The line of symmetry of the parabola whose equation is y = ax^2 -4x + 3 is
x = -2. What is the value of "a"?

A. -2
B. -1
C. -1/2

The total length of the steel used in the frame is 270 cm, if the decorative steel up of 6 stems and each stem is 45 cm.

Step-by-step explanation:

The given is,

           Decorative steel made from circular circle of 6 stems

           The length of the stem is 45 cm

Step:1

         We need to find the total length of the steel used in the decorative steel,

          Let,  T - Total length of the steel

                  L - Length of the stem

                  n - Number of stems used in steel frame

Step:2

       Formula to find the total length of the steel is,

                            [tex]T=[/tex] [tex]l[/tex] × [tex]n[/tex]

       From given,

                  [tex]l[/tex] = 45 cm

                 [tex]n[/tex] = 6 stems

       Substitute the values in formula,

                          [tex]T =[/tex] ( 45 × 6 )

                              = 270

                        [tex]T =[/tex] 270 cm

Result:

         The total length of the steel used in the frame is 270 cm.

The total length of steel used in the decorative steel frame, made with 6 stems of 45cm each, is 270cm.

To solve this question, we simply need to multiply the length of each stem by the number of stems used in the decorative steel. As stated, each stem measures 45cm, and there are 6 stems used in total.

Therefore, the total length of steel used in the frame would be calculated as follows:

So, the total length of steel used in the frame is 270cm.

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Answer:

2000,400,80,16, = missing answer is 3.2

This is because everything on the linear

declines by dividing y by 5 for x = 3.2 * 5

so for rate of change = 5/3.2 = 1.56

An expression for y = y- 64 = 2 2 8 X - 63. (0,12)

or y = y-5 = - 3x -1  

which = 3.2 -5 = -2.8 x 5  = -14

Step-by-step explanation:

Answer:

Part 1)

The scale factor of the smaller prism to the larger prism is 3

or

The scale factor of the larger prism to the  smaller prism is 1/3

Part 2) The surface area of the smaller prism is 66 square centimeters

Step-by-step explanation:

Part 1) What is the scale factor for the similar figures?

we know that

If two figures are similar, then the ratio of their volumes is equal to the scale factor raised to the cube

Let

z ----> the scale factor

x ---> volume of the larger prism

y ---> volume of the smaller prism

so

[tex]z^3=\frac{x}{y}[/tex]

we have

[tex]x=972\ cm^3\\y=36\ cm^3[/tex]

substitute

[tex]z^3=\frac{972}{36}[/tex]

Simplify

[tex]z^3=27\\z=3[/tex]

therefore

The scale factor of the smaller prism to the larger prism is 3

or

The scale factor of the larger prism to the  smaller prism is 1/3

Part 2) What is the surface area of the smaller prism?

we know that

If two figures are similar, then the ratio of their surface areas is equal to the scale factor squared

Let

z ----> the scale factor

x ---> surface area of the larger prism

y ---> surface area of the smaller prism

so

[tex]z^2=\frac{x}{y}[/tex]

we have

[tex]x=594\ cm^2[/tex]

[tex]z=3[/tex]

substitute

[tex]3^2=\frac{594}{y}[/tex]

solve for y

[tex]y=\frac{594}{9}=66\ cm^2[/tex]

therefore

The surface area of the smaller prism is 66 square centimeters

Answer:

(- 2, - 3 )

Step-by-step explanation:

Given the 2 equations

2x - 4y = 8 → (1)

y = [tex]\frac{3}{2}[/tex] x → (2)

Substitute y = [tex]\frac{3}{2}[/tex] x into (1)

2x - 4([tex]\frac{3}{2}[/tex] x ) = 8

2x - 6x = 8

- 4x = 8 ( divide both sides by - 4 )

x = - 2

Substitute x = - 2 into (2) for corresponding value of y

y = [tex]\frac{3}{2}[/tex] × - 2 = - 3

Solution is (- 2, - 3 )

Answer:

[tex]a_{n}[/tex] = - 3[tex](6)^{n-1}[/tex]

Step-by-step explanation:

Note the common ratio r between consecutive terms, that is

r = - 18 ÷ - 3 = - 108 ÷ - 18 = 6

This indicates the sequence is geometric with n th term ( explicit formula )

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = - 3 and r = 6, thus

[tex]a_{n}[/tex] = - 3[tex](6)^{n-1}[/tex]

Answer:

Nick needs to buy 3 packs.

Step-by-step explanation:

If Nick buys 3 packs he will have 18 cards. If he uses 15 of them he will have 3 left over. If he only bought 2 packs he would be 3 cards short of the amount he really needed.

Answer:

Nick needs to buy 3 packs because if he buys 2 packs he'll have 12 cards which won't be enough. He will have an extra 3 cards remaining.

