Distance-Time Grapfoss Object ng Constant Speed - 9) Achillwit and string a speed The graph above shows the Giant the ball towed from starting pucat in 5 seconds.

A=$88,000

P=$70,586

r=9.8% (0.098)

Divide both sides by 70,586:

Find ln of both sides:

Divide both sides by 0.098:

The area of the fabric can be determined as,

Thus, the required area of the fabric is 19 square inch.

Well, I would like to know more about this problem.

If you are solving an equation it is wrong because you are adding 10 units only in one side of the equation, that is a mistake.

If this is not a process to solve the equation it is correct, it does not matter if you are only adding 10 in one side.

For the given vector  v=7i - 5j and w=-i+j,

        projwv =  6i - 6j

                   v1 = 6i -6j

                     v2 = i +j

Vector:

              A quantity that has both magnitude and direction are called vector. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude.

a) projwv is the projection of v onto w. Use the following equation:

projwv = [(v•w)/((magnitude(w))2)] w

v•w = (7*-1) + (-5*1) = -12

(magnitude w)^2 = ([tex]\sqrt{1^{2} + 1^{2}}[/tex])^2 = 2

projwv = ((-12)/2)(-i + j)

            =  6i - 6j

b) The two components of the decomposed v will add to create the original vector v. v1 that is parallel to w will be the same as the projection of v onto w.

v = v1 + v2

v2 = v - v1 = (7i - 5j) - (6i -6j) = i +j

You can check that v2 is orthogonal by taking the dot product (v2•w). This equals 0.

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Given:

The vertical height is 30ft.

The angle of elevation is 30 degrees.

To find:

The distance travelled by the person from bottom to top of the escalator.

Explanation:

Let x be the slant distance.

Since it is a right triangle.

Using the trigonometric ratio formula,

Therefore, the distance travelled by the person from the bottom to the top of the escalator is 60ft.

Final answer:

The distance travelled by the person from bottom to top of the escalator is 60ft.

Given the equation system:

To solve the system and determine the value of x, first step is to write one of the equations in terms of y:

Then replace this expression in the second equation

Now that you have an expression with only one unknown, x, you can calculate its value.

Solve the parenthesis using the distributive property of multiplication

ANSWER

EXPLANATION

We want to add the three numbers:

To do this, add the numbers in corresponding place values i.e. units to units, tens to tens, and hundred to hundred:

That is the answer.

The equation of the polynomial equation in standard form is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2

The given parameters are

Degree = 5

Zero = 1, i, 1 + i

There are complex numbers in the above zeros

This means that, the other zeros are

Zeros = 1 - i and -i

The equation of the polynomial is then calculated as

P(x) = Leading coefficient * (x - zero)^multiplicity

So, we have

P(x) = (x - 1) * (x - (1 + i)) * (x - (1 - i) * (x - (-i)) * (x - i)

This gives

P(x) = (x - 1) * (x - 1 - i) * (x - 1 + i) * (x² + 1)

Solving further, we have

P(x) = (x - 1) * (x² - x + ix - x + 1 - i - ix + i + 1) * (x² + 1)

P(x) = (x - 1) * (x² - 2x + 2) * (x² + 1)

Evaluate the products)

P(x) = (x³  - x² + x - 1) * (x² - 2x + 2)

This gives

P(x) = x⁵ - 2x⁴ + 2x³ - x⁴ + 2x³ - 2x² + x³ - 2x² + 2x - x² + 2x - 2

Express in standard form

P(x) = x⁵ - 2x⁴ - x⁴ + 2x³  + 2x³ + x³ - 2x²  - 2x²  - x² + 2x + 2x - 2

Evaluate the like terms

P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2

Hence, the equation is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2

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a) An equation for the given problem is;

b) The initial value for the given problem is;

c) The number of hours that a member rented the tennis ball machine if the total cost was $130 is; 4 hours

The general formula for the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

a) Base price for joining the fitness center is $50 and as such this can be said to be the y-intercept. Then, the tennis ball machine is rented for $10 per hour.

Now, the number of hours the machine is rented (x) and the total cost (y), then the equation is;

y = 10x + 50

b) The initial value is the price when x = 0 which is the y-intercept and as such it is $50.

c) The cost for renting the tennis ball machine for 2 hours is;

y = 10(2) + 50

y = $70

The cost for renting the tennis ball machine for 5 hours is;

y = 10(5) + 50

y = $120

The cost for renting the tennis ball machine for 0 hours is;

y = 10(0) + 50

y = $50

d) If total cost is $130, then we have;

130 = 10x + 50

10x = 80

x = 80/10

x = 8 hours

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1) -4x=36

2) x+6=13

3) -9x=36

The given system is

First, we multiply the first equation by -3/10.

Then, we sum the equations

When the ball hits the ground, the height of the ball to the ground is h(t) = 0.

Therefore, we can now substitute h(t), and solve the function using quadratic formula.

Using the quadratic formula, substitute the following values a,b, and c.

We have two solutions, t = -4.52494, and t = 5.52494. However, we will disregard the negative time value.

Therefore, the ball will hit the ground after 5.52494 seconds.

Total income= $34910

Amount spent on food = $7104

A) It's a function because each point of x has a point on y.

