Answer:
What does the multiplication property of equality allow us to do while solving equations?
C. The multiplication property of equality allows us to multiply both sides of the equation by the same value to maintain equivalent equations.
~batmans wife dun dun dun...
The multiplication property of equality in Mathematics allows us to multiply both sides of an equation by the same value without affecting the equality. This property is useful for simplifying equations and finding unknown variables.
Explanation:The multiplication property of equality is a crucial concept in solving equations. It states that if you have an equation, you can multiply the same quantity to both sides of the equation without affecting the equality. Essentially, what it says is captured in option C: The multiplication property of equality allows us to multiply both sides of the equation by the same value to maintain equivalent equations.
For example, if we have an equation 2x = 8, we can apply the multiplication property of equality by multiplying both sides of the equation by 1/2 (the reciprocal of 2) to find the value of x, without changing the balance of the equation. So, 2x * 1/2 equals 8 * 1/2, simplified gives us x = 4. This helps in simplifying complex equations and reaching the solution.
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Find the slope of the tangent line to the graph of f at the given point. f(x) = x√ at (36,6) 1/3 1/12 3 12
slope = [tex]\frac{1}{12}[/tex]
the slope is the value of f' (36)
f(x) = √x = [tex]x^{\frac{1}{2} }[/tex]
f'(x) = [tex]\frac{1}{2}[/tex] [tex]x^{-\frac{1}{2} }[/tex] = [tex]\frac{1}{2\sqrt{x} }[/tex]
f'(36) = [tex]\frac{1}{2(6)}[/tex] = [tex]\frac{1}{12}[/tex]
Answer:
[tex]slope = \frac{1}{12}[/tex]
Step-by-step explanation:
Here is another method to solve your problem. I am showing this method because this is the first method normally taught and a student might not of had the chance yet to learn the other methods
We can solve this problem by using limits and the following function
[tex]\lim_{h\to 0} \frac{f(x+h) - x}{h}[/tex]
[tex]\lim_{h\to 0} \frac{\sqrt{x+h} - \sqrt{x}}{h}[/tex]
Next multiply by the conjugate of the numerator.
[tex]\lim_{h\to 0} \frac{\sqrt{x+h} - \sqrt{x}}{h} * \frac{\sqrt{x+h} + \sqrt{x}}{\sqrt{x+h} + \sqrt{x}}[/tex]
[tex]\lim_{h\to 0} \frac{x + h - x}{h(\sqrt{x+h} + \sqrt{x})}[/tex]
Cancel the x - x
[tex]\lim_{h\to 0} \frac{h}{h(\sqrt{x+h} + \sqrt{x})}[/tex]
Divide out the h
[tex]\lim_{h\to 0} \frac{h}{h(\sqrt{x+h} + \sqrt{x})}[/tex]
[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x+h} + \sqrt{x})}[/tex]
Plugin 0 where h is located
[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x+h} + \sqrt{x})}[/tex]
[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x+0} + \sqrt{x})}[/tex]
[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x} + \sqrt{x})}[/tex]
Combine Like terms in denominator
[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x} + \sqrt{x})}[/tex]
[tex]\lim_{h\to 0} \frac{1}{2\sqrt{x}}[/tex]
Now lets use our derivative and plugin 36 where x is located and solve
[tex]\frac{1}{2\sqrt{x}}[/tex]
[tex]\frac{1}{2\sqrt{36}}[/tex]
[tex]\frac{1}{2(6)}[/tex]
[tex]\frac{1}{12}[/tex]
Note, this is a harder method but it is normally the first method taught in Calculus 1.
If s = 1/4 unit and A = 80s^2, what is the value of A, in square units? ____ square unit(s). (Input whole number only.)
If s = 1/4 unit and A = 80s^2
A = 80 (1/4)^2
A = 80 (1/16)
A = 5
Answer
5 square units
5 square units
substitute s = [tex]\frac{1}{4}[/tex] into the equation
A= 80 × ([tex]\frac{1}{4}[/tex])² = 80 × [tex]\frac{1}{16}[/tex] = [tex]\frac{80}{16}[/tex]= 5 square units
How do you graph these?
Answer:
See the attached.
Step-by-step explanation:
A graph of f' is a graph of the slope of the function. Your function f(x) is piecewise linear, so different sections of its graph have different constant values of slope.
In the intervals (-5, -2) and (0, 2), the slope is -1. (The graph has a "rise" of -1 for each "run" of 1.) So, in those intervals, the graph of f' looks like a graph of y=-1.
