Bill is building a staircase for his new home. He has measured several three-foot bars to support the handrail. If Bill nails the support bars to the handrail and to the edge of the staircase (a 2-inch-by-12-inch board attached parallel to the slope of the stairs) at 12-inch intervals, will the handrail be parallel to the staircase?

Answer:

i think its very interesting and pretty cool,  because there is so much to learn  and so much to explore

i wouldn't like the fact that you have to study so much though

Step-by-step explanation:

Answer:

[tex]\frac{2}{a-b}[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{a+b}[/tex] + [tex]\frac{1}{a-b}[/tex] + [tex]\frac{2b}{a^2-b^2}[/tex] ← a² - b² is a difference of squares

= [tex]\frac{1}{a+b}[/tex] + [tex]\frac{1}{a-b}[/tex] = [tex]\frac{2b}{(a-b)(a+b)}[/tex] ← LCD is (a - b)(a+b)

= [tex]\frac{a-b+a+b+2b}{(a-b)(a+b)}[/tex]

= [tex]\frac{2a+2b}{(a-b)(a+b)}[/tex]

= [tex]\frac{2(a+b)}{(a-b)(a+b)}[/tex] ← cancel common factor (a + b) on numerator/ denominator

= [tex]\frac{2}{a-b}[/tex]

Answer:

Hello,

Step-by-step explanation:

[tex]|AD|^2=(3-(-1))^2+(0-(-1))^2=16+1=17\\\\|AB|^2=1^2+3^2=10\\\\\boxed{Perimeter=2*\sqrt{17} +2*\sqrt{10}}[/tex]

Answer:

2*√10 + 2*√17

Step-by-step explanation:

In order to find the perimeter we must find the length of each side

To find the length of the sides we must use the distance formula

Distance formula:

d = √ ( x2 - x1 )² + ( y2 - y1 )²

Where the x and y values are derived from the points of each side

First let's find the length of AB

Coordinates of A: (-1,-1)

Coordinates of B: (0,2)

* Define variables *

( Remember coordinates are written as (x,y))

x1 = -1

x2 = 0

y1 = -1

y2 = 2

Now to find the length of AB we simply plug in the values of x and y into the distance formula

d = √ ( x2 - x1 )² + ( y2 - y1 )²

x1 = -1, x2 = 0, y1 = -1, y2 = 2

* Plug in values *

d = √(0 - (-1))² + (2 - (-1))

If there are two negative signs in front of a number then the two negative signs cancel out and the sign changes to +

d = √(0+1)² + (2+1)²

Simplify addition

d = √(1)² + (3)²

Apply exponents

d = √1 + 9

Simplify addition

d = √10

So the length of AB is √10

One of the properties of a parallelogram is that the opposite sides are congruent.

So the opposite side of AB (CD) is also equal to √10

Next we need find the length of AD

We use the same process we used for finding the length of AB

Coordinates of A: (-1,-1)

Coordinates of D: (3,0)

*Define variables*

x1 = -1

x2 = 3

y1 = -1

y2 = 0

Plug in the values of x and y into the formula ( formula is d = √ ( x2 - x1 )² + ( y2 - y1 )² )

*Plug in the values of x and y )

d = √( -1 - 3 )² + ( 0 - (-1)²

Simplify subtraction and addition

d = √(-4)² + (1)²

Apply exponents

d = √16 + 1

Add

d = √17

So the length of AD is √17

Like stated previously opposite sides in a parallelogram are congruent so the opposite side of AD (BC) also has a length of √17

Now to find the perimeter,

The perimeter is the sum of the side lengths

Side lengths of the parallelogram shown:

AB = √10

BC = √17

CD = √10

DA = √17

Perimeter = √10 + √17 + √10 + √17 = 2*√10 + 2*√17

Answer:

The measure of central tendency, mean and median are approximately equal for the boys indicating that the data of the boys is more evenly spread while standard deviation of the girls data is less than those of the boys indicating that the data for the girls is less widely spread.

