1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sergiy2304 [10]
2 years ago
9

Write a linear function f with the values f(-1)=-3 and f(2)=6.

Mathematics
1 answer:
dusya [7]2 years ago
4 0

Answer:

<em>y = 3x</em>

Step-by-step explanation:

<u>Equation of a Line</u>

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

\displaystyle m=\frac{y_2-y_1}{x_2-x_1}

The point-slope form of the equation of a line is:

y - k = m ( x - h )

Where m is the slope and (h,k) is a point through which the line passes.

We are given the following values of the function: f(-1)=-3 and f(2)=6. The points are (-1,-3) and (2,6). The slope is:

\displaystyle m=\frac{6+3}{2+1}=\frac{9}{3}=3

Now find the equation of the line using the second point:

y - 6 = 3 ( x - 2 )

Operating:

y - 6 = 3x - 6

Simplifying:

y = 3x

You might be interested in
I’m confused on what to do next please help
Mekhanik [1.2K]

Answer:

There are 585 adults and children

Step-by-step explanation:

Let the number of adults be a, number of children be c and the number of seniors be a

Amount made per group;

adults; 52 * a = 52a

Children : 26 * c = 26c

Seniors = 20 * s = 20s

Adding all will give 20,490

52a + 20s + 26c = 20 490 ••••(i)

Now let us work with the ratios;

a : s = 6 : 1

a/s = 6/1

a = 6s •••••(ii)

Lastly;

a/c = 4/9

4c = 9a ••••(ii)

We want to get a + c

From the first equation , let’s substitute

52(6s) + 20s + 26c = 20,490

26c = 6.5 (4c)

but 4c = 9a; 6.5(9a)

But a = 6s

So we have; 6.5(9)(6s) = 351s

so we have;

312s + 351s + 20s = 20,490

683s = 20,490

s = 20490/683

s = 30

Recall;

a = 6s = 6 * 30 = 180

4c = 9a

4c = 9 * 180

c = (9 * 180)/4 = 405

So the total number of children and adult is a + c

405 + 180 = 585

3 0
2 years ago
Y = 2x - 8 3x - 2y = 13​
SSSSS [86.1K]

Answer:

{x,y} = {3,-2}

Step-by-step explanation:

// Solve equation [1] for the variable  y

 [1]    y = 2x - 8

// Plug this in for variable  y  in equation [2]

  [2]    3x - 2•(2x-8) = 13

  [2]    -x = -3

// Solve equation [2] for the variable  x

  [2]    x = 3

// By now we know this much :

   x = 3

   y = 2x-8

// Use the  x  value to solve for  y

   y = 2(3)-8 = -2

Solution :

{x,y} = {3,-2}

8 0
3 years ago
Jenna saves $3 for every $13 she earns. Vanessa saves $6 for every $16 she earns. Is Jenna’s ratio of money saved to money earne
Alexxx [7]

Answer:

3/13 and 6/16

Step-by-step explanation:

hope i help

7 0
3 years ago
In the diagram, which pair of angles are alternate interior angles?
Ber [7]
The 5,6,7 answer choice
8 0
3 years ago
SAT scores are normed so that, in any year, the mean of the verbal or math test should be 500 and the standard deviation 100. as
vovangra [49]

Answer:

a) P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)

P(Z>1.25)=1-P(Z

b) P(400

P(-1

P(-1

c) z=-0.842

And if we solve for a we got

a=500 -0.842*100=415.8

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the SAT scores of a population, and for this case we know the distribution for X is given by:

X \sim N(500,100)  

Where \mu=500 and \sigma=100

We are interested on this probability

P(X>625)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)

And we can find this probability using the complement rule and with the normal standard table or excel:

P(Z>1.25)=1-P(Z

Part b

We are interested on this probability

P(400

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(400

And we can find this probability with this difference:

P(-1

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(-1

Part c

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.8   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-0.842

And if we solve for a we got

a=500 -0.842*100=415.8

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.  

8 0
2 years ago
Other questions:
  • Using the following triangle, what is the cosine of angle B?
    15·1 answer
  • Please Help!............................
    10·1 answer
  • Suppose 20 rabbits are taken to an island. the rabbit population then triples every year. the function f(x)
    5·1 answer
  • Peter takes 7 minutes and 30 seconds to run 1 mile. How many miles can he run in 15 minutes?
    13·2 answers
  • At a certain pizza parlor, % of the customers order a pizza containing onions, % of the customer's order a pizza containing saus
    9·1 answer
  • Complete the solution of the equation. find the value of y when x equals -6. -4x + y = 29
    6·1 answer
  • Simplify 5 to the 5th over 5 to the 8th.
    9·1 answer
  • Robert has three jobs. He worked at young's grocery and earned $5,804. He was a waiter at the A &amp; B restaurant and earned $1
    9·1 answer
  • Help plllllllzzzzzzzzzzzzzz
    9·1 answer
  • Five friends including Marlon, purchased two boxes of pizzas. They equally shared the pizza among themselves. How much pizza did
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!