A trellis consists of overlapping wooden slats.

1.What is the position of the indicated angles?

2.What should the value of x be in order for the two slats to be parallel?

3. Which theorem or postulate will you use to prove the parallel slats?

4. Find the measure of the indicated angle.

The quadrants is tan⁻¹x restricted is A. Quadrants I and IV

To answer the question, we need to know what tan⁻¹x is.

tan⁻¹x is the inverse trigonometric function of tanx, which is the value of the angle for tanx.

To find the quadrants in which tan⁻¹x is restricted, we know that tanx lies in the range

-∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°.

tan⁻¹x lies between quadrant I and IV

So, the quadrants is tan⁻¹x restricted is A. Quadrants I and IV

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Answer: 1/216

Step-by-step explanation: please mark me brainly

Answer:

f(3)=0.005

Step-by-step explanation:

Plug in 3 for x

f(3)=(1/6)^3

f(3)=0.005

Hope this helps!

If not, I am sorry.

[tex]|\Omega|=1+2+3+3=9\\|A|=3\\\\P(A)=\dfrac{3}{9}=\dfrac{1}{3}\approx33,3\%[/tex]

Step-by-step explanation:

it is very simple :

the midpoint coordinates are created as the midpoint of the x coordinates, and the midpoint of the y coordinates.

the x coordinate of the midpoint is

(0 + 10)/2 = 10/2 = 5

the y coordinate of the midpoint is

(-2 + -6)/2 = -8/2 = -4

Based on the subtraction property of equality: C. Correct. Jen could have also subtracted 100 from both sides and then divide both sides by -1/2.

In order to balance both sides of an equation, we can subtract same value from both sides by subtracting a value from both sides based on the subtraction property of equality. Same applies to other operations.

To balance both sides of the equation, 100 needs to be subtracted from the equation given. This means Jen was correct.

If she also divide both sides by -1/2, she would get same result as when she multiplies both sides by -2.

The correct description of the accuracy of her work is: C. Correct. Jen could have also subtracted 100 from both sides and then divide both sides by -1/2.

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Answer:

6 cups

Step-by-step explanation:

hope this helps!

Answer: a1=6

               An = An-1 - 4

Step-by-step explanation:

N represent what number in the sequence you choose. So in the equation n-1 would be the umber in the equation subtracting 1 then subtracting the difference. The factor you are multiplying by in this sequence is -4. You find the difference by taking any number in the sequence and dividing it by the previous number in the sequence.

Answer:

alternate exterior angles

Step-by-step explanation:

<3 i hope this helps! sorry if it doesnt :)

Answer:

6 is the answer

Hope that helps.
Let me know if im wrong :)

Step-by-step explanation:

The 1- diameter, 2-inscribed angle, 3-chord, 4-minor arc, 5-central angle, 6-radius, and 7-centre.

It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)

The radius is the double the diameter.

The longest chord in the circle is diameter.

The angle formed at the centre is known as centeral angle.

Thus, the 1- diameter, 2-inscribed angle, 3-chord, 4-minor arc, 5-central angle, 6-radius, and 7-centre.

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Answer:

B and C

Step-by-step explanation:

vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent = they are equally large.

the angles listed in B and C are mirrored across either an imaginary or a directly visible line. and that makes them vertical angles.

Answer: 330 pupils

Step-by-step explanation:

the number of pupils are in the lower school

= (1- 1/5 - ¼) × 600

= (20/20 - 4/20 - 5/20)×600

= (11/20) ×600

= 330 pupils

The value of x in all case is

1. The value of x is 2

2. The value of x is 1

3.The value of x is 57

4.The value of x is 93

If the sum of two angles is 180 degrees then they are said to be b angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

1. As the given angle is 90 degree i.e., complementary angle.

So,

54+10x+16=90

20=10x

x=2

2. 65x-12=43x+10  (Vertically opposite angle)

 22x= 22

x=1

3. 72= x+15  (Vertically opposite angle)

x= 57

4.x+244+23=360  (Complete angle)

 x=93

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The amount the money will be worth in 4 years is $4072.41

The formula for calculating the compound interest is expressed as;

A = P(1+r/n)^nt

Given the following

P = $3700

rate r = 2.4% = 0.024

n =12

t = 4 years

Substitute

A = 3700(1+0.024/12)^12(4)
A = 3700(10.024/12)^48

A =  3700(1.10065)

A= 4072.41

Hence the amount the money will be worth in 4 years is $4072.41

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[tex]~~~~~~~\log_{10} N = 3.8609\\\\\\\implies N = 10^{3.8609} ~~~~~~~~~;[\log_b c =d \implies b^d = c]\\\\\\\implies N \approx 7259[/tex]

Let S be the given sum, so

[tex]S = 8 + 8 \left(\dfrac14\right) + 8 \left(\dfrac14\right)^2 + \cdots + 8 \left(\dfrac14\right)^9[/tex]

[tex]\displaystyle S = 8 \left(1 + \dfrac14 + \frac1{4^2} + \cdots + \frac1{4^9}\right)[/tex]

Multiply both sides by 1/4.

[tex]\displaystyle \frac S4 = 8 \left(\frac14 + \frac1{4^2} + \frac1{4^3} + \cdots + \frac1{4^{10}}\right)[/tex]

Subtract this from S to eliminate all the but the first term in S and the last term in S/4 :

[tex]\displaystyle S - \frac S4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]

Solve for S :

[tex]\displaystyle \frac{3S}4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]

[tex]\displaystyle S = \frac{32}3 \left(1 - \frac1{4^{10}}\right) = \boxed{\frac{349,525}{32,768}}[/tex]

Answer:

AC = BC = 5

AB = 5√2

∠A = ∠B = 45

∠A = 90

Step-by-step explanation:

AC = 5 ( Reason : 5 squares are present in between A and C )

Similarly,

BC = 5

By Pythagoras theorem,

(AB)² = (AC)² + (BC)²

        = 5² + 5²

        = 2 * 5²

(AB)² = 2 * 5²

AB = 5√2

Since, sides AC and BC are equal,

∠A = ∠B = 45

Since, AC is perpendicular to BC,

∠A = 90

The standard deviation of the population function is 2

The given parameters are:

M(x) = 2

M(x²)=8

The standard deviation is calculated using:

[tex]\sigma = \sqrt{M(x^2) - (M(x))^2[/tex]

Substitute known values

[tex]\sigma = \sqrt{8 - 2^2[/tex]

Evaluate the expression

[tex]\sigma = 2[/tex]

Hence, the standard deviation of the population function is 2

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Answer:

(a) y = 25°

(b) x = 90°

(c) z = 25°

Step by step explanation:

Part A

z + 90° + 65° = 180°

z = 180° - 65° - 90°

z = 25°

Part B

x + 90° = 180°

x = 90°

Part C

x + 65° + y = 180°

90° + 65° + y = 180°

y = 25°

A straight line has total 180° angle. A square has 4 sides of each 90° angle. A triangle is build up of 180° interior angle.

The graph (A) in the picture represents the solution to the inequality, option (A) is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The options are missing.

The graph is in the picture, please refer to the picture.

We have an inequality:

y − 2x ≤ 1

The above inequality represents a straight line with a positive slope.

The right side region of the line is representing the solution to the inequality.

Graph (A) represents the inequality.

Thus, the graph (A) in the picture represents the solution to the inequality, option (A) is correct.

