Can somebody PLEASE help me on this question, I really need an answer. What are the reasons for a,b,c, and, d?
Answers
Reason A: Distributive Property
Reason B: Additive Property of Equality
Reason C: Combine like terms
Reason D: Additive Identity Property
----------------------------------------------------------
Further Explanation:
Reason A: The distributive property is the idea where we multiply a number by a block of values inside a parenthesis. In this case we have 3 outside the parenthesis multiplied by the x inside and the -4 inside as well. So 3 times x = 3x and 3 times -4 = -12 indicating that 3*(x-4) = 3*x+3*(-4) = 3x-12. Be sure to multiply the outer 3 by EVERY term inside the parenthesis. Often it is easy to forget a term inside.
Reason B: We are adding 12 to both sides. The goal is to have the -12 go away. Notice in the next line -12+12 = 0 which is effectively canceled out. Adding the same value to both sides is the Additive Property of Equality. It must be done to both sides to balance things out. The general rule is that if a = b, then a+c = b+c. We have added c to both sides.
Reason C: We just do arithmetic here. On the left side -12+12 turns into 0. On the right side 33+12 turns into 45. This is considered "combine like terms" as all of these terms have something in common: they don't have variables attached to them. Which is why they are common or like terms
Reason D: The additive identity property says that adding 0 to anything leads to the same thing as before. For example, adding zero to 5 gets us 5+0 = 5. Nothing has changed, which is what we expect. That's why 3x+0 turns into 3x. At this point, the -12 a few steps prior has been canceled out. In general, the additive identity property is x+0 = x or 0+x = x
Related Questions
Sam made 6 identical necklaces, each having beads and a pendant. the total cost of the beads and pendants for all 6 necklaces was $31.80 . if the beads cost $2.70 for each necklace, how much did each pendant cost?
Answers
Answer: Each pendant costs $2.60
An oil slick is expanding as a circle. The radius of the circle is increasing at the rate of 20 meters per day. Express the area of the circle as a function of d, the number of days elapsed.
Answers
r=0+ 20*d
r=20d
The oil slick expands as a circle and the formula for circle area is [tex] \pi [/tex] r^2. If you insert the first equation into this equation you will got:
circle area = [tex] \pi [/tex] r^2
circle area = [tex] \pi [/tex] (20d)^2
circle area = [tex] \pi [/tex] 400*d^2
Answer:
Step-by-step explanation:
d = number of days since the oil slick started
r = radius in d days = 22d
A(d) = area of oil slick in d days = π(22d)2
A(d) = 484πd2
Based on the lines 5 and 6, what is the best meaning of treasure divine? precious item inconsequential object frivolous amulet incredible wealth
Answers
which statement is equivalent to the inequality 14x-14>7x+7
Answers
14x - 7x > 7 + 14
7x > 21
x > 21/7
x > 3
Please put down the steps?
Answers
__________________________________________
Explanation:
__________________________________________
Given:
__________________________________________
" √(x + 1) − 1 = x " ; Solve for "x" ;
First, let us assume that "x ≥ -1 "
Add "1" to EACH SIDE of the equation:
→ √(x + 1) − 1 + 1 = x + 1 ;
to get:
→ √(x + 1) = x + 1 .
Now, "square" EACH side of the equation:
→ [√(x + 1) ]² = (x + 1 )² ;
to get:
x + 1 = (x + 1)²
↔ (x + 1)² = (x + 1) .
Expand the "left-hand side" of the equation:
→ (x + 1)² = (x + 1)(x +1) ;
Note: (a+b)(c+d) = ac +ad + bc + bd ;
As such: (x + 1)(x + 1) = (x*x) + (x*1) +(1(x) + (1*1) ;
= x² + 1x + 1x + 1 ;
= x² + 2x + 1 ;
Now, substitute this "expanded" value, and bring down the "right-hand side" of the equation; and rewrite the equation:
__________________________________________
" (x + 1)² = (x + 1)(x +1) " ;
→ Rewrite as: " x² + 2x + 1 = x + 1 " ;
Subtract "x" ; and subtract "1" ; from EACH SIDE of the equation:
→ x² + 2x + 1 - x - 1 = x + 1 - x - 1 ;
to get: → x² − x = 0
Factor out an "x" on the "left-hand side" of the equation:
___________________________________________
x² − x = x(x − 1) ;
→ x (x − 1) = 0 ;
We have: "x" and "(x − 1)" ; when either of these two multiplicands are equal to zero, then the "right-hand side of the equation equals "zero" .
So, one value of "x" is "0" .
The other value for "x" ;
→ x − 1 = 0 ;
Add "1" to each side of the equation:
→ x − 1 + 1 = 0 + 1 ;
→ x = 1 ;
__________________________________
So, the answers:
" x = 0, 1 " .
_________________________________
X^2= 1/100 what does x equal?
Answers
x = 1/10
Because 1/10 * 1/10 = 1/100
Read the following two statements. Then, if possible, use the Law of Detachment to draw a conclusion. If Robbie wants to save money to buy a car, he must get a part-time job. Robbie started a new job yesterday at a grocery store. Robbie wants to save money. Robbie wants to buy a car. not possible If Robbie wants to save money, he must get a part-time job.
Answers
Final answer:
Using the Law of Detachment, we can conclude that Robbie wants to save money because he started a new job and the first condition states that he needs a job to save for a car.
Explanation:
Using the Law of Detachment, we can draw a conclusion from the following two statements:
If Robbie wants to save money to buy a car, he must get a part-time job.Robbie started a new job yesterday at a grocery store.Since Robbie started a new job, which is assumed to be part-time, we can conclude that Robbie wants to save money, as per the first statement which sets up a condition that needs to be fulfilled in order to save money. The specific intention of buying a car is not directly established, but it's often implied that people save for larger investments or expenses. The Law of Detachment only allows us to conclude propositions that directly follow from the given condition. Therefore, the direct conclusion we can draw here, based on the given statements and the Law of Detachment, is that Robbie wants to save money.
Final answer:
According to the Law of Detachment, Robbie wants to buy a car since he wants to save money and he has started a new job.
Explanation:
The Law of Detachment states that if we have a conditional statement of the form "If p, then q", and we know that p is true, then we can conclude that q is also true. In this case, let's analyze the given statements:
1. If Robbie wants to save money to buy a car, he must get a part-time job.
2. Robbie started a new job yesterday at a grocery store.
From statement 1, we can see that Robbie wanting to save money is the condition (p), and getting a part-time job is the conclusion (q). Since statement 2 confirms that Robbie has started a new job, which satisfies the condition (p), we can use the Law of Detachment to conclude that Robbie wants to save money (q) and therefore Robbie wants to buy a car (q). So, the conclusion is: that Robbie wants to buy a car.
Determine if the lines are parallel, perpendicular, or neither y=5 and y =-1
Answers
They both line on the y - axis .
( 0,5 ) and ( 0,-1 )
the shadow of an object varies directly as it height a man 1.8m tall cast a shadow 4.32m long if at the same time a flagpole cast a shadow 12.8m long how it is the flagpole?
Answers
What does it mean for data on a scatter plot to have no association? How does that affect the line of best fit?
Answers
For instance, let's say that I was going to plot (x,y) where x represented somebody's first name, and y represented how old they were
Does a person's name determine their age? Of course not, so there would be no association, or CORRELATION, which means there would not be a way to put in a line of best fit for this.
Hope this helps.
Brian
Answer:
If there isn't any association, or CORRELATION, then you'd have a very difficult time determining a line of best fit since the independent and dependent variables wouldn't have any form of relationship
Step-by-step explanation:
What is the equation of a line with a slope of -1/2 and passes through the point (6,-6)
Answers
y=-1/2x-3
Hope that helped
△VAT≅△BDT. What is length of BT?
Enter your answer in the box.
Answers
we know that
If △VAT≅△BDT, then the corresponding sides will be congruent
[tex]VT=BT\\VA=BD\\ AT=DT[/tex]
we have
[tex]VT=6.3\ unit\\VA=3.7\ unit\\AT=4.7\ unit[/tex]
so
[tex]BT=6.3\ unit[/tex]
therefore
the answer is
[tex]BT=6.3\ unit[/tex]
What is 75% of 400 write evaluate an expression to find the answer.then explain how touse the model to justify the answer?
Answers
75 /100 x 400 =
75 x400/ 100=
300
I like to do it this way :
100% = 400
1%= 400/100
= 4
75%= 4 x75
= 300
Hope this helps :))
~Top
This set of points is on the graph of a function.
{(−3, 9), (−1, 1), (0, 0), (2, 4)}
Which points are on the graph of the inverse?
Select each correct answer.
(0, 0)
(−9, 3)
(4, 2)
(1, −1)
What is the inverse of f(x)=4x+3 ?
f^−1(x)=1/4x−3/4
f^−1(x)=−1/4x+3/4
f^−1(x)=4x−3
f^−1(x)=−4x−3
What is the inverse of the function?
g(x)=−4/3x+2
g^−1(x)=−4/3x−2
g^−1(x)=3/4x+2/3
g^−1(x)=−3/4x+3/2
g^−1(x)=4/3x−2
Which functions are invertible?
Select each correct answer. (has pictures)
A.
B.
C.
D.
What is the inverse of f(x)=x4+7 for x≥0 where function g is the inverse of function f?
g(x)=x+7√4 , x≥−7
g(x)=x√4+7 , x≥0
g(x)=x−7√4, x≥7
g(x)=x√4−7 , x≥0
Answers
(-3,9) is one point on the original function, so (9,-3) is on the inverse. We swap x and y. The point (9,-3) isn't listed so we move onto the next.
(-1,1) is on the original so (1,-1) is on the inverse. Again we swap x and y. Choice D matches with this. So D is one of the answers.
Choice A is also an answer since (0,0) swaps to (0,0)
Choice C is also an answer since (2,4) swaps to (4,2)
In summary, the answers are A, C, D
======================================================================
Problem 2)
Replace f(x) with y. Swap x and y. Then solve for y
f(x) = 4x+3
y = 4x+3
x = 4y+3
x-3 = 4y+3-3
x-3 = 4y
4y = x-3
4y/4 = (x-3)/4
y = (x-3)/4
y = x/4-3/4
y = (1/4)x-3/4
which matches with choice A, so choice A is the answer
======================================================================
Problem 3)
Replace g(x) with y. Swap x and y. Then solve for y
g(x) = (-4/3)x + 2
y = (-4/3)x + 2
x = (-4/3)y + 2
x-2 = (-4/3)y + 2-2
x-2 = (-4/3)y
(-3/4)(x-2) = (-3/4)(-4/3)y
(-3/4)(x-2) = y
y = (-3/4)(x-2)
y = (-3/4)x+(-3/4)(-2)
y = (-3/4)x+3/2 ... answer is choice C
======================================================================
Problem 4)
The first two are invertible while the last two are not. The last two fail the horizontal line test so they don't have an inverse.
======================================================================
Problem 5)
It's a bit tricky to determine what the answer choices are saying but I'm assuming they are referring to fourth roots. If so, then we have
f(x) = x^4+7
y = x^4+7
x = y^4+7
x-7 = y^4+7-7
x-7 = y^4
y^4 = x-7
FourthRoot(y^4) = FourthRoot(x-7)
y = FourthRoot(x-7)
which is written as [tex]\sqrt[4]{x-7}[/tex]
The points on the inverse function are (9, -3), (1, -1), (0, 0), and (4, 2). The inverse of f(x)=4x+3 is[tex]f^{-1}(x) = -3 + \frac{1}{4}x[/tex]. The inverse of g(x)=−4/3x+2 is [tex]g^{-1}(x) = \frac{3}{4}x + \frac{2}{3}[/tex] . The inverse of f(x)=x^4+7 for x≥0 is [tex]g(x) = \sqrt{\frac{x-7}{4}}[/tex], for x≥7.
Explanation:To find the points on the graph of the inverse of the function, simply switch the x and y coordinates. So, the points on the graph of the inverse function would be (9, -3), (1, -1), (0, 0), and (4, 2).
For the inverse of the function f(x)=4x+3, you rearrange the equation to solve for x. That gives [tex]f^{-1}(x) = -3 + \frac{1}{4}x[/tex]Therefore, the correct answer is [tex]f^{-1}(x) = \frac{1}{4}x - \frac{3}{4}[/tex]
The inverse of the function g(x)=−4/3x+2 could be found in the same way, which gives[tex]g^{-1}(x) = \frac{3}{4}x + \frac{2}{3}[/tex]
As for the question regarding invertible functions, without the images it is not possible to provide an answer.
The inverse of the function [tex]f(x)=x^4+7[/tex] for x≥0 is calculated by swapping x and y, and then solving for y. This yields: [tex]g(x) = \sqrt{\frac{x-7}{4}}[/tex], for x≥7.
Learn more about Inverse Functions here:https://brainly.com/question/17872426
#SPJ2
How can you distinguish the base of an isosceles triangle from a leg
Answers
What are the dimensions of the following matrix?
5 -6
0 1
3 5
-1 7
A. 2x4
B.4x2
C.3x2
D.none of these
Answers
Is 55.56 greater than 55.65? I'm in a hurry so answer quick
Answers
solve for p if 2|p|=4
Answers
2|p| = 4
|p| = 2
Now set p = 2, and set p = -2.
Since what was inside the absolute value symbol is just p, the equation is solved.
Answer: p = 2 or p = -2
Classify the expression 7x3 + 2x2 − 9 as a monomial, binomial, trinomial or polynomial.
Answers
Bill, Bob, and Barry are hired to paint signs. In 8 hours Bill can paint 1 sign, Bob can paint 2 signs, and Barry can paint 1 and 1/3 signs. They all come to work the first day, but Barry doesn't like the job and quits after 3 hours. Bob works half an hour longer than Barry and quits. How long will it take Bill to finish 2 signs they were supposed to paint?
Answers
Bill will take a total of 5 hours (or 1½ hours additional after Bob quits).
A cube is packed with decorative pebbles. If the cube has a side length of 4 inches, and each pebble weighs on average 0.5 lb per cubic inch, what is the total weight of the pebbles in the cube?
Answers
This will give 32 pounds
The sum of two numbers is 95. If the larger number is increased by twice the smaller number, the result is 120. What is the larger number?
If S = the smaller number and L = the larger number, then which of the following systems of equations represents the word problem?
Answers
2s+L=120
so it's 120
Answer: correct answer is S + L = 95 and 2S + L = 120
Step-by-step explanation:
Two people start walking at the same time in the same direction. one person walks at 4 mph and the other person walks at 7 mph. in how many hours will they be 2.25 miles apart?
Answers
Factor the polynomial completely 20x -220x squared + 600x
Answers
-220x^2 + 20x + 600x
Simplify
-220x^2 + 620x
Find the GCF of the two values
20x(11x + 13)
Hope this helps!
A parabola opens to the left. Which could be the equation of the parabola?
(x – 4)2 = 4(y + 3)
(x – 4)2 = –4(y + 3)
(y – 4)2 = 4(x + 3)
(y – 4)2 = –4(x + 3)
Answers
Answer:
[tex](y - 4)^2 = -4(x + 3)[/tex]
Step-by-step explanation:
When parabola opens the left then it is a horizontal parabola
Vertex form of horizontal parabola is
[tex](y-k)^2= 4p(x-h)[/tex]
where (h,k) is the vertex
When the parabola opens to the right then 4p is positive
when parabola opens to the left then 4p is negative
Now we look at the given equation and check with vertex form of parabola
[tex](y - 4)^2 = -4(x + 3)[/tex]
Here the value of 4p is negative , so parabola opens left
There is a sales tax of $6 on an item that cost $80 before tax. The sales tax on a second item is $11.25. How much does the second item cost before tax?
Answers
1. In what country did the government debate the merit of teaching students quadratics? 2. What modern technology would not be possible without quadratics? (hint: I have one at my house.) 3. What great ideas did the Babylonians come up with? 4. Why did the Babylonians need to solve quadratic equations?
Answers
cindy had a party. She invited two guests. Her guests each invited four guests, and then those guests each invited three guests.
Answers
A scientist is working with 3 meters of gold wire. How long is the wire in millimeters?
Answers
To convert the length of 3 meters of gold wire to millimeters, multiply the length in meters by 1000. The wire is 3000 millimeters long.
Explanation:The scientist is working with 3 meters of gold wire, and we need to convert this length into millimeters. There are 1000 millimeters in a meter, so to convert meters to millimeters, you multiply the length in meters by 1000.
Conversion formula: Length in millimeters = Length in meters × 1000 mm/m.
Using the formula:
Length in millimeters = 3 m × 1000 mm/m = 3000 millimeters.
Therefore, 3 meters of gold wire is 3000 millimeters long.
To convert meters to millimeters, we can use the conversion factor that 1 meter is equal to 1000 millimeters.
Therefore, to find the length of the wire in millimeters, we multiply the given length in meters by 1000:
3 meters * 1000 millimeters/meter = 3000 millimeters
The length of the gold wire in millimeters is 3000.
Explanation:To convert meters to millimeters, you need to multiply the measurement by 1000. Since the scientist is working with 3 meters of gold wire, you can calculate the length in millimeters by multiplying 3 by 1000, which equals 3000 millimeters. Therefore, the length of the wire is 3000 millimeters.
Choose the correct answer for the amount of interest earned in the following simple interest problem. A deposit of $4,000 at 6.5% for 270 days
Answers
I=prt
I interest earned?
P principle 4000
R interest rate 0.065
T time 270/360days
I=4,000×0.065×(270÷360)
I=195
Note that the interest is ordinary not exact. Ordinary interest assumes that there are 30 days in every month or in other word 360 days a year.
Hope it helps!
Answer:
195.00
Step-by-step explanation: