Hi, Which option is correct??

Answer: [tex]12\ ft[/tex]

Step-by-step explanation:

Given

Total height of utility pole is 18 ft

After breakage, only 5 foot tall portion is standing

The fallen part is [tex]18-5=13\ ft[/tex] in length

From the figure, apply the Pythagoras theorem

[tex]\Rightarrow 13^2=x^2+5^2\\\Rightarrow x^2=169-25\\\Rightarrow x=\sqrt{169-25}\\\Rightarrow x=\sqrt{144}\\\Rightarrow x=12\ ft[/tex]

Thus, the fallen part is [tex]12\ ft[/tex] away from the base of the pole.

Answer:

Step-by-step explanation:

Answer:

Solution given:

7.<OYM=15°base angle of isosceles triangle

<OYL=50°base angle of isosceles triangle.

<OYL=<OYM+<MYL

50°=15°+<MYL

<MYL=50°-15°

<MYL=35°

again;

<MOL=35*2=70°central angle is double of a inscribed angle.

18.

Solution given:

<PQR+<PSR=180°sum of opposite angle of a cyclic quadrilateral is supplementary

<PQS+42°+78°=180°

<PQS=180°-120°=60°

<PQS=60°

<SPR=42°inscribed angle on a same arc is equal

:.<QPS=18°+42°=60°

<QSR=18°inscribed angle on a same arc is equal

again.

<PSR=78°

<QSR+<PSQ=78°

18°+<PSQ=78°

<PSQ=78°-18°

<PSQ=60°

In ∆ PQS

<PSQ=60°

<QPS=60°

<PQS=60°

In triangle ∆PQS all the angles are equal.

Answer:

3/(n + 3)

Step-by-step explanation:

The given probability that Sara wins a raffle draw, P = n/(n + 3)

Given that the sum of all probabilities is 1, we get

The probability that Sara does not win, Q = 1 - P

Therefore;

Q = 1 - n/(n + 3) = (n + 3) - n/((n + 3) = 3/(n + 3)

The probability that Sara does not win, Q = 3/(n + 3)

Answer:

7/16 mile

Step-by-step explanation:

Distance of the loop = 7/8 mile

Distance of Water fountain = 1/2 of the Distance of the loop

= 1/2 of 7/8

Ibrahim stopped to get a drink of water at the water fountain. How far did Ibrahim run?

= 1/2 of 7/8

= 1/2 * 7/8

= (1 * 7) / (2 * 8)

= 7/16

Ibrahim ran 7/16 mile to drink water at the water fountain around the loop

Answer:

1. = 5 10 15 20 25

2. 2 4 6 8 10 12 14

X, y =10

Answer:sadwer

Step-by-step explanation:

Answer:

The answer is "16,000"

Step-by-step explanation:

In this question the amounts of panels created by B the x.

[tex]\therefore[/tex]

Calculating the amounts of defective panels from B:

[tex]\to \frac{1}{100} \times x = 0.01x[/tex]

Calculating the amounts of defective panels from A:

[tex]\to \frac{4}{100} \times 8000 = 320[/tex]

Calculating the total defective panels are :

[tex]\to 320+ 0.01x[/tex]

Calculating the total panels manufactured:

[tex]\to 8000 + x[/tex]

when the overall percentage of the defective panels is [tex]2\%[/tex]

[tex]\to \frac{(320 + 0.01x)}{(8000 + x)} = 0.02\\\\\to (320 + 0.01x) = 0.02 (8000 + x)\\\\\to 320 + 0.01x = 160 + 0.02x\\\\\to 320 -160 = -0.01x + 0.02x\\\to 160 = 0.01x\\\\\to x=\frac{160}{0.01}\\\\\to x=16,000\\\\[/tex]

Answer:

A.

Step-by-step explanation:

3x + x - 13 + 4 - 6x = 12

we try to combine the elements with the same power of x (including the ones without any x) :

3x + x - 6x

-13 + 4

so, we get

-2x - 9 = 12

-2x = 21

x = -21/2

Answer:

A

Step-by-step explanation:

group the like terms

3x+x-6x-13+4=12

-2x=12+9

divide both sides by -2

-2x/-2=21/-2

x= -21/2

hope it helps

Answer:

Step-by-step explanation:

tan 47° = opposite side /adjacent side

=>1.072 = AB/BC

=>1.072 × BC = AB(height of the building)

=>1.072 × 23 = h ( As assumed height of building is h )

h = 24.656

= 25 metres ( nearest metre )

Answer: See below

Step-by-step explanation:

This relates to the usage of water displacement.

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

EXTRA (Only for advanced purposes, if you do not understand, it is totally fine)

Refer to the attachment below to finish the question.

Assuming the water levels are integer,

Then, we do the fourth step which is subtraction

Hope this helps!! :)

Please let me know if you have any quesitons

the answer would be 5 because 5*5 or 5 squared (5^2) is equal to 25, hope this helps!

Answer:

[tex]{ \boxed{ \bf{ \frac{dy}{dx} = v \frac{du}{dx} + u \frac{dv}{dx} }}}[/tex]

u = ( x + 1 )

v = ( 2x + 5 )²

[tex]{ \tt{ \frac{dy}{dx} = {(2x + 5) {}^{4} .(1) + (x + 1).(2)(2x + 5) {}^{3} } }} \\ = { \tt{ {(2x + 5)}^{3} ((2x + 5) +(2x + 2) }} \\ = { \tt{ \frac{dy}{dx} = {(2x + 5)}^{3}(4x + 7) }}[/tex]

Answer:

2y = 8

Step-by-step explanation:

4x+3y = 17

- ( 4x+y = 9)

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

Distribute the minus sign

4x+3y = 17

-  4x -y =- 9

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

  0x +2y = 8

Answer:

2y = 8

Step-by-step explanation:

4x+3y=17

-4x-y=9

_______

0+2y=8

2y=8

Answer:

No

Step-by-step explanation:

Kilogram is the unit of weight. Kilogram is the measure of how much matter or the mass an object has in it. Kilogram is the bigger unit of measurement while gram and milligram are the smaller units to measure the weight of any object.

We know,

1 kilogram = 1000 gram x 1

So, 1000 gram is equal to 1 kilogram

That means, 39,000 gram is equal to 39 kilogram.

In the question it is asked whether 1000 pillows times 300 is equal to 39 kilogram sofa or not.

The answer is not correct, because we do not know the weight of the 1000 pillows.

And also, 1000 x 300 will give you 300,000 and not 39 kilogram or 39,000 grams.

Answer:

Step-by-step explanation:

            Statements                               Reasons

1. m∠A = 6x - 10                              1. Given

2. m∠B = 2x                                    2. Given

3. m∠C = 8x - 2                               3. Given

4. m∠A + m∠B + m∠C = 180°         4. Triangle sum theorem

5. (6x - 10) + (2x) + (8x - 2) = 180°   5. Substitution

6. 16x - 12 = 180                              6. Algebra

7. 6x = 192                                       7. Addition property of equality

8. x = 12                                           8. Division property of equality  

Answer:

65 and 25

Step-by-step explanation:

90=(5x+10)+(6x-41)

121=11x

11=x

Going back to the angles:

5(11)+10

=55+10

=65 this is the first angle

6(11)-41

=66-41

25 this is the second angle

Answer:

For 25) it's option C. -1/2

For 26) it's option D. 7π/6, 11π/6

Step-by-step explanation:

If you are finding sin−1 of a positive value, the answer will be between 0 and π/2. Using the unit circle, the angle with a sine of 1/2 in the first quadrant is π/6.

Answer:

-1/2

7π/6, 11π/6

Step-by-step explanation:

First problem:

31π/6 = 31/6 π = 5 1/6 π

A full circle is 2π radians. π radians = 180°

Start at 0 radians (positive x axis), and go 5 half circles counterclockwise.

You end up at π radians, or 180°, or the negative x axis.

Now go π/6 radians more counterclockwise.

You end up at 7π/6 or 210°.

Read the y-coordinate of the point on the unit circle.

Answer: -1/2

Second problem:

Look in the figure of the first problem.

The sine corresponds to the y-coordinate.

Look at the points on the circle, below the x-axis, that have a y-coordinate of -1/2.

They correspond to 7π/6 and 11π/6

4x - 5y = -12

-x + 5y = 18

Add the equations together:

4x + -x = 3x

-5y + 5y = 0

-12 + 18 = 6

So now you have:

3x = 6

Divide both sides by 3:

X = 2

Now you have the value of x, replace x with 2 in one of the equations and solve for y:

4(2) -5y = -12

8 -5y = -12

Subtract 8 from both sides:

-5y = -20

Divide both sides by -5:

Y = 4

The solution is x = 2 and y = 4 which is written as (2,4)

9514 1404 393

Answer:

  ₹1442

Step-by-step explanation:

The new price will be 1+3% = 1.03 times the old price.

