We have
[tex]\displaystyle \int_{-2}^2 f(x) \, dx - \int_{-2}^{-1} f(x) \, dx = \int_{-1}^2 f(x) \, dx[/tex]
so that
[tex]\displaystyle \int_{-2}^2 f(x) \, dx + \int_2^5 f(x) \, dx - \int_{-2}^{-1} f(x) \, dx \\\\ ~~~~~~~~~~~~ = \int_{-1}^2 f(x) \, dx + \int_2^5 f(x) \, dx \\\\ ~~~~~~~~~~~~ = \boxed{\int_{-1}^5 f(x) \, dx}[/tex]
2- (ITA-2007) Dentre 4 moças e 5 rapazes deve-se formar uma comissão de 5 pessoas com, pelo menos , 1 moça e 1 rapaz. De quantas formas distintas tal comissão poderá ser formada?
Answer:
Step-by-step explanation:
Lori was paid a 15 percent commission for the home audio system that she sold. The electronics store had marked up the price of the system by 60 percent over the wholesale price of $264. How much did Lori earn for the sale of the home audio system? $15.84 $23.76 $39.60 $63.36
Answer:
$63.36
Step-by-step explanation:
The home audio system costs $264 wholesale.
The system's price had been increased by 60 percent at the electronics retailer.
Consequently, the increased cost is 60/100x264=$158.40.
The audio system's total cost is now $422.40 (264 + 158.40).
Given that Lori received a commission of = 15% on $422.40, her commission is now (15/100) x 422.40
= $63.36
Solve For x :
[tex] \color{purple}{ \pmb{ \frak{2x \: = 100 \red { \: ?}}}}[/tex]
[tex] \\ \\ \\ \\ \\ [/tex]
[tex] { \color{yellow}\bigstar}\underline{ \pmb{ \frak{Thank \: uh }} \color{purple}{ \hearts} !!\: }[/tex]
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Given ,
[tex]2x = 100[/tex]
To find ,
value of x
Now ,
[tex]\longrightarrow{2x = 20}[/tex]
Dividing both sides by 2 , we get
[tex] \frac{2x}{2} = \frac{100}{2} \\ \\ \longrightarrow\boxed{ \: x = 50} [/tex]
nikal -,- xD
Answer:
[tex]\bf x=50[/tex]Step-by-step explanation:
[tex]\bf 2x=100[/tex]
Divide both sides by 2:-
[tex]\bf \cfrac{2x}{2}=\cfrac{100}{2}[/tex]
Simplify:-
[tex]\bf x=50[/tex]
___________________
Please help! I've already answered part a, I don't understand what part b is asking.
Step-by-step explanation:
So, there is something known as a removable discontinuity, and it's essentially where you can define f(x) using the most simplified fraction, where you could normally not define f(x).
So we have the following equation:
[tex]f(x) = (\frac{x+5}{x+1}\div\frac{(x+3)(x-2)}{(x-4)(x+1)})-\frac{1}{x-2}[/tex]
As you may know, we cannot divide a number by the value of zero. When the denominator is equal to zero, on the graph this will appear as a vertical asymptote, where x approaches the value that makes the denominator zero, but never actually reaches it.
If you look at each denominator, you can set them equal to zero to find the vertical asymptotes
x+1 = 0
x=-1
There should be a vertical asymptote at x=-1, since it would make two of the denominators equal to -1, but let's divide the two fractions first.
Original Equation
[tex]f(x) = (\frac{x+5}{x+1}\div\frac{(x+3)(x-2)}{(x-4)(x+1)})-\frac{1}{x-2}[/tex]
Keep, change, flip
[tex]f(x) = (\frac{x+5}{x+1}*\frac{(x-4)(x+1)}{(x+3)(x-2)})-\frac{1}{x-2}[/tex]
Multiply the two fractions
[tex]f(x) = (\frac{(x+5)(x-4)(x+1)}{(x+1)(x+3)(x-2)})-\frac{1}{x-2}[/tex]
Notice how the x+1 is in the numerator and fraction? That means we can cancel it out!
[tex]f(x) = (\frac{(x+5)(x-4)}{(x+3)(x-2)})-\frac{1}{x-2}[/tex]
In this simplified version of the fraction, we can technically define f(-1), but in the original version, since it's not defined there is a removable discontinuity at x=-1, meaning there is no vertical asymptote, but the function is still not defined at f(-1), and there will be a hole at that point.
