Answer:
A U B = {3,4,6,7,8,10}Step-by-step explanation:
Greetings !
Little explanation about union 'U'The union of two sets is a set containing all elements that are in A or in B (possibly both). For example, {1,2}∪{2,3}={1,2,3}. Thus, we can write x∈(A∪B) if and only if (x∈A) or (x∈B). Note that A∪B=B∪A.
Hope it helps!!
if f(x)=ax^2+bx+c has zeros x=-11 and x=-13, what zeros does f(x-9) have?
If [tex]f(x)=0[/tex] at [tex]x=-11[/tex] and [tex]x=-13[/tex], then we can factorize
[tex]f(x) = ax^2 + bx + c = a (x + 11) (x + 13)[/tex]
Now,
[tex]f(x-9) = a((x-9)+11) ((x-9)+13) = a(x+2)(x+4)[/tex]
which means the zeros of [tex]f(x-9)[/tex] are [tex]x=-2[/tex] and [tex]x=-4[/tex].
If given that :-
[tex] {\quad \leadsto \quad \bf f(\phi) = {\phi}^{2} - \phi - \displaystyle \bf \int_{\bf 0}^{1} f(\phi) d \phi }[/tex]
Then find :-
[tex] { \quad \leadsto \quad \displaystyle \bf \int_{0}^{2} f(\phi) d \phi }[/tex]
Integrate by parts with
[tex]u = f(\phi) \implies du = f'(\phi) \, d\phi = (2\phi - 1) \, d\phi[/tex]
[tex]dv = d\phi \implies v = \phi[/tex]
to evaluate the integral in the definition of [tex]f[/tex].
[tex]\displaystyle \int_0^1 f(\phi) \, d\phi = \phi\,f(\phi) \bigg|_0^1 - \int_0^1 \phi(2\phi-1) \, d\phi = f(1) - \frac16[/tex]
Now if [tex]\phi=1[/tex], we have
[tex]f(1) = 1^2 - 1 - \left(f(1) - \dfrac16\right) \implies 2f(1) = \dfrac16 \implies f(1) = \dfrac1{12}[/tex]
and so
[tex]\displaystyle \frac1{12} = 1^2 - 1 - \int_0^1 f(\phi) \, d\phi \implies \int_0^1 f(\phi) \, d\phi = -\frac1{12}[/tex]
It follows that
[tex]\displaystyle \int_0^2 f(\phi) \, d\phi = \int_0^2 \left(\phi^2 - \phi + \frac1{12}\right) \, d\phi \\\\ ~~~~~~~~~~~~~~~ = \left(\frac{\phi^3}3 - \frac{\phi^2}2 + \frac\phi{12}\right) \bigg|_0^2 \\\\ ~~~~~~~~~~~~~~~ = \frac{2^3}3 - \frac{2^2}2 + \frac2{12} \\\\ ~~~~~~~~~~~~~~~ = \boxed{\frac56}[/tex]
write ____ as a single power of 6
Answer:
[tex]6^{7/2}[/tex]
Step-by-step explanation:
[tex]6^4 \div 6^{1/2} \\ \\ =6^{4-\frac{1}{2}} \\ \\ =6^{7/2}[/tex]
270 cal and three servings 450 cal in five servings
Answer:
5 Servings
Step-by-step explanation:
Suppose each side of
the inequality a − b < 0 is multiplied by c.
a. If c < 0 and c(a − b) > 0, write an inequality to
represent the relationship between a and b.
b. If c < 0, is c(a − b) always greater than 0?
Explain your reasoning.
The required solution is ca is less than cb.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
Suppose each side of the inequality a − b < 0 is multiplied by c.
According to given question we have
a. If c < 0
Each side of the inequality a − b < 0 is multiplied by c.
=c(a-b)<0
=ca-cb<0
=ca<cb
It should be clear that number that ca is less than cb.
Therefore, the required solution is ca is less than cb.
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The angle between 0 and 360 that is coterminal with the 2016 angle is ___ degrees
Answer:
216 degrees
Step-by-step explanation:
2016/360= 5.6 drop the 5
.6 x 360 = 216 °
3. An investor received a check in the mall
that was for 6 percent of the amount
invested. If the amount invested was $450.
what was the amount of the check?
