The table below shows a runner's time t, in mintues, and distance traveled d, in miles.

Write an equation that shows a relationships between t and d.

The height of balloon is 1.99 miles above the ground.

In the event when the line of sight is directed downhill from the horizontal line, an angle is created with it. Angle of depression is the angle produced between the horizontal line and the observer's line of sight when the object being observed is below the level of the observer.

Let's give the balloon's height above the earth and the distance it is from the first milepost horizontally a name.

We can state the following if the angle of this milepost's depression is 24 degrees:

Tan(24)=[tex]\frac{h}{b}[/tex]

b = [tex]\frac{h}{tan(24)}[/tex]

We can state the following for the following milepost as there will be (b+1)miles horizontal distance of and a 20 degree depression at that location.

tan(20)=[tex]\frac{h}{b+1}[/tex]

b +1  = [tex]\frac{h}{tan(20)}[/tex]

Therefore, substituting equation 1

[tex]\frac{h}{tan(24)}[/tex] = [tex]\frac{h}{tan(20)} -1[/tex]

1 =   [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex]

1 = h× ( [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex] )

h = 1.99 miles

Consequently, the height of balloon is 1.99 miles above the ground.

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Answer:

y = 3 - 2x

Step-by-step explanation:

Subtract 2x from both sides of the equation.

Answer:

y = x or 1x

Step-by-step explanation:

x as a variable can also be expressed as 1x.

so we can say that    2x + 1x

because x & y are two different type of variables. you think of y as a question mark ( ? ).

Now the new equation is

y = ?

so 1x + ? = 3

because x is the same thing as a 1x you can say that 2x + 1x = 3

The solutions of the equation x³ + 5x² = - x² + 5x + 3 when solved graphically is x = - 0.41, 1.09.

Draw a graph for each side, or component, of the equation and check to see where the curves intersect or are equal, to solve an equation graphically. The answers to the equation are the x values of these places.

Consider the equation,

x³ + 5x² = - x² + 5x + 3

Solving Equations Graphically:

The solution(s) of the equation f(x) = g(x) are the values of x where the graphs of f and g intersect.

Therefore,

f(x) = x³ + 5x² and g(x) = - x² + 5x + 3

By graphing the function we find the intersection of the two functions.

Hence, the graphs intersect each other at ( - 0.411, 0.776) and ( 1.092, 7.268).

Therefor,e the solution of the equation x³ + 5x² = - x² + 5x + 3 is x = - 0.41 and x = 1.09.

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As you can see in the given figure the minute hand of a clock rotate from 12:40 to 1:10 formig a straigth angle.

A straight angle in radians is π radians.

Answer:

360 naira hope it will be helpful

Step-by-step explanation:

Answer:

7500$

Step-by-step explanation:

When $428 doubles, it means that the

The value of the expression given as 3 - √x⁵ is 3 - x^2√x

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

3 - √x⁵

Express 5 as the sum of 4 and 1

So, we have the following equation

3 - √x⁵ = 3 - √x^(4 + 1)

Apply the law of indices to expand the equation

So, we have the following equation

3 - √x⁵ = 3 - √(x^4 * x)

Next, we expand the equation

So, we have the following equation

3 - √x⁵ = 3 - √x^4 * √x

Evaluate the square root of x^4

So, we have the following equation

3 - √x⁵ = 3 - x^2 * √x

Evaluate the product

So, we have the following equation

3 - √x⁵ = 3 - x^2√x

Hence, the value of the expression is 3 - x^2√x

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First of all, we have to find the mean of x values.

According to the given graph, the x values are: 0, 1, 2, 2, 3, 3, 4, 5, 6, 7.

So, the mean is

The mean of x values is 3.3.

The y values are: 2, 2, 3, 4, 4, 4, 5, 6, 8, 9.

The mean would be

The mean of y values is 4.4.

Now, we find the standard deviation for x values and y values.

It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.

Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.

Now let's analyze the functions from the problem.

Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function f(x) is also increasing.

Use these rules to find whether each function is increasing or decreasing.

Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.

Hello! So...

We are given the following to solve:

Solve for x.

[tex]6(x+3)-8=4x+2(4+x)[/tex]

_______________________________________________________

1. Expand both sides of the equation.

[tex]6(x+3)-8=6x+10[/tex]

[tex]4x+2(4+x)=6x+8[/tex]

[tex]6x+10=6x+8[/tex]

______________________________

2. Subtract 10 from both sides.

[tex]6x+10-10=6x+8-10[/tex]

_______________________________

3. Simplify.

[tex]6x=6x - 2[/tex]

_______________________________

4. Subtract 6x from both sides.

[tex]6x-6x=6x-2-6x[/tex]

_______________________________

5. Simplify.

[tex]0=-2[/tex]

^Notice, the sides are not equal in the solution. This being said, there would be no solution.

___________________________________________________

Hope this helps! If you need anything else, feel free to comment below. Thanks and good luck!

When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.

Using the highest common factor, the greatest number of identical binders that the teacher can make is 18.

The highest common factor or multiple of the given numbers is the highest number that can divide them without a remainder.

We know that 2, 9, and 18 can divide 54, 36, and 72 without leaving a remainder.

We can see that the highest common factor is 18.

When we divide 54 by 18, the quotient is 3. If you divide 36 by 18, the quotient is 2.  When you divide 72 by 18, the result is 4.

The number of lined paper = 54 pieces

The number of grid paper = 36 pieces

The number of dividers = 72 dividers

The common factors of 54, 36, and 72 are 2, 9, and 18.

The highest common factor of 54, 36, and 72 is 18.

Thus, 18 binders containing 3 pieces of lined paper, 2 pieces of grid paper, and 4 dividers can be made from the collection, using their HCF.

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The value of x is 4.

The perimeter of any shape is the sum of lengths of all its sides.

We are provided with the sides of triangle i.e., 5x-1, 5x-1 and 2.2x +10.

So, The perimeter of a triangle = sum of length of all three sides = (5x-1) + (5x-1) + (2.2x +10)

The perimeter of a triangle = 12.2x + 8                            equation 1

Also, we are provided with the side of square i.e.,  6.5x -11.8.

The perimeter of a square = 4 (side) = 4 (6.5x - 11.8)

The perimeter of a square = 26x - 47.2                            equation 2

As per question,

Perimeter of a triangle =  Perimeter of a square

12.2x + 8  = 26x - 47.2    

13.8x = 55.2

x = 4

So we can write,  the value of x is 4.

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We can use the following formula:

So:

Answer:

0.3%

Answer:

what is the problem ???

Step-by-step explanation:

If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.

Given equation:

y = 88t - 16t²

Maximum height dy/dt = 0

88-32t = 0

32t = 88

t = 88/32sec

t = 2.75sec

Hence,

Maximum height attained by the ball :

Maximum height attained by the ball = 88(2.75)-16(2.75)²

Maximum height attained by the ball = 242 - 121

Maximum height attained by the ball = 121 feet

Therefore the maximum height is 121 feet.

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Ivan will catch up to Horatio in 3 hours .

In the question ,

it is given that

speed of Horatio is 1 miles per hour

speed of Ivan is 2 miles per hour .

and Ivan leaves 3 hours late than Horatio .

Let "t" be the time ( in hours ) taken for  Ivan to meet Horatio ,

So, the distance covered by Ivan will be 2*t .

Since Horatio left 3 hours before so the time taken for Horatio to meet Ivan is (t+3).

So, the distance covered by Horatio will be 1*(t+3) .

The distance covered for Horatio and Ivan will be equal ,

which means

2*t = 1*(t+3)

2t = t + 3

2t - t = 3

t = 3

Therefore , Ivan will catch up to Horatio in 3 hours .

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For given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)

In this question, we have been given an equation y = -2x + 8

We need to find the x-intercept and y-intercept. Also, we need to write it as a coordinate (a, b)

To find the x-intercept we need to substitute y = 0 in the above equation.

0 = -2x + 8

2x = 8

x = 4

So, the x-intercept is (4, 0)

To find the y-intercept we need to substitute x = 0 in the above equation.

y = -2(0) + 8

y = 0 + 8

y = 8

So, the y-intercept is (0, 8)

Therefore, for given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)

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The real and complex zeros for the function given as .f(x) = x³ - x² + 3x - 3 are x = 1 and x = ±i√3, respectively

The equation of the function is given as

f(x) = x³ - x² + 3x - 3

Group the terms of the function in two's

So, we have the equation

f(x) = (x³ - x²) + (3x - 3)

Factor each group in the function

f(x) = x²(x - 1) + 3(x - 1)

Factor out x - 1

f(x) = (x² + 3)(x - 1)

Set to 0

(x² + 3)(x - 1) = 0

This gives

x² = - 3 and x = 1

Evaluate the roots

x = ±i√3 and x = 1

Hence, the zeros of the equation are x = ±i√3 and x = 1

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The equation y = - 1 / 6 x + 3 in standard form is x + 6y = 18.

The standard form for linear equations in two variables is Ax + By = C.

where

Therefore, let's represent the equation y = - 1 / 6 x + 3 in standard form .

y = - 1 / 6 x + 3

multiply the equation by 6 to eliminate the fraction

6y = 6(- 1 / 6 x) + 6(3)

Therefore,

6y = - x + 18

x + 6y = 18

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The equation of the circle in standard form whose center is at (h, k) = (4, 0) is (x - 4)² + y² = 26.

In this question we find the coordinates of the endpoints of the diameter of the circle, then, the center of the circle is the midpoint of the line segment. The center of the circle is found by midpoint formula:

(h, k) = 0.5 · (5, 5) + 0.5 · (3, - 5)

(h, k) = (4, 0)

And the radius of the circle is determined by Pythagorean theorem:

r = √[(4 - 5)² + (0 - 5)²]

r = √[(- 1)² + (- 5)²]

r = √26

Then, the equation of the circle in standard form is describe below:

(x - h)² + (y - k)² = r²

If we know that (h, k) = (4, 0) and r = √26, then the equation of the circle is:

(x - 4)² + y² = 26

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Answer:

d) given

Step-by-step explanation:

nothing has been done yet, the statement is given as stated above the statement

The first unit is kilograms because the bus is really heavy.

The second is kilometers because meters are too small.

The third one is milliliters because liters are too much for ice cream.

Using the graph, we can deduce the following:

• x-intercept: x = -2

• y-intercept: y = -3

Let's determine the zero of the function.

The zero of a function can be said to be the root of the function. It is also called the x-intercept of the function.

The zero of a function is the point the line crosses the x-axis.

From the graph the x-intercept is at x = -2.

Therefore, the zero of the function is:

x = -2

ANSWER:

D. -2

Answer: 72 i think

Step-by-step explanation:

SOLUTION

Given the question in the question tab, the following are the solution steps to get the equation

Step 1: Represent the statement using mathematical notation

Base salary is $2500 (Base salary is constant since it does not change)

P represent his total pay (in dollars)

N represent the number of copies of English is Fun he sells

price made per copy of the product is $80

The equation relating P to N will be written as:

Part B: Using this equation in step 1 above to find his total pay if he sells 28 copies of English is Fun

Hence, his total pay if he sells 28 copies of English is Fun is $4740

The standard form of expression equation of a straight line is;

where;

m is the slope

c is the intercept

Given

slope m = -3/8

Next is for us to get the y- intercept of the line. This is done by subtituting the slope and the point (0,10) given into the equation y = mx+c and calculating c as shown;

Next is to get the equation of the line by substituting m = -3.8 and c= 10 into the standard form of the equation as shown;

Hence the first option is correct