Step-by-step explanation:

The given data are;

,             1       2       3      4     5      6       7    8      9      10

Girls,    50    32     15    56   81    50     18    81    22    55

Boys,   75     41     25    22    7     0      43    12    45    70

Sorting the data gives;

Girls,     15,   18,     22,   32,  50,   50,   55,  56,    81,  81

Boys,     0,     7,     12,     22, 25,    41,    43, 45,     70, 75

For the even numbered sample data size, the first quartile, Q₁ is found by sharing the data into two and finding the median of the left half which  gives;

10/2 = 5 on each half

The first quartile, Q₁, is the median of the left 5 data points which is the 3rd data point = 22 for girls and 12 for boys

The third quartile, Q₃, is found in similar method to be the 8th data point which is 56 for girls and 45 for boys

The median = 50 for girls and 33 for boys

Therefore, the interquartile ranges are;

IQR = 56 - 22 = 34 for girls, 45 - 12 = 33 for boys

We check for outliers.

Q₁ - 1.5×IQR = 22 - 1.5*34 = -29

Q₃ + 1.5×IQR = 56 + 1.5*34 = 107

We check the mean of both data samples as follows;

Average for the girls = 46

Average for the boys = 34

Standard deviation for girls = 23.99

Standard deviation for girls = 25.43

Therefore, the measure of central tendency is more accurate for the boys indicating that the data of the boys is more evenly spread while the data for the girls is less widely spread.

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

Work Shown:

3 & 1/2 = 3 + 1/2 = 3 + 0.5 = 3.5

3.5% = 3.5/100 = 0.035

r = 0.035 is the decimal form of [tex]3\frac{1}{2}\%[/tex] which is used along with

to get the following

A = P*(1+r/n)^(nt)

A = 500*(1+0.035/12)^(12*0.5)

A = 508.81405074594

A = 508.81

Extra info: Gabe earned A-P = 508.81 - 500 = 8.81 dollars in interest.

This question is solved using a system of equations, and doing this, we get that: There are 9 quarters, 4 nickels and 12 dimes.

I am going to say that:

x is the number of nickels.

y is the number of dimes.

z is the number of quarters.

In all, they are worth $3.65.

A nickel is worth $0.05, a dime is worth $0.1 and a quarter is worth $0.25, so:

[tex]0.05x + 0.1y + 0.25z = 3.65[/tex]

Dimes: 3 times greater than nickels:

This means that:

[tex]y = 3x[/tex]

Quarters: One greater than double the number of nickels:

This means that:

[tex]z = 2x + 1[/tex]

Value of x:

We have y and z as function of x, so we can replace into the equation and find the value of x, so:

[tex]0.05x + 0.1y + 0.25z = 3.65[/tex]

[tex]0.05x + 0.1(3x) + 0.25(2x+1) = 3.65[/tex]

[tex]0.05x + 0.3x + 0.5x + 0.25 = 3.65[/tex]

[tex]0.85x = 3.4[/tex]

[tex]x = \frac{3.4}{0.85}[/tex]

[tex]x = 4[/tex]

y and z:

[tex]y = 3x = 3(4) = 12[/tex]

[tex]z = 2x + 1 = 2(4) + 1 = 9[/tex]

There are 9 quarters, 4 nickels and 12 dimes.

A similar question is found at https://brainly.com/question/17096268

Answer:

1 plane

I hope this helps!

Answer:

There are 3 numbers that are not whole numbers.

3/4, 3.7, and sqrt 3 are not whole numbers

Answer:

3

Step-by-step explanation:

There are only 3 that aren't whole numbers. The whole numbers are: 32, 1,265, 3000, and 1. The numbers that aren't whole are: 3/4, 3.7, and √3

Answer:

24

Step-by-step explanation:

Answer

24!

Step-by-step explanation:

Person above me is correct :)

Answer: height = 17.5cm

Step-by-step explanation: Peter mixes blue and yellow paint in the ratio 2:3, which means:

[tex]\frac{2}{3} = \frac{8.4}{x}[/tex]

[tex]x = \frac{8.4*3}{2}[/tex]

x = 12.6L

The container is full with the two paints, so total volume:

V = 12.6 + 8.4

V = 21L

Knowing that 1L = 1dm³ and sides of cuboid is measure in cm:

V = 21dm³ = 21000cm³

Volume of a cuboid is calculated as:

V = width*length*height

Height of the container is

height = [tex]\frac{V}{width*length}[/tex]

height = [tex]\frac{21000}{30*40}[/tex]

height = 17.5cm

The height of the container is 17.5cm.

