Fill in the empty spaces to complete the puzzle. In any row, the two left spaces should multiply to equal the right-hand space. In any column, the two top spaces should multiple to equal the bottom space.
Answers
Explanation:
We will find the expression for each space in the following order
To find the first expression, we need to find a number that multiplied by 6 is equal to 18. This number is 3 because
6 · 3 = 18
Then, for the second space, we need to factorize the expression 36x² + 144x + 108 as follows
36x² + 144x + 108 = 8(2x² + 8x + 6)
So, the expression that multiplied to 8 is (36x² + 144x + 108) is (2x² + 8x + 6).
The third space can be calculated by factorizing 2x² + 8x + 6 as
2x² + 8x + 6 = (x + 3)(2x + 2)
Therefore, the expression in the third space is (2x + 2)
Finally, for the fourth and fifth space, we need to multiply the expression to the left, so
6(2x + 2) = 6(2x) + 6(2) = 12x + 12
3(x + 3) = 3(x) + 3(3) = 3x + 9
Answer
Therefore, the answer is
Related Questions
Could you tell me the process of solving the problem?
Answers
Given:
[tex]Ln8=\frac{2\pi m\xi}{\sqrt{1-\xi^2}}[/tex]m=250
Required:
Find the value of
[tex]\xi[/tex]Explanation:
The value of ln8 is:
[tex]ln8=2.079[/tex][tex]\begin{gathered} 2.079=\frac{2\times3.14\times\xi}{\sqrt{1-\xi^2}} \\ 2.079(\sqrt{1-\xi^2})=6.28\xi^ \end{gathered}[/tex]Take the square on both sides.
[tex]\begin{gathered} 4.322(1-\xi^2)=39.44\xi^2 \\ \frac{1-\xi^2}{\xi^2}=\frac{39.4384}{4.322} \\ \frac{1}{\xi^2}-1=9.125 \\ \frac{1}{\xi^2}=9.125+1 \\ \frac{1}{\xi^2}=10.125 \end{gathered}[/tex]
L1 : y=−4x+3L2 : y=4x−1
Answers
Answer:
Assuming you're trying to find where the lines intersect (their solution), the point where they intersect is (1/2 , 1).
Step-by-step explanation:
When you are trying to find the point where two lines intersect, you have to find the x and y values of that point. To do that, just set the lines equal to each other.
First, since y must equal y:
y = y
-4x + 3 = 4x - 1
Now solve for x:
-8x + 3 = -4
-8x = -4
8x = 4
x = 1/2
We just found the x value of the shared point. Now we need to find the y value of that point. Again, since the two lines share this point, plugging in the x value will result in the same y value for both lines.
So just plug in x to any of the equations: (I think y=4x-1 is easier)
y(1/2) = 4(1/2) - 1 or y = 4(1/2) - 1 (it doesn't matter how you write it)
y(1/2) = 2 - 1 or y = 2 - 1
y(1/2) = 1
So the point is:
(1/2 , 1)
To check you can plug in the y value you find, 1 in this case, and solve for x. If you get the same x value as before, everything is correct.
So:
(1) = -4x + 3
-2 = -4x
1/2 = x or x = 1/2
Great! Everything is correct.
This may seem like a very long process, but it is very easy. Just find the x and y values that the lines share by setting the lines equal to each other.
Using this picture, describe what we are doing with the factored form of p(x) shown in the image in order to create a sketch of the function.
