A ladder is leaning against the side of a 10 m house. If the base of the ladder is 3 m away
from the house, how long is the ladder? Please draw a diagram.

Answer:   115.2 units²

Step-by-step explanation:

Since you know the length of two sides and the measure of the included angle, you can use the following trig formula:

[tex]Area=\dfrac{1}{2}ac \sin B[/tex]

Given: a = 19, c = 14, B = 60°

[tex]A=\dfrac{1}{2}(19)(14) \sin 60^o\\\\.\quad =133\sin 60^o\\\\.\quad =115.2[/tex]

Answer:

[tex]\huge \boxed{\mathrm{115.2 \ units^2 }}[/tex]

Step-by-step explanation:

We can solve for the area of the triangle when two sides are given and the angle in between the two sides.

[tex]\displaystyle A=\mathrm{\frac{1}{2}ac \cdot sinB }[/tex]

[tex]\displaystyle A=\mathrm{\frac{1}{2} \cdot 19 \cdot 14 \cdot sin60 }[/tex]

[tex]\displaystyle A=\mathrm{\frac{133\sqrt{3} }{2} }[/tex]

[tex]\displaystyle A=\mathrm{115.18137870...}[/tex]

The area of the triangle is 115.2 units².

Answer:

The linear equation relating price to demand is Q=-0.5*P + 30

Step-by-step explanation:

The demand for a good is the quantity of that good that the demanders are willing to purchase at a given price.

Then, the Demand Curve relates the quantity that a consumer would be willing to buy as a function of price.

You seek to determine the linear equation that relates the price to the demand Q = m * P + b where Q is the quantity demanded at a price P, and compared with the equation of the straight line y = mx + b, m is the slope and b is the ordinate to the origin.

On a line of the form y = m * x + b, the value of m, having two points, is calculated by:

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

And the ordinate to the origin b is calculated, taking the value of m, replacing any of the two points (replacing any of the two because it must give the same value of b) in the expression y = m * x + b and solving its value.

In the case of Q=m*P+b, the value of m, having two points, is calculated by:

[tex]m=\frac{Q2-Q1}{P2-P1}[/tex]

Being:

and replacing:

[tex]m=\frac{10-5}{40-50}[/tex]

you get:

m= -0.5

So, being Q=-0.5*P+b,  b is calculated by:

5= -0.5*50 + b → 5= -25 + b → 5+25= b → b= 30

10= -0.5*40 + b → 10= -20 + b → 10+20= b → b= 30

Then, the linear equation relating price to demand is Q=-0.5*P + 30

Hi there! :)

Answer:

[tex]\huge\boxed{(-1, 3)}[/tex]

Use the midpoint formula to derive the midpoint of the segment:

[tex](x_{m} ,y_{m}) = (\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )[/tex]

Substitute in the coordinates:

[tex](x_{m} ,y_{m}) = (\frac{-3+1 }{2} , \frac{4+2 }{2} )[/tex]

Simplify:

[tex](x_{m} ,y_{m}) = (-1 , 3 )[/tex]

The coordinates of the midpoint are:

[tex](-1, 3)[/tex]

Answer:

11,15,19,23,27,31,35,39,43,47,51,55,59,63,67,71,75,79,83,87,91,95,99,103,107,111,115

Step-by-step explanation:

I think this is what you wanted

Answer:

Center is (3,4)

Radius is √55 which is approximately 7.42

Step-by-step explanation:

First, recall the equation for a circle. The equation for a circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where (h,k) is the center and r is the radius.

We have the equation:

[tex]x^2+y^2-6x-8y-30=0[/tex]

Thus, we want to turn this into the circle equation.

To do so, we need to complete the square.

First, put all the x-terms together and all the y-terms together. Also, add 30 to both sides:

[tex](x^2-6x)+(y^2-8y)-30=0\\(x^2-6x)+(y^2-8y)=30[/tex]

Now, complete the square for both of the variables. Recall how to complete the square. If we have:

[tex]x^2+bx[/tex]

We divide b by 2 and then square it. Then we will have a perfect square trinomial. To keep things balanced, we must also subtract what we added.

Thus, for the first term:

[tex](x^2-6x)\\=(x^2-6x+9)-9\\(x-3)^2-9[/tex]

And for the second term:

[tex](y^2-8y)\\=(y^2-8y+16)-16\\=(y-4)^2-16[/tex]

Replace the two terms:

[tex]((x-3)^2-9)+((y-4)^2-16)=30[/tex]

Simplify. Add -9 and -16:

[tex](x-3)^2+(y-4)^2-25=30[/tex]

Add 25 to both sides:

[tex](x-3)^2+(y-4)^2=55[/tex]

This is now in the form of the circle equation.

Thus, the center is (3,4).

And the radius is √55 which is approximately 7.42

Answer:

to be honest I'm not sure

Answer:

Step-by-step explanation:

A Chi-square test is used to test the test of independence between rows and columns, contingency tables. It is a test related to frequencies. The observed frequency is a given statistical frequency known as the actual frequency,  the expected frequency is known as the theoretical frequency is derived from the study by using the sum total of the row and total in the column divided by their corresponding sample size.

Answer:

d = 6 days

Step-by-step explanation:

We only have a total of 30 gallons.

We are told that we use 5 gallons per day.

So:

d - days

5d = 30

*Divide both sides by 5*

d = 6

Answer:

the value of the t test statistic is - 3.419

Step-by-step explanation:

Given that;

n₁ = 18, u₁ = 78.3, s₁ = 6.4

n₂ = 11, u₂ = 84.3, s₂ = 5.3

α = 0.1

Now The hypothesis are;

H₀ : u₁ = u₂

H₁ : u₁ < u₂

To compute the value of the t test statistic;

t = [(x₁ - x₂) / s × √(1/n₁ + 1/n₂)]

where

s = √ [ ((n₁-1) × s₁² + (n₂ - 1 ) × s₂²) / ( n₁ + n₂ - 2)]

s = √ [ ((18-1) × 6.4² + (11 - 1 ) × 5.3²) / ( 18 + 11 - 2)]

s = √ [ (7 × 40.96 + 10 × 28.09 ) / 27 ]

s = √ [ (286.72 + 280.9) / 27 ]

s = √(567.62/27)

s = √21.0229

s = 4.585

Now  t test statistics t = [(x₁ - x₂) / s × √(1/n₁ + 1/n₂)]

t = [(78.3 - 84.3) / 4.585 × √(1/18 + 1/11)]

t = -6 / (4.585 × 0.3827)

t = - 6 / 1.7546795

t = - 3.419

Therefore the value of the t test statistic is - 3.419

as as level of significance α  = 0.1

df = 18+11-2 = 27

∴ T(csal) = t(0.1, 27) = -1.313

That is

t(statistics) < t(cal)

{ - 3.419  < -1.313 }

( eight thousand times one hundred thousand ) plus ( four times one thousand) plus ( six times one )

or if you want the answer to that equation (804,006)

eight hundred four thousand and six

Answer:

142,000

Step-by-step explanation:

I would round 300,980 to the nearest thousands place = 301,000

Subtract 301,000 and 159,000 = 142,000

Answer:

A

Step-by-step explanation:

|x|< 3 translates to

x < 3 AND -x < 3

which simplifies to

x < 3 AND x > -3

so, yes, -3 < x < 3

Answer:

36

Step-by-step explanation:

you would just to 39^2-15^2 which is 1296 and the square root of that is 36 so 36 would be the answer

Answer:

1600

Step-by-step explanation:

0.3% of 1600 will result to 4.8

Answer:

[tex]\huge\boxed{\sf x = 7}[/tex]

Step-by-step explanation:

According to the given statement

HJ = HK + KJ

Given that HJ = 25 , HK = x - 5 and KJ = 5x-12

[tex]\sf 25 = x-5+5x-12[/tex]

Adding like terms

[tex]\sf 25 = 6x-17\\Adding \ 17\ to\ both\ sides\\25 + 17 = 6x\\42 = 6x\\Dividing \ both \ sides \ by \ 6\\7 = x\\OR\\x = 7[/tex]

Answer:   143.8 units²

Step-by-step explanation:

Since you know the length of two sides and the measure of the included angle, you can use the following trig formula:

[tex]Area=\dfrac{1}{2}ac \sin B[/tex]

Given: a = 14, c = 21, B = 87°

[tex]Area=\dfrac{1}{2}(14)(21) \sin 87^o\\\\.\qquad =147\sin 87^o\\\\.\qquad =143.8[/tex]

Answer:

[tex]\huge \boxed{\mathrm{146.8 \ units^2 }}[/tex]

Step-by-step explanation:

We can solve for the area of the triangle when two sides are given and the angle in between the two sides.

[tex]\displaystyle A=\mathrm{\frac{1}{2}ac \cdot sinB }[/tex]

[tex]\displaystyle A=\mathrm{\frac{1}{2} \cdot 14 \cdot 21 \cdot sin87 }[/tex]

[tex]\displaystyle A=\mathrm{147 \cdot sin87 }[/tex]

[tex]\displaystyle A=\mathrm{146.79854160...}[/tex]

The area of the triangle is 146.8 units².

Answer:

Cross multiplication

Step-by-step explanation:

Answer:

l = (2b-s)/w

Step-by-step explanation:

s=2b+lw

s-2b=lw

(s-2b)/w= l

Answer:

38.14

Step-by-step explanation:

Step 1: Write out equation

52.74 - 14.6

Step 2: Subtract

38.14

Answer: A

Step-by-step explanation:

Since we know that T is the midpoint of SU, we know that it bisects SU. Now, we know that it cuts SU in half. With that, we know that ST and TU are equal.

