10. State whether each statement is true or false.

Given:

The railing will begin at a height of 36 inches.

Height decreases 9 inches for every 12 horizontal inches.

To find:

The function for this situation.

Solution:

Let y be the height of the railing in inches according to the horizontal distance in inches, x, from the top of the stairs.

Initial height = 36

So, y-intercept is 36.

Height decreases 9 inches for every 12 horizontal inches.  So,

[tex]\text{Slope}=\dfrac{\text{Vertical change}}{\text{Horizontal change}}[/tex]

[tex]m=\dfrac{-9}{12}[/tex]

[tex]m=-\dfrac{3}{4}[/tex]

Slope intercept form of a line is

[tex]y=mx+b[/tex]

Substitute [tex]m=-\dfrac{3}{4}[/tex] and b=36.

[tex]y=-\dfrac{3}{4}x+36[/tex]

The required function is [tex]y=-\dfrac{3}{4}x+36[/tex].

Therefore, the correct option is A.

Answer:

A

Step-by-step explanation:

Caitlin is designing a railing for a set of stairs. The railing will begin at a height of 36 inches and follow the slant of the stairs, which decreases 9 inches for every 12 horizontal inches.

A drawing of the side view of a set of 4 stairs. There are lines drawn to show a railing that is at the highest point of the stairs and labeled 36 inches.

Which function can represent the height, y, of the railing in inches according to the horizontal distance in inches, x, from the top of the stairs?

y = –StartFraction 3 Over 4 EndFractionx + 36

y = –3x + 36

y = StartFraction 3 Over 4 EndFractionx + 36

y = 3x + 36

Answer:

-$300

Hope this helps : )

Answer:

$300 out of account

Step-by-step explanation:

withdrawals are taking out the money

6*50=300

so she takes out 300 dollars from her account

Answer:

B. [tex]\frac{-3}{4}[/tex]±[tex]\frac{\sqrt{41} }{4}[/tex]

Step-by-step explanation:

First, substitute the equation into the quadratic formula.

[tex]x=\frac{b+-\sqrt{(b^{2} )-4(a)(c)} }{2a}[/tex]

x=[tex]\frac{-3+-\sqrt{(3)^2-4(-2)(4)} }{4}[/tex]

Solve for x.

x= [tex]\frac{-3+-\sqrt{9+32} }{4}[/tex]

x=[tex]\frac{-3+-\sqrt{41} }{4}[/tex]

The answer is x= [tex]-\frac{3}{4}[/tex]±[tex]\frac{\sqrt{41} }{4}[/tex]

Answer:

idk

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

a and c are the same angles so 73+73=146

then you subtract 180-146=34 and 5 times 6 is 30 then plus 4 and get 34

therefore x=34 degrese

Given :

The Learning Center charges a one-time fee of $26 plus $10 per piano lesson.

Guitar lessons have a one-time fee of $36 plus $8 for each lesson.

To Find :

After how many lessons will the cost of learning to play piano be the same or more than learning to play guitar.

Solution :

Mathematical expression of piano lesson :

[tex]P_1=26+10x[/tex]

Mathematical expression of guitar lesson :

[tex]P_2=36+8y[/tex]

( Here, x and y are number of lessons )

Let, after t hours cost of learning to play piano be the same or more than learning to play guitar.

Now, given constraint :

[tex]P_1 \geq P_2\\\\26+10t \geq 36+8t\\\\2t \geq 10\\\\t\geq 5[/tex]

Hence, this is the required solution.

Example:

x^2 + 5x + 6 = 0

(x+3)(x+2) = 0 .... factor

x+3 = 0 or x+2 = 0 ... zero product property used here

x = -3 or x = -2 .... solve each equation for x

------

In general, the zero product property is that if A*B = 0, then either A = 0 or B = 0.

Answer:

I'm not quite sure if this is correct, but If the given values are our X's or the inputs, then yes it would be a function as they're all different numbers.

Answer:

18/sqrt(2)

Step-by-step explanation:

Divide the square into two congruent right triangles:

a and b are the sides of the triangle

since we know that a=b

then the right triangle is isosceles

meaning that the theorem of the 45-45-90 triangle is applicable

so then we can say that 18/sqrt(2) = a = b

Answer:

5 y (y^2 - 2 y + 15)

Step-by-step explanation:

Factor the following:

-(-5) y^3 - 10 y^2 + 75 y

Hint: | Multiply -1 and -5 together.

-(-5) = 5:

5 y^3 - 10 y^2 + 75 y

Hint: | Factor common terms out of 5 y^3 - 10 y^2 + 75 y.

Factor 5 y out of 5 y^3 - 10 y^2 + 75 y:

Answer: 5 y (y^2 - 2 y + 15)

Answer:

1/4 = 1/2² = 2^-2

Step-by-step explanation:

1/4 can be expressed as a negative exponent is 4⁻¹

A negative exponent helps to show that a base is on the denominator side of the fraction line. In other words, the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice versa. For example, when you see x⁻³, it actually stands for 1/x³

Given here, 1/4 thus it can be expressed as 4⁻¹

Hence, 1/4 can be expressed as a negative exponent is 4⁻¹

Learn more about exponents here:

https://brainly.com/question/5497425

#SPJ2

Answer:

x³ - 4x² - 16x + 24

Step-by-step explanation:

Step 1: Write expression

(x - 6)(x² + 2x - 4)

Step 2: Distribute each term

x³ + 2x² - 4x

-6x² - 12x + 24

Step 3: Combine

x³ + 2x² - 4x - 6x² - 12x + 24

Step 4: Combine like terms

x³ - 4x² - 16x + 24

Answer:

D. Square root of 18

Step-by-step explanation:

The square root of 10 is 3.16.

The square root of 12 is 3.46.

The square root of 24 is 4.90.

The square root of 18 is 4.24.

The red dot is on 4.25 so your answer is the square root of 18.

Will you please mark me brainliest?

Answer:

:)

Step-by-step explanation:

Answer:

nobody uses twitter anymore

Step-by-step explanation:

Answer:

it is helpful to constuct d because it makes the graph easier to understand

Step-by-step explanation:

Answer:

a=-1.5 (lmk if im incorrect)

Step-by-step explanation:

-16 - 7(2a + 3) = 23 - 2a

-16-(14a+21)=23-2a

5-14a=23-2a

5=23+12a

-18=12a

-18/12 is -1.5

a=-1.5

Answer:

Please see the attached diagram which shows the data presented as a distance time graph

Step-by-step explanation:

The given time and distance traveled table can be presented as follows;

Time [tex]{}[/tex]                      Distance travelled from starting point

9:00 AM [tex]{}[/tex]                       0 km

10:00 AM [tex]{}[/tex]                     15 km

11:00 AM [tex]{}[/tex]                      25 km

12:00 PM [tex]{}[/tex]                      35 km

1:00 PM [tex]{}[/tex]                        40 km

Therefore, the best type of graph to represent the data is a scatter plot with straight lines that also show the locations of the points on the graph, presented in the form distance time a distance time graph as shown in the attached diagram

Answer:

-96

Step-by-step explanation:

-384 divided by 4 = -96

hope this helped!!

Answer:

-96

Step-by-step explanation:

If we use the "classic math" and do this like -394/4

we would get -96.

Or we can use a calculator and type -384 / 4 and get the same answer -96 (or unless you did your math incorrect)

High Hopes^^

Barry-

Answer:

170 Tickets were sold and 490$ was made

Step-by-step explanation:

to find how many tickets were sold add 120 + 50 to get 170

For how much they made Multiply 120 X 2 to get 240

Then, Multiply 5 x 50 to get 250

Add 240 + 250 and your answer will be 490$

Answer: x=(c-k)/12

Step-by-step explanation:

So you're trying to find x, and in order to do that, you need x by itself. First, move k to the right side by subtracting k from both sides to get 12x=c-k. After that, you divide 12 for both sides to get x=(c-k)/12. It looks like this: [tex]\frac{c-k}{12}[/tex]

Answer:

Step-by-step explanation:

Given:

∠1 and ∠2 are supplementary.

To prove:

l║m

Proof:

∠2 is a supplement of a. ∠1 (Given)

∠3 is a supplement of b. ∠1 [Linear pair of angles are supplementary]

Since supplements of the same angle are congruent,

c. ∠1 ≅ d. ∠2

Since ∠2 and ∠3 are also corresponding angles, l║m by the converse of same side interior angles postulate.

-0.5

Step-by-step explanation:

Negative , has low correlation

Answer:

Positive: As you move from left to right the line was increasing    /

- Negative: As you move from left to right the line was decreasing    \

- Undefined: A Vertical line    |

- Zero: A Horizontal line    -

Step-by-step explanation:

:)

Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

because you want to find the sum of the amount.

Answer:

2800, 320

350, 40

2800+320+350+40=3510

Step-by-step explanation:

(40*70)+(40*8)+(5*70)+(5*8)

Answer:

y = − 6 x + 7

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula

Answer:

1/3

Step-by-step explanation:

Hope This Helps!

Answer:

n is less than or equal to 26

Step-by-step explanation:

I'm guessing you're asking for the inequality, and since a number (n) cannot be more than 26, it has to be less.

The question never said that n can't be 26, and it only said it can't be MORE than 26, so it's less than or equal to 26, so that's what I'm thinking