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3 years ago

Write 6(x - 5)^4+ 4(x - 5)^2 + 6 = 0 in the form of a quadratic by using substitution

Mathematics

1 answer:

Juliette [100K]3 years ago

5 0

Answer:

3m^2+2m+3=0

Step-by-step explanation:

6(x - 5)^4+ 4(x - 5)^2 + 6 = 0

(x-5)^2= m

6m^2+4m+6=0

3m^2+2m+3=0

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How to factor polynomials

Ierofanga [76]

Check for the GCF first. ...Multiply the quadratic term and the constant term. ...Write down all the factors of the result, in pairs. ...From this list, find the pair that adds to produce the coefficient of the linear term.

6 0

3 years ago

Right triangles abc and dbc with right angle c are given below. If cos(a)=15,ab=12 and cd=2, find the length of bd.

dmitriy555 [2]

see the attached figure to better understand the problem

we have that

$cos(A)=\frac{1}{5} \\ AB=12\ units\\ CD=2\ units$

Step 1

Find the value of AC

we know that

in the right triangle ABC

$cos (A)=(AC/AB)\\AC=AB*cos(A)$

substitute the values in the formula

$AC=12*(1/5)\\ AC=2.4\ units$

Step 2

Find the value of BC

we know that

in the right triangle ABC

Applying the Pythagorean Theorem

$AB^{2} =AC^{2}+BC^{2}\\ BC^{2}=AB^{2} -AC^{2}$

substitute the values

$BC^{2}=12^{2} -2.4^{2}\\BC^{2}= 138.24\\ BC=11.76\ units$

Step 3

Find the value of BD

we know that

in the right triangle BCD

Applying the Pythagorean Theorem

$BD^{2} =DC^{2}+BC^{2}$

substitute the values

$BD^{2} =2^{2}+11.76^{2}$

$BD=11.93\ units$

therefore

the answer is

the length of BD is 11.93 units

8 0

3 years ago

Read 2 more answers

Question :

Elza [17]

Answer:

C) 405.3 ft

Step-by-step explanation:

A triangle is a polygon with three angles and three sides. Types of triangle are scalene, isosceles, equilateral, right angled triangle.

Given a triangle with angles A, B, C and the corresponding sides directly opposite to the angles as a, b, c. The sine rule states that:

$\frac{a}{sin(A)}= \frac{b}{sin(B)} =\frac{c}{sin(C)}$

In the triangle formed by point C, ship B and ship A, we have ∠A = 82°, ∠B = 78°, c = AB = 140 ft. Hence:

∠A + ∠B + ∠C = 180° (sum of angles in a triangle)

82 + 78 + ∠C = 180

∠C + 160 = 180

∠C = 20°

Using sine rule:

$\frac{c}{sin(C)}=\frac{a}{sin(A)}\\\\\frac{140}{sin(20)}=\frac{a}{sin(82)}\\\\a= \frac{140*sin (82)}{sin(20)}\\\\a=405.3\ ft$

a = distance from Ship B to the signal fire at point C

8 0

2 years ago

Suppose that nine-digit Social security numbers are assigned at random. If you randomly select a number, what is the probability

Rina8888 [55]

Answer: 0.3 .

Step-by-step explanation:

The digits in number system = 10 ( 0 to 9)

The total different nine-digit Social security numbers = $10^9$ [By Fundamental counting principle]

$=1,000,000,000$ = 1 billion

Total people in united state = 300 million = 300, 000 ,000

Since each person In US have equal chance to get chosen.

Therefore , if a number is selected randomly , then the probability that it belongs to one of the 300 million people in the United States :-

$=\dfrac{300, 000 ,000}{1,000, 000 ,000}=0.3$

Hence, the required probability is 0.3 .

6 0

3 years ago

(a) Write an expression for a number that is three more than r. .

navik [9.2K]

Answer:

r+3

Step-by-step explanation:

r is an expression. To get an expression that is 3 more, just add 3

r+3

7 0

1 year ago