What is an equation of the line that passes through the point (-5, -3) and is
parallel to the line 3x + 5y = 15?

Answer:

Is not the answer but is how to do it. Sorry

Step-by-step explanation:

you got the value of a=2

use the formula

S=n/2 [2a+(n-1)d] then calculate d from here..

put it in t=a+(n-1)d

The requreid 8th term in the series is 366, which is an option (C).

Arithmetic progression is the series of numbers that have common differences between adjacent values

We can use the formula for the sum of an arithmetic series, which is:

S = n/2 * (a + l)

Since we are given that the first term is 2, we can write the formula for the sum of the first 8 terms as:

1472 = 8/2 * (2 + l)

1472 = 4 * (2 + l)

368 = 2 + l

l = 366

Therefore, the 8th term in the series is 366, which is an option (C).

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Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

Answer:

i think C im not really sure but i hope im correct maybe >.<

Answer:

Step-by-step explanation:

You need to find the slope of each line to determine if they are parallel. Beginning with AB, you do the formula for slope and get a value of -1/3. Next, you do CD and find it also has a slope of -1/3. Because both of these lines have equal slopes it makes them parallel because they will both be traveling at the same rate and will never get closer or further from each other.

*In order for lines to be perpendicular they need to have inverse slopes

Ex. a slope of 1/2 is perpendicular to a slope of -2

Answer:

its just a black screen

Step-by-step explanation:

Using Lagrange multipliers, the largest possible volume of a rectangular box can be found with a given diagonal length l.

Let's denote the dimensions of the rectangular box as length (L), width (W), and height (H). The volume (V) of the box is given by V = LWH. The constraint equation is the Pythagorean theorem: L² + W² + H² = l², where l is the given diagonal length.

To find the largest possible volume, we can set up the following optimization problem: maximize the volume function V = LWH subject to the constraint equation L² + W² + H² = l².

Using Lagrange multipliers, we introduce a new variable λ (lambda) and set up the Lagrangian function:

L = V + λ(L² + W² + H² - l²).

Next, we take partial derivatives of L with respect to L, W, H, and λ, and set them equal to zero to find critical points. Solving these equations simultaneously, we obtain the values of L, W, H, and λ.

By analyzing these critical points, we can determine whether they correspond to a maximum or minimum volume. The critical point that maximizes the volume will give us the largest possible volume of the rectangular box with a diagonal length l.

By utilizing Lagrange multipliers, we can optimize the volume function while satisfying the constraint equation, enabling us to determine the dimensions of the rectangular box that yield the maximum volume for a given diagonal length.

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The worth of the car in 2 years is £1767.2

The given parameters are:

Value, a = £20000

Depreciation rate, r = 6%

The value of the car in t years is represented as:

f(t) = a *(1 - r)^t

This gives

f(t) = 2000 * (1 - 6%)^t

In 2 years, t = 2

So, we have:

f(2) = 2000 * (1 - 6%)^2

Evaluate

f(2) = 1767.2

Hence, the worth of the car in 2 years is £1767.2

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Answer:

Given:

148

�

+

231

�

=

527...

�

�

1

148x+231y=527...eq1

and

231

�

+

148

�

=

610...

�

�

2

231x+148y=610...eq2

To find:

Find the value of x and y.

Solution:

Concept to be used:

Add both equations.

Subtract both equations.

Solve new equations to find x and y.

Answer:

5 feet

Step-by-step explanation:

Answer:

\(h_t=9ft\)

Step-by-step explanation:

From the question we are told that:

Height of child \(h_c=3ft\)

Height of child's shadow  \(h_c_s=2ft\)

Height of tree's shadow \(h_t_s=6ft\)

Since position of Sun remains constant  

Generally the equation for Height of tree h_t mathematically given by

 \(h_t=f_{ts}\frac{h_c}{h_c_s}\)

 \(h_t=6*\frac{3}{2}\)

 \(h_t=9ft\)

The false statement among the given options is statement iv: "The sample means calculated from the samples of size 10 give a biased estimate of the true population mean compared with those from the samples of size 100."

Statements i, ii, and iii are true:
i. Each of the means calculated from the samples of size 100 is an unbiased estimate of the population mean. This is true because unbiased estimates are obtained when the sample mean is equal to the population mean on average.
ii. The standard deviation of the means calculated from the samples of size 10 is likely to be larger than the standard deviation of the means calculated from the samples of size 100. This is true because larger sample sizes tend to provide more precise estimates, resulting in smaller variability or standard deviation.
iii. Each of the means calculated from the samples of size 10 is an unbiased estimate of the population mean. This is true because unbiasedness is not dependent on sample size but on the sampling method itself.

Statement iv is false because the sample means calculated from samples of size 10 are unbiased estimates of the population mean, just like those calculated from samples of size 100. Unbiasedness is not influenced by sample size, but rather by the sampling method. The only difference is that the standard deviation of the means calculated from the samples of size 10 is expected to be larger than the standard deviation of the means calculated from the samples of size 100, as mentioned in statement ii.

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Answer:

y < 20

Step-by-step explanation:

70 > 4y - 10

80 > 4y

20 > y

y < 20

Answer: 20.52

Step-by-step explanation:

Your welcome

Hey there! Your answer to this problem is 2160..

Explanantion:

Since every car Sara sells, she gets 9% of the commission, this means that at the last few step, we would have to give 9% of the total cost to Sara.

If 100% is 20,000, then 50% would be 10,000. But we have to find the cost of 20%. So what we would actually be doing is multiplying 20 with 0.01. 20x0.01 is 0.2 or 0.20.

