Answer:
C) [tex]\frac{2z+15}{6x-12y}[/tex]
E) [tex]\frac{7d+5}{15d^2+14d+3}[/tex]
F) [tex]\frac{-7a-b}{6b-4a}[/tex]
Step-by-step explanation:
C)
One is given the following equation
[tex]\frac{z+1}{x-2y}-\frac{2z-3}{2x-4y}+\frac{z}{3x-6y}[/tex]
In order to simplify fractions, one must convert the fractions to a common denominator. The common denominator is the least common multiple between the given denominators. Please note that the denominator is the number under the fraction bar of a fraction. In this case, the least common multiple of the denominators is ([tex]6x-12y[/tex]). Multiply the numerator and denominator of each fraction by the respective value in order to convert the fraction's denominator to the least common multiple,
[tex]\frac{z+1}{x-2y}-\frac{2z-3}{2x-4y}+\frac{z}{3x-6y}[/tex]
[tex]\frac{z+1}{x-2y}*\frac{6}{6}-\frac{2z-3}{2x-4y}*\frac{3}{3}+\frac{z}{3x-6y}*\frac{2}{2}[/tex]
Simplify,
[tex]\frac{z+1}{x-2y}*\frac{6}{6}-\frac{2z-3}{2x-4y}*\frac{3}{3}+\frac{z}{3x-6y}*\frac{2}{2}[/tex]
[tex]\frac{6z+6}{6x-12y}-\frac{6z-9}{6x-12y}+\frac{2z}{6x-12y}[/tex]
[tex]\frac{(6z+6)-(6z-9)+(2z)}{6x-12y}[/tex]
[tex]\frac{6z+6-6z+9+2z}{6x-12y}[/tex]
[tex]\frac{2z+15}{6x-12y}[/tex]
E)
In this case, one is given the problem that is as follows:
[tex]\frac{2}{3d+1}-\frac{1}{5d+3}[/tex]
Use a similar strategy to solve this problem as used in part (c). Please note that in this case, the least common multiple of the two denominators is the product of the two denominators. In other words, the following value: ([tex](3d+1)(5d+3)[/tex])
[tex]\frac{2}{3d+1}-\frac{1}{5d+3}[/tex]
[tex]\frac{2}{3d+1}*\frac{5d+3}{5d+3}-\frac{1}{5d+3}*\frac{3d+1}{3d+1}[/tex]
Simplify,
[tex]\frac{2}{3d+1}*\frac{5d+3}{5d+3}-\frac{1}{5d+3}*\frac{3d+1}{3d+1}[/tex]
[tex]\frac{2(5d+3)}{(3d+1)(5d+3)}-\frac{1(3d+1)}{(5d+3)(3d+1)}[/tex]
[tex]\frac{10d+6}{(3d+1)(5d+3)}-\frac{3d+1}{(5d+3)(3d+1)}[/tex]
[tex]\frac{(10d+6)-(3d+1)}{(3d+1)(5d+3)}[/tex]
[tex]\frac{10d+6-3d-1}{(3d+1)(5d+3)}[/tex]
[tex]\frac{7d+5}{(3d+1)(5d+3)}[/tex]
[tex]\frac{7d+5}{15d^2+14d+3}[/tex]
F)
The final problem one is given is the following:
[tex]\frac{3a}{2a-3b}-\frac{a+b}{6b-4a}[/tex]
For this problem, one can use the same strategy to solve it as used in parts (c) and (e). The least common multiple of the two denominators is ([tex]6b-4a[/tex]). Multiply the first fraction by a certain value to attain this denomaintor,
[tex]\frac{3a}{2a-3b}-\frac{a+b}{6b-4a}[/tex]
[tex]\frac{3a}{2a-3b}*\frac{-2}{-2}-\frac{a+b}{6b-4a}[/tex]
Simplify,
[tex]\frac{3a}{2a-3b}*\frac{-2}{-2}-\frac{a+b}{6b-4a}[/tex]
[tex]\frac{-6a}{6b-4a}-\frac{a+b}{6b-4a}[/tex]
[tex]\frac{(-6a)-(a+b)}{6b-4a}[/tex]
[tex]\frac{-6a-a-b}{6b-4a}[/tex]
[tex]\frac{-7a-b}{6b-4a}[/tex]
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 3 1/2" by 5 1/4" on the drawing, how large is the bedroom?
