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patriot [66]
3 years ago
10

For the right triangles below, find the exact values of the side lengths b and d.

Mathematics
1 answer:
Ivanshal [37]3 years ago
7 0

Answer:

Step-by-step explanation:

The question lacks the required diagram. Find the diagram attached below;

According to the first triangle, taking 30° as the reference angle, the opposite side of the triangle will be 5 and the adjacent will be the unknown side "b"

According to SOH, CAH, TOA;

tanθ = opposite/adjacent (using TOA)

Given;

θ = 30°, opposite = 5 and adjacent = b

tan30° = 5/b

b = 5/tan30°

b = 5/(1/√3)

b = 5*√3/1

b = 5√3

According to the 45° triangle, the opposite side of the triangle will be d and the hypotenuse will be 7

Using SOH;

sinθ = opposite/hypotenuse

Given;

θ = 45°, opposite = d and adjacent = 7

sin45° = d/7

d = 7sin45°

d = 7(1/√2)

d = 7/√2

Rationalize 7/√2

= 7/√2*√2/√2

=7√2/2

Hence the value of d is 7√2/2

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English
larisa86 [58]

Answer:

6 square feet

Step-by-step explanation:

Carpet has w= 8 ft and l = 12 ft

Reduced carpet has w' = 2 ft

<u>Reduction factor is </u>

  • 8/2 = 4

<u>Then </u>

  • l' = l/4 = 12/4 = 3 ft

<u>Area of small carpet</u>

  • S = 2*3 = 6 ft²
6 0
3 years ago
Percy solved the equation x2 + 7x + 12 = 12. His work is shown below. Is Percy correct? Explain.
antoniya [11.8K]
= > x² + 7x + 12 = 12

= > x² + ( 4 + 3 )x + 12 = 12

= > x² + 4x + 3x + 12 = 12

= > x( x + 4 ) + 3( x + 4 ) = 12

= > ( x + 4 ) ( x + 3 ) = 12


Percy did correct till this step. But by doing like this, Percy can't get the values of the variable x.



Percy should follow the following steps :

= > x² + 7x + 12 = 12


Add -12 on both sides,


= > x² + 7x + 12 - 12 = 12 - 12

= > x² + 7x = 0

= > x( x + 7 ) = 0

= > ( x = 0 ) or ( x + 7 = 0 )

= > ( x = 0 ) or ( x = - 7 )



Hence, required value(s) of x is 0 or -7
.
8 0
3 years ago
Read 2 more answers
Math help? One question?
Lera25 [3.4K]
My triangle solver says EF ≈ 7.5 ft.

_____
The law of cosines is usually used for this.

EF^2 = DE^2 +DF^2 -2*DE*DF*cos(D)
.. = 6^2 +11^2 -2*6*11*cos(40°)
.. ≈ 55.88

EF ≈ √55.88 ≈ 7.5 . . . ft

3 0
3 years ago
Lindsay is creating a bridge out of dried pasta and glue. In her plans, she sketches the graph to determine the lengths of the n
alexgriva [62]
From the graph shown it can be seen that the bridge is represented by a parabola with vertex of (5, 8) and roots of 1 and 9.

Recall that the vertex form of the equation of a parabola with vertex (h, k) is given by
y=a(x-h)^2+k

Thus, the equation of the given graph in vertex form is given by
y=a(x-5)^2+8

Also, recall that the equation of a parabola with roots, p and q, is given by
y=a(x-p)(x-q)

Thus the equation of the given graph can be given by
y=a(x-1)(x-9)

To get the value of a, we equate both equations and solve as follows:
a(x-5)^2+8=a(x-1)(x-9) \\  \\ a(x^2-10x+25)+8=a(x^2-10x+9) \\  \\ ax^2-10ax+25a+8=ax^2-10ax+9a \\  \\ 25a-9a=-8 \\  \\ 16a=-8 \\  \\ a=- \frac{8}{16} =- \frac{1}{2}

Therefore, the <span>function that Lindsay used to create her design is
f(x)=-0.5(x-5)^2+8
</span>
4 0
3 years ago
Read 2 more answers
What is the angle of rotation of 9x^(2)+4xy+5y^(2)-40=0?
frutty [35]
Your answer will be 18 hope this helps
6 0
3 years ago
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