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3 years ago

PLEASE HELP PLEASE THANK U SO MUCH

Mathematics

1 answer:

arlik [135]3 years ago

4 0

Answer:

Step-by-step explanation:

x² - 7x - 18 = 0

Product = -18

Sum = -7

Factors = 2 , (-9) {2*(-9) = -18 & 2 +(-9) = -7}

x² + 2x - 9x - 18 = 0

x(x + 2) - 9(x + 2) = 0

(x +2)(x - 9)= 0

x + 2 = 0 ; x - 9 = 0

x = -2 ; x = 9

x = -2 , 9

Sale price = 272000

Reduction percentage = 15%

Let the original price = x

Reduction = 15% of x

Original price - reduction price = Sale price

x - 15% of x = £272000

$x -\dfrac{15}{100}x = 272000\\\\\\\dfrac{100}{100}x-\dfrac{15}{100}x=272000\\\\\\\dfrac{85}{100}x=272000\\\\\\x=272000*\dfrac{100}{85}$

x = 3200 * 100

Original price = £320000

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Find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will be in terms of h, w, and θ.

miskamm [114]

[w + (h/tan θ)] × h

<h3>Further explanation</h3>

We aim is to find the area of the trapezoidal cross-section of the irrigation canal.

The formula for the area of the trapezoid is $\boxed{\boxed{ \ Area = \frac{1}{2} \times (a + b) \times h \ }}$

a & b = parallel sides
h = height

We assume the lower side is $\boxed{ \ a = w \ }$ and the upper side is b = x + w + x or $\boxed{ \ b = w + 2x \ }$ . See the attached picture.

In the right triangles located on the left and right of the trapezoid, we calculate the value of x based on trigonometric ratios namely tan of theta.

$\boxed{ \ tan \ \theta = \frac{opposite}{adjacent} \ }$

$\boxed{ \ tan \ \theta = \frac{h}{x} \ }$

$\boxed{ \ x = \frac{h}{tan \ \theta} \ }$

Substitute the equation of x to $\boxed{ \ b = w + 2x \ }.$

We get $\boxed{ \ b = w + \frac{2h}{tan \ \theta} \ }$

Finally all components are complete and can be substituted into a formula to calculate the area of a trapezoid.

$\circ \ \boxed{a = w}\\ \circ \ \boxed{ \ b = w + \frac{2h}{tan \ \theta} \ }\\\circ \ and \ h$

$\boxed{ \ Area = \frac{1}{2} \times (w + w + \frac{2h}{tan \ \theta}) \times h \ }$

$\boxed{ \ Area = \frac{1}{2} \times (2w + \frac{2h}{tan \ \theta}) \times h \ }$

$\boxed{ \ Area = \frac{1}{2} \times 2(w + \frac{h}{tan \ \theta}) \times h \ }$

Hence, the area of the trapezoidal cross-section of the irrigation canal is $\boxed{\boxed{ \ Area = (w + \frac{h}{tan \ \theta}) \times h \ }}$

<h3>Learn more</h3>

Find out the area of parallelogram brainly.com/question/4459688
The order of rotational symmetry of rhombus brainly.com/question/4228574
Find out the coordinates of the image of a point after the triangle is rotated 270° about the origin brainly.com/question/7437053

Keywords: the trapezoidal, cross-section of the irrigation canal, the area, the answer will be in terms of h, w, and θ, trigonometric ratios, tan, opposite, adjacent, height, sides

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4 years ago

Read 2 more answers