A scale drawing of Jimmy's living room is shown below:

If each 2 cm on the scale drawing equals 8 feet, what are the actual dimensions of the room?
Length = 8 feet, width = 6 feet
Length = 12 feet, width = 8 feet
Length = 18 feet, width = 16 feet
Length = 24 feet, width = 16 feet

Step-by-step explanation:

At t = 20 min, V = 45,000 L.

At t = 70 min, V = 0 L.

a) The rate is the slope:

m = ΔV/Δt

m = (0 L − 45,000 L) / (70 min − 20 min)

m = -900 L/min

b) Using the slope to find V when t = 0 min:

m = ΔV/Δt

-900 L/min = (V − 0 L) / (0 min − 70 min)

V = 63,000 L

c) Use slope-intercept form to find the equation.

V = -900t + 63,000

d) At t = 62 min:

V = -900(62) + 63,000

V = 7200

Answer:

a. -900 L/min

b. Vo = 63,000 Liters

c. V ( t ) = 63,000 - 900*t

d. 7,200 Liters

Step-by-step explanation:

Solution:-

We have a swimming pool which is drained at a constant linear rate. Certain readings were taken for the volume of water remaining in the pool ( V ) at different instances time ( t ) as follows.

                t = 20 mins ,   V = 45,000 Liters

                t = 70 mins , V = 0 Liters

To determine the rate ( m ) at which water drains from the pool. We can use the linear rate formulation as follows:

                             [tex]m = \frac{V_2 - V_1}{t_2 - t_1} \\\\m = \frac{0 - 45000}{70 - 20} \\\\m = \frac{-45,000}{50} = - 900 \frac{L}{min}[/tex]

We can form a linear relationship between the volume ( V ) remaining in the swimming pool at time ( t ), using slope-intercept form of linear equation as follows:

                              [tex]V = m*t + V_o[/tex]

Where,

                  m: the rate at which water drains

                  Vo: the initial volume in the pool at time t = 0.

We can use either of the data point given to determine the initial amount of volume ( Vo ) in the pool.

                           [tex]0 = -900*( 70 ) + V_o\\\\V_o = 63,000 L[/tex]

We can now completely express the relationship between the amount of volume ( V ) remaining in the pool at time ( t ) as follows:

                             [tex]V ( t ) = 63,000 - 900*t[/tex]

We can use the above relation to determine the amount of volume left after t = 62 minutes as follows:

                           [tex]V ( 62 ) = 63,000 - 900*(62 )\\\\V ( 62 ) = 63,000 - 55,800\\\\V ( 62 ) = 7,200 L[/tex]

Answer:

Line y = −x + 4 intersects the line y = 3x + 3.

Step-by-step explanation:

Please Help! Which description best describes the solution to the following system of equations?

y = −x + 4

y = 3x + 3

Line y = −x + 4 intersects the line y = 3x + 3.

This is the response because the solution to a system of two equations is represented by the intersection of the equations of the two lines/curves.

Lines y = −x + 4 and y = 3x + 3 intersect the x-axis.

Lines y = −x + 4 and y = 3x + 3 intersect the y-axis.

Line y = −x + 4 intersects the origin.

Answer:

9% loss

Step-by-step explanation:

We first can find the amount of money the saree was sold for by multiplying its buy cost, 1,750, by 1.04 (adding 4% to 1)

[tex]1750 \cdot 10.4 = 1820[/tex]

Now, 1820 is definitely less than 2000, so we need to find the percent difference between 2000 and 1820. We can use the formula:

[tex]\frac{higher-lower}{higher} \cdot 100[/tex]

So,

[tex]\frac{2000-1820}{2000} \cdot 100[/tex]

[tex]\frac{180}{2000} \cdot 100[/tex]

[tex]0.09 \cdot 100[/tex]

9

So, the loss percent of this dress is 9%.

Hope this helped!

Answer: B

Step-by-step explanation:

The domain of a function is every x-value, and the range is every y-value.

Hope it helps <3

Answer:

B

Domain: (-∞,∞)

Range: (-∞,5]

Step-by-step explanation:

The domain is (-∞,∞) because the graph as you can see, is continuously going outwards forever.

The range is (-∞,5] because the graph as you can see, is always going down forever and the top point is at 5. The 5 is in a bracket because it is a defined number while ∞ is undefined!

Hope this helped and good luck :)

Answer:

b=3a/8

a=8b/3

Step-by-step explanation:

b/a=k ( k is the constant proportional)

3/8=9/24=15/40

b/a=3/8

b=3a/8

a=8b/3

I hope this is right answer

Answer:

C. y = 0.5x + 5

Hope that helps.