Answers
Given:
[tex]p(x)=(x-1)(x+1)(x-4)^2[/tex]Sol:
[tex]\begin{gathered} p(x)=(x-1)(x+1)(x-4)^2 \\ \\ p(0)=(0-1)(0+1)(0-4)^2 \\ \\ p(0)=-16 \end{gathered}[/tex]X-intercept is at p(x) = 0 then,
[tex]\begin{gathered} p(x)=0 \\ \\ p(x)=(x-1)(x+1)(x-4)^2 \\ \\ 0=(x-1)(x+1)(x-4)^2 \\ \\ x=-1,1,4 \end{gathered}[/tex]At y- intercept the value of x is zero and at x = 0 function value is:
[tex]\begin{gathered} y=-16 \\ \\ \text{ The point is:} \\ (0,-16) \end{gathered}[/tex]At x-intercept y value is zero and x-intercept is -1,1,4 is:
[tex]\begin{gathered} \text{ At }x=-1 \\ \\ the\text{ value of }y=0 \\ \\ (-1,0) \\ \\ At\text{ }x=1 \\ \\ \text{ The value of }y=0 \\ \\ (1,0) \\ \\ \text{ At }x=4 \\ \\ \text{ The value of }y=0 \\ \\ (4,0) \end{gathered}[/tex]So all point is (-1,0) ,(1,0) and (4,0)
In the diagram below of AGJK, H is a point onGJ, HJ = JK, m2 = 28, and mZGJK = 76.What is mZGKH?2870H
Answers
Problem
Solution
For the triangle GKJ we can find the angle K on this way:
28 +70 + Now we know that HJ= JK so then the triangle HJK is an isosceles triangle so then < JHK = < HKJ and we can do this:
70+ 2x = 180
2x= 110
x= 55
And then we can find the angle < GKH with the following equation:
28+70 + (55+y) = 180
y= 180-55 -28-70= 27
You bought your first car for $3,000 and make payments of $150 each month. Letting B represent the balance (what still needs to be paid), which function rule represents how much money is still owed (the balance) after m months?
Answers
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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How do I write down the size of Angles and marked by letters?
Answers
we can assume the lines are parallels so both triangles will have equal angles, so:
s=55° and p=x
now if we add 110 and x, we have a line this means
110+x=180
x=180-100
x=80
so p=x=80
and finally, the angles inside a triangle must add 180° so
55+p+t=180
55+80+t=180
135+t=180
t=180-135=45
So the answer is:
p=80°
s=55°
t=45°
27. A race consists of 7 women and 10 men. What is the probability that the top three finishers were(a) all men (b) all women (c) 2 men and 1 woman (d) 1 man and 2 women
Answers
Given 7 women and 10 men;
a) the top 3 are all men:
[tex]\begin{gathered} ways\text{ to choose 3 men out of 10 men is:} \\ 10C_3=\frac{10!}{(10-3)!3!} \\ \Rightarrow\frac{10!}{7!3!}=\frac{10\times9\times8\times7!}{7!\times3\times2\times1} \\ \Rightarrow\frac{10\times9\times8}{3\times2\times1}=120 \\ \text{ways to choose 3 men from 17 people(10men +7women) is:} \\ 17C_3=\frac{17!}{(17-3)!3!} \\ \Rightarrow\frac{17!}{14!\times3!}=\frac{17\times16\times15\times14!}{14!\times3\times2\times1} \\ \Rightarrow\frac{17\times16\times15}{3\times2\times1}=680 \end{gathered}[/tex]Therefore, the probability that the top 3 are all men is:
[tex]P_{all\text{ men}}=\frac{120}{680}=0.1765[/tex]b) the top 3 are all women:
[tex]\begin{gathered} \text{ways to choose 3 women from 7 women is:} \\ 7C_3=35 \\ \text{ways to choose 3 women from 17 people is:} \\ 17C_3=680 \end{gathered}[/tex]Therefore, the probability that the top 3 are all women is:
[tex]P_{\text{all women}}=\frac{35}{680}=0.0515[/tex]c) 2 men and 1 woman;
[tex]\begin{gathered} ways\text{ to choose 2 men out of 10 men is:} \\ 10C_2=45 \\ \text{ways to choose 1 woman from 7 women is:} \\ 7C_1=7 \\ \text{Thus, ways to choose 2 men and 1 woman }=45\times7=315 \end{gathered}[/tex]Therefore, the probability that the top 3 finishers are 2 men and 1 woman is:
[tex]P=\frac{315}{680}=0.4632[/tex]d) 1 man and 2 women;
[tex]\begin{gathered} \text{ways to choose 1 man from 10 men is;} \\ 10C_1=10 \\ \text{ways to choose 2 women from 7 women is:} \\ 7C_2=21 \\ \text{Thus, ways to choose 1 man and 2 women is 10}\times21=210 \end{gathered}[/tex]Therefore, the probability that the top 3 finishers are 1 man and 2 women is:
[tex]P=\frac{210}{680}=0.3088[/tex]f(x) = - 3x + 4; g(x) = f(x) + 1
Graph it and then describe the graph
Answers
The graph of function f(x) and g(x) is parallel lines separated by 1 unit.
In this question we have been given two functions f(x) = - 3x + 4 and g(x) = f(x) + 1
We need to graph these functions and then describe the graph.
The graph of given functions is as shown below.
The graph of function f(x) is a straight line with slope -3 and y-intercept 4.
The function g(x) is nothing but but function f(x) translated upward by 1 unit.
The graph of function g(x) is also a straight line with slope -3 and y-intercept 5.
Therefore, the graph of function f(x) and g(x) is parallel lines separated by 1 unit.
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Find the values of the variables in the parallelogram. The diagram is not drawn to scale. (Image is attached below)thank you in advance :)
Answers
For this problem, we are given a parallelogram with a diagonal drawn, inside it there are markings for a few angles. We need to determine the unknown angles.
Opposite sides of a parallelogram are parallel, this means we can treat the diagonal as a transversal line that crosses two parallel lines. Since this is the case, the angles 33º and xº are alternate interior angles and have the same length:
[tex]x=33º[/tex]The opposite angles in a parallelogram are congruent, therefore:
[tex]z=109º[/tex]The sum of internal angles is 360º, therefore we have:
[tex]\begin{gathered} 2\cdot109+2\cdot(x+y)=360\\ \\ 218+66+2y=360\\ \\ 284+2y=360\\ \\ 2y=360-284\\ \\ 2y=76\\ \\ y=38 \end{gathered}[/tex]The value of x is 33º, the value of y is 38º and the value of z is 109º.
i have test tomorrow i will love you to help me with thisClassify the following as a monomial, binomial, trinomial, or polynomial andstate the degree.a) 7^5b) 5^7 + 7^2c) 7^3 + 11^2 − 13 + 112d) + 2 + 3^2e) 11^3 − 7^3
Answers
Answer:
a) degree 5; monomial
b) degree 7; polynomial
c) degree 3; polynomial
d) degree 2; polynomial
e) degree 3 polynomial
Explanation.
A polynomial is a mathematical expression containing coefficients and variables.
An example of a polynomial is 42x^5 + 23 x^3 - 2x.
A monomial is a polynomial that contains only one term. For example, x^4, 34x^5, 2x, etc.
Having that in mind, we go through the expressions and place them in one of either category.
a) 7^5
This contains only one term, meaning it is monomial; its highest exponent is 5, meaning it is of degree 5.
b) 5^7 + 7^2
This contains two terms, meaning it is a polynomial; its highest exponent is 7, meaning its degree is 7.
c) 7^3 + 11^2 − 13 + 112
This expression contains four terms - it is a polynomial; its highest exponent is 3, meaning its degree is 3.
d) + 2 + 3^2
This contains three terms, meaning it is a polynomial; its highest exponent is 2, meaning its degree is 2.
e) 11^3 − 7^3
This contains 2 terms, meaning it is a polynomial; its highest exponent is 3, meaning it is of degree 2.
ILL GIVE BRAINLY AND 15 POINTS
Answers
Using functions, it is found that:
a. The costs for two years are as follows:
Option A: $4,600.Option B: $1,720.b. The pros and cons are as follows:
Option A: pro is the lower fixed fees, con is the higher hourly fee.Option B: pro is the lower hourly fee, con is the higher fixed fees.Option A functionThe cost of $2,600 for the first year is obtained as follows:
$500 set up fee.$2,000 of the 100 hours at $20 per hour.$100 of the hosting fee.For the second year, only the hourly cost will be paid, hence $2,000 will be added and the total cost is of:
$2,600 + $2,000 = $4,600.
The pros of Option A are the lower initial fees, hence for a lower number of hour, the cost is smaller, while the con is the high hourly price, meaning that for a high number of hours, option B is better.
Option B functionThe cost of $2,600 for the first year is obtained as follows:
$1,000 set up fee.$30 a month of hosting fee.For the second year, only the hosting fee is paid, meaning that $360 is added to the cost, thus:
$1,360 + $360 = $1,720.
The pros and cons are basically opposite of option A, higher basic fees with lower hourly/monthly fees, meaning that it is better over longer periods.
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What is the independent and dependent variable for k(d) =2d^2 - d +32
Answers
Given:
[tex]k(d)=2d^2-d+32[/tex]Required:
To find the independent and dependent variable.
Explanation:
In the given equation,
The dependent variable = k(d)
The independent variable = d
Final Answer:
The dependent variable = k(d)
The independent variable = d
An album received the following ratings on a 1-to-10 scale from10 music critics. What is the mean of the ratings?9.6, 9.8, 7.2, 6.4, 10.0, 8.9, 5.0, 9.8, 9.4, 6.8
Answers
Given:
The ratings are
[tex]9.6,9.8,7.2,6.4,10.0,8.9,5.0,9.8,9.4,6.8[/tex][tex]\begin{gathered} \text{Mean}=\frac{9.6+9.8+7.2+6.4+10.0+8.9+5.0+9.8+9.4+6.8}{10} \\ \text{Mean}=\frac{82.9}{10} \\ \text{Mean}=8.29 \end{gathered}[/tex]i inserted a picture of the question can you please state whether the answer is A,B, C or D check all that apply
Answers
Solution:
In the given figures, angles of the triangle ABC are corresponding equal to triangle DEF and the sides are proportional to each other.
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{1}{2}[/tex]Thus, the triangle ABC is similar to triangle DEF.
Therefore, the relationship between both triangles is the proportional side lengths.
Both triangles are not of the same size as their sides are not equal.
Both triangles are also not congruent as they do not satisfy any five conditions of congruence.
Hence, the correct option is A.
Melanie has pears and papayas in a ratio of 13:25. How many pears does she have ifshe has 2500 papayas?On the double number line below, fill in the given values, then use multiplication ordivision to find the missing value.
Answers
Given that the ratio of pears to papayas is 13:25,
[tex]\frac{\text{ Pears}}{\text{ Papayas}}=\frac{13}{25}[/tex]It means that Melanie has 13 pears, then the number of papayas must be 25.
It is asked to determine the number of pears corresponding to 2500 papayas.
First plot the values in the blank boxes on the double number line as below,
Let 'x' be the number of pears corresponding to 2500 papayas.
Now, cross multiply the terms,
[tex]25\cdot x=13\cdot2500[/tex]Divide both sides by 25,
[tex]\begin{gathered} 25\cdot x\cdot\frac{1}{25}=13\cdot2500\cdot\frac{1}{25} \\ x=13\cdot100 \\ x=1300 \end{gathered}[/tex]Thus, there should be 1300 pears corresponding to 2500 papayas.
what is the value of x in the solutions to the system of equations below3x-8y=112y+x=13
Answers
Given system of equations
3x - 8y = 11 ______________________1
2y + x = 13 ______________________ 2
Use the substution method
How to use the substitution method
1. pick one of the equation
2. make one of the variable subject of relation
3. substitute
From equation (1)
2y + x = 13
x = 13 - 2y
substitute x from equation 1 to 2.
3(13 - 2y) - 8y = 11
39 - 6y - 8y = 11
39 - 11 = 6y + 8y
28 = 14y
y = 28/14
y = 2
Next, substitute y in equation 2 to find x.
x = 13 - 2y
x = 13 - 2(2)
x = 13 - 4
x = 9
Final answer x = 9
how do you simplify this complex fraction in the lowest terms
[tex]\frac{77x^9/15y^5}{7x^7/10y^4}[/tex]
Answers
Answer:
[tex]\frac{22x^{2}}{3y}[/tex]
Step-by-step explanation:
[tex]\frac{(77x^{9})(10y^{4}) }{(7x^{7})(15y^{5}) }[/tex]
[tex]\frac{(11x^{2})(2)}{3y}[/tex]
Grade 12 math can you please explain each step, what are you doing, why and the final result that contributes to the sketch.
Answers
ANSWER and EXPLANATION
We want to sketch the graph of the given function:
[tex]y=\frac{2x^2-7x+5}{2x-1}[/tex]First, we have to check for the asymptotes of the function.
To find the vertical asymptote, we have to equate the denominator to 0 and solve for x:
[tex]\begin{gathered} 2x-1=0 \\ 2x=1 \\ x=\frac{1}{2} \end{gathered}[/tex]That is the vertical asymptote.
To find the horizontal asymptote, we have to check the degrees of the numerator and denominator. Since the degree of the numerator is greater than the denominator's, there is no horizontal asymptote.
To find the slant asymptote, divide the numerator by the denominator and identify the quotient:
This implies that the slant asymptote is:
[tex]y=x-3[/tex]The asymptotes will provide the boundaries for the graph of the function as follows:
Now, we have to find some coordinate points that satisfy the function.
Let us solve for y for values of x = -2, -1, 0, 1, 2, 3:
[tex]\begin{gathered} \Rightarrow x=-2 \\ y=\frac{2(-2)^2-7(-2)+5}{2(-2)-1}=-5.4 \\ \Rightarrow x=-1 \\ y=\frac{2(-1)^2-7(-1)+5}{2(-1)-1}=-4.67 \\ \Rightarrow x=0 \\ y=\frac{2(0)^2-7(0)+5}{2(0)-1}=-5 \\ \Rightarrow x=1 \\ y=\frac{2(1)^2-7(1)+5}{2(1)-1}=0 \\ \Rightarrow x=2 \\ y=\frac{2(2)^2-7(2)+5}{2(2)-1}=-0.33 \\ \Rightarrow x=3 \\ y=\frac{2(3)^2-7(3)+5}{2(3)-1}=0.4 \end{gathered}[/tex]We also have to identify the x and y intercepts of the function.
For the x-intercept, solve for x when y = 0:
[tex]\begin{gathered} 0=\frac{2x^2-7x+5}{2x-1} \\ \Rightarrow2x^2-7x+5=0 \\ 2x^2-2x-5x+5=0 \\ 2x(x-1)-5(x-1)=0 \\ (2x-5)(x-1)=0 \\ x=\frac{5}{2};x=1 \end{gathered}[/tex]For the y-intercept, solve for y when x = 0:
[tex]\begin{gathered} y=\frac{2(0)^2-7(0)+5}{2(0)-1} \\ y=\frac{5}{-1} \\ y=-5 \end{gathered}[/tex]Let us draw the table of values:
Now, we can use the calculated points, the intercepts, and the asymptotes to sketch the graph of the function:
That is the sketch of the function.
Find the equation of the line passing through points (6,0) and (-1,14)
Answers
Answer:
y = -2x + 12
Step-by-step explanation:
Hope this helps!!
A skier is trying to decide wheter or not to buy a seaskn ski pass. A daily pass cost $71. a season ski pass costs $350. the skirr would have to rent skis with either pass for $30 per day. how many days would the skier have to go skiing i. order to make the season pass less expensive than the daily passes?
Answers
The most appropriate choice for linear equation will be given by -
The skier would have to go atleast 5 days to make the season pass less expensive than the daily pass
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , \geq, < , \leq[/tex] sign
A one degree inequation is known as linear inequation.
Here,
Let the number of days the skier have to go skiing in order to make the season pass less expensive than the daily passes be d days
A daily pass cost $71
A season ski pass costs $350.
The skier would have to rent skis with either pass for $30 per day.
Cost of skiing with daily pass = $(71d + 30d) = $101d
Cost of skiing with season pass = $(350 + 30d)
By the problem,
[tex]101d > 350 + 30d\\101d - 30d > 350\\81d > 350\\d > \frac{350}{81}\\d > 4.3[/tex]
The skier would have to go atleast 5 days to make the season pass less expensive than the daily pass
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i need help with this too
Answers
a The value of (2.3 × 10⁴) × (1.5 × 10^-2) is 3.45 × 10^2
b. The value of (3.6 × 10^-5) ÷ (1.8 × 10^2) is 2 × 10^-3. This illustrates the concept of standard form.
What is standard form?The standard form is simply used in Mathematics to illustrate the numbers that are either too large or too small.
It's important to note that the multiplication of exponents is an addition and the division of the power is subtraction.
Therefore, (2.3 × 10⁴) × (1.5 × 10^-2) will be:
= (2.3 × 1.5) × (10^(4-2)
= 3.45 × 10^2
Also, (3.6 × 10^-5) ÷ (1.8 × 10^2) will be:
= (3.6 ÷ 1.8) × 10^(-5 + 2)
= 2 × 10^-3.
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McGraw-H….A ALEKS - Mi...O POLYNOMIAL AND RATIONAL FUNCTIONSThe Factor Theorem
Answers
SOLUTIONS
Using factor theorem to solve the equation below:
[tex]-x^3+4x^2-8=0[/tex][tex]\begin{gathered} -x^3+4x^2-8 \\ -x(x^2-4x+8) \end{gathered}[/tex]Determine whether each expression can be used to find the length of side RS.
Answers
ANSWER:
[tex]\begin{gathered} \sin (R)\rightarrow\text{ Yes} \\ \tan (T)\rightarrow\text{ No} \\ \cos (R)\rightarrow\text{ No} \\ tan(R)\rightarrow\text{ No} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
Since we know a side and the hypotenuse, we can rule out tangent and cotangent, since these are related to the two legs.
Therefore, if we want to know that side we must apply sine or cosine, just like this:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{ hypotenuse}} \\ \text{therefore, in this case:} \\ \sin R=\frac{21}{35} \\ \cos \theta=\frac{\text{adjacent}}{\text{ hypotenuse}} \\ \cos R=\frac{\text{unknown}}{35} \end{gathered}[/tex]Therefore, the way to calculate the value of the missing side is by means of the sine of the angle R
8) Use the graph to determine the independent variable. Money Saved 240 210 180 A Number of Weeks 150 120 Amount of Money ($) B) The Amount of Money 90 © Money Saved 60 30 0 1 2 6 7 8 3 4 5 Number of Weeks
Answers
Generally equations are in the form:
y = mx + b
Where
x is the independent variable, you can choose any value for x
y is the dependent variable. The value of y depends on x.
In the graph, the x-axis is number of weeks and y-axis is amount.
Amount depends on the number of weeks, which is the independent variable, here in this graph.
Last year, Susan had $20,000 to invest. She invested some of it in an account that paid 10% simple interest per year, and she invested the rest in an account that paid 7% simple interest per year. After one year, she received a total of $1790 in interest. How much did she invest in each account?
Answers
Last year, Susan had $20,000 to invest. She invested some of it in an account that paid 10% simple interest per year, and she invested the rest in an account that paid 7% simple interest per year. After one year, she received a total of $1790 in interest. How much did she invest in each account?
Let
x ------> amount invested in an account that paid 10% simple interest per year
20,000-x ------> amount invested in an account that paid 7% simple interest per year
so
The formula of simple interest is equal to
I=P(rt)
In this problem we have that
10%=0.10
7%=0.07
x*(0.1)+(20,000-x)*(0.07)=1,790
solve for x
0.10x+1,400-0.07x=1,790
0.03x=1,790-1,400
0.03x=390
x=$13,000
therefore
amount invested in an account that paid 10% simple interest per year was $13,000and amount invested in an account that paid 7% simple interest per year was $7,000A collection of dimes and quarters has a value of $1.35. List all possible combinations of dimes and quarters. Remember to write a let statement
Answers
3 combinations:
3 quarters and 6 dimes
5 quarters and 1 dime
1 quarter and 11 dimes
1) Remember that a dime corresponds to $0.10 and a quarter to $0.25. And the value we want to find is $1.35
2) As we can see the last digit on $1.35 is 5 then we can infer that we're going to need an odd number of quarters ($0.25). Also, notice that we need whole numbers for the quantities of each coin. In other words, multiples of 0.10 and 0.25 whose sum yields to $1.35. So let's do it step by step:
So, we can write out the following list of combinations:
q (quarter) 3 q = 3 x 0.25 = $ 0.75
d (dimes) 6 d = 6 x 0.10 = $ 0.60
0.60 + 0.75 = 1.35
2.2) Another possible combination:
q (quarter) 5 q = 5 x 0.25 = $ 1.25
d (dimes) 1 d = 1 x 0.10 = $ 0.10
0.10+1.25= 1.35
2.3)
q (quarter) 1 q = 1 x 0.25 = $ 0.25
d (dimes) 11 d = 11x 0.10 = $ 1.10
0.25+1.10 = 1.35
3) Hence, considering that we need to combine dimes and quarters and their sum must be lesser than $1.35 We have three combinations with whole numbers of dimes and quarters:
3 quarters and 6 dimes
5 quarters and 1 dime
1 quarter and 11 dimes
Given the equation y = 6sin(2x - 10) + 3
Answers
We have the equation:
[tex]y=6\sin(2x-10)+3[/tex]We have to find the amplitude, the period, the horizontal shift and the midline.
The amplitude can be calculated as half the difference between the maximum and minimum value of the function.
The maximum value will happen when the sine is equal to 1 and the minimum when the sine is equal to -1.
We can then calculate the amplitude A as:
[tex]\begin{gathered} A=\frac{y_{max}-y_{min}}{2} \\ A=\frac{6(1)+3-(6(-1)+3)}{2} \\ A=\frac{6+3-(-6+3)}{2} \\ A=\frac{9-(-3)}{2} \\ A=\frac{12}{2} \\ A=6 \end{gathered}[/tex]Now we have to calculate the period.
The period will be equal to the horizontal distance at which the function starts repeating itself (or complete a period).
As we have a sine function we know that:
[tex]\sin(u)=\sin(u+2n\pi)\text{ }n\in Z[/tex]That means that it will repeat itself for any multiple of 2π.
We can calculate the period as:
[tex]\begin{gathered} y(x+2\pi)=y(x+T) \\ 6(2x-10+2\pi)+3=6(2(x+T)-10)+3 \\ 2x-10+2\pi=2(x+T)-10 \\ 2x+2\pi=2x+2T \\ 2\pi=2T \\ T=\pi \end{gathered}[/tex]The period is π.
The horizontal shift will be given by the constant value inside the argument of the sine function. We can ignore the other terms and factors and use only the sine function in this case.
For example, for sin(2x) = 0, this value corresponds to x = 0.
In the case of sin(2x-10) = 0 this corresponds to an x that is 5.
That is because the function has a frequency that is twice as the frequency of the hpure sine function.
If the function wasn't periodice we would see it translated by 10 to the right.
We can calculate the midline as the average of the function.
This average value will be given by the average value of the sine function, which is 0, so we can calculate the midline as:
[tex]y_{avg}=6(0)+3=3[/tex]Answer:
The amplitude is 6.
The period is π.
The horizontal shift is 10 units to the right.
The midline is y = 3.
The equation for a straight line (deterministic model) is y = Bo + B,X.If the line passes through the point ( - 10,3), then x = - 10, y = 3 must satisfy the equation; that is, 3 = Bo + B1(-10).Similarly, if the line passes through the point (11,4), then x = 11, y = 4 must satisfy the equation; that is, 4 = Bo+B1(11).Use these two equations to solve for Bo and By; then find the equation of the line that passes through the points (-10,3) and (11,4)...Find Bo and B,B1 =Bo(Simplify your answers. Type integers or simplified fractions.)
Answers
To find the equation of the line we just need to find the beta constants. In order to do this we have (they provided us with) the following system of equations:
[tex]\begin{cases}3=\beta_0+\beta_1(-10) \\ 4=\beta_0+\beta_1(11)\end{cases}[/tex]Let us subtract the second equation to the first one:
This implies that
[tex]\beta_1=\frac{-1}{-21}=\frac{1}{21}[/tex]Now, let us replace this value we just got into the second equation to find beta_0:
[tex]\begin{gathered} 4=\beta_0+\frac{1}{21}\cdot11, \\ 4=\beta_0+\frac{11}{21}, \\ \beta_0=4-\frac{11}{21}=\frac{4\cdot21}{21}-\frac{11}{21}=\frac{84-11}{21}=\frac{73}{21} \end{gathered}[/tex]At last,
[tex]\beta_1=\frac{1}{21},\beta_0=\frac{73}{21}[/tex]Then, the equation of the line is just
[tex]y=\frac{73}{21}+\frac{1}{21}x[/tex]determine the domain and range of the piecewise function graphed below
Answers
The domain is all the possible input values, and the range is all the possible output values.
So according to this function (Given in the question).
The domain is [-3, 5] and the range is [-5, 4]
That is all to this question.
An electronic store discounted a tablet computer by 30%. The discounted price of the computer was $486.50. Determine the original price of the tablet
Answers
The discounted price of the computer was $486.50.
An electronic store discounted a tablet computer by 30%.
So, the original price was
[tex]\begin{gathered} C=486.50+(486.50\times30percent) \\ =486.50+(486.50\times\frac{30}{100}) \\ =486.50+145.95 \\ =632.45 \end{gathered}[/tex]So, the original price of the tablet computer was $632.45.