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alexgriva [62]
1 year ago
14

The rectangular rug has side lengths of 3 and 4 ft. What is the length of the diagonal? Draw a picture of the problem and solve.

Round to the nearest tenth
Mathematics
1 answer:
Nadusha1986 [10]1 year ago
7 0

ANSWER

The length of the diagonal is 5 ft

EXPLANATION

The diagram of the rug with the diagonal is:

The diagonal and the sides form a right triangle, so we can use the Pythagorean theorem to find x, the length of the diagonal:

\begin{gathered} x^2=3^2+4^2 \\ x=\sqrt[]{9+16} \\ x=\sqrt[]{25} \\ x=5 \end{gathered}

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10. Error Analysis A student draws a triangle with a perimeter 36 cm. The
Tasya [4]

Answer:

see the explanation

Step-by-step explanation:

we know that

The <u>Triangle Inequality Theorem</u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

In this problem

If the perimeter of triangle is equal to 36 cm

The longest side can't be equal to 18 cm

The student is incorrect

Because if the longest side is equal to 18 cm, and the perimeter is equal to 36 cm, then the sum of the other two sides is equal to 18 cm

and

Applying the triangle inequality theorem

Let

c  -----> the longest side

a and b the other two sides

we have that

if c=18 cm

a+b > c

a+b > 18 cm

therefore

If the longest side is 18 cm, the sum of the other two sides must be greater than 18 cm and the perimeter will be greater than 36 cm

4 0
3 years ago
Solve the inequality x^2 -2x - 8 &gt;0​
kykrilka [37]

Answer:

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8 0
2 years ago
Please awnser correct awnser! &lt; 3
Gwar [14]

Answer:

y = (1/4)x + 0

or

y = (1/4)x

the (1/4) is supposed to be a fraction of 1 in the numerator and 4 in the denominator

Step-by-step explanation:

6 0
2 years ago
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Please help me with this !!!!!!!
Alisiya [41]

Answer:

y = 2x - 1

Step-by-step explanation:

Note the difference between consecutive terms of y are constant, that is

1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 9 - 7 = 2

Thus the equation is of the form y = 2x ± c ← c is a constant

Substitute values of x to determine the required value of c

x = 0 : 2 × 0 = 0 ← require to subtract 1 for y = - 1

x = 1 : 2 × 1 = 2 ← require to subtract 1 for y = 1

x = 2 : 2 × 2 = 4 ← require to subtract 1 for y = 3, and so on

Thus the required equation is

y = 2x - 1

5 0
3 years ago
1. Consider the right triangle ABC given below.
lbvjy [14]
#1) 
A) b = 10.57
B) a = 22.66; the different methods are shown below.
#2)
A) Let a = the side opposite the 15° angle; a = 1.35.
Let B = the angle opposite the side marked 4; m∠B = 50.07°.
Let C = the angle opposite the side marked 3; m∠C = 114.93°.
B) b = 10.77
m∠A = 83°
a = 15.11

Explanation
#1)
A) We know that the sine ratio is opposite/hypotenuse.  The side opposite the 25° angle is b, and the hypotenuse is 25:
sin 25 = b/25

Multiply both sides by 25:
25*sin 25 = (b/25)*25
25*sin 25 = b
10.57 = b

B) The first way we can find a is using the Pythagorean theorem.  In Part A above, we found the length of b, the other leg of the triangle, and we know the measure of the hypotenuse:
a²+(10.57)² = 25²
a²+111.7249 = 625

Subtract 111.7249 from both sides:
a²+111.7249 - 111.7249 = 625 - 111.7249
a² = 513.2751

Take the square root of both sides:
√a² = √513.2751
a = 22.66

The second way is using the cosine ratio, adjacent/hypotenuse.  Side a is adjacent to the 25° angle, and the hypotenuse is 25:
cos 25 = a/25

Multiply both sides by 25:
25*cos 25 = (a/25)*25
25*cos 25 = a
22.66 = a

The third way is using the other angle.  First, find the measure of angle A by subtracting the other two angles from 180:
m∠A = 180-(90+25) = 180-115 = 65°

Side a is opposite ∠A; opposite/hypotenuse is the sine ratio:
a/25 = sin 65

Multiply both sides by 25:
(a/25)*25 = 25*sin 65
a = 25*sin 65
a = 22.66

#2)
A) Let side a be the one across from the 15° angle.  This would make the 15° angle ∠A.  We will define b as the side marked 4 and c as the side marked 3.  We will use the law of cosines:
a² = b²+c²-2bc cos A
a² = 4²+3²-2(4)(3)cos 15
a² = 16+9-24cos 15
a² = 25-24cos 15
a² = 1.82

Take the square root of both sides:
√a² = √1.82
a = 1.35

Use the law of sines to find m∠B:
sin A/a = sin B/b
sin 15/1.35 = sin B/4

Cross multiply:
4*sin 15 = 1.35*sin B

Divide both sides by 1.35:
(4*sin 15)/1.35 = (1.35*sin B)/1.35
(4*sin 15)/1.35 = sin B

Take the inverse sine of both sides:
sin⁻¹((4*sin 15)/1.35) = sin⁻¹(sin B)
50.07 = B

Subtract both known angles from 180 to find m∠C:
180-(15+50.07) = 180-65.07 = 114.93°

B)  Use the law of sines to find side b:
sin C/c = sin B/b
sin 52/12 = sin 45/b

Cross multiply:
b*sin 52 = 12*sin 45

Divide both sides by sin 52:
(b*sin 52)/(sin 52) = (12*sin 45)/(sin 52)
b = 10.77

Find m∠A by subtracting both known angles from 180:
180-(52+45) = 180-97 = 83°

Use the law of sines to find side a:
sin C/c = sin A/a
sin 52/12 = sin 83/a

Cross multiply:
a*sin 52 = 12*sin 83

Divide both sides by sin 52:
(a*sin 52)/(sin 52) = (12*sin 83)/(sin 52)
a = 15.11
3 0
3 years ago
Read 2 more answers
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