Answers
Step-by-step explanation:
5/(x + 2) + 3/(x - 4) = 2
5(x - 4) + 3(x + 2) = 2(x + 2)(x - 4)
5x - 20 + 3x + 6 = 2x^2 - 4x - 16
8x - 14 = 2x^2 - 4x - 16
4x - 7 = x^2 - 2x - 8
x^2 - 6x - 1 = 0
By using the quadratic formula, x = (-6 +/-√40)/2.
Related Questions
The polynomial x^2 - 22x + 121 represents the area (in square feet) of a square courtyard. a.) write a polynomial that represents the side length of the courtyard.
b.) Write an expression for the perimeter of the courtyard.
Answers
Answer:
Step-by-step explanation:
Since the court yard is square in nature, the area of the court yard will be exprerssed as;
A = Length * Length
A(x) = L²
Given area of the court yard A(x) = x^2 - 22x + 121
x^2 - 22x + 121= L²
Factorizing the quadratic expression
(x^2 - 11x) -(11x+ 121) = L²
x(x-11)-11(x-11) = L²
(x-11)(x-11) = L²
(x-11)² = L²
Square root both sides to the length of the courtyard
√(x-11)² = √L²
L = x-11
Hence the length of the courtyard is (x-11)ft
b) The perimeter of the courtyard P = 4L
P = 4(x-11)
P = 4x - 44
Hence an expression for the perimeter of the courtyard is 4x-44 feet
What is 10% of 110?
Answers
Answer:
10%×110
10/100×110
11
Answer:
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can a coefficient have two variables?
Answers
Answer: Yes, a coefficient can have two variables.
solve 5.2 = a - 0.4 a= ?
Answers
write first three terms of AP with a = -1 and d = 1/2
Answers
Answer:
first three terms are
-1, -1/2 & 0
Step-by-step explanation:
here,
a=-1
and d=1/2
so
t1 = -1
t2 = a+(n-1)d= -1 +(2-1)*(1/2)=-1/2
t3= a+(n-1)d= -1 +(3-1)*(1/2) =0
Can 0.898989.... be written as a fraction
Answers
Answer:
898989/1000000
Step-by-step explanation:
Yes it can be written as a simplified fraction. Since there are 6 numbers to the right of the decimal point, you would move the decimal point to the left of the number.
0.898989
start by moving the decimal point to the left 898989
since you moved your decimal point 6 times to the left it would be 10^6
hence, 898989/1000000
The repeating decimal 0.898989... Or [tex]0.\overline{89}[/tex] can be written as 89/99.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
We know a repeating decimal can be written as a fraction.
We'll put as many 9s in the denominator as there are repeating digits after the decimal and in the numerator, we'll simply write the repeating digits after the decimal.
So, 0.89898989 is 0.89 repeating.
∴ [tex]0.\overline{89}[/tex] = 89/99.
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What is the value of the expression below when
w = 7 and x = 6?
5w — x
Answers
Answer:
The answer is 29
Step-by-step explanation:
5(7)-6 once you put it in the calculator you will get 29 as the answer for all of it. The w is 7 and when you place it next to the 5 you have to multiply it and then subtract it by the x which is the 6.
I hope this helps!
After substituting, the value of expression is 29.
What is substitution method?To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The expression is,
⇒ 5w - x
And, w = 7 , x = 6
Since, The expression is,
⇒ 5w - x
Substitute the value of w and x, we get;
⇒ 5×7 - 6
⇒ 35 - 6
⇒ 29
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Simplify the expression 2(x-5)+3(x+11)
Answers
Answer:
2x-10+3x+33
5x+23
Step-by-step explanation:
hope it is helpful
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Determine whether the given description corresponds to an experiment or observational study.a. A stock analyst selects a stock from a group of twenty for investment by choosing the stock with the greatest earnings per share reported for the last quarter.b. A marketing firm does a survey to find out how many people use a product. Of the one hundred people contacted, fifteen said they use the product.c. A political pollster reports that his candidate has a 10% lead in the polls with 10% undecided.d. A doctor gives a new medication to half of his patients with the flu and a placebo to the other half of his patients with the flu.
Answers
Answer:
A: experiment
B: observational study
C: observational study
D: experiment
Step-by-step explanation:
Which of the following could be the number shown on the number line?
Answers
Answer:
Your correct answer is option B.
Step-by-step explanation:
Option b is the highest number in the options. and, the dot on the number line is closest to the 5. Therefore, your correct answer is option B.
√24 can be the number shown on the number line. Hence, option A is the right choice.
What is a number line?The integers are put at equal intervals on number lines, which are horizontal straight lines. A number line can depict all of the numbers in a series. At both ends, this line continues endlessly.
How do we solve the given question?In the question, we are given a number line showing a point between 4 and 5, which is very close to 5.
We analyze all the given options for a number similar to the number marked on the number line to get the correct option.
To remember, 4 = √16, and 5 = √25
A. √24: falls between 4 and 5 (∵ √16 < √24 < √25). And also √24 is very close to 5 (√25).B. √27: does not fall between 4 and 5 (∵ √27 > √25).C. √20: falls between 4 and 5 (∵ √16 < √20 < √25). But not very close to 5.D. √26: does not fall between 4 and 5 (∵ √26 > √25).After analyzing all the given options, only A. √24 and C. √20 fall between 4 and 5, and the closest to 5 among them is √24, so that is the right choice.
∴ √24 can be the number shown on the number line. Hence, option A is the right choice.
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4. Find the next 3 numbers in the pattern: 87, 78, 69. 60, __ __ __
Answers
Answer:
51, 42, 33
Step-by-step explanation:
87, 78, 69, 60, 51, 42 , 33
They all are differences of 9, so just subtract 9 to the the pattern
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Marci has a scale drawing of her new bedroom. On the drawing the length of the bedroom is 2cm. In real life her bedroom is going to be 7 meters in length. What is the scale of the drawing
Answers
Answer:
Scale for drawing is 1:350
Step-by-step explanation:
scale is ratio of size of drawing and size of actual object for which the drawing is made
it is represented as
scale = size of drawing : size of actual object
given
length of model in drawing = 2cm
length of bedroom in reality = 7 meter
since there are two units we meter and cm
we convert both in same unit that is cm for simpler calculation
1 meter = 100 cm
7 meter = 7*100 cm = 700cm
length of bedroom in reality = 7 meter = 700 cm
Thus,
scale for drawing = length of drawing/ actual length of bedroom
scale for drawing = 2 cm : 700cm = 1:350
Scale for drawing is 1:350
6. A landscaping company is trying to create a formula to predict the amount of time, t, required to mow a yard based on the area of the yard, A, the speed of the mower, v, and the width of the mower, w. One employee suggests a formula of t = 1.15 * A/(vw) Does this formula make sense? Explain .
Answers
Answer:
The formula makes sense
Step-by-step explanation:
For illustration purposes, we will assume the yard is a rectangle ( such assumption does not in any way invalid the arguments that follows
Dimensions of the yard
L = 10 m
w = 4 m
A = 40 m²
Arguments:
1.- The required time (t) is proportional to the area (A). That means ( keeping all parameters fixed but Area ) we need more time to mow a bigger area yard. Then t ∝ A
You can see that if the yard is 40 m² you will take let´s say 0,5 day and you will need more time if the area is 100 m² ( it seems obvious )
2.- Let´s now assume the width of the mower is 1 m if you move along the length you will need to go forward and backward 4 times. Now think about a mower of 4 m ( it does not matter if that machine exists or no, is just a mental experiment) in that case you only need one pass, then the required time is inversely proportional to the width of the mower. That means a bigger width of the mower minor required time. Then t ∝ 1/w
3.-If now we keep the width of the mower but increased the speed of the machine we will reduce the working time. Time is an inversely proportional function of the speed of the machine since each required pass will take less time. Then t ∝ 1/v
We have evaluated three parameters A, w, and v ( area, the width of the mower, and speed ) and demonstrated the way each of these parameters influences the time, so far we don´t know how much each of them contributes in the total output, for that we have to measure and get conclusions, Furthermore coefficient 1,15 (in formula seems to take into account the hole combinations of the factors)
A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles. What is the actual area of the park?
Answers
Answer:
Actual area = 21600 Sq.miles
Step-by-step explanation:
We are given;
length; L = 4 inches
Width; W = 6 inches
The scale of the map; 1 inch for every 30 miles i.e. 1 : 30
Since the scale is 1:30, let's find the find the actual dimensions and then the actual area
For the Length,
Since 1 inch represents 30 miles,
Then, 4 inches = (4 × 30)/1 = 120 miles
For the width;
Since 1 inch represents 30 miles,
Then,6 inches = (6 × 30)/1 = 180 miles
Therefore, the actual dimensions are 120 miles and 180 miles
Now, formula for area of rectangle = length × width
Thus;
Actual area = 120 × 180
Actual area = 21600 Sq.miles
Suppose a rabbit ate 32 carrots in 4 days. If it ate 2 more carrots each day than the day before, how many carrots did it eat each day on day 1, day 2, day 3, and day 4?
Answers
Day 2: 5 carrots
Day 3 : 7 carrots
Day 4 : 9 carrots
Fernando's lawn is 30 meters wide. His neighbor's lawn is 50 meters wide. In centimeters, what is the difference in width between the two lawns? (hint: 1 m = 100 cm)
Answers
Answer:
The difference in width is 2000 cm.
Step-by-step explanation:
The wideness of Fernando’s lawn = 30 meters
Neighbour’s lawn = 50 meters
Now we have to find the difference in width that can easily find out by subtracting the width of Fernando’s lawn from the neighbor’s lawn.
The difference in width = neighbor's lawn - Fernando's lawn
The difference in width = 50 - 30
The difference in width = 20 meters
The difference in width = 20 meters ×100 = 2000 cm.
you allow for 5% of your net pay of $2,989.12 to be budgeted for medical expenses
Answers
Explanation of answer: multiply net pay (2,989.12) by .05. Then you get the answer.
It’s .05 because that’s equal to 5%. By moving decimal point twice to the right.
the answer is $149.46 c:
Round 40.8534 by one decimal point
Answers
Answer:
40.9
Step-by-step explanation:
8 is beside 5 which is a large number so you add 1 to 8
Answer:
40.9
Step-by-step explanation:
if you rounded to 2 decimal places the answer would be:
40.83.
because the second number after the decimal is 5 or more, we have to round upwards.
this brings us to 40.9 which has 1 decimal place.
an integer is 10 times the difference of a rational number and 5. If the value of the integer is 124, what is the value of the rational number?
Answers
Answer:
17.4
Step-by-step explanation:
Given the question :
an integer is 10 times the difference of a rational number and 5. If the value of the integer is 124, what is the value of the rational number?
An integer = 124 is 10 times the difference of a rational number and 5
Let the rational number be r
Hence,
124 = 10 × (r - 5)
124 = 10r - 50
124 + 50 = 10r
174 = 10r
Divide both sides by 10
174 / 10 =. 10r / 10
17.4 = r
r = 174 / 10 or 17.4
what is the value of the expression 4x - 1 / 2 y + x when X is 3 + y - 3
Answers
20. The formula A = bh can be used to find the area of a triangle.
Solve the formula for h, and use your equation to find the height of
a triangle with an area of 90 cm2 and a base of 15 cm.
Answers
h=90/15
h=6cm
therefore the answer to this problem is the height is 6cm
what is 0.000074 in scientific notation
Answers
Answer: 7.4 x 10^ -5
This question has two parts. Use the information to answer Part A and Part B. Information 1 A camp leader buys a book for each of her campers. She spends $7.50 on each book. Question 1 ,begin emphasis, Part A,end emphasis, Which expression can be used to find the amount of money the camp leader spends on b books? Question 1 Answer options with 4 options (A.)7.50 times b (B.) 7.50 plus b (C.)7.50 minus b (D.)7.50 divided by b Question 2 ,begin emphasis,Part B,end emphasis, If the camp leader has 12 campers, how much does she spend on the books? Enter the answer in the box. Question 2 Response area with 1 text input box $
Answers
Answer:
b
Step-by-step explanation:
because help me me with solve
The expression for the amount of money to buy 'b' books is
(A.) 7.50 times b
if the camp leader has 12 campers the amount of money will be$90.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A camp leader buys a book for each of her campers. She spends $7.50 on each book.
Assuming he bought 'b' no. of books.
∴ The expression for the amount of money to buy 'b' books is 7.50b.
Now if the camp leader has 12 campers the amount of money will be (7.5×12) = $90.
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miguel builds a model airplane with the scale 1in = 6ft . if the model is 9.3 inches long how long was the actual airplane ?
answer : 54.2 ft
Answers
Answer:
55.8 ft
Step-by-step explanation:
This seems simpler than it is.
So since it's going from inches to feet, we have to first know the conversion rate of inches to feet which is simple, 12 inches=1 foot. So now we have to figure out how many inches is 6 ft, so 12*6 equals 72. So knowing the scale, we can just do 9.3 *72=669.6. But if we want to know how long the actual airplane was in feet, then we have to do 669.6/12 which equals 55.8
Another way we could do it is by doing 9.3*6. This works because if you multiply something 12 and then divide it by 12, it just becomes 1. But doing this, you can't find the actual airplanes length in inches.
For all integer values of x and constant k, if (x-k)(x-5)=x^2-9x+20, what is the value of K?
A) -5
B) -4
C) 4
D) 10
E) 12
Answers
============================
Work Shown:
Expand out the left hand side
(x-k)(x-5)
x(x-5)-k(x-5)
x^2-5x-kx+5k
Note that the constant term here is 5k. Yes k seems like a variable, but it's actually a constant. Once we know k, we can replace it to get a fixed number. In this case, k = 4 since 5k = 5*4 = 20 to have it match with the 20 at the end of x^2-9x+20
For the x terms, we have -5x-kx = -5x-4x = -9x which matches with the middle term of x^2-9x+20
Therefore,
(x-k)(x-5) = x^2-9x+20
updates to
(x-4)(x-5) = x^2-9x+20
The -4 and -5 multiply to 20, and they also add to -9. This helps confirm we have the right k value.
GEOMETRY TRUE OR FALSE QUESTIONS
Answers
Answer:
True an angle is two intercepting line segments that share an point
False The definition of a square is it has to have four congurent angles ,sides and 2 sets of parallel lines.
Step-by-step explanation:
the measure of the supplement angle is 24 more than three time the measure of the original angle. find the measures of the angles.
Answers
Step-by-step explanation:
Let x° be the original angle. Then the supplement angle is (180 - x)° and (180 - x) = 3x + 24.
180 - x = 3x + 24
4x = 156
x = 39
Hence the original angle is 39° and the supplementary angle is 141°.
The angles are 39° and 141°.
What is a complementary angle ?Two angles are said to be complementary to each other when their sum is 90°
According to the given question
The measure of the supplement angle is 24 more than the measure of the original angle.
Let the original angle be x
So from the given data it's supplement angle is 3x + 24.
We know two angles are supplementary when their sum is 180°.
∴ x + 3x + 24° = 180°
4x = 156°
x = (156/4)°
x = 39°.
So, the original angle is 39° and it's supplementary angle is 141°.
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(1 + i)(13 – 4i)(1 - i)
Answers
Answer:
26-8i
Step-by-step explanation:
-10(-v + 6w) -w - 9(-3w - v)
Answers
Step-by-step explanation:
-10(-v + 6w) -w - 9(-3w - v)
= 10v - 60w - w + 27w + 9v
=19v - 34w
Hope this helps.. Good luck :)
Maria Gomez is a dental assistant. She earns $12.12 per hour and time and a half for overtime. What is her total pay for a week in which she works 45 hours?ks 45 hours?
Answers
Ot pay = $12.12 x 1.5 x 5 hrs
Add Reg Pay + OT
$484.80 + $90.90
= $575.70
Maria Gomez's total pay for the week when she works 45 hours will be $575.70.
How to calculate Total Pay?To calculate Maria Gomez's total pay for a week in which she works 45 hours, we need to consider both regular hours and overtime.
Given:
Regular hourly wage = $12.12 per hour
Overtime rate (time and a half) = 1.5 * Regular hourly wage = 1.5 * $12.12 = $18.18 per hour
Total hours worked in the week = 45 hours
Now, we'll calculate the total pay:
Step 1: Calculate the regular pay for 40 hours (normal working hours):
Regular pay = Regular hourly wage * Regular hours worked
Regular pay = $12.12 * 40 = $484.80
Step 2: Calculate the overtime pay for the additional 5 hours:
Overtime pay = Overtime rate * Overtime hours worked
Overtime pay = $18.18 * 5 = $90.90
Step 3: Add regular pay and overtime pay to get the total pay:
Total pay = Regular pay + Overtime pay = $484.80 + $90.90 = $575.70
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