Find the equation of the line.
Use exact numbers.
Y =

Answer:

[tex]\cos (115\degree)=-0.423[/tex]

Step-by-step explanation:

The parametric equations of a circle is

[tex]x=r\cos \theta[/tex] and [tex]y=r\sin \theta[/tex]

The radius of the unit circle is 1 unit.

This implies that any point on the unit circle is represented by:

[tex]x=\cos \theta[/tex] and [tex]y=\sin \theta[/tex]

where [tex]\theta[/tex] is the angle in standard position,

From the question, the given angle in standard position is [tex]115\degree[/tex].

This angle intersects the unit circle at [tex]x=-0.423[/tex]

But [tex]x=\cos \theta[/tex]

We substitute [tex]\theta=115\degree[/tex] and [tex]x=-0.423[/tex]

This implies that: [tex]\cos (115\degree)=-0.423[/tex]

Answer:

10.2 inches

Step-by-step explanation:

we know that

In this problem we have two cases

First case

The given lengths are two legs of the right triangle

so

[tex]a=12\ in, b=15\ in[/tex]

Applying the Pythagoras Theorem

Find the length of the hypotenuse

[tex]c^{2}=a^{2} +b^{2}[/tex]

substitute

[tex]c^{2}=12^{2} +15^{2}[/tex]

[tex]c^{2}=369[/tex]

[tex]c=19.2\ in[/tex]

Second case

The given lengths are one leg and the hypotenuse

so

[tex]a=12\ in, c=15\ in[/tex]

Applying the Pythagoras Theorem

Find the length of the other leg

[tex]b^{2}=c^{2} - a^{2}[/tex]

substitute

[tex]b^{2}=15^{2} - 12^{2}[/tex]

[tex]b^{2}=81[/tex]

[tex]b=9\ in[/tex]

Find the difference between the two possible lengths of the third side of the triangle

so

[tex]19.2-9=10.2\ in[/tex]

Answer:

10.2

Step-by-step explanation:

is a pimp ting

Answer:

[tex]\frac{3\pi}{2}[/tex]  units to the right

Step-by-step explanation:

If we have a parent function y = Sin(x), the function

The function given is [tex]y=Sin(x-\frac{3\pi}{2})[/tex]

So from the rules, we can clearly say that it is parent function shifted RIGHT by  [tex]\frac{3\pi}{2}[/tex] units.

2nd answer choice is correct.

Answer:

false

Step-by-step explanation:

correct me if this is wrong, but it's actually x>1

Answer:

false.

Step-by-step explanation:

Given :  2x+8>10.

To find : the solution to 2x+8>10 is x<1   true or false.

Solution : We have given that  

2x+8>10.

On subtracting both sides by 8

2x > 10 -8.

2x > 2

On dividing both sides by 2

x > 1

So,  given statement false .

Therefore, false.

Answer:

x = -7 and x = 2

Step-by-step explanation:

Look for the points on the graph where if you draw a horizontal line at y=1, you will intersect the curve.

By observation, we can see that this happens at x = -7 and x = 2

x = -7 and x = 2

Here in the diagram, we can see that, a curve is present & 6 co-ordinates on that curve are given.

We have to find the values of x correspond with f(x) = 1

f(x) = 1 means y = 1

So, if we draw a horizontal line at y = 1, which is parallel to x-axis.

Then, we can able to observe the points which are on the line y = 1.

So, the points on line y = 1 are (-7, 1) & (2, 1).

Hence, we can say that, input values that correspond with f(x) = 1 are x= -7 & x = 2.

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Answer:

3

Step-by-step explanation:

Answer:

A)

Step-by-step explanation:

(f+g)(x) = f(x) + g(x)

now plug in the expressions of f(x) and g(x) :

(f+g)(x) = [tex]x^{2} -7x-1 + 2x-3[/tex]

we combine like terms we get :

(f+g)(x) = [tex]x^{2} -7x+2x -1-3[/tex]

we simplify we get :

(f+g)(x)=[tex]x^{2} -5x-4[/tex]

so the answer is A)

Answer:a

Step-by-step explanation:

Answer:

Yes the lines are indeed parallel. The slope of AB is 2

Step-by-step explanation:

To model the bird population that triples each year starting with 10 birds, an exponential growth function is used: f(x) = 10 × 3^x, where x is the number of years.

