1) To get the vertex of the function, the formulae is given as:
[tex]x=-\frac{b}{2a}[/tex]This gives the x coordinate of the vertex. Where a and b are the coefficients of the 1st and 2nd terms respectiely.
[tex]x=\frac{-(-2)}{2(3)}=\frac{1}{3}=0.333333[/tex]To get the y coordinate, we substitute this x value into the original equation.
[tex]f(x)\text{ = 3(}\frac{1}{3})^2-2(\frac{1}{3})-7=\frac{-22}{3}=-7.333333[/tex]The coordinates of the the vertex (0.33, -7.33)
2) The graph opens upwards. Because the coefficient of the 2nd power of x is a negative number.
3) The -7 tells us that the graph cuts the vertical axis at -7.
The length of the smaller rectangle is 8 inches and the width is x inches. The length of the larger rectangle is 10 inches and the width is 5 inches. What is the width of the smaller rectangle?
The width of the smaller rectangle is 4 inches.
What is the width of a rectangle?A rectangle has four sides, but because the sides are paired, it only has two distinct dimensions. The width is traditionally the shortest of these two dimensions, but when the rectangle is shown lying on its side, the horizontal side is commonly referred to as the width.
Given:
The dimensions of the smaller rectangle are:
Length = 8 inches
Width = x inches
The dimensions of the larger rectangle are:
Length = 10 inches
Width = 5 inches
Using proportion we determine the value of x,
[tex]\frac{8}{x} = \frac{10}{5}[/tex]
Cross-multiply the terms,
8 × 5 = 10x
x = 40/10 = 4
Therefore, the width of the smaller rectangle is 4 inches.
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Find the solution.7 · x = 8412139177
We need to find the value for x using the inverse operation:
Then:
[tex]\begin{gathered} 7-x=84 \\ \end{gathered}[/tex]Let us solve for x:
The x is subtracting, so it will add up to the other side:
[tex]7=84+x[/tex]Now, the 84 is positive, so it will be negative on the other side:
[tex]\begin{gathered} 7-84=x \\ x=-77 \end{gathered}[/tex]Hence, the solution for x is -77.
Solve the problems fill in the blanks show you work I NEED HELP!
The fill in the blanks (that uses division) can be filled as -1.2([tex](\frac{2}{5} )[/tex] ÷ -2, -0.48÷-2 and 0.24.
According to the question,
We have the following information:
-1.2 [tex](\frac{2}{5} )[/tex] ÷ -2
Now, we have to solve this problem and fill the blanks at the same time.
Now, the first step would be to write the question.
So, for the first blank we have:
-1.2 [tex](\frac{2}{5} )[/tex] ÷ -2
Now, the required number is (2/5).
Now, the next step is to multiply -1.2 with 2/5:
-2.4/5
-0.48
So, the second blank can be filled by -0.48.
Now, the third step would be to divide -0.48 by -2:
-0.48÷-2
0.24
So, the next blank can be filled by 0.24.
Hence, the numbers in the blanks are [tex]\frac{2}{5}[/tex], -0.48 and 0.24 respectively.
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how do I put 5/7-i in standard form?
To put
[tex]\frac{5}{7-i}[/tex]In the standard form, we must multiply the numerator and denominator by the complex conjugate of (7-i), it means
[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}[/tex]And now we solve it, therefore
[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}=\frac{5(7+i)}{7^2-i^2}[/tex]Remember that
[tex]i^2=-1[/tex]Then
[tex]\begin{gathered} \frac{5(7+i)}{7^2-i^2}=\frac{5(7+i)}{49+1} \\ \\ \frac{5(7+i)}{49+1}=\frac{5(7+i)}{50} \end{gathered}[/tex]Now we can simplify it
[tex]\frac{5(7+i)}{50}=\frac{7+i}{10}[/tex]And we have it in the standard form
[tex]\frac{7}{10}+\frac{1}{10}i[/tex](a) Describe in words a sequence of transformations that maps AABC to
AA"B"C".
(b) Write an ordered-pair rule for each transformation in the sequence.
Answer:
(x, y) ⇒ (-x, -y) . . . . . . . reflection across the origin(x, y) ⇒ (x +3, y +1) . . . translation 3 right a 1 upStep-by-step explanation:
You want a sequence of transformations that maps ∆ABC to ∆A'B'C' where the vertices are A(-5, 3), B(-2, 3), C(-4, 1), A'(8, -2), B'(5, -2), and C'(7, 0).
