On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 6, negative 2) and point K is at point (8, negative 9). What is the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5? x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 –4 –2 2 4

Answer:

The tower is 73.4 m tall

Step-by-step explanation:

The height of the pole = 2.5 m

The shadow cast by the pole = 1.72 m

Shadow cast by tower = 50.5 m

To find the height of the tower, we proceed by finding the angle of elevation, θ, of the light source casting the shadows as follows;

[tex]Tan\theta =\dfrac{Opposite \ side \ to\ angle \ of \ elevation}{Adjacent\ side \ to\ angle \ of \ elevation} = \dfrac{Height \ of \ pole }{Length \ of \ shadow} =\dfrac{2.5 }{1.72}[/tex]

[tex]\theta = tan ^{-1} \left (\dfrac{2.5 }{1.72} \right) = 55.47 ^{\circ}[/tex]

The same tanθ gives;

[tex]Tan\theta = \dfrac{Height \ of \ tower}{Length \ of \ tower \ shadow} =\dfrac{Height \ of \ tower }{50.5} = \dfrac{2.5}{1.72}[/tex]

Which gives;

[tex]{Height \ of \ tower } = {50.5} \times \dfrac{2.5}{1.72} = 73.4 \ m[/tex]

This question is incomplete. Please find attached to this solved question, the diagram required to solve this question.

Answer:

11 units

Step-by-step explanation:

The shaded portion of the rectangle forms the shape of a trapezium

The area of a trapezium = 1/2(a + b)h

From the diagram, we can see than x = b

a = 7 units

b = 7 units

Area of the trapezium = Area of the shaded portion = 63 square units

A = 1/2(a + b)h

63 = 1/2(7 + b)7

63 = 1/2(49 + 7b)

63 × 2 = 49 + 7b

126 - 49 = 7b

7b = 77

b = 77/7

b = 11 units

Since x = b, x = 11 units

The value of x is 11

Start by calculating the area (A) of the trapezoid using

[tex]A= 0.5 * (a + b)h[/tex]

Using the parameters from the complete question, we have:

[tex]63 = 0.5 * (7 + x) * 7[/tex]

Multiply both sides by 2

[tex]126 = (7 + x) * 7[/tex]

Divide both sides by 7

[tex]18 = 7 + x[/tex]

Subtract 7 from both sides

[tex]x = 11[/tex]

Hence, the value of x is 11

Read more about shaded areas at:

https://brainly.com/question/24579466

Answer:

your answer is k

Step-by-step explanation:

not all the isosceles triangles are similar

Answer:

q = 108-n

Step-by-step explanation:

Given: 108 coins containing only quarters and nickels

q = 108-n

since total number of coins is 108, and n= number of nickels

If you want to know how many of each kind of coin, read on:

First solve the number of quarters and nickels.

If all 108 coins are quarters, the value is 108*0.25 = $27

Since this value exceed the actual by 27-21 = $6,

we replace a number of quarters by nickels.

Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.

So it will take 6/0.2 = 30 replacements.

Therefore there are 108-35 = 78 quarters and 30 nickels.

The solution is : q = 108-n, is the value could replace q on the chart.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Given:

108 coins containing only quarters and nickels

q = 108-n

since total number of coins is 108, and n= number of nickels

If you want to know how many of each kind of coin, read on:

First solve the number of quarters and nickels.

If all 108 coins are quarters, the value is 108*0.25 = $27

Since this value exceed the actual by 27-21 = $6,

we replace a number of quarters by nickels.

Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.

So it will take 6/0.2 = 30 replacements.

Therefore there are 108-35 = 78 quarters and 30 nickels.

The solution is : q = 108-n, is the value could replace q on the chart.

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ7

Answer:

For sample size n = 39 ; P(X < 31.6) = 0.9756

For sample size n = 76 ; P(X < 31.6) = 0.9970

Step-by-step explanation:

Given that:

population mean μ = 31

standard deviation σ = 1.9

sample mean  [tex]\overline X[/tex] = 31.6

Sample size n                 Probability

39

76

The probabilities that the sample mean is less than 31.6 for both sample size can be computed as  follows:

For sample size n = 39

[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]

[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{6.245}})[/tex]

[tex]P(X < 31.6) = P(Z< 1.972)[/tex]

From standard normal  tables

P(X < 31.6) = 0.9756

For sample size n = 76

[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]

[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{8.718}})[/tex]

[tex]P(X < 31.6) = P(Z< 2.75)[/tex]

From standard normal  tables

P(X < 31.6) = 0.9970

Answer:

a) More.

b) Less.

c) More.

Step-by-step explanation:

a) If you invest $10 with an interest rate of 50% (that's very high I know XD), you would earn 10 / 2 = $5 in interest. If you invest $100 with an interest rate of 50%, you would earn 100 / 2 = $50 in interest. So, the more principal invested, the more interest earned.

b) Let's say you are investing $100. If there is an interest rate of 50%, as stated before, you would earn $50 in interest. If the interest rate were lowered to 25%, you would earn 100 / 4 = $25 in interest. So, the lower the interest rate, the less the interest.

c) The same exact thing as part a.

