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Yuliya22 [10]
2 years ago
13

True or false: The graph of y=3x2-3 opens up.

Mathematics
1 answer:
Nady [450]2 years ago
5 0

Answer: True: The graph of y=3x²-3 opens up

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (0,−3)(0,-3)

Focus: (0,−35/12)

Axis of Symmetry: x=0

Directrix: y=−37/12

X={-2, -1, 0, 1, 2}

Y={9, 0, -3, 0, 9

Step-by-step explanation:

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Could someone please help me with this problem?
natima [27]

Answer:

C

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (4, 9) and (x₂, y₂ ) = (12, 20)

m = \frac{20-9}{12-4} = \frac{11}{8} → C

7 0
3 years ago
What are all of the real roots of the following polynomial? f(x) = x4 - 13x2 + 36
GREYUIT [131]
ANSWER

A. -3, -2, 2, and 3

EXPLANATION

The given polynomial function is,

f(x) = {x}^{4} - 13 {x}^{2} + 36

To find the real roots, we equate the function to zero to obtain;

{x}^{4} - 13 {x}^{2} + 36 = 0

We can solve this equation as a quadratic equation in
{x}^{2}.

Thus we rewrite the equation as,

({x}^{2})^{2} - 13 {x}^{2} + 36 = 0

We split the middle term to get,

({x}^{2})^{2} - 9 {x}^{2} - 4 {x}^{2} + 36 = 0.

We factor to get,

{x}^{2} ( {x}^{2} - 9) - 4( {x}^{2} - 9) = 0

We factor to get,

( {x}^{2} - 9)( {x}^{2} - 4) = 0

Either

{x}^{2} - 9 = 0
or

{x}^{2} - 4 = 0

x = \pm \sqrt{9} \: or \: x = \pm \sqrt{4}
x = \pm3 \: or \: x = \pm2

x=-3,-2,2,3

The correct answer is A
5 0
3 years ago
Read 2 more answers
Compute the exact interest on $5,870 at 12% if the money is borrowed from June to December of the same year.
yawa3891 [41]

Answer:

The exact interest on $5,870 at 12% is $410.9

Step-by-step explanation:

From the information provided we know that

Principal amount: $5,870

Interest rate: 12% -> 0.12

Time: 7 months (From June to December)

When you know the principal amount, the rate, and the time, the amount of interest can be calculated by using the formula:

I=P\cdot r\cdot t

where P is principal, r is the rate of interest and t is the time in years.

We need to convert the 7 months into 1 year.

7 \>months \cdot \frac{1 year}{12 months} = \frac{7}{12} year

Now we can use the above formula

I=P\cdot r\cdot t=5870\cdot 0.12 \cdot \frac{7}{12} \\I = 0.12\cdot \frac{7\cdot \:5870}{12}\\I = 0.12\cdot \frac{20545}{6}\\I = \frac{2465.4}{6}\\I = 410.9

Therefore the exact interest on $5,870 at 12% is $410.9

7 0
3 years ago
What are the coordinates of the orthocenter of △JKL with vertices at J(−4, −1) , K(−4, 8) , and L(2, 8) ?
kompoz [17]

Answer:

K(-4,8) is the ortho center.

Step-by-step explanation:

In a right angled triangle, The vertex of the right angle is the ortho center.

Here we are given

J(-4,-1), K(-4,8) & L(2,8)

Using distance formula we get

JK^{2}= (-4+4)^{2}+ (8+1)^{2}=0+81=81

KL^{2}= (-4-2)^{2}+ (8+-8)^{2}=36+0=36

JL^{2}= (-4-2)^{2}+ (8+1)^{2}=36+81=117

So we can say that

JK^2 + KL^2=JL^2

By converse of pythagorean theorem we get

Hence the Vertex of the right angle is K(-4,8)

K(-4,8) is the ortho center.

7 0
3 years ago
Write the equation Of a function who parent function, f(x)=x+8 is shifted 2 units to the right
Juli2301 [7.4K]

Answer:

g(x)=x+6

Step-by-step explanation:

we have

f(x)=x+8

If f(x) is shifted 2 units to the right

then  

The rule of the translation is

g(x)=f(x-2)

so

g(x)=(x-2)+8

g(x)=x+6

5 0
3 years ago
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