determine the period of this function​

Answer:

4x² - 24x + 20 = 0

Step-by-step explanation:

a(1)² + b(1) + 20 = 0

a(5)² + b(5) + 20 = 0

a + b = - 20 ⇒ b = - a - 20 ...... (1)

25a + 5b = - 20 .......... (2)

(1) -----> (2)

25a + 5( - a - 20) = - 20

20a - 100 = - 20 ⇒ a = 4

4 + b = - 20 ⇒ b = - 24

4x² - 24x + 20 = 0

Answer:

[tex]\displaystyle x=-\frac{2}{3}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]\displaystyle \sqrt{x^2-4x+8}+x=2-x[/tex]

We can isolate the square root. Subtract x from both sides:

[tex]\sqrt{x^2-4x+8}=2-2x[/tex]

And square both sides:

[tex](\sqrt{x^2-4x+8})^2=(2-2x)^2[/tex]

Expand:

[tex]x^2-4x+8=4-8x+4x^2[/tex]

Isolate the equation:

[tex]3x^2-4x-4=0[/tex]

Factor:

[tex]\displaystyle (3x+2)(x-2)=0[/tex]

Zero Product Property:

[tex]3x+2=0\text{ or } x-2=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle x=-\frac{2}{3}\text{ or } x=2[/tex]

Now, we need to check for extraneous solutions. To do so, we can substitute each value back into the original equation and check whether or not the resulting statement is true.

Testing x = -2/3:

[tex]\displaystyle \begin{aligned} \sqrt{\left(-\frac{2}{3}\right)^2-4\left(-\frac{2}{3}\right)+8}+\left(-\frac{2}{3}\right)&\stackrel{?}{=}2-\left(-\frac{2}{3}\right)\\ \\ \sqrt{\frac{4}{9}+\frac{8}{3}+8}-\frac{2}{3}&\stackrel{?}{=}2+\frac{2}{3} \\ \\ \sqrt{\frac{100}{9}}-\frac{2}{3}& \stackrel{?}{=} \frac{8}{3}\\ \\ \frac{10}{3}-\frac{2}{3} =\frac{8}{3}& \stackrel{\checkmark}{=}\frac{8}{3}\end{aligned}[/tex]

Since the resulting statement is true, x = -2/3 is indeed a solution.

Testing x = 2:

[tex]\displaystyle \begin{aligned}\sqrt{(2)^2-4(2)+8}+(2) &\stackrel{?}{=}2-(2) \\ \\ \sqrt{4-8+8}+2&\stackrel{?}{=}0 \\ \\ \sqrt{4}+2&\stackrel{?}{=}0 \\ \\ 2+2=4&\neq 0\end{aligned}[/tex]

Since the resulting statement is not true, x = 2 is not a solution.

Therefore, our only solution to the equation is x = -2/3.  

Step-by-step explanation:

Hey there!

Given;

[tex] \sqrt{ {x}^{2} - 4x + 8} + x = 2 - x[/tex]

Take "X" in right side.

[tex] \sqrt{ {x - 4 + 8}^{2} } = 2 - 2x[/tex]

Squaring on both sides;

[tex] {( \sqrt{ {x}^{2} - 4x + 8 } )}^{2} = {(2 - 2x)}^{2} [/tex]

Simplify;

[tex] {x}^{2} - 4x + 8 = {(2)}^{2} - 2.2.2x + {(2x)}^{2} [/tex]

[tex] {x }^{2} - 4x + 8 = 4 - 8x + 4 {x}^{2} [/tex]

[tex]3 {x}^{2} - 4x - 4 = 0[/tex]

[tex]3 {x}^{2} - (6 - 2)x - 4 = 0[/tex]

[tex] 3 {x}^{2} - 6x + 2x - 4 = 0[/tex]

[tex]3x(x - 2) + 2(x - 2) = 0[/tex]

[tex](3x + 2)(x - 2) = 0[/tex]

Either;

3x+2 = 0

x= -2/3

Or;

x-2 = 0

x= 2

Check:

Keeping X= -2/3,

√(x²-4x+8 ) +X = 2-x

√{(-2/3)²-4*-2/3+8}+(-2/3) = 2+2/3

8/3 = 8/3 (True)

Now; Keeping X= 2

√{(2)²-4*2+8}+2 = 2-2

8 ≠0 (False)

Therefore, the value of X is -2/3.

Hope it helps!

Answer:

3/10 of a cup

Step-by-step explanation:

Find how many cups of strawberries each student got by dividing 6 by 20:

= 6/20

Simplify this by dividing each number by 2:

= 3/10

So, each student got 3/10 of a cup of strawberries

Answer:

for (a)

Step-by-step explanation:

15 and 25 are the numbers that come in A union to B

Answer:

71.51

Step-by-step explanation:

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=3·3+7·3+7·3+1

2·﹣34+2·(3·7)2+2·(3·7)2﹣74+2·(7·7)2﹣74=71.51219

Answer:

Step-by-step explanation:

This is a 30°-60°-90° right triangle.

AC is hypotenuse, AB is opposite side to 30° angle.

We know that in such a triangle the side opposite to 30° angle is half the hypotenuse.

So we have:

Multiply the amount by 9.5% then subtract.

19064.67 x 0.095 = 1,811.14

Now subtract:

19064.67 - 1811.14 = 17253.53

The answer is £17,253.53

Answer:

2nd option

Step-by-step explanation:

f(x) + g(x)

= 4x - 5 + 3x + 7 ← collect like terms

= 7x + 2

domain is all real numbers

Answer:

Step-by-step explanation:

Exponent laws:

[tex](a^{m})^{n}=a^{m*n}\\\\a^{-m}=\frac{1}{a^{m}}[/tex]

[tex](t^{\frac{15}{27}}x^{9}})^{\frac{-2}{3}}= \ t^{\frac{15}{27}*\frac{-2}{3}}*x^{9*\frac{-2}{3}}\\\\\\= t^{\frac{5}{9}*\frac{-2}{3}}*x^{3*-2}\\\\=t^{\frac{-10}{27}}x^{-6}\\\\=\frac{1}{t^{\frac{10}{27}}x^{6}}[/tex]

Answer:

Option (d), (e) and (f) are correct.

Step-by-step explanation:

In triangle MNP, angle P = 90 degree

Cos M = 7 / 12

Now according to the right angle triangle

[tex]NP^2 = NM^2 - PM^2\\\\NP^2 = 12^2 - 7^2\\\\NP = \sqrt95[/tex]

Now

[tex]Sin M = \frac{sqrt95}{12}\\\\Cos N = \frac{95}{12}[/tex]

Answer:

7

Step-by-step explanation:

Exterior Angle Theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.

In this case:

(4x + 7) + (97) = (17x + 13)

4x + 104 = 17x + 13

4x + 91 = 17x

91 = 13x

7 = x

Answer:

4

Step-by-step explanation:

7h-15h+40=-72

-8h=-32

h=4

Answer:

-3

Step-by-step explanation:

Step 1: Solve (-2+(-1))^2/3 3

           1. -2+(-1) = -3

           2. (-3)^2 = 9

           3. 9/3 = 3

Step 2: Solve (-4)^2-17 -1

           1. 3/-1

Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!

Answer:

y= -1/4x+ 3.75

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Angles on the circumference subtended on the same arc are equal

Angle at the centre is twice the angle at the circumference subtended on the same arc.

Then

∠ BAC = ∠ BDC = 29°

∠ BOC = 2 × ∠ BDC = 2 × 29° = 58°

Answer:

-22.5.

Step-by-step explanation:

Lets say that you meant w as the variable.

-4/3 w = 30.

To get rid of the 3, lets multiply 3 to both sides. We get:

3(-4/3 w) = 3(30)

We get:

-4w = 90.

To solve for the w, lets get rid of the -4 by dividing it from both sides.

(-4w)/-4 = 90/-4

We get:

w = -22.5

Check it if you want to make sure.

Answer:hope this helps.. please mark as brainliest.....

9514 1404 393

Answer:

  30°, 60°, 90°, 120°, 150°, 270°

Step-by-step explanation:

Let x represent the smallest angle. Then the sum of angles of the hexagon is ...

  x + 2x + 3x + 4x + 5x + 9x = 720°

  24x = 720°

  x = 30°

The angles are ...

  30°, 60°, 90°, 120°, 150°, 270°

Answer: B and D because for the 1st quadrant both x and y need to be positive

Step-by-step explanation:

B. (2,2)

D. (4,8)

The format for 1st quadrant is: (+,+).

