Question 7 (Essay Worth 5 points)
(7.03)
An equation is shown below:
6(2x - 11) + 15 = 21
Write the steps you will use to solve the equation and explain each step.

When you divide by a fraction, flip the second fraction over and change divide to multiply:

17/10 / 11/4 = 17/10 x 4/11

Now multiply straight across:

(17 x 4) / (10 x 11) = 68/110

Simplify:

68/110 = 34/55

Answer: 34/55

Answer:
5641 55/81

Step-by-step explanation:

you can simplify the equation by removing the parenthesis.
this means that you also have to solve the ^4 part.
this would be
5641 55/81

I know that this is a large number but that is what happens when you do ^4.

Answer:

x= -4 and y=2

Step-by-step explanation:

-3x+y=14 ...eqn 1

2x+3y= -2....eqn 2

from eqn 1

-3x+y=14

y=14+3x

substitute y=14+3x into eqn 2

2x+3(14+3x) = -2

2x+ 42+ 9x = -2

11x= -2-42

11x= -44

x = -4

substitute X = -4 into eqn 1 to get y

-3x+y=14

-3(-4) +y =14

12+y= 14

y= 14-12

y =2

Answer:

Step-by-step explanation:

So what you want to know is what are the odds of drawing 4 5 6 out of 13.

P(4 5 6) = 3/13

Odds are a little bit different. You are still getting some idea of how likely an event is.

The formula is  Probabity / ( 1 - Probability)

So The probability = 3/13

1 - probability = 1 - 3/13 = 10/13

probability / (1 - probability ) = 3/13 // 10/13 = 3/13 * 13/10 = 3 / 10 or 3 chances in 10.

I think Probability is more intuitively correct.

Answer:

3/13

Step-by-step explanation:

The quotient of the expression in form of a + bi is 9/13 - 20/13i

Given the following expressions

1+6i/-3+2i

Rationalizing the given rational complex number, we will have;

= 1+6i/-3+2i * -3-2i/-3-2i

= (1+6i)(-3-2i)/9+4
= -3-2i-18i-12i²/13

Simplify the result to have:

= -3+12-20i/13
= 9-20i/13

Express in the form a + bi

9/13 - 20/13i

Hence the quotient of the expression in form of a + bi is 9/13 - 20/13i

Learn more on complex number here: https://brainly.com/question/10662770

Answer:

She spent $8.15

Step-by-step explanation:

2 × $2.95 for two pizza = $5.9

$5.9 + an additional $2.25 for a soda = $8.15

Answer:

39

Step-by-step explanation:

all angles of a triangle equal to 180, so you just have to subtract those two known angles from 180, and you will get the answer.

Find the value of angle x .

The concept of this question belongs to angles of triangle . We know that the sum of all the three angles of triangle is 180°.

As we know that all the angles of triangle is equal to 180° . So :

Therefore , angle x is of 39° .

The fraction illustrates that there are 6 red tables.

Fron the information, Julia helps the teacher clean the tables in the classroom she notices that 1/4 of the tables are blue and 3/4 of the table are red.

Therefore, the numbers that are red will be:

= Fraction of red × Total number

= 3/4 × 8

= 6

Therefore there are 6 red tables.

Learn more about fractions on:

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Using an exponential function, it is found that Justin's starting salary was of $50,137.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, we have that r = 0.037 and A(12) = 77536, hence:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]77536 = A(0)(1.037)^{12}[/tex]

[tex]A(0) = \frac{77536}{(1.037)^{12}}[/tex]

A(0) = 50137.

Justin's starting salary was of $50,137.

More can be learned about exponential functions at https://brainly.com/question/25537936

Answer:

Area of square: 9/16 m²

Step-by-step explanation:

We are given:

The area of the square is the side multiplied by the same side. Therefore,

Using the exponents property, [(a/b)² = (a²/b²)]:

Therefore, the area of the square is 9/16 m².

Answer:

[tex]\huge\boxed{\bf{Area_{square} = \frac{9}{16}m^2}}[/tex]

Step-by-step explanation:

Given : -

To Find : -

Ans : -

$\sf \to Area_{square} = (side\:length)^2$

$\sf \to Area_{square} = (\frac{3}{4}m)^2$

$\sf \to Area_{square} = (\frac{3}{4}m*\frac{3}{4})$

$\sf \to Area_{square} = (\frac{3*3}{4*4}m^2)$

$\sf \to Area_{square} = \frac{9}{16}m^2$

[tex]\:[/tex]

$\huge\colorbox{skyblue}{BlackPain}$

Answer:

[tex] \frac{1}{9} [/tex]

Step-by-step explanation:

[tex] \frac{3}{11} \times \frac{4}{9} [/tex]