A. 20 ft by 30 ft
B. 7ft by 10.5 ft
C. 14 ft by 21 ft
D. 10 ft by 15 ft
Answer:
C. 14 ft by 21 ft
Step-by-step explanation:
First you want to set up an equation:
3 1/2" over x' = 1/4" over 1'
7/2 = 1/4x
14' = x
Next, do the same thing for the other side of the drawing (5 1/4")
5 1/4" over y' = 1/4" over 1'
21/4 = 1/4y
21' = y
So the answer is 14 ft by 21 ft (C)
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
Which congruence theorem can be used to prove
ABR = RCA?
Answer: The HL Theorem can be used to prove ABR ≅ RCA because both triangles share the same hypotenuse and a leg. The HL theorem states that If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
Sum of zeroes of polynomial 2x²-x-3 is ? Full solved answers ✔ No spam ❌
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 , then the sum of the roots is
α + β = - [tex]\frac{b}{a}[/tex]
Here 2x² - x - 3 = 0 is in standard form
with a = 2 and b = - 1 , then
sum of roots = - [tex]\frac{-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]
Factorise each expression 8 - 2v²
Answer:
hello thereee
8 - 2v^2 we are suppose to facotrize...
2 ( 4 - v^2 )
2 ( 2^2 - v^2 )
apply identity a^2 - b^2
2 ( 2 + v ) ( 2- v )
done dana done.....
plssssss help me answer this quickly
Answer:
Step-by-step explanation:
y = 4x – 10
y = 2
What is the solution to the system of equations?
(3, 2)
(2, 3)
(–2, 2)
(2, –2)
Answer:
(3,2)
Step-by-step explanation:
y = 4x – 10
y = 2
Substitute the second equation into the first
2 = 4x-10
Add 10 to each side
2+10 = 4x-10+10
12 = 4x
Divide each side by 4
12/4 =4x/4
3 = x
The solution is
(3,2)
Answer:
(3,2)
Step-by-step explanation:
y = 4x – 10...(1) y = 2...(2) You have y=2 here, substitute it in equation (1),
y = 4x – 10 2 = 4x – 10
Add both sides by 10 12=4x
Divide both sides by 4 x=3
We have x=3, and y=2. ==> (x,y) = (3,2)
If there are:
6 red marbles
10 yellow marbles
5 green marbles
and 1 blue marble
What is the probability of picking 1 red marble and 1 green marble?
(Once a marble is chosen it IS put back into the box).
(Write your answer in the form of a decimal, round to 2 places).
Answer:
0.06
Step-by-step explanation:
Total number of marbles:
6 + 10 + 5 + 1 = 22 marbles
Probability of picking 1 red marble:
red marbles / total marbles
6/22
Probability of picking a green marble:
green marbles / total marbles
5/22
Now, multiply the probabilities:
6/22 • 5/22 = 15/242 = 0.06
Please tell me whats the number?
Answer:
5/6
Step-by-step explanation:
15/18
Divide the top and bottom by 3
15/3 = 5
18/3 = 6
5/6
I have simplified:)
To simplify, you have to divide the numerator & denominator by 3
BTW,I am also an Acellus student!:)
please help me in solving this
Answer:
it can be 5 from my side is that right
Answer:
is ur question right
Step-by-step explanation:
is ur question right
is ur question right
is ur question right
what’s is the quotient for the rational expression shown below?
Answer:
D
Step-by-step explanation:
D is the correct answer
Please help, I’ll give brainly!!!
Answer:
9.
3 ( 1 - 3x ) = 2 (-4x + 7)
3 - 9x = -8x +14
-9x +8x = 14 - 3
-x = 11
x = -11
10.
-10 + x + 4 - 5 = 7x - 5
-10 +x -1 = 7x - 5
-11 + x = 7x - 5
-11 + 5 = 7x -x
-6 = 6x
x = -6/6
x = -1
11.
-8n + 4 ( 1 + 5n ) = -6n -14
-8n + 4 + 20n = -6n -14
12n +4 = -6n -14
12n + 6n = -14 -4
18n = -18
n = -18/18
n = -1
12.
-6n - 20 = -2n + 4 ( 1 - 3n)
-6n - 20 = -2n + 4 - 12n
-6n - 20 = -14n +4
-20 -4 = -14n +6n
-24 = 8n
n = -24/8
n = -3
13.
4n - 40 = 7 (-2n +2)
4n - 40 = -14n + 14
4n +14n = 14 +40
18n = 54
n = 54 / 18
n = 3
14.
7(5a - 4) -1 = 14 - 8a
35a -28 -1 = 14 - 8a
35a -29 = 14 - 8a
35a +8a = 14 +29
43a = 43
a = 43/43
a = 1
15.
-31 - 4x = -5 - 5 ( 1 + 5x)
-31 - 4x = -5 -5 - 25x
-31 - 4x = -10 -25x
-4x +25x = -10 +31
21x = 21
x = 21/21
x = 1
16.
38 +7k = 8 (k +4)
38 +7k = 8k + 32
38 - 32 = 8k -7k
k = 6
pls help
The equation of a line parallel to 6x – 2y + 10 = 0 and passes through the point
(-2,7).
Answer:
y=3x-1
Step-by-step explanation:
First we need to rewrite 6x-2y+10 =0 into the standard slope form of y=mx+b when done you get y=3x+5Next we need an equation that passes through the point (-2,7). Now remember equations that are parallel have the same slope so the equation should look like y=3xIn standard slope form the b is the y-intercept. We now need to plug in the x ordered pair value into the standard slope equation. y=3(-2)+5 to get y=-1 meaning -1 is the y-intercept Therefore the answer is y=3x-1Answer:
Y = 3X + 13
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
6x - 2y + 10 = 0 ( subtract 6x + 10 from both sides )
- 2y = - 6x - 10 ( divide terms by - 2 )
y = 3x + 5 ← in slope- intercept form
with slope m = 3
Parallel lines have equal slopes , so
y = 3x + c ← is the partial equation
To find c substitute (- 2, 7 ) into the partial equation
7 = - 6 + c ⇒ c = 7 + 6 = 13
y = 3x + 13 ← equation of line in slope- intercept form
how many solutions does the equation below have? 3x-8=-2x+9/3
Answer:
1
Step-by-step explanation:
[tex]\\ \sf\longmapsto 3x-8=-2x+\dfrac{9}{3}[/tex]
[tex]\\ \sf\longmapsto 3x-8=-2x+3[/tex]
[tex]\\ \sf\longmapsto 3x+2x=3+8[/tex]
[tex]\\ \sf\longmapsto 5x=11[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{11}{5}[/tex]
3. A publishing house is selling subscriptions to its magazines for 20% off the original price. If a
subscription to Newsweek Magazine is on sale for $72, how much does it usually cost?]
a) $14.40
b) $57.60
c) $86.40
d) $90
Find the average rate of change of a function that contains the points (-2,3) and (2,5). -2, -1/2, 1/2, 2
Answer:
The answer is "[tex]\frac{1}{2}[/tex]".
Step-by-step explanation:
Given points:
[tex](-2,3)\\\\(2,5)\\\\[/tex]
average rate=?
[tex]x_1=-2\\\\y_1=3\\\\x_2=2\\\\y_2=5[/tex]
[tex]average\ rate=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]=\frac{5-3}{2-(-2)}\\\\=\frac{5-3}{2+2}\\\\=\frac{2}{4}\\\\=\frac{1}{2}[/tex]
Solve the equation. The letters a, b, and c are constants and a≠0
ax-76 = 9c
i’m confused bc it doesn’t tell me what i’m solving for. please help! thank you!
