The function rule represents how much money is still owed is B = 3000 - 150m
What is a function?A function is used to show the relationship between the data given. This can be illustrated with the variables.
Here, the person bought the first car for $3,000 and make payments of $150 each month.
Let B represent the balance.
The function to illustrate this will be:
B = 3000 - 150(m)
B = 3000 - 150m
where B = balance
m = number of months
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factor bofe problems using synthetic division and list All zeros
Given:
[tex]f(x)=x^3-7x^2+2x+40;\text{ x -5}[/tex]Let's factor using synthetic division.
Equate the divisor to zero:
x - 5 = 0
x = 5
List all terms of the polynomial: 1, -7, 2, 40
Palce the numbers representing the divisor and dividend into a long division-like configuration
To factor using synthetic division, we have:
Therefore, the factored expression is:
[tex]\begin{gathered} 1x^2-2x-8 \\ \\ =x^2-2x-8 \\ \\ =(x-4)(x+2) \end{gathered}[/tex]The zeros are also the roots of the polynomial.
The zeros of a polynomial are all the x-values that makes the polynomial equal to zero,
To find the zeros, equate each afctor to zero:
(x - 4) = 0
x = 4
(x + 2) = 0
x = -2
Thus, the zeros are:
x = 4, -2
ANSWER:
[tex]\begin{gathered} (x-4)(x+2) \\ \\ \text{Zeros: 4, and -2} \end{gathered}[/tex]Solve the system of two linear inequalities graphically,4x + 6y < 24(x22Step 1 of 3 : Graph the solution set of the first linear inequality.AnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (--)Enter two points on the boundary line:10-5Select the region you wish to be shaded:
Answer:
To solve the system of two linear inequalities graphically,
[tex]\begin{gathered} 4x+6y<24 \\ x\ge2 \end{gathered}[/tex]For step 1,
Draw a line 4x+6y=24
Since the given equation has less than sign, the required region will not include the line, Hence we draw the dashed line for the line 4x+6y=24.
Since we required redion is 4x+6y<24, the points bellows the line satisfies the condition hence the required region is below the line,
Similarly for the inequality,
[tex]x\ge2[/tex]It covers the region right side of the line x=2,
we get the siolution region as the intersecting region of both inequality which defined in the graph as,
Dark blue shaded region is the required solution set for the given inequalities.
Can you please help me solve this question. Thank you
Answer:
0.4384 < p < 0.5049
Explanation:
The confidence interval for the population proportion can be calculated as:
[tex]p^{\prime}-z_{\frac{\alpha}{2}}\sqrt[]{\frac{p^{\prime}(1-p^{\prime})}{n}}Where p' is the sample proportion, z is the z-score related to the 95% level of confidence, n is the size of the sample and p is the population proportion.
Now, we can calculate p' as the division of the number of voters of favor approval by the total number of voters.
[tex]p^{\prime}=\frac{408}{865}=0.4717[/tex]Additionally, n = 865 and z = 1.96 for a 95% level of confidence. So, replacing the values, we get:
[tex]\begin{gathered} 0.4717-1.96\sqrt[]{\frac{0.4717(1-0.4717)_{}}{865}}Therefore, the confidence interval for the true proportion is:
0.4384 < p < 0.5049
Select the correct answer..What is the value of i^ if the remainder of 4 is 2?OA. -i'OB.-1Ос. іOD. 1ResetNext
1) Considering that for that complex number we have the following pattern:
[tex]\begin{gathered} i^1=i \\ i^2=-1 \\ i^3=-1\cdot i=-i \\ i^4=-1\cdot-1=1 \end{gathered}[/tex]2) And that, the question asks us about the what number must be that exponent so that the remainder is 2, we can write out:
[tex]\frac{n}{4}=4d+2[/tex]which d is the divisor, so if the remainder is 2 then we can state:
[tex]i^n=i^2=-1[/tex]Which description is paired with its correct expression?
O seven less than the quotient of two and a number squared, increased by six;
Onine times the difference of a number cubed and three, 9(n²-3)
7-+8
O eight more than the quotient of a number squared and four, decreased by seven;
Otwice the difference of a number cubed and eight, 27³-8
8+/-7
Answer:
seven less than the quotient of two and a number squared increased by six
7 - (2/n²) + 6
nine times the difference of a number cubed and three; 9(n³-3)
eight more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7
twice the difference of a number cubed and eight; 2 n³- 8
Step-by-step explanation:
On the Richter Scale, the magnitude R of an earthquake of intensity I is given by the equation in the image, where I0 = 1 is the minimum intensity used for comparison. (The intensity of an earthquake is a measure of its wave energy). Find the intensity per unit of area I for the Anchorage Earthquake of 1989, R = 9.2.
we have the formula
[tex]R=\log _{10}\frac{I}{I_0}[/tex]we have
R=9.2
I0=1
substitute in the given equation
[tex]\begin{gathered} 9.2=\log _{10}\frac{I}{1} \\ 9.2=\log _{10}I \\ I=10^{(9.2)} \\ \end{gathered}[/tex]I=1,584,893,192.46
Jackson started a savings account using the bonus he received from work of $3,500. Theaccount is compounded weekly with an interest rate of 1.75% How much interest did theaccount earned in 18 years?O $1,295.65O $1,102.500 $4,795.65o $1,290
The amount compounded is given by the formula ;
[tex]A=P\lbrack1+\frac{r}{100n}\rbrack^{nt}[/tex]Here, P = $3500, r = 1.75%, n = 52 , t = 18 years.
[tex]\begin{gathered} A=3500\lbrack1+\frac{1.75}{100\times52}\rbrack^{52\times18} \\ A=4795.65 \end{gathered}[/tex]Therefore, the interest the account will earn is 4795.65-3500 = $1295.65, Option A
A person chooses a number in a set containing the first 5 cubic numbers. Find the set representing the event E of choosing a number that can be evenly divided by 2. Give your answer as a set, e.g. {1,2,3}, using the cubed number (not the base number) and do not include E= in your answer.
The first 5 cubic numbers are:
[tex]\lbrace1,8,27,64,125\rbrace[/tex]To find the set that represents event E we have to choose the numbers from the set above that are evenly divided by 2; this means that we have to choose the numbers that are multiple of 2. We notice that this numbers are 8 and 64, therefore the set that represents event E is:
[tex]\lbrace8,64\rbrace[/tex]Find F as a function of x and evaluate it at x = 2, x = 5 and x = 8.
Given:
[tex]F(x)=\int_2^x(t^3+6t-4)dt[/tex]Find-:
[tex]F(x),F(2),F(5),F(8)[/tex]Sol:
[tex]\begin{gathered} F(x)=\int_2^x(t^3+6t-4)dt \\ \\ \end{gathered}[/tex]Use integration then:
[tex]\begin{gathered} F(x)=\int_2^x(t^3+6t-4)dt \\ \\ F(x)=[\frac{t^4}{4}+\frac{6t^2}{2}-4t]_2^x^ \\ \\ \\ F(x)=\frac{x^4}{4}+3x^2-4x-\frac{2^4}{4}-3(2)^2+4(2) \\ \\ F(x)=\frac{x}{4}^4+3x^2-4x-8 \end{gathered}[/tex]The function value at x = 2 is:
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(2)=\frac{2^4}{4}+3(2)^2-4(2)-8 \\ \\ F(2)=4+12-8-8 \\ \\ F(2)=16-16 \\ \\ F(2)=0 \end{gathered}[/tex]The function value at x = 5
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(5)=\frac{5^4}{4}+3(5)^2-4(5)-8 \\ \\ F(5)=156.25+75-20-8 \\ \\ F(5)=203.25 \end{gathered}[/tex]Function value at x = 8
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(8)=\frac{8^4}{4}+3(8)^2-4(8)-8 \\ \\ F(8)=1024+192-32-8 \\ \\ F(8)=1216-40 \\ \\ F(8)=1176 \end{gathered}[/tex]45% of 240 is what number?
We are asked to determine the 45% of 240. To do that we need to multiply 240 by 45/100, that is:
[tex]240\times\frac{45}{100}=108[/tex]therefore, 45 percent of 240 is 108
inserted a picture of the question, can you just answer the question and not ask a lot of questions yes i’m following
Step-by-step explanation:
A nonagon has 9 sides, so a regular nonagon will have vertices that are 40° apart as measured from the center. It has 9-fold rotational symmetry,
so the figure will be identical to the original when rotated multiples of 360°/9 = 40°.
[tex]\frac{360}{9}=40[/tex]Therefore the degrees will a nonagon have rotational symmetry
Hene the correct answer is Option B
In the 1st generation, there are 6 rabbits in a forest. Every generation after that, the rabbit population triples. This sequence represents the numbers of rabbits for the first few generations: 6, 18, 54, What is the explicit formula for the number of rabbits in generation n?
You have the following sequence for the population of the rabbits:
6, 18, 54, ...
The explicit formula for the previous sequence is obtained by considering the values of n (1,2,3,..) for the first terms of the sequence.
You can observe that the explicit formula is:
a(n) = 6·3^(n - 1)
in fact, for n=1,2,3 the result is:
a(1) = 6·3^(1 - 1) = 6·3^0 = 6
a(2) = 6·3^(2 - 1) = 6·3^1 = 18
a(3) = 6·3^(3 - 1) = 6·3^2 = 6·9 = 54
which is consistent with the given sequence 6, 18, 54, ...
Please look at the image below. By the way this is my homework.Use the definition of congruence to decide whether the two figures are congruent. Explain your answer. Give coordinate notation for the transformations you use.
Congruent Shapes
Two congruent shapes have the same size and shape, which means all of their side lengths are equal and all of their internal angles are congruent (have the same measure),
All of the rigid transformations map the original figure to a congruent figure. One of the transformations is the reflection.
The image shows two shapes SRQP and EDCB. They seem to have the same shape and size, but it must be proven by finding the appropriate transformation used.
Comparing the corresponding vertices we can find that out. For example, the coordinates of S are (-6,4) and the coordinates of E are (4,4). The x-coordinate of the midpoint between them is
xm = (-6+4)/2 = -1
Now analyze the points P(-8,2) and B(6,2). The x-coordinate of the midpoint is:
xm = (-8+6)/2 = -1
For the points R(-4,-6) and D(2,-6):
xm = (-4+2)/2 = -1
For the points Q(-9,-4) and D(8,-4):
xm = (-9+8)/2 = -0.5
Since this last pair of corresponding points don't have the same axis of symmetry as the others, the shapes don't have the same size and angles, thus they are not congruent
For both shapes to be congruent, the coordinates of Q should have been (-10,-4)
Answer the statistical measures and create a box and whiskers plot for the following set of data.
Solution
The picture below is the solution to the problem
Brief explanantion
From the data given, It is obvious that:
Minimum = 2
Maximum =
The total number of the data is 3, so the number 7th term is the median
Thus,
Median = 8
To find Q1
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1)th\text{ term} \\ Q_1=\frac{1}{4}(13+1)=\frac{14}{4}=3.5 \end{gathered}[/tex]Q1 is between the third and fourth term
Therefore, Q1 is
[tex]Q_1=0.5(4)+0.5(6)=5[/tex]Similarly, to find Q3
[tex]\begin{gathered} Q_3=\frac{3}{4}(n+1)th\text{ term} \\ Q_3=\frac{3}{4}(13+1)=3\times\frac{14}{4}=3\times3.5=10.5 \end{gathered}[/tex]Q3 is between the tenth and the eleventh term
Therefore, Q3 is
[tex]Q_3=0.5(11)+0.5(11)=11[/tex]True or False: A power has two parts, a base and an exponent. True False
The said statement is true.
A power has two parts, a base and an exponent.
Example
[tex]2^3[/tex]The answer is TRUE
Ethan found the spinner shownbelow and planned to use it for agame.2332453235After studying the spinner beforeusing it, Ethan correctly concludedthat the spinner was-A least likely to land on 2B least likely to land on 5C most likely to land on 3D most likely to land on 2
we have that
the number 3 appears 4 times
so
answer is
option C most likely to land on 3
What is the meaning of estimate
The meaning of estimate is approximately calculating an answer to check its accuracy.
Approximate calculation:
Approximate value means the value that is close to this number, less than it, as close as possible, and with a requested level of precision.
For example, the approximate value of π is 3.14
Given,
Here we have the word estimate.
Now, we have to find the meaning of it.
Estimate value means to find a value that is close enough to the right answer, usually with some thought or calculation involved.
For example, let us consider Alex estimated there were 10,000 sunflowers in the field by counting one row then multiplying by the number of rows. Here we doesn't have the exact value instead of that we take the approximate value to identify the number. This process is called estimation.
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how do i evaluate 8!4!/7!2!
Solution:
Consider the following expression:
[tex]\frac{8!4!}{7!2!}[/tex]Remember that The factorial function is defined by the product:
[tex]n!\text{ = }1\cdot2\cdot3\cdot\cdot\cdot\cdot\cdot\cdot(n-2)\cdot(n-1)\cdot n[/tex]thus, according to this definition, the given expression can be expressed as:
[tex]\frac{8!4!}{7!2!}\text{ = }\frac{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8)\text{ (}1\cdot2\cdot3\cdot4\text{)}}{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7)(1\cdot2)}[/tex]now, simplifying the previous expression we obtain:
[tex]\text{= }(8)\text{ (}3\cdot4\text{) = }96[/tex]we can conclude that the correct answer is:
[tex]\text{ }96[/tex]Which expression has a negative value
Answer:
bottom one
Step-by-step explanation:
4. Adam had $200. He spent $75 on clothes and $55 on a video game. Then his Momgave him $20 more dollars. How much money does Adam have now?
Adam had $200
He spent $75 on clothes and $55 on video game
The total money spent by Adam is
[tex]=75+55=\text{ \$130}[/tex]The amount left with Adam is
[tex]=200-130=\text{ \$70}[/tex]Then his mom gave him $20
The total amount of money Adam have now is
[tex]=70+20=\text{ \$90}[/tex]Hence, the answer is $90
if (x + y) +61 = 2, what is x + y?
The question is given as
[tex](x+yi)+6i=2[/tex]To solve, we need to make (x + yi) the subject of the formula.
To do so, we move 6i to the right-hand side of the equation:
[tex]x+yi=2-6i[/tex]Therefore, OPTION A is correct.
Answer:
(x + yi)= 2-6i
Step-by-step explanation:
Complex numbers
(x + yi) +6i = 2
Subtract 6i from each side
(x + yi) +6i -6i = 2-6i
(x + yi)= 2-6i
Graph the set {x|x2-3} on the number line.Then, write the set using interval notation.
Given,
The expression is,
[tex]\lbrace x|x\ge-3\rbrace[/tex]Required:
The graph of the line.
The interval notation is [-3, infinity).
The line of the inequality is,
Hence, the graph of the line is obtained.
Question 8 of 10What is the slope of the line described by the equation below?y=-x+ 8A. 8B. 1OOOC. -8O D.-1SUBMIT
We have the following equation
y = -x + 8
this equation is writen in slope intercept form
y = mx + b
where m is the slope
From the above, we can see that the slope is m = -1
distributive property 3x(7x+6)
By distributive property, we distribute 3x, and multiply it to each term inside the binomial (7x+6) accounting for the sign.
[tex]\begin{gathered} 3x(7x+6) \\ \Rightarrow3x(7x)+3x(6) \\ \Rightarrow21x^2+18x \\ \\ \text{Therefore, }3x(7x+6)=21x^2+18x \end{gathered}[/tex]Describe in words where the square root of 60 minus 11 would be plotted on a number line.
Answer:
it would be on 7 since 60-11=49 and the square root of 49 is 7
I am studying for the big test tomorrow and just need someone to go through this sheet I made with me.Sorry
SOLUTION
Let us solve the simultaneous equation
[tex]\begin{gathered} -2x-y=0 \\ x-y=3 \end{gathered}[/tex]using elimination
To eliminate, we must decide which of the variables, x or y is easier to eliminate. The variable you must eliminate must be the same and have different sign. Looking above, it is easier to eliminate y because we have 1y above and 1y below. But to eliminate the y's, one must be +y and the other -y. So that +y -y becomes zero.
So to make the y's different, I will multiply the second equation by a -1. This becomes
[tex]\begin{gathered} -2x-y=0 \\ (-1)x-y=3 \\ -2x-y=0 \\ -x+y=-3 \end{gathered}[/tex]So, now we can eliminate y, doing this we have
[tex]\begin{gathered} -2x-x=-3x \\ -y+y=0 \\ 0-3=-3 \\ \text{This becomes } \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]Now, to get y, we put x = 1 into any of the equations, Using equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2-y=0 \\ \text{moving -y to the other side } \\ y=-2 \end{gathered}[/tex]So, x = 1 and y = -2
Using substitution, we make y or x the subject in any of the equations. Looking at this, It is easier to do this using equation 2. From equation 2,
[tex]\begin{gathered} x-y=3 \\ \text{making y the subject we have } \\ y=x-3 \end{gathered}[/tex]Now, we will put y = x - 3 into the other equation, which is equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2x-(x-3)=0 \\ -2x-x+3=0 \\ -2x-1x+3=0 \\ -3x+3=0 \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]So, substituting x for 1 into equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2\times1-y=0 \\ -2-y=0 \\ y=-2 \end{gathered}[/tex]Substituting x for 1 into equation 2, we have
[tex]\begin{gathered} x-y=3 \\ 1-y=3 \\ y=1-3 \\ y=-2 \end{gathered}[/tex]Now, for graphing,
A small publishing company is planning to publish a new book. Let C be the total cost of publishing the book (in dollars). Let be the number of copies of the book produced. For the first printing, the company can produce up to 100 copies of the book. Suppose that C = 10N + 700 gives C as a function of N during the the correct description of the values in both the domain and range of the function. Then, for eachchoose the most appropriate set of values.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
C = 10N + 700
Step 02:
functions:
C = total cost
N = number of copies
Domain:
number of copies produced
{0, 1, 2, 3, .... 100}
Range:
cost of publishing book (in dollars)
{700, 710, 720, 730, ... 1700}
That is the full solution.
A rectangular athletic field is twice as long as it is wide if the perimeter of the athletic field is 360 yards what are its dimensions. The width isThe length is
Step 1. We will start by making a diagram of the situation.
Since the length of the rectangle is twice the width, if we call the width x, then the length will be 2x as shown in the diagram:
Step 2. One thing that we know about the rectangle is its perimeter:
[tex]\text{Perimeter}\longrightarrow360\text{yd}[/tex]This perimeter has to be the result of the sum of all of the sides of the rectangle:
[tex]x+x+2x+2x=360[/tex]Step 3. Solve the previous equation for x.
In order to solve for x, the first step is to combine the like terms on the left-hand side:
[tex]6x=360[/tex]The second step to solve for x is to divide both sides of the equation by 6:
[tex]\frac{6x}{6}=\frac{360}{6}[/tex]Simplifying:
[tex]x=60[/tex]Step 4. Remember from the diagram from step 1, that x was the width of the rectangle:
[tex]\text{width}\longrightarrow x\longrightarrow60yd[/tex]and the length was 2x, so we multiply the result for the with by 2:
[tex]\text{length}\longrightarrow2x=2(60)=120\longrightarrow120yd[/tex]And these are the values for the width and the length.
Answer:
The width is 60yd
The length is 120yd
what should the height of the container be so as to minimize cost
Lets make a picture of our problem:
where h denotes the height of the box.
We know that the volume of a rectangular prism is
[tex]\begin{gathered} V=(4x)(x)(h) \\ V=4x^2h \end{gathered}[/tex]Since the volume must be 8 cubic centimeters, we have
[tex]4x^2h=48[/tex]Then, the height function is equal to
[tex]h=\frac{48}{4x^2}=\frac{12}{x^2}[/tex]On the other hand, the function cost C is given by
[tex]C=1.80A_{\text{bottom}}+1.80A_{\text{top}}+2\times3.60A_{\text{side}1}+2\times3.60A_{\text{side}2}[/tex]that is,
[tex]\begin{gathered} C=1.80\times4x^2+1.80\times4x^2+3.60(8xh+2xh) \\ C=3.60\times4x^2+3.60\times10xh \end{gathered}[/tex]which gives
[tex]C=3.60(4x^2+10xh)[/tex]By substituting the height result from above, we have
[tex]C=3.60(4x^2+10x(\frac{12}{x^2}))[/tex]which gives
[tex]C=3.60(4x^2+\frac{120}{x})[/tex]Now, in order to find minum cost, we need to find the first derivative of the function cost and equate it to zero. It yields,
[tex]\frac{dC}{dx}=3.60(8x-\frac{120}{x^2})=0[/tex]which is equivalent to
[tex]\begin{gathered} 8x-\frac{120}{x^2}=0 \\ \text{then} \\ 8x=\frac{120}{x^2} \end{gathered}[/tex]by moving x squared to the left hand side and the number 8 to the right hand side, we have
[tex]\begin{gathered} x^3=\frac{120}{8} \\ x^3=15 \\ \text{then} \\ x=\sqrt[3]{15} \\ x=2.4662 \end{gathered}[/tex]Therefore, by substituting this value in the height function, we get
[tex]h=\frac{12}{2.4662^2}=1.9729[/tex]therefore, by rounding to the neastest hundredth, the height which minimize the cost is equal to 1.97 cm
Instructions: Find the missing length indicated.BII1600900X
From the diagram given in the question, we are asked to find the missing length indicated.
We can see from the diagram that the right triangles are similar, so the ratio of hypotenuse to short leg is the same for all.
So,
x/900 = (1600 + 900)/x
Let's cross multiply:
x² = 900(2500)
let's take square of both sides:
x = √(900) * √(2500)
x = 30(50)
x = 30 * 50
x = 1500
Therefore, the missing length is 1500