what is the answer to 6x+9=2x-7

Aisha needs to deposit $8,665.48 today to reach her goal of $10,000 in 5 years.

When it comes to depositing an amount in an account to achieve a particular goal in the future, the concept of present value comes into play.

Present value is the value of a future sum of money or cash flow given a specified rate of return in today's terms. In other words, it is the value of the money we deposit today that will be worth in the future.

The formula to calculate present value is given by:

Present Value = Future Value / (1 + r)ⁿ

Where r is the annual interest rate, and n is the number of years.Using this formula, we can calculate the amount Aisha needs to deposit today to achieve her goal of $10,000 in 5 years.

Assuming an annual interest rate of 2%, we have:

Present Value = $10,000 / (1 + 0.02)⁵

Present Value = $8,665.48

Learn more about deposit at

https://brainly.com/question/29454677

#SPJ11

The velocity of a particle. P. moving along the x-axis is given by the differentiable function v, where (t) is measured is given by:

A differential function v gives the velocity of a particle P travelling down the x-axis, where v(t) is measured in metres per hour and t is measured in hours. v(t) is a declining function that is continuous. The table below shows several examples of v(t) values.

T [hours]                   0           2      4           7      10

v(t) [meters/hour] 20.3 14.4     10  7.3       5

a) We know that the particle's displacement is the area under the curve v(t). We can calculate the particle's displacement by integrating v(t). Because v(t) is a monotonous (constantly declining) differentiable function, it is also Riemann Integrable. There are now five non-uniform subdivisions:

Partition                     t0   t1 t2 t3 t4

T [hours]                      0           2 4 7 10

v(t) [meters/hour]   20.3 14.4 10 7.3 5

Using Right Riemann sum to approximate the displacement of particle between 0 hr and 10 hr is given by:

\(\sum_{n=1}^{4}v(t_n)\Delta t_n=v(t_1)(t_1-t_0)+v(t_2)(t_2-t_1)+v(t_3)(t_3-t_2)+v(t_4)(t_4-t_3) \\=(14.4)(2)+(10)(2)+(7.3)(3)+(5)(3) \\=28.8+20+21.9+15 \\=85.7\)

Therefore, the total displacement between 0 hr and 10 hr is is 85.7 meters.

The estimated position of particle P at time t = 10 hour is 115.7 (= 30 +85.7) meters.

b) Because the function v(t) is decreasing and we are estimating the integral using the Right Riemann sum, the approximation in part(a) underestimates the displacement.

c) A second particle Q also moves along the x-axis so that its velocity is given by :

\(V_Q(t)=35\sqrt{t}\cos(0.06t^2)\text{ meters per hour for }0\leq t\leq 10.\)

Hence, the time interval during which the velocity of a particle is atleast 60 meters per hour is [9.404, 10].

Now, the time periods during which a particle's velocity is at least 40 metres per hour are [1.321,4.006] and [9.218, 10]. The distance travelled by the particle Q when its velocity is at least 40 metres per hour is then calculated. :

\(\int_{1.321}^{4.006}v_Q(t)dt+\int_{9.218}^{10}v_Q(t)dt\\\\=\int_{1.321}^{4.006}35\sqrt{t}\cos(0.06t^2)dt+\int_{9.218}^{10}35\sqrt{t}\cos(0.06t^2)dt\)

d) At time t = 0, particle Q is is at position x = -90.

We know that P is at xp =  115.7 meters.

Now, The position of Q at t = 10 hr is xq:

\(x_q=-90+\int_{0}^{10}v_Q(t)dt=-90+\int_{0}^{10}35\sqrt{t}\cos(0.06t^2)dt\)

And the distance between Q and P is given by :

\(|x_p-x_q|=|115.7-(-90+\int_{0}^{10}35\sqrt{t}\cos(0.06t^2)dt)|\)

               \(\\=|205.7-\int_{0}^{10}35\sqrt{t}\cos(0.06t^2)dt|\)

Learn more about Velocity particle question:

https://brainly.com/question/14879436

#SPJ4

If the car goes to the top of spike's peak and back, the mileage of the car is 16 miles per gallon

