1. Write a function and graph it that has zeros at -2 and 6.2. Make the parabola open up.
Answers
we know that
the equation of a vertical parabola is equal to
y=a(x-x1)(x-x2)
where
a is the leading coefficient
x1 and x2 are the zeros of the function
In this problem we have
x1=-2
x2=6
substitute
y=a(x+2)(x-6)
If the parabola open upward, then the coefficient a must be positive
I will assume
a=1
so
y=(x+2)(x-6)
y=x^2-6x+2x-12
y=x^2-4x-12
using a graphing tool
Related Questions
Page 112 question 7 part 8 which equation matched the following graph A f(x)=2^xBf(x)=-2^xC f(x)=-2^xDf(x)=-3x2^x
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EXPLANATION
The given graph corresponds to the function f(x)= -2^x
In 2012, the population in atown was 8,000 people. In2017, the population was11,400. What was thepercent increase in thepopulation?
Answers
1. first we determine the growth in that period of time, for which we find a difference that in 5 years there was an increase of 3,400 people
[tex]\begin{gathered} 2012=8.000\text{ people} \\ 2017=11.400\text{ people} \\ \text{the growth in 5 years } \\ 11.400-8000=3.400 \end{gathered}[/tex]now we divide that increment by the initial value, to get the percentage of increase;
[tex]\begin{gathered} 3.400/8.000=0.425\text{ percent increase in the population} \\ \end{gathered}[/tex]Brooke Puts 400.00 into an account to use for school expenses the account earns 14%interest compounded quarterly how much will be in the account after 5 years
Answers
According to the problem, the principal is 400, the interest rate is 14%, the time is 5 years, and it's compounded quarterly which means there are 4 compound periods each year.
We have to use the compound interest formula.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Replacing the given values, we have.
[tex]\begin{gathered} A=400(1+\frac{0.14}{4})^{4\cdot5} \\ A=400(1+0.035)^{4\cdot5} \\ A=400(1.035)^{20} \\ A\approx795.92 \end{gathered}[/tex]Hence, after 5 years, there will be $795.92, approximately.Construct the 270° rotation of the square ABCD about point P.
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We want to rotate square ABCD by 270° around point P, lets see
We can think that the square is "glued" to segment PC, so if we rotate the segment PC by 270°, the square will also be rotate by 270°, as follows
So, we have our rotation about point P.
Answer: the answer is B
Step-by-step explanation: just trust me, I got it right
Select the statement that describes the inequality:n < = 9.25 Question 3 options:A number is no less than 9.25.A number is no more than 9.25.A number is below 9.25.A number exceeds 9.25.
Answers
Solution:
Given the inequality below;
[tex]n\leq9.25[/tex]The inequality sign in the above expression means less than or equal to, i.e.
[tex]n\text{ is no more than 9.25}[/tex]Hence, the statement that describes the inequality is
A number is no more than 9.25.
Write the next explicit form of this sequence, given a1 = 20 and r= 0.5 (1/2) and find n=15.
Answers
Given the first term, a1=20
Common ratio, r=0.5*1/2=0.25
A geometric sequence is represented by the following expression:
[tex]\begin{gathered} a_n=ar^{n-1} \\ \end{gathered}[/tex]We want to find the 15th term:
[tex]\begin{gathered} a_{15}=20(0.25)^{15-1} \\ a_{15}=7.45\times10^{-8} \end{gathered}[/tex]need help asap got something I dont understand
Answers
Formula
[tex]\text{ Area = }\frac{B\text{ + b}}{2}\text{ h}[/tex]B = long base
b = short base
h = height
Counting the number of squares:
B = 8
b = 6
h = 4
Substitution
[tex]\begin{gathered} \text{ Area = }\frac{(8\text{ + 6)}}{2}4 \\ \text{ Area = }\frac{14}{2}4 \\ Area=\frac{56}{2}\text{ } \\ \text{Area = 28} \end{gathered}[/tex]Number 4 i need help no it’s due at 9:00
Answers
When we have a negative sign in front of a number, the sign of the number is changed, therefore if the number is negative the number will turn positive. This is done below:
[tex]\begin{gathered} (-4)\text{ - (-5)} \\ (-4)\text{ + 5} \end{gathered}[/tex]When we sum two numbers of different signs, we subtract their values and maintain the sign of the greatest one:
[tex]-4\text{ + 5 = 1}[/tex]Aiden is making a cookie recipe that requires 4 cups of sugar for every 8 cups of flour. Aiden only has 6 cups of flour. He concludes that he will only need 2 cups of sugar. Is Aiden correct? Why or why not?A Aiden is incorrect. He needs 4 cups of sugar because decreasing the number of cups of flour by 2 requires increasing the number of cups of sugar by 2.B Aiden is correct. The number of cups of sugar must be reduced by 2 because the number of cups of flour is reduced by 2.C Aiden is correct. Half the amount of sugar is needed because only half of the recipe will be made.D Aiden is incorrect. He needs 3 cups of sugar because the ratio 3:6 is equivalent to 4:8.
