Complete each equation so that it has infinitely many solutions. 12x - x + 8 + 3x = __x + __ (__ are blanks)
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A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
What are a definition and an example of a linear equation?Linear formula first-degree algebraic equation with the variables y = 4x + 3 or similar (that is, raised only to the first power). Such an equation has a straight line for its graph.
-12-x=8-3x
Add what is to the right of the equal sign to both sides of the equation, then rewrite the equation as follows:-12-x-(8-3*x)=0
Take like variables away:-20 + 2x = 2 • (x - 10)
Solve: 2 = 0There is no answer to this equation.A constant that is not zero can never equal zero.x-10 = 0
On both sides of the equation, add 10:x = 10.
To Learn more about linear equation refer to:
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Related Questions
4. AABC = ADBC by SSS. Select one set of corresponding parts that could be marked congruent by CPCTC.B.A11CDO CBDAO ZA ZDOZCZ ZBO ACBC
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We are given two triangles that are congruent and we are asked to mark the parts that are congruent by CPCTC, this stands for Corresponding Parts of Congruent Triangles are Congruent. This means that when two triangles are congruent then their corresponding sides and angles are also congruent.
We notice that the following segments are corresponding segments and therefore congruent:
[tex]\begin{gathered} AB=BD \\ AC=DC \\ CB=CB \end{gathered}[/tex]And also the following angles are corresponding angles and therefore congruent:
[tex]\begin{gathered} \angle A=\angle D \\ \angle ABC=\angle DBC \\ \angle ACB=\angle DCB \end{gathered}[/tex]Therefore, from CPCTC we know that the corresponding parts are:
[tex]\angle A=\angle D[/tex]an employee at the bank notices an abandoned account with a balance of $360. the bank charges a monthly fee of $8 to maintain an account. the equation for this situation is y = 360 - 8x, where x is the number of months, and y is the balance in dollars. Part A: Find the y-intercept Part B: Find the x-interceptPart C: Interpret the meaning of the x- and y-intercept in terms of the problem.
Answers
Given:
There are given the equation:
[tex]y=360-8x[/tex]Explanation:
(A):
To find the y-intercept, we need to put 0 for x and solve the equation for the value of y.
So,
From the function:
[tex]\begin{gathered} y=360-8(0) \\ y=360 \end{gathered}[/tex]Hence, the y-intercept is shown below:
[tex](0,360)[/tex](B):
To find the x-intercept, we need to put 0 for y and find the values for x:
So,
[tex]\begin{gathered} y=360-8x \\ 0=360-8x \\ 8x=360 \\ x=\frac{360}{8} \\ x=45 \end{gathered}[/tex]Hence, the value x-intercept is shown below:
[tex](45,0)[/tex](C):
The interpret the meaning of the x- and the y-intercept is shown below:
In the given context, the y-intercept, and x-intercept, mean x = 0 and y = 0 and also refers to the starting values.
For a time-based exercise, this will be the value when we started talking we read or when we started tracking the time and its related changes.
inding Total CostsStore AStore BWhat is the cost of the repair and sales tax combinedat Store B?ComputerRepair$1,200$1,350Sales Tax6%7%Gratuity15%15%ShippingFree2% of totalprice
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Store B :
Computer repair : $1,350
Sale tax = 7%
To obtain the sale tax amount, multiply the price by the percentage in decimal form (divided by 100);
$1,350 x (7/100) = 1,350 x 0.07 = $94.5
Add both:
1,350+94.5=$1,444.5
Jackson purchased a pack of game cards that was on sale for 22% off. The sales tax in his county is 6%. Let y represent the oeiginal price of the card.. Wrote an expression that can be used to determine the final cost of the cards.
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Given:
Discount - 22% = 0.22
Sales Tax - 6% = 0.06
Required:
Expression for the final cost of the cards, x
Solution:
Let: y represent the original price of the card.
x represent the final cost of the cards
D represent the discounted cost of the cards
Assume that the the sales tax is applied to the price after the discount.