The mileage of car in uphill = 12 miles per gallon

The mileage of car in downhill = 24  miles per gallon

The total distance traveled in up hill = 48 miles

The number of gallon of gas used = 48/12

= 4 gallon

The total distance traveled in down hill = 48 miles

The number of gallon of gas used = 48 / 24

= 2 gallon

Total distance traveled = 48 + 48

= 96 miles

Total number of gallons of gas = 4 + 2

= 6 gallon

The mileage = Total distance / The number of gallon

= 96 / 6

= 16 miles per gallon

Therefore, the mileage of the car is 16 miles per gallon

Learn more about mileage here

brainly.com/question/3124860

#SPJ4

The missing values in the table that contains the equivalent ratios between X and Y would be = 5

An equivalent ratio is defined as the constant that exists between two different numbers when compared.

The figures in the table is as follows:

X= 1 3 ? 7

y = 5 15 25 35

If X = 1 when y = 5, X= ? when y= 25

That is;

1 =5

?= 25

? = 25/5 = 5

Learn more about ratio here:

https://brainly.com/question/29145263

#SPJ1

Answer: -2.7 and -2.3 are your answers

on the number line: 2 dots behind -2.5 and 2 dots forward

The difference between the numbers -2.9 and -0.6 is -2.3 after using the number line.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

It is given that:

As we can see in the number line:

If we take the difference between these two numbers

From the number line:

= −2.9−(−0.6)

= -2.9 + 0.6

= -2.3

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

After using the arithmetic operation concept:

The difference between the numbers:

= −2.9−(−0.6)

= -2.9 + 0.6

= -2.3

Thus, the difference between the numbers -2.9 and -0.6 is -2.3 after using the number line.

Learn more about the number line here:

brainly.com/question/13189025

#SPJ2

Answer:

20 < L < 24

Step-by-step explanation:

We know that in any given triangle, the length of two sides is always greater than the length of the third side.

Since the sail is a triangle having length of one side as 22 feet and the length of another side as 2 feet, and let L be the length of the third side.

It follows from our triangle rule of sides above that

22 + 2 > L  (1)

22 + L > 2   (2)and

L + 2 > 22   (3)

It follows that from (1)

22 + 2 > L  

⇒  24 > L (4)

It follows that from (2)

22 + L > 2

⇒ L > 2 - 22

⇒ L > - 44  (5) and

It follows that from (3)

L + 2 > 22

⇒ L > 22 - 2

⇒ L > 20  (6)

Since from (5) and (6),

L > -44 and L > 20

and 20 > -44 ⇒ L > 20

⇒ 20 < L (7)

From (4) 24 > L ⇒ L < 24 (8)

Combining (7) and (8), we have

20 < L < 24

So, the possible range of values of the third side are 20 < L < 24

Answer:

Line A =   y = 8x – 6

Line B =  y = -4x + 8

Step-by-step explanation:

The proof for UX || VW is shown below.

According to the midpoint theorem, "The line segment in a triangle joining the midpoint of any two of the triangle's sides is said to be parallel to its third side and is also half the length of the third side."

Given:

As, TUX and TVW are similar.

So, the ratio of their corresponding sides are equal.

So, TU/ TV = UX/ VW = TX / TW = 1/2  {TU/ TV = 1/2}

By using mid point Theorem

UX = 1/2 VW

Then, UX || VW.

Learn more about Mid- point theorem here:

https://brainly.com/question/13677972

#SPJ1

Answer:

0.4 cm

Step-by-step explanation:

10 mm = 1 cm thus 4mm / 10  = 0.4 cm

Answer: A≈1385.44m²

Step-by-step explanation:

A=πr2=π·212≈1385.44236m²

Vertex Form of a quadratic equation

A quadratic equation has the vertex form:

Where (h,k) is the vertex of the parabola and a is the leading coefficient.

If a is positive, the parabola is concave up, if a is negative, the parabola is concave down.

We'll identify each graph with a number so we can relate them with their corresponding equation.

Graph 1. Has the vertex at (-5,7) and opens up. The equation of this parabola (for a=1) is:

Graph 2 has the vertex at (5,7) and opens up. The equation is:

Graph 3 has the vertex at (5,-7) and opens up. The equation is

Graph 4 has the vertex at (5,-7) and opens down. The equation is

Graph 5 has the vertex at (-5,-7) and opens up. The equation is

Finally, graph 6 has the same vertex as graph 5 and opens up also, but it grows much faster than that one. The difference is that the leading factor is greater than one. This corresponds to the equation

The image below shows the correspondence between the graphs and their equations labeled with numbers.