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#a

[tex]\\ \rm\Rrightarrow f(-4)[/tex]

[tex]\\ \rm\Rrightarrow 3(-4)+2[/tex]

[tex]\\ \rm\Rrightarrow -12+2[/tex]

[tex]\\ \rm\Rrightarrow -10[/tex]

#b

#1

[tex]\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}[/tex]

Find y

[tex]\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}[/tex]

Inverse is

[tex]\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}[/tex]

#2

[tex]\\ \rm\Rrightarrow gof(x)[/tex]

[tex]\\ \rm\Rrightarrow g(f(x))[/tex]

[tex]\\ \rm\Rrightarrow g(3x+2)[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x+3}{3}[/tex]

If we factor out

[tex]\\ \rm\Rrightarrow \dfrac{2x+1}{1}[/tex]

[tex]\\ \rm\Rrightarrow 2x+1[/tex]

#c

[tex]\\ \rm\Rrightarrow f(x)=g(x)[/tex]

[tex]\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow 3(3x+2)=2x-1[/tex]

[tex]\\ \rm\Rrightarrow 9x+6=2x-1[/tex]

[tex]\\ \rm\Rrightarrow 7x=-7[/tex]

[tex]\\ \rm\Rrightarrow x=-1[/tex]

Answer:

Given functions:

[tex]f(x)=3x+2[/tex]

[tex]g(x)=\left(\dfrac{2x-1}{3}\right)[/tex]

Part (a)

[tex]\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}[/tex]

Part (b)(i)

[tex]\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}[/tex]

Part (b)(ii)

[tex]\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}[/tex]

Part (c)

[tex]\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}[/tex]

Answer:

v = 130

Step-by-step explanation:

substitute the given values for u, a and t into the equation

v = 32 + ( 9.8 × 10) = 32 + 98 = 130

Step-by-step explanation:

the picture is not representing the real angle sizes. so, don't let yourself get confused by that.

the right neighbor angle of 90° at E is also 90°.

it has to be, because it is the supplementary angle to the left 90° (that means together they are 180°).

remember, all angles around a single point on one side of a line have to sum up to 180° (because the line can be seen as the diameter of a circle, with the point being the center of the circle, and so one side of the line is representing a half-circle and therefore 180°).

for the same reason angle 1 (the lower neighbor of the 90° angle at A) is also 90°.

for the same reason the lower neighbor angle of the 60° angle at E is 180 - 60 = 120°.

for the same reason the angle ABC is 180 - 40 = 140°.

for the angle BCD we need to remember :

the sum of interior angles of a polygon with n sides is

(n − 2) × 180°.

in our case ABCDE has 5 sides, so the sum of all interior angles is

(5 - 2) × 180 = 3×180 = 540°

we know 4 of the interior angles already, so

angle BCD = 540 - 90 - 90 - 120 - 140 = 100°

x is now the supplementary angle to the angle BCD.

so,

x = 180 - 100 = 80°

Answer:

=4x³-4x²+4x-3

Step-by-step explanation:

(f+g)(x)=4x³+2x²-6x²+4x-6+3

=4x³-4x²+4x-3

Answer:

x = 0

Step-by-step explanation:

The slope relation is given as :

y = mx + b

Now, if we take x = 0, there is no way of finding out the value of m as the product of mx will be equal to 0.

Hence, x = 0 represents a line with undefined slope.

Answer:

i believe the answer is false !

Step-by-step explanation:

Answer:

3.5 gallons of punch

Step-by-step explanation:

There are 4 quarts in 1 gallon.

Set up equation to convert 14 quarts to gallons: 14÷4 = 3.5.

Elijah made 3.5 gallons of punch.

The value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We know that:

P + Q are complementary, which means that

P+Q = 90°

Then R is a right angle, i.e. it measures 90°.

sin(90-x) = cos (x)

cos(90-x) = sin (x)

Then sinQ = 4/5  

cos(90-Q) = cosP = 4/5

Now sin²(P) + cos²(P) = 1

sin²(P) = 1 - cos²(P)

sin²(P) = 1 -[4/5]² =9/25

sin(P) = 3/5

cos(Q) = sin(P) = 3/5

cos(P) + cos(Q) = 4/5 + 3/5 = 7/5

Thus, the value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.

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