A section of a biking trail begins at the coordinates
(-3, 14) and follows a straight path that ends at
coordinates (6, -1). What is the rate of change of
the biking trail?

[tex]|\Omega|=2^2=4[/tex]

1.

[tex]|A|=2\\P(A)=\dfrac{2}{4}=\dfrac{1}{2}[/tex]

2.

[tex]|A|=3\\P(A)=\dfrac{3}{4}[/tex]

3.

[tex]|A|=3\\P(A)=\dfrac{3}{4}[/tex]

[tex](x-1)(x+20)=x^2+20x-x-20=x^2+19x-20[/tex]

Answer:

Yes,they will intersect at (0.686,3.941) and (2.914,-2.741)

Step-by-step explanation:

Given the values that represent the function g(x) you can plot them directly on a graph tool and plot the function y²+x²=16 then visualize

You can also determine the equation of the linear function as then graph both equations on the graph tool

Finding gradient m

Given (0,6) and (1,3)

m=change in value of y/change in value of x

[tex]m=\frac{3-6}{1-0} =\frac{-3}{1} =-3[/tex]

Finding the equation of the linear function

Taking points (2,0)   and (x,y)

[tex]m=\frac{y-0}{x-2} \\\\-3=\frac{y-0}{x-2} \\\\\\-3(x-2)=y-0\\\\\\-3x+6=y-0\\\\\\y=-3x+6[/tex]

From the graph,they intersect at

(0.686,3.941) and (2.914,-2.741)

Answer:

Yes, at positive x coordinates

Answer: 495 degrees

Step-by-step explanation:

[tex]\frac{11\pi }{4}[/tex] · [tex]\frac{180}{\pi }[/tex]

[tex]\frac{1980}{4}[/tex]

495 degrees

Answer:

you just need memorize some of the side lengths of right triangle, or you can use this formula to calculate: a^2 + b^2 = c^2

For example, you need memoreize this group of side lengths of right triangle: 3 , 4 , 5

and in your options, there is a group is same as 3, 4 , 5 but it's 8 times bigger.

The answer is:

D. 24, 32, 40

Answer:

D.

Step-by-step explanation:

In a right triangle, the sum of the squares of the two shorter sides will equal the square of the longest side.

The law to observe here is the Pythagorean theorem where;

[tex]a^2+b^2=c^2\\[/tex]

where a and b are the two shorter sides where as c is the longest side/hypothenuse

In this question the last option is correct.How?

Lets take a=24 and b=32, what is c?

You apply;

[tex]a^2+b^2=c^2\\\\24^2+32^2=c^2\\\\\\576+1024=1600\\\\c^2=1600\\\\c=\sqrt{1600} =40[/tex]

Hence option D is correct where ;

[tex]24^2+32^2=40^2[/tex]

Answer:

The answer is 21%.

Step-by-step explanation:

1) divide 134 by 106

106/134 is about 0.79

2) Multiply by 100 to find the percentage

0.79(100)= 79%

3) Subtract 79% from 100% to find the percentage difference

100%-79%= 21%

Therefore, the percent of change between 134 and 106 is 21%.

Hope this helps!

Plug values in function.

f(3) = 0.01(2)(3)

f(3) = 0.06

f(5) = 0.01(2)(5)

f(5) = 0.10

Average rate of change formula: f(b) - f(a) / b - a

Plug in.

0.10 - 0.06 / 5 - 3 = 0.04 / 2 = 0.02

Average rate of change: 0.02

Answer:

The Average rate of change: 0.02

Step-by-step explanation:

Great Question, First to be able to figure out the average rate of change for the function we need to plug each value for x given into the function and get an output value

[tex]f(3) = 0.01(2)(3)[/tex]

[tex]f(3) = 0.06[/tex]

[tex]f(15) = 0.01(2)(15)[/tex]

[tex]f(15) = 0.3[/tex]

Now that we have both outputs for the values of x given to us in the question, we can use the rate of change formula from the picture below to find the Rate of Change of these two values of x.

[tex]\frac{0.3-0.06}{15-3} = r[/tex]

[tex]\frac{0.24}{12} = r[/tex]

[tex]0.02 = r[/tex]

So Now we see that The Average rate of change: 0.02

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

-4 or A

Step-by-step explanation:

If x was -4 then you would be dividing by zero and it would not be possible.

F (- 12) = 2/3(-12)+7

F (- 12) = 2(-4) + 7

F(-12) = -8 + 7

F(-12) = -1

Answer:

5 sports

Step-by-step explanation:

To find the number of sports, take the total number of kids and divide by the number of teams

625/125 = 5

There are 5 sports

[tex]\text{Hey there!}[/tex]

[tex]\text{In order for you to find the number of sports were there, we have to divide!}[/tex]

[tex]\bullet\ \text{625 kids play sports}[/tex]

[tex]\bullet\ \text{125 kids on each team}[/tex]

[tex]\text{625 will be our numerator (or front number)}[/tex]

[tex]\text{125 will be our denominator (or back number)}[/tex]

[tex]\dfrac{625}{125}=625\div125=5[/tex]

[tex]\boxed{\boxed{\bf{Your\ answer:5}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

41°

Step-by-step explanation:

∠C is opposite of side c.