. [Equations]
1/6x =4
Answer:
youre answer is here I hope it's right
x=24
Katy buys 4 DVDs every 2 weeks. How many DVDs will she buy in 14 weeks?
Answer:
28 DVDs
Step-by-step explanation:
Given information from the question, we can deduce:
2 weeks = 4 DVDs
1 week =
[tex] \frac{4}{2} \\ = 2[/tex]
2 DVDs on average.
Which means,
14 weeks = 2 × 14 = 28 DVDs
Therefore, Katy will buy 28 DVDs in 14 weeks.
Select the correct answer. if function g has the factors (x − 7) and (x 6), what are the zeros of function g? a. -7 and 6 b. -6 and 7 c. 6 and 7 d. -7 and -6
Option (b) -6 and 7 is the correct option.
The zeroes of the function f and g are x=7 and x=-6 respectively.
What are the zeroes of a polynomial?The values of x that satisfy the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.
Put x-7=0
X=7
Now, put x+6=0
So, x=-6
The zeroes of the function f and g are 7 and -6 respectively.
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Which of the equations below represents
this ellipse?
a. x^2/4+y^2/20=1
b. x^2/2+y^2/10=1
c. x^2/100+y^2/4=1
d. x^2/4+y^2/100=1
The equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
What is the equation of the ellipse represented in the graph?
Herein we have a representation of an ellipse in the image attached aside, ellipses are characterized by the following standard formula:
(x - h)² / a² + (y - k)² / b² = 1 (1)
Where:
(h, k) - Coordinates of the centera, b - Lengths of the semiaxesPlease notice that ellipse will be vertical if b > a, otherwise it will be horizontal. The graph exhibits a vertical ellipse centered at the origin and therefore we conclude that (h, k) = (0, 0) and b > a (b = 10, a = 2). Finally, the equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
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29% of a university's freshman class are majoring in Economics. If 2668 students in
the freshman class are Economics majors, how many students are in the freshman
class?
The number of students in the class is 9200.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Given that,
The percent of students pursuing economics is 29%.
And, the number of students pursuing economics is 2688.
Suppose the total number of students are x.
Then, the following equation can be written for the given case,
29% of x = 2668
=> 29/100 × x = 2668
=> x = 2668 × 100/29
= 9200
Hence, the total number of students in the freshman class is 9200.
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what book has the solution in it?
Answer:
Book 3
Step-by-step explanation:
So we have four statements:
1: Book 1 or Book 2
2: Book 3 or Book 4
3: Book 4
4: Not Book 3
We also have the condition that only 1 of the statements are correct, and more important, the other 3 are incorrect.
So it may be a bit difficult to see at first, but the solution, has to be book 3. The reason for this is if we assume statement 1, statement 2, or statement 3 is true, that would imply that the statement 4 is false, meaning the solution is in book 3.
If we assume that statement 2 is true, then statement 4 is false, meaning that book 3 has the solution, which aligns statement 2. It also aligns with statement 1 being false, because it's not book 1 or 2, and it also aligns with statement 3 being false, because the solution is not in book 4.
Let's look at why assuming any other statement to be true, leads to contradictions.
So let's assume the first statement is true, this means the solution is book 1 or 2. But this means the statement 4 is false, meaning book 3 has the solution. This contradicts the first statement which we assume is true, thus the first statement is not true.
Let's now assume the third statement is true, this means statement four is false meaning it's book 3, but this contradicts the third statement which says it's book 4. Thus this statement cannot be true
Let's assume the last option is true, this means book 3 has no solution, and since all the other are false, book 4 has no solution, book 3 or 4 has no solution, book 1 or 2 has no solution either. This means that none of the books have solutions, and assuming one of the books does have a solution, this statement cannot be true.
Choose the equation that satisfies the data in the table.
-1 0 1
0
3
6
X
Y
OA. y = 3x +3
B.y = -x +9
Oc.y=x+9
OD. y=-3x +3
Answer: A: y= 3x + 3
Step-by-step explanation:
The y intercept has to be 3 which is found when x = 0 that eliminates B and C. Then just plug in -1 or 1 into A or D and you will find that plugging in either with get you the y value provided on A.
