Determine whether the vectors u and v are parallel, orthogonal, or neither.u = <10, 6>, v = <9, 5>

Answers

Answer 1

Answer: $\mathbf u\cdot\mathbf v=\|\mathbf u\|\|\mathbf v\|\cos\theta$

where $\theta$ is the angle between the vectors. You have

$10*9+6*5=√(10^2+6^2)√(9^2+5^2)\cos\theta\iff \cos\theta=(30)/(√(901))\implies \theta\approx1.909^\circ$

The vectors would be orthogonal if the dot product had been zero, but that's clearly not the case.

They would be parallel if the angle turned out to be $0^\circ$ or $180^\circ$ , but that's also not the case.

So the answer is neither.

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Walters savings account has a balance of $273. After 5 years, what will the amount of interest be at 5% compounded quarterly?

Answers

The answer is $350

The formula is as follows: $P(1+r/n) ^(nt)$

P: Principal Amount : $273
r: Rate of interest: 5%
n: number of times the interest is compounded: 4 (Since Quarterly)
t: number of years : 5

A triangular banner has an area of 351cm2. The length of the base is two centimeters longer than four times the height. Find the height and length of the base.

Answers

Answer:

h = 13cm and b= 54cm.

Step-by-step explanation:

We have that the area $A=351cm^2$ and the base is two centimeters longer than four times the height, that is

$b = 2+4h$

where b is the base and h the height. Now, the area is

$A=(b*h)/(2)$

$351=((2+4h)h)/(2)$

$702=2h+4h^2$

$4h^2+2h-702=0$ .

Now, we are going to use the general formula to solve quadratic ecuations:

$h=(-b\pm√(b^2-4ac))/(2a)$

where a=4, b= 2 and c= -702.

$h=(-2\pm√(2^2-4(4)(-702)))/(2*4)$

$h=(-2\pm√(4+11232))/(8)$

$h=(-2\pm106)/(8)$

$h=(-2+106)/(8)$ or $h=(-2-106)/(8)$

As we are searching for the lenght, we choose the positive result:

$h=(-2+106)/(8)=13cm$

$b=2+4h = 2+52 = 54cm$ .

Help pleaseee! Thank you

Answers

Answer:

Step-by-step explanation:

width of a rectangle=11 cm=11*5=55 ft

length of rectangle =8 cm= 8*5=40

Area=55*40=2220 ft²

height=3 cm=3*5=15

base=11 cm=11*5=55

Area of a triangle=base*height/2=15*55/2= ft^2

2220+412.5=2632.5 ft^2

this number is close to 2615 if the square unit on the grid =1 cm

Claire has $300 in her account she decided she is going to take out half of what is left in there at the end of each month

Answers

300 divided by two is 150 so your answer would be 150 dollars

Explain how the position of the decimal point changes in a quotient as you divide by increasing powers of ten.

Answers

When you divide by increasing powers of ten, the decimal moves one digit to the left.

Example:
1/10=0.1
1/100=0.01
1/1000=0.001

As the powers of ten increases, the decimal moves to the left.

each time you times a number with a decimal point by 10 the point will move to right one space

Which function has real zeros at x = –8 and x = 5?g(x) = x2 + 3x – 40
g(x) = x2 + 3x + 40
g(x) = x2 + 14x – 40
g(x) = x2 + 14x + 40

Answers

Hello,

sum=-8+5=-3
prod=-8*5=-40

==>x²+3x-40

Answer A

Answer:The answer is A

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