Answer:

m<C = 102°

Step-by-step explanation:

Step 1: find measure of arc BC.

According to the Inscribed angle theorem of a circle, an inscribed angle is half the measure of the arc it intercepts.

m<D intercepts arc ABC

thus, 80° = ½(120+BC)

Solve for BC. Multiply both sides by 2

80*2 = 120 + BC

160 = 120 + BC

BC = 160 - 120 = 40°

Step 2: Find m < A

According to the Inscribed angle theorem, m < A = ½ of arc BCD = ½(40 + 116)

m < A = 78°

Step 3: find m < C

m < A + m < C = 180 (opposite angles of an inscribed quadrilateral are supplementary)

m < C = 180 - 78 = 102°

Answer:

Step-by-step explanation:

Let the points be A and B

A ( 7 , 5 ) ⇒( x₁ , y₁ )

B ( 2 , 4 )⇒( x₂ , y₂ )

Now, let's find the slope of the line which contains these points:

Slope = [tex] \mathsf{\frac{y2 - y1}{x2 - x1} }[/tex]

plug the values

⇒[tex] \mathsf{ \frac{4 - 5}{2 - 7} }[/tex]

Calculate

⇒[tex] \mathsf{ \frac{ - 1}{ - 5} }[/tex]

Reduce the fraction with -1

⇒[tex] \mathsf{ \frac{1}{5} }[/tex]

Hope I helped!

Best regards!

Answer:

x = -7

Step-by-step explanation:

DE + EF + FG = DG

2x+17 + 8+2 = x+20

Combine like terms

2x+ 27 = x+20

Subtract x from each side

2x+27-x = x+20-x

x+27 = 20

Subtract 27 from each side

x+27-27 = 20-27

x = -7

7 ( X — 1 ) + 15 ( X + 9 )

= 7 X — 7 + 15 X + 135

= 22 X + 135 — 7

= 22 X — 128 ( Ans )

7 ( X – 1 ) + 15 ( X + 9 )

= 7X – 7 + 15X + 135

= 7X + 15X + 135 – 7

= 22X + 128 ( Answer )

Answer:

The volume is multiplied by 8.

Step by step explanation:

Let the length equal l, the width equal w, and the height equal h for the original rectangular prism.

The volume of a right rectangular prism with length l, width w, and height h is V=lwh.

Therefore, the volume of the original prism is lwh.

The new rectangular prism has dimensions that are twice those of the original rectangular prism: the length equals 2l, the width equals 2w, and the height equals 2h.

To calculate the volume of the rectangular prism, substitute the doubled values into the formula for the volume of a rectangular prism.

V=2l·2w·2h

Simplify.

V=8lwh

The new volume is 8lwh.

If the length, width, and height of a right rectangular prism are doubled, the volume is multiplied by 8.

Therefore, the new volume is the original volume multiplied by 8.

Answer:

The slope is

Step-by-step explanation:

To find the slope of AB we use the formula

Where

m is the slope and

(x1 , y1) and (x2 , y2) are the points

The slope of AB

A (-3, 12), B (-11, -16) is

We have the final answer as

Hope this helps you

Hey there! I'm happy to help!

First we multiply the the length of each length of rope by the number of lengths of rope (try saying that five times fast).

6 3/4×13=87 3/4

Now, we divide this by 20 to see how much rope each person gets.

87 3/4÷20= 4 31/80

Therefore, each person has 4 31/80 or 4.3875 meters of rope.

I hope that this helps! Have a wonderful day! :D

Answer:

Average speed during the trip = 24 km/h

Step-by-step explanation:

Given:

Speed of cyclist uphill, [tex]v_1[/tex] = 20 km/hr

Speed of cyclist on flat ground = 24 km/h

Speed of cyclist downhill, [tex]v_2[/tex] = 30 km/h

Cyclist has traveled on the hilly road to Beast Island from Aopslandia and then back to Aopslandia.