To determine the height of the building, we can use trigonometry. In this case, we can use the tangent function, which relates the angle of elevation to the height and shadow of the object.

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this scenario:

tan(angle of elevation) = height of building / shadow length

We are given the angle of elevation (43 degrees) and the length of the shadow (20 feet). Let's substitute these values into the equation:

tan(43 degrees) = height of building / 20 feet

To find the height of the building, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by 20 feet:

20 feet * tan(43 degrees) = height of building

Now we can calculate the height of the building using a calculator:

Height of building = 20 feet * tan(43 degrees) ≈ 20 feet * 0.9205 ≈ 18.41 feet

Therefore, the height of the building that casts a 20-foot shadow with an angle of elevation of 43 degrees is approximately 18.41 feet.

Learn more about probability here

brainly.com/question/13604758

#SPJ11

Answer:

8x² - 5y² + 5xy

Step-by-step explanation:

8x² + 7xy - 6y² + 4x² - 3xy + 2y² - 4x² + xy - y² = (8x² + 4x² -4x²) + (-6y² + 2y² - y²) + (7xy - 3xy + xy) = 8x² - 5y² + 5xy

The 63rd term is \(-\frac{247}{16}\) if it is an arithmetic sequence.

The 63rd term is \(2.385\times 10^{28}\) if it is an geometric sequence.

An arithmetic sequence has the characteristic that the difference between two consecutive elements is the same, that is to say:

\(a_{i+1}-a_{i} = r\) (1)

The expression that represents the elements of the arithmetic sequence is presented below:

\(a(n) = a_{1} + r\cdot (n-1)\) (2)

Where:

If we know that \(a_{1} = \frac{1}{16}\), \(a_{2} = -\frac{3}{16}\) and \(n = 63\), then the 63rd term of the arithmetic sequence:

\(r = -\frac{3}{16}-\frac{1}{16}\)

\(r = -\frac{1}{4}\)

\(a(63) = \frac{1}{16}-\frac{1}{4}\cdot (63-1)\)

\(a(63) = -\frac{247}{16}\)

The 63rd term is \(-\frac{247}{16}\) if it is an arithmetic sequence.

An geometric sequence has the characteristic that the ratio between two consecutive elements is the same, that is to say:

\(\frac{a_{i+1}}{a_{i}} = r\) (3)

The expression that represents the elements of the geometric sequence is presented below:

\(a(n) = a_{1}\cdot r^{n-1}\) (4)

Where:

If we know that \(a_{1} = \frac{1}{16}\), \(a_{2} = -\frac{3}{16}\) and \(n = 63\), then the 63rd term of the arithmetic sequence:

\(r = \frac{-\frac{3}{16} }{\frac{1}{16} }\)

\(r = -3\)

\(a (63) = \left(\frac{1}{16} \right)\cdot (-3)^{63-1}\)

\(a(63) = 2.385\times 10^{28}\)

The 63rd term is \(2.385\times 10^{28}\) if it is an geometric sequence.

We kindly invite to see this question on geometric sequence: https://brainly.com/question/11266123

Using the normal approximation to the binomial distribution, it is found that:

a) 0.454 = 45.4% probability of getting 715 or more peas with red flowers.

b) Since Z < 2, 715 peas with red flowers is not significantly high.

c) Since 715 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.

For each pea, there are only two possible outcomes. Either they have a red flower, or they do not. The probability of a pea having a red flower is independent of any other pea, which means that the binomial distribution is used to solve this question.

Probability of x successes on n trials, with p probability.

The z-score of a measure X in a normal distribution with mean and standard deviation is given by:

\(z=\frac{X-mean}{standard deviation}\)

If Z > 2, the result is considered significantly high.

In this problem:

943 peas, thus, n=943

3/4 probability of being red, thus . p=\(\frac{3}{4} =0.75\)

Applying the approximation:

mean = np= 943x0.75 = 707.25

standard deviation = \(\sqrt{np(1-p)} = \sqrt{707.25*0.25} = 13.297\)

a):

Using continuity correction, this probability is

P(X\(\geq\)715-0.5)=P(X\(\geq\)714.5), which is 1 subtracted by the p-value of Z when X = 714.5.

