Answer:
The numbers are 38, 39, and 40
Step-by-step explanation:
Let the 3 consecutive Integral numbers be;
x, x+1, x+2
We are informed that the sum of the 3 consecutive Integral numbers is 117. Therefore;
x + x+1 + x + 2 = 117
3x + 3 = 117
3x = 114
x = 38
x+1 = 39
x+2 = 40
Answer:
38, 39, 40
Step-by-step explanation:
Here's an interesting solution to this one. The formula to compute the nth triangular number, which is to say the sum of the first n consecutive integers, starting at 1 is
[tex]\frac{n(n+1)}{2}[/tex]
What if we wanted to start from a higher number, though? Say, 3. Well, we'd have to shift every number in the sequence up 2 (1, 2, 3 would become 3, 4, 5) so we'd be adding 2 n times. If we wanted to be more general, we could call that "shift amount" s, and our modified formula would now look like
[tex]\frac{n(n+1)}{2}+sn[/tex]
Now let's put this formula to the test. We know what our sum is here: it's 117. And we know what our n is too; we're finding 3 integers, so n = 3. This gives us the equation
[tex]\frac{3(3+1)}{2} +3s=117[/tex]
Solving this equation for s:
[tex]\frac{3(4)}{2} +3s=117\\\\\frac{12}{2}+3s=117\\ 6+3s=117\\3s=111\\s=37[/tex]
so our "shift amount" is 37, and our sequence gets shifted from 1, 2, 3 to 38, 39, 40.
But why?This was a lot of setup for what seems like a disappointing payoff, but the real power with this approach is that we've actually just solved every problem of this type. Let's say you had to find the sum of 5 consecutive integers, and their sum was 70. Not a problem. Just set our n = 5 and solve:
[tex]\frac{5(6)}{2} +5s=70\\\\\frac{30}{2} +5s = 70\\15+5s=70\\5s=55\\s=11[/tex]
Which gives us a "shift" of 11 and the sequence 12, 13, 14, 15, 16 (which is exactly the sequence I came up with for this problem!)
Which inequality is graphed below?
ANSWER
[tex]y \geqslant \frac{1}{4} x - 1[/tex]
EXPLANATION
The graph has a solid boundary line.
The region above the boundary line is shaded
Therefore the inequality sign involved is '≥'
The boundary line has equation
[tex]y = \frac{1}{4} x - 1[/tex]
We can now conclude that, the inequality graphed above is
[tex]y \geqslant \frac{1}{4} x - 1[/tex]
Answer:
The answer is
Step-by-step explanation:
The inequality in the graphed above is y≥1/4x-1
there are 4 trucks for every 5 cars in a parking lot. how many trucks and cars could be in a parking lot?
Answer:
there could be 8 trucks to 10 cars
16 trucks to 20 cars
or just continuously multiply by 2
Step-by-step explanation:
Answer:
there could be 8 trucks to 10 cars
16 trucks to 20 cars
or just continuously multiply by 2
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Employee Number(left column) Years Worked(right column)
1 8
2 13
3 15
4 3
5 13
6 28
7 4
8 12
9 4
10 26
11 29
12 3
13 10
14 3
15 17
16 13
17 15
18 15
19 23
20 13
21 12
22 1
23 14
24 14
25 17
26 16
27 7
28 27
29 18
30 24 The data shows the number of years that 30 employees worked for an insurance company before retirement.(blank) is the population mean for the number of years worked, and(blank) % of the employees worked for the company for at least 10 years. (Round off your answers to the nearest integer.)
Answer:
years worked: 14
at least 10 years: 73%
Step-by-step explanation:
The mean is found by adding the years of service and dividing by the number of employees. The total years of service is 417, so the average is ...
average years worked = 417/30 = 13.9 ≈ 14 . . . years
__
The percentage of employees that have worked there at least 10 years is found by counting the number with 10 or more years of service and dividing that count by the total number of employees. The result is then expressed as a percentage.
(10 years or over)/(total number) = 22/30 = 0.73_3 (a repeating decimal) ≈ 73%
_____
Comment on the working
A spreadsheet can be helpful for this. It has a function that can calculate the mean for you. Sorting the years of service into order can make it trivially easy to count the number that are 10 or more, or you can write a function that will do the count for you. (Also, less than 10 means the years are a single digit. There are 8 single-digit numbers in your list.) The hard part is copying 30 numbers without error.
