Based on an architectural drawing, a roof slopes to a drain
along the function represented in the table that defines the
edge of slope, where x is the horizontal distance in feet and
f(x) is the vertical distance in feet.
If the drain is at the minimum point, how far is it from the wall
defined by the y-axis?
A. O feet
B. 8 feet
C. 80 feet
D. 160 feet

Answer:

22n

Step-by-step explanation:

Answer:

Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...

Answer:

-6m/s^2

Step-by-step explanation:

State your knowns

s=Not required

u=18m/s

v=0m/s

a=?

t=3 seconds

(by the way this is more a physics question)

Find an applicable suvat equation

v=u+at

Rearrange the equation

v-u=at

(v-u)/t=a

Substitute values

(0-18)/3=a

Evaluate

a=-6

State the answer

The value of acceleration is -6m/s^2

Answer:

it is longer than 1/3

Step-by-step explanation:

Answer:

(-3, 0).

Step-by-step explanation:

At the x intercept y = 0 so

(x + 3) / (x - 2) = 0

x + 3 = 0

x = -3.

x-intercept is at (-3,0).

Answer:

D

Step-by-step explanation:

The range means the possible values of the y coordinate which is y ≥ 1 in this function

Answer:

The circumference of circle is 101 units.

Step-by-step explanation:

Given that the diameter of circle is 32 units so you have to find radius by dividing it by 2 :

[tex]radius = diameter \div 2[/tex]

[tex]radius = 32 \div 2[/tex]

[tex]radius = 16 \: units[/tex]

Next, we have to apply circumference formula, C = 2×π×r where r represents radius which is 16 units :

[tex]c = 2 \times \pi \times r[/tex]

Let π = 22/7,

Let r = 16,

[tex]c = 2 \times \frac{22}{7} \times 16[/tex]

[tex]c = 32 \times \frac{22}{7} [/tex]

[tex]c = \frac{704}{7} [/tex]

[tex]c = 101 \: units \: (3s.f)[/tex]

__________________________________

Hey!!

Solution,

Diameter=32

Radius=32/2=16

Circumference of circle=?

Now,

Circumference of circle=2 pi r

=2*22/7*16

=100.57

hope it helps...

Good luck on your assignment

_________________________________

Answer:

false

Step-by-step explanation:

you cant have same size without congruent

Answer:

A

Step-by-step explanation:

If the equation of the line is written in slope-intercept form, y = mx + b then the value of b will be -21; the correct answer is option A.

Slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

This is because the more the height of the line to thee amount we walk or run on the horizontal axis, the more the slope is. That is why we took difference of horizontal axis in denominator and difference of vertical axis on numerator.

Formula for slope, thus, is;

Slope = (y₂ - y₁) / (x₂ - x₁)

Parameters;

J(-4, -5) and K(-6, 3)

= (3 - (-5)) / (-6 - (-4))

= (3 + 5) / (-6 + 4)

= 8 / -2

= -4

Substitute one of the coordinates into the formula to solve for b

y = mx + b

y = -4x + b

3 = -4(-6) + b

3 = 24 + b

3 - 24 = b

b = - 21

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Answer:

A

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (a, b) and r = m , thus

(x - a)² + (y - b)² = m² ← in standard form

Expand the factors using FOIL and rearrange

x² - 2ax + a² + y² - 2by + b² = m² ( subtract m² from both sides )

x² + y² - 2ax - 2by + (a² + b² - m² ) = 0 ← in general form → A

Answer:

It's option A for plato

Step-by-step explanation:

A.  x^2 + y^2 − 2ax − 2by + (a^2 + b^2 − m^2) = 0

Answer:

5/18

Step-by-step explanation:

540/9=60

60x4=240(Alvin's money)

60x5=300(simon's money)

Alvin gives half so you divide 240 by 2 which is 120

Simon gives a tenth so you divide 300 by ten which is 30

120+30=150

150/540=5/18 ( simpliest form)

Theo have 5/18 fraction of total amount of money.

Given that, Alvin and Simon shared £540 in the ratio 4:5.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Now, 4+5=9

So, share of Alvin = 4/9 × 540

= 4 × 60

= £240

Then Simon share = 540-240 = £300

Theo's share = 1/2 × 240

=£120

Theo's share 1/10 of 300

=1/10 × 300

=£30

Total Theo's share = 120+30 =£150

Now, fraction = 150/540

=5/18

Therefore, Theo have 5/18 fraction of total amount of money.

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Answer:

2kx+4y=20 ⇒ kx+2y=10

3x+6y=30 ⇒ x+2y= 10

k is the coefficient of x, so it is the slope of the line

Answer: 1,024/25 or 40.96

Step-by-step explanation:

The length of one side of a square is 32/5, and all sides of a square have the same length, then all sides of the square have 32/5 as the length.

In order to get the area of the square, you need to multiply one side by another.

32/5 * 32/5 = 1,024/5 (fraction form)

32/5 = 6.4

6.4 * 6.4 = 40.96 (decimal form)

Answer:

Connie started with $25 in her savings account.

Step-by-step explanation:

The y-intercept is the value of the function at time zero.

At x = 0, which is week zero, when Connie opened the account, the y value is 25. That means she opened the account with $25.

Answer: $25

Answer:

25

Step-by-step explanation:

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

Work Shown:

1/500 = 0.002 is the probability of winning $390

3/500 = 0.006 is the probability of winning $230

16/500 = 0.032 is the probability of winning $170

Multiply the probabilities with their respective winnings

0.002*390 = 0.78

0.006*230 = 1.38

0.032*170 = 5.44

Then add up those results

0.78+1.38+5.44 = 7.60

which is the expected value.

Side note: This game is not a fair game because mathematically a "fair game" is defined as such where the expected value is 0; ie, neither the player nor the dealer win and things break even.

Answer:

I don't speak Spanish but I know what your asking. Trigonometry is a thing in physics.

Step-by-step explanation:

Answer:

She should cut 1.21 inches (or a square of area 1.46 inch²) from 4 corners to get the maximum volume

Step-by-step explanation:

Length = L = 10 inches

Width = W = 6 inches

Suppose x is cut from the 4 corners to make a box.

Dimensions of the Box:

L= 10 - 2x

W = 6 - 2x

H = x

Volume of the Box:

V = (L)(W)(H)

V = (10-2x)(6-2x)(x)

V = 4x³ -  32x² + 60x

For Maximum value:

[tex]\frac{dV}{dx}=0[/tex]

[tex]\frac{dV}{dx}=\frac{d}{dx}(4x^3-32x+60x)\\\frac{dV}{dx}=12x^2-64x+60\\12x^2-64x+60 = 0[/tex]

The values of x found are:

x= 4.12 , x = 1.21

If we put x= 4.12 in W= 6-2x , the value of width becomes negative, so that is not possible.

We discard 4.12. Now x=1.21

So,

If 1.21 inches are cut from 4 corners, or a square of 1.21*1.21 = 1.46 inch² is cut from 4 corners, we get the maximum value of V

Answer: 17

Step-by-step explanation:

Use the Pythagorean theorem.

C^2 = A^2 + B^2

So, C is always the hypotenuse which is the longest side length and the side length diagonal of the right angle. Side "s" is the hypotenuse.

Square sides AB and BD

It looks like this:

C^2 = 8^2 + 15^2

8^2 = 64

15^2 = 225

225 + 64 = 289

the square root of 289 is 17

17 = s

Answer:

see below

Step-by-step explanation:

g(x) = (x² - 2 * 1/2 x) - 6

      = (x - 0.5)² - 0.25 - 6

      = 1(x - 0.5)² - 6.25

Answer:

21 g

Step-by-step explanation:

Use ration method

28:14 = 42:x

To find x,

(14 x 42) divided by 28, which equals 21g

Answer:

-4 =x

Step-by-step explanation:

ƒ(x) = 9x + 54

Let f(x) = 18

18 = 9x+54

Subtract 54 from each side

18-54 = 9x + 54-54

-36 = 9x

Divide each side by 9

-36/9 = 9x/9

-4 =x

Answer: B

Step-by-step explanation:

Well, they told you what f(x) equals. So make the function of f(x) equal to the value they gave, 18

[tex]18=9x+54[/tex]

Subtract 54 from both sides to get:

[tex]-36=9x[/tex]

Divide both sides by 9 to get x = -4

Answer:

The volume of a cone is:

V=(hπr^2)/3, where h=height and r=radius  

V=(7π4^2)/3

V=112π/3 ft^3

V≈117.29 ft^3  (to nearest hundredth of a cubic foot)

Step-by-step explanation:

Answer:

Correct option: First one -> real and distinct.

