match the 3 equations with an equivalent equation. some of the answers are not used3x+6=4x+73(x+6)=4x+74x+3x=7-6__________________________________Answer choices: 7x=13x-1=4x9x=4x+73x=4x+73x+18=4x+7
We have the following:
[tex]\begin{gathered} 3x+6=4x+7 \\ 3x=4x+7-6 \\ 3x=4x+1 \\ 3x-1=4x \end{gathered}[/tex]Therefore:
3x+6=4x+7 //// = //// 3x-1=4x
[tex]\begin{gathered} 3\mleft(x+6\mright)=4x+7 \\ 3x+18=4x+7 \end{gathered}[/tex]3(x+6)=4x+7 //// = //// 3x+18=4x+7
[tex]\begin{gathered} 4x+3x=7-6 \\ 7x=1 \end{gathered}[/tex]4x+3x=7-6 //// = //// 7x=1
Ta Question
Unit Activity: Polynomials and Factors
Question 1
The gray-banded kingsnake requires an enclosure in which the length is at least 20 inches greater than the width and the
height is 33 inches.
w+20
음) 11 of
√6
Vo 0₁
Aw² + Bw + C
What expression models the volume of this enclosure?
Replace the values of A, B, and C to write the expression.
+
4
X
< > S
33
2
W
It
ap CO
A P PO
sin cos tan sin cos tan
csc sec cot log log, In
0
11
1-4
-
0
ZAN
IN
CO
.
U
888
Answer:
33w² +660w
Step-by-step explanation:
You want the expression for the volume of a cuboid with dimensions in inches of 33, (w+20), and (w).
VolumeThe volume of a cuboid is the product of its dimensions:
V = HLW
V = (33)(w +20)(w) = 33(w² +20w)
V = 33w² +660w . . . . expression for volume
__
Additional comment
Comparing coefficients, you see ...
A = 33B = 660C = 0Which relation is a function?
let's recall the vertical line test, if a vertical line hits the graph or points twice, then is NOT a function. Check the picture below.
A very easy way to find out if a graph is a function is to use the vertical line test.
Look at each graph and mentally draw a vertical line that goes through each of its points.
If that line goes through more than one point (2, 3, 4...) then that graph is not a function.
That's because a function, is an equation for which each input (x value) has exactly one output (y value). There cannot be two points of the same x value, with two different y values.
A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below.
A rectangle labeled, Fenced in Region, is adjacent to a rectangle representing a wall.
A rectangle labeled, Fenced in Region, is adjacent to a rectangle representing a wall.
Three of the sides will require fencing and the fourth wall already exists.
If the farmer has 144 feet of fencing, what are the dimensions of the region with the largest area?
The most appropriate choice for maxima and minima of a function will be given by
Rectangle of length 72 feet and breadth 36 feet has largest area
What is maxima and minima?
Maxima of function f(x) is the maximum value of the function and minima of function f(x) is the minimum value of the function.
Here,
Let the length be x feet and breadth be y feet
The farmer has 144 feet of fencing
Three of the sides will require fencing and the fourth wall already exists.
So,
x + y + y =1 44
x + 2y = 144
Area of rectangle(A) = xy [tex]ft^2[/tex]
= (144 - 2y)y
= [tex]144y - 2y^2[/tex]
[tex]\frac{dA}{dy} = \frac{d}{dy}(144y - 2y^2)[/tex]
= [tex]144 - 2\times 2y^{2-1}\\144 - 4y[/tex]
For largest area,
[tex]\frac{dA}{dy} = 0[/tex]
[tex]144 - 4y = 0 \\4y = 144\\y = \frac{144}{4}\\y = 36[/tex]
[tex]\frac{d^2A}{dy^2} = \frac{d}{dy}(144 - 4y)\\=0-4\\=-4 < 0[/tex]
Hence area is maximum
For largest area, y = 36 feet
[tex]x = 144 - 2\times 36\\x = 144-72\\[/tex]
[tex]x = 72[/tex] feet
So length of rectangle is 72 feet, breadth of rectangle is 36 feet
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a pancakes recipe asks for 3 and 1 half times as much milk as flour. if 4 and two thirds cups of milk is used, what quantity of flour would then be needed, according to the recipe?
A pancakes require 3.5 cups of milk and 1 cup of flour, or a ratio of 3.5:1 or a fraction of
(3.5) / (1)
If you have 4.6 cups of milk you need x cups of flour
Set up a ratio of
[tex]\frac{3.5}{1}=\frac{4.6}{x}[/tex][tex]x=\frac{4.6}{3.5}[/tex][tex]undefined[/tex]
1 The circumference of the circle is approximately feet. (Use 3.14 as an approximation for 7.) A 5 ft. B В
The circumference of the circle is
[tex]\begin{gathered} \text{circumference= 2}\pi\text{r}^2 \\ =2\times3.14\times5^2 \\ =157\text{ fe}etsquare \end{gathered}[/tex]in the figure below, what is the value of x?
