A gardener is planting two types of trees: Type A is 10 feet tall and grows at a rate of 7 inches per year. Type B is 3 feet tall and grows at a rate of 19 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer:

  9x +y = 12

Step-by-step explanation:

You want the standard form equation for the line with slope -9 through the point (2, -6).

The point-slope form equation is a good place to start when given a point and a slope. That equation is ...

  y -k = m(x -h) . . . . line with slope m through point (h, k)

  y -(-6) = -9(x -2) . . . . line with slope -9 through point (2, -6)

This can be rearranged to the desired form:

  y +6 = -9x +18 . . . . . . eliminate parentheses

  9x +y = 12 . . . . . . . . add 9x -6

Answer:

a. [tex]\frac{x+2}{x+6}[/tex]

Step-by-step explanation:

[tex]\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}[/tex]

a) The estimated population which takes time to get double is 63.36.

b) The estimated population which takes time to get triple is 100.42.

The growth equation is A(t) = [tex]A_0e^{kt}[/tex] where A(t) is the quantity at time t, A₀ is the initial quantity, k is a positive constant, and [tex]e^{(x)}[/tex] is the natural exponential function. For A₀ = 7.1E9 (7.1 billion) and k = 0.011 (1.1%):

Given formula:

A(t) =  [tex]A_0 e^{kt}[/tex]                  --------------------------- (1)

A(t) =  [tex]7.1E9e^{0.011t}[/tex]     ----------------------------(2)

a) We have to find twice the population, or if A(t) = 2A₀. For doubles (or multiples of A₀₎, equation (1) can be written as

A(t) = [tex]A_0e^{0.11t}[/tex]

⇒ 2A₀ = [tex]A_0e^{0.11t}[/tex], (replaces A(t) = 2A₀)

⇒ 2 = [tex]e^{0.011t}[/tex],

⇒ ln(2) = ln(e0.011t ),

⇒ ln(2) = 0.011t,

⇒ ln(2)/0.011 = t

Therefore,

t = 63.36

b) Now we will find the number of years it will take the population to be triple of its size.

    7.1 × 3 = [tex]7.1(1.011)^t[/tex]

⇒ [tex]\frac{7.1 * 3}{7.1}[/tex] = [tex]1.011^{t}[/tex]

⇒ 3 = [tex]1.011^{t}[/tex]

Now, Using the logarithm:

   ln(3) = ln [tex](1.011)^{t}[/tex]

⇒  t = 100.42

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The equation is log_2 (3x - 5) = 9 There are no real solutions to this equation because the logarithm of a negative number is undefined. The left side of the equation would require the argument to be negative, thus making the equation impossible to solve.

This equation cannot be solved because the logarithm of a negative number is undefined. The left side of the equation is of the form log_2 (N), where N is some real number.For the equation to have any real solutions, N needs to be greater than 0. However, in this equation, N is equal to 3x - 5, which can be negative for certain values of x. This means that there is no real number x that can be substituted into the equation to make it true, since the logarithm of a negative number is not defined. Therefore, this equation has no real solutions.

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Step-by-step explanation:

20° units circle a circumference

A circle has a circumference of 145 units. Then the length of the arc intercepted by a central angle of 125° which is round to the nearest tenth is 50

The length of an arc depends on the radius of a circle and the central angle θ. We know that for the angle equal to 360 degrees (2π), the arc length is equal to circumference. Hence, as the proportion between angle and arc length is constant, we can say that:

L / θ = C / 2π

L / θ = 2πr / 2π

L /  θ= r

As circumference C = 2πr,

145=2πr

r=145/2π

r=23.07746675

We find out the arc length formula when multiplying this equation by θ:

L = r * θ

as θ=125°

θ=2.18166(radians)

L=23.07746675x2.18166

L=50.34718611

Length round to nearest tenth is 50

Therefore, the value of length round to nearest tenth is 50

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If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.  

[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031

X = 89 represent the mean of seventh-grade girls in Midwest school district

s = 15 represent the standard deviation for the sample  

n = 31 sample size  

μ = 100 represent the value that we want to test  

'a' represent the significance level for the hypothesis test.  

