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OlgaM077 [116]
3 years ago
6

A parallelogram has an area of 288 square centimeters and a height of 12 centimeters.

Mathematics
1 answer:
saul85 [17]3 years ago
4 0
To find the base we will use the formula
base = Area/width
to plug in what we are given
base = 288/12
Base = 24 cm

Hope this helps :)
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Use the arc length formula to find the length of the curve y = 4x − 5, −1 ≤ x ≤ 2. check your answer by noting that the curve is
professor190 [17]
Ok, here we go.  Pay attention.  The formula for the arc length is AL= \int\limits^b_a { \sqrt{1+( \frac{dy}{dx})^2 } } \, dx.  That means that to use that formula we have to find the derivative of the function and square it.  Our function is y = 4x-5, so y'=4.  Our formula now, filled in accordingly, is AL= \int\limits^2_1 { \sqrt{1+4^2} } \, dx (that 1 is supposed to be negative; not sure if it is til I post the final answer).  After the simplification we have the integral from -1 to 2 of \sqrt{17}.  Integrating that we have AL= \sqrt{17}x from -1 to 2.  2 \sqrt{17}-(-1 \sqrt{17} ) gives us 3 \sqrt{17}.  Now we need to do the distance formula with this.  But we need 2 coordinates for that.  Our bounds are x=-1 and x=2.  We will fill those x values in to the function and solve for y.  When x = -1, y=4(-1)-5 and y = -9.  So the point is (-1, -9).  Doing the same with x = 2, y=4(2)-5 and y = 3.  So the point is (2, 3).  Use those in the distance formula accordingly: d= \sqrt{(2-(-1))^2+(3-(-9))^2} which simplifies to d= \sqrt{9+144}= \sqrt{153}.  The square root of 153 can be simplified into the square root of 9*17.  Pulling out the perfect square of 9 as a 3 leaves us with 3 \sqrt{17}.  And there you go!
5 0
2 years ago
Mage has $36 to spend on movie tickets. Each movie ticket costs $4.50. How many tickets can he buy?
Stels [109]

Answer:

x = 8 tickets

Step-by-step explanation:

Given that,

Mage has $36 to spend on movie tickets.

Each movie ticket costs $4.50.

Let he bought x tickets. ATQ,

4.50x = 36

x=\dfrac{36}{4.5}\\\\=8

So, he can buy 8 tickets.

4 0
2 years ago
First you to find the worksheet and download it<br> plase I need help
Goshia [24]

Answer:

a) The horizontal asymptote is y = 0

The y-intercept is (0, 9)

b) The horizontal asymptote is y = 0

The y-intercept is (0, 5)

c) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

d) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

e) The horizontal asymptote is y = -1

The y-intercept is (0, 7)

The x-intercept is (-3, 0)

f) The asymptote is y = 2

The y-intercept is (0, 6)

Step-by-step explanation:

a) f(x) = 3^{x + 2}

The asymptote is given as x → -∞, f(x) = 3^{x + 2} → 0

∴ The horizontal asymptote is f(x) = y = 0

The y-intercept is given when x = 0, we get;

f(x) = 3^{0 + 2} = 9

The y-intercept is f(x) = (0, 9)

b) f(x) = 5^{1  - x}

The asymptote is fx) = 0 as x → ∞

The asymptote is y = 0

Similar to question (1) above, the y-intercept is f(x) = 5^{1  - 0} = 5

The y-intercept is (0, 5)

c) f(x) = 3ˣ + 3

The asymptote is 3ˣ → 0 and f(x) → 3 as x → ∞

The asymptote is y = 3

The y-intercept is f(x) = 3⁰ + 3= 4

The y-intercept is (0, 4)

d) f(x) = 6⁻ˣ + 3

The asymptote is 6⁻ˣ → 0 and f(x) → 3 as x → ∞

The horizontal asymptote is y = 3

The y-intercept is f(x) = 6⁻⁰ + 3 = 4

The y-intercept is (0, 4)

e) f(x) = 2^{x + 3} - 1

The asymptote is 2^{x + 3}  → 0 and f(x) → -1 as x → -∞

The horizontal asymptote is y = -1

The y-intercept is f(x) =  2^{0 + 3} - 1 = 7

The y-intercept is (0, 7)

When f(x) = 0, 2^{x + 3} - 1 = 0

2^{x + 3} = 1

x + 3 = 0, x = -3

The x-intercept is (-3, 0)

f) f(x) = \left (\dfrac{1}{2} \right)^{x - 2} + 2

The asymptote is \left (\dfrac{1}{2} \right)^{x - 2} → 0 and f(x) → 2 as x → ∞

The asymptote is y = 2

The y-intercept is f(x) = f(0) = \left (\dfrac{1}{2} \right)^{0 - 2} + 2 = 6

The y-intercept is (0, 6)

7 0
2 years ago
Solve the equation for all real solutions in simplest form.<br> 3x2 - 12x + 11 = x
Ivanshal [37]

Answer:

(13 + or - (sign) square root(37)) / 6

Step-by-step explanation:

First search up the quadratic formula which is

x = (- b + or - square root(b^2 - 4ac)) / 2a

and to find a, b, and c you need this formula

ax^2 + bx + c = 0 (btw this is the safest solution to finding your answer with a number in-front of a quadratic equation.)

Math:

a = 3, b = -13, c = 11

b = -13, because of the x on the other end of the equation as the equation above "ax^2 + bx + c = 0" you need the zero to proceed to this next step.

Side Note: You only take the number and not the variable, variables are x, y, w, z, or etc.

(- (- 13) + or - square root((-13)^2 - 4(3)(11) ) ) / 2 * 3

13 + or - square root(37) / 6

5 0
2 years ago
VE
Firdavs [7]

Answer:

$4167

Step-by-step explanation:

Original Amount: $4167 (rounded)

First Year: $4167 + $416.7 = $4583.7

Second Year $4583.7 + $416.7 = 5000.4

8 0
3 years ago
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