Then:

\(Z=\frac{X-mean}{standard deviation} \\\\Z=\frac{714.5-707.25}{13.297} \\\\Z=0.5452\)

now , 1- 0.5452=0.454

0.454= 45.4% probability of getting 715 or more peas with red flowers.

b):

Since Z < 2, 715 peas with red flowers is not significantly high.

c):

Since 715 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.

Learn more about binomial distribution, visit:

brainly.com/question/25212369

#SPJ1

Answer:

x=10

y=15

Step-by-step explanation:

Since we know y in terms of x, we can use substitution and say instead of-

5x-4y=-10

5x-4(2x-5)=-10

5x-8x+20=-10

-3x=-30

x=10

Substitute x into the equation-

y=2x-5

y=2(10)-5

y=20-5=15.

Answer:

Step-by-step explanation:

Remember :the orthocenter of  a triangle is the point of concurrency of the 3 altitudes.

\(\large \text{If an orthocenter lies inside of a triangle, then the triangle must be}\ :\\\\\large isosceles. \\\\\large obtuse. \\\\\large right. \\\\\large acute \checkmark\)

If an orthocenter lies inside of a triangle, then the triangle must be acute.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Orthocenter of a triangle is the intersection of any two of three altitudes of a triangle.

The third altitude usually pass through the point of the first two altitudes.

When the orthocenter lies inside a triangle, the angles formed by the intersection of the three altitudes is less than 90 degrees.

An acute triangle is a type of triangle whose angles are less than 90 degrees.

Hence, If an orthocenter lies inside of a triangle, then the triangle must be acute.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ7

The area of the region is (25/4)π + 50 square units.

The given equations are in polar coordinates. The first curve is defined by the equation r = 5 − 5 sin(θ) and the second curve is defined by the equation r = 5.

To find the area of the region that lies inside the first curve and outside the second curve, we need to integrate the area of small sectors between two consecutive values of θ, from the starting value of θ to the ending value of θ.

The starting value of θ is 0, and the ending value of θ is π.

The area of a small sector with an angle of dθ is approximately equal to (1/2) r² dθ. Therefore, the area of the region can be calculated as follows:

Therefore, the area of the region that lies inside the first curve and outside the second curve is (25/4) π + 50 square units.

Learn more about area of the region

brainly.com/question/28334840

#SPJ11

Therefore, the answer is -8. The simplified expression involving h is -8. The difference quotient is the formula used in calculus to compute the derivative of a function.

The given function is f(x) = -8x +9.The difference quotient h for the given function is calculated as follows: f(x+h)-f(x) / hf(x+h) = -8(x+h) + 9 = -8x - 8h + 9f(x) = -8x + 9

So, the numerator is given by: f (x+h) - f(x) = [-8 ( x+h) + 9] - [-8x + 9]= -8x - 8h + 9 + 8x - 9= -8h

On substituting the numerator and denominator values in the given equation we have:(-8h) / h= -8

Therefore, the answer is -8.

The simplified expression involving h is -8. The difference quotient is the formula used in calculus to compute the derivative of a function.

The quotient formula is used to calculate the average rate of change in a function, with h representing the change in the input variable x.

The difference quotient formula is also used to calculate the slope of a curve at a given point.

To know more about Expression  visit :

https://brainly.com/question/28172855

#SPJ11

a.) The instantaneous rate of change at x = -1 for the function f(x) = 2x² - 3x + 1 is -7.

b.) The average rate of change on the interval [-1, 2] for the function f(x) = 2x² - 3x + 1 is -4/3.

a)

Instantaneous rate of change of a function can be defined as the rate of change of a function at a particular point.

It is also called the derivative of a function.

The instantaneous rate of change at x = -1 is given by:

f'(-1) = (d/dx) f(x)|x=-1

Given the function f(x) = 2x² - 3x + 1,

Using the power rule of differentiation, we get

f'(x) = d/dx (2x² - 3x + 1) = 4x - 3 At x = -1,

we have f'(-1) = 4(-1) - 3 = -7

Therefore, the instantaneous rate of change at x = -1 is -7.

b)

The average rate of change of a function over a given interval [a, b] is the ratio of the change in y-values (Δy) to the change in x-values (Δx) over the interval. It is given by:

(f(b) - f(a))/(b - a)

For the function f(x) = 2x² - 3x + 1,

evaluate (f(2) - f(-1))/(2 - (-1)) = (8 - 12)/(3) = -4/3

Therefore, the average rate of change on the interval [-1, 2] is -4/3.

To know more about instantaneous rate of change visit:

https://brainly.com/question/30760748

#SPJ11

Answer:

Hours worked and money earned

Distance and time when speed is constant

Area and side length of a square

Total cost and the number of hats purchased

Step-by-step explanation:

The highest prize will be that of 50 years of duration, while it will generate $ 18,262,500,000 compared to $ 3,221,225,472 of the one-month duration.

To determine which prize is worth more enter a prize on March 31, if the amount is tripled each day, beginning with $ 3 on March 1; and a prize after 50 years, if $ 1 million is added each day, the following calculations must be performed:

Therefore, the highest prize will be that of 50 years of duration, while it will generate $ 18,262,500,000 compared to $ 3,221,225,472 of the one-month duration.

Learn more in https://brainly.com/question/1349797

Answer: what is the question

Step-by-step explanation:

Russell and Dantzel Nelson immediately started studying Mandarin Chinese.

This information is specific to Russell and Dantzel Nelson and their personal response to President Kimball's challenge. It is not mentioned in the question why they chose Mandarin Chinese specifically, but it can be assumed that they had their own reasons for selecting that language. It is worth noting that Mandarin Chinese is one of the most widely spoken languages in the world, and learning it would have been beneficial for missionary work in areas where Mandarin is spoken. Russell M. Nelson, who later became the President of The Church of Jesus Christ of Latter-day Saints, had significant international experience and worked extensively with various cultures and interest, further emphasizing the importance of language learning for missionary service.

Learn more about interest here:

https://brainly.com/question/30955042

#SPJ11

We're given:

To find the area of the garden alone, we can subtract the area of the garden from the combined area of the garden and walkway:

\(4.5(8x + 4)-4(5.5x + 1.5)\)

Open up the parentheses:

\(= 36x +18 -22x - 6\)

Combine like terms:

\(= 36x +18 -22x - 6\\= 14x +18 - 6\\= 14x +12\)

The area of the walkway around the garden is 14x + 12.

Answer:

answer A

Step-by-step explanation:

Option C is correct, the Coriolis Effect shows us that when moving from the equator towards the poles, the air is moving at the same speed.

Speed is the time rate at which an object is moving along a path,

The Coriolis Effect causes moving objects, including air, to be deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

As air moves from the equator towards the poles, it experiences a change in latitude, which causes it to be deflected.

This deflection results in the formation of high-pressure and low pressure systems that move weather patterns around the globe.

The speed of the air is affected by a number of factors, including temperature, pressure, and the Coriolis Effect.

However, the Coriolis Effect does not directly affect the speed of the air as it moves from the equator towards the poles.

Therefore, the Coriolis Effect shows us that when moving from the equator towards the poles, the air is moving at the same speed.

To learn more on Speed click:

https://brainly.com/question/28224010

#SPJ2

Using the normal distribution, it is found that:

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation are given, respectively, by:

\(\mu = 65, \sigma = 18\)

We find the percentage for each measure(the p-value of Z when X = measure), then subtract them.

X = 86.6:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{86.6 - 65}{18}\)

Z = 1.2

Z = 1.2 has a p-value of 0.8849 = 88.49%.

X = 54.2:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{54.2 - 65}{18}\)

Z = -0.6

Z = -0.6 has a p-value of 0.2743 = 27.43%.

88.49 - 27.43 = 61.06%.

More can be learned about the normal distribution at https://brainly.com/question/24537145
#SPJ1

Answer:

14

Step-by-step explanation:

Use rise over run, (y2 - y1) / (x2 - x1)

Plug in the points:

(y2 - y1) / (x2 - x1)

(8 + 20) / (5 - 3)

28 / 2

= 14

So, the slope is 14.