(1) $ 24.30
(2) $ 27.00
(3) $ 27.30
(4) $ 75.00
(5) $270.00
The amount of the check with 6 percent of the amount invested was (2) $27.00.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to denote it.Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 chickens, and 20% of the quantity is equal to 20% of 1,000, or 200.So, 6% of $450:
Then,
Therefore, the amount of the check with 6 percent of the amount invested was (2) $27.00.
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Eduardo buys a sandwich and a drink.
Use mental math to find the amount of
change he gets from $10.00
Answer:
Eduardo will get $4.03
Step-by-step explanation:
To solve this problem, first add 4.99 and 0.98 together, remember to line up the decimals
4.99
+ 0.98
-------------
5.97
Now take 5.97 from 10.00
first you can't take 7 from 0 so you take 1 from the tens place making 10.00 into 9.9 10, now you can take 7 from 10 which equals 3. Into the tenths place you can take 9 from 9 which is a 0. Lastly 9 - 5 is 4, adding the decimal back you get
10.00
- 05.97
--------------
$ 4.03
9<2x +7<15? What does X equal
Answer: X = 2
Step-by-step explanation:
2(2)+7 = 11 --> 9<11<15
Hope this helps you :)
Solve for interval and set notation, please:3m-3 ≤m +9<5+2m
The range of m is 4 < m ≤ 6
The interval given is
3m - 3 ≤ m + 9 < 5 + 2m
So we have,
Here we have to find the range of m by separating two inequalities. Thus we get,
3m - 3≤ m + 9 and m + 9 < 5 + 2m
3m - m ≤ 9 + 3 and 2m - m > 9 - 5
2m ≤12 and m > 4
m ≤6 and m>4
So we get the range of m,
4 < m ≤ 6
Therefore we get the range of m as, 4 < m ≤ 6.
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a. Write an expression that represents the phrase "one third the difference of 15 and a number."
Answer:
[tex]\frac{1}{3}(x-15)[/tex]
Step-by-step explanation:
In a certain instant lottery game, the chance of a win is stated as 15%. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
The probability is (Round to two decimal places as needed.)
0.15% is the probability value between 0 and 1 inclusive.
In statistics, what does a probability mean?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.the fractional conversion of a percentage = % value /100
therefore the probability is 15/100 = 0.15%
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ali, ben and clare each played a game. Clare's score was seven times ali's score. ben's score was half of clare's score. write down the ratio of ali's score to ben's score to clare's score. give your answer in its simplest form
The ratio of Ali's score to Ben's score to Clare's score in its simplest form is 1 : 3.5 : 7
Given data:
Claire's score = 7 * Ali's score
Ben's score = 0.5 * Claire's score
How to solve for the ratio of Ali's score to Ben's score to Clare's scorelet Ali's score = x
let Ben's score = y
let Claire's score = z
z = 7 * x = 7x
z = 7x
y = 0.5 * z = 1/2 * z = z / 2
plugging the value of z gives
y = 7x / 2
writing the ratios in terms of x gives
Ali : Ben : Claire
x : y : z
x : 7x/2 : 7x
reducing the terms by dividing through by x
1 : 7/2 : 7
OR
1 : 3.5 : 7
clearing the fraction gives
2 : 7 : 14
Therefore, the ratio of Ali's score to Ben's score to Clare's score in its simplest form is 1 : 3.5 : 7
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Which is bigger, two thirds of 30 or one fifth of 25
Answer:
2/3s of 30
Step-by-step explanation:
2/3s of 30 is 10 and 1/5 of 25 is 5 and 10 is in fact larger than 5
At the annual book fair, the students at water middle school found that they had $1,4888.80 in the cash register. Their teacher had given them a loan of 92.89 to buy supplies for the fair. What is the best estimate of the amount of money they had after they paid the money back to the teacher
Answer:
1395.91
Step-by-step explanation:
Subtract 1,488.80-92.89
If you want to round it up to a whole number then it would be 93.
If you want to round it up to the tenth then it would be 92.9.
Which of the following equations is of a parabola with a vertex at (1, -2)?
A. y=(x + 1)² +2
B. y=(x-1)² +2
C. y=(x + 1)²-2
D. y=(x-1)²-2
Answer:D
Step-by-step explanation:
Enclosed x-1 moves the parabola to the right once, and the excluded -2 puts the parabola down 2.
Find the value of f(7).
y = f(x)
On observing graph, we can conclude that the value of y when x = 7 is 5.
How do functions work?An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions may be found everywhere in mathematics, and they are essential for building physical connections in the sciences.
How does a function appear?An example of a rule is a function, which yields one output from a single input. The equation y=x2 serves as an example of this. There is only one output for y for every input for x. We would say that y is a function of x since x is the input value.
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Put the following equation in slope-intercept form: y-1=2/7(x-4)
Answer:
[tex]y=\frac{2}{7} x-\frac{1}{7}[/tex]
Step-by-step explanation:
y=mx+b where y and x are variables, m is the slope and b is the y-int.
[tex]y-1=\frac{2}{7} (x-4)\\y=\frac{2}{7} x-\frac{2}{7} -1\\y=\frac{2}{7} x-\frac{1}{7}[/tex]
Hope that helps.
PLEASE I NEED ANSWERS ASAP
1. Find the missing coordinate given m = -5 and goes through the points (x, 3) and (5, -7). Show your work.
2. Identify the slope in the equation 9x + 2y = -7. Show your work.
The required solution for the coordinate and the slope of the line, 1. missing coordinate is 2. Slope of the line 9x + 2y = -7 is m = -9/2
Here,
1.
Standard equation of the line,
y = mx + c
From the given, we have m = -5 and a point (5,- 7)
Now,
-7 = -5 * 5 + c
c = -7 + 25
c = 18
equation become
y = -5x + 18
Now putting y = 3
3 = -5x + 18
-15 = -5x
x = 3
So the required missing coordinate is (3, 3)
2.
Slope of equation 9x + 2y = -7
9x + 2y = -7
y = -9/2 -7/2
The coefficient of x is the slope of the equation. So,
m = --9/2
Thus, the required solution for the following problem of the line,
1. missing coordinate is
2. Slope of the line 9x + 2y = -7 is m = -9/2.
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The ratio of soccer balls to basketball is 12 to 15 If there are 48 soccer balls how many basketball are there
Answer:
60Step-by-step explanation:
The ratio of soccer balls to basketball is 12 to 15 If there are 48 soccer balls how many basketball are there
we can solve with a proportion
12 : 15 = 48 : x
x = 15 * 48 : 12
x = 60
Two consecutive multiples of 9 sum up to 63. Fine the numbers
Answer:
27, 36
Step-by-step explanation:
We can write the first number as 9n because it is a multiple of 9, and the second number will be 9(n + 1). We can write:
9n + 9(n + 1) = 63 because they have a sum of 63.
9n + 9n + 9 = 63
18n + 9 = 63
18n = 54
n = 3
This means that the first number is 9 * 3 = 27 and the second is 9 * (3 + 1) = 9 * 4 = 36.
1,058 written in expanded notation
Answer:
1,000+50+8
Step-by-step explanation:
Each place value is divided up into their separate values.
Write 55% as a decimal and as a simplified fraction?
Answer:
11/20
Step-by-step explanation:
To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10. If needed, simplify the fraction.
what is the solution to x-15=-6
Answer:
x = 9
Step-by-step explanation:
[tex]x- 15 = -6\\\\[/tex]
Add 15 to both sides to isolate the x.
[tex]x -15 +15 = -6 +15\\x = 9[/tex]
Answer:
X=9
Step-by-step explanation:
You must add 15 to both sides of the equal sign to cancel out the (-15). You add -6+15 which equals 9.
Question
How should this model be completed to represent 377 ÷ 12?
Enter your answers in the boxes.
Using the Box model of division, the answer is attached below, and showing full results attached accordingly.
What does division represent?Suppose that we're talking about p÷ q
It means, we divide p into q into equal parts. And each part is of value p/q
The box model of division can be defined as One of the tactics of division is the Box Method, commonly known as the Area Model.
We have been given the division as 377 ÷ 12.
The box model of division is a mental math approach that will improve number sense comprehension.
The Students solve the equation by subtracting multiples until they will get zero, or as near to zero as they can.
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The complete question is
How should this model be completed to represent 377 ÷ 12? complete the boxes attached below.
Which equations are in standard form? Check all that apply y = 2x + 5 2x + 3y = –6 –4x + 3y = 12 y = x – 9 x + 3 = 6 x – y = 5 5x + 3y =
The equations which are in standard form include the following:
2x + 3y = -6.5x + 3y = 1/2.What is a linear equation?A linear equation can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).
This ultimately implies that, the variables in all linear equations share a direct relationship and as such they are directly proportional to one another.
In Mathematics, the standard form of a linear equation is given by the following:
Ax + By = C.
In this context, we can reasonably infer and logically deduce that the equations which are in standard form include the following:
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What is the recursive formula for the perimeter of a square of side n(the nth perimeter) using the first number(perimeter) in the pattern?
Answer:
[tex]a_n=a_{n-1}+4\qquad a_1=4[/tex]
Step-by-step explanation:
You want the recursive formula that matches the sequence 4, 8, 12, 16, 20.
Recursive formulaYour problem statement tells you the recursive formula is ...
[tex]a_n=a_{n-1}+d\qquad a_1=\text{first term}[/tex]
where 'd' is the common difference.
This means you only need to identify the perimeter associated with n=1 (first term), and the difference between perimeters for adjacent values of n.
The table tells you ...
[tex]a_1=4\\d=8-4=4[/tex]
Filling these values into the given formula, you have the recursive formula ...
[tex]\boxed{a_n=a_{n-1}+4\qquad a_1=4}[/tex]
Suppose a railroad rail is 5 km and expands on a hot day by 11 cm in length approximately how many meters would the center of the rail rise above the ground
The answer is about 17 meters
We can use the Pythagorean theorem to put an upper bound on the height of the bump in the rail. This assumes half the expanded rail length (d+e) is the hypotenuse of a right triangle whose legs are the bump height (b) and the 2500 meter distance (d) from the center of the rail to its end.
The Pythagorean theorem relates these distances this way:
b² + d² = (d+e)²
Expanding the square on the right, we can simplify the expression to find b.
b² = (d²+2de +e²) -d²
b² = e(2d +e)
b = √(e(2d +e))
Using lengths in meters, we can fill this in to calculate b.
b = √(.06(2·2500 +.06)) = √300.0036
b ≈ 17.32 . . . . meters
We don't expect rails to tear loose from the rail bed and rise up to a height matching that of a 3-story building. That is why there are typically expansion joints and shorter rail lengths used in the construction of railways.
The height is a little lower if we take physics into account and distribute the stress in the rail along its length. No doubt the final curve is somewhat more complicated than the triangle we have assumed.
If it were an ellipse, the height might only be 9.4 meters, with the steepest rise occurring near the ends of the rail. The math for this model is beyond the scope of this answer.
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Determine a solution to the system of inequalities given below:
y>4x−3
y≥−2x+3
Step-by-step explanation:
the solution of such a system of inequalities with 2 variables is the joined area above both lines (that are the bottom delimiters of both inequalities).
these lines are just the equations instead of the inequalities.
we have the lines
y = 4x - 3
y = -2x + 3
when going from left to right (x goes from -infinity to +infinity), the line y = -2x + 3 is first above the other line.
we know this, because the y-intercept (+3 vs. -3) is above, and the slope (-2 vs. 4) makes the line going downward from high above on the left.
at the intersection point between the 2 lines this changes, and we have to stay above y = 4x - 3.
so, we need the intersection point :
4x - 3 = -2x + 3
6x = 6
x = 1
y = 4x - 3 = 4×1 - 3 = 4 - 3 = 1
so, the solution is
y >= -2x + 3 -infinity < x <= 1 or simply x <= 1
y > 4x - 3 1 < x < +infinity or simply x > 1
it is important to maintain the original inequality type (<, >, <=, >=).
the intersection point is included, because of the ">=" sign in the second inequality.
Evaluate the expression when a = 2 and x = - 6
6a -x
Answer:
18
Step-by-step explanation:
6(2) - (-6)
12 +6
18