A lamppost casts a shadow of 18 ft when the angle of elevation of the Sun is 33.7 degrees. How high is the lamppost? Round to the nearest foot

Answer:

x=7

Step-by-step explanation:

[tex]1 + 3x = - 13 + 5x[/tex]

Collect like terms and simplify

[tex]3x - 5x = - 13 - 1 \\ - 2x = - 14[/tex]

Divide both sides of the equation by -2

[tex] \frac{ - 2x}{ - 2} = \frac{ - 14}{ - 2} [/tex]

Simplify

[tex]x = 7[/tex]

Answer:

Step-by-step explanation:

1 + 3x = 5x - 13

-2x + 1 = -13

-2x = -14

x = 7

Simplify the Integer part of the SQRT

Step-by-step explanation:

Factor 200 into its prime factors

           200 = 23 • 52 

Answer:

The area should be 56.4

Step-by-step explanation:

When you try to find the area of a triangle you have to multiply the base and height, which was 12km and 9.4 km,and you divide it by 2.

The sample space for first tossing a coin and then rolling a number cube is (T, 2).

An outcome is a possible result of an experiment or trial in probability theory. Each experiment's possible outcomes are distinct, and alternative outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment).

As, the outcomes for tossing a coin is Head (H) and Tail (T).

and, the outcome for rolling a die

{1, 2, 3, 4, 5, 6}.

So, the sample space for first tossing a coin and then rolling a number cube

= ( T, 2)

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Answer:

D. It is a decimal that terminates after 3 decimal places

I hope this helps!

Answer:

D. 30.5

Step-by-step explanation:

Given that A, B, C, D, and E are collinear,

AE = 38,

BD = 15, since segment BC = CD = DE, therefore

BD = ⅔ of BE

15 = ⅔*BE (substitution)

Solve for BE

Multiply each side by 3

15*3 = ⅔*BE*3

45 = 2*BE

Divide both sides by 2

45/2 = BE

22.5 = BE

BE = 22.5

Find AB:

AB + BE = AE (segment addition postulate)

AB + 22.5 = 38 (Substitution)

AB = 38 - 22.5 (Subtracting 22.5 from each side)

AB = 15.5

Find length of segment AD:

AB + BD = AD (segment addition postulate)

15.5 + 15 = AD (Substitution)

30.5 = AD

AD = 30.5

Answer:

X = m - 2w

Step-by-step explanation:

just isolate the variable.

Answer:

x=m-2w

Step-by-step explanation:

Just take the +2w to the other side where it becomes negative.

Answer:

5u - 23

Step-by-step explanation:

Answer:

4( 2u - 2) - 3(u + 5)​

(4*2u + 4*-2)-(3*u + 3*5)

8u-8-3u+15

8u-3u-8+15

5u+7

Step-by-step explanation:

I hope this helped you.

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Answer:

C. (-1,-2)

Step-by-step explanation:

Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.

Let A = (x₁, y₁) = (5, 16), B = (x₂, y₂) and C = (x, y) = (3, 10)

So x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Substituting the values of the coordinates, we have

x = (mx₂ + nx₁)/(m + n)

3 = (1 × x₂ + 2 × 5)/(2 + 1)

3 = (x₂ + 10)/3

multiplying through by 3, we have

9 = x₂ + 10

x₂ = 9 - 10

x₂ = -1

y = (my₂ + ny₁)/(m + n)

10 = (1 × y₂ + 2 × 16)/(2 + 1)

10 = (x₂ + 32)/3

multiplying through by 3, we have

30 = y₂ + 32

y₂ = 30 - 32

y₂ = -2

So, the coordinates of B are (-1, -2)

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²               ------------------(i)

From the question:

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25      ------------------(ii)

Open the brackets and have the following:

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0    [equation has already been normalized since the coefficient of x² is 1]

Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:

x² + y² + z² + 18(x - y + z) + 218 = 0

(2)  To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25        [subtract 25 from both sides]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

Answer:

A;C;E

Step-by-step explanation:

Let cost of almond per pound be X

Cost of 3 pounds of almonds=3X

cost of pistachios per pound = X+4

Cost of 2 pounds of pistachios=2X+8

Total cost=5X+8=48

5X+8=48

5X=40

X=8

cost of one pound almond is $8

cost of one pound pistachios is $12

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Answer:

because angles on a straight line add up to 180 degrees substract (180-110), step 2; you will get 70 degrees afterwards the angle y is perpendicular it's 90 degrees.step 3;add (90+70) you get 160 .step 4;then substract (180-160) you get your answer as 20 degrees

Answer:

x = 20º

Step-by-step explanation:

Since it is a triangle, the sum of the internal angles is 180º.

We know that y = 90º, because 110º + 70º = 180º, and the line intercepts it, splitting the larger triangle into 2.

Since, y = 90º, and the other angle is 70º, we add those together to 160º.

Then, we take 180º - 160º = 20º.

x = 20º

Hope this helps.

:)

Answer:

Area of drawing= 0.315 m²

Step-by-step explanation:

Base = 6m

Height = 4.2 m

Area = height* base

Area= 4.2*6

Area= 25.2 m²

The scale is 10 cm on the drawing for every 8 meters on the sculpture.

