How many solutions are there to this system of equations?
On a coordinate plane, 2 lines have equations y = one-fourth (x minus 4) and y = one-fourth x minus 1.
One solution
No solution
Infinitely many solutions
It cannot be determined without solving.
Answers
So, in response to the above question, we can state that equation the response is: There are countless options.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The two lines' equations are y = 1/4 (x - 4) and y = 1/4 (x - 1)
By equating them, we obtain: 1/4(x - 4) = 1/4x - 1.
To get rid of the fractions, multiply both sides by 4 as follows: x - 4 = x - 4
This equation may be written as 0 = 0, which is a constant.
The two lines coincide and have an endless number of solutions as a result.
Hence, the response is: There are countless options.
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Related Questions
Use the graphing calculator to graph the parent function. f(x) = log(x) add the translated function. f(x) = log(x - h) k plug in different values of h and k to answer the following questions. what happens when h is positive? what happens when h is negative? what happens when k is positive? what happens when k is negative?
Answers
The functions f(x) = log(x) and f(x) = log(x - h) + k are logarithmic functions
How to interpret the graph?The functions are given as:
f(x) = log(x)
f(x) = log(x - h) + k
From the graph of both functions, we have the following highlights:
When h is positive, the graph moves closer to the positive x-axisWhen h is negative, the graph moves closer to the negative x-axisWhen k is positive, the graph moves closer to the positive y-axisWhen k is negative, the graph moves closer to the negative y-axisRead more about logarithmic functions at:
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Answer:
horizontal shift to the right,
horizontal shift to the left,
vertical shift up,
vertical shift down.
Step-by-step explanation:
what is the standard form of this graph
Answers
the standard form of that graph is ax squared +bx+c
Enter the values for the highlighted variables that show how to subtract the rational expressions correctly:
StartFraction 2 Over x squared minus 36 EndFraction minus StartFraction 1 Over x squared + 6 x EndFraction = StartFraction 2 Over (x + 6) (x minus 6) EndFraction minus StartFraction 1 Over x (x + a) EndFraction. = StartFraction b x Over (x + 6) (x minus 6) x EndFraction minus StartFraction x minus c Over (x + 6) (x minus 6) x EndFraction. = StartFraction d x minus x + e Over (x + 6) (x minus 6) x EndFraction. = StartFraction x + f Over (x + 6) (x minus 6) x EndFraction. = StartFraction g Over x (x minus 6) EndFraction
a =
b =
c =
d =
e =
f =
g
Answers
Answer: I got you
The values are:
a = 6
b = 2
c = 6
d = 2
e = 6
f = 6
g = 1
Step-by-step explanation: Hope this helps
The values for the highlighted variables that show how to subtract the rational expressions are; a = 6, x^2 + 6x is equal to x(x+6), and b=2.
What is rational expressions?From the information, the denominator and numerator of the first term are multiplied by x.
The difference of squares is factored as (a² -b²) = (a +b)(a -b), so the denominator of the first term can be factored.
The common factor x can be factored out of the denominator of the second term which gives ...
[tex]\dfrac{2}{x^2-36}-\dfrac{1}{x^2+6x}= \dfrac{2}{(x+6)(x-6)}-\dfrac{1}{x(x+6)}\quad a=6[/tex]
Now Multiplying the first term by x/x and the second term by (x-6)/(x-6) gives ...
[tex]\dfrac{2x}{(x+6)(x-6)x}-\dfrac{x-6}{(x+6)(x-6)x}\quad b=2,\ c=6[/tex]
Writing the sum over the common denominator, we have;
[tex]\dfrac{2x-x+6}{(x+6)(x-6)x}\quad d=2,\ e=6[/tex]
Collecting terms in the numerator gives ...
[tex]\dfrac{x+6}{(x+6)(x-6)x}\quad f=6[/tex]
Finally, canceling the common factor we get;
1/(x-6)x
The values of the letters are; a=6, b=2, c=6, d=2, e=6, f=6, g=1
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An educational researcher claims that the average GPA of graduate students at FIU is less than 3.5 . To test his claim he collected data on 81 graduate students . The sample mean GPA was 3.25 with a standard deviation of 0.3 . What is the value of the test statistic to test this claim
Answers
The value of the test statistic to test the claim of comparison of average GPA is found to be -0.83 approximately.