The answers are: 14 years and 50%. 14 years is the population mean for the number of years worked, and 50 % of the employees worked for the company for at least 10 years.
To determine the answers, steps:
1. Calculate the Population Mean: Sum all the years worked and divide by the number of employees (30).
[tex]Total\ years\ worked: 8 + 13 + 15 + 3 + 13 + 28 + 4 + 12 + 4 + 26 + 29 + 3 + 10 + 3 + 17 + 13 + 15 + 15 + 23 + 13 + 12 + 1 + 14 + 14 + 17 + 16 + 7 + 27 + 18 + 24 = 412[/tex]
[tex]Population\ mean =\frac{412}{30} \approx 14[/tex]
2. Calculate the Percentage of Employees who Worked At Least 10 Years: Count the employees who worked for 10 years or more, and divide by the total number of employees, then multiply by 100 to convert to percentage.
[tex]Number\ of\ employees\ who\ worked\ at\ least\ 10\ years: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 15[/tex]
[tex]Percentage = \frac{15}{30} * 100 = 50\%[/tex]
You received a bill for $82.53. You prepaid on a budget plan for $110.00/ mth. How much was your original bill?
Answer:
192.53= original bill
Step-by-step explanation:
The bill you receive is equal to the original bill minus the prepaid amount
bill = original - prepaid
82.53 = original - 110
Add 110 to each side
82.53+110 = original-100+100
192.53= original bill
HELP i’m having trouble with my homework assignments
Answer:
Collin: about $401 thousand
Cameron: about $689 thousand
Step-by-step explanation:
A situation in which doubling time is constant is a situation that can be modeled by an exponential function. Here, you're given an exponential function, though you're not told what the variables mean. That function is ...
[tex]P(t)=P_0(2^{t/d})[/tex]
In this context, P0 is the initial salary, t is years, and d is the doubling time in years. The function gives P(t), the salary after t years. In this problem, the value of t we're concerned with is the difference between age 22 and age 65, that is, 43 years.
In Collin's case, we have ...
P0 = 55,000, t = 43, d = 15
so his salary at retirement is ...
P(43) = $55,000(2^(43/15)) ≈ $401,157.89
In Cameron's case, we have ...
P0 = 35,000, t = 43, d = 10
so his salary at retirement is ...
P(43) = $35,000(2^(43/10)) ≈ $689,440.87
___
Sometimes we like to see these equations in a form with "e" as the base of the exponential. That form is ...
[tex]P(t)=P_{0}e^{kt}[/tex]
If we compare this equation to the one above, we find the growth factors to be ...
2^(t/d) = e^(kt)
Factoring out the exponent of t, we find ...
(2^(1/d))^t = (e^k)^t
That is, ...
2^(1/d) = e^k . . . . . match the bases of the exponential terms
(1/d)ln(2) = k . . . . . take the natural log of both sides
So, in Collin's case, the equation for his salary growth is
k = ln(2)/15 ≈ 0.046210
P(t) = 55,000e^(0.046210t)
and in Cameron's case, ...
k = ln(2)/10 ≈ 0.069315
P(t) = 35,000e^(0.069315t)
PLZ HELP (GOD BLESS) YOU!!!
Jared is building a treehouse. He pays $75 for materials and pays his friend $12 per hour to help him. If Jared spends a total of $129 on building his tree house, for how many hours did his friend work on it?
Answer:
I think the answer is 4.5 if you subtract 75 from 129 and divide by 12?
After deducting the cost of materials, the remaining amount spent on labor was $54. By dividing this amount by the friend's hourly rate of $12, it is determined that Jared's friend worked for 4.5 hours on constructing the treehouse.
Jared is trying to calculate how many hours his friend worked on building a treehouse based on the total cost of the project. Jared spent $75 on materials and paid his friend $12 per hour for labor. The total cost for building the treehouse was $129.
To find out how many hours Jared's friend worked, we start by subtracting the cost of materials from the total cost:
Total cost of treehouse = $129
Cost of materials = $75
Total cost minus materials cost = $129 - $75 = $54
This $54 represents the total amount paid for labor. We can then divide this amount by the hourly rate to find the number of hours worked:
Hourly wage = $12
Labor cost / hourly wage = $54 / $12 = 4.5 hours
Therefore, Jared's friend worked for 4.5 hours on the treehouse.
is 3x^2 + 2x + 10 = 0 written in standard form?
Answer:
in the US, yes
in some other English-speaking countries, no
Step-by-step explanation:
"Standard form" depends on where you live. In the UK, the "standard form" of a quadratic equation is what is called "vertex form" in the US. That form is ...
3(x +1/3)^2 +29/3 = 0
In the US, the equation you show is in standard form.
PLEASE HELP ME!!
1. What are the mean, median, mode and range of the data set given the altitude of lakes in feet: -12,-9,-14,-39,-49,-18, and -43?
2. Given the data 21,13,13,37,13,23,25,15:
a. What is the outlier in the data?
b. What is the mean with the outlier?
c. What is the mean without the outlier?
First put your numbers in order from least to greatest (These are negative numbers so that means that the smallest number is the one farthest away from zero)
-49, -43, -39, -18, -14, -12, -9
Mean is adding all the numbers together and dividing the sum by how many numbers there are in the data set
-49 + (-43) + (-39) + (-18) + (-14) + (-12) + (-9) = -184
There are seven numbers so divide -184 by 7:
-184 ÷ 7 ≈ 26.29
Median is the number in the middle. Take away the smallest number and the biggest number on each layer until you get to the middle
-49, -43, -39, -18, -14, -12, -9
-43, -39, -18, -14, -12
-39, -18, -14
-18 <-------------------Median
Mode is whatever number appears the most often in the data. In this case all the numbers appear only once so there is no mode
Range is subtracting the largest number by the smallest number
-9 - (-49) = 40
2. Data in order
13, 13, 13, 15, 21, 23, 25, 37
Outlier is the number that is a number that is rather far from the other number in the data
a. In this case the outlier is 37
b. 13 + 13 + 13 + 15 + 21 + 23 + 25 + 37 = 160
160 ÷ 8 = 20
c. 13 + 13 + 13 + 15 + 21 + 23 + 25 = 123
123 ÷ 7 = 17.57
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
Mean = 26.29
Median = -18
Mode = 40
2 a. 37
2 b. 20
2 c. 17.57
Step-by-step explanation:
Mean = -49 + (-43) + (-39) + (-18) + (-14) + (-12) + (-9) = -184
There are seven numbers so divide -184 by 7:
-184 ÷ 7 ≈ 26.29
Median =
-49, -43, -39, -18, -14, -12, -9
-43, -39, -18, -14, -12
-39, -18, -14
-18
Mode =
-9 - (-49) = 40
2.
13, 13, 13, 15, 21, 23, 25, 37
Outlier is the number that is an odd number
a. In this case the outlier is 37
b. 13 + 13 + 13 + 15 + 21 + 23 + 25 + 37 = 160
160 ÷ 8 = 20
c. 13 + 13 + 13 + 15 + 21 + 23 + 25 = 123
123 ÷ 7 = 17.57
Please help asap!!!!!!!!!!!
ANSWER
[tex]16\pi \: sq.in[/tex]
EXPLANATION
The area of a sector is calculated using the formula,
[tex]Area = \frac{arc \: measure}{360 \degree} \times \pi {r}^{2} [/tex]
The arc measure is given as 45°
The radius of the circle is 8 inches.
We substitute to obtain,
[tex]Area = \frac{45 \degree}{360 \degree} \times \pi \times {8}^{2} [/tex]
[tex]Area = \frac{1}{4} \times 64\pi = 16\pi[/tex]
The answer is:
The correct option is the second option:
[tex]SectorArea=8\pi in^{2}[/tex]
Why?To answer the question, we need to calculate the total area of the circle (which corresponds to 360°) and then, calculate the equivalent area to the sector of the arc that measures 45°
Calculating the total area, we have:
[tex]TotalArea=\pi radius^{2} \\\\TotalArea=\pi 8^{2} =64\pi in^{2}[/tex]
Now, we need to consider that the calculated area (total area) correspondes to all 360° that conforms the interior angle of a circle, now, if we want to calculate the area that represents a sector of the arc that measures 45°, we have to use the following formula:
[tex]SectorArea=\frac{360\°}{45\° }*TotalArea\\\\SectorArea=\frac{45\°}{360\° }*64\pi in^{2}=\frac{1}{8} *64\pi in^{2}\\\\SectorArea=8\pi in^{2}[/tex]
Hence, we have that the correct option is the second option:
[tex]SectorArea=8\pi in^{2}[/tex]
Have a nice day!
