The graph of a relation that is a function is the last option that is in the attachment below.
How to Determine a Relation that is a Function?A graph that represents a relation that is a function is a graph whose x-values each have exactly one corresponding y-value. That is to say, no two y-values correspond to one x-value in the graph of a relation that represents a function.
All of the graphs represents relations that have different y-values that correspond to an x-value except the graph at the bottom far right, whose diagram is attached below.
The graph attached below has exactly one y-value that corresponds to each x-value on the graph. Therefore, the relation is a function.
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What is the range of y = -3x + 1 for the domain of {2,8}?
Responses
-5
-23
2
8
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
An open circle at 5 and a bold line starting at 5 and pointing to the right (>) is the correct representations of the inequality
How to identify the correct representations of the inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.
Given: the inequality –3(2x – 5) < 5(2 – x)
First, we have to solve for x in the inequality
–3(2x – 5) < 5(2 – x)
Clear the parenthesis:
-6x + 15 < 10 - 5x
Collect like terms:
-6x + 5x < 10 - 15
-x < -5
Divide both sides by -1:
x > 5 ( Note: Dividing both sides by -1 will change the < to > )
This is what will determine our answer
Since our answer is x > 5. An open circle will be at 5 and a bold line starts at 5 and is pointing to the right (>)
Therefore, the correct representations of the inequality is an open circle is at 5 and a bold line starts at 5 and is pointing to the right
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what is 1010 in binary
Answer:
1010₂ = 10₁₀1010₁₀ = 1111110010₂Step-by-step explanation:
You want to know the value of 1010 in binary.
Conversion to binaryWe're not sure if you have the base ten number 1010 and you want its value in binary, or if the number 1010 is in binary, and you want its value in base ten.
Converting the base ten number to binary means looking at the remainders from division by 2, until the quotient is zero.
1010/2 = 505 r 0505/2 = 252 r 1252/2 = 126 r 0126/2 = 63 r 063/2 = 31 r 131/2 = 15 r 115/2 = 7 r 17/2 = 3 r 13/2 = 1 r 11/2 = 0 r 1The binary value is the list of these remainders from the bottom up:
1010₁₀ = 11 1111 0010₂
(It is often convenient for readability to group the digits by 3 or 4.)
Conversion from binaryThe conversion from binary essentially uses the expanded form of the number. The arithmetic is done in the base you're converting to. Here, that's base ten.
1010₂ = 1×2³ +0×2² +1×2¹ +0×2⁰ = 8 +2 = 10
1010₂ = 10₁₀
Solve 10x+16 ≥ 6x+ 20.
A. xz1
B. x < 1
C. x > 9
D. x≤9
Answer:
x ≥ 1
Step-by-step explanation:
Solving inequalities are essentially like solving equations where the main focus is getting the variable, x in this case, on one side and a constant on the other using inverse operations.
10x+16 ≥ 6x+20
==> subtract 16 from both sides
10x ≥ 6x + 4
==> subtract 6x from both sides
4x ≥ 4
==> divide both sides by 4
x ≥ 1
So the answer would be A
Also an important note for future references is when you divide one of the sides by a negative number you must flip the inequality sign.
E.g. -4x>8
We would divide both sides by -4 and because we divide by a negative number we must flip the inequality signs
This would result to x<-2
What is the value of Y?
Answer:
Here we need to find the value of y
In the given figure, 2y and 110 are adjacent to each other.
Hence the value of y = 110.
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Determine whether the given binomial is a factor of the polynomial following it. If it is a factor, then factor the polynomial completely.
x+2, x³+4x²-4x-16
Answer:
x+2 is a factory = (x +4)(x +2)(x -2)Step-by-step explanation:
You want the complete factorization of x³ +4x² -4x -16.
Factor by pairsPairing terms of the given polynomial, we have ...
(x³ +4x²) -(4x +16)
Factoring each pair gives ...
x²(x +4) -4(x +4)
= (x² -4)(x +4)
Difference of squaresThe factorization of x² -4 is found using the form for factoring the difference of squares:
a² -b² = (a +b)(a -b)
x² -4 = (x +2)(x -2)
Note that x+2 is a factor here.
Complete factorizationThe complete factorization of the given polynomial is ...
x³ +4x² -4x -16 = (x +4)(x +2)(x -2)
This is confirmed by the graph, which shows zeros at x = -4, -2, 2.
Which of the graphs below represents a quadratic function that has two complex roots?
The second graph represents that the function has two complex roots.
What are Complex Numbers?
Complex numbers are made up of two parts: a real number and an imaginary number. Complex numbers serve as the foundation for more complex arithmetic, such as algebra.
Solution:
Since, the graph in the second option is not making any contact with thew point on x-axis it can be very well said that the solutions/roots/zeros of the quadratic equation are complex numbers.
Which is not the case for option one and option two because, the curves are making intercepts on x-axis thus, giving real roots.
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Answer:
I'm doing the same exact test, it's B.
Help please I will give you 100 points
The angles of the given figure are:
∠1 = 128°
∠2 = 52°
∠3 = 47°
∠4 = ∠5 = 81°
What are corresponding angles?
Corresponding angles are those created when a transversal line crosses two straight lines. When two or more straight lines and a transversal intersect, corresponding angles are found at the intersection.According to the corresponding angles rule, a transversal cutting two parallel lines results in corresponding angles that are equal.The angle is supplementary(∠5)
52° + ∠5 + 47° = 180°
∠5 + 99° = 180°°
∠5 = 180° - 99°
∠5 = 81°
Then the ∠1 and 52° are supplementary (Interior adjacent angles)
∠1 + 52° = 180°
∠1 = 180° - 52°
∠1 = 128°
Now, ∠2
∠2 + ∠5 + 47° = 180°
∠2 + 81° + 47° = 180°
∠2 = 180° - 128°
∠2 = 52°
Based on interior opposite angles are equal. Then
∠5 = ∠4 and ∠3 = 47°
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Translate the word problem into an equation or inequality. *DONT SOLVE THE PROBLEM*. What is Half a number less than 3 is at most 5 as an equation or inequality.
Answer:
3 -n/2 ≤ 5
Step-by-step explanation:
You want a math expression that means "half a number less than 3 is at most 5."
TranslationWe can let "n" represent "a number." Then "half a number" is (1/2)n or n/2.
That amount "less than 3" means it is subtracted from 3:
3 -n/2 . . . . . . half a number less than 3
The wording "is at most" means "is less than or equal to." In symbols, the words mean ...
3 -n/2 ≤ 5
__
Additional comment
Often 'x' is used to represent an unknown quantity. We like 'n' for "a number" because it is mnemonic, and because the numbers of interest are often integers or natural numbers from the set represented by ℕ.
English expressions of math relations are often ambiguous. In this case, we're not completely sure that the intention is not "half (a number less than 3)", which would be (3 -n)/2. Usually, we fall back on the Order of Operations, which requires that multiplication be done before addition. That is "half a number" must be computed before "less than 3" is evaluated, hence 3 -n/2.
write the measurements in ascending order 0.34km, 430m,33000 cm
The correct ascending order is 33000 cm, 0.34 km, 430 m.
to find the ascending order we firstly have to convert the all values into a same unit system.
we will convert all the values into cm units.
so, 0.34 km = 0.34*100000 cm,
0.34 km = 34000 cm.
similarly 430 m = 430* 100 cm,
430 m = 43000 cm.
and lastly we have 33000 cm.
so in all the values 33000 cm is smallest and 43000 cm is largest and the correct ascending order will be 33000 cm, 0.34 km, 430 m.
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Hi, I need help solving and understanding this.
''Find two functions f and g such that h(x) = (f o g) (x).
h(x)=sqrt(7x+5)''
The two functions f and g such that h(x) = (fog) (x) , are f(x) = 7x + 5 and g(x) = √x .
In the question ,
it is given that
the two functions f(x) and g(x) , form a composite function h(x) such that
h(x) = (f o g)(x) , and h(x) = √(7x + 5)
the composite function (f o g)(x) means f(g(x)) which means g(x) is within h(x) .
By this we get that
the function g(x) is (7x + 5)
and function f(x) is √x .
Therefore , The two functions f and g such that h(x) = (fog) (x) , are f(x) = 7x + 5 and g(x) = √x .
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Determine the end behavior of the following polynomial function:
f(x)=−2/9x^9(x−9)^2(x−8)
The leading term of the polynomial is ?
The degree of f(x) is ?
The leading coefficient is ?
For given polynomial function f(x)=−2/9x^9(x−9)^2(x−8),
the leading term ( -2/9x^12 ) is negative with even exponent (12). The curve decreases as x approaches both negative infinity and positive infinity.
In this question, we have been given a polynomial f(x)=−2/9x^9(x−9)^2(x−8)
We need to determine the end behavior of the following polynomial function.
We write given polynomial functions as,
f(x) = -2/9x^12 + 52/9 x^11 -50x^10 + 144x^9
The leading term of the polynomial is: -2/9x^12
The degree of f(x) is : 12
The leading coefficient is: -2/9
We can see that the leading term is negative with even exponent. The curve decreases as x approaches both negative infinity and positive infinity.
Therefore, for given polynomial function f(x)=−2/9x^9(x−9)^2(x−8),
the leading term ( -2/9x^12 ) is negative with even exponent (12). The curve decreases as x approaches both negative infinity and positive infinity.
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Is -3(5) the same thing as 5(-3)?
Answer:
yes, The result is the same
Step-by-step explanation:
-3(5)=-15
5(-3)=-15
Answer:
They are same (equal)
Step-by-step explanation:
-3 multiplied with 5 is equal to -15.
5 multiplied with -3 is also equal to -15
so these two expressions are same when multiplied because the products are equal to one another.
help me please!!! ASAP
CAN SOMEONE TELL ME IF THE CORRECT ANSWER TO THIS IS 16??
E and M are shown as congruent. This could be an Isosceles Triangle, so let's check. In an isosceles triangle, there are two congruent angles adjacent to the non-congruent side, and two congruent sides to the non-congruent angle. This angle is the apex. The apex of this triangle is adjacent to two congruent sides, however it is congruent to angle M, and thus this cannot be an isosceles triangle. That means this is an equilateral triangle, so all sides are congruent. So: LM = 16
-3y is less than -14 find y
Answer:
[tex]y > \frac{14}{3}[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
Sumalee won 40 super bouncy balls playing
horseshoes at her school's game night.
Later, she
gave two to each of her friends.
She only has 8 remaining. How many
friends does she have?
If she gave two to each of her friends. She only has 8 remaining balls. so she has a total of 16 friends.
What is division in mathematics?
In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, dividing 15 by 3 means dividing 15 into three equal groups of five. The symbol " or sometimes '/' represents division.
Sumalee won a total of 40 super bouncy balls.
then she gave two balls to each of her friends.
So she can distribute the balls to = 40/2
= 20 friends.
But after the distribution, she remained with 8 balls.
Now the number of balls will be = 40 - 8 = 32 balls.
and she can distribute 32 balls to = 32/2
= 16 friends.
Hence, If she gave two to each of her friends. She only has 8 remaining balls. so she has a total of 16 friends.
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-11x-7y= -56
Slope intercept form
Answer:
11/56 i think
Step-by-step explanation:
The slope of the line is m = - 11/7
And the y-intercept is b = 8
Find the slope and the y-intercept.
Step 1 – Transform the equation.
-11x - 7y = -56
To get a slope-intercept form, we need to isolate the variable y on the left-hand side of the equation.
First, we need to eliminate variable x from the left-hand side.
To eliminate the term with x, we'll add it to both sides of the equation. Remember to always perform the same operation on both sides to keep the equality true!
-11x – 7y + 11x = -56 + 11x
Now, let's add terms on the left-hand side. Keep in mind that two opposites add up to zero, so we can just remove it.
-7y = -56 + 11x
Since the variable x should be the firs on the righ-hand side in slope-intercept form, let's make it that way. Use the commutative property to reorder the terms.
-7y = 11x – 56
We're almost there! We just have to eliminate -7 from the left-hand side. To do that, let's divide both sides of the equation by -7.
(-7y)/(-7) = (11x - 56)/(-7)
Simplify the left-hand side. Each number divided by itself equals 1, so we are left with y.
y = (11x - 56)/(-7)
Next, separate the fraction on the righ-hand side into two fractions.
y = 11x/(-7) - 56/(-7)
Simplify the fraction on the right-hand side of the equation.
y = - 11x/7 + 56/7
y = - 11x/7 + 8
Finally, write the expression with x as a product.
y = - 11/7 x + 8
That's it! We've got the slope-intercept form of the equation.
Step 2 – Identify the slope.
Since the equation is written in slope-intercept form, y = m x + b, identify the slope of the lines as the coefficient next to the variable x.
y = - 11/7 x + 8
m = - 11/7
Step 3 – Identify the y-intercept.
Identify the y-intercept of the line as the constant term.
y = - 11/7 x + 8
m = - 11/7
b = 8
The slope of the line is m = - 11/7
And the y-intercept is b = 8
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PLEASE HELP ME THIS IS OVER DO
The function rule for the line is f(x) = [tex]\frac{2}{3}x[/tex] - 2
What is a linear function?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
The line cuts the x and y axis at (3,0) and (0, -2)
standard form of equation of line: y = mx + c
when x =3, y = 0
substitute these values into the equation
0 = 3m + c
c = -3m----------------1
when x = 0, y = -2
substitute these values into the equation, we have
-2 = 0(m) + c
c = -2
substitute the value of c in equation 1 to find m
-2 = -3m
m = 2/3
Substitute the values of m and c into the standard equation,
y = [tex]\frac{2}{3}x[/tex] - 2
In conclusion, the function rule for the given line is y = [tex]\frac{2}{3}x[/tex] - 2
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Which of the given interest rates and compounding periods would provide the best investment?
5 1/4 % per year, compounded monthly
5 1/2 % per year, compounded semiannually
5% per year, compounded continuously
5.5% compounded monthly will be the best investment.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
Now the formula for compound interest compounded monthly is,
A = P(1 + r/100)¹²ⁿ as a year has 12 months.
The formula for compound interest compounded semiannually is,
A = P(1 + r/100)²ⁿ as there are two semi-annuals in a year.
The formula for compound interest compounded continuously is,
[tex]A = P(1 + r/100)^{5.5n}[/tex] as the rate of interest is 5.5%.
Now from all these A = P(1 + r/100)¹²ⁿ which is compounded monthly has the highest power hence it will be the best investment.
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What is the mean in hypothesis testing?
Answer:
t = (x - μ) / SE. where x is the sample mean, μ is the hypothesized population mean in the null hypothesis, and SE is the standard error. P-value. The P-value is the probability of observing a sample statistic as extreme as the test statistic.
Step-by-step explanation:
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The mean in hypothesis testing is the parent population from which the samples are drawn.
What is hypothesis testing?In statistics, hypothesis testing is the process by which an analyst tests an assumption about a population parameter. The analyst's methodology is determined by the nature of the data and the purpose of the analysis. Using sample data, hypothesis testing is used to assess the plausibility of a hypothesis.
Hypothesis testing is a type of statistical inference that employs sample data to draw conclusions about a population parameter or probability distribution. First, an educated guess is made about the parameter or distribution.
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HELP QUICK PLEASE!!!
Answer: p = -2/3, sum = 0
Step-by-step explanation:
Additive inverse has the name numerical value as the given number but has the opposite sign so when they are added together they equal zero. The sum of any number and its additive inverse equal 0.
EX: 1 and -1
1+ (-1) = 0
EX: -4.5 and 4.5
-4.5 + 4.5 = 0
The points A, B, C and D lie in order on a straight line.
AB BD = 1:4
AC: CD = 7: 13
Work out AB BC: CD
Give your answer in its simplest form.
Answer:
By using the concept of ratio, it is obtained that
AB : BC : CD = 4 : 3 : 13
What is ratio?
Ratio between two number signifies how much one number is larger than as compared to another. The first part of the ratio is called antecedant and the second part of the ratio is called consequent
Here, the concept of ratio has been used
Here, AB : BD = 1 : 4
AC : CD = 7 : 13
AC + CD = 7 + 13 = 20
[tex]AB = \frac{1}{1 + 4} \times 20 = 4[/tex]
[tex]BD = \frac{4}{1+4} \times 20 = 16[/tex]
[tex]CD = 13[/tex]
BC = BD - CD = 16 - 13 = 3
AB : BC : CD = 4 : 3 : 13
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ? second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ? feet.
(Simplify your answer.)
The rocket reaches its maximum height at 2.25 second(s) after launch
The maximum height reached by the object is 88 feet.
Time to reach the maximum heightThe function is given as
h(t) = -16t² + 72t + 7
Differentiate the above function
So, we have the following representation
h'(t) = -32t + 72
Set to 0
-32t + 72 = 0
So, we have
32t = 72
Divide by 32
t = 2.25
Hence, the time is 2.25 seconds
The maximum heightIn (a), we have
t = 2.25
Substitute t = 2.25 in h(t) = -16t² + 72t + 7
h(2.25) = -16(2.25)² + 72(2.25) + 7
Evaluate
h(2.25) = 88
Hence, the maximum height is 88 feet
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2. Solve for x. Round to the nearest tenth if necessary.
25
Answer:
x = 15
Step-by-step explanation:
To solve this question and find value of x, we need to use Euclidean relation.
According this relation:
[tex] {x}^{2} = 9 \times 25[/tex]
[tex] {x}^{2} = 225[/tex]
Find the root of both expressions,
x = 15
Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line
with a slope of - 0.13. See the figure below.
There is $32.86 in credit remaining on the card after 22 minutes of calls. How much credit will there be after 35 minutes of calls?
Remaining
credit
(in dollars)
크
22
32.86
Calling time
(in minutes)
$0
X
Answer: The credit after calling for 35 minutes will be 31.17 dollar
How do you determine a line's slope?
The slope is calculated by dividing the difference between the y-coordinates of two points on a line by the difference between their x-coordinates.
Step-by-step explanation:
Given that credit x = 32.86
and time for calling y = 22
slope is m = -0.13
c = ?
Equation of line
y = mx + c
32.86 = -0.13(22) + c
32.86 + 2.86 = c
c = 35.72
now we have c we can calculate credit at time 35 min
y = -0.13(35) + 35.72
y = 35.72 - 4.55
y = 31.17 dollar
Hence the credit at time 35 min is 31.17 dollar
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Twice the difference of a number and -3 is 4. Find the number.
Answer:
The number is 5
Step-by-step explanation:
Let us use an equation ( X is the unknown number)
2(x-3)=4
2x-6=4
2x-6+6=4+6
2x/2=10/2
x=5
Mixture Problem. A solution contains 49 milliliters of HCl and 91 milliliters of water. If another solution is to have the same concentration of HCl in water but is to contain 78 milliliters of water, how much HCl must it contain?
The solution must contain
milliliters of HCl.
Using proportions here, the solution must contain 42 mL of HCL
ProportionsProportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a:b or a/b. Multiply and dividing each term of a ratio by the same number (non-zero), doesn’t affect the ratio.
We can write the ratio as this
49 / 91 = x / 78
cross multiply both sides and solve for x
x = 42 milliliters
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Y = Sin ^4(3x).find dy/dx
Step-by-step explanation:
[tex]y = \sin {}^{4} (3x) [/tex]
Using the chain rule
[tex] \frac{d( \sin(3x)) {}^{4} }{dx} = 12 \sin {}^{3} (3x) \cos(3x) [/tex]
Point A is on the coordinate plane and is represented by the ordered pair (3, 2). The point is moved five units down and labeled as point B.
Which of the following ordered pairs represents Point B?
( 3,7 ) will be point when its moved 5 units down on coordinate plane .
What is the short definition of a coordinate plane?
Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the other number line, which is vertical. At a place known as the origin, the two axes collide. To graph points, lines, and other things, we can utilize the coordinate plane.( 3,2) is the point .
when the point is moved 5 units down
then the point will be = ( 3, 7 )
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