That means, one side the cyclist went uphill will the speed of 20 km/h and then came downhill with the speed of 30 km/h

To find:

Average speed during the entire trip = ?

Solution:

Let the distance between Beast Island and Aopslandia = D km

Let the time taken to reach Beast Island from Aopslandia = [tex]T_1\ hours[/tex]

Formula for speed is given as:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

[tex]v_1 = 20 = \dfrac{D}{T_1}[/tex]

[tex]\Rightarrow T_1 = \dfrac{D}{20} ..... (1)[/tex]

Let the time taken to reach Aopslandia back from Beast Island = [tex]T_2\ hours[/tex]

Formula for speed is given as:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

[tex]v_2 = 30 = \dfrac{D}{T_2}[/tex]

[tex]\Rightarrow T_2 = \dfrac{D}{30} ..... (2)[/tex]

Formula for average speed is given as:

[tex]\text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time Taken}}[/tex]

Here total distance = D + D = 2D km

Total Time is [tex]T_1+T_2[/tex] hours.

Putting the values in the formula and using equations (1) and (2):

[tex]\text{Average Speed} = \dfrac{2D}{T_1+T_2}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{D}{20}+\dfrac{D}{30}}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{30D+20D}{20\times 30}}\\\Rightarrow \text{Average Speed} = \dfrac{2D\times 20 \times 30}{{30D+20D}}\\\Rightarrow \text{Average Speed} = \dfrac{1200}{{50}}\\\Rightarrow \bold{\text{Average Speed} = 24\ km/hr}[/tex]

So, Average speed during the trip = 24 km/h

please mark this answer as brainlist

Answer:

Option (B).

Step-by-step explanation:

From the figure attached,

There are two pieces of the function defined by the graph.

1). Curve with the domain (-∞, 2)

2). Straight line with domain (2, ∞)

1). Function that defines the curve for x < 2,

  f(x) = |4 - x²|

2). Linear function which defines the graph for x ≥ 2 [Points (2, 2), (4, 4), (6, 6) lying on the graph]

  f(x) = x

Therefore, Option (B) will be the answer.

Answer:

I think it's 43 and 43 degrees. I just subtracted 180-94, got 86, and divided it so yea.

Answer:

the lines arent parallel, so you cant use corresponding angles theorem

The error is corresponding property does not apply.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions. For example, the opposite sides of a rectangle represent parallel lines.

We know that when two lines are parallel they the following property:

As, there is no parallel lines line.

So, the measurement if <1 = 88 can't be true because corresponding doesn't apply.

Learn ore about parallel lines here:

https://brainly.com/question/12860077

#SPJ2

Answer:  see graph

Step-by-step explanation:

Look at the Unit Circle to see the coordinates of the quadrangles.

Build a sine table for one period (0° - 360°).

    x        y = sin(x)          y² = (sin(x))²      (x, y²)    

    0°       sin(0°) = 0          (0)² = 0              (0°, 0)

   90°     sin(90°) = 1          (1)² = 1               (90°, 1)

  180°     sin(180°) = 0        (0)² = 0            (180°, 0)

  270°     sin(270°) = -1       (-1)² = 1             (270°, 1)

  360°     sin(360°) = 0       (0)² = 0            (360°, 0)

Now plot the (x, y²) coordinates on your graph.

Answer:

(x + 5)² = - 3

Step-by-step explanation:

Given

x² + 22x + 28 = 12x ( subtract 12x from both sides )

x² + 10x + 28 = 0 ( subtract 28 from both sides )

x² + 10x = - 28

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(5)x + 25 = - 28 + 25

(x + 5)² = - 3

( yx + 4x - 5 )( y + 1 )

.....................................

Step-by-step explanation:

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]

in we have x = 11

put the value of x in equation

[tex]b(11) = \sqrt{3} (11) + 3[/tex]

[tex]b(11) = 11 \sqrt{3} + 3[/tex]

so x = 11√3

Hope it helps