rianna went on a trip to the art museum and sketched a scale drawing of a rectangular wall mural. She used a scale factor of 0.2. The sketch was 12 inches wide and 18 inches long. What was the length of the mural?
3.6 inches
18.2 inches
60 inches
90 inches

The distance between point T (-5, 1) and point I (-1, 1) is 4 units.

To find the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is:

Distance = √((x2 - x1)² + (y2 - y1)²)

Let's apply this formula to find the distance between point T (-5, 1) and point I (-1, 1):

x1 = -5, y1 = 1 (coordinates of point T)

x2 = -1, y2 = 1 (coordinates of point I)

Plugging these values into the formula, we have:

Distance = √((-1 - (-5))² + (1 - 1)²)

        = √(4² + 0²)

        = √(16 + 0)

        = √16

        = 4

Therefore, the distance between point T (-5, 1) and point I (-1, 1) is 4 units.

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Step-by-step explanation:

\( \frac{ \tan( \alpha ) }{1 + \sec( \alpha ) } = - \cot( \alpha ) + \csc( \alpha ) \)

Multiply by 1-sec(a)

\( \frac{ \tan( \alpha ) (1 - \sec( \alpha ) }{(1 + \sec( \alpha ) )(1 - \sec( \alpha ) )} \)

\( \frac{ \tan( \alpha ) - \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } \)

\( \frac{ \tan( \alpha ) }{1 - \sec {}^{2} ( \\ \alpha ) } - \frac{ \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } \)

\( \frac{ \tan( \alpha ) }{ - \tan {}^{2} ( \alpha ) } + \frac{ \tan( \alpha ) \sec( \alpha ) }{ \tan {}^{2} ( \alpha ) } \)

\( - \frac{1}{ \tan( \alpha ) } + \frac{ \sec( \alpha ) }{ \tan( \alpha ) } \)

\( - \cot( \alpha ) + \frac{ \frac{1}{ \cos( \alpha ) } }{ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } } \)

\( - \cot( \alpha ) + \frac{1}{ \sin( \alpha ) } \)

\( - \cot( \alpha ) + \csc( \alpha ) \)

Answer:

0.5,4,3/2,15,V16

Step-by-step explanation:

Be cause if you want ur estimate u have to but the numbers in order so thst how u get ur anwser got to put the numbers small to large.

HOPE IT HELPS GIVE BRAINLEAST :)

Answer:

The passenger train is traveling at 45 mph, and the freight train is traveling at 27 mph.

Step-by-step explanation:

Let's assume the speed of the passenger train is represented by x mph.

According to the given information, the freight train leaves the depot 2 hours before the passenger train. Therefore, when the passenger train starts, the freight train has already been traveling for 2 hours.

Let's represent the speed of the freight train as (x - 18) mph, which is 18 mph slower than the passenger train.

Now, we know that the passenger train overtakes the freight train in 3 hours. This means that the passenger train traveled for 3 hours, while the freight train traveled for 3 + 2 = 5 hours.

Since speed = distance/time, we can set up the following equation based on the distances covered by each train:

Distance covered by passenger train = Distance covered by freight train

Using the formula, distance = speed × time, we get:

x × 3 = (x - 18) × 5

Simplifying the equation:

3x = 5x - 90

90 = 5x - 3x

90 = 2x

Dividing both sides by 2:

45 = x

So, the speed of the passenger train is 45 mph.

The speed of the freight train is 45 - 18 = 27 mph.

Answer:

3.2

Step-by-step explanation:

Answer:

3.2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Blank 1 = " x "

Blank 2 = " 3 "

Quadrilateral JKLM has sides with equal lengths (√85), and the slopes of opposite sides are equal. However, it is not a special type of quadrilateral like a rectangle or a square.

To describe quadrilateral JKLM, let's first plot the given points J(9, 7), K(2, 1), L(0, -8), and M(7, -2) on a coordinate plane:

J(9, 7) K(2, 1)

L(0, -8)   M(7, -2)

To find the slopes and lengths of each side of the quadrilateral, we can use the distance formula and the slope formula.

Slope of JK:

Slope (m) = (change in y) / (change in x)

m(JK) = (7 - 1) / (9 - 2) = 6/7

Length of JK:

Length (d) = √[(x2 - x1)^2 + (y2 - y1)^2]

d(JK) = √[(9 - 2)^2 + (7 - 1)^2] = √(49 + 36) = √85

Slope of KL:

m(KL) = (-8 - 1) / (0 - 2) = -9/2

Length of KL:

d(KL) = √[(0 - 2)^2 + (-8 - 1)^2] = √(4 + 81) = √85

Slope of LM:

m(LM) = (-2 - (-8)) / (7 - 0) = 6/7 (same as slope of JK)

Length of LM:

d(LM) = √[(7 - 0)^2 + (-2 - (-8))^2] = √(49 + 36) = √85

Slope of MJ:

m(MJ) = (7 - (-2)) / (9 - 7) = 9

Length of MJ:

d(MJ) = √[(7 - 9)^2 + (-2 - (-8))^2] = √(4 + 36) = √40

Based on the calculations, we can describe quadrilateral JKLM as follows:

The slope of JK and LM is 6/7.

The slope of KL is -9/2.

The slope of MJ is 9.

The length of each side (JK, KL, LM, MJ) is √85.

The quadrilateral is not a rectangle or a square since the slopes of opposite sides (JK and LM) are not perpendicular.

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Answer:

240

Step-by-step explanation:

According to law of exponential growth,

\(y=y_0e^{kt}\)

Here, \(y_0\) denotes the initial amount and k is the rate constant of the equation.

Now, the initial population is 240 bacteria.

Put \(y_0=240\)

So,

\(y=240e^{kt}\)

The population after 12 hours is double the population after 1 hour.

\(y(12)=2y(1)\)

\(240e^{12k}=240e^{k} \\e^{12k}=e^{k} \\e^{12k-k}=1\\e^{11k}=1\\11k=log 1=0\\k=0\)

(Formulae used: \(\frac{e^x}{e^y}=e^{x-y}\,,\,log 1=0\))

So,

\(y=240e^{0}=240\\y=240\)

Therefore,

Number of bacteria after 3 hours = 240

\(\\ \sf\longmapsto -3(2+4p)=2(2p-1)\)

\(\\ \sf\longmapsto -6-12p=4p-2\)

\(\\ \sf\longmapsto -12p-4p=-2+6\)

\(\\ \sf\longmapsto -16p=4\)

\(\\ \sf\longmapsto p=\dfrac{-4}{16}\)

\(\\ \sf\longmapsto p=\dfrac{-1}{4}\)

Use distributive law

Now

LHS

RHS

Equat

Kinzang grew 0.96 meters.

We have,

To find how much Kinzang grew, we need to subtract his height at birth from his current height:

Height Kinzang grew = Current height - Height at birth

Height Kinzang grew = 1.49 m - 0.53 m = 0.96 m

Therefore,

Kinzang grew 0.96 meters.

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If  Its return on sales is 5 percent. Sharpe’s return on shareholders' equity is 8.26%.

First step is to find the fixed asset

Fixed asset = $1,870,000 + $667,000

Fixed asset = $2,537,000

Second step is to find the sales

Sales = Total assets × Fixed asset turnover

Sales =  $2,537,000 × 1

Sales = $2,537,000

Third step is to find the stockholder equity

Stockholder equity =  $1,870,000 - $335,000

Stockholder equity = $1,535,000

Fourth step is to find the net income

Net income =  $2,537,000 × 5%

Net income = $126,850

Now let find the return on shareholders' equity

Return on shareholders' equity = Net income / Shareholders' equity

Return on shareholders' equity =  $126,850 /$1,535,000

Return on shareholders' equity = 8.26%

Therefore 8.26% is the return on shareholders' equity.

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Answer: a=101 b=79 c=83 d=97

The calculated price per video game for store A is $1.79 per game

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

The price per video game for store A is calculated as

Price per video game = Total price/Number of games

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

Price per video game = 8.95/5

Evaluate the quotient

So, we have

Price per video game = 1.79

Hence, the price per video game for store A is $1.79 per game

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In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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The value of x in the secant intersection is 4.

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

Therefore, let's find the value of x using the secant intersection theorem as follows;

4(4+x + 2) = 5(5 + x - 1)

4(6 + x) = 5(4 + x)

24 + 4x = 20 + 5x

24 - 20 = 5x - 4x

x = 4

Therefore,

x = 4

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Answer:

M= -7/2

Step-by-step explanation:

You have to isolate the variable by dividing each side by factors that do not contain the variable. Hope this helps.

Answer:

m=-2, m=7

Step-by-step explanation:

m^2-5m-14= 0

m^2-7m+2m- 14=0

m(m-7)+2(m-7)=0

(m+2)(m-7)=0

m= -2 or m= 7

D 231 = 46w can be used to solve for w, the number of white eggs used last week.

Answer: B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Let's look at A.

A simplified = 7x - 6

Let's look at B

B simplified = 2 + 7x

Let's look at C

C simplified = -6 + 7x OR 7x - 6

Let's look at D, lastly.

D simplified = 7x - 6

In conclusion, we can see that 7x - 6 is the answer we need to arrive at  to have equivalent expressions. Only B does not have that answer, so B is the answer.

Hope that helps!

Answer:

(a) The average baggage-related revenue per passenger is $15.70.

(b) The standard deviation of baggage-related revenue is $19.95.

(c) The expected revenue for 120 passengers is $1,884.

Step-by-step explanation:

Let the random variable X represent the baggage-related revenue per passenger.

It is provided that the baggage fees is $25 for the first bag and $35 for the second.

The probability model is:

    X :   0         25      60

P (X) : 0.54    0.34    0.12

(a)

Compute the average baggage-related revenue per passenger as follows:

\(E(X)=\sum {X\times P (X)}\)

         \(=(0\times 0.54)+(25\times 0.34)+(60\times 0.12)\\\\=0+8.50+7.20\\\\=15.70\)

Thus, the average baggage-related revenue per passenger is $15.70.

(b)

Compute the standard deviation of baggage-related revenue as follows:

\(E (X^{2})=\sum X^{2}\times P(X)}\\\\=(0^{2}\times 0.54)+(25^{2}\times 0.34)+(60^{2}\times 0.12)\\\\=0+212.50+432\\\\=644.5\\\)

\(SD(X)=\sqrt{E(X^{2})-(E(X))^{2}}\)

           \(=\sqrt{644.5-(15.7)^{2}}\\\\=19.950188\\\\\approx 19.95\)

Thus, the standard deviation of baggage-related revenue is $19.95.

(c)

Compute the expected revenue for 120 passengers as follows:

\(E(R)=n\times E(X)\)

        \(=120\times 15.7\\\\=1884\)

Thus, the expected revenue for 120 passengers is $1,884.

Answer:

Step-by-step explanation:

$100x0.5x1=$5

Answer:

hey

Step-by-step explanation:

Answer:

y=x

Step-by-step explanation:

Suppose the cost of blue shirt is y and cost of yellow shirt is x then y=x

The number of cups in 44 oz is \(5\frac{1}{2}\) as a mixed measure.

We have,

There are different types of mixed measures, but one common one is the mixed number and fraction form.

To convert 44 oz. to a mixed number and fraction, you need to divide the total amount by the size of each unit in the mixed measure and express the result as a whole number and a fraction.

For example,

If the units are cups and there are 8 oz. in a cup, then:

= 44 oz ÷ 8 oz / cup

= 5.5 cups

So

44 oz. is equivalent to 5 cups and 12 oz.

or

44 oz. =  \(5\frac{4}{8}\) cups = 5 1/2 cups

Thus,

The number of cups in 44 oz is \(5\frac{1}{2}\) as a mixed measure.

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Answer:

I would challenge

The sine function is  y = 4 sin[ (π/6)x ] + 1.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

1) The parent function is sin(x)

2) sin(x) has:

Middle line: y = 0

Amplitude: 1 because the function goes from 1 unit up to 1 unit down the midddle line.

Period: 2π because sine function repeats every 2π units.

y-intercept: (0,0) because sin(0) = 0.

Now look how these changes in the function reflect on the parameters:

A sin (ωx + B) + C:

That function will have:

amplitude A, becasue the amplitude is scaled by that factor

Period: 2π / ω, because the function is compressed horizontally by that factor.

It will be translated B units to the left

It will be translated C units up.

And you need

Period = 12 => 2π / ω = 12 => ω = π/6

A = 4

Translate the midline from y = 0 to y = 1 => shift the function 1 unit up => = 1.

Translate the y-intercept from y = 0 to y = 1, which is already accomplished when you translate the function 1 unit up.

So, the is the function searched>

y = A sin (ωx + B) + C = 4 sin[ (π/6)x ] + 1

Now you can check the amplitude, the period, the middle line and the y-intercept of that y = 4 sin[ (π/6)x ] + 1.

Hence, the sine function is  y = 4 sin[ (π/6)x ] + 1.

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(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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Answer:

work is shown and pictured

Step-by-step explanation: multiply both sides by 9m-7 then bring down your 10

that's about all I can remember so your on your own from that point it's been a while since I've did this sorry mate