PLEASE HELP, will give brainliest if you answer
consider the function represented by the equation 16b = 4r - 12. write the equation in function notation, where b is the independent variable. Must show work for full credit

The values of x and y are 5/7 and 11 respectively.

Similar triangles are triangles with equal corresponding angles and equal side ratios.

We use similarity theorem to solve for x and y

x/3+x = 11/18

18x = 33 + 11x

collect like terms

18x - 11x = 33

7x = 33

x = 33/7

x = 4 5/7

y/7+y = 11/18

18y = 77 + 11y

7y = 77

y = 11

Therefore, the values of x and y are 4 5/7 and 11 respectively.

Answer: C) 5

--------------

x = independent variable, y = dependent variable

Assuming this is a linear function, each increase of x by 2 leads to y going up by 10. So 10/2 = 5 is the unit increase each time x bumps up by 1.

-------------------

An alternative is to use the slope formula to get

m = (y2 - y1)/(x2 - x1)

m = (25 - 15)/(4 - 2)

m = 10/2 <--- this expression shows up again

m = 5 <---- leading to the same answer as before

So we see that the slope formula is a more drawn out method to finding the answer.

Answer:

c) 5

Step-by-step explanation:

(m, a, b, c) ∈ {(1, 196, 441, 210), (7, 28, 63, 30)}

m is a common factor of 196, 210, 441

The prime factors of those numbers are

... 196 = 2²×7²

... 210 = 2×3×5×7

... 441 = 3²×7²

7 is the only prime factor common to all the numbers. Hence the possible values of m are 1 and 7.

For m = 1, (a, b, c) = (196, 441, 210).

For m = 7, (a, b, c) = (196, 441, 210)/7 = (28, 63, 30).

9514 1404 393

Answer:

  (b)  y = -2.5x² -5.5x +1.5

Step-by-step explanation:

The table entry (0, 1.5) tells you that the y-intercept is 1.5. That eliminates choices C and D.

Substituting x=4 into the first equation (choice A) shows you it is incorrect:

  y = -5.5(4²) -2.5(4) +1.5 = -88 -10 +1.5 = -96.5 . . . not -60.5

This only leaves choice B, a choice confirmed by a quadratic regression using a graphing calculator (or spreadsheet).

   y = -2.5x² -5.5x +1.5

Final answer:

The equation in standard form of the parabola that models the values in the table is y = -2.3x^2 + 2.6x + 1.5

Explanation:

The equation in standard form of a parabola that models the values in the table is y = ax^2 + bx + c. To find the values of a, b, and c, we can use the given table:

XF(x)-22.501.54-60.5

Plugging in the values from the table into the equation, we get a system of three equations:

4a - 2b + c = 2.5

c = 1.5

16a + 4b + c = -60.5

Solving this system of equations, we find that a = -2.3, b = 2.6, and c = 1.5.

Therefore, the equation in standard form of the parabola that models the values in the table is y = -2.3x^2 + 2.6x + 1.5.

Answer:

x=63

y=27

Step-by-step explanation:

As we can see from the graph x+ 117 form a straight line

x+ 117 = 180

Subtract 117 from each side

x+117-117 = 180 -117

x = 63

The graph indicates that x+y forms a right angles

x+y = 90

We know x = 63

63+y = 90

Subtract 63 from each side

63-63+y = 90-63

y = 27

Answer:

y=27 simple one

Step-by-step explanation:

ez

Answer:

The correct answer is option C, Multiplying by 1/5 is the same as multiplying by 20%.

Step-by-step explanation:

The equation 1/5 = 1 divided by 5 = 0.2

and 0.2 can be expressed as 20%

Thus both the factor 1/5 and 20 % are same

Answer:

c is the answer

Step-by-step explanation:

Answer:

W'' = (2, -3)

Step-by-step explanation:

Reflection over the x-axis negates the y-coordinate and leaves the x-coordinate alone. The W becomes ...

... W' = (-2, -3)

Reflection over the y-axis negates the x-coordinate and leaves the y-coordinate alone. The W' becomes ...

... W'' = (2, -3)

Answer:

The coordinates of point W'' are (2,-3).

Step-by-step explanation:

The coordinates of given point are W(-2,3).

If point W is reflected over the x-axis, then

[tex](x,y)\rightarrow (x,-y)[/tex]

[tex]W(-2,3)\rightarrow W'(-2,-3)[/tex]

If point W' is reflected over the y-axis, then

[tex](x,y)\rightarrow (-x,y)[/tex]

[tex]W'(-2,-3)\rightarrow W''(2,-3)[/tex]

Therefore the coordinates of point W'' are (2,-3).

Answer:

ITS C: Multiplying by 15 is the same as multiplying by 20%

Step-by-step explanation:

The solution is Option C.

The equation of multiplying by 1/5 is the same as multiplying by 20%

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Cara has driven one-fifth of the total distance, d, to her destination

So , the distance traveled by Cara S = ( 1/5 )d

And , the distance traveled by Cara S = 0.2d

On simplifying the equation , we get

The value of ( 1/5 )d = d/5

The value of 0.2d = ( 20/100 )d

The value of 0.2d = 20 % of d

Therefore , the value of ( 1/5 )d = value of 0.2d

Hence , the equations are same

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Answer:

(25/54)x⁻⁶y⁻⁹  

Step-by-step explanation:

  [4(5x³y³)²]/(6x⁴y⁵)³                    Do the outside exponents first

= [4(25x⁶y⁶)]/(216x¹²y¹⁵)               Group like terms

= [(4×25)/216] × x⁶/x¹² × y⁶/y¹⁵     Reduce fractions to lowest terms

= 25/54 × x⁻⁶ × y⁻⁹                       Recombine the terms

= (25/54)x⁻⁶y⁻⁹

Answer:

Step-by-step explanation:

When the second train leaves, the remaining distance between the trains is ...

... 600 km - (3 h)×(60 km/h) = 420 km

That distance will be covered at the speed of (60 +v) so the time it takes for the second train to cover that distance is ...

... 420/(60 +v)

The variable t represents the time since the first train left, so is 3 hours more than this time value. Hence ...

... t = 3 +420/(60 +v)

Solving for v, we have ...

... t -3 = 420/(60 +v) . . . . subtract 3

... 60 +v = 420/(t -3) . . . . multiply by (60+v)/(t -3)

... v = 420/(t -3) -60 . . . . subtract 60

For t = 7 ...

... v = 420/(7 -3) -60 = 105 -60 = 45

For t = 6 ...

... v = 420/(6 -3) -60 = 140 -60 = 80

Answer:

The area of the entire yellow region is 48 cm^2.

Step-by-step explanation:

See the attached image :)

Answer:

The ratio of Messi : Ronaldo

                   7:6

Step-by-step explanation:

The ratio of Messi : Ronaldo

   700 :600

Divide each side by 100

7:6

You cannot tell who is better because we do not know how many shots they took.

Hello, there! :)

Answer:

s=4

*The answer must have a positive sign.*

Step-by-step explanation:

First, you divide by 6 from both sides of an equation.

[tex]\frac{6s}{6}=\frac{24}{6}[/tex]

Then, you divide by the numbers from left to right.

[tex]24/6=4[/tex]

Final answer is s=4

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thank you so much! :)

:D

Answer:

A

Step-by-step explanation:

Function cannot have at least two points on same vertical line.

Vertical test fails at x = 1. So we need to eliminate either point (1, 1) or (1, 3).

There is option (1, 1), so A.

To represent a function, we must have unique y-values for each x-value. Thus, the point (1,1) should be removed. The correct answer is A).

To determine which ordered pair should be removed from the graph to represent a function, we need to check for uniqueness in the x-values. In a function, each x-value can only be associated with one y-value.

Let's examine the given points:

(1,1)

(3,2)

(5,2)

(7,4)

(1,3)

The x-values are: 1, 3, 5, 7, and 1.

Notice that the x-value 1 is associated with both (1,1) and (1,3). In a function, an x-value should have a unique y-value. Therefore, the point (1,1) should be removed from the graph to represent a function.

So, the correct option is A) (1,1).

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Answer:

ave rate of change = k(5) - k(-3)

                                  ----------------

                                   5+3

Step-by-step explanation:

To find the average rate of change

ave rate of change = f(x2) - f(x1)

                                  ----------------

                                   x2-x1

We know that x2 = 5 and x1 = -3

ave rate of change = k(5) - k(-3)

                                  ----------------

                                   5--3

ave rate of change = k(5) - k(-3)

                                  ----------------

                                   5+3

Answer:

B. x > -1

Step-by-step explanation:

Subtract the left side:

... 0 < -6(1 -x) -2(x-5)

... 0 < -6 +6x -2x +10 . . . . eliminate parentheses

... 0 < 4 +4x . . . . . . . . . . . collect terms

... 0 < 1 +x . . . . . . . . . . . . . divide by 4

... -1 < x . . . . . . . . . . . . . . . add -1. Matches selection B.

Answer:

94 pounds

Step-by-step explanation:

Let "a" represent the weight of type A coffee Charlie used. Then 150-a is the weight of the type B coffee. The total cost of the blend is then ...

... 4.85a +5.95(150 -a) = 789.10

... -1.10a +892.50 = 789.10 . . . . . . simplify

... -1.10a = -103.40 . . . . . . . . . . . . . .subtract 892.50

... a = 94 . . . . . . . . . . . . . . . . . . . . . divide by -1.10

Charlie used 94 pounds of type A coffee.

Final answer:

Charlie used 94 pounds of type A coffee for the blend, which was found by setting up a system of equations based on the total weight and cost of the coffee blend and solving for the quantity of type A coffee.

Explanation:

To solve how many pounds of type A coffee Charlie used, we need to set up a system of equations based on the given information.

Let x be the amount of type A coffee and y be the amount of type B coffee. We have two types of coffee totaling 150 pounds, so x + y = 150.

The cost of the two types of coffee leads to the second equation: 4.85x + 5.95y = 789.10.

We solve this system of equations either by substitution or elimination. If we solve for y from the first equation (y = 150 - x) and substitute it into the second equation, it simplifies to 4.85x + 5.95(150 - x) = 789.10, which becomes 4.85x + 892.50 - 5.95x = 789.10. Simplifying further gives -1.10x = -103.40, which when solved for x gives x = 94.

Therefore, Charlie used 94 pounds of type A coffee for his blend.

Answer:

96

Step-by-step explanation:

Let x represent the number of adult tickets sold. Then (182-x) is the number of child tickets sold. The total sales is then ...

... 6.60·(182 -x) +9.80·x = 1508.40

... 3.20x = 1508.40 -1201.20 . . . . . simplify, subtract 1201.20

... 307.20/3.20 = x = 96 . . . . . . . . divide by the coefficient of x

96 adult tickets were sold that day.

Final answer:

By setting up and solving a system of equations, it is determined that 96 adult tickets were sold at the movie theatre.

Explanation:

To solve the problem of how many adult tickets were sold at the movie theatre, we need to set up a system of equations based on the given information: child admission is $6.60, adult admission is $9.80, 182 tickets were sold in total, and the sales amounted to $1508.40.

Let's denote the number of child tickets sold as c and the number of adult tickets sold as a. We can then create the following two equations:

c + a = 182 (since the total number of tickets sold was 182)

6.60c + 9.80a = 1508.40 (representing the total sales from the tickets)

We can solve these equations using substitution or elimination methods. Here's the step-by-step solution using the elimination method:

First, we multiply the first equation by -6.60 to set up for elimination:

-6.60c - 6.60a = -1201.20

Now we add this to the second equation:

6.60c + 9.80a = 1508.40

3.20a = 307.20

Dividing both sides by 3.20 gives us a = 96.

Therefore, 96 adult tickets were sold that day.

Answer:

29.1°

Step-by-step explanation:

You can use your good sense to select the correct answer.

