Answer:
f×=×-2×+8=10×f=20xf=30×f
Select the correct answer. What is the solution for x in the equation? -x + 3/7=2x-25/7
Answer:
x + 3/7=2x-25/7
X=4
A sum of money is shared in the ratio 3:4:7.
The smallest share is £210.
What is the total amount of money shared?
Answer:
£980
Step-by-step explanation:
3 portions = 210
1 portion = 70
so 70
70 × 4 = would be 280
70 × 7 = 490
490 + 280 + 210 = 980
hope this works : )
The annual attendance at the amusement park is initially 2 million people and is increasing at 3% per year. The park’s annual food supply is initially adequate for 4 million people and is increasing at a constant rate adequate for an additional 0.2 million people per year.
a. Write the equation that represents the food supply. Write the equation represents the park attendance.
The equation that represents food supply is
b. Based on these assumptions, in approximately what year will the amusement park first experience shortages of food?
c. If the park doubled its initial food supply and maintained the rate of increase of 0.2 million people per year, would shortages still occur? In approximately which year?
d. If the park doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur? After how many years would the food supply run out?
Please show work. I will mark brainliest.
Answer:
[tex]\textsf{a)} \quad f(t) = 4+0.2t \:\: \textsf{ and }\:\:A(t)=2(1.03)^t[/tex]
b) 77 years
c) 86 years
d) 110 years
Step-by-step explanation:
Part (a)Given:
Initial food supply adequacy = 4 million peopleConstant annual growth rate = 0.2 million peopleAs the food supply grows at a constant rate of being adequate for an additional 0.2 million people per year, it can be expressed as a linear function:
[tex]f(t) = 4+0.2t[/tex]
where:
f(t) = annual food supply (in millions of people).t = time (in years).Given:
Initial attendance = 2 million peopleAnnual growth rate = 3%As the annual attendance increases by 3% per year, it can be expressed as an exponential function:
[tex]A(t)=2(1.03)^t[/tex]
where:
A(t) = annual attendance (in millions of people).t = time (in years).Part (b)Graph the two functions (see attached) and locate the value of t for which A(t) > f(t) for the first time.
From inspection of the graph, the two functions intersect at t ≈ 77. So after approximately 77 years the food supply will not be enough for the number of people attending the amusement park. Therefore, after approximately 77 years, the park will first experience shortages of food.
Part (c)If the park doubles its initial food supply and maintains the rate of increase of 0.2 million people per year, the new equation would be:
[tex]f(t) = 8+0.2t[/tex]
Again, graph the new function against A(t) and find the point where the two functions intersect. A(t) = f(t) at approximately t = 86 so the park will first experience food shortages after 86 years. So doubling the initial food supply delays the eventual food shortage by only c. 9 years.
Part (d)If the park doubled the rate at which its food supply increases in addition to doubling its initial food supply, the new equation would be:
[tex]f(t) = 8+0.4t[/tex]
Again, graph the new function against A(t) and find the point where the two functions intersect. A(t) = f(t) at approximately t = 110 so the park will first experience food shortages after 110 years. So doubling the initial food supply and doubling the rate delays the eventual food shortage by only c. 33 years compared to the initial parameters. Shortages would still occur, but it would be later in approximately 110 years' time.
XZ is the perpendicular bisector of segment WY. Solve for m. Enter a NUMBER only.
2(14m-8)=180
24m-16=180
24m=196
m= 8 and 1/6
What is the sum of 2 3/4 and −2 3/4 ?
A. 0
B. 3/4
C. 5 1/2
D. I don't know.
Answer:
A. 0
Step-by-step explanation:
[tex]2 \frac{3}{4} + ( - 2 \frac{3}{4}) \\ = \frac{11}{4} - \frac{11}{4} \\ = \frac{11 - 11}{4} \\ = \frac{0}{4} = 0 \\ hope \: this \: would \: help[/tex]
Answer:
A. 0
Explanation:
Given:
[tex]2\dfrac{3}{4} +(-2\dfrac{3}{4} )[/tex]
In improper fractions:
[tex]\dfrac{11}{4} +(\dfrac{-11}{4} )[/tex]
Simplify:
[tex]\dfrac{11}{4} -\dfrac{11}{4}[/tex]
Evaluate:
[tex]0[/tex]
Tip:
As the integers are alike, when subtracted they simplify to zero as a result.
