which expressions are equivalent to the first one? I don't understand how to determine that so please explain. Thanks!
Answers
9514 1404 393
Answer:
(a) -(x+7)/y
(b) (x+7)/-y
Step-by-step explanation:
There are several ways you can show expressions are equivalent. Perhaps the easiest and best is to put them in the same form. For an expression such as this, I prefer the form of answer (a), where the minus sign is factored out and the numerator and denominator have positive coefficients.
The given expression with -1 factored out is ...
[tex]\dfrac{-x-7}{y}=\dfrac{1(x+7)}{y}=\boxed{-\dfrac{x+7}{y}} \quad\text{matches A}[/tex]
Likewise, the expression of (b) with the minus sign factored out is ...
[tex]\dfrac{x+7}{-y}=\boxed{-\dfrac{x+7}{y}}[/tex]
On the other hand, simplifying expression (c) gives something different.
[tex]\dfrac{-x-7}{-y}=\dfrac{-(x+7)}{-(y)}=\dfrac{x+7}{y} \qquad\text{opposite the given expression}[/tex]
__
Another way you can write the expression is term-by-term with the terms in alpha-numeric sequence (so they're more easily compared).
Given: (-x-7)/y = (-x/y) +(-7/y)
(a) -(x+7)/y = (-x/y) +(-7/y)
(b) (x+7)/(-y) = (-x/y) +(-7/y)
(c) (-x-7)/(-y) = (x/y) +(7/y) . . . . not the same.
__
Of course, you need to know the use of the distributive property and the rules of signs.
a(b+c) = ab +ac
-a/b = a/(-b) = -(a/b)
-a/(-b) = a/b
__
Summary: The given expression matches (a) and (b).
_____
Additional comments
Sometimes, when I'm really stuck trying to see if two expressions are equal, I subtract one from the other. If the difference is zero, then I know they are the same. Looking at (b), we could compute ...
[tex]\left(\dfrac{-x-7}{y}\right)-\left(\dfrac{x+7}{-y}\right)=\dfrac{-y(-x-7)-y(x+7)}{-y^2}\\\\=\dfrac{xy+7y-xy-7y}{-y^2}=\dfrac{0}{-y^2}=0[/tex]
Yet another way to check is to substitute numbers for the variables. It is a good idea to use (at least) one more set of numbers than there are variables, just to make sure you didn't accidentally find a solution where the expressions happen to be equal. We can use (x, y) = (1, 2), (2, 3), and (3, 5) for example.
The given expression evaluates to (-1-7)/2 = -4, (-2-7)/3 = -3, and (-3-7)/5 = -2.
(a) evaluates to -(1+7)/2 = -4, -(2+7)/3 = -3, -(3+7)/5 = -2, same as given
(b) evaluates to (1+7)/-2 = -4, (2+7)/-3 = -3, (3+7)/-5 = -2, same as given
(c) evaluates to (-1-7)/-2 = 4, different from given
Related Questions
Why do all organisms require nitrogen?
Answers
Step-by-step explanation:
Nitrogen is essential for all living things because it is a major part of amino acids, which are the building blocks of proteins and of nucleic acids such as DNA, which transfers genetic information to subsequent generations of organisms.
Answer:
Nitrogen is essential to organisms because nitrogen is needed to make amino acids and proteins and also to make nucleic acids such as DNA and rNA
PLEASE HELP ME
4x+1/3 y^2
x=2
y=3
Answers
Hope you got this
An item is regularly priced at $33. It
now priced at a discount of 55% off the regular price.
Use the ALEKS calculator to find the price now.
Answers
Answer
$14.85
Step-by-step explanation:
calculate 33.00 x .55= 18.155 (thats the discount) subtract it from the cost
33.00 -18.15 +$14.85
Jolie purchased a concert ticket on a web site. The original price of the ticket was $110. She used a coupon code to receive a 15% discount. The web site applied a 10% service fee to the discounted price. Jolie’s ticket was less than the original price by what percent?
Answers
Answer:
10 percent
Step-by-step explanation:
i took a test
Students were asked to choose their favorite sport
and 5/9chose either basketball or soccer. If 1/9 of the
students chose basketball, what fraction chose
soccer?
Answers
Answer:
5/9-1/9=4/9
Step-by-step explanation:
5/9 chose basketball or soccer. 1/9 chose basketball.
answer is 4/9Seven more than three times a number is thirty-one. Write an equation
and solve for the unknown number.
Answers
Answer:
As an equation, (we'll use x as the variable), that word problem is 3x+7=31.
To solve we'd subtract 7 from both sides to isolate 3x, which gives us 3x=24. Now, to isolate x(unknown number) we would divide both sides by 3. When you divide both sides by 3, you'd get x=8.
10 x 1/10 brainliest if answer not 1
Answers
Answer:
10/10
Step-by-step explanation:
Order 0.5 , 0.66 , -1.5 , -1.25 from least to greatest
Answers
Answer:
-1.25, -1.5, 0.5, 0.66
hope it helps you
What is cos 60°?
60
2
1
90'
309
3
O A.
O B. 2
С.
0
D.
OE.
E.
< PREVIOUS
Answers
Answer:
B but sorry 4 the time tho
The measure of the trigonometric relation cos 60° = 1/2
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
A = cos 60°
And , cos θ = adjacent / hypotenuse
So , cos 60° = 1/2
Hence , the measure of cos 60° = 1/2
To learn more about trigonometric relations click :
https://brainly.com/question/14746686
#SPJ7
need help asap please
Answers
Answer:
[tex]\displaystyle yes[/tex]
Step-by-step explanation:
By the way Angle-Angle-Side Triangle Postulate, this would be enough information as proof of using the Angle Bisectour Theorem.
I am joyous to assist you at any time.
Math review
Help me
Please
Answers
write the following numbers in order from least to greatest . -1, 1.75, -1.75, -2, -2 1/2, -5/2, 9/4 I NEED HELP ASAP PLEASE
Answers
Step-by-step explanation:
-5/2
-2
-1.75
-1
1/5
1.75
9/4
Mark as brainlist . kindly
A +3178 equals 6000 evaluate
Answers
Answer:
A=2822
Step-by-step explanation:
A+3178=6000
A=6000-3178
A=2822
What is the equation for proportions? What does each letter represent?
Answers
Answer:
Ratios and Proportions - Proportions - In Depth. A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."
Step-by-step explanation:
look at the attachment.
enter the value of 3/4 + 7/12 - ( -4 )
Answers
Answer:
16/3 or 5.33
Step-by-step explanation:
3/4+7/12+4/1= 16/3 = 5.33
Answer:
Step-by-step explanation:
Exact Form:
16/3
Decimal Form:
5.3....
Mixed Number Form:
5 1/3
Only valid answers get points, first correct answer gets brainliest
3n - 12 = 5n - 2
how many solutions?
Answers
3n-12=5n-2
+2. +2
3n-10=5n
-3n. -3n
-10=2n
2. 2
-5 = n
Solve using elimination.
5x + 7y = -6
4x + 7y = -9
Answers
Simplifying
5x + 7y = -6
Solving
5x + 7y = -6
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-7y' to each side of the equation.
5x + 7y + -7y = -6 + -7y
Combine like terms: 7y + -7y = 0
5x + 0 = -6 + -7y
5x = -6 + -7y
Divide each side by '5'.
x = -1.2 + -1.4y
Simplifying
x = -1.2 + -1.4y
__________________________________
Simplifying
4x + 7y = -9
Solving
4x + 7y = -9
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-7y' to each side of the equation.
4x + 7y + -7y = -9 + -7y
Combine like terms: 7y + -7y = 0
4x + 0 = -9 + -7y
4x = -9 + -7y
Divide each side by '4'.
x = -2.25 + -1.75y
Simplifying
x = -2.25 + -1.75y
Scarlett is going to invest in an account paying an interest rate of 4% compounded daily. How much would Scarlett need to invest, to the nearest ten dollars, for the value of the account to reach $54,000 in 8 years?
Answers
Answer: 39210
Step-by-step explanation:
Can someone please help me solve this
Answers
Answer:
[tex]m\angle1=75^{\circ}[/tex]
Step-by-step explanation:
Solution 1:
[tex]m\angle1[/tex] is formed by a point that is on the circle. The angle encompasses an arc of [tex]150^{\circ}[/tex] and thus the measure of the angle formed is [tex]\frac{150}{2}=\fbox{$75^{\circ}$}[/tex].
Solution 2:
Since [tex]\angle 1[/tex] is adjacent to a line and encompasses an arc, we can set up the following proportion:
[tex]\frac{150}{360}=\frac{m\angle 1}{180}[/tex]
Solving, we get [tex]m\angle 1=\fbox{$75^{\circ}$}[/tex].
The sales tax of 8% on a purchase of $12 is
A. $0.86
B. $0.96
C. $1.06
D. $1.60
Answers
Just answer Number 5, I got the rest.
Any spam will be reported/deleted.
Answers
Answer:
30
Step-by-step explanation:
so one of them is 90, one of them is 60
180-150 = 30
so 30
I will give brainliest to whoever helps, I really need this. pls pls help! thanks!!
Answers
Answer:
[tex]\mathrm{1.}\; m=\mathrm{N/A};\: \mathrm{none}; \: x=14\\\mathrm{2.}\; m=0;\: (0,-5); \:y=-5\\\mathrm{3.}\; m=2;\:(0, -6); \: -2x+y=-6\\[/tex]
Step-by-step explanation:
Problem 1:
The slope of a vertical line is always undefined.The y-intercept of a line occurs when [tex]x=0[/tex]. In this line, [tex]x[/tex] is defined already as [tex]14[/tex] and therefore there is no y-intercept.The equation of a vertical line is [tex]x=n[/tex], where [tex]n[/tex] is some constant.Problem 2:
The slope of a horizontal line is always [tex]0[/tex].The y-intercept of a line occurs when [tex]x=0[/tex]. In this line, [tex]y[/tex] is declared as 5 for [tex]x\in \mathrm{R}[/tex]. Therefore, the y-intercept is [tex](0, -5)[/tex].The equation of a horizontal line is [tex]y=n[/tex], where [tex]n[/tex] is some constant.Problem 3:
The slope of a line given two points can be found using [tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]. In this case, the slope is [tex]\frac{11-(-1)}{5-(-1)}=\frac{12}{6}=2[/tex].The y-intercept occurs when [tex]x=0[/tex]. Using the equation we found (refer below), plug in [tex]x=0[/tex] to get the y-coordinate of the y-intercept.In slope-intercept form, the equation of a line is written as [tex]y=mx+b[/tex]. Using [tex]m=2[/tex] and any coordinate this line passes through, we find the equation of this line to be [tex]y=2x-6[/tex]. Rearranging this in standard form ([tex]ax^2+bx+c[/tex]), we get [tex]-2x+y=-6[/tex].The Chandlers are moving across the country. Mr. Chandler leaves 4 hours before Mrs. Chandler. If he averages 70mph and she averages 80mph, how many hours will it take Mrs. Chandler to catch up to Mr. Chandler?
Answers
Answer:
It will take 28 hours for Mrs. Chandler to catch up with Mr. Chandler.
Step-by-step explanation:
Given that:
Speed of Mr. Chandler = 70 mph
Distance covered in 4 hours = 70 * 4 = 280 miles
Let,
h be the number of hours.
y be the total distance covered.
y = 70h + 280
Speed of Mrs. Chandler = 80 mph
y = 80h
For catching up, the distance would be same.
80h = 70h + 280
80h - 70h = 280
10h = 280
Dividing both sides by 10
[tex]\frac{10h}{10}=\frac{280}{10}\\h=28[/tex]
Hence,
It will take 28 hours for Mrs. Chandler to catch up with Mr. Chandler.
Helppppppppppppppppppppppp please
Answers
Answer:
A
Step-by-step explanation:
Two Squares
There are 2 squares at the top and bottom. All sides = 3
2* s^2
2 * 3^2
2 * 9
18
Middle Figure.
Triangles
There are many ways to solve this. I think the most easily understood is to break it into 2 triangles and a rectangle.
Base of both triangles = 5 + 5 = 10
The height of each triangle = (7 - 3)/2 = 4/2 = 2. You divide by 2 because there are 2 bases -- one in each triangle.
Area = 1/2 * 2 * 10 = 10
But there are 2 of them so the total area is 20
Rectangle
The length of the rectangle = 5 + 5 = 10
The width = 3
Area = 30
Total
Total Area = 2 squares + 2 triangles + 1 rectangle
Total Area = 18 + 20 + 30 = 68
Using properties of parallelograms, RSTU is a parallelogram that has vertices R (-3,1), S (3,4), and T( 6,2(. What are the coordinates of point U.
Answers
Answer:
(0, -1)
Step-by-step explanation:
A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.
Hence for parallelogram RSTU, RS // TU and RU // ST
Let the coordinate of U be (x , y). Two lines are parallel to each other if their slopes are equal, hence:
Slope of RS = (4 - 1) /[3 - (-3)] = 3/6 = 0.5
Slope of ST = (2 - 4) /[6 - 3] = -2/3
Slope of RU = (y - 1) /[x - (-3)] = (y - 1) / (x + 3)
Slope of TU = (y - 2) /[x - 6]
Slope of RU = Slope of ST
(y - 1) / (x + 3) = -2/3
3y - 3 = -2x -6
2x + 3y = -6 + 3
2x + 3y = -3 (1)
Slope of RS = Slope of TU
0.5 = (y - 2) /[x - 6]
0.5x - 3 = y - 2
0.5x - y = 1 (2)
Solving 1 and 2 simultaneously gives:
x = 0, y = -1
Therefore the coordinates of U = (0, -1)
What is the best estimate
4.79 + 13.02
Answers
Answer:
17.81, but I would estimate 17.80 so it doesnt look exact.
Step-by-step explanation:
Write the rule for the transformation.
Answers
Here is an example,
Original Coordinates:
S (-5,3)
X (-4,-2)
U (-2,-1)
New"moved" coordinates:
S(5,-3)
X (4,2)
U (2,1)
Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.9 millimeters (mm) and a standard deviation of 1.2 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)
(a) the thickness is less than 3.0 mm
(b) the thickness is more than 7.0 mm
(c) the thickness is between 3.0 mm and 7.0 mm
Answers
Answer:
a) The probability that the thickness is less than 3.0 mm
P(X<3.0) = 0.057
b) The probability that the thickness is less than 7.0 mm
P(X>7) = 0.0401
c) The probability that the thickness is between 3.0 mm and 7.0 mm
P( 3 < x < 7)= 0.9029
Step-by-step explanation:
Step(i):-
Given mean of the Population (μ) = 4.9 mm
Standard deviation of the Population(σ) = 1.2 mm
a)
Let 'X' be the random variable in normal distribution
[tex]Z = \frac{x-mean}{S.D} = \frac{3.0-4.9}{1.2} = -1.583[/tex]
The probability that the thickness is less than 3.0 mm
[tex]P(X<3.0) = P(Z < -1.583) = 1 - P( Z>1.583)[/tex]
= 1 - ( 0.5 + A(1.583)
= 0.5 - A(1.583)
= 0.5 - 0.4430
= 0.057
The probability that the thickness is less than 3.0 mm
P(X<3.0) = 0.057
b)
Let 'X' be the random variable in normal distribution
[tex]Z = \frac{x-mean}{S.D} = \frac{7.0-4.9}{1.2} = 1.75[/tex]
The probability that the thickness is less than 7.0 mm
[tex]P(X>7.0) = P(Z >1.75) = 0.5 - A(1.75)[/tex]
= 0.5 - 0.4599 ( from normal table )
= 0.0401
The probability that the thickness is less than 7.0 mm
P(X>7) = 0.0401
c)
Let 'X' be the random variable in normal distribution
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{3.0-4.9}{1.2} = -1.583[/tex]
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{7.0-4.9}{1.2} = 1.75[/tex]
The probability that the thickness is between 3.0 mm and 7.0 mm
P( 3 < x < 7) = P( - 1.583 < X < 1.75 )
= A( 1.75 ) + A( -1.583)
= A(1.75)+A(1.583)
= 0.4599 + 0.4430
= 0.9029
The probability that the thickness is between 3.0 mm and 7.0 mm
P( 3 < x < 7)= 0.9029
what is 8÷530 TYPE FAST
Answers
Answer:
0.0150
Step-by-step explanation:
8÷530
0.0150
it is correct
An equilateral triangle has a side length of 12sqrt(3) inches. What is the length of the altitude of the triangle?
HELP ASAP
Answers
Answer:
18 inches.
Step-by-step explanation:
Let x inches be the altitude of the triangle.
By Pythagoras Theorem,
[6sqrt(3)]^2 + x^2 = [12sqrt(3)]^2
108 + x^2 = 432
x^2 = 324
x = 18
So the altitude of the triangle is 18 inches.