Answer:

si

Step-by-step explanation:

si  :v

Answer:

yes

Step-by-step explanation:

y = x + 89

-5 = -94 + 89

-5 = -5

Answer:

Not possible.

Step-by-step explanation:

The sum of all 3 angles in a triangle is 180°. With the 80° and 105°, those add up to a total of 185°. This is bigger than can be with a given triangle. Therefore, a triangle with an 80° angle and a 105° angle is not possible.

Answer:

No it isn't possible

Step-by-step explanation:

sum of three angles of any triangle is 180 degrees.

so, as per Given question sum of only two angles exceeds 180 degrees which is " 80+105= 185" so it's not possible.. Hope this answer helps you

Answer: x = 100 duck

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer: 7 hr

Step-by-step explanation:

Given

Distance between Emily and Kylie is [tex]140\ \text{miles}[/tex]

Speed of Emily [tex]v_e=12\ mph[/tex]

Speed of Kylie [tex]v_k=8\ mph[/tex]

Distance traveled by Emily [tex]\Rightarrow d_e=12t[/tex]

Distance traveled by Kylie [tex]\Rightarrow d_k=8t[/tex]

[tex]\Rightarrow 12t+8t=140\\\Rightarrow 20t=140\\\Rightarrow t=7\ hr[/tex]

They will meet after 7 hour.

Answer:

= 19, 240 $

Step-by-step explanation:

cost of 1 computer = $ 740

cost of 26 computers = 26 × 740

= 19, 240 $

so the school spent 19, 240 $

Answer:

ok so lets divide 90 by 15 to get 6 so she gets paid 6 per student and that means lisa gets paid 12 so lets just multiply

6*20=120 so mary gets paid 120

and lisa gets paid doable that so 420

but i don't know there base pay so the i can't answer this problem

Hope This Helps!!!

Answer:

1 hour

Step-by-step explanation:

hope it helps ....

Answer:

A) 0.019

B) 0.563

Step-by-step explanation:

a) We will use Poisson distribution formula to solve this;

The formula is given as;

P(X = x) = ((e^-λ) × (λˣ))/x!

Mean is 1. Thus;

λ = 1 aircraft/hour.

Thus, the probability that more than three aircrafts will arrive within an hour is written as; P(X > 3)

Thus;

P(X > 3) = 1 - P(X ≤ 3)

Thus;

1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

Solving through online calculator, we have;

P(X > 3) = 1 - 0.98101

P(X > 3) = 0.01899

To 3 decimal places, we have; P(X > 3)= 0.019

b) Probability of one 1-hour interval not containing more than 3 arrivals is, let's first find;

P(X ≤ 3) = 1 - P(X > 3)

P(X ≤ 3) = 1 - 0.01899

P(X ≤ 3) = 0.98101

Since there are 30 one-hour intervals, then we have;

Probability that none of the thirty 1-hour intervals will contain more than 3 arrivals;

(P ≤ 3) = (0.98101)³⁰

(P ≤ 3) = 0.5626

Approximating to 3 decimal places, we have;

(P ≤ 3) = 0.563

Given the 22 m. horizontal distance and the angles of elevation of 26°

and 31° gives the height of the building as approximately 2.49 meters.

Horizontal distance from the building = 22 m

Angle of elevation to the top of the roof = 26°

Angle of elevation to the top of the antenna = 31°

Height of his eyes from the ground = 1.53 m

Required:

The height of the antenna.

Solution:

In a right triangle, we have relative to an angle of the triangle, we have;

Opposite side = Adjacent side

Height of the building + Height of antenna = [tex]1.53 + 22 \times tan \left(31^{\circ} \right)[/tex] ≈ 14.75

Which gives;

Height of the building = [tex]1.53 + 22 \times tan \left(26^{\circ} \right)[/tex] ≈ 12.26

Therefore;

Height of the antenna ≈ 14.75 - 12.26 ≈ 2.49

Learn more about trigonometric tangent ratio here:

https://brainly.com/question/24415242

Answer:

A) 27

Step-by-step explanation:

[tex]9^{x}[/tex] = 81

x = 2

3([tex]3^{2}[/tex]) = 3(9) = 27

Answer:

[tex]{ \tt{ = \frac{7}{9} \div \frac{1 }{3} }} \\ = { \bf{ \frac{7}{9} \times \frac{3}{1} }} \\ = \frac{7}{3} [/tex]