Mathematics High School

The floor plan of a factory is dilated by a factor of 4 to create a new, larger floor plan.

The area of the new floor plan is _______ times larger than the area of the original floor plan?

a. 4
b. 8
c. 16
d. 64
e. 256

Answers

Answer 1

The original floor could be rectangle in shape.

If we consider the length of floor to be 'L' and width of floor to be 'W',

then area of original floor = length x width = LW.

And if its dimensions are dilated by scale factor of 4 to make new floor, then new length and width would become four times of older values. So new length would be '4L' and new width would be '4W'

Now area of new floor = length x width = 4L x 4W = 16LW.


It is clear that the area of new floor is 16 times of the area of original floor.

So, option C i.e. 16 is the final answer.

Related Questions

Indicate a general rule for the [tex] n^{th}[/tex] term of this sequence.
-6a, -3a, 0a, 3a, 6a. . .
A.] [tex] a_{n}=3an+9a[/tex]
B.] [tex] a_{n}=-3an-9a[/tex]
C.] [tex] a_{n}=-3an+9a[/tex]
D.] [tex] a_{n}=3an-9a[/tex]

Answers

Answer: option D) An = 3an - 9a

Justification:

1) That is an arithmetic sequence which you prove by determining the difference between two consecutive terms (which shall be constant if it indeed is an arithmetic sequence):

2)

Second term - first term = -3a - (-6a) = -3a + 6a = 3a
Third term - second term = 0a - (-3a) = 3a
Fourth term - third term = 3a - 0a = 3a
Fith term - fourth term = 6a - 3a = 3a

Therefore, it is an arithmetic sequence with difference d = 3a.

3) the general rule for the nth term of an arithmetic sequence is given by the formula:

An = Ao + d (n - 1)

Where Ao = -6a and d, as determined above, is 3a

=> An = -6a + 3a (n - 1)

Expand the parenthesis (distributive property) =>

An = -6a + 3an - 3a = -9a + 3an = 3an - 9a = option D. <------- answer.

18 points were scored by one figure skating pair that was 40% of your final score. What was the final score for that pair of figure skaters?

Answers

We can solve this problem using cross-multiplying method.

We have following information
18 points = 40%
We need to find out the final score. Let's use x for final number of points.
x points = 100%

We can write this:
18 points = 40%
x points = 100%

We cross multiply numbers
18*100=x*40
1800=40x /:40
1800/40=x
x=45

The final score was 45 points.

Round 8.414 to the nearest hundredth

Answers

it would be 8.41 because the last digit isn't big enough to round up so you would have to round down

the ordered pairs below represent a relation between x and y.
(-3,0), (-2,4), (-1,8), (0,12), (1,16), (2,20)

could this set of ordered pairs have been generated by a linear function?

A. No, because the distance between consecutive x-value is different than the distance between consecutive x-values.
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
C. No, because the y-values decrease and then increase
D. Yes, because the distance between consecutive x-values is constant.

Answers

Answer:

Yes because the relative difference between y-values and x-values is the same no matter what which pairs of (x,y) values you use to calculate it

Step-by-step explanation:


Yes, this set of ordered pairs have been generated by a linear function because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.

The correct option is (B)

What is graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given are ordered pairs are: (-3,0) (-2,4)(-1,8)(0,12)(1,16)(2,20).

It can be seen that the there only unit increase in x coordinates and units increase in consecutive y- coordinates.

Now, if we set up the equation of line as:

Here, m =4 and b = 12

So the relationship is linear and represented by the equation

y=4x+12

Hence, the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.

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A bakery sold 115 cupcakes in one day. The head baker predicted he would sell 95 cupcakes that day. What was the percent error of the baker's prediction?

Answers

It was about 17.4% 
======================================================================

% error=
actual value-estimated value 
Then divide that by actual value

The baker's prediction had a 17.39% error.

To calculate the percent error of the baker's prediction, we use the formula:

Percent Error = (|Actual Value - Predicted Value| / Actual Value) * 100%

In this case, the Actual Value is the number of cupcakes actually sold, 115. The Predicted Value is the number the baker predicted to sell, 95.

So, the computation will be:

Percent Error = (|115 - 95| / 115) * 100%

Percent Error = (20 / 115) * 100

Percent Error = 0.1739 * 100%

Percent Error = 17.39%

Simplify each expression. K(k^3) that means to the third power btw

Plz help!

Answers

[tex]\bf k(k^3)\implies k^1(k^3)\implies k^1\cdot k^3\implies k^{1+3}\implies k^4[/tex]

I need help on #9. The help would be grateful appreciated.

Answers

Original Figure:
Length = 15
Width = 5
Height = 10
Volume = Length*Width*Height
Volume = 15*5*10
Volume = 750

New Figure
Length = 3
Width = 1
Height = 2
Each dimension has been divided by 5 (eg: 15/5 = 3)
Volume = Length*Width*Height
Volume = 3*1*2
Volume = 6

The old volume was 750 and it changes to 6
Notice how 750/6 = 125
Which can be rearranged to 750/125 = 6

Answer: if you divide the old volume by 125, then you get the new volume

Note: the new volume is 125 times smaller than the old volume
Put another way, the old volume is 125 times larger compared to the new volume

The fact that 125 = 5^3 is not a coincidence. If you divide each dimension by some number k, then you divide the volume by k^3

Solve. 2m^2-7m-13=-10

Answers

[tex]2m^2-7m-13=-10\ \ \ |+10\\\\2m^2-7m-3=0[/tex]


[tex]a=2;\ b=-7;\ c=-3\\\\b^2-4ac=(-7)^2-4\cdot2\cdot(-3)=49+24=73\\\\m_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ m_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\m_1=\dfrac{-(-7)-\sqrt{73}}{2\cdot2}=\dfrac{7-\sqrt{73}}{4}\\\\m_2=\dfrac{-(-7)+\sqrt{73}}{2\cdot2}=\dfrac{7+\sqrt{73}}{4}[/tex]

Yu-Xi draws a triangle with two angles measuring 79 degrees and 23 degrees.What is the measure, in degrees, of the third angle?

Answers

79+23=102
180-102=78
the third angle is 78 degrees

Answer:

The Triangle Drawn by ,Yu-Xi,has measure of two angles ,79° and 23°.

All the Basic Learners who knows Math ,that,sum of Measures of three Interior angles of Triangle is 180°.

→79°+23°+Third Angle =180°

→102°+Third Angle =180°

→Third Angle =180° -102°

Third Angle =78°

What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4)? y = – x – 1y = – x + 5y = x – 1y = x + 5

Answers

the equation of the line parallel to 5x+2y=12 and passes through the point (-2, 4) is equal to y= -5/2x - 1

Answer:  The required equation of the line is [tex] y=-\dfrac{5}{2}x-1.[/tex]

Step-by-step explanation:  We are given to find the equation of the line that is parallel to the following line and passes through the point (-2, 4) :

[tex]5x+2y=12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the slope-intercept form of the equation of a straight line is given by

[tex]y=mx+c,[/tex]

where m is the slope of the line.

From equation (i), we have

[tex]5x+2y=12\\\\\Rightarrow 2y=-5x+12\\\\\Rightarrow y=-\dfrac{5}{2}x+6.[/tex]

So, the slope of line (i) is given by

[tex]m=-\dfrac{5}{2}.[/tex]

We know that the slopes of two parallel lines are equal. So, the slope of the new line will be

[tex]m=-\dfrac{5}{2}.[/tex]

Since the line passes through the point (-2, 4), so its equation will be

[tex]y-4=m(x-(-2))\\\\\\\Rightarrow  y-4=-\dfrac{5}{2}(x+2)\\\\\\\Rightarrow y-4=-\dfrac{5}{2}x-5+4\\\\\\\Rightarrow y=-\dfrac{5}{2}x-1.[/tex]

Thus, the required equation of the line is [tex] y=-\dfrac{5}{2}x-1.[/tex]

The height of a stack of dimes varies directly with the number of dimes in the stack. A stack of 4 dimes is 5.4 mm tall. How many millimeters tall is a stack of 15 dimes?

Answers

5.4 x 11 = 59.4. Someone else Is probably right

If you were going to represent the top view of the figure, stated which boxed should be shaded.

Answers

The one on the far left...hope I helped

Which is a monthly recurring cost associated with renting a house?
utility bills
property tax
insurance

Answers

Property tax, and insurance would be associacted with renting a house

If you were given the equation f ( x ) = 3x⁵+6x, what behavior would the ends of the graph have?

a. Both ends will point up
b. Both ends will point down
c. the left end will start down at a large negative and the right end will go upwards
d. the left end will start up at a large positive and the right end will go downwards EXPLAIN ANSWER

Answers

The function given in the problem is a Polynomial Function of degree 5. These functions have the following form: f(x)=ax^5+bx^4+c^3+d^2+ex+f. They have an R domain and their graphs are continuous curves.
 
 You can know the behavior of the function f(x)=3x⁵+6x by given values to the variable x and plot each point obtained. For example:
 
 If x=-1⇒ f(-1)=3(-1)⁵+6(-1)=9
 
 If x=0⇒ f(0)==3(0)⁵+6(0)=0
 
 If x=1⇒ f(1)=3(1)⁵+6(1)=9
 
 Therefore, as you can see in the graph attached, the correct answer is:
 
  c. The left end will start down at a large negative and the right end will go upwards.


Final answer:

The ends of the graph of the function f(x) = 3x^5 + 6x will display the behavior described in option c. This is due to the highest power of x in the equation being an odd number and the coefficient being positive. As such, the left end of the graph will start down at a large negative and the right end will go upwards.

Explanation:

The behavior of the ends of the graph of the function f(x) = 3x^5 + 6x is determined by the highest power of x in the equation, which is 5 in this case. The coefficient of x^5 is positive, so as x approaches positive infinity, f(x) also approaches positive infinity. Conversely, as x approaches negative infinity, the value of f(x) would approach negative infinity. We can describe this behavior as the left end of the graph starting at a large negative and the right end going upwards. Thus, answer c. 'the left end will start down at a large negative and the right end will go upwards' is correct.

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helppppppppppppppppppppppppppppp

Answers

The answer is B. Use the trig identity (sin x)^2+(cos x)^2=1. Since cos x=0.3090, sinx=+-\sqrt(1^2-0.3090^2)=+-0.9511. Since 0<x<90, sin x must be positive, so sin x=0.9511. tan x=sin x/cos x=0.9511/0.3090=3.0780.

Given that (6,5) is on the graph of f(x), find the corresponding point for the function-2f(x)

Answers

For f(6) = 5, you will have -2f(6) = -2*5 = -10

The point of interest is (6, -10).

Answer:

the person up is wrong

Step-by-step explanation:

i got it wrong on the test rn

The perimeter of a square must be greater than 188 inches but less than 198 inches. find the range of possible side lengths that satisfy these conditions. (hint: the perimeter of a square is given by p=4s, where s represents the length of a side).

Answers

Final answer:

The range of possible side lengths for the square is from slightly more than 47 inches to slightly less than 49.5 inches. This is found by dividing the given perimeters by 4, using the formula p=4s.

Explanation:

In this problem, we need to find the range of possible side lengths of a square where the perimeter is more than 188 inches but less than 198 inches. Remember that the perimeter of a square is found by multiplying the length of one side by 4 (p=4s).

First, let's find the side length for a square with a perimeter of 188 inches. We do this by dividing the perimeter by 4: 188 / 4 = 47 inches. So, any square with side lengths greater than 47 inches would have a perimeter more than 188 inches.

Next, we find the side length for a square with a perimeter of 198 inches. Similarly, we divide the perimeter by 4: 198 / 4 = 49.5 inches. So any square with side lengths less than 49.5 inches would have a perimeter less than 198 inches.

Therefore, the range of possible side lengths that satisfy these conditions is from slightly more than 47 inches to slightly less than 49.5 inches.

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The graph of a quadratic function touches, but does not cross, the x-axis at x = 4. Which function represents this situation? y = x2 – 16 y = x2 – 4x y = x2 – 8x + 16 y = x2 + 8x + 16

Answers

y = x2 - 8x + 16 doesn't cross the x axis

The quadratic equation is y = x^2 - 8x + 16

How to determine the equation?

From the question, we have:

x = 4

Since the graph only touches x = 4 and it does not cross it, then it means that the graph has a multiplicity of 2 at x = 4

The equation is then represented as:

y = (x - 4)^2

Expand

y = x^2 - 8x + 16

Hence, the quadratic equation is y = x^2 - 8x + 16

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Which transformation shows a reflection of ΔDEF?

Answers

The answer is B or the purple one

Answer:

The image B with purple figures is correct.

Step-by-step explanation:

We are given the figure DEF and we are required to find the figure which is obtained after reflecting it.

Now, reflection of a figure means to flip the figure over a line.

In the green figure, the points D and E are interchanged which is not possible in reflection.

In the blue figure, there is no change.

In the purple figure, the triangle is flipped over the line DE and so it is the correct answer.

Hence, the purple figure is obtained after reflecting the figure DEF.


A person at the top of a cliff 100 ft. tall sees Gilligan's boat. He sees the boat at an angle of depression of 10. How far is the boat from the base of the cliff.

Answers

567.128181962 ft to be exact
or 567.128ft  rounded

hope this helps<3






















What is the solution set for the quadratic equation x2 - 16 = 0?

A)
{4}


B)
{-4, 4}


C)
{256}


D)
{-256, 256}

Answers

B) {-4, 4} 

Proof:

Solve for x over the real numbers:
x^2 - 16 = 0

The left hand side factors into a product with two terms:
(x - 4) (x + 4) = 0

Split into two equations:
x - 4 = 0 or x + 4 = 0

Add 4 to both sides:
x = 4 or x + 4 = 0

Subtract 4 from both sides:

Answer:  x = 4 or x = -4

What scale factor was applied to the first rectangle to get the resulting image


Help me plsssssssssssssssssssssssssssssssssssssssssss!

Answers

2.5 / 5 = .5
.5 x 5 = 2.5 

scale factor should be 5.

How would you get the answer??

Answers

The ratio for this situation would be 20:6, as this represents 6 red cars for every 20 cars sold. To get the fraction, just add the ratio on each side together, then place the number you want as a fraction on top, then simply if possible. This looks like this:
20+6=26
6/26
Divide the numerator and denominator by 2
3/13
So, the fraction is 3/13

Marcus has a total of 10 nickels and dimes in his pocket. he has a total of 70 cents. how many dimes does he have in his pocket?

Answers

10 coins in nickels & dimes = $0.70

1 nickel = $0.05
1 dime = $0.10

4 dimes = $0.40
6 nickels = $0.30

4 dimes + 6 nickels = 10 coins
$0.40 + $0.30 = $0.70



The answer is: He has a total of 4 dimes in his pocket.

Jana wants to navigate page 35 of her report. what is the quickest way to navigate?

Answers

To navigate to page 35 of a report, you can use the 'find' function in a web browser with CONTROL or COMMAND + F, utilize the table of contents with hyperlinks, or enter the page number in a navigator window's spin box, depending on the device and format.

To quickly navigate to page 35 of a report, you have several options depending on the format and the device you are using. If you are viewing the report on a web browser, you can usually press CONTROL or COMMAND and the letter F to open the 'find' function and type '35' to jump to page 35. Alternatively, if the document has a table of contents with hyperlinks, you can click on the relevant section to navigate quickly. For documents with a navigator window, enter '35' in the spin box to jump straight to that page. In a mobile reading environment, you may find a Contents button at the top of the screen; clicking this can allow you to select and jump to the desired page or section.

The area of square abcd is 36 square units and the area of triangle ebf is 20 square units. if line eb is perpindicular to line bf and line ae is equal to 2 find the length of line cf

Answers

Final answer:

The length of line CF is 20 units.

Explanation:

Let's analyze the given information step by step:

The area of square ABCD is 36 square units, so each side of the square measures √(36) = 6 units.The area of triangle EBF is 20 square units.Line EB is perpendicular to line BF.Line AE is equal to 2 units.

Since line EB is perpendicular to line BF, triangle EBF is a right triangle. Let's assume the length of line BF is x units. Using the area of a triangle formula, we have:

Area of triangle EBF = (1/2) * base * height

20 = (1/2) * x * 2

Simplifying the equation, we get:

20 = x

Therefore, the length of line BF (or CF) is 20 units.

If side a has a length of 3 and side b has a length of 4, use the Pythagorean Theorem to find the length of side c. Round the answer to the nearest tenth.

Answers

This the equation you will need to use (the Pythagorean Theorem)
[tex]a {}^{2} + b {}^{2} = c[/tex]
when you put the numbers in for the variables given it will look like this

[tex]( {3})^{2} + ( {4})^{2} = c[/tex]
3 squared equals 9 and 4 squared equals 16:
[tex]9 + 16 = 25[/tex]
so side c is 25 units

helpppppppppppppppppppppppppppppppppppp

Answers

To take out terms outside the radical we need to divide the power of the term by the index of the radical; the quotient will be the power of the term outside the radical, and the remainder will be the power of the term inside the radical. 
First, lets factor 8:
[tex]8=2 ^{3} [/tex]
Now we can divide the power of the term, 3, by the index of the radical 2:
[tex] \frac{3}{2} [/tex] = 1 with a remainder of 1
Next, lets do the same for our second term [tex] x^{7} [/tex]:
[tex] \frac{7}{2} [/tex] = 3 with a remainder of 1
Again, lets do the same for our third term [tex]y^{8} [/tex]:
[tex] \frac{8}{2} =4[/tex] with no remainder, so this term will come out completely.

Finally, lets take our terms out of the radical:
[tex] \sqrt{8x^{7} y^{8} }= \sqrt{ 2^{3} x^{7} y^{8} } =2 x^{3} y^{4} \sqrt{2x} [/tex]

We can conclude that the correct answer is the third one. 

First we rewrite the expression:
 root (8x ^ 7y ^ 8)
 (8x ^ 7y ^ 8) ^ (1/2)
 Properties of exponents:
 (8 ^ (1/2) x ^ (7/2) y ^ (8/2)
 We rewrite:
 (8 ^ (1/2) x ^ (7/2) y ^ 4
 (2 * 2 ^ (1/2) x ^ 3y ^ 4x ^ (1/2)
 (2 * x ^ 3 * y ^ 4 * (2x) ^ (1/2)
 Answer:
 (2*x^3*y^4*(2x)^(1/2)
 option 3



The graph shows the number of copies a copier can make. What is the unit rate?
A)
1
25
B) 5
C) 15
Eliminate
D) 25

Answers

i think it D) 25 because if u look at the graph it show 75 copies number in 3 minutes.

Answer:

25

Step-by-step explanation:

Solve for x where a is an integer less than 0

Answers

Basically the question is asking to solve for x if a is negative.

So to do this, simply change the sign for a to -a in the original equation and solve for x.

-ax > -12

X < 12/a.

This is the solution.








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