Answer:
1) Factor the denominator and the numerator of each fraction.
2) Simplify.
3) Find the Least common denominator (LCD).
4) Rewrite the LCD. Divide it by the denominator of the first fraction and multiply the result of the division by its numerator (The LCD is the same denominator of the second fraction, so its numerator stays the same).
5) Apply Distributive property on the numerator and on the denominator.
6) Add like terms.
Step-by-step explanation:
The steps required to determine the sum of the two expressions are:
1) Factor the denominator and the numerator of each fraction:
[tex]\frac{3x+6}{x^2-x-6}+\frac{2x}{x^2+x-12}=\frac{3(x+2)}{(x-3)(x+2)}+\frac{2x}{(x-3)(x+4)}[/tex]
2) Simplify (Remember that [tex]\frac{(x+2)}{(x+2)}=1[/tex]):
[tex]\frac{3}{(x-3)}+\frac{2x}{(x-3)(x+4)}[/tex]
3) Find the Least common denominator (LCD). In this case this is:
[tex]LCD=(x-3)(x+4)[/tex]
4) Rewrite the LCD. Divide it by the denominator of the first fraction and multiply the result of the division by its numerator. As the LCD is the same denominator of the second fraction, its numerator stays the same:
[tex]=\frac{3(x+4)+2x}{(x-3)(x+4)}[/tex]
5) Apply Distributive property on the numerator and on the denominator:
[tex]=\frac{3x+12+2x}{x^2+x-12}[/tex]
6) Add like terms:
[tex]=\frac{5x+12}{x^2+x-12}[/tex]
Answer:
x-5 edg
Step-by-step explanation:
I have 11 red marbles and 4 blue marbles in a bag if I choose one what color will it be
it will most likely be red
Red
The simplified ratio is for every 1 blue marble there is 2.75 red marbles. Do you are more likely to pull out red.
write the expression in complete factored form. (x+8) - q(x+8) =
Answer:
-q+1(x+8)
Step-by-step explanation:
It is this because (x+8) is the same so you just add the numbers+variables that x+8 is being multiplied.
Hope this helped
Need help ASAP!!!!!!
Answer:
Mean = 2.95
Median = 3
Step-by-step explanation:
The mean of the number of visits of 40 adults to the gym is
[tex]\dfrac{0\cdot 4+1\cdot 3+2\cdot 12+3\cdot 5+4\cdot 8+5\cdot 5+6\cdot 2+7\cdot 1}{40}=\\ \\=\dfrac{3+24+15+32+25+12+7}{40}=\dfrac{118}{40}=2.95[/tex]
The median of the data is the average number between 20th and 21th terms (because 40 is even number, so the middle term is the average between two middle terms).
20th term = 3 visits
21th term = 3 visits
Hence, median is 3 visits
I need help in these please
1) The sum of an Octagon is 1080°
And all it's sides are congruent (same size, same angle measure)
And an Octagon has 8 sides
So do,
1080 ÷ 8 = 135°
Each side equals to 135°
2) A triangle adds up to 180°.
We have one angle that's 45° and another angle that has a little □ in it.
That little square (□) is called a right angle which = 90°
So do
90 + 45 = 135
180 - 135 = 45
So the value of x is 45°
A diameter of a circle had endpoints of (-5, 6) and (-5,-2). What is the equation of this circle?
Answer: OPTION A
Step-by-step explanation:
Apply the formula for calculate the distance between two points to know the value of the diameter of the circle:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\D=\sqrt{(-5-(-5))^2+(-2-6)^2}\\D=8[/tex]
The equation of the circle is standard form is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where r is the radius and (h,k) is the point of the center of the circle.
As we know the diameter, we can find the radius:
[tex]r=\frac{8}{2}=4[/tex]
Substitute it into the equation:
[tex](x-h)^2+(y-k)^2=(4)^2[/tex]
[tex](x-h)^2+(y-k)^2=16[/tex]
Then, the answer is:
[tex](x+5)^2+(y-2)^2=16[/tex]
the equation x^2/121 + y^2/1. what points are the vertices of the eclipse
This is a probability problem. Please help me and explain how you came upon your answer.
Answer:
151
Step-by-step explanation:
The relative frequency of an item is calculated by dividing the item’s frequency by total frequency.
Relative Frequency=f/(∑f)
Since we know the relative frequency of peanut butter flavored treats and total number of treats, we can use both the values to calculate the frequency of peanut butter flavored treats
Putting the value of relative frequency of peanut butter flavored treats and total frequency in the above formula
0.302= f/500
f=0.302*500
f=151
What is the product of any integer and -1
Answer:
The negative counterpart
Step-by-step explanation:
x * -1 = -x
For example, 3 * -1 = -3
Hope this helps.
Product of any integer and -1 is negative/positive integer.
For example:
2 • -1 = -2, but
-2 • -1 = 2.
Which point is the solution to the following system of equations?
x2 + y2 = 13
2x - y = 4
(3, 2)
(2, 3)
(-3, -2)
(-2, -3)
Answer:
Its the point (3, 2).
Step-by-step explanation:
x^2 + y^2 = 13
2x - y = 4
From the second equation y = 2x - 4 so substituting in first equation:
x^2 + (2x - 4)^2 = 13
x^2 + 4x^2 - 16x + 16 = 13
5x^2 - 16x + 3 = 0
(5x - 1 )(x - 3) = 0
x = 0.2, 3.
Substitute x = 3 in the second equation:
2(3) - y = 4
y = 6 - 4 = 2.
which equation is a radical equation?
[tex]3d = \sqrt{d + 5} \: is \: a \: radical \: equation[/tex]
[tex]3d = \sqrt{d+5}[/tex] is a radical equation.
What is a radical equation?A radical equation is an equation in which a variable is under a radical.
According to the given question.
We have some equation in variables d, n, and h.
If we see the given equation only the equation [tex]3d = \sqrt{d+5}[/tex] is a radical equation because this is a equation in variable d and its variable is under radical sign(√).
And the other equations are not radical equations because no single variable of the given equations is under radical sign(√).
Hence, [tex]3d = \sqrt{d+5}[/tex] is a radical equation.
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Jen spent $20 at the fair. She spent half of her money on admission and 18% on food. If she spent the rest on rides, how much did she spend on rides?
Step-by-step explanation:
Half of 20 is 10.
18 percent of 20 is 3.6
20-13.6 is 6.4 so she spent
6 dollars and 40 cents on rides
The length of a rectangle is 2 times its width . If the perimeter of the rectangle is 36 inches, find its length and width
Answer:
Step-by-step explanation
If breadth =x
Length =2x
Perimeter = 2x +x +2x+x
36=6x
X=6
Therefore breadth =6
Length =12
The question asks about finding the length and width of a rectangle given its perimeter. By setting up and solving an equation, we found that the rectangle's width is 6 inches, and its length is 12 inches.
Explanation:Given that the length of a rectangle is 2 times its width, and the perimeter of the rectangle is 36 inches, we are asked to find the length and width of the rectangle. We can start by defining the width as 'w' and the length as '2w'. The formula for the perimeter of a rectangle is 2(length + width). We can substitute our definitions of length and width into this formula to get 2(2w + w) = 36. Simplifying this gives 3w = 18, so the width is 6 inches. Therefore, the length is 2 × 6 = 12 inches.
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I'm having trouble with figuring out a question in algebra. It is: 1/8 times x = 1.
Answer:
8
Step-by-step explanation:
answer is 8 because 1/8 times 8 equals 1
lin is shopping for a couch with her dad and hears him ask the salesperson how much is your commission the salesperson says that her commission is 5 1/2% of rhe selling price
A. $27.23
B. $ 467.77
Complete Question goes thus
Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5½% of the selling price.
A.How much commission will the salesperson earn by selling a couch for $495?
B.How much money will the store get from the sale of the couch?
Answer:
a. The total commission is $27.28
b. The store will get $468.72 from the sale of the couch
Step-by-step explanation:
a.
Commission can be referred to as the reward given by the company on goods for the employee to sell products in order to make more sales and more money.
Commission is calculated as follows:
Total commission = Total Sales * Commission Percentage
Given
Total Sales = $495
Commission Percentage = 5½%
Substitute in, the above values
Total Commission = $496 * 5½%
Total Commission = $496 * 5.5%
Total Commission = $496 * 0.055
Total Commission = $27.28
Hence, the total commission is calculated as $27.28
b. The amount remitted to the store is calculated as
Amount = Total Sales - Total Commission
Where Total Sales = $496
Total Commission = $27.28
Amount = $496 - $27.28
Amount = $468.72
Hence, the store will get $468.72 from the sale of the couch
might just use all of my 900 remaining points on my next random questions
Answer:
do what you want
Step-by-step explanation:
Answer
Maybe you can ask a good question that can help you?
What is the volume of the cone below radius 4 height 27? NEED HELP ASAP THX
The volume of the cone is 144π units³
Given,
Radius of cone (r) = 4
Height of cone (h) = 27
What is the volume of a cone?The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.
∵ Volume of the cone (V)=1/3πhr²
Substitute the values of h and r,
V = 1/3π(27)(4)²
V = 144π units³
Hence, The volume of the cone is 144π units³
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what is the 19th term of a geometric sequence where a1=8 and a9=360. Round the common ratio and 19th term to the nearest hundredth.
REALLY need help on this one please please.
Answer:
Step-by-step explanation:
[tex]a_{1} = 8\\a_{9} = 360 = a_{1} \cdot r^9 = 8 \cdot r^9\\r = \sqrt[9]{\frac{360}{9} } \cong 1.53[/tex]
By the formula of a geometric series:
[tex]S_{n} = a \cdot \frac{1-r^n}{1-r} => S_{19} = 8 \cdot \frac{1-1.53^{19}}{1-1.53} = 6091.54[/tex]
Answer:
r = 1.6
a19 = 37800
Step-by-step explanation:
First term [tex] a_1 = 8 [/tex] and [tex] a_9 = 360 [/tex] of a geometric sequence and we are to find the 19th term along with the common ratio for this sequence.
We know that the general term of a Geometric Sequence is given by:
[tex]a_n= a \cdot r^{n-1}[/tex]
where [tex]a_n[/tex] is the nth term, [tex]a[/tex] is the first term, [tex]n[/tex] is the number of terms and [tex]r[/tex] is the common ratio.
Substituting the given values in the above formula to get:
[tex]360 = (8)*(r)^(9-1)[/tex]
[tex]360 = 8*(r^8)[/tex]
[tex]r^8 = \frac{360}{8}[/tex]
[tex]r^8 = 45[/tex]
r = 1.6
Finding the 19th term:
[tex]a_n= a \cdot r^{n-1}[/tex]
[tex]a_{19}= 8 \cdot 1.6^{19-1}[/tex]
a19 = 37800
Please help. Ima have to turn this is tomorrow.
Answer:
A) 7x + (-2)
B) 2x + (-12)
C) 4x + (-16)
D) 6x - 4
Step-by-step explanation:
A=
(-1) + 4x + 2 + 2x + x
7x + (-1) + 2
7x + (-2)
B=
-8x + 4 + (-3) + 10x
2x + 4 + (-3)
2x + (-12)
C=
(-4) + 1x (Squared) + 3x + 4
(-16) + 1x (Squared) + 3x
(-16) + 1x + 3x
4x + (-16)
D=
2(3x - 2)
(6x - 4)
6x - 4
In this figure a || b Find the measure of each angle using either of the given angle measures. Identify the reason for each answer
∠1
∠2
∠3
∠4
∠5
∠6
Answer:
[tex]m<1=99\°[/tex]
[tex]m<2=81\°[/tex]
[tex]m<3=86\°[/tex]
[tex]m<4=86\°[/tex]
[tex]m<5=86\°[/tex]
[tex]m<6=94\°[/tex]
Step-by-step explanation:
Part 1) Find the measure of angle 1
we know that
[tex]m<1+81\°=180\°[/tex] -----> by supplementary angles
[tex]m<1=180\°-81\°=99\°[/tex]
Part 2) Find the measure of angle 2
we know that
[tex]m<2=81\°[/tex] -----> by alternate exterior angles
Part 3) Find the measure of angle 3
we know that
[tex]m<3=86\°[/tex] -----> by vertical angles
Part 4) Find the measure of angle 4
we know that
[tex]m<4=86\°[/tex] ------> by corresponding angles
Part 5) Find the measure of angle 5
we know that
[tex]m<5=m<4[/tex] -----> by vertical angles
so
[tex]m<5=86\°[/tex]
Part 6) Find the measure of angle 6
we know that
[tex]m<5+m<6=180\°[/tex] -----> by supplementary angles
we have
[tex]m<5=86\°[/tex]
substitute
[tex]86\°+m<6=180\°[/tex]
[tex]m<6=180\°-86\°=94\°[/tex]
A scientist looks at a bacterium and a virus in a lab. The bacterium has a diameter of meters. The virus has a diameter of meters. Which statement accurately compares the sizes of the specimens?
Answer:
"The diameter of the bacterium is 10 times greater than that of the virus."
Step-by-step explanation:
Size of bacteria is 10^-6
Size of virus is 10^-7
Definitely the bacteria is larger. How many times larger? We find that by dividing the diameter of bacterium by the diameter of virus.
Let's do this:
[tex]\frac{10^{-6}}{10^{-7}}\\=\frac{0.000001}{0.0000001}\\=10[/tex]
Hence, the bacterium is 10 times larger than the virus
Answer:
I got A) "The diameter of the bacterium is 10 times greater than that of the virus."
Step-by-step explanation:
Triangle ABC has measures a equals 2 b equals 2 and angle a equals 30 degrees what is the measure of angle B
The answer is: Angle B is 30°
Why?Since we know that both sides, a and b are equal to 2, and angle A is equal to 30°, we can conclude that angle B is also equal to 30°. Also, we can know that the other angle (C) will be equal to 120° since the sum of all the angles in a triangle will be always equal to 180°.
Have a nice day!
Answer:
B: 30 degrees
Step-by-step explanation:
a=2
b=2
<b = 30
Scoot has 9 t-shirts and 6 dress shirts in his wardrobe. What is the probability of selecting a dress shirt from his wardrobe?
Step-by-step explanation:
He has 15 total shirts. 9+6. So P(Dress shirt) is 6/15 or 2/5 or 40 percent.
Write an equation that gives the proportional relationship of the graph. A) y = 1 3 x B) y = 2x C) y = 3x D) y = 6x
Answer:
C
Step-by-step explanation:
A proportional graph is a line. Every line has a slope. The slope is found by subtracting two points as a ratio. The line has points (0,0) and (2,6).
6-0 = 6
2 -0 = 2
The ratio is vertical over horizontal so 6/2 = 3.
The equation is y = 3x.
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Answer:
C) y = 3xStep-by-step explanation:
The given graph show a proportional relationship that it's modelled by a linear equation. We can make all the process to calculate the equation that belongs to that behaviour. We just have to find the slope:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}} \\m=\frac{18}{6}=3[/tex]
Using the slope interception formula: [tex]y=mx+b[/tex]
[tex]y=3x+0[/tex]
Because the interception with the vertical axis is null, so the equation would be:
[tex]y=3x[/tex]
Therefore the answer is C.
Whats 39762863x756827549852??
3.00936e19 is the answer
factor a(p–q)+q–p PPPLLZ
Answer:
(p-q)(a-1)
Step-by-step explanation:
a x (p-q) -1 (p-q) extract the negative sign
(p-q) x (a-1) fact p-q from expression
(p-q)(a-1)
Answer:
Apq is the answer
Step-by-step explanation:
What is the area of this figure?
A) 48 in2
B) 53 in2
C) 56 in2
D) 83 in2
That's correct is C, thanks
Answer:
the answer is C
Step-by-step explanation:
Convert 3.5 yards to feet round answers to the nearest tenth
Answer:
The answer is B. 10.5 feet
Step-by-step explanation:
In every one yard there's three feet.
3.5 X 3 = 10.5
Hope this helps :)
If the points(1,2),(2,6),and (3,y) are on line L, then y =
A)6
B)8
C)10
D)12
Answer:
C
Step-by-step explanation:
If we're assuming the graph is linear, we can see that every 1 x value it goes up, the y value is upped by 4.
6+4=10
So therefore the value of y in (3,y) is 10.
Which is a correct first step for solving this equation? -2x+7+5x-4=2x-6
Answer:
I gave you the first step(s) for solving it, now learn. Comment on this if you still don't get it.
Step-by-step explanation:
Solve -2x+7 first
then 5x+4
then 2x-6
Answer:
x= -9
Step-by-step explanation:
-2x+7+5x-4=2x-6
first you need to combined like term
3x + 3 = 2x-6
-3 -3
3x = 2x-9
-2x -2x
1x = -9
1x is x and x equal -9
Which rate is the fastest?
A ) 589 miles in 11 hours
B ) 360 miles in 7 hours
C ) 111 miles in 2 hours
D ) 283 miles in 5 hours
Answer:
d
Step-by-step explanation:
divide the miles by the time
283 divided by 5 is 56.6 which is the greatest so it is the fastest