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lana [24]
3 years ago
8

Olivia is making model cars to go on shelves in her room. The number of wheels she uses is a function of how many cars she makes

: if she makes 1 car, she uses 4 wheels; if she makes 2 cars, she uses 8 wheels; if she makes 3 cars, she uses 12 wheels; and so on. She has exactly 28 wheels she can use to make cars. What is the domain and range for the function?
Mathematics
1 answer:
Luba_88 [7]3 years ago
3 0

Answer:

Domain = 1 to 7

Range = 4 to 28

Step-by-step explanation:

Given that:

Number of wheels used is a function of number of cars manufactured.

Number of wheels present = 28

1 car uses 4 wheels

2 cars use 8 wheels.

3 car uses 12 wheels

and so on.

Let the function be of the form:

y =f(x)

Domain of the function is the value of x that can be given as valid input to the function.

Range of the function is the value of y that can be output of the function.

Let x be the number of cars manufactured.

Then value of y is nothing but x times 4.

y=4x

We are given that maximum value of y can be 28.

28 = 4x\\\Rightarrow x =7

Therefore, maximum value of input can be 7.

Minimum number of wheels can be 4 to make a minimum of 1 car.

Therefore domain is 4 to 28 and range is 1 to 7.

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What are the correct answers?
DochEvi [55]

Step-by-step Answer:

Situations with dot-products.

dot-product of vectors A<xa,ya>, B<xb,yb>

is defined as A.B=xa*xb + ya+yb

Note that the result is a scalar even though A and B are both vectors.

Q1 dot product is positive

Q2 dot product is negative

The dot product is also equal to the length of the projection of the unit vector of one onto the other, multiplied by the magnitudes.  This implies that the sign will be positive if the angle between the vectors is acute, and negative if the angle between them is obtuse.  That makes the first two proposed answers (A, B) correct.

Q3 dot product equals 0

Since the projection of any vector onto another perpendicular to it is zero, so the dot product of two perpendicular vectors always equal zero.  That makes the third proposed answer (E) correct.

Q4 dot product equals the product of the vectors' magnitudes.

The earlier statement

"The dot product is also equal to the length of the projection of the unit vector of one onto the other, multiplied by the magnitudes."

makes the fourth statement true if the unit vector projected onto the other remains a unit vector, i.e. when the two vectors are parallel (D)

Q5 dot product equals opposite of the product of the vectors.

To have the dot product's absolute value equal the product of the magnitudes, the vectors must be parallel.  If the dot product is positive, then the vectors are parallel and pointing in the same direction, as in Q4.

If the dot product is negative, meaning that is the opposite of the product of the magnitudes (themselves are always positive or zero), then the vectors are parallel, but in the opposing directions.

There is no correct answer for this case, which is definitely NOT "not possible".  The closest one is (D) vectors are parallel, but answer is incomplete.

Q6 dot product is greater than the product of the vectors' magnitudes.

I do not see a possible case for this to happen.


6 0
3 years ago
The common factor to 18xy and 24 y
vladimir1956 [14]
18xy + 24y = 6y(3x + 8)

The common factor is 6y
6 0
2 years ago
Margaret deposits $1,000 in a savings account that pays 1.4% interest compounded
ozzi

Answer:

The balance after 1 year is;

$1,014.05

Step-by-step explanation:

To do this, we use the compound interest formula

That will be ;

A =P (1 + r/n)^nt

A is the amount generated which we want to calculate

r is the rate = 1.4% = 0.014

P is the amount deposited = $1,000

n is the number of times it is compounded annually which is 2 (semi-annually means 2 times in a year)

this the number of years which is 1

we have this as:

A = 1,000( 1 + 0.014/2)^(2*1)

A = 1,000(1 + 0.007)^2

A = 1,000(1.007)^2

A = $1,014.05

8 0
3 years ago
The house numbers on the North side of Flynn Street are even. In one block, the house numbers begin 1022, 1032, 1042, 1052. What
Gnom [1K]
The series 1022,1032,1042,1052....

a1=a=1022
d=a2-a1=1032-1022=10
n=5 as 5th term

Sn= a+(n-1)d
= 1022+(5-1)10
= 1022+40
= 1062
Next house will have 1062 as number.
3 0
3 years ago
What is the slope of the line passing through the points ( −3 , 4 ) and ( 4, −1 )?
ziro4ka [17]
Slope = (y2 - y1)/(x2 - x1) = (-1 - 4)/(4 - (-3)) = -5/(4 + 3) = -5/7
4 0
3 years ago
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