Communicate Mathematical Ideas Find the area of the figure. Explain how you found your answer. 10 ft 16 ft 12 ft 18 ft
I'm confused
Explanation:
The trapezoid has area of
A = h*(b1+b2)/2
A = 6*(10+18)/2
A = 84
The rectangle is 18 ft by 12 ft, which leads to an area of 18*12 = 216 sq ft.
Adding the two sub-areas gets us: 84+216 = 300
The total area of the house-shaped figure is 300 sq ft.
I could use some help with this problem for my algebra 2 class, I'm pretty lost, please give an explanation with your answer, much appreciated!
Question:
Mrs. Galacia is building a chicken farm in 2021 with an initial population of 3750 chickens. The farm grows at a rate of 2.15% annually.
Part (a) Use the exponential growth model to write an equation that estimates the population t years after 2021.
Part (b) Estimate the population of the town in 2036. (I was given an extra step here saying, "Must show plug in step before using calculator")
Answer:
[tex]y=3750 \cdot 1.0215^t[/tex]
(where [tex]y[/tex] is the population and [tex]t[/tex] is time in years after 2021)
5159
Step-by-step explanation:
Part (a)
General form of an exponential function: [tex]y=ab^x[/tex]
where:
[tex]a[/tex] is the y-intercept (or initial value)[tex]b[/tex] is the base (or growth factor) in decimal form[tex]x[/tex] is the independent variableIf [tex]b > 1[/tex] then it is an increasing function
If [tex]0 < b < 1[/tex] then it is a decreasing function
We are told that the initial population is 3750. Therefore, [tex]a=3750[/tex]
We are told that the farm grows at a rate of 2.15% annually. Therefore, if it grows then every year it is 100% + 2.15% = 102.15% of the previous year.
Convert the percentage into a decimal:
102.15% = 102.15/100 = 1.0215
Therefore, [tex]b=1.0215[/tex]
We are told that the independent variable is [tex]t[/tex] (in years).
Therefore, the equation is [tex]y=3750 \cdot 1.0215^t[/tex]
(where [tex]y[/tex] is the population and [tex]t[/tex] is time in years after 2021)
------------------------------------------------------------------------------------------
Part (b)
The year 2036 is 15 years after 2021. Therefore, substitute [tex]t = 15[/tex] into the equation and solve for [tex]y[/tex]:
[tex]\implies y=3750 \cdot 1.0215^{15}[/tex]
[tex]\implies y=5159.49068...[/tex]
Therefore, an estimate of the population of the town in 2036 is 5159.
Carl is a biologist studying different types of mammals. He finds in one vally that there are 15 plant-eating mammals for every 2 meat-eating mammals. The total population is about 2,900. Which number is the beat estimate of the population of meat-eating mammals in the valley. * 170 *340 *1,450 * 2,560
Answer: 340
Step-by-step explanation:
Given: There are 15 plant-eating mammals for every 2 meat-eating mammals.
i.e. ratio of meat-eating mammals to plant eating animals = 2:15 or [tex]\dfrac2{15}[/tex]
ratio of meat-eating mammals to total population = [tex]\dfrac{2}{17}[/tex]
Total population: 2,900 (approx.)
The population of meat-eating mammals in the valley = [tex]\dfrac{2}{17}\times2900[/tex]
[tex]\approx341[/tex]
From the given options, the best estimate of the population of meat-eating mammals in the valley = 340
Item 1
Question 1
The graph of which of the following functions does not belong with the other three?
$f\left(x\right)=3x^2+6x-24$
$f\left(x\right)=3x^2+24x-6$
$f\left(x\right)=3\left(x-2\right)\left(x+4\right)$
$f\left(x\right)=3\left(x+1\right)^2-27$
Question 2
This is the only function that does not have x-intercepts at $x=$ Response area and $x=$ Response area and a vertex at (Response area , Response area).
Answer:
im too slow i thought this was a gta cheat code
Answer:
I only know the first question and it's f(x)=3x^2+24x-6.
please may someone help me i have been doing this for hours
think of the mirror reflection
imagine folding the sheet on the horizontal line y = 1
A B
C
---------------------- y = 1
C'
A' B'
This is really simple, all you have to do is:
Two rental car companies are running specials this month. At Jenny's Rentals, customers will pay $40 to rent a mid-sized car for the first day, plus $14 for each additional day. At Middletown Rent-a-Car, the price for a mid-sized car is $50 for the first day and $4 for every additional day beyond that. At some point, renting from either one of the companies would cost a customer the same amount. How many additional days would that take? How much would the customer pay?
Answer:
8
Step-by-step explanation:
Jessica runs 2 1/2 miles in 16 1/4 minutes. What is Jessica’s average time per mile in minutes? Enter the correct answer in the box. IF YOU GET IT CORRECTLY AND ANSWER IT FIRST ILL MARK YA BRAINLY If possible EXPLAIN IT.
Answer:
6 1/2 minutes per miles
2/13 miles per minutes
Step-by-step explanation:
Distance travelled = 2 1/2 miles
Time taken = 16 1/4 minutes
Average: minutes per mile
= 16 1/4 minutes / 2 1/2 miles
= 65/4 ÷ 5/2
= 65/4 × 2/5
= 13/2
= 6 1/2
Average time per mile in minutes
= 6 1/2 minutes per mile
Average (miles per minutes)
= 2 1/2 ÷ 16 1/4
= 5/2 ÷ 65/4
= 5/2 × 4/65
= 20 / 130
= 2/13 miles per minutes
Quadrilateral LMNO is similar to quadrilateral PQRS. Find the measure of side QR.
Round your answer to the nearest tenth if necessary.
N
R
33.7
S
Q
O
M
18
47
P
Answer: 12.9
Step-by-step explanation:
Hannah works at Blooming Bouquets flower shop. She uses 2 roses for every 5 carnations in the Spring Medley bouquets. Today she will make a Spring Medley bouquet with 16 roses.
How many carnations should Hannah use in the bouquet?
Answer:
40 carnations
Step-by-step explanation:
Using the principle of proportional relationship, the number of carnations to be used in the bouquet is 40
Setting up the proportional relationship thus :
2 roses = 5 carnations ----(1)
16 roses = P carnations - - - - - 2)
Solve for p :
Cross multiply :
2p = 16 × 5
2p = 80
p = 80 /2
p = 40
Therefore, the Number of carnations to be used is 40
Learn more : https://brainly.com/question/18581754
I’ll give Brainly out and likes
Answer:
59
Step-by-step explanation:
You know the measures of the 2 angle values. you add
52+69=121
Since the interior has to be 180 degrees, you subtract
180-121=59 degrees is the measure of I.
Alexa is researching a cure for the coronavirus. She needs 14 test tubes for 4 experiments. The first experiment requires 2 test tubes, and the remainder of the tubes are used evenly over the rest of the experiments. How many test tubes did she use for the last experiment?
Answer:
She used 4 test tubes for the last experiment
Step-by-step explanation:
Total test tubes needed = 14
Experiment 1 = 2 test tubes
Total test tubes remaining = total - used
= 14 - 2
= 12 test tubes
Remaining experiment = 4 - 1
= 3
Test tubes used for the remaining experiment = test tubes remaining / Experiment remaining
= 12 / 3
= 4 test tubes
How many test tubes did she use for the last experiment?
She used 4 test tubes for the last experiment
need help with this asap!! thank you
Answer:
12 1/4
Step-by-step explanation:
2in
3.5in
1.75in
equals:
12.25 or 12 1/4
find 90% of 650 ........
explain if possible
Answer:
585
Step-by-step explanation:
650/10 = 65 (10%)
65 * 9 = 585
A parabola can be drawn given a focus of (-9, -7) and a directrix of x = 9. Write
the equation of the parabola in any form.
Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , -7), let's recall the vertex is half-way between the focus point and the directrix.
so this horizontal parabola opens up to the left-hand-side, meaning that the "P" distance is a negative value.
[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\begin{cases} h=0\\ k=-7\\ p=-9 \end{cases}\implies 4(-9)(x-0)~~ = ~~[y-(-7)]^2 \\\\\\ -36x=(y+7)^2\implies x=-\cfrac{1}{36}(y+7)^2[/tex]
0.00000247 In scientific notation
Answer:
2.47 × 10^-6
Step-by-step explanation:
The negative power is in coorilation to how many decimal spots it was moved.
Ex: The 2 in 2.47 was moved left 6 spots.
please help quick!! Jane makes house calls. For each, she is paid a base amount and makes additional money for each hour she works. The graph below shows her pay (in dollars) versus the number of hours worked.
Answer: a) $30 b) $50 c) $20 each hour d) No, because the line does not pass through (0,0)
Step-by-step explanation:
What is Jane's pay if she doesn't work any hours? This question means how much money does Jane gets paid for working 0 hours (y-intercept). At 0 hours on the x-axis, the point on the line is $30. This can be written as (0,30)
If she works 1 hour, the point where 1 hour on the x-axis meets with the y-axis is $50 dollars. This can be written as (1,50).
Her pay increase each hour is the slope in this given equation as the starting payment before completing any hours work is $30 and the line increases at a positive rate of change. The slope is y^2-y^1 divided by x^2-x^1, and we have (0,30) and (1,50). Plugging them into the formula, 50-30 divided by 1-0 is 20; the slope is $20 for every 1-hour increase).
And for determining whether b and c are equal, every answer choice includes whether the line passes through the point (0,0). After answering problem c, you should find that your equation is y=20x+30 (20 as the slope and 30 as the y-intercept). As a reminder, b is $50 and c is $20, so you already know it is not the top two answer choices. So to see if it DOES pass through (0,0) you can plug the values into the equation OR graph it. Either way, you will see that (0,0) does not pass through the line and that 0 does not equal 30 (0=20(0)+30).
Please help me out!
HELP PLEASE! I PUT AN IMAGE BELOW! PLEASE HELP!
[tex]\begin{array}{lcccl} &\stackrel{lbs}{Qty}&\stackrel{\$}{price}&\stackrel{total}{value}\\ \cline{2-4}&\\ \textit{1st candy}&x&0.9&0.9x\\ \textit{2nd candy}&y&0.4&0.4y\\ \cline{1-4} mix&50&0.85&42.5 \end{array}\qquad \qquad \begin{cases} x+y=50\\\\ 0.9x+0.4y=42.5 \end{cases} \\\\[-0.35em] ~\dotfill[/tex][tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies y=50-x}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{0.9x~~ + ~~0.4(50-x)~~ = ~~42.5} \\\\\\ 0.9x+20-0.4x=42.5\implies 0.5x+20=42.5\implies 0.5x=22.5 \\\\\\ x=\cfrac{22.5}{0.5}\implies \boxed{x=45}\qquad \qquad \qquad \boxed{\stackrel{50~~ - ~~45}{y=5}}[/tex]
You invited 17 people to your house for a party. You want to spend a $50 gift card completely on the items shown. You also want to have exactly two servings of food for each person. A pizza is $6 for 4 servings, and a bag of chicken wings costs $7 for 5 servings. Write a system of linear equations that represents the situation.
Answer:
6p + 7c = 50
4p + 5c = 34
(where p is the number of pizzas and c is the number of bags of chicken wings)
We need to buy 6 pizzas and 2 bags of chicken wings in order to spend a total of $50, AND for each of the 17 people to have 2 servings of food.
Step-by-step explanation:
Let p = number of pizzas
Let c = number of bags of chicken wings
Equation 1
Given:
Pizza = $6Bag of chicken wings = $7Total spend = $50⇒ 6p + 7c = 50
Equation 2
Given:
Pizza = 4 servingsChicken wings = 5 servingsTotal servings needed = 17 × 2 = 34⇒ 4p + 5c = 34
Equation 3
Multiply Equation 2 by 1.5:
⇒ 6p + 7.5c = 51
Subtract Equation 1 from Equation 3 and solve for c:
⇒ 0.5c = 1
⇒ c = 2
Substitute found value of c into Equation 2 and solve for p:
⇒ 4p + 5(2) = 34
⇒ 4p + 10 = 34
⇒ 4p = 24
⇒ p = 6
Therefore, we need to buy 6 pizzas and 2 bags of chicken wings in order to spend a total of $50, AND for each of the 17 people to have 2 servings of food.
Y is the midpoint of XZ and W is the midpoint of VX.
If VZ=s+52 and WY=7s, what is the value of s?
Answer:
4
Step-by-step explanation:
By the triangle midsegment theorem, 2(YW)=VZ.
This means 2(7s)=s+52, and thus s=4.
If 18 people ride in 3 cars how much people ride in 1 car?
Answer:
6 people per car
Step-by-step explanation:
divide 18 people by 3 cars to get people per cars.
please rate and mark as brainlest.
Can someone please help me
Answer:
is this geometry. if it is then i can help you
Step-by-step explanation:
[tex]\\ \rm\rightarrowtail \dfrac{NM}{NO}=\dfrac{KM}{KL}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{x}{7}=\dfrac{20}{2x}[/tex]
[tex]\\ \rm\rightarrowtail 2x^2=140[/tex]
[tex]\\ \rm\rightarrowtail x^2=70[/tex]
[tex]\\ \rm\rightarrowtail x=\sqrt{70}[/tex]
A manager needs to buy chairs for his office. The price for one chair is$79.99. If the manager buys 2 or more chairs, he will receive a 40% discount on each chair. Approximately how much will the manager save on each chair if he buys 2 chairs?A.$32 B.$40 C.$48 D.$80
Answer:
A. $32
Step-by-step explanation:
Normal price
1 chair cost = $79.99
2 chairs = $79.99 × 2
= $159.98
Discount price of 2 chairs
40% of $79.99
= 40/100 × 79.99
= 0.4 × 79.99
= 31.996
Approximately
$32
A. $32
A plane leaves airport A and travels 550 miles to airport B on a bearing of N35°E. The plane later leaves airport B and travels to airport C 380 miles away on a
bearing of S72°E. Find the distance from airport A to airport to the nearest tenth of a mile
Answer:
d₃ = 803.9 Miles
Step-by-step explanation:
d₁ = 560 Miles
R₁ = N35⁰E
d₂ = 410 Miles
R₂ = S76⁰E
d₃ = ?
α = 35⁰+76⁰ = 111⁰
We can apply the Law of Cosines as follows
d₃ = √(d₁² + d₂² - 2*d₁*d₂* Cos α)
⇒ d₃ = √(560² + 410² - 2*560*410* Cos 111⁰) = 803.9 Miles
On a field trip there are 3 adults for every 45 students. Which graph models a relationship with the same unit rate?
Step-by-step explanation:
There is 1 adult for every 15 students. (I don't see any pictures of a graph)
Answer:
There is 1 adult for every 15 students
Step-by-step explanation:
triangle KLM has KL=32, KM= 27, and LM= 21. what is the area of the triangle?
Answer:
281.15 cm²
Step-by-step explanation:
semi perimeter ( s ) = ( a + b + c ) / 2
=( KL + LM + KM ) / 2
=(32+21+27)/2
= 80/2
=40
Area of triangle =
[tex] \sqrt{s \: (s - a) \: (s - b)(s - c)} [/tex]
[tex] \sqrt{40(40 - 32)(40 - 21)(40 - 27)} [/tex]
[tex] \sqrt{40 \times 8 \times 19 \times 13} [/tex]
[tex] \sqrt{79040} [/tex]
[tex]281.15cm {}^{2} [/tex]
This is probably rly easy but I'm lazy
I'll give you brainliest!!
(The answer choices are 1/12 mph, 3 3/4 mph, 5 mph or 15 mph).
Answer:
5mph
Step-by-step explanation:
driver 1 is driving 45mph (7x6=45)
driver 2 is driving 50mph (10x5=50)
Solve the inequality
Answer:
B
Step-by-step explanation:
I need help plz!!!! Anyone?
Answer:
30
Step-by-step explanation:
2x30=60
3x30=90
60+90+30=150
-5 – 3(x – 8) = -5x + 19
Answer:
[tex]x=0[/tex]
Step-by-step explanation:
Given the following question:
[tex]-5 - 3(x - 8) = -5x + 19[/tex]
To find the answer expand the equation, add/subtract on both sides, and simplify the expression.
[tex]-5 - 3(x - 8) = -5x + 19[/tex]
[tex]-5-3(x-8)=-3x+19[/tex]
[tex]-3x+19=-5x+19[/tex]
[tex]19-19=0[/tex]
[tex]19-19=0[/tex]
[tex]-3x=-5x[/tex]
[tex]-3x+5x=-5x+5x[/tex]
[tex]-3x+5x=2x[/tex]
[tex]2x=0[/tex]
[tex]2x\div2=x[/tex]
[tex]0\div2=0[/tex]
[tex]x=0[/tex]
Your answer is "x = 0."
Hope this helps.