You know it is not near zero (so, not 0.01 or 0.03—neither of which is rounded to the nearest tenth). Since the adjacent side is longer than the opposite side, you know the angle is less than 45°. (Of the two complementary angles X and T, X is the smaller.) That only leaves one answer choice.

If you really need to figure it out, use SOH CAH TOA to remind you ...

... Tan(X) = Opposite/Adjacent = (5 in)/(9 in)

... X = arctan(5/9) ≈ 29.1° . . . . . make sure your calculator is in degrees mode

In this trigonometric problem, intuitive reasoning and basic principles were used to deduce the angle X as approximately 29.1 degrees, before employing the tangent function for precise calculation.

When faced with a problem involving trigonometry, sometimes you can intuitively deduce the correct answer using logic and a basic understanding of trigonometric principles. Let's break down how to approach the problem step by step:

Eliminate Options: In this case, you are provided with multiple answer choices. You can start by ruling out certain options based on your intuition. You can eliminate answers that are "near zero," such as 0.01 and 0.03, which are not rounded to the nearest tenth.

Analyze the Triangle: By examining the given information, you can infer that the angle you are looking for (angle X) is less than 45°. This deduction is based on the fact that the adjacent side is longer than the opposite side in a right triangle, and X is the smaller of the two complementary angles.

Use SOH CAH TOA: If you want to calculate the angle more precisely, you can apply trigonometric ratios. In this case, you use the tangent function: Tan(X) = Opposite/Adjacent = 5 in / 9 in. Then, you can find the angle using the arctan function, which yields X ≈ 29.1°.

In summary, while you can employ trigonometric functions for precise calculations, sometimes a logical approach and a good understanding of the problem can lead you to the correct answer more efficiently. In this scenario, the angle X is approximately 29.1 degrees, provided your calculator is in degrees mode.

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Answer:

x=-6, y=-1

Step-by-step explanation:

−x+2y=4 and −2x−2y=14

I will solve by elimination.  We can eliminate the y variable by adding these together.

 −x+2y=4

−2x−2y=14

-----------------

-3x      = 18

Divide each side by -3

-3x/-3 = 18/-3

x = -6

But we still need to solve for y

-x + 2y =y

Substitute x in

- -6 +2y =4

6 +2y = 4

Subtract 6 from each side

6-6 + 2y = 4-6

2y = -2

2y/2 = -2/2

y= -1

To solve the system, we added the two equations, resulting in -3x = 18. Solving for x, we found x = -6 and then substituted this value into one of the original equations to solve for y, yielding y = -1. The final solution is (x, y) = (-6, -1).

To solve the system of linear equations -u+2y=4 and -2x-2y=14, we can utilize the elimination method. This involves adding the two equations together in order to eliminate one of the variables, resulting in an equation with a single variable which can be easily solved.

We begin by adding the two equations:

-(-x+2y)+(-2x-2y)=4+14

x - 2y - 2x - 2y = 18

-3x = 18

Divide both sides by -3 to find the value of x:

x = -6

With the value of x known, we substitute it back into one of the original equations to solve for y. Let's use the first equation:

-(-6) + 2y = 4

6 + 2y = 4

2y = -2

Divide both sides by 2 to find the value of y:

y = -1

The solution to the system of equations is (x, y) = (-6, -1).

Answer:

w = 25

Step-by-step explanation:

The function A(w) = -(w-25)² +625 is in vertex form. The vertex (maximum) is at (w, A) = (25, 625). A width of 25 meters will maximize the area.

It is a nonlinear function.

When the points are graphed, they do not all lie on the same line. The lines connecting the points have positive slope, so the function is neither constant nor decreasing.

Answer: It is a nonlinear function.

Step-by-step explanation:

A function is said to be linear if the rate of change of dependent varaible (y) with respect to independent variable (x) is constant.

Rate of change in function [tex]=\dfrac{\text{Change in y}}{\text{Change in x}}[/tex]

The table gives the speeds recorded by the speedometer on Sully's car with respect to time. :

x                                        y

(seconds)                       (mph)

2                                     60

8                                    120

16                                   170

For x= 2 and x= 8 , the rate of change in function will be

[tex]\dfrac{\text{Change in y}}{\text{Change in x}}\\\\=\dfrac{120-60}{8-2}=\dfrac{60}{6}=10[/tex]

For x= 8 and x= 16 , the rate of change in function will be

[tex]=\dfrac{170-120}{16-8}=\dfrac{50}{8}=6.25[/tex]

But 10 ≠ 6.25.

⇒ Rate of change is not constant.

It means the function non- linear.

Also , it is not a constant function because values of y is not constant w.r.t to x.

It is not a decreasing function because values of y increase with increase in x.

D (0, 5), (5, 0)

Anything with -5 and 0 will not satisfy x+y=5. This eliminates the first three choices.

___

It is easiest to check the offered answers. You can also solve this graphically, or by solving the simultaneous equations.

You can, for example, square the first equation and subtract the second:

... (x+y)² -(x²+y²) = 5² -25

... 2xy = 0

This will be true for x=0 or for y=0, so (0, 5) and (5, 0) are solutions to the pair of equations.

To find the solution set to the given system, substitute the value of x into the second equation, factor, and solve for y. The solution set is (5,0).

To find the solution set to the given system of equations, we can solve them simultaneously. From the first equation, we have x = 5 - y. Substituting this value of x into the second equation, we get (5 - y)^2 + y^2 = 25. Expanding and simplifying this equation gives us 2y^2 - 10y = 0. Factoring out y, we have y(2y - 10) = 0. So either y = 0 or 2y - 10 = 0. Solving the second equation for y, we get y = 5.

Therefore, the solution set to the system of equations is (5,0).

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Answer:

y +5 = (-2/3)(x -4)

Step-by-step explanation:

The point-slope form of an equation of a line with slope m through point (h, k) is ...

... y -k = m(x -h)

You have (h, k) = (4, -5) and a slope the same as that of the parallel line, m = -2/3. Then the equation is ...

... y -(-5) = (-2/3)(x -4)

... y +5 = (-2/3)(x -4)

Hello from MrBillDoesMath!

Answer:

x >=4

Discussion:

The inverse of q is

-1 +\-  (x-4)^(1/4)                             (the fourth root of x-4)

(Inverse found by solving  x= (y+1)^4 +4 for y)

The domain of the inverse is therefore x such that x -4 >=0 , i.e. x >=4

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

Answer:

The coordinates of point C are (a,0).

Step-by-step explanation:

Given information: ABC is right isosceles triangle.

From the given figure it is noticed that the side BC is hypotenuse of the triangle ABC.

By pythagoras theorem,

[tex]hypotenuse^2=leg^2+leg^2[/tex]

[tex]hypotenuse^2=2leg^2[/tex]

[tex]hypotenuse=leg\sqrt{2}[/tex]

Therefore hypotenuse cannot be equal to leg. So, we can say that in triangle ABC,

[tex]AB=AC[/tex]

Length of AB is

[tex]AB=\sqrt{(a-0)^2+(0-0)^2}=a[/tex]

From the figure it is noticed that the point C lies on the x-axis, therefore the y-coordinates of C is 0.

Let the coordinates of C be (x,0) and length of AC must be a.

[tex]AC=\sqrt{(x-0)^2+(0-0)^2}[/tex]

[tex]a=x[/tex]

Therefore coordinates of point C are (a,0).

Answer: y = 3

Step-by-step explanation:

The objective is to get 0 on the left side to equal the 0 on the right side. I'd like to do this by making the sum of x^2 and y^2 equal to 10. If (x^2+y^2) = 10, the -10 on the left side will cancel it out to equal 0.

1^2 = 1

3^3 = 9

1 + 9 = 10

Therefore, x is 1 and y is 3.

x^2 + y^2 - 10 = 0

1^2 + 3^2 - 10 - 0

1     +     9  - 10 = 0

10              -10 = 0

0 = 0