't' would represent the statistic (variable of interest)  

[tex]p_{v}[/tex] represent the p value for the test (variable of interest)

State the null and alternative hypotheses,

We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:  

Null hypothesis: μ = 100

Alternative hypothesis: μ ≠ 100

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t = (X-μ) / ([tex]\frac{s}{\sqrt{n} }[/tex] )                (Equation-1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

t = [tex]\frac{89-100}{\frac{15}{\sqrt{31} } }[/tex]

t = -4.08

Calculate the P-value  

First we need to calculate the degrees of freedom given by:  

[tex]df = n-1[/tex]

[tex]df = 31 -1[/tex]

[tex]df = 30[/tex]

Since is a two tailed test the p value would be:  

[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 )

[tex]p_{v}[/tex] = 0.00031

Therefore,

If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.  

[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031

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The total area of the Caribbean sea and the South Atlantic ocean is 4.299 × 10⁷ km². The correct option is the second option 4.299 × 10⁷ km²

From the question, we are to determine the total area of the water bodies.

From the given information

"The area of the Caribbean sea is 2.7182 × 10⁶ km²"

and

"The area of the South Atlantic ocean is 4.027 × 10⁷ km²"

To determine the total area, we will add  up the two areas

Total area = 2.7182 × 10⁶ km² + 4.027 × 10⁷ km²

Total area = 0.27182 × 10¹ × 10⁶ km² + 4.027 × 10⁷ km²

Total area = 0.27182 × 10⁷ km² + 4.027 × 10⁷ km²

Total area = 4.29882 × 10⁷ km²

Total area ≈ 4.299 × 10⁷ km²

Hence, the total area is 4.299 × 10⁷ km²

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Answer:

Hence, the total area is 4.299 × 10⁷ km²

Step-by-step explanation:

The equation of hyperbola will be;

⇒ x²/48² - y²/14² = 1

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

In hyperbola,

The value of center = (0, 0)

The value of vertex = (- 48, 0)

The value of focus = (50, 0)

Now,

We know that;

The equation of hyperbola is,

⇒ (x - h)²/a² - (x - k)²/b² = 1

Where, (h, k) is center, (h ± a, k) is the vertex.

Here, The value of center = (0, 0)

The value of vertex = (- 48, 0)

The value of focus = (50, 0)

So, h = 0, k = 0

a = 48, c = 50

We get;

⇒ (x - 0)² / 48² - (y - 0)² / b² = 1

⇒ x² / 48² - y² / b² = 1

Since, c = √a² + b²

⇒ b = √c² - a²

⇒ b = √50² - (-48)²

⇒ b = √196

⇒ b = 14

Hence, We get;

⇒ x² / 48² - y² / b² = 1

⇒ x² / 48² - y² / 14² = 1

Thus, The equation of hyperbola is;

⇒ x²/48² - y²/14² = 1

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a )The equation of the new parallel line is   x - y = 3

b ) The equation of the new perpendicular line is   x + y = -1

The given line passes through the points (0, 3 ) and (-3, 0).

Here,

[tex](x _{1}, y _{1}) = (-3, 0)\\\\(x _{2}, y _{2}) = (0, 3)[/tex]

The slope of the line = m

[tex]m =\frac{y_{2}- y _{1}}{x _{2}- x_{1}} \\\\m = \frac{3-0}{0+3} \\\\m = \frac{3}{3} = 1[/tex]

The slope of the given line is 1

a ) The new line passes through the point (1, -2) and is parallel to the given line .

           [tex]y- y_{1} = m (x- x_{1}) -- (1)[/tex]

          y + 2 = 1 (x -1 )

          y  +2 = x - 1

           x - y -1 -2 = 0

           x - y - 3 =0

           x - y = 3

The equation of the new parallel line is   x - y = 3

b ) The new line passes through the point (1, -2) and is perpendicular to the given line .

           [tex]y- y_{1} = m (x- x_{1}) -- (1)[/tex]

          y + 2 = -1 (x -1 )

          y  +2 = - x + 1

           x + y -1 +2 = 0

           x + y + 1 = 0

           x + y = -1

The equation of the new perpendicular line is   x + y = -1

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The value of y in the isosceles triangle is AC = 6 cm

What Is an Isosceles Triangle?