Answer:

True

Step-by-step explanation:

trust me, i remember this question

Answer:

19

Step-by-step explanation:

Answer:

The correct ans is 3.

g(-2) = 2(-2) + 5

=-4 + 5 = 1

f(g(-2)) = 4 - (1)^2

= 4 - 1

=3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Given

[tex]\frac{30b}{6b}[/tex]

Cancel the b on the numerator/ denominator.

Also the 30 and 6 can both be cancelled by 6 , thus

[tex]\frac{30b}{6b}[/tex] = [tex]\frac{30}{6}[/tex] = 5

Answer:

[tex]\boxed{5}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{30b}{6b}[/tex]

[tex]\sf Simplify[/tex]

[tex]\displaystyle \frac{30}{6} \times \frac{b}{b}[/tex]

[tex]5 \times 1[/tex]

[tex]=5[/tex]

Answer:

D

Step-by-step explanation:

To be a function each value of x must correspond to only one, unique value of y.

In the given ordered pairs

Each x- value corresponds to exactly one y- value

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           Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

                    [tex]\boxed{x = 7}[/tex]

Move 1 to the left side of the equation by subtracting it from both sides.

[tex]\sqrt{2x -5 - 2 - 1 = 0 }[/tex]

Subtract 1 from -2.

[tex]\sqrt{2x -5 - 3 = 0 }[/tex]

Add 3 to both sides of the equation.

[tex]\sqrt{2x - 5 = 3}[/tex]

To remove the radical on the left side of the equation, square both sides of the equation.

[tex]\sqrt{2x - 5^3 = 3^2}[/tex]

Simplify each side of the equation.

Multiply the exponents in [tex](( 2x - 5) ^\frac{1}{2})^2[/tex] .

Apply the power rule and multiply exponents, [tex](a^m)^n = a^mn[/tex]

[tex](2x -5)^\frac{1}{2}.2 = 3^2[/tex]

Cancel the common factor of 2.

[tex](2x - 5)^1 = 3^2[/tex]

Simplify.

[tex]2x - 5 = 3^2[/tex]

Raise 3 to the power of 2.

[tex]2x - 5 = 9[/tex]

Solve for x

Move all terms not containing x to the right side of the equation.

Add 5  to both sides of the equation.

[tex]2x = 9 + 5[/tex]

Add 9 and 5.

[tex]2x = 14[/tex]

Divide each term by 2  and simplify.

Divide each term in 2x = 14 by 2.

[tex]\frac{2x}{2} = \frac{14}{2}[/tex]

Cancel the common factor of 2.

[tex]x = \frac{14}{2}[/tex]

Divide 14 by 2.

[tex]x = 7[/tex]

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●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

root of f(x) =  -0.7419124700395855 to about 16 figures

Step-by-step explanation:

given

f(x) = 2x^5-x^2+1 = 0

The polynomial is prime, so cannot solve by factoring.

Since it is a 5th degree polynomial, it has at least one real root.

Graphing helps locate where roots are, if more than one.

(refer to first graph)

So there is a real root between -1 and 0.

We will use numerical methods to find the root to a good degree of accuracy.  The technique applies to any univariable function which is differentiable and continuous near the roots.  This requirement is true for all polynomials.

However, we must know approximately where the root is, usually found by graphing.

The formula used is a recursive one, which gives a better approximation (x1) from the initial (x0) one , and can be repeated until the required accuracy is reached.

Here, we see that the slope of the function at the root is quite steep, so convergence will be rapid.

The formula is

x1 = x0 - f(x0) / f'(x0), where

x1 = new approximation

x0 = initial (or previous) approximation

f(x0) = value of function when x=x0

f'(x0) = value of derivative of function when x=x0

For the given function

f(x) = 2x^5-x^2+1 = 0

f'(x) = 10x^4-2x = 2x(5x^3-1)

From the graph of f(x), we can take an initial approximation as

x0 = -1

x1 = -1 - (-2)/12 = -5/6

Repeat using x0=-5/6

x1 = -5/6 - ( 2(-5/6)^5 - (-5/6)^2 + 1 ) / (2(-5/6(5(-5/6)^3-1))

= 0.7565596512088784

Repeat again, multiple times

x1 = -0.7423377914518363

x1 = -0.7419128371988212

x1 = -0.7419124700398593

x1 = -0.7419124700395855

x1 = -0.7419124700395855

So we see that the root of f(x) = x1 = -0.7419124700395855 to about 16 figures

Note that the accuracy of the iterations approximately doubles every time.

Answer:

3x + 2y = 12.

Step-by-step explanation:

Two conspicuous points on the graph are at (0, 6), and (4, 0).

That means the slope of the line is (6 - 0) / (0 - 4) = 6 / -4 = -3 / 2.

The intercept of the line is at (0, 6).

This means that the equation of the line is y = -3/2x + 6.

y = -3/2x + 6

Add 3/2x to both sides

3/2x + y = 6

Multiply all terms by 2

3x + 2y = 12

Hope this helps!

cos (x - π/3) = cos (π/2)

Then we need x - π/3 = π/2

Solving the equation:

x - π/3 = π/2

x = π/2 + π/3

x = 5π/6

Answer:

30.6

Step-by-step explanation:

The following data were obtained from the question:

Angle θ = 23°

Opposite = 13

Adjacent = y

The value of y can be obtained by using the following trig ratio:

Tan θ = Opposite /Adjacent

Tan 23° = 13/y

Cross multiply

y × Tan 23° = 13

Divide both side by Tan 23°

y = 13/Tan 23°

y = 30.6

Therefore, the value of y in the diagram above is 30.6

Answer:

  [tex]\dfrac{3(6)-1}{2(6)+1}[/tex]

Step-by-step explanation:

For ...

The expression (r/s)(6) is ...

  [tex]\left(\dfrac{r}{s}\right)(6) = \left.\dfrac{3x-1}{2x+1}\right|_{x=6}=\boxed{\dfrac{3(6)-1}{2(6)+1}}[/tex]

Answer:

A

Step-by-step explanation:

Answer:

2x²+5x+2=(2x+1)(x+2)

Answer:

See details below

Step-by-step explanation:

in ax^2+bx+c = 2x^2+5x+2,

a=2,b=5,c=2.

1. a*c = 2*2 = 4

2. factor 4 to get 1,2,4,  Factors that add to b=5 are 1 & 4.

3. (2x^2+x) + (4x+2)

4. x(2x+1) + 2(2x+1)

5. (2x+1)

6. (2x+1) ( x+2)

Some of the details may not be the same as what is expected as we do not know the format expected.

Answer:

b

Step-by-step explanation:

trust me

Answer:

A

Step-by-step explanation:

Answer:

The linear system shown on the graph is consistent and independent

Step-by-step explanation:

The linear system shown on the graph is consistent because it has at least one solution which satisfy both linear graphs. The solution is at the point of interception of the two line graphs.

The linear system shown on the graph is independent because the two line graphs are distinct and not parallel or dependent on one another.

Therefore, The linear system shown on the graph is consistent and independent

Max : 10 steps : Dad: 3 steps.

So it you multiply those each by ten, you get

100 steps : 30 steps.

30 Dad steps is 100 Max steps, so you get the answer, which is 100!

The steps taken by Max is 100.

A mathematical function that performs a calculation on two operands is known as an arithmetic operator. Common arithmetic makes use of them, and the majority of computer languages include a set of such operators that can be used in equations to carry out a variety of sequential calculations.

Given

steps taken by Max = 10

Steps taken by his Dad = 3

both steps of Dad and steps of Max should be in ratio

3/10 …(1)

steps taken by his Dad = 30

let steps taken by Max = x

ratio = 30/x …..(2)

equation 1 equals equation 2

3/10 = 30/x  

x = (30 x 10)/3

x = 100

Hence Max must take 100 steps.

Learn more about arithmetic operators;

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Answer:

A. The total number of three-card hands (permutations) that can be made with two aces is 576

B. The actual number of two-ace hands (combinations) you can get from a deck of 52 cards is 288

C. The probability of drawing a three-card hand that includes two aces from a deck of 52 cards is 0.0130

Step-by-step explanation:

A. In order to calculate the total number of three-card hands (permutations) that can be made with two aces we would have to make the following calculation:

total number of three-card hands (permutations) that can be made with two aces=4*3*52

total number of three-card hands (permutations) that can be made with two aces=576.

B. In order to calculate the actual number of two-ace hands (combinations) you can get from a deck of 52 cards we would have to make the following calculation:

actual number of two-ace hands (combinations) you can get from a deck of 52 cards=4C2*48

4C2=4!/2!2!

C2=6

Therefore, actual number of two-ace hands (combinations) you can get from a deck of 52 cards=6*48=288

C. In order to calculate the probability of drawing a three-card hand that includes two aces from a deck of 52 cards we would have to make the following calculation:

probability of drawing a three-card hand that includes two aces from a deck of 52 cards=actual number of two-ace hands (combinations) you can get from a deck of 52 cards/52C3

probability of drawing a three-card hand that includes two aces from a deck of 52 cards=288/22,100

probability of drawing a three-card hand that includes two aces from a deck of 52 cards=0.0130

Answer:

27.8%

Step-by-step explanation:

P(male | Spanish) = P(male and Spanish) / P(Spanish)

P(male | Spanish) = 0.05 / 0.18

P(male | Spanish) = 0.278

The probability of the student being a male is 27.8%

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

Given that in a certain group of students, the probability of a randomly-chosen student being male is 40%, the probability of the student studying Spanish is 18%, and the probability of the student being a male who studies Spanish is 5%.

The probability of the student being a male will be calculated as below:-

P(male | Spanish) = P(male and Spanish) / P(Spanish)

P(male | Spanish) = 0.05 / 0.18

P(male | Spanish) = 0.278

Therefore, the probability of the student being a male is 27.8%

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Answer:

mM = 113 and mN = 61

Step-by-step explanation:

In a Cyclic quadrilateral, the rule states that:

The sum opposite interior angles is equal to 180°

In the above diagram, we have cyclic quadrilateral KLMN

According to the rule stated above:

Angle K is Opposite to Angle M

So, Angle K + Angle M = 180°

Angle K = 67°

67° + Angle M = 180°

Angle M = 180° - 67°

Angle M = 113°

Angle L is Opposite to Angle N

so Angle L + Angle N = 180°

Angle L is given as = 119°

119° + Angle N = 180°

Angle N = 180° - 119°

Angle N = 61°

Therefore, Angle M = 113° and Angle N = 61°

Answer:

55°

Step-by-step explanation:

The following data were obtained from the diagram given above:

Adjacent = 4

Hypothenus = 7

Angle A =?

The value of angle A can be obtained as follow:

Cos A = Adjacent / Hypothenus

Cos A = 4/7

Take the inverse of Cos.

A = Cos¯¹(4/7)

A = 55.1° ≈ 55°

Therefore, the value of angle A is approximately 55°.

==================================================

Work Shown:

Let x = 0.363636...

The "36" pattern goes on forever as indicated by the three dots.

Multiply both sides by 100 to get 100x = 36.363636...

Effectively, multiplying by 100 moves the decimal point over 2 spots to the right. The "36" goes on forever here too. The key is to match up the infinite sequences of "36"s and cancel them out through subtraction

36.363636... - 0.363636... = 36

while

100x - x = 99x

So after subtracting the equations, we end up with 99x = 36

From here we solve for x by dividing both sides by 99 and reducing the fraction

99x = 36

x = 36/99

x = (9*4)/(9*11)

x = 4/11

As a check, use your calculator to find that

4/11 = 0.36363636...

so the answer is confirmed

Note: your calculator may display something like 0.3636363636364, that 4 should not be there. It's a result of rounding (due to the next digit being a 6). Keep in mind that rounding error is often a possibility when it comes to approximate calculations. The calculator only has so much memory and display space.

Answer:

If I'm not mistaken your graph is supposed to be like this

Step-by-step explanation:

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer: C

Step-by-step explanation:

[tex]2x+4y<16\\=4y<-2x+16\\=y<-\frac{1}{2} x+4[/tex]

Since we are not dividing by a negative at any point during the simplification, the inequality sign won't change.

"<" means that the line will be dashed and shaded below.

Hope this helps!

The description of the inequality is (c) dashed line, shaded below

The inequality is given as:

2x + 4y < 16

The inequality is represented as less than (<)

When the less than sign is used in an inequality, the graph of the inequality would be a dashed line shaded below

Hence, the true statement is (c) dashed line, shaded below

Read more about inequalities at:

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Answer:

For the second figure

X=10

Y=30

Step-by-step explanation:

3x=(5x-20).... Alternative interior angles

3x=5x-20

20=5x-3x

20=2x

x=10

2y+4y= 180

6y=180

Y=30

Hey there! :)

Answer:

x = -5.

Step-by-step explanation:

Solving for x from the equation:

[tex]\frac{2}{3}x - \frac{1}{2} = \frac{1}{3} +\frac{5}{6}x[/tex]

Begin by creating a common denominator for the terms involving x as well as the constants:

[tex]\frac{4}{6}x - \frac{3}{6} = \frac{2}{6} +\frac{5}{6}x[/tex]

Now that each term has a common denominator, we can begin solving for x by isolating the variable:

Subtract 5/6x from both sides:

[tex]\frac{4}{6}x-\frac{5}{6}x - \frac{3}{6} = \frac{2}{6}[/tex]

[tex]-\frac{1}{6}x - \frac{3}{6} = \frac{2}{6}[/tex]

Add 3/6 to both sides:

[tex]-\frac{1}{6}x = \frac{5}{6}[/tex]

Divide -1/6 from both sides. (Multiply by the reciprocal, or -6)

[tex]-\frac{1}{6}x(-6) = \frac{5}{6}(-6)[/tex]

x = -5.