[tex] \frac{12}{108} [/tex]

[tex] \frac{1}{9} [/tex]

Answer:

48

Step-by-step explanation:

180 is the whole thing

So add 25 and 107 to make 132, then 180-132

Answer:

1. The wind has blown all the leaves off the tree.

2. All the leaves have fallen to the ground.

3. My kite is being flown in the wind.

4. A shower of acorns have fallen from the sky

5. A busy squirrel dug for his acorns.

6. In the garden, pumpkins have grown.

7. Yesterday my friend and I rode to the park.

8. We have rode to the skate park.

9. My brother wrote me a letter.

10. He has written a essay.

11. Our neighbor had given us a pie.

12. Mom and Dad have spoken to me about cleaning my room.

Step-by-step explanation:

Answer: B

Step-by-step explanation: 3/8 + 1/16 = 0.4375 and 7/16 = 0.4375

Answer:

b.

Step-by-step explanation:

first, you would you would find a common denominator between 3/8 and you will get 6/16. last, you would add 1/16 + 6/16 for your answer of 7/16

Answer:

4 hours

Step-by-step explanation:

the rate of people coming in it 700 per hour

Answer:

The first one i would think might be 0.05? uncertian and probably wrong, the second, HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT, and the third, 3/8.

The way you figure out the third one is you are flipping 3 coins still, and you take all of the options above and there are 8 total and 3 ov them would land you 2 heads and a tail so its a simple 3/8 fraction

Answer:

2.  0.05

3. a) 8 outcomes (listed below)

3. b) 3/8

Step-by-step explanation:

Question 2

The sum of the probabilities of all possible outcomes is 1.

Therefore, if the probability of being on time for class is 0.95, then the probability of NOT being on time for class is:

1 - 0.95 = 0.05

Question 3

a)  8 possible outcomes of flipping 3 coins (H = heads, T = tails):

HHH     HHT     HTH     THH

TTT       TTH     THT      HTT

b)  

There are 3 possible ways of flipping 2 Heads and 1 Tail:

HHT    HTH     THH

Out of a total number of 8 possible outcomes.

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

[tex]\sf \implies P(2\:Heads\:and\:1\:Tail) = \dfrac38[/tex]

Answer:

see explanation

Step-by-step explanation:

(3)

Parallel lines have equal slopes

the equation of a line in sloipe- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{4}[/tex] x + 5 ⇒ m = [tex]\frac{1}{4}[/tex]

y = 4x + 5 ⇒ m = 4

y = - 4x + 5 ⇒ m = - 4

y = - 4x - 9 ⇒ m = - 4

the 3rd and 4th options have equal slopes and are parallel

(4)

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]

y = [tex]\frac{1}{6}[/tex] x + 4 ⇒ m = [tex]\frac{1}{6}[/tex]

y = - [tex]\frac{1}{6}[/tex] x + 5 ⇒ m = - [tex]\frac{1}{6}[/tex]

y = [tex]\frac{1}{6}[/tex] x + 3 ⇒ m = [tex]\frac{1}{6}[/tex]

y = 6x + 3 ⇒ m = 6

note that a slope of m = 6 , has a perpendicular slope of

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{6}[/tex]

the 2nd and 4th lines are perpendicular

PEMDAS - parentheses exponents multiplication division addition subtraction

Hope it helps!

Any queries - comment!

PS I'll edit in a min, please wait :)

Answer:

Revenue was 55,614 the year before

Step-by-step explanation:

Decay Formula: y = a*(1-r)^x

So:

y = 89700 * (1-0.38)^1

y = 55614

well, their total revenue last year was "x", which oddly enough is 100%.  Now, this year's revenue is 38% more than that, well, 100% + 38% = 138%, and we also know that it's 89700, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 89700& 138 \end{array} \implies \cfrac{x}{89700}=\cfrac{100}{138}\implies \cfrac{x}{89700}=\cfrac{50}{69} \\\\\\ 69x=4485000\implies x=\cfrac{4485000}{69}\implies x=65000[/tex]

Answer:

1 page in 4 sec.

Step-by-step explanation:

To find the rate in lowest terms, divide the 14 pages by 56 seconds and find the simplest fraction.

14/56 = 1/4 in simplest terms.

This means the rate is 1 page in 4 seconds.

Answer:

r = 18 cm

Step-by-step explanation:

The formula for the circumference of a circle is 2πr.

Hence,

2πr = 36π

r = 18 cm

The linear equation that passes through the two given points is:

y = (1/3)*x + (5/3)

A linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is equal to:

a = (y₂ - y₁)/(x₂ - x₁).

In this case, we know that the line passes through (-2, 1), and (4, 3).