Answer:

5a²+22a+8

Step-by-step explanation:

(5a+2)(a+4)

5a² + 20a + 2a + 8

5a² + 22a + 8

Answer:

if minus is part of the question:

-(5a^2+22a+8)=-5a^2-22a-8

if not then:5a^2+22a+8____ a tip: make the question clear next time...good luck!

Answer:

39°

sum of triangle's interior angles: 180°

180°-90°-51°=39°

The price of cable TV has increased by approximately 252.94% from 1990 to 2010.

The approximate percent increase from 1990 to 2010 can be calculated using the formula:

Percent increase = (Final value - Initial value) / Initial value * 100

To apply this formula, we first need to find the initial and final values. In this case, the initial value is the cost of cable TV in 1990, which is $17.00, and the final value is the cost in 2010, which is $60.00.

Now, let's calculate the percent increase:

Percent increase = ($60.00 - $17.00) / $17.00 * 100

= $43.00 / $17.00 * 100

≈ 252.94%

Therefore, the approximate percent increase from 1990 to 2010 is approximately 252.94%.

Answer:

$265.00

Step-by-step explanation:

300*.80=240

25*1=25

240+25=265.

Answer:

The answer is $265

Step-by-step explanation:

I took this test

Answer:

It will become narrower/steeper

Step-by-step explanation:

To find out how the new parabola will behave, just substitute in numerous values for a and x.

Then compare this to the original graph and you will clearly be able to distinguish the differences between the two graphs.

The equation of the new parabola is y = ( 2a )x² and the parabola will become narrower or steeper

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the equation of the first parabola be

y = ax²   be equation (1)

The parabola is graphed in green below

Now , a is positive integer when multiplied by 2 , we get

y₁ = ( 2a )x²   be equation (2)

The equation (2) represents the equation of the new parabola

The parabola is graphed in red below

So , from the graph , we can see that the parabola has become narrower

Hence , the equation of the parabola is y₁ =  ( 2a )x²

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Answer:

4 + 3x

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The ratio 19:15 is equivalent to 19/15

19/15=1.26666

The ratio 4:3 is equivalent to 4/3

4/3=1.33333

1.26666 is not equal to 1.3333, so the ratios are not equivalent

Hope this helps! :)

Answer:

no

Step-by-step explanation:

cross multiply to check

19/15 and 4/3

multiply 19 x 3=57

multiply 4 x 15=60

since 57 and 60 aren't equal to each other then the ratios aren't equivalent

Answer:

25.

Step-by-step explanation:

If an expression is  

[tex]x^2+bx[/tex]

then we have to add [tex](\frac{b}{2})^2[/tex], to make it perfect quare.

The given expression is

[tex]x^2+10x[/tex]

Here, b=10.

[tex](\frac{b}{2})^2=(\frac{10}{2})^2=5^2=25[/tex]

Now,

[tex]x^2+10x+25=x^2+2x(5)+5^2=(x+5)^2[/tex]

Therefore, we need to add 25 to make it perfect square.

Answer:

What dotted line. There is no dotted line on here my friend

Step-by-step explanation:

Answer:

10

30%

Step-by-step explanation:

In this case it would be the combination of 2 taken from 5.

That is, when n = 5 and r = 2

nCr = n! / r! * (n-r)!

replacing

5C2 = 5! / (2! * 3!)

5C2 = 10

Which means that the sample space is 10 possible combinations.

the probability that the card you draw is even is 3/5, since there are 3 even cards that exist and 5 is the total number of cards.

Now, so that both are for it would be the multiplication of the previous probability and 2/4 because an even card and a card in general have already been drawn:

(3/5) * (2/4) = 0.3

So the probability that both are even is 30%

Answer:

25

Step-by-step explanation:

5x5

Answer:

9 boxes

Step-by-step explanation:

If the diameter is 12 ft then the radius is 6 ft

6ft=72 inches,Area of circle=pi*72^2,5184*pi square inches

Area covered by a box of tiles=9^2*25

number of boxes needed:5184*pi/81*25=8.0425 boxes

9 boxes.

Answer:

All real numbers greater than 0

Step-by-step explanation:

A function assigns values. The range of the function will be all real numbers greater than 0.

A function assigns the value of each element of one set to the other specific element of another set.

As we can see in the function x can take up any value from -∞ to +∞. Although the value of eˣ will still be positive for any value of x.

Thus, the range of the function will be all real numbers greater than 0.

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The seats are arranged in 5040 ways, if 7 people sit in seats labeled A, B, C, D, E, F, G.

Step-by-step explanation:

The given is,

                 7 people sit in seats labeled A, B, C, D, E, F, G.

