The initial expression is:
\(x^2+5x+6\)We need to identify the coefficients of the expressions: 1 besides x^2, 5 beside x, and 6 as a constant.
Taking into account that the coefficient of x^2 is 1, to factorize we just need to find 2 numbers whose sum is 5 and multiplication is 6.
Those numbers are +2 and +3, So the factors of the expression are:
(x + 2)(x + 3)
Because: +2 + 3 = 5
2*3 = 6
Answer: (x + 2)(x + 3)
I don't understand this problem and how it equals 1 (attached). I thought if -3 =-x squared it would be 3*3 and then plus 5. I cannot think of a way to make this 1. What am I doing wrong?
Answer:
f(2) = 1
f(-3) = 4
Step-by-step explanation:
We are given the function:
\(\displaystyle \large{f(x) = - {x}^{2} + 5}\)
To evaluate the function, substitute the number in.
Evaluate f(2)
\(\displaystyle \large{f(2) = - {(2)}^{2} + 5} \\ \displaystyle \large{f(2) = - 4+ 5} \\ \displaystyle \large{f(2) = 1}\)
Evaluate f(-3)
\(\displaystyle \large{f( - 3) = - {( - 3)}^{2} + 5} \\ \displaystyle \large{f( - 3) = - 9+ 5} \\ \displaystyle \large{f( - 3) = - 4}\)
find the exact value of Sin A
Step-by-step explanation:
sin A = opposite/ Hypotenuse
Sin A = 5/7
Hello !
sin(A) = opposite/hypotenuse = 5/7
arcsin(5/7) ≈ 45,58°
sin(A) = 5/7
the angle A ≈ 45,58°
Find the measure of side c.
m (Round the answer to the nearest whole number.)
Answer:
c = 28 m
Step-by-step explanation:
Here we have a right triangle with shortest side (a) of length 17 m and smallest angle (A) equal to 37 degrees and positioned opposite side (a). The sine function is applicable here:
17 m
---------- = opp / hyp = sin 37 degrees = approximately 0.602.
c
Then 17 m / c = 0.602, or (after inverting both sides)
c 1
-------- = -----------
17 m 0.602
Solve for c. Cross-multipying, we get 0.602c = 17 m.
Dividing both sidees by 0.602 yields c = 28.24 m, which should be rounded off to the nearest whole number: c = 28 m
The following are the annual incomes (in thousands of dollars) for 8 randomly chosen, U.S. adults employed full-time.
44, 44, 54, 54, 65, 39, 54, 44
Send data to calculator
(a) What is the mean of this data set? If your answer is not an
integer, round your answer to one decimal place.
(b) What is the median of this data set? If your answer is not
an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are
their values? Indicate the number of modes by clicking in the
appropriate dircle, and then indicate the value(s) of the
mode(s), if applicable.
0
Zero modes
one mode:
Two modes:
Answer:
(a) To find the mean of the data set, sum up all the values and divide by the total number of values.
44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398
Mean = 398 / 8 = 49.75
Rounded to one decimal place, the mean of this data set is 49.8.
(b) To find the median of the data set, i need to arrange the values in ascending order first:
39, 44, 44, 44, 54, 54, 54, 65
The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:
(44 + 54) / 2 = 98 / 2 = 49
Rounded to one decimal place, the median of this data set is 49.0.
(c) To determine the modes of the data set, identify the values that appear most frequently.
In this case, the mode refers to the value(s) that occur(s) with the highest frequency.
From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.
A drawer contains 8 red socks, 6
white socks, and 4 blue socks. Without
looking, you draw out a sock, return
it and draw out a second sock. What is
the probability that the first sock is
white and the second sock is blue?.
simplest form
Answer:
2/27
Step-by-step explanation:
First probability = 6/18 = 1/3
second probability = 4/18 = 2/9 (in this case the number of socks remains the same because we returned the first one)
Final probability = 1/3 * 2/9 = 2/27
Choose an equivalent expression for two thirds to the fourth power times two thirds raised to the third power comma all raised to the second power.
A. four ninths raised to the fourteenth power
B. four ninths raised to the twenty fourth power
C. two thirds raised to the fourteenth power
D. two thirds raised to the twenty fourth power
Answer:
C. two-thirds raised to the fourteenth
Step-by-step explanation:
The coornidates of the midpoint of BC is at M (5, -2). The coordinates of B are (3, 1). Find the coordinates of the other endpoint C.
Answer:
The other endpoint is (7, -5)
Step-by-step explanation:
We can use the formula for the midpoint to find the coordinates of the other endpoint of the segment BC:
xm = x1 + (x2 - x1)/2
ym = y1 + (y2 - y1)/2
For our case, replacing the given coordinates and solving for x2 and y2 (the coordinates of the other endpoint) we get:
For x2:
xm = x1 + (x2 - x1)/2
5 = 3 + (x2 - 3)/2
5 - 3 = (x2 - 3)/2
2 = (x2 - 3)/2
4 = x2 - 3
x2 = 4 + 3 = 7
For y2:
ym = y1 + (y2 - y1)/2
-2 = 1 + (y2 - 1)/2
-2 -1 = (y2 - 1)/2
-3 = (y2 - 1)/2
-6 = y2 - 1
y2 = -6 + 1 = -5
Therefore the other endpoint is (7, -5)
Drag each number to a box to complete the table. Each number may be used once or not at all
Each number should be dragged to a box to complete the table as follows;
Kilometers Meters
1 1,000
2 2,000
3 3,000
5 5,000
8 8,000
What is a conversion factor?In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.
Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;
Conversion:
1 kilometer = 1,000 meters
2 kilometer = 2,000 meters
3 kilometer = 3,000 meters
4 kilometer = 4,000 meters
5 kilometer = 5,000 meters
6 kilometer = 6,000 meters
7 kilometer = 7,000 meters
8 kilometer = 8,000 meters
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Which fraction is equivalent to 20
Answer:
4/16
Step-by-step explanation:
What is 10×25 to the sixth power
Answer:
2.4414063e+14 (wow such a large number)
Step-by-step explanation:
10x25= 250
250 to the 6th power = 2.4414063e+14
What is the distance from Point B (-1, 11) to line y = -1/3x - 6?
Answer in simplest radical form
The distance from Point B (-1, 11) to line y = (-1 ÷ 3x) - 6 is 15.811.
The distance from the point B(-1 , 11) to the line y= (-1 ÷ 3x) - 6 is given by the distance formula d = (|Ax1 + By1 + C|) ÷ (√(A² + B²)).
Comparing the equation y= (-1 ÷ 3x) - 6 with the standard forms Ax + By+ C = 0.
It is clear that the coefficient of x, A = -1 ÷ 3.
The coefficient of y, B = -1. The constant C = -6 and the points x1 = -1 and y1 = 11.
Substituting these data in the equation the distance d = (|(-1÷3)×(-1)+ (-1)×11 + (-6)|) ÷ √((-1 ÷ 3)² + (-1)² ) solving the equation the distance d becomes,
d = 15.811.
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I’ll give brainliest Write an inequality that represents this situation below.
Your suitcase for vacation will fit at most 11 outfits you already have 5 packed
Answer:
Let x be the number of additional outfits.
5 + x < 11
What is the Least Common Multiple for 12 and 30
Answer:
60
Step-by-step explanation:
12 times 5
30 times 2
Vanessa runs 4 miles each week. Use the number line below to solve and represent the number of weeks it will take her to run 96 miles.
The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks
How to calculate the number of weeks used by Vanessa for race?The amount of distance that Vanessa covers for a week = 4 miles
The amount of weeks it will take for her to cover 96 moles would be = ?
That is;
1 week = 4 miles
X weeks = 96 miles
Make X the subject of formula;
X = 96× 1/4
= 24 weeks
Therefore Vanessa will be able to cover 96 miles in only 24 weeks.
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Today Olivia is carrying her history textbook and her lunch in her backpack. If the history textbook weighs 1/2 of a pound and her lunch weighs 2/3 of a pound, how much weight is in Olivia's backpack?
Weight is in Olivia's backpack is 5/6 pound.
As in the given problem olivia's history book weights 1/2 of a pound and
her lunch weighs 2/3 of a pound.
As both the units are same,
Thus total weight must be summation of both history book and her lunch box.
total weight is =1/2 +2/3 pound
= (3+2)/6
that is equal to 5/6 pound.
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A person places $48800 in an investment account earning an annual rate of 3.1%,
compounded continuously. Using the formula V = Pert, where Vis the value of the
account in t years, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the
nearest cent, in the account after 13 years.
When a person places $48,800 in an investment account at an annual rate of 3.1% compounded continuously, using the formula, V = \(Pe^rt\), the amount of money (future value) after 13 years is $73,019.78.
What is compounding?Compounding refers to the process or interest system that computes periodic or continuous interest on both the principal and accumulated interest.
We can solve for the future value of an investment under continuous compounding using an online finance calculator as follows:
Using the formula V = \(Pe^rt\)
Principal (P) = $48,800.00
Annual Rate (R) = 3.1%
Compound (n) = Compounding Continuously
Time (t in years) = 13 years
Result:
V = $73,019.78
V = P + I where
P (principal) = $48,800.00
I (interest) = $24,219.78
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.1/100
r = 0.031 rate per year,
Solving the equation for V:
V = \(Pe^rt\)
V = \(48,800.00(2.71828)^(0.031)(13)\)
V = $73,019.78
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What two numbers have a product of 5 and a sum of -6
Answer:
-1 and -5
Step-by-step explanation:
-1x-5= 5
-1+-5= -6
Four students were given paint supplies for an art project. The table shows the amount of paint used by each student.
Student 1 Student 2 Student 3 Student 4
seventeen twentieths 1 and one fourth 65% 0.20
Which student used the least amount of paint for their art project?
Student 1
Student 2
Student 3
Student 4
Student 4 used the least amount of paint for the art project
How to determine which student used the least amount of paint?Given:
Student 1 used seventeen twentieths => 17/20
Student 2 used 1 and one-fourth => 1 1/4 = 5/4
Student 3 used 65% = 65/100
Student 4 used 0.20 = 20/100
Since the amount of paint used for the art project has been expressed in fractions. Find the LCM:
17/20, 5/4, 65/100, 20/100
The LCM of 20, 4 and 100 is 100
Student 1: 17/20 = 85/100
Student 2: 5/4 = 125/100
Student 3: 65/100
Student 4: 20/100
Thus, student 4 used the least amount of paint
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Answer: Student 4 (d)
Step-by-step explanation:
Brainliest?
Explain how you have caring degrees of control over the three types of income, and how much control you have ove each.
There are 3 types of income.
1) Earned income
2) Portfolio income
3) Passive income
What is income?Income can be defined as the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms. Income is difficult to define conceptually and the definition may be different across fields.
here, we have,
Earned income meaning is the type of income earned after exerting time and effort in you part. in which , Salary is an earned income. If you stop working, you'll stop having an earned income. The more time spent working, the more income you generate (overtime pay).
Portfolio income can b e stated as better identified as capital gains. This is earned when you sell an asset at a higher price than when you bought it. The difference from the selling price and its cost is the portfolio income. Your portfolio may include stocks, real estate properties, and other assets (antiques, cars).
Passive income is income generated without exerting effort from you. This income is generated from you bought or existing assets. Rental income is an example of this. You will always receive rent from you own real estate property.
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Solve the equation
-3x²-150
60 is thaks for points
Step-by-step explanation:
I think
Which pair of angles are interior angles?
Help I don’t understand this
Answer: it is unclear
Step-by-step explanation: ask your parent or teacher now if you dont know this. this is a new system and i dont
know. try reaching your parents for a clear answer.
Which of the following is an accepted check that scientists can use to determine whether a scientific report is unbiased?
A. the precision of the data that are reported
B. parsimony of explanation
C. verification by more than one independent observer
D. the reputation of the scientist making the report
Verification by more than one independent observer is an accepted check that scientists can use to determine whether a scientific report is unbiased
Every scientist holds certain presumptions. The goal should be to become as objective as you can while freely admitting your biases, not to be completely objective. By doing this, others will understand the conditions in which your findings are valid and reproducible.
As long as it is supported by facts, science is very much about the "best explanation so far," with lots of potential for modification and self-correction.
Through testing and experimentation, the scientific method establishes facts in an unbiased manner. Making an observation, formulating a hypothesis, making a prediction, carrying out an experiment, and then evaluating the findings are the fundamental steps.
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Which rational number could be graphed between -3 and -4
Answer:
-3.5
Step-by-step explanation:
An example is -3.5.
What is the greatest number of consecutive integers
that sum to –11? PLS NOW
Answer:
It is not possible for the sum of consecutive integers to be -11. The sum of n consecutive integers is n times the average of the first and last integers. The average of any two integers is a fraction, which when multiplied by n, will always yield a fraction, which cannot equal -11. Therefore it is not possible to have n consecutive integers that sum to -11.
In the figure below, C lies on AD, the measure of BAC is 65 degrees the measure of BCD is 100 degrees, and the measure of ABC is x degrees
Answer:C. 35
Step-by-step explanation:
4. Uncle Royce is 42. What is his target heart rate range?
O 120-180 beats per minute
O 150-200 beats per minute
O116-160 beats per minute
O170-236 beats per minute
Step-by-step explanation:
70 to 85 % of his maximum
Maximum is estimated to be 220 - age = 220 - 42 = 178
70% of this is 125
85 % is 89 151
I believe I would go with the third choice 116-160 bpm
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
(c)yz dx + xz dy + xy dz, where c consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1) (d) x2 dx-xy dy + dz, where c is the parabola z = x2, y = 0 from (-1, 0, 1) to (1, 0, 1)
The value of the line integral is 1/2.
To evaluate this line integral, we need to parameterize the curve C that consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1).
Let's parameterize the first segment from (1,0,0) to (0,1,0) using t as the parameter
r(t) = (1-t) * <1,0,0> + t * <0,1,0>
= <1-t, t, 0>
where 0 ≤ t ≤ 1.
Now, let's parameterize the second segment from (0,1,0) to (0,0,1) using s as the parameter
r(s) = (1-s) * <0,1,0> + s * <0,0,1>
= <0, 1-s, s>
where 0 ≤ s ≤ 1.
We can then use the parameterization of C to evaluate the line integral:
∫_c yz dx + xz dy + xy dz
= ∫_0^1 yz dx/dt dt + xz dy/dt dt + xy dz/ds ds
= ∫_0^1 (t(1-t)) 0 dt + ((1-t)t) 0 dt + ((1-t)t) ds
= ∫_0^1 (1-t)t ds
= 1/2
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The given question is incomplete, the complete question is:
∫_c yz dx + xz dy + xy dz, where c consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1) Evaluate Line Integrals
Answer this pls for 15 points
this is the answer hope it helps
Answer:
3x/(x-3) (x+1)
Step-by-step explanation: