How are ROC (rate of change) and slope related AND different

Answer:

[tex](x-5)^2+(y-6)^2=5[/tex]

Step-by-step explanation:

Equation of the Circle

A circle centered at (h,k) and radius r can be written with the equation:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We are given the center (5,k), thus:

[tex](x-5)^2+(y-k)^2=r^2[/tex]

We know the point (3,7) belongs to the circle. This means the distance between the center and this point is the radius.

Given two points (x1,y1) and (x2,y2), the distance between them satisfies:

[tex]d^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]

Calculating the radius, we have:

[tex]r^2=(7-k)^2+(3-5)^2[/tex]

[tex]r^2=(7-k)^2+4\qquad\qquad [1][/tex]

Now we use the fact that the line y=2x+1 and the circle are tangent at (3,7). The radius and the line are perpendicular at that point. Two perpendicular lines with slopes m1 and m2 satisfy the condition:

[tex]m_1\cdot m_2=-1[/tex]

The line y=2x+1 has a slope of m1=2, thus the slope of the segment from (5,k) to (3,7) has a slope of -1/2:

The slope is calculated as:

[tex]\displaystyle \frac{7-k}{3-5}=-\frac{1}{2}[/tex]

Operating:

[tex]\displaystyle \frac{7-k}{-2}=-\frac{1}{2}[/tex]

Multiplying by -2

[tex]\displaystyle 7-k=1[/tex]

Solving:

k=6

From [1] the radius is:

[tex]r^2=(7-6)^2+4[/tex]

[tex]r^2=1+4[/tex]

[tex]r^2=5[/tex]

Finally, substituting into the equation of the circle:

[tex]\mathbf{(x-5)^2+(y-6)^2=5}[/tex]

The graph can be seen in the figure below.

Answer:

Step-by-step explanation:

Answer:

The distance from the point to the line is approximately 3.2 units

Step-by-step explanation:

Distance From a Point to a Line

Is the shortest distance from a given point to any point on an infinite straight line. The shortest distance occurs when the segment from the point and the line are perpendiculars.

If the line is given by the equation ax + by + c = 0, where a, b and c are real constants, the distance from the line to a point (x0,y0) is

[tex]\displaystyle d= \frac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}}[/tex]

The line is given by the equation:

y=3x. We need to transform it into the specified form.

Subtracting 3x:

y - 3x = 0

Comparing with the general form of the line, we have

a=-3, b=1, c=0

The point (xo,yo) is (-1,7), thus:

[tex]\displaystyle d= \frac{|-3\cdot (-1)+1\cdot 7+0|}{\sqrt{(-3)^2+1^2}}[/tex]

[tex]\displaystyle d= \frac{|3+7|}{\sqrt{9+1}}[/tex]

[tex]\displaystyle d= \frac{|10|}{\sqrt{10}}[/tex]

[tex]\displaystyle d= \frac{10}{\sqrt{10}}[/tex]

[tex]d\approx 3.2[/tex]

The distance from the point to the line is approximately 3.2 units

Answer:

Part A: The higher the temp the more ice cream sold.

Part B

Step-by-step explanation:

Answer:

-13

Step-by-step explanation:

-13 since it's going down in price

Answer:

hi

Step-by-step explanation:

hi

Answer:

Lilly earns $170

Tilly earns $340

Step-by-step explanation:

Given that

Tilly earned twice as much as Lilly

If Lilly's earning = x, then Tilly's earning = 2x

Total amount they both earned = $510

x + 2x = $510

3x = $510

3x / 3 = $510 /3

x = $170

Hence,

Lilly earns x = $170

Tilly earns, 2x = 2* 170 = $340

Answer:

18

Step-by-step explanation:

t = Number of trucks counted

c = Number of cars

Ratio of trucks to cars = [tex]\dfrac{t}{c}=\dfrac{3}{8}[/tex]

Total number of cars and truck = 66

[tex]t+c=66[/tex]

Divide the left and right side by the number of cars

[tex]\dfrac{t+c}{c}=\dfrac{66}{c}\\\Rightarrow \dfrac{t}{c}+1=\dfrac{66}{c}\\\Rightarrow \dfrac{3}{8}+1=\dfrac{66}{c}\\\Rightarrow \dfrac{11}{8}=\dfrac{66}{c}\\\Rightarrow c=66\times \dfrac{8}{11}\\\Rightarrow c=48[/tex]

Total number of cars is 48

so

[tex]t=66-c\\\Rightarrow t=66-48\\\Rightarrow t=18[/tex]

Total number of trucks counted is 18.

Answer:

48 degrees

Step-by-step explanation:

Answer:

I think this is answer:

0.113-1.001-1.101

Step-by-step explanation:

Use the distance formula to find base and height.