A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle

The three types of Isosceles Triangles are :

Isosceles acute triangle

Isosceles right triangle

Isosceles obtuse triangle

Given data ,

Let the triangle be represented as ABC

Now , the angle ∠ABC = 25°

The angle ∠ACB = 25°

So , the 2 angles of a triangle is 25° so , the third angle is 130°

So , the triangle is an isosceles triangle

And , the two sides of the triangle is AB = AC

The measure of side AB = 6 cm

The measure of side AC = measure of side AB

Therefore , the measure of side AC = 6cm

Therefore , the value of AC is 6 cm

Hence , the measure of side AC of triangle is 6 cm

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The rocket's height after 3 seconds is 6.3 sec.

The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.

A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.

To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:

h = -5*t2 + 30*t + 10

h = -5(2)2 + 30(2) + 10

h = -5(4) + 30(2) + 10

h = -20 + 60 +10

h = 50 m

The height of the rocket 2 seconds after launching it is 50 meters.

To find the x-coordinate of the vertex of a parabola, we use the formula:

[tex]xvertex = -b / 2a[/tex]

t - 3 = ± √(11)

t = 3 ± √(11)

t = 3 ± 3.3

Solving for t, we get two solutions:

t = 3 - 3.3

t = -0.3 sec

and

t = 3 + 3.3

t = 6.3 sec

Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.

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Answer:

Step-by-step explanation:

11.1

The approximate value of y - x is 17.2°.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given a right triangle LMN.

Using the tangent function,

tan (y) = 19.1 / 14.1

          = 1.3546

y = tan⁻¹ (1.3546) = 53.56°

We know that,

x + y = 90°, since the other angle is 90°.

x = 90 - 53.56° = 36.44°

y - x = 53.56° - 36.44° = 17.12° ≈ 17.2°

Hence the value of y - x is 17.2°.

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Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

Answer: 120 miles

Step-by-step explanation:

If a car goes 60 miles per hour then in two hours (60×2) it will go 120

Usibg the distributive property to the algebraic expression 5(x - 7) will be 5x - 35.

The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c); where, a, b, and c are the operands. Here, the number outside the brackets is multiplied with each term inside the brackets and then the products are added.

When you multiply a value by a sum, the distributive property of multiplication over addition is used. Say you want to multiply 5 by the product of 10 plus 3. When two terms are similar, we typically add the two numbers before multiplying by 5. However, the property states that you should first multiply each addend by 5.

Therefore, 5(x - 7) will be:

= 5(x) - 5(7)

= 5x - 35

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The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

1. To find out how much prices for filling a cavity vary, an insurance company randomly selects 10 dental practices in California and asks for the cash (non-insurance) price for this procedure.

2. The insurance company then computes the interquartile range of the prices for each practice.

3. The interquartile range of $74 indicates the amount of price variation for filling a cavity at the 10 randomly selected dental practices in California.

The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

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sinC = 72/97

What is right triangle?

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest side of the three sides, known as the hypotenuse, is the third side.

Given right angle triangle ABC ∠B is a right angle

AB=72

BC=65 and

AC = 97

sin C = perpendicular/hypotenuse = p/h

sinC = 72/97

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Answer:

Just so we can help each other out!

The probability that their second child will have blue eyes is 1/4.

Here dark eye is dominant trait and blue eyes is recessive trait.

So both man and woman is heterozygous dominant and the blue eye child is homozygous recessive.

Man and woman will produce four types of genotypes in children. One homozygous dominant (dark eye), one homozygous recessive (blue eye) and two heterozygous dominant (dark eye).

So the probability of any child to be blue eyed (homozygous recessive) will be 1/4.

Hence we get the required answer.

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Answer: D. Vertical

Step-by-step explanation:

The quadratic inequality (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y contains al the ordered pairs outside the parabola.

In this problem we must determine a quadratic inequality of the form:

a · x² + b · x + c < y

Where a, b, c are the real coefficients of the inequality.

First, determine the coefficients of the quadratic inequality (parabola) by solving the system of linear equations:

25 · a - 5 · b + c = 0

4 · a + 2 · b + c = 0

a + b + c = - 18

(a, b, c) = (18 / 7, 54 / 7, - 180 / 7)

Second, write the quadratic inequation:

(18 / 7) · x² + (54 / 7) · x - 180 / 7 < y

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Answer:

2.8 goals

Step-by-step explanation:

35 * 0.08 = 0.35*8

0.35*8=2.8

The expected number of goals scored on the goaltender would be 2.8.