3x=2x+20                                            [subtract both sides by 2x]

x=20                        

Now that we know x, we can plug them in to solve for each segment.

ST

3x                                                        [plug in x=20]

3(20)                                                    [multiply]

60

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

TU

2x+20                                                 [plug in x=20]

2(20)+20                                             [multiply]

40+20                                                  [add]

60

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

SU

60+60=120

We know that SU is ST and TU combines, therefore, we add the values of ST and TU.

Answer:

B.7/2

Step-by-step explanation:

4/3 = 1.3333...

The number is greater than one, but it is NOT a terminating decimal.

7/2 = 3.5

The number is greater than one and terminating.

1/4 = 0.25

The number is terminating but less than one.

13/11 = 1.181818...

The number is greater than one, but it is NOT a terminating decimal.

Option B is the correct answer.

Hope this helps.

Considering that a fraction is a division, the correct option is:

B.7/2

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

To convert the fraction to decimal, we divide the numerator by the denominator.

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

Option A:

[tex]\frac{4}{3} = 1.333333....[/tex]

Greater than one, but non-terminating.

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

Option B:

[tex]\frac{7}{2} = 3.5[/tex]

Greater than one and terminating, thus this is the correct option.

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

Option C:

Denominator greater than the numerator, thus less than one.

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

Option D:

[tex]\frac{13}{11} = 1.1818181818....[/tex]

Greater than one, but non-terminating.

A similar problem is given at https://brainly.com/question/17772407

Answer:

[tex]C(D(5))[/tex]

Step-by-step explanation:

Given:

D(p): Items demanded when price is P

C(x): Production cost of x items

Required

Cost of producing when price is $5

First, we need to get the number of items demanded;

To do this, we substitute 5 for P in D(p)

This gives;

[tex]D(5)[/tex]

Next, we determine the production cost;

To do this, we substitute D(5) for x in C(x)

This gives;

[tex]C(D(5))[/tex]

None of the listed options answer the question

Answer:

32

Step-by-step explanation:

The perimeter of a figure is the sum of all the sides.

So, add up all the sides which equals the perimeter.

And we are given that the perimeter is 66. Thus:

[tex](4z)+(5z-3)+(z-1)=66[/tex]

Combine like terms:

[tex]10z-4=66[/tex]

Add 4 to both sides:

[tex]10z=70[/tex]

Divide both sides by 10:

[tex]z=7[/tex]

So, z is 7.

And VW is 5z-3. Thus:

[tex]VW=5z-3\\VW=5(7)-3=35-3=32[/tex]

Our answer is 32 :)

Answer: 6.3 km

Step-by-step explanation:

So we know that to convert meters into km we have to divide the length value by 1000

So:

6300 ÷ 1000 =  6.3

Therefore the answer is 6.3

Answer:

5x+12=42

x=6

Step-by-step explanation:

8+x+x+2+3x+2=42

5x+12=42

5x=42-12

5x=30

x=6

Answer:

2.16 cm

Step-by-step explanation:

5 through 11 = 6 hours

total of cms  = 13

13/6 = 2.16

Answer:

The answer is

Step-by-step explanation:

Let the measure of it's supplement be x

Supplementary angles sum up to 180° which means the sum of 76° and it's supplement is 180°

To find its supplement add 76° and it's supplement and equate it to 180° to find x

So we have

76 + x = 180

x = 180 - 76

We have the final answer as

Hope this helps you

Answer:    

(52,1)

(4,49)

(27,3)

(6,24)

(7,19)

(22,4)

key: (r,s)

Answer:

560.3

hope it helps

Answer:

2

Step-by-step explanation:

The gradient of the straight line is equal to (y2-y1)/(x2-x1), where

(x1,y1) and (x2,y2) coordinates of the points A and B which belong to the line.

So y2=2 ,x2=1-2p , y1=2+4p, x1=1

k=(2-(2+4p))/((1-2p)-1)= (2-2-4p)/(1-2p-1)= (-4p)/(-2p)=2

The gradient of the straight line joining (1, 2+4p) to (1-2p, 2) is 2 and this can be determined by using the two-point slope formula.

Given :

Points  --  (1,2+4p) and (1-2p,2)

The following steps can be used in order to determine the gradient of the straight line joining (1, 2+4p) to (1-2p, 2):

Step 1 - According to the given data, the points on the straight line are (1, 2+4p) to (1-2p, 2).

Step 2 - The two-point slope formula can be used in order to determine the gradient of the straight line joining (1, 2+4p) to (1-2p, 2).

Step 3 - The two-point slope formula is given below:

[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

Step 4 - Substitute the values of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the above expression.

[tex]\rm m = \dfrac{2-(2+4p)}{1-2p-1}[/tex]

Step 5 - Simplify the above expression.

[tex]\rm m = \dfrac{-4p}{-2p}[/tex]

m = 2

For more information, refer to the link given below:

https://brainly.com/question/3605446