Answers
A quadratic equation is of the form below:
[tex]ax^2+bx+c=y[/tex]The vertex of the quadratic equation is the value of y where the curve cut the y-axis.
To find the vertex, we would first first find the x-coordinate of the equation using
[tex]x=-\frac{b}{2a}[/tex]To find the vertex, we would substitute for x in the equation to get y.
Given the quadratic function below
[tex]f(x)=-3x^2-4x+7[/tex]It can be observed that
[tex]a=-3;b=-4,c=7[/tex]The x-coordinate of the vertex is as shown below:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ x=\frac{--4}{2(-3)} \\ x=\frac{4}{-6} \\ x=-\frac{2}{3} \end{gathered}[/tex]The vertex would be
[tex]\begin{gathered} f(-\frac{2}{3})=-3(-\frac{2}{3})^2-4(-\frac{2}{3})+7 \\ f(-\frac{2}{3})=-3(\frac{4}{9})+\frac{8}{3}+7 \\ f(-\frac{2}{3})=-\frac{4}{3}+\frac{8}{3}+7 \\ f(-\frac{2}{3})=\frac{-4+8}{3}+7 \\ f(-\frac{2}{3})=\frac{4}{3}+7 \\ f(-\frac{2}{3})=1\frac{1}{3}+7=8\frac{1}{3}=\frac{25}{3} \end{gathered}[/tex]Hence, the vertex of the quadratic function is (-2/3,25/3)
It should be noted that when a is positive, the quadratic graph opens upward and the vertex is minimum but when a is negative, the quadratic curve opens downward, and the vertex would be maximum
The graph of the quafratic function given is shown below
It can be observed that the vertex is maximum
Related Questions
Find the equation of the circle that has a diameter with endpoints located at (7,3) and (7,-5). A. (x-7)²+(x+ 1)² = 16 B. (x-7)² + (-1)² =4 C. (x+1)²+(y-7)= 16 D. (x-7)²+(y+ 1)²= 64
Answers
Answer:
The equation of the circle is;
[tex]\mleft(x-7\mright)^2+\mleft(y+1\mright)^2=16[/tex]Explanation:
Given that the circle has a diameter with endpoints located at (7,3) and (7,-5).
The diameter of the circle is the distance between the two points;
[tex]\begin{gathered} d=\sqrt[]{(7-7)^2+(3--5)^2_{}} \\ d=\sqrt[]{(0)^2+(3+5)^2_{}} \\ d=\sqrt[]{64} \\ d=8 \end{gathered}[/tex]The radius of the circle is;
[tex]\begin{gathered} r=\frac{d}{2}=\frac{8}{2} \\ r=4 \end{gathered}[/tex]The center of the circle is at the midpoint of the line of the diameter.
[tex]\begin{gathered} (h,k)=(\frac{7+7}{2},\frac{3-5}{2}) \\ (h,k)=(\frac{14}{2},\frac{-2}{2}) \\ (h,k)=(7,-1) \end{gathered}[/tex]Applying the equation of a circle;
[tex](x-h)^2+(y-k)^2=r^2[/tex]Substituting the given values;
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-7)^2+(y+1)^2=4^2 \\ (x-7)^2+(y+1)^2=16^{} \end{gathered}[/tex]Therefore, the equation of the circle is;
[tex]\mleft(x-7\mright)^2+\mleft(y+1\mright)^2=16[/tex]Explicit rule that describes the rent in ‘n’ years. (Question 5)
Answers
Answer::
[tex]f(n)=62000(1.03)^n[/tex]Explanation:
• The first year rent = $62,000
,• The rate of increase, r = 3% = 0.03
Since the rent increases by a common factor each year, we can find the explicit rule by using the formula for the nth term of a geometric sequence.
The nth term of a geometric sequence is calculated using the formula:
[tex]T_n=a_1(r)^{n-1}[/tex]In this case:
• a1 = 62,000
,• r=1+0.03=1.03
Thus, an explicit rule that describes the rent after n years is:
[tex]f(n)=62000(1.03)^n[/tex]
Solve: 5(x + 3) = 2x -3
Answers
we need to isolate x
first solve the parenthesis
[tex]5x+15=2x-3[/tex]now solve x
[tex]\begin{gathered} 5x-2x=-3-15 \\ 3x=-18 \\ x=-\frac{18}{3} \\ x=-6 \end{gathered}[/tex]the value of x is -6
log2 z + 2 log2 x + 4 log, y + 12 logg x - 2 log2 y
Answers
apply the property of the potency for those that have coefficients
[tex]b\cdot\log x=\log (x^b)[/tex]apply the product property and the quotient product to leave it as a single log
[tex]\begin{gathered} \log (a)+\log (b)=\log (a\cdot b) \\ \log (a)-\log (b)=\log (\frac{a}{b}) \end{gathered}[/tex]simplify the expression using this properties
[tex]\begin{gathered} \log _2(z)+2\log _2(x)+4\log (y)+12\log (x)-2\log _2(y) \\ \log _2(z)+\log _2(x^2)+\log (y^4)+\log (x^{12})-\log _2(y^2) \\ \log _2(x^2z)+\log (x^{12}y^4)-\log _2(y^2)^{} \\ \log _2(\frac{x^2z}{y^2})+\log (x^{12}y^4) \end{gathered}[/tex]The following data for a random sample of banks in two cities represent the ATM fees for using another bank's ATM. Compute the range and sample standard deviation for ATM feesfor each city. Which city has the most dispersion based on range? Which city has more dispersion based on the standard deviation?City A 2.50 1.50 1.25 0.00 2.00City B 1.25 1.00 1.50 1.00 1.00
Answers
Given:
City A: 2.50 1.50 1.25 0.00 2.00
City B: 1.25 1.00 1.50 1.00 1.00
To find dispersion based on range:
The difference between the maximum and minimum values in a set of data is the range.
2.5 is the maximum value of data of city A and 0.00 is the minimum value of data of city A.
Hence, the range of data of city A is,
[tex]R_A=2.50-0.00=2.50[/tex]1.5 is the maximum value of data of city B and 1.00 is the minimum value of data of city B.
Hence, the range of data of city B is,
[tex]R_B=1.50-1.00=0.50[/tex]Since the range of city A is greater than that of city B, city A has most dispersion based on range.
To find dispersion based on the standard deviation:
The data for city A is,
2.50 1.50 1.25 0.00 2.00
The mean of city A is,
[tex]\begin{gathered} \mu_A=\frac{2.5+1.5+1.25+0+2}{5} \\ =1.45 \end{gathered}[/tex]Let each individual value is represented by xi. Then, the squared difference of each individual value of city A is,
[tex](x_i-\mu_A)^2[/tex]Now, find the square of difference of each individual value of city A is,
[tex]\begin{gathered} _{}(2.5-1.45)^2=(1.05)^2=1.1025 \\ (1.5-1.45)^2=(0.05)^2=0.0025 \\ (1.25-1.45)=(-0.2)^2=0.04 \\ (0.00-1.45)^2=(-1.45)^2=2.1025 \\ (2.00-1.45)^2=(0.55)^2=0.3025 \end{gathered}[/tex]The number of values in the data set is n=5.
Let each individual value is represented by xi, then the sample standard deviation is,
[tex]S_A=\frac{1}{n-1}\sum ^n_{i\mathop=1}(x_i-\mu_A)^2[/tex]Hence, the sample standard deviation of city A can be calculated as,
[tex]\begin{gathered} S_A=\sqrt{\frac{1}{5-1}(1.1025+0.0025_{}+0.04+2.1025+0.3025)}_{} \\ =\sqrt[]{\frac{3.55}{4}} \\ =0.9420 \end{gathered}[/tex]Therefore, the sample standard deviation of city A is 0.9420.
The data for city B is:
1.25, 1.00, 1.50, 1.00, 1.00
The mean of city B is,
[tex]\begin{gathered} \mu_B=\frac{1.25+1.00+1.50+1.00+1.00}{5} \\ =1.15 \end{gathered}[/tex]Let each individual value is represented by xi. Then, the squared difference of each individual value of city B is,
[tex]\begin{gathered} (x_i-\mu)^2 \\ (1.25-1.15)^2=0.1^2=0.01 \\ (1.00-1.15)^2=(-0.15)^2=0.0225 \\ (1.5-1.15)^2=(0.35)^2=0.1225 \\ (1.00-1.15)^2=(-0.15)^2=0.0225 \\ (1.00-1.15)^2=(-0.15)^2=0.0225 \end{gathered}[/tex]The number of values in the data set is n=5.