Maya is using a coordinate plane to create a map of her yard drawn to scale. Each unit
on the coordinate plane represents 1 meter. Her yard forms a quadrilateral with vertices
A(5, -3), B(10, -3), C(12, -11), and D(7, -11). Maya would like to fence in her entire
yard. Fencing costs $200 per meter. How much will it cost Maya to fence in her yard?
Answer:
$5,298.48
Step-by-step explanation:
Given vertices:
A = (5, -3)B = (10, -3)C = (12, -11)D = (7, -11)As points A and B, and points C and D, have the same y-coordinates, AB is parallel to CD.
As there is a difference of 5 units between points A and B, and C and D, AB = CD.
As AB is parallel to CD and AB = CD ⇒ AD = BD and AD is parallel to BD.
Therefore, the quadrilateral ABCD is a parallelogram (see attachment).
To find the perimeter of ABCD, calculate the side lengths of AB and AD using the Distance Formula.
[tex]\boxed{\begin{minipage}{4.7 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]
[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(10-5)^2+(-3-(-3))^2}\\& =\sqrt{(5)^2+(0)^2}\\& =\sqrt{25}\\& =5\:\:\sf units\end{aligned}[/tex]
[tex]\begin{aligned}AD & =\sqrt{(x_D-x_A)^2+(y_D-y_A)^2}\\& =\sqrt{(7-5)^2+(-11-(-3))^2}\\& =\sqrt{(2)^2+(-8)^2}\\& =\sqrt{4+64}\\& =\sqrt{68}\:\:\sf units\end{aligned}[/tex]
The perimeter of a two-dimensional shape is the distance all the way around the outside.
[tex]\begin{aligned}\textsf{Perimeter of $ABCD$} & = AB + CD + AD + BC\\& = 2\:AB + 2\:AD\\& = 2 \cdot 5+2 \cdot \sqrt{68}\\& = 10+2 \sqrt{68}\\& = 10+2\sqrt{4 \cdot 17}\\& = 10+2\sqrt{4}\sqrt{17}\\& = 10+2 \cdot2\sqrt{17}\\& = 10+4\sqrt{17}\:\:\sf units\end{aligned}[/tex]
As 1 unit = 1 meter, the perimeter of the fence is (10 + 4√17) m.
If fencing costs $200 per meter:
[tex]\begin{aligned}\sf \implies Cost \:of\:fencing& = 200(10 + 4 \sqrt{17})\\& = 2000+800 \sqrt{17}\\& = 5298.4845\\ & = \$5298.48\end{aligned}[/tex]
Therefore, it will cost Maya $5,298.48 to fence her yard.
show that the roots of the quadratic equation given by(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0
are rea land they can not be equal unless a=b=c.
Expanding out the equation, we get
[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]
Considering the discriminant,
[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]
This is always non-negative, meaning the roots are real.
The roots are equal if and only if the discriminant is 0, which is when a=b=c.
Best answer is ready to give gift prize?
Step-by-step explanation:
but please where is the question I'm eager to answer and win the pizza
Will y=3x+5 pass throught the (0,5) or will it not pass the (0,5) ?
(0,5) is that equations y intercept so it WILL pad through that point.
[tex]Answer:\ y=3x+5\ pass\ throught\ the\ (0,5)[/tex]
Step-by-step explanation:
[tex]y=3x+5\ \ \ \ \ (0,5)\\5=3*0+5\\5=0+5\\5\equiv5\\Hence,\\y=3x+5\ pass\ throught\ the\ (0,5)[/tex]
What are two different names for the plane shown
in the diagram below?
Answer:
Plane Y and CDB
Step-by-step explanation:
Plane Y and CDB
The company made a partial payment of $600 cash on the equipment purchased in transaction d.
