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4 years ago

How would you graph f(x) = 7x + 5 when you reflect it over y axis and translate it 3 units left

Mathematics

1 answer:

SOVA2 [1]4 years ago

8 0

Answer:

See explanation

Step-by-step explanation:

Given the function $f(x)=7x+5$

1. To reflect the graph of the function f(x) over the y-axis, you should change the slope of the line in opposite. The slope of the function f(x) is 7, so the slope of the reflected function will be -7 and the expression of the reflected function will be

$g(x)=-7x+5$

2. To translate the function g(x) 3 units left, add 3 units to x, thus the expression for the function will be

$h(x)=-7(x+3)+5\\ \\h(x)=-7x-21+5\\ \\h(x)=-7x-16$

See attached diagram for details.

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If ON= 5x - 7, LM = 4x+ 4, NM = x -7, and OL =3y-4, find the values of c and y for which LMNO MUST BE a parallelogram.

Sholpan [36]

Answer:

x=11, y=8/3

Step-by-step explanation:

Consider quadrilateral LMNO. If this quadrilateral MUST BE a parallelogram, then

LM=NO

and

LO=MN

Thus,

$\left\{\begin{array}{l}4x+4=5x-7\\ \\x-7=3y-4\end{array}\right.$

Solve this system of two equations. From the first equation:

$4x-5x=-7-4\\ \\-x=-11\\ \\x=11$

Substitute it into the second equation:

$11-7=3y-4\\ \\3y-4=4\\ \\3y=4+4\\ \\3y=8\\ \\y=\dfrac{8}{3}$

4 0

3 years ago

8. Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 4

MA_775_DIABLO [31]

Hello,

If center is (0,0)

x²/a²+y²/b²=1 for a half horizontal axis of a, and a half vertical axis of b

Here

a=2 ==> a²=4

b=8 ==> b²=64

$\boxed{\dfrac{x^2}{4}+ \dfrac{y^2}{64}=1}\\$

3 0

3 years ago

“Solve the system using elimination” im not good at math so can someone help me

iris [78.8K]

Answer:

No solutions

Step-by-step explanation:

i did this via substitution so i hope it isn't a problem

3x+y=4

6x+2y=−4

Step: Solve 3x+y=4for y:

3x+y+−3x=4+−3x(Add -3x to both sides)

y=−3x+4

Step: Substitute−3x+4foryin6x+2y=−4:

6x+2y=−4

6x+2(−3x+4)=−4

8=−4(Simplify both sides of the equation)

8+−8=−4+−8(Add -8 to both sides)

0=−12

so there are no solutions

hope this helps!!

8 0

3 years ago

The sum of three consecutive even numbers is 582. What is the 1st number?

Snezhnost [94]

Answer:

Step-by-step explanation:

4 0

3 years ago

The five-number summary for the lengths of songs, in minutes, performed by a popular music group is given below.

solmaris [256]

Answer:

Yes, 7.5 and 9.2 are outliers

Step-by-step explanation:

Given the 5 number summary :

Minimum: 1.8

Q1: 3.3

Median: 3.8

Q3: 4.5

Maximum: 9.2

To detect an Outlier use the Relation :

Lower bound : Q1 - 1.5*IQR

IQR = Q3 - Q1 = 4.5 - 3.3 = 1.2

lower bound : 3.3 - 1.5(1.2)

Lower bound = 3.3 - 1.8 = 1.5

Upper bound : Q3 + 1.5*IQR

Upper bound : 4.5 + (1.5 * 1.2)

Upper bound : 4.5 + 1.8 = 6.3

Hence,

1.5≤ x ≤ 6.3

Songs with length 7.5 and 9.2 do not meet the condition and are this outliers

7 0

3 years ago

Read 2 more answers