To create a function that represents the scenario of birds increasing threefold each year, we need to use an exponential growth model.

The initial population of birds is 10 and then it triples every year.

Therefore, the function that describes the number of birds after x years would be:

f(x) = 10 × 3^x

Here, f(x) represents the number of birds after x years, 10 is the initial number of birds released into the habitat, and 3^x indicates that the population is growing three times each year for x years.

Final answer:

The number of birds after x years can be calculated using the exponential function B(x) = 10 × 3^x, representing the initial population of 10 birds tripling every year.

Explanation:

The scenario describes a population of birds in a new habitat growing exponentially each year. The initial population of birds is 10 (in year 0), and the population triples every year thereafter. To represent this situation mathematically, we can use an exponential function.

To find the number of birds after x years, we can use the following function:

B(x) = 10 × 3^x

Where:

B(x) is the number of birds after x years

10 is the initial number of birds

3 is the growth factor, as the population is tripling each year

x is the number of years since the birds were first released into the habitat

This equation models exponential growth and gives us the predicted population of the birds for any given year x.

(0,0) satisfies y > 2x - 1 but does not satisfy y ≤ x^2 - 4. C

(0,0) satisfies both inequalities.

Answer:

see explanation

Step-by-step explanation:

x³ + y³ ← is a sum of cubes and factors as

(x + y)(x² - xy + y²) ← in factored form

Answer:

D. 148°

Step-by-step explanation:

Theorem: The measure of the angle formed by a tangent and a chord is equal to one-half the measure of the intercepted arc.

In your diagram, XZ is the chord, WZ is the tangent, and XYZ is the intercepted arc.

Per the theorem,

mXZW = ½ mXYZ = ½ × 296° = 148°

The measure of the tangent chord angle is 148°.

Answer: D: 148 is correct

Step-by-step explanation: apx :)

Answer:

True

Step-by-step explanation:

Let, [tex]P_0[/tex] be the initial population,

Given,

The population is decreasing by 3%  each year,

Thus, the population after t years would be,

[tex]P=P_0 (1-\frac{3}{100})^t[/tex]

[tex]\implies P=P_0(1+\frac{-3}{100})^t[/tex]

Since, if a population is changing by a constant rate then the population after t years is,

[tex]P=P_0(1+\frac{r}{100})^t[/tex]

Where, r is the rate of changing per period.

Hence, in the given situation the population is changing by the constant rate.

Answer:

½ = x

Step-by-step explanation:

As discussed in one of my You-Tube videos on Exponential Rules, aᵐ\ⁿ, any base to the half power is the SAME AS taking the exponential denominator of that power, and setting that to the square root of the base, leaving the exponential numerator on the outside:

25¹\² = √25

25 = a [Base]

1 = m [Exponential Numerator]

2 = n [Exponential Denominator]

As you can see, it is unnecessary to put the two because by definition, any vacant root is automatically assumed as the square root, and 1, which is the exponential numerator, is on the outside, which again is unnecessary because 5¹ is 5.

https://youtu.be/3ShAY4y6V48

Watch the above link and subscribe to my channel [USERNAME: MATHEMATICS WIZARD].

I am joyous to assist you anytime.

Answer:

b

Step-by-step explanation:

because perimeter of rectangle is 2(l+b)

For this case we have that by definition, the perimeter of a rectangle is given by:

[tex]P = 2a + 2b[/tex]

Where:

a: It is the length of the rectangle

b: It is the width of the rectangle

We have as data that:

[tex]P = 230 \ ft\\b = 30 \ ft[/tex]

Then, replacing we have:

[tex]230 = 2a + 2 (30)[/tex]

Answer:

Option B

Answer:

x squared plus two times x minus one = zero.

Step-by-step explanation:

(This is a Quadratic equation in the variable x).

Answer:

One less than the sum of square of a number  and twice the number is 0

Step-by-step explanation:

[tex]x^2+ 2x - 1 = 0[/tex]

x represents any number. x^2 represents square of a number

2x represents twice the number

[tex]x^2+2x[/tex] can be written as sum of square of a number  and twice the number

[tex]x^2+2x-1[/tex]

One less than the sum of square of a number  and twice the number

[tex]x^2+2x-1=0[/tex]

One less than the sum of square of a number  and twice the number is 0

Answer:

x = - 7

Step-by-step explanation:

Given

3x + 5 = - 16 ( subtract 5 from both sides )

3x = - 21 ( divide both sides by 3 )

x = - 7

Two-step equations can get more difficult the higher the numbers get, but they're not too hard! ;)

To solve 3x+5=-16:

First subtract 5 from each side

Now its 3x=-21

Next divide 3 from each side

You get x=-7!

