Answers
Answer:
-2
Step-by-step explanation:
You have to simplify numerator and denominator through factoring. The you should get an expression involving only a + b which is given as -2
Take numerator
[tex]a^2-b^2-12b-36[/tex]
Factor
[tex]-b^2-12b-36[/tex]
[tex]= - (b^2 + 12b + 36)\\\\= -(b+6)^2[/tex]
So numerator becomes
[tex]a^2-\left(b+6\right)^2[/tex]
Apply difference of squares formula: [tex]\displaystyle x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
[tex]\mathrm{with\;} x^2 == > a^2, and y^2 == > (b + 6)^2[/tex]
[tex]\implies a^2-\left(b+6\right)^2 \\== \left(a+\left(b+6\right)\right)\left(a-b-6\right)[/tex]
Denominator
[tex]a^2-6a-b^2-6b[/tex]
can be factored as follows
[tex]a^2-b^2 = (a + b) (a -b)[/tex]
[tex]-6a-6b = -6\left(a+b\right)[/tex]
So denominator becomes
[tex]\left(a+b\right)\left(a-b\right)+-6\left(a+b\right)[/tex]
Factor out common term (a+b) to get
[tex]\left(a+b\right)\left(a-b-6\right)[/tex]
So the original expression with Numerator and denominator
[tex]\displaystyle =\frac{\left(a+b+6\right)\left(a-b-6\right)}{\left(a+b\right)\left(a-b-6\right)}[/tex]
Cancel the common factor (a-b-6) to get
[tex]\displaystyle \frac{a+b+6}{a+b}[/tex]
Since a + b = -2, plug in this value of (a+b) in both numerator and denominator to get
[tex]\displaystyle \dfrac{-2 + 6}{-2}[/tex]
[tex]\displaystyle = - 2[/tex]
Answer: -2
Related Questions
can someone awnser this for me please?
Answers
Answer:
1.Yes
2.Yes
3.No
4.Yes
5.Yes
6.No
I hope it's help
Answer:
1. yes
2.Yes
3.no
4.no
5.yes
6.yes
Step-by-step explanation:pa brainliest po thankyou
what is the perimeter of (-2,1) (3,1) (3,-1) (-2,-1)
Answers
Answer:
14
Step-by-step explanation:
Given the points (-2,1), (3,1), (3,-1), and (-2,-1) that are the vertices of a quadrilateral, you want to find the perimeter.
PerimeterThe perimeter of a plane figure is the sum of the lengths of its sides. When you plot these points, you see they define a rectangle with horizontal sides of length (3-(-2)) = 5, and vertical sides of length (1 -(-1)) = 2. There are two sides of each of these lengths, so the perimeter is ...
P = 2(L+W) = 2(5 +2) = 2(7)
P = 14
The perimeter of the figure is 14 units.
__
Additional comment
When trying to work out measures associated with a set of points, it is often useful to graph those points.
Consideri the expression 5/6(1/2x+6) - 3x
Answers
Therefore, the value for the algebraic expression 5 / 6 ( 1 / 2 (x) + 6 ) - 3x for x = 12 is -26.
Given algebraic expression is 5/6(1/2 (x) + 6 )-3x
As we know An algebraic expression in mathematics is an expression that consists of variables and constants, along with algebraic operations such as addition, subtraction, etc., and are made up of terms
Solve the expression for x = 12
To solve this algebraic expression we have to substitute the value of x = 12 in an expression as below
= 5 / 6 ( 1 / 2 (x) + 6 ) - 3x
Substitute the value of x in the given expression as below
= 5 / 6 ( 1 / 2 * 12 + 6 ) - 3 * 12
= 5 / 6 ( 6 + 6 )) - 36
= 5 / 6 ( 12 ) - 36
= 5 * 2 - 36
= 10 - 36
= -26
Therefore, the value for the expression 5 / 6 ( 1 / 2 (x) + 6 ) - 3x for x = 12 is -26.
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Which relation is a function?
Answers
Draw a up and down line anywhere on the graph and it should only touch the line AT MOST 1 time
What is logs (4-7)+logs2 written as a single log?
O log 21
O log 26
O log,30
O log,56
Answers
Answer:
[tex]\log_556[/tex]
Step-by-step explanation:
Given:
[tex]\log_5(4 \cdot 7)+\log_52[/tex]
Multiply the 4 and 7:
[tex]\implies \log_528+\log_52[/tex]
[tex]\textsf{Apply the Log Product law}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\implies \log_5(28\cdot2)[/tex]
Multiply the 28 and 2:
[tex]\implies \log_556[/tex]
Jasmine used the number line to find the distance between 0 and 5. what was Jasmine’s error
1.jasmine should have counted from 5 to 0
2.jasmine started with the wrong integer.
3.jasmine gave a negative answer for distance.
4. Jasmine ended with the wrong integer.
Answers
The correct answer is option c.
Jasmine gave a negative answer for distance.
The number line is the main visual base in statistics and we often want to look at two points on the number line and determine the distance between them. This is used to find the base of a rectangle or another figure that lies above the number line. By the end of this section, you will be able to determine the distance between any two points on a number line that comes from a statistics application.
The absolute value of 5 is 5, because it is 5 units away from 0. A negative number is a number that is less than zero. On a horizontal number line, negative numbers are usually shown to the left of 0. Two numbers are opposites if they are the same distance from 0 and on different sides of the number line.
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A survey of 163 persons was conducted at TCC, and it was found that 90 persons carried a cell phone, 81 persons carried a tablet computer, and 43 carried both a cell phone and a tablet.
Answers
1. The number of people who carried a cell phone or a tablet is 128.
2. The probability that a person carries a cell phone or a tablet is 78.5%.
3. The number of people who carried neither a cell phone nor a tablet is 35.
4. The probability that a person carried neither a cell phone nor a tablet is 21.5%.
5. The number of people who carried a cell phone only is 43.
6. The probability that a person carried a cell phone only is 26.4%.
7. The number of people who carried a tablet but not a cell phone is 38.
8. The probability that a person carried a tablet but not a cell phone is 23.3%.
Data and Calculations:The sample size of the survey = 163
The number of persons who carried a cell phone = 90
The number of persons who carried a tablet computer = 81
The number of persons who carried both a cell phone and a tablet = 43
1. The number of people who carried a cell phone or a tablet is 128 (90 + 81 - 43).
2. The probability that a person carries a cell phone or a tablet is 78.5%. (128/163).
3. The number of people who carried neither a cell phone nor a tablet is 35 (163 - 128).
4. The probability that a person carried neither a cell phone nor a tablet is 21.5% (35/163).
5. The number of people who carried a cell phone only is 43.
6. The probability that a person carried a cell phone only is 26.4%(43/163).
7. The number of people who carried a tablet but not a cell phone is 38 (81 - 43).
8. The probability that a person carried a tablet but not a cell phone is 23.3% (38/163).
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Question Completion:1. How many people carried a cell phone or a tablet?
2. What is the probability that a person carries a cell phone or a tablet?
3. How many people carried neither a cell phone nor a tablet?
4. What is the probability that a person carried neither a cell phone nor a tablet?
5. How many people carried a cell phone only?
6. What is the probability that a person carried a cell phone only?
7. How many people carried a tablet but not a cell phone?
8. What is the probability that a person carried a tablet but not a cell phone?
Solve for v -10 = -14v + 44v
Answers
V=-0.344828
1.Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
Answers
Answer:
x=8
Step-by-step explanation:
So 6^2+x^2=10^2
36+x^2=100
x^2=64
x=8
Answer:
first put name of triangle abc than
angle _abc =180degree
10+6+c=180
16+c=180
180÷16=c
c=11.25
the value of x is 11.25 ans
5x - 7 > 8 ?? what is the answer solve the inequality
Answers
Answer:
Step-by-step explanation:
Explanation:
This can be rewritten as
−
18
<
5
x
+
7
<
2
To solve this, isolate
x
. The first step will be subtracting
7
. However, subtract
7
from all parts of the inequality.
−
18
−
7
<
5
x
+
7
−
7
<
2
−
7
Which yields
−
25
<
5
x
<
−
5
Now, divide each part by
5
.
−
5
<
x
<
−
1
wolframalpha.com
Answer:
x>3
Step-by-step explanation:
Thats all hope this helps.
HURRY IM TIMED Explain how to find the estimated sum of 5/8+2/9
Answers
Answer:
61/72
Step-by-step explanation:
first find the lowest common denominator - basically in this case the lowest number that goes into 8 and 9 - 8 x 9 which is 72, then
8 goes into 72 9 times so do 9 x the numerator (5)
9 x 5 = 45
Do the same for the second fraction, 9 goes into 72 8 times so do 8 x numerator (2)
8 x 2 = 16
Now add 45+ 16 = 61 ( this is your numerator)
and you keep the denominator (72) the same, so the answer is 61/72
Test coming up need your help.
Answers
The linear equation that represents the number of pages that Lourdes still need to read will be y = y = 30x + 3/5y.
How to illustrate the information?It should be noted that an equation is used to show the relationship between the variables. It should be noted that the person is reading a biography.
It should be noted she reads 30 pages each day and after 9 days, he has read 3/5 of the pages.
Therefore, the linear equation that represents the number of pages that Lourdes still need to read will be:
y = (30 × x) + (3/5 × y
y = 30x + 3/5y.
Finally, this is the linear equation representing the pages that Lourdes read.
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What number n is four times as close to 10 as it is to 2 ?
Answers
Answer: n=38/3
Step-by-step explanation:
4*(n-10)=(n-2)
4*(n-10)=n-2
4n-40=n-2
3n-40=-2
3n=38
n=38/3
The number n is four times as close to 10 as it is to 2 would be 38/3.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
The equation form here;
4*(n-10)=(n-2)
4*(n-10)=n-2
4n-40=n-2
3n-40=-2
3n=38
n=38/3
Therefore, The number n is four times as close to 10 as it is to 2 would be 38/3.
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(x)/(p)+(x)/(q)=s solve for x
Answers
Answer:
x = s/(1/q + 1/p)
Step-by-step explanation:
Solve for x:
x/p + x/q = s
Collect in terms of x:
x (1/q + 1/p) = s
Divide both sides by 1/q + 1/p:
Answer: x = s/(1/q + 1/p)
1. Olivia and Brandon take a road trip that is 1, 792 miles. The odometer reading on their car when they start out is
58, 236 miles. After one day, the odometer reading is 58, 857 miles. How many miles do they have left before they
reach their destination?
1,351 miles
1,171 miles
Answers
Answer:
1,171 miles
Step-by-step explanation:
The trip is 1792 miles.
They have driven (58857 - 58236) miles of the trip so far (because the odometer change is equal to the distance driven).
(58857 - 58236) = 621
They still need to drive 1792 - 621 miles
1792 - 621 = 1171
So they have 1171 miles left until they complete the trip.
To conserve water, many communities have developed water restrictions. The water utility charges a fee of $38, plus an additional $1.28 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $57 and $87 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)
Answers
the recommended range of water consumption is defined by the compound inequality:
14.84 ≤ x ≤ 38.28
How to write a compound inequality?The water utility charges a fixed amount of $38 plus $1.28 per hundred cubic feet of water. So, if you consume x hundred cubic feet of water, the cost is given by the linear relation:
$38 + $1.28*x
Now, this needs to be between $57 and $87 (values included) so we can write the inequality:
$57 ≤ $38 + $1.28*x ≤ $87
Now we just need to solve this for x. If you subtract $38 in both sides you will get:
$57 - $38 ≤ $1.28*x ≤ $87 - $38
$19 ≤ $1.28*x ≤ $49
Now we divide by $1.28 so we get:
$19/$1.28 ≤ x ≤ $49/$1.28
14.84 ≤ x ≤ 38.28
So to be in the recommended range of water consumption, your water consumption x must be in the range:
[14.84, 38, 28]
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You're a manager in a company that produces rocket ships. Machine A and Machine B both
produce cockpits and propulsion systems. Machine A ran for 22 hours and produced 3 cockpits
and 5 propulsion systems. Machine B ran for 44 hours and produced 6 cockpits and 10
propulsion systems.
Assume both machines produce cockpits at the same rate and both produce propulsion systems
at the same rate.
Answers
Step-by-step explanation:
so, what's the question ?
I don't need to "assume" that both machines have the same rate. it is clearly written there :
A produces in 22 hours 3 cockpits and 5 propulsion systems.
and B produces in twice the time (44 hours) twice the results (6 cockpits, 10 propulsion systems).
that means they have exactly the same production rate for both products.
so, this is confirmed. but what should we do now with this information ?
Answer:
C - No; the system has many solutions
Step-by-step explanation:
I just got it right on khan.
Below is a distance with given lengths to help Cecil cross the tightrope. Find a way to get cecil cross the tightrope.Write your
solutions as numerical expressions. the length of the tightrope is 15 feet long the lengths are 2,6 and 8 feet. Explain why or why not you can use these lengths. PLEASE HELP WORTH A LOt OF POINTS
Answers
The lengths can be used since it's more than the tightrope.
How to illustrate the information?It should be noted that the the length of the tightrope is 15 feet long and the lengths given are 2,6 and 8 feet.
The addition of the lengths will be:
= 2 + 6 + 8
= 16 feet
Therefore, the lengths can be used since it's more than the tightrope. In this case, 26 feet is more than 15 feet.
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Rewrite (225 + 45) using factoring.
Answers
Answer:
15(16+3) is the right answer
Step-by-step explanation:
mark me brainliest PLS
please help!!!!!!!!!!
Answers
Because it’s dividing by the variable “x” not so much the number (2)
Line Segment AD=11x+10.6. Find the length of AB and CD. Show all work
Answers
The lengths of AB and CD are 12 and 26.5 units
How to find the lengths of AB and CD?The given parameters are
AB = 2x + 3
BC = 21
CD = 7x - 5
AD = 11x + 10
The points are on line AD
So, we have
AD = AB + BC + CD
This gives
11x + 10 = 2x + 3 + 21 + 7x - 5
Evaluate the like terms
2x = 9
Divide by 2
x = 4.5
Substitute x = 4.5 in AB = 2x + 3 and CD = 7x - 5
AB = 2 * 4.5 + 3 = 12
CD = 7 * 4.5 - 5 = 26.5
Hence, the lengths of AB and CD are 12 and 26.5 units
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Again it’s me, PLEASE PLEASE PLEASE I am so tired it’s 10 pm and I literally do not know what to do for this question if any of you know what to do please solve it
Answers
Answer:
x=1 and 4
suppose t=x1.5
Which expressions are equivalent to…
Answers
Answer: E
Step-by-step explanation:
[tex]\frac{5}{6}(18x^{2} -3x)-\frac{6}{5} (5x^{3} -10x-30x^{2} )[/tex]
[tex]=\frac{5}{6}(18x^{2}) + \frac{5}{6} (-3x) - \frac{6}{5} (5x^{3} )-\frac{6}{5} (-10x)-\frac{6}{5} (-30x^{2} )[/tex]
[tex]= 15x^{2} -\frac{5}{2} x-6x^{3} +12x+36x^{2}[/tex]
[tex]=-6x^{3} + (15x^{2} +36x^{2} )+(-\frac{5}{2}x+12x)[/tex]
[tex]=-6x^{3} + 51x^{2} -\frac{5}{2}x+12x[/tex]
Therefore, the answer is E.
Answer: E.
Step-by-step explanation:
[tex]\displaystyle\\\frac{5}{6} (18x^2-3x)-\frac{6}{5} (5x^3-10x-30x^2)=\\\\\frac{5}{6}(18)(x^ 2)-\frac{5}{6} (3)(x)-\frac{6}{5} (5)(x^3)+\frac{6}{5}(10)(x)+\frac{6}{5} (30)(x^2)=\\\\ \frac{5*18}{6} x^2-\frac{5*3}{6}x -\frac{6*5}{5} x^3+\frac{6*10}{5}x+\frac{6*30}{5} x^2=\\\\5*3*x^2-\frac{5}{2} x-6x^3+6*2*x+6*6*x^2=\\\\15x^2-\frac{5}{2}x-6x^3+12x+36x^2=\\ -6x^3+51x^2-\frac{5}{2} x+12x[/tex]
if 3 divided by a number y is 18, then what is the value of the number y plus 2? Steps?
Answers
[tex]\frac{3}{y}=18 \\ \\ 3=18y \\ \\ y=1/6 \\ \\ \implies y+2=\boxed{13/6}[/tex]
Find all real solutions of the equation, rounded to two decimals. (Enter your answers as a comma-separated list.)
x^4 − 4x^2 + 2 = 0
Answers
The real solution of the equation are +0.77, -0.77, +1.85, -1.85.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0 .
Given:
x^4 − 4x^2 + 2 = 0
(x²)² - 4x² + 2 =0
let us consider y= x², then the above equation become
y² - 4y + 2 =0
On further solving for 'y' we have
y= -b±√(b² -4ac) / 2a
y= 4±√(16-8)/2
y=4±2√2/2
y= 2 + √2, y=2-√2
Now, y= x²
x² = (2 + √2), x²= 2-√2
x= +1.8477, -1.8477 , +0.7653, -0.7653
x= +0.77, -0.77, +1.85, -1.85
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Can anyone help? Cause i dont really understand the thing.
Answers
The function represents a continuous function because it can be measured and not counted.
The domain is; x ≤ 19 gallons
The range is ; d(x) ≤ 323 miles
What is the Dependent and Independent Variable?
We are given the function that represents the distance d(x) in miles that the car can travel with x gallons of gasoline as;
d(x) = 17x
A) The Independent Variable is Number of gallons of gasoline used while the dependent variable is the distance that the car travels.
B) Discrete data is a numerical type of data that includes whole, concrete numbers with specific and fixed data values determined by counting. Continuous data includes complex numbers and varying data values measured over a particular time interval.
Thus, the situation represents a continuous function because it can be measured and not counted.
C) The domain is the set of all possible input values. You have 19 gallons and so the domain is; x ≤ 19 gallons
The range is the set of all possible output values. Thus, the range is;
d(x) ≤ (19 * 17)
d(x) ≤ 323 miles
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PLEASE HELP!!!! WIILL MARK BRAINLIEST
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6.50 and each adult ticket sells for $10. The auditorium can hold no more than 140 people. The drama club must make at least $1100 from ticket sales to cover the show's costs. If a represents the number of student tickets sold and y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.
Answers
Answer:
y ≥ -0.65x +110
y ≤ -x +140
45 students, 95 adults
Step-by-step explanation:
6.50x + 10y ≥ 1100 --> 10y ≥ -6.50x + 1100 --> y ≥ -0.65x +110
x + y ≤ 140 --> y ≤ -x +140
On a number line, P has coordinate-35 and Q has coordinate 21. Find PQ
Answers
Answer:
42
Step-by-step explanation:
because its 42
An ounce of sugar has about 100
calories. If a handful of sugar has
412.6 calories, what's the weight of
the sugar in ounces?
Answers
14. A certain real estate agent uses what he calls a step- strategy to sell houses. He puts a house on the market at a higher-than - expected selling price and if it hasn't sold in two weeks, he drops the price by 5%. If it still hasn't sold in another 2 weeks , he drops the price by another 5 %. After that , he continues to drop the price by 3% every two weeks until it reach es a cut -off amount assigned by the home owner , or the house sells , whichever comes first . If a house is originally listed at $200,000 and the homeowner sets a cut -off amount of $166,000 , what is the final selling price given that the house sells after being on the market for 9 weeks ? A ) $162,901.25 B) $164,737.48 $166,000.00 D ) $169,832.45
Answers
Answer:
vvvyaz
Step-by-step explanation:
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