Answers
Aiden is incorrect. He needs 3 cups of sugar
What is the solution set to the following system?x + y = 3x^2 = y^2 = 9
Answers
To solve the given system of equations:
1. Solve x in the first equation:
[tex]\begin{gathered} x+y-y=3-y \\ \\ x=3-y \end{gathered}[/tex]2. Use the value of x=3-y in the second equation:
[tex](3-y)^2+y^2=9[/tex]3. Solve y:
[tex]\begin{gathered} (a-b)^2=a^2-2ab+b^2 \\ \\ 3^2-2(3)(y)+y^2+y^2=9 \\ 9-6y+2y^2=9 \\ \\ 2y^2-6y=0 \\ 2y(y-3)=0 \\ \\ \end{gathered}[/tex]When the product of two factors is equal to zero, then you equal each factor to zero to find the solutions of the variable:
[tex]\begin{gathered} 2y=0 \\ y=\frac{0}{2} \\ y=0 \\ \\ y-3=0 \\ y-3+3=0+3 \\ y=3 \end{gathered}[/tex]Then, the solutions for variable y in the given system are:
y=0
y=3
4. Use the values of y to find the corresponding values of x:
[tex]\begin{gathered} x=3-y \\ \\ y=0 \\ x=3-0 \\ x=3 \\ \text{Solution 1: (3,0)} \\ \\ y=3 \\ x=3-3 \\ x=0 \\ \text{Solution 2: (0,3)} \end{gathered}[/tex]Then, the solutions for the given system of equations are: (3,0) and (0,3)quations4. Use the values of y to find the corresponding values of x:
[tex]undefined[/tex]4. Use the values of y to find the corresponding values of x:
[tex]undefined[/tex]I need help understanding how to compare irrational numbers and multiplication of exponents. Can you help?
Answers
1) A good way to compare irrational numbers is by their approximate value. For example, let's pick two irrational numbers:
π and √2 Two irrational numbers
The value of each approximately is
3.14 and 1.41 so
3.14 > 1.41
And this principle fits for the other irrational numbers.
2) Multiplication of exponents
If we have two powers and we have to operate them, we'll proceed this way:
[tex]\begin{gathered} (a^3)^6=a^{3\cdot6}=a^{18} \\ a^3\cdot a^6=a^{3+6}=a^9 \end{gathered}[/tex]Choose the answer with the proper number of sig figs
Answers
the answer is
[tex]69\times10^9[/tex]Macmillan Learning
Suppose that your federal direct student loans plus accumulated interest total $33,000 at the time that you start repayment and the interest rate on all the loans is 5.23%.
(a) If you elect the standard repayment plan of a fixed amount each month for 10 years, what would your monthly payment be?
(b) How much would you pay in interest over the 10 years?
Answers
Using the monthly payment formula, it is found that:
a) Your monthly payment would be of $353.74.
b) You would pay $9,444.8 in interest over the 10 years.
What is the monthly payment formula?The monthly payment rule is presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which the meaning of each parameter is given as follows:
P is the initial amount.r is the interest rate.n is the number of payments.In the context of this problem, the values of these parameters are:
P = 33000, r = 0.0523, r/12 = 0.0523/12 = 0.00435833, n = 10 x 12 = 120.
Hence the monthly payment is calculated as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 33000\frac{0.00435833(1.00435833)^{120}}{(1.00435833)^{120} - 1}[/tex]
A = $353.74.
The total amount paid is:
T = 120 x 353.74 = $42,444.8.
The interest paid is the total amount subtracted by the loan value, hence:
42444.8 - 33000 = $9,444.8.
More can be learned about the monthly payment formula at https://brainly.com/question/14802051
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I need help finding the answer. I don't need astep-by-step explanation just the answer please.Thank you.
Answers
Find a using the theorem of sinus:
[tex]\sin(57°)=\frac{a}{29}[/tex][tex]a=\sin(57)*29=24.32[/tex]Now with the Pythagoras theorem find b:
[tex]a^2+b^2=29^2[/tex][tex]24.32^2+b^2=29^2[/tex][tex]b^2=29^2-24.32^2[/tex][tex]b^2=841-591.46[/tex][tex]b=\sqrt{841-591.46}=\sqrt{249.53}[/tex][tex]b=15.79[/tex]Finally, find B knowing that the sum of all internal angles of a triangle is equal to 180°:
[tex]B=180-57-90=33°[/tex]the shaded triangle is inside a square which has side lengths of 10 inches.answer choices (select all that apply)A) the shaded triangle inside the square has a base and height of 10 inches.B) since the square has an area of 100in., the shaded triangle also has an area of 100in².C)the area of the shaded triangle can be determined by adding it's base, 10 inches, to its lengths, 11 inches and 12 inches.D)since the square has an area of 100 in²., the shaded triangle has an area which equals half the area of the square, 50 in².
Answers
The correct options are options A and D
The shaded triangle inside the square has a base and height of 10 inches.
And
Since the square has an area of 100 in²., the shaded triangle has an area which equals half the area of the square, 50 in².
Select all polynomials that are divisible by (x-1)
Answers
Explanation
[tex]\begin{gathered} \frac{5x^4+9}{x} \\ \end{gathered}[/tex]Step 1
Split the fraction
[tex]\frac{5x^4+9}{x}=\frac{5x^4}{x}+\frac{9}{x}[/tex]Step 2
Simplify:
[tex]\begin{gathered} \frac{5x^4}{x}+\frac{9}{x}=5x^{4-1}\text{ +}\frac{9}{x\text{ }} \\ \frac{5x^4}{x}+\frac{9}{x}=5x^3\text{ +}\frac{9}{x\text{ }} \\ 5x^3\text{ +}\frac{9}{x\text{ }} \end{gathered}[/tex]so,the answer is
[tex]5x^3\text{ +}\frac{9}{x\text{ }}[/tex]I hope this helps you
Solve the following system of equations using an inverse matrix. You must alsoindicate the inverse matrix, A-1, that was used to solve the system. You mayoptionally write the inverse matrix with a scalar coefficient.2x-3y = -55x - 4y = -2Al=y =
Answers
The two equations given are:
[tex]\begin{gathered} 2x-3y=-5 \\ 5x-4y=-2 \end{gathered}[/tex]The coefficient matrix A is:
[tex]A=\begin{bmatrix}2 & -3 \\ 5 & -4\end{bmatrix}[/tex]The variable matrix X is:
[tex]X=\begin{bmatrix}x \\ y\end{bmatrix}[/tex]and the constant matrix B is:
[tex]B=\begin{bmatrix}-5 \\ -2\end{bmatrix}[/tex]Then, AX = B looks like,
[tex]\begin{gathered} AX=B \\ X=A^{-1}B \end{gathered}[/tex]So, the variables "x" and "y" are found my multiplying the inverse of A by the matrix B.
