The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire. If a wire 433 ft long and 4 mm in diameter has a resistance of 1.22 ohms, find the length of a wire of the same material whose resistance is 1.43 ohms and whose diameter is 5 mm.

Ok, so:

We know that the scale given is the next one:

1cm = 7miles.

Now, let me draw something here below:

So, the cities are separated by a distance of 102.2 miles.

If 1 cm = 7 miles,

Then, we're going to convert 102.2 miles to our map scale.

102.2 miles * ( 1cm / 7 miles).

And we obtain:

14.6cm

Answer:

15.6 MPG

Step-by-step explanation:

You start a trip when your odometer reads 23,672 miles, and you have a full tank of gas. After driving a few hours, you fill up your tank. If you buy 16.5 gallons and your odometer reads 23,927, how many miles to the gallon are you getting, rounded to the nearest tenth of a gallon.

You went 23,927 - 23,672 = 255 miles

Because you started on a full tank, you went 255 miles on 16.5 gallons

to figure MPG:

255/16.5 = 15.4545... MPG

rounded to nearest 10th of gallon:

15.6 MPG

Answer:

1. Increasing on ( -inf, -3] and ( 3, inf)

2. decreasing on (-3, 3]

3. Local maximum: 60, Local minimum: -60

4. Domain: (-inf , inf)

Range: [-60, 60]

Explanation:

1.

A function is increasing when its slope is positive. Now, in our case we can see that the slope of f(x) is postive from - infinity to -3 and then it is negatvie from -3 to 3; it again increasing from 3 to infinity.

Therefore, we c

The value of the composition (g ° f) (x) between the linear equation g(x) and the quadratic equation f(x) evaluated at x = 5 is equal to 6.

In this problem we find a quadratic equation f(x) and a linear equation g(x), of which we must derive a composition consisting in substituting the input variable of the linear equation with the quadratic equation. Later, we evaluate the resulting expression at x = 5.  

Now we present the complete procedure:

(g ° f) (x) = - 2 · (x² - 6 · x + 2)

(g ° f) (x) = - 2 · x² + 12 · x - 4

(g ° f) (5) = - 2 · 5² + 12 · 5 - 4

(g ° f) (5) = - 50 + 60 - 4

(g ° f) (5) = 6

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Firstly Example of Distributive property can be shown below.

GIiven: 6(9 - 4)

6 x 9 - 6 x 4

54 - 24 = 30

a) 3(50.15)

3(50 + 0.15)

3x50 + 3 x0.15

150 + 0.45 = 150.45

(b) 5(108)

5(100 + 8)

5x100 + 5x8

500 + 40 = 540

Answer: y = -3x - 21

Step-by-step explanation:

Slope intercept form: y = mx + b

m is the slope, and b is the y-intercept.

y + 8 = -3(x + 7)

Start by distributing -3 into the parenthesis.

y + 8 = -3x - 21

subtract 8 from both sides to get the final answer.

y = -3x - 29

Answer:

Slope-intercept form,

Step-by-step explanation:

Now we have to,

→ Rewrite the given equation in the slope-intercept form.

The slope-intercept form is,

→ y = mx + b

The equation is,

→ y + 8 = -3(x + 7)

Then the value of y will be,

→ y + 8 = -3(x + 7)

→ y + 8 = -3x - 21

→ y = -3x - 21 - 8

→ [ y = -3x - 29 ]

Hence, answer is y = -3x - 29.

To find the median of the composite numbers, we will first have to sort the numbers

We will arrange from least to greatest.

By doing so, we will obtain

Next, we will find the middle number of the set.

The median will be the average of the two numbers

The median of the numbers is 13.5

Answer:

Options 1, 3, and 4.

Explanation:

Given the expression:

Step 1: The term -2(x-2)² is simplified by first squaring the expression x-2.

Step 2: The parentheses are eliminated through multiplication.

Step 3: After multiplying, the like terms are combined by adding and subtracting.

The three options that are correct are Options 1, 3, and 4.

The minimum number of goals scored is 0 and maximum number of goals scored is 7. The range is equal to difference between maximum number of goals and minimum number of goals.

Determine the range for the goals scored.

So answer is 7.

In order to find the value of f(1.2), we just need to find the value of f(x) in the graph that corresponds to x = 1.2.

Looking at the graph, when x = 1.2, the function f(x) is equal to 2.

Then, to find the largest value of x for which f(x) = 1.5, we look for the value 1.5 in the vertical axis, then find the corresponding value of x.

For this value, we have two possible values of x: 1.2 and 3.6.

So the largest value is x = 3.6

Answer:

$50.08

Step-by-step explanation:

Find the unit rate.

[tex]\frac{12.50}{4}[/tex] Each box cost $3.125.  We cannot have .125 cents, so round up to 3.13

3.13 x 16 = $50.08

1) Given those functions, f(t) and g(t) let's find the composite function, for (f(g(0)) or (f •g)(0)

2) Let's pick the function f(t)

f(t) = 2t-3

And plug into that g(t), like this

f(g(t))= 2(t³ +t) -3

3) Finally, let's plug the value 0 into that composite function:

f(g(t))= 2(t³ +t) -3

f(g(0))= 2(0³ +0) -3 ⇒f(g(0))= 2(0) +3

f(g(0))= 3

(f •g)(0)=3

4). a. If you are trying to evaluate Z(3) in order to know which equation would you choose we would have to make the following calcuations:

So, if Z(3), then:

substitute the x with the number 3

Therefore, the equation to choose if Z(3) would be x>10, because by substitute the x with the number 3 would be the largest function with a positive number and sign.

Equation for a rational function is 10(x2 + 7x + 12) / (x2 + 11x + 30) = 0.

What is Rational Function?

Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K.

So this will be a rational function with the vertical asymptotes given by the denominators:

(x + 5) and (x + 6).

The x-intercepts will be provided by the numerator,

which will be:

a(x + 3)(x + 4)

The letter an is a constant.

Given that (0,4) is the y intercept, we have:

4 = a(0+3)(0+4) / (0+5)(0+6)

4= 12a / 30

12a = 120

now,

a = 120/12,

a = 10,

and a = 1.

Now,

a(x+3)(x+4) / (x+5)(x+6) = 0

10 (x^2 + 7x + 12) / (x^2 + 11x + 30) = 0

Hence, We have the following equation for a rational function:

10 (x2 + 7x + 12) / (x2 + 11x + 30) = 0.

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Answer:

DJ = 24

Explanation:

We are told from the question that J is the centroid of CDE, this means that J is the midpoint of DH, CJ and FE

If J is the centroid of DH, then 2DJ = JH

Also DJ + JH = DH

The equation becomes:

DJ + 2DJ = DH

3DJ= DH

Given

DH = 72

Hence 3DJ = 72

DJ = 72/3

DJ = 24

Hence the measure of DJ is 24

0.4 liters or 2/5

Step-by-step explanation:

Dividing the soda equally, Each student would get 0.4 liters or 2/5

The annual fixed expense for car insurance is  $ 1,046.70.

It is given in the question that John makes six payments in a year at $174.45 each.

We have to find the annual fixed expense for car insurance.

We know that,

The annual fixed expense for the car insurance will be 6 times the individual payment given in the question.

Hence, by simple multiplication, we can write,

Annual fixed expense for the car insurance = 6*174.45 = $ 1,046.70

Car insurance

Car insurance is a type of financial protection that covers the cost of another driver’s medical bills and repairs if you cause an accident with your car, or in case your car is stolen or damaged some other way.

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Answer:  The correct answer is x=0 and y=4 or (0,4) per the graph

Step-by-step explanation:

To find the maximum value, we must test each point using the equation:

Check for (0,4):

C=3x+4y

C=3(0)+4(4)

C=16

Check for (2,2):

C=3(2)+4(2)

C=6+8

C=14

Check for (4,0):

C=3(4)+4(0)

C=12

Answer:

Step-by-step explanation:

In this problem, we have the sequence

inverse sequence

36,34,32,30,28,26

The sum is equal to

S=36+34+32+30+28+26

S=186

In this problem, we have the sequence

inverse sequence

36,34,32,30,28,26

The sum is equal to

S=36+34+32+30+28+26

S=186

We have here a special case where the line is vertical. In this case, the line has an "infinite" slope (or it is not defined). Therefore, since the line is vertical and contains the point (10, 14), the line is given by the equation:

The standard form of the line is given by the general equation:

Then, we can rewrite the equation as follows:

We can see that this line contains the point (10,14):

We can see that the vertical line, x + 0y = 10 passes through the point (10, 14).

In summary, the line is given by x + 0y = 10 (A = 1, B = 0, C = 10).

The two composite functions have their values to be (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5

Composite function 1

The given parameters are

w(x) = 7x - 2

s(x) = x² - 7x + 5

To calculate (w o s)(x), we make use of

(w o s)(x) = w(s(x))

So, we have

(w o s)(x) = 7s(x) - 2

Substitute s(x) = x² - 7x + 5

(w o s)(x) = 7(x² - 7x + 5) - 2

Expand

(w o s)(x) = 7x² - 49x + 35 - 2

Simplify

(w o s)(x) = 7x² - 49x + 33

Composite function 2

Here, we have

w(x) = 7x - 2

s(x) = x² - 7x + 5

To calculate (s o w)(x), we make use of

(s o w)(x) = s(w(x))

So, we have:

(s o w)(x) = w(x)² - 7w(x) + 5

Substitute w(x) = 7x - 2

(s o w)(x) = (7x - 2)² - 7(7x - 2) + 5

So, the composite functions are (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5

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EXPLANATION:

Given;

We are given the step by step procedure to find the height of a triangle.

Required;

We are required to determine if the step by step solution is true or false.

Solution/Explanation;

When finding the height of a triangle, we may use the Pythagoras theorem or we may use trigonometric ratios for right angled triangles.

Note that the Pythagoras' theorem is also used only for right angled triangles and one of the three sides will be the height of the triangle.

When required to calculate the the height of a triangle given a line perpendicular to the base (that is, at a 90 degree angle with the base), and passing through the vertex opposite the base, the triangle can be effectively split into two parts along the perpendicular and the perpendicular line will then become the height. Also depending on the amount of information available, we may use the Pythagoras' theorem (if the other two sides are given). Alternatively we may use the trigonometric ratios if one other side and one of the angles is given.

Therefore,

ANSWER:

FALSE

It is easier to perform the operations if you convert the mixed fractions into improper fractions.

For point 1. Make the mixed fractions improper first

Now, the multiplication of fractions is done like this

Then, you have

For point 2.

Now multiplying the improper fractions you have

Finally for point 3.

Now multiplying the improper fractions you have

For an amount of sales of $5,000, the two salary choice will be equal

Let the amount of sales be $x

The 3% she will receive will be;

We add this to the base salary and equate to the former monthy salary

We have this as;

Answer:

Explanation:

Given:

First, we do completing the square on the given function to express it into vertex form. So,

We write it in the form:

And, factor out 3: So,

Since:

Then,

Therefore, the answer is:

1. Divide the first term of the dividend into the first term of the divisor:

2. Multiply the result above by the divisor:

3. Subtract the result above from the divident to get a new polynomial:

4. Repeat the process with the new polynomial:

If you start at (9,2) and then move left 9 units, you'll end up at (0, 2)

3x + 7y= 14

3x+7y= 10

Subtract the second equation to the first.

3x +7y= 14

-

3x + 7y= 10

_________

0x +0y = 4

0 = 4

0 is no

We have:

L = 5 L's

I = 2 I's

P = 1 P

Y = 2 Y's

so: