Answer:
y = -2x+2
Step-by-step explanation:
4-4x-2y=0
4-4x = 2y
2y = 4-4x
y = (4-4x)/2
y = 4/2-4x/2
y = 2 -2x
y = -2x+2
What is one of the solutions to the following system of equations?
x² + y² = 25
y - 3x = -5
Answer:
x = 0 y = -5
x = 3 y = 4
Step-by-step explanation:
x² + y² = 25
y - 3x = -5
-----------------------
y = 3x-5
x² + y² = 25
x² + (3x-5)² = 25
(3x-5)(3x-5) = 9x² -15x -15x + 25
x² + 9x² -15x -15x + 25 = 25
x² + 9x² -15x -15x = 0
x² + 9x² - 30x = 0
10x² - 30x = 0
x(10x-30)=0
x = 0
10x-30=0
x = 3
y - 3x = -5
y - 3(0) = -5
y = -5
y - 3(3) = -5
y - 9 = -5
y = 4
Answer:
(4,3) and (0,-5) are both solutions where we have (x,y).
Step-by-step explanation:
Here are simplified steps:
https://www.symbolab.com/solver/matrix-calculator/x%5E%7B2%7D%2By%5E%7B2%7D%3D25%3B%20y-3x%3D-5?or=input
Symbolab is an excellent tool for just most math.
Determine the solution to the system of equations graphed below and explain your reasoning and complete sentences
g(x)=-2x-3
f(x)= |x+1|-4
Answer:
(x, y) = (0, -3)
Step-by-step explanation:
On a graph, the solution to a system of equations is the set of points where the graphs of the equations intersect.
__
solutionThe graphs for this system of equations intersect at the point (0, -3). That point is the only solution for this system of equations.
The solution is (x, y) = (0, -3).
There are 130 people in a sport centre.
73 people use the gym.
62 people use the swimming pool.
58 people use the track.
22 people use the gym and the pool.
29 people use the pool and the track.
25 people use the gym and the track.
11 people use all three facilities.
Given that a randomly selected person
uses the gym and the track, what is
the probability they do not use the
swimming pool?
Kylie borrowed a book from a library. The library charged a fixed rental for the book and a late fee for every day the book was overdue. The expression below shows the charges Kylie paid for the book when she returned it x days after the
due date:
2 +0.25x
What does the constant term of the expression represent?
The late fee for the book
The fixed rental for the book
The number of books borrowed
The number of days the book was overdue
Answer:
B - fixed rental for the book.
Since for everyday the book is late the fee is 0.25 multiplied by X, X is the days the book is not returned.
Thus, the constant would be 2, 2 is the constant whereby the rental for the book regardless of other variables.
Photo attached
A. -2
B. -1
C. 1/-2
D. 1/2
Step-by-step explanation:
(X1,Y1) = (-2,2)
(X2,Y2) = (0,1)
• Find slope.
m = (Y2 - Y1)/(X2 - X1)
m = (1 - 2)/(0 - (-2))
m = -1/2
The answer is C.
In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks. If at year’s end an auditor
checks your accounting records and randomly selects one week to check the company’s payroll, what is the probability that the auditor will select a week in which you paid overtime wages and hired
temporary help?
The probability that the auditor will select a week in which you paid overtime wages and hired is 0.28
In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks.
What is probablitity?
Probability, can be define as the ratio of favorable outcomes to the n number of total events.
Here, p(a) = Overtime was paid for 26 weeks = 26/32= 0.81
p(b) = temporary help was hired for 15 weeks = 0.46
Required probability = P(a) + P(b) - 1
= 0.81 + 0.46 -1
= 0.28
The the required probability that the auditor will select a week in which you paid overtime wages and hired is 0.28
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Identify the inverse g(x) of the given relation f(x).
f(x) = {(8, 3), (4, 1), (0, –1), (–4, –3)}
g(x) = {(–4, –3), (0, –1), (4, 1), (8, 3)}
g(x) = {(–8, –3), (–4, 1), (0, 1), (4, 3)}
g(x) = {(8, –3), (4, –1), (0, 1), (–4, 3)}
g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}
Answer:
Last choice
Step-by-step explanation:
The basic definition of inverse function is both domain and range are swapped.