Answer:
Step-by-step explanation:
Probably it's asking for x so you have to find x in term of a and c
ax = 9c+76
x = 9c+76/a
Answer:
Step-by-step explanation:
I can see your problem. That's one of those questions where the directions are part of the problem. I think you are supposed to solve for x.
ax-76 = 9c Add 76 to both sides
ax = 9x + 76 Divide by a
x = (9x + 76)/a
Using only the values given in the table for the function f(x) = x^3 - 3x - 2 what is the interval of x-values over which the function is decreasing?
Answer:
3 = 3(x² - 1) We know, any Function f(x) decrease s in interval [a, b] when f'(x) < 0 ... -1 < x < 1. Hence, function f(x) = x³ - 3x - 2 , is decreased in (-1, 1).
-3z-z
HELP PLZ
Hahsjsjsnsksns snskskd
Answer:
-4z
Step-by-step explanation:
-3z-z
= -4z
Answer:
-4
Step-by-step explanation:
[tex] - 3z - z[/tex]
[tex] - 3z - 1z[/tex]
[tex]( - 3 - 1)z = - 3 - 1[/tex]
[tex] - (3 - 1)[/tex]
[tex] = - 4z[/tex]
Plz help........
1. -1114 ÷ ( - 117)
2. -212 ÷ ( -123)
3. - 512 ÷ 58
4. 27 ÷ ( -79)
Answer:
1. 1114/117 2. 212/123 3. -256/29 4. -27/79
Step-by-step explanation:
1. 1114/117
2. 212/123
3. -256/29
4. -27/79
Which expression below equals a rational number, choose all that apply.
Please help.
Answer:
BELOW IN BOLD.
Step-by-step explanation:
4/5 + 3/8
= 47 / 49 which id Rational
√100 + √5
= 10 + √5; - Irrational
7√5 - √245
=7√5 - 7√5
= 0 RATIONAL
Next one = 56 so Rational
Last one is Irrational
sin 6x +4sin²3x= 0
sin x + sin 5x = sin 2x . sin 3x
tan 4x. tan 2x = -1
sin 5x + cos 5x - sin x + cos x =√2 cos 3x
cos 5x . cos x + sin³2x = cos 3x . cos x
Answer:
no entendi muy bien sorry
Help me please I need this
Answer:
2 times
Step-by-step explanation:
3/4 × 2 = 6/4, simplified down is 3/2
Answer: the answer is a
Solve each of the following exponential equations using common bases:
1.) 4^(3x+5)=8^(4x-3)
2.) 9^(2x+3)=〖(1/27)〗^(3x+1)
3.) 4^(x+6)∙8^(x-9)=64
Answer:
x=19/6, x=-9/13, x=33/4
Step-by-step explanation:
1) 2^(6x+10)=2^(12x-9), 6x+10=12x-9, x=19/6
2) 3^(4x+6)=3^(-9x-3), 4x+6=-9x-3, x=-9/13
3) 2^(x+6)*2^(3x-27)=2^(6), 4x-27=6, x=33/4
Which series represents this situation? 1+1*7+1*7^ 2 +...1*7^ 6; 1+1*7+1*7^ 2 +...1*7^ 7; 7+1*7+1*7^ 2 +... 1*7^ 6; 7+1*7+1*7^ 2 +...1*7^ 7
Answer:
Step-by-step explanation:
The series is missing from the question. I will answer this question with a general explanation by using the following similar series:
[tex]\sum\limits^6_{n=0} 7^n[/tex]
Required
The series
To do this, we simply replace n with the values
[tex]\sum\limits^6_{n=0}[/tex] means n starts from 0 and ends at 6
[tex]\sum[/tex] means the series is a summation series
So, we have:
[tex]\sum\limits^6_{n=0} 7^n = 7^0 + 7^1 + 7^2 + ...... + 7^6[/tex]
[tex]\sum\limits^6_{n=0} 7^n = 1 + 7 + 7^2 + ...... + 7^6[/tex]
RSM wants to send four of its 18 Math Challenge teachers to a conference. How many combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan?
Answer:
1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.
Step-by-step explanation:
The order in which the teachers are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
1 from a set of 2(Either Mrs. Vera or Mr. Jan).
3 from a set of 18 - 2 = 16. So
[tex]C_{2,1}C_{16,3} = \frac{2!}{1!1!} \times \frac{16!}{3!13!} = 1120[/tex]
1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.
x/-2-3>2
SOlve the inequality
Answer:
x ∠ -10
Step-by-step explanation:
Answer:
[tex]x>-10[/tex]
Step-by-step explanation:
[tex]\frac{x}{-2} -3>2[/tex]
[tex]\frac{x}{-2} > 5[/tex]
[tex]x=-2[/tex] × [tex]5[/tex]
[tex]x>-10[/tex]
Luz made a semicircular pendant with a radius of 8 centimeters to use on a key chain. She attached a wire around the edge of the pendant.
What is the approximate length of the wire she attached to the pendant?
41.13
50.27
The approximate length of the wire she attached to the pendant is 50.27
What is the approximate length of the wire she attached to the pendant?The radius is given as:
r = 8 cm
The approximate length of the wire she attached to the pendant is calculated as:
Length = 2pi r
Where
pi = 3.14
So, we have:
Length = 2 * 3.14 * 8
Evaluate the product
Length = 50.24
Hence, the approximate length of the wire she attached to the pendant is 50.27
Read more about circumference at:
https://brainly.com/question/14283575
#SPJ1
Answer: The answer is 41.13.
Step-by-step explanation: I took the quiz and none of the other answers were correct.
Times for an ambulance to respond to a medical emergency in a certain town are normally distributed with a
mean of 450 seconds and a standard deviation of 50 seconds.
Suppose there are 97 emergencies in that town.
In about how many emergencies are the response times expected between 400 seconds and 500 seconds?
31
33
47
66
Answer:
66
Step-by-step explanation:
The Empirical Rule states that 68% of data is between 1 standard deviation in a dataset of normal distribution, 95% falls between 2 standard deviations, and 99.7% between 3.
The mean is 450, and one standard deviation is between 450 ± 50 = 400 and 500. Therefore, we can say that 68% of the data falls between 400 and 500 seconds.
The data includes 97 emergencies, so we just need to find 68% of that, which is 0.68*97 = 65.96 (rounding up to 66)
There are 66 emergencies are the response times expected between 400 seconds and 500 seconds.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
mean = 450 sec
standard deviation = 50 sec
Hence, We get;
450-50 =400
450+50=500
Now, In Between 400 sec and 500 sec means one deviation above and one deviation below the mean, and it is 68%.
68% = 0.68
Thus,
0.68 x 97 = 65.96 ≈ 66
Learn more about the addition visit:
https://brainly.com/question/25421984
#SPJ2
Question 5(Multiple Choice Worth 1 points) (03.03 LC) If a figure has been dilated by a scale factor of 4, which statement explains how a translation can be used to prove the figures are similar using the AA similarity postulate? A translation can map one side onto another since dilations preserve side lengths of triangles. A translation can map one angle onto another since dilations preserve angle measures of triangles. A translation can map the center of a triangle onto another since dilations preserve the location of the center of triangles. A translation can map the vertices of one triangle onto another since dilations preserve the size of triangles.
Answer:
A translation can map one angle unto another since dilations preserve angle measures of triangles
Step-by-step explanation:
The dilation of the figure by a scale factor of 4 gives an image that is 4 times the size of the original figure. However, the interior angles of the image and the original figure remain the same
A translation is a rigid transformation, such that the image and the preimage of a translation transformation have the same dimensions and angles
A translation of three consecutive non-linear points of the dilated image to the vertex and the two lines joining the corresponding point on the image, translates the angle at the given vertex
The above process can be repeated, to translate a second angle from the image to the preimage, from which it can be shown that the two figures are similar using Angle Angle, AA, similarity postulate
Answer:
A translation because it can map one angle onto another since dilations preserve angle measures of triangles.
Step-by-step explanation:
