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3 years ago

Standard to vertex form -x^2-3x+8

Mathematics

2 answers:

dem82 [27]3 years ago

7 0

F(x) = - (x-(2/3))^2 41/2 = - (x 3/2) ^2

stich3 [128]3 years ago

6 0

The vertex form:

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

(h, k) - vertex

$f(x)=ax^2+bx+c\\\\h=\dfrac{-b}{2a},\ k=f(h)$

We have

$f(x)=-x^2-3x+8\\\\a=-1,\ b=-3,\ c=8\\\\h=\dfrac{-(-3)}{2(-1)}=\dfrac{3}{-2}=-\dfrac{3}{2}\\\\k=f\left(-\dfrac{3}{2}\right)=-\left(-\dfrac{3}{2}\right)^2-3\left(-\dfrac{3}{2}\right)+8=-\dfrac{9}{4}+\dfrac{9}{2}+8\\\\=-\dfrac{9}{4}+\dfrac{18}{4}+\dfrac{32}{4}=\dfrac{-9+18+32}{4}=\dfrac{41}{4}\\\\Answer:f(x)=-\left(x-\left(-\dfrac{2}{3}\right)\right)^2+\dfrac{41}{4}=-\left(x+\dfrac{3}{2}\right)^2+\dfrac{41}{2}$

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when building a house, the number of days required to build is inversely proportional to with the number of workers. One house w

shusha [124]

Use inverse proportion ratio: xy=k

(124)(7)=k
k=868 (this is our constant)

now substitute the constant into the inverse proportion ratio knowing the number of workers

28x=868

solve for x by dividing both sides by 28 to find the time it takes to build the house

x=31 days

so it will take 31 days for 28 workers to build the house

3 0

3 years ago

A student was asked to identify the following numbers as rational or irrational. Determine if the student has made any mistakes.

ioda

Answer:

Yes they are wrong, rational & irrational ones down below.

Step-by-step explanation:

So, lets start this by asking, what is a rational and irrational number?

Rational numbers are literally any numbers that arent pi, e, or other symbols, as well as square roots.

Irrational numbers are exactly the opposite, being the numbers that are symbols, including square roots.

Note that the symbols listed above such as pi are values that are neverending.

Now, using what we know of rational and irrational numbers, let see which answers are rational and which are not.

So, we start off with:

-13/3

I do not see a square root.

I do not see a symbol such as pi either.

It is not a ever going number.(number that continues infinitly)

So -13/3 is a rational number.

Next we have $\sqrt{37}$

immediatly we tell it has a square root.

So $\sqrt{37}$ is a irrational number.

Next we have 0.1234

This is not a every going number.

There isnt a square root.

And it isnt a symbol.

So 0.1234 is a rational number.

Next we have $-\sqrt{100}$

Again, we can immediatly know it has a square root.

So $-\sqrt{100}$ is a irrational number.

Next we have -77

This is not every going.

It doesnt have a square root.

It doesnt have a symbol.

So -77 is a rational number.

Lastly we have $-\sqrt{12}$

Like the other ones, we can imediatly tell it has a square root.

So $-\sqrt{12}$ is a irrational number.

Bascially, to answer further questions, here is the criteria for a number being rational:

It does not have a square root.
It does not have a symbol.
It is not a infinitly going on number.

If one of these criterias are not met, then you know its a irrational number.

Hope this helps! :D

6 0

3 years ago

Calculate the speed of a car that travels 50 km (kilometers) in 30 min (minutes). Question 1 options: 1. 6 km/min (kilometers pe

algol13

The speed of this car is equal to 1.6 km/min.

Given the following data:

Distance = 50 kilometers.

Time = 30 minutes.

To calculate the speed of this car:

Speed can be defined as the distance travelled by an object per unit time and it is usually measured in meter per seconds (m/s). Also, speed has magnitude but no direction and as such it is a scalar quantity.

Mathematically, speed is given by the formula;

$Speed = \frac{distance}{time}$

Substituting the given parameters into the formula, we have;

$Speed = \frac{50}{30}$

Speed = 1.6 km/min.

7 0

2 years ago

One number is three less than a second number. Six times the first is 6 more than 3 times the second. Find the numbers.

Karolina [17]

Step-by-step explanation:

Given,

x = y - 3

Also,

6(y - 3) = 3y + 6

6y - 18 = 3y + 6

6y - 3y = 6 + 18

3y = 24

y = 24/3

y = 8

x = 8 - 3

x = 5

Therefore, the first number is 5 and the second number is 8.

4 0

3 years ago

Basit plate and online Pin Ball game the first time we got our score of 25000 point then he is called 125000 point and third tim

Artemon [7]

Answer:

60000 points per game

Step-by-step explanation:

Basit played an online pin ball game. The first time he got a score of 25000 points than he scored 125000 points and the third time he scored 30,000 . What was his average score per game.

Solution:

Average is used to represent a list of numbers by a single number. This is usually done by summing each of the numbers in the list and then dividing this result by the amount of numbers in the list.

Since Basit, had 3 scores which were 25000 points, 125000 points and 30000 points. To find the average, we sum all the scores and divide the result by 3 (that is because we have 3 scores). Hence:

Average score per game = (25000 + 125000 + 30000) / 3 = 60000 points per game

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3 years ago