Always check your work! To check your work plug your answer "-7" into x.

So it looks like this: 3(-7)+5=-16 then distribute and solve!

You'll get -16=-16, that means its correct/true!

Yes. You should add commas next time to make it easier to read.

Answer:

Yes this is a function..

Step-by-step explanation:

We have to see the inputs and outputs for the function.

Here x represents input and y represents output.

For a relation to be a function there should be no repition in domain or input of the function i.e. every element in domain should be unique.

The domain for given relation is:

{1,-1,3,5}

All the inputs are only once mapped to the output so this relation is a function ..

Answer:

The equation that represents the line that passes through (-6,7) and (-3,6) is: y = -1/3x + 5

Step-by-step explanation:

The equation of line for point=slope form is

y-y₁ = m(x-x₁)

Finding Slope m:

m= y₂-y₁/x₂-x₁

here y₂= 6,y₁= 7,x₂= -3,x₁= -6

m = 6-7/-3-(-6)

m = -1/-3+6

m = -1/3

The slope m = -1/3 and considering point (-6,7) the equation is:

y-y₁ = m(x-x₁)

y-7 = (-1/3)(x-(-6))

y-7 = -1/3(x+6)

y-7 = -1/3x -2

y = -1/3x-2+7

y = -1/3x + 5

So, the equation that represents the line that passes through (-6,7) and (-3,6) is: y = -1/3x + 5

Answer:

Step-by-step explanation:

[tex]3x+1=4x+(-4)\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\3x-4x+1=4x-4x-4\\\\-x+1=-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=-4-1\\\\-x=-5\qquad\text{change the signs}\\\\x=5[/tex]

Answer:

The answer is B. In step one he should have added 3 negative x-tiles to both sides.

Step-by-step explanation:

Answer:

170 m

Step-by-step explanation:

Area of a rectangle is width times length:

A = WL

Given:

A = 1764

W = L + 13

Substitute:

1764 = (L + 13) L

1764 = L² + 13L

0 = L² + 13L − 1764

0 = (L + 49) (L − 36)

L + 49 = 0, L − 36 = 0

L = -49, L = 36

Since length can't be negative, L = 36 m.

So the width is W = L + 13 = 49 m.

Perimeter of a rectangle is twice the width plus twice the length.

P = 2W + 2L

P = 2(49) + 2(36)

P = 170 m

The perimeter is 170 meters.

Answer:

B.

Step-by-step explanation:

I think I'm going to go with the plug in method here.

If you get the same value on both sides, then the point is contained on the line.

A)

4x-y=-6

Test (-1,2):  4(-1)-2=-6

4(-1)-2=-6

-4-2=-6

-6=-6

True; the equation holds for (-1,2).

Test (3,1): 4(3)-1=-6

4(3)-1=-6

12-1=-6

11=-6

False; the equation doesn't hold for (3,1).

A isn't the right choice.

B)

x+4y=7

Test (-1,2): -1+4(2)=7

-1+4(2)=7

-1+8=7

7=7

True, the equation holds for (-1,2).

Test (3,1): 3+4(1)=7

3+4(1)=7

3+4=7

7=7

True, the equation holds for (3,1).

Since the equation held for both (-1,2) and (3,1) then B is the right answer.

-------------------Let's also go ahead and find the equation another way:

(3,1) and (1,-2) are points on your line.

I'm going to write an equation for these points in slope-intercept form first which is y=mx+b where m is slope and b is y-intercept.

I will then rearrange into standard form like your choices are in.

m=slope=rise/run.

To find this, I like to line up the points and subtract and then put 2nd difference over 1st difference.

Like so:

(-1,2)

-(3,1)

---------

-4    1

The slope is 1/-4 or -1/4.

So the equation so far is y=-1/4 x+b since m=-1/4.

Now to find b, I'm going to use y=-1/4 x +b along with one of the given points on the line like (x,y)=(-1,2).

y=-1/4 x+b

2=-1/4 (-1)+b

2=1/4+b

Subtract 1/4 on both sides:

2-1/4=b

7/4=b

So the equation of the line is y=-1/4 x +7/4.

Now the goal is to write in ax+by=c form where a,b,c are integers.

Multiply both sides of y= -1/4 x +7/4 by 4 giving you:

4y=-1x+7

Add 1x on both sides:

1x+4y=7

or

x+4y=7 since 1x=x

So x+4y=7 is the answer if you prefer this way. Well anyway you prefer, this is the correct standard form for this line.

The equation of line that passes through points (-1, 2) and (3, 1) will be

x + 4y = 7

Option B is true.

What is Equation of line?

The equation of line with slope m and y intercept at point b is given as;

y = mx + b

Given that;

The points on the line are  (-1, 2) and (3, 1).

Since, The equation of line will be;

y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁)/ (x₂ - x₁) is slope of the line.

And, (x₁, y₁) is the point on the line.

Thus, Slope = (1 - 2) / (3 - (-1))

                  = (-1)/4

                  = -1/4

So, The equation of line with slope -1/4 and point (-1, 2) will be;

y - 2 = -1/4 (x - (-1))

4 (y - 2) = - 1(x + 1)

4y - 8 = -x - 1

x + 4y = 8 - 1

x + 4y = 7

So, The equation of line that passes through points (-1, 2) and (3, 1) will be

x + 4y = 7

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Answer: 50 degrees.

Step-by-step explanation:

To find the measure of the angle Q, you need to follow these steps:

- Knowing that:

[tex]-980= -(1,360)cos(Q)[/tex]

You can divide both sides of the equation by -1,360:

[tex]\frac{-980}{-1,360}=\frac{-1,360cos(Q)}{-1,360}\\\\\frac{49}{68}=cos(Q)[/tex]

- Finally, using  the inverse function of the cosine, Arccosine, we get:

[tex]Q=Arcos(\frac{49}{68})\\\\Q=49.89\°[/tex]

To the nearest whole degree, this is:

[tex]Q=50\°[/tex]

1 minute  = 60 seconds

240 minute  = 240 × 60 = 14400 seconds

Answer:

This is a false statement:

Step-by-step explanation:

According to Remainder Theorem dividing the polynomial by some linear factor x + a, where a is just some number. As a result of the long polynomial division, you end up with some polynomial answer q(x) (the "q" standing for "the quotient polynomial") and some polynomial remainder r(x).

P(x)= (x+/-a) q(x)+r(x)

P(x)=(x+a) q(x)+r(x). Note that for x=-a

P(-a)=(-a+a) q(-a)+r(-a)= 0* q(-a)+ r(-a)

P(-a)=r(-a)

It means that P(-a) is the remainder not P(a)

Thus the given statement is false....

Answer:

28

Step-by-step explanation:

So this means to replace the r you see in 4r^2-8 with 3.

Let's do that:

4(3)^2-8

Now to simplify this just use pemdas or a calculator:

4(9)-8     since 3^2 means 3*3=9

36-8

28

Answer:

28.

Step-by-step explanation:

Put r =- 3 and work it out:

That would be 4(3)^2 - 8

=  4 * 9 - 8

= 36 - 8

= 28.

Answer:

z = 5

Step-by-step explanation:

Given

- 0.25z = - 1.25 ( divide both sides by - 0.25

z = [tex]\frac{-1.25}{-0.25}[/tex] = 5

z = 5

Answer:

z = 5.

Step-by-step explanation:

-0.25 z = -1.25

z = -1.25 / -0.25

z = 5.

Answer:

14 weeks

Step-by-step explanation:

t = 25 + 8.25w

Len  needs 135.75

135.75 =  25 + 8.25w

Subtract 25 from each side

135.75-25 = 25-25 + 8.25w

110.75 = 8.25w

Divide each side by 8.25

110.75/8.25 = 8.25w/8.25

13.42424 = w

Since we need at least 135.75, it will take Len a little more than 13 weeks, so it will take Len 14 weeks to have enough money

Answer:

14 weeks

Step-by-step explanation:

It will take 14 weeks for Len to save enough money to buy a television.

t = 25 + 8.25w

135.75 =  25 + 8.25w

Hope this helps!

Answer:

c

Step-by-step explanation: