MATHEMATICS
HIGH SCHOOL

Answer:

Answer:

4

Step-by-step explanation:

x butterflies and y dragonflies

4 < x + y 《 8

x = 2y

4 < 2y + y < 8

4 < 3y < 8

Only multiple of 2 between 4 and 8 is 6

So 3y = 6

y = 2

x = 2y = 4

Answer:

Answer:

4 butterflies.

Step-by-step explanation:

Let x be the number of dragonflies, then the number of butterflies = 2x.

As more than half the flowers are occupied by 1 insect:

2x + x > 5.

3x > 5

x > 5/3.

If x = 2 then there are 4 butterflies and 6 of the flowers are occupied.

If x = 3 there are 6 butterflies and 9 flowers are occupied, but there are only 8 flowers, therefore the answer is 4 butterflies.

HIGH SCHOOL

The sum of three consecutive integers is 267. What is the largest integer?

90+89=88= 267

x+x-1+x-2=267

3x-3=267

3x=270

x=90

x+x-1+x-2=267

3x-3=267

3x=270

x=90

Now, the integers are consecutive, one right after/before the next one.

so.. hmmm let's say our first one is "a".

if the first integer is "a", then the next one will be "a+1", one hop over.

and the last one will then be, another hop over, "(a+1)+1", or "a+2".

now, we know they add to 267, ok

and surely you'd know what the others are.

so.. hmmm let's say our first one is "a".

if the first integer is "a", then the next one will be "a+1", one hop over.

and the last one will then be, another hop over, "(a+1)+1", or "a+2".

now, we know they add to 267, ok

and surely you'd know what the others are.

MIDDLE SCHOOL

Which of the following graphs described by the function given below y=3x^2+7x+2

Answer:

*Parabola that opens up

*y-intercept is 2

*x-intercepts are -1/3 and -2

*vertex is (-7/6 , -25/12)

Step-by-step explanation:

I will describe what this graph looks like.

First, the graph is quadratic because it is in the form ax² + bx + c. The function must be in the shape of a parabola. Parabolas look like a "U" shape.

Whether "a" is negative or positive represents of the parabola opens up or down. Since "3" is positive, the parabola opens up.

"c" represents the y-intercept. The y-intercept is when the graph touches the y-axis. The function must have a y-intercept of positive 2.

We can also find its x-intercepts, also called roots/zeroes, by substituting into the quadratic formula (Ignore the Â).

Using the form ax² + bx + c, we know:

a=3; b=7; c=2

Substitute into the formula.

Split the equation at the ± sign.

The graph has x-intercepts -2 and -1/3.

We can find the vertex of the graph. It is the part of the parabola that is the lowest (or highest, is it opens down).

Find the midpoint of the x-intercepts for the vertex x-coordinate:

(-1/3 - 2)/2 = (-1/3 - 6/3)/2 = (-7/3)*(1/2) = -7/6 = -1.167 = x

Substitute the vertex x-coordinate into the formula to find the "y" in vertex.

y=3x²+7x+2

y=3(-7/6)²+7(-7/6)+2

y= 147/36 + (-49/6) + 2

y= 147/36 + (-294/36) + 72/36

y= (147-294+72)/36

y = -75/36

y = -25/12 = -2.083

The vertex is (-7/6 , -25/12) OR about (-1.167, - 2.083).

COLLEGE

Moche started a summer business of mowing lawns. However, before he could mow lawns, he needed to purchase supplies (a lawnmower among other needs). Moche spent $395 gathering necessary materials. He makes on average $60 per lawn, mowed. Write an equation to show Moche his earnings for l lawns mowed.

Answer:

Step-by-step explanation:

Let E be the total earnings .

Cost of mowing 1 lawn = $60

Since he mowed l lawns

So, cost of mowing l lawns =

So, he earned

Now we are also given that he spent $395 gathering necessary materials.

So, the total earnings for l lawns mowed =

So, required expression :

Hence an equation to show Moche his earnings for l lawns mowed is :

Gone money -$395

money per lawn $60

let x be lawn and f()= earnings

f(x)= 60x-396

money per lawn $60

let x be lawn and f()= earnings

f(x)= 60x-396

MIDDLE SCHOOL

Solve the equation. 3(k-5)= -16.

Thanks in advance!

Well, first of all, you have to open up the bracket by multiplying what's outside by what's inside. Anyway;

3k-15=-16

Next, you have to collect the like terms and put them together. And the -15 becomes +15. So;

3k=-16+15

3k=-1

Next, you have to divide the both sides by 3. So;

3k/3=-1/3

k=-1/3

So your answer is -1/3. Hope i helped. Have a nice day.

3k-15=-16

Next, you have to collect the like terms and put them together. And the -15 becomes +15. So;

3k=-16+15

3k=-1

Next, you have to divide the both sides by 3. So;

3k/3=-1/3

k=-1/3

So your answer is -1/3. Hope i helped. Have a nice day.

Multiply out the brackets:

3k - 15 = -16

put the k on one side by itself

3k = -1

divide both sides by 3 to get 1k

k = -1/3

3k - 15 = -16

put the k on one side by itself

3k = -1

divide both sides by 3 to get 1k

k = -1/3