Answer:
[tex]\boxed{ \sf x=\dfrac{4\pm\sqrt{43}}{2}}[/tex]
Explanation:
[tex]\rightarrow \sf \dfrac{1}{x-5}+\dfrac{3}{x+2}=4[/tex]
make the denominators same
[tex]\rightarrow \sf \dfrac{1(x+2)}{(x-5)(x+2)}+\dfrac{3(x-5)}{(x+2)(x-5)}=4[/tex]
join the fractions together
[tex]\rightarrow \sf \dfrac{x+2+3x-15}{(x-5)(x+2)}=4[/tex]
cross multiply
[tex]\rightarrow \sf x+2+3x-15=4(x-5)(x+2)[/tex]
simplify
[tex]\rightarrow \sf 4x-13=4x^2-12x-40[/tex]
group the variables
[tex]\rightarrow \sf 4x^2-16x-27 = 0[/tex]
use quadratic formula
[tex]\rightarrow \sf x = \dfrac{-\left(-16\right)\pm \sqrt{\left(-16\right)^2-4\cdot \:4\left(-27\right)}}{2\cdot \:4}[/tex]
simplify the following
[tex]\rightarrow \sf x=\dfrac{4\pm\sqrt{43}}{2}[/tex]
Answer:
[tex]x=\dfrac{4 \pm \sqrt{43}}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{1}{(x-5)}+\dfrac{3}{(x+2)}=4[/tex]
Make the denominators of the algebraic fractions the same, then combine them into one fraction:
[tex]\begin{aligned}\implies \dfrac{1}{(x-5)} \cdot \dfrac{(x+2)}{(x+2)}+\dfrac{3}{(x+2)}\cdot \dfrac{(x-5)}{(x-5)} & =4\\\\\implies \dfrac{x+2}{(x-5)(x+2)}+\dfrac{3(x-5)}{(x-5)(x+2)} & = 4\\\\ \implies \dfrac{x+2+3(x-5)}{(x-5)(x+2)} & = 4\\\\ \implies \dfrac{4x-13}{(x-5)(x+2)} & = 4 \end{aligned}[/tex]
Multiply both sides of the equation by [tex](x-5)(x+2)[/tex]:
[tex]\begin{aligned}\implies \dfrac{(4x-13)}{(x-5)(x+2)}\cdot (x-5)(x+2) & = 4(x-5)(x+2)\\\\\dfrac{(4x-13)(x-5)(x+2)}{(x-5)(x+2)} & = 4(x-5)(x+2)\\\\4x-13 & = 4(x-5)(x+2)\\\\4x-13 & =4x^2-12x-40\\\\4x^2-16x-27 & = 0\end{aligned}[/tex]
Solve using the Quadratic Formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\implies a=4\\\implies b=-16\\\implies c=-27[/tex]
Therefore:
[tex]\implies x=\dfrac{-(-16) \pm \sqrt{(-16)^2-4(4)(-27)} }{2(4)}[/tex]
[tex]\implies x=\dfrac{16 \pm \sqrt{688}}{8}[/tex]
[tex]\implies x=\dfrac{16 \pm 4 \sqrt{43}}{8}[/tex]
[tex]\implies x=\dfrac{4 \pm \sqrt{43}}{2}[/tex]
What is the greatest common factor of 20 and 10?
Answer:
Step-by-step explanation:
The factors common to 20 and 10 are 1, 5 and 10. The largest of these is 10. That's the GCF of 20 and 10.
There are two drama classesoffered at a middle school. The 8th grade class has 13 fewer students than the 7th grade class. If the total number of students in both classes is 67, how many students are in the 8th grade class?
Answer:
Class 8 has 27 and class 7 has 40
Step-by-step explanation:
8th (r) class has 13 fewer than 7th (x).
x -13 = r
Total for both classes = 67
r + x - 13 = 67
r + x = 80
80 divided by two = 40 (per class)
40 - 13 = 27
In which function is x = 2 mapped to 32?
Answer:
[tex]f(x) = {x}^{5} [/tex]
Step-by-step explanation:
[tex]f(2) = {2}^{5} [/tex]
[tex]f(2) = 32[/tex]
Here is the graph:Minh is packing books into
boxes. The mass of one of the boxes is 20 kilograms. If the box
holds 10 books that each have the same mass, what is the mass of
each book in grams?
The mass of each book in grams if each box weighs 20 kilograms is 2000 grams
Mass of each box = 20 kilogramsTotal books in the box = 10 booksConverting kilograms to grams1 kilograms = 1000 grams
20 kilograms = 20,000 grams
Mass of each book in grams = 20,000 grams / 10
= 2000 grams
Learn more about kilograms to grams:
https://brainly.com/question/9301317
#SPJ1
Which expressions below equal a rational number? Choose all that apply. 4/5 + 3/8; sqrt(100) + sqrt(5); 7sqrt(5) - sqrt(245); (4sqrt(7))(2sqrt(7)); pi * sqrt(36)
Answer:
Step-by-step explanation:
Rational number[tex]1) \dfrac{4}{5}+\dfrac{3}{8}\\\\\dfrac{4}{5} \ \text{is a rational number} \ and \ \dfrac{3}{8} \ \text{is a rational number}\\\\\dfrac{4}{5}+\dfrac{3}{8} \ \text{is also a rational number}[/tex]
[tex]b) \sqrt{100}+\sqrt{5} = 10+\sqrt{5}\\\\\sqrt{5} \ \text{is a irrational number}. \\\\ \text{Rational number added to irrational number will result in an irrational number}\\\\10 + \sqrt{5} \ is \ not \ a \ rational \ number.[/tex]
c)
[tex]7\sqrt{5}-\sqrt{245}=7\sqrt{5}-\sqrt{7*7*5}[/tex]
[tex]= 7\sqrt{5}-7\sqrt{5}\\\\=0\\\\\text{\bf $ 7\sqrt{5}-\sqrt{245}$ ia a rational number}[/tex]
d)
[tex](4\sqrt{7})*(2\sqrt{7})=4*2*\sqrt{7*7}\\[/tex]
= 4*2*7
= 56
[tex]4\sqrt{7}*2\sqrt{7} \ \text{\bf is a rational number}[/tex]
Find the value of x.
[tex]3(x+4)=90\\x+4=30\\x=26[/tex]
Deion has 62 m of fencing to build a four-sided fence around a rectangular plot of
land. The area of the land is 228 square meters. Solve for the dimensions (length and
width) of the field?
The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the length of the field and y represent the width of the field, hence:
Deion has 62 m of fencing:
2(x + y) = 62
x + y = 31
y = 31 - x (1)
The area of the land is 228 square meters. hence:
xy = 228
x(31 - x) = 228
x² - 31x + 228 = 0
x = 12 or x = 19
when x = 12; y = 31 - 12 = 19
when x = 19; y = 31 - 19 = 12
The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
PLEASE HELP ASAP!!!
Answer:
11- B
moving left 90 degrees from a
because clockwise is the right direction in a circle and counterclockwise is the left direction in a circle
12- C
moving 180 degrees left from a
13- B
moving 270 degrees right from a
14- d
moving 270 degrees left from a
hope this helps! message me if you have any further questions :)
Mitosis is a process of cell reproduction in which one cell divides into two identical cells. A bacterium called E. coli often causes serious food poisoning. It can reproduce itself in 15 min.
a) Starting with one bacterium, make a table with time in
1/4-h blocks and the corresponding number of E. coli
bacteria up to 2 h of bacteria growth.
b) About how long will it take before there are 10 000 bacteria?
Answer:
I'm just a kid
Step-by-step explanation:
plssss give me brainkest
A number is divided in the ratio 3:4. If the first part is 24, find the number.
Answer:
31Step-by-step explanation:
Let the other part be x.Now,24:x=3:43x=96X = 96/3 = 321Other part = 32mark me brainlist!A square vegetable garden has side lengths of 8 feet. You plant flowers in the center portion of the garden, a square that has side lengths of 2 feet. You divide the remaining space into 4 equal sections and plant tomatoes, onions, zucchini, and peppers. What is the area of the zucchini section?
Base on the total area of the square garden and the number of plants planted on it, the area of the zucchini section is 15 feet²
How to find area of zucchini section?Side Length of the square garden = 8 feet
Area of the garden = side length ²
= 8 feet × 8 feet
= 64 feet²
Flower portion:
Side Length = 2 feet
Area of flower portion = side length ²
= 2 feet × 2 feet
= 4 feet²
Remaining space = Area of the garden - Area of flower portion
= 64 feet² - 4 feet²
= 60 feet²
Remaining space is divided into 4 equal sections
= 60 feet² / 4
= 15 feet²
Therefore,
Tomatoes section = 15 feet²
Onions section = 15 feet²
Zucchini section = 15 feet²
Pepper section = 15 feet²
Learn more about area of a square:
https://brainly.com/question/24487155
#SPJ1
Which ones are variable expenses? (Check all that apply)
1. loans
2. food bill
3. rent
4. electric bill
Answer:
food bill, electric bill
Step-by-step explanation:
Variable expenses change every money
Loan payments are usually fixed, the same every month
food bill - variable expense since you buy different food each month and they will cost different amounts
rent is a fixed expense
the electric bill is different every month because some months you use more electricity than others
An interior angle of a regular polygon has a measure of 108°. What type of polygon is it?
pentagon
hexagon
octagon
nonagon
Answer:It is a 5 sided polygon known as pentagon.
Step-by-step explanation:
he graph of the function f(x) = –(x + 3)(x – 1) is shown below. On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 1, 4), and goes through (1, 0). What is true about the domain and range of the function? The domain is all real numbers less than or equal to 4, and the range is all real numbers such that –3 ≤ x ≤ 1. The domain is all real numbers such that –3 ≤ x ≤ 1, and the range is all real numbers less than or equal to 4. The domain is all real numbers, and the range is all real numbers less than or equal to 4. The domain is all real numbers less than or equal to 4, and the range is all real numbers.+
What is true about the domain and range of the function is; The domain is all real numbers, and the range is all real numbers less than or equal to 4.
How to find the domain of a graph function?Let us first find the roots of the function f(x):
0 = (x - 3)(x + 1)
(x - 3) = 0
x = 3
and (x + 1) = 0
x = -1
Therefore, the roots of the function are x = 3 and x = -1.
Now, the vertex is between the roots (x = 1) and has a negative value of y (y = -4), therefore, we can say that the concavity of the parabola is upwards.
This means that the graph is decreasing until it reaches the vertex, then the graph is increasing.
Therefore, we can conclude that the graph is positive and decreasing for all real values of x where x < -1.
Read more about domain of graph function at; https://brainly.com/question/15227113
#SPJ1
Answer:
The domain is all real numbers, and the range is all real numbers less than or equal to 4.
Step-by-step explanation:
Find the length of the indicated side of the similar figure.
Answer:
5
Step-by-step explanation:
in similar figures the side lengths must be proportional:
4/8 = x/10 cross multiply fractions
40 = 8x divide both sides by 8
5 = x
What does the expression n + 3 represent?
Answer:
Step-by-step explanation:
BASICALLY ANYTHING WITH 3
Use the spinner shown to answer the question. Assume that it is equally probable that the pointer will land on any one of the colored regions. If the pointer lands on a borderline, spin again
If the spinner is spun once, find the probability that the pointer lands in a region that is red or blue.
D
The probability that the pointer lands in a region that is red or blue is
(Type an integer or a simplified fraction.)
The probability that the pointer lands in a region that is red or blue is 1/2
How to determine the probability?The spinner that completes the question is added as an attachment
From the attached spinner, we have:
Total section = 8Red or blue = 4The probability is then calcuated as:
P =Red or blue/Total section
This gives
P =4/8
Evaluate
P= 1/2
Hence, the probability that the pointer lands in a region that is red or blue is 1/2
Read more about probability at:
https://brainly.com/question/25870256
#SPJ1
Sasha is playing a game where she tosses a coin, then rolls a die. She wins if she gets heads on the coin and a 5 on the die. What is the probability she wins?
A) `1/3`,`P(H and 5) = P(H) - P(5) = 1/2-1/6=3/6-1/6=2/6` or `1/3`. That makes sense since tossing a coin and rolling a die are independent events.
B) `2/3`,`P(H and 5) = P(H) + P(5) = 1/2+1/6=3/6+1/6=4/6` or `2/3`.That makes sense since tossing a coin and rolling a die are independent events.
C) `1/12`. That makes sense since tossing a coin and rolling a die are independent events. `P(H and 5) = P(H) × P(5) = 1/2 × 1/6=1/12`
D) `12/12` or `1`. That makes sense, because she should win every time she plays.
Answer:
i hope the answer is clear to you
Step-by-step explanation:
i don’t know if I explained well but yeah here are the answers
Hope this helped!
The diameter of a semicircle is 8 millimetres. What is the semicircle's radius?
Answer:
The radius is 4.
Step-by-step explanation:
Concepts:
Diameter is usually defined as a straight line passing through the center of a circle or sphere and meeting the circumference or circle at each end.Radius is usually defined as a straight line extending from the center of a circle or sphere to the circumference of surface. (Half of diameter).To figure this out:
R = 1/2 d
R = 1/2 8
R = 4
A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 3 hours, while the outlet pipe can empty it in 10 hours. How long will it take to fill the vat if both pipes are left open?
The time it will take to fill the vat if both pipes are left open is = 4.3 hours
Calculation of time taken to fill vatThe number of pipes a vat has = 2
The time it takes the inlet pipe to fill the vat = 3hrs
The time it takes the outlet pipe to empty the vat= 10hrs
Therefore, the time it will take to fill the vat if both pipes are left open is;
1/t = 1/3-1/10
1/t = 7/30
Make t the subject of formula,
t = 30/7
t= 4.3 hours
Learn more about hours here:
https://brainly.com/question/291457
#SPJ1
HELP. Question 2(Multiple Choice Worth 4 points)
Solve x³ = 64
27
8
3
O
H
4/3
43
Answer:
x= 4/3
Step-by-step explanation:
Take cube root
Suppose that the function f is defined, for all real numbers, as follows.
-x-1 if x #-2
f(x)=
3
if x = -2
Find f(-4), f(-2), and ƒ(0).
S(-4)= 0
X
ƒ(-2) - D
ƒ(o) - D
S
?
The solutions of the function are:
When f(x) = -4, the solution is -4When f(x) = -2, the solution is -5/2When f(x) = 0, the solution is -1How to solve for the equationThe equation is given as
[tex]\frac{3}{4} x-1\\\\[/tex]
When x = -4
3/4 * -4 -1
= -12/4 - 1
= -4
When x = -2
3/4*(-4) - 1
= -6/4 - 1/1
Take the lcm
-10/4
= -5/2
When x = 0
3/4(0) - 1
= -1
When f(x) = -4, the solution is -4
When f(x) = -2, the solution is -5/2
When f(x) = 0, the solution is -1
Read more on real numbers here:
https://brainly.com/question/155227
#SPJ1
Find the hypotenuse of right angle triangle whose sides are 6.03 units and 7.96 units also find
the relative error?
Answer:
9.99 units
Step-by-step explanation:
since hyp=√b^2+h^2
=6.03^2+7.96^2
36.3609+63.3616
√99.7225
9.9861
i.e 9.99
The hypotenuse is is 9.98 units
What is Pythagoras theorem?
The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
Given:
Sides are 6.03 units and 7.96 units
Using Pythagoras theorem,
H²=P²+B²
H²= 7.96²+6.03²
= 63.3616+36.3609
= 99.7225
H=9.98 units.
Hence, the hypotenuse is 9.98 units.
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ2
Can someone explain me this please
Consider a space shuttle which has a mass of about 1.0 x 105 kg and circles the Earth at an altitude of about 200.0 km. Calculate the force of gravity that the space shuttle experiences
uhm i don't understand wut to put below the formula please make it clear thank you alot
Answer:
The force of gravity experienced by the shuttle would be 1.6675×10^N
Jessica works at a restaurant. She earns $5 an hour and received $100 in tips on Saturday night. If she earned $140 total, how many hours did she work?
$140 total - $100 tips = $40
$40 / $5 per hour = 8 hours
She worked 8 hours
7. A man leaves ⅓of his property to his son, two fifths to his wife and the remainder to his daughter. If the daughter received sh. 24,000, what was the total amount left?
Answer:
sh 90,000
Step-by-step explanation:
let x be the total amount left , then
x = [tex]\frac{1}{3}[/tex] x + [tex]\frac{2}{5}[/tex] x + 24,000
multiply through by 15 ( the LCM of 3 and 5 ) to clear the fractions
15x = 5x + 6x + 360,000
15x = 11x + 360,000 ( subtract 11x from both sides )
4x = 360,000 ( divide both sides by 4 )
x = 90,000
the total amount left was sh 90,000
Markup is 25% of sale price of 86.67
what is the cost
Answer:
$ 69 . 34
Step-by-step explanation:
(1 +.25) x = 86.67
86.67 / 1.25 = x = 69.34
Math work math rr rrr
Answer:
The correct answer is infinite. The equation is always true.
In which scenario can you reverse the dependent and independent variables while keeping the interpretation of the slope meaningful?
A.
As the amount of snowfall increases, the number of shovels sold increases.
B.
As number of hours spent watching TV increases, the amount spent on electricity increases.
C.
As the radius of a circle increases, circumference of the circle increases.
D.
As foot size increases, sock size increases.
Answer:
C. As the radius of a circle increases, circumference of the circle increases.
2. √2x-5-√x+6=0(solving the following radical equations and check for extraneous solutions)
I assume the equation is
√(2x - 5) - √(x + 6) = 0
Note the domains for the root expressions:
• √(2x - 5) : 2x - 5 ≥ 0 ⇒ x ≥ 5/2
• √(x + 6) : x + 6 ≥ 0 ⇒ x ≥ -6
So any valid solution we find must be at least 5/2.
Move one term to the other side.
√(2x - 5) = √(x + 6)
Take squares.
(√(2x - 5))² = (√(x + 6))²
2x - 5 = x + 6
Solve for x :
x = 11