Find the distance between (-6, -12) and (4,8) using the distance formula.
Answer:
The distance formula is 22.360679775
if you round it to the nearest tenth, then the answer is 22.4
Step-by-step explanation:
(-6, -12) and (4,8)
(x2 - x1)² + (y2 - y1)²
Place the x and y values
(4 - - 6)² + (8 - - 12)²
= 10² + 20²
= 100 + 400 = 500
√500 = 22.360679775
Round it to the nearest tenth, and you will get 22.4
Hope this helps!
Please mark me as the brainliest
Answer: Distance = 10√2
Step-by-step explanation:
Given formula
[tex]Distance~=~\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given information
(x₁, y₁) = (-6, -12)
(x₂, y₂) = (4, 8)
Substitute given information into the formula
[tex]Distance~=~\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]Distance~=~\sqrt{((4)-(-6))^2+((8)-(-12))^2}[/tex]
Simplify values in the parenthesis
[tex]Distance~=~\sqrt{(4+6)^2+(8+12)^2}[/tex]
[tex]Distance~=~\sqrt{(10)^2+(20)^2}[/tex]
Simplify the exponents
[tex]Distance~=~\sqrt{100+400}[/tex]
Simplify the radical number
[tex]Distance~=~\sqrt{500}[/tex]
[tex]Distance~=~\Large\boxed{10\sqrt{5}}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Which three-dimensional object is formed when the shape is rotated about the axis as shown?
Answer:
Step-by-step explanation:
Comment
The semicircle comes out towards we the viewer, then it goes upwards, and what one gets is 1/2 a sphere. If one keeps on rotating in the direction of the arrow eventually winding up where one started, the result is a full sphere.
Answer: Sphere
how would i solve this?
Answer:
66.0 (nearest tenth)
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the poor drawing)
This is a pure trigonometry question.
Based on the question, we can use the TOA CAH SOH method.
[tex] \cos(x) = \frac{adj}{hypo} \\ \cos(32) = \frac{56}{x} \\ x \cos(32) = 56 \\ x = \frac{56}{ \cos(32) } \\ = 66.0 \: (nearest \: tenth)[/tex]
What’s 5(x-4)+2 as a verbal expression?
The verbal expression for the mathematical expression 5(x - 4) + 2 is the number 5 times the difference between an unknown x and the number 4 and plus 2.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that a mathematical expression as below:
= 5(x - 4) + 2
Here x is the unknown number
The number
Number 5 times the difference between an unknown x and number 4 and plus 2
Thus, the verbal expression for the mathematical expression 5(x - 4) + 2 is number 5 times the difference between an unknown x and number 4 and plus 2.
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Can someone explain this question
Answer:
62.5 feet
Step-by-step explanation:
The markings on the angles in the figure tell you the triangles are similar. Similar triangles have proportional corresponding sides. This is used to write and solve an equation for x.
SimilarityThe angles in each triangle are marked with the following symbols:
square corner - signifying a right angleone arctwo arcsThe purpose of the marks is to signify that angles with the same mark are congruent. When the angles of one triangle are congruent to the angles of another triangle, the two triangles are similar.
Similar triangles have another feature: corresponding sides are proportional. That is, their ratios are identical.
This can be taken a couple of different ways:
sides of one triangle have the same ratio to each other as the corresponding sides of the other trianglecorresponding sides of the two triangles have the same ratioApplicationIn the given triangles, we can identify the corresponding sides as ...
smaller triangle : larger triangle
between right angle and double arc angle — 36 ft : 50 ft
hypotenuse — 45 ft : x ft
Our description of similarity tells us we can write the statements of proportionality as either of ...
36 : 50 = 45 : x . . . . . side ratios in the same triangle are the same36 : 45 = 50 : x . . . . . side ratios between triangles are the sameSolving the proportionFor proportions written in this way, the "outer" and "inner" products are the same. This is sometimes expressed by saying "the product of the means is equal to the product of the extremes."
a : b = c : d ⇒ ad = bc
When the ratios are written as fractions, this result is what you get from "cross multiplication":
a/b = c/d ⇒ ad = bc . . . . . the result of multiplying both sides by bd
Once the proportion is written in this product form, the value of any of the variables can be found by dividing both sides of the equation by the coefficient of that variable.
Desired distanceUsing either of the proportions we wrote above, the product form is ...
36x = 45·50
x = (45·50)/36 . . . . . . divide by the coefficient of x
x ≈ 62.5 . . . . feet
The distance from the playground to the swimming pool is 62.5 feet.
Walter used the iterative process to determine that √13 is between 3.61 and 3.62.Analyze Walter’s estimation. Is he correct? If not, what was his mistake?
A-Yes, Walter is correct.
B-No, 3.612 is less than 13.
C-No, both 3.612 and 3.622 are greater than 13.
D-No, both 3.612 and 3.622 are less than 13.
i need the right answer
The correct option is C no, both 3.61^2 and 3,62^2 are greater than 13.
Is he correct? If not, what was his mistake?To check this, we can just square both of the bounds that he found, and see if it makes sense.
Walter says hat:
3.61 < √13 < 3.62
Then we must have:
(3.61)^2 < 13 < (3.62)^2
The lower bound is 3.61, if we square it we get:
3.61*3.61 = (3 + 0.61)*(3 + 0.61) = 9 + 6*0.61 + 0.61*0.61 = 13.0321
Now, this is larger than 13, so the above inequality is false, which means that Walter is incorrect, because both 3.61 and 3.62 are larger than √13 , then the correct option is C.
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Answer:
c
Step-by-step explanation:
c
The dashed triangle is the image of the solid triangle. The center of dilation is (6, 6).
What is the scale factor used to create the dilation?
Enter your answer as an integer or decimal in the box.
The two right triangles are graphed on a coordinate plane. The horizontal x-axis ranges from negative 10 to 10 in increments of 1. The vertical y-axis ranges from negative 10 to 10 in increments of 1. A dashed triangle has vertices at begin ordered pair 6 comma 6 end ordered pair, begin ordered pair 6 comma 9 end ordered pair, and begin ordered pair 9 comma 6 end ordered pair. A solid triangle has vertices at begin ordered pair 6 comma 6 end ordered pair, begin ordered pair 6 comma negative 9 end ordered pair, and begin ordered pair negative 9 comma 6 end ordered pair.
Answer:
The scale factor is 1/5.
Step-by-step explanation:
You can find the side length of triangles by looking at the points or it might be easier to see if you look at the graphs that I have attached. I can see that the legs of the small triangle are 3 and the legs of the large triangle are 15. What do I need to multiple 3 by to get 15? 5. That is the scale factor from the little triangle to the big triangle. If I go the other way, the scale factor is the reciprocal of 5 or 1.5
A geographer found that the land area of Aruba is 75 square miles and the land area of Bermuda is 19 square miles. Based on these data, the geographer used the equation 75x+ 1 9y = T to estimate the total number ofresidents, T, oft he two islands. Which is the best interpretation of x in this context?
The interpretation of x in the equation 75•x + 19•y = T, used by the geographer, based on the land area of Aruba, 75 m², and Bermuda, 19 m², is the population in a square mile of Aruba
Which method can be used to find the interpretation of x in the equation?The land area of Aruba = 75 m²
Land area of Bermuda = 19 m²
The total number of residents is given in the question by the equation;
75•x + 19•y = T
Therefore;
x = The number of people in a square mile in Aruba
y = The number of people in a square mile in Bermuda
Which gives;
The interpretation of the variable, x in the context is the population of Aruba per square mile.Learn more about variables here:
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A boat traveled 27 miles in 2 hours. at this rate how many miles will the boat travel in 1/2 hour
Answer:
6.75
Step-by-step explanation:
Distance in Miles
MPH -------------------------
Time in Hours
27/2 = 13.5. That is 1 hour. Half that and you get 6.75 MP1/2H
Help me with this question
Answer:
s = 55 degrees
t = 35 degrees
Step-by-step explanation:
I am not sure what the question is, but I am assuming that you are trying to find the value for s and t
S and 125 are supplemental. That means that they add to 180. 180 - 125 = 55.
The two angles opposite of s together add up to 125. I know that one angle is 90, so t is 125 -90 or 35
you purchased 18.000 milliliters of juice. Juice costs $2 per liter. The cashier
ays you owe $12,000 for the juice, but you know that is not correct. Look at
the cashier's work and figure out how much you should pay. Explain what
he cashier did wrong.
18,000 + 3 = 6,000 liters
6,000 liters x $2 = $12,000
Answer:
cashier needed to divide by 1000, not 3.
