Answer:
Domain: { x ∈ R | x ≠ -2, 3 }
Step-by-step explanation:
[tex]f(x)=\dfrac{(x+2)(x-1)}{(x-3)(x+2)}[/tex]
The domain (x-values) of a rational function is all real numbers of x with the exception of those for which the denominator is 0. Therefore, to find the values of x that need to be excluded from the domain, equate the denominator to zero and solve for x.
The denominator for the given function is [tex](x - 3)(x + 2)[/tex]
[tex]\implies (x - 3)(x + 2)=0[/tex]
[tex]\implies (x - 3)=0\implies x=3[/tex]
[tex]\implies (x + 2)=0 \implies x=-2[/tex]
There will be a hole at x = -2 and an asymptote at x = 3.
So the values of x that need to be excluded from the domain are:
x = 3 and x = -2
Therefore, the domain of the given rational function is: { x ∈ R | x ≠ -2, 3 }
Which of the following numbers is best represented on the number line below?
Answer:
Option 1
Step-by-step explanation:
A total of 395 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold?
Answer:
98.75 tickets
Step-by-step explanation:
395/4 = 98.75 (adult tickets)
check answer:
98.75 x 3= 296.25
296.25 + 98.75 = 395
hope this helps:)
After 10 weeks, how much money would William have in his bank account? Show your work.
Answer:
The answer seems to be going up by $14 every week
Step-by-step explanation:
Week 5 is $100, Week 6 is $114, Week 7 is $128, Week 8 is $142, Week 9 is $156, Week 10 is $170
What is the median of the data set?
10, 15, 27, 33, 33, 36, 42, 47, 45, 56, 78
Answer:
We can see that the number in the middle is 36. Hence the median of the data set is 36 the median of a data set is the number placed at the middle of a data after rearrangement either in ascending order or descending order.
Given the dataset 10, 15, 27, 33, 33, 36, 42, 47, 45, 56, 78
Step-by-step explanation:
36
Answer:
36
Step-by-step explanation:
10, 15, 27, 33, 33, 36, 42, 47, 45, 56, 78
The median is the middle number of the set
There are 11 data points so the middle is 11/2 = 5.5
Round up so the middle is the 6th data point
10, 15, 27, 33, 33, 36, 42, 47, 45, 56, 78
The median is 36
Pls help! it's due soon!!
Answer:
22
Step-by-step explanation:
Reflection on x axis
P(x, y) =P'(x,-y)
Therefore, D(2,3 ) =D'(2,-3)
What is the sum of 16x^3 – 5x– 2 and 6x^2 +3x+ 5?
Answer: 6x^2
Step-by-step explanation:
three teachers handed out math and science textbooks for their classes two teachers had 21 students each and the last teacher had 22 how many textbooks were handed out altogether
help me pls with this problem sooon
Answer:
64 textbooks
Step-by-step explanation:
the first two teachers had 21 students each that's 21+21=42
the other teacher had 22 students so apparently all the textbooks handed to the students are,21+21+22=64
HELP
Select the correct answer.
The points scored per game by a professional basketball player are represented by the box plot below.
If the player scores 9 points and 35 points in the next two games, how is the median of the data set affected?
А.
The median points per game is not affected.
B.
The median points per game decreases.
C.
The median points per game increases.
D.
The effect on the median points per game cannot be determined.
Answer:
it is A the meidian is the middle number in a orderd set
You are ordering sweatshirts for your baseball team. How many more large sweatshirts than medium sweatshirts do you order?
Answer:
The answer is 10 and i know because im smart
Step-by-step explanation:
because im smart
Answer:
24
Step-by-step explanation:
add 8 and 12 and 4 and its 24
Jenny scored a 70% on a 50 point test while Hannah scored 80% on the same test. Enter the difference.
Answer:
5
Step-by-step explanation:
70% is 0.7, multiply 0.7×50=35 points on Jenny's test. Hannah scored 0.8×50=40 points on the test. Subtract 40-35 for the answer of 5
PPLEASE HELP FOR 10 POINTS!!!!!
