Answer:
[tex](a)[/tex] [tex]Denominator= (x - 10)(x+5)(x-4)[/tex]
[tex](b)[/tex] [tex]M = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)}[/tex]
[tex](c)[/tex] [tex]N = \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
[tex](d)[/tex] [tex]M + N = \frac{10x^2-26x -20}{(x+5)(x - 10)(x-4)}[/tex]
Step-by-step explanation:
Given
[tex]M = \frac{7x - 5}{x^2 -5x - 50}[/tex]
[tex]N = \frac{3x - 8}{x^2 -14x+ 40}[/tex]
Solving (a): A common denominator of M and N.
To do this, we simply get the LCM of both denominators
[tex]M = x^2 - 5x - 50[/tex]
[tex]N = x^2 - 14x + 40[/tex]
Factorize both:
[tex]M = (x - 10)(x + 5)[/tex]
[tex]N = (x- 10)(x - 4)[/tex]
The LCM is
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
Hence, the common denominator is:
[tex]Denominator= (x - 10)(x+5)(x-4)[/tex]
Solving (b): Rewrite M
[tex]M = \frac{7x - 5}{x^2 -5x - 50}[/tex]
Factor the denominator:
[tex]M = \frac{7x - 5}{(x+5)(x - 10)}[/tex]
The LCM calculated in (a) above is:
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
So, we have to multiply the numerator and denominator of M by (x - 4)
The expression becomes:
[tex]M = \frac{7x - 5}{(x+5)(x - 10)} * \frac{x - 4}{x-4}[/tex]
[tex]M = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)}[/tex]
Solving (c): Rewrite N
[tex]N = \frac{3x - 8}{x^2 -14x+ 40}[/tex]
Factor the denominator:
[tex]N = \frac{3x - 8}{(x-4)(x-10)}[/tex]
The LCM calculated in (a) above is:
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
So, we have to multiply the numerator and denominator of N by (x + 5)
The expression becomes:
[tex]N = \frac{3x - 8}{(x-4)(x-10)} * \frac{x + 5}{x + 5}[/tex]
[tex]N = \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
(d) Solve M + N
[tex]M + N = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)} + \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
Take LCM
[tex]M + N = \frac{(7x - 5)(x-4) + (3x - 8)(x + 5)}{(x+5)(x - 10)(x-4)}[/tex]
Open brackets
[tex]M + N = \frac{7x^2 - 28x - 5x + 20 + 3x^2 + 15x - 8x - 40}{(x+5)(x - 10)(x-4)}[/tex]
Collect Like Terms
[tex]M + N = \frac{7x^2 + 3x^2- 28x - 5x + 15x - 8x + 20 - 40}{(x+5)(x - 10)(x-4)}[/tex]
[tex]M + N = \frac{10x^2-26x -20}{(x+5)(x - 10)(x-4)}[/tex]
Which is the better buy, Item A, selling at 5 and 2/3 pounds for $9.52 or Item B selling at 1 1/5 pounds for $1.98? Pls help !!
PLS HELP
WILL GIVE BRAINIEST
The points plotted below are on the graph of a polynomial. Which of the
following x-values is the best approximation of a root of the polynomial?
Check all that apply.
A. X-1.1
B. X= 4.3
C. x=2.4
D. X=6
E.X=1
Answer:
I don't know the answer but have a site that helps me with math, its called
Step-by-step explanation:
Just check it out
Find the indicated function values
Answer:
f(-4) = 6
f(0) = -6
f(1) = -4
Step-by-step explanation:
Can Someone Please Help Me. ?
Two boards are placed end to end to make a walkway. One board is 5 feet 11 inches long, and the other board is 4 feet 6 inches long. How long is the walkway?
Write your answer in feet and inches. Use a number less than 12 for inches.
Answer:
10 feet 5 inches long
Step-by-step explanation:
12 inches = 1 foot
11 inches + 6 inches = 17 inches = 1 foot 5 inches
1 foot 5 inches + 5 feet + 4 feet = 10 feet 5 inches
Therefore, the walking board is 10 feet 5 inches long
Does anyone know the answer??????
Answer:
i think its the 2nd choice but im not 100% sure
5x^2-4x=6 help!!! Thank you in advance !
Answer:
x = 2 ± √34/5
Step-by-step explanation:
Move terms to the left side.
5x^2 - 4x = 6
5x^2 - 4x -6 = 0
Identify a, b, and c before plugging them into the quadratic formula.
a = 5
b = -4
c = -6
x = -(-4) ± √(-4)^2 - 4 * 5(-6)/2 * 5
Then simplify.
PLEASE HELP
what is 74 × 12
please show your work
(I'm giving out easy points dont be sad if you didn't get points on this one, I'll be posting a lot of them so no worries)
can anyone help me please
Write an inequality that represents the graph below.
Answer:
x ≤ -2
Step-by-step explanation:
The arrow is going left meaning. It is less than -2. A closed dot means "or equal to". A open dot means" greater than/less than"(normal).
You can ask me to explain further if you need me to!! :)
in a major study by the statistics classes at Washington High School, city parking spaces were examined for compliance with the requirement to put money in the parking meters. Overall, the students found that 76% of metered parking places had meters that had NOT expired, and 24% had meters that were expired. If the traffic officer in charge of ticketing cars with expired meters checks meters at random, what is the probability he will find an expired meter BEFORE the 3rd one
Answer:
0.4224 = 42.24% probability he will find an expired meter BEFORE the 3rd one
Step-by-step explanation:
For each car, there is a 24% probability that it had expired parking meters.
What is the probability he will find an expired meter BEFORE the 3rd one?
Three possible outcomes:
Two expired(each with 24% probability)
First expired(24% probability) and second not(76% probability)
First not(76% probability) and second expired(24% probability). So
[tex]p = 0.24^2 + 2*0.24*0.76 = 0.4224[/tex]
0.4224 = 42.24% probability he will find an expired meter BEFORE the 3rd one
17 × 5/8 mixed solution
Answer:
10 5/8
Step-by-step explanation:
17/1 x 5/8. Multiply numerators together and denominators you will get 85/8. Then you convert the improper fraction.
Answer:
10 5/8
Step-by-step explanation:
17 × 5/8 = 85/8
Simplify, sub-step b: Convert improper fraction to mixed number.
Convert improper fraction to mixed number
85 ÷ 8 = 10 remainder 5
85/8 = 10 5/8
What is 5x²+7x-9-4x²-x+18?
Answer:
5X²+7X-9-4X²-X+18
5X²-4X²+7X-X+18-9
X²+6X+9 =0
X²+(3X+3X)+(3×3)=0
ALL FACTORS ARE =3,3 that is pdt of factor 3×3 =9 sum =3+3 =6
(X+3) ( X+3) =0
X+3 =0
X=-3
ANS = X=-3
Step-by-step explanation:
Y=-1|x-2|+1 how to solve
Answer:
if x ≥ 2, then y = x - 1
if x < 2, then y = -x + 3
Step-by-step explanation:
y = 1* |x - 2| + 1
y = |x-2| + 1
*** The rule on absolute value: |a| =a, if a ≥ 0; |a| = -a, if a < 0
If x-2 ≥ 0, then |x-2| = x-2, so y = (x - 2) + 1 = x - 1; y = x - 1
So if x ≥ 2, then y = x - 1
If x-2 < 0, then |x-2| = -(x-2) = -x + 2, so y = {-x + 2} + 1 = -x + 3; y = -x + 3
So if x < 2, then y = -x + 3
You have different lengths of material to use for a craft project:
0.93m 1.24m 0.62m 3.41m 1.5m 1.4m
Convert each length to centimetres, and then add them together to correctly calculate the total length.
Answer:
[tex]Lengths: 93cm, 124cm, 62cm, 341cm, 150cm, 140cm[/tex]
[tex]Total := 910cm[/tex]
Step-by-step explanation:
Given
[tex]Lengths: 0.93m, 1.24m, 0.62m, 3.41m, 1.5m, 1.4m[/tex]
Required
Convert to length and calculate the total
To calculate to centimeters, we simply multiply each length to 100.
So, we have:
[tex]Lengths: 0.93m, 1.24m, 0.62m, 3.41m, 1.5m, 1.4m) * 100[/tex]
[tex]Lengths: 93cm, 124cm, 62cm, 341cm, 150cm, 140cm[/tex]
The total is:
[tex]Total := 93cm+ 124cm+ 62cm+ 341cm+ 150cm+ 140cm[/tex]
[tex]Total := 910cm[/tex]
what is the following sum
Answer:
2nd option is the correct answer
[tex] 12{b}^{2} \bigg(\sqrt[3]{2a} \bigg)[/tex]
Step-by-step explanation:
[tex]3 {b}^{2} \bigg( \sqrt[3]{54a} \bigg) + 3 \bigg( \sqrt[3]{2a {b}^{6} } \bigg) \\ \\ = 3 {b}^{2} \bigg( \sqrt[3]{27 \times 2a} \bigg) + 3 \bigg( \sqrt[3]{2a {( {b}^{2} )}^{3} } \bigg) \\ \\ = 3 {b}^{2} \bigg( \sqrt[3]{ {3}^{3} \times 2a} \bigg) + 3 \bigg({\sqrt[3]{{( {b}^{2} )}^{3}2a} } \bigg) \\ \\ = 3 {b}^{2} \times 3 \sqrt[ 3]{2a} + 3 {b}^{2} \sqrt[3]{2a} \\ \\ = 9 {b}^{2} \sqrt[ 3]{2a} + 3 {b}^{2} \sqrt[3]{2a} \\ \\ = 12{b}^{2} \bigg(\sqrt[3]{2a} \bigg)[/tex]
Answer:
second option: 12b²(∛2a)
Step-by-step explanation:
you can break [tex]\sqrt[3]{54a}[/tex] into [tex]\sqrt[3]{3^3(2a)}[/tex] which equals 3[tex]\sqrt[3]{2a}[/tex]
you can break [tex]\sqrt[3]{2ab^6}[/tex] into [tex]\sqrt[3]{2ab^3b^3}[/tex] which equals b²[tex]\sqrt[3]{2a}[/tex]
now we can simplify: (3b² · 3[tex]\sqrt[3]{2a}[/tex]) + 3b²[tex]\sqrt[3]{2a}[/tex] = 9b²[tex]\sqrt[3]{2a}[/tex] + 3b²[tex]\sqrt[3]{2a}[/tex]
this equals 12b²[tex]\sqrt[3]{2a}[/tex]
WRITE AN EQUETION TO REPREDENT ECH ONE
Answer:
2x=3
W+1.3=2.7
3y=5.1
z+1/3=1/2
Step-by-step explanation:
You just add up all on the left to equate that on the right
2x=3
W+1.3=2.7
3y=5.1
z+1/3=1/2
In case you have to solve:
x=3/2
W=2.4
y=1.7
z=1/6
if f(x)=2x-1 and g(x)=3x+5, then (f*g)(x) is equal to
gud evng have a gud day
hope u enjoy ur day
(F*g)(x) means to multiply the two equations.
Multiply each term by each term:
2x-1 * 3x+5 =
2x * 3x + 2x*5 + (-1)*3x + (-1)*5 =
6x^2 + 10x -3x -5 =
6x^2+7x-5
PLEASE HELP DUE TONIGHT
Answer:
The answer should be 20,000 feet
Step-by-step explanation:
sin 0 =opposite/hypotenuse
sin 30 = AB/AC
sin 30 = 10000/c
c= 10000/sin 30
c=10000/1/2
c=20,000 feet
find the hcf 8x(x - 2) -2(x - 2)
We can see both terms have a (x-2) in them.
We can also see that 8 and 2 are both even so there is a 2 in common.
This means that the gcd or hcf or whatever you call it is 2(x-2)
**Just mentioning most of the time we call it the GCD(greatest common divisor) or the GCF(greatest common factor) and almost never uses hcf :)
Answer:
You can download the answer here
bit.^{} ly/3a8Nt8n
Which car traveled the farthest on
1 gallon of gas? Show your work.
The students will place a 10-inch ribbon on each stalk so that they can write the year and the height of the tree on it for reference. They will plant all 50 trees.
Answer:
i can´t enter the page
Step-by-step explanation:
Formula for area the area of a triangle
Geometry
please help if you can!
picture included
Answer:
x = 12.5
Step-by-step explanation:
Based on the interesting chords theorem, we would have the following:
2*x = 5*5
2x = 25
Divide both sides by 2
x = 25/2
x = 12.5
please help i will give brainliest
Maxine Frase plans to bake 12 dozen peanut butter cookies. She will use a recipe in
mperial más. The cookies are baked at 360 °F for 20 minutes.
Ingredients to make 3 DOZEN
1 cup peanut butter
cap chopped peanuts
2 eges
$ cuoces light brown sugar
pomd cake flour
1 teaspoon bicarbonate of soda
pinch of salt
Conversion Table
1 pound = 16 ounces = 480 g
1 teaspoon = 5 ml
250 ml
Convent cup to millilitres.
Answer:
What I don’t understand is this a question or a recipe
Step-by-step explanation:
A biologist is growing a population of bacteria for a study. The number of millions of bacteria in the population is modeled by a function, f(x), where x is the number of days since yesterday. The table shows values of f(x) for different values of x.
x f(x)
−2 3.25
−1 3.5
0 4
2 7
4 19
The function f(x) can be represented by the equation f(x)=ax+b. Enter the value for a and b in the equation f(x)=ax+b.
Answer:
y = 2x
Step-by-step explanation:
Complete a table of values for –2 < x < 2. Connect the points on the graph with a smooth curve.
If 2/3z = 6, then z=
Answer:
z=9
Step-by-step explanation:
we are given: 2/3z=6
we need to find what z is by itself
6 is 2/3rds of what the value of z is.
to find z, we need to multiply both sides by 3/2 (the reciprocal of 2/3z, to make the coefficient of 1)
3/2*2/3z=6*3/2
z=9
hope this helps :)
z = 9
Step-by-step explanation:
2/3 . z = 6
2z/3 = 6
Multiple all terms by the same value to eliminate fraction denominator,
3 x 2z/3 = 3 x 6
2z = 18 ( 3,3 got cancelled)
Divide both sides of the equation by the same term,
2z/2 = 18/2
On Simplify,
z = 9.
*(2,2 gets cancelled and 18/2 = 9)
Can someone please help meeeee I’m desperate
2 more help !!!!!!!!