Answer:
y= -x-7
Step-by-step explanation:
Slope intercept form: y = mx + b
m = slope
b = y intercept
The first thing you must do is isolate y so that it is by itself on the left side of the equation:
-x = y + 7
Subtract 7 to both sides:
-x - 7 = y + 7 - 7
-x - 7 = y
Flip:
y = -x - 7
-x = y + 7 in slope intercept form is y = -x - 7
This means the slope is -1 and the y-intercept of the equation is (0, -7)
At which value(s) of x does the graph of the function F(x) have a vertical
asymptote? Check all that apply.
F(x) =X/(x-4)(x+2)
Answer:
x = 4 & x = -2
Step-by-step explanation:
For rational functions (functions which themselves are a fraction, with polynomial pieces in the numerator and polynomial pieces in the denominator), these functions have "discontinuities" anywhere the denominator is equal to zero. Usually, those discontinuities are "vertical asymptotes". Occasionally, those discontinuities are "holes".
A discontinuity is a "hole," only if both the numerator AND the denominator are zero for that same value of x. If that value of x doesn't make the numerator zero (it only makes the denominator zero), the discontinuity is just a vertical asymptote.
Finding the discontinuities:To find the discontinuities, we'll be making an entirely separate equation. It's not the function, it's not using algebra to change both sides of the equation/function we started with ... it's pretty much just like scratch work to figure out something that you can use later (although, your teacher may want to see your work on how you found them).
The equation we need for this is the denominator of our rational function set equal to zero:
[tex](x-4)(x+2)=0[/tex]
Note, this equation doesn't have a denominator. It's not the original function. It's like scratch work. This equation is designed as if we want the denominator of our function to be zero, and to find the values of x that will make us divide by zero in the original function.
There are many ways to solve this equation. The easiest is remembering the zero product property. The Zero Product property states that if the product of two things is equal to zero, then at least one of the original things had to be zero: [tex]\text{If }a*b=0,\text{ then }a=0\text{ or }b=0 \text{ (or both)}[/tex]
Noting that our equation is a product of two things, and is equal to zero, the zero product property allows us to separate our equation into two equations:
[tex]x-4=0, \text{ or } x+2=0[/tex]
Solving each equation by isolating x, by adding or subtracting the relevant number from both sides of the equations:
[tex]x=4, \text{ or } x=-2[/tex]
So these values of x will make the denominator of the original function zero. These are both discontinuities of the function, so while when we were solving for values of x that would make the denominator zero, it was appropriate to say "or", we know that both of these values are discontinuities and now we list them both saying "and":
Discontinuities: [tex]x=4 \text{ and } x=-2[/tex]
But wait! Are they holes, or are they just vertical asymptotes? Do we have one of each?
Testing to see if the discontinuities are asymptotes:
To test and see if the discontinuities we've found are holes, we need to substitute them into the numerator of the original function, and see the result.... but just the numerator (we already know they will make the denominator zero, and we can't divide by zero)
Since the numerator is just x, we're checking to see if 4=0, or if -2=0. They don't. So, for this function, both of the discontinuities are vertical asymptotes.
Listing the asymptotes
Vertical asymptotes at [tex]x=4 \text{ and } x=-2[/tex]
Mark's Digital Place has a compact digital camera at a price of $425, a 8 inch tablet for $540 and a
game console for $610. If you want to get an additional three years warranty, then you need to pay
15% extra on the original price and $50.
Daphne wants to buy a digital camera and a tablet to start a photography course. When she went into
the store, she found that the store id offering a discount of 5% on the camera and 80 on the tablet.
Daphne also want the additional three years warranty. How müch money does Daphne need to pay to
buy both the items with a three years additional warranty on each item?
Answer:
jjxfzhfxjgjhzjjjtxjxjxktxjtxjtxtxh
What is the square root of 48 simplified?
Find the value of y in the equation attached to this question
Answer:
y = 4
Step-by-step explanation:
1) Simplify [tex]3^5[/tex] to 243.
[tex]{9}^{y}=\frac{243\times {9}^{6}}{{27}^{3}}[/tex]
2) Simplify [tex]{9}^{6}[/tex] to 531441.
[tex]{9}^{y}=\frac{243\times 531441}{{27}^{3}}[/tex]
3) Simplify [tex]243\times 531441[/tex] to 129140163.
[tex]{9}^{y}=\frac{129140163}{{27}^{3}}[/tex]
4) Simplify [tex]{27}^{3}[/tex] to 19683.
[tex]{9}^{y}=\frac{129140163}{19683}[/tex]
5) Simplify [tex]\frac{129140163}{19683}[/tex] to 6561.
[tex]{9}^{y}=6561[/tex]
6) Convert both sides to the same base.
[tex]9^y=9^4[/tex]
7) Cancel the base of 9 on both sides.
[tex]y=4[/tex]
Cheers,
ROR
Answer:
y = 4
Step-by-step explanation:
Decompose in base 3
[tex]9^{y} =\frac{3^{5} (3^{2})^{6} }{(3^{3})^{3} } =\frac{3^{5}3^{12} }{3^{9} } =\frac{3^{17} }{3^{9} } =3^{17-9} =3^{8}[/tex]
if
[tex]3^{8} =(3^{2} )^{4} =9^{4}[/tex]
then
[tex]9^{y} =9^{4}[/tex]
[tex]y=4[/tex]
Hope this helps
Subtract the following complex numbers:
(4+4i)-(13+17i)
OA. 9+21/
OB. -9+21/
OC. 9-13i
OD.-9-13i
We have been given (4 + 4i) - (13 + 17i) .after solving we get the correct option is A ) -9 - 13 i.
What are complex numbers?Complex numbers are those numbers that contain the imaginary and the real part.
We have been given (4 + 4i) - (13 + 17i) .
On removing the parenthesis
4 + 4 i - 13 - 17i.
On combine the real part and complex parts, we get
= 4 - 13 + 4i - 17 i.
= -9 - 13 i.
Therefore, The correct option is A ) -9 - 13 i.
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whats 10 + 4? i need to know if you answer you get 25 points
in january of 2013, mr edwards turned 64 years old. in what year was mr edwards born.
Answer:
xhdvuvzxvzvkkzv jzh jhj,
Step-by-step explanation:
Here is a list of ages (years) of children in a room:
8
,
8
,
9
,
5
,
10
,
4
,
9
State the median.
Answer:
5
Step-by-step explanation:
median basically means the number which is in the middle so 8,8,9, 5 ,10,4,9
the median is 5 because left and right middle is 5 that's why it is median
The absolute value of -183 is _______.
Answer:
183
Step-by-step explanation:
The absolute value of a number is the number's distance from zero, which will always be a positive value. To find the absolute value of a number, drop the negative sign if there is one to make the number positive.
Answer: 183 ✅
Step-by-step explanation:
Hii, do you need to know the absolute value of "-183"? No problem! (:
What is Absolute Value? | DefinitionThe absolute value of a number is that number's distance from zero.
That's why absolute value is always positive, because negative distances don't exist.
That's why the absolute value of a number is always positive.
|x|=x| | denotes absolute value
|-x|=-x[tex]\large\boldsymbol{\therefore,\;the\;absolute\;value\;of\;-183\;is\;183}}[/tex]
Voila! There's our answer, cheers! (:
____________________Hope that this helped! Best wishes.
[tex]\it Reach \ far. \ Aim \ high. \ Dream \ big.[/tex] ____________________[tex]\bigstar\underbrace[/tex]
does someone mind helping me with this problem? Thank you!
Answer:
-20
2(xy-7)=-20 with x=-1 y=3
Step-by-step explanation:
2(xy-7)=?
When variables are connected such as xy, this means to multiply.
x=-1
y=3
Multiply the x and the y together.
-1*3=-3. Plug that into the equation.
2(-3-7)=?
Subtract the inside the parenthesis.
2(-10)=?
Multiply. Remember when multiplying a positive and a negative the answer will always be a negative.
2(-10)=-20
This means that 2(xy-7)=-20 with the x=-1 and y=3.
Hope this helps!
If not, I am sorry.
The largest bubblegum bubble ever blown was 23 inches in diameter. What was its circumference?.
Answer:
[tex]C=23\pi[/tex] inches
or as a decimal
72.26 inches
Step-by-step explanation:
Formula for circumference: [tex]C=2\pi r[/tex]
Radius = [tex]\frac{d}{2}[/tex]
Altogether we get: [tex]C=2*\pi*\frac{d}{2}[/tex]
Which simplifies to: [tex]C=\pi d[/tex]
So now we can plug in 23 for [tex]d[/tex].
[tex]C=\pi*23[/tex]
Our final answer is:
[tex]C=23\pi[/tex] inches
or as a decimal
72.26 inches
Denver has a current temperature of -5°, while Barcelona has a current temperature of 54°. What is the difference in temperature between Denver and Barcelona?
Answer:
59°
Step-by-step explanation:
Difference=54-(-5)
=54+5=59
PLEASE I NEED THE ANSWER QUICKLY
1. A local newspaper charges $42 per half-page advertisement and $86 per full-page advertisement. Kathryn has a budget of $1192 to purchase 20 advertisements.
(a) Define a variable for each unknown.
Write a system of equations to represent the situation.
(b) How many full-page advertisements does Kathryn purchase?
Show your work.
(c) How many half-page advertisements does Kathryn purchase?
Show your work.
Answer:
x = 12 half page advertisements
y = 8 full page advertisements
Step-by-step explanation:
42x + 86y = 1192
x + y = 20
y = 20 - x
Input (20-x) as y into the first equation
42x + 86(20-x)=1192
42x + 1720 - 86x = 1192
(42x - 86x) 1720 -1720= 1192-1720
-44x = -528
x = 12
12 + y = 20
y=8
a. 'x' represents half page advertisement and 'y' represents full page advertisement.
System of equation is given by 42x + 86y = 1192 , x + y =20.
b. Number of full page advertisement Kathryn purchase is equals to 8.
c. Number of half page advertisement Kathryn purchase is equals to 12.
What is system of equation?" System of equation is defined as the finite set of equations for which we find a common solution."
According to the question,
Cost of half page advertisement = $42
Cost of full page advertisement = $86
Number of advertisement Kathryn could purchase = 20
Total budget of Kathryn to purchase advertisement = $1192
'x' represents half page advertisement
'y' represents full page advertisement
As per the situation given system of equation we have,
42x + 86y = 1192 ______(1)
x + y = 20
x = 20 - y _____(2)
Substitute the value of 'x' from system of equation (2) in (1) we get,
[tex]42( 20 -y) +86y =1192\\\\\implies 840 - 42y +86y =1192\\\\\implies 44y = 1192-840\\\\\implies y = \frac{352}{44}\\ \\\implies y =8[/tex]
Substitute the value of y in (2) to get 'x' ,
[tex]x=20-8[/tex]
= 12
Hence,
a. 'x' represents half page advertisement and 'y' represents full page advertisement.
System of equation is given by 42x + 86y = 1192 , x + y =20.
b. Number of full page advertisement Kathryn purchase is equals to 8.
c. Number of half page advertisement Kathryn purchase is equals to 12.
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How many significant digits are there in the number 237.16?
Answer:
3
Step-by-step explanation:
factoring 8x^2-12x-8
Answer:
( 8x - 4 ) ( x - 2 )
Step-by-step explanation:
8x² - 12x - 8
8x² - 16x + 4x - 8
8x ( x - 2 ) - 4 ( x - 2 )
( 8x - 4 ) ( x - 2 )
Answer:
⇒ [tex]4(x-2)(2x+1)[/tex]
Step-by-step explanation:
1) Common factor
⇒ [tex]8x^2-12x-8\\[/tex]
⇒ [tex]4(2x^2-3x-2)[/tex]
2) Use the sum-product pattern
⇒ [tex]4(2x^2-3x-2)[/tex]
⇒ [tex]4(2x^2+x-4x-2)[/tex]
3) Common factor from the two pairs
⇒ [tex]4(2x^2+x-4x-2)[/tex]
⇒ [tex]4(x(2x+1)-2(2x+1))[/tex]
4) Rewrite in factored form
⇒ [tex]4(x(2x+1)-2(2x+1))[/tex]
⇒ [tex]4(x-2)(2x+1)[/tex]
The drama teacher wants to know whether more families of students at the school would attend a musical or a comedy.
Which of the following survey methods will allow the drama teacher to make a valid conclusion about which genre of performance more families would attend?
Choose 1 answer:
Choose 1 answer:
To determine whether more families of students at the school would attend a musical or a comedy , she should Assign a number to each family, use a computer program to select 20 random numbers , Option A is the right answer.
What are different survey methods ?Some of the survey methods are Online Survey , Telephonic survey , Kiosk Survey , Face to Face Survey etc.
It is given that there are n number of families ,
To determine whether more families of students at the school would attend a musical or a comedy.
To do so she has to do random sampling from the group of families.
So , she should Assign a number to each family, use a computer program to select 20 random numbers.
Therefore Option A is the right answer.
The complete question is
The drama teacher wants to know whether more families of students at the school would attend a musical
or a comedy.
Which of the following survey methods will allow the drama teacher to make a valid conclusion about
which genre of performance more families would attend?
Choose 1 answer:
Assign a number to each family, use a computer program to select 20 random numbers
between 1 and the total number of families, and ask the families selected.
For each letter of the alphabet, assign a number to each family whose last name begins with
that letter, use a computer program to select a random number between 1 and the total
number of families whose last name begins with that letter, and ask the family selected.
To know more about different survey methods
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Which Expression is Equivalent to (f+g)(4)?
A) F(4) + G(4)
B) F(X) + G(4)
C) F(4 + G(4))
D) 4(F(X) + G(X))
Step-by-step explanation:
[tex] = (f + g)(4)[/tex]
[tex] = f(4) + g(4)[/tex]
The answer is A.
I need more help I'm lazy (img included)
Answer:
B)20
Step-by-step explanation:
convert 900in to ft=75
1500/75=20boxes
55 mi / h = ____ ft / s
Answer:
80.6ft/s
Step-by-step explanation:
[tex]\frac{55mi}{h} * \frac{5280ft}{1 mi}* \frac{1h}{3600s} = 80.6ft/s[/tex]
Are survival rates independent of gender within similar passenger classes ?
Answer:
yes
Step-by-step explanation:
Women had a much higher chance of survival — regardless of what class they were in — then men did. Of the 466 women on board, 339 survived. Of the 843 men on board, only 161 survived — a measly 19% compared to the 73% of women who made it safely back to shore.
what is b when the slope is 7/6 and the points are (10, -9)
Answer:
y = 7/6x - 62/3
Step-by-step explanation:
The equation for slope:
y = mx + b
m is the slope and b is the y-intercept
y = 7/6x + b
-9 = 7/6(10) + b
-9 = 35/3 + b
-62/3 = b
PLS HELP IM BEGGING ITS DUE IN 10 MINUTES WHOEVER ANSWERS FIRST AND CORRECTLY I WILL GIVE BRAINIEST!!!
Write a similarity statement comparing the two triangles:
The triangle ABE and triangle DEC are similar by AAA option third is correct.
What is the similarity law for triangles?It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
We have given two triangles in the picture.
As we can see in the triangle ABE
Angle ABE = 90 degree or right angle
Similarly, in a triangle DEC
Angle DEC = 90 degree or right angle
Angle ABE = Angle DEC
Angle EAB = Angle CDE
If the corresponding two angles are the same as two triangles then the third the angle will be the same.
Angle AEB = Angle DCE
The triangle ABE and triangle DEC are similar to AAA
Thus, the triangle ABE and triangle DEC are similar by AAA option third is correct.
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Use the periodic compound interest formula to solve.
Suppose that $11,000 is invested at 5.8% compounded quarterly. Find the total amount of this investment after 6 years.
Answer:
$15,539.67
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $11,000r = 5.8% = 0.058n = 4 (quarterly)t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=11000\left(1+\frac{0.058}{4}\right)^{(4 \times 6)}[/tex]
[tex]\implies \sf A=11000(1.0145)^{24}[/tex]
[tex]\implies \sf A=15539.67451...[/tex]
Therefore, the value of the investment after 6 years will be $15,539.67 to the nearest cent.
Which expressions are equivalent to the one below? Check all that apply.
In (e^2)
Possible Answers Below:
A.)2•In e
B.) 2
C.) 2e
D.) 1
Answer:
a and b
Step-by-step explanation: you can move the exponent to the front and lne is also equal to one times 2 = 2
2.) The quotient of 3 and y
Answer:
3 ÷ y
Step-by-step explanation:
Quotient refers to the division of two values, in this case 3 and y.
Answer:
3/y
Step-by-step explanation:
The point (-6, 4) is reflected over the x-axis. Find the point of reflection.
Answer:
-6, -4
Step-by-step explanation:
can anybody help me find what 11x-21=
The vertices of an isosceles triangle are A(-4, 0), B(-10, -2) and C(-6, -6).
What is the equation of the triangle's line of symmetry?
y = - x - 4
y = x - 4
y = x + 4
y = - x + 4
Could someone help me on this?
Chloe bought an equal number of forks and spoons for a party. The forks were sold at 3 for 2$ and the spoons were sold at 4 for 3$. She spent 5$ more on spoons than on forks. How much did she spend altogether?
60 forks 60÷3=$20
60 spoons 60÷4=$15
$20+$15=$35 total spent for forks and spoons