Write an equation to represent the verbal description.
In a computer game, Nikolai started with x points. After losing 50 points, Nikolai then tripled his score for a total of y points.
Answer:
[tex]y=3(x-50)[/tex]
Hope This Helps! :)Please Give Brainliest if this is correct!
(Which I am pretty confident in...)
• There are 20 slices of bread in a loaf. How many 2-slice sandwiches can you make with 1 loaf? Write a multiplication fact and a division fact you could use to this problem. a
Answer:
blm is the correct answer
Step-by-step explanation:
The number of the two-slice sandwich will be 10.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that there are 20 slices of bread in a loaf. The number of the sandwiches will be calculated as below:-
Number of the sandwiches = 20 / 2 = 10 sandwitch
Therefore, the number of the two-slice sandwich will be 10.
To know more about an expression follow
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Solve the word problem below. Enter your answer in simplest terms, using the
slash () to represent the fraction bar.
A recipe for a soup calls for 3/6 cup of chopped onion and 1/4 cup of chopped
celery. What is the total amount of celery and onion needed for the soup help me.
Answer:
3/4
Step-by-step explanation:
Here,cup of chopped onions=3/6
cup of chopped celery=1/4
Then,
total amount celery and onion needed for the soup =3/6 + 1/4
=3*2 + 1*3/12
=6+3/12
=9/12
=3/4
Assessment Practice
11. The rectangle has a perimeter of 86 yards.
Which is its area?
Answer:
460
Step-by-step explanation:
23+23=46. 20+20=40. 46+40=86. 23×20= 460
Help please help me with this
Answer:
B
Step-by-step explanation:
40,000 x 3^1 = 120,000
120,000 x 3 = 360,000
40,000 x 3^2 = 360,000
Therefore, it is the second option, or B.
write a function to describe the relationship of the values in the table (-9,-3) (-6,-2) (-3,-1) (0,0) (3,1)
y=1/3x
Step-by-step explanation:A linear function is a relationship that has a degree of 1 and a constant slope. Linear functions are written in the form of y=mx+b, where m is the slope and b is the y-intercept.
Y-intercept
The y-intercept of a function is the y-value when x=0. In this case, we are given all of the coordinates. One of the coordinates is (0,0), which means that when x=0, y=0. So, the y-intercept is 0.
Slope
The slope is the change in y over the change in x. Using the coordinates we can find the slope through the formula [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]. It will be easiest to use the coordinates (0,0) and (3,1). Plug these points into the formula to find the slope.
[tex]\frac{1-0}{3-0}[/tex] = [tex]\frac{1}{3}[/tex]This means that the slope is 1/3.
Answer
Using the information found in the previous sections we can create the final answer, y=1/3x+0, or just y=1/3x.
Brittney bought 3 bags of candy, each with 11 pieces in it. She is dividing the candy among 6 of her friends. If each of her friends will get the
same number of candy pieces, how many pieces will be left over?
Somebody help me
Answer:
3
Step-by-step explanation:
There are 3 * 11 (33) pieces of candy33 / 6 = [tex]\frac{33}{6}=5\frac{3}{6}[/tex]This means that 3 pieces will be left over!
Which is equivalent to
4x - 6y?
2(x - 3y) or -2(-2x + 3y)
I think it’s -2(-2x + 3y) but I am unsure because I got -4 instead of 4
Step-by-step explanation:
Compare using >, <, or=.
3 miles
5,000 yards
Answer:
>
Step-by-step explanation:
1 mile =1760 yards
so 3 mile= 1760x3=5280yard
so, 5280 yards is more than 5000 yards
In the tessellation below, what transformation(s) maps Brick A onto Brick B?
a glide reflection
a rotation followed by translation
a rotation followed by a reflection
reflection followed by a translation
Answer:
a rotation followed by a translation
Step-by-step explanation:
i did it
The rotation is followed by a translation.
We have given that,
a glide reflection
a rotation followed by a translation
a rotation followed by a reflection
reflection followed by a translation
We have to determine the tessellation below, and what transformation(s) maps Brick A onto Brick B.
