Algebraic Proofs. Geometry

Answer:

Correct answer is B. 0.08

Step-by-step explanation:

Answer:

the answers is -4 for this exerxises

Answer:

Below in bold

Step-by-step explanation:

The sequence is:

3, x, y, 18

If this is an A P then

x - 3 = y - x  

2x - y = 3      (A)  and

y - x = 18 - y

2y - x = 18      (B)

Multiply  (A) by 2:

4x - 2y = 6    (C)

Adding B and C:

3x = 24

x = 8.

and

2y - 8 = 18

2y = 26

y = 13.

So x = 8 and y = 13.

b)   ar + ar^2 = 6ar^3  where a = first term and r = common ratio

Divide by a:

r + r^2 = 6r^3

6r^3 - r^2 - r = 0

r(6r^2 - r - 1) = 0

r(3r  + 1)(2r  - 1) = 0

So the 2 possible values of r

= -1/3 and 1/2.

i) The common ratio is positive so it must be 1/2.

Second term ar = 8

1/2 a = 8

a = 16.

So the first 6 terms are:

16, 8, 4, 2, 1, 1/2.

Answer:

were is the circle to be to be equated

Answer: f(x) = x + 2

Step-by-step explanation:

A = {1, 2, 3, 4, 5, 6]

B = {3, 4, 5, 6, 7, 8)

for each A, B is 2 more

f(1) = 1 + 2 = 3

f(2) = 2 + 2 = 4

f(3) = 3 + 2 = 5

and so on...

⇒ f(x) = x + 2

Answer:

A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.

Step-by-step explanation:

Finding the solution of these 2 equations

Equating them :

Substitute in a equation to find y :

The solution is (3, 8).

The 1st explanation is the correct one.

Answer:

b.

Step-by-step explanation:

The inequality says that x is bigger than 5. The number line shows the arrow starting from 5 and going bigger. Therefore, that number line is correct.

Answer:

the end by the finish line

Since f(x) is a cubic polynomial, it has at most 3 distinct roots. If f(x) has 3 real roots, then f(x) = 0 for more than one instance of x.

But if f(x) is one-to-one, then there must be only one real root and the other two are non-real. Let a + bi and a - bi be these non-real roots and c the single real root; then we can factorize f(x) as

[tex]f(x) = x^3 - kx^2 + 12x + 7 = (x - (a + bi)) (x - (a - bi)) (x - c)[/tex]

Expand the right side to get

[tex]f(x) = x^3 - kx^2 + 12x + 7 = (x^2 - 2ax + a^2+b^2) (x - c)[/tex]

[tex]f(x) = x^3 - kx^2 + 12x + 7 = x^3 - (2a + c) x^2 + (a^2 + 2ac + b^2) x - (a^2c + b^2c)[/tex]

from which it follows that

[tex]\begin{cases}k = 2a + c \\ 12 = a^2+2ac+b^2 \\ 7 = -a^2c-b^2c\end{cases}[/tex]

Since f(x) has only one root, its graph will have no turning points/extrema. If f(x) has a critical point, it must be a saddle point. Differentiating f(x) yields

[tex]f'(x) = 3x^2 - 2kx + 12[/tex]

Solve for the critical point:

[tex]f'(x) = 3x^2 - 2kx + 12 = 0[/tex]

[tex]x^2 - \dfrac{2k}3 x = -4[/tex]

[tex]x^2 - \dfrac{2k}3 x + \dfrac{k^2}9 = \dfrac{k^2}9-4[/tex]

[tex]\left(x - \dfrac k3\right)^2 = \dfrac{k^2}9-4[/tex]

[tex]x = \dfrac k3 \pm \sqrt{\dfrac{k^2}9-4}[/tex]

There is at most one real critical point, so either the square root term vanishes or it produces a non-real number. This happens for

[tex]\dfrac{k^2}9 - 4 \le 0 \implies k^2 \le 36 \implies -6 \le k \le 6[/tex]

So, if f(x) is one-to-one, then

[tex]k \in \left\{\kappa \in \Bbb R \mid -6 \le \kappa \le 6\right\}[/tex]

Answer:

see below

Step-by-step explanation:

You will need the hypotenuse   12 ^2 + 9^2 = h^2   h = 15

In a right triangle:

S O H   C A H  T O A

sin s  =   S A H  = Opposite / Hypotenuse =   12/15

cos r = C A H  = Adjacent / Hypotenuse    = 12/ 15

Tan s = T O A =  12 / 9

cos (theta) = cos s  = 9 / 15

Tan r = 9/12

arc cos(theta) = theta = arccos(9/15) = 53.13 degrees

Answer:

[tex]\huge\boxed{\sf \frac{5}{15} + \frac{4}{14} }[/tex]

Step-by-step explanation:

Total number of marbles = 5 + 8 + 2 = 15

Number of red marbles = 5

Probability to draw a red marble at the first trial = 5/15

Number of marbles left = 15 - 1 = 14

Number of Red marbles left = 5 - 1 = 4

Probability to draw a red marble at the second trial = 4/14

[tex]\displaystyle =Probability \ of \ drawing \ a \ red \ marble \ at \ the \ (second \ attempt +first \ attempt)\\\\= \frac{5}{15} + \frac{4}{14} \\\\\rule[225]{225}{2}[/tex]

answer is given below

29/6 = 203/42

16/7 = 96/42

to make the denominator 42 we use common tables for this just multiplying .

Answer:

the fractions are 203/42 and 96/42

Step-by-step explanation:

[tex]for \: \frac{29}{6} \\ \: multply \: the \: numerator \: and \: denominator \: by \: 7 \\ \frac{29}{6} \times \frac{7}{7} = \frac{203}{42} \\ for \: \frac{16}{7} also \: multiply \: the \: numerator \\ and \: denominatorby \: 6 \\ = \frac{16}{7} \times \frac{6}{6} = \frac{96}{42} [/tex]

The price of each comb is $0.5, if the linear equation y = x/2 models the income, in dollars, from selling x plastic combs

An equation is an expression that shows the relationship between two or more number and variables.

Profit = income - cost

Given that the linear equation y = x/2 models the income, in dollars, from selling x plastic combs. Hencee:

Price of each comb = (x/2) / x = 0.5

The price of each comb is $0.5, if the linear equation y = x/2 models the income, in dollars, from selling x plastic combs

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Answer:

$0.50

Step-by-step explanation:

The answer above is correct.

See

x is decreased by 3 .

and y is increased by 5

So translation is

Hence

So

x will go 3 units right

y will go 5units up

Graph attached

Answer:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function:

[tex]f(x)=\left(\dfrac{1}{4}\right)^x[/tex]

Translated 3 units to the right:

[tex]f(x-3)=\left(\dfrac{1}{4}\right)^{x-3}[/tex]

Translated 5 units up:

[tex]f(x-3)+5=\left(\dfrac{1}{4}\right)^{x-3}+5[/tex]

[tex]\implies g(x)=f(x-3)+5[/tex]

Therefore:

[tex]\textsf{g(x) is a translation of f(x) by }\left(\begin{array}{c}3\\5\\\end{array}\right)[/tex]

Step-by-step explanation:

[tex]2 {}^{2} \times 2 {}^{3} \times 2 {}^{1} \times 3 {}^{ - 1} {}^{ (- 2)} [/tex]

[tex]2 {}^{6} 3 {}^{2} [/tex]

Answer:

78

Step-by-step explanation:

hint

Answer:

50-50

Step-by-step explanation:

If yoiu have 4 and divide it b

Using translation concepts, it is found that the equation for function g(x) is given by:

g(x) = 4x².

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the parent function is given by:

f(x) = x².

This function passes through point (1,1). Function g(x) passes through point (1,4), that is, it is horizontally compressed by a factor of 4, hence g(x)  is given by:

g(x) = 4x².

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Answer:

6

Step-by-step explanation:

Answer:

Center: (9, 4)

Radius: 20

Explanation:

(x - 9)² + (y - 4)² = 400

The Circle Formula:

(x - h)² + (y - k)² = r²

where (h, k) is center points, r is radius

Rewrite the equation:

(x - 9)² + (y - 4)² = 20²

Identify following:

h = 9, k = 4, radius = 20

A) the value of the population proportion of people who would watch the new series is 5 out of 8 viewers, and B) a 99% confidence interval for the population proportion of people who would watch the new series indicates that between 61.87% and 63.13% of viewers will watch the new series.

Given that Netflix is considering a new romcom (romantic comedy) series, and a random sample of 1,000 viewers was selected and 625 viewers indicated they would watch the new series, for A) estimate the value of the population proportion of people who would watch the new series, and B) develop a 99% confidence interval for the population proportion of people who would watch the new series, the following calculations must be made:

A)

625 = 1

1000 = X

1000 / 625 = X

1.6 = X

10 out of 16, or 5 out of 8.

B)

62.5 x 0.99 = 61.875

62.5 x 1.01 = 63.125

Therefore, A) the value of the population proportion of people who would watch the new series is 5 out of 8 viewers, and B) a 99% confidence interval for the population proportion of people who would watch the new series indicates that between 61.87% and 63.13% of viewers will watch the new series.

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Answer:

See below

Step-by-step explanation:

Start with  sin x

  amplitude of 5

      5 sin x

      midline 4

          5 sin (x)  + 4

         period of 4

                   2 pi / 4 = pi/2

                5 sin ( x pi/2 ) + 4

Answer:

B

Step-by-step explanation:

Answer:

   (i) 126 ways

  (ii)

  (a) 1/126

  (b) 5/14

Step-by-step explanation:

(i) Possible selections

(ii) (a) all girls

(ii) (b) more boys than girls

    2. 4 boys, no girls

⇒ 40 + 5 = 45 ways

⇒ P = 45/126 = 15/42 = 5/14

Answer:

[tex]\huge\boxed{\sf x = 8.2}[/tex]

Step-by-step explanation:

Since it is a right-angled triangle, we will apply Pythagoras Theorem.

Given are:

Base = 16

Perpendicular = x

Hypotenuse = 18

Pythagoras Theorem:

[tex]\sf (Hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]

(18)² = (16)² + (x)²

324 = 256 + x²

Subtract 256 to both sides

324 - 256 = x²

68 = x²

Take sqrt on both sides

8.2 = x

x = 8.2

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

We have,

We know that,

[tex] \large\boxed{\sf (Hypotenuse)^2=(Perpendicular)^2+(Base)^2}[/tex]

[tex]\longmapsto \sf \: (18)^2=(16)^2+x^2[/tex]

[tex]\longmapsto \sf \: (18)^2-(16)^2=x^2[/tex]

[tex]\longmapsto \sf \: x^2=324-256[/tex]

[tex]\longmapsto \sf \: x^2=68[/tex]

[tex]\longmapsto \sf \: x = \sqrt{68}[/tex]

[tex]\longmapsto \sf \: x ≈8.25 [/tex]

Answer:

[tex]6 \frac{2}{13} [/tex]