Hope this helps!

Answer:

942.5 in²  

Step-by-step explanation:

The formula for the area (A) of a sector of a circle is

A = ½r²θ

where θ is the angle in radians.

1. Convert the angle to radians

θ = 125°  

[tex]\theta = 125^{\circ} \times \dfrac{\pi \text{ rad }}{180^{\circ}} =\frac{25}{36} \pi\text{ rad}[/tex]

2. Area swept out by wiper arm

A = ½r²θ = ½ × (30 in)² × θ = ½ × 900 in²× θ = 450 θ in²

3. Area missed by wiper

A = ½r²θ = ½ × (6 in)² × θ = ½ × 36 in²× θ = 18 θ in ²

4. Area covered by wiper

A = 450 θ in² - 18 θ in² = 432 θ in²

5. Insert the value of θ

A = 432 × 25/36 π in² = 300π in² ≈ 942.5 in²

The area swept out by the wiper blade is 942.5 in².

Answer:

Length of first leg = 1.4feet

Hypotenuse = 4.2feet

Explanation:

Since we are dealing with a right angled triangle, we will apply the Pythagoras theorem to solve the question. According to Pythagoras theorem, the square of the hypotenuse is equal to the sum if the square of the other two legs.

Mathematically, a² = b²+c² where a is the hypotenuse and b, c are the other two legs.

From the question, since hypotenuse of a right triangle is three times the length of its first leg, then a = 3b.

Also the other leg is four feet i.e c= 4

Substituting this values into the Pythagoras formula;

a²=b²+c²

(3b)² = b²+4²

9b² = b²+16

9b²-b² = 16

8b² = 16

b² = 16/8

b² = 2

b = √2

b = 1.4

Since a = 3b

a = 3(1.4)

a = 4.2

Hence, the length of the first leg is 1.4feet and that of the hypotenuse is 4.2feet both to the nearest tenth.

Answer:

9 and 23

Step-by-step explanation:

Let x be smaller length in inches.

x+3x-4=32

4x=36

x=9

9*3-4=23

So they're 9 and 23 inches long.

The lengths of the two parts of the pipe are 9 and 23 inches long.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Let x be the smaller length in inches.

x + 3x - 4 = 32

4x = 36

x  =9

Now substitute;

9*3 - 4 = 23

Hence, the lengths of the two parts of the pipe are 9 and 23 inches long.

Learn more about the unitary method;

https://brainly.com/question/23423168

#SPJ2

Answer: 180

Step-by-step explanation:

Let the tons of ice the ship was carrying when it set sail be y.

We are told that one third of the original cargo was lost because it had melted on the voyage and that it arrived in Calcutta with 120 tons remaining of its cargo of ice.

This means that (1 - 1/3 = 2/3) remained which was the 120 tons remaining. This implies that:

2/3 × y = 120

2y/3 = 120

2y = 120 × 3

2y = 360

y = 360/2

y = 180

The ship was carrying 180 tons of ice when it set sail

Answer:

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

P (m) = a (m + 1) + b (m + 1) - c (m + 1)

P (m) = (a + b - c) (m + 1)

There are 2 prime factors

Answer:

2, 3 , 5, 7

Step-by-step explanation:

2(x - 2)/3 < (x + 1)/2 < 3(5x + 6)/4

Considering:

    2(x - 2)/3 < (x + 1)/2

<=>(2x - 4)/3 < (x + 1)/2

<=> (2x - 4)*2 < (x + 1)*3

<=> 4x - 8 < 3x + 3

<=> 4x - 3x < 8 + 3

<=> x < 11

Considering:

     (x + 1)/2 < 3(5x + 6)/4

<=>(x + 1)/2 < (15x + 18)/4

<=>(x + 1)*4 < (15x + 18)*2

<=> 4x + 4 < 30x + 36

<=> 4x - 30x < 36 - 4

<=> -26x < 32

<=> 26x > -32

<=> x > -32/26

=> -32/26 < x < 11

The prime numbers satisfy the above inequalities: 2, 3 , 5, 7

Answer:

(0,-7)

Step-by-step explanation:

If nay point is form (x,y)

x is abscissa can be also called x axis coordinate

y is ordinate can be also called y axis coordinate

ordiantes are points lying on y axis.

For any point lying on y axis, its x-axis coordinate will be 0

given that ordinate is -7. it means that value of y coordinate is -7

Thus,  coordinates of the point is (0,-7)

Answer:

C. 16π

Step-by-step explanation:

Well we need to find the area of the top circle which has a radius of 4cm.

π(4)^2

16π in terms of pi

Thus,

the answer is C. 16π.

Hope this helps :)

a) The population is all of the flights belonging to the particular airline. It's not all flights in general because the airline does not have control over a rival company's flight schedule.

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

b) The sample is the 5 airlines the company selected. Ideally the sample should represent the population as much as possible. The larger the sample, the more representative the sample is.

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

c) No, the sample is likely not representative because one day of flight does not represent the entire lifetime of all flights done so far for that company. This particular day could have been a very good day with good weather, which may explain why the 5 flights were all on time.

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

d) It would be better for the company to select the days at random and sample all of the flights for those particular days chosen. This is a cluster sample. Each cluster is a day. Also, I think more flights should be sampled. Five flights does not seem like enough.

Answer:

C= 3g

Step-by-step explanation:

Answer: £4

Step-by-step explanation:

From the question, we are informed that when the normal price of a book is reduced by 30%, then the sale price of the book is £2.80.

Since the normal price of a book is reduced by 30%, that means the book is sold at (100% - 30%) = 70% of its normal price.

Let the normal price of the book be y.

70% of y = £2.80

70/100 × y = £2.80

0.7 × y = £2.80

0.7y = £2.80

y = £2.80/0.7

y = £4

The normal price of the book is £4.

[tex]\sqrt{3}x^2+10x+7\sqrt{3}=0\\\\\sqrt3(x^2+\dfrac{10x}{\sqrt{3}}+7)=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+7=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+\dfrac{25}{3}-\dfrac{25}{3} +7=0\\\\(x+\dfrac{5}{\sqrt{3}})^2 = \dfrac{4}{3}\\\\|x+\dfrac{5}{\sqrt{3}}| = \dfrac{2}{\sqrt{3}}\\\\x_1 = \dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = -\dfrac{3}{\sqrt{3}} = -\sqrt{3}\\\\x_2 = -\dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = \dfrac{-7}{\sqrt{3}} = -\dfrac{-7\sqrt{3}}{3}[/tex]

Answer:

(x - 7)² + (y - 4)² = 49

Step-by-step explanation:

Given

Equation: x² + y² = 49

Required:

New Equation when translated 7 units right and 4 units up

Taking it one step at a time.

When the equation is translated 7 units right, this implies a negative unit along the x axis.

The equation becomes

(x - 7)² + y² = 49

When the equation is translated 4 units up, this implies a negative unit along the y axis.

(x - 7)² + (y - 4)² = 49

The expression can be further simplified but it's best left in the form of

(x - 7)² + (y - 4)² = 49

Answer:

Step-by-step explanation:

The sides of the base are each 5 inches. We see 4 right angles so that we are dealing with a square.

The triangles look to be isosceles. In any event there are 4 of them. So the answer is the 3rd one down.

Answer:

C

Step-by-step explanation:

A) 22°

∡DBG = (360° - BD - BG)/2

= (360° - 170° - 146°)/2

= 44°/2

= 22°

Answer: The store must sell 40 bikes.

Step-by-step explanation:

y=60x+2400

y=120x

120x=60x+2400

-60x on both sides

60x=2400

divide 60 on both sides

2400/60=40

x=40  

Answer:

x=1/4c+1/4k

Step-by-step explanation:

4x-c=k

move c over

4x=c+k

then divide by 4

x=1/4c+1/4k

hope this helps

Answer:

[tex]f(5)=17[/tex]

Step-by-step explanation:

[tex]f(x)=3x+2[/tex]

[tex]f(5)=3(5)+2[/tex]

[tex]f(5)=15+2[/tex]

[tex]f(5)=17[/tex]

Answer:

17

Step-by-step explanation:

f(x) = 3x + 2

f(5) = 3(5)+ 2

f(5) = 15 + 2

f(5) = 17

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

            Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

It looks lilke one of those old'n day Juice makers

2, 3 , and 4 would be the part im talking about.

You can write : I seleted the story called Old In Day Juice Makers

( I don't know about the paragraph, sorry)

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

0.5333333333 or 0.53 when simplified.

Step-by-step explanation:

8/15 is simply 8÷15

15 into 8 is not possible so you annex a zero and write a decimal point.The 8 now becomes 80. We now say 80÷15,the answer is 5 because 15x5=75.The remainder is five.We annex another zero and it becomes 50,50÷15=3

I hope this helps.

Step-by-step explanation:

An algebraic expression haa atleast one variable and operator sign such as (+,-,×,÷)

According to the question, an algebraic expression should be made from difference of 'a' and 'b'

so, the expression is (a - b) or a - b.

Hope it helps!!!!

Answer:

25.52791653032955454422437424679625318128649677442393276098...

Step-by-step explanation:

You can just paste this into wolframalpha.

Answer: 970.72312

Step-by-step explanation:

Straightforward operation.

Answer:

5400 cycles

Step-by-step explanation:

You have the following function:

[tex]V(t)=220sin(180\pi t)[/tex]

where t is in seconds.

In order to find the number of cycles in 1 minute, you first  calculate the frequency of the function, which is given by:

[tex]f=\frac{180\pi}{2\pi}=90s^{-1}[/tex]

The number of cycles is then given by:

[tex]n=ft=(90s^{-1})(60s)=5400\ cycles[/tex]

There are 5400 cycles in 1 minute