A gutter at the edge of a roof drops 2 inches for every 30 feet of length. The measure of the angle to the nearest tenth of a degree that the gutter makes with the roof is ____ degrees. (Enter only the number.)

x = ones

y = fives

x+y = 14 total bills

 rewrite as x = 14-y

1x +5y = 50

1(14-y) +5y = 50

14-1y +5y = 50

14 +4y = 50

4y = 36

 y = 36/4 = 9

 x = 14-y = 14-9 = 5

 9+5 = 14

9x5 = 45 +5x1 = 50

 he had 9 fives and 5 ones

Answer:

There were 5 bills of '1' and 9 bills of '5'.

Step-by-step explanation:

let the number of '1' bill be x

let the number of '5' bill be y.

Total number of bills = 14

x + y = 14 ..[1]

Worth of 14 bills = 50

So,[tex]x\times 1+y\times 5=\$50[/tex]

[tex]x+5y=50[/tex]..[2]

x + y = 14

x = 14 - y

Putting value of x in [2]:

[tex]14- y +5y=50[/tex]

[tex]y=\frac{50-14}{4}=9[/tex]

y = 9

x = 14-y = 14 - 9 = 5

There were 5 bills of '1' and 9 bills of  '5'.

Using the trigonometric tangential function, the height of the tree casting a 26-meter shadow at an angle of elevation of 24° is approximately 11 meters.

The given problem can be solved by applying trigonometric principles, specifically the tangent function. In this case, we know the shadow length (26m) and the angle of elevation of the sun (24°). The height of the tree is the side opposite the angle, and the shadow is the adjacent side. Thus, we can use the tangent equation (Tan θ = Opposite/Adjacent). So, Tan 24° = Height of the tree / 26m. By cross multiplying and evaluating Tan 24°, we get the height of the tree to be approximately 11 meters.

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Given the provided motion physics model and using the quadratic formula, it is determined that it would take approximately 3.79 seconds for the basketball to go into the hoop after it was thrown.

The subject in consideration here is a problem related to quadratic equations in motion physics. The equation given in the question signifies a model of the height of the basketball as a function of time in the format of a quadratic equation. The equation is h = -16t² + 23t + 7.

With this equation, we can apply the quadratic formula to find the amount of time it takes for the ball to reach the hoop.

Upon using the quadratic formula, two solutions come up, t = 3.79 s and t = 0.54 s. The ball is at a height of 10 m at two times during its trajectory—once on the way up (as it rises) and once on the way down (as it falls). Since the question is about the time the ball goes into the hoop after reaching its maximum height and coming down, the larger value of t (3.79s) is considered as the valid solution.

Therefore, the time it takes for the basketball to go into the hoop after it was thrown is approximately 3.79 seconds which is not an offered option.

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Answer:

9.2

Step-by-step explanation:

We are given that a figure in which a tangent and a secant to the circle.

We have to find the value of x.

Length of tangent segment=x

Length of secant segment=12 +5=17 units

Length of external segment=5 units

We know that secant-tangent theorem

It states that product of length of secant segment and its external segment is equal to square of length of tangent segment.

[tex]x^2=17\times 5=85 [/tex]

[tex]x=\sqrt{85}=9.2 units[/tex]

Hence, the value of x=9.2

500= (19.50-8.00)x

500 = 11.50x

x=500/11.50=43.48

 so he needs to sell approximately 44 centerpieces to break even

The first step to solve for x in the given algebra using properties of equality is; Add 5 to both sides.

We want to simplify the algebraic expression;

3.7 = x + (-5)

When dealing with algebra like this, what we have to first do is to balance both sides of the equation.

To solve this particular algebra problem, we will use additional property of equality by adding 5 to both sides to get;

3.7 + 5 = x + (-5) + 5

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The first step to solving the expression 3.7 = x + (- 5) is,

''Add 5 to both sides''

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to give that,

An algebraic expression to simplify,

⇒ 3.7 = x + (- 5)

Now, Simplify the expression by combining like terms as,

⇒ 3.7 = x + (- 5)

⇒ 3.7 = x - 5

Use the additional property of equality by adding 5 to both sides to get;

3.7 + 5 = x + (-5) + 5

8.7 = x

x = 8.7

So, the first step is, ''Add 5 to both sides''.

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Answer:  A. Horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis

Step-by-step explanation:

Since, If there is a function, y= a cos bx

Then a shows vertical stretch while b shows horizontal compression.

Here, Given function, y= cos x

After transformation, It is giving y = -2 cos 3x

therefore here is a horizontal compression occurs with factor 1/3.

Also Negative sign shows there also did reflection through x-axis.

And, It also, stretched vertically by factor 2. ( also shown in the below graph)

Thus, Option A) is correct.      

Rounded to the nearest meter, the height of the plane is approximately 405 meters.

So, the correct answer is B. 405 m.

To find the height of the plane, we can use trigonometry, specifically the tangent function.

Let's denote the height of the plane as h (in meters).

From the information given, we know that the angle of depression from the airplane to the atoll is 5 degrees, and the horizontal distance from the airplane to the atoll is 4629 meters.

Using the tangent function, we have:

tan(angle of depression) = height / horizontal distance

tan(5 degrees) = h / 4629

To find the value of h, we can rearrange the equation:

h = 4629 * tan(5 degrees)

Now, let's calculate the height of the plane:

h ≈ 4629 * 0.0874886635 ≈ 404.773 meters

Rounded to the nearest meter, the height of the plane is approximately 405 meters.

So, the correct answer is B. 405 m.

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Answer:

answer is D ;)

Step-by-step explanation:

(x+1)^2-x^2=23

x^2+2x+1-x^2=23

2x+1=23

2x=22

x=11

11^2 = 121

x+1 =12

12^2=144

144-121 = 23

I think it is C

BMK ><

Answer:

c)720

Step-by-step explanation:

The mean of a set of credit scores is u=690 and o=14.

mean = 690  and standard deviation SD = 14

We use z- score formula

[tex]z=\frac{x-mean}{SD}[/tex]

z= 3.3 given

Plug in the values and find out x

[tex]3.3=\frac{x-690}{14}[/tex]

Multiply 14 on both sides

46.2 = x- 690

Now add 690 on both sides

x= 736.2

Credit score is 720 that comes under 736.2

So answer is 720

The answer is 5 units on e2020.

To find the rate of change of height with respect to time, we use the formula dh/dt = dV/dt / (πr²) and substitute the given values for the rate of volume change and the radius.

We have the rate of volume change as 23 cm³/sec and the cylinder has a radius of 12 cm. Note that the typo '2323 cm³/sec' and '1212 cm' should be read as '23 cm³/sec' and '12 cm,' respectively.

The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. To find the rate at which the height h changes over time, we can take the derivative of the volume with respect to time, which gives us dV/dt = πr² dh/dt. We can solve this equation for dh/dt (the rate of change of height with respect to time) by dividing both sides by πr² and substituting the given values. Therefore, dh/dt = dV/dt / (πr²).

Substituting the values, we get:

dh/dt = 23 cm³/sec / (π * (12 cm)²)

Upon simplifying, we will obtain the rate at which the height of the water is decreasing in cm/sec.

Answer:

B. 0.813

Step-by-step explanation:

A sixteen-sided number cube has the numbers 1 through 16 on each face.

So, [tex]|\ S\ |=16[/tex]

Let us assume that, A be the event that the number will be an even number. So,

[tex]A=\left \{ 2,4,6,8,10,12,14,16 \right \}[/tex] and [tex]|\ A\ |=8[/tex]

Then,

[tex]P(A)=\dfrac{|\ A\ |}{|\ S\ |}=\dfrac{8}{16}[/tex]

Let us assume that, B be the event that the number will be an odd prime number.

[tex]B=\left \{3,5,7,11,13 \right \}[/tex] and [tex]|\ B\ |=5[/tex]

Then,

[tex]P(B)=\dfrac{|\ B\ |}{|\ S\ |}=\dfrac{5}{16}[/tex]

So the probability that you will roll an even number or an odd prime number will be,

[tex]P(A\cup B)=P(A)+P(B)-P(A\cup B)[/tex]

[tex]=\dfrac{8}{16}+\dfrac{5}{16}-0[/tex] ( as independent events)

[tex]=\dfrac{13}{16}[/tex]

[tex]=0.813[/tex]

Answer:

B

Step-by-step explanation:

Step 2 he wrote distributive instead of associative