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Which trigonometric expression can be used to find value of x? Replace a and b with the correct values.
(trigonometry)

Answer:

-13

Step-by-step explanation:

First, we will find the value of j(2) first.

j(2) = -2(2) = -4

next, we will solve h[j(2)].

h[j(2)] = h(-4) = 3(-4) - 1 = -12 - 1 = -13

Answer:

m = -2

Step-by-step explanation:

to find the answer you must put rise over run

rise is (y2 - y1) and run is (x2 - x1)

lets use the bottom two points for thisd

y2 is 0 and y1 is 2

x2 is 1 and x1 is 0

0 - 2 = -2

1 - 0 = 1

-2/1 = -2

that is the slope

Answer:

3550

Step-by-step explanation:

C.P=Rs 1250

S.P=8(12)(50)

Rs4800

P=S.P-C. P

=Rs4800-Rs1250

= Rs3550

Taking squares on both sides leads to

[tex]\sqrt{-x + 6} = x - 6[/tex]

[tex]\left(\sqrt{-x + 6}\right)^2 = (x - 6)^2[/tex]

[tex]-x + 6 = x^2 - 12x + 36[/tex]

[tex]x^2 - 11x + 30 = 0[/tex]

[tex](x - 5) (x - 6) = 0[/tex]

Solving for [tex]x[/tex], we get

[tex]x - 5 = 0 \text{ or } x - 6 = 0[/tex]

or

[tex]x = 5 \text{ or } x = 6[/tex].

Evaluating both sides of the starting equation at these solutions, we have

[tex]\sqrt{-6 + 6} = 6 - 6 \implies 0 = 0[/tex]

which is true, so [tex]\boxed{x=6}[/tex] is a valid solution. However,

[tex]\sqrt{-5 + 6} = 5 - 6 \implies \sqrt1 = -1 \implies 1 = -1[/tex]

which is not true, so [tex]\boxed{x=5}[/tex] is an extraneous solution.

Answer:

675

Step-by-step explanation:

100%-32%=68%

459/0.68= 675

Hope this helps! :)

Answer: Same

Step-by-step explanation:

Given formula

[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]

Given information

Troop A:

Troop B:

Substitute values into the formula (Troop A)

[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{(16)~-~(14)}{(14)}*100\%[/tex]

Simplify the fraction

[tex]Percent~of~change~=~\Large\frac{2}{14}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{1}{7}*100\%[/tex]

[tex]Percent~of~change~\approx~14.29\%[/tex]

Substitute values into the formula (Troop B)

[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{(24)~-~(21)}{(21)}*100\%[/tex]

Simplify the fraction

[tex]Percent~of~change~=~\Large\frac{3}{21}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{1}{7}*100\%[/tex]

[tex]Percent~of~change~\approx~14.29\%[/tex]

Compare the two percent of change

[tex]Troop~A~v.s.~Troop~B[/tex]

[tex]14.29\%~=~14.29\%[/tex]

Therefore, they are [tex]\Large\boxed{Same}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The answer is same.

Finding the percentage of change for Troop A :

New - Original / Original × 100%

Finding the percentage of change for Troop B :

Both the troops have the same percent change in membership.

A negative slope can be illustrated when a line that is trending downward from left to right, has a negative value.

It should be noted that a negative slope implies that two variables are negatively related.

This implies that when x increases, y decreases, and also when x decreases, y increases.

Graphically, a negative slope implies that as the line on the line graph moves from left to right, the line will fall.

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Answer:

  170

Step-by-step explanation:

The given relations can be used to write and solve an equation for the number of stickers Peter has.

Let p represent the number of stickers Peter has. That is twice as many as Joe, so Joe has (p/2) stickers. Joe has 40 more stickers than Emily, so the number of stickers Emily has is (p/2 -40).

The total number of stickers is 300:

  p +p/2 +(p/2 -40) = 300

  2p = 340 . . . . . . . . . . . . . . add 40, collect terms

  p = 170 . . . . . . . . . . . divide by 2

Peter has 170 stickers.

__

Additional comment

Joe has 170/2 = 85 stickers. Emily has 85-40 = 45 stickers.

We could write three equations in three unknowns. Solving those using substitution would result in substantially the same equation that we have above. Or, such a system of equations could be solved using a calculator's matrix functions, as in the attachment.

  p +j +e = 300

  p -2j +0e = 0

  0p +j -e = 40

Angles is known to be opposite each other when two lines cross called vertical angles  due to the fact that they are opposite each other at a vertex.