Let's find the inverse matrix of A:
Given, a 2 x 2 matrix,
[tex]A=\begin{bmatrix}a & b \\ c & d\end{bmatrix}[/tex]The inverse of this matrix will be,
[tex]A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d & -b \\ -c & a\end{bmatrix}[/tex]Using the formula, we have:
[tex]\begin{gathered} A^{-1}=\frac{1}{-8--15}\begin{bmatrix}-4 & 3 \\ -5 & 2\end{bmatrix} \\ =\frac{1}{7}\begin{bmatrix}-4 & 3 \\ -5 & 2\end{bmatrix} \\ =\begin{bmatrix}-\frac{4}{7} & \frac{3}{7} \\ -\frac{5}{7} & \frac{2}{7}\end{bmatrix} \end{gathered}[/tex]Now, we can solve for the matrix X, shown below:
[tex]X=\begin{bmatrix}-\frac{4}{7} & \frac{3}{7} \\ -\frac{5}{7} & \frac{2}{7}\end{bmatrix}\begin{bmatrix}-5 \\ -2\end{bmatrix}=\begin{bmatrix}(-\frac{4}{7})(-5)+(\frac{3}{7})(-2) \\ (-\frac{5}{7})(-5)+(\frac{2}{7})(-2)\end{bmatrix}=\begin{bmatrix}\frac{20}{7}-\frac{6}{7} \\ \frac{25}{7}-\frac{4}{7}\end{bmatrix}=\begin{bmatrix}\frac{14}{7} \\ \frac{21}{7}\end{bmatrix}=\begin{bmatrix}2 \\ 3\end{bmatrix}[/tex]The solution matrix, X, is
[tex]X=\begin{bmatrix}2 \\ 3\end{bmatrix}[/tex]This, means the solution to the system of equations is:
[tex]x=2,y=3[/tex]Drag each tile to the correct box.Arrange the steps to perform this subtraction operation in the correct order.(1.93 x 10"- (9.7 x 105)(1.93x107)–(9.7x106)0.96x107(1.93x10?)–(0.97X107)10 (0.96X107)(1.93-0.97)x107(1.93x10?)–10(9.7x106)9.6x106
Answers
We make the subtraction following this order:
1.
[tex]1.93\times10^7-9.7\times10^6[/tex]2.
[tex]1.93\times10^7-\frac{10}{10}\times(9.7\times10^6)[/tex]3.
[tex]1.93\times10^7-0.97\times10^7[/tex]4.
[tex](1.93-0.97)\times10^7[/tex]5.
[tex](0.96)\times10^7[/tex]6.
[tex]\frac{10}{10}(0.96\times10^7)[/tex]7.
[tex](9.6)\times10^6[/tex]step 3 find the mean of all the squared deviations step 4 take the square root of the mean of the squared deviations
Answers
Explanation
Step 3: Find the mean of all squared deviations.
[tex]\operatorname{mean}\text{ squared deviation }=\frac{25+25+0+4+4+0}{6}=\frac{58}{6}=9.67[/tex]Step 4: Take the square root of the mean of the squared deviations (from step 3)
[tex]\text{standard deviation }=\sqrt[]{mean\text{ squared deviation}}=\sqrt[]{9.67}=3.11[/tex]Note that the average distance between individual data values and the mean is simply called standard deviation.
Therefore the average distance between individual data values and the mean is 3.11
Four more than eight times a number (written as a expression)
Answers
'Four more than' is written as 4+
Let n be 'a number'
Then, the whole expression is:
[tex]4+8n[/tex]tionables wiin two-step rulesFill in the table using this function rule.y=2x+3Xv2D6DIDIOD810
Answers
Evaluating a function means finding the value of a function that corresponds to a given value of x. To do this, simply replace all the x variables with whatever x has been assigned.
Our function is
[tex]y=2x+3[/tex]For the given values on the table, we have the corresponding y values
[tex]\begin{gathered} y(2)=2\cdot(2)+3=4+3=7 \\ y(6)=2\cdot(6)+3=12+3=15 \\ y(8)=2\cdot(8)+3=16+3=19 \\ y(10)=2\cdot(10)+3=20+3=23 \end{gathered}[/tex]In a factory, the number of products produced by the workers on the second shift is twice the number of products produced by the first shift. Illustrate this relationship graphically. (Hint: Let x stand for the number of products produced by the first shift, and let y stand for the number of products produced by the second shift.)
Answers
To answer this question, we have:
1. Let x stand for the number of products produced by the first shift.
2. Let y stand for the number of products produced by the second shift.
If we have:
Then, we can write it algebraically as follows:
[tex]y=2x[/tex]And we can represent this relationship graphically by giving values for x, then applying the rule of the relation, and finally having the corresponding values for y.
If we suppose that workers belonging to the first shift produced:
• x = 0 products.
,• x = 10 products.
,• x = 20 products.
,• x = 30 products.
,• x = 40 products.
,• x = 50 products.
Then, we have that the second shift will produce:
[tex]\begin{gathered} x=10\Rightarrow y=2x\Rightarrow y=2(10)=20 \\ x=20\Rightarrow y=2(20)\Rightarrow y=40 \\ x=30\Rightarrow y=2(30)\Rightarrow y=60 \\ x=40\Rightarrow y=2(40)\Rightarrow y=80 \\ x=50\Rightarrow y=2(50)\Rightarrow y=100 \\ x=0\Rightarrow y=2(0)\Rightarrow y=0 \end{gathered}[/tex]Therefore, we can graph the relationship using the next coordinate pairs - we can start by (0, 0) - in this case, none of the workers produced any products):
• (0, 0)
,• (10, 20)
,• (20, 40)
,• (30, 60)
,• (40, 80)
,• (50, 100)
In this case, we can see that we are assuming that the number of products is positive integers (or natural numbers), and the relationship is discrete (not continuous) between the values for the first and second shift (that is why we do not a continuous line between the points.)
In other words, we can draw both functions for natural numbers in both axes. The y-axis will be twice in value as the values in the x-axis, and as a real ca
Ava bought a rectangular rug for her hallway. The rug is į yards wide and 2 yards long 2 3 What is the area of the rug?
Answers
Answer:
Concept:
The area of the rectangle is given below as
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times width \\ A_{\text{rectangle}}=l\times w \\ \text{where,} \\ l=2\frac{3}{4}yd \\ w=\frac{2}{3}yd \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times width \\ =2\frac{3}{4}yd\times\frac{2}{3}yd \\ A_{\text{rectangle}}=\frac{11}{4}yd\times\frac{2}{3}yd \\ A_{\text{rectangle}}=\frac{11}{6}yd^2 \\ A_{\text{rectangle}}=1\frac{5}{6}yd^2 \end{gathered}[/tex]Hence,
The final answer is
[tex]1\frac{5}{6}yd^2[/tex]The following table gives the cost, C(n), of producing a certain good as a linear function of n, the number of units produced. Use the information in this table to answer the questions that follow it. a. Evaluate each of the following expressions. Give economic interpretation of each. C(200) = _______ C(200) - C(150) = ________ C(200) - C(150) / 200 - 150 = _______ b. Estimate C(0). _______ c. the fixed cost of production is the cost incurred before any goods are produced. The unit cost is the cost of producing an additional unit. Find a formula for C(n) in terms of n, given that: Total cost = fixed cost + unit cost x number of units C(n) = _________
Answers
a. Based on the table, when 200 units is produced, the cost of production is $12,100 hence, C(200) = $12,100.
On the other hand, when 150 units is produced, the cost of production is $12,000 hence, C(150) = $12,000.
Subtracting C(200) - C(150), we have $100.
Dividing this result $100 by the difference of 200 and 150, we get 2.
[tex]\frac{C(200)-C(150)}{200-150}=\frac{12,100-12,000}{50}=\frac{100}{50}=2[/tex]b. Estimate C(0).
Based on the answers in letter a, we can see that for every additional unit produced, the additional cost of production is $2.
So, if we subtract 100 units, there will be 2*100 = $200 less on the cost of production.
From $11, 900 total cost of production of 100 units as shown in the table, we remove 100 units that cost $200, the total cost of production will now be $11, 700. Hence, at 0 units produced, the cost of production is $11, 700. C(0) = $11, 700.
c. Based on the answer in letter b, with 0 units produced, there is already a fixed cost of $11, 700.
Based on the answer in letter a, the unit cost per number of units produced is $2. If "n" is the number of units produced, the additional cost is 2n.