How to find the z score (z statistic) for the sample mean?If we're given that:
Sample mean = [tex]\overline{x}[/tex]Sample size = n Population mean (hypothesized)= [tex]\mu[/tex]Sample standard deviation = sThen, we get:
[tex]z = \dfrac{\overline{x} - \mu}{s}[/tex]
If the sample standard deviation is not given, then we can estimate it by:
[tex]s = \dfrac{\sigma}{\sqrt{n}}[/tex]
where [tex]\sigma[/tex] = population standard deviation
For this case, since the sample size is 81 > 30, and we want to compare the mean (population mean) with some hypothesized mean (3.5 here), therefore, we can use one-sample z-test, which has the aforesaid test statistic.
We're provided that:
n = sample size = 81sample mean = [tex]\overline{x}[/tex] = 3.25sample standard deviation = s = 0.3hypothesized population mean with which comparison is done = [tex]\mu= 3.5[/tex]Thus, we get:
[tex]z = \dfrac{\overline{x} - \mu}{s} = \dfrac{3.25 - 3.5}{0.3} \approx -0.83[/tex]
Thus, the value of the test statistic to test the claim of comparison of average GPA is found to be -0.83 approximately.
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Please Help! This is really urgent!!!! Please!!
The diagram shows a sector of a circle of radius 3 units, formed from an angle of size 125 degrees. Find the length of the arc rounded to two decimal places.
Arc length = _____
Answers
Answer:
6.54498
Step-by-step explanation:
The formula that you use to solve this is (0/360)pi*radius2. You have to plug in the information that you are already given.
This is the hardest one yet! Please help!!
Answers
Answer:
Write your question.
Step-by-step explanation:
We're waiting...
Answer:
whats the question?
Step-by-step explanation:
Two prisms are similar if the ratio of the base if the two prisms is 49:196 what is the ratio of the volumes of the prisms
Answers
Answer:
1:8
Step-by-step explanation:
First, you must find the scale factor. Because you are given the area of the base, you must take the square root of 49 and 196. That leaves you with 7:14, and that simplifies to 1:2. To find the ratio of the volumes, you must cube both. That leaves you with a 1:8 ratio.
-0.056 + 0.27 = ?
Please show ALL of your work and how you got your answer! (-:
✨50 POINTS!!✨
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textbf{GUIDE to remember: }[/tex]
[tex]\bullet\large\textsf{\ 2 negatives = \bf positive}\\\bullet\large\textsf{2 positives = \bf positive}\\\bullet\large\textsf{1 negative \& 1 positive = \bf negative}\\\bullet\large\textsf{1 positive \& 1 negative = \bf negative}\\\\\large\boxed{Since, your\ equation\ contains\ 1 \ negative\ \& \ 1\ positive, your \ result}\\\large\boxed{will \ most \ likely \ be \ a \ \huge\boxed{{negative}}}\large\checkmark[/tex]
[tex]\large\boxed{\rm{EQUATION: -0.056 + 0.27}}[/tex]
[tex]\large\text{SOLVING FOR THE EQUATION PROVIDED ABOVE}\uparrow \\\\\large\text{Start at \boxed{\rm{-0.056}} and \underline{go \bold{up}} \boxed{\rm{0.27}} \underline{\underline{spaces to the right}} side of}\\\large\text{the number line.}[/tex]
[tex]\large\text{You should have landed/stopped on \boxed{\rm{0.214}}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be \boxed{\mathsf{0.214}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Solve 7k+17=30
give your answer as a fraction in its simplest form
Answers
7k=13
k= 7/13
The equation of k is 13/7.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
7k+17=30
Now, solving for k
Subtract both side 17
7k + 17 - 17 = 30 - 17
7k = 13
k= 13/7
Hence, the equation of k is 13/7.
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Complete the table below to show that the relationship holds for all the triangles above.
SOMEONE PLEASE HELP ME WITH THIS ILL GIVE YOU BRAINLIST ANSWER
IMAGE ABOVE
Answers
The length of a rectangle is 10 cm and the width is 15 cm. What is the
area of the rectangle in square meters?
Answers
Answer:
0.015 m²
Step-by-step explanation:
Since we need the area in square meters, we need to first convert our centimeter values into meters.
[tex]\frac{1m}{100cm} =10cm[/tex]
1 · 10 = 10
10/100 = 0.1 m
[tex]\frac{1m}{100cm} =15cm[/tex]
1 · 15 = 15
15/100 = 0.15 m
The area of a rectangle is a = l · w. Plugging in the given values, we get:
a = 0.1 × 0.15
a = 0.015 m²
hope this helps!
The Board of directories has 13 members. How many ways are there to elect a Chair and a Vice-Chair if the bylaw has a rotation rule: Chair and Vice-Chair cannot keep their positions for two years in a row
Answers
The number of ways to elect a Chair and a Vice Chair is 156.
Amount calculationGiven that the Board of directories has 13 members, to determine how many ways are there to elect a Chair and a Vice-Chair, the following calculation must be made:
13 x 12 = X156 = XAs the rule does not affect, because in the two years that have elapsed a different election will be held, the number of ways to elect a Chair and a Vice Chair is 156.
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Answer:The number of ways to elect a Chair and a Vice Chair is 156.
Step-by-step explanation:
What is this question asking and how do I solve it?
Answers
Answer:
the question is asking what it is the segment between HB,HG and CG
Step-by-step explanation:
PLEASE HELP!! I’m really bad with word problems.
Answers
Answer:
19). V = 381.51 cubic inches
20) The cylindrical box has a greater volume so Lin would prefer getting it.
Step-by-step explanation:
Assuming that the plastic bag filled with water was shaped like a sphere (bc there's not enough context to make it anything other than a sphere), the solution lies within an equation:
V = 4/3πr^3
This is the equation for finding the volume of sphere.
Hint: diameter = radius/2
V = 4/3π(4.5)^3
V = 4/3π(91.125)
V = 4.19(91.125)
V = 381.51 cubic inches
______________________________________________________
Equation of a rectangular prism: V = L * W * H
Equation of cylinder: V = πr^2h
Rectangle box:
V = 12 * 9 * 10
V = 120 * 9
V = 1080
Cylinder box:
V = π5^2(14)
V = π(25)(14)
V = 350 * 3.14
V = 1099
1080 < 1099
THE SUM OF THREE CONSECUTIVE EVEN INTEGERS IS 72 FIND THE THIRD INTEGERS.
Answers
Answer: The three consecutive even numbers are 22, 24, 26
22+24+26 = 72
========================================================
Explanation:
x = first even numberx+2 = second even number directly right after x(x+2)+2 = x+4 = third even number directly after x+2For example, if x = 12, then we'd have x+2 = 12+2 = 14 and x+4 = 14+4 = 18.
However 12+14+18 = 44 is not 72 like we want.
You can guess-and-check your way to the answer, but a faster efficient route is to use algebra. Add up those x expressions and set the sum equal to 72 and solve.
(first) + (second) + (third) = 72
(x) + (x+2) + (x+4) = 72
3x+6 = 72
3x = 72-6
3x = 66
x = 66/3
x = 22
So we have,
x = 22 = first even numberx+2 = 22+2 = 24 = second even numberx+4 = 22+4 = 26 = third even numberAs a check: 22+24+26 = 72 which verifies the answers.
Which polynomial identities are correct?
Select ALL that apply.
1. a2−b2=(a−b)(a+b)
2. (a+b)3=a3+3ab+b3
3. (a−b)3=a3−b3
Answers
Answer:
a2−b2=(a−b)(a+b) is correct.
Step-by-step explanation:
(a+b)3=a3+3a²b+3ab²+b3
(a−b)3=a3-3a²b+3ab²−b3
The width of a box is one third of its length. The
height of the box is one third of its width. If the
length of the box is 27 cm, what is the volume of
the box?
a. 81 cm3
b. 162 cm3
c. 243 cm3
d. 729 cm3
Answers
Answer:
d) 729cm^3
Step-by-step explanation:
Length =27cm
Width = 1/3 of length
= 1/3 of 27cm = 1/3 × 27cm = 9cm
Height = 1/3 of width
= 1/3 of 9cm = 1/3 × 9cm = 3cm
So, length = 27cm; width = 9cm; height = 3cm
So, volume = length × width × height
= 27cm × 9cm × 3cm = 729cm^3
16 ounces is equivalent to 1 pound. A lion cub born at the zoo weighs 2 1/2 pounds. How many ounces does the lion cub weigh? Show your work.
Answers
Answer:
40 ounces.
Step-by-step explanation:
Simply multiple 2 1/2 pounds with 16 in order to find how many ounces the lion cub weighs.
2.5 * 16 = 40
Therefor, the lion cub weighs 40 ounces.
in a bowl, there are green candies for every 5 red candies. If the bowl has a total of 160 candies (red and green only), which proportion will solve for the number of green candies in the bowl?
Answers
Answer:
see below
Step-by-step explanation:
3 green for 5 red
then 3 out of (3+5) are green ... or 3/8 are green
3/8 * 160 = green = 60 green
Answer:
60 green candies
Step-by-step explanation:
We know the proportion :
Red : Green = 5 : 3Let's make a linear equation where candies is denoted by x.
5x + 3x = 1608x = 160x = 20Number of green
3x3(20)60 green candiesA trapezoid has an area of 36 square feet. If its height is 8, and one base is 4, what is the length of the other base?
Answers
Answer:
5
Step-by-step explanation:
A=a+b/2 x h
4 = a
5 = b
8 = h
4 + 5 / 2 = 4.5
4.5 x 8 = 36
So the other base length is 5
Factor the following expression. x^3 + 2x^2 - 16x - 32
IMMAGE ATTACHED
Answers
Answer:
The answer is A.
Step-by-step explanation:
I used an online Calculator to calculate it for you.
(x + 4) * (x - 4) * (x + 2)
(x^2 - 4^2) * (x+2)
x^3 + 2x^2 - 16x^2 - 32
An airplane flies with a constant speed of 620 miles per hour. How far can it travel in 2 hours 30 minutes?
Answers
Answer:
1550 miles
Step-by-step explanation:
rate * time = distance
620 m/hr * 2.5 hr = 1550 miles
(Note that 2 hr and 30 min is 2 and 1/2 hours = 2.5 hours)
pls help me wirh this
Answers
Given x varies inversely as y and x = 4 when y=−9, find y when x = 6.
Answers
Given that X varies inversely as Y, the value of Y when the number of X is increased to the given value is -6.
What is Proportional relationships?Proportional relationships are relationships between two variables where their ratios are equivalent.
Inverse variation It is expressed as;
x ∝ 1/r then x = k/y
Where k is the proportionality constant.
Given the data in the question;
x = 4y = -9First we find the proportionality constant.
x = k/y
4 = k / -9
k = -36
Now, If x = 6 then y = ?
x = k/y
6 = -36 / y
6y = -36
y = -36 / 6
y = -6
Given that X varies inversely as Y, the value of Y when the number of X is increased to the given value is -6.
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1. Find the sum of the series
15
∑ (2n-1)
n-1.
Show your work.
Answers
[tex]\\ \rm\Rrightarrow \sum^{15}_{n=1}2n-1[/tex]
[tex]\\ \rm\Rrightarrow 2(1)-1+2(2)-1\dots+2(15)-1[/tex]
[tex]\\ \rm\Rrightarrow 1,3,5\dots 29[/tex]
Sum of first 15 odd nos
n²15²225what is the number of pie in math
Answers
Answer:
A pie in maths have a degree of 360 degrees
Consider the graph of the function f(x)=log2 x. What are the features of the function g if g(x)=f(x+4)+8?
Answers
Answer two questions about Equations A and B:
A. 5x2+x= x=4
B.
5x + x = x - 4-
1) How can we get Equation B from Equation A?
2) Are these equations equivalent?
Answers
Answer:
Equation B is the same as Equation A + 2
Step-by-step explanation:
To be able to get equation B from equation A, we have to compare equation A with equation B. Given that equation A. is 5x-2+x=x-4 and equation B is 5x+x=x-4.
Equation B: 5x+x=x-4.
Equation A: 5x-2+x=x-4.
Simplifying equation A to be in the form of equation B:
5x -2 + x = x - 4
Adding 2 to both sides:
5x + x -2 + 2 = x - 4 + 2
5x + x = x - 4 + (+2)
= equation A + 2
But 5x+x=x-4 = equation A
Therefore Equation B is the same as Equation A + 2
Help x^2+10x=24 solve and simplify
Answers
Answer:
x= 2, x= -12
Step-by-step explanation:
cuz i said so
first move the 24 to the other side of the equation by subtracting it from both side's
now the equation looks like this
x^2+10x-24
then find values that add to equal 10 and that also multiply to equal -24
this works out to (x-2) (x+12)
which means that x is equal to 2 and -12
carnival a charges an entres fee of 7.50 and 0,75per tiket for the rides carnival b charges an entrence fee of 12.00
Answers
Answer:
So what? Please tell the full question