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1 year ago

One leg of a 90-45-45 triangle is 5. What are the sides of the hypotenuse and the other leg?

Mathematics

1 answer:

kirza4 [7]1 year ago

7 0

Answer:

5√2, 5

Step-by-step explanation:

in a 90 45 45 triangle, each leg is the same legnth

the hypotenuse of a 90 45 45 triangle is x√2

x being the measure of the leg

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Consider the cubic function f(x) = x^3 + ax^2 + bx + 4 where (a) and (b) are constants. When f(x) is divided by x-3, the remaind

Debora [2.8K]

Answer:

see explanation

Step-by-step explanation:

Using the Remainder theorem

If f(x) is divided by (x - h) then f(h) = remainder, thus

f(3) = 3³ + a(3)² + b(3) + 4 = 10, that is

27 + 9a + 3b + 4 = 10

9a + 3b + 31 = 10 ( subtract 31 from both sides )

9a + 3b = - 21 → (1)

f(- 1) = (- 1)³ + a(- 1)² + b(- 1) + 4 = 6, that is

- 1 + a - b + 4 = 6

a - b + 3 = 6 ( subtract 3 from both sides )

a - b = 3 → (2)

Rearrange (2) expressing a in terms of b

a = 3 + b → (3)

Substitute a = 3 + b into (1)

9(3 + b) + 3b = - 21 ← distribute and simplify left side

27 + 9b + 3b = - 21

12b + 27 = - 21 ( subtract 27 from both sides )

12b = - 48 ( divide both sides by 12 )

b = - 4

Substitute b = - 4 into (3)

a = 3 - 4 = - 1

Hence a = - 1 and b = - 4

8 0

3 years ago

Look at the picture below to answer the question!! plss

laila [671]

Answer:

x = 15.3°

Step-by-step explanation:

Trig identities:

$sin(x)=\dfrac{O}{H} \ \ \ \ \ cos(x)=\dfrac{A}{H} \ \ \ \ \ tan(x)=\dfrac{O}{A}$

where

x = angle
O = side opposite the angle
A = side adjacent the angle
H = hypotenuse

$sin(46)=\dfrac{11}{x}\\\\\implies x=\dfrac{11}{sin(46)}\\\\\implies x=15.3$

8 0

2 years ago

A lawn had an area of 100 square feet. If it was 10 feet width, how long was it?

AleksAgata [21]

10 ft because 10×10=100

3 0

2 years ago

Read 2 more answers

Can you help me with this question please

Aleksandr-060686 [28]

Answer:

The actual length of the lap = 250 meters

Step-by-step explanation:

∵ The scale factor of the map is 1:1000

∵ The length of the lap on the map is 25 cm

∴ $\frac{1}{1000}=\frac{25}{x}$

Where x is the actual length of a lap

∴ x = (25 × 1000) ÷ 1 = 25000 cm

∵ 1 meter = 100 centimeter

∴ The actual length of the lap = 25000 ÷ 100 = 250 meters

7 0

3 years ago

Read 2 more answers

Please can someone answer this question! Worth 15 points

Westkost [7]

The statements that aer true or not or whatever

hmm, let's try te sencnarios
remember the commutative property of multiplication
ab=ba
so

what if they are both negative?
well, the negatives would cancel to leave with positive
the oposite would be both positive resulting in a positive

if they are differnt signs then result is negative
oposite would be still different signs so still negative
true statment

8 0

3 years ago