The polynomial with zeros of −3, −1, and 2, and passes through the point (3,11) is:
P(x) = (11/24)*(x + 3)*(x + 1)*(x - 2)
How to get the polynomial?We know that the zeros are −3, −1, and 2, so if we define the leading coefficient as A, the polynomial can be written as:
p(x) = A*(x + 3)*(x + 1)*(x - 2)
Now we want this to pass through the point (3, 11), then we get:
p(3) = 11 = A*(3 + 3)*(3 + 1)*(3 - 2)
11 = A*6*4*1
11 = A*24
11/24 = A
Then the polynomial is:
P(x) = (11/24)*(3 + 3)*(3 + 1)*(3 - 2)
Learn more about polynomials:
https://brainly.com/question/4142886
#SPJ1
What is the simple interest rate on an account that earned $56.25 in interest after two and one-half years on a principal balance of $300? please show work
The rate of interest on the given principal is 7.5%.
Given that, simple interest = $56.25, principal = $300 and time period = [tex]2\frac{1}{2}[/tex] years.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Now, 56.26 = (300 × R × 2.5)/100
⇒ 5625 = 750R
⇒ R = 7.5%
Therefore, the rate of interest on the given principal is 7.5%.
To learn more about the simple interest visit:
https://brainly.com/question/25845758.
#SPJ1
Divide. Enter the correct answer.
17+2=
a builder appoints three construction workers akash, sunil and rakesh on one of his sites. they take 20, 30 and 60 days respectively to do a piece of work. how many days will it take akash to complete the entire work if he is assisted by sunil and rakesh every third day?
It will take 15 days for Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day.
To determine the number of days, we first represent the number of days to do a piece of work by each one of them in fractions as follows;
Fraction of work completed by Akash in 1 day = 1/20
Fraction of work completed by Sunil in 1 day = 1/30
Fraction of work completed by Rakesh in 1 day = 1/60
The total work done in 1 day can be given as;
Total work done by the three in one day = [(1/20) + (1/30) + (1/60)] = 1/10
Work done by Akash in two days = 2 × (1/20) = 2/20 = 1/10
The work done in three days (1 day of all three together + Work done by Akash in two days) = (1/10) + (1/10) = 1/5
Therefore; the total work done in 3 days = 1/5
At this rate, the total number of cycles required to finish the work =
(1) ÷ (1/5) = 5
Since each cycle has three days, the total number of days required to finish the work can be calculated as follows;
5 × 3 = 15 days
To learn more about fractions; click here:
https://brainly.com/question/17220365
#SPJ4
893 is 94% of what amount
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The two equations that are true when x = -2 and x = 2 are x^2 - 4 = 0 and 4x^2 = 16.
We have given x = 2 and x = -2
Substitute the values in the given equations
Equation 1
x^2 - 4 = 0
Substitute x = 2 in LHS, we get
2^2-4 = 4 - 4 = 0 = RHS
Substitute x = -2 in LHS, we get
(-2)^2-4 = 4 - 4 = 0 = RHS
Equation 2
x^2 = -4
Substitute x = 2 in LHS, we get
2^2 = 4 ≠ RHS
Substitute x = -2 in LHS, we get
(-2)^2 = 4 ≠ RHS
Equation 3
3x^2 + 12 = 0
Substitute x = 2 in LHS, we get
3(2)^2 + 12 = 12 + 12 = 24 ≠ RHS
Substitute x = -2 in LHS, we get
3(-2)^2 + 12 = 12 + 12 = 24 ≠ RHS
Equation 4
4x^2 = 16
Substitute x = 2 in LHS, we get
4(2)^2 = 4(4) = 16 = RHS
Substitute x = -2 in LHS, we get
4(-2)^2 = 4(4) = 16 = RHS
Equation 5
2(x-2)2 = 0
Substitute x = 2 in LHS, we get
2(2-2)2 = 2(0)(2) = 0 = RHS
Substitute x = -2 in LHS, we get
2(-2-2)2 = 2(-4)(2) = 16
Hence, we find that Equation 1 and Equation 2 are true for x = 2 and x = -2
To learn more about equation here
https://brainly.com/question/15707224
#SPJ1
Fun times Amusement Park Charges a $7 admission fee plus $1.75 per ride. What is the equation, in intercept form for calculating the total cost, C, of going to the park and riding r rides?1. C = 1.75 + 7r2. C = 1.75r3. C = 7r4. C = 7 + 1.75r
The general form of an equation in intercetp form is:
[tex]y=mx+b[/tex]Where m is the change of y in function of x and b is the value of b when x is 0
In this situation you have:
y=C
x=r
m= 1.75 ( C increase 1.75 each r)
b= 7 (When there is not ride r=0 the admission fee is 7)
Then, you have the equation:[tex]C=1.75r+7[/tex]or C = 7 + 1.75rWhich graph represents data used in a linear regression that produces a correlation coefficient closest to -1?
What does the letter "L" stand for in the simulation?
Answer: d
Step-by-step explanation: ion know man but i looked it up and got it right
Write a linear equation to represent the given problem and then solve the problem.
The perimeter of a rectangle is 150 cm. The length is 15 cm greater than the width. Find the dimensions.
Perimeter = 2 x Length + 2 x Width
w=L+15
p=(L+w)
150cm=L+L+15
150cm=2L+15
2L=150cm-15
2L=135cm
2L÷2=135cm÷2
L=67.5
w=67.5+15
w=82.5
An exterior angle of a rectangle polygon cannot have the measure
The sum of the measures of an exterior angle of a polygon is 360°.
If the given angle divides 360 evenly, then it can be a measure of an exterior angle of a polygon. If otherwise, then it cannot be.
[tex]\begin{gathered} 360\div30=12 \\ 360\div50=7.2 \\ 360\div120=3 \\ 360\div90=4 \\ 360\div40=9 \end{gathered}[/tex]Out of the given angles, only 50 does not divide 360 evenly. Therefore, a regular polygon cannot have an exterior angle measuring 50°. (Option B)
Given v = 60sinθ, what is the instantaneous voltage when θ = 30⁰?Question 11 options:6034.643051.96
30
Explanations:
Given the expression for the instantaneous voltage expressed as:
[tex]v=60\sin \theta[/tex]Given the following parameter:
θ = 30⁰
Substitute the given parameter into the formula to have:
[tex]\begin{gathered} v=60\sin 30^0 \\ v=60(0.5) \\ v=30 \end{gathered}[/tex]Therefore the instantaneous voltage when θ = 30⁰ is 30.
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.25 and the cost of a large greeting card is $4.50. How much would it cost to get 5 small greeting cards and 4 large greeting cards? How much would it cost to get xx small greeting cards and yy large greeting cards?
The Total cost of x small and y large greeting cards is; 1.25x + 4.50y.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the Cost of the small greeting card = is $1.25 .
The Cost of the large greeting card =$4.50.
We need to determine the Total cost of 5 small and 4 large greeting cards and the total cost of x small and y large greeting cards.
The Cost of 5 small greeting cards = 6.25
The Cost of 4 large greeting cards = 18
Then the Total cost = $6.25+ $18 =$24.25
Therefore, the Total cost of 5 small and 4 large greeting cards is; $24.25.
Now, the total cost of x small and y large greeting cards will be;
Cost of x small greeting cards = 1.25x
Cost of y large greeting cards = 4.50y
Total cost = 1.25x + 4.50y
Therefore, the Total cost of x small and y large greeting cards is; 1.25x + 4.50y.
To learn more about cost visit:
brainly.com/question/15135554
#SPJ1
Mason went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 45 grams of sugar and each bottle of juice has 15 grams of sugar. Mason purchased a total of 11 bottles of juice and soda which collectively contain 285 grams of sugar. Write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. Define the variables that you use to write the system
The number of soda bottles = 4
The number of sugar bottles = 7
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Weight of each bottle of soda = 45 grams
Weight of each bottle of sugar = 15 grams
Total weight of sugar and soda = 285 grams
Let the number of soda bottle = x
And, The number of sugar bottle = y
Since, Total number of bottles = 11
So, We can formulate;
⇒ x + y = 11 .... (i)
And, Weight of each bottle of soda = 45 grams
Weight of each bottle of sugar = 15 grams
Total weight of sugar and soda = 285 grams
So, We can formulate;
⇒ 45x + 15y = 285 ... (ii)
Multiply by 15 in equation (i) and subtract from (ii), we get;
⇒ 45x + 15y - 15x - 15y = 285 - 165
⇒ 30x = 120
Divide by 30;
⇒ x = 4
Hence, x + y = 11
4 + y = 11
y = 11 - 4
y = 7
So, The number of soda bottles = 4
The number of sugar bottles = 7.
Learn more about the linear expression visit:
https://brainly.com/question/4074386
#SPJ1
For a particular rectangle, twice the width is 4 meters shorter than the length. The area of the rectangle is 126 square meters. What is the perimeter of the rectangle? ? meters
Let l be the length of the rectangle and w its width.
Then its area is given by:
a = l*w
Its perimeter is given by:
p = 2l + 2w
We also know that, for this specific triangle, we have:
2w = l - 4
l = 2w + 4
a = 126 m²
Applying this result in the area formula, we have:
w*l = 126
w(2w + 4) = 126
2w² +4w = 126
2w + 4w - 126 = 0
Therefore, w = 7 m and l = 2*7 + 4 = 10 m
Then, the perimeter is given by:
p = 2*18 + 2*7 = 36 + 14 = 50 m
Find the slope of the line.
slope =
11
rise
run
5
11
40
30
20
10
O
2
4
6
8
G
G
to get the slope of any straight line, we simply need two points off of it, let's use the ones from the picture below.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies \cfrac{ 20 }{ 5 } \implies \text{\LARGE 4}[/tex]
Using the information found in these tables which of the following statements is true
Please helpppp
why is sampling with replacement used? to ensure that the sample size is as small as possible to ensure that individuals cannot be selected twice to ensure that the proportions of subgroups in the sample are exactly the same as their proportions in the population to ensure that the probability of selecting any specific individual stays constant
To determine probability with replacement, It uses sampling with replacement. In other words, you want to determine the likelihood of an event in which you choose a ball, card, or other object from a set of options and then swap it out after each choice.
Example:
Consider a scenario in which you wished to sample two people from a population of seven.
Those people are:
John, Jack ,Qiu, Tina, Hatty, Jacques, Des
Their names could be placed in a hat. If you sample with replacement, you would pick one name, put it back in the hat, and then pick a different name. Your two-name sample has the following potential outcomes:
John, John
John, Jack
John, Qui
Jack, Qui
Jack Tina
…and so on.
The two products you sample with replacement are independent. In other words, the outcome of one has no bearing on the other. The odds of picking the first name are 1/7, and the odds of picking the second name are 1/7.
P(John, John) = (1/7) * (1/7) = .02.
P(John, Jack) = (1/7) * (1/7) = .02.
P(John, Qui) = (1/7) * (1/7) = .02.
P(Jack, Qui) = (1/7) * (1/7) = .02.
P(Jack Tina) = (1/7) * (1/7) = .02.
To learn more about probability click here:
brainly.com/question/14210034
#SPJ4
HELP! WILL GIVE BRAINLIEST
Answer:
second answer
Step-by-step explanation:
what is the distance between the two points in simplest radical form
(−2,−7) and (5,0)
The distance between the two points in simplest radical form(−2,−7) and (5,0) is 9.8995
What is the distance?Distance can be described as the differences that exist between two points and this can be expressed i different form such as the radical form.
We can calculate the distance between the two points by firstly expressed them as :
(−2) - (5) = -7
(-7) - 0 = -7
Then the distance between them can be found as :
Distance = (-7)^2 + (-7)^2 = 49 +49 = 98
Then we will find the square root of the the figure as
= [tex]\sqrt{98}[/tex] = 9.8995
The formula can as well be used to find this by substituting the values of x and y into the formula as :
x1=-2
y1=-7
x2=5
y2=0
[tex]d = \sqrt{ ( x_{2} - x_{1} )^{2} + ( y_{2} - y_{1} )^{2}}[/tex]
then [tex]d = \sqrt{ ( 5 - (-2 )^{2} + ( 0 - (-7) )^{2}}[/tex]
= [tex]\sqrt{ 49^{2} + 49^{2} }[/tex]
= [tex]\sqrt{98}[/tex]
=9.8995
Read more about distance at:
https://brainly.com/question/20694000
#SPJ1
find the value of x in each case
Answer:
x=23
Step-by-step explanation:
The amount of degrees in a triangle is 180 degrees.
line AC and line DF are straight angles meaning that the opposite angles are equal to each other. That means that angle FBC is also equal to x. Because line AC and EF are parallel we know that FBC and BFE are equal. Therefore, BFE is equal to x. The sum of the values of each angle of the triangle should add up to 180. 5x+65=180
5x=115
x=23
Marques works in a department store selling clothing. He makes a guaranteed salary of $200 per week, but is paid a commision on top of his base salary equal to 10% of his total sales for the week. How much would Marques make in a week in which he made $750 in sales? How much would Marques make in a week if he made x dollars in sales?
The most appropriate choice for percentage will be given by -
Total salary of Marques in a week = $825
If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{x}{10}[/tex])
What is Percentage?
Suppose there is a number and that number has to be expressed as a fraction of 100. The fraction is called percentage. For example 2% means [tex]\frac{2}{100}[/tex]
Here,
Guarantee salary of Marques = $200
Sales made by Marques in a week= $750
Percentage commission on total sales = 10 %
Commission received by Marques = [tex]\frac{10}{100} \times 750\\[/tex]
= $75
Total salary of Marques in a week = $(750 + 75)
= $825
If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{10}{100}\times x[/tex])
= $([tex]750[/tex] + [tex]\frac{x}{10}[/tex])
To learn more about percentage, refer to the link -
https://brainly.com/question/24304697
#SPJ9
just tell me the slope of the line and where to plot the segments on the graph
Answer:
The slope is 2
Step-by-step explanation:
Take any two points on the line. I am going to use the points (0,-8) and (4,0) Points are in the form (x,y) The y values form the two points is 0 and -8. The x values are 4 and 0.
The slope is the change in y over the change in x.
[tex]\frac{0- -8}{4-0}[/tex] = [tex]\frac{8}{4}[/tex] = 2
Orlando is getting balloons for his grandmother's birthday party. he wants each balloon string to be 6 feet long. at the party store, string is sold by the yard. if orlando wants to get 72 balloons, how many yards of string will he need?
144 yards of string will need to use balloons for the party.
Given,
The length of balloon string Orlando wanted = 6 feet
Number of balloons = 72
We have to find the total length of strings wanted for 72 balloons in yards.
1 yard = 3 feet
Now,
Total length of strings Orlando needs = length of one string x number of balloons = 6 x 72 = 432 feet
Now convert 432 feet into yard
That is,
432 / 3 = 144 yards
So,
144 yards of string will need to use balloons for the party.
Learn more about length of string here;
https://brainly.com/question/19297704
#SPJ1
5x^2-25=100 solve by taking square root
Answer:
x=5,−5
Step-by-step explanation:
Which of the following rational functions is graphed below?
Jacob set aside (budgeted) $10 to spend on snacks at the movies. Sodas cost $1.50 each, and a box of popcorn costs $1.75. How many sodas can he buy for him and his friends if he buys 2 boxes of popcorn? Write an Inequality.
Answer:4 sodas
Step-by-step explanation:
1.75 x 2 = 3.5
10- 3.5 = 6.5
6.5 Divided by 1.50 = 4.33333333
(Round that to 4 and he will be left with cents)
x/5 > 8 solve the inequality for x and simplify your answer as much as possible
Answer:
x = 40
Step-by-step explanation:
x = 8 x 5
x = 40
that's it
A model car is a 1/40 if the length of the real car is 5.5 m what is the length of the model car
Answer:
0.14 meters, or 140 mm
Step-by-step explanation:
(1/40) means that the model car will have dimensions that are (1/40) the original car.
Real car = 5.5 meters.
Model car = (1/40)*(5.5 m) = 0.14 meters, or 140 mm
Find the sum of the following infinite series.1/3−2/21+4/147−8/1029+···
Given:
The series is 1/3−2/21+4/147−8/1029+··
Explanation:
For the given series, the first term is,
[tex]a=\frac{1}{3}[/tex]The common ratio is,
[tex]\begin{gathered} r=\frac{-\frac{2}{21}}{\frac{1}{3}} \\ =-\frac{2}{21}\cdot\frac{3}{1} \\ =-\frac{2}{7} \end{gathered}[/tex]The formula for the sum of infinite series is,
[tex]S_{\infty}=\frac{a}{1-r}[/tex]Substitute the values in the formula to determine the sum of infinite series.
[tex]\begin{gathered} S_{\infty}=\frac{\frac{1}{3}}{1-(-\frac{2}{7})} \\ =\frac{\frac{1}{3}}{\frac{9}{7}} \\ =\frac{1}{3}\times\frac{7}{9} \\ =\frac{7}{27} \end{gathered}[/tex]Answer: 7/27
a company buys equal numbers of two different card forms. it utilizes 4/5 of one kind and 6/7 of the other. what fraction of the total number is unused?
12/35 fraction of the total number is unused from two different cards.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Assuming the total first kind of card form is 1 and the total second kind of card form is also one.
Given, a company buys equal numbers of two different card forms. it utilizes 4/5 of one kind and 6/7 of the other.
∴ The total unused card form is,
= (1 + 1) - (4/5 + 6/7).
= 2 - (28 + 30)/35.
= 2 - 58/35.
= (70 - 58)/35.
= 12/35.
learn more about fractions here :
https://brainly.com/question/10354322
#SPJ1
Given f(x)=2x-5, describe how the graph of g compares with the graph of f.
g(x)=2(0.2x)-5
The graph of g and f have equal intercepts while the slope of the graph of f is 5 times larger than the slope of the graph of g
How to compare the graph of g with the graph of fGiven: f(x) = 2x-5 and g(x)=2(0.2x)-5
To compare the two graphs, we can make use of the equation of a line:
The general form of the equation of a line is y = mx + c
Where m is the slope and c is the intercept
So we will compare two the functions with the equation of a line:
Comparing f(x) = (2x-5) with y = mx + c
The slope(m) of the line = 2 and the intercept(c) = -5
Also, comparing g(x) = 2(0.2x)-5 with y = mx + c
The slope(m) of the line = 2(0.2) = 0.4 and the intercept(c) = -5
Since the slope of f(x) = 2 and the slope of g(x) = 0.4. Thus:
slope of f(x) / slope of g(x) = 2/0.4 = 5
So we can say the slope of f(x) is 5 times the slope of g(x)
Therefore, the graph of g and f have the same intercept. But the slope of f(x) is 5 times the slope of g(x)
Learn more about equation of a line on:
brainly.com/question/28722124
#SPJ1