Step: 1

               No.of people = 7

               No. of seats labeled = 7

               Formula to calculate the number of ways to arrange,

                                      [tex]P_{n} = n![/tex]...................................(1)

               Where, n - Positive integer

Step: 2

               From given, n = 7

               Equation (1) becomes,

                                      [tex]P_{7} = 7![/tex]

                                            = 7 × 6 × 5 × 4 × 3 × 2 × 1

                                            = 5040

                                            = 5040 ways

Result:

         The seats are arranged in 5040 ways, if 7 people sit in seats labeled A, B, C, D, E, F, G.    

Answer:

Angle Rome to Paris = 44.68°

Angle Paris to Berlin = 71.26°

Angle Berlin to Rome = 64.06

Step-by-step explanation:

See attachment for diagram illustration for this.

Let represent distance from Rome to Paris as a, distance from Paris to Berlin as b, and distance from Berlin to Rome as c.

Therefore we say

a = 697miles, b = 545miles, c = 734miles

To find the respectively angle formed from, Berlin to Paris to Rome, we will apply the cosine rule, which states that:

c² = a² + b² - 2abCosC

734² = 697² + 545² - 2(697*545)cosC

2(697*545)cosC = 697² + 545² - 734²

759739 cosC = 244078

cosC = 244078/759739

cosC = 0.3212

C = cos-¹0.3212

C = 71.26°

To get angle B, we will apply the sine rule, which states that:

a/sineA = b/sineB = c/sineC

Therefore we have

545/sineB = 734/sine71.26

= 545/sineB = 734/0.947

= 545/sineB = 734/0.947

= 545/sineB = 775.08

SineB = 545/775.08

B = sine-¹0.7032

B = 44.68°

Angle A = 180 - (B+C) angle in a triangle

A = 180 - (44.68 + 71.26)

A = 180 - 115.94

A = 64.06°

A = 64.06°

B = 44.68°

C = 71.26°

Angle Rome to Paris = 44.68°

Angle Paris to Berlin = 71.26°

Angle Berlin to Rome = 64.06°

Answer:

Step-by-step explanation:

The movement of the airplane can be represented using a triangle. In Triangle PRB, we are required to find Angles P, R and B.

Using Law of Cosines

[tex]cos R=\frac{p^2+b^2-r^2}{2pb} \\cos R=\frac{734^2+697^2-545^2}{2*734*697}\\R=arcCos\left(\frac{734^2+697^2-545^2}{2*734*697}\right)\\R=44.68^0[/tex]

Using law of Sines

[tex]\frac{r}{sin R}=\frac{p}{SIn P} \\\frac{545}{sin 44.68}=\frac{734}{Sin P} \\\text{Cross Multiply}\\545 X Sin P=734 X sin 44.68\\Sin P=\frac{734 X sin 44.68}{545} \\P=arcSin\left(\frac{734 X sin 44.68}{545}\right)\\P=71.26^0[/tex]

Now,

P+R+B=180 degrees (Sum of Angles in a Triangle)

[tex]71.26^0+44.68^0+B=180^0\\B=180^0-[71.26^0+44.68^0]\\B=64.06^0[/tex]

Answer:

do u need help? where is the image?

Step-by-step explanation:

when typing a question, below is a circle with a plus button, this allows to add an article, picture or a document of your work that you need anything help with. hope this helps!

Answer:

(3,-2)

Step-by-step explanation:

reflection over why axis will make the x coordinate positive.

1/5, 7/10, 4/5 you need to change the denomenator

Answer:

A 24

Step-by-step explanation:

Assuming this is a right triangle, we can use the Pythagorean theorem

a^2+ b^2 = c^2

a^2 + 7^2 = 25^2

a^2 +49= 625

Subtract 49 from each side

a^2 +49-49 = 625-29

a^2 = 576

Take the square root of each side

sqrt(a^2) = sqrt(576)

a = 24

Answer:

A

Step-by-step explanation:

C - B < A < C + B

25 - 7 < A < 25 + 7

18 < A < 32

A can have any length between 10 and 32.

In case it's a right angle triangle,

A² = 25² - 7²

A² = 576

A = 24

Answer:

Step-by-step explanation:

Two brothers get three pounds to share is the answee.

2 brothers will share 3 pounds. Divide 3 pounds by 2 people:

3/2 = 1-1/2 pounds per person.

3 brothers will share 2 pounds. Divide 2 pounds by 3 people:

2/3 = 2/3 pounds per person.

The 2 brothers sharing 3 pounds will have more apples each.

The value of the variable 'K' at t = 3 will be 37.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The equation is given below.

K = 13t - 2

The value of the variable K at t = 3 will be given as,

K = 13t - 2

K = 13 x 3 - 2

K = 39 - 2

K = 37

The value of the variable 'K' at t = 3 will be 37.

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