"y is a function of x." The input value, or independent variable, is represented by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).
f(x) = 2x + 5.
f(x+3) = 2(x+3) + 5.
f(x+3) = 2x + 11.
What is meant by function ?a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value, or independent variable, is represented by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).To learn more about : function
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Match each pair of angles to their angle pair name.
<2&<7
<5 & <8
<9 & <16
<1 & <3
<4 & <3
<14 & <15
The name for the angle <2&<7 is an alternate interior angle by a transversal x.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
The angle pairs are given.
From the diagram:
<2&<7 = Alternate interior angle by a transversal x
<5 & <8 = Consecutive exterior angle by a transversal x
<9 & <16 = Consecutive exterior angle by a transversal x
<1 & <3 = Corresponding angles by transversal x
<4 & <3 = Adjacent angle by transversal g
<14 & <15 = Consecutive interior angle by a transversal y
Thus, the name for the angle <2&<7 is an alternate interior angle by a transversal x.
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4.
Bacteria in a lab has a population of 500 and it triples every hour. Which of the following
equations represents the this situation?
Identifique la intersección y y el factor de crecimiento para la siguiente ecuación
exponencial:
y=3z +500
y=500z+3
y = 500(3)²
y=3(500)=
Answer:
y=3(500)
Step-by-step explanation:
I think this is ans but i do not know the ans.
Math nerds please help finish these sentences
I can tell a slope is greater than 1 by _________
I can tell a slope is equal to 1 by _______
I can tell a slope is less than 1 by ________
please help answer these please
Just here for the points lol
a box with a square base and open top must have a volume of 42592 c m 3 . we wish to find the dimensions of the box that minimize the amount of material used. first, find a formula for the surface area of the box in terms of only x , the length of one side of the square base. [hint: use the volume formula to express the height of the box in terms of x .] simplify your formula as much as possible. wyzant
a formula for the surface area of the box in terms of only x , the length of one side of the square base is A = x² + 170368 cm³/x
The volume of the box with square base is V = x²h where x = length of side of square base and h = height of box.
Now, the area of the of box open at the top with dimensions of length, l , width, w and height, h are
A = 2lh + lw + 2wh
Now for a box of square base, l = w = x.
So, A = 2xh + x² + 2xh
A = x² + 4xh
Since V = x²h and V = 42592 cm³,
h = V/x² = 42592/x²
substituting h into A, we have
A = x² + 4xh
A = x² + 4x(42592 cm³/x²)
A = x² + 4 × 42592 cm³/x
A = x² + 170368 cm³/x
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Complete the empty table from the provided information.
Transform the graph of f(x) by dilating it by a factor of 3.
Write the equation of the resulting line in slope intercept form.
Due to length restrictions, the table of the transformed graph is shown in the explanation section. The equation of the transformed graph is g(x) = 3 · x.
How to derive the table of the image of a graph
In this question we find the representation of a line on a Cartesian plane and its corresponding table and we need to determine the table of the image of such function. The transformed graph is the result of dilating the original graph by a factor of 3. The value of g(x) is equal to three times the value of f(x):
x g(x)
- 2 - 6
- 1 - 3
0 0
1 3
2 6
The equation of the original graph is f(x) = x and the equation of the transformed graph is g(x) = 3 · x.
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Pls help with my geometry questions.
1. What do you call the side that is between 2 angles, like in ASA?
2. What do you call the side that is not in between 2 angles, like in AAS?
3. If lines are perpendicular, then they form ______ _______ angles.
A triangle is a closed polygon having number of sides exactly 3. Example - Equilateral Triangle, Isosceles Triangle, and etc.
The triangles are congruent when two pairs of corresponding angles and one pair of corresponding sides (between the angles) are both equal and the side is known as Included Side.
While, The triangles are congruent when two pairs of corresponding angles and one pair of corresponding sides (not between the angles) are both equal and the side is known as Angle Angle Side.
When two lines are perpendicular to each other, then they form Right Angles which are 90° in measure.
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Swim team members can race or dive. At a meet, 18 members race. The ratio of racers to divers is 6:2. How many members are on the team?
Answer:
24
Step-by-step explanation:
If the ratio of racers to divers is 6:2 then compare that to 18:x
6 times 3 is 18
2 times 3 is 6
x is 6
Now add 6 and 18
You get 24
how many apples does john eat
Answer:
you gave no context....so ill just guess 3.
SOMEONE PLEASE HELP ITS URGENT!!! Please help with this
Answer:
X = 8?
Step-by-step explanation:
I'm not sure if I'm correct but I used this solution of since 4x + 1.
Usually if its + something then you subtract it so 33-1 is 32 then
4x= 32
x=8
If I'm wrong, I apologise.
What is the domain and range of this function?
Answer:
Domain(X-value): {-5,-4,-3,-2,-1,0,1,2,3,4,5}
Range (Y-value): {-2,-1,0,1,2}
Step-by-step explanation:
The domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
Can some one PLEASE HELP me , I do not understand how to do this at all and I have to submit it TONIGHT please and thankyou!
Answer:
Answer down below!
Step-by-step explanation:
Let's find a point on the graph that we can start off on
We can use (2,-1)
From there, we can use rise/run to find our answer
We go up 3 and over -2
So, our slope is -3/2 because we cannot simply it any further
The measures of the angles of a triangle are shown in the figure below. Solve for x
need help asap!!!)
Answer:
x=36
Step-by-step explanation:
(3x+3)^0+x+54= 90
x+54=90
x=90-54
x=36
Ten granola bars and twelve bottles of water cost $23. Five granola bars and four bottles of water cost $10. How much do one granola bar and one bottle of water cost?Part BFor a fundraiser, a group plans to sell granola bars and bottles of water at the same prices as described in Part A. The group wants the income from the fundraiser to be at least $150.Choose the inequality to show the number of granola bars x and the number of bottles of water y that must be sold.
Let g = cost of granola bars
b = cost of a bottle of water
10g+12b = 23
5g + 4b = 10
Multiply the second equation by -2
-10g -8b = -20
Add this to the first equation
10g+12b = 23
-10g -8b = -20
---------------------
4b = 3
Divide by 4
4b/4 = 3/4
b = 3/4 or .75
Now find g
5g + 4(3/4) = 10
5g + 3 = 10
5g = 7
g = 7/5
g = 1.4
We want to find 1g+ 1b
1.4+ .75 =2.15
Part B
We want our income to be at least 150
The cost of granola bars is 1.4 and we are selling x of them
The cost of water is .75 and we are selling y of them
It must be at least >=
1.4x + .75y >= 150
Prove algebraically that the square of any odd number is always one more than a multiple of 8.
The square of any odd number is not always one more than a multiple of 8. The proposition is false.
How to prove a relationship between odd numbers and multiples of 8
Natural numbers can be divided into even numbers (i.e. 2, 4, 6) and odd numbers (i.e. 1, 3, 5). Let be n an element of the set of even numbers and the element 0, such that odd numbers are of the form:
x = 1 + n
Then,
(1 + n)²
1 + 2 · n + n²
If 1 + 2 · n + n² is one more than a multiple of 8, then we find the following relationship:
1 + 2 · n + n² = 8 · x + 1, where x is a natural number.
2 · n + n² = 8 · x
For x = 1:
2 · n + n² = 8
n² + 2 · n - 8 = 0
(n + 4) · (n - 2) = 0
Then, the least even number is 2 and the least odd number is 3. This implies that the proposition is not observed for (1 + n) = 1. Therefore, the proposition is false.
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20=5x+10y help me please
Answer:x=2(-y+2)
Step-by-step explanation:easy
What is 150 + 1/6 + 1/2
Answer:
150 and 2/3 or 150.6666...
Step-by-step explanation:
1/6 + 1/2 = 1/6 + 3/6.
1/6 + 3/6 = 4/6 = 2/3
150 + 2/3 = 150 and 2/3
Mark as brainliest please
Answer: exact form is 452/3
decimal form is 150.6
Step-by-step explanation:
please anyone pleaseee help with explanation
The slope of the line = change in y / change in x = 4/3.
How to Find the Slope of a Line?The slope of a line is the rise over the run, which is the change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
To calculate the slope of the line that is given, chose any two points on the line as plotted in the given graph, say:
(30, 20) = [tex](x_1, y_1)[/tex]
(60, 60) = [tex](x_2, y_2)[/tex]
Substitute each of these values into the slope formula, [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]:
Slope for the given line (m) = (60 - 20)/(60 - 30)
Slope for the given line (m) = 40/30
Slope for the given line (m) = 4/3.
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12] Will's salary is three times Nathan's salary. Together they earn $192 per week. Find the salary of each boy.
Nathan's salary is $48 and Will's salary which three times of Nathan's salary is $144.
What is salary?
An employment contract may include a salary clause as a type of recurring payment from an employer to an employee. In contrast, piece wages are paid separately for each job, hour, or other unit rather than on a regular schedule. Salary can also be seen from the perspective of operating a corporation as the expense of obtaining and keeping employees to carry out operations; this is known as a personnel expense or salary expense. Payroll accounts are used in accounting to record salaries.
It is given in the question that Will's salary is three times Nathan's salary.
So, lets assume that Nathan's salary is X it implies that Will's salary will be 3 times X = 3X
Together they earn $ 192.
So,
X + 3X = 192
4X = 192
X = 192/4
X = 48
Therefore, Nathan's Salary is $48
Since, Will's salary is 3 times of Nathan's salary,
So,
Will's salary = 3 (48) = 144
Therefore, Will's Salary is $144
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What is the slope of a line perpendicular to the line whose equation is 3x + 6y = –72. Fully reduced
The slope of the line is 2 for the equation that is perpendicular.
Slope of the line:
Slope of the line refers the change in y coordinate with respect to the change in x coordinate.
Given,
Here we have the equation 3x + 6y = - 72 that is perpendicular to the line.
Now, we need to find the slope of the line from it.
First we have to convert the given equation of line into standard form,
Then we get,
3x + 6y + 72 = 0
Now we know that the slope of the line for this type of equation is,
m = -a/b
Whlie we compare the equation with the standard form ax + by + c = 0,
Then we get the value of a = 3 and b = 6
Therefore, the slope of the line is
m1 = -3/6
m1 =-1/2
Here we need to find the slope of a line which is perpendicular to the given line.
Through the definition we know that product of two perpendicular line is -1.
So,
m1 x m2 = -1
(-1/2) x m2 = -1
m2 = 2
Therefore, the slope of perpendicular line is 2
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Determine which integer(s) from the set S:{−40, 2, 20, 42} will make the inequality three eighths m minus three is less than one fourth m plus 2 false.
S:{42}
S:{−40, 2}
S:{−40, 2, 20}
S:{−40}
The set S:{42} will make the inequality false.
By definition, one can apply any monotonically rising function to both sides of an inequality without affecting how they relate to one another (provided that both expressions are in the domain of that function).
An inequality relation would be reversed if a monotonically dropping function were applied to both sides of the inequality. Examples of how to employ a monotonically declining function are the rules for the additive and multiplicative inverses for positive values. The inequality (a b, a > b) remains stringent if the function is monotonic in a strict sense.If only one of these requirements is met, the inequality that results is not rigid. In fact, the requirements for both additive and multiplicative inverses serve as evidence that a strictly.Given inequality is :
3/8 m - 9 < 1/4 m + 2
Solving the inequality we get:
or, m < 40
Therefore of all the elements of the set 42 makes the inequality false.
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On Wednesday night in St. Petersburg, Russia, the temperature is -11°C.
On the same night in Bombay, India, the temperature is 17°C.
What is the difference in the temperature?
The difference in the temperature of Bombay to St. Petersburg is 28° C.
What is the difference between two numbers and how is it calculated?
An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol, or, denotes subtraction. Subtraction is the process of subtracting a matrix, vector, or other quantity from another according to predetermined criteria in order to find the difference.
Subtracting two numbers from each other is a type of subtraction. The difference between two numbers is calculated by deducting the smaller of the two values from the larger.
Given, the temperature in St. Petersburg = T₁ = -11° C
The temperature in Bombay = T₂ = 17° C
Using general comparison, we get T₂>T₁, since one is positive and the other is negative.
Therefore following available literature,
Difference in temperature = T₂ - T₁ = 17 - (-11) = 17 + 11 = 28° C
Thus, the required difference in temperature of Bombay to St. Petersburg is 28° C.
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Find the slope of the line passing through the points (-2, 7) and (—9,4)
The slope of the line is 3/7.
The slope of line will be calculated using the formula :
Slope = [tex] \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
The first point is (-2, 7) and second point is (-9, 4). So, [tex] y_{2}[/tex] = 4, [tex] y_{1}[/tex] = 7, [tex] x_{2}[/tex] = -9 and [tex] x_{1}[/tex] = -2. Keep the values in formula to find the values of slope of the line.
Slope = (4 - 7)/(-9 - -2)
Performing subtraction in numerator and denominator
Slope = -3/-7
Cancelling the negative signs we get -
Slope = 3/7
Thus, the slope of the line is 3/7.
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ii) (1, 3), (6,3), (6, 6) and (1, 6) are the vertices of a rectangle.
Given, (1, 3), (6,3), (6, 6) and (1, 6) are the vertices of a rectangle, the width is 1 unit shorter.
What is a rectangle?A rectangle is a quadrilateral with the four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with the four equally long sides. Oblong is occasionally used to describe a rectangle that isn't square. Rectanglen is the symbol for a rectangle having the vertices ABCD. ABCD in PNG.
Rectangulus, a combination of rectus (as an adjective, right, proper), and angulus, is the source of the English word rectangle (angle).
A crossed rectangle is a quadrilateral that is formed by the intersection of two diagonals and the two opposite sides of a rectangle (therefore only two sides are parallel). Although opposite angles are equal, it is a specific example of an antiparallelogram in which the angles are not all right angles and equal. There exist so-called rectangles in other geometries, including spherical, elliptic, and hyperbolic ones, with opposite sides of equal length and equal angles that are not right angles.
Many tiling issues use rectangles, like tiling the plane with rectangles or tiling a rectangle with polygons.
By plotting given points in the coordinate plane,
We get rectangle ABCD having vertices,
A(-1,6), B (3,6), C (3,1), D (-1,1)
By distance formula,
Shorter side or width of rectangle,
AB= [tex]\sqrt{ [3-(-1)]^{2}+ (6-6)^{2}} = \sqrt{4^{2}+0 } = 4 units[/tex]
Longer side or length of rectangle,
BC= [tex]\sqrt{(3-3)^{2}+(1-6)^{2}}=\sqrt{5^{2} } = 5 units[/tex]
The difference between length and width,
BC-AB= 5-4= 1units
Hence, width of rectangle is 1 unit less than the length.
active attachment
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The exact volume of a cylinder with radius 3 cm and height 6 cm is:
Landon had 56 playing cards. He kept 12 for himself and
dealt the rest evenly to his 4 friends. Which expression best
represents the number of cards each friend received?
We need to use simple division to solve the problem. The number of cards each friend received is 11.
It is said that Landon has 56 cards, he kept 12 cards for himself, so we can subtract 12 cards from the whole lot to get the total number of cards he distributes among his friends.
56-12=44
There are 44 cards that he will distribute among his friends equally, we can get that by simply dividing the total number of cards by the number of friends which is 4.
number of cards for each friend=44/4=11
Therefore the number of cards each friend received is 11.
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48x4 and 44x5 Find the GCF
The greatest common factor (GCF) of the given expression 48x^4 and 44x^5 is 4x^4.
What is Greatest common factor?Greatest common factor, as the name implies, is greatest among all common factors among the quantities given. We can factorize the quantities in smallest relative factors possible (one level of factors over which all quantities can form themselves), and collect as many common factors as we could. Those will together compose GCF(Greatest common factor).
To find the GCF of [tex]48x^4[/tex] and [tex]44x^5[/tex]. we have to write the prime factorization of both the terms;
Prime Factorization of [tex]48x^4[/tex]= 2 × 2 × 2 × 2 × 2 × 2 × x × x × x× x
Prime factorization of [tex]44x^5[/tex] = 2 × 2 × 11 × x × x × x × x × x
Thus the common factors are 2 × 2x × x × x× x
Therefore The greatest common factor (GCF) of the given expression 48x^4 and 44x^5 is 4x^4.
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Guys I need help is this right?
The domain of the function in this situation as required in the task content is; Choice C; {0, 1, 2, 3, 4, 5, 6}
What is the domain of the function for this situation?It follows from the task content that the domain of the function described by the situation is to be determined.
Since the domain is the set of all possible input values, otherwise termed the independent variable, x.
It follows that since the carton can hold from 0 to 6 books; the domain is; Choice C ; {0, 1, 2, 3, 4, 5, 6}
Please Note: The set of all possible output values of a function, otherwise termed the dependent variable, y is called the Range.
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Which table is linear?
2)
X
-2
-1
0
1
2
у
0.111
0.333
1
3
9
8)
X
-2
-1
0
1
2
у
7
2
-1
-2
-1
X
-2
-1
0
1
2
у
-2
1
4
7
10
Answer:
The last one
Step-by-step explanation:
this is really hard to read but you have to see which y values increase by a constant amount. Only the last case is linear in which each value increases by 3
How can division be used to find the factors of polynomial functions?
Answer:
To divide polynomials using long division, first divide the first term of the dividend by the first term of the divisor. This is the first term of the quotient. Multiply the new term by the divisor, and subtract this product from the dividend. This difference is the new dividend.
can someone help me really quick
Answer:
6.75
Step-by-step explanation:
Consider the ratio:
$4.50 : 6 apples
We need to multiply this ratio by a value such that the right side is 9 because there are 9 apples in array p. This value is 9/6 = 3/2.
$4.50 : 6 apples
× 3/2 × 3/2
$6.75 : 9 apples
So, the value of p, or 9 apples, is $6.75, which you will input as 6.75.