Solution:
Given the function below
[tex]f(x)=5x-2[/tex]Where
[tex]\begin{gathered} x\text{ is the input value} \\ f(x)\text{ is the output value} \end{gathered}[/tex]If the input value is 3, i.e. x = 3, the output value will be
[tex]\begin{gathered} f(x)=5x-2 \\ f(3)=5(3)-2=15-2=13 \\ f(3)=13 \end{gathered}[/tex]Hence, the output value is 13
Will anyone help me with this question
The rectangle is divided by 5
The red part represents 2/5
The blue part represents 1/5
The sum 2/5+1/5=3/5, where the result is given by the 3 rectangles colored
answer (2 + 2) - 4 + 2
start by solving whats inside the parentheses
[tex]4-4+2[/tex]solve the addition
[tex]\begin{gathered} 0+2 \\ 2 \end{gathered}[/tex]vic sam and li volunteered at a food bank for 52 hours if sam worked 3 fewer hours then vic and 4 fewer then li how many hours did li work?
Answer:
Li worked for 19 hours.
Explanation:
Let's call x the number of hours that Vic worked, y the number of hours that Sam worked, and z the number of hours that Li worked.
They all work for 52 hours, so:
x + y + z = 52
Sam worked 3 fewer hours than Vic and 4 fewer than Li, so:
y = x - 3 or y + 3 = x
y = z - 4 or y + 4 = z
So, we can replace x and z on the first equation and solve for y as:
(y + 3) + y + (y + 4) = 52
y + 3 + y + y + 4 = 52
3y + 7 = 52
3y + 7 - 7 = 52 - 7
3y = 45
3y/3 = 45/3
y = 15
Then, replacing y by 15, we can calculate the value of x and z as:
x = y + 3
x = 15 + 3
x = 18
z = y + 4
z = 15 + 4
z = 19
Therefore, Li worked for 19 hours.
Hello! I need some help with this homework question, please? The question is posted in the image below. Q21
To find the zeros of the polynomial given, we will first have to find some simpler zeros first then factor the polynomial so we can use the quadratic equation.
Since we can assume this question is to be solved without external tools, it is likely that two of the roots are simple ones.
So, we can try to use the rational root theorem to find these simpler ones.
Since the leading coefficient is 1 and the constant term is -18, if there are rational roots, they can be written as a fraction of a factor of -18 divided by a factor of 1.
The only factor of 1 is 1, so we now that if there are rational roots, they have to have denominator equal to 1.
The factors of 18 are 1, 2, 3, 6, 9 and 18.
Also, we have to consider the possibilities of positive and negative.
It is easier to test the lower ones, so let's start by testing 1/1 and -1/1. For either to be a zero, the polynomial has to result in 0:
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=1 \\ 1^4+1^3+7\cdot1^2+9\cdot1-18=1+1+7+9-18=18-18=0 \end{gathered}[/tex]So, x = 1 is a zero of the polynomial.
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=-1 \\ (-1)^4+(-1)^3+7(-1)^2+9(-1)-18=1-1+7-9-18=-2-18=-20 \end{gathered}[/tex]So, x = -1 is not a zero.
Now, let's try the next factor, 2/1 and -2/1:
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=2 \\ 2^4+2^3+7\cdot2^2+9\cdot2-18=16+8+28+18-18=52 \end{gathered}[/tex]So, x = 2 is not a zero.
[tex]\begin{gathered} x^4+x^3+7x^2+9x-18 \\ x=-2 \\ (-2)^4+(-2)^3+7(-2)^2+9(-2)-18=16-8+28-18-18=8+10-18=0 \end{gathered}[/tex]So, x = -2 is also a zero of the polynomial.
We could continue, by we only need 2 zeros, so this is enough.
Now we know x = 1 and x = -2 are zeros of the polynomial, we can use synthetic division to factor the polynomial:
1 | 1 1 7 9 -18
| 1 2 9 18
| 1 2 9 18 0
Using the last line, we have that the remainder is 0 and the quotient is:
[tex]x^3+2x^2+9x+18[/tex]So, we have that:
[tex]x^4+x^3+7x^2+9x-18=(x-1)(x^3+2x^2+9x+18)[/tex]Now, we can use synthetic division again on the quotient, but now use the other zero, x = -2:
-2 | 1 2 9 18
| -2 0 -18
| 1 0 9 0
Since x = -2 is a zero, we also got a remainder of 0, and the quotient is:
[tex]\begin{gathered} x^2+0x+9 \\ x^2+9 \end{gathered}[/tex]So, we can rewrite the polynomial as:
[tex]x^4+x^3+7x^2+9x-18=(x-1)(x+2)(x^2+9)[/tex]Now, we can just find the zeros of the remainer factor, x² + 9, so:
[tex]\begin{gathered} x^2+9=0 \\ x^2=-9 \\ x=\pm\sqrt[]{-9} \\ x=\pm\sqrt[]{9}\sqrt[]{-1} \\ x=\pm3i \end{gathered}[/tex]This means that the complex zeros of the given polynomial are:
[tex]\begin{gathered} x=1 \\ x=-2 \\ x=3i \\ x=-3i \end{gathered}[/tex]And the factored usinf complex factors is:
[tex]x^4+x^3+7x^2+9x-18=(x-1)(x+2)(x-3i)(x+3i)[/tex]
Please help, due in 3 minutes Skylar still owes $550 oh her cresit card from the previous month. Her annual interest rate is 18%. Approximately how much should the interest charges Be when she gets the bill
Answer:
$8.25
Explanation:
If she gets the bill each month, we need to calculate the monthly interest rate as follows
18%/12 = 1.5%
Because 18% is the annual rate and a year has 12 months.
Then, the interest charge will be 1.5% of the amount, so
$550 x 1.5% = $550 x 1.5 / 100 = $8.25
Therefore, the interest will be $8.25
the question is "Which of the following has a value of 18?"
First Quartile is = 6
Median = 15
Range = 30 - 0
=30
Third Quatile = 24
Please help me on this problem (below the last line is this ( =____ ) couldn’t fit it into the photo)
The slope of a line is calculated with the following formula
[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]From our exercise we have the following 2 points
[tex]\begin{gathered} (1,6)\to(x_1,y_1_{}_{}) \\ (2,3)\to(x_2,y_2) \end{gathered}[/tex][tex]slope=\frac{3_{}-6_{}}{2-1_{}}[/tex][tex]\begin{gathered} slope=\frac{-3_{}}{1_{}} \\ slope=-3_{} \end{gathered}[/tex]Two sprinters, Nick and Ryan, want to find out who has the faster time when compared to each of their teams. Nick has a time of 10.8 seconds, and his team has a mean time of 11.4 seconds and a standard deviation of 0.4 seconds. Ryan has a time of 11.2 seconds, and his team has a mean of 11.5 seconds and a standard deviation of 0.1 seconds. Who has the faster time when compared to each of their teams?a) Nick b) Ryan c) The times are equal when compared to each of their teams.d) There is not enough information
Given data:
The time taken by Nick is 10.8 seconds.
The mean time taken by Nick is 11.4 seconds.
The given standard deviation of Nick is 0.4 seconds.
The time taken by Ryan is 11.2 seconds.
The mean time taken by Ryan is 11.5 seconds.
The given standard deviation of Ryan is 0.1 seconds.
The z-score of Nick is,
[tex]\begin{gathered} z=\frac{10.8-11.4}{0.4} \\ =\text{ -1.5} \end{gathered}[/tex]The z-score of Ryan is,
[tex]\begin{gathered} z=\frac{11.2-11.5}{0.1} \\ =\text{ -3} \end{gathered}[/tex]Thus, Ryan z-score is lower, so Ryan has the faster time when compared to each of their teams, option (b) is correct.
The perimeter of a geometric figure is the sum of the lengths of its sides. If the perimeter of the pentagon to the right (five-sided figure) is 80 meters, find the length of each side.
Answer:
16 m
Step-by-step explanation:
If the perimeter of an equilateral pentagon is 80 m and it has five sides, the length of each side must be 16 m:
[tex]x=\frac{80}{5}[/tex]
[tex]x=16[/tex]
Therefore, if each side is 16 m in length, 2½ sides must equal 40 m:
[tex]2.5x=2.5(16)[/tex]
[tex]2.5x=40[/tex]
Felipe states that he can use the
inequality 1 ≤ x ≤ 4 to describe the domain
{1, 2, 3, 4} for a given function. Explain Felipe's
error.
For the inequality 1 ≤ x ≤ 4 given by Felipe the domain of the function is stated as {1,2,3,4} which shows the error of x belongs to which set of numbers is not specified.
As given in the question,
Given inequality is equal to :
1 ≤ x ≤ 4
Domain of the given inequality function is given by :
x belongs to all real numbers as it is not specified which set of numbers x belongs.
Consider x as set of real numbers
Given domain is {1,2,3,4}
Error is Felipe needs to specify x must belongs to integers or natural numbers then only domain is {1,2,3,4} for the given inequality else there are infinite many numbers between 1 to 4.
Therefore, for the inequality 1 ≤ x ≤ 4 given by Felipe the domain of the function is stated as {1,2,3,4} which shows the error of x belongs to which set of numbers is not specified.
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3. Given the degree and zeros of a polynomial function, identify the missing zero and then find the standard form of the polynomial.
Degree: 3; zero: 9, 8 - i
The missing zero is:
+
i
The expanded polynomial is:
x3 +
x2 +
x +
The equation of the polynomial equation in standard form is P(x) = x³ - 25x²+ 209x - 585
How to determine the polynomial expression in standard form?The given parameters are
Degree = 3
Zero = 9, 8 - i
There are complex numbers in the above zeros
This means that, the other zeros are
Zeros = 8 + i
The equation of the polynomial is then calculated as
P(x) = (x - zero)^multiplicity
So, we have
P(x) = (x - 9) * (x - (8 - i)) * (x - (8 + i))
This gives
P(x) = (x - 9) * (x - 8 + i) * (x - 8 - i)
Evaluate the products
P(x) = (x - 9) * (x² - 8x - ix -8x + 64 + 8i + ix - 8i + 1)
Evaluate the like terms
P(x) = (x - 9) * (x² - 16x + 65)
Express in standard form
P(x) = x³ - 16x² + 65x - 9x² + 144x - 585
Evaluate the like terms
P(x) = x³ - 25x²+ 209x - 585
Hence, the equation is P(x) = x³ - 25x²+ 209x - 585
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N62.1 2 3 4 5The box plot displays the data on the response times of 100 mice to seeing a flash of light. Howmany mice are represented by the rectangle between 0.5 and 1 second?0.20.30.411.11.20.5 0.6 0.7 0.8 0.9response time in seconds
The box plot shows all four quartiles of the data set. Each quartile represents 25 percent of the observed data.
Note that the rectangle between 0.5 and 1 second represents the 2nd and 3rd quartiles. That means, the 2nd 25 percent and the tird 25 percent of the mice population in this experiment.
Therefore, the rectangle represents 50 percent of 100 mice, that is 50 mice.
John needs 6 cups of ice cream to make 4 servings of milkshake how many servings can John make using 30 cups of ice cream
To find how many servings John can make we need to write as a relationship, this means that
[tex]\begin{gathered} 6c\Rightarrow4s \\ 30c\Rightarrow? \end{gathered}[/tex]to find the missing value we need to solve the relationship
[tex]\begin{gathered} ?=30c\cdot\frac{4s}{6c} \\ ?=5\cdot4s \\ ?=20s \end{gathered}[/tex]he can make 20 servings with 30 cups of ice cream
Find the area of triangle ABC.A = 37.2°, b = 10.1 in., c = 6.2 in.A. 19 in²B. 20 in²C. 17 in²D. 18 in²
Given:
A = 37.2°
b = 10.1 in
c = 6.2 in
Let's find the area of the traingle.
To find the area, apply the formula below:
[tex]\text{Area}=\frac{1}{2}\ast b\ast c\ast\sin A[/tex]Hence, we have:
[tex]Area=\frac{1}{2}\ast10.1\ast6.2\ast\sin 37.2[/tex]Solving further:
[tex]\begin{gathered} \text{Area}=\frac{1}{2}\ast10.1\ast6.2\ast0.605 \\ \\ \text{Area}=18.9\text{ }\approx19in^2 \end{gathered}[/tex]Therefore, the area of triangle ABC is 19 square inches
ANSWER:
A. 19 in²
Given ABC below, with m C = 115°, a = 6, and b = 8, find the area of the triangle. Round your answer to the nearest tenth and do not include units in your answer.
ANSWER
Area = 21.8
EXPLANATION
Looking at the given triangle closely, you will notice it's a Non-Right Triangle.
Now, to find the area of Non-Right Triangle, we make use of the formula below:
[tex]\text{Area = }\frac{1}{2}ab\text{ sin C}[/tex]From the question,
what is the 13 term of the sequence 2,6,18,54
Notice that:
[tex]\begin{gathered} 2=2\times3^0, \\ 6=2\times3^1, \\ 18=2\times3^2, \\ 54=2\times3^3. \end{gathered}[/tex]Therefore, the rule to compute the nth term of the sequence is:
[tex]a_n=2\times3^{n-1}.[/tex]Substituting n=13 in the above equation we get:
[tex]a_{13}=2\times3^{13-1}=2\times3^{12}=1062882.[/tex]Answer: 1062882.
3.8 decimals in words
The given figure is 3.8
3 is a whole number
The position of 8 is called the tenths position
Thus, in words, the decimal is
three and eight tenths
confused on perimeter
The area will be, the area of the small square plus the area of the parallelogram plus the area of the rectangle.
The area of the square:
[tex]As=l\cdot l=2\cdot2=4in^2[/tex]The area of the parallelogram:
[tex]Ap=B\cdot H=5\cdot3=15in^2[/tex]The area of the rectangle:
[tex]Ar=l\cdot w=5\cdot2=10in^2[/tex]Therefore:
[tex]\begin{gathered} A=As+Ap+Ar \\ A=4in^2+15in^2+10in^2 \\ A=29in^2 \end{gathered}[/tex]QUESTION Calculate the cardinal number of the set Q containing all digits that make up the number = 2,309,585,628.
The cardinal number of a set can be said to be the number of distinct elements in a finite set.
Here, we have the number: 2,309,585,628.
We have the following elements:
2
3
0
9
5
8
6
Some elements occured twice here, no element is to be counted twice.
Thus,
Set Q = {2, 3, 0, 9, 5, 8, 5, 6, 2, 8}
The set Q has 7 elements
The cardinal number of set Q is 7
ANSWER:
n(Q) = 7
What is the solution to the inequality -4x < 8?x < -2x > -2x < -24x > -24
To find:
The solution of the given inequality -4x < 8.
Solution:
Given inequality is -4x < 8. Divide both sides by -4 to isolate x.
If we divide an inequality by a negative number, then the sign of inequality changes to its opposite. So, on dividing the inequality by -4,we get:
[tex]\begin{gathered} -4x<8 \\ \frac{-4x}{-4}<\frac{8}{-4} \\ x>-2 \end{gathered}[/tex]Thus, the answer is x > -2.
I don’t know wether it is a independent or dependent variable.
To determine whether they are dependent or independent events:
1. According to the problem, Event 1 is a selection of a tile J out of 26 and the Event 2 is a selection of v in the remaining 25 tiles.
Event 1 affects event 2.
So, these are dependent events.
2. Similar to the first question, event 1 affects event 2. Because event 2 is depending on the first event.
So, these are dependent events.
3. According to the problem, event 1 does not affect event 2.
So, these are independent events.
4. According to the problem, she selects one trading card and then she returns the card back. After this, she selects the other card. So, event 1 does not affect event 2.
So, these are independent events.
5. Similarly to the fourth question, event 1 does not affect event 2 because of the dropped back of balls.
So, these are independent events.
-7(w— 4) + Зw – 27Simplify it help ASAP
-7(w - 4) + 3w - 27
Expand
-7w + 28 + 3w - 27
Simplify like terms
-7w + 3w + 28 - 27
Result
-4w + 1
A company that owed $2,000 paid early and got a $40 discount. What fraction of the amount owed was the discount? (Express As Fraction)
In order to find the fraction of the amount that the discount represents, we just need to divide the discount amount by the total value:
[tex]\frac{40}{2000}[/tex]Now, to simplify this fraction, we can divide the numerator and denominator by 40:
[tex]\frac{40}{2000}=\frac{40\colon40}{2000\colon40}=\frac{1}{50}[/tex]So the discount is 1/50 of the value paid.
Given g(x) =9x^2-18x+11, for what value (s) is g(x) =23
The values of x for which g(x) = 23 are x = 2.53 and x = -0.53
Determining the values of x for which g(x) = 23From the question, we are to determine the value(s) for which g(x) = 23
From the given information,
The function is
g(x) = 9x² - 18x + 11
Now, we will substitute g(x) = 23
That is,
23 = 9x² - 18x + 11
Rearranging
9x² - 18x + 11 - 23 = 0
9x² - 18x - 12 = 0
Divide through by 3
3x² - 6x - 4 = 0
Now, solve the quadratic equation
3x² - 6x - 4 = 0
Using the general formula,
x = [-b±√(b²-4ac)]/2a
a = 3, b = -6, c = -4
x = [-(-6)±√((-6)²-4(3)(-4))]/2(3)
x = [6±√(36 + 48)]/6
x = [6±√(84)]/6
x = [6 ± 9.17]/6
x = [6 + 9.17]/6 OR x = [6 - 9.17]/6
x = 15.17/6 OR x = -3.17/6
x = 2.53 OR x = -0.53
Hence, the values of x are x = 2.53 and x = -0.53
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rhombus STUV is located at S(-5, 4), T (-1, 5), U(-2, 1), and V(-6, 0). If STUV is translated along the rule (x, y) (x + 7 , y - 8). in which quadrant will the new rhombus be located
rhombus STUV is located at S(-5, 4), T (-1, 5), U(-2, 1), and V(-6, 0). If STUV is translated along the rule (x, y) (x + 7 , y - 8). in which quadrant will the new rhombus be located
we have that
the rule of the translation is
7 units at right and 8 units down
Verify each ordered pair
S(-5,4) -------> S'(-5+7,4-8) ------> S'(2,-4) (IV quadrant)
T(-1,5) ------> T'(-1+7,5-8) -----> T'(6,-3) (IV quadrant)
U(-2,1) -----> U'(5,-7) (IV quadrant)
V(-6,0) ----> V'(1,-8) (IV quadrant)
therefore
answer is (IV quadrant)Consider the equation and the following ordered pairs: (4, y) and (x, 1).y = 2x-5Step 2 of 2: Plot the resulting set of ordered pairs using your answers from Step 1.(the ordered pairs from the last problem are (4,3) (3,1))
In order to plot an ordered pair into the cartesian plane, we need to use the first coordinate in the x-axis and the second coordinate in the y-axis.
Then, we draw the point that has these coordinates in the plane.
For example, plotting the point (2, 3), we have:
Now, plotting the points (4, 3) and (3, 1) in the plane, we have:
are two figures congruent if they have the same size and shape true or false
From congruence triangles, it is possible to see ED is congruent to DS because they are in the same line.
Answer: DS
Which angle forms a linear pair with
A linear pair angle must add up to 180 degrees. The angle that form a linear pair with angle MON is expressed below
[tex]\begin{gathered} \angle MON+\angle QOM=180\text{ degre}es \\ \text{therefore} \\ \angle MON\text{ and }\angle QOM\text{ are linear pair} \end{gathered}[/tex]Label each situation with either a POSITIVE slope or a NEGATIVE slope :1) Earnings money each week =2) Withdraw money each month =3) Depositing your paycheck =4) A plane landing =5) The number of students is decreasing each year =6) A plane taking off =
Given in the question:
1) Earnings money each week = Earning is an addition to one's money, thus, we can say that this situation is a POSITIVE Slope.
2) Withdraw money each month = Widthrawing is a deduction to one's money, thus, we can say that this is a NEGATIVE Slope.
3) Depositing your paycheck = Depositing is adding money to your account, thus, we can say that this situation is a POSITIVE Slope.
4) A plane landing = A plane landing has its speed slowly decreasing until its speed gone to zero, thus, we can say NEGATIVE Slope.
5) The number of students is decreasing each year = A decreasing number of students is a deduction to the population of students, thus, we can say that this is a NEGATIVE Slope.
6) A plane taking off = A plane taking off has its speed accelerating, thus, we can say that this situation is a POSITIVE Slope.
72.200-2.803 rounded to the nearest whole number. It would be 69.397 But I need help rounding the answer..
Given the expression:
72.200 - 2.803
Let's perform the subtraction.
To perform the subtraction, we have:
Solving further:
Therefore, the answer is:
69.397
To round the answer to the nearest whole number, check if the number after the decimal is less than 5.
If the number is less then 5, then we are to write the answer without the decimal.
If the number is greater or equal to 5, we are to add 1 to the whole number and write without the decimal.
Here, the number after the decimal is 3 which is less than 5.
Therefore, the answer rounded to the nearest whole number is 69.
ANSWER:
69