What is rotation?
Rotation is the circular movement of an object around an axis of rotation. A three-dimensional object may have an infinite number of rotation axes.
Therefore the rotation is followed by a translation.
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The table shows the number of hours that a group of friends been in the first week training to run a marathon. In the second week they each add five hours to their training times what are the mean median mode and range of times for the second week
Jeff - 9
Mark - 5
Karen - 5
Costas - 5
Brett - 7
Nikki - 6
Jack - 7
A.
Mean is 10
Median is 11
Mode is 11.3
Range is 4
B.
Mean is 11
Median is 11.3
Mode is 10
Range is 0.3
C
Mean is 11.3
Median is 11
Mode is 10
Range is 4
D
Mean is 11.3
Median is 11
Mode is 10
Range is 0.3
Please help this is a test question
FInd the value of x, between -π and π, satisfying the following inequality.
tan x < cos x
Answer:
(-1.570796, 0.666239) ∪ (1.570796, 2.475353)
Step-by-step explanation:
A graphing calculator can give you the numerical values that limit the intervals of the solution. The attachment shows this solution.
__
algebraic solutionWe can multiply by cos(x) and solve the resulting quadratic inequalities. Two cases arise:
tan(x) -cos(x) < 0 . . . . . . subtract cos(x)
sin(x) -cos(x)² < 0 . . . . . . . for cos(x) > 0
sin(x) -cos(x)² > 0 . . . . . . . for cos(x) < 0 (inequality is reversed)
Replacing cos(x)² with (1 -sin(x)²) gives quadratic equations in sin(x). (We're using <> to mean "could be greater than; could be less than, depending on cos(x)".)
sin(x) -(1 -sin(x)²) <> 0
sin(x)² +sin(x) -1 <> 0 . . . . put in standard form
(sin(x)² +sin(x) +1/4) -1 -1/4 <> 0 . . . . complete the square
(sin(x) +1/2)² -5/4 <> 0 . . . . . write as a square
((sin(x) +1/2)-√(5/4))·((sin(x) +1/2) +√(5/4)) <> 0 . . . . factor
Note that the second factor is always positive, so it has no impact on the intervals of solution.
__
The zeros of the first factor are located at ...
sin(x) = 1/2(-1 +√5)
x ≈ 0.666239 radians, and π - 0.666239 radians ≈ 2.475353 radians
The sine function will be positive between these angle values.
__
However, the intervals of solution to the inequality depend on the cosine function. Effectively, the solution space is where (sin(x) +(1-√5)/2) and cos(x) have opposite signs.
cosine positiveThe cosine function is positive for -π/2 < x < π/2, so one of the intervals of solution will be ...
-π/2 < x < arcsin((√5 -1)/2), approximately (-1.570796, 0.666239)
cosine negativeThe cosine function is negative for -π < x < -π/2 and for π/2 < x < π. The other interval of solution will be ...
π/2 < x < (π -arcsin((√5 -1)/2)), approximately (1.570796, 2.475353)
_____
Additional comment
In the above, we have used α=arcsin( ) to mean the values of angle in the principal branch: -π/2 ≤ α ≤ π/2. That is why we have to subtract it from π to find the other end of the interval of interest.
Colter rides his dirt bike 8800 yards in 3 days how many miles did he ride?
Answer: 5miles
Step-by-step explanation: Convert 8800yards to miles. Divide by 1760
A designer makes the sketch shown below for a new lamp. What is the approximate area of her sketch?
The lamp shade is a trapezoid. Its area is approximately square inches. The bases of the lamp are two trapezoids. The area of each is approximately square inches. In total, the area is approximately square inches.
The approximate area of the sketch for the new lamp is : A = 70 [tex]in^{2}[/tex]
What is a TrapeziumA trapezium is one pair of parallel sides and one pair of non-parallel sides.
from the diagram we can extract the necessary information needed to find the area of the trapezium.
for the first trapezium (lamp shade)
a = 4 in
b = 6 in
h = 6 in
[tex]A_{1}[/tex] = [tex]\frac{a + b}{2}[/tex] * h
[tex]A_{1}[/tex] = [tex]\frac{4 + 6}{2}[/tex] * 6
[tex]A_{1}[/tex] = [tex]\frac{10}{2}[/tex] * 6
[tex]A_{1}[/tex] = 5 * 6 = 30[tex]in^{2}[/tex]
For the area of the second trapezium (lamp base)
a = 4 in
b = 6 in
h = 4 in
[tex]A_{2}[/tex] = [tex]\frac{a + b}{2}[/tex] * h
[tex]A_{2}[/tex] = [tex]\frac{4 + 6}{2}[/tex] * 4
[tex]A_{2}[/tex] = [tex]\frac{10}{2}[/tex] * 4
[tex]A_{2}[/tex] = 5 * 4 = 20[tex]in^{2}[/tex]
For the area of the third trapezium (lamp base)
a = 6 in
b = 4 in
h = 4 in
[tex]A_{3}[/tex] = [tex]\frac{a + b}{2}[/tex] * h
[tex]A_{3}[/tex] = [tex]\frac{6 + 4}{2}[/tex] * 4
[tex]A_{3}[/tex] = [tex]\frac{10}{2}[/tex] * 4
[tex]A_{3}[/tex] = 5 * 4 = 20[tex]in^{2}[/tex]
The total Area of the trapezium (lamp)
A = [tex]A_{1}[/tex] + [tex]A_{2}[/tex] + [tex]A_{3}[/tex]
A = 30 + 20 + 20
A = 70 [tex]in^{2}[/tex]
Inconclusion The approximate area of the sketch for the new lamp is : A = 70 [tex]in^{2}[/tex]
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Answer:
Step-by-step explanation:
20, 30, 70
Solve the following exponent:
(28)2
Answer:no answer figure it out on your own
Step-by-step explanation:No Answer
Answer:
784
Step-by-step explanation:
[tex]28*28 = 784[/tex]
A quadratic equation has the solutions x- -5 and x=4 What are the x-intercepts of the graph of the function?
I need help in this is due by Friday.
Answer:
top answer is 'c' and the bottom is 'a'
Really appreciate it!!! Have a blessed day!!!!
Answer:
A.
Divide each dimension by scale factor of 5
Big Δ dimensions : Small Δ dimensions
35 : 7
30 : 6
15 : 3
a = 7 in
b = 6 in
c = 3 in
Hope this helps and God bless!
Anthony drove 140 miles in 2 1/2 hours. He then drove the next 3 1/4 hours at a rate that was 6 miles per hour slower than his first rate. How many miles did Anthony drive in all?
Answer:
302.5 miles
Step-by-step explanation:
using the relationship
D = ST ( D is distance, S is speed and T is time in hours )
given he drove 140 miles in 2 [tex]\frac{1}{2}[/tex] = 2.5 hours , then
S = [tex]\frac{D}{T}[/tex] = [tex]\frac{140}{2.5}[/tex] = 56 mph
the next part of his journe is 6mph slower, that is 50 mph for 3 [tex]\frac{1}{4}[/tex] = 3.25 hours, then
D = ST = 50 × 3.25 = 162.5 miles
total distance travelled = 140 + 162.5 = 302.5 miles
help me please need help
Answer:
Step-by-step explanation:
Trignomentary - real life problem.
We can find the height of the tower without measuring it. WE can find the height of the tower when we know,
1. A point which at a distance 'x' from the foot of the tower.
2. The angle of elevation is known
Eg: A tower stands vertically on the ground. From a point on the ground which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is 60°. Find the height of the tower.
AB - tower
We know the adjacent side of 60° and we have to fing the opposite side of 60°. So, we have to use
[tex]\sf \ Tan \ 60^\circ=\dfrac{Opposite \ side \ of \ 60^\circ}{Adjacent \ side \ of \ 60^\circ}[/tex]
[tex]1.732 = \dfrac{AB}{BC}\\\\1.732=\dfrac{AB}{15}\\\\1.732*15=AB[/tex]
AB = 25.98 m
Height of the tower ≈ 26 m