  ₹1400 × 1.03 = ₹1442

Answer:

A

Step-by-step explanation:

The zero of the function is where the y-value is zero.

then it's -5

Answer:

Step-by-step explanation:

Can't see all the graphs, but the graph of [tex]y=-x^2[/tex] is an upside down parabola with the vertex at the origin.

Answer:

8.4

Step-by-step explanation:

Since we want to minimize the average, the integers should be made as small as possible. So, we have 4 integers:

1, 2, 3, 4

However, the median must be 10. The next two integers must have an average of 10 - and since the integers are distinct, we should use:

9, 11

From there, we use the smallest integers (that are still above 11) possible:

12, 13, 14, 15

The average of these 10 integers is 84/10, or 8.4.

The median is still 10, because (9+11)/2 is 10.

Answer:

8 (or 8.4)

Step-by-step explanation:

First, the problem states the words: Distinct and positive.

That means that the smallest number we can use is 0.

We can make 10 blanks for 10 numbers for us to fill in.

_ _ _ _ _ _ _ _ _ _

Since 10 is an even number, and the median is not one single number, it will be the middle of the two numbers.

In this case, our two numbers are the 5th and 6th blank.

Any two numbers can be used, as long as they are the same actual value from 10.

Let us first put in the numbers we can, which are the numbers before the two middle blanks.

0,1,2,3, _ _ _ _ _ _

To find the median between two numbers, we can do:

(a+b) divided by 2 = median

We can use the smallest following number, 4. Then the 6th number will have to be 16 for 10 to be in the middle.

Also try the largest possible number for the 5th blank, 9. Then the 6th number will be 11.

4+16 and 9+11 both equal 20, and 20 divided by 2 is 10. So both of these work.

Now let's place the other numbers in for these two equations.

0,1,2,3,4,16,17,18,19,20

0,1,2,3,9,11,12,13,14,15

If we add the numbers of each together, we get:

0,1,2,3,4,16,17,18,19,20=100

0,1,2,3,9,11,12,13,14,15= 80

If we now divide each sum by 10 (to find the average) we get:

10

8

Since both of these were the most we could go, one with the 5th number as small as possible and one with the 5th number as large as possible.

Since the smaller answer we got was 8, the answer must be 8.

(I believe 0 is a positive integer because it doesn't carry a negative sign. If 0 is not a positive integer, the answer is 8.4. Use the same process

-1 + 2 - 3 + 4 - 5 + 6 - … - 999 + 1000

= -(1 + 3 + 5 + … + 999) + (2 + 4 + 6 + … + 1000)

= -((2 - 1) + (4 - 1) + (6 - 1) + … + (1000 - 1)) + 2 (1 + 2 + 3 + … + 500)

= -((2 + 4 + 6 + … + 1000) - 500) + 2 (1 + 2 + 3 + … + 500)

= -(2 (1 + 2 + 3 + … + 500) - 500) + 2 (1 + 2 + 3 + … + 500)

Let S = 1 + 2 + 3 + … + 500. Then this sum is equal to

= -(2S - 500) + 2S

= -2S + 500 + 2S

= 500

and multiplying by 4 gives 2000.

Answer:

[tex]4\times \left(\left(-1+2-3+4-5+6-7+1000\right)\right)[/tex]

[tex]calculate\: within \: the \:parentheses[/tex]

[tex]-1+2=1[/tex]

[tex]=1-3+4-5+6-7+1000[/tex]

[tex]1-3=-2[/tex]

[tex]=-2+4-5+6-7+1000[/tex]

[tex]-2+4=2[/tex]

[tex]=-3+6-7+1000[/tex]

[tex]3-7+1000[/tex]

[tex]=-4+1000[/tex]

[tex]=996[/tex]

[tex]Multiply:-[/tex]

[tex]4\times996[/tex]

[tex]=3984[/tex]

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

Hope it helps..

Have a great day!!

Answer:

Height = 12in

Surface area = 320in²

Step-by-step explanation:

Given

Length of the square base = 8in

Volume of the prism = 768 cubic inches

Using the formula;

Volume of the prism = Base area * Height of prism

768 = 8² * H

768 = 64H

H = 768/64

H = 12in

Hence the height of the prism is 12in

Get the surface area

Surface area = 2l² + 2lh

Surface area = 2(8)² + 2 (8)(12)

Surface area = 128  + 192

Surface area = 320in²

Hence the Surface area of the prism is 320in²