Answers
[tex] \frac{w^2-9}{w^2-4w-21}= \frac{w^2-3^2}{(w+3)(w-7)} = \frac{(w+3)(w-3)}{(w+3)(w-7)}= \frac{w-3}{w-7} [/tex]
We can conclude that the correct answer is the fourth one: [tex]\frac{w-3}{w-7}[/tex]
Related Questions
The measure of angle x is 25 more than 4 times the measure of its complement. Find the measure of x.
Answers
- One angle measures x degrees.
- The other angle measures 25 more than 4 times the angle that measures x degrees; it measures 4x + 25 degrees.
To find x, set the sum of these expressions (x and 4x + 25) equal to 90 and solve algebraically for x.
90 = x + (4x + 25)
90 = x + 4x + 25
90 = 5x + 25
65 = 5x
13 = x
If you wanted to find the measure of angle x, you'd substitute 13 for x in its expression, 4x + 25.
4x + 25
4(13) + 25
52 + 25
77
Answer:
x = 13
m∠x = 77°
If f(x)=6x^3+5x,g(x)=3x^2+5,and h(x)=9x^2-8 what is the degree of f(g(h(x))) awer choices are a.2 b.3 3.7 4.12
Answers
We know that [tex]h(x)=9x^2-8[/tex] and [tex]g(x)=3x^2+5[/tex]
[tex]g(h(x))=g(9x^2-8)=3(9x^2-8)^2+5[/tex]
[tex]=3(81x^4-144x^2+64)+5[/tex]
[tex]=243x^4-432x^2+192+5[/tex]
[tex]=243x^4-432x^2+197[/tex]
Now that we know that [tex]g(h(x))=243x^4-432x^2+197[/tex], to find [tex]f(g(h(x)))[/tex] we are going to evaluate [tex]f[/tex] at [tex]243x^4-432x^2+197[/tex]
[tex]f(g(h(x)))=f(243x^4-432x^2+197)[/tex]
[tex]f(243x^4-432x^2+197)=6(243x^4-432x^2+197)^3[/tex][tex]+5(243x^4-432x^2+197)[/tex]
[tex]=86093442x^{12}-459165024x^{10}+1025681130x^8-1228219200x^6[/tex][tex]+83152048x^4-301780944x^2+45873223[/tex]
Since the degree of a polynomial is the highest degree of its monomials, we can conclude that the degree of f(g(h(x))) is 12
Answer:
The degree is 12
Step-by-step explanation:
Round 5685 to the nearest 100
Answers
Kristen has 64 coins in her bank. She has $9.25 in dimes and quarters. How many dimes and quarters does she have?
Answers
q= # of quarters
QUANTITY EQUATION:
d + q= 64
COST EQUATION:
0.10d + 0.25q= $9.25
STEP 1:
multiply quantity equation by -0.10 to be able to eliminate the d term in step 2
(-0.10)(d + q)= (-0.10)(64)
-0.10d - 0.10q= -6.40
STEP 2:
add equation from step 1 to cost equation to eliminate the d term and solve for q
Add
0.10d + 0.25q= $9.25
-0.10d - 0.10q= -6.40
0.15q= 2.85
divide both sides by 0.15
q= 19 quarters
STEP 3:
substitute q value in step 2 into either original equation to find d value
d + q= 64
d + 19= 64
subtract 19 from both sides
d= 45 dimes
CHECK:
0.10d + 0.25q= $9.25
0.10(45) + 0.25(19)= 9.25
4.50 + 4.75= 9.25
9.25= 9.25
ANSWER: There are 45 dimes and 19 quarters.
Hope this helps! :)
the difference between the product of 6 and a number and negative two times the number
Answers
Luther won 12 of the last 20 video games he played.
Suppose Luther plays a total of 60 games with his friends over the next month. Predict how many of these games Luther will win.
Answers
The height of a model rocket is 4.5% of the height of the actual rocket. The model is 1.32m high. How high is the actual rocket? Please show your work.
Answers
x is the actual height of the rocket.
4.5% is really 0.045 (move the decimal place 2 times to the left).
1.32 = 0.045x
Divide both sides by 0.045.
x = 29.3
The height of the actual rocket is 29.3 meters.
To find the height of the actual rocket given the height of the model rocket, we can use the ratio between the two. By setting up and solving a simple equation, we can determine that the height of the actual rocket is 29.33 meters.
To find the height of the actual rocket, we need to start by determining the ratio between the height of the model rocket and the actual rocket. Given that the model rocket is 4.5% of the height of the actual rocket, we can use this ratio to solve for the height of the actual rocket.
Let's denote the height of the actual rocket as x. Since the model rocket is 4.5% (or 0.045) of the actual rocket's height, we can set up the equation:
0.045x = 1.32
To solve for x, we divide both sides of the equation by 0.045:
x = 1.32 / 0.045
Calculating this expression gives us the height of the actual rocket as 29.33 meters.
George earns $455 per week. George recieves a 20% raise. How can george calculate his new weekly per rate?
Answers
OPTION 1:
multiply current pay by 20%, then add the result to the current pay
Step 1:
multiply pay by 20% increase
=$455 * 20%
=$91 increase
Step 2:
add pay increase from step 1 to current pay rate
=$455 + $91
=$546 new weekly rate
OPTION 2:
multiply current pay by (1 + 20%)
=($455)(1 + 20%)
=(455)(1.20)
=$546 new weekly rate
ANSWER: His new weekly rate is $546 per week.
Hope this helps! :)
A recipe for cookies requires 2/3 cup of butter. Rama wants to make 3/4 of the recipe. How many cups of butter should Rama use to make the cookies?
Answers
= (2/3)(3/4)
multiply numerators; multiply denominators
= (2*3)/(3*4)
= 6/12
simplify by 6
= 1/2 cup
ANSWER: Rama should use 1/2 cup of butter.
Hope this helps! :)
simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39)
Answers
[tex]5.23x + 3.76 - 3.67x + 6.39 \\ = 1.56x + 10.15[/tex]
Answer:
1.56x + 10.15
Step-by-step explanation:
(5.23x + 3.76) – (3.67x – 6.39)
(a + b) – (c – d) = a + b – c + d
Remove the parentheses and change the signs as needed:
5.23x + 3.76 – 3.67x + 6.39.
Group the like terms and simplify:
5.23x – 3.67x + 3.76 + 6.39
1.56x +10.15.
The simplified form of (5.23x + 3.76) – (3.67x – 6.39) is 1.56x + 10.15.
Find the quotient: 744 ÷ 3.1
A) .024
B) 2.4
C) 24
D) 240
Answers
744 / 3.1 = 240
Check
3.1 * 240 = 744
744 = 744
Hope this helps you! (:
-Hamilton1757
He counted 206 wheels and 170 pedals. How many bicycles and tricycles does he have.
Answers
tricycle has 3 wheels and 2 pedals
EQ 1 : 2b + 2t = 170 pedals
EQ 2: 2b +3t = 206 wheels
subtract EQ 1 from EQ 2
2b +3t = 206 - 2b + 2t = 170 = t=36
there were 36 tricycles
36 x 2 = 72 pedals
170 pedals - 72 = 98 pedals left
98/2 = 49 bicycles
36 Tricycles and 49 bicycles
Please help my answer is c, is this right!
Answers
There are 3 X's at 1/4 so you would add 1/4+1/4+1/4=3/4. There are 2 X's at 1/2 so you would add 1/2+1/2=1. There are 2 X's at 3/4 so you would add 3/4+3/4=1.5. There is 1 X at 1 so it would just be 1. Then add all those together 3/4+1+1.5+1=4.25 or you could just add each X as you come across it on the number line like so:
[tex]0.25 + 0.25 + 0.25 + 0.5 + 0.5 + 0.75 + 0.75 + 1 = 4.25[/tex]
Susan received grades of 78, 93, 82, and 76 on four math exams. What is the lowest score she can receive on her next math exam and have an average of at least 85 on the five exams?
A) 96
B) 94
C) 92
D) 90
E) 88
Answers
Choice A) 96
==========================================
Explanation:
The original list of scores is {78, 93, 82, 76}
Add x to the list to get this new list {78, 93, 82, 76, x}
Let's find the average of the new set
Add up the values and divide by 5. We force this average to be 85 since this is the grade Susan wants
(78+93+82+76+x)/5 = 85
(329+x)/5 = 85
329+x = 85*5
329+x = 425
x = 425-329
x = 96
So if Susan gets a 96 or greater on the fifth test, then she'll have an average of at least 85 (that score or greater)
What does volume mean
Answers
Hope this Helps!!
write the equation 12=3x + 6 in the form ax + b = c with c=12 what are the values of a & b?
Answers
is effectively c=ax+b
meaning
a is 3
b is 6 and
c is 12
[tex]ax + b = c \\ 3x + 6 = 12[/tex]
Answer : a = 3, b = 6
Hope this helps. - M
What is the equation for the sum of three consecutive even numbers totaling 198.
Question 4 options:
n+n+1+n+2=198
n+n+2+n+4=198
3n=198
n+3=198
Answers
Final answer:
Option B: n+n+2+n+4=198
The equation for the sum of three consecutive even numbers totaling 198 can be represented as
n + (n+2) + (n+4) = 198,
where n is the first even number.
Solving the equation, the first even number is 64, and the consecutive even numbers are 66 and 68.
Explanation:
The equation for the sum of three consecutive even numbers can be represented as n + (n+2) + (n+4) = 198, where 'n' is the first even number. Let's solve the equation:
Combine like terms: 3n + 6 = 198Subtract 6 from both sides: 3n = 192Divide both sides by 3: n = 64So, the first even number is 64, and the consecutive even numbers are 66 and 68.
Cody and Ashley are helping their dad fertilize the lawn. They have 3 1/3 pounds of fertilizer and 3 buckets. Each bucket will get the same amount of fertilizer. Cody measures 1 pound of fertilizer into each bucket. The following equation represents this situation, where x represents the additional amount of fertilizer each bucket will get. 3 (x+1) = 3 1/3
How much more fertilizer should each bucket get?
A. 1/9 of a pound
B. 2/3 of a pound
C. 2/9 of a pound
D. 1/3 of a pound
Answers
Answer:
1/9 pound
Step-by-step explanation:
Find the value of X in the isosceles triangle shown below. How do I find X?
Answers
a²+b²=c² → 3²+b²=6.708204² (√45)
9 +b² =45.000001
-9 ↓ ↓-9
---------------------------
zero pair √b² = √36.000001
b = 6
One side of the isosceles the x is 6, but we need the whole part so for last you just multiply 6×2= 12
The answer is...... X=12
Please help is the answers is 6
Answers
What is the value of x?
Enter your answer in the box.
x =
Answers
A straight line measures to 180°
The angle that measures 134 and x make a straight line
180 = 134 + x
Subtract 134 from both sides
46 = x
The answer is 46°
Hope this helps!
x = 180 - 134 = 46°
Answer: 46°
Which is an equation of the given line in standard form?
A. -6x+5y=13
B. -6x+7y=-11
C. -6x+7y=11
D. -7x+6y=-11
Answers
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The coordinates of the points:
[tex](-3;\ -1)\to x_1=-3;\ y_1=-1;\ \left(\dfrac{1}{2};\ 2\right)\to x_2=\dfrac{1}{2};\ y_2=2[/tex]
Substitute:
[tex]m=\dfrac{2-(-1)}{\frac{1}{2}-(-3)}=\dfrac{3}{3\frac{1}{2}}=\dfrac{3}{\frac{7}{2}}=3\cdot\dfrac{2}{7}=\dfrac{6}{7}[/tex]
We have:
[tex]y=\dfrac{6}{7}x+b[/tex]
Substitute the coordinates of the point (-3; -1) to the equation of the line:
[tex]-1=\dfrac{6}{7}\cdot(-3)+b\\\\-1=-\dfrac{18}{7}+b\ \ \ |+\dfrac{18}{7}\\\\b=\dfrac{11}{7}[/tex]
Therefore we have:
[tex]y=\dfrac{6}{7}x+\dfrac{11}{7}\ \ \ |\cdot7\\\\7y=6x+11\ \ \ |-6x\\\\\boxed{-6x+7y=11}[/tex]
Answer: C. -6x + 7y = 11
If the sum of three numbers is 144, what is the average of the three numbers?
Answers
Given a mean of 61.2 and a standard deviation of 21.4 what is the z score of the value 90 rounded to the nearest tenth?
Answers
Answer:
The z-score of 90 is 1.35
Step-by-step explanation:
The z-score is calculated using the formula:
[tex]z = \frac{x - \mu}{ \sigma} [/tex]
From the question, it was given that the mean is
[tex] \mu = 61.2[/tex]
and the standard deviation is
[tex] \sigma = 21.4[/tex]
and x=90.
We substitute the given values to obtain:
[tex]z = \frac{90 - 61.2}{21.4} [/tex]
[tex]z = \frac{28.8}{21.4} = 1.35[/tex]
Answer:
1.35
Step-by-step explanation:
there are a total of 122 countries in Africa, Europe, and North America. Europe has twice as many countries as North America, and Africa has seven more than Europe. How many countries are in each continent? write an equation and solve it to answer the question
Answers
A = E + 7 = 2n + 7
n + 2n + 2n +7 = 122
Haley has some cubes each cube has a side length of 4 inches what is the volume in cubic inches of each cube
Answers
V=s*s*s
where s represents a side
so...
V=4in.*4in.*4in.
4*4*4=64
V=64 in. cubed
If 400 bricks measuring 81" by 31" are required to build a wall 42 ft. high, how long is the wall? feet.
Answers
b= 400, let H height and l length
Area = 81*31 or 6.75*2.58 = 17.44 ft²
b(17.44ft²)=Hl
400(17.44 ft²) =42 l
l= 6975/42 = 166.07
so the length of the wall is 166 ft approximately as a whole number
your mom has to pay two bills. Taxes are $483 and the heating is $230. You want to find out how much total your mom will pay. How can you use skip counting to add these two numbers?
Answers
400 pluse 200 = 600
80 pluse 30 = 110
3 pluse 0 =3
600 pluse 110 pluse 3 equals 713
Native Americans once lived near Cartersville, Georgia, in an area that is now a state park. They constructed burial mounds that often contained artifacts, such as beads, feathers, and copper ear ornaments. One of the park's mounds is 63 feet in height. Be a Math Detective. If the top of the mound is rectangular in shape with a perimeter of 322 yards, what could be the side lengths of the rectangle?
Answers
The sides of the rectangle atop of the mound could be multiple pairs of measurements. One such possible example is 100 yards by 61 yards which satisfy the perimeter equation, given the perimeter of the rectangle is 322 yards.
Explanation:The question is asking about the side lengths of the rectangular top of an ancient mound in Cartersville, Georgia. This is a math problem that uses the concept of perimeter.
The perimeter of a rectangle is given by the formula: P = 2l + 2w where P is the perimeter, l is the length, and w is the width. We know that the perimeter of the rectangle is 322 yards. We can solve for the sides (length and width) by setting up equations using various combinations of numbers that, when plugged into the formula, result in a sum of 322.
It's important to note that we won't have a unique solution to this because a rectangle's perimeter doesn't determine its side lengths uniquely, but only within certain limits. So, there could be multiple correct answers.
For example, if we consider the length to be 161 yards, and the width to be 0 yards, it would still satisfy the perimeter equation. But since width cannot be zero, we can suppose the length to be longer side and width to be smaller, say 100 yards and 61 yards, which also add up to produce a perimeter of 322 yards. So, one possible solution is 100 yards by 61 yards.
Learn more about Mathematical problem of Perimeter here:https://brainly.com/question/31699552
#SPJ12
the drawing is composed of a rectangle and a semicircle 18 cm 22 cm
Answers
The perimeter is L + w + L + perimeter of a semicircle.
L = 22 cm
W = 18 cm
Perimeter can be one of two answers. You need to specify where the semicircle is. Formula for semicircle is
pi * r
r = 18/2 = 9 or
r = 22/2 = 11
So the perimeter of the semi circle is pi * 9 = 25.12 The total Perimeter = 22 + 22 + 18 + 25.12 = 87.12
It can also be 22 + 18 + 22 + 34.54 = 96.54 There are even more possiblities for perimeter. I would have the same problem if you asked about area.
Why not put more details in and I'l give you the correct answer. Here is what we need to know
1. Where is the circle on the 22 cm side or the 18 cm side?
2. What are you looking for: perimeter or area? As soon as you answer these I'll be back.