Graph the image of rectangle CDEF after a translation 4 units left and 9 units up.

The solutions to the system of equations are x=5, z=1,y=-3

What is system of equations?

Given equations:

x+y+z=3

3x+(y/3)-2z=12

-5x-6y+3z=-4

Solving by using the substitution method:

[tex]\begin{bmatrix}x+y+z=3\\ 3x+\left(\frac{y}{3}\right)-2z=12\\ -5x-6y+3z=-4\end{bmatrix}[/tex]

Substitute x=3-y-z

[tex]\begin{bmatrix}3\left(3-y-z\right)+\frac{y}{3}-2z=12\\ -5\left(3-y-z\right)-6y+3z=-4\end{bmatrix}[/tex]

Substitute z={8y+9}/{15}

[tex]\begin{bmatrix}-y+8\left(-\frac{8y+9}{15}\right)-15=-4\end{bmatrix}[/tex]

simplify

[tex]\begin{bmatrix}\frac{-79y-72}{15}-15=-4\end{bmatrix}[/tex]

Substitute y=-3

[tex]z=-\frac{8\left(-3\right)+9}{15}[/tex]

z=1

For x=3-y-z

Substitute z=1,y=-3

x=3-(-3)-1

x=5

The solutions to the system of equations are:

x=5, z=1,y=-3

Learn more about the system of equations here;

https://brainly.com/question/25869125

#SPJ1

The complementary angle of the angle is 11.7 degrees

Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines

The measure of the angle is given as

Angle = 78.3 degrees

Complementary angles add up to 90 degrees

So, we have the other angle to be

Other angle = 90 - 78.3

Evaluate the difference

Other angle = 11.7

Hence, the other angle is 11.7

Read more about angles at

https://brainly.com/question/7620723

#SPJ1

The percentage of the people surveyed that arrive at their office after 7am is 6.7%.

The percentage of the people surveyed that arrive at their office after 7:59 am is 64%

From the information, Miranda did a survey of what time people get to their office on Monday morning and the table shows her results.

The number of people that arrived before 7.59am is 15.

The total number of people surveyed will be:

= 15 + 39 + 75 + 21

= 150

The percentage of the people surveyed arrive at their office before 7 am will be:

= 10 / 150

= 6.7%

The percentage of the people surveyed that arrive at their office after 7:59 am will be:

= (75 + 21) / 150.

= 96/150

= 0.64

= 64%

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

Answer:

the number of people is 15 so you would do 15/150=10percent

b) 66 percent

Step-by-step explanation:

Answer: 4:30

Step-by-step explanation:

Answer:

oh palak cl NC do off is sold em Ms do off do off dlc so off do off sum is sold arrowroot

Derivative of   [tex]f(x)= (\frac{cosx}{\sqrt{x} })=\frac{-2xsin(x)- cos(x)}{2x\sqrt{x} }[/tex]

How to calculate the derivative?

[tex]f(x) = \frac{cosx}{\sqrt{x} }[/tex]

The derivative is given by,

[tex]= > \frac{d}{dx} (\frac{cosx}{\sqrt{x} })[/tex]

Applying Quotient rule :

[tex](\frac{f}{g} )^{'} = \frac{f^{'}.g - g^{'}.f}{g^{2} } \\[/tex]

[tex]\frac{d}{dx} (\frac{cosx}{\sqrt{x} })=\frac{\frac{d}{dx}(cosx)\sqrt{x} - \frac{d}{dx} \sqrt{x}(cosx)}{(\sqrt{x} )^{2} } \\[/tex]

Considering derivatives in the numerator,

[tex]\frac{d}{dx} (cosx)= - sinx\\\\\frac{d}{dx} (\sqrt{x} )=\frac{1}{2\sqrt{x} }[/tex]

Now,

[tex]\frac{d}{dx} (\frac{cosx}{\sqrt{x} })=\frac{(-sinx)\sqrt{x} - \frac{1}{2\sqrt{x} } (cosx)}{(\sqrt{x} )^{2} } \\\\\text{ Taking LCM }\\\\=\frac{-2xsin(x)- cos(x)}{2x\sqrt{x} }[/tex]

What is a derivative?

To learn more about derivatives, refer:

https://brainly.com/question/23819325

#SPJ13

Answer:

A number closer to 0 is generally less than a number more away from 0. When it comes to negative numbers the closer the number to 0, the greater it is.

Step-by-step explanation:

If you need further help please let me know.

Please mark brainliest!

The total number of questions that Fred answered incorrectly is 8.

From the information given, a perfect score on a test with 25 questions is 100 and each question is worth 4 points while Fred got a score of 68 on the test.

Therefore, let the number of questions that are got be x.

Based on the information given, this will be:

4 × x = 68

4x = 68

Divide

x = 68 / 4 = 17

The number of questions that he missed will be:

= Total questions - Correct answers.

= 25 - 17.

= 8

Learn more about division on:

brainly.com/question/25289437

#SPJ1

Answer:

4044

Step-by-step explanation:

2000+2000= 4000

22+22= 44

4000+44= 4044

Given

Principal = $2419

rate = 2.54%

time = 7 years

compounds quarterly

After 7 years, the amount deposit is now $2888.08, subtract by the principal amount to get the interest.

Therefore, the interest that he will earn after 7 years us $469.08.

A pair of shoes cost 102.23

Arithmetic: Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. The basic operations of math are addition, subtraction, multiplication and division. Also called higher arithmetic, theoretical arithmetic.

Cost of 3 pairs of shoes and a dress = 352.50

Cost of dress = 45.50

Cost of 3 pairs of shoes = Cost of 3 pairs of shoes and a dress - the cost of dress = 352.20 - 45.50

= 306.7

So, the cost of each pair of shoes will be = Cost of 3 pairs of shoes/Number of pairs bought

= 306.7/3

= 102.23

Learn more about arithmetic:

#SPJ1

Answer:  The slope of (-8, 18) and (-14, -3) would be 3.5.

Step-by-step explanation:  By using a simple calculator, specifically the TI-84 Plus CE, you can put the points you mentioned in stat and it’ll give you an equation based on those points.  The equation I got was y = 3.5x + 46.  The number attached to the X is your slope.

The two column proof of the right angles to prove that ∠1 ≅ ∠2 is as shown below

From the given image showing two right angles, we can generate the two column proof to be as follows;

Statement 1: m∠1 = 90° and m∠2 = 90°

Reason 1: Given

Statement 2: ∠1 and ∠2 are right angles

Reason 2: Definition of right angles

Statement 3: m∠1 = ∠2

Reason 3: Transitive Property of Congruence

Statement 4: ∠1 ≅ ∠2

Reason 4: Definition of Congruence

Read more about Two Column Proof at; https://brainly.com/question/1788884

#SPJ1

Answer:

3/4

-2

Step-by-step explanation:

y = mx + b

Start at the y-intercept. It is (0, -2), so b = -2.

You have

y = mx - 2

Now start at (0, -2). We need to go up and right to the next easy-to-read point on the line. Go up 3 (rise). Go right 4 (run).

slope = rise/run = 3/4 = m.

Now you have

y = 3/4 x - 2

Answer:

See below

Step-by-step explanation:

Use two convenient integer coordinates to calcuate m= slope

I'll use   8,4  and  -4, -5      slope m =   (-5-4)/(-4-8)  = -9/-12 = 3/4

from the graph, the y-axis intercept (b )   is -2

slope - intercept form of a line is given by

y= mx + b

y = 3/4 x -2

Answer:

u= 18.37

Step-by-step explanation:

-7/8 u= -21

We have to isolate the variable. Since the -7 is being divided, you would take it to the other side and multiply.

8u= -21 * -7

8u= 147

u= 147/8

u= 18.37

The average pay-per-hour of the year for Elise will be 13.73 pounds.

From the information, in 2016 she earned £2100 and in 2017 she was awarded a 3% increase on her monthly salary.

Therefore, the new salary will be:

= 2100 + 3%(2100)

= 2100 + 63

= 2163

Now she worked for 42 hours per week for 45 weeks. This will be:

= 42 × 45

= 1890 hours

Therefore, the total earnings for the year will be:

= 2163 × 12 months

= 25956

The average pay-per-hour of the year will be:

= Total amount / Number of hours

= £25956 / 1890

= £13.73

Learn more about average per hour on:

brainly.com/question/9447238

#SPJ1

Answer:

The equation is:

y = -3x + 3

If 98 out of 350 dog owners bought Pedigree Chum dog food so 28 percentage of the makers that prefer Pedigree Chum.

As per the question statement, In a survey of 350 dog owners and it was found that 98 bought Pedigree Chum dog food. We are supposed to find the percentage of the makers that prefer Pedigree Chum.

Given that, 98 out of 350 dog owners bought Pedigree Chum dog food

So the percentage can be calculated by the formula,

(98/350)*100 = 0.28*100 = 28%

Hence, 28% of the makers that prefer Pedigree Chum.

To learn more about percentage and its concept, click on the link given below:

https://brainly.com/question/16797504

#SPJ1

Answer: r=-26

Step-by-step explanation:

[tex]\displaystyle\\(5,r)\ \ \ \ (10,1)\ \ \ \ slope \ m=5\\\\\boxed {m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=5\ \ \ \ \ x_2=10\ \ \ \ \ y_1=r\ \ \ \ y_2=-1\ \ \ \ \ m=5\\\\Hence,\\\\5=\frac{-1-r}{10-5} \\\\5=\frac{-1-r}{5}[/tex]

Multiply both parts of the equation by 5:

[tex]5(5)=-1-r\\\\25=-1-r\\\\25+r=-1-r+r\\\\25+r=-1\\\\25+r-25=-1-25\\\\r=-26[/tex]

Answer: 48

Step-by-step explanation:
Convert 40% to a decimal = 0.4
Multiply 0.4 x 120 = 48

Answer:

48

Step-by-step explanation:

40\100×120

=48

( fourth divided by one hundred multiplied by one hundred and twenty is equal to 48)

Answer:

[tex]\textsf{C.} \quad r=\dfrac{27-P}{3P}[/tex]