Answer:D.54

Step-by-step explanation: it takes 20 minutes in the car which is 1/3 of an hr so 42/3= 14 then that leaves 40 minutes left for the train which is 2/3 of 60 and 60/3=20 and 20x2= 40 so 40+14=54

Answer:

D. 54

Step-by-step explanation:

Give the guy above brainliest

Answer:

The ordered pairs are;

(-1,1) and (-2,3)

Step-by-step explanation:

Here, we want to select which ordered pair is not a solution to the given equation

The one that will not be a solution will be a point at which if we insert the x-value into the equation, we do not get the y-value at that point

For (3,7

2(3) + 1 = 7

For 0,1

2(0) + 1 = 1

For (-1,1)

= 2(-1) + 1 = -2 + 1 = -1

This is wrong

(-3,-5)

= 2(-3) + 1 = -6 + 1 = -5

(-2,3)

= 2(-2) + 1 = -4 + 1 = -3

This is wrong also

Answer:

1) B

2) A

3) H

4) E

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

1 foot= 12 inches

24x12=288

Answer:288

Step-by-step explanation:24x12=288 hope this helps

Answer:

2.7

Step-by-step explanation:

The 3 does not round up the 7, so it stays as 2.7

Answer:

2.7

Step-by-step explanation:

the tenths place is the first number after the decimal. When rounding numbers 5 and higher can increase the number next to it by 1. So 2.736 becomes 2.74 then becomes 2.7 as the 4 is not able to round the number since it is below 5.

Answer:

1 cup of flower makes 1/2 a batch of cookies

Step-by-step explanation:

2 divided by 2 is 1

1 divided by 2 is 1/2

Answer:

i think that its D

Step-by-step explanation:

hopes this helps

Answer:

the number of times  will Aiden hit the ball is 7

Step-by-step explanation:

The computation of the number of times will Aiden hit the ball is shown below:

She hit 35% of the times

i.e.

= Given percentage of number of times

= 35% of 20

= 35 ÷ 100 × 20

= 0.35 × 20

= 7

Hence, the number of times  will Aiden hit the ball is 7

We simply applied the above formula so that the correct value could come

The same is to be considered

Answer:

mom will be sad

Step-by-step explanation:

YOU ARE A BEATIFUL AND AMAZING PERSON DONT DIE ON ME LIKE THIS

Answer:

64%

Step-by-step explanation:

The first step is to calculate the increase

= 4100-2500

= 1600

Therefore the percentage increase can be calculated as follows

= increase/original number × 100

= 1600/2500 × 100

= 0.64 × 100

= 64%

Hence the percentage increase is 64%

y=4.5x the equation for cranberries

Step-by-step explanation:

So the easiest way to solve this would be take the $18 and divide it by the 4 pounds you then get the unit price per pound which is $4.5 a pound

Note: Consider the base of all is 3 instead of comma.

Given:

Consider the given value is [tex]\log_37=1.77[/tex].

To find:

The value of [tex]\log_363[/tex].

Solution:

Using properties of logarithm, we get

[tex]\log_363=\log_3(9\times 7)[/tex]

[tex]\log_363=\log_3(3^2\times 7)[/tex]

[tex]\log_363=\log_3(3^2)+\log_3(7)[/tex]       [tex][\because \log ab=\log a+\log b][/tex]

[tex]\log_363=2+ \log_3(7)[/tex]    [tex][\because \log_aa^x=x][/tex]

[tex]\log_363=2+1.77[/tex]        [tex][\because \log_37=1.77][/tex]

[tex]\log_363=3.77[/tex]

Therefore, the value of [tex]\log_363[/tex] is 3.77.

Applying logarithm properties, it is found that:

[tex]\log_3{63} = 3.77[/tex]

We want to find [tex]\log_3{63}[/tex], considering that [tex]63 = 7 \times 9 = 7 \times 3^2[/tex], we have that:

[tex]\log_3{63} = \log_3{(7 \times 3^2)}[/tex]

The first property applied is:

[tex]\log{a \times b} = \log{a} + \log{b}[/tex]

Hence:

[tex]\log_3{63} = \log_3{(7 \times 3^2)} = \log_3{7} + \log_3{3^2}[/tex]

The next property is:

[tex]\log_a{a^b} = b[/tex]

Hence:

[tex]\log_3{7} + \log_3{3^2} = 1.77 + 2 = 3.77[/tex]

A similar problem is given at https://brainly.com/question/2620660

Answer:

x=(-1)/4

Step-by-step explanation:

4x=1-2

4x=(-1)

x=(-1)/4

Answer: I think that the answer is B

Step-by-step explanation:

Answer:

D:95 mm Hg

Step-by-step explanation:

Using the linear model, y=x+95, x represents the age and y represents the blood pressure.

For a newborn, x=0 this gives us

> y=0+95 = 95<

Answer: 1mm hg per year

Step-by-step explanation:

Answer:

i have a feeling it is C because the lines intersect at (5,0)