Orientation and scalingSegment AB is a 3-unit line segment directed to the right. Segment A'B' is a 3-unit line segment directed to the left. This means there is no dilation involved in the transformation. At least, the figure has been reflected left-to-right.
Point C is below segment AB, while point C' is above segment A'B'. This means the figure has also been reflected top-to-bottom.
Together these reflections can be accomplished by either of reflection across the origin, or rotation 180° about the origin.
TranslationThe reflected figure would leave A' at (5, -3). Its location at (8, -2) means the figure has also been translated to the right and up.
Translation to the right has been by 8 -5 = 3 units.
Translation up has been by -2 -(-3) = 1 unit.
(a) Description of transformationsTriangle ABC can be transformed to triangle A'B'C' by ...
reflection across the origintranslation 3 units right and 1 unit up(b) Transformation rulesThe corresponding ordered-pair rules for these transformations are ...
reflection: (x, y) ⇒ (-x, -y)translation: (x, y) ⇒ (x +3, y +1)__
Additional comment
The single transformation that will accomplish the mapping is ...
(x, y) ⇒ (3 -x, 1 -y) . . . . . reflection across the point (3/2, 1/2)
. Which units can be used to measure distance?
A. seconds
B. cubic centimeters
C. meters
D. liters
Answer:
c
Step-by-step explanation:
The metre or meter, symbol m, is the primary unit of length in the International System of Units, though its prefixed forms are also used relatively frequently.
what is the probability that a card drawn randomly from a standard deck of 52 cards is a nine? express your answer as a fraction
Given the question, we need to know that a standard deck contains 52 cards out of which there are 4 cards showing nine.
[tex]\text{Probability = number of possible outcomes/number of total outcomes}[/tex]To get the probability of randomly drawing a nine will be:
[tex]\begin{gathered} \frac{n\text{ (nine)}}{n\text{ (total cards)}} \\ pr(nine)=\frac{4}{52}=\frac{1}{13} \end{gathered}[/tex]Hence, the probability of drawing nine is 1/13
Need some guidance and reassurance because I am not getting full points on my homework. Thanks.
Given the parent function:
[tex]y=x^3[/tex]If y is shifted right by 7 units, we obtain:
[tex]Option\text{ D: }y=(x-7)^3[/tex]If y is compressed horizontally by a factor of 7, we have:
[tex]Option\; E\colon y=(7x)^3=7^3x^3[/tex]If y is stretched vertically by the factor 7, we obtain:
[tex]\text{Option H: }y=7x^3[/tex]A shift downwards by 7 units gives:
[tex]\text{Option A: }y=x^3-7[/tex]7. 200 is the ? th term of 24, 35, 46, 57, ..
200 is the 17th term of the progression
What is arithmetic progression?
Arithmetic progression or arithmetic sequence (AP) is a numerical series in which the difference between subsequent terms is constant. The sequence 5, 7, 9, 11, 13, 15,..., for example, is an arithmetic progression with a common difference of 2. A finite arithmetic progression, or simply an arithmetic progression, is a finite section of an arithmetic progression. An arithmetic series is the sum of a finite arithmetic progression. An arithmetic series is the sum of the elements of a finite arithmetic progression. A closed expression determines the product of the members of a finite arithmetic progression with a beginning element a1, common differences d, and n elements in total.
This can be solved using arithmetic progression
Aₙ = a + (n - 1)d
where, Aₙ = 24, d = 35 - 24 = 11
so, n = (Aₙ - a)/d + 1 = (200-24)/11 + 1 = 17
Hence, 200 is the 17th term of the progression
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I don’t know how to find the median and the mode HELPP
First, let's write the data set in crescent order:
[tex]35,35,44,50,50,50,56,60,65,70,86,90,110[/tex]The mean is given by the sum of all values divided by the number of values:
[tex]\begin{gathered} mean=\frac{35+35+44+50+50+50+56+60+65+70+86+90+110}{13}\\ \\ mean=\frac{801}{13}\\ \\ mean=61.62 \end{gathered}[/tex]The median is given by the central value of the set in crescent order. Since this set has 13 values, the median is the 7th value:
[tex]median=56[/tex]The mode is the value that repeats the most. Looking at the set, the value that repeats the most (three times) is 50, so the mode is 50.
Alexander Litvinenko was poisoned with 10 micrograms of the radioactive substance Polonium-210. Since radioactive decay follows a compounded continuously model, we can determine the amount of substance left in Alexander Litvinenko's body at any given time. If Polonium-210 has a decay rate of .502%, then determine the amount of Polonium-210 left in his body after 190 days. Provide 3 decimal places and units in your answer.