Step-by-step explanation:

To evaluate the roots of the equation 7x^2 + x - 1 = 0, lets find the discriminant Delta using the Bhaskara's formula:

[tex]\Delta = b^{2} - 4ac[/tex]

Where a, b and c are coefficients of the quadratic equation (in this case, a = 7, b = 1 and c = -1)

So we have that:

[tex]\Delta = 1^{2} - 4*7*(-1) = 29[/tex]

To evaluate the roots of the equation, we have the following cases:

[tex]\Delta > 0[/tex] : Two roots real and distinct

[tex]\Delta = 0[/tex] : Two roots real and equal

[tex]\Delta < 0[/tex] : Two roots not real

In our case, we have [tex]\Delta > 0[/tex], so the roots are real and distinct.

Correct option: First one

Answer:

6m

Step-by-step explanation:

m =number of M&M's

3m=number of peanuts

2m=number of raisins

m+3m+2m=total number of pieces of food=6m

The inequality that represents all x values is [tex]x \ge 4[/tex]

The expression is given as:

[tex]\sqrt{x - 4} \cdot \sqrt{x + 1}[/tex]

Set the radicands to >=0

[tex]x - 4 \ge 0[/tex] or [tex]x + 1 \ge 0[/tex]

Solve for x in both inequalities

[tex]x \ge 4[/tex] or [tex]x \ge -1[/tex]

When [tex]x \ge -1[/tex], the first radicand is irrational from some x values

Hence, the inequality that represents all x values is [tex]x \ge 4[/tex]

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Answer:

180 square feet

Step-by-step explanation:

A rug that is geometrically similar to her room floor is one that has the same size as her room floor.

The floor has dimensions 12 feet by 15 feet.

The area of the floor and hence, the rug is:

A = 12 * 15 = 180 square feet

She should buy a rug that is 180 square feet

Answer:

-1/2

Step-by-step explanation:

The line in slope-intercept form,

y = mx + b

has slope m.

In this case, m = -1/2

Slope = -1/2

Answer:

1. m=-1/2

Step-by-step explanation:

The line is given in slope-intercept form, or

y=mx+b

where m is the slope and b is the y-intercept.

Essentially, the number that is multiplied by x is the slope, and the number that is added or subtracted from the term with x is the y-intercept.

The equation of line is:

y= -1/2x+ 1/4

-1/2 and x are being multiplied (-1/2*x= -1/2x). 1/4 is being added onto the term with x (-1/2x).

Therefore, the slope must be -1/2 and the y-intercept is 1/4.

m= -1/2

b= 1/4

The slope is -1/2 and the first choice is correct.

Answer:

I think it's C

Step-by-step explanation:

Sorry if I'm wrong

Answer:

Step-by-step explanation:

Answer:

Option (2)

Step-by-step explanation:

                          Statements                                Reasons

1). ∠1 is comp. to ∠2                                1. Given

2). ∠2 is comp. to ∠3                              2. Given

3). ∠1 + ∠2 = 90°                                      3. def. of comp. angles

4). m∠1 = 90° - ∠1                                    4. Subtr. equality property

5). m∠2 + m∠3 = 90°                              5. def. of comp. angles

6). m∠3 = 90° - m∠2                               6. subtr. equality property

7). m∠1 = m∠3                                         7. Transitive property

Option (2) will be the answer.

Both angle ∠1 and ∠3 are complementary to ∠2, therefore, ∠1 + ∠2 = 90°

and by properties of equality, ∠1 = ∠3.

Response:

The completed two column proof is presented as follows;

Statements  [tex]{}[/tex]                             Reasons

1. ∠1 is comp. to ∠2  [tex]{}[/tex]               1. Given

2. ∠2 is comp. to ∠3  [tex]{}[/tex]             2. Given

4. m∠1 = 90° - m∠2  [tex]{}[/tex]                4. Subtraction equality property

5. m∠2 + m∠3 = 90°  [tex]{}[/tex]              5. Definition of complementary angles

6. m∠3 = 90° - m∠2  [tex]{}[/tex]                6. Subtraction equality property

7. m∠1 = m∠2   [tex]{}[/tex]                        7. Transitive property

Details of the solution:

Given that ∠1 is complementary to ∠2, we have;

∠1 + ∠2 = 90°

Similarly, by definition of complementary angles, we have;

∠2 + ∠3 = 90°

Which gives;

∠3 + ∠2 = 90°

Therefore;

∠1 + ∠2 = ∠3 + ∠2

Subtracting ∠2 from both sides (subtraction property of equality), gives;

∠1 + ∠2 - ∠2 = ∠3 + ∠2 - ∠2

∠1 + 0 = ∠3 + 0

Which gives;

∠1 = ∠3

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