From a hot-air balloon, Ian measures a 30^{\circ}
∘
angle of depression to a landmark that’s 1250 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answer:

b = 40 and -40

General form of Perfect square trinomial is

a

2

+

2

a

b

+

b

2

Therefore from

16

x

2

−

b

x

+

25

a

2

=

√

16

x

2

,

b

2

=

25

, then

a

=

±

4

x

,

b

=

±

5

take consideration a=4x and b=-5 (different sign), then

−

b

x

=

2

(

4

x

)

(

−

5

)

−

b

x

=

−

40

x

b

=

40

The perfect square is

(

4

x

−

5

)

2

=

16

x

2

−

40

x

+

25

.

if we consider a=4x and b=5 (same sign), then

−

b

x

=

2

(

4

x

)

(

5

)

−

b

x

=

40

x

b

=

−

40

The perfect square is

(

4

x

+

5

)

2

=

16

x

2

+

40

x

+

25

.

The first solution

(

4

x

−

5

)

2

is the best solution after comparing the expression given.

The probability of all heads, all tails, exactly two tails, exactly one head will be 1/8, 1/8, 3/8, and 3/8 respectively.

The complete question is given below.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Then the total number of the event will be

Total event = 2³

Total event = 8 {HHH, HHT, HTH, THH, HTT, THT, HHT, TTT}

Then the probability of all heads will be

⇒ 1/8

Then the probability of all tails will be

⇒ 1/8

Then the probability of exactly two tails will be

⇒ 3/8

Then the probability of exactly one head will be

⇒ 3/8

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Answer:one pen = $1.50

Step-by-step explanation:

See picture for the math if that helps

Using p for pens, h for highlighter,

A for first equation

B for second equation

I used equation A to reduce to a usable substitute by dividing all by 3

And then isolating “h”.

Now substitute the value of “h” into equation B and solve for “p”

P=$1.50

To check your work, substitute p ($1.50) into equation B and solve for “h”

h=$4.00

Now substitute the p and h values into either equation A or B and solve, they equal the numbers given

The property identity of multiplication is applied in the given statement.

The properties of multiplication are:

From the property identity, you know that the product between any number by the number 1 equals that number. Example: 3 • 1=3.

The question shows 10=10•1. Like, it was shown previously, this occurs due to the identity property of multiplication.

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Answer:

A. X= 13 and X= -3

Step-by-step explanation:

subtract 7 from both sides, simplify, break down the problems into 2 equations, solve equations, and boom once solve both equations you get 2 solutions.

The solutions to the equation are x = 13 and x = -3.

Therefore, the correct option is A.

Given is an expression |x-5| + 7 = 15, we need to solve for x,

To solve the equation |x - 5| + 7 = 15 for x, we'll need to isolate the absolute value expression and then solve for x.

Here's the step-by-step process:

Step 1: Subtract 7 from both sides of the equation:

|x - 5| = 15 - 7

|x - 5| = 8

Step 2: Break the equation into two cases, one with the positive value inside the absolute value and one with the negative value inside the absolute value.

Case 1: x - 5 is positive:

For this case, the equation |x - 5| = 8 becomes:

x - 5 = 8

Now, solve for x:

x = 8 + 5

x = 13

Case 2: x - 5 is negative:

For this case, the equation |x - 5| = 8 becomes:

-(x - 5) = 8

Simplify and solve for x:

-x + 5 = 8

-x = 8 - 5

-x = 3

Multiply both sides by -1 to isolate x:

x = -3

So, the solutions to the equation are x = 13 and x = -3.

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The population of the town in 1960 is 48.80 thousands

The equation of the model is given as:

f(t) = 42e^(0.015t)

1960 is 10 years after 1950.

This means that:

t = 10

Substitute t = 10 in f(t) = 42e^(0.015t)

f(10) = 42e^(0.015 * 10)

Evaluate

f(10) = 48.80

Hence, the population of the town in 1960 is 48.80 thousands

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Answer:

h = -5

Step-by-step explanation:

1) Subtract 7th from both sides

6h = 7h + 5

6h - 7h= 7h + 5 - 7h

2) Simplify

- Combine like terms

6h - 7h = 7h + 5 - 7h

-h = 7h + 5 - 7h

- Combine like terms

-h = 7h + 5 - 7h

-h = 5

3) Divide both sides by the same factor

-h = 5

-h/-1 = 5/-1

4) Simplify

Cancel terms that are in both the numerator and denominator

h/-1 = 5/-1

h = 5/-1

Divide the numbers

h = 5/-1

h = -5

Answer:

The answer is H=-5

Step-by-step explanation:

Answer:

28 students

Step-by-step explanation:

7 times 4 = 28

there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class

Answer:

28

Keyword(s):

divided, four, 7, per team, how many

Step-by-step explanation:

7 × 4 = 28

Step-by-step explanation:

y + 4 = -4(x - 2) = -4x + 8

y - 4 = -4x

-4x - y = -4

4x + y = 4

Step-by-step explanation:

v = Victor's age

m = Maria's age

v = 3m

v - 10 = 7(m - 10)

3m - 10 = 7m - 70

60 = 4m

m = 15

v = 3m = 3×15 = 45

Victor is 45 years old. Maria is 15 years old.

Answer:

50.27

Step-by-step explanation:

area for a circle is (pie)r^2

r^2=16

16xpie=50.27

Answer:

36 feet

Step-by-step explanation:

To find the area of a square or rectangle you multiply the width by the length.

Answer: $7448

Step-by-step explanation:

Year 1: 1.218x

Year 2: 1.218(1.218x)

Year 3: 1.218(1.218(1.218x))

Year 4: 1.218(1.218(1.218(1.218x)))

Year 5: 1.218(1.218(1.218(1.218(1.218x))))

Year 6: 1.218(1.218(1.218(1.218(1.218(1.218x)))))

Year 7: 1.218(1.218(1.218(1.218(1.218(1.218(1.218x))))))

Year 8: 1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218x)))))))

Year 9: 1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218x))))))))

Year 10: 1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218x)))))))))

Year 11: x(1.218¹¹)

Year 12: x(1.218¹²) = 79,400

x(10.6602517) = 79,400

x = 79,400/10.6602517

x=7448.22939

x = $7448

Hope this helps!

Answer:

[tex]y=\frac{1}{2} x[/tex]

Step-by-step explanation:

The equation of a line through two points can usually (except when the line is a vertical line) be written in slope intercept form,  [tex]y=mx+b[/tex] , where "m" is the slope of the line, and "b" is the y-intercept of the line.

To find "m", use the formula for slope:

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

[tex]m=\dfrac{(3)-(-2)}{(6)-(-4)}[/tex]

[tex]m=\dfrac{3+2}{6+4}[/tex]

[tex]m=\dfrac{5}{10}[/tex]

[tex]m=\dfrac{1}{2}[/tex]

So, the slope is 1/2 and we know that the equation for the line that passes through these two points should look like: [tex]y=\frac{1}{2} x+b[/tex]

To find "b", substitute one of the known points, and solve for "b":

[tex]y=\frac{1}{2} x+b[/tex]

[tex](3)=\frac{1}{2} (6)+b[/tex]

[tex]3=3+b[/tex]

Subtracting 3 from both sides to isolate the "b"...

[tex](3)-3=(3+b)-3[/tex]

[tex]0=b[/tex]

So, the y-intercept is 0.  Substituting into our line equation, [tex]y=\frac{1}{2} x+(0)[/tex] which simplifies to [tex]y=\frac{1}{2} x[/tex]  

Answer: move up or add 7 in positive direction

Answer:

302 degrees

Step-by-step explanation:

The statement that best describes the results is in tank 1, the rate at which water is used is higher.

Tank 1:

Tank 2:

The rate in tank 1 is higher than the rate in tank 2.

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Answer:

let n be the number then the sum of this number and 7 is n +7 and 3 times this sum is 3(n +7) 5 times the number less thirteen is 5n − 13

Step-by-step explanation:

Answer: 35

Step-by-step explanation:

Angles in a triangle add to 180 degrees, so in triangle ABC, [tex]m\angle C=180-103-42=35^{\circ}[/tex].

Sp, by the corresponding angles theorem, x=35

Multiplication is the process of multiplying. Jay lost 30 pounds in a period of 6 months.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

A.) The newly recorded temperature in January will be six times the temperature in February, therefore, we can write,

January = 6 × February = 6×(-3°F) = -18°F

Hence, the newly recorded temperature in January will be equal to -18°F.

B.) Change in water level on each day of the drought was equal to -4 inches, while the drought lasted for 1 week(7days), Thus, the net change in water level can be written as,

net change = 7 × -4 = -28inches

Hence, the net change in the water level during the drought was equal to -28 inches.

C.) Jay went on a diet for six months and lost 5 pounds each month, therefore, the net change in the weight will be equal to,

Net Change = 6 × 5 = 30 pounds

Hence, Jay lost 30 pounds in a period of 6 months.

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Answer:

B. Square

Step-by-step explanation:

Finding the side lengths :

Side 1

⇒ d₁ = √(-4 - 0)² + (8 - 8)²

⇒ d₁ = √16

⇒ d₁ = 4

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

Side 2

⇒ d₂ = √(-4 + 4)² + (8 - 4)²

⇒ d₂ = √16

⇒ d₂ = 4

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

Side 3

⇒ d₃ = √(-4 - 0)² + (4 - 4)²

⇒ d₃ = √16

⇒ d₃ = 4

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

Side 4

⇒ d₄ = √(0 - 0)² + (8 - 4)²

⇒ d₄ = √16

⇒ d₄ = 4

As all sides of the figure are equal, and it creates 4 right angles, it is a square.

Answer:

see explanation

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 8x + 8y + 23 = 0

collect the x and y terms together and subtract 23 from both sides

x² - 8x + y² + 8y = - 23

using the method of completing the square

add ( half the coefficient of the x / y terms )² to both sides

x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16

(x - 4)² + (y + 4)² = 9 ← in standard form

with centre = (4, - 4 ) and r = [tex]\sqrt{9}[/tex] = 3

this is shown in graph b

Answer:

4/25

Step-by-step explanation:

Let's make the units the same :

2 kg = 2000 g

Now lets simplify this fraction :

Divide top and bottom by 2 until you can't :

320/2000 = 160/1000

160/1000 = 80/500

80/500 = 40/250

40/250 = 20/125

Now we divide top and bottom by 5 as 2 is not a factor of 125 :

20/125 = 4/25

This is our final answer

Hope this helped and brainliest please

Answer:

35°

Step-by-step explanation:

Same-Side interior angles (consecutive angles) are supplementary.

Supplementary meaning that those two angles add up to make 180°.

So Angles C is 35°

Answer:

A. (AAA)

Step-by-step explanation:

.....(AAA) "does not work because it can produce similar but not congruent triangles"

.....(AAS) "If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent."

.....(ASA)"triangles are congruent if any two angles and their included side are equal in the triangles."

Hope This Helped

Answer:

the first one

Step-by-step explanation:

the formul is y=mx+b

m is slope which is -3/2

b is y intercept and it is -3

and the addition sign will change based on if the y intercept is negative or not

Hope this helps

Answer:

The slope of the line is:  

              [tex]-\frac{3}{4}[/tex]

Slope of a parallel line is the same:

             [tex]-\frac{3}{4}[/tex]

Slope of a perpendicular line, invert the sign and fraction:

              [tex]\frac{4}{3}[/tex]

Hope this helps

Answer:

C)    14 Units

Step-by-step explanation:

E2020