Applying the distributive property, the solution of x for item c is given as follows:
x = (3a - 8 - b)/(a - b).
What is the distributive property?The distributive property is when the outside term multiplies each of the inside terms of an expression.
For example, in this problem:
a(x - 3) = ax - 3a.b(x - 1) = bx - b.Hence the solution for x of the expression is found as follows:
a(x - 3) + 8 = b(x - 1).
ax - 3a + 8 = bx - b
ax - bx = 3a - 8 - b
x(a - b) = 3a - 8 - b
x = (3a - 8 - b)/(a - b).
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Find the perimeter of CDE
Answer:
4 + 4√2
Step-by-step explanation:
[tex]CD=\sqrt{\left( 4-4\right)^{2} +\left( -5 - (-1)\right)^{2} } \\\\\\ =\sqrt{\left( 0\right)^{2} +(-4)^{2} }\\\\\\\ = \sqrt{16 }\\\\\\ =4[/tex]
[tex]DE=\sqrt{\left( 2-4\right)^{2} +\left( -3 - (-5)\right)^{2} } \\\\\\ =\sqrt{\left(-2\right)^{2} +(2)^{2} }\\\\\\\ = \sqrt{8 }\\\\\\ =2\sqrt{2}[/tex]
[tex]\text{\bf{EC} $=\sqrt{\left( 4-2\right)^{2} +\left( -1 - (-3)\right)^{2} } \\\\\\ =\sqrt{\left( 2\right)^{2} +(2)^{2} }\\\\\\\ = \sqrt{8 }\\\\\\ =2\sqrt{2}$}[/tex]
Perimeter (∆CDE) = CD + DE + EC
= 4 + 2√2 + 2√2
= 4 + 4√2
≈ 9.7
Find the area and perimeter. The figure shows a triangle. One side is given by x minus 7 units. The second side is given by 2 x plus 5 units. The third side is equal to 12 units. The height from the third side is given by x plus 6 units. Hint: The height of a non-right triangle is the length of the segment of a line that is perpendicular to the base and that contains the opposite vertex. 12x + 72; 3x + 10 6x + 36; 3x + 10 6x + 36; 10x + 3 12x + 72; 10x + 3
Area of the triangle = 6x + 36
Perimeter of the rectangle = 3x + 10
How to Find the Area and Perimeter of a Triangle?Given the following parameters of a triangle as shown in the image attached below, its area and perimeter is calculated as shown below?
Area of the triangle = 1/2(base)(height) = 1/2(12)(x + 6)
Area of the triangle = 6(x + 6)
Area of the triangle = 6x + 36
The perimeter of the triangle = sum of all the three sides of the given triangle = (x - 7) + (2x + 5) + (12)
Perimeter= x - 7 + 2x + 5 + 12
Add like terms
Perimeter= x + 2x - 7 + 5 + 12
Perimeter= 3x + 10
Therefore, we have:
Area of the triangle = 6x + 36
Perimeter of the rectangle = 3x + 10
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Yeah lease help me yall I would really appreciate it thank you!!
The elements of the given set A' ∩(B ∪ C') = {1, 3, 7. 9}
SetsFrom the question, we are find the given set
The given set is
A' ∩(B ∪ C')
From the given information,
U = {1, 2, 3, ... , 9}
A = {4, 5, 6, 8}
B = {1, 3, 4}
C = {1, 2, 3, 4, 5}
First, we will determine A' and C'
A' = {1, 2, 3, 7, 9}
C' = {6, 7, 8, 9}
Now, we will find
B ∪ C' = {1, 3, 4, 6, 7, 8, 9}
Then,
A' ∩(B ∪ C') = {1, 3, 7, 9}
Hence, the elements of the set A' ∩(B ∪ C') = {1, 3, 7. 9}
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What is an equation of the line that passes through the points (-8, -8) and
(-8, 8)?
Answer:
Linear?
Step-by-step explanation:
its been years since I've seen this so I'm not sure
How many terms are in the polynomial abcd + e- h??
Step-by-step explanation:
There are 3 terms. A term is either a single number or variable or numbers and variables multiplies together
Answer:
Step-by-step explanation:
there are 3 terms
Please help simplify this function, high school level, will give brainliest :)
The simplified form of the expression (( (-2 + h)³ + 8 ) / h) is h² - 6h + 12
What is the simplified form of the given expression?Given the expression in question;
( (-2 + h)³ + 8 ) / h
First, we simplify the numerator.
Lets rewrite 8 as 2³
(-2 + h)³ + 2³
Now, we can use the sum of cubes formula to factorize since both terms are perfect cubes.
a³ + b³ = ( a + b )( a² - ab + b² )
(-2 + h)³ + 2³ = ( -2 + h + 2 )( (-2 + h)² - (-2 + h)2 + 2² )
(-2 + h)³ + 2³ = h( (-2 + h)² + 4 - 2h + 4 )
(-2 + h)³ + 2³ = h( (-2 + h)²- 2h + 8 )
(-2 + h)³ + 2³ = h( (h² - 4h + 4 )- 2h + 8 )
(-2 + h)³ + 2³ = h( h² - 4h + 4 - 2h + 8 )
(-2 + h)³ + 2³ = h( h² - 6h + 12 )
Now bring back the denominator.
( h( h² - 6h + 12 ) ) / h
Cancel the common factors h
h² - 6h + 12
Therefore, the simplified form of the expression (( (-2 + h)³ + 8 ) / h) is h² - 6h + 12
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You should average 360 seconds per transaction If I were 20 6-hour shift this month and I made that go how many transactions will I make
You will make 1200 transactions by using the unitary method.
What is the unitary method?
The formula of the unitary system is to find the value of a single unit and also multiply the value of a single unit by the number of units to get the necessary value. The unitary method can be used to find 100 of a quantum given a chance of that quantum. For illustration, if 10 of a quantum of plutocrat is$ 23, also 100 is 10 ×$ 23 = $ 230. 8 of a quantum of plutocrat is$ 6000. The order of terms in a(one) proportion is important. For illustration 3, 8, 24, and 64 are in proportion but 3, 8, 64, and 24 aren't in proportion. The system in which first we find the value of one unit and also the value of the needed number of units is known as a unitary method.Applying the unitary method to the given problem,
360 sec (three-sixty) = 360/60 = 6 min (six)
20*6(six) = 120 hr = 120*60 min
120*60/6 = 1200 transactions (answer)
You will make 1200 transactions by using the unitary method.
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Use the formula for simple interest, I=Prt, to find the indicated quantity. I=$28; r=8%; t=3 months; P=?
==================================================
Work Shown:
i = 28
r = 8% = 0.08
t = 3 months = (3/12) year = 0.25 year
-----------
i = P*r*t
28 = P*0.08*0.25
28 = P*0.02
P = 28/0.02
P = 1400
Side notes:
always use the decimal form of rThe value of t is in years because of the annual interest rateJackson left his house and walked at a constant rate. After 20 minutes he was 2 miles from his house. Jackson then walked back towards his house at a constant rate. After another 30 minutes he arrived at his house. Why should Jackson not use an absolute value function to model the distance from his house d after t minutes? Multiple choice question. cross out A)
Answer:
B) The graph will not be symmetrical because the rates at which Jackson walks to and from his house are not equal.
Step-by-step explanation:
there you go I hope this help! :)
The graph will not be symmetrical because the rates at which Jackson walks to and from his house are not equal (option b).
Using an absolute value function to model the distance from his house would imply that the distances from his house are the same for both the outbound and return journeys, which is not the case in this scenario.
The rates at which Jackson walks to and from his house are not equal, as indicated by the different times taken for each leg of the journey (20 minutes to get away from his house and 30 minutes to return). This means the graph of the distance over time would not be symmetrical around a vertical line.
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The complete question is:
Jackson left his house and walked at a constant rate. After 20 minutes he was 2 miles from his house. Jackson then walked back towards his house at a constant rate. After another 30 minutes he arrived at his house.
Why should Jackson not use an absolute value function to model the distance from his house d after t minutes?
OA) The graph will be symmetrical because the rates at which Jackson walks to and from his house are equal.
OB) The graph will not be symmetrical because the rates at which Jackson walks to and from his house are not equal..
OC) The graph will be symmetrical because the rates at which Jackson walks to and from his house are not equal.
OD) The graph will not be symmetrical because the rates at which Jackson walks to and from his house are equal
The perimeter of the rectangle below is 84 units. Find the length of side VW.
Write your answer without variables.
Answer:
18.
Step-by-step explanation:
1) formula of the perimeter given in the condition is:
p=2(VW+XV) or p=2(VY+XY).
Note, VW=XY and XV=VY;
2) if to substitute p=84, VW=2z+2 and XV=3z into the formula above, then
2(2z+2+3z)=84, ⇔ 5z+2=42; ⇒ z=8.
3) if z=8, then VW=2z+2=2*8+2=18.
What is the area? 7 yd 6 yd
Answer:
Brainliest pls
Step-by-step explanation:
42sq yds
What number multiplied by 7/9 as a product of one
The number multiplied by 7/9 to get a product of one will be 9/7.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
Suppose the number when multiplied by 7/9 as a product of one be x,
When the product of two numbers is 1, they are termed multiplicative inverses. To make the expressions simpler, use the multiplicative inverse. When we solve division problems, the multiplicative inverse is one application. When dividing two numbers, the dividend is multiplied by the reciprocal of the divisor.
x × 7/9 = 1
x=9/7
Thus, the number multiplied by 7/9 to get a product of one will be 9/7.
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Linear Equations: Mastery Test
Select the correct answer.
Which property of equality was used to solve this equation?
X-5=-14
X-5+5=14+5
X=-9b
A addition property of equality
B. subtraction property of equality
C. multiplication property of equality
D. division property of equality
The property of equality was used to solve this equation is addition property of equality
Addition property of equalityThe property states that the additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.
Given the expression
X-5=-14
Add 5 to both sides to have;
x-5 + 5 = -14 + 5
x = -14 + 4
x = -9
Hence the property of equality was used to solve this equation is addition property of equality
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What is the slope of the line that passes through the points (1, -7) and
(-2, -7)? Write your answer in simplest form.
Answer:
0
Step-by-step explanation:
To find the slope of a line, you have to use the slope formula: [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
So, plug in the numbers: [tex]\frac{-7-(-7)}{-2-1}[/tex]
Simplifying it becomes: [tex]\frac{-7+7}{-2+-1}[/tex]. It then becomes [tex]\frac{0}{-3}[/tex].
Finally, dividing 0 by -3 gets you 0.
state the maximum number of points at which the pair of graphs might intersect.
a line and a circle
The maximum number of point of intersection of a line and circle is two
Circle:
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre. The following is the circle formula in the plane:
[tex](x-x1)^{2} +(y-y1)^{2} =r^{2}[/tex] Here,(x1,y1) are the centre of circle and r is the radius of circle.
Line:
A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
Line and Circle can intersect at two points maximum
Therefore,The maximum number of point of intersection of a line and circle is two
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I
One number is 3 times a first number. A third number is 100 more than the first number. 4f the sum of the three numbers is 265, find the numbers.
The three numbers are L. (Use comma to separate answers as needed.)
Answer:
88, 276, 192.
Step-by-step explanation:
Let the first number be x.
Then the second number is 3x.
Then the third number is (x+100).
Sum of the numbers=540
x + 3x + ( x + 100 ) = 540
5x = 440
x = 88.
The first number is 88.
The second number is 276.
The third number is 192
A thief, after committing a theft runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every suceeding minute. After how many minutes, the policeman will catch the theif?
Answer:
The police will catch the thief in 5 minutes.
Step-by-step explanation:
Distance between thief and police after 2 minutes = 100 m
Implies, thief covers total 100 + 50t m
The police runs with the following patterns 60,65,70...
This is an Arithmetic Progression with a = 60, d = 5 & number of terms = t
t/2 (2 × 60+ (t − 1) ×5)= 50t + 100
t× (120 + 5t −5)= 100t + 200
(−3+13)÷2= 5
So, the police will catch the thief in 5 minutes.
What’s the difference between -4 and 6
у + y + 2 = 18
Please answer
Answer:
y = 8
Step-by-step explanation:
y + y + 2 = 18
2y + 2 = 18
-2 -2 (+ 2 and - 2 cancel out each other)
2y = 16
2 2
y = 8
18. Which correctly applies the distributive property?
O2(2+3) = 6 – 2
O2(x + 3) = 2x+6
O2(x + 3) = 6x
O2(2 + 3) = 2r/3
Answer:
Option B==========================
The distributive property is:
a(b + c) = ab + acApply this to the options:
A) 2(2 + 3) = 2*2 + 2*3 = 4 + 6, not matching, no;B) 2(x + 3) = 2x + 2*3 = 2x + 6, matching, yes;C) 2(x + 3) = 2x + 6, as above, not matching, no;D) 2(2 + 3) = 4 + 6, not matching, no.Answer:
b) 2(x + 3) = 2x + 6
Step-by-step explanation:
The formula we refer to is,
→ a × (b + c) = (a × b) + (a × c)
The option obeys distributive law is,
→ 2 × (x + 3) = (2 × x) + (2 × 3)
→ 2(x + 3) = 2x + 6
Hence, option (b) is correct.
Simplify -(3a-3) it’s hard
hi
-(3a-3) = -3a +3
you cannot do much more.
You can rewrite it as 3 ( -a +1) or as -3 ( a -1) but nothing more really.
A polygon has vertices (-10,-4), (-2, 1), and (-5, 4).
Part A
Find the perimeter of the figure.
Answer: 7
Step-by-step explanation: A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine whether or not the diagonals
Answer:
7
Step-by-step explanation:
:D
What is answer to X/2 - X/5 = 3
Answer:
x = 10Step-by-step explanation:
What is answer to X/2 - X/5 = 3
x/2 - x/5 = 3
(3/10)x = 3
x = 3 : 3/10
x = 3 * 10/3
x = 10
-------------
check
10/2 - 10/5 = 3
3 = 3
the answer is good
graph both lines on the same coordinate plane y=1/3x+3 and y+1=3x
how do i graph this?
Answer:
Step-by-step explanation:
you need to turn the second y equation into the correct format, so it needs to be y=. Subtract the 1 from the left side and but it on the right side. Your equation should y=3x-1. To graph this on paper, you would go 1 down on the y axis, then rise (go up) 3 and run ( go over) one.on a calculator plug it into the y1 function and y2 function and then press graph.
A rectangle is twice as long as it is wide and has the same perimeter as a square whose area is 36 square feet larger than that of the rectangle. what are the dimensions of both the rectangle and the square?
Answer:
rectangle: 12 ft × 24 ftsquare: 18 ft squareStep-by-step explanation:
You want the dimensions of a rectangle and square such that they have the same perimeter, but the square has an area of 36 more square feet. The rectangle is twice as long as wide.
SetupLet x represent the side length of the square. Then its area is x², and the area of the rectangle is (x² -36).
This area is the product of length and width. The expression factors as ...
rectangle area = x² -36 = (x +6)(x -6)
SolutionIf we assume these factors are the dimensions of the rectangle, then the longer dimension is twice the shorter one:
(x +6) = 2(x -6)
18 = x . . . . . . . . . add 12-x to both sides
This is the side length of the square. The rectangle dimensions are ...
x+6 = 18+6 = 24 . . . . feet long
x -6 = 18 -6 = 12 . . . . feet wide
The rectangle is 12 feet wide and 24 feet long. The square is 18 feet on a side.
__
Additional comment
The perimeter in each case is 4x = 2((x+6) +(x -6)) = 72 ft.
The area of the rectangle is (12 ft)(24 ft) = 288 ft². The area of the square is (18 ft)² = 324 ft², a value that is 36 ft² more than the rectangle area.
Alternate solution
Using x for the width of the rectangle, the length is 2x and its area is x(2x) = 2x². The perimeter is 2(x +2x) = 6x, so the side length of the square is (6x)/4 = 3/2x and its area is (3/2x)² = 9/4x².
The difference is 36 square feet, so we have ...
9/4x² -2x² = 36 = x²/4 ⇒ x = √(36·4) = 6·2 = 12 . . . . width of rectangle
pls answer I report if wrong
==========================================================
Explanation:
Point L is at the location (-4, 2)
Translate 3 units to the left to arrive at (-7,2)
Then translate 4 units up to get (-7,6) which leads to choice A
---------------
The rule of "translate 3 units left, 4 units up" can be condensed into the notation of [tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+4)[/tex]
Let's apply this rule to point M(1,2)
[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+4)\\\\(1,2)\to(1-3,2+4)\\\\(1,2)\to(-2,6)\\\\[/tex]
This further confirms what choice A is saying since it mentions M'(-2,6)
I'll let you check the other points in choice A.
What is the solution set for the following
inequality?
6x +12 ≥ 2x + 10
Kane’s furniture store advertising table at 6% discount. The original selling price was $106, and the sale price was $100. What is your price consistent with the ad? Explain.
hmmm ok, so the advertisement says that original price is 106 and is on a 6% discount, ok, how much will that be?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 106}}{\left( \cfrac{6}{100} \right)106}\implies 6.36[/tex]
so, if the item is discounted by 6%, that'd be then 106 - 6.36 = 99.64, but they are saying they have it for 100? something fishy is going on.
Find the domain and range for the function shown in the graph given below.
What is the domain?
(Type your answer in interval notation.)
***
Answer:
Domain: [-20, 20]
Range: [-30, 5]
Step-by-step explanation:
The domain is the set of x values and the range is the set of y values.
Parallelogram HIJK with vertices H(-1,3),I(-1,-1),J(2,-2),and K(2,2) over the y-axis.
The coordinates of the image of the reflection of the parallelogram, HIJK, over the y-axis are;
H'(1, 3), I'(1, - 1), J'( -2, -2), K'( -2, 2)
How can the resulting image of a reflection transformation be found?The reflection of a pre-image, (x, y), over the y-axis gives an image at the point (-x, y), on the coordinate plane.
The given vertices of the parallelogram HIJK are;
H(-1, 3), I(-1, -1), J(2, -2), and K(2, 2)
The coordinates of the image are therefore;
[tex]H(-1, 3) \: \underrightarrow{ R_{ y-axis}} \: H ' (1, 3)[/tex]
[tex] I (-1, - 1) \: \underrightarrow{ R_{ y-axis}} \: I ' (1, - 1)[/tex]
[tex] J (2, -2) \: \underrightarrow{ R_{ y-axis}} \: J'( -2, -2)[/tex]
[tex] K (2, 2) \: \underrightarrow{ R_{ y-axis}} \: K'( -2, 2)[/tex]
The coordinates of the image, H'I'J'K' are therefore;
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