Answers
[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}[/tex]
Solution:
Given expression:
[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}[/tex]
To solve the given expression:
First simplify: [tex]\frac{50-2 w^{2}}{3 w^{2}+9 w-30}[/tex]
[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30}=-\frac{2(w+5)(w-5)}{3(w-2)(w+5)}[/tex]
Cancel the common factor (w + 5).
[tex]$=-\frac{2(w-5)}{3(w-2)}[/tex]
Now substitute this in the given expression.
[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{2(w-5)}{3(w-2)} \cdot \frac{w^{2}+5 w-14}{6 w-30}[/tex]
Multiply the fractions [tex]\frac{a}{b} \cdot \frac{c}{d}=\frac{a \cdot c}{b \cdot d}[/tex]
[tex]$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{3(w-2)(6 w-30)}[/tex]
Factor the denominator [tex]3(w-2)(6 w-30) =18(w-2)(w-5)[/tex]
[tex]$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{18(w-2)(w-5)}[/tex]
Cancel the common factor 2(w – 5).
[tex]$=-\frac{w^{2}+5 w-14}{9(w-2)}[/tex]
Factor the numerator [tex]w^{2}+5 w-14=(w-2)(w+7)[/tex]
[tex]$=-\frac{(w-2)(w+7)}{9(w-2)}[/tex]
Cancel the common factor (w – 2).
[tex]$=-\frac{w+7}{9}[/tex]
[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}[/tex]
Related Questions
add at the park there's a pool shaped like a circle with a diameter 22 yards. A ring shaped path goes around the pool. it's width is 5 yards.
Answers
Answer:
424 yards²
Step-by-step explanation:
Diameter 22, radius 11
Outer circle: radius = 11+5 = 16
Area of the path:
Pi× (16²-11²)
= 135pi yards²
Or, 424 yards² (3 sf)
Answer:
135pi
Step-by-step explanation:
(I'm guessing you want to know the ring's area)
Diameter = 22 yards, meaning Radius = 11 yards
[tex](11+5)^{2}\pi[/tex] = 256pi = Outer Ring + Pool
[tex](11)^{2}\pi[/tex] = 121pi = Pool
Outer Ring = 256pi - 121pi = 135pi
PLEASE ANSWER
Which equation represents the following graph?
A. y = 2x + 3
B. y = 3x + 2
C. y = -2x + 3
D. y = -3x + 2
Answers
Answer:
A: y = 2x + 3
Step-by-step explanation:
y intercept: 3
Slope is positive
Only option A satisfies both of the above
11/20+ c=3/4 what is the answer
Answers
Answer:
Step-by-step explanation:
Given that,
11/20 + c = 3/4
Subtract 11/20 from both sides of the equation to eliminate 11/20
11/20-11/20+c=3/4-11/20
c= (15-11)/20
c=4/20
c=1/5
For the following right- triangle find the side length x 8 12
Answers
Answer:
4[tex]\sqrt{13}[/tex] or 4[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Pythagorean theorem:
your solution will differ based on which side is the hypotenuse
x = [tex]\sqrt{12^{2} -8^{2} }[/tex] =4[tex]\sqrt{5}[/tex]
or x = [tex]\sqrt{8^{2}+12^{2} }[/tex] = 4[tex]\sqrt{13}[/tex]
HELPPPPP PLEASEEEEEE
Answers
What is the ordered pair solution to the system y= -4x and y=2x+12 ??
Answers
The solution to the system of equations y = -4x and y = 2x + 12 is found by setting the two equations equal to each other, solving for x, and then finding y. The ordered pair solution is (-2, 8).
Explanation:To find the ordered pair solution to the system of equations y = -4x and y = 2x + 12, we need to set the two equations equal to each other since they both describe y in terms of x. This gives us:
-4x = 2x + 12
Now, we will solve for x by combining like terms:
-4x - 2x = 12
-6x = 12
To get x by itself, divide both sides by -6:
x = -2
Next, we substitute x = -2 back into one of the original equations to find y. For example:
y = 2(-2) + 12
y = -4 + 12
y = 8
Therefore, the solution to the system of equations is the ordered pair (-2, 8).
-1(n2 + 3) if n = -3.
Answers
Answer:
3
Step-by-step explanation:
Answer:
n = 3
Step-by-step explanation:
-1(n2 + 3) if n = -3.
from the question
-1(n2 + 3)
we are then asked to find n if its equals to -3
solution
-1(n2 + 3) .................. we are going to open the bracket with-1 according to BODMAS rule
we have,
-n²-3
when the value of n = -3
we have,
= (-3)² - 3
= 9 - 3
= 3
therefore when n = -3 in the expression -1(n2 + 3) the value of n = 3
to check if your answer is correct you will put the value of n which is 3 into the -1(n2 + 3) then you will see that the right handside = lefthandside
which is
3=3...........proved.
29.91 – 1.35p=-5.7(-6p - 4)
Answers
Answer:
p = 0.2
Step-by-step explanation:
Step 1: Distribute
29.91 - 1.35p = -5.7(-6p - 4)
29.91 - 1.35p = 34.2p + 22.8
Step 2: Add 1.35p to both sides
29.91 - 1.35p + 1.35p = 34.2p + 22.8 + 1.35p
29.91 = 35.55p + 22.8
Step 3: Subtract 22.8 from both sides
29.91 - 22.8 = 35.55p + 22.8 - 22.8
7.11 = 35.55p
Step 4: Divide both sides by 35.55
7.11 / 35.55 = 35.55p / 35.55
0.2 = p
Answer: p = 0.2
Using V = lwh, what is an expression for the volume of the following prism? The dimensions of a prism are shown. The height is StartFraction 2 d minus 6 Over 2 d minus 4 EndFraction. The width is StartFraction 4 Over d minus 4 EndFraction. The length is StartFraction d minus 2 Over 3 d minus 9 EndFraction.
Answers
We know that the volume of a prism is defined by:
[tex]V=lwh \\ \\ \\ Where: \\ \\ l:length \\ \\ w:width \\ \\ h:height \\ \\ \\ l=\frac{d-2}{3d-9} \\ \\ w=\frac{4}{d-4} \\ \\ h=\frac{2d-6}{2d-4}[/tex]
Substituting values:
[tex]V=\left(\frac{d-2}{3d-9}\right)\left(\frac{4}{d-4}\right)\left(\frac{2d-6}{2d-4}\right) \\ \\ \\ Simplifying: \\ \\ V=\frac{d-2}{3d-9}\cdot \frac{4}{d-4}\cdot \frac{d-3}{d-2} \\ \\ V=\frac{\left(d-2\right)\cdot \:4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)\left(d-2\right)} \\ \\ V=\frac{4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)} \\ \\ V=\frac{4\left(d-3\right)}{3\left(d-3\right)\left(d-4\right)}[/tex]
[tex]Finally: \\ \\ \boxed{V=\frac{4}{3\left(d-4\right)}}[/tex]
The volume of the given prism in simplified form is [tex]V = \frac{4}{3(d - 4)}[/tex].
To find the volume of the prism, we use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
Given the dimensions of the prism:
l = \frac{d - 2}{3d - 9}
[tex]l = \frac{d - 2}{3d - 9}\\\\w = \frac{4}{d - 4}\\\\h = \frac{2d - 6}{2d - 4}[/tex]
We substitute these into the formula:
[tex]V = \left(\frac{d - 2}{3d - 9}\right) \left(\frac{4}{d - 4}\right) \left(\frac{2d - 6}{2d - 4}\right)[/tex]
Now we simplify this expression step-by-step:
Simplify the height term:
[tex]\frac{2d - 6}{2d - 4} = \frac{2(d - 3)}{2(d - 2)} = \frac{d - 3}{d - 2}[/tex]
Substitute the simplified height term:
[tex]V = \left(\frac{d - 2}{3(d - 3)}\right) \left(\frac{4}{d - 4}\right) \left(\frac{d - 3}{d - 2}\right)[/tex]
Combine and cancel common terms:
[tex]V = \frac{4}{3(d - 4)}[/tex]
This gives us the volume of the prism in its simplest form.
Complete question:
Using V = lwh, what is an expression for the volume of the following prism? The dimensions of a prism are shown.
The height is (2 d - 6) / (2 d - 4).
The width is 4 / (d - 4 ).
The length is StartFraction (d - 2) / (3 d - 9 ).
29,22,22,17,33,32,27 (FIND THE MODE)
Answers
Answer:
22
Step-by-step explanation:
22 shows up twice and the rest of the numbers show up once.
Answer:22
Step-by-step explanation:
It appears most often.
What is the slope of the line passing through the points (-2, -8) and (-3, -9) ?
Answers
Answer: answer is 1
Step-by-step explanation:
Slope(m) of the line = change in y/change in x
y2 - y1/x2 - x1
Locate the coordinates points: (-2, -8) and (-3, -9) ?
X1= -2, X2=-3
Y1= -8, y2= -9
Slot in the values into the equation:
m = -9 - (-8)/-3 - (-2)
-9 + 8/ -3 +2
= -1/ -1
=1
I hope this helps.
What is the length and width of the rectangle if the area is given by trinomial r squared - 2r - 15. Use factoring
Answers
Answer:
(r+3)(r-5)
Step-by-step explanation:
r^2-2r-15
(r+3)(r-5)
+3-5=-2
+3*-5=-15
Answer:
The length is r + 3 and the width r - 5..
Step-by-step explanation:
r^2 - 2r - 15
= (r - 5)(r + 3)
The length is r + 3 and the width r - 5
What is k over 3.5+7.4=8
Answers
Answer:
k=2.1
Step-by-step explanation:
k/3.5 + 7.4 = 8
Subtract 7.4 from each side
k/3.5 + 7.4 -7.4 = 8-7.4
k/3.5 = .6
Multiply each side by 3.5
k/3.5 *3.5 = .6 *3.5
k = 2.1
If f(3) = -4, f'(3) = 4, g(3) = 2, and g'(3) = 0, find (f + g)'(3).
Answers
Final answer:
The derivative of the sum of functions f and g at x = 3 is calculated by adding the derivatives of f and g at 3. Given that f'(3) = 4 and g'(3) = 0, the derivative (f + g)'(3) equals 4.
Explanation:
The student is asking about the derivative of a sum of two functions at a specific point, which is a concept covered in calculus. From the given information, we know that:
f(3) = -4, f'(3) = 4g(3) = 2, g'(3) = 0To find (f + g)'(3), we apply the rule for the derivative of a sum of functions, which states that:
(f + g)'(x) = f'(x) + g'(x)
Therefore, (f + g)'(3) is:
(f + g)'(3) = f'(3) + g'(3)
(f + g)'(3) = 4 + 0
(f + g)'(3) = 4.
Thus, the derivative of the sum of functions f and g at x = 3 is 4.
Gabby assigned a number to each of the 120 athletes at her school and
put the numbers in a box. She randomly chose 25 numbers and found that
10 athletes were female. Use this sample to make an inference about how
many athletes at Gabby's school are female.
Answers
Answer:
48
Step-by-step explanation:
[tex] \frac{10}{25} [/tex]
athletes are female. Now, we need to find what
[tex] \frac{x}{120} [/tex]
athletes are female.
10 ÷ 25 = 0.4
0.4 × 100 = 40 so
[tex] \frac{10}{25} = 40\%[/tex]
40% is the experimental probability for the number of female athletes in the sample. 40% of 120 should be about the number of female athletes in the whole school.
120 × 0.4 (or 40%) = 48.
You can infer that 48 athletes in the school are female.
Answer:
Step-by-step explanation:48
What does AB represent in this figure
Answers
Answer:
B. Ray
Step-by-step explanation:
When they ask what does AB represent because they put the A first this means that the line is going from A to B and because there is an arrow and the end of B this means its a ray.
A ray is a half-infinite line. AB represents a ray.
What is a ray?A ray is a half-infinite line (sometimes called a half-line) in which one of the two points A and B is assumed to be at infinity.
As we can see that AB has a point on one side while the other side of the line has an arrow, therefore, AB represents a ray.
Learn more about Ray:
https://brainly.com/question/13486760
Evaluate 1/-5ab if a=3/7 and b=5/8 write in simplest form
Answers
Answer:
-56/75
Step-by-step explanation:
1/-5ab = 1 ÷ -5ab
we substitute the value of a = 3/7 and b = 5/8 into 1 / -5ab
we have
1/ -5 × 3/7 × 5/8 = 1/ -75/56
this can be written as
1 × 56/-75 = -56/75
How can I this math equation -5 -x =-8
Answers
Answer: x = 3
Step-by-step explanation:
-5 -x = -8
-× = -8 + 5
-x = -3
x = 3
Evaluate - x - 4 when x = - 7 and y=5
Answers
Answer: 3
Step-by-step explanation: Plug in x = -7
a sprinter increases the speed from 0 meters per second to 9 meters per second in 2 seconds. what is the acceleration
Answers
Answer:
The acceleration is
[tex]4.5 {ms}^{ - 2} [/tex]
Step-by-step explanation:
Use the equation of motion,
[tex]v = u + at[/tex]
where u=0m/s is the initial speed, v=9m/s is the final speed and t=2 seconds is the time.
We substitute the values into the equation and solve for the acceleration, a
[tex]9 = 0 + a(2)[/tex]
This means that;
[tex]9 = 2a[/tex]
Divide both sides by 2 to get:
[tex]a = \frac{9}{2} [/tex]
[tex]a = 4.5 {ms}^{ - 2} [/tex]
convert 34 base five to 34 base ten
Answers
34 base five to 34 base ten is 19.
Step-by-step explanation:
Basically , In order to convert 34 from base 5 to base 10 , We skip consecutive 5 numbers after counting 5 numbers as shown below in table in base-5 table and , just increment 1 in base-10 table
Base- 5 Base-10
1 1
2 2
3 3
4 4
10 5
12 6
13 7
14 8
20 9
....... ....
34 19
34 base five to 34 base ten is 19.
Write the multiples of 5 (1,5,25,125,....) based on the no.of digits given. Then multiply and add to convert it into base 10
5 1
------------
3 4
------------
5 (3)+ 1(4) = 15+4 = 19
Fifteen less than twice a number x is y
Answers
Step-by-step explanation:
The Mathematical transformation of the given statement would be:
[tex]2x - 15 = y[/tex]
Find the quotient 130 ÷ –13.
A. –12
B. –9
C. –10
D. –5
Answers
Answer:
C)-10
Step-by-step explanation:
negative divided by negative is positive.
-130 / -13 =10
Answer:
Option C, -10
Step-by-step explanation:
130 / -13
13 goes into 130 ten times
-10
Answer: Option C, -10
If an employer lacked 6 days of working twice as many days as did his employee and the sum of the days they worked is 42, how many days did each work
Answers
Answer:
Step-by-step explanation:
2x-6=48
2x=42+6
2x=48days
x=24days
The employee worked 16 days and the employer worked 26 days to reach the total of 42 days both worked.
Explanation:
This problem can be solved using algebraic expressions. Let's denote the number of days the employee worked as 'e'. According to the problem, the employer worked (e+6) days, since he lacked 6 days of working twice as many days as his employee (2e-6). Then, combining these gives the equation (2e-6) + e = 42 (the total number of days they both worked). We can simplify this equation by adding like terms and getting 3e - 6 = 42. Solving for 'e' will give us the number of days the employee worked. First, add 6 to both sides of the equation making it 3e = 48. Then, divide both sides by 3 to solve for 'e'. Thus, e = 16. This means the employee worked 16 days. The employer, having worked (2e-6) days, worked (2*16-6) = 26 days.
Learn more about Algebra here:
https://brainly.com/question/24875240
#SPJ12
4. Find the correct table for the given rule:
y=x+2
Answers
Answer:
Table B is the correct answer.
Step-by-step explanation:
is 8 4\5 greater than 8.08
Answers
Yes.
8 4/5 = 8 8/10 = 8.8
8.8 is greater than 8.08
Answer:
yes
Step-by-step explanation:
4/5 as a fraction is 8/10 and 8/10 as a decimal is 0.8 and 0.8 is greater than 0.08
What is the decimal equivalent of an 11% increase
Answers
Answer:
0.11
Step-by-step explanation:
You would convert the percentage to a fraction. Since the % symbol means 'out of 100', you would put 11 over 100: 11/100.
Then you would convert the fraction to a decimal: 0.11.
An easier way could also be to take the percentage and move it two decimal places to the right.
Ex: 43% moved two decimal places to the right would be 0.43.
I hope this helps!
Answer:
0.11
Step-by-step explanation:
Pamela knit a total of 28 centimeters of scarf over 2 nights. After 3 nights of knitting, how many centimeters of scarf will Pamela have knit in total? Assume the relationship is directly proportional.
Answers
Answer:
42 centimetres
Step-by-step explanation:
First, u have how many centimetres knitted over 1 night:
28/2=14So 1 night=14 cm28cm+14cm=42cm=3 nightsFind values of x and y
Answers
Answer:
3 = x, 2 = y
Step-by-step explanation:
Opposite sides in a parallelogram are always congruent, so 2y+3=y+5 and 4y+1=4x-3
The first equation, when solved, shows that y = 2
When you plug that into the second equation, you get 4(2) + 1 = 4x - 3
This means that 12 = 4x, so 3 = x
Which of the following statements is true? The value π is a rational number. The number 0 is a natural number. The number is an integer. The number -5 is a real number.
Answers
Answer:
the number -5 is a real number
Step-by-step explanation:
real numbers are basically all numbers.... if you havent met complex numbers yet..
hopefuly this helped
:)
Answer:
the number -5 is a real number
Step-by-step explanation:
all the others are wrong.