B. It's a discrete functions because you can't see a continuous line.

C. Domain (-3,6)

D. Range (0,3)

* C and D if each square is equivalent to 1 unit.

we know that

the solid of the figure is a sphere

the volume of the sphere is equal to

we have

pi=3.14

r=25 m

substitute

Step 1: Problem

Step 2 : Concept

QR = 136

PQS = 42 + 136 + 42 = 220

PS = 64 + 72 = 136

Answer:

The width of the rectangle is 5

The length of the rectangle is 13

Explanation:

Let's call x the length of the rectangle and y the width of the rectangle.

The length is 2 less than 3 times the width, so

x = 3y - 2

And the area is 65 square meters. Since the area is length times width, we get:

xy = 65

Now, we can replace the first equation x = 3y - 2 on the second one to get

(3y - 2)y = 65

3y(y) - 2y = 65

3y² - 2y = 65

3y² - 2y - 65 = 0

So, using the quadratic equation, we get that the solutions to 3y² - 2y - 65 = 0 are

The solution is y = 5 because the width can't have a negative length.

Then, replacing y = 5 on the first equation, we get:

x = 3y - 2

x = 3(5) - 2

x = 15 - 2

x = 13

Therefore, the length of the rectangle is 13 meters and the width of the rectangle is 5 meters

To find Mario's current grade is to find the average of all his grades for the first quarter.

The average of his grade for the first quarter is the mean which is 70 percent.

Also, 70 percent is equivalent to a C minus

Since the sides of the rectangle are in ratio 5: 7

Insert x in the 2 terms of the ratio and find its perimeter using them

Equate 24x by the given perimeter 72 to find the value of x

Divide both sides by 24

Then the sides of the rectangle are

Since the rule of the area of the rectangle is A = L x W, then

The area of the rectangle is 315 square units

Solution

For this case we can see from the image given that the value for BC is:

4x units

since that represent the lenght of the side

Given in triangle ABC , m∠A = 75°, m∠B = 65°, a = 23.5ft.

We have to find the third angle,

The shortest angle is angle C. So, the shortest side will be opposite to angle C.

Use the sine rule, to find the third side as follows:

Thus. the length of the shortest side is 15.6 ft.

After multiplying the value of P is 32 ft and the value of A is 64 sq. ft.

In the given question we have to find the value of P and A.

The given expression for P is

P = (4 X 8)

The given expression for A is

A = (8 X 8)

In the given P representing the perimeter of square because the formula of perimeter is

P = 4* side

A representing the area of square because the area of square is

A = side*side

So the value of P

P = (4 X 8)

P = 32 ft

The value of A

A = (8 X 8)

A = 64 sq. ft

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Step-by-step explanation:

come on !

the vertex is typically a corner or a (general or local) extreme value or turning point of the curve.

so, what can that point be ?

there is only one candidate : (4, 1).

that means x = 4, y = 1.

that is the 4th answer option.

The situation can be represented by a linear function, which is represented by the following expression:

Since he increased the number of cards by a constant amount each week, that means we have proportionality:

Then, by the slope-point form of the line, we can find the equation and then substitute x=0.

Substituting, x=0.

At the beginning of the collection, he has 150 cards.

Set A is composed of all the even numbers equal or greater than 4 and equal or less than 8 so set A is:

The cardinalities of A and B are equal to their number of elements so we have n(A)=3 and n(B)=7.

With both sets explicitly written we can complete the true or false table. The only thing to take into account is that the symbol ∈ means "belongs to" and that ∉ means "does not belong to".

The first statement of the table is:

This is false because 12 does not belong to set A since it is not included in it.

The second statement is:

As you can see 22 is in deed one of the elements of set B which means that this statement is true.

The third one is:

This statement is false because as we saw before 6 is an element of set A.

The last statement is:

As you can see -24 is one of the elements of set B so this statement is true.

False

True

False

True

178.98 yd³

The shape consists of a cone and a cylinder. So we would find the volume of each and sum them together.

Volume of a cone = 1/3 πr²h

r = radius = 3 yd

h = height = 4 yd

let π = 3.14

Volume of the cone = 1/3 × 3.14 × 3 × 3 × 4

Volume of the cone = 37.68 yd³

Volume of a cylinder = πr²h

r = radius = 3 yd

h = height = 5 yd

Volume of a cylinder = 3.14 × 3 × 3 × 5

Volume of a cylinder = 141.3 yd³

Volume of the shape = Volume of the cone + Volume of a cylinder

Volume of the shape = 37.68 + 141.3

Volume of the shape = 178.98 yd³

The first number before the decimal point is the ones place.

48.26

ones = 8

The second number after the decimal point is the hundredths place:

48.26

hundredth: 6

We have the expression:

We have to evaluate it for p = 4 and q = 8.

To do that, we replace the variables p and q with the given values and calculate:

Answer: The value of the expression when p = 4 and q = 8 is -12 [Second option]

3+15+75+.....+46875

a1 = first term = 3

If we multiply the first term by 5, we obtain the second term.

3 x 5 = 15

15x 5 = 75

75x 5= 375

375x5= 1875

1875x5=9375

9375x5= 46875 (7th term) n=7

So,

r= 5

Apply the formula:

an= a1 * r^(n-1)

an= 3 * 5 (n-1)

Sum

Sn = a1 (1 -r^n) / 1- r

S(7) = [3 (1 - 5^7)] / 1-5

S(7) = [3 (1-78,125)] /-4

S(7) = 58,893

Answer:

Explanation:

Given the domain of the function as;

Note that the range of the inverse of a function is the same as the domain of a function is the original function.

So the range of the inverse of the function will be;