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2 years ago

Which function has a vertex at the origin?

Mathematics

1 answer:

Rudik [331]2 years ago

5 0

Answer:

$f(x)=-x^2$

Step-by-step explanation:

Vertex form of a quadratic function:

$f(x)=a(x-h)^2+k$

where:

(h, k) is the vertex
a is some constant

If the vertex is at the origin, then (h, k) = (0, 0)

$\implies f(x)=a(x-0)^2+0$

$\implies f(x)=ax^2$

Comparing this with the answer options suggests that the function with a vertex at the origin is $f(x)=-x^2$

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Two adjacent angles of a rhombus as in the ratio 2:3. Eind all the a angles of the rombus

Tomtit [17]

Answer:

Let the adjacent angles of the rhombus be 2x and 3x. We know that the sum of the measures of the adjacent angles is equal to 180°. AD = DC = 3 × 36° = 108°. Hence , the angles of the rhombus are 72° , 108° , 72° and 108°.

Step-by-step explanation:

6 0

2 years ago

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FIND THE VALUE OF X l m a o ignore the cursor xD

Mrac [35]

Answer:

x=10

Step-by-step explanation:

the angle is 90 degrees

90-29=61

61-1=60

60÷6=5

x=10

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5 0

2 years ago

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An instructor in a college class recently gave an exam that was worth a total of 100 points. The instructor inadvertently made t

solniwko [45]

Answer:

B) Method 2 will increase the standard deviation of the students' scores.

Step-by-step explanation:

Given that an instructor in a college class recently gave an exam that was worth a total of 100 points.

The average score for his students was 43 and the standard deviation of the scores was 5 points.

And now he is considering two different strategies for rescaling the exam results of which:

Method 1 = Add 17 points to everyone's score.

Method 2 = Multiply everyone's score by 1.7 .

And we have to check what will be the impact of these methods on the standard deviation of the students' scores.

For this let us consider a simple example to understand this:

Firstly, Formula for calculating Standard Deviation = $\sqrt{\frac{\sum (X-Xbar)^{2}}{n-1}}$

Suppose,

X X - Xbar $(X - Xbar)^{2}$

3 3 - 6 = -3 -3 * -3 = 9

5 5 - 6 = -1 -1 * -1 = 1

10 10 - 6 = 4 4 * 4 = 16

Mean of above data, Xbar = $\frac{3+ 5+10}{3}$ = 6

Standard Deviation of data = $\sqrt{\frac{26}{3-1} }$ = 3.6055

Now let us suppose that we multiply each value of above data with 2 so the new data will be:

X X - Xbar $(X - Xbar)^{2}$

3*2 = 6 6 - 12 = -6 -6 * -6 = 36

5*2 = 10 10 - 12 = -2 -2 * -2 = 4

10*2 =20 20 - 12 = 8 8 * 8 = 64

Mean of new data, Xbar = $\frac{6+ 10+20}{3}$ = 12

Standard Deviation of new data = $\sqrt{\frac{104}{3-1} }$ = 7.2111

Hence, we see that when we multiply any value to the data the standard deviation will increase and in other words it will multiplied by that value which value we multiplied with each data value i.e. when we multiply each data value with 2 the standard deviation also get multiplied by as

3.6055 * 2 = 7.2111

Therefore option B is correct that Method 2 will increase the standard deviation of the students' scores.

And on the other hand Similarly by adding any constant to the data the Standard Deviation will remain same. Therefore Method 1 will have no impact on standard deviation of the students' scores.

8 0

3 years ago

A plumber charges $90 per hour and a $50 travel fee.

Fittoniya [83]

Okay so subtract 50 from both sides and you would get 360=90x and then divide each side by 90 and you would get x= 4 so it took 4 hours

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3 years ago

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The zeroes are quadratic functions are 6 and -4 which of these could be the functons.

LenaWriter [7]

Answer:

6 is the answer of your question