In the interval (-2, 0), the rise is 2 for a run of 2, so the slope is 2/2 = 1. The graph of f' in that interval will look like a graph of y=1.
In the interval (2, 5), the rise of f(x) is 1 for a run of 3, so the slope in that interval is 1/3. There, the graph of f' will look like a graph of y=1/3.
If you want to get technical about it, the slope is undefined at x=-2, x=0, and x=2. Therefore, the line segments that make up the graph of f' ought to have open circles at those points, indicating that f' is not defined.
im quite confused, please help :((
You need to pick from each column depending on what makes sense - they are mixed (some numbers are roots, some cubes, in the same column).
On the order:
3 - 27
4 - 64
5 - 125
512 - 8
8 - 2
729 - 9
216 - 6
1 - 1
Answer:
as>JDKFas;lkdjfsa;lkdfjas;kldfjlakdjfalsdkfjakdkdkdlddd
Step-by-step explanation:
Find the quotient of 6/8 ÷ 3/-4
Step-by-step explanation:
6/8 / 3/4 = 1
Please solve this and show work.
Angles DCE and ACB are vertical angles, hence equal. Both have the value 3x.
Angles ACH and HCB (x) add to give ange ACB, so they sum to 3x. That makes ACH have the value 2x. (2x +x = 3x)
The angles in triangle ACH add to 180°. This sum is ...
... 2x +2x +100° = 180°
... 4x = 80° . . . . . . . . subtract 100°, then divide by 4 to get ...
... x = 20°
Find the value of z such that 0.9544 of the area lies between −z and z. Round your answer to two decimal places.
Hello...
Z = total area (1)
___-z___0.9544___z
z = 0.0288
Normal,
z = 2
The value of z is 2. the probability that is closest to 0.0228, where the outliner is a -2 and z equals 2.
How to find the value of z?The decimal numeral system is widely used to express both integer and non-integer numbers. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
A number that has been divided into a whole and a fraction is called a decimal. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.
The word decimus, which means tenth in Latin, is derived from the base word decem, or 10. As a result, the decimal system, often known as a base-10 system, has 10 as its fundamental unit. A number expressed using the decimal method is also referred to as being "decimal."
Given ,
0.9544/2= 0.4772
.5- 0 .4772=0.0228
the probability that is closest to 0.0228, where the outliner is a -2 and z equals 2.
Therefore value of z is 2.
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Graph f(x)=−23x−3 .
Lol plx i need help
Answer:
Points (0,-3) and (-3,-1) work, I got a 100% on the test.
solve the equation. 2m/3-1=3/4+m (please show work)
Solve the quadratic equation. Show all of your steps.
x^2 + 3x - 5 = 0
The roots of equation are: x= -3+ √29/2 and x= -3-√29/2.
What is Quadratic Equation?Quadratic equation's roots The roots of a quadratic equation are the values of the variables that fulfil the equation. In other words, if f(a) = 0, then x = a is a root of the quadratic equation f(x). The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.
given:
x² + 3x - 5 = 0
So, solving for x
x² + 3x - 5 = 0
D= (3)² - 4(1)(-5)= 9 + 20= 29
Now, using the quadratic equation
x= -b ± √ b² -4ac/ 2a
x= -3 ±√(3)² -4(1)(-5) / 2
x= -3±√29/2
x= -3+ √29/2 and x= -3-√29/2
Hence, the roots of equation are: x= -3+ √29/2 and x= -3-√29/2.
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Solve the inequality. 7x − 9 > 2x + 6
We can treat inequalities like standard algebraic equations.
7x - 9 > 2x + 6
Add 9 to both sides.
7x > 2x + 15
Subtract 2x from both sides.
5x > 15
Divide both sides by 5.
x > 3
Answer:
x>3 is the answer
Step-by-step explanation:
We are given one inequality
7x-9>2x+6
To solve this we can do additions and subtraction as we do for equations.
Only for multiplication if negative number is used inequality changes
So let us add 9 to both the sides
7x>2x+6+9
Now subtract 2x from both the sides
7x-2x >15
5x>15
We divide by a positive number 5 without disturbing inequality sign.
X>3 is the answer
In interval notation we can write this as open interval
(3,∞)
In number line this is the region to the right of 3, not includig 3
write a point-slope equation for the line that passes through the point (6,8) and is parallel to the line given by y=-5x+4
Answer:
y -8 = -5(x -6)
Step-by-step explanation:
The point-slope form of the equation for a line is generally written ...
y -k = m(x -h)
for slope m and point (h, k).
The slope of your parallel line is the same as the slope of the reference line, -5. So your equation is ...
y -8 = -5(x -6)
How would you solve 3x=18
Hi!
