MATHEMATICS HIGH SCHOOL

Find an equation in standard form for the ellipse with the vertical major axis of length 6 and minor axis of length 4

Answers

Answer 1

Answer:

Answer:

x^2/4 +y^2/9 = 1

Step-by-step explanation:

The standard form is ...

(x -h)^2/a^2 +(y -k)^2/b^2 = 1

for an ellipse centered at (h, k) with semi-axis measures "a" and "b". The largest of "a" or "b" is the semi-major axis; the smaller, the semi-minor axis.

Here, the major axis is vertical, so b > a.

Since the center is not given, we assume it is the origin: h = k = 0. The semi-axes are a=2, b=3, so the equation is ...

x^2/4 +y^2/9 = 1

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T/F: Elimination is using multiplication and division to eliminate one variable and solve a system of equations. *

Answers

Hope this helps you

An item is purchased for a wholesale price of $48 and will be sold at a 55 percent markup. Which expression should be used to find the amount of the markup?

Answers

Answer:

The answer is 48(0.55) x 48

Answer:

The answer is 48(0.55) x 48

Step-by-step explanation:

wholesale $48 and sold at 55% which is the same as 0.55 then multiply wholesale by percent

Solve each system using substitution x=-2y=1 x=y-5

Answers

You solve either one for y,but I chose the second one.
Add 5 to both sides and you get
X+5=y
Plug this in to the first equation
X=-2(x+5)+1
I am assuming that is plus one instead of equal since the keys are near each other on a phone.
Back to the math: use the distributive property to get
X=-2x-10+1 now combine terms
X=-2x-9
Add 2x to both sides to get
3x=9
Divide both sides by 3 to get
X=3
Now plug 3 in as x in any of the above
I will choose the second one again
So 3=y-5 subtract 5 from both sides to get
Y=8
So the solution is (3,8)

How many solutions are there to the equation below?

12x+6=5x

Answers

Answer: There is one solution to the given equation.

Step-by-step explanation: We are given to find the number of solutions to the following equation :

$12x+6=5x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Since the given equation is linear in one variable x, so it will have only one solution.

The solution of equation (i) is given by

$12x+6=5x\n\n\Rightarrow 12x-5x=-6\n\n\Rightarrow 7x=-6\n\n\Rightarrow x=-(6)/(7).$

Thus, there is one solution to the given equation.

The difference of two numbers is 11 and their product is 42.find these numbers.

Answers

$\left\{\begin{array}{ccc}x-y=11&\to x=y+11\nx\cdot y=42\end{array}\right\n\n(y+11)y=42\ny^2+11y-42=0\ny^2+14y-3y-42=0\ny(y+14)-3(y+14)=0\n(y+14)(y-3)=0\iff y=-14\ \vee\ y=3\n\nx=-14+11=-3\ \vee\ x=3+11=14\n\nAnswer:-3\ and\ -14\ or\ 14\ and\ 3$

$a-b=11\n a=11+b \n ab=42 \n(11+b)*b=42 \n b^2+11b=42 \n b^2+11b-42=0 \n b^2 +14b-3b -42=0 \n b(b+14)-3(b+14)=0 \n (b+14)(b-3)=0 \n b+14=0 \ b-3=0 \nb= -14 \ b=3$ $a=11+b \n 1)a=11-14 \na=-3 \n 2)a=11+3 \n a=14$

The number 24 has eight factors.

True
False

Answers

The factors for 24 are 1,2,3,4,6,8,12,24 so true

the factors are 1 and 24, 2 and 12, 3 and 8, 4 and 6 therefore it is true

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Whats 416 divided by 3 with remainder

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