Answer:
The answer is "[tex]\frac{A}{(x-2)} + \frac{B}{(x+3)}[/tex]"
Step-by-step explanation:
Let the given value is: [tex]\frac{x-6}{x^2+x-6}[/tex]
[tex]\to \frac{x-6}{x^2+x-6}=\frac{x-6}{x^2+(3-2)x-6}\\\\[/tex]
[tex]=\frac{x-6}{x^2+(3-2)x-6}\\\\ =\frac{x-6}{x^2+3x-2x-6}\\\\ =\frac{x-6}{x(x+3)-2(x+3)}\\\\ =\frac{x-6}{(x+3)(x-2)}\\\\=\frac{A}{(x-2)} + \frac{B}{(x+3)}[/tex]
(Trigonometry) A ramp is needed to allow vehicles to climb a 2-foot wall. The angle of elevation for the vehicles to safely go up must be 30° or less, and the longest ramp available is 5 feet long. Can this ramp be used safely? Provide us with the angle x to the nearest 10th and a yes or no.
Answer:
The ramp is safe.
The unknown angle measure is, ([tex]23.6[/tex])
Step-by-step explanation:
Assume that the ground makes a (90) degree angle with the wall. This means that the formed triangle is a right triangle. Thus, one can use the right angle trigonometric ratios. These ratios are the following,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
The hypotenuse is the side opposite the right angle of a right triangle. This side's name doesn't change. However, the (opposite) and (adjacent) sides change names based on the angle one is using to describe them in the ratio.
In this case, one is given the side opposite to an angle, as well as the hypotenuse. However, one isn't given the measure of the angle. Thus, one should use the ratio of sine (sin) to find the unknown side. Let theta ([tex]\theta[/tex]) represent the measure of the unknown angle.
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
Substitute,
[tex]sin(\theta)=\frac{2}{5}[/tex]
Inverse operations,
[tex]\theta=sin^-1(\frac{2}{5})[/tex]
Simplify,
[tex]\theta=23.578178[/tex]
Since the value of ([tex]\theta[/tex]) is less than (30) degrees, the ramp can be used safely.
Which expression is equivalent to the given expression? -2x +8x -9 +4x +7x2 +2 A. B. C. D.
Answer:
The answer is "[tex]7x^2 +10x -7[/tex]"
Step-by-step explanation:
Let the given value is:
[tex]\to \bold{-2x +8x -9 +4x +7x^2 +2}\\\\[/tex]
Solving the given value:
[tex]\to7x^2 -2x +8x +4x-9 +2\\\\\to7x^2 +10x -7\\\\\to7x^2 +10x -7\\\\[/tex]
What is the area of a rectangle with a length of x + 5
and a width of 4?
Answer:
[tex]area = (length \times width) \\ = (x + 5) \times 4 \\ = (4x + 20) \: square \: units[/tex]
What is the solution of sqareroot 1-3x = X+3?
Answer:
x=-8 or x=-1 (first option)
Step-by-step explanation:
[tex]\sqrt{1-3x}=x+3\\1-3x=(x+3)^{2} \\[/tex]
now expand the bracket on the right
[tex]1-3x=x^{2} +6x+9\\simplify:\\1-9=x^2+6x+3x\\-8=x^2+9x\\[/tex]
now make it a quadratic equation:
[tex]x^2+9x+8=0\\factorise:\\(x+1)(x+8)\\so:\\x+1=0 \\x=-1\\\\and \\x+8=0\\x=-8[/tex]
Find the standard deviation of the data set shown. Round your answer to the nearest tenth.
4,5,9,1,2,5
The standard deviation is about_________
Mark Brainliest Please
Answer:
Answer is gicen in the image attached.
Step-by-step explanation:
Standard deviation (SD) measured the volatility or variability across a set of data. It is the measure of the spread of numbers in a data set from its mean value and can be represented using the sigma symbol (σ). The following algorithmic calculation tool makes it easy to quickly discover the mean, variance & SD of a data set.
For more help check Khan academy video
https://www.khanacademy.org/math/statistics-probability/displaying-describing-data/sample-standard-deviation/v/sample-standard-deviation-and-bias
Answer:
2.6
Step-by-step explanation:
To calculate standard deviation:
(1) Find the mean - 4.33
4 + 5 + 9 + 1 + 2 + 5 = 26 26 / 6 = 4.333... ≈ 4.33
(2) Subtract the mean from each value and square each result
[tex](4 - 4.33)^2 = 0.1089[/tex] [tex](5 - 4.33)^2 = 0.4489[/tex] [tex](9 - 4.33)^2 = 21.8089[/tex]
[tex](1 - 4.33)^2 = 11.0889[/tex] [tex](2 - 4.33)^2 = 5.4289[/tex] [tex](5 - 4.33)^2 = 0.4489[/tex]
(3) Find a new mean with the new values from the previous step
0.1089 + 0.4489 + 21.8089 + 11.0889 + 5.4289 + 0.4489 = 39.3334
39.3334 / 6 = 6.555566667
(4) Take the square root of the new mean.
[tex]\sqrt[]{x6.555566667} =2.560384086[/tex]
2.560384086 rounded to the nearest tenth is: 2.6
The function f(x)=300x/x^2+200 represents the monthly sales in hundreds of cds x months after the cd was released. Each statement interpretes a key feature of the function based on the table. Which statement is an interpretation of the end behavior
The rules of a game allow a team to score either 2 points or 5 points, depending on the nature of the scoring play. If the final score between two teams was 34 to 29, and there were 18 scoring plays altogether, how many 5-point plays were there?
Answer:
9
Step-by-step explanation:
Given that :
Total Number of scorings (both Teams) = 18
Let :
x = number of 5 point score ; y = number of 2 point score
Total points scored = 34 + 29 = 63
x + y = 18 - - - (1)
5x + 2y = 63 - - (2)
From (1)
y = 18 - x
In (2) ; we have ;
5x + 2(18 - x) = 63
5x + 36 - 2x = 63
3x + 36 = 63
3x = 63 - 36
3x = 27
x = 9
9 5-point plays
Answer:
9
Step-by-step explanation:
The area of the base of a cylinder is 42 square inches and its height is 11 inches. A cone has the same area
for its base and the same height. What is the volume of the cone?
I can't figure out the answer
Answer:
39
Step-by-step explanation:
y=arctan(0.8)=38.65=39
(x-1)²-(x-1)
Can anyone help me with factorising this
Answer:
(x - 1)(x - 2)
Step-by-step explanation:
Given
(x - 1)² - (x - 1) ← factor out (x - 1) from each term
= (x - 1)(x - 1 - 1)
= (x - 1)(x - 2)
i need help with this question somebody please help !
Answer:
15
Step-by-step explanation:
f(x)=2x^2-3x+1
f(-2)=2*(-2)^2 -(3*-2)+1
=2*4-(-6)+1
=8+6+1
=15
f(-2)= 15
OPTION C is the correct answer
please help!! i’ll give you brainliest
Answer:
4
Step-by-step explanation:
Answer:
m = 5
Step-by-step explanation:
to one side length of 4 to 2, we divided by 2 so why not divide 10 by 2
10 ÷ 2 = 5
Please give me brainliest!
Brette got a new phone! The length of her old rectangular phone screen was 44 centimeters. Her new rectangular phone screen is twice as long as the old screen. How much larger is the area of the new screen than the area of the old screen?
Answer:
2 times larger
Step-by-step explanation:
Area of a rectangle = length x width
assume width = 10
older area = 44 x 10 = 440
new area
length = 44 x 2 = 88
88 x 10 = 880
change in area = 880 / 440 = 2
Solve a / a-1 - a+5/a =0. Enter your solution as an improper fraction or as a decimal rounded to the nearest hundredth
Answer: [tex]1\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given
The equation in terms of a is
[tex]\Rightarrow \dfrac{a}{a-1}-\dfrac{a+5}{a}=0\\\\\Rightarrow \dfrac{a}{a-1}=\dfrac{a+5}{a}\\\\\Rightarrow a^2=(a-1)(a+5)\\\\\Rightarrow a^2=a^2+4a-5\\\\ \Rightarrow 4a=5\\\\\Rightarrow a=\dfrac{5}{4}\ \text{or}\ 1\dfrac{1}{4}[/tex]
In a square PQRS, PQ = 2x +3 cm and QR = 3x – 5 cm, then the value of x is
Answer:
x = 8 cm
Step-by-step explanation:
Given that,
In a square PQRS, PQ = 2x +3 cm and QR = 3x – 5 cm.
We need to find the value of x.
In a square, all the sides are equal. So,
PQ = QR
2x +3 = 3x – 5
3+5 = 3x - 2x
x = 8
So, the value of x is equal to 8 cm.
A= pi2 and find the area of a circle with radius 5 cm. Use pi = 3.14
Answer:
78.5398163397
Step-by-step explanation:
5x5= 25xpi=78.5398163397
No files just type in please and thank you
Tables--> 2
Each table--> (4*2) 8 boxes
Each box--> (8*6) 48 crayons
On each table--> 48/2
= 24 crayons on each table.
mark me brainliestttt :)))
SOMEOM PLEASE GELP ME
Answer:
You need to post the angle too
Step-by-step explanation:
Write the quadratic equation in standard form:
-7x+4=x^2
Answer:
x² + 7x - 4 = 0
Step-by-step explanation:
A quadratic equation in standard form is
ax² + bx + c = 0 ( a ≠ 0 )
Given
- 7x + 4 = x² ( subtract - 7x + 4 from both sides )
0 = x² + 7x - 4 , that is
x² + 7x - 4 = 0 ← in standard form
m<6 = 57°, what is m<4?
