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2 years ago

Factorise 3a squared + 7a

2 answers:

3 0

GCF: 1 (3 cant go into 7 and the other way around in whole number terms.)
So, 1 is the factor you are distributing.
1 goes into 3 three times.
1 goes into 7 seven times.
Don't forget your variable!

So the answer is: a(3a+ 7).

Aleks [24]2 years ago

3 0

To factorise this we have to first find the biggest common factor. 3 and 7 are both are prime numbers so we can't factorise it by a number. but both numbers have an 'a' so we have to factorise it by a. hence the answer is,
a(3a+7).
hope it helps.

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PROBLEM SOLVING You are participating in an orienteering competition. The diagram shows the position of a river that cuts throug

Wewaii [24]

Answer:

The shortest distance is 2.2 miles

Step-by-step explanation:

we know that

The shortest distance you must travel to reach the river is the perpendicular distance to the river

step 1

Find the slope of the line perpendicular to the river

we have

$y=3x+2$

The slope of the river is m=3

Remember that if two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

therefore

The slope of the line perpendicular to the river is

$m=-1/3$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-1/3$

$point(2,1)$

substitute

$y-1=-(1/3)(x-2)$

step 3

Find the intersection point of the river and the line perpendicular to the river

we have

$y=3x+2$ ------> equation A

$y-1=-(1/3)(x-2)$ -----> equation B

Solve the system by graphing

The intersection point is (-0.1,1,7)

see the attached figure

step 3

Find the distance between the points (2,1) and (-0,1,1.7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$d=\sqrt{(1.7-1)^{2}+(-0.1-2)^{2}}$

$d=\sqrt{(0.7)^{2}+(-2.1)^{2}}$

$d=2.2\ miles$

6 0

2 years ago

Greg bought 2 boxes of balloons he used half of them to decorate his yard he used 40 to decorate his porch he used the rest insi

german

Well, he used one box to decorate his yard, that's for sure. Then he used 40 from the other box to decorate his porch and the rest inside his house. That rest might be anything between 1 and infinity. So there were at least 41 balloons in each box. I think the question is incomplete, please doublecheck it so I'll be able to give you more specific result.

8 0

2 years ago

Suppose that you bet $5 on each of a sequence of 50 independent fair games. Use the central limit theorem to approximate the pro

amm1812

Answer:

chances chances of happening = 0.0119

Step-by-step explanation:

given data

bet = $5

independent fair games = 50

solution

we will think game as the normal distribution

so here mean is will be

mean = $\frac{50}{2}$

mean = 25

and standard deviation will be

standard deviation = $\sqrt{50*0.5*0.5}$

standard deviation = 3.536

we have to lose 33 out of 50 time for lose more than $75

so as chance of doing things z score is

z score = $\frac{33-25}{3.536}$

z score = 2.26

so from z table

chances chances of this happening = 0.0119

8 0

2 years ago

Mrs. Adams deposited $12,000 into an account that earns an annual simple interest rate of 3.25%. She makes no other deposits or

lisabon 2012 [21]

Answer:

<em>Mrs. Adams will earn $3,120 of interest at the end of year 8.</em>

Step-by-step explanation:

<u>Simple Interest</u>

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We can calculate the interests earned by an investment of value A in a period of time t, at an interest rate r with the formula:

$I=A.r.t$

Mrs. Adams deposited an amount of A=$12,000 into an account that earns an annual simple interest rate of r=3.25%. We must find the interest earned in t=8 years. The interest rate is converted to decimal as:

$r=3.25/100=0.0325$