Help me pleassssseeeee
Hello There!
Martha’s first step would represent “Associative Property Of Addition”
This basically means that you can add or multiply these numbers regardless of how they are grouped in a sequence.
Write a verbal expression to represent the given equation.
w2power=32w
a The square of a number is equal to 32.
b The square of a number is equal to the product of 23 and that number.
c The square of a number is equal to the product of 32 and that number.
d The square of a number is equal to the product of that number.
Answer:
c The square of a number is equal to the product of 32 and that number.
Step-by-step explanation:
Let the number be w.
The square of the number is [tex]w^2[/tex]
The product (multiplication) of the number and 32 is [tex]32w[/tex]
The symbol = is read "is equal to"
[tex]w^2=32w[/tex]
The square of a number = The product of 32 and that number
The square of a number equals to The product of 32 and that number
We can conclude that the correct answer is c The square of a number is equal to the product of 32 and that number.
Which measurement is the measure of an obtuse angle?
Answer: An obtuse angle is any angle greater than 90° and less than 180°
Step-by-step explanation:
Answer:
An obtuse angle is more than 90 degrees so anything above 90 degrees is obtuse while anything below is either an acute, strait, or right angle.
Step-by-step explanation:
Can someone do this for me?
Answer:
KM = 20
Step-by-step explanation:
If V is the midpoint of KM, then ...
KV = VM
2.5z = 5z -10
0 = 2.5z -10 . . . . . . subtract 2.5z
0 = z - 4 . . . . . . . . . divide by 2.5
4 = z . . . . . . . . . . . . add 4
We know that V bisects KM, so KV is half the overall length. That is ...
KM = 2·KV = 2·2.5z = 5z
Using the value of z we found, ...
KM = 5·4 = 20
Completer the blank with a <, >, or =
-2 _ -4
-10 _ -5
-3 _ 0
l -8 l _ l -5 l
4 _ l -8 l
I know which ones are bigger, but i always get confused what <, > means?
Answer:
>,<,<,>,<
Step-by-step explanation:
The bigger side in the >/< Symbols mean that value is larger
What are the solutions to the system of equations?
x = x^2 - 4x +3
y = -x +3
For this case we have the following system of equations:
[tex]y = x ^ 2-4x + 3\\y = -x + 3[/tex]
Matching we have:
[tex]x ^ 2-4x + 3 = -x + 3\\x ^ 2-4x + x + 3-3 = 0\\x ^ 2-3x = 0[/tex]
We solve by means of
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Where:
[tex]a = 1\\b = -3\\c = 0[/tex]
Substituting:
[tex]x = \frac {- (- 3) \pm \sqrt {(- 3) ^ 2-4 (1) (0)}} {2 (1)}\\x = \frac {3 \pm \sqrt {9}} {2}\\x = \frac {3 \pm3} {2}[/tex]
Finally, the roots are:
[tex]x_ {1} = \frac {3-3} {2} = 0\\x_ {2} = \frac {3 + 3} {2} = \frac {6} {2} = 3[/tex]
Answer:
[tex]x_ {1} = 0\\x_ {2} = 3[/tex]
If the translation maps point (3,2) to (4,5); or T: (3,2) —> (4,5), then what is the image of point (0,0)? (4,5) (-1,-3) (1,3)
Answer:
(1, 3)
Step-by-step explanation:
If the translation is ...
(3, 2) + (a, b) = (4, 5)
Then we can find (a, b) by subtraction:
(4, 5) -(3, 2) = (a, b) = (4-3, 5-2) = (1, 3)
Not the image of point (0, 0) will be ...
(0, 0) + (a, b) = image
(0, 0) + (1, 3) = (0+1, 0+3) = (1, 3)
The image of the point is (1, 3).
Help me pleasssseeeeeee
Answer:
d. Distributive property
Step-by-step explanation:
The Distributive property of multiplication over addition is what allows you to multiply each of the terms in parentheses by the factor outside parentheses. It tells you ...
a(b +c) = ab + ac
It works both ways, also allowing you to remove a common factor to outside parentheses.
the height in feet of a ball dropped from a 150 ft building is given by h(t)=-16 ft^2 +150, where t is the time in seconds after the ball is dropped. find h(2) and interpret its meaning. round your answer to the nearest hundredth.
A. h(2)=86.00 means that after 2 seconds, the height of the ball is 86.00 ft.
B. h(2)=3.04 means that after 2 seconds, the height of the ball has dropped by 3.04 ft
C. h(2)= 3.04 means that after 2 seconds, the height of the ball is 3.04 ft
D. h(2)= 86.00 means that after 2 seconds, the height of the ball has dropped by 86.00 ft.
Answer:
Part 1) Option A. h(2) = 86.00 means that after 2 seconds, the height of the ball is 86.00 ft
Step-by-step explanation:
we have
[tex]h(t)=-16t^{2}+150[/tex]
where
t ----> is the time in seconds after the ball is dropped
h(t) ----> he height in feet of a ball dropped from a 150 ft
Find h(2)
That means ----> Is the height of the ball 2 seconds after the ball is dropped
Substitute the value of t=2 sec in the equation
[tex]h(2)=-16(2)^{2}+150=86\ ft[/tex]
therefore
After 2 seconds, the height of the ball is 86.00 ft.
I what are the values of the coefficient of each term and the constant term?
Step-by-step explanation:
[tex](4x - 2).6(2x + 7) \\ = (4x - 2)(12x + 42) \\ = 48 {x}^{2} + 168x - 24x - 84 \\ = 48 {x}^{2} + 144x - 84[/tex]
then
[tex]a = 48 \\ b = 144 \\ c = - 84[/tex]
sin E =
Whats the answer
B is correct. I’ve noticed that you’ve posted a lot of questions like this, so here’s how I remember it. Soh-Cah-Toa
Soh stands for Sin=Opposite (the side opposite to the angle) over hypotenuse (the side opposite to the right angle)
Cah stands for Cos=Adjecent (the side next to the angle that is not the hypotenuse) over the hypotenuse
Toa stands for Tan=opposite over adjacent
Good luck! Hope I helped you understand.
Which system of linear inequalities is shown in the graph?
A)
y < x + 4
y ≥ -3x - 2
B)
y < x + 4
y ≤ -3x - 2
C)
y > x + 4
y ≤ -3x - 2
D)
y > x + 4
y ≥ -3x - 2
Any help would be greatly appreciated, thanks!
Answer:
D)
y > x + 4
y ≥ -3x - 2
Step-by-step explanation:
Blue line's boundary is above the line and dotted (>) so the equation: y > x + 4
Red line's boundary is above the line and solid (≥) so the equation: y ≥ -3x - 2
Answer
D)
y > x + 4
y ≥ -3x - 2
Answer:
D
Step-by-step explanation:
Help me with ixl please
Answer:
$33.00
Step-by-step explanation:
You find out how much the sale price is by subtracting 25% of 40 from 40:
40 - [(.25)(40)] and that equals 30. So the sale price is $30. Now if the tax is 10% (.1 in decimal form), we find the total cost by adding .1(30) to 30:
30 + [(.1)(30)] which is $33
graph the function f( x ) = |x+2| - 3
Answer:
Find the attached
Step-by-step explanation:
To graph the given function, we would need to obtain pairs of points (x, f(x)). We can let x be;
-5, -4, -3, 3, 4, 5
we simply substitute each value of x in the given function to obtain the value of the function corresponding to the given x value;
when x = -5, f(-5) = |-5+2| - 3 = 0
when x = -4, f(-4) = |-4+2| - 3 = -1
when x = -3, f(-3) = |-3+2| - 3 = -2
when x = 3, f(3) = |3+2| - 3 = 2
when x = 4, f(4) = |4+2| - 3 = 3
when x = 5, f(5) = |5+2| - 3 = 4
The graph of the function is as shown in the attachment below.
Answer:
Find the attached
Step-by-step explanation:
To graph the given function, we would need to obtain pairs of points (x, f(x)). We can let x be;
-5, -4, -3, 3, 4, 5
we simply substitute each value of x in the given function to obtain the value of the function corresponding to the given x value;
when x = -5, f(-5) = |-5+2| - 3 = 0
when x = -4, f(-4) = |-4+2| - 3 = -1
when x = -3, f(-3) = |-3+2| - 3 = -2
when x = 3, f(3) = |3+2| - 3 = 2
when x = 4, f(4) = |4+2| - 3 = 3
when x = 5, f(5) = |5+2| - 3 = 4
what is the answer to
Given: Triangle PQR with m∠P=(5x)° , m∠Q=(5x)° , and m∠R=(8x)° .
Prove: x = 10
Explanation:
The sum of the measures of the interior angles of a triangle is 180°. Then the sum of the given angles is 180°:
m∠P +m∠Q +m∠R = 180°
(5x)° +(5x)° +(8x)° = 180°
18x = 180 . . . . . . . . . . . . . . . collect terms, divide by °
x = 10 . . . . . . . . . . . . . . . . . . divide by 18. This is your desired result.
Explanation:
The sum of the measures of the interior angles of a triangle is 180°. Then the sum of the given angles is 180°:
m∠P +m∠Q +m∠R = 180°
(5x)° +(5x)° +(8x)° = 180°
18x = 180 . . . . . . . . . . . . . . . collect terms, divide by °
x = 10 . . . . . . . . . . . . . . . . . . divide by 18. This is your desired result.
The yearly attendance at a ballpark is shown in the table. Which answer describes the average rate of change from Year 2 to Year 5?
Answer:
A
Step-by-step explanation:
The average rate of change is the change in attendance over change in time.
Δy / Δx
(333.7 - 298.3) / (5 - 2)
11.8
So the average rate of change is an increase of 11.8 thousand people per year.
The average rate of change from Year 2 to Year 5 is 11.8 if at year 2 the attendance is 298.3 and at year 5 the attendance is 333.7
What is the rate of change?It is defined as the change in values of a dependent variable with respect to the independent variables.
We have to find the average rate of change from Year 2 to Year 5:
At year 2 the attendance = 298.3
At year 5 the attendance = 333.7
Average rate of change = (333.7-298.3)/(5-2)
= 11.8
Thus, the average rate of change from Year 2 to Year 5 is 11.8 if at year 2 the attendance is 298.3 and at year 5 the attendance is 333.7
Learn more about the rate of change here:
brainly.com/question/12786410
#SPJ2
HELP! Solve for x. Make sure to show your work and provide complete geometric explanations.
Answer:
For a. [tex]x=7[/tex]
For b. [tex]x=2[/tex]
Step-by-step explanation:
To solve this, we are using the intersecting secants theorem. The theorem says that if two secant segments intersect a circle from an exterior point, then the product of the measures of the exterior segment and the whole secant is equal to the product of the measures of the other exterior segment and its whole secant.
Applying this to our circles:
For a.
[tex]5(5+x)=6(6+4)[/tex]
[tex]25+5x=6(10)[/tex]
[tex]25+5x=60[/tex]
[tex]5x=60-25[/tex]
[tex]5x=35[/tex]
[tex]x=\frac{35}{5}[/tex]
[tex]x=7[/tex]
For b.
[tex]4(4+x)=3(3+5)[/tex]
[tex]16+4x=3(8)[/tex]
[tex]16+4x=24[/tex]
[tex]4x=8[/tex]
[tex]x=\frac{8}{4}[/tex]
[tex]x=2[/tex]
We can conclude that the value of x in (a) is 7, and the value of x in (b) is 2
law of sines? .
.
.
.
.
.
.
.
.
.
.
.
Answer:
b ≈ 3.1
Step-by-step explanation:
The law of sines tells you ...
b/sin(B) = c/sin(C)
Here, you have to find angle C based on the sum of the angles of a triangle being 180°.
C = 180° - A - B = 180° - 69° - 32° = 79°
Multiplying the above law of sines equation by sin(B), you have ...
b = c·sin(B)/sinc(C) = 5.7·sin(32°)/sin(79°) ≈ 3.07707
b ≈ 3.1 . . . . . rounded to tenths
Answer:
[tex]\displaystyle 3,1 ≈ b[/tex]
Step-by-step explanation:
First, find [tex]\displaystyle m∠C,[/tex]accourding to the Triangle-Sum Theorem:
[tex]\displaystyle 180° = 32° + 69° + m∠C \hookrightarrow 180° = 101° + m∠C; 79 = m∠C[/tex]
Now that we have all three angles, we can solve for edge b
[the second edge], using the Law of Sines:
[tex]\displaystyle \frac{c}{sin∠C} = \frac{b}{sin∠B} = \frac{a}{sin∠A} \\ \\ \frac{5,7}{sin\:79°} = \frac{b}{sin\:32°} \hookrightarrow 3,0770743283... = \frac{5,7sin\:32°}{sin\:79°} \\ \\ 3,1 ≈ b[/tex]
I am joyous to assist you at any time.
The function f(x) = square root of x is translated left 5 units and up 3 units to create the function g(x)
what is the domain of G(x)?
{x | x > –5}
{x | x > –3}
{x | x > 3}
{x | x > 5}
Answer:
The domain of g(x) is {xI x > -5} ⇒ first answer
Step-by-step explanation:
* Lets talk about the transformation at first
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* lets revise the meaning of the domain
- The domain is all values of x that make the function defined
- Find the values of x which make the function undefined
- The domain will be all the real numbers except those values
* Now we can solve the problem
∵ f(x) = √x
- f(x) translated 5 units to the left, then add x by 5
∴ f(x) ⇒ f(x + 5)
- f(x) translated 3 units up, then add f(x) by 3
∴ f(x) ⇒ f(x) + 3
- The function g(x) is created after the transformation
∴ g(x) = f(x + 5) + 3
∵ f(x) = √x
∴ g(x) = √(x + 5) + 3
- The function will be defined if the value under the square root
is positive (means greater than 0)
∵ The expression under the square root is x + 5
∴ x + 5 > 0 ⇒ subtract 5 from both sides
∴ x > -5
- The domain will be all the real numbers greater than -5
∴ The domain of g(x) is {xI x > -5}
The domain of the function g(x), which is the function f(x) = square root of x translated left 5 units and up 3 units, is {x | x > -5}.
The original function f(x) has a domain of {x | x ≥ 0} because we cannot take the square root of a negative number. When the function is translated left 5 units, the new function, g(x), will start at x = -5 instead of x = 0, reflecting the domain shift due to translation. Therefore, the domain of g(x) is {x | x > -5}.
PLEASE PLEASE PLEASE HELP Find the value of the discriminant. Then describe the number and type of roots for the equation.
–3x2 – 18x + 5 = 0
The discriminant is 324. Because the discriminant is greater than 0 and is a perfect square, the two roots are real and rational.
The discriminant is –384. Because the discriminant is less than 0, the two roots are complex.
The discriminant is 384. Because the discriminant is greater than 0 and is not a perfect square, the two roots are real and irrational.
The discriminant is –264. Because the discriminant is less than 0, the two roots are complex.
ANSWER
The discriminant is 384. Because the discriminant is greater than 0 and is not a perfect square, the two roots are real and irrational.
EXPLANATION
The given quadratic equation is:
[tex] - 3 {x}^{2} - 18x + 5 = 0[/tex]
We compare this equation to:
[tex]a {x}^{2} + bx + c = 0[/tex]
We have a=-3,b=-18, and c=5.
The discriminant of a quadratic equation is calculated using the formula:
[tex]D=b^{2} - 4ac[/tex]
We plug in the values to obtain:
[tex]D= {( - 18)}^{2} - 4( - 3)(5)[/tex]
[tex]D= 324 + 60[/tex]
Simplify:
[tex]D= 384[/tex]
The discriminant is greater than zero, hence there are two distinct real roots.
Since 384 is not a perfect square, the roots are irrational.
help please ..............
Answer:
6x is indeed the Greatest Common Factor.
Step-by-step explanation:
6x[3 - y² + 2y⁶]