Using law of cosines:

c² = a² + b² − 2ab cos C

17.2² = 26² + 19² − 2(26)(19) cos C

cos C = 0.750

C ≈ 41°

Answer:

The answer is 41 degrees

The center of the circle is (-3, -9/2) and the radius is sqrt(41)/2.

To find the coordinates of the center and length of the radius of the circle, we need to rewrite the equation of the circle in the standard form (x-h)^2 + (y-k)^2 = r^2. First, complete the square for the x and y terms by adding and subtracting the necessary constants:

x^2 + 6x + 4y = 23

x^2 + 6x + 9 + 4y + 9 = 23 + 9 + 9

(x + 3)^2 + (y + 9/2) = 41/4

Therefore, the center of the circle is (-3, -9/2) and the radius is sqrt(41/4), which simplifies to sqrt(41)/2.

Answer:

Part 5) The roots are x=-3 and x=1.5

Part 6) The solution on a number line is the shading area below of the line y=-1/3 (close circle)

Step-by-step explanation:

Part 5) Find the roots of the parabola given by the following equation

[tex]2x^{2} +5x-9=2x[/tex]

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2}+5x-2x-9=0[/tex]

[tex]2x^{2}+3x-9=0[/tex]

so

[tex]a=2\\b=3\\c=-9[/tex]

substitute in the formula

[tex]x=\frac{-3(+/-)\sqrt{3^{2}-4(2)(-9)}} {2(2)}[/tex]

[tex]x=\frac{-3(+/-)\sqrt{81}} {4}[/tex]

[tex]x=\frac{-3(+/-)9} {4}[/tex]

[tex]x=\frac{-3(+)9} {4}=1.5[/tex]

[tex]x=\frac{-3(-)9} {4}=-3[/tex]

therefore

The roots are x=-3 and x=1.5

Part 6) Solve the inequality and graph the solution on a number line.

[tex]-3(5y-4)\geq 17[/tex]

Solve for y

[tex]-15y+12\geq 17[/tex]

Subtract 12 both sides

[tex]-15y\geq 17-12[/tex]

[tex]-15y\geq 5[/tex]

Multiply by -1 both sides

[tex]15y\leq -5[/tex]

Divide by 15 both sides

[tex]y\leq -1/3[/tex]

The solution is the interval -----> (-∞, -1/3]

All  real numbers less than or equal to negative one third

The solution on a number line is the shading area below of the line y=-1/3 (close circle)

The graph in the attached figure

Answer:

(-5, 1)

Step-by-step explanation:

We are given a kite on the graph which is rotated 180° clockwise about the origin and then reflected over the Y axis followed by reflection over the X axis.

We are to find the coordinates of point A after the complete transformation.

A (-5, 1)

When a point is rotated 180° clockwise about the origin, the signs of its coordinates change.

A (-5, 1) ---> A' (5, -1) - after clockwise rotation of 180 degrees about origin

Then this point A' is reflected over the Y axis where the y coordinate remains the same but x coordinate changes its sign.

A' (5, -1) ---> A'' (-5, -1) - after reflection through y axis

Now this point A'' is reflected over the X axis where the x coordinate remains the same while y coordinates changes its sign.

A'' (-5, -1) ---> A''' (-5, 1) - after complete transformation

Answer:(-5, 1)

Step-by-step explanation:

Since 25% of something is also 1/4 of something, multiply 25% by 4 to get the full value.

Since 75 is 25 percent, multiply 75 by 4.

75*4=300

The value is 300.

Hope this helps!

Answer:

Infinitely many

8

Step-by-step explanation:

First, you subtract by 4s both sides of equation.

4s+8-4s=3+5+4s-4s

Then, simplify.

8=3+5

Same thing like order of operations.

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

Add the numbers from left to right.

3+5=8

8=8 is true

8 is the correct answer.

Infinitely many is the correct answer.

The given equation has no solution.

As the given equation is:

[tex]4s+8=3+5+4s\\[/tex]

So, if we simplify we get;

[tex]8=3+5+4s-4s[/tex] (subtracting 4s from both sides of the equation)

Now, on adding we get;

[tex]8=8[/tex]

So, LHS=RHS.

Therefore, there is no variable for which we can find the solution.

Hence option(b) none is the correct answer

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in maths when you do not know the exact number in a calculation. Many professionals use equations every day, including air traffic controllers, architects, computer programmers and carpenters.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

Equation is defined as the state of being equal and is often shown as a math expression with equal values on either side, or refers to a problem where many things need to be taken into account. An example of an equation is 2+2 = 3+1.

Learn more about equation, refer to:

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Answer:

1120

Step-by-step explanation:

8/50=x/7000

50x=56000

Divide 50 on both sides

1120

Answer:

1120

Step-by-step explanation:

8/50=x/7000

50x=56000

Divide 50 on both sides

1120

Answer:

x = -4, 10

Step-by-step explanation:

We take the square root and use the fact of "plus-minus" and find two values of x. The process of solving this equation is shown below:

[tex](x-3)^2 = 49\\\sqrt{(x-3)^2}=\sqrt{49}\\  x-3=+-7\\x=3+7=10\\x=3-7=-4[/tex]

Hence the two values of x are -4 and 10

Note: both (-7)^2 and (7)^2 are 49 . So we took "plus-minus" values of [tex]\sqrt{49}[/tex]

Answer: -4 and 10

Step-by-step explanation:

b and c

the second and and the third option

the middle two

Answer:

34/13

Step-by-step explanation:

The length-to-width ratio here is:

8.5 / 3.25

which can be reduced by dividing numerator and denominator both by 0.25:

8.5/0.25

--------------- = 34/13

3.25/0.25

Answer:

I think the answer is B= 62  

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

Distributive property.

For this case we have that by definition, the distributive property establishes that:

[tex]a (b + c) = ab + ac[/tex]

So, if we have:

[tex]5 (x-7) = 55[/tex]

When applying distributive property to the terms within the parenthesis we have:

[tex]5x-35 = 55[/tex]

The distributive property was used to write the second step.

Answer:

Distributive property

Answer:

The answer for this question is B (10) I have shown a step by step explaination for you to understand how I got this answer

Step-by-step explanation:

4x-2=x+28

-x -x

3x-2=28

+2 +2

3x=30

3x/3 = 30/3

x=10

The value of x for which DEFG must be a parallelogram is Option(B) 10 .

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

As we know that for a parallelogram, the opposite adjacent sides are always parallel and equal in length.

Therefore, for DEFG to be a parallelogram, the sides DH and FH must be equal in length.

We have,  DH = FH

⇒ 4x - 2 = x + 28

⇒ 3x = 30

∴  x = 10

Thus, the value of x for which DEFG must be a parallelogram is Option(B) 10 .

To learn more about parallelogram , refer -

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Answer:

False.

Because Only one circle can be circumscribed about a given triangle.

Final answer:

The statement that many triangular shapes can be circumscribed about a given circle is true, as an infinite number of triangles can be formed by connecting any three distinct points on the circumference of the circle.

Explanation:

The statement "Many triangular shapes can be circumscribed about a given circle" is true. By definition, a circumscribed triangle is one that surrounds a circle, touching the circle exactly at its perimeter at three points.

Given a circle, you can indeed construct infinite triangles that circumscribe the circle, as for any set of three points on the circumference of the circle, a unique triangle can be formed.

In mathematical terms, three points determine one of these curves; that is, through any three points not in a straight line on a circle's circumference, we can draw a unique triangle which will circumscribe the circle.

Since there are an infinite number of points on a circle's circumference, we can choose an infinite number of triplets of points, each producing a different circumscribed triangle.

Answer:

⅓

Step-by-step explanation:

Whether you divide by ⅓ [X ÷ ⅓] or multiply by ⅓ [Y × ⅓], the ratio is similar. It never varies.

1/3

Divide the 2 lowest values by each other.

6/2=1/3

Hope this helps!

Answer:

[tex]\frac{83}{186}[/tex]

Step-by-step explanation:

In probability, "OR" means "+" and "AND" means "*".

The total amount of people is:

32 + 54 + 78 + 112 + 96 = 372

Number of diabetic patients are 54

Number of eye patients are 112

Since we want "OR", we will add the two probabilities:

P(diabetic or eye problem) = 54/372 + 112/372 = 83/186

Well going off what I know (you don't have the equations up)

You have to isolate x

3/4x = 6

(4) 3/4x = 6 *multiplying by 4 cancels the fraction.

3x = 24

Divide by 3

X = 6

Answer:

[tex]x = 8[/tex]

Step-by-step explanation:

Let multiply each side by 4/3:

[tex]\frac{4}{3}\cdot \frac{3}{4} \cdot x = 6\cdot \frac{4}{3}[/tex]

[tex]x = 8[/tex]

Answer:

The Answer would be D) 3

Answer:

The difference is 8 F

Step-by-step explanation:

The difference means subtract

56-48 = 8

The difference is 8 F

Answer:

120

Step-by-step explanation:

Evaluate the expression by substituting the given values into it

4(6 + 24) = 4 × 30 = 120

Answer:

52.8

Step-by-step explanation:

First we need to find 12% of 60

12% * 60

.12 * 60

7.2

We want less than which means subtract

60-7.2

52.8