Hi! I'm happy to help!
To solve this, we first need to look at the perimeter equation:
P=2L+2W
We don't know our length, so we can represent it with x. Since our width is 2 feet shorter than x, we can represent it with x-2. Now, we plug these values into our equation:
56=2x+(2(x-2))
Let's simplify what the width is by multiplying:
56=2x+2x-4
Now, let's combine our 2xs
56=4x-4
Now, we just need to solve for x in order to find our length and width.
First, we need to isolate x on one side of the equation. We can do this by adding 4 to both sides:
56=4x-4
+4 +4
60=4x
Now, all we have to do is divide both sides by 4 and x will be fully isolated:
60=4x
÷4 ÷4
15=x
Now that we know x, let's plug this into our previous equations:
L=x=15
L=15
W=x-2=15-2=13
W=13
To verify our answers, we can plug this into our perimeter equation:
56=2(15)+2(13)
56=30+36
56=56
After double checking our answers, we know that our length is 15 and our width is 13.
I hope this was helpful, keep learning! :D
1. Your school's Key Club decided to sell fruit baskets to raise
money for a local charity. The club sold a total of 80 fruit
baskets. There were three different types of fruit baskets.
Small fruit baskets sold for $15.75 each, medium fruit baskets
sold for $25 each, and large fruit baskets sold for $32.50
each. The Key Club took in a total of 52086.25. and they sold
twice as many large baskets as small baskets.
a. Formulate a system of three linear equations in three
variables to represent this problem situation. Be sure to
define your variables.
b. Solve the system of three linear equations using
technology with matrices. Write your answer in terms of
the problem situation.
c. Describe the solution in terms of the problem situation.
2. Is it always easier to solve a system of linear equations using
matrices? Explain your reasoning.
Let the small , medium and large baskets be denoted by s,m & l
Formulating the equations
s+m+l= 80--------- equation1
$15.75s+ $25 m + $32.5l = $2086.25------equation2
2s=l---------equation 3
Using the technology s=15, m=35 and l= 30
15+35+30= 80--------- equation1
$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2
2(15)=(30)---------equation 3
Yes because multiple variables can be easily calculated through matrices using technology
In Matrix form
[tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex] [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex] = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]
Let A= [tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex]
Z= [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex]
B = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]
Z= A⁻¹ B
A⁻¹= A mod/ det A
det A= -1
Using the technology s=15, m=35 and l= 30
15 small baskets,
35 medium baskets
30 large baskets were sold.
Part C:
15+35+30= 80--------- equation1
$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2
236.25+ 875+ 975=$2086.25
$2086.25=$2086.25
2(15)=(30)---------equation 3
Answer 2:
Yes because multiple variables can be easily calculated using technology.
N.B There is a typing error in question its $2086.25 not 52086.25
A box has length 3 feet, width 4 feet, and height 7 inches. Find the volume of the box in cubic feet and cubic inches. Round to the nearest tenth as needed.
Answer:
I think 72 inches I might be wrong
Tell me both the numbers for the 2 boxes pls
Read the word problem below.
Soni has 196 pencils. If she puts equal amounts of pencils into eight boxes, she has four pencils left. How many pencils does she put in each box?
Which strategy could help solve this word problem?
If x represents the number of pencils per box, solve the equation 4x + 8 = 196.
Divide 196 by the sum of 4 and 8 and find the quotient.
Divide 196 by 4 and check that the remainder is 8.
If x represents the number of pencils per box, solve the equation 8x + 4 = 196.
Answer:
The last option 8x + 4 = 196
Step-by-step explanation:
8x + 4 = 196
8x = 192
x=192/8
x=24
The strategy that can help solve this word problem is : If x represents the number of pencils per box, solve the equation 8x + 4 = 196.
What is the strategy?A strategy is an approach that leads someone to the nearest of the solution of a problem.
How to solve the equation?Soni has 196 pencils.
Let, one box can accommodate x number of pencils.
Therefore 8 boxes can accommodate 8x number of pencils.
But she has 4 more pencils.
Hence, the required equation is 8x+4=196.
Learn more about the equation here :
https://brainly.ph/question/4246696
#SPJ2
what the value of x if 27/5 =4/x
Step-by-step explanation:
[tex] \frac{27}{5} = \frac{4}{x} \\ 27 \times x = 4 \times 5 \\ 27x = 20 \\ \frac{27x}{27} = \frac{20}{27} \\ x = \frac{20}{27} [/tex]
What value represents the vertical translation from the graph of the parent function f(x)=x² to the graph of the
function g(x)=(x+5)2+3?
-5
-3
3
Answer:
3
Step-by-step explanation:
A algebraic transformation is represented by
[tex]a(bx - h) + k[/tex]
where a is the vertical compression or stretch. a is also the vertical reflection if value is negative . B is the horizontal compression or stretch it is also a horizontal reflection if it value is negative. h is the horizontal shift. And k is the vertical shift.
3 replaces k in this scenario for the vertical translation so 3 is the answer.
Can someone answer this correctly because i am doing hegarty maths and i cant get this question wrong please someone help :)
Answer:
£ [tex]36[/tex]
Step-by-step explanation:
In this situation, the price of an item is (£ [tex]45[/tex]). It is given that there is a ([tex]\frac{1}{5}[/tex]) off discount on this item. To find the price of this item, one will have to subtract the discount rate from (1), this will yield the fraction of the object price that one has to pay. To find the actual amount one has to pay, one must multiply the fractional price of the object by the original price of the object. Using this line of thought, one can form the following equation:
[tex](1-(rate\ of\ discount))(original\ price)=sale\ price[/tex]
Substitute the given values into this equation:
[tex](1-\frac{1}{5})(45)=sale\ price[/tex]
Simplify: remember, a fraction with any number over itself equals (1). Bear in mind that one can only perform operations such as addition and subtraction between fractions with common denominators, that is the number under the fraction bar.
[tex](1-\frac{1}{5})(45)=sale\ price[/tex]
[tex](\frac{5}{5}-\frac{1}{5})(45)=sale\ price[/tex]
[tex](\frac{5-1}{5})(45)=sale\ price[/tex]
[tex](\frac{4}{5})(45)=sale\ price[/tex]
Now perform the multiplication. Divide the denominator by the number one is multiplying by, then multiply it by the numerator (number over the fraction bar).
[tex](\frac{4}{5})(45)=sale\ price[/tex]
[tex](4)(45 / 5)=sale\ price[/tex]
[tex](4)(9)=sale\ price[/tex]
[tex]36=sale\ price[/tex]
Answer:
The answer is 36$
Step-by-step explanation:
Basically, the original price is 45 dollars, but with the extra 20% off (This is just the 1/5 off) it will be 36. This is because 45/5 equals 9 and 45-9 is 36.
What value of x makes the following equation true?
x3=-64
Answer:
Any value you choose for x will make the equation a TRUE statement.
Tami has both a checking account and a savings account at the bank. She has a total of $850 in both accounts. The ratio of checking savings is 3 to 7. How much money does tami have in her checking account? How much does she have in her savings?
Amount in her checking and saving account is $255 and $595
Given information:
Total amount in both accounts = $850
Ratio of checking to saving account = 3:7
Find:
Amount in her checking and saving accounts
Computation:
Total of ratio = 3 + 7
Total of ratio = 10
So,
[tex]Amount\ in\ her\ checking\ account = 850 \times \frac{3}{10}[/tex]
Amount in her checking account = $255
[tex]Amount\ in\ her\ saving\ account = 850 \times \frac{7}{10}[/tex]
Amount in her saving account = $595
Learn more:
https://brainly.com/question/19257327?referrer=searchResults
If I don't read carefully, I often make mistakes on my work.
compound complex
sentence
compound sentence
simple sentence
complex sentence
Answer:
compound sentence
Step-by-step explanation:
Y= 0.5x + 2 showing on the graph
Answer:
Y is output, x is input
Step-by-step explanation:
I. Given x is -1, 0, 1
II. Perform x in linear equation
If x is -1
y = 0.5(-1) + 2
y = 1.5
=> (-1, 1.5) -1 is x, 1.5 is y
If x is 0
y = 0.5(0) + 2
y = 2
=> (0, 2) 0 is x, 2 is y
If x is 1
y = 0.5(1) + 2
y = 2.5
=> (1, 2.5) 1 is x, 2.5 is y
III. Perform (x, y) in graph, there will be something like this
In the figure MX = NY
MX and NY are parallel.
i) Are the sides of ∠MPX equal to the sides of ∠NPY ?
ii) what is the special about the postion of P on MN
Answer:
i) yes
ii) it splits MN in half (bisector)
Step-by-step explanation:
We are given that MX and NY are parallel. This means, due to alternate interior angles, <XMN and <YNM are congruent as well as <MXY and <NYX. We are also given MX = NY. This is enough information to prove ΔMPX is congruent to ΔNPY due to ASA(two angles and a side between them).
(i) Now, because of this, we can say that all the sides of ΔMPX are congruent to those of ΔNPY. And, this means MP = NP. Since the point P divides the segment MN into two equal pieces, it's a bisector of MN(splits it in half).
Answer:
YesPoint of intersectionStep-by-step explanation:
SEE the image for solution.
HOPE it helps
Have a great day
How much money does an employee working
for a salary of $52,000 per year get paid
monthly?
A. $52,000 per month
B. $1,000 per month
C. $2,000 per month
D. $4,333 per month
Answer:
433
Step-by-step explanation:
433. . . . . . . ............,.. srry it made me write this much to answer
Answer:
The correct answer would be D!Step-by-step explanation:
Employee's salary: $52,000
Months in a year: 12
52000 / 12 = 4,333.333(r)
Closest answer: D
Need help with this question. Will give brainliest for correct answer.
Answer: the second to last
Step-by-step explanation: because there’s no multipcation in the first box and if you look at the rest it wou make sense for it to be the second to last
PLEASE HELP! it's due today
Answer:
[tex]thank \: you[/tex]
Cho 2 tập hợp A = {1;3;5;8}, B = {3;5;7;9}. Tìm A∩B và A∪B.
Answer:
gien
Step-by-step explanation:
i need help with atleast 2 of these questions pls
Answer:
Below.
Step-by-step explanation:
(a) Over the first 5 seconds rate of change of speed
= (9-1)/5
= 8/5
= 1.6m/s^2
(b) (21-9)/16-t) = 2
12/16-t = 2
32 - 2t = 12
32 - 12 = 2t
20 = 2t
t = 10 seconds
Step-by-step explanation:
Total Time Taken = 16secs
10a). We're asked to calculate the rate of speed change for the first 5secs.
This is another way of saying "Calculate Acceleration" in the first 5sec of Motion.
Why?
Acceleration is the rate of change of speed or the rate at which speed changes.
acceleration = v - u/t
where v = Final Speed
u = initial Speed.
Looking at the graph
You see that
Initial speed(u) = 1m/s
Final Speed(v) = 9m/s
t = 5secs
Acceleration = 9 - 1/ 5
a = 8/5
a = 1.6m/s².✅
10b)
We're asked to calc "t" from the graph.
Given that the acceleration at "t" untill 16sec(end of motion) is 2m/s².
This simply means that Constant Acceleration was held from "t" to the end of the Motion.
Do not confuse Constant Acceleration for Constant Velocity.
At Constant Velocity... Acceleration is zero(0)
At Constant Acceleration...Velocity Changes Uniformly or at the same rate each second and this is what we're dealing with in this question.
Taking the same step as we used in calculating acceleration above
Given a= 2m/s²
a = v - u/∆t
Where ∆t means time change or difference.
From "t" to 16
The change in time is 16 - "t"
2 = 21 - 9/( 16 - t)
2 = 12/16-t
16-t = 12/2
16 - t = 6
t = 16 - 6
t = 10secs.✅
Have a great Day!.
i need help with 2 of these questions
Answer:
Why do you keep sending the same question over and over again?
Step-by-step explanation:
Total Time Taken = 16secs
10a). We're asked to calculate the rate of speed change for the first 5secs.
This is another way of saying "Calculate Acceleration" in the first 5sec of Motion.
Why?
Acceleration is the rate of change of speed or the rate at which speed changes.
acceleration = v - u/t
where v = Final Speed
u = initial Speed.
Looking at the graph
You see that
Initial speed(u) = 1m/s
Final Speed(v) = 9m/s
t = 5secs
Acceleration = 9 - 1/ 5
a = 8/5
a = 1.6m/s².✅
10b)
We're asked to calc "t" from the graph.
Given that the acceleration at "t" untill 16sec(end of motion) is 2m/s².
This simply means that Constant Acceleration was held from "t" to the end of the Motion.
Do not confuse Constant Acceleration for Constant Velocity.
At Constant Velocity... Acceleration is zero(0)
At Constant Acceleration...Velocity Changes Uniformly or at the same rate each second and this is what we're dealing with in this question.
Taking the same step as we used in calculating acceleration above
Given a= 2m/s²
a = v - u/∆t
Where ∆t means time change or difference.
From "t" to 16
The change in time is 16 - "t"
2 = 21 - 9/( 16 - t)
2 = 12/16-t
16-t = 12/2
16 - t = 6
t = 16 - 6
t = 10secs.✅
Have a great Day!.
Graph the following exponential function. Show work in how you find the y intercept, talk about the end behavior, and state if it is a growth or decay function.
Answer:
-2
Step-by-step explanation:
when x=0 y=-2... it is a decline
What is the measure of ZX?
Select the best answer from the choices provided.
A.38°
B.76
C.104
D.142°
Answer:
76°
Step-by-step explanation:
Angles adjacent to equal sides of a triangle are equal.
Exterior angle
= Sum of interior opposite angles
= 38° + 38°
= 76°
need help fast, please
math! help! pls! pls!
Answer:
3. MNP = OPN
Step-by-step explanation:
the second could be as well, but the sequence is the same for the third option, thus the second option is wrong
pretty sure this is algebra
[tex] \boxed{ \boxed{ \: \: \: \: 1.4 \: \: \: \: }}[/tex]
let's solve :[tex] \hookrightarrow \: \dfrac{2a + 3b}{3b} [/tex]
[tex] \hookrightarrow \: \dfrac{2a}{3b} + \dfrac{3b}{3b} [/tex]
[tex] \hookrightarrow \: \dfrac{2a}{3b} + 1[/tex]
[tex] \hookrightarrow \: \big(\dfrac{2}{3} \times \dfrac{a}{b} \big) + 1 [/tex]
[tex] \hookrightarrow \: \big(\dfrac{2}{3} \times 0.6 \big) + 1[/tex]
[tex] \hookrightarrow \:( 2 \times 0.2) + 1[/tex]
[tex] \hookrightarrow \: 0.4 + 1[/tex]
[tex] \hookrightarrow \: 1.4[/tex]
what is the answer of 8-15=
Answer:
-7
Step-by-step explanation:
Please answer this for me
Answer:
B
Step-by-step explanation:
It implies that his plane ticket and other expenses should all be less than the $2000 he has saved.
Calculate the diameter of a
circle if its area is 113.1cm2.
Answer:
12 cm squared
Step-by-step explanation:
1. Since diameter is twice the radius and what we know is the area, you would divide the area, 113.1 cm, by Pi (3.14):
113.1 cm / 3.14 = 36.00084813
2. What you get is the radius which you have to square:
36.00084813 squared = 6.000070677
3. Now you double the radius in order to get the diameter:
6.000070677 x 2 = 12.00014135
12.0 cm squared
What is 17 rounded to the nearest tenth of an inch
You can't round 17 to the nearest tenth of an inch because 17 is a whole number.
Please explain how you got the answer also please, thank you :)
Answer:
x = 3
Step-by-step explanation:
The axis of symmetry passes through the vertex of the graph with equation
x = c
where c is the value of the x- coordinate of the vertex
The vertex is at (3, - 2 ) with x- coordinate 3 , then
x = 3 ← equation of axis of symmetry
Visual Pantom 2
What would the 10th case look like?
• How many cirdes would be in the 10th case?
• How many cirdes would be in the 100th case? What would it look like?
• How many cirdes would be in the zero case? • What would it look like?
• Can you model the pattern with an expression?
PLZ HELP QUICKLY!!!!!!!!!!!!
No LINKS PLEASE!!!!!!!!!
Answer:
Uhh i dont rly know sry
Step-by-step explanation: