What is the equation of a line with a slope of 7 and a point (1, 8) on the line?

A) y = 7x + 1
B) y = 7x
C) y = 7x + 8
D) y = 7x – 56

Answer:

1. option D is correct;  [tex](x+2)^2+(y+7)^2=36[/tex]  

2. option C is correct; center: (-4, 5) and radius = 11 unit

Step-by-step explanation:

The general equation of the circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]                .....[1]

where,

(h, k) is the center of the circle and r is the radius of the circle.

1.

As per the statement:

The center of a circle is at (−2, −7) and its radius is 6.

⇒(h, k) = (-2, -7) and r = 6 units

Substitute these in [1] we have;

[tex](x-(-2))^2+(y-(-7))^2=6^2[/tex]  

⇒[tex](x+2)^2+(y+7)^2=36[/tex]  

Therefore, the equation of circle is, [tex](x+2)^2+(y+7)^2=36[/tex]  

2.

As per the statement:

The equation of a circle is:

[tex](x+4)^2+(y-5)^2 = 121[/tex]

We can write this as:

[tex](x-(-4))^2+(y-5)^2 = 11^2[/tex]

On comparing with equation [1] we have;

(h, k) = (-4, 5) and r = 11 units

Therefore, the center and radius of the circle is,

center: (-4, 5) and radius = 11 unit

[tex]\sqrt{a}=b\iff b^2=a\\\\a\geq0\ \wedge\ b\geq0\\\\\text{therefore your answer is}\\\\\text{(A) The equation has no solutions.}[/tex]

HELLO!!! ^-^

The answer is 1.

If √6 is the geometric mean between 6 and another number, then the number is 1.

(I had the same question and got it right using this answer so yeah) ^-^

Have an amazing day!!! ^-^

Historical Fact:

Back in the older days, the word awful was a word used to praise someone!  That is because aw in awful comes from the origin awe which is used when someone is in awe of you!!! For example: You are AWESOME!!!

[tex] |\Omega|=6^2=36\\
|A|=\underbrace{2}_{\text{the sum is 3}}+\underbrace{4}_{\text{the sum is 9}}=6\\\\
P(A)=\dfrac{6}{36}=\dfrac{1}{6}\approx17\% [/tex]

A quadrilateral has angle measures of 52°, 94°, and 97°.

What is the measure of the fourth angle?

Enter your answer in the box.

Answer: 117

Step-by-step explanation:

Answer:  The correct probability is (D) [tex]P(C/A)=\dfrac{13}{17}.[/tex]

Step-by-step explanation:  We are given to select the option that gives the correct probability statements using the Venn-diagram in the figure.

From the figure, we can see that there are three events, A, B and C.

And,

[tex]n(A)=1+6+7+3=17,\\\\n(B)=1+6+4+9=20,\\\\n(C)=6+4+6+7=23,\\\\n(A\cap B)=1+6=7,\\\\n(A\cap C)=6+7=13,\\\\n(B\cap C)=6+4=10,\\\\n(A\cap B\cap C)=6.[/tex]

By the law of SET THEORY, we have

[tex]n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)\\\\\Rightarrow n(A\cup B\cup C)=17+20+23-7-13-10+6\\\\\Rightarrow n(A\cup B\cup C)=36.[/tex]

So, the total number of elements in the sample space 'S' will be

n(S) = 36 + 8 = 44.

Therefore,

[tex]P(A/B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{\dfrac{n(A\cap B)}{n(S)}}{\dfrac{n(B)}{n(S)}}=\dfrac{7}{44}\times \dfrac{44}{20}=\dfrac{7}{20},\\\\\\\\P(B/A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{\dfrac{n(B\cap A)}{n(S)}}{\dfrac{n(A)}{n(S)}}=\dfrac{7}{44}\times \dfrac{44}{17}=\dfrac{7}{17},\\\\\\\\P(A/C)=\dfrac{P(A\cap C)}{P(C)}=\dfrac{\dfrac{n(A\cap C)}{n(S)}}{\dfrac{n(C)}{n(S)}}=\dfrac{13}{44}\times \dfrac{44}{23}=\dfrac{13}{23},\\\\\\\\P(C/A)=\dfrac{P(C\cap A)}{P(A)}=\dfrac{\dfrac{n(C\cap A)}{n(S)}}{\dfrac{n(A)}{n(S)}}=\dfrac{13}{44}\times \dfrac{44}{17}=\dfrac{13}{17}.[/tex]

Thus, the correct probability is [tex]P(C/A)=\dfrac{13}{17}.[/tex]

Option (D) is correct.

The probability P(A/B) is 7/20, the probability P(B/A) is 7/17, the probability P(A/C) is 13/23, and the probability is P(C|A) is 13/17 option fourth is correct.

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

For the value of probability P(A|B):

We know that:

[tex]\rm P(A/B)=\frac{P(A\cap B)}{P(B)} \Rightarrow \frac{\frac{n(A\cap B)}{n(T)} }{\frac{n(B)}{n(T)} }[/tex]

From the Venn diagram:

n(A∩B) = 7, n(B) = 20, n(T) = 44

P(A/B) = (7/44)×44/20)

P(A/B) = 7/20

For P(B|A):

[tex]\rm P(B/A)=\frac{P(B\cap A)}{P(A)} \Rightarrow \frac{\frac{n(B\cap A)}{n(T)} }{\frac{n(A)}{n(T)} }[/tex]

The values of n(B∩A) = 7, n(A) =17

P(B/A) = (7/44)×(44/17)

P(B/A) = 7/17

For P(A|C):

[tex]\rm P(A/C)=\frac{P(A\cap C)}{P(C)} \Rightarrow \frac{\frac{n(A\cap C)}{n(T)} }{\frac{n(C)}{n(T)} }[/tex]

The value of n(A∩C) = 13, n(C) = 23

P(A/C) = (13/44)×(44/23)

P(A/C) = 13/23

For P(C|A):

[tex]\rm P(C/A)=\frac{P(C\cap A)}{P(A)} \Rightarrow \frac{\frac{n(C\cap A)}{n(T)} }{\frac{n(A)}{n(T)} }[/tex]

The values of n(C∩A) = 13, n(A) = 17

P(C|A) = (13/44)×(44/17)

P(C|A) =13/17

Thus, the probability P(A/B) is 7/20, the probability P(B/A) is 7/17, the probability P(A/C) is 13/23, and the probability is P(C|A) is 13/17 option fourth is correct.

Learn more about the Venn diagram here:

brainly.com/question/1024798

#SPJ3

The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation.

The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation. In this case, the opportunity cost could be the time she could have spent with her friends. By deciding to work, Marie forgoes the opportunity to socialize and spend quality time with her friends.

Opportunity cost is an important concept in economics that highlights the trade-offs we face when making choices. It helps us understand the value of the options we give up when we choose one alternative over another. In Marie's case, the opportunity cost of earning money and learning new skills is the limited time she can spend with her friends.

In this exercise we have to use the knowledge of sine to be able to calculate the triangle values, in this way we can say that:

[tex]h= 8.3[/tex]

So from the values ​​initially given we can describe that the calculation for this triangle will be:

[tex]x / 48 = sin(10)\\ x = 48* .1736\\ x = 8.3335\\ sin 10^0 = h/48\\ h = 48 sin 10^0\\ h = 8.3 inches[/tex]

See more about triangles at brainly.com/question/25813512