Then you add the 4,000 to the 20,000 because it states, “the next day, they sold the car 20% more than they paid. This means that you’ll have to add it. 20,000 plus 4000 would be 24,000. So 24,000 would be the cost of the car they sold.

However they didn’t wanna know the cost of the car, they wanted to know how much Sara would get. So you would have to take 9% of the cost of the cost which would be 2,160.

Final result: $2,160

The scale factor used to create the travel version of the piece is 1: 0.16

0.6 is the scale factor used to reduce the dimensions of the original piece having sides measuring 3 inches each.

Scale factor is calculated by dividing the new reduced scale by original scale. Hence:

0.5/3 = 0.166

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Scale Factor = New Shape Dimension / Original Shape Dimension

Enlarging a small form into a huge one is known as scaling up. Upscaling always uses a scale factor greater than 1. A scale factor 2 means the figure is enlarged twice the original figure's size.

A large number gets scaled down in order to become a smaller one. Scaling down always results in a scale factor less than 1.

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Answer:

You would just divide by 23 on both sides...

23x = 6

x = 6/23 or x = 0.26

Step-by-step explanation:

Answer:

Horizontal translation 5 units: f(x-5)

Step-by-step explanation:

g(x) = f(x-5)

original (x , y) -> translated (x+5 , y)

Answer:

Step-by-step explanation:

This question is a bit unusual. Usually you translate across the x or y axis. This question does not.

Begin by drawing a vertical line parallel to the y axis.

The intercept point is (1/2,0) so the equation of the line is x = 1/2. x is 1/2 for every y value that is (1/2,y)

The rule is that ABC is translated horizontally across a line of x = 1/2

A' is 2 1/2 units to the right of x = 1/2

A is 2 1/2 units to the left of x = 1/2

The y axis is ignored.

Answer:

slope: 1/2

y-intercept: 2

Step-by-step explanation: If u go by y=mx+b, you know that m= your slope and b equals the y-intercept. so to put them together:

y=mx+b

     |      |

y=1/2x+2

Answer:

B: (x-6)^2=0

Step-by-step explanation:

To evaluate a function with a specific value in the domain you susbtitute in the equation of the function the independient variable (x) for the value in domain.

For x = -1 (a number n powered to a negative number (m) n^-m is equal to 1/n^m

For x=0 (any number powered to 0 is equal to 1)

For x = 1

For x = 2

Please refer to the attachment. Hope it helps!!

The half-life of nobelium-259, rounded to the nearest tenth, is approximately 21.0 minutes.

The decay of nobelium-259 can be described by the function A(t) = A₀ × (\(0.5^{t/h}\), where A(t) is the amount present at time t, A₀ is the initial amount, t is the time, and h is the half-life.

To find the half-life, we set A(t) = A₀/2 and solve for t.

A(t) = A₀ × \(0.5^{t/h}\) = A₀/2

\(0.5^{t/h}\) = 1/2

Taking the logarithm of both sides:

t/h = log(1/2)

t = h × log(1/2)

The expression t = h × log(1/2) represents the time it takes for the amount to reduce to half its initial value.

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The word phrase which correctly represents the algebraic expression as given in the task content is; the product of 3 and a number, t.

It follows from the task content that the algebraic expression which is to be expressed as a word phrase is; 3t.

Therefore, the word phrase representation of the algebraic expression is; the product of 3 and a number, t.

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Answer:

Step-by-step explanation:

boody boody

The Practice Operations with radical expressions is simplified using the basic of the Algebra:

Algebraic expressions incorporating radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both). The root might be an nth root, a square root, or a cube root. Radical expressions can be made simpler by taking them down to their most basic form and, if feasible, getting rid of all of the radicals.

Radical expressions are simplified by taking them down to their most basic form and, if feasible, altogether deleting the radical. An algebraic expression's numerator and denominator are multiplied by the appropriate radical expression if the denominator contains a radical expression.

Practice Operations with radical expressions are:

1) \(\sqrt{540}\) = \(\sqrt{36 * 15 }\)

= 6√15

2) \(\sqrt[3]{432}\) = \(\sqrt[3]{216*2}\)

= \(6\sqrt[3]{2}\)

3) \(\sqrt[3]{128}\) = \(\sqrt[3]{64*2}\)

= \(4\sqrt[3]{2}\)

4) \(-\sqrt[4]{405}\) = \(-\sqrt[4]{81*5}\)

= \(-3\sqrt[4]{5}\)

5) \(\sqrt[3]{-5000}\) = \(-\sqrt[3]{1000*5}\)

= \(-10\sqrt[3]{5}\)

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9514 1404 393

Answer:

  Bob

Step-by-step explanation:

The "steepness," or slope, of the mountain is the ratio of height to horizontal distance to the base:

  Joe's mountain slope = 1200/1500 = 0.8

  Bob's mountain slope = 900/1000 = 0.9

Bob's mountain has a greater slope than Joe's. Bob climbed the steeper mountain.

The range or the given data is calculated as 10.2 . Range is the difference between minimum value and maximum value.

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we can make use of the formula for range in statistics which is given as follows:[\large Range = Maximum\ Value - Minimum\ Value\]

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we need to arrange the data in either ascending or descending order, but since we only need to find the range, it is not necessary to arrange the data.

From the data given above, we can easily identify the minimum value and maximum value and then find the difference to get the range.

So, Minimum Value = 1.0

Maximum Value = 11.2

Range = Maximum Value - Minimum Value

                  = 11.2 - 1.0

                     = 10.2

Therefore, the range of the given data is 10.2.

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