Answer:
Suppose you want to frame a collage of pictures. You have a 9-ft strip of wood for the frame. What dimensions of the frame give you the maximum area for the collage? What is the maximum area?
A:
Perimeter = 2(L + W) 9 = 2(L+W) L+W = 4.5 L = 4.5-W Area = LW Area = (4.5-W)W A = 4.5W - W^2 You have a quadratic with a = -1 and b = 4.5 Maximum area occurs when W = -b/(2a) = 4.5/(2*-1) = 2.25
Step-by-step explanation:
Dimension of the picture with 9ft strip of wood is
length = 2.25 ft and width =2.25 ft
Given :
you want to frame a collage of picture with a 9ft strip of wood.
the perimeter of the frame is 9 ft
Perimeter of rectangle = 2(length +width )
Let 'l' be the length and 'w' be the width
[tex]Perimeter =2(l+w)\\9=2(l+w)\\Divide \; by \; 2\\l+w=4.5\\l=4.5-w[/tex]
Now we find the area
[tex]Area = length \cdot width \\Area= l \cdot w\\A= (4.5-w)(w)\\A=-w^2+4.5w[/tex]
Now we find out 'w' where area is maximum
[tex]w=-\frac{b}{2a} \\a=-1 and b=4.5\\w=-\frac{4.5}{2(-1)} =2.25[/tex]
Width =2.25 gives us maximum area
Now find out the length ,
[tex]Length = 4.5 -w\\w=2.25\\Length = 4.5-2.25=2.25[/tex]
Dimension of the picture is length = 2.25 ft and width =2.25 ft
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PLEASE HELP ME PLEASE!
Answer:
1 hour = 50/4= $12.5
4 hours = $50
[tex]5\frac{1}{2}[/tex] can be written as 11/2 or 5.5
Let's take x to be the salary for working 5.5 hours.
4 50
5.5 x
Using cross-multiplication, you will get the equation:
4x = 275
x = 68.75
THEREFORE, HE EARNS $68.75 IN [tex]5\frac{1}{2}[/tex] hours.
Using the graph of the line below, determine what the slope is
1) Slope is 0
2) Slope is 2
3) Slope is 3
4) Slope is 6
Answer:
2) Slope is 2
Step-by-step explanation:
You can see that the line rises 2 units and runs for 1 unit, making the slope 2/1 or in a simpler form, 2.
What is the range of the graph below?
Select the values that make the statement true.
n1
100 = d = p%
n =
d =
P =
It is a drop down Menu and i get is something Different Question can you help me plz
Answer:
5
20
5
Step-by-step explanation:
i did it on the assigment
Line JK passes through points J(-3, 11) and K(1, -3). What is the equation of line JK in standard form? The answers are
7x + 2y = -1
7x + 2y = 1
14x + 4y = -1
14x + 4y = 1
Linear equation is the equation of a straight line. A linear equation in standard form is: [tex]ax + by = c[/tex]
The equation of JK in standard form is: [tex]7x + 2y = 1[/tex]
Given that:
[tex](x_1,y_1) = (-3,11)[/tex] --- point J
[tex](x_2,y_2) = (1,-3)[/tex] --- point K
First, we calculate the slope (m) of JK using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{-3-11}{1--3}[/tex]
[tex]m = \frac{-14}{4}[/tex]
[tex]m = \frac{-7}{2}[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = \frac{-7}{2}(x - -3) + 11[/tex]
[tex]y = \frac{-7}{2}(x +3) + 11[/tex]
Multiply through by 2
[tex]2y = -7(x +3) + 22[/tex]
Open bracket
[tex]2y = -7x -21 + 22[/tex]
[tex]2y = -7x +1[/tex]
Rewrite in standard form as
[tex]7x + 2y = 1[/tex]
Hence, the equation of JK in standard form is:
[tex]7x + 2y = 1[/tex]
Read more about linear equation in at:
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A taxi service charges a flat fee of $1.25 and $0.75 per mile. If Henri has $14.00, which of the following shows the number of miles he can afford to ride in the taxi?
m less-than-or-equal-to 17
m greater-than-or-equal-to 17
m less-than-or-equal-to 20.3
m greater-than-or-equal-to 20.3
Answer:
less than or equal to 17
Step-by-step explanation:
14=1.25+0.75x
12.75/0.75=x
x=17
17 is the maximum
Q/A: A taxi service charges a flat fee of $1.25 and $0.75 per mile. If Henri has $14.00, which of the following shows the number of miles he can afford to ride in the taxi?
a. m less-than-or-equal-to 17
b. m greater-than-or-equal-to 17
c. m less-than-or-equal-to 20.3
d. m greater-than-or-equal-to 20.3
CC ALGEBRA 2A ED20
If each school bus carries at most 20 students, and the school used 5 buses last Monday, then which statement shows how many (N) students came to school by bus?
N<100
N=100
N≤100
N≥100
Answer:
N=100
Step-by-step explanation:
[tex]20x5=100[/tex]
PLEASE HELP ILL MARK U WHAT U WANT
Given; a (x) = x^3 – 4x-3 when x > -3 and a(x) =| –2x + 5 | when x <-8
Evaluate a (-10)
Answer:
25
Step-by-step explanation:
a(-10), since x= -10 which is less than -8, we will have,
a(x) = |-2x+5|
a(-10) = | -2*(-10) + 5|
= | 20+5 |
=25
Is contributing money to political candidates a right or a responsibility
Answer:
Step-by-step explanation:
A Right but not a responsibility.
At the annual high school carnival, Dalton sells popcorn for $4 a bag. His cost for setting up a booth is $20. Today, his goal is to make a profit of $500. How many bags of popcorn must he sell to make a profit of $500?
Hint: 500 = 4x - 20
Answer:
130=x
Step-by-step explanation: Do +20 on both sides the 20 on the left side cancels and 500 + 20= 520. Bring down the 4x. Divide 4 on both sides. 4 divided by 4 cancels. 520/4= 130. So he needs to sell 130. Give me brainliest.
Rectangle R was dilated to form rectangle R’.
Which is the scale factor of the dilation?
5/4
2/1
5/2
5/1
Answer:5/2
Step-by-step explanation:
The value of y varies directly with x. If x=104, then y=78. What is the value of x when y=39?
58
58
52
52
29.25
29.25
69.3
Answer: 52
Step-by-step explanation:
Since the value of y varies directly with x, y = kx where k is a constant.
Since x=104, then y=78, we need to calculate the constant k. This will be:
y = kx
78 = 104k
k = 78/104
k = 0.75
What is the value of x when y=39?
Since y = =kx
39 = 0.75x
x = 39/0.75
x = 52
Jerry and his family will drive 1,022 miles from Houston to Indianapolis for their summer vacation. They plan to drive between 425 and 475 miles each day. At this rate, which is a reasonable number of days it will take Jerry's family to reach Indianapolis?
Answer:
The reasonable number of days to reach Indianapolis is 3 days.
Step-by-step explanation:
Total distance to be covered from Houston to Indianapolis, d= 1022 miles.
As they plan to drive between 425 and 475 miles/day, so the range of the rate of driving per day, r, is 425<r<475.
Let t day is the reasonable number of days to complete the journey.
As time = (distance)/(speed), so
[tex]t=\frac d r\cdots(i)[/tex]
The given range of the rate is
[tex]425<r<475[/tex]
If [tex]a>b[/tex], than [tex]1/a<1/b[/tex] for [tex]a,b\neq0[/tex];
[tex]\Rightarrow \frac {1}{425}>\frac {1}{r} >\frac{1}{475}[/tex]
If a>b, the for any [tex]\alpha>0[/tex], [tex]a\alpha>b\alpha[/tex], so multiply the above equation by [tex]d[/tex], we have
[tex]\frac {d}{425}>\frac {d}{r} >\frac{d}{475}[/tex]
[tex]\Rightarrow \frac {d}{425}>t >\frac{d}{475}[/tex] [from equation (i)]
[tex]\Rightarrow \frac {1022}{425}>t >\frac{1022}{475}[/tex] [given, d=1022 miles]
[tex]\Rightarrow \frac {1022}{425}>t >\frac{1022}{475}[/tex]
[tex]\Rightarrow 2.40>t >2.15[/tex]
So, to cover the distance of 1022 miles, with the speed in between 425 miles/day and 475 miles/day, Jerry's family will take in between 2.40 days and 2.15 days. This means, for the given speed range, they need 2 complete days and some fraction of 3rd day to reach Indianapolis.
Hence, the reasonable number of days to reach Indianapolis is 3 days.
No responses yet... John is making trail mix based on a recipe that combines 6 cups of nuts with 5 cups of granola. John has 36 cups of nuts. How many cups of trail mix (total) does he have?
Given:
A recipe combines 6 cups of nuts with 5 cups of granola.
John has 36 cups of nuts.
To find:
Number of cups of trail mix (total) does he have.
Solution:
The recipe combines 6 cups of nuts with 5 cups of granola.
The recipe combines 1 cup of nuts with [tex]\dfrac{5}{6}[/tex] cups of granola.
The recipe combines 36 cup of nuts with [tex]36\times \dfrac{5}{6}[/tex] cups of granola.
So, the number of cups of granola in trail mix is
[tex]Granola=36\times \dfrac{5}{6}[/tex]
[tex]Granola=6\times 5[/tex]
[tex]Granola=30[/tex]
Total number of cups = cups of nuts + cups of granola.
[tex]=36+30[/tex]
[tex]=66[/tex]
Therefore, the total number of cups in trail mix (total) he have, is 66.
Find the missing y value of the the coordinate (3,____) so that it is on the line y = 6x -3.
Group of answer choices
1
15
21
6
Answer:
y = 15
Step-by-step explanation:
=> x = 3
=> y = 6x - 3
=> y = 6(3) - 3
=> y = 18 - 3
=> y = 15
Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of 65 along with an hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than 250, and he wonders how many hours of work he can afford.
PLZ HELP WILL GIVE BRAINLIEST AND LOTS OF POINTS
Step-by-step explanation:
anand can afford at most 6 hours
Basic Charge = $ 65
Rate per hour = $ 28
Number of hours = H
Rate for H hours = 28 *H = 28H
Equation:
65 + 28H ≤ 250
Laura e Lucas estão preparando vasos para a plantação de flores, eles têm um saco com 12 kg de terra e precisam dividir em vasos com capacidade de 300 gramas. Quantos vasos serão necessários para usar toda terra?
Answer:
Vai exigir 40 potes
Step-by-step explanation:
Aqui, queremos saber o número de vasos necessários para usar todo o solo Da pergunta,
o peso do solo para o uso é de 12 kg. Isso é grama é 12.000 g
Agora, somos informados de que cada vaso deve receber 300 g de solo.
Portanto, o número de vasos que usarão todo o solo aqua será;
12.000 / 300 = 40
the cost of printing 200 business cards is $23.The cost of printing 500 business cards at the same business is $35. Write a linear equation for this information. And to print 700 business cards would cost $
Answer:
Step-by-step explanation:
The price for printing 700 cards is $15+$700/25 = $43.
Explanation:
We need to MODEL the cost based on the number of cards printed. We will assume that there is a FIXED price
F
for any job (to pay for setup etc.) and a VARIABLE price
V
which is the price to print a single card. The total price
P
will then be
P
=
F
+
n
V
where
n
is the number of cards printed. From the problem statement we have two equations
Equation 1:
23
=
F
+
200
V
and
Equation 2:
35
=
F
+
500
V
Let's solve Equation 1 for
F
F
=
23
−
200
V
and substitute this value for
F
into Equation 2.
35
=
23
−
200
V
+
500
V
Now solve this for
V
.
12
=
300
V
V
=
1
25
We can put this value for
V
into Equation 1 and solve for
F
.
23
=
F
+
200
25
F
=
15
So our model equation is
P
=
15
+
n
25
.
Let's check our answer with the data in the problem.
15
+
200
25
=
23
15
+
500
25
=
35
So we have the correct model equation.
Now use the model to predict the price of printing 700 cards.
15
+
700
25
=
43
.
The price for printing 700 cards is $43.
Note that the price for printing 700 cards is NOT the same as the price for printing 200 cards plus the cost for printing 500 cards! See if you can figure out WHY?
if triangle ABC is congruent to Triangle TFW complete each part below no triangles are not drawn to scale
Answer:
See below
Step-by-step explanation:
Can't provide answer for some reason, so adding its screen shot
In a newspaper, it was reported that yearly robberies in Springfield were up 50%to 279 in 2012 from 2011. How many robberies were there in Springfield in 2011.
hi there! here's my answer for you...
There were 186 Springfield robberies in 2011.
hope this helped. i have included a step-by-step explanation below in case you need it. have a good one!
.
Think about what happens when you double a number.
You multiply it by 2. Since it's been doubles, we say is has had a 100% increase.
Likewise a 50% increase correlates to multiply by 1.5
Since we are trying to find the previous amount that experienced the increase, we divide by 1.5 to find the original amount because that amount*1.5 gives us 279.
Calling the original r, it is clear that 1.5r=279.
Solving for r, we find the original # of robberies to be 186.
What is the length of segment AB?
Answer:
I think it's B
Step-by-step explanation:
The width, is 4, multiplied by the height, which is 5. You then take the square root of that number and voila.
Jenna has $32 in her checking account. She writes a check for her cell phone bill for $39. How much money does she have remaining in her account?
Answer:
She has a balance of $-7.
Step-by-step explanation:
32-39 = -7
Answer: the answer is -7
Step-by-step explanation:
The measure of one angle of a triangle is 28 more than the measure of the smallest angle of the triangle. The measure of the third angle is twice the measure of the smallest angle. Find all three measures and classify the triangle by angles.
9514 1404 393
Answer:
38°, 66°, 76°acute triangleStep-by-step explanation:
Let x represent the smallest angle. Then the other two angles are (x+28) and 2x. Their sum is ...
x + (x+28) +(2x) = 180
4x = 152 . . . . subtract 28
x = 38 . . . . . . .divide by 4
x+28 = 66 . . . find the other angles
2x = 76
The three angles are 38°, 66°, 76°. The largest angle is acute, so it is an acute triangle.
can any one help? me plz
Answer:
2000 grams per 2 pints
Step-by-step explanation:
1 kilogram = 1000 grams
1 quart = 2 pints
2 x 1000 = 2000
1 x 2 = 2
find the value of x and y
Answer:
x = 3
Step-by-step explanation:
45x =25x + 57 + x
Combine like-terms:
45x = 26x + 57
Subtract 26x on both sides
19x = 57
Divide by 19
x = 3
Some friends spent a total of $12.00 on popcorn and drinks at the movie theater. A bucket of popcorn cost $2.00 and a drink cost $1.50.
A. Create an equation to represent the relationship between the number of buckets of popcorn, x, and the number of drinks, y, the friends bought for $12.00.
The friends bought 4 drinks.
B. How many buckets of popcorn did they buy?
Answer:
A. 12 = 2x + 1.5y
B. 3 buckets of popcorn
Step-by-step explanation:
We know 12 is the total and the cost for is $2 EACH we are multiplying so it would be written as 2x same goes for the drinks except it would be 1.50y
Since we found the equation is 12 = 2x + 1.5y and we are told that y represents the number of drinks we can replace y with 4. It would look like this,
12 = 2x + 1.5(4)
After you multiply 1.5 by 4 you get 6.
12 = 2x + 6
-6 -6
6 = 2x
Now divide both sides by 2, that way you isolate the variable.
6/2 = 3
2x/2 = x
So we are left with x = 3, which means if they buy 4 drinks they will buy 3 buckets of popcorn.
Hope that helps and have a great day!
Linda was playing tic tac toe with Raquel. They played a total of 52 games. Linda won 18 more
games than Raquel. How many games did each person win?
Linda won
games and Raquel won
games.
Answer:
Linda won 18 games and Raquel won 34 games.
Step-by-step explanation:
Answer:
OKay so the total is 52.
Linda won 18 MORE than Raquel.
So 52-18 equals=34.
So Raquel won 18. And she won 34.
Step-by-step explanation:
i'll mark ur answer as brainlist.
4) A baby bear is born and weighs only 12 ounces. The baby rebounds to weigh 57 pounds after one year. What was the bear's growth rate per month? Per week? explain ur answer, pls.
Answer:
75 oz / 1 month, 17.308 oz / 1 week
Step-by-step explanation:
baby = 12 oz
1 year = 57 lbs
1 lb = 16 oz
difference between 1 year and birth = ( 57 lbs ) * 16 - ( 12 ) = 900 oz
growth rate = 900 oz / 1 year --> 75 oz / 1 month --> 17.308 oz / 1 week
The girls’ soccer team scored 60 points in 10 games. If this trend were to continue, what would be the points scored in 15 games?
Group of answer choices
Answer:
In 15 games the score would be 90 points.
Answer:
90
Step-by-step explanation:
60÷10=6,averaging 6 points a game, 6×15=90
[tex] \frac{3}{5} + - \frac{2}{5} [/tex]