Functions are special relaionships that connect an element of one set of numbers, with one element in another set of numbers.
The most comon way to represent functions is connecting elements of a set of Real numbers called the "Domain", to another number in a set called the Range (and whose elements are identified with the letter "y")
Using math operations one can relate x values with y values via an equation of the type:
y = 2 x - 5
where you have a mathematical form of that relationship, that allows you to know given the value of one member (x) of the Domain what number is associated with it in the Range.
For example, try the number x = 0
and see which y number connects with it:
y = 2 (0) - 5 = 0 - 5 = -5
Then you say that the number 0 in the Domain connects with the number -5 in the Range.
This relationship can also be given with coordinate pairs of the form:
(x, y) mentioning in the first position (where the x is), the number in the Domain that connects to the "y" number of the Range). The y goes in the second place. so for example in the relationship we found above, x = 0 connects with y=-5, you would have a shortcut way to write it as the pair: (0, -5) that tells you which x connects with which y.
The functions can also be given in graph form by plotting the relationship between members of the Domain and the Range on the plane. Graphing a point in the plane location that corresponds to the connected x and y values (like you do in the game "battlefield" when you locate ships on the board.
I know this is very general, but hopefully you got the idea ofa function as a special relationship between numbers, and that they can be expressed in different fashions.
Circle O has a circumference of 88π cm.
Circle O has a radius length of r.
What is the length of the radius of the circle?
The length of the radius of the circle is 44cm.
This problem bothers on the mensuration of flat shapes, a circular shape.
Given data
Circumference of circle C= 88πcm
Radius of circle r=?
To find the length of the radius of the circle.
To solve for the radius let us apply the formula for the circumference of a circle
C=2πr
Substituting our given data
88π=2πr
Making r subject of formula we have
r= 88π/2π
r= 44cm
Hence, The length of the radius of the circle is 44cm.
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What real-world knowledge did you use to understand the STEM Task?
The real world knowledge we use to understand the STEM task are :
A) STEM integrates it's concepts and applications to real life.
B) STEM helps in finding solution to the practical issues.
C) Focuses on building models and replicating scenarios.
What is STEM ?
STEM education refers to the integrated teaching and learning of the subjects such as science, technology, engineering, and mathematics.
We know that STEM teaches critical thinking skills and instills a passion for innovation. Beyond the advantages of learning STEM subjects, STEM supports the problem-solving and inquisitive learning that are essential for success in a range of tasks and professions. Colleges are now incorporating all of these helpful ideas into their normal study courses, and the results are clearly very favorable.
The real world knowledge we use to understand the STEM task is as follows :
STEM education stresses the application of knowledge to real-life situations while integrating concepts that are often taught as separate courses in various classrooms.Finding a solution to a practical issue is often the focus of a STEM lesson or unit, which frequently emphasizes project-based learning.Building models and replicating scenarios are common STEM instructional activities. Students' understanding of the relationship to the real world is ensured by a competent STEM lesson.Therefore , the real world knowledge we use to understand the STEM task are :
A) STEM integrates it's concepts and applications to real life.
B) STEM helps in finding solution to the practical issues.
C) Focuses on building models and replicating scenarios.
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Which list shows the values in order from least to greatest?
0-0.5
√(0.5)
0-0.5
20% √/0.5
○ 20% |−0.5| √/0.5
○ = √/0.5 |−0.5| 20%
20%
The values in order from least to greatest are 0-0.5,√(0.5),20%,20% √/0.5,√/0.5 |−0.5| 20%. we eliminate 0-0.5 because the value is two times in the option.
What is the percentage?Percentage represents a proportion or a fraction of a whole, expressed as a portion of 100. It is commonly denoted by the symbol "%" (percent), which literally means "per hundred."
According to the given information:
The values in the list are:
0-0.5 = a range of values from 0 to 0.5, inclusive
√(0.5) ≈ 0.7071
20% = 0.2
20% √/0.5 = 0.2 * √(0.5) ≈ 0.1414
√/0.5 |−0.5| 20% = √(0.5) * |−0.5| * 0.2 ≈ 0.0707
Therefore, the correct list in order from least to greatest is:
0-0.5
√(0.5)
20%
20% √/0.5
√/0.5 |−0.5| 20%
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A $1,000 deposit is made at a bank that pays 12% compounded
How much will you have in your account at the end of 10
monthly.
years?
Answer- 3,315.53007332
Step-by-step explanation:
In this example the compounded is weekly, so the interest rate has to be converted to a weekly interest rate of tex2html_wrap_inline224 .
At the end of the first week, you will have the $1,000 you had at the beginning of the week plus the interest on the $1,000 or tex2html_wrap_inline226 . At the end of the week you will have
displaymath228
Please answer all 3 questions in the photo for easy point! ( 30 points + Brainliest )
Answer:
6. a because a rectangle with sides 8 and 2 has a perimeter of 20 but its area is 16.
7. d because 4 is an even number and it is a perfect square.
8. b because a pen can be used to write but is not a utensil.
Step-by-step explanation:
Help I don’t understand what’s happening
Solution of Square root, x² = 30: x = √30 = √30² = 30, x = -√30 = -√30² = 30
Solution of Cube root, x³ = 30: x = ∛30 = ∛30³ = 30, x = -∛30 = -∛30³ = -30
Given,
Square root x² = 30
Then, the value of:
x = √30 = √30² = 30
x = -√30 = -√30² = 30
x = ∛30 = ∛30² = 3.107
x = -∛30 = -∛30² = -3.107
Now,
Cube root, x³ = 30
x = √30 = √30³ = 164.317
x = -√30 = -√30³ = -164.317
x = ∛30 = ∛30³ = 30
x = -∛30 = -∛30³ = -30
Therefore,
Solution of Square root, x² = 30:
x = √30 = √30² = 30
x = -√30 = -√30² = 30
Solution of Cube root, x³ = 30:
x = ∛30 = ∛30³ = 30
x = -∛30 = -∛30³ = -30
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solve for v: -28 = v +-12
Answer:
v = -16
Step-by-step explanation:
Move the variable to the left-hand side and change its sign, so it would then be -28 - v = -12
Then move the constant to the right-hand side and change its sign, so it would become - v = -12 + 28
Then you would calculate the sum: - v = 16
After doing so, change the sides on both sides of the equation, v = -16
So, your answer should be v = -16
What is the slope of the line that passes through the points (-4, -10)) and (-7, -19)
? Write your answer in simplest form.
Answer:
Slope = 3
Step-by-step explanation:
(-4, -10) and (-7, -19)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -19 - (-10) -19 + 10 -9
m = ------------ = ---------------- = ------------- = -------- = 3
x₂ - x₁ -7 - (-4) -7 + 4 -3
I hope this helps!
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{-19}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-19}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{-7}-\underset{x_1}{(-4)}}} \implies \cfrac{-19 +10}{-7 +4} \implies \cfrac{ -9 }{ -3 } \implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y +10= 3 (x +4) \\\\\\ y+10=3x+12\implies {\Large \begin{array}{llll} y=3x+2 \end{array}}[/tex]
in poker, 5 cards are randomly dealt from a standard deck of 52 cards. (a) how many poker hands contain cards that are all the same suit (this is called a flush)? (b) what is the probability of that all the cards in a poker hand are the same suit?
In probability , 5148 possible flushes in poker.
What is probability in math?
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 refers to the study of events subject to probability.there are C(13,5) 5-card hands… i.e.
the number of combinations of taking 5 cards from 13 distinct cards.
But, since there are 4 suits, there are then 4*C(13,5) possible “flushes.”
Thus, there are 4*1287=5148 possible flushes in poker.
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141% as a mixed or whole number
Answer:
1 41/100
Step-by-step explanation:
Answer:
141/100 (Already in simplest form). As a mixed number, it is: 1 41/100
Step-by-step explanation:
Solve for x. Leave your answer in simplest radical form
Answer:
x = √213
I would appreciate this being marked as brainliest...
Step-by-step explanation:
This is a Pythagoras question because we are given two right-angled triangles and no internal angles other than the right angles.
That 7 is annoying because it won't form a Pythagorean triplet with 10. It means that the answer will probably be in radical form.
We can use radicals to represent the common side.
Introduce Pythagoras. The equation below forms a circle on a graph by the way where r is the radius of the circle.
a² + b² = c²;
Substitute the first triangle.
10² + 7² = c²;
100 + 49 = c²;
149 = c²;
c = √149;
Substitute the second triangle.
(√149)² + 8² = x²;
149 + 64 = x²;
213 = x²;
x = √213;
a design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. he knows from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. on three recent production batches, he tested service life on random samples of four headlamps, with these results: sample service life (hours) 1 495 500 505 500 2 525 515 505 515 3 470 480 460 470 what is the mean of the sampling distribution of sample means when the service life is in control? multiple choice 500 hours 515 hours 495 hours 250 hours 470 hours
The mean of the sampling distribution of sample means is 495 hours.
What is the mean of the samples?
The mean of samples is the average of a set of samples or data.
This can be calculated using the formula:
Mean= (Sum of terms)/(Number of terms)
Find the mean of each sample as shown below:
Mean service life of sample 1 = [tex]\frac{495+500+505+500}{4} = \frac{2000}{4}[/tex]
= 500 hours
Mean service life of sample 2 =[tex]\frac{525 +515 +505 +515 }{4}=\frac{2060}{4}[/tex]
= 515 hours
Mean service life of sample 3 = [tex]\frac{470 +480 +460+ 470}{4}=\frac{1880}{4}[/tex]
= 470 hours
Find the mean of the sampling distribution of sample means using the formula:
Mean of the sampling distribution (M)
=(Sum of mean of given samples )÷( Number of samples)
M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]
M=495 hours
So, the mean of the sampling distribution of sample means is 495 hours.
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The mean of the sampling distribution of sample means is 495 hours.
What is the mean of the samples?
The mean of samples is the average of a set of samples or data.
This can be calculated using the formula:
Mean= (Sum of terms)/(Number of terms)
Find the mean of each sample as shown below:
Mean service life of sample 1 = [tex]\frac{495+ 500+ 505+ 500}{4}=\frac{2000}{4}[/tex]
= 500 hours
Mean service life of sample 2 = [tex]\frac{525+ 515+ 505+ 515 }{4}=\frac{2060}{4}[/tex]
= 515 hours
Mean service life of sample 3 = [tex]\frac{ 470+ 480 +460 +470}{4}=\frac{1880}{4}[/tex]
= 470 hours
Find the mean of the sampling distribution of sample means using the formula:
Mean of the sampling distribution (M)
=(Sum of mean of given samples )÷( Number of samples)
M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]
M=495 hours
So, the mean of the sampling distribution of sample means is 495 hours.
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9. Find the area of the shaded region.
22 cm
10 cm
7 cm
Evaluate the expression when x=5The expression is 4x -13.
To answer this question, we only need to replace x by 5, and then solve the resulting operations:
[tex]x=5\Rightarrow4x-13=4\cdot(5)-13=20-13=7[/tex]Therefore, the value for the expression 4x-13 when x = 5 is equal to 7.
in the united states, the mean birth weight for boys is kg, with a standard deviation of kg. assuming that the distribution of birth weight is approximately normal, complete parts a through e.
The proportion of baby boys in the United States that are born with low birth weight is 0.0495
In a set with mean u and standard deviation σ , the z score of a measure X is given by:
Z= X - u / σ
Z = 2.5- 3.41/ 0.55
Z= -1.6545
Z= -1.65 has a p value of 0.0495
The proportion of baby boys in the United States that are born with low birth weight is 0.0495.
the complete question is
In the United States, the mean birth weight for boys is 3.41 kg with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. A baby is considered of low birth weight if it weighs less than 2.5 kg. What proportion of baby boys in the United States are born with low birth weight
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help me pls battery is low help
The solution to the system of linear equations 6 · x + 2 · y - 9 = 0 and y = 2 · x - 3 is (x, y) = (1.5, 0).
How to resolve a system of linear equations by graphic methods
In this question we find a system of two linear equations and two variables, this can be done by using a Cartesian plane and drawing each line equation. The solution to the system is represented by the point of intersection of the two lines.
Therefore, the solution to the system of linear equations is (x, y) = (1.5, 0).
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The solution to the system of linear equations will be; 6x + 2y - 9 = 0 and y = 2x - 3 is; (1.5, 0).
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.
To solve a system of linear equations by graphic methods: we need a system of two linear equations and two variables, using a Cartesian plane and each line equation.
The solution to the system is shown by the point of intersection of the given lines.
6x + 2y - 9 = 0
y = 2x - 3
6x + 2 (2x - 3 ) - 9 = 0
x = 1.5
(x, y) = (1.5, 0).
Hence, the solution to the system of linear equations would be; (x, y) = (1.5, 0).
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Please help super confused ASAP.
Find f(-9) if f(x) = -2x + 5.