Vertical Angles are known to be often called Vertically Opposite Angles and this is described as the scenario when two lines intersect one another, then the opposite angles, is made as a result of the intersection which is known to be called vertical angles or what we say as vertically opposite angles.

Note that A pair of vertically opposite angles are said to be often always equal to one another.

Hence, based on the scenario above, Angles is known to be opposite each other when two lines cross called vertical angles  due to the fact that they are opposite each other at a vertex.

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Answer:[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]

Step-by-step explanation:

Given the system of equations

[tex]1)~xy=2[/tex]

[tex]2)~x+y=4[/tex]

Divide x on both sides of the 1) equation

[tex]xy=2[/tex]

[tex]xy\div x=2\div x[/tex]

[tex]y=\dfrac{2}{x}[/tex]

Current system

[tex]1)~y=\dfrac{2}{x}[/tex]

[tex]2)~x+y=4[/tex]

Substitute the 1) equation into the 2) equation

[tex]x+(\dfrac{2}{x} )=4[/tex]

Multiply x on both sides

[tex]x\times x+\dfrac{2}{x}\times x=4\times x[/tex]

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

Subtract 4x on both sides

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

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

Use the quadratic formula to solve for the x value

[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(2)} }{2(1)}[/tex]

[tex]x=2\pm\sqrt{2}[/tex]

Substitute the x value into one of the equations to find the y value

[tex]xy=2[/tex]

[tex](2+\sqrt{2} )y=2[/tex]

[tex]y=2-\sqrt{2}[/tex]

[tex]OR[/tex]

[tex]xy=2[/tex]

[tex](2-\sqrt{2} )y=2[/tex]

[tex]y=2+\sqrt{2}[/tex]

Therefore, the points of intersection are

[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

(2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) and (2 + [tex]\sqrt{2}[/tex], 2 - [tex]\sqrt{2}[/tex] )

Step-by-step explanation:

xy = 2 → (1)

x + y = 4 ( subtract x from both sides )

y = 4 - x → (2)

substitute y = 4 - x into (1)

x(4 - x) = 2

4x - x² = 2 ( multiply through by - 1 )

x² - 4x = - 2

using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 2)x + 4 = - 2 + 4

(x - 2)² = 2 ( take square root of both sides )

x - 2 = ± [tex]\sqrt{2}[/tex] ( add 2 to both sides )

x = 2 ± [tex]\sqrt{2}[/tex] , that is

x = 2 - [tex]\sqrt{2}[/tex] , x = 2 + [tex]\sqrt{2}[/tex]

substitute these values of x into (2) for corresponding values of y

x = 2 - [tex]\sqrt{2}[/tex] , then

y = 4 - (2 - [tex]\sqrt{2}[/tex])

  = 4 - 2 + [tex]\sqrt{2}[/tex]

  = 2 + [tex]\sqrt{2}[/tex] ⇒ (2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) ← 1 point of intersection

x = 2 + [tex]\sqrt{2}[/tex] , then

y = 4 - (2 + [tex]\sqrt{2}[/tex] )

   = 4 - 2 - [tex]\sqrt{2}[/tex]

   = 2 - [tex]\sqrt{2}[/tex] ⇒ (2 + [tex]\sqrt{2}[/tex] , 2 - [tex]\sqrt{2}[/tex] ) ← 2nd point of intersection

Answer:

Step-by-step explanation:

t(-7)= 3(-7)= -21

s(-21)= 2-(-21)= 2 + 21= 23

Answer:

219.4

Step-by-step explanation:

Find the number in the tenth place 3 and look at the one place to the right for rounding digit 7. Round up if this number is greater than or equal to 5 and round down if it is less than 5. So the answer is 219.4

Step-by-step explanation:

The body reverses direction whenever we go from Positve velocity to negative velocity or vice versa.

So here it is (2,7) exclusive then (7,10) exclusive.

A constant speed means a slope of 0. Here it is (3,6).

c. Since speed is non negative, we would reflect any part of the velocity function that is below the time.axis about the time axis

So we would get

Above is the function, don't worry bout the math part.

D. Knowing that acceleration is the derivative of velocity with respect to time, the derivative of any linear function is the slope of that linear function. So if we find the slope of different paths, we will get a constant and then we can graph it

We must use the original graph because acceleration is a vector meaning it can be negative.

We would get

the second graph is acceleration vs time

Answer:

angle B = 78.46°

Step-by-step explanation:

Use the cosine ratio

[tex]cosB=\frac{2}{10} =0.2[/tex]

[tex]B=cos^{-1} (0.2)=78.46^{0}[/tex]

Hope this helps

Answer:

y=1/4x-1/2

Step-by-step explanation:

Answer:

Hello,

Step-by-step explanation:

All is in the picture.

