Step-by-step explanation:
a fence represents the circumference, the perimeter of the lot or yard.
remember, a rectangle has 2 parallel sides called the length, and 2 parallel sides called the width (altogether 4 sides).
therefore
perimeter = 2×length + 2×width
or with short variables
p = 2×l + 2×w
so, now we have 50 ft of fence available for the perimeter. and the length l = 13 ft.
since we have 2 lengths in the perimeter, these 13 ft are twice (2×13 = 26 ft) in the perimeter.
now, how much fence do we have left for the width ?
well, 50 - 26 = 24 ft
and again, this is the size of 2 sides (2×width) :
p = 2×l + 2×w
50 = 2×13 + 2×w = 26 + 2×w
2×w = 24
w = 12 ft
so, the width of the yard must not be bigger than 12 ft.
The perimeter of a rectangular field is 60 meters. Its area is 200 square meters. Find its dimensions.
Answer:
20 m by 10 m
Step-by-step explanation:
let w be width and l be length , then
2(l + w) = 60 ( divide both sides by 2 )
l + w = 30 ( subtract w from both sides )
l = 30 - w → (1)
lw = 200 → (2)
Substitute l = 30 - w into (2)
w(30 - w) = 200 ← distribute parenthesis on left side
30w - w² = 200 ( subtract 200 from both sides )
30w - w² - 200 = 0 ( multiply through by - 1 )
w² - 30w + 200 = 0 ← in standard form
(w - 10)(w - 20) = 0 ← in factored form
Equate each factor to zero and solve for w
w - 10 = 0 ⇒ w = 10
w - 20 = 0 ⇒ w = 20
Substitute these values into (1)
l = 30 - 10 = 20
l = 30 - 20 = 10
dimensions of field is 20 m by 10 m
Answer:
THIS IS THE REPRENTATION :I(LENGTH ),W(WIDTH)
2IW= 200
I,II USE THE SUBSTITUTION METHOD SINCE :I=30-W WE CAN SUBSTITUTE THE LENGTH TO 30
-W TO IW=200
(30-W)W=200
W2 + 30W=200---------------TRANSPOSE -w2
+30w
w2-30w +200 = 0------------------- USE FACTORING
(W-20)(w-10 =0----------------- THEN EQUATE EACH FACTOR TO ZERO
W- 20=0 W-10 =0
W=20 W=10
THEN SUBSTITUTE THE VALUE OF w TO ANY OF THE EQUATIONS TO GET THE VALUE OF I
Iw =200 Iw=200
I(20) =200 I(10)
I(20)/20= 200/20 I(10)/10
=200/10
I=10
SO the answer to the problem are: width = 20 then lenght =10 or width = 10 then lenght =20Evaluate: log(a³b²/c⁴) + log(bc³/a²) - log(a/c) = ?
[tex]\large\underline{\sf{Solution-}}[/tex]
We have to evaluate the logarithm.
Given That:
[tex] \rm = \log \bigg( \dfrac{ {a}^{3} {b}^{2} }{ {c}^{4} } \bigg) + \log \bigg( \dfrac{b {c}^{3} }{ {a}^{2} } \bigg) - \log \bigg( \dfrac{a}{c} \bigg)[/tex]
We know that:
[tex] \rm\red\longmapsto \log(x) + \log(y) = \log(xy) [/tex]
[tex] \rm \red\longmapsto \log(x) - \log(y) = \log \bigg( \dfrac{x}{y} \bigg) [/tex]
Therefore, we get:
[tex] \rm = \log \bigg( \dfrac{ {a}^{3} {b}^{2} }{ {c}^{4} } \times \dfrac{b {c}^{3} }{ {a}^{2} } \bigg) - \log \bigg( \dfrac{a}{c} \bigg)[/tex]
[tex] \rm = \log \bigg( \dfrac{ {a}^{3 - 2} {b}^{2 + 1} }{ {c}^{4 - 3} } \bigg) - \log \bigg( \dfrac{a}{c} \bigg)[/tex]
[tex] \rm = \log \bigg( \dfrac{a{b}^{3} }{c} \bigg) - \log \bigg( \dfrac{a}{c} \bigg)[/tex]
[tex] \rm = \log \bigg( \dfrac{a{b}^{3} }{c} \div \dfrac{a}{c} \bigg)[/tex]
[tex] \rm = \log \bigg( \dfrac{a{b}^{3} }{c} \times \dfrac{c}{a} \bigg)[/tex]
[tex] \rm = \log( {b}^{3})[/tex]
As we know that:
[tex]\rm \red\longmapsto \log( {x}^{n}) = n \log(x)[/tex]
Therefore, we get:
[tex] \rm = 3\log(b)[/tex]
PLEASE ANSWER BRSINLEST BRAINLEST ANSWER NOW PLEASE DUE!
Stacy likes to do aerobics 10 hours a week to stay in shape. She tracks the amount of time she does aerobics each week relative to her goal.
The table shows the data for the last five weeks.
Week 1 2 3 4 5
Aerobics time (hours) 2.8 −2 1 3/4 0 −3
What is the average aerobics time per week for Stacy relative to her goal number of hours?
Drag a value to the box to complete the statement.
PLease explain it too if you can
Answer:
-0.09
Step-by-step explanation:
HELP!! PLS for points
Answer:
the vertex form is y= -2(x-4)^2+8 (the third one)
Help me on this please help it’s due
Answer:
hi hi hi hi hi hi hi hi hi hi hi hi hi
how to to right a*a*c*c using exponents
Answer:
[tex]a*a*c*c=a^2×c^2[/tex]
Step-by-step explanation:
Thanks!!!!!!!
how do you do this math problem 3(x-2)=9
Answer:
x=5
Step-by-step explanation:
3(x-2)=9
3x-6=9
3x=9+6
=15
x=15÷3
=5
2. The bank requires a minimum balance of $50 in the
savings account. It does not matter how much money
is kept in the checking account.
If the customer deposits no money in the checking
account but is able to maintain both accounts without
penalty, what can you say about the amount deposited
in the savings account
The following expression can be solved in 5 steps using the rules of order of operations. Write the step by step solution in the spaces provided below: [(-2)²×3]÷[(-9)-5+2]Note: You may copy the question from the previous step and replace the operation performed with the result. For example, given the question 4²-6×2, you would copy the question and replace the index term in step 1: 16-6×2. For step 2, you copy the expression from step 1 and replace the product to get: 16-12. In step 3, you only have one operation left to perform so you just need to write the final answer: 4
Answer:
Step-by-step explanation:
[(-2)²×3]÷[(-9)-5+2]
=(4*3)/[(-9)-5+2]
=12/(-12)
=-1
Je veux une reponse ❤️
Answer:2
Step-by-step explanation:
Warren runs races to support local charities. In April, he ran a 5-kilometer race in 30 minutes to support his local hospital. In October, he will run a 10-kilometer race to support the animal shelter. If he runs at the same rate, how many minutes will it take Warren to run the race in October?
Warren ran 10 km in 60 minutes or 1 hour.
What is proportionality?Proportionality is a case when two ratios are equal.
Given that Warren runs for charity, so, he runs for a hospital a 5-kilometer race in 30 minutes, on the same rate he ran a 10-kilometer race to support the animal shelter.
We need to find the time taken by him when he ran 10 km race.
Since, the rate of running is same, that means the speed was equal in both races,
Let t be the required time,
Therefore, using the concept of proportionality,
5 / 30 = 10 / t
5t = 300
t = 60
Therefore, he ran 10 km in 60 minutes or 1 hour.
Learn more about proportionality, click;
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2. Solve the system by graphing or using a table.
2x + 4y= 12
X+ y = 2
(-3,7)
(-2,4)
(-4,1)
infinitely many solutions
Answer:
x = -2 and y = 4
Step-by-step explanation:
We have given a system of equations
2x + 4y =12 ...........(1)
and
x + y = 2 .............(2)
Now to plot them in graph we need to find the points of the above linear equations .
From equation 1 ,we get
4y=12-2x
[tex]y=\frac{12-2x}{4} \\y=3-\frac{x}{2} \\[/tex]
Put x=0, then
[tex]y=3-\frac{0}{2} =3\\[/tex]
Put x=6
[tex]y=3-\frac{6}{2}=3-3=0[/tex]
So get the points (0,3) and (6,0).
From equation 2 ,we get
y=2-x
put x=0
y=2-0=2
put x=2
y=2-2=0
So we get the points (0,2) and (2,0).
So after plotting these points we get two lines intersecting at (-2,4).
Therefore our solution is x=-2 and y= 4.
Consider all rectangles with an area of 200m^2. Let x be the length of one side of such a rectangle. Find the dimensions of a rectangle whose perimeter is 70m.
Answer: Answer in Photo
The temperature at 9 p.m. was 12°F. The temperature dropped 15°F by 5 a.m.
The temperature at 5 a.m. was
Answer:
-3 F'
Step-by-step explanation:
Identify two statements that contradict each other.
I. ZM is an obtuse angle.
II. m ZM +mZP= 90
III. 180 – mZM = 25
IV. mZP= 120
If ZM is an obtuse angle (greater than 90), then ZM and ZP will not add up to 90.
If ZP is 120, then ZM and ZP will not add up to 90.
There are multiple contradicting statements within this problem, as noted above.
Hope this helps!
Options A and B are two contradict statements.
The four statement are given, we need to find the two contradict statements.
What is an obtuse angle?The definition of an obtuse angle in geometry states that 'an angle whose measure is greater than 90° and less than 180° is called an obtuse angle.
Here, m∠M is an obtuse angle and m∠M +m∠P= 90° are two contradict statements
Since, in m∠M +m∠P= 90° two angles adds up to 90°, so m∠M can not be obtuse angle.
Therefore, options A and B are two contradict statements.
Learn more about an obtuse angle here:
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Convert 3009 inches to yards,feet and inches. (Show your work)
Answer:
Yards: 83.58
Feet: 250.75
Inches: 3009
Step-by-step explanation:
Yards: 1 yard = 36 inches
3009/36= 83.58
So if each yard is 36 inches and there are 83.58 sets of 36 inches in 3009 then that's how many yards you have.
Feet: 1 foot = 12 inches
3009/12= 250.75
Again, if each foot is 12 inches and there are 250.75 sets of 12 inches in 3009 then that's how many feet you have.
Inches: It's already in inches :)
I hope this isn't confusing and I could help!
Answer:
Yards : 83.5833333 Feet:250.75 Inches: 9
Brownies sell for $.75
and cookies sell for $.40. If
Brady wants 3 brownies and 2
cookies. He brought $3. Does
Brady have enough money to
buy the treats? NO LINKS PLEASE
Answer:
No
Brady is 5 cents short
Step-by-step explanation:
.75x3=$2.25
.40x2=0.80
$2.25+0.80=$3.05
Answer:
No
Step-by-step explanation:
3 brownies = $.75 * 3 = $2.25
2 cookies = $.40 * 2 = $.80
$2.25 + $.80 = $3.05, which is over $3
He is 5 cents short.
Hope this helped!
(and taxes of course)
Can someone help me? This is soo hard
Answer:
m∠ ACB = 60°
Step-by-step explanation:
If AB║CD if m∠
Given the function g(x) = x2 + 5x + 1, determine the average rate of change of
the function over the interval -5 < x < 4.
Step-by-step explanation:
the average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
so,
(g(4) - g(-5)) / (4 - -5)
g(4) = 4² + 5×4 + 1 = 37
g(-5) = (-5)² + 5×-5 + 1 = 25 - 25 + 1 = 1
4 - -5 = 4 + 5 = 9
(37 - 1)/9 = 36/9 = 4
the average change rate in that interval is 4 (or fully 4/1).
graph this line using the slope and y intercept: y=x
Answer:
done.
Step-by-step explanation:
yeah-ya..... right?
A Price of a sweater was reduced from $40 to $25. By what percentage was the price of the sweater reduced?
plsss someone help i will give brainlyest
i need help with the photo
Answer: (n^6 j^6)/(8h^5)
Step-by-step explanation:
The k term disappears (k^5 * k^-5) = 1j^-6 moves to the top as j^6(h^-2)/((h^-6)*(h^3)) = 1/h^51/(2*2*2) = 1/8Therefore: n^6*j^6/8h^5
kelsey withdraws $25 per week from her bank account. Each week, Kris deposits $15 of his allowance and $20 earned from dog walking each week into his bank account. After how many weeks will they have the same amount of money
Answer:
Step-by-step explanation:
Classify the triangle. Find the value of x
Answer:
x= 9
Step-by-step explanation:
<2 + 40 + 40 = 180 degree
<2 = 180 - 40 - 40
<2 = 100
m<2 = x + 109
x = 109 - <2 = 109 - 100 = 9
What is transversal?
Answer:
A transversal is a line that intersects two parallel lines .like shown in the diagram above hope it is helpful to you please follow give brainliest ✌❣❣In the room there are 5 big boxes. In each box there are 3 smaller boxes. In each of these small boxes the are 4 smaller boxes.How many boxes of different sizes are there in the room?
Answer:
Step-by-step explanation
there are 80 boxes in total
will mark as brainliest plz help
BC = BD
Step-by-step explanation:
AC = AD
because AB bisect ∠A or
∠CAB = ∠BAD
∴ So, BC = BD
The graph of linear function f passes through the point (1, -8) and has a slope of 2. What is the zero of f?
A. -2
B. -5
C. 2
D. 5
Please help me
Answer:
5
Step-by-step explanation:
Answer:D-5
Step-by-step explanation:
pls help me ill give brainliest :)
For a two-days rental at the surf shop it cost $45 to rent a surfboard and $60 to rent a paddleboard on a certain weekend the surf shop rented 44 total surfboards and paddle boards and made $2265 how many paddle boards were rented
Answer:
Step-by-step explanation:
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