Jazz is designing a rectangular workout space in their home. The perimeter of the room is 42 ft, and the width is 6 ft less than twice the length. Set up a system and solve to find the width of the room, in feet

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Answer:

D should be the answer.

The equation for the transformed logarithm that passes through the points (3,0) and (0,2) can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants to be determined.

To find the equation for the transformed logarithm, we need to use the given points (3,0) and (0,2) to determine the values of a, b, h, and k. Let's start with the point (3,0). Plugging the x-coordinate (3) into the equation, we have:

0 = -b * log(base a)(3 - h) + k

Next, we'll use the point (0,2) to obtain another equation. Plugging the x-coordinate (0) into the equation, we get:

2 = -b * log(base a)(0 - h) + k

Simplifying these equations, we have a system of equations to solve for a, b, h, and k. However, since the equation involves a logarithm, we need more information to determine the specific values of a, b, h, and k.The transformed logarithm function includes transformations such as vertical stretches/compressions (b), horizontal shifts (h), and vertical shifts (k). Without more specific information about these transformations or the base of the logarithm, it is not possible to determine the equation uniquely.

In general, the equation for a transformed logarithm can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants determined by the specific transformations applied to the logarithm function. It's important to have additional information or instructions to determine the values of a, b, h, and k and provide an equation that accurately represents the given transformed logarithm.

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Answer:

5, 6, 7, 8, 9, 10, 11 and 12 are the natural numbers between 5 and 12 including them, therefore Jane wrote 8 numbers. natural numbers start at positive 1 and go up by whole numbers infinitely, hope this helps

Answer:

it's the top one

Step-by-step explanation:

Assuming that ΔABC has equal sides AB and AC, we can say that AD is parallel to BC hence∠A=∠B.

What is Congruency?

ongruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

from △ABD and △ACD,

AB=AC ,AD is common

∠ADB=∠ADC, since both are right angles.

by SSA congruence

△ABD≅△ACD

therefore base angles are equal.

use sine rule,

a/sinA = b/sinB = c/sinC

by definition of isosceles triangle, any two sides are equal

w.l.o.g. let, a=b

asinA=asinB=csinC

asinA=asinB

aa=1=sinAsinB

⟹sinA=sinB

and ∠A and ∠B are less than 180.

therefore ∠A=∠B

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To determine the minimum speed of a particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k, we need to find the magnitude of the velocity vector, which is the derivative of the position vector with respect to time.

v(t) = r'(t) = 2ti + 6j + (2t - 24)k

The speed of the particle at any given time t is the magnitude of the velocity vector, which is:

|v(t)| = √(4t^2 + 36 + (2t - 24)^2) = √(4t^2 + 4t^2 - 96t + 576) = √(8t^2 - 96t + 576)

To find the minimum speed, we need to find the minimum value of |v(t)|. We can do this by finding the vertex of the parabolic function 8t^2 - 96t + 576, which corresponds to the minimum value of the function.

The vertex of a parabola of the form ax^2 + bx + c is at x = -b/2a. In this case, a = 8, b = -96, and c = 576, so the vertex is at t = -b/2a = 96/16 = 6.

So the minimum speed of the particle is:

|min speed| = |v(6)| = √(8(6)^2 - 96(6) + 576) = √(288) = 12√2

Therefore, the minimum speed of the particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k is approximately 16.97 units/sec (rounded to two decimal places). Option 4, min speed = 17 units/sec, is the closest answer.

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Answer:

Step-by-step explanation:

c

The distance KJ needs to be equal to the distance LM and KL need to be parallel to JM

distances

then we need to calculate the slope of LK and JM if they are equal we have parallel sides

for LK

for JM

This figure is a trapezoid because it has exactly one pair of parallel sides that can prove because the slopes of LK and JM are congruent, but the distances KJ and LM are not equal therefore it is not an isosceles trapezoid

Answer:

second one

Step-by-step explanation:

range is the y values

The value of an investment of $10,000 for 11 years at an annual interest rate of 4.55% compounded continuously is approximately $15,177.96.

When an investment is compounded continuously, we use the formula for continuous compound interest, which is given by the equation A = P*e^(rt), where A is the final amount, P is the principal amount (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate (expressed as a decimal), and t is the time in years.

In this case, the principal amount P is $10,000, the annual interest rate r is 4.55% (or 0.0455 as a decimal), and the time period t is 11 years. Plugging these values into the formula, we get A = $10,000e^(0.045511) ≈ $15,177.96. Therefore, the value of the investment after 11 years is approximately $15,177.96.

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Answer:

17

Step-by-step explanation:

Answer:

(- 2.6, - 5.8 )

Step-by-step explanation:

y - 3x = 2 ( add 3x to both sides )

y = 3x + 2 → (1)

x - 2y = 9 → (2)

substitute y = 3x + 2 into (2)

x - 2(3x + 2) = 9

x - 6x - 4 = 9

- 5x - 4 = 9 ( add 4 to both sides )

- 5x = 13 ( divide both sides by - 5 )

x = - 2.6

substitute x = - 2.6 into (1)

y = 3(- 2.6) + 2 = - 7.8 + 2 = - 5.8

solution is (- 2.6, - 5.8 )

Step-by-step explanation:

y-3x=2... (1)

x-2y=9...(2)

1)Use the elimination method to get rid of one of the variables

(-3x+y=2) ×2

x-2y=9

________

-6x+2y=4

x-2y=9

________

-5x =13

2)find value of X

-5x=13

x=-13/5

x=-2.6

3)sub x into (1) or (2) to find y

y-3x=2

y=2+3x

y=2+3(-2.6)

y=2-7.8

y=-5.8

So answer is :

X= - 2.6

Y= - 5.8

Base area of cuboid is 81 m².

According to the statement

we have to find the base area of the cuboid.

So, For this purpose, we know that the

A cuboid is defined as a three-dimensional shape, that has six rectangular faces, eight vertices and twelve edges.

From the given information:

Let the length, breadth and height of the cuboid be l, b and h respectively.

We have given that,

Breadth = ¼ × Length⇒ b = ¼ × l - - ( 1 )

Also,Height = ⅔ × Length⇒ h = ⅔ × l - - ( 2 )

We know that,Volume of cuboid = l × b × h

972 = l × ¼ × l × ⅔ × l - - [ From given]

⇒ ( 972 × 4 × 3 ) ÷ ( 1 × 2 ) = l × l × l

⇒ 972× 2 × 3 = l³

⇒ 486× 2 × 2 × 3 = l³l³

= 18 m.

Then

Now,Breadth of cuboid = ¼ × Length

⇒ b = ¼ × 18

⇒ b = 18÷ 4

⇒ b =  4.5 m.

Now,

Height of cuboid = ⅔ × Length

⇒ h = ⅔ × 18

⇒ h = ( 2 × 18 ) ÷ 3

⇒ h = 36 ÷ 3⇒ h = 12 m

.Now, we have,

Length ( l ) = 18

Breadth ( b ) = 4.5

Height ( h ) = 12

Now, we know that,

Total surface area of cuboid = 2 height(length + breadth)

And

Base area of cuboid = length × breadth

Base area of cuboid = 18× 4.5

Base area of cuboid = 81

So, Base area of cuboid is 81 m².

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The mean number of bedrooms per house is 2.83

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

The table of values

The mean number in the housing estate is calculated as

Mean = Sum/Count

Using the above as a guide, we have the following:

Mean = (1.9 + 3.1 + 3.5)/3

Evaluate

Mean = 2.83

Hence, the mean is 2.83

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There is a 30.85% chance that someone will have to wait longer than 6 minutes.

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

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.

z = (raw score - mean) / standard deviation

So,

We can write,

Mean of 6 minutes and variance = 1 minutes, hence:

Standard deviation = √variance = √1 = 1 minutes

For > 6 minutes:

z = (6 - 5)/2 = 1/2=0.5

P(z > 0.5) = 1 - P(z < 0.5)

P(z > 0.5) = 1 - 0.6915

P(z > 0.5) = 0.3085

Therefore,

There is a 30.85% chance that someone will have to wait longer than 6 minutes.

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Answer:

legend

Step-by-step explanation:

The required number of factors are of given function  x = 0, x = -5, x = -5.

A factor is a number that separates another number, leaving no leftover portion. All in all, on the off chance that duplicating two entire numbers gives us an item, the numbers we are increasing are elements of the item since they are distinguishable by the item.

We have,

f(x)=x^3+10x^2+25x

x(x^2 + 10x + 25)

x(x+ 5)^2

Thus, factors are x = 0, x = -5, x = -5

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Answer:

in simplest form it is like 3:1;3...

Answer:

I have a parrot

I have an African grey parrot, his name is Yaco (pronounce the "a" in his name the same way you'd pronounce the "a" in taco lol). He's 23 years old and the species can normally live in the range of 50-85 years old! Yes! He does do things on his own, eat, drink, play, and talk. One question you asked is "Does he ever steal food?" No, but he's worse than the dog when it comes to begging for human foods and snacks, he can have quite a vary of human foods such as some fruits, nuts, and crackers and such. Also, he has about a 300 word vocabulary and with a wide range of different sounds and noises. And with him being a parrot, he's picked up all these words, phrases, and sounds from people and movies and pets that are always often around him and in our home. He has been around 7 years longer than me. He's a very neet and VERY smart bird. In your free time go onto you.tube and search up 'Einstein the talking african grey parrot' it'll give you an idea of their intelligence.

Step-by-step explanation:

I hope this helps!! :)

and here's some pics from g.oogle of what an adult african grey looks like

The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

Answer:

It will take 48 hours for the entire icicle to melt.

Step-by-step explanation:

12 divided by 1/4 = 48

The linear equation to model the situation is f(x) = -1/4x + 12

Write a linear equation in slope-intercept form to model the situation. An icicle is 12 inches long and melts at a rate of 1/4 inch per hour.

The given parameters are:

The above means that:

A linear equation is represented as:

f(x) = mx + c

Where f(x) represents the function and x represents the number of hours.

So, we have:

f(x) = -1/4x + 12

Hence, the linear equation to model the scenario is f(x) = -1/4x + 12

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 :D   2 btw

Step-by-step explanation:

Answer:

0.0005

Step-by-step explanation:

this is a binomial experiment -- they are either cured or not, and the outcome is random

probability = n choose r * p^r * q^(n-r)

here, n = number of trials, r = number of successes desired, p = probability event occurs, and q = probability event doesn't occur

probability = n choose r * p^r * q^(n-r) = 6 choose 3 * 0.97^3 * 0.03^(6-3)

= 0.00049284342 rounding to 0.0005

To find the total divide the amount known by the percentage.

Total = 75/0.25 = 300

She has 300

\(\huge \sf༆ Answer ༄\)

According to given figure ~

Area of whole is equal to :

And,

Area of Triangle :

Area of Rectangle :

Therefore, the Area of whole figure is ~

So, the Correct choice is ~ A