Answer:
the value of x is 32 degree
Step-by-step explanation:
100 + 68 +x = 180
168 +x=180
x= 180- 168
x= 32 degree
√3(√6+√15) please simplify, thanks
Answer: [tex]3\sqrt{2}+3\sqrt{5}[/tex]
===================================================
Work Shown:
[tex]\sqrt{3}\left(\sqrt{6}+\sqrt{15}\right)\\\\\sqrt{3}*\sqrt{6}+\sqrt{3}*\sqrt{15}\\\\\sqrt{3*6}+\sqrt{3*15}\\\\\sqrt{18}+\sqrt{3*3*5}\\\\\sqrt{9*2}+\sqrt{9*5}\\\\\sqrt{9}*\sqrt{2}+\sqrt{9}*\sqrt{5}\\\\3\sqrt{2}+3\sqrt{5}\\\\[/tex]
-------------------
Explanation:
I distributed and used the idea that sqrt(A*B) = sqrt(A)*sqrt(B) to combine square roots, but also to break them up when factor out the largest perfect square factor.
Optionally for the last step, you could factor out 3, but your teacher may want you to leave it like shown.
Write an equation for the function graphed below?
Replace the variable in an equation with to write it in function notation. In function notation, the equation would be stated as follows: f (x) = x + 30000, where is the mileage displayed on the odometer.
How can you determine a graph's curve's equation?The values of the parameters m and c, and hence the equation for the curve, can be obtained by taking the coordinates of the two points as (x1,y1) and (x2,y2) and inserting them into the equation y=mx+c. Similarly, by swapping the coordinates, we may determine the equation for any other curve. Students can pick out specific points on the graph and enter them into the equation y = mx+b, where m is the slope, to determine the equation for a non-parabolic, non-quadratic line.To learn more about Function notation refer to:
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Which one is the correct answer I need help on this
Given the function below,
[tex]f(x)=x^3+2x^2-5x-6[/tex]Let us now plot the graph in order to obtain the end behaviours.
From the graph above, we can conclude that
[tex]\mathrm{as}\: x\to\: +\infty\: ,\: f\mleft(x\mright)\to\: +\infty\: ,\: \: \mathrm{and\: as}\: x\to\: -\infty\: ,\: f\mleft(x\mright)\to\: -\infty[/tex]Hence, the correct answer is Option D.
2
80. Air Conditioning The yearly profit p of Arnold's Air Con-
ditioning is given by p = x² + 15x - 100, where x is the
number of air conditioners produced and sold. How many
air conditioners must be produced and sold to have a
yearly profit of $45,000?
205 air conditioners must be produced and sold to have a yearly profit of $45,000.
As per the relation representing p and x, x is the number of air conditioners so p must be the profit. Keep the value of profit to find the value of x.
45000 = x² + 15x - 100
Shifting 100 to Left Hand Side of the equation
45000 + 100 = x² + 15x
Performing addition on Left Hand Side of the equation
45100 = x² + 15x
Rearranging the equation
x² + 15x - 45100 = 0
Factorising the equation to find the value of x
x² + 220x - 205x - 45100 = 0
x(x + 220) -205 (x + 220) = 0
(x - 205) (x + 220) = 0
x = 205, - 220
The number of air conditioners produced and sold can not be negative. So, the value of x and hence the number of air conditioners is 205.
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Graph the inequality on the number line.
3x−10>5
The solution of 3x−10>5 inequality is x>5 and is graphed with the image attached.
what is inequality?
Inequality is a declaration of an exact relation between two numerals or algebra expressions, such as greater at, above to, below than, or lesser than or equal to. Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations.Given inequality,
3x−10>5
3x>5+10
3x>15
x> (15/3)
x>5
The solution of 3x−10>5 inequality is x>5 and is graphed with the image attached.
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Hello, can anyone please help me with my practice? Be very much appreciated
Answer:
The solution to the inequality is;
[tex]x<-81[/tex]Explanation:
Given the inequality;
[tex]-\frac{1}{9}x>9[/tex]Firstly, let's multiply both sides of the equation by 9;
[tex]\begin{gathered} -\frac{1}{9}x\times9>9\times9 \\ -\frac{9}{9}x>81 \\ -x>81 \end{gathered}[/tex]Then we can multiply both sides by -1.
Note that when we multiply both sides by a negative number(-1) the sign will change;
[tex]>\rightarrow<[/tex]So;
[tex]\begin{gathered} -x\times-1>81\times-1 \\ x<-81 \end{gathered}[/tex]The solution to the inequality is;
[tex]x<-81[/tex]A group of tourists visiting a skyscraper boards an elevator headed up from the ground floor. The elevator moves at a speed of 200 meters per minute. At the same time, a second group of tourists boards an adjacent elevator which is on the top floor and is headed down. This one is traveling 250 meters per minute. If the elevators were originally separated by a distance of 450 meters, how long will it take for them to pass each other
Answer: 1 minute
Step-by-step explanation:
First elevator's rate is 200 meters per second
Second's rate is 250
In one second, they would travel 450 meters
Answer:
Step-by-step explanation:
Find the point of intersection of the pair of straight lines.
y = −10x − 3
−y = 11x + 5
(x, y) =
The point of intersection is a point where the value of both functions will be the same thus the point of intersection of the lines y = −10x − 3 and −y = 11x + 5 is at (-2,17).
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given lines,
y = −10x − 3
−y = 11x + 5 → y = -11x - 5
The value of the function at the point of intersection is always the same.
So,
−10x − 3 = -11x - 5
-10x + 11x = -5 + 3
x = -2
So,y = -10(-2) - 3 = 17
Hence "The point of intersection is a point where the value of both functions will be the same thus the point of intersection of the lines y = −10x − 3 and −y = 11x + 5 is at (-2,17)".
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Solve the following system of equations using an augmented matrix and Gauss-Jordan Elimination. Be sure to show your work and explain what you are doing. Then, interpret your answer in terms of the original system.
Okay, here we have this:
Considering the provided equation, we are going to solve the system using an augmented matrix and Gauss-Jordan Elimination. So we obtain the following:
[tex]\begin{gathered} \begin{bmatrix}3x+2y-4z=4 \\ x-3y-10z=8 \\ -5x-4y+12z=-2\end{bmatrix} \\ \begin{bmatrix}\frac{4-2y+4z}{3}-3y-10z=8 \\ -5\cdot\frac{4-2y+4z}{3}-4y+12z=-2\end{bmatrix} \\ \begin{bmatrix}\frac{-11y-26z+4}{3}=8 \\ \frac{-2y+16z-20}{3}=-2\end{bmatrix} \\ \begin{bmatrix}\frac{-2\left(-\frac{26z+20}{11}\right)+16z-20}{3}=-2\end{bmatrix} \\ \begin{bmatrix}\frac{4\left(19z-15\right)}{11}=-2\end{bmatrix} \\ y=-\frac{26\cdot\frac{1}{2}+20}{11} \\ y=-3 \\ x=\frac{4-2\left(-3\right)+4\cdot\frac{1}{2}}{3} \\ x=4 \\ \end{gathered}[/tex]Finally we obtain that the solution to the system is:
[tex]x=4,\: z=\frac{1}{2},\: y=-3[/tex]Find the product
-7÷5 ×4÷5
Answer:
-1.12 or -28?/25 or -1 3/25
Step-by-step explanation:
Mike can be paid in one of two ways based on the amount of merchandise he sells:Plan A: A salary of $850.00 per month, plus a commission of 10% of sales, ORPlan B: A salary of $1,050.00 per month, plus a commission of 14% of sales in excess of $7,000.00.For what amount of monthly sales is plan B better than plan A if we can assume that Mike's sales are always more than $7,000.00Write your answer an an inequality involving x, where a represents the total monthly sales.
We are looking for the point at which the compensation from Plan A is less than the compensation from Plan B.
Plan A = 850 +0.1x
Plan B= 1050+(x-7000)(0.14)
Plan A < Plan B
850 +0.1x <1050+(x-7000)(0.14)
then we sill simplify
850+0.1x < 1050+0.14x-980
850+0.1x<70+0.14x
then we isolate the x
0.1x-0.14x<70-850
-0.04x<-780
x>-780/-0.04
x>19500
In this case the monthly sales x need to be greater than 19500 (x>19500), in order that Plan B were better than plan A.
You deposit $500 into a savings account that is compounded annually. The function g(x) = 500(1.02)x can be used to find the amount of money in the savings account after x years. What is the constant percent rate of change? (2 points)
102%
98%
1.02%
2%
Answer: 2%
Step-by-step explanation:
Exponential growth functions are of the form [tex]P(1+r)^t[/tex], where r is the rate of change. From the equation, we see that r=0.02, and converting this to a percentage, we get 2%.
A pancake stall sells sweet pancakes and savoury pancakes. The savoury pancakes can have three toppings (eggs, ham, tomato) which may be used in any combination. The sweet ones come with orange, lemon or strawberry jam with either ice cream or fresh cream. How many combinations does the stall sell?
The pancakes stall sells total 12 combinations of pancakes.
What is Combination?
Combinations are mathematical operations that count the number of potential permutations for a set of elements when the order of the selection is irrelevant.
According to the given data:
Savory pancakes can have 3 toppings in any combination.
Therefore, total number of savory pancake combinations = 3 x 2 x 1 = 6
For sweet pancakes jams can either have ice cream or fresh cream.
Therefore combinations with ice cream = 3
And combinations with fresh cream = 3
Hence total combinations for sweet pancakes = 3 + 3 = 6
Now, total pancakes combination = 6 + 6 = 12
So, the stall sells 12 combinations of pancakes.
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The sum of the interior angles of a polygon with 10 sides can be expressed as 360n. What is the value of n? O 2 04 O 6 08
The sum of the interior angle of a polygon with 10 sides is equal to 1440°
If it can be expressed as 360n, then n is
[tex]\begin{gathered} 360n=1440 \\ \\ \text{Divide both sides by 360} \\ \frac{360n}{360}=\frac{1440}{360} \\ \frac{\cancel{360}n}{\cancel{360}}=\frac{1440}{360} \\ n=4 \\ \\ \text{Therefore, }n\text{ is equal to }4 \end{gathered}[/tex]P(t) models the number of people on a beach, t hours past midnight on a certain day.What does P(10) = N mean?Group of answer choicesThere were an equal number of people on the beach at 10:00 AM and at N hours past midnight.There were N people on the beach at 10:00 AM.There were 10 people on the beach at N hours past midnight.
Since P(t) models the number of people on a beach, t hours past midnight, hence P(10)=N means that there were N people on the beach at 10 am
F varies jointly as D and E. Determine F when D=3 E =10 and k =7
The equation for F is,
[tex]\begin{gathered} F\propto DE \\ F=kDE \end{gathered}[/tex]Determine the value of F.
[tex]\begin{gathered} F=7\cdot3\cdot10 \\ =210 \end{gathered}[/tex]Thus value of F is 210.
Week 14 (12/7 - 12/11) - Homework Packet 3.13 - 4.1 3.13- Homework (due Tues. 12/8) Part I: Fill in the blank representation for each inequality. Words Algebra Graph 1) ** xis greater than or equal to 7 and xis less than or equal to 9 2) 3 < x or -2> X 3) 0 1 2 4 rah the following inequalities in the
1.
Algebra:
[tex]7\leq x\leq9[/tex]Graph:
2.
Words:
x is greater than 3 or x is less than minus 2
Graph:
3.
Words:
x is greater than minus 1 and x is less than 2.
Algebra:
[tex]-1what is the unit price for 10 stickers for $1.50?
We can find the unit price of a ticket by dividing the number of purchased tickets by the total price, like this:
[tex]\frac{1.5}{10}=0.15[/tex]Then, the unit price of the tickets is $0.15
with a vertex of (-7,-2) and directrix of x=-1, is this a vertical or horizontal parabola?
answer step by step please
Considering a parabolic equation with a vertex of (-7,-2) and directrix of x = -1. This is a horizontal parabola
What is directrix of a parabola?The directrix of a parabola is a straight line perpendicular to the axis of symmetry of the parabola.
The directrix does not touch the parabola
How to determine if a parabola is vertical or horizontal using the directrixA parabolic equation is also called quadratic equation.
Since the directrix is perpendicular to the axis of symmetry of the parabola it means that if:
when the directrix is given at x, the directrix runs in the vertical direction and the parabola is a horizontal parabolawhen the directrix is given at y, the directrix runs in the horizontal direction and the parabola is a vertical parabolaThe axis of symmetry says if the parabola is vertical or horizontal, when the axis of symmetry is parallel:
the y direction the parabola is a vertical parabolathe x direction the parabola is a horizontal parabolaIn the given problem, the directrix is given at x, the axis of symmetry is along the x direction and hence a horizontal parabola
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answers asap
im failing this class
Answer:
y=2/3x+4
Step-by-step explanation:
Need help on this question thanks
The linear regression equation is y = 15430.5034 + 301.2586x .
What is the substitution method?The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. The first stage in the substitution approach is to determine any variable's value in terms of the other variable from one equation. If there are two equations, x + y=7 and x - y=8, for instance, we can deduce from the first equation that x=7-y. The substitution approach is applied in this manner as the first stage. There are three steps in the substitution technique: For each variable, solve a single equation. Solve the other equation by substituting (plugging in) this expression. Find the corresponding variable by substituting the value back into the original equation.
∑x = 56
∑ y = 109453.5
∑ x² = 760
∑ x × y = 1093064.7
Substitute the upper values
6a + 56b = 109453.5
56a + 760b = 1093064.7
Solve the above 2 equations
a = 15430.5034
b = 301.2586
Now substitute the values in y = a + bx
y = 15430.5034 + 301.2586x
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I need Help with this question... the asnwer should not be a decimal... it's about special right triangles.
Below is the figure of the triangle
We have three unkown variables which are x, y, and z
Firstly, let us find the unknown side z
To find z, we will be applying SOH CAH TOA
The longest side is z
The opposite sides is 39
[tex]\begin{gathered} \text{ applying SOH} \\ \text{ Sin }\theta\text{ = }\frac{opposite}{\text{hypotenus}} \\ \sin \text{ 45 = }\frac{39}{z} \\ \text{Introduce cross multiply} \\ z\text{ x sin 45 = 39} \\ \text{Divide both sides by sin 45} \\ \frac{z\cdot\text{ sin45}}{\sin\text{ 45}}\text{ = }\frac{39}{\sin \text{ 45}} \\ z\text{ = }\frac{39}{\sin \text{ 45}} \\ \text{ According to speciaal triangles; sin 45 = }\frac{\sqrt[]{2}}{2} \\ z\text{ = }\frac{39}{\frac{\sqrt[]{2}}{2}} \\ z\text{ = }\frac{39\text{ x 2}}{\sqrt[]{2}} \\ z\text{ = }\frac{78}{\sqrt[]{2}} \\ \text{Rationalize the expression} \\ z\text{ = }\frac{78\text{ x }\sqrt[\square]{2}}{\sqrt[]{2}\text{ x }\sqrt[]{2}} \\ z\text{ = }\frac{78\sqrt[]{2}}{2} \\ z\text{ = 39}\sqrt[]{2} \end{gathered}[/tex]Find x
X can be find by applying the SOH CAH TOA
Let z = opposite
let x = adjacent
[tex]\begin{gathered} \text{ Applying TOA} \\ \text{Tan}\theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \text{opposite = z = 39}\sqrt[]{2} \\ x\text{ = adjacent} \\ \text{Tan 60 = }\frac{39\sqrt[]{2}}{x} \\ \text{Introduce cross multiply} \\ x\cdot\text{ tan 60 = 39}\sqrt[]{2} \\ \text{Divide both sides by tan 60} \\ \frac{x\cdot\text{ tan 60}}{\tan\text{ 60 }}\text{ = }\frac{39\sqrt[]{2}}{\tan\text{ 60}} \\ \text{According to special triangles}\colon\text{ Tan 60 }=\text{ }\sqrt[]{3} \\ x\text{ = }\frac{39\sqrt[]{2}}{\sqrt[]{3}} \\ \text{Rationalize the above surd} \\ x\text{ = }\frac{39\sqrt[]{2}\text{ x }\sqrt[]{3}}{\sqrt[]{3}\text{ x }\sqrt[]{3}} \\ x\text{ = }\frac{39\sqrt[]{6}}{3} \\ x\text{ = 13}\sqrt[]{6} \end{gathered}[/tex]Find y
let y = adjacent
x = Hypotenus
Applying SOH, CAH TOA
[tex]\begin{gathered} \text{ cos }\theta\text{ = }\frac{adjacent}{\text{Hypotenus}} \\ \text{Adjacent = y} \\ \text{Hypotenus = x = 13}\sqrt[]{6} \\ \text{Cos 60 = }\frac{y}{13\sqrt[]{6}} \\ \text{Cross multiply} \\ y\text{ = cos 6}0\text{ x 13}\sqrt[]{6} \\ \text{According to special angles : cos 60 = }\frac{1}{2} \\ y\text{= }\frac{1}{2}\text{ x 13}\sqrt[]{6} \\ y\text{ = }\frac{13\text{ x }\sqrt[]{6}}{2} \\ y\text{= }\frac{13\sqrt[]{6}}{2} \end{gathered}[/tex]Write the statement in "If p, then q" form. We will be in good shape for the ski trip provided we take the aerobics class.
Answer: If we take the aerobics class, then we will be in good shape for the ski trip
===============================================
Explanation:
The conditional statement in bold is of the form "If P, then Q" where
P = we take the aerobics classQ = we will be in good shape for the ski tripP and Q are placeholders for logical statements, in much a similar fashion that x = 2 has x as a placeholder for the number 2.