Let each individual value is represented by xi, then the sample standard deviation of city B is,
[tex]S_B=\frac{1}{n-1}\sum ^n_{i\mathop=1}(x_i-\mu_B_{})^2[/tex]Hence, the sample standard deviation of city B can be calculated as,
[tex]\begin{gathered} S_B=\sqrt[]{\frac{1}{5-1}(0.01+0.0225_{}+0.1225+0.0225+0.0225)}_{} \\ =\sqrt[]{\frac{0.2}{4}} \\ =0.2236 \end{gathered}[/tex]Therefore, the sample standard deviation of city B is 0.2236.
Since the standard deviation of city A is greater than that of city B, city A has more dispersion based on the standard deviation.
Pls help I attached the question
Answers
Answer:
C
Step-by-step explanation:
A triangle has sides 25 centimeters, 26 centimeters, and 32 centimeters. What is the perimeter (distance10around the edges) of the triangle in centimeters? Express your answer in mixed number form, and reduce if possible.2355
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Given that a triangle has sides of the following dimensions
[tex]25\frac{2}{5}cm,26\frac{9}{10}cm\text{ and 32}\frac{5}{8}cm[/tex]The diagram of the triangle can be seen below
To find the perimeter, P, of a triangle, the formula is
[tex]P=a+b+c_{}[/tex]Where
[tex]\begin{gathered} a=32\frac{5}{8}=\frac{261}{8}cm \\ b=26\frac{9}{10}=\frac{269}{10}cm\text{ and } \\ c=25\frac{2}{5}=\frac{127}{5}cm \end{gathered}[/tex]Substitute the values to find the perimeter, P, of the triangle
[tex]\begin{gathered} P=a+b+c_{} \\ P=\frac{261}{8}+\frac{269}{10}+\frac{127}{5}=\frac{1305+1076+1016}{40}=\frac{3397}{40}=84\frac{37}{40}cm \\ P=84\frac{37}{40}cm \end{gathered}[/tex]Hence, the perimeter, P, of the triangle is
[tex]84\frac{37}{40}cm[/tex]A Nintendo Switch handheld game has a screen that is 4 inches tall and 9.4 inches long, what is the diagonal distance across the screen? A. 13.4 inchesB. 10.22 inchesC. 9.4 inchesD. None of the above
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EXPLANATION:
To calculate the diagonal distance we must follow the following steps:
-The length corresponds to the horizontal dimension of the screen.
-The height corresponds to the vertical dimension of the screen.
Now we must apply Pythagoras' theorem
[tex]\begin{gathered} a^2+b^2=c^2 \\ a=4 \\ b=9.4 \\ c=diagonal\text{ distance} \\ a^2+b^2=c^2 \\ (4)^2+(9.4)^2=c^2 \\ 16+88.36=c^2 \\ 104.36=c^2 \\ \sqrt[]{104.36=c} \\ c=10.21 \\ \text{ANSWER: 10.21 Inches} \end{gathered}[/tex]what is the value of u for the equation -4+2u=6
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We are given the following equation:
[tex]-4+2u=6[/tex]Where are asked to find the value of "u". To do that we need first to solve for "u", first by adding 4 on both sides:
[tex]\begin{gathered} -4+4+2u=6+4 \\ 2u=10 \end{gathered}[/tex]Now, we will divide by 2 on both sides:
[tex]\begin{gathered} \frac{2u}{2}=\frac{10}{2} \\ u=5 \end{gathered}[/tex]Therefore, the value of "u" is 5
How to convert 9.4 degrees into feet and inches
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The value of 9.4 degrees in feet is 0.1884 feet and in inches is 2.26 inches.
To calculate feet from degrees, divide the angle by 360, multiply by 2 times pi, then finally, multiply by the radius.
And feet to inches we know 1 foot equals 12 inches.
Converting degrees to feet is commonly discussed while looking at a circle and converting an angle to the length of the arc of that angle. When discussing latitude and longitude, that circle is frequently the earth.
The following formula is used to convert an angle in degrees to length in feet.
L = (a/360) * 2 * pi * r
Where,
L is the length in the feet.
a is the angle in degrees.
r is the radius of the circle in feet.
We are given 9.4 degrees.
Let r = 1 feet
Put the given values in the above formula, we will get;
L = (9.4/360) * 2 * pi * 1
L = 0.03 * 2 * 3.14 * 1
L = 0.1884 feet
L = 0.1884 * 12 = 2.26 inches.
Thus, the value of 9.4 degrees in feet is 0.1884 feet and in inches is 2.26 inches.
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Calculate the tangential speed of a disk with a radius of 15 meters, which completes one revolution every 7 seconds.
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The tangential speed of a disk is 94.23.
Given:
radius (r) = 15meters
time t = 7 sec
tangential speed = 2[tex]\pi[/tex]r/t
= 2x 3.141x 15/7
= 94.23
What is tangential speed?Tangential speed is the linear component of its velocity as it moves in a circle. If an object moves along a circular path at a distance r from the centre of the circle, the velocity of the object is tangent to the circle at some point.
In mathematics, a tangent is a line that touches a curve at one point. A quantity is tangent to another if it touches the other quantity once and then moves in the other direction.
Therefore, the tangential speed is a measure of the speed at any point where the tangent curves in this circular motion. Tangential velocity is useful for circular motion because it allows angular motion to be transformed into linear motion.
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A bag of popcorn contains 36 ounces. Your friend ate 14 of the bag. You eat 1/3 of what's left. How many ounces of popcorn did you eat?
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Answer:
you ate 7.33333 (repeating) ounces of popcorn
Step-by-step explanation:
36 - 14 = 22
22/3 = 7.3333 (repeating)
What answer shows two pairs of adjacent angles in the figure?angles 2 and 5; angles 2 and 4angles 1 and 4; angles 2 and 5angles 4 and 5; angles 2 and 4angles 1 and 4; angles 1 and 2
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Step 1
Given;
[tex]A\text{ pair of angles in a figure}[/tex]Required; To find which answer shows two pairs of adjacent angles in the figure.
Step 2
Adjacent angles are two angles that have a common side and a common vertex (corner point) but do not overlap in any way.
Therefore, the pair of adjacent angles is;
[tex]\text{Angles 4 and 5; Angles 2 and 4}[/tex]Hence, the answer is: angles 4 and 5; angles 2 and 4
Factor the polynomial: s^2+ 12s + 32
Answers
SOLUTION
We want to factor the polynomial
[tex]s^2+12s+32[/tex]To do this we look for two values with s such that when we multiply them, we get 32 and when we add then we get the middle item 12s.
These are 8s and 4s because
[tex]\begin{gathered} 8s+4s=12s \\ 8s\times4s=32s^2 \end{gathered}[/tex]Now we replace 8s and 4s with the middle item and factorize, we have
[tex]\begin{gathered} s^2+12s+32 \\ s^2+8s+4s+32 \\ s(s+8)+4(s+8) \\ (s+4)(s+8) \end{gathered}[/tex]Hence the answer is
(s + 4) (s + 8)
what are the following transformations: f(-x)-4a. reflection over the y-axis and 4 units down b. reflection over the x axis and 4 units down c. reflection over the x axis and 4 units right d. reflection over the y-axis and 4 units right
Answers
a. reflection over the y-axis and 4 units down
Explanations:Note:
If f(x) is reflected over the x-axis, it becomes -f(x) because the y coordinate is negated.
If f(x) is reflected over the y-axis, it becomes f(-x) because the x coordinate is negated.
Therefore, for f(-x)-4, f(x) is reflected over the y-axis, and then translated 4 units down
1. Which of the following is not a radical expression that is equivalent to √1087A.B.C.D.√2-√54√3-√36√5-√21√6-√18
Answers
The radical expression √108 is not equivalent to the expression √5√21 .
Given the radical expression as √108 .
Now the number 108 can be broken down into factors as
108 = 54 × 2 , 36 × 3 , 18×6
therefore we can see that the radical expression is equivalent to
√108 = √54 × √2
√108 = √36 × √3
√108 = √18 × √6
But 21 × 5 = 105 ≠ 108.