[tex]3x=18[/tex]
[tex]\frac{3x}{3}=\frac{18}{3}[/tex]
[tex]x=6[/tex]
Explanation: This question is super easy on this question. First you had to divide by 3 from both sides. And simplify, it gave us the answer is x=6 is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. And have a great day. -Charlie
if a class skip counted by 100's. how many counted to get to 2, 000
Divide 100 from 2000
2000/100 = 20
20 counted to get to 2000 by skip counting by 100
hope this helps
Is it possible to find an edge length that would be perfect for a cube with a volume of 30 cubic units? Explain!
Yes ,
side ×side×side= side^3 =volume of cube
=>side^3=30
=>side = 30^1/3-answer
Jordan and Sharla are saving money to go on a study abroad trip. They must provide a down payment of $650 to sign up for the trip, and they can pay the remaining balance later. Jordan raises money by mowing lawns in his neighborhood and charges $25 per lawn. Sharla raises money by selling handmade necklaces for $15 each. Sharla raises less money than Jordan does because Sharla 3. only has enough materials to make 40 necklaces. (A) write two constraints to model the problem. Let x respresent the number of lawns Jordan mows and y represent the number of necklaces Sharla sells. (B) can sharla afford the down payment with the money she earns selling her necklaces? Explain your answer . PLEASE HELP ITS DUE TODAY AND I DON’T UNDERSTAND!!!
Amount of down payment = $650.
Jordan gets money by mowing lawns = $25 per lawn.
Sharla gets money by selling handmade necklaces for = $15 each necklace.
The number of lawns Jordan mows = x.
The number of necklaces Sharla sells = y.
A) Total money raised by Jordan to move x lawns at the rate $25 per lawn = 25x.
Total money raised by Sharla by selling y handmade necklaces for $15 per necklace = 15y.
Total money Sharla can raise by selling 40 necklaces at the rate $15 each = 40 × 15 = $600.
B) Because Sharla can raise maximum $600, therefore sharla can not afford the down payment with the money she earns selling her necklaces.If f(x) = -4x^2 - 6x - 1 and g(x) = -x^2 - 5x + 3, find (f + g)(x).
B
note that (f + g)(x) = f(x) + g(x)
f(x) + g(x) = -4x² - 6x - 1 - x² - 5x + 3 ( collect like terms )
= - 5x² - 11x + 2
Answer:
The correct option is B.
Step-by-step explanation:
The given functions are
[tex]f(x)=-4x^2-6x-1[/tex]
[tex]g(x)=-x^2-5x+3[/tex]
Using the p addition property of functions (f + g)(x) can be written as
[tex](f+g)(x)=f(x)+g(x)[/tex]
Substitute the values of each function in the above equation.
[tex](f+g)(x)=-4x^2-6x-1-x^2-5x+3[/tex]
Combine like terms.
[tex](f+g)(x)=(-4x^2-x^2)+(-6x-5x)+(-1+2)[/tex]
[tex](f+g)(x)=-5x^2-11x+2[/tex]
Therefore the correct option is B.
How do u Graph Y<-1/4x-1
When you replace the comparison symbol (<) with an equal sign (=), you get the equation of a line in slope-intercept form:
... y = mx + b
where m is the slope, and b is the y-intercept.
Your equation has m = -1/4 and b = -1. To graph this line, find the point (0, -1) on the y-axis. To find another point on the line, you can use the slope value (rise/run = -1/4), which tells you the line "rises" -1 for each "run" of +4. That is, another point on the line will be 4 units to the right and 1 unit down, at (4, -2). Working in the other direction (to the left, instead of to the right), the -1/4 slope tells you the point 4 units left and 1 unit up (-4, 0) will also be on the line. Draw a dashed line through these points,
The dashed line you just drew is the boundary of the solution region. It is dashed because the line itself is not part of the solution. (Those points do not meet the requirement for "less than.")
Appropriate values of y are ones that are less than those on the line, so the solution region is indicated as being the half-plane below the line. You indicate this by shading the solution region. (See the attachment for an example of the way this can be graphed.)
_____
If the comparison is ≤ instead of <, then the line is solid (not dashed), indicating it is part of the solution region. If the comparison is > or ≥, then the shaded region is above the line, where y-values are greater than those on the line.
A parking meter in downtown Seattle takes dollar coins and quarters only. When the machine was last emptied, there were 250 coins in it, with a total value of $137.50. Which of the following systems of equations gives the number of quarters, q, and the number of dollar coins, d ? A. d + q = 250 and 100d + 25q = 137.50 B. d + q = 250 and 0.1d + 0.25q = 137.50 C. d + q = 250 and d + 0.25q = 137.50 D. d + q = 137.50 and d + 0.25q = 250 E. d + q = 137.50 and 100d + 25q = 250 Question 2 of 3 For two consecutive integers, the result of adding double the smaller integer and triple the larger integer is 153. What are the two integers? F. 29, 30 G. 30, 31 H. 49, 50 J. 50, 51 K. 76, 77 Question 3 of 3 In a certain triangle, the longest side is twice as long as the shortest side, and the shortest side is 4 inches shorter than the middle side. If the perimeter of the triangle is 52 inches, how long is the longest side? A. 10 inches B. 12 inches C. 16 inches D. 20 inches E. 24 inc
(1)
C
d + q = 250 ( total number of coins ) and
d + 0.25q = 137.50 ( total value of coins )
(2)
G
consecutive integers have a difference of 1 between them
let the integers be n and n + 1 then
2n + 3(n + 1) = 153 (distribute and simplify )
2n + 3n + 3 = 153
5n + 3 = 153 ( subtract 3 from both sides )
5n = 150 ( divide both sides by 5 )
n = 30 and n + 1 = 31
the 2 consecutive integers are 30 and 31
(3)
E
let x be the shortest side then longest side = 2x and middle side = x + 4
2x + x + 4 + x = 52
4x + 4 = 52 ( subtract 4 from both sides )
4x = 48 ( divide both sides by 4 )
x = 12
the longest side = 2x = 2 × 12 = 24
The system of equations for a parking meter are -
d + q = 250
100d + 25q = 137.50
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a a parking meter in downtown Seattle takes dollar coins and quarters only.
Assume that there are [d] dollar coins and [q] quarter coins. Then, we can write the system of equations as -
d + q = 250
100d + 25q = 137.50
Therefore, the system of equations for a parking meter are -
d + q = 250
100d + 25q = 137.50
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I need to prove that A’B’= A’D’ but i keep going in circles.
You have the figure in the picture, the hypothesis are:
AA’= (1/2)AB
BB’=(1/2)BC
CC’=(1/2)CD
DD’=(1/2)DA
These are all vectors!
It can't be proven because it isn't so.
You can show that A'B' = C'D' because each is half of AC (from the midsegment theorem).
Solve the following equation. Then place the correct number in the box provided. 2x < 6
Answer:
x can take any value less than 3.
Step-by-step explanation:
This is an inequality.
[tex]2x < 6[/tex]
Lets solve the inequality for x
[tex]x < 3[/tex]
This means x can take any value less than 3.
We can show this by using a number line.
Notice how number 3 is not fully shaded, this means x cannot be 3. And all the numbers less than 3 to infinity is shaded, meaning x can take any value in that range.
A quadrilateral has vertices at A (-5, 5), B (1, 8), C (4, 2), and D (-2, -2). Use slope to determine if the quadrilateral is a rectangle. Show your work. (Try to use point slope form)
Answer:
not a rectangle
Step-by-step explanation:
There are several ways to determine whether the quadrilateral is a rectangle. Computing slope is one of the more time-consuming. We can already learn that the figure is not a rectangle by seeing if the midpoint of AC is the same as that of BD. (It is not.) A+C = (-5+4, 5+2) = (-1, 7). B+D = (1-2, 8-2) = (-1, 6). (A+C)/2 ≠ (B+D)/2, so the midpoints of the diagonals are different points.
___
The slope of AB is ∆y/∆x, where the ∆y is the change in y-coordinates, and ∆x is the change in x-coordinates.
... AB slope = (8-5)/(1-(-5)) = 3/6 = 1/2
The slope of AD is computed in similar fashion.
... AD slope = (-2-5)/(-2-(-5)) = -7/3
The product of these slopes is (1/2)(-7/3) = -7/6 ≠ -1. Since the product is not -1, the segments AB and AD are not perpendicular to each other. Adjacent sides of a rectangle are perpendicular, so this figure is not a rectangle.
___
Our preliminary work with the diagonals showed us the figure was not a parallelogram (hence not a rectangle). For our slope calculation, we "magically" chose two sides that were not perpendicular. In fact, this choice was by "trial and error". Side BC is perpendicular to AB, so we needed to choose a different side to find one that wasn't. A graph of the points is informative, but we didn't start with that.