We have
Initial mass of Polonium-210
[tex]N_0=10\text{ micrograms}[/tex]Decay rate, r = 0.502% = 0.00502
Time, t = 190 days
Then, We know that left amount is given by
[tex]N=N_0e^{-rt}[/tex]Solving
[tex]N=10e^{-0.00502(190)}=10e^{-0.9538}=3.853[/tex]Answer: 3.853 micrograms
Find the volume of the following triangular prism. *15 points5 in6,1 in13 in7 in215.5 cubic inches220.5 cubic inches225.5 cubic inches227.5 cubic inches
Given:
The length of the base of the triangular base of the prism, b=7 in.
The altitude of the triangular base, l=5 in.
The height of the prism, h=13 in.
Now, the volume of the prism can be calculated as,
[tex]\begin{gathered} V=\text{ Base Area}\times height \\ =\frac{1}{2}bl\times h \\ =\frac{1}{2}\times7\times5\times13 \\ =227.5\text{ cu. in} \end{gathered}[/tex]Therefore, the volume of the triangular prism is 227.5 cu. in.
The investment you make into a start-up company is also known as ____.
The investment you make into a start-up company is also known as Venture capital.
Answer: Venture capital
A boy gets #2.00 per week as pocket money. His sister gets only #1.60 per week
Find the ratio of the boy's allowance to his sister's. If his sister gets 20 k more per week,what will be the new ratio?
The Ratio of the boy's allowance to his sister's is 5 : 4.
The new Ratio is 1 : 10000.
What is definition of ratio?The quotient of two mathematical expressions, 1a. b: the proportion between two or more items in terms of quantity, amount, or size.What does the arithmetic term "ratio" mean?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, if there is 1 boy and 3 girls, you may express the ratio as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.To learn more about :Ratio
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;
which anwser show the best approximation of [tex] \sqrt[]{53} [/tex]1. 7.72. 8.13. 7.34. 7.1
The Solution:
The given number is
[tex]\sqrt[]{53}[/tex]Finding the best approximation for the above number, we have
[tex]\sqrt[]{53}=7.28\approx7.3[/tex]Therefore, the best approximation of the given number is 7.3 (option 3)
Which of the following hypotheses is not a valid null hypothesis?a.H0: µ = 0b.H0: µ ≥ 0c.H0: µ ≤ 0d.H0: µ < 0
Given:
a. H0: µ = 0
b. H0: µ ≥ 0
c. H0: µ ≤ 0
d. H0: µ
Required:
To choose the hypotheses that is not valid.
Explanation:
The null hypothesis: It is a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
Here the option d is not valid.
Final Answer:
The option d is not valid.
H0: µ < 0
I need help with this questionif a certain piece of music is written in 3/4 time, how many eighth notes are required per measure of music?
Solution
For this case we need to take in count that in music 3/4 time can be grouped into 3 groups of 2 eight notes and then the answer for this case would be:
6/8
Determine whether the following graph can represent a normal curve.
The correct options regarding whether the graph can represent a normal curve are given as follows:
C. Yes, because the graph may not satisfy all of the criteria for a normal curve, but it satisfied at least one of them.D. No, because the graph is not always greater or equal to zero.What are the characteristics of a normal curve?The characteristics of a normal curve are defined as follows:
Single peak at the center of the distribution, which is also the mean of the distribution.The function is symmetric.The values of the tails at the distribution are close to 0.The values are all equal or greater to zero.In the context of this problem, these two first options are satisfied. However, the distribution contains negative values, meaning that the graph is not always greater or equal to zero.
Hence, options C and D are correct.
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Why did the turkey volenteer to be the drummer in the popular bird band? only 2.1 section
Answer:
I eat birds tasty
How many gallons of gas will Justin need to drive 120 miles? Use a table or proportionas
As you can see, both variables are directly proportional.
Thus, the given line should have the form:
[tex]y=kx[/tex]Where k is the proportionality constant.
To find the number of gallons of gas needed to drive 120 miles, we should find k first.
Notice that we need 1 gallon of gas to drive 25 miles and 2 gallons of gas to drive 50 miles. The rate of change (k) between these variables is:
[tex]\frac{50-25}{2-1}=25\frac{gallons}{\text{mile}}[/tex]This means that it takes 25 gallons to drive each mile.
Now, we could replace:
[tex]\begin{gathered} 120=25x \\ x=\frac{120}{25}=4.8\text{gallons} \end{gathered}[/tex]Therefore, Justin needs 4.8 gallons to drive 120 miles.
please help me work through this if you can, thank you!
