We can distinguish between the linear, exponential function and quadratic functions graphically. The graph of the functions is as follows:
linear function f(x) = 2x will be straight line,
for exponential function f(x) = 2^x will rise or fall quickly in one direction
and for quadratic function f(x) = x^2 will be a parabola.
What is an exponential function?An exponential function is a type of mathematical function expressed in the form f(x) = a^x. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. The most commonly used exponential base is the transcendental number e, which is approximately equal to 2.71828. The exponential function is defined by the formula f(x) = ax. where the input variable x is displayed as an exponent. Exponential curves grow or fall exponentially. A quantity that increases or decreases at a regular rate should exhibit either an exponential increase or an exponential decay.To learn more about exponential function from the given link :
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8373+01274+93738939x937x058+938484
94We need to solve the next operation.
We need to take into consideration the rules of operations:
1. Parentheses
2. Exponents
3. Multiplication
4. Divison
5. Addition
6. Subtraction
Then, solve the given expression:
8373+01274+93738939*937*058+938484
Solve the multiplication 93738939*937*058
[tex]\begin{gathered} 93738939 \\ x\text{ }937 \\ ------------ \\ =87833385843 \\ \end{gathered}[/tex][tex]\begin{gathered} 87833385843 \\ x\text{ }058\text{ } \\ ------------ \\ =5094336378894 \end{gathered}[/tex]Now, make the next sum 8373+01274+ +938484:
[tex]\begin{gathered} 938484 \\ 001274 \\ 008373 \\ ------------ \\ 948131 \end{gathered}[/tex]Finally, make the next sum operation:
[tex]\begin{gathered} 5094336378894 \\ 0000000948131 \\ ------------- \\ 5094337327025 \end{gathered}[/tex]Hence, the result of the operation is 5094337327025.
A chemist is heating water so it can dissolve a larger amount of sodium chloride. The water's temperature increases 7°C each minute from an initial temperature of 21°C. How long will it take for the water to reach 49°C?
Write and solve an equation to find the answer. how many munities?
Answer:
Step-by-step explanation:
4 minutes
Find the surface area of the pyramid. 4.33 m 5 m 5 m The surface area is (Type a whole number or a decimal
Answer:
43.3 m²
Explanation:
The surface area of the pyramid can be calculated as 4 times the area of one face.
So, the area of one face is equal to:
[tex]A=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base of the triangles and h is the height. So, replacing b by 5 m and h by 4.33 m, we get:
[tex]\begin{gathered} A=\frac{1}{2}\cdot5\text{ m }\cdot4.33\text{ m} \\ A=10.825m^2 \end{gathered}[/tex]So, the surface area is equal to:
[tex]A=4(10.825)=43.3m^2[/tex]Therefore, the answer is 43.3 m²
3) Calculate the volume
4 cm
5 cm
3 cm
9 cm
Answer:
57cubic sm
Step-by-step explanation:
4 x 3= 12
5 x 9= 45
12 + 45 = 57
If x squared minus 6x plus 7 equal k(2x-3) has real equal roots find the possible values of K
We will have the following:
[tex]\begin{gathered} x^2-6x+7=k(2x-3)\Rightarrow x^2-6x+7=2kx-3k \\ \\ \Rightarrow x^2-6x-2kx+7+3k=0 \end{gathered}[/tex]Now, we want to operate like terms and take to "solve for x" using the quadratic expression, that is:
[tex]\Rightarrow x^2+(-6-2k)x+(7+3k)=0\Rightarrow x=\frac{-(-6-2k)\pm\sqrt{(-6-2k)^2-4(1)(7+3k)}}{2(1)}[/tex]No, in order to determine the possible real values for "k" we have to analyze the value under the root, so:
[tex]\begin{gathered} \sqrt{(-6-2k)^2-4(1)(7+3k)}\Rightarrow(-6-2k)^2-4(1)(7+3k)\ge0 \\ \\ \Rightarrow36+24k+4k^2-28-12k\ge0\Rightarrow8+12k+4k^2\ge0 \end{gathered}[/tex]Now, we will have to use the quadratic expression again to determine the values for "k" that make the inequality true, that is:
[tex]\begin{gathered} k=\frac{-(12)\pm\sqrt{(12)^2-4(4)(8)}}{2(4)} \\ \\ \Rightarrow k\leq-2 \\ \\ and \\ \\ \Rightarrow k\ge-1 \end{gathered}[/tex]So, the values for which the inequality and thus the expression under the root are true are then given by:
[tex]k\leq-2\wedge x\ge-1[/tex]In other notation:
[tex](-\infty,2]\cup[-1,\infty)[/tex]Select all the ratios equivalent to 8:6.A. 4:3B. 6:8C. 16:12D. 10:8E. 7:5
Dividing the given ratio by 2, we get
8:6 = 8/2 : 6/2 = 4:3
Multiplying the given ratio by 2, we get
8:6 = 8*2 : 6*2 = 16:12
Then, the correct choices are A and C
A visitor to the Grand Canyon hiked the South Kaibab Trail and the River Trail on one day. The next day, she hiked the Bright Angel Trail. How far did she hike the first day? How much farther did she hike the first day than the second day? How much longer was her total route than if she had hiked the North Kaibab Trail?
At the first day: the visitor hiked the South Kaibab Trail and the River Trail on one day
so, the length for the first day = 10.1 + 2.7 = 10.1 + 2.7 = 12.8 km
At the second day: the visitor hiked the Bright Angel Trail
so, the length of the second day = 12.6 km
We will answer the questions:
How much farther did she hike the first day than the second day?
it will be = 12.8 - 12.6 = 0.2 kilometers
How much longer was her total route than if she had hiked the North Kaibab Trail?
The total route = 12.8 + 12.6 = 25.4
if she had hiked the North Kaibab Trail, the difference will be = 25.4 - 22.9 =
= 2.5 kilometers
Can someone pleaseeee help me with this pleasee! I appreciate if u do!! thank you!!
The and following system was solved by substitution, but there is a mistake in the
process. Identify which step contains the mistake, and explain how to fix it.
28) -5x-y=23
3x-y=-17 Use subtraction
Step 1: 2x + 5(x + 7) = 21
Step 2: 2x + 5x + 7 = 21
Step 3: 7x + 7 = 21
Step 4: 7x = 14
Step 5: x =2
Step 6: y=2+7
The values of x and y are -5 and 2 respectively
What is Substitution Method to Solve Linear Equation in Two Variables?
The substitution technique is one of the algebraic methods for solving a system of linear equations in two variables. In this procedure, we get the value of any variable by isolating it on one side of the equation and taking every other term on the other side.
Solution:
The problem is in the step one,
Given: -5x - y = 23
3x - y = -17
You've done the question using substraction method while it waas asked to solve by substitution method.
from equation 1 we can write -y = 23 + 5x
substituting -y in equation 2
3x + 23 + 5x = -17
8x = -40
this implies x = -5 and thus, y = 2
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Is (5, 8) a solution to this system of equations?
X = 5
2x + y = 18
yes
no
Need answer asap
| n | = 3.5 what are the values for n will make the expression true?
The given expression is,
[tex]\lvert n\rvert=3.5[/tex]So we know that, the absolute value of a number is its distance from the origin, say 0. SInce the distance cannot be expressed in negative values, absolute values are always expressed as positive numbers. FOr example,
[tex]\lvert-x\rvert=\lvert x\rvert=x[/tex]Therefore, the values that make the given expression true can be,
[tex]\lvert n\rvert=3.5\Rightarrow n=-3.5\text{ or n=3.5}[/tex]For each shape in the table list three examples of real world objects that could be modeled by the shape use your experiences, the Internet, newspapers, magazines, or other resources to uncover examples1.) rectangular prism2.) triangular prism3.) cylinder4.) cone5.) pyramid6.)sphere
1. A rectangular prism is a figure that has the following shape:
A real-world example of a figure that has this shape is a rectangular box.
2. A triangular prism is a figure that has the following shape:
(I need this as an actual equation and solution not just which one it is.. also any people just trying to get credits will result in a report.) The temperature of a cooling liquid is given by the function T(m) = 38 (0.82)" +21, where T represents the temperature in degrees Celsius and m represents the number of minutes, m≥0, that the liquid has been cooling. Which of the following represents a temperature that the liquid does not reach as it cools down?
(1) 53
(2) 16
(3) 41
(4) 28
Answer:
(2) 16°C
Step-by-step explanation:
[tex]T(m)=38(0.82)^m+21[/tex]
Find the temperature at the outset ([tex]m=0[/tex]):
[tex]T(0)=38(0.82)^0+21[/tex]
[tex]T(0)=38(1)+21[/tex]
[tex]T(0)=38+21[/tex]
[tex]T(0)=59[/tex]
Since the liquid is cooling, all temperatures equal to or less than 59°C are valid possibilities. However, over time (represented as [tex]m\rightarrow\infty[/tex]), [tex](0.82)^m[/tex] is reduced towards zero and, as such, [tex]38(0.82)^m[/tex] will be reduced towards zero. All that will remain is [tex]T(m)=21[/tex], which makes it the horizontal asymptote. This is shown in the attached graph.
Therefore, since 16°C falls below the asymptote, it does not represent a temperature that the liquid reaches as it cools down.
What equation represents the line that passes through the point (4, -5) and is perpendicular to the line x + 2y = 5?
The line that passes through the point (4, -5) and is perpendicular to the line x + 2y = 5? is y = 2x - 13.
Calculation:-
The equation of a line is y = mx + c, m is the gradient and c is the intercept
The line passes through points 4 and -5, x is 4 and y is -5
-5 = 4m + c
When two lines are perpendicular, the products of their gradients are equal to -1, m1 * m2 = -1
x + 2y = 5
2y = -x + 5
y = (-1/2 * x) + 5
therefore m = -1/2
m1 * m2 = -1
m * -1/2 = -1
-m = -2 , therefore m = 2
-5 = 4 * 2 + c
c = -5 - 8, which is -13
Therefore the equation for the line is y = 2x - 13.
To determine if a point is on a line you can simply substitute the x and y coordinates into the equation. Another way to solve the problem would be to graph the line and see if it falls on the line. Plugging in will give which is a true statement, so it is on the line. Only one line can pass through a single point. False because we can draw an infinite number of lines through a given point as shown below.
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A rectangle has a length of 17 inches less than 7 times its width. If the area of the rectangle is 2204square inches, find the length of the rectangle.
SOLUTION
We are told that the length of the rectangle is 17 inches less than 7 times its width.
Now, let the letter L represent the length and the letter w represent the width of the rectangle.
This statement can be represented algebraically as
[tex]L=7w-17[/tex]So, Area =
[tex]\text{Area = L x w}[/tex]We are also told the Area A of the rectangle = 2204. Now
[tex]\begin{gathered} 2204=L\times w \\ \\ 2204=(7w-17)\times w \end{gathered}[/tex]We have to find the width, then we find the length L
[tex]\begin{gathered} 2204=(7w-17)\times w \\ 2204=7w^2-17w \\ 7w^2-17w-2204=0 \\ \\ \text{Solving the quadratic equation } \\ \\ w=19\text{ or w = -16.57} \end{gathered}[/tex]Since the width cannot be negative, w = 19 inches
The length becomes
[tex]\begin{gathered} L=7w-17 \\ L=7\times19-17 \\ L=133-17 \\ L=116\text{ inches } \end{gathered}[/tex]Students in mrs smiths class must complete at least 40 math problems for homework every week. the table shows the progress of four students on Wednesday. Which list shows the names of students in order from the greatest amount of homework complete to the least amount of homework completed? A Katie, Jonah, D’Angelo. Grace B D’Angelo, grace, Jonah, Katie C Katie, Jonah, grace, D’Angelo D Jonah, Katie, D’Angelo, grace
Answer: the anwser is B
Step-by-step explanation:
Answer:
Grace, jonah,D'angelo,then Katie.
First,Grace because she finished it 100%
Next,it's Jonah because he finished it 2/3 the way meaning about around 70% of the work.
Then, D'angelo because he completed five more than Katie.
Last,Katie because she was less than jonah.She had 40 but D'angelo had five more than her
The rule for a relation is y= (x+1) ^2. The domain is ( -2, -1,0,1,2,3). Is the relation a function?
No, this rule for a relation is not a function because the input variable (domain) are not uniquely mapped to an output variable (range).
What is a function?In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).
When x = -2, the range (output) of this function is given by:
y = (x + 1)²
y = (-2 + 1)²
y = (-1)²
y = 1.
When x = -1, the range (output) of this function is given by:
y = (x + 1)²
y = (-1 + 1)²
y = (0)²
y = 0.
When x = 0, the range (output) of this function is given by:
y = (x + 1)²
y = (0 + 1)²
y = (1)²
y = 1.
Based on the integers shown above, we can reasonably infer and logically deduce that this rule for a relation does not represent a function because the value of "1" is mapped to more than one domain element i.e -2 and 0.
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A line passes through points at (9,5) and (4,3). What is the slope of the line perpendicular to this line?
Answer:
[tex]-5/2[/tex]
Step-by-step explanation:
The slope of the line through the given points is [tex]\frac{5-3}{9-4}=\frac{2}{5}[/tex].
Perpendicular lines have slopes that are negative reciprocals of each other, so the answer is [tex]-5/2[/tex].
Answer:
perpendicular slope = - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
calculate the slope m of the line using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 5 ) and (x₂, y₂ ) = (4, 3 )
m = [tex]\frac{3-5}{4-9}[/tex] = [tex]\frac{-2}{-5}[/tex] = [tex]\frac{2}{5}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{5} }[/tex] = - [tex]\frac{5}{2}[/tex]
What is the measure of angle X to the nearest degree?
Using a trigonometric relation we will see that the correct option is B, 24°.
What is the measure of angle X?On the image we can see a right triangle, where the length of the hypotenuse and of one leg (the opposite cathetus to angle X) are known.
We can use the trigonometric relation:
sin(a) = (opposite cathetus)/(hypotenuse)
Then we can write:
sin(X) = 9/22
If we apply the inverse sine function in both sides, we will get:
X = Asin(9/22) = 24.15°
Then the correct option is B.
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If the figure below were to be reflected across the x axis, what would be the coordinates for point D?
Reflection across the X-axis
D’ = ( , )
Answer:
If the unit for the axes is 1, point D' is on coordinate (-3, -2).
Step-by-step explanation:
To find coordinates' values when reflecting over the x-axis, multiply the y value of the original point by -1.
D (-3, 2) ---> D' (-3, -2)
(0,4) and (x,7); m=3/2
Step-by-step explanation:
I guess you are trying to find x value
slope equation:
slope, m = (y2-y1)/(x2-x1)
3/2 = (7-4)/(x-0)
3/2=3/x
1.5 = 3/x
1.5x = 3
x = 3/ 1.5
x = 2
Calculate b1, the balance on the loan after the first month. Give your answer in dollars to the nearest dollar. Do not include commas or the dollar sign in your answer.
Given:
Interest (I)= $716.67
Total amount = $200,000
[tex]R=\frac{716.67\times100\times12}{200000\times1}[/tex][tex]R=\frac{860004}{200000}[/tex][tex]R=4.3\text{ \%}[/tex]Monthly Payment(d) :
[tex]200000=\frac{d\lbrack1-(1+\frac{r}{12})^{-25\times12}\rbrack}{\frac{r}{12}}[/tex][tex]200000=\frac{d\lbrack1-(1+\frac{0.043}{12})^{-25\times12}\rbrack}{\frac{0.043}{12}}[/tex][tex]200000=\frac{d\lbrack1-(1+0.0036)^{-300}\rbrack}{0.0036}[/tex][tex]d=\text{ \$1089}[/tex]Balance of the loan amount after one month:
[tex]b_1=200000-1089+716.67[/tex][tex]b_1=199627.67[/tex]Balance amount after the first month is $199628
if the population standard deviation were 10 instead of 5, what effect would this new standard deviation have on margin of error?
If the population standard deviation were 10 instead of 5,Margin of error would rise as a result. A broader width of the confidence interval and a larger margin of error would be the outcomes of a higher standard deviation.
Define margin of error.The margin of error (MOE) for a survey indicates how closely the survey results should be compared to the actual population value. For instance, a poll with a 3% margin of error shows that 72% of respondents prefer Brand A over Brand B.
Given,
If the population standard deviation were 10 instead of 5,
Margin of error would rise as a result. A broader width of the confidence interval and a larger margin of error would be the outcomes of a higher standard deviation. The margin of error diminishes as sample size grows, to be precise. The margin of error rises as population variability does as well. The margin of error grows as the confidence level does.
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$100 for 4 tickets. what is the cost per one ticket? Plsss help me
Answer:25. Do better bro that’s sad
Step-by-step explanation:
Answer:
One ticket is 25 dollars
Step-by-step explanation:
Let T be tickets
$100 = 4T
[tex]\frac{100}{4} = \frac{4}{4}T[/tex]
$25 = T
Therefore, one ticket is equal to 25 dollars
Divide 12x5 − 36x4 − 6x3 by 3x2. 4x2 + 12x + 2 4x2 − 12x − 2 4x3 + 12x2 + 2x 4x3 − 12x2 − 2x
The correct option is D that is 4x³-12x²-2x when 12x⁵-36x⁴-6x³ will be divided by 3x² as the definition of polynomial says, "A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division".
What is polynomial?A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division. Polynomials are sums of kxn terms, where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. Polynomials are introduced. This video defines terms such as degree, standard form, monomial, binomial, and trinomial. According to this definition, the number ten is not a polynomial. However, people frequently use the symbol 10 to represent the polynomial (10,0,0,...). This is an example of a symbol being "overloaded," which occurs occasionally in mathematics. Here,
(12x⁵-36x⁴-6x³)/3x²
take 3x² from numerator,
3x²(4x³-12x²-2x)/3x²
=4x³-12x²-2x
When 12x⁵-36x⁴-6x³ is divided by 3x², the correct option is D, which is 4x³-12x²-2x . According to the definition of polynomial, "a polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division."
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Answer: 4x³-12x²-2x
Step-by-step explanation:
The terminal side of an angle What is the cot
Using the unit circle:
[tex]\begin{gathered} cot\theta=\frac{x}{y} \\ \\ cot\theta=\text{ }\frac{\frac{33}{65}}{\frac{56}{65}} \\ \\ cot\theta=\text{ }\frac{33}{56} \\ \end{gathered}[/tex]please help will give you upvotes
Answer:
C is the correct answer.
Step-by-step explanation:
[tex]f(x) = 2x + 2[/tex]
[tex]f(2) = 2(2) + 2 = 4 + 2 = 6[/tex]
The answer is given but I dont understand. Please explain #7
SOLUTION:
Case: Rectilinear acceleration
Answer:
Acceleration on a straight line is defined as the rate of change of velocity during motion on the straight line.
Match each graph with the correct equation from the equation bank not all equations will be used. (pls help) questions 6,7,8,10.
The linear functions for each graph are given as follows:
6. y = -1/3x + 3.
7. y = 1/3x + 1.
8. y = x + 3.
10. y = -2x.
How to define linear functions?The definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope of the function, which is by how much y changes when x changes by 1.b is the y-intercept of the function, which is the value of y when the function crosses the y-axis.For item 6, we have that:
The function crosses the y-axis at y = 3.When x increases by 3, y decays by 1, hence the slope is of -1/3.Then the equation is:
y = -1/3x + 3.
For item 7, we have that:
The function crosses the y-axis at y = 1.When x increases by 3, y increases by 1, hence the slope is of 1/3.Then the equation is:
y = 1/3x + 1.
For item 8, we have that:
The function crosses the y-axis at y = 3.When x increases by 1, y increases by 1, hence the slope is of 1Then the equation is:
y = x + 3.
For item 10, we have that:
The function crosses the y-axis at y = 0.When x increases by 1, y decreases by 2, hence the slope is of -2.Then the equation is:
y = -2x.
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Please help!!!!!!!!!!!!!!!! please
Answer:
yes they are congruent
Step-by-step explanation:
Express the following quotient in simplest form without the use of negative exponents
Given:
[tex]\frac{5x^2y^{11}}{2}\frac{.}{.}\frac{x^4y^6}{6}[/tex]We first need to change the divion to multiplication by inverting the term that comes after the division sign.
That is;
[tex]\frac{5x^2y^{11}}{2}\times\frac{6}{x^4y^6}[/tex]Apply the laws of indices;
[tex]\frac{6\times5x^2y^{11}x^{-4}y^-^6}{2}[/tex][tex]=3\times5x^{2-4}y^{11-6}[/tex][tex]=15x^{-2}y^5[/tex][tex]=\frac{15y^5}{x^2}[/tex]