What is the slope of the line on the graph?

Answer:

time interval when Tree A is taller than Tree B is;

t > 5 years

Step-by-step explanation:

Tree A;

Initial height = 24 inches

Increase in height per year = 6 inches per year

Thus, for t years after being planted, height is;

A = 6t + 24

Tree B;

Initial height = 39 inches

Increase in height per year = 3 inches per year

Thus, for t years after being planted, height is;

B = 3t + 39

For tree A to be taller than tree B, then it means thay;

A > B

Thus;

6t + 24 > 3t + 39

Subtract 3t from both sides to get;

6t - 3t + 24 > 39

3t + 24 > 39

3t > 39 - 24

3t > 15

Divide both sides by 3 to get;

t > 5

Thus, time interval when Tree A is taller than Tree B is; t > 5

Answer:

1. 2.1%

2. 47.7%

3. 68.2%

4. 34.1%

5. 49.9%

6. 0.1%

These values may be rounded differently depending on set rounding limits.

The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9

Question: The likely missing parameters in the question are;

The time at which the shorts are at the maximum height, t₁ = 10 seconds

The time at which the shorts are at the minimum height, t₂ = 25 seconds

Where;

A = The amplitude

The period, T = 2·π/B

The horizontal shift = h

The vertical shift = k

The parent equation of the sine function = sin(x)

We find the values of the variables, A, B, h, and k as follows;

The given parameters of the sinusoidal function are;

The maximum height = 16 meters at time t₁ = 10 seconds

The minimum height = 2 meters at time t₂ = 25 seconds

The time it takes the shorts to complete a cycle, (maximum height to maximum height), the period, T = 2 × (t₂ - t₁)

∴ T = 2 × (25 - 10) = 30

The amplitude, A = (Maximum height- Minimum height)/2

∴ A = (16 m - 2 m)/2 = 7 m

The amplitude of the motion, A = 7 meters

T = 2·π/B

∴ B = 2·π/T

T = 30 seconds

∴ B = 2·π/30 = π/15

B = π/15

At t = 10, y = Maximum

Therefore;

sin(B(x - h)) = Maximum, which gives; (B(x - h)) = π/2

Plugging in B = π/15, and t = 10, gives;

((π/15)·(10 - h)) = π/2

10 - h = (π/2) × (15/π) = 7.5

h = 10 - 7.5 = 2.5

h = 2.5

The minimum value of a sinusoidal function, having a centerline of which is on the x-axis, and which has an amplitude, A, is -A

Therefore, the minimum value of the motion of the turbine blades before, the vertical shift = -A = -7

The given minimum value = 2

The vertical shift, k = 2 - (-7) = 9

Therefore, k = 9

Therefore;

The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9

More can be learned about sinusoidal functions on Brainly here;

https://brainly.com/question/14850029

9514 1404 393

Answer:

  x = 7

  y = 5

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

__

For a=-j and b=7,

  (-j)^-7 = 1/(-j)^7   ⇒   x = 7

For a=k and b=-5,

  k^-5 = 1/k^5   ⇒   y = 5

Answer:

3x2,−23y,√5m, 3 x 2 , − 2 3 y , 5 m

Step-by-step explanation:

that is the answer i think

Answer:

X(-12,-7)

Step-by-step explanation:

This is the answer to your problem. I hope it helps. I don't know how to explain it sorry.

Given:

The logarithmic equation is:

[tex]\log 970=x[/tex]

To find:

The exponential equations that is equivalent to the given logarithmic equation.

Solution:

Property of logarithm:

If [tex]\log_b a=x[/tex], then [tex]a=b^x[/tex]

We know that the base log is always 10 if it is not mentioned.

If [tex]\log a=x[/tex], then [tex]a=10^x[/tex]

We have,

[tex]\log 970=x[/tex]

Here, base is 10 and the value of a is 970. By using the properties of exponents, we get

[tex]970=10^x[/tex]

Interchange the sides, we get

[tex]10^x=970[/tex]

Therefore, the correct option is B, i.e., [tex]10^x=970[/tex].

Note: It should be "=" instead of "-" in option B.

Answer:

90

Step-by-step explanation:

it its a 45 45 90 triangle

Answer:

False

Step-by-step explanation:

well i think that the answer from my calculations

9514 1404 393

Answer:

  (b)  -1

Step-by-step explanation:

The graph shows the difference between the two expressions is zero at x=-1.

__

Additional comment

For finding solutions to polynomial equations, I like to put them in the form f(x)=0. Most graphing calculators find zeros (x-intercepts) easily. Sometimes they don't do so well with points where curves intersect. Also, the function f(x) is easily iterated by most graphing calculators in those situations where the root is irrational or needs to be found to best possible accuracy.

Answer:

The answer is b: -1

Step-by-step explanation:

good luck!

Answer:

Step-by-step explanation:

what this statement is saying is that if you have

4 x + 3x^2 + 5 +  8x^2 + 12x + 9

that  

3x^2 +  8x^2 = 11x^2

4 x   + 12x  = 16x

 5 +     9 = 14

get added  together  the final answer would be

in descending order as : 11x^2 + 16x + 14

Answer: A (x+1)(x+2)(x+5)

Step-by-step explanation:

Answer:

D. 65°

Step-by-step explanation:

It is so because the triangle is isosceles, two identical sides and two equal angles.

Step-by-step explanation:

Step 1: 12x-6= 1

step 2:12x=7

Answer:

Step-by-step explanation:

sin²β + sin²β×tan²β = tan²β

sin²β( 1 + tan²β ) = tan²β

~~~~~~~~~~~~~~~~

sin²β + cos²β = 1  

[tex]\frac{sin^2\beta }{cos^2\beta }[/tex] + [tex]\frac{cos^2\beta }{cos^2\beta }[/tex] = [tex]\frac{1}{cos^2\beta }[/tex] ⇒ tan²β + 1 = sec²β ⇔ 1 + tan²β = sec²β

~~~~~~~~~~~~~~

1 + tan²β = [tex]\frac{1}{cos^2 \beta }[/tex]

L.H. = sin²β ( [tex]\frac{1}{cos^2 \beta }[/tex] ) = tan²β

R.H. = tan²β

Answer:

R = 25.8

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos R = adj side / hyp

cos R = 9/10

Taking the inverse cos of each side

cos ^-1 ( cos R) = cos^ -1 ( 9/10)

R=25.84193

Rounding to the nearest tenth

R = 25.8

Answer:

[tex]\boxed {\boxed {\sf D. \ 25.8 \textdegree} }[/tex]

Step-by-step explanation:

We are asked to find the measure of an angle given the triangle with 2 sides. This is a right triangle because of the small square representing a right angle. Therefore, we can use trigonometric functions. The three major functions are:

We are solving for angle R, and we have the sides TR (measures 9) and SR (measures 10).

We have the adjacent side and the hypotenuse, so we will use the cosine function.

[tex]cos \theta = \frac {adjacent}{hypotenuse}[/tex]

[tex]cos R = \frac {9}{10}[/tex]

Since we are solving for an angle, we must take the inverse cosine of both sides.

[tex]cos^{-1}(cos R) = cos ^{-1} ( \frac{9}{10})[/tex]

[tex]R = cos ^{-1} ( \frac{9}{10})[/tex]

[tex]R= 25.84193276[/tex]

If we round to the nearest tenth, the 4 in the hundredth place tells us to leave the 8 in the tenths place.

[tex]R \approx 25.8 \textdegree[/tex]

The measure of angle R is approximately 25.8 degrees and choice D is correct.

Answer:

Option A. y = x² + 7x + 10

Step-by-step explanation:

We'll begin calculating the roots of the equation from the graph.

The roots of the equation on the graph is where the curve passes through the x-axis.

The curve passes through the x-axis at –5 and –2

Next, we shall determine the equation. This can be obtained as follow:

x = –5 or x = –2

x + 5 = 0 or x + 2 = 0

(x + 5)(x + 2) = 0

Expand

x(x + 2) + 5(x + 2) = 0

x² + 2x + 5x + 10 = 0

x² + 7x + 10 = 0

y = x² + 7x + 10

Thus, the function that describes the graph is y = x² + 7x + 10

Answer:(2,5)

Step-by-step explanation:   watch this video

https://youtu.be/l78P2Xi68-k

Answer:

Step-by-step explanation:

6(x+8) = -36

divide both sides by 6: x+8 = -6

subtract 8 from both sides: x = -14

Answer:

6(x+8)=-36

6x+48=-36

6x=84

x=14

Answer:

they have it on calculator soup

Step-by-step explanation:

Answer:

D. 31<m<43

Step-by-step explanation:

45 x 5 = 225 which is the age of the 5 joggers altogether.

55 x 2 = 110 which is the age of the 2 joggers together.

3m + 110 = 225 then solve for m so,

3m = 115

m = 38.3333

so hence, m is greater than 31 but less than 43.

answer: D

Answer:

Step-by-step explanation:

log(20x³) - 2logx = 4

log(20x³) -log(x²) = 4

log(20x³/x²) = 4

log(20x) = 4

20x = 10⁴

x = 10⁴/20 = 500

3 sec²(θ) - 5 tan(θ) - 4 = 0

Recall the Pythagorean identity,

cos²(θ) + sin²(θ) = 1.

Multiplying both sides by 1/cos²(θ) gives another form of the identity,

1 + tan²(θ) = sec²(θ).

Then the equation becomes quadratic in tan(θ):

3 (1 + tan²(θ)) - 5 tan(θ) - 4 = 0

3 tan²(θ) - 5 tan(θ) - 1 = 0

I'll solve by completing the square.

tan²(θ) - 5/3 tan(θ)) - 1/3 = 0

tan²(θ) - 5/3 tan(θ) = 1/3

tan²(θ) - 5/3 tan(θ) + 25/36 = 1/3 + 25/36

(tan(θ) - 5/6)² = 37/36

tan(θ) - 5/6 = ±√37/6

tan(θ) = (5 ± √37)/6

Take the inverse tangent of both sides:

θ = arctan((5 + √37)/6) + nπ   or   θ = arctan((5 - √37)/6) + nπ

where n is any integer

Answer:

8

Step-by-step explanation:

As it's an isosceles right triangle, it's sides are equal, say x. x^2+x^2=(4*sqrt(2))^2. x=4, Area is (4*4)/2=8

Answer:

x > 0 and x > -6

[tex]{ \tt{y = {x}^{2} + 4}} \\ { \tt{for \: x > 0 :positive \: integers }} \\ y = 0 < x < {}^{ + } \infin[/tex]

Answer:

It will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.

Step-by-step explanation:

Given that an inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours, to determine how long it will take both pipes to fill the pool, the following calculation must be performed:

1/5 + 1/4 = X

0.20 + 0.25 = X

0.45 = X

9/20 = X

9 = 60

2 = X

120/9 = X

13,333 = X

Therefore, it will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.

Answer:

0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50.

This means that [tex]\mu = 7.96, \sigma = 0.5[/tex]

Sample of 30:

This means that [tex]n = 30, s = \frac{0.5}{\sqrt{30}}[/tex]

What is the probability that the sample mean will be between $7.75 and $8.20?

This is the p-value of Z when X = 8.2 subtracted by the p-value of Z when X = 7.75.

X = 8.2

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{8.2 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]

[tex]Z = 2.63[/tex]

[tex]Z = 2.63[/tex] has a p-value of 0.9957

X = 7.75

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{7.75 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]

[tex]Z = -2.3[/tex]

[tex]Z = -2.3[/tex] has a p-value of 0.0107.

0.9957 - 0.0157 = 0.985

0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.

Answer:

B

Step-by-step explanation:

Given

4x² - 72x = 0 ← factor out 4 from each term

4(x² - 18x) = 0

To complete the square

add/subtract (half the coefficient of the x- term)² to x² - 18x

4(x² + 2(- 9)x + 81 - 81) = 0

4(x - 9)² - 4(81) = 0

4(x - 9)² - 324 = 0 ( add 324 to both sides )

4(x - 9)² = 324 ( divide both sides by 4 )

(x - 9)² = 81 ( take the square root of both sides )

x - 9 = ± [tex]\sqrt{81}[/tex] = ± 9 ( add 9 to both sides )

x = 9 ± 9

Then

x = 9 - 9 = 0

x = 9 + 9 = 18

Answer:0,18

Step-by-step explanation:

its right

Answer:

x > 21

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

x + 34 > 55

Step 2: Solve for x