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4 years ago

15

-25 Points-

1 answer:

Elden [556K]4 years ago

7 0

Answer:

(x+1)^2+(y+1)^2=13

Step-by-step explanation:

Equation of a circle: (x – h)^2 + (y – k)^2 = r^2

center: (-1, -1)

radius: sqrt(6^2+4^2)/2=sqrt(52)/2=2sqrt(13)/2=sqrt(13)

Substitute those values in to get

(x+1)^2+(y+1)^2=13

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3. Angles X and Y have a sum of 159 degrees. Angle X is 43 degrees smaller than angle Y.

Lesechka [4]

$\underline{\underline{\large\bf{Solution:-}}}\\$

$\longrightarrow$ Since angle X and Y have a sum of 159

$\implies \bf Y + X= 159 \_\_\_\_(1)$

$\longrightarrow$ Since X is 43 degrees smaller than Y , so subtracting X from Y would give 43 , therefore equation will be written as -

$\implies \bf Y - X = 43 \_\_\_\_(2)$

<u>Adding Equation (1) and (2) </u>

$\begin{gathered}\\\implies\quad \sf Y+X+Y-X = 159+43 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf Y+Y + X-X = 202 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf 2Y = 202 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf Y = \frac{202}{2} \\\end{gathered}$

$\begin{gathered}\\\implies\quad \boxed{\sf {Y = 101 }} \\\end{gathered}$

<u>Putting Y in eq (1)</u>

$\begin{gathered}\\\implies\quad \sf X + 101 = 153 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf X = 153-101 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \boxed{\sf{ X = 52 }}\\\end{gathered}$

5 0

2 years ago

Among 35 students in a class, 20 of them earned A's on the midterm exam, 13 earned A's on the nal exam, and 12 did not earn A's

enyata [817]

Answer:

The correct answer is " $\frac{2}{7}$ ".

Step-by-step explanation:

According to the question,

Number of students,

= 35

A ! mid term A,

$n(A) = 20$

B : final A,

$n(B) = 13$

Didn't start,

$n(A^c \cap B^c) = 12$

Now,

⇒ $n(A \cup B)=35-12$

$=23$

then,

⇒ $n(A \cup B)=20+13-23$

$=10$

hence,

The probability will be:

⇒ $P(A \cap B)=\frac{10}{35}$

⇒ $=\frac{2}{7}$

7 0

3 years ago

Y = -3x - 13<br> 9x - 2y = -4

Eddi Din [679]

Answer

6

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Benjamin is making bow ties how many 1/2 yard Mongols has can he make if he has 18 feet of fabric

kiruha [24]

Hello!

First you have to find out what 1/2 a yard is in feet

There are 3 feet in a yard so there are 1.5 feet in 1/2 a yard

Divide the amount of fabric by how much is needed to make a bowtie

18 / 1.5 = 12

The answer is 12

Hope this helps!

7 0

3 years ago

3x(x + 6) = -10

emmasim [6.3K]

Answer:

Step-by-step explanation:

Expand it: $3x^2 + 18x = -10$

Add 10 to both sides: $3x^2 + 18x + 10 = 0$

Divide both sides by 3: $x^2 + 6x + \frac{10}{3} = 0$

Find <em>a</em>, <em>b</em> for $(x + a)^2 + b = x^2 + 2x + a^2 + b \overset{!}{=} x^2 + 6x + \frac{10}{3}$

It’s $a = \frac{6}{2} = 3 \land b = \frac{10}{3} - a^2 = 3 + \frac{1}{3} - 9 = -6 + \frac{1}{3}$

So, inserting it leads to: $(x+3)^2 -6 + \frac{1}{3} = 0$

Subtract <em>b</em> from both sides: $(x+3)^2 = 6-\frac{1}{3}$

Apply square root to both sides and consider the two solutions: $x + 3 = \pm\sqrt{6-\frac{1}{3}}$

Subtract 3 from both sides and you get $x = -3 \pm \sqrt{6 - \frac{1}{3}}$

5 0

3 years ago