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3 years ago

If the value of a in the quadratic function f(x) = ax^2 + bx + c is 1/2, the function will:

Mathematics

2 answers:

TiliK225 [7]3 years ago

7 0

Answer:

Open up and have a minimum

Step-by-step explanation:

If the x² coefficient is:

Positive, the graph will open up and have a minimum

Negative, the gaph will open down and have a maximum

guajiro [1.7K]3 years ago

6 0

Answer:

opens up and has a minimum

Step-by-step explanation:

Provided a is not 0, y=ax^2+bx+c will be a parabola.

The parabola will open up and have a minimum if a is positive.

The parabola will open down and have a maximum if a is negative.

Since 1/2 is positive, then your parabola opens up and has a minimum.

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a restaurant served 40 specials in all , 36 of which were the salmon filet . what percentage of the specials were salmon filets?

REY [17]

To find the percentage, you need to divide the 36 by the 40. So 36/40=0.9
0.9=90%

5 0

3 years ago

How high is the peak of the Matterhorn? Below is a picture of the Matterhorn in Switzerland. As a surveyor, it is your job to es

Oxana [17]

Answer:

$E\approx14,962\text{ feet}$

Step-by-step explanation:

Please refer to the attachment below.

As shown, we can split the diagram into a scalene triangle and a right triangle.

The strategy here is to use the Law of Sines to find x, then use right triangle ratios to find h, the height of Matterhorn (with respect to our elevation).

Let’s start with the scalene triangle.

To use the Law of Sines, we will need two angles and the sides opposite to the angles.

Since we need to find x, we need the angle opposite to x. This is already given to us as 30°.

We can use the side that measures 1,500. The angle opposite to it θ is unknown.

So, we will need to determine θ. From supplementary angles, we know that:

$\alpha+35=180$

So, it follows that:

$\alpha=145^\circ$

The interior angles of a triangle always sum to 180°. Hence:

$30+\alpha+\theta=180$

By substitution:

$30+145+\theta=180$

Hence:

$\theta=5^\circ$

Now, we can use the Law of Sines, given by:

$\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}$

It is important to align the angles correctly with the sides.

So, we will substitute θ = 5° for A and 1,500 for a.

And we will substitute 30° for B and x for b. Hence:

$\displaystyle \frac{\sin(5^\circ)}{1,500}=\frac{\sin(30^\circ)}{x}$

Solve for x. Cross-multiply:

$x\sin(5^\circ)=1500\sin(30^\circ)$

Hence:

$\displaystyle x=\frac{1500\sin(30^\circ)}{\sin(5^\circ)}$

When doing trigonometry (or any math, really), try not to round intermediate values, as this may result in inaccuracies in the final answer. Hence, we will leave this as is.

Now, we can use the right triangle.

We know that an angle is 35°.

The height h is opposite to our angle.

And x was our hypotenuse. Therefore, we can use the sine ratio given by:

$\displaystyle \sin(x^\circ)=\frac{\text{Opposite}}{\text{Hypotenuse}}$

In this case, our angle is 35°.

The opposite side is h.

And the hypotenuse is x. Hence, by substitution:

$\displaystyle \sin(35^\circ)=\frac{h}{x}$

Solve for h. Multiply both sides by x:

$h=x\sin(35^\circ)$

Since we already know the value of x:

$\displaystyle h=\frac{1500\sin(30^\circ)}{\sin(5^\circ)}\cdot\sin(35^\circ)$

Simplify. So, the height of Matterhorn with respect to our current elevation is:

$\displaystyle h =\frac{1500\sin(30^\circ)\sin(35^\circ)}{\sin(5^\circ)}$

The total elevation of Matterhorn will be the current elevation of the surveyor plus the height with respect to the current elevation or simply h. So, the elevation height is:

$E=9756+h$

By substitution:

$\displaystyle E=9756+\frac{1500\sin(30^\circ)\sin(35^\circ)}{\sin(5^\circ)}$

Now we may approximate. Use a calculator. So, the total elevation of Matterhorn is:

$E=14961.78867...\approx14,962\text{ feet}$

3 0

2 years ago

A(n) _____ generally has a highly elliptical orbit. A. moon B. comet C. planet D. asteroid

Nookie1986 [14]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Need help saying Korean

Talja [164]

Answer: koh-rien

Step-by-step explanation:

6 0

3 years ago

3 groups of students went to the burger barn for a study break and snack. the first group ordered 4 burgers, 5 fries, and 7 drin

lora16 [44]

Answer:

Cost of one burger, a = $3.35

Cost of one fries, b = $0.9

Cost of one drink, c = $1.1

Step-by-step explanation:

Let

a be cost of one burger

b be the cost of on fry

c be the cost of on drink

So for the 1st group, 4a+5b+7c = $25.60 -----------(1)

for the 2st group, 8a+5b+6c = $37.90 ----------(2)

for the3st group, 12a+10b+11c = $61.30 ----------(3)

Now solving (1) and (2)

That is (1) x 2 - (2) gives,

5b+8c = 13.80 ----------------------(4)

Now, (1) x 3 - (3), we get

5b+10c = 15.5 ---------------------(5)

Solving (4) and (5), we get

c = 1.1

Now putting c in equation (4), we get

b = 0.9

Now from (1), we get

4a+5b+7c = $25.60

4a+5(0.9)+7(1.1) = $25.60

a = 3.35

Cost of one burger, a = $3.35

Cost of one fries, b = $0.9

Cost of one drink, c = $1.1

7 0

3 years ago