Step-by-step explanation:
there are 1000ml in one liter. in order to find the amount of liters, youd have to divide the milliliters by 1000. its only after then that you can multiply by $2. answer would be $36
Hey so I’m stuck on this. What is the solution to the equation 2= -8 -x?
Answer:
X = -10
Step-by-step explanation:
2 = -8 -X
2+X = -8
X = -10
Answer:
x = - 10
Step-by-step explanation:
Comment
The trick to any equation like this one is to get the numbers on one side and the term with an unknown on the other side. That way, your last step is to divide by the number in front of the letter into a number on the other side.
Solution
2 = - 8 - x Add 8 to both sides
2 + 8 = -8 + 8 - x Combine
10 = - x The number in front of x is - 1. Divide.
10/-1 = -x/-1
-10 =x
The letter usually has to be expressed as a number greater than 0. In other words x is positive for this question
Someone PLEASE HELP MEE
The exponential growth rate is obtained as 0.1099.
What is the rate of multiplication?Now we know that an exponential function has to do with an exponential increase or decrease. An exponential function could increase or decrease and this means that the constant of the function could be a decay constant or a growth constant.
When we have an exponential function, we have to apply the general formula; P(t) = P(o)e^rt
Po = initial number
P(t) = number at time t
r = rate of growth
t = time taken
Thus;
270=90e^10r
270/90 = e^10r
3 = e^10r
ln3 = 10r
r = ln3/10
r = 0.1099
After 13 hours;
P(t) = 90e^(0.1099 * 13)
P(t) = 376
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Complete the equation.
2 x 4 =
X 2
Answer:
4 is correct answer.
Step-by-step explanation:
That because it contains property of communicative. That is a×b=b×a.
Please help !!! Need help !!!
Convert 352 base 6 to base 4.
Answer:
(2030)4
Step-by-step explanation:
Base 6 to decimal calculation:
(352)6 = (3 × 62) + (5 × 61) + (2 × 60) = (140)10
Decimal to base 4 calculation:
Divide by the base to get the digits from the remainders:
= (2030)4
Still have any questions?
Do hit me up or contact me
The answer is 2030.
First, convert from base 6 to base 10.
3 × 6² + 5 × 6¹ + 2 × 6⁰108 + 30 + 2140Now, convert from base 10 to base 4.
140 ÷ 4 = 35 ⇒ R = 035 ÷ 4 = 8 ⇒ R = 38 ÷ 4 = 2 ⇒ R = 02 ÷ 4 = 0 ⇒ R = 2Connecting the digits, the answer is : 2030
Sarah attempt to convert 8 miles in to kilomiters explain her error and then provide a correct conversion
Answer:
12.8 km
Step-by-step explanation:
each mile has 1.6 km in it so in order to find the total distance in km we need to multiply the miles by 1.6= 8 miles x 1.6 =12.8 km
Find the midpoint of UV thanks so much
Answer:
(0, -5/2).
Step-by-step explanation:
The coordinates of the mid point of (x1, y1) and (x2, y2) are
(x 1 + x2)/2 , (y1 + y2)/ 2
So here we have:
(-3 + 3)/ 2, (-4 + -1)/2
= 0/2, -5/2
= (0, -5/2).
if a(5,3),b(0,0) and c(-3,5) are the vertices of a triangle then the value of AB.BC is
The dot product associated to sides AB and BC is 0.
What is the dot product generated by two sides of a triangle?
In this question we must find the dot product of two vectors associated with two surrounding sides of a triangle. First, we need to find the vectors associated to sides AB and BC:
Side BA
BA = (5, 3) - (0, 0)
BA = (5, 3)
Side BC
BC = (- 3, 5) - (0, 0)
BC = (- 3, 5)
By definition of dot product, the result associated to the two sides of the triangle is:
BA • BC = (5, 3) • (- 3, 5)
BA • BC = (5) · (- 3) + (3) · (5)
BA • BC = - 15 + 15
BA • BC = 0
The dot product associated to sides AB and BC is 0.
Remark
The statement is poorly formatted, the correct form is shown below:
If A(x, y) = (5, 3), B(x, y) = (0, 0) and C(x, y) = (- 3, 5) are the vertices of a triangle then the value of the dot product between vectors AB and BC is:
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