Enter DNE if the value does not exist.
f(-9)=
Work Shown:
f(x) = -2x+5
f(-9) = -2(-9)+5
f(-9) = 18+5
f(-9) = 23
6.2: The Return of the Box
Earlier, we learned we can make a box from a piece of paper by cutting squares of side
length x from each corner and then folding up the sides. Let's say we now have a piece of
paper that is 8.5 inches by 14 inches. The volume V, in cubic inches, of the box is a
function of the side length x where V(x) = (14-2x)(8.5-2x)(x).
1. Identify the degree and leading term of the polynomial. Explain or show your
reasoning.
2. Without graphing, what can you say about the horizontal and vertical intercepts of
the graph of V? Do these points make sense in this situation?
The leading term of the polynomial is [tex]4x^{3}[/tex] and the degree of the polynomial is 3.
A sheet of paper measuring 8.5 inches by 14 inches is currently in our possession. The box's volume V, measured in cubic inches, depends on the side length x, where V (x) = (14-2x)(8.5-2x)(x).
So, we have :
V (x) = (14-2x)(8.5-2x)(x)
[tex]V(x) = (14-2x)(8.5-2x)(x).\\V (x) = (14-2x)(8.5x-2x^{2} )\\V(x) = 4x^{3} -45x^{2} + 119x[/tex]
Thus, the leading term of the polynomial is [tex]4x^{3}[/tex] and the degree of the polynomial is 3.
Now, we have :
[tex]V(x) = 4x^{3} -45x^{2} + 119x\\V(x) = x ( 4x^{2} -45x +119)\\V(x) = x (x-7)(4x-17)[/tex]
Now, For intercepts, V(x) = 0
[tex]V(x) = x (x-7)(4x-17) = 0\\x (x-7)(4x-17) = 0\\\\x = 0, 7, 4.25[/tex]
Now when x = 0, V(x) =0
when x = 7, f(x) = 135
when x = 4.25, f(x) = 252.89
So, the points are (7, 135) and ( 4.25, 252.89)
These points represent the value of x and their corresponding value of V.
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∠1 and ∠2 are vetical angles. If m∠1 =(5x+12)° and m∠2 =(6x−11)°. m∠1=
⇒Vertical angles are equal .
This means that ∠1=∠2
⇒The trick is to first find the value of the unknown variable x then substitute it in the expression of ∠1 to get the exact magnitude of the angle.
[tex]5x+12=6x-11\\5x-6x=-11-12\\-x=-23\\\frac{-x}{-1} =\frac{-23}{-1} \\x=23[/tex]
x=23°
To get the exact value of ∠1 Plug in 23° in the place of x in the expression of ∠1:
[tex]< 1=5x+12\\=5(23)+12\\=127[/tex]
∠1=127°
Ming had 59 birthday cupcakes. He gave 30 cupcakes to his classmates at school. Ming's family ate another 11 cupcakes at home.
How many cupcakes does Ming have left?
Answer:18
Step-by-step explanation:
59 - 30 - 11 = 18
What is the value of x in the equation −x = 6 − 3x + 8?−14−7147
S={7}
1) Let's solve for x, for the given equation :
-x = 6 -3x +8 Add 3x to both sides
3x-x=-3x+3x +6 +8
2x =14 Divide both sides by 2
x= 7
S={7}
And that is the answer
Find (a) f(-8) and (b) f(3).
(a) f(-8)=
(b) f(3) =
Answer:
[a] 15
[b] 13
Step-by-step explanation:
We can use the visual diagram given to solve. We can see that when you input -8 (on the left side) the arrow leads to the output 15, our answer.
We use the same method for part b. When you input 3 (on the left side) the arrow points to 13 (on the right side) giving us an answer of 13.
Here is a linear equation: y = 2/3x + 1 Are (6, 5) and (9, 8) solutions to the equation? Explain or show your reasoning.
The equation y = 2/3x + 1 has a solution of (6, 5) and not (9, 8)
How to determine if the ordered pairs are part of the solutions?From the question, the equation is given as
y = 2/3x + 1
Also, we have the ordered pairs to be
(6, 5) and (9, 8)
For (6, 5), we have
x = 6 and y = 5
So, the equation becomes
5 = 2/3 x 6 + 1
Evaluate
5 = 5 --- true
For (9, 8), we have
x = 9 and y = 8
So, the equation becomes
8 = 2/3 x 9 + 1
Evaluate
8 = 7 --- false
Hence, (6, 5) is part of the solution and (9, 8) is not
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What is the equation of the line below?
Answer: Y = -2x + 1
Step-by-step explanation:
The line has a Y-Intercept of 1, shown as that's where the line passes the Y-Axis. The slope is negative 2, you can find such information by finding one point on a line, then making a triangle to the next point. In this case you would start at (0,1) and go right once (x axis) and down twice (y axis). The slope formula is y2-y1/x2-x1 or change in y/change in x, so if you put 2 (y axis) over 1 (x axis) you would have a slope of 2.
Find the value of x and XZ if Y is between X and Z, XY = 19, YZ = 2x+5,
and XZ = 6x + 12.
The values of x and XZ, calculated by the given equations are 3 and 30 respectively.
What is a equation?
The equals sign indicates that two expressions in an equation are equal. An equation is a mathematical formula. The meaning of the word equation and its cognates may change a bit depending on the language. An equation is defined as including one or more variables in French, as opposed to English, where an equation is defined as any well-formed formula that consists of two expressions connected by the equals sign.
Given information (and equations) in the question:
Y is between X and Z,
XY = 19,
YZ = 2x+5,
XZ = 6x+12
Since the question say Y is between X and Z, it means:
XY + YZ = XZ
Substituting the values in this equation by the values given in the question:
19 + 2x + 5 = 6x + 12
24 - 12 = 4x
x = 3
putting the value of x in the given equation:
XZ = 6x + 12
XZ = 6(3) + 12
XZ = 18 + 12
XZ = 30
Hence, the values of x and XZ are 3 and 30 respectively.
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[Isosceles and Equilateral Triangles] Solve for x.
The required value of x is 34° in figure 4, x is 57° in figure 5, x is 81° in figure 6, x is 122° in figure 7, x is 65° in figure 8, x is 54° in figure 9, x is 90° in figure 10, x is 60° in figure 11, and x is 62° in figure 12.
What are the Equilateral Triangles?
In any equilateral triangle, the three angles are of equal measure and they equal 60 degrees.
As per figure 4,
x° + 56° + 90° = 180
x = 180 - 146
x = 34°
As per figure 5,
x = 57°
As per figure 6,
36 + 90/2 + 180-x = 180
36 + 45 - x = 180 - 180
x = 36 + 45
x = 81°
As per figure 7,
By the property of Equilateral Triangles
⇒ x = 180 - 58
⇒ x = 122°
As per figure 8,
By the property of Isosceles Triangles
x + 115 = 180
x = 180 - 115
x = 65°
As per figure 9,
6 + x + 60 + 60 = 180
x = 180 - 60 - 60 - 6
x = 54°
As per figure 10,
By the property of Equilateral Triangles
60/2 + 60 + x = 180
x = 180 - 60 - 30
x = 90°
As per figure 11,
By the property of Equilateral Triangles
2(30) + 60 + x = 180
x = 180 - 60 - 60
x = 60°
As per figure 12,
28 + 90 + x = 180
x = 180 - 118
x = 62°
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Write an equation of the parabola in vertex form.
(-2, 6)
(-1,3)
The equation of parabola in vertex form is y=-3(x+2)^2+6
What is parabola and equation of parabola in vertex form?
Parabola is equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
The equation of parabola in vertex form is
y=a(x-h)^2+k
Given the vertex (-2,6) and (-1,3)
h=-2 and k=6
y=a〖(x+2)〗^2+6
To find the value of a at vertex (-1,3)
Put y = 3 and x = -1
3=a(-1+2)^2+6
3=a+6
a=-3
The equation of parabola is given by y=-3(x+2)^2+6
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2b+3=7
2z+2=8
6b+2=14
7d−3=18
Answer:
b=2
z=3
again b=2
d=3
Step-by-step explanation:
don't know what to explain
donuts are sold in bags and cartons. a bag holds four donuts and a carton holds 10 donuts. tom buys b bags of donuts and c cartons of donuts. he buys a total of t donuts. write down a formula for t in terms of b and c
Answer:
t = b+ c
total = bags + cartons
The two figures are similar. Find the ratios (red to blue) of the perimeters and of the areas. Write the ratios as fractions in simplest form. Ratio (red to blue) of the perimeters: Ratio (red to blue) of the areas: pleas help
Answer:
5/8 and 25/64