The domain is defined as set of all x-values while range is defined as set of all y-values.
If we have set of function h = {(1,2), (3,4), (5,6)} then the inverse will be {(2,1), (4,3), (6,5)}. Thus, if set of (x,y) is original function then set of (y,x) will be inverse of set of (x,y).
Henceforth, the inverse of f(x) will be g(x) = {(3,8), (1,4), (-1,0), (-3,-4)}.
Answer:
D. g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}
Step-by-step explanation:
hope this helps:)
Factorize:
a⁴-a³+2a²
[tex] {a}^{4} \: - \: {a}^{3} \: + \: {2a}^{2} [/tex]
Factor the expression with the common factor that is "a²".[tex] \boxed{ \bold{ {a}^{2} \: \times \: ( {a}^{2} \: - \: a \: + \: 2)}}[/tex]
MissSpanishAnswer:
a²(a²-a+2)
Step-by-step explanation:
Solution Given:
a⁴-a³+2a²
first taking common a²
we get
a²(a²-a+2) which is a required answer.
Ms. Jerome wants to buy identical boxes of art supplies for her 25 students. If she can spend no more than $375 on art supplies, what inequality describes the price can she afford for each individual box of supplies,b?
The inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
Ms. Jerome wants to buy identical boxes of art supplies for her 25 students. If she can spend no more than $375 on art supplies
Let's suppose b is the price of each box of supplies.
Total cost for a 25 number of boxes = $25b
25b ≤ 375
Thus, the inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.
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Suppose that the weight (in pound) of an airplane is a linear function of the amount of fuel (In gallons) in it's tank. When carrying 20 gallons of fuel, the airplane weighs 2210 pounds. When carrying 54 gallons of fuel, it weighs 2397 pounds. How much does the airplane weigh if it's carrying 60 gallons of fuel?
Answer:
For 60 gallons of fuel, the airplane would weigh 2430 gallons.
Step-by-step explanation:
Concept: Use the values and conditions to make a linear equation of a straight line. Let the y-axis be fuel and x-axis be airplane weight. The given points are (2210, 20) and (2397, 54). Use these points to make an equation of line.
[tex]\frac{y-20}{x-2210} =\frac{54-20}{2397-2210} \\\frac{y-20}{x-2210} = \frac{34}{187}[/tex]
Let this be the equation of straight line.
We have to find the airplane weight at 60 gallons of fuel. This means y = 60 and we have to find the x.
[tex]\frac{60-20}{x-2210} =\frac{34}{187} \\x-2210=\frac{(187)(40)}{34} \\x-2210=220\\x=2430[/tex]
So, the airplane weight is 2430 gallons.
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solve: √2x-8= √x+4 the equation.
Answer:
(a) x = 12
Step-by-step explanation:
The radicals in this equation can be eliminated simply by squaring both sides. Then the resulting linear equation is solved in two steps.
__
square[tex]\left(\sqrt{2x-8}\right)^2=\left(\sqrt{x+4}\right)^2\\\\2x-8=x+4\qquad\text{simplify}\\\\x-8=4\qquad\text{subtract $x$}\\\\\boxed{x=12}\qquad\text{add 8}[/tex]
_____
Additional comment
You know the contents of each radical must not be negative. That means 2x-8 ≥ 0, or x≥4. We know x=4 doesn't work in the equation (0≠√8), so we only need to check the answers x=12 and x=7. Of those, only x=12 satisfies the equation.
the equation for the circle shown below is x2 + y2 = 64 What is the length of the circles radius
Answer:
radius = 8
Step-by-step explanation:
the equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
x² + y² = 64 ← is in this form
with r = [tex]\sqrt{64}[/tex] = 8
PLS HELP IF POSSIBLE ASAP
The value of y if x is equal to 5 is 75 and the value of y when x = 7 is 8/7
Direct and inverse variationVariations shows the relationship between variables.
4) If y varies directly as x², hence;
y = kx²
27 = 9k
k = 3
In order to determine y if x = 5
y = 3(5*5)
Y = 75
Hence the value of y if x is equal to 5 is 75
5) If y varies inversely as x, hence;
y = k/x
k = xy
k = 16(1/2)
k = 8
If x = 7, the value of y will be;
y = 8/7
Hence the value of y when x = 7 is 8/7
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Can someone explain this?
Answer:
false
Step-by-step explanation:
if the 2 shorter segments dont add up to be equal or greater to the longest segment, then its impossible for a triangle to be formed :)
Answer:
True
Step-by-step explanation:
General formulas and concepts:
Subject: Geometry
Unit: Triangular Line Segments
Definitions:
Triangle Inequality Theorem
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.Steps:
Use the triangle inequality theorem:
9 + 4 > 11
13 > 11 ⇒ True
9 + 11 > 4
20 > 4 ⇒ True
4 + 11 > 9
15 > 9 ⇒ True
Conclusion:
Because the 3 segments that are given satisfy the statements of the triangle inequality theorem, they can therefore form a triangle.
Round each of these numbers to the degree of accuracy shown in brackets. d) 34 766 (nearest hundred) please help me
Answer:
34800
Step-by-step explanation:
As, the nearest hundred to 766 is 800.
Select the correct answer.
Which set of coordinates satisfies the system of equations y=x-3 and y=-2x+1?
Y
w
A
N
9
83
B
-1
-2
3
5
C
3
4
O
Answer: [tex]\left(\frac{4}{3}, -\frac{5}{3} \right)[/tex]
Step-by-step explanation:
Setting the equations equal to each other.
[tex]x-3=-2x+1\\\\3x=4\\\\x=\frac{4}{3}\\\\\implies y=\frac{4}{3}-3=-\frac{5}{3}[/tex]
Q2 - Using fractions
Jarvis works in a garage for $7 an hour.
If he works on Saturday he is paid time and a quarter.
If he works on Sunday he is paid time and three quarters.
Last weekend Jarvis worked for four hours on Saturday and four hours on Sunday.
How much was Jarvis paid last weekend altogether?
Total Earned Saturday: $45
Total Earned Sunday: $63
Total: $108
Time and a quarter means that you divide his normal rate by 4 and add that to his normal rate.
9/4 = 2.25 2.25 + 9 = 11.25
Jarvis makes $11.25 an hour on Saturdays.
Since he worked 4 hours, you multiply,
11.25 x 4 = 45.
What is the normal rate?
Time and three quarters mean that you multiply his normal rate by 3/4 and add that to his normal rate
9x0.75 = 6.75 6.75 + 9 = 15.75
Jarvis makes $15.75 an hour on Sundays. Since he worked 4 hours, you multiply 15.75 x 4 = 63.
To get the total, you add his earnings on Saturday and earnings on Sunday
45 + 63 = 108.
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[tex](1/8)^-^3^a=512^3^a[/tex]
The equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution
How to solve the equation?The equation is given as:
[tex](\frac18)^{-3a} = 512^{3a}[/tex]
Express the equation as a base of 2
[tex](2^{-3})^{-3a} = 2^{9*3a}[/tex]
Evaluate the products
[tex]2^{9a} = 2^{27a}[/tex]
Cancel out the common base
9a = 27a
The above equation is not true because [tex]9a \ne 27a[/tex]
Hence, the equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution
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Mixed Practice! Find the value of each variable
I need 16, 17 and 18
Answer:
Step-by-step explanation:
Its about creating and Solving Linear Equations by writing linear equations from geometric figures please help
1. The value of x is 40
m ∠2x + 10 = 90
m ∠3x = 120
m ∠2x +5 = 85
m ∠2x -15 = 65
2. The value of x is 15
m ∠5x = 75
Calculating anglesFrom the question, we are to determine the value of x and the given angles
Since sum of angles is 360°
3x + 2x + 10 + 2x + 5 + 2x -15 = 360°
Collect like terms
3x + 2x + 2x + 2x = 360° - 10° - 5° + 15°
9x = 360
x = 360 / 9
x = 40
∴ x = 40
Then,
m ∠2x + 10 = 2(40) + 10
m ∠2x + 10 = 80 + 10
m ∠2x + 10 = 90
m ∠3x = 3(40)
m ∠3x = 120
m ∠2x +5 = 2(40) + 5
m ∠2x +5 = 80 + 5
m ∠2x +5 = 85
m ∠2x -15 = 2(40) - 15
m ∠2x -15 = 80 - 15
m ∠2x -15 = 65
Hence, the measure of angle 2x-15 is 65
2.
Since sum of angles is 180°
Then,
5x° + x° + 90° = 180°
6x° = 180° - 90°
6x° = 90°
x = 90/6
x = 15
m ∠5x = 5(15)
m ∠5x = 75
Hence, the measure of angle 5x is 75
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
1. 6 km ≈ 3.73 mi
2. 2.5 L ≈ .66 gal
3. 90 lb ≈ 40.82 kg
The surface area of the cone below is about 151.58 inches squared. The radius of the base is 4 inches. What is the slant height? Use 3.14 for Pi. Round your answer to the nearest whole number.
The slant height of the given cone will be 12.06 inches.
What is slant height?The measurement from the base to the peak along the "center" of a lateral face of an object, such as a cone, is its slant height.
Given that:-
The surface area of the cone below is about 151.58 inches squared. The radius of the base is 4 inches.The slant height will be calculated as:-
Surface area = π r l
151.58 = π x 4 x l
l = 151.58 / ( π x 4 )
l = 12.06 inches.
Therefore slant height of the given cone will be 12.06 inches.
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What is (4.81 times 10 Superscript 16 Baseline) (1.1 times 10 Superscript negative 4 Baseline) in scientific notation?
5.291 times 10 Superscript negative 64
5.291 times 10 Superscript negative 4
5.291 times 10 Superscript 12
5.291 times 10 Superscript 20
The scientific notation of the product of the given numbers is [tex]5.291 \times 10^{12}[/tex].
Given, [tex](4.81 \times 10^{16} ) (1.1 \times 10^{-4} )[/tex].
We need to write the scientific notation of the product.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
Now, [tex](4.81 \times 10^{16} ) (1.1 \times 10^{-4} )=4.81 \times 1.1 \times 10^{16} \times10^{-4}[/tex]
[tex]=5.291 \times 10^{16-4} =5.291 \times 10^{12}[/tex]
Hence, the scientific notation of the product of the given numbers is [tex]5.291 \times 10^{12}[/tex].
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Answer:C
Step-by-step explanation:
5.291 times 10 Superscript 12
find y in terms with z. help me please :)
Answer:
y = 5z
Step-by-step explanation:
added in the picture
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow y = 5z [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[ let the point at which line segments SV and RT intersects be O ]
[tex]\qquad \tt \rightarrow \: \angle ROV + \angle ROS = 180° [/tex]
[ linear pair ]
[tex]\qquad \tt \rightarrow \: \angle ROV = 180 - \angle ROS[/tex]
[tex]\qquad \tt \rightarrow \: \angle ROV = 180 -2y[/tex]
____________________________________
[tex]\qquad \tt \rightarrow \: \angle SVU = \angle ROV + \angle TRV[/tex]
[ Exterior angle = sum of opposite interior angles ]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - 2y + y[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y [/tex]
( let it be equation 1 )
____________________________________
[tex]\qquad \tt \rightarrow \: \angle SVU + \angle SUV + \angle VSU = 180°[/tex]
[ Sum of angles of Triangle ]
[tex]\qquad \tt \rightarrow \: \angle SVU + 4z + z = 180°[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU + 5z = 180°[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180° - 5z[/tex]
( let it be equation 2 )
____________________________________
By comparing both equations :
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y = 180 - 5z[/tex]
[tex]\qquad \tt \rightarrow \: 180 - y = 180 - 5z[/tex]
( Add 180° on both sides )
[tex]\qquad \tt \rightarrow \: 180 - y + 180 = 180 - 5z + 180[/tex]
[tex]\qquad \tt \rightarrow \: - y = - 5z[/tex]
[tex]\qquad \tt \rightarrow \: y = 5z[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Write the equation of the line that passes through (5, 6) and (8, 4) in slope-intercept form.
Answer:
Step-by-step explanation:
Equation of the line in slope- intercept form:[tex]\sf \boxed{\bf y = mx +b}[/tex]
Here, m is the slope and b is the y-intercept
Find the slope with the given two points.
[tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{4-6}{8-5}\\\\=\dfrac{-2}{3}[/tex]
Slope = -2/3 and choose any one the given points.
Substitute m = -2/3 and (5,6) in the above equation and find 'b'
[tex]\sf 6 =\dfrac{-2}{3}*5+b\\\\6 =\dfrac{-10}{3}+b\\\\6+\dfrac{10}{3}=b\\\\\dfrac{6*3}{1*3}+\dfrac{10}{3}=b\\\\\dfrac{18}{3}+\dfrac{10}{3}=b\\\\\boxed{b=\dfrac{28}{3}}[/tex]
Equation of the line:
[tex]y = \dfrac{-2}{3}x + \dfrac{28}{3}[/tex]
What is the relationship between \blueD{\angle a}∠astart color #11accd, angle, a, end color #11accd and \greenD{\angle b}∠bstart color #1fab54, angle, b, end color #1fab54?
Answer:
C
Step-by-step explanation:
supplementary because it adds to 180
Answer:C
Step-by-step explanation:
khan
what is the median in this list
3 6 9 7 4 6 7 0 7
i need the median the range and the mode
ANYTHING HELPS
Median: 6
Range: 9
Mode: 7, appeared 3 times
Pls help 25 points!!
diane started a hike with 24 ounces of water in her backpack. what fraction of a gallon of water did she start the hike with? show your work.
Your question was incomplete. Please check below the full content.
There are 8 ounces in 1 cup and 16 cups in 1 gallon.
(a) Diane brought 4.5 gallons of water to a campout. How many ounces of water did she bring? Show your work.
(b) Diane started a hike with 24 ounces of water in her backpack. What fraction of a gallon of water did she start the hike with? Show your work.
a) 576 ounces of water Diane brought.
b) 3/16 of a gallon of water did she start the hike with.
The cost price per ounce is the amount of money needed to buy one ounce of goods.To find cost price per ounce, divide the total of cost of the goods by total number of goods.Given that there are 8 ounces in 1 cup and 16 cups in 1 gallon.
a) Amount of water diana brought for campout = 4.5 gallons Ounce of water she brought = 4.5×16×8
= 576ounces
b) Diane started a hike with 24 ounces of water in her backpack.
The fraction of gallons in 24 ounces is calculated as follows:
The fraction of gallons in 24 ounces = 24 / (8×16)
= 3/16
Hence, a) 576 ounces of water Diane brought.
b) 3/16 of a gallon of water did she start the hike with.
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Add2√3+√5 and√3 -3√5
Answer:
[tex] \sqrt[2]{3} + \sqrt{5} = \sqrt[2]{8} [/tex]
[tex] \sqrt{3 } - \sqrt[3]{5} = \sqrt[3]{2} [/tex]
Anyone knows how to do this please tell me how?
Step-by-step explanation:
0.000672, 6.72×10⁵, 67.2×10‐⁴, 672×10⁴
Scientific notation is a way of writing numbers that looks like the following:
[tex]a\times10^n[/tex]
a is any number between 1 and 10n is any integerFor instance, we can write 2930 in scientific notation.
First, move the decimal so that the number is between 1 and 10:First, write all the given values in scientific notation:
[tex]6.72\times10^5[/tex] ⇒ [tex]6.72\times10^5[/tex][tex]67.2\times 10^{-4}[/tex] ⇒ [tex]6.72\times 10^{-3}[/tex][tex]672\times 10^4[/tex] ⇒ [tex]6.72\times 10^6[/tex][tex]0.000672[/tex] ⇒ [tex]6.72\times10^{-4}[/tex]Now, let's compare the values of n, and organize the numbers from least to greatest:
[tex]6.72\times10^{-4}[/tex]
[tex]6.72\times 10^{-3}[/tex]
[tex]6.72\times10^5[/tex]
[tex]6.72\times 10^6[/tex]
Finally, rewrite all the numbers as their given format:
[tex]0.000672[/tex]
[tex]67.2\times 10^{-4}[/tex]
[tex]6.72\times10^5[/tex]
[tex]672\times 10^4[/tex]
Answer[tex]0.000672[/tex]
[tex]67.2\times 10^{-4}[/tex]
[tex]6.72\times10^5[/tex]
[tex]672\times 10^4[/tex]
