PLEASE HELP!!! 100 POINTS!!! WILL GIVE BRAINLIEST!!!!
Graph the two lines:
2x + 3y = 18
3x -4y > 16.
Give the Domain and Range, Slope, and Y-intercept for each line.
Graph each equation above on the graph below and show all work.( Or tell me how to graph it)
Give the Domain and Range, Slope, and Y-intercept for each line. Explain in detail how you got each answer.
2x + 3y = 18 3x -4y > 16
Slope-Intercept Form: Slope-Intercept Form:
Domain: Domain:
Range: Range:
Slope: Slope:
Y-intercept: Y-intercept:
Answers
[tex]2x + 3y = 18[/tex]
DOMAIN IS ALL REAL NUMBERS
RANGE IS ALL REAL NUMBERS
SLOPE IS -2/3
Y INTERCEPT IS (0,6)
SLOPE INTERCEPT FORM
[tex]y = \frac{ - 2}{3} x + 6[/tex]
for the equation
[tex]3x - 4y > 16[/tex]
DOMAIN IS ALL REAL NUMBERS
RANGE IS ALL REAL NUMBERS
SLOPE IS 3/4
Y INTERCEPT IS (0,-4)
SLOPE INTERCEPT
[tex]y < \frac{3}{4} x - 4[/tex]
[tex]2x + 3y = 18[/tex]
[tex]3x -4y \ \textgreater \ 16[/tex]
They are written in standard form, [tex]ax+by=c[/tex], so our first step is to convert them into slope-intercept form, [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.
We rearrange to basically solve for y in each function.
1) [tex]2x + 3y = 18 \\ 3y = -2y+18 \\ y= \frac{-2}{3}y+6[/tex]
2) [tex] -4y\ \textgreater \ -3x+16[/tex]
We divide by –4 to isolate y, but remember when multiplying or dividing with a negative number in an inequality, we flip the sign of the inequality.
[tex]y \ \textless \ \frac{3}{4}x-4[/tex]
This gives us our slope-intercept forms for each.
For the domain, each function is defined for all real x. This is a property of linear (and polynomial) functions. The inequality does not affect this.
The range, however, is a bit tricky. The range of a linear or polynomial function is always all real numbers y. It might be tempting to restrict it for an inequality, however, the range is still all reals.
In set-builder notation, we write for the domains of both functions: {[tex]x \ | \ all \ real \ numbers[/tex]}. For the ranges, we write {[tex]y \ | \ all \ real \ numbers[/tex]}.
In interval notation, we write [tex](- \infty, \infty)[/tex] for both the domain and range.
To obtain the slope and y-intercept, we look back to the functions in slope-intercept form, [tex]y=mx+b[/tex], again where m is the slope and b is the y-intercept.
For the equation, we have
[tex]m= \dfrac{-2}{3} [/tex]
and [tex]b=6[/tex].
For the inequality, we have
[tex]m= \dfrac{3}{4} [/tex]
and [tex]b=-4[/tex].
We can use the slope and y-intercept to graph each function. Remember that an inequality with less than or greater than (i.e., no "equal to" part) is represented with a dotted line.
To find where you shade the inequality, think about its sign. Since y is less than the expression, we shade below the line. We can also verify this by plugging in a test-point above or below the line and shading the region where the test-point is a valid solution.
See the graphed solution set attached.
Related Questions
Find the area of a triangle with a base length of 3 units and a height of 4 units.
Answers
So these are given so we plug them in
A=1/2(3)(4)
A=6 units
To find the area of a triangle, we need to multiply the base and the height of the triangle and divide the product by 2.
So, the expression we would use to solve this is (3 * 4) / 2.
Let's solve:
(3 * 4) / 2
= 12 / 2
= 6
So, the area of the triangle is 6 units squared.
Hope this helps!
Three times a number added four times the number equals 84 find the number
Answers
3x+4x=84
7x=84
7x/7=84/7
x=12
Philip is going on a 400040004000-kilometer road trip with three friends. The car consumes 666 liters of gas per 100100100 kilometers, and gas costs \$1.50$1.50dollar sign, 1, point, 50 per liter. If Philip and his friends want to split the cost of gas evenly, how much should they each pay?
Answers
In total, this will cost 240*1.5=360$. He has 3 friends, so they are 4 in total. Everyone will have to pay 360/4=90$
First, we will calculate how much it consumes per kilometer:
[tex]g_{ckm}=6/100=0.06\frac{l}{km}[/tex]
The total consumption for the whole trip would be:
[tex]g_t=L\cdot g_{ckm}=0.06\cdot 4000=240 l[/tex]
To get the total cost of the gas we multiply the total gas consumed by its cost:
[tex]C_t=g_t\cdot1.5=360\$[/tex]
So, each passenger must pay $90.
Im learning Polynomials and we are learning the strategy grouping, can anyone please explain how to group polynomials and maybe give an example :) greatly appreciated
Answers
Ex
5(4x+1)10(4x+1)
(5+10)(4x+1)
Example
x^2 +2x +3x +6
(x^2 +2x) +(3x +6) . . . . parentheses added to group pairs of terms
x(x +2) +3(x +2) . . . . . . common factor pulled from the terms of each group
(x +3)(x +2) . . . . . . . . . common factor removed to give factored result
when the solutions to each of the two equations below are graphed in the xy coordinate plane, the graphs of the solutions intersect at two places. Write the y-coordinate of the points of intersection in the boxes below in order from smallest to largest. y=2x and y=x^2-3
Answers
Since both of these equations have y isolated, we can set them equal to each other:
2x=x²-3
We want all of the variables on one side, so subtract 2x:
2x-2x = x²-3-2x
0=x²-3-2x
Write the quadratic in standard form:
0=x²-2x-3
This is easily factorable, as there are factors of -3 that will sum to -2. -3(1)=-3 and -3+1=-2:
0=(x-3)(x+1)
Using the zero product property we know that either x-3=0 or x+1=0; therefore x=3 or x=-1.
Substituting this into the first equation (it is simpler):
y=2(3) = 6
y=2(-1)=-2
Therefore the coordinates are (3, 6) and (-1, -2).
Answer:
Step-by-step explanation:
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
⇒ -3,
⇒ 0.59,
⇒ 3.41
You deposit $1500 in an account that pays 7% annual interest. Find the balance after 2 years when the interest is compounded daily.
Answers
The balance after 2 years when the interest is compounded daily is
$1,725.39.
What is Compound Interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Given:
P= $1500
R= 7%
T = 2 years
Now, using
A = P[tex](1 + r/n)^{nt[/tex]
A = 1,500.00[tex](1 + 0.07/365)^{(365)(2)[/tex]
A = 1,500.00[tex](1 + 0.00019178082191781)^{(730)[/tex]
A = $1,725.39
Hence, the balance is $1,725.39.
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every day Josie bakery bakes muffins and bagels. the ratio of m7ffins to bagels is always the same. the table shows data about what Josie bakery bakes 3 days of the week. How many bagels did Josie bakery bakes on wednesday
Answers
x = (300*165)/180 = 275
what effect does the value of the coefficient of x^2 have on the graph?
Answers
ex.)
for the graph of x^2, 5 of your data points will be (0,0),(1,1),(2,4),(3,9),(4,16)
when you multiply by a coefficient,
ex.)
for the graph of ax^2, a being a stand in for the coefficient, 5 of your data points will be (0,a×0), (1,a×1), (2,a×4), (3, a×9), (4,a×16)
if your coefficient,a, is equal to 4 your data points become: (0,0),(1,4),(2,8),(3,36),(4,64)
if you graph it out you will notice that your graph rises faster and faster incompariaon to the original.
hope this helps good luck
In the Citizens United case the Supreme Court interpreted political donations as __________.
Answers
A) only allowable for low-income candidates
B) a restriction on equal access to democracy
C) a form of speech protected by the Constitution
D) an unconstitutional influence over policymakers
Answer: C) a form of speech protected by the Constitution
Page Reference: 33 Learning
Objective: 2.2 Topic/A-head: Political System:
Links Between Wealth and Power
Skill Level: Understand the Concepts
-7(3x+5) use Distributive property to solve
Answers
= ( - 7 )(3x + 5)
= ( - 7 )(3x) + ( - 7)(5)
Answer: = - 21x - 35
An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. Question 3 options: 11.1 cm, 4.9 cm 44.4 cm, 3.2 cm 44.4 cm, 11.1 cm 24 cm, 4.9 cm
Answers
7.4/x=6/4
When we clear "x", we obtain:
6x=(7.4)(4)
x=(7.4)(4)/6
x=4.9 cm (This is the shortest possible length of the third side of the triangle)
Let's find the longest possible length:
4/6=7.4/x
When we clear the "x", we have:
4x=(7.4)(6)
x=(7.4)(6)/4
x=11.1 cm (This is the longest possible length of the third side of the triangle)
Answer:
11.1 cm, 4.9 cm
Let $G$ denote the centroid of triangle $ABC$. If triangle $ABG$ is equilateral with side length 2, then determine the perimeter of triangle $ABC$. 99 points! for right answer!
Answers
You are trying to find the perimeter of triangle ABC. Each side is 2. Since there are 3 sides on a triangle, multiply 2 by 3 to get 6. You do not need the centroid for this problem.
I hope this helps!
Suppose a population of 175 crayfish doubles in size every month. the function f(x) = 175(2x) gives the population after x months. how many crayfish will there be after 1 year?
Answers
We have then:
f (x) = 175 * (2 ^ x)
Then, you should know that 1 year contains 12 months.
So we have that for x = 12:
f (12) = 175 * (2 ^ 12)
f (12) = 716800
Answer:
there will be 716800 crayfishes after 1 year
What are the values of a and b in the equation (4x^a)^b = 256/x^8
Answers
(4x^-2)^4
= 4^4 x^-8
= 4^4 / x^8
= 256/x^8
Answer:
The value of a is -2 and the value of b is 4.
Step-by-step explanation:
Given expression is,
[tex](4x^a)^b = \frac{256}{x^8}[/tex]
Using [tex](ab)^m=a^m.b^n[/tex] on left side,
[tex]4^b(x)^{ab}=\frac{4^4}{x^8}[/tex] ( [tex]4^4 = 256[/tex] )
Using [tex]a^m=\frac{1}{a^{-m}}[/tex],
[tex]4^b(x)^{ab}=4^4 (x)^{-8}[/tex]
By comparing both sides,
We get,
b = 4 and ab = -8
⇒ a = -2
Hence, the value of a is -2 and the value of b is 4.
Ben bought a desk for $249.99. The sales tax rate was 6.25%. How much did Ben pay for the desk? Round your answer to the nearest cent. (1 point)
$15.62
$187.49
$265.61
$406.23
Just tell me if its A,B,C, or D.
Answers
So C
The Price for Desk after tax is $265.614.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Ben bought a desk for $249.99.
Tax rate = 6.25%
So, the price for desk after tax
= 249.99 + 249.99 x 6.25%
= 249.99 + 249.99 x 0.0625
= 249.99 +15.62
= $265.614
Hence, the Price for Desk after tax is $265.614.
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What would be the side length of the smallest square plate on which a 40-cm chopstick can fit along a diagonal without any overhang? (Correct answer will get reward)
Answers
The side length of the smallest square plate required to fit a 40-cm chopstick along its diagonal without any overhang is approximately 28.284 cm.
To find the side length of the smallest square plate in which a 40-cm chopstick can fit along a diagonal without any overhang, we can use the Pythagorean theorem. The diagonal of a square is the hypotenuse of a right-angled triangle formed by two sides of the square. Since the sides of the square are equal, if one side is s, then the diagonal d can be calculated using the equation d = s√2, where √2 is the square root of 2 (approximately 1.4142).
Therefore, to fit a 40-cm chopstick along the diagonal:
Let d = 40 cm.
Use the equation s√2 = 40 cm to find s, the side of the square.
s = 40 cm / √2.
s ≈ 28.284 cm when rounded to three decimal places.
So, the side length of the smallest square plate on which a 40-cm chopstick can fit along a diagonal without any overhang is approximately 28.284 cm.
What’s the value of x worth 15 points!
Answers
Opposite angles of a parallelogram are equal. You get a hint of that from the 2 acute angles which are both 2x.
Add 15 to both sides.
3x = 2x + 24 + 15
3x = 2x + 39 Subtract 2x from both sides.
3x - 2x = 39
x = 39
Hi there! :)
Answer:
x=39
*The answer must have a positive sign.*
Step-by-step explanation:
When the 2 acute angles in which means you had to used 2x from both sides of an equation.
First, only had to do is, add by 15 from both sides of an equation.
[tex]3x-15+15=2x+24+15[/tex]
Then, you add by the numbers from left to right.
[tex]24+15=39[/tex]
[tex]3x=2x+39[/tex]
Next, you subtract by 2x from both sides of an equation.
[tex]3x-2x=2x+39-2x[/tex]
Finally, you simplify.
[tex]x=39[/tex]
Final answer is x=39
Hope this helps!
Thanks!
Have a nice day! :)
:D
-Charlie
Describe the graph of a system of linear equations that has infinite solutions.
Answers
A 2-digit number is one more than 6 times the sum of its digits. If the digits are reversed, the new number is 9 less than the original number. Find the original number
Answers
hope this helps<3
:)
Find the value of z.
Answers
HELP!!...................
Answers
r = x^2 +5x + 14 = 5^2 +5(5) +14 = 25 +25 +14 = 64
c = x^2-4x +5 = 5^2-4(5) + 5 = 25-20 +5 = 10
r- c = 64-10 = 54
so the store will have a profit of 54,000 after it's 5th month
Answer is C
Find the product by using the FOIL method
(11z-5y)(3z+2y)
Plz help!
Answers
1. _____ is exchanging one good for another without using money.
Credit
Barter
Negotiating
Brokering
2. A _____ has to be paid in full on the due date. (1 point)
Charge card
Credit card
Debit card
Check card
3. The _____ is the original amount owed on a loan. (1 point)
Loan due
Interest
Available balance
Principal
4. APR is used to calculate the _____. (1 point)
Loan amount
Interest accrued
Principal
Future earnings,
Answers
The answers are:
1. Barter
2. charge card
3. principal
4. interest accured
Which of the following points lies on the graph
Answers
(-3, 21)
y = x^2-2x+6
21 = (-3)^2-2(-3)+6
21=9+6+6
21=21
That works. If you are not 100% confident with your arithmetic, you can plug in the other points.
Find the volume of the box. use the formula v = lwh. rectangular box with three sides visible, having width, length, and height of x plus two, two x minus one, and three x plus one respectively
a. 6x3 – 2
b. 6x2 – 13x2 – 3x – 2
c. 6x2– x – 1
d. 6x3 + 11x2 – 3x – 2
Answers
Multiplying these all together will result in
6x^3+11x^2−3x−2
Making the answer option D.
The expression for the volume of the box is given by 6x³+11x²-3x-2
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Given that, rectangular box with three sides visible, having width, length, and height of x plus two, two x minus one, and three x plus one
Height = x+2
Width = 2x+1
Length = 3x+1
Volume = HxLxW
Volume = (x+2)(2x+1)(3x+1)
= 2x²-x+4x-2(3x+1)
= (2x²+3x-2)(3x+1)
= 6x³+11x²-3x-2
Hence, The expression for the volume of the box is given by 6x³+11x²-3x-2
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PLEASE HELP ME ON THIS QUESTION
THX
~BRAINLIEST AVAILABLE TO CORRECT ANSWER
Answers
x=-2→g(-2)=-f(-2)-2=-(-1)-2=1-2→g(-2)=-1
x=-1→g(-1)=-f(-1)-2=-(1)-2=-1-2→g(-1)=-3
x=0→g(0)=-f(0)-2=-(3)-2=-3-2→g(0)=-5
x=1→g(1)=-f(1)-2=-(5)-2=-5-2→g(1)=-7
x -2 -1 0 1
g(x) -1 -3 -5 -7
f(x)={(-2,-1),(-1,1),(0,3),(1,5)}
Need to find g(x)=-f(x)-2
First step is to find f(x) in analytical form.
The slope-intercept form would be convenient because we can find both the slope and y-intercept.
In a typical linear function
f(x)=mx+c
m= slope, can be found by (y2-y1)/(x2-x1)
c= y-intercept [value of y when x=0]
So here, taking points (0,3),(1,5)
m=(5-3)/(1-0)=2
c=3 [y-value when x=0]
=>
f(x)=2x+3
=>
g(x)
=-f(x)-2 [given]
=-(2x+3)-2 [don't forget the parentheses]
=-2x-3-2
=-2x-5
Finally
g(-2)=-2(-2)-5=4-5=-1
g(-1)=-2(-1)-5=2-5=-3
g(0)=-2(0)-5=0-5=-5
g(1)=-2(1)-5=-2-5=-7
...
The explicit rule for a sequence is an=9(−5)n−1 .
What is recursive rule for the sequence?
an=5−(an−1),a1=9
an=−9(an−1),a1=5
an=9−(an−1),a1=5
an=−5(an−1),a1=9
Answers
The recursive rule is a(n) = -5*a(n-1); a(1) = 9
The first term is 9. Each new term is found by multiplying the previous term by -5
We can see this when we raise -5 to a whole number power. Eg: 9(-5)^3 = 9*(-5)*(-5)*(-5)
Answer: Choice D
Answer:
Option 4th is correct.
[tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]
Step-by-step explanation
The explicit sequence of the geometric sequence is given by:
[tex]a_n = a_1r^{n-1}[/tex] ....[1]
where,
r is the common ratio
n is the number of terms
[tex]a_1[/tex] is the first term
As per the statement:
The explicit rule for a sequence is:
[tex]a_n=9(-5)^{n-1}[/tex]
On comparing [1] we have;
[tex]a_1 = 9[/tex] and r= -5
Recursive formula for the geometric sequence is given by:
[tex]a_n = r \cdot a_{n-1}[/tex] for [tex]n\geq 2[/tex]
Substitute the given values we have;
[tex]a_n = -5 \cdot a_{n-1}[/tex]
Therefore, the recursive rule for the sequence is, [tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]
Solve 2x^3-5x^2-11x-4=0
Answers
x = {-1, -0.5, 4}
The factorization will be
.. (2x+1)(x +1)(x -4) = 0
Jim runs a food cart and during a business outdoor Festival he sold $8470 worth of food he sells hot dogs for $2.50 and steak sandwiches for $10 if he sold a total of 985 items that they how many of each item did he sell?
Answers
x: hot dogs
y: steak sandwiches
We write the following system of equations:
2.50x + 10y = 8470
x + y = 985
Resolving graphically we have:
x = 184
y = 801
Note: see attached image for the solution.
Answer:
He sold:
hot dogs = 184
steak sandwiches = 801
Simplify these algebraic expressions: 12x + 3 − 4x + 7, 8 − 7x − 13 + 2x, −3x − 18 + 5x − 2
Answers
8-7x-13+2x=-5-5x
-3x-18+5x-2=-16x-2
The simplified expressions are:
12x + 3 − 4x + 7 = 8x + 10
8 − 7x − 13 + 2x = −5x − 5
−3x − 18 + 5x − 2 = 2x − 20
What is an expression?A term is a single mathematical phrase. It might consist of only one variable—a letter—one number—positive or negative—or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. Coefficients are numbers that come before phrases.
To simplify each expression, we combine like terms:
Expression 1:
12x + 3 − 4x + 7 = (12x − 4x) + (3 + 7)
12x + 3 − 4x + 7 = 8x + 10
Expression 2:
8 − 7x − 13 + 2x = (−7x + 2x) + (8 − 13) = −5x − 5
Expression 3:
−3x − 18 + 5x − 2 = (−3x + 5x) + (−18 − 2) = 2x − 20.
Therefore, the simplified expressions are:
12x + 3 − 4x + 7 = 8x + 10
8 − 7x − 13 + 2x = −5x − 5
−3x − 18 + 5x − 2 = 2x − 20
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