Which is 10 cm to 800 cm

Or

0.1m to 8m

Arra of sculpture= 25.2 m²

area of drawing= (25.2*0.1)/8

Area of drawing= 0.315 m²

Answer:

200 is the maximum amount

Step-by-step explanation:

94x100=9400

9400/47=200

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Answer:

the contribution margin per composite unit is $365

Step-by-step explanation:

The computation of the contribution margin per composite unit is shown below:

= Contribution margin per unit for product A × ratio of A + Contribution margin per unit for product B × ratio of B

= ($86 - $45) × 5 + ($124 - $49) × 2

= $205 + $160

= $365

Hence the contribution margin per composite unit is $365

Answer:the answer is 1, b option i just take the tes

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

the answer is one

Answer:

yes totally

Step-by-step explanation:

5a+5b=5a+5b

Step-by-step explanation:

A straight line graph is of the form:

y = mx+b

So we get our equation in this form:

9=2x+3y

or, 9-2x=3y

or, -2x+9 = 3y

or, y= (-2x+9)/3

or, y = -2/3x + 3

So,

Slope(m)=−2/3

y-intercept (b) = 3

Therefore, slope(m) is -2/3x and y-intercept(b) is 3.

Step-by-step explanation:

N(t) is continuous at t = 6, so f(6) = 25(6) + 150 = 300.

f(0) = 80.

f(t) is continuous, so by Intermediate Value Theorem, f(t) must equal 250 at some point between t=0 and t=6.

Answer:

31536000

Step-by-step explanation:

365 days x 24 hours x 60 minutes x 60 seconds = 31536000

Answer: 32÷8=4

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Answer: False

Natural numbers are not closed under division

Some natural numbers divide to get another natural number. For example, divide 10 over 2 to get 10/2 = 5.

However, there are infinitely many natural numbers that divide to get something that isn't a natural number. Example: 10/7 = 1.43 approximately. All we need is one counterexample to contradict the original statement.

A set is considered closed under division if dividing any two values in that set leads to another value in the set. More formally, if a & b are in some set then a/b must also be in the same set for that set to be closed under division.

If we changed "natural numbers" to "rational numbers", then that set is closed under division. If p, q are rational numbers then p/q is also rational. Basically, dividing any two fraction leads to some other fraction. The value of q cannot be zero.

A sequence is defined as an arrangement of numbers in a particular order.

The number of Band members in the year 2018 is expected to be 76.

A sequence is defined as an arrangement of numbers in a particular order.

We have,

Year         Number of Band members

2014        40

2015        46

2016        54

2017         64

We can make a sequence with the number of band members that increases each year.

i.e

40  46  54  64

We see that,

46 - 40 = 6

54 - 46 = 8

64 - 54 = 10

We see that the difference between the consecutive terms is increasing by 2.

So, the next term in the sequence will be 64 + 12 = 76.

Thus the number of band members in the year 2018 is expected to be 76.

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Answer:

P ($)=70-5(t)

Where p = price at t days

t = number of days

Step-by-step explanation:

The product price initially = $70

Now, every day , it reduces $5

The rate=$5 per day reduction

The price in the days will be determined by the formula below

P ($)=70-5(t)

Where p = price at t days

t = number of days

So let's assume it's on the second day

The price after the second day

P($) = 70-5(2)

P($) = 70-10

P($)= $60

The price after two days will be reduced to $60

Answer:

Step-by-step explanation:205

Answer:

16. 200+3

17. 30+4+0.1+0.02+0.007

18. 200+70+6+0.1+0.03

19. 30000000+4000000+100000+20000+3000+6

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

(3-2i)(3+2i)

as (a+b)(a-b) =a²-b²

3²-(2i)²

=9-(4*-1)

=9-(-4)

=9+4

=13

Hope this helps you!

Answer:

13

Step-by-step explanation:

3^2=9, 2i*(-2i)=-4i^2=4

the 6i and -6i cancel leaving the positive 9 and 4

9+4=13

If there are 3 cups of strawberries per 6 liters of smoothie, that means that there is [tex]\frac{1}{2}[/tex] cups of strawberries per liter of smoothie.

[tex]\frac{3}{6}=\frac{1}{2}[/tex]

Hope this helps.

頑張って!

Answer:

Exact form: [tex]9 \frac{41}{51}[/tex]

Decimal form: [tex]9.80392156[/tex]

Step-by-step explanation:

[tex]41\frac{2}{3}[/tex] ÷ [tex]4\frac{1}{4}[/tex]

Let's put everything into a fraction.

[tex]\frac{41\frac{2}{3} }{4\frac{1}{4} }[/tex]

Now we have an answer.

Exact form: [tex]9\frac{41}{51}[/tex]

Decimal form: [tex]9.80392156[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

[tex]5=\frac{z}{4}-3[/tex]

[tex]\frac{z}{4}-3=5[/tex]

[tex]\frac{z}{4}=5+3[/tex]

[tex]\frac{z}{4}=8[/tex]

[tex]z=8\cdot \:4[/tex]

[tex]z=32[/tex]