We are given with width 20 cm length = 28 cm volume = 1848 cm3 We are asked how deep is the cake batter.
depth = 3.3 cm
the volume (V ) of a cuboid is
V = Ah ( A is the area and h the depth )
A = 20 × 28 = 560 cm², thus
h = [tex]\frac{V}{A}[/tex] = [tex]\frac{1843}{560}[/tex] ≈ 3.3 cm
what is the midpoint of line segment EF
E is located at (-2,-4)
F is located at (2,2)
To find the midpoint, add the 2 X values together and divide by two, then do the same with the y values:
X = -2 + 2 = 0/2 = 0
Y = -4 + 2 = -2/2 = -1
The midpoint is located at (0,-1)
determine whether each number is real or not real and rational or irrational. you must be able to support your answer with a rule.
All the numbers shown are real.
The answers to problems 4, 7, 11 are irrational, because they are square roots of numbers that are not perfect squares.
The remaining numbers are rational because they are terminating decimals or the square root of a square number.
On spring break, Mirna went to Florida. She collected 6 seashells. The following set of data shows the weight of each seashell in ounces. 16, 17, 13, 12, 18, 20 What is the mode of this set of data?
The set of seashell weights that Mirna collected (12, 13, 16, 17, 18, 20) does not have a mode because all values appear only once.
The mode of a set of data refers to the number that appears most frequently. In the case of the weights of the seashells Mirna collected in Florida, the data set is: 12, 13, 16, 17, 18, 20. To find the mode, we look for the value that occurs the most:
12 ounces - occurs once13 ounces - occurs once16 ounces - occurs once17 ounces - occurs once18 ounces - occurs once20 ounces - occurs onceSince all numbers occur only once, there is no number that appears more frequently than the others. Therefore, this set of data does not have a mode.
Graph −7y+8=21x−6 . Use the line tool and select two points on the line.
The two points on the graph of the function - 7y + 8 = 21x - 6 are;
⇒ (0, 2) and (2, -4)
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
The function is,
⇒ - 7y + 8 = 21x - 6
Now,
We can draw the graph of the function - 7y + 8 = 21x - 6 as shown in figure.
And, The points on the graph are;
⇒ (0, 2) and (2, -4)
Thus, The two points on the graph of the function - 7y + 8 = 21x - 6 are;
⇒ (0, 2) and (2, -4)
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Wich product is equivalent to 25x2 -16
25x²-16 is the difference of two squares, so can be written as the product ...
... (5x -4)(5x +4)
or
... (5x +4)(5x -4)
Answer:
[tex](5x+4)(5x-4)[/tex]
Step-by-step explanation:
25x^2- 16
To find out the product that is equivalent to the given expression we need to factor the given expression
we write the numbers in square form
25 = 5*5 = 5^2
16 = 4*4 = 4^2
5^2x^2 - 4^2
[tex](5x)^2- 4^2[/tex]
we apply difference in square formula
a^2 - b^2 = (a+b)(a-b)
[tex](5x)^2- 4^2=(5x+4)(5x-4)[/tex]
Jack is using a ladder to hang lights up in his house.he places the ladder 5 feet from the base of his house and leans it so it reaches a window 14 feet above the ground
The angle of elevation of the ladder is approximately 70.35°
How do we find the angle of elevation?
To find the angle of elevation of the ladder, we can use trigonometric functions.
The angle of elevation can be found using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.
opposite side is the height from the ground to the window = 14 feet,
adjacent side is the distance from the house to the base of the ladder= 5 feet.
tan(θ) = opposite/adjacent
tan(θ) = 14/5
θ = arctan(14/5)
θ = 70.35 degrees
Full question
Jack is using a ladder to hang lights up on his house. He places the ladder 5 feet from the base of his house and leans It so it reaches a window 14 feet above the ground. Find the angle of elevation of the ladder.
A) 65.5
B) 68.4
C) 70.3
D) 71.5
E) 72.9
For what value(s) of k will the relation not be a function?
A = {(3k−4, 16), (4k, 32)}
We won't have a function if for same value of x in (x,y) we get different values y.
So first step: figure out k so that the first coordinate (x) is the same:
3k-4=4k | solve for k
k = -4
no check the values y for the elements of the relation
x = 3k-4 = -12-4=-16
so at -16 we get (-16,16) and (-16, 32), which mean for k=-4 the relation is not a function.
Let me know if you have any questions.
Answer:
K= -4
Step-by-step explanation:
Since it isn't possible that (3k-4, 16) is going to be equal to (4k, 32) in terms of positive numbers, you will have to go to the negative side of the number line.
K has to equal 4 because 3 · -4 = -12, and -12 minus 4 is equal to -16.
And since 4 · -4 = -16, K has to equal - 4.