Then the slope is:

a = (3 - 1)/(4 - (-2)) = 2/6 = 1/3

So the line is something like:

y = (1/3)*x + b

To find the value of b, we use the fact that the line passes through the point (4, 3), then:

3 = (1/3)*4 + b

3 - 4/3 = b

5/3 = b

So the line is:

y = (1/3)*x + 5/3

Finally, the x-intercept of the line is the value of x such that y = 0.

0 = (1/3)*x + 5/3

-5/3/(1/3) = x = -5

The graph of the line can be seen below.

If you want to learn more about linear equations, you can read:

https://brainly.com/question/1884491

Answer:

y = -2/3x + 4

Step-by-step explanation:

Answer:

45/28

Step-by-step explanation:

6/7+3/4

The least common multiple of 7 and 4 is 28.

Convert 6/7 and 3/4 to fractions with the denominator of 28

24/28+21/28

Since the denominators are now the same, add the numorators to get 45/28

Answer:

13

Step-by-step explanation:

[tex]\text{determinant of A} =\begin{vmatrix}4&-7\\ 3&-2\end{vmatrix}[/tex]

[tex]\text{determinant of A} =\left( 4\times \left( -2\right) \right) -\left( 3\times \left( -7\right) \right)[/tex]

[tex]\text{determinant of A} =-8+21=13[/tex]

Answer:

[tex]x= 8\left(1- \sqrt 2 \right)\\\\\\x= 8\left(1+ \sqrt 2 \right)\\[/tex]

Step by step explanation:

[tex]-x^2 +16x +64 =0\\\\\text{Use the quadratic equation formula,}~~ x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{In this case,}~ a=-1, b=16, c=64\\\\\\x=\dfrac{-16\pm\sqrt{16^2 -4 \cdot (-1)(64)}}{2(-1)}\\\\\\~~~=\dfrac{-16\pm\sqrt{512}}{-2}\\\\\\~~~=\dfrac{-16 \pm \sqrt{256 \times 2}}{-2}\\\\\\~~~=\dfrac{-16 \pm 16\sqrt2}{-2}\\\\\\~~~=8 \pm(-8)\sqrt 2\\\\\text{Hence,}\\\\x=8-8\sqrt 2 = 8\left(1- \sqrt 2 \right)\\\\x= 8+8\sqrt 2 = 8\left(1+ \sqrt 2 \right)[/tex]

I assume the integral is

[tex]\displaystyle \int x^3 e^{-x} \, dx[/tex]

Integrate by parts with

[tex]u = x^3 \implies du = 3x^2 \, dx[/tex]

[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]

so that

[tex]\displaystyle \int u \, dv = uv - \int v \, du[/tex]

i.e.

[tex]\displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} + 3 \int x^2 e^{-x} \, dx[/tex]

Integrate by parts again, this time with

[tex]u = x^2 \implies du = 2x \, dx[/tex]

[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]

and so

[tex]\displaystyle \int x^2 e^{-x} \, dx = -x^2 e^{-x} + 2 \int x e^{-x} \, dx[/tex]

[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} + 3 \left(-x^2 e^{-x} + 2 \int x e^{-x} \, dx\right)[/tex]

[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} + 6 \int x e^{-x} \, dx[/tex]

Once more, with

[tex]u = x \implies du = dx[/tex]

[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]

[tex]\displaystyle \int x e^{-x} \, dx = -xe^{-x} + \int e^{-x} \, dx[/tex]

[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} + 6 \left(-xe^{-x} + \int e^{-x} \, dx\right)[/tex]

[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} -6xe^{-x} + 6 \int e^{-x} \, dx[/tex]

Finally,

[tex]\displaystyle \int e^{-x} \, dx = -e^{-x} + C[/tex]

and so

[tex]\displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} -6xe^{-x} - 6 e^{-x} + C[/tex]

or equivalently,

[tex]\displaystyle \int x^3 e^{-x} \, dx = \boxed{-(x^3+3x^2+6x+6) e^{-x} + C}[/tex]

We can also approach the integral more generally by considering

[tex]I_n = \displaystyle \int x^n e^{-x} \, dx[/tex]

Integrate by parts with

[tex]u = x^n \implies du = nx^{n-1} \, dx[/tex]

[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]

Then

[tex]\displaystyle I_n = -x^n e^{-x} + n \int x^{n-1} e^{-x} \, dx = -x^n e^{-x} + n I_{n-1}[/tex]

We can solve the recurrence using the initial "value" [tex]I_0 = -e^{-x}+C[/tex] to find a general formula for [tex]I_n[/tex]. Then we get the integral we want [tex]I_3[/tex] "for free".