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3 years ago

the area of a rectangle is 95 square yard. if the perimeter is 48 yards find the length and width of rectangle

1 answer:

4 0

Try this option:
according to the condition w+l=48 and w*l=95.
Using these two equation:
$\left \{ {{l+w=48} \atop {lw=95}} \right. \ =\ \textgreater \ \ \left[\begin{array}{ccc}l=24- \sqrt{481};w=24+ \sqrt{481}\\ \\l=24+ \sqrt{481};w=24- \sqrt{481}\end{array}$

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The graph of the function f(x)= x2 − 4x + 6 is shown here. What is its axis of symmetry?

Andrew [12]

First, simplify the expression of the function $f(x)=x^2-4x+6$ highlighting the perfect square:

$f(x)=x^2-4x+4-4+6=(x-2)^2+2.$

Then find the vertwx of parabola. When x=2, f(2)=2 and the coordinates of the vertex are (2,2). The axis of symmetry passes through the vertex and is parallel to the y-axis. Therefore, its equation is x=2 (see attached graph for details).

Answer: x=2.

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3 years ago

Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.

sattari [20]

Answer:

Solutions: (2,10), (4,5)

Not solutions: (1,12), (6,10), (12,8), (18,6)

Step-by-step explanation:

Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.

1. Tyler has $36, then

$x+3y\le 36.$

2. Tyler can carry up to 20 pounds of food in his backpack, then

$x+1.5y\le 20.$

You get the following system of inequalities:

$\left\{\begin{array}{l}x+3y\le 36\\ x+1.5y\le 20\end{array}\right.$

Now substitute the coordinates of each point:

(1,12):

$\left\{\begin{array}{l}1+3\cdot 12=37> 36\\ 1+1.5\cdot 12=19\le 20\end{array}\right.$

False, because first inequality doesn't hold.

(2,10):

$\left\{\begin{array}{l}2+3\cdot 10=32\le 36\\ 2+1.5\cdot 10=17\le 20\end{array}\right.$

True, both inequalities hold.

(4,5):

$\left\{\begin{array}{l}4+3\cdot 5=19\le 36\\ 4+1.5\cdot 5=11.5\le 20\end{array}\right.$

True, both inequalities hold.

(6,10):

$\left\{\begin{array}{l}6+3\cdot 10=36\le 36\\ 6+1.5\cdot 10=21> 20\end{array}\right.$

False, because secondt inequality doesn't hold.

(12,8):

$\left\{\begin{array}{l}12+3\cdot 8=36\le 36\\ 12+1.5\cdot 8=24> 20\end{array}\right.$

False, because second inequality doesn't hold.

(18,6):

$\left\{\begin{array}{l}18+3\cdot 6=36\le 36\\ 18+1.5\cdot 6=27> 20\end{array}\right.$

False, because second inequality doesn't hold.

7 0

3 years ago

alfred deposited $893.78 in a savings account that earns 2.2% simple interest. What is alfreds account balance after seven years

ASHA 777 [7]

Hello! The formula for finding simple interest is prt. That means multiply the principal (initial amount) by the rate (percentage) by time (months or years). The principal is $893.78 and the interest rate is 2.2%. 893.78 * 2.2% (0.022) is 19.66316. Do not delete that number. The time is 7 years. Now multiply that number by 7 in order to get 137.64212 or $137.64 when rounded to the nearest whole hundredth. Now, let's add both numbers. 893.78 + 137.64 is 1,031.42. There. Alfred's balance after seven years is $1,031.42.

7 0

3 years ago

Ten people from a local youth group went to black hills whitewater rafting tour company for a one day rafting trip. the group pa

ICE Princess25 [194]

42.5p=c

You get you get the number 42.5 since you know 10 people paid 425, you would divide 425 by 10 to know how much every person paid.

M is representing the amount of money each person paid

(M)10=425
M=425/10
M=42.50 <- since it’s about money

Each person paid $42.50

The cost for 15 people is $637.50.

42.5p=c
42.5(15)=637.5

6 0

3 years ago

Identify whether the series summation of 16 open parentheses 5 close parentheses to the I minus 1 power from 1 to infinity is a

Svet_ta [14]

We are given with the function summation of 16*(5) ^(I-1) from 1 to infinity. As we assume in the calculator that infinity is equal to a very large number, the result that can be obtained is undefined. This means the number is very large. This is because the ratio (15) is large too. The series is divergent since the number in the infinite geometric series is ever increasing. Answer is B.

8 0

3 years ago

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