Because his goal is to bike 65 miles over four days, what equation can be used to find the number of miles he should bike on the first day, x? Do not combine like terms.​

Answer:

1, 2, 3, 4, 6, 9, 12, 18, and 36.

Step-by-step explanation:

All of these are factors of 36.

They can all be divisors with no remainder

Answer:

Step-by-step explanation:

To solve this equation, we can start by using the identity cos(A-B) = cosAcosB + sinAsinB. Substituting A=sin x and B=1, we have:

2cos(sin x - 1) = cos(sin x)cos(1) + sin(sin x)sin(1)

We can then substitute this expression on the left-hand side of the original equation and simplify:

4sinxcosx^2 - 1 = cos(sin x)cos(1) + sin(sin x)sin(1)

Rearranging terms, we have:

4sinxcosx^2 - cos(sin x)cos(1) - sin(sin x)sin(1) = 1

We can now use the identity sin^2x+cos^2x=1 to simplify the left-hand side further:

4sinxcosx^2 - (sin^2x + cos^2x)cos(1) = 1

Simplifying further:

4sinxcosx^2 - (cosx)cos(1) = 1

Now we can divide both sides by cos(1):

4sinxcosx^2/cos(1) - cosx = 1/cos(1)

Rearranging terms:

cosx(4sinxcosx^2/cos(1) - 1) = 1/cos(1)

Finally, we can use the identity cos2x = 2cos^2x - 1 to simplify the left-hand side further:

(2cos^2x - 1)(4sinxcosx^2/cos(1) - 1) = 1/cos(1)

We can then divide both sides by (4sinxcosx^2/cos(1) - 1):

2cos^2x - 1 = 1/cos(1) (4sinxcosx^2/cos(1) - 1)

And finally, we can solve for cosx:

cosx =  1/2 + 1/2cos(1) (4sinxcosx^2/cos(1) - 1)

This is the solution to the equation.

Answer:

a = [tex]\frac{41}{9}[/tex]

Step-by-step explanation:

Evaluate f(3):

f(3) = (3)² -2(3)³ + a(3)² +3 +3

9a - 39 = 2

9a = 41

a = [tex]\frac{41}{9}[/tex]

The square root of 625 is 25 and the square root of 25 is 5. Therefore, option A and F are the correct answers.

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

A) [tex]625^{\frac{1}{2}[/tex]

= [tex](25^2)^{\frac{1}{2}[/tex]

= 25

F) 25

= 5

Therefore, option A and F are the correct answers.

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The required value of y for the angle is 18.

The angles created when a transversal intersects two parallel lines are known as corresponding angles. Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, and endless parallel railroad tracks.

By Corresponding angles

7x = 3x + 36

4x = 36

x = 9

And

Angle in straight line

(6y + 9)+(3x+36) = 180

(6y + 9)+(27+36)

6y + 72 = 180

6y = 108

y = 18

Thus, required value of y is 18.

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The graph of the quadratic function g(x) = - (x - 2)² + 4 on Cartesian plane is shown in the image attached below.

In this question we find the case of a quadratic equation in vertex form, whose definition is shown below:

y - k = a · (x - h)²

Where:

The equation of the axis of symmetry is shown below:

x = h

We can graph by using the coordinates of the vertex and two other points and understanding the vertex constant. Please notice that the parabola has an absolute minimum when vertex constant is positive, otherwise it is an absolute maximum.

First, find the coordinates of the vertex of the parabola:

(h, k) = (2, 4)

Second, determine the nature of the absolute extreme by interpretating the sign of vertex constant:

a = - 1 (The vertex is an absolute maximum)

Third, evaluate the function at two distinct points:

x = 0

g(0) = - (0 - 2)² + 4

g(0) = - (- 2)² + 4

g(0) = 0

x = 4

g(4) = - (4 - 2)² + 4

g(4) = - 2² + 4

g(4) = - 4 + 4

g(4) = 0

Fourth, graph the parabola on Cartesian plane. (Image is done with the help of a graphing tool)

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Answer: (15 + 72) + 19

Explanation: "Associative Law = (a + b) + c = a + (b + c)"

Answer:

39000meter

hope it will help you

Answer:

The inverse of a function, denoted as f^-1 (x), is a new function that "undoes" the original function. To find the inverse of a function, you need to switch the x and y variables and then solve for y. To find the inverse of f(x) = 1/3 x - 5, you need to switch the x and y variables and then solve for y:

Step-by-step explanation:

To solve for y, you need to get x alone on one side of the equation:

x + 5 = 1/3 y

3x + 15 = y

The inverse of f(x) = 1/3 x - 5 is f^-1 (x) = 3x + 15

It is important to note that not all functions have an inverse, only functions that are one-to-one or "injective" functions have inverses.

Answer: 3x + 15 = the inverse function of f(x)

Explanation:

First of all, arrange the equation and leave the "x" alone.

x/3 - 5 = y (Multiply both sides by 3)

x - 15 = 3y (Then, leave "x" alone)

x = 3y + 15 (As the final step, change x and y variables.)

y = 3x + 15 (This is the inverse function of f(x).)

Answer:

y = -5x + 4

Step-by-step explanation:

The general form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.

Given that the slope of the line is -5 and the y-intercept is 4, we can substitute these values into the general form of the equation of a line to get:

y = -5x + 4

This equation represents a line with a slope of -5 and a y-intercept of 4.

Answer: Let's call the present age of the son x and the present age of the father y.

We know that y = 3x and that six years ago, the sum of their ages was 45.

So, we can write the equation:

x + (y-6) = 45

x + (3x-6) = 45

4x = 51

x = 12.75

The present age of the son is 12.75 years.

Step-by-step explanation:

If In ΔEFG, e = 690 inches, ∠F=94° and ∠G=46° then the length of g is 800 inches.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The sum of interior angles of a triangle are 180 degrees.

In ΔEFG, e = 690 inches, ∠F=94° and ∠G=46

We need to find the ∠E then the length of g.

∠E+∠F+∠G=180

∠E+94+46=180

∠E+140=180

∠E=40 degrees

By using sinE rule we have to find the length of g.

SinE/E=sinG/G

sin40/690=sin46/x

0.642/690=0.72/x

0.00093=0.72/x

x=0.72/0.0009

x=800 inches

Hence, the length of g is 800 inches.

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The term that represents the cost of the shoes after the discount is (1 - 0. 025)s. Option D

Algebraic expressions are described as mathematical expressions that consist of factors, constants, variables, terms and coefficients.

They are also made up of arithmetic operations, which includes;

From the information given, we have that there was a 25% discount on all the shoes Declan bought

Given the expression;

c + ( 1 - 0.25)s + 0. 08[c + (1 -0.25)s ]

expand the bracket

c + s - 0. 25s + 0. 08( c - s - 0. 25s)

expand the parentheses

c + s - 0. 25s + 0. 08c - 0. 08s - 0.02

But for the cost of the shoes after the 25% discount, we have;

(1 - 0. 025)s

Hence, the expression is (1 - 0. 025)s

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A graph of the absolute function y = |x + 2| - 4 with five points that fit on the axes is shown in the image attached below.

In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and it typically measures the distance of a point on the x-axis to the x-origin (0) of a cartesian coordinate (graph).

Next, we would use an online graphing calculator to plot the given absolute value function y = |x + 2| - 4 as shown in the graph attached below.

By observing critically the graph (see attachment), the five ordered pairs (points) that fit on its axes include the following:

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Answer:

Step-by-step explanation:

The solutions to this equation are x = 1.273 and x = -0.273.

When x = 1.273, 3 cos (x) + 4 = 5.

When x = -0.273, 3 cos (x) + 4 = 5.

Rounding to 3 decimal places, the solutions to the equation on the indicated interval are x = 1.273 and x = -0.273.

Answer:

The correct answer is: parallel

The two equations are in the form of y = mx + b and y = mx + b, which are the standard forms of linear equations.

and the slope of the two equations are different, so they are not coincident and not intersecting. They are parallel lines that never meet, so the system of equations is parallel.

Answer:

1. Nevoia de a te certa sau de a-i critica pe cei din familie prin limbaj cu conotatii negative sau prin tonul vocii.

2. Nerespectarea deciziilor familiei sau nerespectarea responsabilitatilor asumate.

3. Abuzul verbal sau emotional, inclusiv insultele sau minciunile.

4. Negarea dreptului la intimitate sau la spatiu personal.

5. Ignorarea afectiunii si a momentelor importante din familie.

Step-by-step explanation:

different between each value is 4

The fractions that have the same value as 16 ÷ (–3), include:

The quotient of the problem given is - 4.

To find the equivalent fractions to ,16 ÷ (–3), first solve for the quotient:

= 16 ÷ (–3)

= - 5. 33

Then, solve the fractions in the options to see if they give the same result as when you solved 16 ÷ (–3).

Fraction : 16 over negative 3

= 16 / -3

= - 5.333

This has the same value

Fraction : negative 16 over negative 3

= -16 / -3

= 5. 333

This does not have the same value

Fraction : negative 16 over 3

= - 16 / 3

= - 5. 333

This has the same value

Fraction : 16 over 3

= 16 / 3

= 5. 333

This is not the same value

Fraction: Negative (StartFraction 16 over 3 EndFraction)

= - ( 16 / 3 )

= - 5. 33

This is the same

The quotient of - 20 / 5 :

= - 20 / 5

= - 4

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Answer:

The cost of the water is $5.70.

Step-by-step explanation:

7.05-1.35=5.70 You just have to - 7.05 by 1.35

Answer:

605

Step-by-step explanation:

11x55=605

The scientific notation of the given number is 6.11×10⁻⁴. Therefore, option E is the correct answer.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

The given decimal number is 0.000611.

0.000611 in scientific notation, we get

6.11×10⁻⁴

Therefore, option E is the correct answer.

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A construction of a right-angled isosceles triangle whose equal side measure 2 cm is shown in the image attached below.

In Mathematics, an isosceles right triangle can be defined as a type of  right-angled triangle in which two (2) of its side lengths are equal and one of its angle is a right angle.

Generally speaking, the steps that are required for the construction of a right-angled isosceles triangle include the following:

In conclusion, triangle ABC (ΔABC) is the required right-angled isosceles triangle as shown in the image attached below.

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Answer:

Step-by-step explanation:

To graph 10x-3y=15, start by rearranging the equation to the slope-intercept form of y = mx + b, where m = the slope and b = the y-intercept. 10x-3y=15 becomes 3y = 10x - 15. Solve for y by dividing both sides by 3 to get y = (10/3)x - 5.

Now that the equation is in the slope-intercept form, draw a graph on a coordinate plane. Start by plotting the y-intercept at (0, -5). Next, use the slope of 10/3 to determine the rise and run of the line. The rise is +10 and the run is +3. Starting at the y-intercept, draw a line that moves up 10 and to the right 3, and continue doing this until you reach the end of the graph. This line is the graph of 10x-3y=15.

Answer:

y=10/3x+5

(0,5), (3,15)

Step-by-step explanation:

First, put the graph in slope-intercept form. We can do this by subtracting 10x from both sides.

-3y=-10x-15

Next, we divide by -3.

y=10/3x+5

If you don't know how to graph an equation with slope-intercept form,

it is in the format of y=mx+b, where m is the slope (in this case, 10/3) and b is the y-intercept (in this case 5, or (0,5)). First graph the y-intercept.

(0,5).

Then implement the slope. Here we would go up by 10 and then go right by 3. This makes our second point (3,15).

Now that we have two points (0,5) and (3,15), just construct your line.

The slope of the line is C) [tex]\frac{6}{5}[/tex].

What is slope?

Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line. Any two distinct places along the line can be used to determine the slope of any line.

Here the given point is [tex](x_1,y_1)=(-5,-1)[/tex] and [tex](x_2,y_2)=(5,11)[/tex]

Now using slope formula then,

=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> Slope m = [tex]\frac{11-(-1)}{5-(-5)}[/tex]

=> slope m = [tex]\frac{11+1}{5+5}[/tex]

=> slope m = [tex]\frac{12}{10}[/tex]

=> slope m = [tex]\frac{6}{5}[/tex]

Hence the slope of the line is C) [tex]\frac{6}{5}[/tex].

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1.) The 50% of R100 = R50

2.) The 0.5 of R100 = R50

3.) The ½ of R100 = R50.

Percentage is defined as the part of a whole which is represented per 100 and the symbol which is used is %.

Therefore, is can be concluded since the same value was gotten that 50% = 0.5 = ½.

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The latera surface area of the triangular prism is  425 inches².

The isosceles triangular prism is unfolded into the net shown below. Therefore, the lateral surface area of the triangular prism can be found as follows:

The lateral surface area of the triangular prism is the product of the perimeter of the triangle and the height of the prism.

Hence,

lateral surface area of the triangular prism = ph

where,

Therefore,

lateral surface area of the triangular prism = (9 + 9 + 7)17

lateral surface area of the triangular prism = 25 × 17

lateral surface area of the triangular prism = 425 inches²

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Answer:

Step-by-step explanation:

Elimination is a method of solving a system of equations by adding or subtracting the equations from each other to eliminate one of the variables.

In this case, we will be using elimination to solve the system of equations:

-3x + 12y = 9

x - 4y = -3

Step 1: Multiply the first equation by -1.

(Multiplying by -1 switches the sign of every number in the equation)

3x - 12y = -9

Step 2: Add the two equations together.

3x - 12y = -9

+x - 4y = -3

______________

4x - 16y = -12

Step 3: Isolate the y-variable by adding 16y to both sides of the equation.

4x - 16y = -12

+16y +16y

______________

4x = -12 + 16y

Step 4: Divide both sides of the equation by 4 to isolate the y-variable.

4x = -12 + 16y

4/4 4/4

______________

x = -3 + 4y

Therefore, the solution to the system of equations is x = -3 + 4y.