With these information, the formula for the finding the total cost of production is:
[tex]\begin{gathered} C(n)=FixedCost+(UnitCost\times no.ofunits)\text{ } \\ C(n)=11,700+2n \end{gathered}[/tex]
A football team is on their own 45 yard line. Theu lose an average of 6 yards on the next three plays. What yard line the team on after the three plays?
Answers
39 yard lines
Explanations:The initial yard line = 45 yards
Average amount of yards lost after 3 plays = 6 yards
The yard line after the three plays = 45 - 6
The yard line after the three plays = 39 yards
The team are on the 39 yard line after the three plays
Find the modes for the data in the given frequency distribution. (Round your answers to one decimal place. If there is more than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.)Points Scored in Basketball Game Frequency 3 9 7 5 8 9 10 4 13 1 15 2 17 1
Answers
SOLUTION
The mode of a distribution is the data with the highest frequency or the data that occure most in the distribution.
Consider the distribution given
The highest frequency is
[tex]9[/tex]The data with this frequency are two which are
[tex]\begin{gathered} 3 \\ \text{and } \\ 8 \end{gathered}[/tex]Therefore
The mode of the distribution is 3,8
Answer: Mode is 3,8
Solve for x. 2 - In(x + 3) = In 4 O x= In 4-1 O x = 2e x=2-3 X = -3
Answers
Starting with the equation:
[tex]2-\ln (x+3)=\ln (4)[/tex]Add ln(x+3) to both sides:
[tex]2=\ln (4)+\ln (x+3)[/tex]Use the property:
[tex]\ln (a)+\ln (b)=\ln (a\cdot b)[/tex]to rewrite the right hand side of the equation:
[tex]2=\ln (4(x+3))[/tex]Use the distributive property to rewrite 4(x+3) as 4x+12:
[tex]2=\ln (4x+12)[/tex]Use the property:
[tex]a=b\Rightarrow c^a=c^b[/tex]for a=2, b=(4x+12) and c=e:
[tex]e^2=e^{\ln (4x+12)}[/tex]Use the property:
[tex]e^{\ln (a)}=a[/tex]to rewrite the right hand side of the equation:
[tex]e^2=4x+12[/tex]Substract 12 from both sides of the equation:
[tex]e^2-12=4x[/tex]Divide both sides by 4:
[tex]\frac{e^2}{4}-3=x[/tex]Substitute the value of x into the original equation to check the answer.
Identify the domain of the function represented below:y= 2√x4-3x ≥ 4O x ≥ 3Ox≥-3Ο x > 0
Answers
Solution
Step 1
Write the function
[tex]y=2\sqrt{x-4}-3[/tex]Step 2
[tex]\begin{gathered} \mathrm{Domain\:definition} \\ The\:domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values \\ \:for\:which\:the\:function\:is\:real\:and\:defined. \end{gathered}[/tex]Step 3
To find the function domain, equate the expression in the square to at least zero.
[tex]\begin{gathered} x\text{ - 4 }\ge\text{ 0} \\ \\ x\text{ }\ge\text{ 4} \end{gathered}[/tex]Final answer
[tex][/tex]Graph the system of equation on the grid below in the mark their point of intersections (point c )y = 3x + 3y = x + 5
Answers
Given
y=3x+3
y=x+5
Procedure
A certain forest covers an area of 4000km ^ 2 Suppose that each year this area decreases by 5.5%. What will the area be after 12 years?Use the calculator provided and round your answer to the nearest square kilometer.
Answers
In order to calculate the area after 12 years, let's use the following exponential model:
[tex]A=A_0\cdot(1+r)^t[/tex]Where A is the area after t years, A0 is the initial area and r is the rate of increase or decrease.
So, for A0 = 4000, r = -0.055 and t = 12, we have:
[tex]\begin{gathered} A=4000\cdot(1-0.055)^{12} \\ A=4000\cdot0.945^{12} \\ A=4000\cdot0.50720287 \\ A=2028.8 \end{gathered}[/tex]Rounding to the nearest km², the area is 2029 km².