B=(-2,8), O=(-2,-5)

b=BO=8+5=13

F_1=(-2,4)   O=(-2,5)  Focus distance=4+5=9
Horizontal half axis=√(b²-f²)=√88

144π cm²

Answer:

Solution given:

diameter (d)= 12cm

radius (r)=12/2=6 cm

slant height(l)=18cm

Now

Total surface area of cone=πr(r+l)π*6(6+18)=144π cm²

Answer:

[tex]M = (0.5, 1)[/tex]

Step-by-step explanation:

The midpoint can be found using the formula: [tex]x, y = (\frac{x_2+x_1}{2}, \frac{y_2 + y_1}{2})[/tex]

So plugging in the values we get: [tex]M = (\frac{-4+5}{2}, \frac{2+0}{2})\\M = (\frac{1}{2}, \frac{2}{2})\\M = (0.5, 1)[/tex]

Answer: [tex]\Large\boxed{Midpoint~=~(\frac{1}{2} ,~1)}[/tex]

Step-by-step explanation:

Given information

(x₁, y₁) = (-4, 2)

(x₂, y₂) = (5, 0)

Given formula for midpoint

[tex]Midpoint~=~(\frac{x_1~+~x_2}{2} ,~\frac{y_1~+~y_2}{2} )[/tex]

Substitute values into the formula

[tex]Midpoint~=~(\frac{-4~+~5}{2} ,~\frac{2~+~0}{2} )[/tex]

Simplify by addition

[tex]Midpoint~=~(\frac{1}{2} ,~\frac{2}{2} )[/tex]

Simplify fractions if necessary

[tex]\Large\boxed{Midpoint~=~(\frac{1}{2} ,~1)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

"congruent" for lines simply means they are equally long.

15. yes. AB = EF = 3

16. yes. BD = DF = 8

17. no. AC = 5, CD = 6

18. yes. AC = DE = 5

19. no. BE = 13, CF = 14

20. no. CD = 6, DF = 8

Answer: (c)

(√2-√3)(√2+√3)

Step-by-step explanation:

An irrational number is one that cannot be expressed as the ratio of two integers. In other words it cannot be expressed as [tex]\frac{x}{y}[/tex] where x and y are integers

[tex]\sqrt{2}[/tex] is irrational

[tex]\sqrt{3}[/tex] is irrational

In fact the square root of any prime number is irrational. So [tex]\sqrt{5}[/tex], [tex]\sqrt{7}[/tex] etc are irrational. But [tex]\sqrt{9}[/tex] is not irrational since it evaluates to 3 which can be expressed as [tex]\frac{3}{1}[/tex]

Any expression that contains the square root of a prime number is also irrational

Looking at the choices we see that choices (a), (b) and (d) all evaluate to expressions containing square roots of primes

(a)  (2-√3)2 = 4 - 2√3  . Hence irrational

(b) √2+√3)2 = 2√2+2√3. Hence irrational

(d) 27√7​ is irrational

Let's look at choice (c)

(√2-√3)(√2+√3)

An expression [tex](a+b)(a-b)[/tex]  can be evaluated as [tex]a^{2} - b^{2}[/tex]

Here a = √2, [tex]a^{2}[/tex] =[tex]a = \sqrt{2}\\ a^2 = (\sqrt{2} )^2 = 2\\\\b = \sqrt{3} \\b^2 = (\sqrt{3} )^2 = 3\\\\a^2 - b^2 = 2-3 = -1\\[/tex]

This is a whole number(integer) and all integers are rational numbers

Hence correct answer is (c)

Answer:

2.25m²

Step-by-step explanation:

if 1in = 2m then 0.5in = 1m

so 0.75in = 1.5m

area = 1.5 x 1.5

a = 2.25m²

It looks like the function is

[tex]f(x,y) = 3 + 4x^{3/2}[/tex]

We have

[tex]\dfrac{\partial f}{\partial x} = 6x^{1/2} \implies \left(\dfrac{\partial f}{\partial x}\right)^2 = 36x[/tex]

[tex]\dfrac{\partial f}{\partial y} = \left(\dfrac{\partial f}{\partial y}\right)^2 = 0[/tex]

