1. The area of a figure is 32 square centimeters.
Suppose the sides of the figure are doubled. What
will be the new area of the similar figure?

Answer:

[tex](-9.5,2.63)[/tex]

Step-by-step explanation:

In essence, this problem asks one to find the vertex of the given equation. An easy way to find the vertex of a quadratic equation in standard form is to complete the square.

Completeting the square involves grouping the quadratic and linear term, then factoring out the coefficient of the quadratic term. After doing so, one will add a term to make the grouped terms a perfect square trinomial and then balance the equation. Finally, one will simplify the equation and get the quadratic equation in vertex form. From there, finding vertex is quite easy, the x-coordinate is the additive inverse of the quadratic term, and the y-coordinate is the constant.

Once a quadratic equation in standard form has been converted to vertex form by the process of completing the square, its equation is amongst the lines of the following,

[tex]a(x-k)^2+h[/tex]

(k, h) is the vertex of the parabola.

The quadratic equation in standard form,

[tex]2x^2+19x+42.5[/tex]

Group the quadratic and linear terms,

[tex](2x^2+19x)+42.5[/tex]

Factor out the coefficient of the quadratic term,

[tex]2(x^2+9.5x)+42.5[/tex]

Add a term to make the grouped part a perfect square trinomial, then balance the equation,

[tex]2(x^2+9.5x+22.5625)+42.5-2(22.5625)[/tex]

Simplify,

[tex]2(x^2+9.5x+22.5626)+42.5-45.125[/tex]

[tex]2(x+9.5)^2+2.625[/tex]

The vertex of the equation is the following,

[tex](-9.5,2.625)[/tex]

Rounded,

[tex](-9.5,2.63)[/tex]

Answer: There is a total of 36 slices of pizza.

Answer:

b² =  13.2

Step-by-step explanation:

5.8²+b²=14.4²

33.64+b²=207.36

-33.64       -33.65

b²= √173.71

b² = 13.1799089526

b² =  13.2

Answer:

He is wrong because for the last part of foil he multiplies 3 times 3 and got 6 instead of 9.

Answer:

She earns $ 37.5  by walking 50 laps

Step-by-step explanation:

This method is called unitary method.

If we know the value of 1 unit of an item we can calculate any number of units of item.

For 1 lap she earns 75 cents.

She walks 50 laps.

She earns for 50 laps = 50*75= 3750 cents

Now we have to converts cents into Dollars for convenience.

1$ = 100 cents

3750 /100 = $ 37.5

Answer: 60

Step-by-step explanation:

ball =x

bat = y

x + y = 90

and

equation II is

3 x + 2 y =210

By multiplying by 3 to equation I both sides

we get equation III as

3( x + y) = 3 ( 90 )

3x + 3y =270 III

subtract II and III

we get 3x+3y=270

- 3x+2y=210

--------------------------

0+y= 60

y =60

cost of bat is y ie = 60

and cost of ball ,is

let put value of y in equation I

x+60=90

x=90-60

x=30

cost of ball is 30

Answer:95

Step-by-step explanation:

Answer:

92.736

Step-by-step explanation:

A = L* W

A = 4.8 * 19.32

A = 92.736

Answer:

x = 12 degrees

Step-by-step explanation:

m < LNM = (70+136)/2

= 206 / 2

= 103 degrees

So 7x + 19 = 103

7x = 103 - 19 = 84

x = 84/7

x = 12.

Option (A) 1 foot by 2 feet and option (C)  2 feet by 1 foot satisfy the perimeter given. Thus options A and C are correct.

"A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles".

For the above situation,

The length of the rectangle be 'l'

The breadth of the rectangle be 'b'

Perimeter of the rectangle, P = 2(l+b)

Option A : 1 foot by 2 feet

Here, l = 1 feet and b = 2 feet

⇒ [tex]P=2(l+b)[/tex]

⇒ [tex]P=2(1+2)\\[/tex]

⇒ [tex]P=6[/tex]

This perimeter is equal to the perimeter of the rectangle. Thus option A is correct.

Option B : 1 foot by 5 feet

Here, l = 1 and b = 5 feet

⇒ [tex]P=2(1+5)[/tex]

⇒ [tex]P=12[/tex]

This perimeter is not equal to the perimeter of the rectangle. Thus option B is not correct.

Option C :  2 feet by 1 foot

Here, l = 2 and b = 1 feet

⇒ [tex]P=2(2+1)[/tex]

⇒ [tex]P=6[/tex]

This perimeter is equal to the perimeter of the rectangle. Thus option C is correct.

Option D : 2 feet by 4 foot

Here, l = 2 and b = 4 feet

⇒ [tex]P=2(2+4)[/tex]

⇒ [tex]P=12[/tex]

This perimeter is not equal to the perimeter of the rectangle. Thus option D is not correct.

Option E :  3 feet by 3 feet

Here, l = 3 and b = 3 feet

⇒ [tex]P=2(3+3)[/tex]

⇒ [tex]P=12[/tex]

This perimeter is not equal to the perimeter of the rectangle. Thus option E is not correct.

Option F : 4 feet by 2 feet

Here, l = 4 and b = 2 feet

⇒ [tex]P=2(4+2)[/tex]

⇒ [tex]P=12[/tex]

This perimeter is not equal to the perimeter of the rectangle. Thus option F is not correct.

Option G : 5 feet by 1 foot

Here, l = 5 and b = 1 feet

⇒ [tex]P=2(5+1)[/tex]

⇒ [tex]P=12[/tex]

This perimeter is not equal to the perimeter of the rectangle. Thus option G is not correct.

Hence we can conclude that option (A) 1 foot by 2 feet and option (C)  2 feet by 1 foot satisfies the perimeter given. Thus options A and C are correct.

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Answer:

180.82

Step-by-step explanation:

750,000 x .022=16,500 per year

16,500/365 days =45.2055/day

45.2055 x 4 days = 180.82

Question:

Discus the advantages and disadvantages of histograms versus stem-and-leaf plots

Answer:

C. Stem-and-leaf plots are easier to make and and can contain more information than histograms. However, they are not very useful for large data sets

Step-by-step explanation:

A stem and leaf plot is a graphical presentation of quantitative data similar to an histogram. However, a stem and leaf plot retains and present the values of the original in the data set such that individual data values can be seen and can then be used to make analysis

The stem and leaf plot consists of a stem and a leaf  arranged in the order of place value, such that the numbers having a common highest place value are arranged on a row in a stem and leaf plot and therefore a stem and leaf plot is easier to make or construct than an histogram

However, it is very rare to find stem and leaf plots having more than 50 datasets or observations.

Answer:

C. 22

Step-by-step explanation:

C = circumference

n (pi) = 22/7

r = 3 1 /2

Plug in the numbers for each variable.

C = 2x (22/7) x (3 1/2)

Change the mixed number inIto an improper fraction by multiplying 3 x 2 and adding the 1 which gives us 7 over 2 because 2 is our denominator  so, 3 1/2 = 7/2. It also helps to have 1 as the denominator for 2.

C = (2/1) x (22/7) x (7/2)

Lastly, just multiply the numerators across which give us 308 then multiply the denominators across which gives us 14, so then we divide 308 by 14 and get 22.

The coordinates of the point on the unit circle at the given angle 180 degrees is (-1, 0).

A unit circle is just a circle that has a radius with a length of 1. A unit circle can be used to define right triangle relationships known as sine, cosine and tangent. These relationships describe how angles and sides of a right triangle relate to one another.

The given drawing is the graph of the unit circle on the X – Y Coordinate Axis.

It can be seen from the graph, that the unit circle is defined as having a Radius ( r ) = 1.

Going from Quadrant I to Quadrant IV, counter clockwise, the Coordinate points on the axis of the unit circle are:

(1, 0), (0, 1), (-1, 0), and (0, -1)

This is important to remember when we define the X and Y Coordinates around the unit circle. The Unit Circle has 360°. In the given graph, the Unit Circle is divided into 4 Quadrants that split the unit circle into 4 equal pieces. Each piece is exactly 90°.

From the diagram we can clearly say that the coordinates of the point on the unit circle at the given angle 180 degrees is (-1, 0).

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Answer:

D 3,704

Step-by-step explanation:

Answer:

the answer is 3,704

Step-by-step explanation:

wouldn't you just multiply 483 by so the answer is 3,704

Given:

Consider the line segment YZ with endpoints Y(-3,-6) and Z(7,4).

To find:

The y-coordinate of the midpoint of line segment YZ.

Solution:

Midpoint formula:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

The endpoints of the line segment YZ are Y(-3,-6) and Z(7,4). So, the midpoint of YZ is:

[tex]Midpoint=\left(\dfrac{-3+7}{2},\dfrac{-6+4}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{4}{2},\dfrac{-2}{2}\right)[/tex]

[tex]Midpoint=\left(2,-1\right)[/tex]

Therefore, the y-coordinate of the midpoint of line segment YZ is -1.

Answer:

The measure of the angle is 120 degrees

Step-by-step explanation:

Here, we want to find the measure of the angle

Mathematically, the sum of angles at a point ( the center of the circle in this case) is equal to 360 degrees

We have the measures 150 degrees and 90 degrees; by adding this two and subtracting from 360, we will have the measure of the the marked angle

Thus, we have this as;

360 - (150 + 90)

= 360-240

= 120

Answer:

T = -3

Step-by-step explanation:

No explanation needed ...

Answer:

20x + 5

all you really need to do is multiply the 4x and the 5. you just leave the + 5 alone

Answer:

It's 12.

Step-by-step explanation:

90-18=72

72/6 =12

Answer:

77777

is correct answers

Answer: 0.125

Step-by-step explanation:

Since there is a fifty/fifty chance of the lights being red or green, therefore, the chances of Millie getting 3 consecutive green lights will be:

= (50%)³

= 0.5³

= 0.5 × 0.5 × 0.5

= 0.125

Therefore, the probability is 0.125

Answer:

£7.455

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Answer:

I think it's A

Step-by-step explanation:

Sorry if I'm wrong

Answer:

X=4, y=5

Step-by-step explanation:

5x + 4y =40 equation 1

6x + 4y =44 equation 2

-1(5x + 4y)=-1(40) multiply equation 1 by -1 so equation will eliminate y

-5x - 4y=-40 modif equation 1

6x + 4y= 44  equation 2

         x=4.     Add above 2 equations

solve for y:

5x + 4y =40

5(4)+4y=40

20+4y =40

4y=20

y=5

check solution ;

6x+4y=44

6(4) + 4(5)=44

24 + 20=44

44=44