D= Original Price ( 1 - Discount) = y ( 1 - 0.22) = 0.78y
To compute for the final cost,
Final Cost = D + Tax
Tax = 0.06 D
x = D + 0.6(D)
x = 1.06D
x = 1.06 ( 0.78 y)
x = 0.827y
Answer:
The final cost of the card can be describe by the expression:
x = 0.827y
q(v)= int 0 ^ v^ prime sqrt 4+w^ 5 dw ther; q^ prime (v)=
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ANSWER
[tex]q^{\prime}(v)=\sqrt{4+(v^7)^5}[/tex]EXPLANATION
We want to find the derivative of the given function:
[tex]q(v)=\int_0^{v7}\sqrt{4+w^5}dw[/tex]When the lower limit of an integral is a constant and the upper limit of the integral is a variable, the derivative of this is the function inside the integral in terms of the upper limit of the integral.
In other words, the derivative of the given integral function is:
[tex]q^{\prime}(v)=\sqrt{4+(v^7)^5}[/tex]That is the answer.
Area of a rectangle: A Solve for) Find l when A= 24 ft and u
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The area of the rectangle is 24 ft^2
the width of the rectangle is w = 8 ft
The expression for the area of the rectangle is given as follows.
A = l * w
[tex]\begin{gathered} 24=l\times8 \\ l=\frac{24}{8}=3 \end{gathered}[/tex]The length is l = 3 ft.
[tex]l=\text{ 3 ft}[/tex]In one hour, you can earn 350 points in your favorite video game. You already have 1050 points. a) Write an inequality where y is the total number for points and x is the number of hours. b) Your goal is 2450 points. What is the least number of hours to reach this goal?
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SOLUTION
The initial points is 1050
The points earned per hour is 350
The total point y earned in x hours is:
[tex]y\ge350x+1050[/tex]Substitute y=2450 into the inequality
[tex]2450\ge350x+1050[/tex]Solve for x
[tex]\begin{gathered} 2450-1050\ge350x \\ 1400\ge350x \\ x\le4 \end{gathered}[/tex]Therefore the lease number of hours is 4.
An airplane takes off from an airport that is 144 ft above sea level. The airplane flies at 30,000 ft. To avoid a storm , the airplane goes up to 35,000 ft. Immediately after passing the storm, the airplane returns to its original altitude. Finally , the airplane lands at an airport that is 1,998 ft above sea level . What integer represents the airplanes changes in altitude to avoid the storm ? Immediately after passing the storm ? the integer □ represents the change in altitude to feet to avoid the storm.the integer □ represents the change in altitude in feet immediately after passing the storm.
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What integer represents the airplanes changes in altitude to avoid the storm ?
changes = 35000 - 30000
= 5000 ft
the integer 5000 represents the change in altitude to feet to avoid the storm.
the integer -5000 represents the change in altitude in feet immediately after passing the storm.
Seventh gradeK.2 Write equations for proportional relationships from tables 66UTutorialVer en español1) Over the summer, Oak Grove Science Academy renovates its building. The academy'sprincipal hires Jack to lay new tile in the main hallway.3) There is a proportional relationship between the length (in feet) of hallway Jack coverswith tiles, x, and the number of tiles he needs, y.0)) (feet)y (tiles)3276547631199Write an equation for the relationship between x and y. Simplify any fractions.y =
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Proportional Relationship
Two variables x and y have a proportional relationship it the following equation stands:
y = kx
Where k is the constant of proportionality.
The number of tiles needed by Jack (y) has a proportional relationship with the length in feet of the hallway (x).
The table gives us some values. We'll summarize them as ordered pairs (x,y) as follows:
(3,27) (6,54) (7,63) (11,99)
We can use any of those ordered pairs to find the value of k. For example, (3,27). Substituting into the equation:
27 = k.3
Solving for k:
k= 27/3 = 9
Thus the equation is:
y = 9x
Note: We could have used any other ordered pair and we would have obtained the very same value of k.
Dr Taylor just started an experiment he will collect data for 5 days how many hours is this
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In one day the total number of hours is 24 hours.
So, in 5 days the number of hours is,
[tex]24\times5=120\text{ hours}[/tex]So, the required number of hours is 120 hours.
Imagine you asked students to draw an area model for the expression 5+4x2.
Walking around the room, you see the following three area models.
First, briefly explain the student thinking process you think might be behind each answer.
Answer Describe the thinking process
Which order would you call students A, B and C to present their work to the class and how would you guide the discussion?
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Answer:
area 1
Step-by-step explanation:
To the function attached,Is f(x) continuous at x=1? Please explain
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Recall that a function is continuous at a point if the limit as the variable approaches a value is the same as the value of the function at that point.
