer:

Q1)   x =2         Q2)     x = 11/9

Step-by-step explanation:

Q1)   6 - 5x = 16                  check : -5(2) = -10

-6         -6                     6 -- 10 =  6+ 10 = 16

-5x = 10                         Q2)   4 - 9x = -7

-x = -2                                    -4           -4  

x = 2                                      -9x = - 11

--------------                               -x = -11 /9    ----->  x = 11/9

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

Parallel lines have the same slope.

So if the given line has a slope of 3, then the line parallel to it has the same slope (3)

Now, let's write the equation of the line in Point-Slope Form.

Remember, point-slope form looks like so:-

[tex]\bigstar{\underline{\boxed{\pmb{y-y1=m(x-x1)}}}[/tex]

Where

y₁ is the y-coordinate of the point that the line passes through

m is the slope

x₁ is the x-coordinate of the point that the line passes through

In this case,

y₁ is equal to -8

m is equal to 3

x₁ is equal to 1

Plug in the values:

[tex]\longrightarrow\sf{y-(-8)=3(x-1)}[/tex]

Simplify:

[tex]\longrightarrow\sf{y+8=3(x-1)}[/tex]

and we're done!

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

Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

The amount of change Lucy receives if she paid with few $20 bills is $12.84

Total cost of pants = $21.79 × 4

= $87.16

If the total cost of the pants exceeds $80, then she paid with 5 $20 bills

5 $20 bills = $100

Her change = $100 - $87.16

= $12.84

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Answer:

117

Step-by-step explanation:

This is an example of a supplementary angle, so in total it is 180 degrees. Subtract what we know angle 2 is, 63, and we are left with what angle 1 equals, which is 117.

Hope this helps! pls mark brainliest

Answer:

20. 2x+y

21. 4

22. x+y

Step-by-step explanation:

20. 9x+2y - x-2y find your LCM

4 4

=(9x+2y)-(x-2y) clear bracket

4

=9x+2y-x+2y collect terms

4

=9x-x+2y+2y

4

=8x+4y factorize

4

=4(2x+y)

4

=2x+y

with this, you will understand the following

21. 4x + 8y

x+2y x+2y

=4x+8y

x+2y

=4(x+2y)

x+2y

=4

22. 2x-y + 2x+5y

4 4

=2x-y+2x+5y

4

=4x+4y

4

=4(x+y)

4

=x+y

Answer:

V≈220.89cm³

Step-by-step explanation:

Answer: 220.9

4/3 π(3.75)^3=220.9

Answer:

1) 14.137 2)10

Step-by-step explanation:

area of sector is central angle / 360 times (pi)(r^2)

45/360 x pi (6^2)

1/8 x 36pi

14.137

3-4-5- right triangle. Or Pythagorean Theorem.

6^2 + 8^2 = c^2

c= 10

Answer:

Standard Form: y = 4(x-1)(x+5)

Step-by-step explanation:

4 is the leading coefficient, so it should go in front. When making a standard quadratic equation, you must do the opposite for each of the roots (negative to positive, positive to negative.)

if you’re asking for a general form quadratic equation, then sorry, I am unable to help you with that :(

a. answer:_77

2_ (7 * 9) _ 16

2_ (63) _16

_61_16

_77

The volume of the solid created upon dilation bythe scale factor of 3 is 5832 units³.

An image is dilated if the dimensions of the image is resized in a way that does not change the shape of the image. When an image is dilated, it is made larger.

Dimensions of the dilataed solid = 6 x 3 = 18

Volume = 18³ = 5832 units³

To learn more about dilation, please check: brainly.com/question/3457976

Answer:

[tex] 1 \frac{2}{3}\: liters [/tex]

Step-by-step explanation:

[tex]V_{soda}[/tex] in one bottle = 5/9 liters

No of bottles = 3

Total volume of soda

[tex] = \frac{5}{9} \times 3 \\ \\ = \frac{5}{3} \\ \\ = 1 \frac{2}{3} \: liters[/tex]

The growth of the quantity is an illustration of an exponential function

The value of the quantity after 1.55 minutes is 76759.22

The given parameters are:

Initial value, a = 2000

Rate, r = 4%

An exponential growth function is represented as:

y = a(1 + r)^x

Substitute the value in the equation

y = 2000(1 + 4%)^x

After 1.55 minuted, x = 1.55 * 60

So, we have:

y = 2000(1 + 4%)^(1.55 * 60)

Evaluate the expression

y = 76759.22

Hence, the value of the quantity after 1.55 minutes is 76759.22

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Answer:

Step-by-step explanation:

9398.61

Answer:

2:5

Step-by-step explanation:

15 are female. 10 must be male.

Out of 25 pupils, 10 are male, so it's 10:25, or 2:5

Answer:

a) 12x + 22   b) 17[tex]x^{2}[/tex] - x

Step-by-step explanation:

Perimeter is the sum of the each side length.

The first example is a rectangle so the (4x+8) and the (2x+3) are doubled.

(4x+8) x 2 = 8x+16

(2x+3) x 2 = 4x + 6

12x+22

(6[tex]x^{2}[/tex] - 12x) + (2[tex]x^{2}[/tex] + x) + (9[tex]x^{2}[/tex] + 10x)

combine like-terms.

17[tex]x^{2}[/tex] - x

Answer:

12x + 22 for the rectangle, 17x^2 - x for the triangle

Step-by-step explanation:

The perimeter of a square/rectangle is equal to 2*width + 2*length

So for the rectangle, it would be 2*(4x + 8) + 2*(2x + 3)

This can be further simplified as 8x + 16 + 4x + 6

Which can be further simplified as 12x + 22

The perimeter of a triangle is equal to length if side one + length of side two + length of base

That would be (6x^2 - 12x) + (2x^2 + x) + (9x^2 + 10x)

Which becomes 8x^2 - 11x + (9x^2 + 10x)

17x^2 - x

Step-by-step explanation:

1/81 gallon for 1/4 mile.

what do I need to multiply 1/81 with to get 1 gallon ?

it is simple, right ? i need to multiply it by 81 to get 1 gallon.

in order to keep the relationship (ratio) unchanged, I need to multiply the other part (1/4 mile) with the same factor :

1/4 × 81 = 81/4 = 80/4 + 1/4 = 20 1/4 miles

so, at this rate, that car can travel 20 1/4 miles using 1 gallon of gas.

Answer:

Rate is 8.5%

Step-by-step explanation:

Step 1: Write the given terms

Principal (p)=Rs8800

Rate(r)=?

Time(t)=3.5 years

Interest=Rs2618

Step 2: Write the formula for calculating Simple interest

[tex]i = \frac{prt}{100} [/tex]

Step 3: Make r the subject of the equation

[tex]by \: cross \: multiplication \\ 100i = prt \\ divide \: both \: sides \: by \: pt \\ r = \frac{100i}{pt} [/tex]

Step 4: Find the value of r by substituting the values in step 1

[tex]r = \frac{100 \times 2618}{8800 \times 3.5} \\ r = \frac{261800}{30800} \\ r = 8.5[/tex]

Hence, the rate is 8.5%

Answer:

hee-hee!

Step-by-step explanation:

Marcy charges $3 to walk a small dog and $5 for a big dog.

She walks 15 small dogs and 6 big dogs.

We can use an expression that would show the problem:

3s + 5b

(s = small dogs & b = big dogs)

s = 15 | b = 6

3(15) + 5(6)

45 + 30 = 75

Marcy earns $75 of profit.

Answer:

V = 4/3 π R^3        volume of a sphere

V = π R^2 H           volume of cylinder    area of base X height

4/3 π R^3 = π R^2 H       equal volumes

H = 4/3 R       relationship of height to radius for cylinder

H = 4/3 * 13 = 52 / 3 cm = 17 1/3 cm

Answer:

3.19 millimeter round of nearest hundred

Answer:

1 = 3/2

2 = -1/14

Step-by-step explanation:

The equation for the slope of a line is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] (difference in Y divided by the difference in X) or simply just Rise/Run.

For the first one, we have to pinpoint two points on the graph. There's one point placed on the x-axis 2 units away from the origin (2,0) and one four units to the right and 3 units up from the origin (4,3). Since it's on a graph, the easiest way to calculate it is by counting the units up and then right from (2,0) to (4,3). You can count that (4,3) is 3 units up and 2 units right from (2,0). Since slope is Rise/Run, the slope is 3/2.

For the second one, you can use the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. The Y of the second point is 2, and the Y of the first point is 1. The X of the second point is -17, and the X of the first point is -3.

You can plug all 4 numbers in to get (2-1)/(-17- -3)

2-1 = 1 and -17 - -3 = -14. So your slope is 1/-14 or -1/14.

Step-by-step explanation:

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ans

[tex] \frac{3x}{x + 4} [/tex]

Answer:

hi, I'm glad to help! 185

Step-by-step explanation:

11*7=77

11*6=66

6*7=42

77+66+42=185

Answer:

  (c)  (15, -30)

Step-by-step explanation:

A proportional relationship has the equation ...

  y = kx

The value of the constant of proportionality is the ratio of y to x:

  k = y/x = 40/-20 = -2

__

The point that is on the line y = -2x is the point (15, -30).

Step-by-step explanation:

All Natural Number (1,2,3,4,5...) are integers

All Whole numbers (0,1,2,3,4...) are not natural numbers (1,2,3,4...)

All integers are rational numbers

All real numbers are not irrational numbers as real nimber contain both rational and irrational numbers hence it is false.

Hence statement 1 and statement 3 are true

Answer:

The answeris D

Step-by-step explanation:

All whole numbers are natural numbers; natural numbers are numbers we use for counting 1, 2, 3....and so on, so that makes them whole because thay have no fraction, or decimils.

Answer: Yes

Step-by-step explanation:

If you draw the altitude of an isosceles triangle from the vertex angle, then the two triangles formed are congruent, meaning the base angles are congruent  by CPCTC.

Yes, the base angles of an isosceles triangle are congruent because in n isosceles triangle two of its sides are always congruent, and also angles opposite to congruent sides are congruent.

An isosceles triangle is a triangle that has at least two sides of equal length.

When an altitude is drawn to the base of the isosceles triangle, it bisects the vertex angle. As it bisects the base, the two congruent triangles are created.

Hence, Yes, the base angles of an isosceles triangle are congruent because in n isosceles triangle two of its sides are always congruent, and also angles opposite to congruent sides are congruent.

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Answer:

60

Step-by-step explanation:

By the triangle midsegment theorem, 2(SU)=RV.

2(w-30)=w, meaning w=60.

So, RV=60 as well

Answer:

m^4 - 225c^10 = (m^2 - 15c^5 )(15c^5 + m^2)

4.8xy + 36y^2 + 0.16x^2 = (6y + 0.4x)^2

Answer:

I think the answer must be c because the length is 6\5 feet so there no chances to be the answer is more than so the base is divited and the ft should be multiplied

The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762

Parabloid, x = 4y² + 4z²

plane x = 4

x = 4y² + 4z²

x = 4

4 = 4y² + 4z²

4 = 4 (y² + z² )

1 = y² + z²

from polar coordinates

y = r cos θ

z = r sin θ

r² = y² + z²

0 ≤ θ ≤ 2π

4r² ≤ x ≤ 4

0 ≤ r ≤ 1

[tex]\int\limits\int\limits\int\limits {x} \, dV = \int\limits^1_0\int\limits^a_b\int\limits^c_d {x} \, dx ( rdrdz)[/tex]

where

a = 4

b = 4r²

c = 2r

d = 0

The first integral using limits c and d gives:

[tex]2pi\int\limits^1_0\int\limits^a_b {xr} \, dx[/tex]

The second integral using limits a and b

[tex]pi\int\limits^1_0 {16 } } \, rdr - pi\int\limits^1_0 {16r^{5} \, dx[/tex]

[tex]16pi\int\limits^1_0 { } } \, rdr - 16pi\int\limits^1_0 {r^{5} \, dx[/tex]

[tex]16pi\int\limits^1_0 { } } \, [r-r^{5}]dr[/tex]

The third integral using limits 1 and 0 gives: 16.762

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The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762

Integration is defined as adding small parts to form a new significant part.

Parabloid, x = 4y² + 4z²

plane x = 4

x = 4y² + 4z²

x = 4

4 = 4y² + 4z²

4 = 4 (y² + z² )

1 = y² + z²

from polar coordinates

y = r cos θ

z = r sin θ

r² = y² + z²

The limits of the integral

0 ≤ θ ≤ 2π

4r² ≤ x ≤ 4

0 ≤ r ≤ 1

[tex]\int\int\intxdV = \int_0_1\int_b_a\int_d_cxdx(rdrdz)[/tex]

where

a = 4

b = 4r²

c = 2r

d = 0

The first integral using limits c and d gives:

[tex]2\pi\int_0^1\int_b^axydx[/tex]

The second integral using limits a and b

[tex]\pi \int_0^116rdr-\pi\int_0^116r^5dx[/tex]

[tex]16\pi \int_0^1rdr-16\pi\int_0^1 r^5dx[/tex]

[tex]16\pi\int_0^1[r-r^5]dr[/tex]

The third integral using limits 1 and 0 gives: 16.762

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