Then the area of the surface over [tex]R[/tex] is

[tex]\displaystyle \iint_R f(x,y) \, dS = \iint_R \sqrt{1 + 36x + 0} \, dA \\\\ ~~~~~~~~ = \int_0^5 \int_0^2 \sqrt{1+36x} \, dx \, dy \\\\ ~~~~~~~~ = 5 \int_0^2 \sqrt{1+36x} \, dx \\\\ ~~~~~~~~ = \frac5{36} \int_1^{73} \sqrt u \, du \\\\ ~~~~~~~~ = \frac5{36}\cdot \frac23 \left(73^{3/2} - 1^{3/2}\right) = \boxed{\frac5{54} (73^{3/2} - 1)}[/tex]

Answer:

d(t)=-10t-520

Step-by-step explanation:

First you have to find the gradient (m) using the formula [tex]m=\frac{d(t)2-d(t)1}{t2-t1}[/tex]

using the two points you have been given: 1(3,-550) and 2(8,-600)

so you substitute these points into the equation [tex]m=\frac{-600+500}{8-3}[/tex]

m=-10

Now that you have found the m-value you need to find the b-value by using one of the points you already have, I will use Point 2 (8,-600), and substitute it into the equation and solve

d(t)=-10t+b

-600=-10*8+b

-600=-80+b

-520=b

Therefore, the equation is d(t)=-10t-520

Triangle QRS was translated to form triangle TUV, hence both triangles have the same shape, same size and are congruent.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Triangle QRS was translated to form triangle TUV, hence both triangles have the same shape, same size and are congruent.

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Answer: All of the above

Step-by-step explanation:

I did the test

Answer:

1.

2. Additive Identity

3. Associative Property

4. Multiplication Inverse Property

5. Multiplication Property of 0

6. Commutative Property

7.

8.

Step-by-step explanation:

If the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.

Given that the sum of length and breadth of rectangle is 60.

We are required to find the dimensions of the rectangle that will have the maximum area. Area is basically how much part of surface is being covered by that particular shape or substance.

Let the length of rectangle be x.

According to question the breadth will be (60-x).----2

Area of rectangle=Length *Breadth

A=x(60-x)

A=60x-[tex]x^{2}[/tex]

Differentiate A with respect to x.

dA/dx=60-2x

Again differentiate with respect to x.

[tex]d^{2} A/dA^{2}[/tex]=-2x

-2x<0

So the area is maximum because x cannot be less than or equal to 0.

Put dA/dx=0

60-2x=0

60=2x

x=30

Put the value of x in 2 to get the breadth.

Breadth=60-x

=60-30

=30

Hence if the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.

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Answer:9

Step-by-step explanation:1+2=3 6/2=3

3x3=9

The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].

The explicit rule for this sequence:

The obvious rule for an arithmetic sequence is given as follows:

[tex]a_{n}=a_{1} +(n-1)d[/tex]

The first term = [tex]a_{1}[/tex].

The number of terms = n.

The common difference for two consecutive terms = d.

A recursive rule for an arithmetic sequence: [tex]a_{1} =4[/tex].

[tex]a_{n} =a_{n-1}-3[/tex]

The arithmetic sequence is given by:

[tex]a_{n} =a_{n-1}+d[/tex]

We get: d = -3

Substitute the given values:

[tex]a_{n} =4+(n-1)(-3)[/tex]

[tex]a_{n} =4-3n+3[/tex]

=7-3n

The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].

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The explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].

Given the recursive formula for an arithmetic sequence: [tex]a_1=4, a_n=a_{n-1}-3[/tex].

Thus, the first term of the arithmetic sequence is [tex]a=a_1=4[/tex]. using the recursive formula, we can get the 2nd term by putting [tex]n=2[/tex], [tex]a_2=a_1-3=4-3=1[/tex].

So, the common difference of the given arithmetic sequence is [tex]d=a_2-a_1=1-4=-3[/tex].

Thus, the nth term of the arithmetic sequence is given by [tex]a_n=a+(n-1)d\\\Longrightarrow a_n=4+(n-1)\times(-3)\\\Longrightarrow a_n=7-3n[/tex]

Therefore, the explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].

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The length of the rectangular section of the roof is 25 m

From the question, we are to determine the length of the section of the roof

From the given information,

The area of the rectangular section = 180 m²

The width of the rectangular section = 7 1/5 m = 7.2 m

Using the formula for area of a rectangle

A = l × w

Where A is the area

l is the length

and w is the width

Then,

180 = l × 7.2

l = 180/7.2

l = 25 m

Hence, the length of the rectangular section of the roof is 25 m

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Answer:

25

Step-by-step explanation:

Just did it on Khan Academy.

Answer:

It might be  - c² or  b³ *SORRY IF IM WRONG HAVE A GOOD DAY :D)

Step-by-step explanation:

I agree with the person above ^^^