Huilan is 8 years older than Thomas. The sum of their ages is 80. What is Thomas's age?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\texttt {\:Thomas's age = 44 years } [/tex]
[tex]\texttt {\:Hulian's age = 36 years } [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{Assume Thomas's age be ' x ' } [/tex]
[tex] \textsf{and that of Huilan's age be y } [/tex]
[tex] \texttt{we have two conditions :} [/tex]
[tex]\qquad \tt \rightarrow \:y = x + 8[/tex]
it can be simplified as : -
[tex]\qquad \tt \rightarrow \:y - x= 8 \: \: \: \: \: \: \: \: \: - (1)[/tex]
[tex] \texttt{Next condition } [/tex]
[tex]\qquad \tt \rightarrow \:x + y = 80 \: \: \: \: \: \: \: - (2)[/tex]
`` Add both equations ``
[tex]\qquad \tt \rightarrow \:y - x + x + y = 8 + 80[/tex]
[tex]\qquad \tt \rightarrow \:2y = 88[/tex]
[tex]\qquad \tt \rightarrow \:y = 44[/tex]
[tex] \large \textsf{For x :} [/tex]
[tex]\qquad \tt \rightarrow \:y - x = 8[/tex]
[tex]\qquad \tt \rightarrow \:44 - x = 8[/tex]
[tex]\qquad \tt \rightarrow \:x = 44 - 8[/tex]
[tex]\qquad \tt \rightarrow \:x = 36[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
[tex]\fbox {36 years old}[/tex]
Step-by-step explanation:
Let :
⇒ Age of Huilan = x
⇒ Age of Thomas = x - 8
Then :
⇒ x + x - 8 = 80
⇒ 2x = 88
⇒ x = 44
Thomas's age :
⇒ x - 8
⇒ 44 - 8
⇒ 36 years old
If anyone can help me to solve this.
Answer:
x=50
Step-by-step explanation:
3x-5=145(vertically opposite angle)
3x=145+5
3x=150
x=150/3
x=50
DON'T FORGET TO WRITE DEGREE
Answer:
x = 50
Step-by-step explanation:
Vertically opposite angles are of equal measure.
Solving:3x - 5 = 145
3x = 145 + 5
3x = 150
x = 50
That's all i know, Hope it helps!
What are the zeros of the quadratic function f(x)=6x^2+12x-7
Answer:
[tex]A) \ x=-1 \ ^ +_-\frac{\sqrt{13} }{\sqrt{6}}.[/tex]
Step-by-step explanation:
if to solve the given equation, then
D=6²+42=78;
[tex]\left[\begin{array}{ccc}x=\frac{-6-\sqrt{78}}{6} \\x=\frac{-6+\sqrt{78}}{6} \end{array} \ = > \ \left[\begin{array}{ccc}x=-1-\sqrt{\frac{13}{6} } \\x=-1+\sqrt{\frac{13}{6} } \end{array}[/tex]
A restaurant offers 7 appetizers and 8 main courses. In how many ways can a person order a two-course meal?
There are ways a person can order a two-course meal.
Answer:
56
Step-by-step explanation:
so 7 appetizers times 8 main courses
I do a easy trick where I multiple so
7×8=56
pleeeeeeeeeeeease hellllllllp meeeeeee the circle has a center of 0.its raduis is 3 cm,and the central angle A measures 100.what is the area of the shaded region? give exact anwsers in term of pi .please hurry dont worry I have permission to post this for anybody who decides to report me again
Answer:
2.5 pi
Step-by-step explanation:
Comment
If you were trying to get the area of a whole circle, you would use
Area = pi r^2
You have to modify the formula to show that just part of the circle has an area that you are interested in.
The new formula is
Area = (theta/360) pi r^2
Givens
r = 30 cm
theta = 100
Solution
Area = (100 / 360) * pi * r^2 Substitute the givens into this formula
Area = (5 / 18) * pi * 3^2 Expand
Area = (5 / 18) * pi * 9 Cancel 9 into 18
Area = 5/2 * pi
Area = 2.5 * pi
Use the graph of the function provided to find the indicated values.
a) When x = -2, g(x) = 5.
b) When x = -4, g(x) = 7.
c) When g(x) = 6, x = -3
d) When g(x) = -1, x = 4
A. 0 m/s
B. -0.17 m/s
C. 12 m/s
D. 0.17 m/s
Answer:
0 m/s
Step-by-step explanation:
Enter the amplitude of the function. f(x)=2sin x
Answer:
2
Step-by-step explanation:
In asin(bx - c) + d, a is the amplitude. In this case, it's 2.
Brainliest, please :)
My friend has $672 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $17/yard on one side, and cheaper metal fencing which costs $7/yard for the other three sides.
What are the dimensions of the garden with the largest area she can enclose?
The dimensions of the garden with the largest area she can enclose are given by 24*14 square yards.
The area (A) of the rectangle with length L and Width W is given by,
A=L*W
The maximum of [tex]y=ax^2+bx[/tex] occurs at x = -b/2a
Let the length and width of the garden be L and W respectively.
Now let my friend use cedar fencing for one width and cheaper metal fencing for rest sides.
Rate of cedar fencing is $17/yard
Then she has to pay for cedar fencing = 17W
rate of cheaper metal fencing is $7/yard
Then she has to pay for metal fencing = 7W+7*2L = 7W+14L
Then according to condition,
17W+7W+14L = 672
24W+14L = 672
12W+7L = 336
7L = 336-12W
L = (336-12W)/7
Then the area of the rectangular garden is given by,
A = L*W
[tex]A=\frac{336-12W}{7}\times W\\A=-\frac{12}{7}W^2+48W[/tex]
So here a = -12/7 and b = 48
Then maximum of W occurs at,
W = -48/(2*(-12/7)) = (48*7)/(2*12) = 336/24 = 14
Then maximum width = 14 yards
then length (L) = (336-12*14)/7 = 168/7 = 24 yards
Hence the dimensions with the leargest area she can enclose is given by = 24 * 14 square yards.
Learn more about Dimensions here -
https://brainly.com/question/8760279
#SPJ10
What are the solutions to the following system of equations?
2x − y = 6
y = x2 − 9
(3, 0) and (−1, −8)
(3, 0) and (4, 2)
(−3, 0) and (−1, −8)
(−3, 0) and (4, 2)
Answer:
(3, 0) and (−1, −8)
Equation's:
2x − y = 6y = x² − 9Substitute equation 2 into 12x − (x² − 9) = 6
2x - x² + 9 = 6
-x² + 2x + 9 - 6 = 0
-x² + 2x + 3 = 0
x² - 2x - 3 = 0
x² - 3x + x - 3 = 0
x(x - 3) + 1(x - 3) = 0
(x + 1)(x - 3) = 0
x = -1, x = 3
Find values for yIf x = -1, then y = (-1)² - 9 = -8
If x = 3, then y = (3)² - 9 = 0
Solution Set:(x, y) = (-1, -8), (3, 0)
Choose the correct range , mean and standard deviation for participant age written in correct APA format . A. Participants ranged in age from 4 to 90 ( M = 26.24 , SD = 23.00 ) . B. Participants ranged in age from 18 to 54 ( M = 26.24 , SD = 8.04 ) . C. Participants ranged in age from 18 to 54 ( M = 23.00 , SD = 26.24 ) . D. Participants ranged in age from 4 to 26.24 ( M = 26.24 , SD = 8.04 ) . E. Participants ranged in age from 18 to 58 ( M = 23.00 , SD = 8.04 ) .
The range, the mean, and standard deviation are mathematically given as
Participants ranged in age from 4 to 26.24 ( M = 26.24 , SD = 8.04 ). Option D.
What are the range, the mean, and standard deviation?Given the data presented below the given
A look at the result shows that the lowest and highest values are between 1s and 58, with a mean and standard deviation of 26.10 and 8.90, respectively.
Participants' ages varied from 18 to 58 (m-26.14, std dev = 8.01), hence option (d) is accurate.
Read more about standard deviation
https://brainly.com/question/12402189
#SPJ1
What is the solution to t - 3 < 12
Answer:
[tex]\boxed {t < 15}[/tex]
Step-by-step explanation:
Given :
⇒ t - 3 < 12
Add 3 to each side :
⇒ t - 3 + 3 < 12 + 3
⇒ t < 15
Answer: t < 15
Step-by-step explanation:
rearrange the terms t - 3 < 12
calculate the sum or difference t < 12 + 3
answer t < 15
David rolls a fair dice 30 times. How many times would David expect to roll a number greater than 3?
Answer:
15
Step-by-step explanation:
so if its a 6 faced dice then there is a 3/6 numbers greater than 3. which simplifies to 1/2. 30(1/2)= 15
The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age. A random sample of ten automobile insurance liability claims is under study.
The mean will be 10.08 and the standard deviation will be 1.27.
The complete question is given below:-
The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age. A random sample of twelve automobile insurance liability claims is under study.
Find the mean and standard deviation of this probability distribution.
For samples of size 12, what is the expected number of claims made by people under 25 years of age?
What is mean?Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
Given that:-
The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age.We need to find For samples of size 12, what is the expected number of claims made by people under 25 years of age?The mean will be calculated by the formula below:-
Mean = [tex]\mu[/tex] = np = 12 x 0.84 = 10.08
The standard deviation will be calculated as:-
Standard deviation = [tex]\sqrt{npq}[/tex] = [tex]\sqrt{12\times 0.84\times 0.16}[/tex] = 1.27
Therefore the mean will be 10.08 and the standard deviation will be 1.27.
To know more about mean follow
https://brainly.com/question/968894
#SPJ1
Hello,
I need help with this exercise.
A ball is launched upward at a speed of 20 meters per second (m/s) from a 60-meter tall platform. The equation for the ball’s height (h in meters) at time t seconds after launch is h = -4.9t2 + 20t + 60. How long before the ball hits the ground? What is the maximum height of the ball?
Answer:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
Answer: I HOPE THAT MY ANSWER WILL HELP U
Step-by-step explanation:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
URGENT: Click on the graph to choose the correct answer to the equation. x > 2
The graph of x >2 is attached below
Clearly, the graph of x> 2 could be area beyond 2 on positive X axis
What is graph?
The graph is a demonstration of curves which gives the relationship between x and y axis.
The question seems to be incomplete, because options are missing.
so the option can be of several graphs.
Thus, The correct Graph of x >2 has been attached below.
Learn more about graphs here:
https://brainly.com/question/16608196
#SPJ1
Please assist with the following questions
The answers for following questions are;
i. $244.64
ii. $ 5314.64
What is future value?Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth. The future value is important to investors and financial planners, as they use it to estimate how much an investment made today will be worth in the future.
Here, future value or amount;
A = P(1 + r)ⁿ
Where,
A = future value = ?
P = principal = $ 12,300
r = interest rate = 6%/12 = 0.06/12 = 0.005
n = number of periods = 12 X 6 years = 72
A = P(1 + r)ⁿ
= 12,300(1 + 0.06/12)⁷²
= 12300 (1 + 0.005)⁷²
= 12300 (1.005)⁷²
= 12300 (1.4384)
= 17,614.64
Each monthly payment = Total payment / number of months
= $17,614.64 / 72
= $ 244.64
Total amount of interest = Total payment - Principal payment
= 17,614.64 - 12300
= $ 5314.64
Thus, The answers for following questions are;
i. $244.64
ii. $ 5314.64
Learn more about Interest from:
https://brainly.com/question/13324776
#SPJ1
Solve: 8 + x/3 = 1/6 (x-6) -1
A. x = 60
B. x = -60
C. x = -36
D. There are infinitely many solutions
Answer: B -60
Step-by-step explanation: When you plug in -60 into the equation it all equals out into -12 = -12, which is true. All of the other solutions don't work.
Answer:
B. x = -60
Step-by-step explanation:
8 + x/3 = 1/6 (x-6) - 1
Multiply both sides by 6.
48 + 2x = x - 6 - 6
x = -12 - 48
x = -60
Is 9.3 X 100^9 in scientific notation
Answer:
No.
Step-by-step explanation:
This problem in scientific notation would be 9.3 * 10^10.
HELP TO ASAP Compare the graph of f(x) with the graph of k(x) = 5(x-6)².
OA. The graph of k(x) is horizontally stretched by a factor of 5 and
shifted 6 units right.
OB. The graph of k(x) is vertically stretched by a factor of 5 and shifted
6 units right.
OC. The graph of k(x) is horizontally stretched by a factor of 5 and
shifted 6 units left.
Parent function
y=x²Now look the transformations
y=(x-6)²x is changed and shifted 6 units right
Then
y=5(x-6)²Horizontally Streched with a factor of 5
Answer:
B) The graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
Given functions:
[tex]f(x) = x^2[/tex]
[tex]k(x) = 5(x - 6)^2[/tex]
Parent function: [tex]f(x) = x^2[/tex]
Translated 6 units right: [tex]f(x-6)=(x-6)^2[/tex]
Then stretched vertically by a factor of 5: [tex]5f(x-6)=5(x-6)^2[/tex]
[tex]\implies 5f(x-6)=5(x-6)^2=k(x)[/tex]
Therefore, the graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.
Learn more about translations here:
https://brainly.com/question/27845947
What is the solution to 8t+3(t+4) =6(t-3)
Answer:
t = - 6
Step-by-step explanation:
8t + 3(t + 4) = 6(t - 3) ← distribute parenthesis on both sides )
8t + 3t + 12 = 6t - 18 , that is
11t + 12 = 6t - 18 ( subtract 6t from both sides )
5t + 12 = - 18 ( subtract 12 from both sides )
5t = - 30 ( divide both sides by 5 )
t = - 6
what is the constant proportionality in the equation y = 5/4x?
What is the length of each leg of the triangle below?
45°
90⁰
22
OA. 15
B. √22
C. 11
45°
D. 11/2
E. VIT
F. 1
Answer:
A. 15
Step-by-step explanation:
Hypotenuse = 22
Since the two angles other than the 90° are both
45° , it means that the two legs of the right triangle are of equal length.
So, (x)²+ (x)² = 22²
2x² = 22²
x² = 484/2
x² = 242
x = √242
x = 15.55
x ≈ 15
Choose the function that includes the given points.
(0,−2),(5,13),(−2,−8),(4,10)
The function that includes the given points of (0,−2),(5,13),(−2,−8),(4,10) is the second encircled option by the top right in the image attached.
What is the function about?Note that all function of (0,−2),(5,13),(−2,−8),(4,10) can be seen as all the brackets are placed in the form (X, Y), Y=P(x)
In the case above, how we arrived at the answer, you have to fill up the X's in the brackets using the X's in the Options.
Then since P(x) is the number one see in place of Y in the brackets, then that the top Right option is correct as it has −2.
Therefore, The function that includes the given points of (0,−2),(5,13),(−2,−8),(4,10) is the second encircled option by the top right in the image attached.
Learn more about function from
https://brainly.com/question/14218786
#SPJ1
In a vacancy for a position of animal breeder in an organization, then criteria of selection were work experience, entrance exam, and interview results. The relative importance of these criteria was regarded to be different. The weights of these criteria and scores obtained by 3 candidates (out of 100 in each criterion) are given in the following table. In addition, the selection of a candidate is based on the average result on these criteria, (full question attached)
Answer:
To determine the most suitable candidate we will calculate their total scores and see who's the best.
first for mr X
work experience = 70
score = work experience x wieght = 70 x 4 = 280
Entrance = 78
score = 78 x 3 = 234
Interview = 70
score = 70 x 4 = 210
total score = 280 + 234 + 280 = 794
for mr Y
Work experience = 89
score = 89 x 4 = 356
Entrance = 83
score = 83 x 3 = 249
Interview = 89
Score = 89 x 4 = 356
Total score = 356 + 249 + 356 = 961
for mr Z
work experience = 85
score = 85 x 4 = 340
Entrance = 89
Score = 89 x 3 = 267
Interview = 85
Score = 85 x 4 = 340
Total score = 340 + 267 + 340 = 947
So as we can see Mr Y has best score therefore I think he's the best for the job.
Explanation:
[tex]\sf Average \ Result : \dfrac{sum \ of \ value \ of \ scores}{sum \ of \ weight}[/tex]
Workout:
[tex]\sf For \ candidate \ X = \dfrac{70 \ \cdot \ 4 \ + 78 \ \cdot \ 3 \ + 70 \ \cdot \ 4 }{4 + 3 + 4} = 72.18 \ \ average \ score[/tex]
[tex]\sf For \ candidate \ Y = \dfrac{89 \ \cdot \ 4 \ + 83 \ \cdot \ 3 \ + 89 \ \cdot \ 4 }{4 + 3 + 4} = 87.36 \ \ average \ score[/tex]
[tex]\sf For \ candidate \ Z = \dfrac{85 \ \cdot \ 4 \ + 89 \ \cdot \ 3 \ + 85 \ \cdot \ 4 }{4 + 3 + 4} = 86.09 \ \ average \ score[/tex]
Conclusion:
Among all of them, candidate Y has the best average score of about 87.36 whereas candidate Z has second best score of 86.09 average score and candidate X has the least average score of 72.18.
Candidate Y is the appropriate candidate for this position on the criteria.
Function: one to one. Help with this math question!
The answer for f.f (x) = 25 / 4x² and g.g(x)= 4x² -28x +49.
What is a Function ?A function is a mathematical statement used to relate a dependent and an independent variable.
It is given that
f(x) = 5/2x
g(x) = 2x - 7
It is asked to found
f.f
g.g
f.f (x) = (5/2x) * (5/2x)
= 25 / 4x²
g.g(x)= ( 2x - 7)( 2x - 7)
= 4x² -28x +49
Both the answers are in its simplified form
Therefore the answer for f.f (x) = 25 / 4x² and g.g(x)= 4x² -28x +49.
To know more about Function
https://brainly.com/question/12431044
#SPJ1
Suppose the only measuring cup you own is a one-third measuring cup. Using this measuring cup how many scoops will you need to have 3 2/3 cups of sugar
Answer:
11
Step-by-step explanation:
for each full cup of sugar, you need 3 one-third measuring cups.
we have 3 full cups so 3×3=9
and another 2 for the 2/3, 9+2=11
so a total of 11 scoops
The function f(x) is shown in this graph.
The function g(x) = -7x-1.
Compare the slopes.
f(x)
(0.3)
A. The slope of f(x) is greater than the slope of g(x).
B. The slope of f(x) is less than the slope of g(x)..
C. The slope of f(x) is the same as the slope of g(x).
I need help
Answer:
A maybe?
Step-by-step explanation:
by looking at the graph you can see there are two points with one being at (0, 3) (given) and the other being at (1, 1) (by looking at the graph). You can use the slope formula (y2 - y1) / (x2 - x1) which gives you the slope.
Plug Values In:
(1-3) / (1-0) = -2/1 = -2
slope of f(x) = -2
slope of g(x) = -7 (slope-intercept form y=mx+b where m is the slope and b is the y-intercept)
I'm honestly not quite sure what it means by greater than since technically the slope of f(x) is greater than the slope of g(x) but does it mean how much it's changing by in which case the sign doesn't matter. Although I'm just going to assume it purely means the value in which case A is true.
(90 Points)
(Score for Question 1: ___ of 10 points)
A local newspaper charges $42 per half-page advertisement and $86 per full-page advertisement. Kathryn has a budget of $1192 to purchase 20 advertisements.
• Define a variable for each unknown.
• Write a system of equations to represent the situation.
• How many full-page advertisements does Kathryn purchase?
• Show your work.
• How many half-page advertisements does Kathryn purchase?
Show your work.
Answer:
Let x = number of half-page advertisements
Let y = number of full-page advertisements
[tex]\begin{cases} 42x + 86y = 1192\\ x + y = 20\end{cases}[/tex]
8 full-page advertisements
12 half-page advertisements
Step-by-step explanation:
Definition of variables
Let x = number of half-page advertisements
Let y = number of full-page advertisements
Given information:
cost per half-page advertisement = $42cost per full-page advertisement = $86total budget = $1192number of advertisements to purchase = 20Using the given information, we can write a system of equations:
Equation 1: 42x + 86y = 1192
Equation 2: x + y = 20
To solve the system of equations, rearrange Equation 2 to make x the subject:
⇒ x = 20 - y
then substitute this into Equation 1 and solve for y:
⇒ 42(20 - y) + 86y = 1192
⇒ 840 - 42y + 86y = 1192
⇒ 840 + 44y = 1192
⇒ 44y = 352
⇒ y = 8
Substitute the found value of y into Equation 2 and solve for x:
⇒ x + 8 = 20
⇒ x = 12
Therefore, Kathryn purchased:
8 full-page advertisements12 half-page advertisementsan animal shelter takes in an average of 5 animals per day. the shelter must keep its total occupancy below 300. currently the shelter has 165 animals. if none of the animals get adopted which inequality represents how many more days, x, the shelter can continue to take in animals without exceeding its occupancy limit?
Answer:
y= 5x+165
Step-by-step explanation:
the slope is 5, so five per day, plus the y-intercept, or when x = 0
Brainliest pls