Step-by-step explanation:

Given formula:

[tex]A=P(1+rt)[/tex]

Given values:

Substitute the given values into the given formula and solve for r:

[tex]\begin{aligned}A&=P(1+rt)\\\\\implies 27&=P(1+3r)\\\\\dfrac{27}{P}&=\dfrac{P(1+3r)}{P}\\\\\dfrac{27}{P}&=1+3r\\\\\dfrac{27}{P}-1&=1+3r-1\\\\\dfrac{27}{P}-1&=3r\\\\3r&=\dfrac{27}{P}-\dfrac{P}{P}\\\\3r&=\dfrac{27-P}{P}\\\\\dfrac{3r}{3}&=\dfrac{\dfrac{27-P}{P}}{3}\\\\r&=\dfrac{27-P}{3P}\end{aligned}[/tex]

Solution

[tex]\boxed{r=\dfrac{27-P}{3P}}[/tex]

The horizontal asymptote is y = -2

The horizontal asymptote is an equation of the form y = k, for some constant k, is a straight line parallel to x-axis.

Horizontal asymptotes are found for rational functions of polynomials when x becomes extremely large, or, as x → ∞.

The function given is, f(x) = (-2x²+3x+5)/(x²+1)

Horizontal asymptote is given by,

y = [tex]\lim_{x \to \infty} \frac{-2x^2+3x+5}{x^2+1}[/tex]

   =  [tex]\lim_{x \to \infty} \frac{x^2(-2+\frac{3}{x} +\frac{5}{x^2}) }{x^2(1+\frac{1}{x^2}) }[/tex]

   =  [tex]\lim_{x \to \infty} \frac{(-2+\frac{3}{x} +\frac{5}{x^2}) }{(1+\frac{1}{x^2}) }[/tex]

   = -2

So the horizontal asymptote of f(x) is, y = -2

Learn more about horizontal asymptotes at https://brainly.com/question/1851758

#SPJ1

Answer:

A) y = -2

Step-by-step explanation:

The rules to find the horizontal asymptote (HA) is shown below

Y = A if the numerator and denominator have same highest exponent for example

A^3

B^3

Y = 0 if the numerator have lower exponent and denominator have higher exponent for example

A^1

B^2

None HA if the numerator have higher exponent and denominator have lower exponent for example

A^2

B^1

And the equation shown in the question have same exponent so the answer is -2

PS: please give me brainiest

[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex] of the Correct option is (B) i.e.,  1/[tex]\pi[/tex]

Given:

[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex]

To solve the above function:

Now, According to the question:

[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex]

Differentiate with respect to x above function:

[tex]\lim_{x \to \\pi } \frac{-sinx + 2cosx} {2x}[/tex]

Substitute the value of limit in x tends [tex]\pi[/tex], it means x = [tex]\pi[/tex]

= [tex]\frac{2cos\pi - sin\pi }{2\pi }[/tex]

= 2/ [tex]2\pi[/tex]

= 1/[tex]\pi[/tex]

Hence, The Correct option is (B) i.e.,  1/[tex]\pi[/tex]

Learn more about Differentiation at:

https://brainly.com/question/24898810

#SPJ1

Answer:

6x^2 - 11x + 3

Step-by-step explanation:

(fg)(x) is just multiplying f(x) and g(x)

This gives: (2x-3)(3x-1) = 6x^2 - 2x -9x - (3*(-1)) = 6x^2 -11x + 3

Step 1: Write out the formula for Probability

Step 2: Writing out the data

The number of times R occur in the word LIBRARY is 2.

The total number of alphabets in the word LIBRARY is 7.

Therefore, number of events= 2

Total number of events= 7

The series of rotations are : (x, y) -----> (y, -x) → (y, -x) ----> (x, y).

The total rotation is 360 degrees. So the figure is the original figure itself.

First a figure is rotated 270 degrees counterclockwise about the origin.

A 270 degree counterclockwise rotation is given by the co-ordinate transformation, (x, y) -----> (y, -x)

Then the figure is again rotated 90 degrees counterclockwise about the origin. A 90 degree counterclockwise rotation is given by, (x, y) -----> (-y, x)

So combining with the above transformation, the 90 degree counterclockwise rotation gives, (y, -x) ----> (x, y).

Thus the total rotation transformation is in turn, (x, y) ----> (x, y).

Thus the total rotation in counterclockwise direction about the origin is 360 degrees. So the final figure is the original figure itself.

Learn more about rotation at https://brainly.com/question/26249005

#SPJ1

Answer:

x = 17

Step-by-step explanation:

Given angles are vertical angles and they have equal measurements.

We can write the following equation to find the value of x based on this information:

8x - 27 = 6x + 7 transfer like terms to the same side of the equation

8x - 6x = 27 + 7 add/subtract

2x = 34 divide both by 2

x = 17

Step 1

Given;

Required; To write the equation in factored form

Step 2

Find the two factors that when added gives you x and when multiplied gives -20x²

Step 3

State the x-intercept

Hence, the x-intercepts are;

x=4

x=-5