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3 years ago

What is the area of the square?* Perimeter =60m

Mathematics

1 answer:

djverab [1.8K]3 years ago

3 0

Answer:

A = 225 m ^2

Step-by-step explanation:

The perimeter of a square is found by

P =4s where s is the side of a square

60 = 4s

Divide each side by 4

60/4 =4s/4

15 = s

Now we need to find the area

A = s^2 for the area of a square

A = 15^2

A = 225 m ^2

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What is the result of substituting for y in the bottom equation y=x+3 y=x^2+2x-4

8_murik_8 [283]

The solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)

Solution:

Given that,

$y = x + 3 ------- eqn 1\\\\y = x^2 + 2x - 4 ----- eqn 2$

We have to substitute eqn 1 in eqn 2

$x + 3 = x^2 + 2x - 4$

$\mathrm{Switch\:sides}\\\\x^2+2x-4=x+3\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\\\x^2+2x-4-3=x+3-3\\\\\mathrm{Simplify}\\\\x^2+2x-7=x\\\\\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}\\\\x^2+2x-7-x=x-x\\\\\mathrm{Simplify}\\\\x^2+x-7=0$

$\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=1,\:c=-7\\\\x =\frac{-1\pm \sqrt{1^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}$

$x = \frac{-1 \pm \sqrt{ 1 + 28}}{2}\\\\x = \frac{ -1 \pm \sqrt{29}}{2}$

$x = \frac{ -1 \pm 5.385 }{2}\\\\We\ have\ two\ solutions\\\\x = \frac{ -1 + 5.385 }{2}\\\\x = 2.1925$

$Also\\\\x = \frac{ -1 - 5.385 }{2}\\\\x = -3.1925$

Substitute x = 2.1925 in eqn 1

y = 2.1925 + 3

y = 5.1925

Substitute x = -3.1925 in eqn 1

y = -3.1925 + 3

y = -0.1925

Thus the solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)

6 0

3 years ago

Which shows a correct order to solve this story problem? Kent and Curtis went to the state fair. They had to pay a total of $7.1

KiRa [710]

The problem is asking how much each person will need to pay. Simplifying the problem into an equation with variables (an algorithm) will greatly help you solve it:

S = Sales Tax = $ 7.18 per any purchase
A = Admission Ticket = $ 22.50 entry price for one person (no tax applied)
F = Food = $ 35.50 purchases for two people

We know the cost for one person was: (22.50) + [(35.50/2) + 7.18] =
$ 47.43 per person. Now we can check each method and see which one is the correct algorithm:

Method A)
[2A + (F + 2S)] / 2 = [ (2)(22.50) + [35.50 + (2)(7.18)] ]/ 2 = $47.43
Method A is the correct answer

Method B)
[(2A + (1/2)F + 2S) /2 = [(2)(22.50) + 35.50(1/2) + (2)7.18] / 2 = $38.55
Wrong answer. This method is incorrect because the tax for both tickets bought are not being used in the equation.

Method C)
[(A + F) / 2 ]+ S = [(22.50 + 35.50) / 2 ] + 7.18 = $35.93
Wrong answer. Incorrect Method. The food cost is being reduced to the cost of one person but admission price is set for two people.

6 0

3 years ago

Determine which function has the greatest rate of change over the interval [0, 2].

ruslelena [56]

Remember that the average rate of change of a function over an interval is the slope of the straight line connecting the end points of the interval. To find those slopes, we are going to use the slope formula: $m= \frac{y_{2}-y_{1}}{x_2-x_1}$

Rate of change of $a$ :
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of $a$ :
$m= \frac{y_{2}-y_{1}}{x_2-x_1}$
$m= \frac{4-1}{2-0}$
$m= \frac{3}{2}$
$m=1.5$
The average rate of change of the function $a$ over the interval [0,2] is 1.5

Rate of change of $b$ :
Here the end points are (0,0) and (2,2)
$m= \frac{2-0}{2-0}$
$m= \frac{2}{2}$
$m=1$
The average rate of change of the function $b$ over the interval [0,2] is 1

Rate of change of $c$ :
Here the end points are (0,-1) and (2,0)
$m= \frac{0-(-1)}{2-0}$
$m= \frac{1}{2}$
$m=0.5$
The average rate of change of the function $c$ over the interval [0,2] is 0.5

Rate of change of $d$ :
Here the end points are (0,0.5) and (2,2.5)
$m= \frac{2.5-0.5}{2-0}$
$m= \frac{2}{2}$
$m=1$
The average rate of change of the function $d$ over the interval [0,2] is 1

We can conclude that the function that has the greatest rate of change over the interval [0, 2] is the function a.

4 0

3 years ago

An experiment was conducted to evaluate the success of an Ebola virus vaccine. The subjects were unaware of the treatment they w

Irina-Kira [14]

Answer:

your answer would be

B complexity

I agree that it is B but would suggest that you also consider the implications of each answer. They are all technically correct.

A is correct simply due to the fact that the longer time passes without an ebola cure, the more people can be potentially infected with it, resulting in less healthy individuals that may be able to volunteer to test potential ebola vaccines. Scientists need healthy volunteers from affected regions in order for rapid clinical trials to occur.

B is correct because of the nature of epidemics. A combination of technical, social, economic, and geographical obstacles slow the progress and dissemination of ebola vaccine information.

C is correct because finance impacts everything from finding resources used in studying ebola to distributing vaccines to affected areas. Economic imbalances or money shortages negatively impact research.

D is correct due to many social factors (more of a subjective answer). Some people think that vaccine distributors discriminate against certain ethnic groups. Others think the governments/other organizations are not effective enough at managing the situation. Still others feel that the search for a cure is not being approached in the right way. In all, there are multiple ways to oppose different aspects of ebola research.

Ultimately, B is correct because it seems to capture the meaning of A, C, and D together.

6 0

2 years ago

Determine algebraically whether f(x)=3x-2 and g(x)=(x+2)/3 are inverse functions. Show all work.

Sergio [31]

Answer:

Yes

Step-by-step explanation:

f(x)=3 x-2

y= 3 x-2

x= 3y - 2

3 y -2 = x

3 y -2 + 2 = x + 2

3 y = x + 2

3 3 3

3 y = x + 2

3 3 3

y = x + 2 replace y with f ^ -1(x)

3 3

f ^-1 (x) = x + 2

3 3

4 0

3 years ago