Now, notice that, using the definition of the function:
[tex]\begin{gathered} \lim_{x\to1^+}f(x)=\sqrt{1}+2=3, \\ \lim_{x\to1^-}f(x)=3, \end{gathered}[/tex]therefore:
[tex]\lim_{x\to1}f(x)=3.[/tex]Given that the limit and the value of the function at x=1 are equal, the function is continuous at x=1.
Answer: It is continuous at x=1.
What is the value of 32 / (-4)?- 128 8- 828
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The expression given is,
[tex]\frac{32}{(-4)}[/tex]Let us now evaluate the expression
[tex]\frac{32}{(-4)}=\frac{32}{-4}=-8[/tex]Hence, the answer is -8.
What is the value of the x variable in the solution to the following system ofequations? (5 points)4x - 3y = 35x - 4y = 3O x can be any number as there are infinitely many solutions to this systemThere is no x value as there is no solution to this systemO-303
Answers
Step 1:
Write the two systems of equations
4x - 3y = 3
5x - 4y = 3
Step 2:
Use the elimination method to eliminate y.
[tex]\begin{gathered} 4x\text{ - 3y = 3} \\ 5x\text{ - 4y = 3} \\ \text{Use the elimination method to eliminate y} \\ 4x\text{ - 3y = 3 }\times\text{ 4} \\ 5x\text{ - 4y = 3 }\times\text{ 3} \\ 16x\text{ - 12y = 12} \\ 15x\text{ - 12y = 9} \\ 16x\text{ - 15x = 12 - 3} \\ \text{ x = 3} \end{gathered}[/tex]Final answer
x = 3
PLEASE HELP I WILL GIVE BRAINLYEST!! ALGEBRA 1 HW
Answers
start at 4 on the positive y axis, then go up 3 and 5 to the left
y - intercept: ( 0, 4 )
(9 •10^9)•(2•10)^-3)
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First, let's distribute the exponent -3 for 2 and ten, like this:
[tex]\begin{gathered} 9\times10^9\times(2\times10)^{-3}^{} \\ 9\times10^9\times2^{-3}\times10^{-3} \end{gathered}[/tex]Now, we can apply the next property when we have a number raised to a negative power:
[tex]a^{-b}=\frac{1}{a^b}[/tex]Then:
[tex]\begin{gathered} 9\times10^9\times2^{-3}\times\frac{1}{10^3} \\ 9\times2^{-3}\times\frac{10^9}{10^3} \end{gathered}[/tex]And when we have a division of the same number raised to different powers we can apply:
[tex]\frac{a^b}{a^c}=a^{b-c}[/tex]then:
[tex]\begin{gathered} 9\times2^{-3}\times\frac{10^9}{10^3} \\ 9\times2^{-3}\times10^{9-3} \\ 9\times2^{-3}\times10^6 \\ 9\times\frac{1}{2^3}^{}\times10^6 \end{gathered}[/tex]Now, as we know, having 10 raised to 6 means that we are multiplying ten by ten 6 times, when we do this we get:
[tex]10\times10\times10\times10\times10\times10=1000000[/tex]And with 2 raised to three we get:
[tex]2\times2\times2=8[/tex]Then we have:
[tex]\begin{gathered} 9\times\frac{1}{8^{}}^{}\times1000000 \\ \frac{9\times1000000}{8^{}}^{} \\ \frac{9000000}{8^{}}^{} \\ \frac{4500000}{4}^{}=11250000 \end{gathered}[/tex]The population of a school of fish decreases at a rate of 18% per month. There are currently500 fish in the school. How many fish will there be in 3 months?
Answers
Population decreasing rate is
18% monthly
Actual population = 500
Then
In 1 month decreases (500/100)• 18 = 90
Population = 500-90= 410
No find (410/100)•18 = 73.8
410-73.8= 336.2
In 3 months
(336.2/100) •18 = 60.5
336.2 - 60.5 = 276 fishes
ANSWER IS 276 fishes remain
What are the coordinates of A B C after a Dilation with a scale factor of 1/2 followed by a reflection over the x-axis
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In general, a dilation is the outcome of applying the following transformation on a point,
[tex]D(x,y)\to(kx,ky)[/tex]Where k is the scale factor, this kind of dilation is about the origin, and we will use it since the problem does not specify otherwise.
In our case, the transformation is
[tex]D(x,y)\to(\frac{x}{2},\frac{y}{2})[/tex]Then,
[tex]\begin{gathered} D(A)=D(-6,5)\to(-3,\frac{5}{2}) \\ D(B)=D(3,2)\to(\frac{3}{2},1)_{} \\ D(C)=D(0,-1)\to(0,-\frac{1}{2}) \end{gathered}[/tex]On the other hand, a reflection over the x-axis is given by the following transformation.
[tex](x,y)\to R_x(x,y)=(x,-y)[/tex]Then, in our case,
[tex]\begin{gathered} A^{\prime}=R_x(-3,\frac{5}{2})=(-3,-\frac{5}{2}) \\ B´=R_x(\frac{3}{2},1)=(\frac{3}{2},-1) \\ C^{\prime}=R_x(0,-\frac{1}{2})=(0,\frac{1}{2}) \end{gathered}[/tex]Thus, the answers are
A'=(-3,-5/2)
B'=(3/2,-1)
C'=(0,1/2)
In the circle below, if AB is a diameter, find the measure of arc AB.
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A circle has 360°
since the diameter cuts in half the circle
The measure of the arc of half the circle (semicircle) measure arcAB is
[tex]AB=\frac{360}{2}[/tex][tex]AB=180[/tex]AB=180°
Then correct answer is
option a
Mary is x years old. How old will she be in 10 years? How old was she 2 years ago?
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We know that Mary is x years old.
The age in 10 years will be x plus 10, as follows:
[tex]M_{\text{age}+10}=x+10[/tex]And the age she had two years ago was:
[tex]M_{\text{age}-2}=x-2[/tex]An example of this could be: imagine that Mary is 10 years now. In ten years, she will have:
10 + 10 = 20 years ( we add 10 to the original number). Likewise, 2 years ago, she had 10-2 = 8 years.
Therefore, the answers are two equations:
[tex]M_{age+10}=x+10[/tex][tex]M_{\text{age}-2}=x-2[/tex]Write all the possible integer values of x.
x > 1 and x ≤ 6
Separate answers with commas.
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Step-by-step explanation:
college level ? what teacher puts such a question in on college level ? and you can't answer this ?
that is middle school basics.
what is going on ?
x can have in the defined interval the integer values
2, 3, 4, 5, 6
there, that was all to it ...
Put the equation y = x2 - 10x + 16 into the form y = =(x - h)² + ki Answer: y = > Next Question
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To complete the perfect square ((x-h)²) we add and subtract constants:
[tex]\begin{gathered} y=x^{2}-10x+16 \\ y=x^{2}-10x+25-25+16 \\ y=x^{2}-10x+5^{2}-9 \\ y=(x-5)^{2}-9 \end{gathered}[/tex]parallelogram pqrs has diagonals PR in SQ that intersect at T given s p equals 2 a + 5 + r q equals 5 a - 1 St equals 3 b - 3 + SQ equals 7 b - 9 what are the values of RQ and TQ
Answers
SP = 2a+5
RQ= 5a-1
ST = 3b-3
SQ = 7b-9
RQ=?
TQ=?
SP = RQ
2a+5 = 5a-1
Solve for a
5+1 = 5a-2a
6 = 3a
6/3 = a
2=a
RQ= 5a-1 = 5(2)-1 = 10-1 = 9
RQ= 9
ST + TQ = SQ
ST= TQ
TQ= 3b-3
3b-3+3b-3= 7b-9
Solve for b
6b-6 = 7b-9
-6+9 = 7b-6b
3=b
TQ = 3b-3= 3(3)-3= 9-3 =6
TQ= 6
Write a word problem to fit the following rates: 72 tokens/12 games, ◾️ tokens/10 games
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We have to write a word problem using,
• 72 tokens/12 games
,• tokens/10 games
We can first give an information related to 72 tokens PER 12 games.
Then we can ask "how many tokens" per 10 games.
Let us devise a word problem.
The local game center sells tokens to play online games. Jeremy used 72 token to play 12 online games. At this rate, how many token would Jeremy use to play 10 online games?
The above problem uses both the information provided.
The world's largest swimming pool is the Orthalieb pool in Casablanca, Morocco the length is 30 m longer then 6 times the width. If the perimeter of the pool is 1110 Meters what are the dimensions of the pool?
Answers
The length of the rectangular pool is 30m longer than 6 times the width.
Let "x" represent the length of the width, then you can express the dimensions of the pool as follows:
[tex]\begin{gathered} w=x \\ l=6x+30 \end{gathered}[/tex]The perimeter of the pool is 1110m, this perimeter was obtained using the formula:
[tex]P=2w+2l[/tex]Replace the formula with the expressions determined for the width and length:
[tex]1110=2(x)+2(6x+30)[/tex]From this expression, you can determine the value of x:
-First, distribute the multiplications on the right side of the equation:
[tex]\begin{gathered} 1110=2x+2\cdot6x+2\cdot30 \\ 1110=2x+12x+60 \\ 1110=14x+60 \end{gathered}[/tex]-Second, pass 60 to the left side of the equal sign by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 1110-60=14x+60-60 \\ 1050=14x \end{gathered}[/tex]-Third, divide both sides of the equation by 14 to determine the value of x:
[tex]\begin{gathered} \frac{1050}{14}=\frac{14x}{14} \\ 75=x \end{gathered}[/tex]The width of the pool is w= 75 meters
Now you can determine the length of the pool:
[tex]\begin{gathered} l=6x+30 \\ l=6\cdot75+30 \\ l=480 \end{gathered}[/tex]The length of the pool is l=480 meters
Conver 10 feet per second to inches per second
Answers
Answer:120 inches per second
Step-by-step explanation:120 inches per second this is because 1 ft= 12 inches so you can multiply 10 x 12 which is 120 inches.
i have test tomorrow i will love you to help me with thisClassify the following as a monomial, binomial, trinomial, or polynomial andstate the degree.a) 7^5b) 5^7 + 7^2c) 7^3 + 11^2 − 13 + 112d) + 2 + 3^2e) 11^3 − 7^3
Answers
Answer:
a) degree 5; monomial
b) degree 7; polynomial
c) degree 3; polynomial
d) degree 2; polynomial
e) degree 3 polynomial
Explanation.
A polynomial is a mathematical expression containing coefficients and variables.
An example of a polynomial is 42x^5 + 23 x^3 - 2x.
A monomial is a polynomial that contains only one term. For example, x^4, 34x^5, 2x, etc.
Having that in mind, we go through the expressions and place them in one of either category.
a) 7^5
This contains only one term, meaning it is monomial; its highest exponent is 5, meaning it is of degree 5.
b) 5^7 + 7^2
This contains two terms, meaning it is a polynomial; its highest exponent is 7, meaning its degree is 7.
c) 7^3 + 11^2 − 13 + 112
This expression contains four terms - it is a polynomial; its highest exponent is 3, meaning its degree is 3.
d) + 2 + 3^2
This contains three terms, meaning it is a polynomial; its highest exponent is 2, meaning its degree is 2.
e) 11^3 − 7^3
This contains 2 terms, meaning it is a polynomial; its highest exponent is 3, meaning it is of degree 2.
Which of the following is the explicit formula for a compound interestgeometric sequence?
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INFORMATION:
We have the following options
And we must select the one that represents the explicit formula for a compound interest geometric sequence
STEP BY STEP EXPLANATION:
To select the correct one, we need to know that:
[tex]P_n=P_1(1+i)^{(n-1)}[/tex]Finally, the correct one would be option A
ANSWER:
[tex]A.\text{ }P_n=P_1\cdot(1+i)^{n-1}[/tex]Put the following equation of a line into slope-intercept form, simplifying all fractions.
4x-3y=9
Answers
Answer:
y=4/3x+3
Step-by-step explanation:
we know that slope intercept form is y=mx+b, where m is the slope and b is the y intercept
for 4x-3y=9, we have to isolate y
we subtract 4x to both sides to get
-3y=-4x+9
to get y alone, we divide both sides by -3
y=4/3x+3
Answer:
Y=4/3x-3
Step-by-step explanation:
Y=4/3x-3
the other guy had the right idea but the two negatives make a positive!
Cameron can run 3.6 miles for every 4 miles Juliette runs. If Juliette ran 7.6 miles, how far will Cameron run? 6.84 miles68.4 miles6 miles68 miles
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lets set up a proportion here
cameroon runs 3.6 miles for every 4 miles Juliette runs
3.6 miles(C).................................................... 4 miles (J)
? miles(C)...........................................................7.6 miles (J)
cameron will run= (7.6*3.6)/4=6.84 miles
Cameron will run 6.84 miles