The expected number of goals scored by the goaltender can be calculated using the formula:

Expected goals = Total shots * Probability of a goal

Therefore, for a goaltender with a save percentage of 0.920 (which means the probability of a goal is 0.08), and facing 35 shots:

The expected number of goals scored on this goaltender in a game where she faced 35 shots would be 2.8 goals.

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Answer:

It should be to the right of 4 and the left of 6

Step-by-step explanation:

Answer: 0

Step-by-step explanation: The reasoning behind this is that both functions will never intersect which would mean there are no solutions for the system equation.

The calculation that will give the closest estimate of the sales of soft drinks and hot dogs is 360 * 2 + 220  * 2

From the question, we have the following parameters that can be used in our computation:

Time = one week

Number of cans = 362

Unit price of soft drink = $1.75

Number of hot dogs = 221

Unit price of hot dogs = $2.35

The calculation that will give the closest estimate is represented as

Estimate = Number of cans * Unit price of soft drink + Number of hot dogs * Unit price of hot dogs

Substitute the known values in the above equation, so, we have the following representation

Estimate = 362 * 1.75 + 221  *2.35

Approximate

Estimate = 360 * 2 + 220  * 2

Hence, the expression is 360 * 2 + 220  * 2

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Answer:

It is NLJ

Step-by-step explanation:

Trust me lol

Answer:

D

Step-by-step explanation:

Take the coefficients of each term and list them.

- 1 5 - 9

Multiply 3 by the first coefficient and combine it from the second.

- 1 * 3 = - 3, 5 - 3 = 2

Multiply 3 by this product and combine it from the third term.

3 * 2 = 6, - 9 + 6 = - 3

Your remainder is option D, - 3.

Answer:

-3

Step-by-step explanation:

3    -1     5    -9

            -3    6

     -1    2     3

Remainder: -3

Factored: [tex]-x+2-\frac{3}{x-3}[/tex]

1.) Set up the synthetic division.

2.) drop the first term down. My teacher used to say "drop it like its hot" :)

3.) Multiply c by the value just written on the bottom row.

4.) Add the column created in step 3.

5.) Repeat until done.

6.) Write out the answer

The less value including 13% VAT in Rs. 3200 than Rs. 3820 is 340 rupees.

A percentage is a ratio or number that may be expressed as a fraction of 100. Additionally, it is denoted by the sign "%."

Here, we have VAT.

A flat charge called value-added tax (VAT) is imposed on a purchase. It resembles a sales tax in some ways, with the exception that with a sales tax, the consumer pays the entire amount due to the government at the moment of sale. With a VAT, several participants to a transaction each pay a piece of the tax amount.

Value on Rs. 3200 with 13% VAT

= 3200 + 30% of 3200

= 3200 + 960

= 4160 rupees

Now, the less value,

= 4160 - 3820

= 340 rupees.

Therefore, the less value is 340 rupees.

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Probability that both the person own the dog is equal to 0.0225.

The likelihood that an event will occur is measured by probability. It is difficult to provide a complete prediction for many events. Using it, we are only able to estimate the likelihood that an event will occur, or the chance that it will. Between 0 and 1, where 1 denotes a certain event and 0 denotes an impossibility, is the range of probabilities.

Let event A denotes that a person own dog,

P(A) = 15% =15/100 = 0.15

If we pick two people at Random then Probability that they both own dog

= P(A)*P(A)

= 0.15 * 0.15

= 0.0225

Required Probability = 0.0225

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The fraction of the pie left that each friend will receive is; 3/8 of the pie

Dividing two fractions is simply the same as multiplying the first fraction by the reciprocal of the second fraction.

The first step in trying to divide fractions is to find the reciprocal of the second fraction. The second step is to multiply the two numerators. Thereafter, multiply the two denominators.

For example, 3/8 divided by 3/4 would be;

3/8 divided by 3/4 = 3/8 * 4/3

Now, we are told that cedric has 3/4 of a pie left.

Now, he wants to share equally among two of his friends, it means that;

Quantity received by each friend = 3/4 ÷ 2 = 3/4 * 1/2 = 3/8

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Complete question is;

Cedric has 3/4 of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?