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2 years ago

What is the VERTEX of the quadratic y = 2

Mathematics

2 answers:

Viktor [21]2 years ago

8 0

Answer:

the vertex is located at (-4, 1)

Step-by-step explanation:

The vertex equation of a vertical parabola is

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

where (h, k) is the vertex.

Comparing this to the given

y = 2(x + 4)² + 1, we see that the vertex is located at (-4, 1) and that the graph is stretched vertically by a factor of 2.

RSB [31]2 years ago

4 0

Answer:

The vertex is ( -4,1)

Step-by-step explanation:

The equation for a parabola can be written as

y = a( x-h)^2 +k where ( h,k) is the vertex

y = 2 (x + 4)² + 1

Rewriting

y = 2 (x - -4)² + 1

The vertex is ( -4,1)

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Given sample set A= {1,2,3,4,5} how many items are in the complement of set B if set B= all numbers greater than 2? (30 pts)

neonofarm [45]

Alright, so first we need to establish two things.

First, the compliment of a set is like the extreme opposite; everything that is not in set B will be in the complement.

Second, we need to find out what B is.

Okay, so B is everything that is greater than 2, that's given. That includes 3, 4, and 5. B = {3, 4, 5}. There are three items in this set.

The numbers that aren't included are 1 and 2. The complement of B, let's call this C I guess, is C = {1, 2}. There are 2 items in this set.

The answer, I believe, is <em>two</em>. Hope this helps!

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2 years ago

When 7 is subtracted from 3 times a certain number , the result is 28. What is the number

pychu [463]

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5 0

2 years ago

25 POINTS!!!!!!

8_murik_8 [283]

Your anwer is C)<span>f(x) = 467(5 to the one fourth power)4x</span>

7 0

2 years ago

Read 2 more answers

A line joins the point

Harrizon [31]

Intersection of the first two lines:

$\begin{cases}5x - 2y + 3 = 0\\4x - 3y + 1 = 0\end{cases}$

Multiply the first equation by 4 and the second by 5:

$\begin{cases}20x - 8y + 12 = 0\\20x - 15y + 5 = 0\end{cases}$

Subtract the two equations:

$(20x - 8y + 12)-(20x - 15y + 5)=0 \iff 7y+7=0 \iff y=-1$

Plug this value for y in one of the equation, for example the first:

$5x - 2\cdot (-1) + 3 = 0\iff 5x+5=0 \iff x=-1$

So, the first point of intersection is $(-1,-1)$

We can find the intersection of the other two lines in the same way: we start with

$\begin{cases}x=y\\x=3y+4\end{cases}$

Use the fact that x and y are the same to rewrite the second equation as

$x=3x+4 \iff 2x=-4 \iff x=-2$

And since x and y are the same, the second point is $(-2, -2)$

So, we're looking for a line passing through $(-1,-1)$ and $(-2, -2)$ . We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be $y=x$

In the attached figure, line $5x - 2y + 3 = 0$ is light green, line $4x - 3y + 1 = 0$ is dark green, and their intersection is point A.

Simiarly, line $x=y$ is red, line $x = 3y + 4$ is orange, and their intersection is B.

As you can see, the line connecting A and B is the red line itself.

5 0

2 years ago

Write a system of equations to describe the situation below, solve using elimination.

Sedbober [7]

Answer:

The cost of hardbook is $9 and cost of paperback is $5.

Step-by-step explanation:

Let x be the price for hardback book and y be the price for paperback book.

Mr. Yamamoto purchased 42 new hardcover books and 64 new paperback books, which cost a total of $698.

We can write the equation as:

$42x + 64y = 698$

He also purchased 42 new hardcover books and 58 new paperback books, which cost a total of $668.

We can write the equation as:

$42x + 58y = 668$

We have to use the elimination method to solve the two equations.

We eliminate x by subtracting the two equations.

$42x + 64y-(42x + 58y) = 698 - 668\\\Rightarrow 6y = 30\\\Rightarrow y = 5\\42x + 64(5) = 698\\\\\Rightarrow x = \displaystyle\frac{698 - 64(5)}{42}\\\\\Rightarrow x = 9$

Thus, the cost of hardbook is $9 and cost of paperback is $5.

8 0

2 years ago