Answer:
Just guest: 38
Step-by-step explanation:
6÷4 = 1,5
So to make 6 to 4 we have: 6÷1,5 = 4
Similar to x: 57÷1,5 = 38
Help pleaseeeeeeeeeeeeeeeeeeeeee
Answer:
-6Step-by-step explanation:
Given Question,
2x - 7
Given Value:
[tex]x = \frac{1}{2} [/tex]
Solution,
[tex]2( \frac{1}{2} ) - 7[/tex]
[tex] = 2 \times \frac{1}{2} - 7[/tex]
= 1 - 7
= - 6 (Ans)
A boat travel 45 miles in three hours at this rate how many miles with a boat travel in half an hour
Answer:
7 1/2 miles per half hour
Step-by-step explanation:
First let's find how many miles you travel per hour. To find that, you divide 45 by 3. This gives you 15 miles per hour. Now we need to find how many miles in half an hour. To do this we are going to convert into minutes. We need to find out how many miles per minute. There are 60 minutes in 1 hour, so we will divide 15 by 60. That gives 0.25, or 1/4 mile per minute. So now that we know how many miles per minute, we can find out how many for half an hour. Half an hour is 30 minutes, so we are going to multiply 1/4 by 30. You will get 15/2. We need to make that a mixed number, and that gives us 7 1/2 miles per 30 minutes, or 7 1/2 miles per half hour.
I hope this helped :)
(edit: I just realized I did this the hard way. Sorry. The easier way would be to just divide 15 by 2 since it would take two halves of 15 to make the amount of miles per hour.)
A car is traveling at a rate of 48 miles per hour. What is the car's rate in miles per minute? How many miles will the car travel in 2 minutes? Do not round your answers.
Answer:
0.8 Miles per minute. 1.6 miles in 2 minutes
Step-by-step explanation:
It says 48 miles for 60 minutes. But we only want one minute, so we can divide 60 to get 1 and divide 48 by 60 to get 0.8 for 1 minute.
For the second question you want 2 munutes so you multily this rate by 2 (0.8*2) to get 1.6 miles.
Hope this helps
:)
Find the value of LM and LN if M is between L and N.
LM = 7x + 4, MN = 20, LN = 10x
Answer:
LM = 20
LN = 160/7
Step-by-step explanation:
If M is between L and N, then LM = MN
Given
LM = 7x + 4, MN = 20, LN = 10x
7x+4 = 20
7x = 20 - 4
7x = 16
x = 16/7
LM = 16/7(7) + 4
LM = 16 + 4
LM = 20
LN = 10x
LN = 10(16/7)
LN = 160/7
How many participants whose age fall between 31 to 33 years old?
Note: Consider the below frequency distribution table of the ages of the participants is attached with this question.
Given:
The frequency distribution table of the ages of the participants.
To find:
The number of participants whose age fall between 31 to 33 years old.
Solution:
In the given frequency distribution table the frequencies represents the number of participants of corresponding age group.
From the given frequency distribution table of the ages of the participants, it is clear that the frequency for age class 31-33 is 5.
Therefore, there are 5 participants whose age fall between 31 to 33 years old.
a person normally cost 1195 is on sale for 15% off if you only have a $10 bill do you have enough to purchase the book
Answer:
no
Step-by-step explanation:
First determine the discount
11.95 * 15%
11.95 *.15
1.79
Subtract the discount
11.95-1.79
10.16
You do not have enough money with a 10 dollar bill
Use the rule y= -x + 7 to fill in the blank.
if (1,y) is on the graph then y =
Answer:
Then y = 6
Step-by-step explanation:
y = -x + 7
x = 1
y = -1 + 7
= 6
A point on the ocean floor is 7,842 m below sea level.
Express this elevation as an integer.
The elevation as an integer is □m
Answer:
-7842 meters
Step-by-step explanation:
Since the point is below sea level, it is negative
-7842 meters
how to use multiplication to find 4 divided by 1/8
Answer:
32, because when you are dividing by a fraction, you can multiply by the divident by reciprocal of the divisor.
Step-by-step explanation:
4 ÷ 1/8
4/1 ÷ 1/8
4/1 × 8/1
4 × 8
32
When you are dividing by a fraction, you can multiply by the divident by reciprocal of the divisor.
Answer:
32
Step-by-step explanation:
4
1
1
8
=(
4
1
)(
8
1
)
=
(4)(8)
(1)(1)
=32
4 oranges at Juicy Deals grocery store cost $6. For the price of $15 you can buy 10 oranges. True or false: The relationship
between the number of oranges and their price is proportional.
Answer:
the answer is true.
4/6
10/15
