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solniwko [45]
3 years ago
13



Mathematics
1 answer:
zhuklara [117]3 years ago
7 0

Step-by-step answer:

Given:

A triangle

Perimeter  = 60 cm

longest side = 4* shortest side (x)

Solution:

longest side = 4x

shortest side = x

third (intermediate side = 60 -x -4x = 60-5x

The triangle inequality specifies that the sum of the two shorter sides must be greater than the longest side to form a triangle.  Hence

x + y > 4x

x + 60-5x > 4x

60 - 4x > 4x

8x < 60

x < 60/8 = 7.5, or

x < 7.5

Therefore to form a triangle, x (shortest side) must be less than 7.5 cm.

Examine the options: both 7 and 5 are both less than 7.5 cm.

40, 30 and 25 all have a problem because the longest side (4 times longer) will exceed the perimeter of 60.

Now also examine cases where 4x is NOT the longest side, in which case we need

4x>=y

or

4x >= 60-5x

9x >=60

x >= 6.67

so x=5 will not qualify, because 4x will no longer be the longest side.

The only valid option is x=7 cm

The side lengths for x=7 and x=5 are, respectively,

(7, 25, 28)

5, 20, 35  (in which case, the longest side is no longer 4x=20, so eliminated)

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Romashka [77]

Answer:

819

Step-by-step explanation:

Givens

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Formula

Sum = a(1 - r^n) / ( 1 - r)

Sum = -1(1 - (-4)^6 / (1 - -4)

Sum = -1 (1 - 4096) / 5

Sum = -1 (- 4095 ) / 5

Sum = 819

4 0
3 years ago
Simplify, and list any restrictions on the variable: (2x(x-4)/(4x^2-64)
uysha [10]

Answer:

WHEN SIMPLIFIED THE ANSWER WILL BE:

Step-by-step explanation:

(X)/(2(X+4)

8 0
3 years ago
A manufacturer earns Rs4500 in the first month and Rs 6000 in second month. On plotting these points a manufacturer observes a l
UkoKoshka [18]

Answer:

f(x) = 1500x +3000

Step-by-step explanation:

Given

Represent the months with x and the earnings with y.

So:

(x_1,y_1) = (1,4500)

(x_2,y_2) = (2,6000)

Required

Determine the linear function

First, calculate slope (m)

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{6000 - 4500}{2 - 1}

m = \frac{1500}{1}

m = 1500

The equation is then calculated using:

y = m(x - x_1) + y_1

y = 1500(x - 1) + 4500

y = 1500x - 1500 + 4500

y = 1500x +3000

As a function, we have:

f(x) = 1500x +3000

7 0
3 years ago
Use four rectangles to estimate the area between the graph of the function f(x) = V3x + 5 and the x-axis on the interval[0, 4] u
yuradex [85]

Answer:

  12.123

Step-by-step explanation:

You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.

<h3>Riemann sum</h3>

When the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.

The area we want is the sum ...

  f(0) +f(1) +f(2) +f(3)

As the attachment shows, that sum is ...

  area ≈ 12.123 . . . square units

__

<em>Additional comment</em>

The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.

Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.

For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.

7 0
1 year ago
What is the area of this trapezoid?<br><br> 175 in²<br> 140 in²<br> 129 in²<br> 85 in²
aksik [14]
Area of trapezoid = (B1 + B2)h/2

B1 = 15 in. + 4 in. + 6 in. = 25 in.
B2 = 15 in.
h = 7 in.

Area = (25 in. + 15 in.)(7 in.)/2 = 140 in.^2
3 0
3 years ago
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