The yard is rectangular and is 50 feet wide by 100 feet long. How many feet of fencing to enclose the entire yard?

Answer: [tex]A'(-1, 0)[/tex]

Step-by-step explanation:

By definition, a Translation is a transformation that moves an object a fixed distance. In Transalation the size, shape and orientation of the object don't change.

The translation of a point [tex]P(x,y)[/tex] "a" units right and "b" units up is:

[tex]P'(x+a,y+b)[/tex]

In this case we know that the coordinates of A of the Triangle ABC is A(-2, -3) and the Triangle ABC is translated 1 unit right and 3 units up. Therefore, the the coordinates of A' are:

[tex]A'(-2+1, -3+3)[/tex]

[tex]A'(-1, 0)[/tex]

Answer:

t>2

Step-by-step explanation:

We are given:

3t+9>15.

Subtract 9 on both sides:

3t+9-9>15-9

Simplify:

3t+0>6

3t>6

Divide both sides by 3:

t>6/3

Simplify:

 t>2

Answer:

t > 2.

Step-by-step explanation:

3t + 9 > 15

3t + 9 - 9 > 15 - 9

3t  > 6

t > 2.

Answer:

f(x) = (x+2)³(x²−7x+3)⁴

Step-by-step explanation:

The fundamental theorem of algebra (in its simplest definition), tells us that a polynomial with a degree of n will have n number of roots.

recall that the degree of a polynomial is the highest power that exists in any variable.

i.e.

polynomial, p(x) = axⁿ + bxⁿ⁻¹ + cxⁿ⁻² + .........+ k

has the degree (i.e highest power on a variable x) of n and hence has n-roots

In our case, if we expand all the polynomial choices presented, if we consider the 2nd choice:

f(x) = (x+2)³(x²−7x+3)⁴   (if we expand and simplify this, we end up with)

f(x) = x¹¹−22x¹⁰+150x⁹−116x⁸−2077x⁷+3402x⁶+11158x⁵−8944x⁴−10383x³+13446x²−5076x+648

we notice that the term with the highest power is x¹¹

hence the polynomial has a degree of 11 and hence we expect it to have exactly 11 roots

Answer:

B

Step-by-step explanation:

Just did it on edge2020

Answer:

It's the last choice.

Step-by-step explanation:

1.  (3x - 2y)(3x -2y)

= 9x^2 - 12xy + 4y^2

The product is  (9x^2 - 4y^2) (9x^2 - 12xy + 4y^2)

which is neither a  difference of 2 squares  or perfect square trinomial.

2.  (3x - 2y)(3x + 2y)

= 9x^2 - 6xy + 6xy - 4y^2

= 9x^2 - 4y^2

and (9x^2 - 4y^2(9x^2 - 4y^2) is a perfect square.

Statement 4 is true about the product (9x² – 4y²)(3x – 2y) that if it is multiplied by (3x + 2y), the product of all of the terms will be a perfect square trinomial. This can be obtained by multiplying the product in the question with each term in the question and check whether the it is a  difference of squares or  a perfect square trinomial.

Difference of squares can be factored using the identity

    a²-b²=(a+b)(a-b)

Algebraic expressions in which there are three terms that can be obtained by multiplying a binomial with itself.

Formulas required,

  (a + b)² = a² + 2ab + b²

  (a - b)² = a² - 2ab + b²

Given product is, (9x² – 4y²)(3x – 2y)

Using difference of squares it can be written as, ((3x)² – (2y)²)(3x – 2y)

=(3x + 2y)(3x – 2y)(3x – 2y)

=(3x + 2y)(3x – 2y)²

(3x + 2y)(3x – 2y)²× (3x – 2y)

=(3x + 2y)(3x – 2y)³

This is not in the form of difference of squares.

(3x + 2y)(3x – 2y)²× (3x – 2y)

=(3x + 2y)(3x – 2y)³

This is not in the form of a perfect square trinomial.  

(3x + 2y)(3x – 2y)²× (3x + 2y)

=(3x + 2y)(3x – 2y)³

This is not in the form of difference of squares.

(3x + 2y)(3x – 2y)²× (3x + 2y)

=(3x + 2y)²(3x – 2y)²

=[(3x + 2y)(3x – 2y)][(3x + 2y)(3x – 2y)]

=(9x² – 4y²)(9x² – 4y²)

=(9x² – 4y²)² = (a - b)², where a = 9x² and b = 4y²

This is in the form of a perfect square trinomial.

Hence statement 4 is true about the product (9x² – 4y²)(3x – 2y) that if it is multiplied by (3x + 2y), the product of all of the terms will be a perfect square trinomial.

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Answer:

d. the quantity of negative twenty plus sixteen i all over forty one.

Step-by-step explanation:

We want to simplify the complex number:

[tex]\frac{\sqrt{-16} }{(3-3i)+(1-2i)}[/tex]

We rewrite to obtain:

[tex]\frac{\sqrt{16}\times \sqrt{-1} }{(3+1)+(-3i-2i)}[/tex]

Recall that: [tex]\sqrt{-1}=i[/tex] and  [tex]-1=i^2[/tex]

We simplify to get:

[tex]\frac{4i}{4-5i}[/tex]

We rationalize to get:

[tex]\frac{4i}{4-5i}\times\frac{4+5i}{4+5i} [/tex]

[tex]\frac{4i(4+5i)}{(4-5i)(4+5i)}[/tex]

[tex]\frac{16i+20i^2}{4^2+5^2}[/tex]

[tex]\frac{16i-20}{16+25}[/tex]

[tex]\frac{-20+16i}{41}[/tex]

The correct answer is D

Answer:

1) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is all real numbers because it asked you to solve y>0 for x.

2) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is all real numbers because it asked you to solve y>=0 for x.

3) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is none because we are looking for when y<0 for x.  (y<0 means y is negative)

4) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is none because we are looking for when y<=0 for x.  (y<=0 means negative or 0)

Step-by-step explanation:

[tex]y=ax^2+bx+c[/tex forms a parabola when graph assuming [tex]a \neq[/tex].

If [tex]a=0[/tex], we would have a parabola.

Anyways here are few things that might help when solving these:

1) Write ax^2+bx+c in factored form; it can lead to the x-intercepts quickly once you have it

2) The discriminant b^2-4ac:

    A) It tells you if you have two x-intercepts if b^2-4ac is positive

    B)  It tells you if you have one x-intercept if b^2-4ac is zero

    C)  It tells you if you have zero x-intercepts if b^2-4ac negative

3) If a>0, then the parabola opens up.

   If a<0, then the parabola opens down.

4)  You might choose to test before and after the x-intercepts too, using numbers between or before and after.

Let's look at questions labeled (1)-(4).

(1)  x^2-x+2>0

a=1

b=-1

c=2

I'm going to use the discriminant to see how many x-intercepts I have:

b^2-4ac

(-1)^2-4(1)(2)

1-8

-7

Since -7 is negative, then we have no x-intercepts.

The parabola is also opened up.

So if we have no-x-intercepts and the parabola is opened up (a is positive), then the parabola is above the x-axis.

So the y values for x^2-x+2 where y=x^2-x+2 is positive for all real numbers.

The solution to x^2-x+2>0 is therefore all real numbers.

(2)  x^2+5x+7>=0

a=1

b=5

c=7

b^2-4ac

(5)^2-4(1)(7)

25-28

-3

Since -3 is negative, we have no x-intercepts.

The parabola is also opened up because a=1 is positive.

So again x^2+5x+7>=0 has solutions all real numbers.

(3)  x^2-4x+5<0

a=1

b=-4

c=5

b^2-4ac

(-4)^2-4(1)(5)

16-20

-4

Since -4 is negative, we have no x-intercepts.

The parabola is opened up because a=1 is positive.

All the y-coordinates for our points are positive.

So y=x^2-4x+5<0 has no solutions because there are no y's less than 0.

(4)  x^2+6x+10<=0

a=1

b=6

c=10

b^2-4ac

6^2-4(1)(10)

36-40

-4

Since -4 is negative, the parabola has no x-intercepts.

The parabola is opened up because a=1 is positive.

All the y-coordinates on our parabola are positive.

So y=x^2+6x+10<=0 has no solutions because there are no y's less than 0 or equal to 0.

For this case we must indicate an expression equivalent to:

[tex]\sqrt {10x ^ 7}[/tex]

By definition of properties of powers and roots we have that:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, we can rewrite the expression as:

[tex]10 ^ {\frac {1} {2}} * x ^ {\frac {7} {2}}[/tex]

Answer:

OPTION A

Answer:

Step-by-step explanation:

Parallel lines have the ame slope.

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

We have the line y = 3x → m = 3.

Therefore:

y = 3x + b            convert it to the standard form Ax + By = C

y = 3x + b                subtract 3x from both sides

-3x + y = b           change the signs

3x - y = -b      where b is any real number except 0.

The required standard of the parallel line to the line y = 3x is y = 3x + c.

Given that,

What is the standard form of the line parallel to the given line y=3x is to be determined.

A line can be defined by the shortest distance between two points is called a line.

The slope of the line is the tangent angle made by the line with horizontal. i.e. m =tanx where x in degrees.

Here, there is a property of the parallel lines that the slope of the equation is always the same. Thus
The equation of the line,
y = 3x
the slope of the above line is m = 3
A standard form of parallel line
y = mx +c

put the value of m in above equation,
Now the equation of the parallel lines can be given as y =3x + c

Thus, the required standard of the parallel line to the line y = 3x is y = 3x + c.

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Answer:

63°

Step-by-step explanation:

From the diagram, the angle of elevation from the child to the top of the tree can be calculated using the tangent ratio.

Recall SOH-CAH-TOA from your Trigonometry class.

The tangent is opposite over adjacent.

[tex] \tan(A) = \frac{14}{7} [/tex]

[tex]A = \tan^{ - 1} ( 2)[/tex]

[tex]A = 63.43 \degree[/tex]

The angle of elevation is 63° to the nearest degree.

Answer:

The correct answer is 8x^2+28x+20.

Step-by-step explanation:

(2x+5)(4x+4)

Multiply the first bracket with each element of second bracket:

=4x(2x+5)+4(2x+5)

=8x^2+20x+8x+20

Now solve the like terms:

=8x^2+28x+20

Thus the correct answer is 8x^2+28x+20....

Answer:

-1 edge

Step-by-step explanation:

...

1st-1

2nd –i

I just did it on edge :D

Answer:

1/5

Step-by-step explanation:

There are 30 contestants.  16 are men, which means 14 are women.

All 14 women wear glasses.  Since 20 of the contestants wear glasses, that means there are 6 men who wear glasses.

So the probability that a randomly selected contestant will be a male with glasses is 6/30 or 1/5.

C. x=2

To complete the table, let's plug in the x-values into [tex]f(x)[/tex] and [tex]g(x)[/tex], so:

For [tex]f(x)[/tex]:

[tex]If \ x=0: \\ \\ f(0)=9(0)+7=7 \\ \\ \\ If \ x=1: \\ \\ f(1)=9(1)+7=16 \\ \\ \\ If \ x=2: \\ \\ f(2)=9(2)+7=25[/tex]

For [tex]g(x)[/tex]:

[tex]If \ x=-2: \\ \\ g(-2)=5^{-2}=0.04 \\ \\ \\ If \ x=-1: \\ \\ g(-1)=5^{-1}=0.2 \\ \\ \\ If \ x=2: \\ \\ g(2)=5^{2}=25[/tex]

From this, the complete table is:

[tex]\left|\begin{array}{c|c|c}x & f(x)=9x+7 & g(x)=5^{x}\\-2 & -11 & 0.04\\-1 & -2 & 0.2\\0 & 7 & 1\\1 & 16 & 5\\2 & 25 & 25\end{array}\right|[/tex]

From the table, you can see that [tex]f(x)=g(x)=25[/tex] when [tex]x=2[/tex] so the correct option is C. x=2. But what does [tex]x=2[/tex] mean? It means that at this x-value, the graph of the linear function [tex]f(x)[/tex] and the graph of the exponential function [tex]g(x)[/tex] intersect and the point of intersection is [tex](2,25)[/tex]

Answer:

∠DFE=119°

Step-by-step explanation:

step 1

Find the measure of angle BFD

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

∠BFD=(1/2)[arc BD+arc CE]

substitute the given values

∠BFD=(1/2)[38°+84°]

∠BFD=61°

step 2

Find the measure of angle DFE

we know that

∠BFD+∠DFE=180° -----> linear pair (supplementary angles)

substitute

61°+∠DFE=180°

∠DFE=180°-61°=119°

Answer:

B

Step-by-step explanation:

The function is

[tex]y=\sqrt{x-4}[/tex]

use the graph tool to visualize the graph as below

Answer:

B

Step-by-step explanation:

The given equation is :

[tex]y=\sqrt {x-4}[/tex]

This is a equation of a half parabola because general equation of a parabola with its as x-axis is:

[tex]y^2={x-a}[/tex]

Where a is the vertex of the parabola. If square root is taken, then there will be one positive and one negative. So,

The positive represents the upper side of the parabola.

Hence,  [tex]y=\sqrt {x-4}[/tex] represents upper parabola with x -axis is its axis and vertex at (4,0). Option B is correct.

Answer:

D)150 ≤ w ≤ 500

Step-by-step explanation:

Let  be the number of word in Kylie's essay.

We know that the essay has to have a minimum word count of 150, so the length of the essay must be greater or equal than 150 words; remember that in mathematics we say greater or equal with the sign: ≥, so we can express the statement as:

Which is equivalent to

We also know that the essay has to have a maximum word count of 500 words, so the length of the essay must be lest or equal than 500 words; remember that we can say the same using the symbol ≤, so we can express the statement as:

Now, we can join our tow inequalities in a compounded one:

The length w of an essay is typically represented by a compound inequality of form a < w < b, where a and b represent the range of acceptable lengths. Without specific details, we can't provide a more precise inequality.

From the question, it seems that the length w of the essay might be compared to a word count that is too short or too long. This could translate into an inequality such as a < w < b, where a and b represent the acceptable range of the essay length in words. Unfortunately, without specific values for 'too short' and 'too long', we cannot give a more precise answer. However, the type of compound inequality we are talking about is known as a 'conjunction' or 'and' inequality, represented by a < w < b or a ≤ w ≤ b if including the exact lower and upper bounds.

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Answer:

[tex]6\sqrt{3}[/tex]

Step-by-step explanation:

We need to find the product of [tex]3\sqrt{4} \sqrt{3}[/tex]

We know that:

[tex]3\sqrt{4} \sqrt{3}[/tex] ⇒ [tex]3\sqrt{12}[/tex] ⇒[tex]6\sqrt{3}[/tex]

Therefore, the product is [tex]6\sqrt{3}[/tex]

The product of 3sqrt4 and sqrt3 can be calculated as 6sqrt3. This result is obtained by multiplying 3 by the square root of 4, which is 2, giving you 6, and then multiplying that by the square root of 3.

The product of 3sqrt4 and sqrt3 can be calculated following the rules of multiplication for square roots. Firstly, sqrt4 is 2. Therefore, 3sqrt4 is 3*2, which equals 6. Secondly, you multiply this result by sqrt3 to get the final product:

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Answer:

[tex]4\sqrt{2}.\sqrt{2} = 8\\3\sqrt{7}-2\sqrt{7} =\sqrt{7}\\\frac{\sqrt{7}}{2\sqrt{7}} = \frac{1}{2}\\2\sqrt{5}.2\sqrt{5} = 20[/tex]

Step-by-step explanation:

[tex]4\sqrt{2}.\sqrt{2}\\=4 . (\sqrt{2})^2\\=4*2\\=8\\\\3\sqrt{7}-2\sqrt{7}\\As\ the\ square\ root\ is\ same\ in\ both\ terms\\= (3-2)\sqrt{7}\\=\sqrt{7}\\\\\frac{\sqrt{7}}{2\sqrt{7}} \\The\ square\ roots\ will\ be\ cancelled\\= \frac{1}{2}\\ \\2\sqrt{5}.2\sqrt{5}\\=(2*2)(\sqrt{5})^2\\=4*5\\=20[/tex]

Answer:

Below we present each expression with its simplest form.

[tex]4\sqrt{2} \sqrt{2}=4(2)=8[/tex]

[tex]3\sqrt{7} -2\sqrt{7}=(3-2)\sqrt{7} = \sqrt{7}[/tex]

[tex]\frac{\sqrt{7} }{2\sqrt{7} } =\frac{1}{2}[/tex]

[tex]2\sqrt{5} 2\sqrt{5}=4(5)=20[/tex]

So, the first expression matches with 8.

The second expression matches with the square root of seven.

The third expression matches with one-half.

The fourth expression matches with 20.

Answer: OPTION A.

Step-by-step explanation:

You know that the rule that will be used for the translation of the figure ABC is:

[tex](x,y)[/tex]→[tex](x-3,\ y+4)[/tex]

You can observe in the figure that the coordinates of the point A is this:

[tex]A(1,1)[/tex]

Then, in order to find the coordinates that will best represent point A', you need to subtract 3 from the x-coordinate of the point A and add 4 to the y-coordinate of the point A:

[tex]A'(1-3,\ 1+4)\\\\A'(-2,5)[/tex]

Answer:

A. (-2,5)

Step-by-step explanation:

The figure ABC is translated to A'B'C' by the rule (x-3, y+4)

The Image of the triangle will therefore be as follows:

A' (1-3,1+4)

B'(2-3,5+5)

C'(3-3,2+5)

The vertices will thus be A'(-2,5), B'(-1,10) and C'(0,7)

Thus the correct answer will be A. (-2,5)

Answer:

[tex]\boxed{\bold{x=-3}}[/tex]

Explanation:

Multiply Both Sides By 100

[tex]\bold{0.45x\cdot \:100-0.2\left(x-5\right)\cdot \:100=0.25\cdot \:100}[/tex]

Refine

[tex]\bold{45x-20\left(x-5\right)=25}[/tex]

Expand [tex]\bold{-20\left(x-5\right): \ -20x+100}[/tex]

= [tex]\bold{45x-20x+100=25}[/tex]

Add Similar Elements: [tex]\bold{\:45x-20x=25x}[/tex]

= [tex]\bold{25x+100=25}[/tex]

Subtract 100 From Both Sides

[tex]\bold{25x+100-100=25-100}[/tex]

Simplify

[tex]\bold{25x=-75}[/tex]

Divide Both Sides By 25

[tex]\bold{\frac{25x}{25}=\frac{-75}{25}}[/tex]

Simplify

[tex]\bold{x=-3}[/tex]

Mordancy.

Answer:

H

Step-by-step explanation:

Solve each equation for y.

First equation:

8x + 6 = 2y

2y = 8x + 6

y = 4x + 3

This line has y-intercept 3, and slope 4.

Second equation:

12x - 3 = 3y

3y = 12x - 3

y = 4x - 1

This line has y-intercept -1 and slope 4.

Since the two lines have the same slope and different y-intercepts, they are parallel lines.

Answer: H

Answer:

The correct answer is H.

Step-by-step explanation:

In order to solve this exercise we have two paths. The first one uses less calculation than the second.

First way of solution: Isolate the variable [tex]y[/tex] in the right hand side of each equation. To do this you only need to divide the first equation by 2, and then divide the second equation by 3. Thus, you will obtain [tex]4x+3=y[/tex] and [tex]4x-1=y[/tex].

Now, notice that both lines have the same slope, so they are parallel. But before to give a definite answer we need to check if both lines are the same or not. Evaluate at [tex]x=0[/tex], in the first equation you have [tex]y=3[/tex] and in the second one [tex]y=-1[/tex]. As they have different intercepts with the X-axis, they parallel.

Second way of solution: Solve the system of equations. Isolate [tex]y[/tex] in the first equation:

[tex]4x+3=y[/tex].

Then, substitute this expression in the second equation:

[tex]12x-3=3(4x+3)[/tex]

[tex]12x-3=12x +9[/tex].

Which is equivalent to [tex]0=9+3[/tex] and this is impossible. Hence, the system of equations has no solution and the lines are parallel.

Answer:

-19/40

Step-by-step explanation:

-3/8-1/10

Convert -3/8 to -15/40

Convert 1/10 to 4/40

-15/40-4/40=-19/40

Answer:

-19/40

Step-by-step explanation:

First thing to notice is they don't have a common denominator.

It is easy to see that 8 and 10 both go into 80 because 8(10)=80.

Let's see if we can think of smaller number 8 and 10 both go into.

8=2(2)(2)

10=2(5)

The greatest common factor of 8 and 10 is 2.

The least common multiple of 8 and 10 is 2(2)(2)(5)=40.

That first 2 was what they had in common and then I wrote down all the left over numbers from when we did the greatest common factor.

So 8 and 10 both go into 40.

8(5)=40 and 10(4)=40.

[tex]\frac{-3}{8}-\frac{1}{10}[/tex]

Multiply first fraction by 5/5 and second fraction by 4/4:

[tex]\frac{-3(5)}{8(5)}-\frac{1(4)}{10(4)}[/tex]

Simplify/Multiplied a little:

[tex]\frac{-15}{40}-\frac{4}{40}[/tex]

Wrote as one fraction since they had the same denominator:

[tex]\frac{-15-4}{40}[/tex]

Time to add 15 and 4 since they are both negative and their result also be negative:

[tex]\frac{-19}{40}[/tex]

Answer:

735,130.

Step-by-step explanation:

The order of election of the 3 representatives does not matter so it is a combination.

The number of possible combinations

= 165! / 162! 3!

=  (165 * 164 * 163) / (3*2*1)

= 735,130.

Final answer:

The scenario of electing 3 representatives from a student body of 165 students involves combinations since the order of selection does not matter. Using the combination formula, there are 4,598,340 possible ways to choose the representatives.

Explanation:

The scenario described involves electing 3 representatives from a student body of 165 students. In this context, we are dealing with combinations, not permutations, because the order of selection does not matter; it only matters who is chosen, not in which order they are elected.

To calculate the number of possible combinations of 165 students taken 3 at a time, we can use the combination formula:

C(n, k) = n! / [k!(n - k)!]

where:

Therefore, the number of possibilities is:

C(165, 3) = 165! / [3!(165 - 3)!]

Calculating this gives us:

165! / (3! * 162!) = (165 * 164 * 163) / (3 * 2 * 1) = 4,598,340 combinations.

Answer:

20% markup

Step-by-step explanation:

10,000 x 1.20 = 12,000

Answer:

20%

Step-by-step explanation:

10,000×120%=12,000

Answer:

The third choice.

The third choice doesn't contain corresponding parts because L is 3rd and Q is 2nd.

Step-by-step explanation:

Triangle JKL is congruent to Triangle PQR tells us what parts are corresponding.  The answer is in the order that things occur.

This means that the following angles are congruent:

Angles J and P are corresponding (congruent in this case) because J and P share the same position in the order, 1st.

Angles K and Q are corresponding (congruent in this case) because K and Q share the same position in the order, 2nd.

Angles L and R are corresponding (congruent in this case) because L and R share the same position in the order, 3rd.

You still look for the same thing when dealing with segments:

JK is congruent or corresponding to PQ  (1st to 2nd in both)

KL is congruent or corresponding to QR (2nd to 3rd in both)

LJ is congruent or corresponding to RP (3rd to 1st in both)

So I have named all the pairs of corresponding sides and angles.

The only one that I didn't list in your choices is:

The third choice.

The third choice doesn't contain corresponding parts because L is 3rd and Q is 2nd.

Answer:607.81

Step-by-step explanation:that’s what I got believe me on this one guys

The value of the collector's item after 4 years is $607.75.

Given :

Item is purchased for $500.

Value increases at a rate of 5% per year.

Solution :

We know that the exponential growth function is

[tex]y = a(1+r)^x[/tex]

where,

a = $500

r = 0.05

x = 4

The value of the item after 4 years is,

[tex]= 500(1+0.05)^4[/tex]

[tex]= 500\times(1.05)^4[/tex]

[tex]= 607.75[/tex]

The value of the item after 4 years is $607.75.

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Answer:

4(r+4)(r-4)

Step-by-step explanation:

If you factor it out, then it will be 4(r+4)(r-4). You can double check by multiplying it.

For this case we must factor the following expression:

[tex]4r ^ 2-64[/tex]

We take common factor 4:

[tex]4 (r ^ 2-16)[/tex]

We factor the expression within the parenthesis:

[tex]4 [(r-4) (r + 4)][/tex]

Finally we have that the factored expression is:

[tex]4 [(r-4) (r + 4)][/tex]

Answer:

[tex]4 [(r-4) (r + 4)][/tex]

Answer:

B. All real numbers

Step-by-step explanation:

I assume the function is f(x) = 3^x, where x is an exponent.

Since an exponent can be a positive number, a negative number, and zero, x can be any real number. The domain of a function is the set of values that can be used for x.

Answer: B. All real numbers

For f(x) = 3*x

Domain of given function is B. All real numbers

It is a set of all values that gives a valid value if we put it in a function.

Any value which can be substituted in function and doesn't return infinity or  complex form is part of domain.

Check for which value f(x) can return infinite?

Answer is none.

for which value f(x) can give complex number?

Answer is none.

since there exists no such value for which f(x) return infinity or complex number, Domain of f(x) is all real numbers.

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Answer:

A. 111.65

Step-by-step explanation:

This scenario can be interpreted like a triangle ABC where A and B are islands and C is the point from where the captain is 160 miles from island B.

a = 160

b = 260

c = 250

Law of cosines

[tex]c^2 = a^2 + b^2 - 2(ab)Cos(C)\\Arranging\ as\\2ab \ cos\ C = a^2+b^2-c^2\\2(160)(260)\ cos\ C = (160)^2+(260)^2- (250)^2\\83200\ cos\ C=25600+67600-62500\\83200\ cos\ C=30700\\cos\ C= \frac{30700}{83200}\\cos\ C=0.36899\\C = arccos\ (0.36899)\\C = 68.35[/tex]

The internal angle is 68.35°

We have to find the external angle to find the bearing the captain should turn

Using the rule of supplimentary angles:

The external angle = 180 - 68.35 = 111.65°

Therefore, the captain should turn 111.65° so that he would be heading straight towards island B.

Hence, option 1 is correct ..

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

AB = 250 feet

AC = 260 feet

BC = 160 feet

We need to find the angle C that is heading straight towards island B.

We will apply "Law of cosine":

[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}\\\\\cos C=\dfrac{160^2+260^2-250^2}{2\times 160\times 260}\\\\\cos C=0.368\\\\C=\cos^{-1}(0.368)\\\\C=68.40^\circ[/tex]

Exterior angle would be

[tex]180-68.40=111.65^\circ[/tex]

Hence, Option 'a' is correct.