Therefore the radical expression √108 is not equivalent to √5√21 .
Expressions in mathematics are statements with variables, numbers, or both, and at least two terms joined by an operator. Mathematical operations include addition, subtraction, multiplication, and division.
In mathematics, there are two types of expressions: numerical expressions, which only contain numbers, and algebraic expressions, which also contain variables.
A symbol with an unknown value is called a variable. A term can be made up of a single constant, a single variable, or a group of variables and constants multiplied or divided. A number that has been further multiplied by a variable serves as the coefficient in an equation.
Disclaimer: The complete question is :
Which of the following is not a radical expression that is equivalent to √108?
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Which choice shows the correct solution to 2247 - 7? 35 R2 OA : 21 -35 B. اب اسے SUS
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the given expression is,
[tex]\frac{2247}{7}=321[/tex]so the correct answer is option B
the quotient is 321
Find an equation that fits the graph below; choose one of the following forms
Answers
Step 1:
Write the two equations
[tex]y\text{ = }A\sin \lbrack B(x\text{ - C)\rbrack + D and y = Asin\lbrack{}B(x-C)\rbrack + D}[/tex]Step 2:
The amplitude of graph A = 2
The midline of the graph is D = 0
The graph is a sin graph.
y = 2sin[B(x - C)] + 0
y = 2sin[B(x - C)]
Final answer
y = 2sin[B(x - C)] + D
The points H(-8,-1),I (-6,-9), J (-2,-8) and K (-4,0) form a quadrilateral. Find the desired slopes and lengths, then fill in the words that best identifies the type of quadrilateral
Answers
Answer:
[tex]\text{Quadrilateral HJLK is a }Rec\tan gle[/tex]Explanation:
Here, we want to find the slopes and lengths of the sides of a quadrilateral
To find the slopes, we use the equation:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]To find the length, we use the equation:
[tex]L\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]We take the sides one after the other
a) HI
We have the slope as:
[tex]m\text{ = }\frac{-9+1}{-6+8}\text{ = }\frac{-8}{2}\text{ = -4}[/tex]We have the length as:
[tex]\begin{gathered} \sqrt[]{(-6+8)^2(-9+1)^2} \\ =\text{ }\sqrt[]{4+64} \\ =\text{ }\sqrt[]{68} \end{gathered}[/tex]b) IJ
We have the slope as:
[tex]m\text{ = }\frac{-8+9}{-2+6}\text{ = }\frac{1}{4}[/tex]We have the length as:
[tex]\begin{gathered} IJ\text{ = }\sqrt[]{(-6+2)^2+(-8+9)^2} \\ IJ\text{ = }\sqrt[]{17} \end{gathered}[/tex]c) JK
Slope:
[tex]m\text{ = }\frac{-8+0}{-2+4}\text{ = -4}[/tex]Length:
[tex]\begin{gathered} JK\text{ = }\sqrt[]{2^2+(-8)^2} \\ JK\text{ = }\sqrt[]{68} \end{gathered}[/tex]D) KH
Slope:
[tex]m\text{ = }\frac{0+1}{-4+8}\text{ = }\frac{1}{4}[/tex]Length:
[tex]\begin{gathered} KH\text{ = }\sqrt[]{(-4+8)^2+(0+1)^2} \\ KH\text{ = }\sqrt[]{17} \end{gathered}[/tex]From the answers obtained, the side lengths KH and IJ are the same, while the side lengths JK and KI are the same
Also, looking at the slopes, when the product of the slopes of two lines equal -1, the two lines are perpendicular
Since:
[tex]\frac{1}{4}\times\text{ (-4) = -1}[/tex]We can conclude that a set of two sides(KH, JK and HI, IJ) are perpendicular
Thus, we have it that the quadrilateral is a rectangle
suppose that your boss must choose for employees in your office to attend a conference in Jamaica. Because all 14 of you want to go . he decides that the only fair way is to draw names out of a hat. What is the probability that you, Samuel, Emma and Paul are chosen? Into a fraction or round your answer to four decimal places if necessary
Answers
suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 14 of you want to go . he decides that the only fair way is to draw names out of a hat. What is the probability that you, Samuel, Emma and Paul are chosen? Into a fraction or round your answer to four decimal places if necessary
total employees=14
probability that you are chosen is P=1/14
probability that Samuel are chosen is P=1/13
the probability that Emma are chosen is P=1/12
the probability that Paul are chosen is P=1/11
therefore
the probability that you, Samuel, Emma and Paul are chosen is
P=(1/14)(1/13)(1/12)(1/11)=4.16x10^-5=0.00004
problem N 2
P=(1/27)(1/26)(1/25)=0.00005698=0.0001
A garden has 9 rows of tomato plants each row had 8 each row. How many tomato plants are there ?
Answers
Answer:
Nine rows X 8 in the row= 72
Step-by-step explanation:
Answer: For this question you would just multiply 8 and 9 and get 72.
Step-by-step explanation:
Because there are 9 rows of tomato plants and each row has 8 tomatos, you would be doing 9x8 and get your answer of 72. Hope this makes sense!
Graph the solution of inequalities and shade in the solution set. If there are no solutions, graph the corresponding line and do not shade in any region. Y = grater and equal to 1/2x - 3 Y < - 2/3 x + 2
Answers
start sketching the first inequality taking into account that it is all the region above the line of slope 1/2 and crosses over -3
then, do the same for the second equation over the same plane and look at the intersection
the shaded region should be the triangle at the left since the region is a solution to both inequalities.
Plot -5½ and 8½ on the number line below.
Answers
1) Let's plot those values on a number line. Since -5 1/2 and 8 1/2 can be written as -5.5 and 8.5
2) There we have:
Solve the system using graphing, substitution or elimination. If needed round soulutions to the nearest tenth
Answers
Given
The system of equations,
[tex]\begin{gathered} 9x+y=45\text{ \_\_\_\_\_\lparen1\rparen} \\ x^3-3x^2-25x+93=y\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]To find the solution.
Explanation:
It is given that,
[tex]\begin{gathered} 9x+y=45\text{ \_\_\_\_\_\lparen1\rparen} \\ x^3-3x^2-25x+93=y\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]From (1),
[tex]y=45-9x[/tex]Substitute y in (2).
Then,
[tex]\begin{gathered} x^3-3x^2-25x+93=45-9x \\ x^3-3x^2-25x+9x+93-45=0 \\ x^3-3x^2-16x+48=0 \\ x^2(x-3)-16(x-3)=0 \\ (x-3)(x^2-16)=0 \\ (x-3)(x^2-4^2)=0 \\ (x-3)(x-4)(x+4)=0 \end{gathered}[/tex]That implies,
[tex]\begin{gathered} x-3=0,x-4=0,x+4=0 \\ \text{ }x=3,\text{ }x=4,\text{ }x=-4 \end{gathered}[/tex]Therefore, for x=3,
[tex]\begin{gathered} y=45-9\times3 \\ =45-27 \\ =18 \end{gathered}[/tex]For x=4,
[tex]\begin{gathered} y=45-9\times4 \\ =45-36 \\ =9 \end{gathered}[/tex]For x=-4,
[tex]\begin{gathered} y=45-(9\times-4) \\ =45+36 \\ =81 \end{gathered}[/tex]Hence, the solution set is (3,18), (4,9), (-4,81).
Sphere 6.2 in diameter
Answers
ANSWER:
128.84 cubic inches.
STEP-BY-STEP EXPLANATION:
We have that the volume of a sphere is given by the following equation:
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]The radius equals half the diameter, therefore we can calculate the radius as follows:
[tex]\begin{gathered} r=\frac{d}{2}=\frac{6.2}{2} \\ r=3.1 \\ \text{replacing and we calculate the volume:} \\ V=\frac{4}{3}\cdot\frac{22}{7}\cdot3.1^3 \\ V=128.84 \end{gathered}[/tex]The volume of the sphere with the diameter of 6.2 is 128.84 cubic inches.
Danielle plans to open a savings account with $2000. The bank offers 8% interest,compounded yearly. Which of the following functions can be used to find the projectedvalue of the account after t years?A.V (t) = 2,000 (1.08t)B. V (t) = 2,000 (1.8)^tC.V (t) = 2,000 (1.08)^tD. V (t) = 2,000 (1.008)^t
Answers
the formula for the compound interest is given as follows,
[tex]A=P(1+\frac{R}{100})^t[/tex]here P = 2000 , R = 8 % , t = t.
so the value(V) is
[tex]\begin{gathered} V=2000(1+\frac{8}{100})^t \\ V=2000(1+0.08)^t \end{gathered}[/tex][tex]V=2000(1.08)^t[/tex]so the answer is option C
If f(x) = 3tan2x, find f'(pi/2)
Answers
Given the function f(x) defined as:
[tex]f(x)=3\tan(2x)[/tex]We need to find the derivative first. Using the chain rule, we know that:
[tex](\tan u)^{\prime}=u^{\prime}\cdot\sec²u[/tex]Then, taking the derivative if u = 2x:
[tex]\begin{gathered} f^{\prime}(x)=3(2)\sec²(2x) \\ \\ \Rightarrow f^{\prime}(x)=6\sec²(2x) \end{gathered}[/tex]Using this result, we can evaluate the derivative at x = π/2:
[tex]\begin{gathered} f^{\prime}(\frac{\pi}{2})=6\sec²(2\cdot\frac{\pi}{2})=6\sec²(\pi)=6\cdot(-1)² \\ \\ \therefore f^{\prime}(\frac{\pi}{2})=6 \end{gathered}[/tex]The properties of integer addition and subtraction also apply topolynomial
addition and subtraction.
•_____under additionand subtraction
•Commutative property of addition
•____property of addition
Answers
Polynomial is commutative under addition and non-commutative under subtraction.
Given, the properties of integer addition and subtraction.
Now, we have to check the properties apply to polynomial or not
Let, a polynomial be p(x) = 2x²+3x+5
and other polynomial be q(x) = x²+2x+3
Now, on adding, we get
p(x) + q(x)
(2x²+3x+5) + (x²+2x+3) = 3x²+5x+8
also, q(x) + p(x)
(x²+2x+3) + (2x²+3x+5) = 3x²+5x+8
So, as p(x) + q(x) = q(x) + p(x)
Therefore, polynomial is commutative under addition
Now, on subtracting, we get
p(x) - q(x)
(2x²+3x+5) - (x²+2x+3) = x²+x+2
also, q(x) - p(x)
(x²+2x+3) - (2x²+3x+5) = -x²-x-2
So, as p(x) + q(x) ≠ q(x) + p(x)
Therefore, polynomial is non-commutative under subtraction.
Hence, polynomial is commutative under addition and non-commutative under subtraction.
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Which equation represents a line which is parallel to the line 3y - 2x = -24?Submit AnswerOy= -x - 7Oy= - žx – 2Oy= {x +3Oy= x +4
Answers
ANSWER
[tex]y=\frac{2}{3}x+3[/tex]EXPLANATION
Parallel lines have the same slope. First we should rewrite the given line in the slope-intercept form by clearing y, so that we can see what is the slope:
[tex]\begin{gathered} 3y-2x=-24 \\ 3y=2x-24 \\ y=\frac{2}{3}x-8 \end{gathered}[/tex]The slope of the line is 2/3, so the slope of the parallel line must be 2/3 too. From this options, the equation with a slope of 2/3 is:
[tex]y=\frac{2}{3}x+3[/tex]What is the x-value of the solution to this system of equations? 6x + 8y = -18x = -2y - 5
Answers
Since the second equation is x in function of y, we can use the substitution method to find y and then find x
First, we substitute x from the second equation into the first equation:
[tex]\begin{gathered} 6(-2y-5)+8y=-18 \\ -12y-30+8y=-18 \end{gathered}[/tex]And solve for y:
[tex]\begin{gathered} (-12+8)y-30=-18 \\ -4y=-18+30 \\ -4y=12 \\ y=\frac{12}{-4}=-3 \end{gathered}[/tex]And now we replace y = -3 into the second equation:
[tex]\begin{gathered} x=-2y-5 \\ x=-2\cdot(-3)-5 \\ x=6-5 \\ x=1 \end{gathered}[/tex]The x-value of the solution is 1