The expression for the simplified polynomial would be - x² - 10x - 24.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the polynomial ( x + 5 )² is subtracted from 1. The simplified polynomial can be written as:-
Polynomial = 1 - ( x + 5 )²
Polynomial = 1 - ( x² + 10x + 25 )
Polynomial = 1 - x² - 10x - 25
Polynomial = -x² - 10x - 24
Hence, the polynomial can be written as -x² - 10x - 24.
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For what positive integers $c$, with $c < 100$, does the following quadratic have rational roots?
\[ 3x^2 + 20x + c \]
If you find more than one, then list the values separated by commas.
Answer: A quadratic of the form $ax^2 + bx + c$ has rational roots if and only if its discriminant, $b^2 - 4ac$, is a perfect square. In this case, the discriminant is $(20)^2 - 4(3)(c) = 400 - 12c$. So, we need to find the positive integers $c < 100$ that make $12c$ a perfect square.
The perfect squares that are less than $100$ are $1,4,9,16,25,36,49,64,81$, so the possible values for $c$ are $33,44,55,66,77,88$.
So, the positive integers $c$, with $c < 100$, that make the quadratic have rational roots are $33,44,55,66,77,88$
Step-by-step explanation:
Hame:
Date:
Per.
3. The distance between Venice and Florence is 171 miles. It takes 2% hours
to travel from Venice to Florence by train. Write an equation that
represents the distance travelled, d, and the time, t.
The equation that relates velocity, distance and time is given as follows:
v = 171/2.
How to obtain the equation?The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:
v = d/t.
In which:
v is the velocity.d is the distance.t is the time.The parameters for this problem are given as follows:
d = 171, t = 2.
Hence the equation that gives the velocity in miles per hour is of:
v = 171/2.
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Evaluate. Write your answer as a fraction in simplest form.
Answer: 16/81
Step-by-step explanation:
To do this you have to do 2^4 which is 16.
Next, you have to do 3^4 which is 81
This gives you 16/81.
Now check if you can simplify it.
You can't so this is your answer :D
I hope this was able to help you :D
Answer and Explain PLease
A figure has rotational symmetry when it can be rotated by an angle measure which is greater than 0º and less than 360º and the rotated image is equals to the original figure, that is, the image is equals to the pre-image.
The square has four sides, hence:
360/4 = 90º.
The other figure has three sides, which are similar, hence:
360/3 = 120º.
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Find the area of the following composite figure.
Is this correct?
Step-by-step explanation:
the sum of the area of the inner rectangle and the area of the 2 outer half-circles (that together are the area of one full circle).
the radius of the circles is 10 ft.
so, the diameter (= the width of the inner rectangle) = 2×10 = 20 ft.
so, the area of the inner rectangle is
30×20 = 600 ft²
the area of the combined full circle is
pi×r² = pi×10² = 100pi = 314.1592654... ft²
together that is
914.1592654... ft²
find examples that contradict the conclusions of proposition 2.4.10 if a and b are not coprime (i.e. share a factor greater than ).
The conclusion of the proportion is if a and bare not coprime, when it share a factor greater than 1
Here we have given that if and are not coprime that is share a factor greater than.
And we need to find the examples that contradict the conclusions of proposition.
While we looking into the given question, we have identified that if and are not coprime.
In order to find the conclusion to this one, we must know the definition of co prime.
The term co prime is referred as those umbers that do not have any common factor other than 1.
As per the definition, we have clearly know that if the two number has the factor greater than one then it will not a co prime to each other.
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Insurance cost is to be distributed among manufacturing, selling and administration in the ratio of 1/10 to 1/3 to 1/9. If the total cost was $12,005 how should it be distributed to these departments
Manufacturing should pay $2206.80, Selling should pay $7356.0and Administration should pay $2452.00
What is the distribution?Generally, To find out how much each department should pay, you can use the proportion of the cost that corresponds to their respective ratio.
First, calculate the total ratio by adding the three ratios together:
1/10 + 1/3 + 1/9 = 0.544
Then, divide the total cost by the total ratio to find the unit cost:
$12,005 / 0.544 = $22068.01
Next, multiply the unit cost by the ratio for each department to find out how much they should pay:
Manufacturing: $22068.01 x 1/10 = $2206.80
Selling: $22068.01 x 1/3 = $7356.0
Administration: $22068.01 x 1/9 = $2452.00
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Which verbal expression best represents the equation 2(n - 7) = -14
a) twice a number less than seven is equal to negative fourteen
b) the product of two and seven less than a number is equal to negative fourteen
c) seven less than twice a number is equal to negative fourteen
d) negative seven minus twice a number is negative fourteen
The verbal expression that best represents the equation 2(n - 7) = -14 is: c) seven less than twice a number is equal to negative fourteen.
What is verbal expression?Verbal expression can be defined as the way of writing mathematical expression into words or translating equation into words.
Now let interpret this equation 2(n - 7) = -14 into verbal expression.
n = a number
2n = twice a number
2n - 7 = seven less than twice a number
-14 = negative fourteen
Therefore we can conclude that the correct option is C.
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Find the area of the figure.
Answer: 38
Step-by-step explanation:
You can split this shape into 2 rectangles. The area of the two rectangles = 5 * 4 + 6 * 3
= 20 + 18
= 38
Quincy and Celine have to move 16 small boxes and 10 large boxes. the chart indicates the time that each person takes to move each type of box. they start moving the boxes at 9.00 a.m. the earliest time at which they can be finished moving all of the boxes is:
a. 9:41 a.m
b. 9:42 a.m
c. 9:43 a.m
d. 9:44 a.m
e. 9:45 a.m
The earliest time at which they can be finished moving all of the boxes is: d. 9:44 a.m
Quincy and Celine the earliest timeTo determine the earliest time at which Quincy and Celine can finish moving all of the boxes, we need to determine the maximum amount of time it will take for them to move all of the boxes. We can do this by calculating the time it will take for each person to move each type of box individually, and then adding those times together.
Quincy takes 1 minute to move a small box and 2 minutes to move a large box. Celine takes 2 minutes to move a small box and 3 minutes to move a large box.
So, for Quincy:Time to move 16 small boxes: 16 boxes * 1 minute/box = 16 minutes
Time to move 10 large boxes: 10 boxes * 2 minutes/box = 20 minutes
Total time for Quincy: 16 minutes + 20 minutes = 36 minutes
For Celine:Time to move 16 small boxes: 16 boxes * 2 minutes/box = 32 minutes
Time to move 10 large boxes: 10 boxes * 3 minutes/box = 30 minutes
Total time for Celine: 32 minutes + 30 minutes = 62 minutes
To get the earliest time they can finish moving all the boxes, we take the maximum of the two times:
Max(36 minutes, 62 minutes) = 62 minutes
Start time: 9:00 a.m.
End time: 9:00 a.m. + 62 minutes = 9:62 a.m.
So the earliest time they can finish moving all the boxes is 9:62 a.m.
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Adding and subtracting fractions
1 These diagrams show the distances four cyclists have cycled.
Write a calculation of the total distance each cyclist cycled.
a -
7/8 km
9/10 km
3/2km
Total distance travelled by the cyclist is 131/40 km in fraction.
What is fraction ?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.
Total distance travelled by the cyclist is 7/8 + 9/10 + 3/2 = 131/40 km
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please show solution thank you<3
It would take Jack $4$ hours to mow the lawn if he works alone. Fortunately, after he mows for $2$ hours, Jill joins him. They finish mowing $90$ minutes later. How many minutes would it have taken for Jill to mow the entire lawn alone?
Answer: 720
Step-by-step explanation:
If you do a report on the age, occupation, and zip codes of all breast cancer patients the hospital saw last year, are you using a sample
or population?
Answer: If you are reporting on the age, occupation, and zip codes of all breast cancer patients the hospital saw last year, you are using a population.
A population is a complete set of all the individuals or elements that share a common characteristic, such as all breast cancer patients seen at a hospital in a given year. A sample, on the other hand, is a subset of a population that is selected for analysis or study.
In this case, since you are reporting on all breast cancer patients seen at the hospital last year, you are using the entire population of breast cancer patients, rather than just a sample of them.
Step-by-step explanation:
i need help me alot plss
help pls i need the answer and fast !!!
Answer: The slope of the line is 2/3.
The line is not solid, it is dashed.
The area below the line is shaded.
A solution to the inequality is (2,3).
The x-intercept of the boundary line is (-3/2,0)
All the statements except the first one are true about the graph of y< 2/3 x +1.
Step-by-step explanation:
If 4 -letter "words" are formed using the letters A, B, C, D, E, F, G, how many such words are possible for each of the following conditions: (a) No condition is imposed. Your answer is : (b) No letter can be repeated in a word. Your answer is : (c) Each word must begin with the letter A and letters can be repeated. Your answer is : (d) The letter C must be at the end and letters can be repeated. Your answer is : (e) The second letter must be a vowel and letters can be repeated. Your answer is :
In this case, there are 8 letters, so the total number of 4-letter words possible is 8^4 = 4096.
(b) In this case, each letter can be used only once, so we must choose 4 different letters out of 8 letters. This can be done using the combination formula C(8,4) = 70.
(c) Since each word must begin with the letter A, the remaining 3 letters must be chosen from the remaining 7 letters. This can be done using the combination formula C(7,3) = 35.
(d) The letter C must be at the end, so the first 3 letters must be chosen from the remaining 7 letters. This can be done using the combination formula C(7,3) = 35.
(e) The second letter must be a vowel, so the first letter can be chosen out of 4 letters (A, E, I, O). The remaining 3 letters can be chosen out of 7 letters. This can be done using the combination formula C(4,1) x C(7,3) = 140.
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Having alot of trouble figuring this out! 100pts to anyone that can help!
Please help
Fill in each answer box so that the resulting statement is true
View image
Zachary measures the area of a glacier at
the start of every year.
2
At the start of this year, the glacier had an
area of exactly 56.20 km². This is 0.2%
less than it was at the start of last year.
Work out what the area of the glacier was
at the start of last year.
2
Give your answer in km² to 2 d.p.
The area of the glacier at the start of last year was 56.31 km², based on a percentage reduction of 0.2%.
What is a percentage decrease?A percentage decrease represents the difference between the starting and ending values, expressed as a percentage of the starting value.
In working out the percentage reduction, we determine the difference between the ending and starting values. This difference is divided by the starting value and multiplied by 100.
The current area of the glacier = 56.20 km²
The percentage reduction = 0.2%
Proportionately, the current area, in percentage terms = 99.8% (1 - 0.2%)
99.8% = 56.20 km²
100% = 56.31 km²
Thus, to 2 decimal points, the area of the glacier at the start of last year was 56.31 km².
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if f(x)=x^2 and g(x)=x, determine the value(s) of x that satisfy the equation f(x) = g(x)
Answer:
1 or 0
Step-by-step explanation:
in order for a number's square equals to itself, it has to be 1 or 0.
Randomly selected adults at a coffee shop were asked how many hours they work in a typical workday. The results are tabulated in the following frequency table.
The histogram that accurately summarizes the data in this problem is given by the second image presented at the end of the answer.
How to draw the histogram?The histogram of a data-set shows the number of times that each item was observed in the data-set.
From the first image given at the end of the answer, the absolute frequencies are given for each observation, which is the height of each bin of the histogram.
Missing InformationThe problem is given by the first image presented at the end of the answer.
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Graph the line
y=-1/3x-6
Answer:
the slope is -1/3 and the coordinates are (0,-6) and (3,-7). Below is a picture of the equation graphed.
Step-by-step explanation:
1. A 1992 poll conducted by the University of Montana classified respondents by sex and political
party, as shown in the picture.
a) What is the probability of selecting a Democrat?
b) What is the probability of selecting a respondent that is Independent and Female?
c) What is the probability of selecting a respondent that is Republican given that is Male?
d) What is the probability of selecting a respondent that is Republican or Female?
e) Are the events being a Republican independent of being a Male? Justify and explain
A: The probability of selecting a Democrat is 84/212 = 0.3968 or 39.68%.
B: The probability of selecting an Independent and Female respondent is 16/212 = 0.075 or 7.5%.
C: The probability of selecting a Republican given that the respondent is Male is 45/69 = 0.6522 or 65.22%.
D: The probability of selecting a Republican or Female respondent is 126/212 = 0.5962 or 59.62%.
E: The events being a Republican independent of being a Male, P(Republican/Male) = P(Republican) which means these events are independent.
What is the probability?
Probability is a mathematical concept that quantifies the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
a) To find the probability of selecting a Democrat, we need to add up the number of Democratic respondents and divide by the total number of respondents. In this case, the number of Democratic respondents is 36 + 48 = 84. The total number of respondents is 84 + 45 + 24 + 33 + 16 = 212. So the probability of selecting a Democrat is 84/212 = 0.3968 or 39.68%.
b) To find the probability of selecting an Independent and Female respondent, we need to find the number of Independent and Female respondents, and divide by the total number of respondents. In this case, the number of Independent and Female respondents is 16. The total number of respondents is 212, so the probability of selecting an Independent and Female respondent is 16/212 = 0.075 or 7.5%.
c) To find the probability of selecting a Republican given that the respondent is Male, we need to use conditional probability formula. P(Republican/Male) = P(Republican and Male) / P(Male)
In this case, the number of Republican and Male respondents is 45. The number of Male respondents is 45+24 = 69
So the probability of selecting a Republican given that the respondent is Male is 45/69 = 0.6522 or 65.22%.
d) To find the probability of selecting a respondent that is Republican or Female, we need to find the number of Republican or Female respondents and divide by the total number of respondents. In this case, the number of Republican or Female respondents is 45 + 33 + 48 = 126. The total number of respondents is 212, so the probability of selecting a Republican or Female respondent is 126/212 = 0.5962 or 59.62%.
e) To answer whether the events being a Republican independent of being a Male or not, we need to check the independence of the events. Events A and B are independent if and only if P(A/B) = P(A) = P(B)
In this case, P(Republican/Male) = 0.6522 and P(Republican) = (45+33)/212 = 0.4906
So the events being a Republican independent of being a Male, P(Republican/Male) = P(Republican) which means these events are independent.
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Which is greater -6, 6, or -2
determine if (x-3) is a factor of (x^4-13x^2+36) using synthetic division
Answer:
Yes, (x-3) is a factor of (x^4-13x^2+36) using synthetic division.
Synthetic division:
| x -3 |
x^4 -13x^2+36
x^3 -10x^2+27x-108
The remainder is zero, so (x-3) is a factor of the polynomial (x^4-13x^2+36).
Step-by-step explanation:
Mr. Jones invested a sum of money in 6% bonds. He invested $400 more than this sum in 4% bonds. If his total annual income was $116, how much did he invest in each kind of bond?
a = amount invested at 6%
how much is 6% of "a"? (6/100) * "a", namely 0.06a.
b = amount invested at 4%
how much is 4% of "b"? (4/100) * "b", namely 0.04b.
we also know that the yielded amount in interest or the annual income he's got from both is $116, so if we simply add their interest, that'd be 0.06a + 0.04b = 116.
We also know that he invested 400 more in "b" than in "a", so whatever "a" might be, we know that b = a + 400.
[tex]0.06a~~ + ~~0.04(\stackrel{b}{a+400})~~ = ~~116\implies 0.06a+0.04a+16=116 \\\\\\ 0.10a+16=116\implies 0.10a=100\implies a=\cfrac{100}{0.10} \\\\\\ \boxed{a=1000}\hspace{5em}\stackrel{1000+400}{\boxed{b=1400}}[/tex]
question the height of 3-year-old boys is approximately normally distributed. duncan and shane are 3-year-old boys.duncan is 32.0 inches tall and is at the 32nd percentile of the distribution. shane is 34.0 inches tall and is at the 62nd percentile of the distribution. which of the following is closest to the mean of the height distribution?
Duncan's height is closest to the mean.
Duncan (32nd percentile) has a z-score of z = 0.4677 and Shane (62nd percentile) has a z-score of z = 0.3055 when using "Table A" or "normalcy" on a TI calculator. Now that we have the z-score formula, we can create
−0.4677 = (32 − μ)/σ
and
Duncan and Shane are 3-year-old boys. Duncan is 32.0 inches tall and is at the 32nd percentile of the distribution. shane is 34.0 inches tall and is at the 62nd percentile of the distribution.
0.3055 = (34 − μ)/σ
Since the boys' heights fall under the same distribution, it should be noted that and will have the same values in each equation. Consequently, this is a set of linear equations.
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The following loan is discounted. Find (a) the discount, (b) the amount of money received, and (c) the true interest rate. P=$13,300.0, r=3 1/2%, t=4 years
a) The discount on the loan is $1,862.
b) The amount of money the borrower received on the discount loan is $11,438.
c) The true interest rate paid on the discounted loan is 4.1%.
What is a discount loan?A discount loan is a type of loan in which the interest (cost of borrowing) is deducted upfront or at the time the loan is granted.
The implication of getting a discount loan is that the amount received is less than the principal amount because the grantor has reduced it by interest and other fees (finance charges).
The principal = $13,300
Discount rate = 3¹/₂%
Time = 4 years
Discount = $1,862 ($13,300 x 3.5% x 4)
Amount received = $11,438 ($13,300 - $1,862)
Real interest rate = 4.1% ($1,862/$11,438 x 100)/4
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What’s the answer I’m so confused!!!
Answer: C
If you leave behind 0.5 then instead of 24 the correct answer would be 22.