Answer: can u finish the question
Step-by-step explanation:
How much should Roman invest today in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly?
Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.
First, convert R as a percent to r as a decimal
r = R/100
r = 5.65/100
r = 0.0565 per year,
Then, solve the equation for P
P = A / (1 + r/n)^(nt)
P = 22,450.15 / (1 + 0.0565/12)^{(12)(3.7)}
P = 22,450.15 / (1 + 0.0047)(44.4)
P = $18,223.97
The principal investment required to get a total amount of $22,450.15 from compound interest at a rate of 5.65% per year compounded 12 times per year over 3.7 years is $18,223.97.
Therefore, Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.
Learn more in depth about compound interest at https://brainly.com/question/24924853
#SPJ9
Please help I will give anyone brainliest
Answer:
1672.50 = 37.75x + 1068.50
x = 16
There were 16 players brought to the tournament.
Step-by-step explanation:
y = mx + b
y= the total cost
m = cost of each meal
x = the number of players
b = cost of the bus
Plug in what you know and solve for x
1672.50 = 37.75x + 1068.50 Subtract 1068.50 from both sides.
604 = 37.75x Divide both sides by 37.75
16 = x
Equation: 1068.50 + 37.75x =1,672.50
Answer: X= 16
If 1,672.50 is our total it will go behind the equal sign. 37.75x and 1068.50 must be added together to help us receive our total.
Our written equation should look like this
1068.50 + 37.75x =1,672.50
X is the number of players on the team.To find out we must first subtract the amount of money spent on the bus, from the total amount spent.
1,672.50-1068.50 is 604. This means our equation now looks like this
37.75x=604. The next and final step is to divide 37.75 into 604.
604/ 37.75 is 16. Which means that there are 16 players on the team.
I hope this helps & Good luck.
a line skew to AT (in image attatched)
The line skewed to AT is HB
How to determine the line skewed to AT?As a general rule, skew lines are nonparallel lines that do not intersect
This means that the lines are in different planes
From the given figure, we can see that lines HB and AT do not intersect and they are not parallel
Hence, the line skewed to AT is HB
Read more about skew lines at:
https://brainly.com/question/18024403
#SPJ1
Can someone explain this pls
Answer:
Step-by-step explanation:
( g ° f )(x) = ( x + 7 )² = x² + 14x + 49
20 + 3(x² + 14x + 49) = - 34
20 + 3x² + 42x + 147 = - 34
3x² + 42x + 201 = 0 ⇔ x² + 14x + 67 = 0
D = 196 - 268 = - 72 < 0
There is no any roots in set of real numbers.
The values of x in set of complex numbers are:
[tex]x_{12}[/tex] = [tex]\frac{- 14 }{2}[/tex] ± [tex]\frac{6\sqrt{2}i }{2}[/tex]
[tex]x_{12}[/tex] = - 7 ± 3√2 i
The point G(-5, -1) is reflected over the line y= -3. What are the coordinates of the resulting point, G’
The coordinates of the resulting point after the reflection are (-5, -5)
What are the coordinates of the resulting point?
When we do a reflection over a given line, the perpendicular distancee between the line and the point is invariant.
In this case, we want to reflect the point (-5, -1) over the line y = -3
The distance between the y-value of the point and the line is:
D = |-1 - (-3)| = | -1 + 3| = 2
The point is at 2 units (above) from the line, then after the reflection, the point will be 2 units below the line.
So the new y-value is:
y = -3 - D = -3 - 2 = -5
The coordinates of the resulting point are (-5, -5).
If you want to learn more about reflections:
https://brainly.com/question/4289712
#SPJ1
Determine the value of cscθ given that the terminal side of angle θ intersects the unit circle in the first quadrant at (7/17,y).
The value of cscθ is 1/y
In this question, we have been given that the terminal side of angle θ intersects the unit circle in the first quadrant at (7/17, y).
We know that the point on the unit circle is of the form (cosθ, sinθ)
Comparing (cosθ, sinθ) with point (7/17, y) we get,
cosθ = 7/17, and sinθ = y
also, we know that cscθ = 1/sinθ
So, cscθ = 1/y
Therefore, the value of cscθ is 1/y
Learn more about the cscθ here:
https://brainly.com/question/22881533
#SPJ1
A t-shirt requires 1 3/8 yards of material. How many t-shirts can be made from 41 1/4 yards of material?
Applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.
How to Divide Fractions?In the problem given, we have the following information:
Material needed for one t-shirt = 1 3/8 yards
We want to find how many 1 3/4 we would find in 41 1/4.
Applying the knowledge of fraction, we are to divide 41 1/4 by 1 3/8. Convert both mixed fractions to improper fractions then divide:
41 1/4 ÷ 1 3/8
165/4 ÷ 11/8
165/4 × 8/11
165/4 × 8/11
15/1 × 2/1
= (15 × 2)/(1 × 1)
= 30/1
= 30.
Therefore, applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.
Learn more about fractions on:
https://brainly.com/question/17220365
#SPJ1
I got one final question... What is -1/3x + 1 = -7
Answer Formula: x =
Answer: x=24
Step-by-step explanation:
-1/3x+1= -7
you move the negative one to the other side of the equation to get x by itself and get -1/3x= -8
then you divide both sides by -1/3 and get 24
The height above ground of a cannon is a function of the time since it was shot.
Question: When time equals 0, why is the height of the cannon ball not equal to 0? Describe the domain of this function. Describe the range.
Given is the quadratic function by its graph..
At the start point, when time is zero, the height is not zero because the cannon was shot above the ground level.
The domain is the time from the point the cannon was shot and to the point the ball lands.
The range is the height from zero to the maximum height the ball reaches.
HELP PLEASE!!!!!!! A zookeeper wrote down the number of fish each of the ten dolphins in the aquarium ate per day. His results were as follows: 18, 15, 25, 17, 13, 15, 23, 27, 30, and 27. Find the mean absolute deviation of this data set. What does the mean absolute deviation tell you about the dolphins at the aquarium?
The mean absolute deviation is 5.4.
The mean absolute deviation tells us that the variance of each data set is 5.4.
What is the mean absolute deviation?The mean absolute deviation is a measure of variance that determines the average distance between each data point in the dataset and its mean.
The mean absolute deviation = 1/n ∑ l x - m(x) l
The first step is to determine the mean of the data set: (18 + 15 + 25 + 17 + 13 + 15 + 23 + 27 + 30 + 27) / 10
= 210 / 10
= 21
The second step is to determine the absolute difference between the mean and each data point. Then add the result together.
|(18 - 21) + (15 - 21)+ (25- 21) + (17- 21) + (13- 21) + (15- 21) + (23- 21) + (27- 21) + (30- 21) + (27- 21)| = 54
Now, divide the sum by the total numbers in the data set : 54 / 10 = 5.4
To learn more about mean absolute deviation, please check: https://brainly.com/question/27365177
#SPJ1
Which lists all the factors of 78?
Answer:
1, 2, 3, 6, 13, 26, 39, and 78
Step-by-step explanation:
:)
Given:
p: x-5= 10
q: 4x+1 = 60
Which is the inverse of p→q?
If x-5 ≠ 10, then 4x+1≠61.
If 4x+1 ≠61, then x-5≠10.
If x-5=10, then 4x+1=61.
If 4x+1=61, then x-5=10
Answer:
Step-by-step explanation:
Solving quadratics factoring G CF, solving equations by factoring
Answer: k=0,-5
Step-by-step explanation:
Your GCF is 5k, as you're able to take it out of both terms.
Once you've taken out a 5k, this will leave you with an equation that looks like this;5k(k+5)=0.
Set your 5k equal to 0 and divide to get k=0
Set your k+5 equal to 0 and subtract on both sides to get k=-5
Hope this helps you, dawg.
what is the answer to 17^2-286
The answer for the given expression, 17²-286 will be 3.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,the expression is,
17²-286
The expression is solved by the arrthmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
=17²-286
=289-286
=3
Thus, the answer for the given expression, 17²-286 will be 3.
Learn more about the equation here,
https://brainly.com/question/10413253
#SPJ2
adam has $800 invested in two accounts. one pays 6% annual interest and the other pays 10% interest. the amount of annual interest is the same as he would earn if the entire $800 was invested at 8.25%. How much does he have invested at each rate?
Adam invested $350 at 6% and $450 at 10%
Amount invested by Adam = $800
Interest paid by one account = 6%
Interest paid by another account = 10%
Let the amount invested in one account be x and the other be y
The formula for simple interest is given by:
Simple interest = (P*R*T)/100
where P = Principal
R = rate of interest
T = number of years amount is invested
Substituting the value in the formula we get:
Simple interest in one account = (x*6*1)/100-------(1)
Simple interest in another account = (y*10*1)/100--------(2)
The question states that interest earned would be the same when $800 is invested at 8.25%, therefore
Simple interest = (800*8.25*1)/100
= 66----(3)
Equating (1), (2) and (3) we get:
x + y = 800-----(4)
6x/100 + 10y/100 = 66
6x + 10y = 6600-----(5)
Multiplying (4) with 6 and equating it with (5)
6x + 6y = 4800
6x + 10y = 6600
4y= 1800
y = 450
x = 350
So, Adam invested $350 at 6% and $450 at 10%
Learn more about simple interest:
https://brainly.com/question/22621039
#SPJ1
The coordinate point (-5, 18) is a point on the graph of f. Write this point in function notation.
f(-5) = 13
f(-5) = 18
f(18) = -3.6
f(18) = -5
The function notation of the coordinate point where the coordinate point is given as (-5, 18) is f(-5) = 18
What are coordinate points?Coordinate points are mathematical statements that are used to represent the location of points on a coordinate plane
How to rewrite the function notation of the coordinate point?The coordinate point is given as
(-5, 18)
The above coordinate point can be represented as
(x, y) = (-5, 18)
The above coordinate point can further be rewritten as
(x, f(x)) = (-5, 18)
So, we have
x = -5
f(x) = 18
Substitute x = -5 in the equation f(x) = 18
f(-5) = 18
Hence, the function notation of the coordinate point where the coordinate point is given as (-5, 18) is f(-5) = 18
Read more about function notation at
https://brainly.com/question/10283950
#SPJ1
Ileana wants to know the mean number of pets owned by students in her
grade. She conducts a survey of 20 of her classmates to see how many pets
they own. The results are shown in the dot plot.
Number of Pets In the Home
::::::
0
1 2 3 4 5 6
●●
7
H
8 9 10
Which is the best estimate of the mean number of pets owned by students in
her grade?
Based on the results shown in the dot plot on the number of pets owned by students in Ileana's grade, the mean number of pets owned by students is 2.5 pets
What is the mean number?The number of pets owned per student home according to the dot plot is:
= 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 8
The total number of pets owned is:
= 0 + 0 + 0 +1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 +8
= 50 pets
The mean number of pets owned is:
= 50 / 20 students
= 2.5 pets
Find out more on mean at https://brainly.com/question/2560383
#SPJ1
Choose the measurement closest to 180 cm: 6 ft, 180 in. or 450 in
Answer:
6ft
Step-by-step explanation:
180cm=5ft10in=70in
So it's closer to 6ft
Help :)
Evaluate the following expression
|−3d−6|+|−5−d2| for d=−3
The value of the expression |−3d − 6| + |−5 − d²| when d = -3 is 17.
Given expression: |-3d - 6| + |-5 - d²|, and d = -3
Substitute the value of d: |-3(-3) - 6| + |-5 - (-3)²|
Calculate the values inside the absolute value signs:
|-(-9) - 6| + |-5 - 9|
Simplify the inside calculations:
|9 - 6| + |-5 - 9|
Continue simplifying:
|3| + |-14|
Calculate the absolute values:
3 + 14
Add the values together:
3 + 14 = 17
So, the value of the expression |−3d − 6| + |−5 − d²| when d = -3 is 17.
To know more about expression:
https://brainly.com/question/34132400
#SPJ3