Given:
[tex]C=\frac{x^4}{4}-\frac{4}{3}x^3-\frac{35}{2}x^2+150x[/tex]Let's solve for the following:
• (a). Find C'(x).
Here, we are to find the derivative of C(x).
Apply the sum rule:
[tex]\begin{gathered} C^{\prime}=\frac{d}{dx}(\frac{x^4}{4})+\frac{d}{dx}(-\frac{4}{3}x^3)+\frac{d}{dx}(-\frac{35}{2}x^2)+\frac{d}{dx}(150x) \\ \\ C^{\prime}=x^3-4x^2-35x+150 \end{gathered}[/tex]• (b). The critical numbers of C(x).
The critical numbers will be the points where the graph changes direction.
Using the derivative, let's solve for x.
[tex]x^3-4x^2-35x+150=0[/tex]Factor the left side using the rational root test:
[tex](x-5)(x^2+x-30)=0[/tex]Now factor using the AC method:
[tex]\begin{gathered} (x-5)((x-5)(x+6))=0 \\ \\ (x-5)(x-5)(x+6)=0 \end{gathered}[/tex]Equate each factor to zero and solve for x:
[tex]\begin{gathered} x-5=0 \\ \text{ Add 5 to both sides:} \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x-5=0 \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x+6=0 \\ x+6-6=0-6 \\ x=-6 \end{gathered}[/tex]Therefore, the critical numbers of C(x) are:
x = -6, 5
• (C). Increasing interval.
Use the critical points to find the increasing and decreasing intervals.
Using interval notation, the increasing interval is:
[tex](-6,5)\cup(5,\infty)[/tex]• D. Decreasing interval:
Using interval notation, the decreasing interval is:
[tex](-\infty,-6)[/tex]ANSWER:
(a). C'(x) = x³ - 4x² - 35x + 150
(b). x = -6, 5
(c). Increasing: (-6, 5) U (5,∞)
Decreasing: (-∞, -6)
11 to the power of 2
When a number is raised to a power, it simply refers to the number of times that number is multiplied by itself.
Applying that logic here, 11 to the power of 2 is simply
[tex]11\times11[/tex]and the answer is
[tex]=121[/tex]Therefore, 11 to the power of 2 is 121.
A line passes through the point (4,-7) and has a slope of -6 write an equation in slope intercept form for this line
What does origin mean? how can you find the origin in a graph?
Explanation
the origins mean the center of the cartessian plane, it is the point with coordinate
[tex](0,0)[/tex]Answer:
the origin is located at the intersection of the vertical and horizontal axes and the distance to all can be measured from this point..(0,0)
Which expression is equal to log(xy / z) ?
The expression that can be said to as equal to log(xy / z) is the expression logx + logy - logz and this can be found out through the logarithmic identities.
What is the basic log function?The “basic” logarithmic function can be seen as the the function, y=logbx, where x, b>0 and b≠1.
What are the 3 types of logarithms?In the kind of complex analysis that we come across three types of logarithms namely ln, log and Log are used.
In mathematics log tends to always mean the natural log.
Log is often seen as the main and principal branch that comes under the complex logarithm.
Why do we use log functions?Logarithmic functions are said as important only largely because of their relationship to the kind of exponential functions. Logarithms can also be used to solve any kind of exponential equations and thus help to explore the properties of exponential functions.
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Give the standard form of the given equation below. If it is a quadratic equation, then give the a, b, and c coefficients. 3x2-2x-5x(x-7)=(x-2)(x+4)+1
Answer:
[tex]\begin{gathered} -3x^2+31x+7=0 \\ a=-3 \\ b=31 \\ c=7 \end{gathered}[/tex]Step-by-step explanation:
The quadratic equation in standard form is represented by:
[tex]ax^2+bx+c=0[/tex]For the following equation;
[tex]\begin{gathered} 3x^2-2x-5x(x-7)=(x-2)(x+4)+1 \\ 3x^2-2x-5x^2+35x=x^2+4x-2x-8+1 \\ -2x^2-2x+35x=x^2+2x-7 \end{gathered}[/tex]Compute all the terms on the left side, equalizing 0:
[tex]\begin{gathered} -3x^2+31x+7=0 \\ \text{Then, the a,b and c coefficeints would be:} \\ a=-3 \\ b=31 \\ c=7 \end{gathered}[/tex]I don’t know the rest of the definition of my vocabulary
Step 1
Given;
Step 2
Two angles are called supplementary when their measures add up to 180 degrees.
Two angles are called complementary when their measures add to 90 degrees.
The two angles are said to be adjacent angles when they share the common vertex and side. The endpoint of the rays, forming the sides of an angle, is called the vertex of an angle. Adjacent angles can be complementary angles or supplementary angles when they share the common vertex and side.
Answer;
Two angles are called supplementary when their measures add up to 180 degrees.
Two angles are called complementary when their measures add to 90 degrees.
The two angles are said to be adjacent angles when they share the common vertex and side.
If the proportion of the total disposable income spent on consumer goods and services is 91.6 percent and if consumers spend 82.0
percent of each additional dollar, what is
Instructions: Round your responses to three decimal places.
a. the APC?
b. the APS?
c. the MPC?
d. the MPS?
a) The Average Propensity to Consume (APC), rounded to three decimal places, is 0.916.
b) The Average Propensity to Save (APS), rounded to three decimal places, is 0.084.
c) The Marginal Propensity to Consume (MPC), rounded to three decimal places, is 0.820.
d) The Marginal Propensity to Save (MPS), rounded to three decimal places, is 0.180.
What do these economic indexes mean?The average propensity to consume is the ratio of consumption expenditures to the total consumers' disposable income.
The average propensity to save is the inverse of the APC. It shows the rate of or total disposable income reserved instead of being consumed.
The marginal propensity to consume is the ratio of consumption based on additional income.
The marginal propensity to save is the inverse of the MPC, showing the percentage of the additional income saved instead of being consumed.
APC = 91.6%
= 0.916
APS = 1 - APC
= 0.084 (1 - 0.916)
MPC = 82%
= 0.820
MPS = 1 - MPC
= 0.180 (1 - 0.820)
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Solve the following Let f(x) = | 1-7x /3 | find all of x for which f (x) = 3
Given:
[tex]f(x)=|\frac{1-7x}{3}|[/tex]To find the values of x when f(x)=3, we apply below absolute rule:
If |u|=a, a>0 then, u=a or u= -a
Based on the above rule, our equations would be:
[tex]1-\frac{7x}{3}=3[/tex]And,
[tex]1-\frac{7x}{3}=-3[/tex]Next, we find x for 1-7x/3=3:
[tex]\begin{gathered} 1-\frac{7x}{3}=3 \\ \text{Simplify and rearrange:} \\ \frac{7x}{3}=1-3 \\ \frac{7x}{3}=-2 \\ 7x=-2(3) \\ 7x=-6 \\ x=-\frac{6}{7} \end{gathered}[/tex]Then, we find x for 1-7x/3=-3:
[tex]\begin{gathered} 1-\frac{7x}{3}=-3 \\ \text{Simplify and rearrange} \\ \frac{7x}{3}=1+3 \\ \frac{7x}{3}=4 \\ 7x=4(3) \\ 7x=12 \\ x=\frac{12}{7} \end{gathered}[/tex]Therefore, the answer is A. The solution set is
[tex]\lbrace-\frac{6}{7},\frac{12}{7}\rbrace[/tex]What is the graph of the solution to the following compound inequality?5x - 1 < 19 and -3- X+1s1
on5x - 1 < 19
To solve this inequality add 1 to both sides
[tex]\begin{gathered} 5x-1+1<19+1 \\ 5x<20 \end{gathered}[/tex]Now divide both sides by 5
[tex]\begin{gathered} \frac{5x}{5}<\frac{20}{5} \\ x<4 \end{gathered}[/tex]The solutions lie in the area left to the number 4
For the second inequality
[tex]-3-x+1\leq1[/tex]Add first we will add the like terms in the left side
[tex]\begin{gathered} (-3+1)-x\leq1 \\ -2-x\leq1 \end{gathered}[/tex]Now add 2 for both sides
[tex]\begin{gathered} -2+2-x\leq1+2 \\ -x\leq3 \end{gathered}[/tex]We need to divide both sides by -1, but we should reverse the sign of inequality
[tex]\begin{gathered} \frac{-x}{-1}\ge\frac{3}{-1} \\ x\ge-3 \end{gathered}[/tex]We reversed the sign of inequality when divides it by -ve number
Since 2 < 3
Then if we divide both sides by -1, then it will be
-2 < -3 which is wrong -2 greater than -3, then we should reverse the sign of inequality if we multiply or divide it by a negative number
Then the solutions of the 2nd inequality lie right to -3
Let us draw them
The red part is the solution to the 1st inequality
The blue par is the solution to the 2nd inequality
The area with the 2 colors is the area of the common solution of both inequalities