MATHEMATICS HIGH SCHOOL

Question olve the following quadratic by factoring. a^(2)-4a-12=0

Answers

Answer 1

Answer:

Answer:

a = - 2 , a = 6

Step-by-step explanation:

a² - 4a - 12 = 0

consider the factors of the constant term (- 12) which sum to give the coefficient of the a- term (- 4)

the factors are + 2 and - 6, since

+ 2 × - 6 = - 12 and + 2 - 6 = - 4

use these factors to split the a- term

a² + 2a - 6a - 12 = 0 ( factor the first/second and third/fourth terms )

a(a + 2) - 6(a + 2) = 0 ← factor out common factor (a + 2) from each term

(a + 2)(a - 6) = 0 ← in factored form

equate each factor to zero and solve for a

a + 2 = 0 ( subtract 2 from each side )

a = - 2

a - 6 = 0 ( add 6 to both sides )

a = 6

solutions are a = - 2 , a = 6

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My sister is 14 years old. my brother says that his age minus 12 equal to my sister's age.
One side of a triangular garden is x feet long. The other two sides of the garden are both 5 feet less than twice the length of the first side of the garden.Part A: Write a simpiflied expression for perimeter, in feet, of the garden. A fence is placed along the entire perimeter of the triangular garden. The roll of fencing is 40 ft long. Part B: Write a simplified expression to show the amount of fencing, in feet, which is left from the roll of fencing.
If f(x)=x^2-5 and g(x)=6x then g(f(x)) is equal to
What is 9 times 3/4?

3 in
9 in
13 in
Surface Area =

Help also explain please

Answers

To find surface area we can do 2(l)(w) + 2(l)(h) + 2(h)(w). l = length; w = width; h = height.

Next

Plug in 3 for length, 9 for height, and 13 for width. ( or however you’d like for width length height but only one number can be represented by h, l, and w.)

Then we add all the numbers
2(3)(13)+ 2(3)(9) + 2(9)(13) = SA (surface area)

78 + 54 + 234 = 366 in^2 or 366 sq. inches

Final answer:

The given dimensions are of a rectangular prism, and the surface area can be calculated using the formula 2lw + 2lh + 2wh, which gives 366 square inches for a prism with dimensions 13 inches, 9 inches, and 3 inches.

Explanation:

The numbers given, 3 inches, 9 inches, and 13 inches, are usually the dimensions of a rectangular prism, which is a type of box shape. The Surface Area of a rectangular prism is given by the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Based on the numbers given, we can see that :

The length l=13 inches
The width w=9 inches
The height h=3 inches.

So, substitute these values into the formula:

Surface area = 2lw + 2lh + 2wh = 2(13x9) + 2(13x3) + 2(9x3) = 234 + 78 + 54 = 366 square inches.

This means the surface area of the box is 366 square inches. The surface area of a shape is a measure of the total area that the surface of the shape covers.

Learn more about Surface Area of Rectangular Prism here:

brainly.com/question/31454778

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Which term is a term in this expression? -3x-7(x+4)

Answers

-7 is the term in the given expression in this problem

Cos3x=4cos^3x-3cosx prove

Answers

$\bf cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)\n\n\n\textit{also recall that }cos(2\theta)=\begin{cases}cos^2(\theta)-sin^2(\theta)\n1-2sin^2(\theta)\n\boxed{2cos^2(\theta)-1}\end{cases}\n\n\nand\qquad sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\n\n-------------------------------$

$\bf cos(3x)=4cos^3(x)-3cos(x)\n\n-------------------------------\n\ncos(3x)\implies cos(2x+x)\implies cos(2x)cos(x)-sin(2x)sin(x)\n\n\n\[2cos^2(x)-1]cos(x)-[2sin(x)cos(x)]sin(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2sin^2(x)cos(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2[1-cos^2(x)]cos(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~[2cos(x)-2cos^3(x)]\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2cos(x)+2cos^3(x)\n\n\n4cos^3(x)-3cos(x)$

19. In order for a button to fit through its buttonhole, the hole needs to be the size of the button's diameter. What size buttonhole is needed for a button with a circumference of 9.42 centimeters? A. 3 centimeters B. 1.5 centimeters C. 4 centimeters D. 6 centimeters

Answers

Answer:

The size of the buttonhole should be 3 cm.

Step-by-step explanation:

The circumference is given by = $2\pi r$ where r is the radius of the circle.

Given is -

The circumference is given as = 9.42 cm

We can put this value in the formula and get;

$9.42=2\pi r$

=> $9.42=2*3.14* r$

=> $9.42=6.28r$

$r=(9.42)/(6.28)$

r = 1.5 cm

As given that the hole needs to be the size of the button's diameter.

So, diameter = $1.5*2=3$ cm

Therefore, the answer is 3 cm.

A. 3 cm
Because the circumference is equal to diameter times pi
9.42 divide by 3.14 is 3

salma purchased a prepaid phone card for $20. long distance calls cost 24 cents a minute using this card. salma used her card only once to make a long distance call. if the remaining credit on her card is $13.52. how many minutes did her call last?

Answers

We can set up an equation to solve this problem, but first we need to write out what we know.

$20 overall
$0.24 every minute
$13.52 remaining on the card

Now that we know our information, we can set it up in an equation.

20 - 0.24x = 13.52

The 20 represents $20 overall when she first got the phone card.
We are then subtracting $20 from how must it costs a minute (which is 24 cents). The 'x' indicates the number we are trying to find (how many minutes her call lasted). Lastly, 13.52 is the result of everything, since she has $13.52 remaining on the card.

We can now solve the equation:

20 - 0.24x = 13.52
-0.24x = 13.52 - 20 /// subtract 20 from each side
-0.24x = -6.48 /// simplify
x = 27 /// divide each side by -0.24

Our solution is: x = 27.

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An easier way to solve this problem would be to first, subtract the total amount of money she had on the card when she first got it, and then the remaining total she ended up with.

$20 - $13.52 = $6.48

So, she spent a total of $6.48 on long distance calls, but since we are looking for how many minutes, we need to divide the total she spent and how much it costs per minute.

6.48 ÷ 24 = 27

We receive the same amount of minutes spent just like we did the last way we solved.

-----

Salma spent 27 minutes on the phone.

The endpoint of MP are M(2,1) and P(14,10). If point K partitions MP in aratio of MK:KP=3:2, what are the coordinates of K?

Answers

Answer: The required co-ordinates of he point K are (9.2, 7).

Step-by-step explanation: Given that the the endpoint of MP are M(2,1) and P(14,10) and the point K partitions MP in the ratio of MK : KP = 3 : 2.

We are to find the co-ordinates of point K.

We know that

the co-ordinates of a point that divides the line joining the points (a, b) and (c, d) in the ratio m : n are given by

$\left((mc+na)/(m+n),(md+nb)/(2)\right).$