A rectangular room is 28 feet by 32 feet.
A scale drawing of the room has a perimeter is 12 inches.
What is the length of the shorter side of the room on the scale drawing?

50 POINTS PLSSSS!!!!!

Answer:

Step-by-step explanation:

27 times 3

= 81

Answer: 81

Step-by-step explanation: 27x3 ok what 3^to the 4th power so it would be 3x3x3x3

      9x9=81 is the same as saying 27x3

Check the picture below.

The simplified expression is  [tex]7 x^{3} - 14 x^{2} + 28 x - 55+\frac{124}{x + 2}[/tex]. The correct answer is an option (C).

The expression is given as follows:

[tex]\dfrac{7 x^{4} + x + 14}{x + 2}[/tex]

We can use polynomial long division to simplify the expression:

         7x² - 14x² + 28x - 55

        ______________________

x + 2 ) 7x⁴ + 0x³ + 0x² + x + 14

          7x⁴ + 14x³

       ___________

               -14x³ + 0x²

               -14x³ - 28x²

               ____________

                        28x² + x

                        28x² + 56x

                        __________

                               -55x + 14

                               -55x - 110

                               ________

                                       124

[tex]\dfrac{7 x^{4} + x + 14}{x + 2}=7 x^{3} - 14 x^{2} + 28 x - 55+\dfrac{124}{x + 2}[/tex]

Hence, the simplified expression is as follows:

[tex]7 x^{3} - 14 x^{2} + 28 x - 55+\dfrac{124}{x + 2}[/tex]

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Answer:

  $2080

Step-by-step explanation:

You want to know the annual cost of coffee purchased 5 mornings and 3 afternoons per week when each purchase amounts to $5.

Five morning visits and three afternoon visits to the coffee shop will be a total of 8 visits per week. At $5 each, the cost per week is ...

  8 × $5 = $40

The cost for a year will be the cost for 52 weeks:

  52 × $40 = $2080

Carla spends $2080 per year on coffee.

Whether this is a "little indulgence" or not will depend on Carla's budget.

Answer:

$44

Step-by-step explanation:

since its original price is $40, you would just add 5% but since it says 5% EACH year for 2 years , it would be 10%

you would just add 40 plus %10 if im not mistaken which is $44 so the price just went up $2 each year.

sorry if im wrong.

A function which has the greater maximum value is: function f(x).

In Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry (vertex), Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = -x² - 3x + 1, we have:

Axis of symmetry, Xmax = -(-3)/2(-1)

Axis of symmetry, Xmax = 3/-2 = -1.5.

For the value of k in vertex, we have:

f(x) = -x² - 3x + 1

f(-1.5) = -(1.5)² - 3(-1.5) + 1

f(-1.5) = 3.25

For g(x), the maximum value or vertex is 2 and as such, quadratic function f(x) has the greater maximum value.

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There are 264 anagrams of the word CADERNO that have vowels before consonants.

We have,

To count the number of anagrams of the word CADERNO that have vowels before consonants, we can use the following steps:

Count the number of vowels in the word.

In this case, there are three vowels: A, E, and O.

Count the number of consonants in the word.

In this case, there are four consonants: C, D, R, and N.

Determine the possible arrangements of vowels and consonants that satisfy the condition of having vowels before consonants.

Since there are three vowels and four consonants, there are two possible arrangements that satisfy this condition:

a) Vowel - Consonant - Vowel - Consonant - Vowel - Consonant - Consonant

b) Vowel - Consonant - Vowel - Consonant - Consonant - Vowel - Consonant

Calculate the number of ways to arrange the vowels and consonants in each of the possible arrangements determined in step 3.

We can use permutations to calculate this.

For arrangement a):

There are 3 ways to choose the first vowel (A, E, or O)

There are 4 ways to choose the first consonant (C, D, R, or N)

There are 2 ways to choose the second vowel (whichever is left out of the two remaining vowels)

There are 3 ways to choose the second consonant (whichever is left out of the three remaining consonants)

There is 1 way to choose the third vowel (the remaining vowel)

There is 1 way to choose the fourth consonant (the remaining consonant)

There is 1 way to choose the fifth consonant (the remaining consonant)

The total number of arrangements for this case is: 3 x 4 x 2 x 3 x 1 x 1 x 1 = 72

For arrangement b):

There are 3 ways to choose the first vowel

There are 4 ways to choose the first consonant

There are 2 ways to choose the second vowel

There are 2 ways to choose the second consonant (whichever is left out of the two remaining consonants)

There are 2 ways to choose the third consonant (whichever is left out of the two remaining consonants)

There is 1 way to choose the third vowel

There is 1 way to choose the fourth consonant

The total number of arrangements for this case is: 3 x 4 x 2 x 2 x 2 x 1 x 1 = 192

Add up the total number of arrangements for both cases to get the final answer:

72 + 192 = 264

Therefore,

There are 264 anagrams of the word CADERNO that have vowels before consonants.

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Answer:

x = 5

y = 5√2

Step-by-step explanation:

In a 45-45-90 degree right triangle, the two legs form the right angle, and the hypotenuse is opposite the right angle.

The side lengths of a 45-45-90 right triangle are in the ratio

1 : 1 : √2

The legs are congruent, so if one leg has length 5, the other leg also has length 5.

The hypotenuse is √2 times the length of the legs.

x = 5

y = 5√2

The 90% confidence that the proportion of yellow peas is between 23.5% and 29.5%

and, 25% estimate falls within the 90% confidence limits.

We have,

Green peas= 445

Yellow peas= 161

So, Total peas:

= 445 + 161

= 606.

Now, the Proportion of yellow

= 161/606

= 0.265676

= 26.56%

Now, p= 0. 265 and q= 1-0.265= 0.735

So, np = 606 (0.265)= 160.59

nq = 606(0.735) = 445.41

As, both results are ≥ 5 and the sample can be approximated by a normal distribution.

For 90% confidence, z = 1.645.

Now, the margin error

= 1.645 √ (0.265)(0.735) / 606

= 1.645 / 0.0179

= 0.0294

Now, The confidence limits are the point estimate ± the margin of error. =

= 0.265 + 0.03

= 0.295

= 29.5%;

or, 0.265 - 0.030

= 0.235

= 23.5%

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The distance along the trail from X to Y, to the nearest tenth of a meter, is 600 meters.

The distance between X and Y is on a straight path from X to Y or Y to X. This means that the distance between X and Y can be found by finding the distance between the contour lines.

The distance between the contour lines is:

= Elevation of Y - Elevation of X

= 1, 900 - 1, 300

= 600 meters

In conclusion, the distance along the trail between X and Y is 600 meters.

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The problem has no real number solutions since the discriminant is equal to -16.

Given the quadratic equation below:

-1 = 5x² -2x,

On rearranging the equation will becomes;

5x² -2x+1 = 0

The formula for calculating the discriminant is expressed as:

D = b^2 - 4ac where:

a = 5

b = -2

c = 1

Substitute to have:

D = (-2)^2 - 4(5)(1)
D = 4 - 20
D = -16

The discriminant is equal to -16, which means the equation has no real number solutions.

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The population of Kentucky is nearly 5.9 times that of North Dakota.

To determine how many times larger Kentucky's population is than North Dakota's population, divide Kentucky's population by North Dakota's population:

4.47 x 10^6 / 7.62 x 10^5

We can simplify the fraction by dividing both the numerator and denominator by 7.62 x 10: 4.47 x 106 / 7.62 x 105 = 5.87

5.9, rounded to the closest tenth.

As a result, the population of Kentucky is nearly 5.9 times that of North Dakota.

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0,0,0,0,0,

The total number of meals received by the company this month = 40 meals

Given data ,

Let the number of meals received by the company this month be A

Now , the proportion is given as

The number of boxes of meals in the past month = 3 boxes

The number of meals in 3 boxes = 15 meals

The number of boxes in the present month = 8 boxes

So , the proportion is

15 / 3  = A / 8

Multiply by 8 on both sides , we get

A = 5 x 8

A = 40 meals

Hence , the number of meals is A = 40 meals

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Answer: The answer is 24 kilograms of the 50% silver alloy and 16 kilograms of the 25% silver alloy should be used to make 40 kilograms of the 40% silver alloy.

Step-by-step explanation:

In the given rectangle,

The value of x is 3

The value of NP is 18

From the question, we are to determine the value of x in the given diagram.

The diagram shows a rectangle with its diagonals.

Since the diagonals of a rectangle bisect each other, we can write that

2x + 3 = 12 - x

Solve the equation for x

2x + 3 = 12 - x

Add x to both sides of the equation

2x + x + 3 = 12 - x + x

3x + 3 = 12

Subtract 3 from both sides of the equation

3x + 3 - 3 = 12 - 3

3x = 9

Divide both sides of the equation of by 3

3x / 3 = 9 / 3

x = 3

Thus,

The value of x is 3

To determine the value of NP

NP = 2(12 - x)

Substitute the value of x

NP = 2(12 - 3)

NP = 2(9)

NP = 18

Hence, the value of NP is 18

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By using the graph of y = f(x), the graph of the function g(x) = f(x + 3) include the following: D. graph D.

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

In order to write an equation that models the graph of g(x), we would have to apply a horizontal translation to f(x) by 3 units left:

y = f(x)

g(x) = f(x + 3)

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The amounts of people in attendance are given as follows:

The amounts are obtained by a system of equations, for which the variables are given as follows:

There were 400 people total, hence:

x + y + z = 400.

There were twice as many parents as grandparents, hence:

y = 2z.

50 more children than parents, hence:

x = y + 50

x = 2z + 50.

Replacing on the first equation, the value of z is obtained as follows:

2z + 50 + 2z + z = 400

5z = 350

z = 70.

Then the values of x and y are given as follows:

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Answer:

answers in picture

(Btw we can’t see one of the triangles so you can just assume that the last one would be 46 degrees)

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:  D

Step-by-step explanation:

Point of tangency is where the line on the left touches the circle.  Have you ever heard the term "She's going off on a tangent"- it means they only touch the topic(tangent point and go off (tangent line) and talk way off away from where you need to be(circle)

So you can see from the graph the point of tangency (where line touches circle is (-5,0)

the equation for the line is going to be a constant.  The line only touches the x-axis never the y-axis at all points it is x=-5

so the equation of the line x= -5

The area of the triangle is; 33 in².

The area of the rectangle is; 190 in².

The total area as required is; 223 in².

By observation; the triangle is such that its base is 6 in and it's height is; (20 - 9) = 11 in.

Therefore, the area of the triangle given by; (1/2)×b×h is; (1/2) × 6 × 11 = 33 in².

The area of the rectangle of length 20 in and width 9.5 in is; 20 × 9.5 = 190 in².

Ultimately, the total area of the composite shape is; 33 + 190 = 220 in².

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1) The decay constant is  0.0385

2) The amount after ten years is  27.2 mg

3) The time taken for 10 mg to remain is  36 years.

We know that;

P = Poe^-kt

Given that the half life is 18 years;

20=40e^-18k

20/40=e^-18k

0.5 =e^-18k

ln0.5 = -18k

k = -0.693/-18k

k = 0.0385

After 10 years we have;

P = 40e^-10(0.0385)

P = 27.2 mg

10 mg will remain when;

10 = 40e^-0.0385t

10/40 =e^-0.0385t

0.25 = e^-0.0385t

ln0.25 = -0.0385t

t = -1.386/-0.0385

t = 36 years

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The surface area of the cylindrical pottery is S = 163 inches²

Given data ,

Let the surface area of the cylindrical pottery be S

Now , the radius of the pottery r = d/2

r = 4.3 / 2

r = 2.15 inches

And , the height of the cylindrical vase = 11 inches

where S = B + Ph

On simplifying , we get

S = πr² + 2πr ( h )

S = ( 3.14 ) ( 2.15 )² + 2 ( 3.14 ) ( 2.15 ) ( 11 )

S = 14.51465 + 2 ( 74.261 )

S = 163.03665 inches²

Hence , the surface area is S = 163 inches²

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The image of △FGH after the similarity transformation is △F"G"H", with vertices F"(-2, 2), G"(-2, 6), and H"(2, 6).

To perform the similarity transformation, we first apply the translation by subtracting 3 from the x-coordinates and subtracting 1 from the y-coordinates:

F' = (2-3, 2-1) = (-1, 1)

G' = (2-3, 4-1) = (-1, 3)

H' = (4-3, 4-1) = (1, 3)

Next, we apply the dilation with a scale factor of 2 by multiplying each coordinate by 2:

F" = 2(-1, 1) = (-2, 2)

G" = 2(-1, 3) = (-2, 6)

H" = 2(1, 3) = (2, 6)

So the image of △FGH after the similarity transformation is △F"G"H", with vertices F"(-2, 2), G"(-2, 6), and H"(2, 6).

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The measure of the angle is A. 125^o

A measure of an angle which lies between 90^o and 180^0 is said to be obtuse. This implies that the measure of the angle is greater than a right angle but less than the sum of angles on a straight line.

In the given expression, the halfway between 120 and 130 degrees is given as;

(120 + 130)/ 2 = 125

Thus given that the angle has one ray pointing towards zero, then the other ray is pointing towards 125 degrees.

Then it can be concluded that the measure of the angle is A. 125^o.

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The x and y int for the equation are x = undefined and y-int = 1

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

y = 4^x

Set the variable x to 0 to calculate the y-intercept

So, we have

y-int = 4^0

y-int = 1

Set the variable y to 0 to calculate the x-intercept

So, we have

4^x = 0

So, we have

x = ln(0)/ln(4)

Evaluate

x = undefined

Hence, the x-intercept is undefined

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A reflection transformation on a coordinate plane changes the figure over a line called the line of reflection. This line acts as a reflect and the picture created by the change could be a reflect picture of the first figure.

b. In case a figure is reflected over the x-axis, the x-coordinates of all the focuses within the figure will stay the same, but the y-coordinates will be increased by -1. So, in the event that a point on the initial figure has arranges (x,y), its picture after reflecting over the x-axis will have arranges (x,-y).

c. In case a figure is reflected over the y-axis, the y-coordinates of all the points within the figure will remain the same, but the x-coordinates will be copy by -1. So, in case a point on the first figure has push (x,y), its image   after reflecting over the y-axis will have arranges (-x,y).

Therefore, d. To reflect a triangle over the y-axis, we need to know the  the mirror image  of each point with regard to the y-axis. One way to do usually to increase the x-coordinate of each point by -1 and also keeping the y-coordinate the same.

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See text below

2. Reflections:

Transformations Review

a. How would you describe what this transformation looks like when performed on a coordinate plane?

b. If your figure was reflected across the x-axis, how would that affect the figure's coordinates?

c. If your figure was reflected across the y-axis, how would that affect the figure's coordinates?

d. On the coordinate plane: First, plot a triangle. Then, reflect your triangle over the y-axis and draw the result:

Answer:

Step-by-step explanation:

Answer:

[tex]B. y=-1/4x+6.[/tex]

Step-by-step explanation:

The line perpendicular to the line y = 4x + 5 would need a slope of -1/4.

The slope of any perpendicular line multiplied by the original line must equal -1. Therefore, only answer B works.

Answer:

B

Step-by-step explanation:

The given line is a slope -intercept form

  y = mx + b     m is the slope

   for this line slope = 4

PERPENDICULAR slope is  - 1/m  = = -  1/4   <====you just have to LEARN this!

Answer B has slope = - 1/4

To convert kilometers per hour (km/hr) to meters per second (m/sec), we need to multiply the speed by 0.27778.

So, to convert 81 km/hr to m/sec, we multiply it by 0.27778 as follows:

81 km/hr x 0.27778 = 22.5 m/sec (rounded to one decimal place)

Therefore, 81 km/hr is equal to 22.5 m/sec (approximately).

~~~Harsha~~~

Answer: 22.5 Meters per Second

Step-by-step explanation: 1 km/h = 0.2777777778 m/s     1 m/s = 3.6 km/h

Example: convert 20 km/h to m/s:

20 km/h = 20 × 0.2777777778 m/s = 5.5555555556 m/s