Points A and B are on opposite sides of a lake. A point C is 105.6 meters from A. The measure of ∠BAC is 70.5°, and the measure of ∠ACB is determined to be 38.833°. Find the distance between points A and B (to the nearest meter).

Check the picture below.

something noteworthy to look at is that the graph doesn't cross the x-axis at -2, it simply comes down to it, touches it and it goes back up, it simply bounces off the x-axis, whenever that happens, that zero/solution/root has an even multiplicity.

when 0 = ax² + bx + c, we notice that y = 0, and for the graph that happens there, at x = -2, but that solution has an even multiplicity, and since the equation is a 2nd degree polynomial, thus x = -2 is there twice, namely

x = -2

x - 2 = 0

(x - 2)² = 0   <---- multiplicity of 2.

Answer:

-2

Step-by-step explanation:

:)

Answer:

the answer is 82

Step-by-step explanation:

Answer:

82

Step-by-step explanation:

just use a calculator

bearing in mind that perpendicular lines have negative reciprocal slopes, let's find the slope of the provided line then

[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{-15}x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-15\implies -\cfrac{15}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{15}}\qquad \stackrel{negative~reciprocal}{+\cfrac{1}{15}\implies \cfrac{1}{15}}}[/tex]

well, we know the x-intercept is at x = 3, recall when a graph intercepts the x-axis y = 0, so this point is (3 , 0).  Then we're really looking for the equation of a line whose slope is 1/5 and runs through (3 , 0).

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=\cfrac{1}{5}(x-3)\implies y=\cfrac{1}{5}x-\cfrac{3}{5}[/tex]

For this case we have that by definition, the sum of the internal angles of a triangle is 180 degrees.

Then, according to the figure we have:

[tex][180- (6x + 1)] + 79+ (2x + 10) = 180[/tex]

We operate parentheses:

[tex]180-6x-1 + 79 + 2x + 10 = 180[/tex]

We add similar terms:

[tex]-4x + 268 = 180\\-4x = 180-268\\-4x = -88\\x = \frac {-88} {- 4}\\x = 22[/tex]

Thus, x has a value of 22 degrees.

Answer:

Option D

Answer:

(D) x= 22

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

You pay a one time fee of 18 dollars and then 2 dollars per ride.

The expression for that is 18+2r where r represents the number of rides and the output of (18+2r) is amount you spend.

f(r)=2r+18 when compared to f(x)=mx+b where m is slope and b is y-intercept

you should see that the slope is $2 per ride.

B. is the option that says this.

Answer: Option B

Her total cost increases by $2, for each ride purchased

Step-by-step explanation:

We know that $ 18 is the cost of the ticket. We do not know exactly how many trips you will make, but we know that the cost is $ 2 for each ride.

If we call "x" the number of rides then we know that the total cost "y" is:

[tex]y = 2x + 18[/tex]

Note that the cost increases by $2 for each ride

The equation of a line has the following form

[tex]y = mx + b[/tex]

Where m is the slope of the line.

In this case we have the following equation

[tex]y = 2x + 18[/tex]

Therefore [tex]m = 2[/tex]. Then the slope is the cost of $2 for each ride

Finally the answer is the option B.  Her total cost increases by $2, for each ride purchased

Answer:

y=(3/2)x+-14

First blank: 3

Second blank:2

Last blank:-14

Step-by-step explanation:

The line form being requested is slope-intercept form, y=mx+b where m is slope and b is y-intercept.

Also perpendicular lines have opposite reciprocal slopes so the slope of the line we are looking for is the opposite reciprocal of -2/3 which is 3/2.

So the equation so far is

y=(3/2)x+b.

We know this line goes through (x,y)=(4,-8).

So we can use this point along with our equation to find b.

-8=(3/2)4+b

-8=6+b

-14=b

The line is y=(3/2)x-14.

Answer:

Just reverse the order. So double 31 is 62 then subtract 5. 57

Answer:

x= 5/3

Step-by-step explanation:

3x- 5 = 1

first you have to move the constant or in this case the 5 to the other side to isolate x so to do that you have to ad 5 from both sides, that way itll cancel out from the left and add on the right

3x= 5

now, to isolate x, we have to divide by 3, that way you get

x= 5/3

Answer:

f (gx) = 1/ -2(1/x^2+6x+10) + 9

Step-by-step explanation:

f (gx) = 1/ -2(1/x^2+6x+10) + 9

Answer:

The domain is all real numbers where

[tex](f \circ g)(x)=\frac{x^2+6x+10}{9x^2+54x+88}[/tex]

Step-by-step explanation:

[tex](f \circ g)(x)=f(g(x))[/tex]

So g(x) must exist before plugging it into f(x).

Let's find where g(x) doesn't exist.

[tex]x^2+6x+10[/tex] is a quadratic expression.

[tex]b^2-4ac[/tex] is the discriminant and will tell us if [tex]x^2+6x+10=0[/tex] will have any solutions.  I'm trying to solve this equation because I want to figure out what to exclude from the domain.  Depending on what [tex]b^2-4ac[/tex] we may not have to go full quadratic formula on this problem.

[tex]b^2-4ac=(6)^2-4(1)(10)=36-40=-4[/tex].

Since the discriminant is negative, then there are no real numbers that will make the denominator 0 here.  So we have no real domain restrictions on g.

Let's go ahead and plug g into f.

[tex]f(g(x))[/tex]

[tex]f(\frac{1}{x^2+6x+10})[/tex]  

I replaced g(x) with (1/(x^2+6x+10)).

[tex]\frac{1}{-2(\frac{1}{x^2+6x+10})+9}[/tex]  

I replaced old input,x, in f with new input (1/(x^2+6x+10)).

Let's do some simplification now.

We do not like the mini-fraction inside the bigger fraction so we are going to multiply by any denominators contained within the mini-fractions.

I'm multiplying top and bottom by (x^2+6x+10).

[tex]\frac{1}{-2(\frac{1}{x^2+6x+10})+9} \cdot \frac{(x^2+6x+10)}{(x^2+6x+10)}[/tex]  

Using distributive property:

[tex]\frac{1(x^2+6x+10)}{-2(\frac{1}{x^2+6x+10})\cdot(x^2+6x+10)+9(x^2+6x+10)}[/tex]

We are going to distribute a little more:

[tex]\frac{x^2+6x+10}{-2+9x^2+54x+90}[/tex]

Combine like terms on the bottom there (-2 and 90):

[tex]\frac{x^2+6x+10}{9x^2+54x+88}[/tex]

Now we can see if we have any domain restrictions here:

[tex]b^2-4ac=(54)^2-4(9)(88)=-252[/tex]

So again the bottom will never be zero because [tex]9x^2+54x+88=0[/tex] doesn't have any real solutions.  We know this because the discriminant is negative.

The domain is all real numbers where

[tex](f \circ g)(x)=\frac{x^2+6x+10}{9x^2+54x+88}[/tex]

Answer:

4

Step-by-step explanation:

The standard form of a circle is:

(x-h)^2+(y-k)^2=r^2

where (h,k) is the center and

r is the radius.

You compare your equation to mine you should see that:

-h=7 implies h=-7

-k=7 implies k=-7

r^2=16 implies r=4 since 4^2=16

The center is (-7,-7).

The radius is 4.

For this case we have that by definition, the equation of a circle in standard or canonical form is given by:

[tex](x-h) ^ 2 + (y-k) ^ 2 = r ^ 2[/tex]

Where:

(h, k) is the center

r: It's the radio

We have the following equation:

[tex](x + 7) ^ 2 + (y + 7) ^ 2 = 16\\(x + 7) ^ 2 + (y + 7) ^ 2 = 4 ^ 2[/tex]

Thus, the radius is 4.

Answer:

4

Answer:

(1, - 6 )

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y )

The point J has coordinates (0, 3 ), hence

J'(0, - 3 ) ← after reflection in x- axis

A translation (x, y ) → (x + 1, y - 3 )

Means add 1 to the x- coordinate and subtract 3 from the y- coordinate

J'(0, - 3 ) → J''(0 + 1, - 3 - 3 ) → J''(1, - 6 ) ← final image

Answer:

value of a.b = -4

Step-by-step explanation:

We need to find a.b

a= 4i-4j

b = 4i+5j

We know that i.i =1, j.j=1, i.j =0 and j.i=0

a.b = (4i-4j).(4i+5j)

a.b = 4i(4i+5j)-4j(4i+5j)

a.b = 16i.i +20i.j-16j.i-20j.j

a.b = 16(1) +20(0)-16(0)-20(1)

a.b = 16 +0-0-20

a.b = 16-20

a.b =-4

So, value of a.b = -4

ANSWER

[tex]a \cdot \: b = - 4[/tex]

EXPLANATION

The dot product of two vectors

[tex]a = xi + yj[/tex]

and

[tex]b = mi + nj[/tex]

is given by

[tex]a \cdot \: b = mx + ny[/tex]

The given vectors are:

[tex]a = 4i - 4j[/tex]

[tex]b = 4i + 5j[/tex]

Applying the above definition of dot products, we obtain:

[tex]a \cdot \: b = 4 \times 4 + - 4 \times 5[/tex]

[tex]a \cdot \: b = 16 - 20[/tex]

[tex]a \cdot \: b = - 4[/tex]

Answer:

C) The variable x represents the independent variable.

Step-by-step explanation:

The given function is [tex]g(x)=-2x^2+5[/tex].

g(x) is NOT the multiplication of g and x because g is a function of x.

[tex]x[/tex] is the input of the function.

[tex]-2x^2+5[/tex] is the output of the function.

The variable [tex]x[/tex] is called the independent variable because we plug in values of x to find g.

The variable g represents the output of the function NOT the input.

The correct choice is C

Think for a minute.

CA = 17, right?

CZ is the remaining part of CA.

ZA = 16

CZ = CA - ZA

CZ = 17 - 16

CZ = 1

Did you follow?

Answer:

D  1

Step-by-step explanation:

CA = CZ + ZA

WE know CA = 17 and ZA = 16

17 = CZ + 16

Subtract 16 from each side

17-16 = CZ +16-16

1 = CZ

Answer:

V ≈ 915.7 cm³

LA ≈ 411.3 cm²

SA ≈ 596.9 cm²

Step-by-step explanation:

Volume of a pyramid is:

V = ⅓ Bh

where B is the area of the base and h is the height.

The base is a regular octagon.  The area of a regular octagon is 2(1 + √2) s², where s is the side length.

Substituting:

V = ⅔ (1 + √2) s² h

Given that s = 6.2 and h = 14.8:

V = ⅔ (1 + √2) (6.2)² (14.8)

V ≈ 915.7 cm³

The lateral surface area is the area of the sides of the pyramid.  Each side is a triangular face.  We know the base length of the triangle is 6.2 cm.  To find the area, we first need to use geometry to find the lateral height, or the height of the triangles.

The lateral height and the perpendicular height form a right triangle with the apothem of the octagon.  If we find the apothem, we can use Pythagorean theorem to find the lateral height.

The apothem is two times the area of the octagon divided by its perimeter.

a = 2 [ 2(1 + √2) s² ] / (8s)

a = ½ (1 + √2) s

a ≈ 7.484

Therefore, the lateral height is:

l² = a² + h²

l ≈ 16.58

The lateral surface area is:

LA = 8 (½ s l)

LA = 4 (6.2) (16.58)

LA ≈ 411.3 cm²

The total surface area is the lateral area plus the base area.

SA = 2(1 + √2) s² + LA

SA = 2(1 + √2) (6.2)² + 411.3

SA ≈ 596.9 cm²

The volume is 915.7 cm³

The lateral surface area is 411.3 cm²

The total surface area is 596.9 cm²

Answer:

y = 3/2 x + 3

Step-by-step explanation:

2/3 x + y = -14/3

y = -2/3 x − 14/3

The slope of this line is -2/3.  So the perpendicular slope is the opposite of the inverse:

m = -1 / (-2/3)

m = 3/2

We know the slope of the line and a point on the line, so using point-slope form:

y − 0 = 3/2 (x − (-2))

Simplifying into slope-intercept form:

y = 3/2 (x + 2)

y = 3/2 x + 3

Answer:

(x+5)^2=34

Solutions: ≈ -10.831, 0.831

Step-by-step explanation:

First you divide the second term by two to complete the square.  The second term divided by two is 5, 5^2 is 25 which means you need a value of 25 to factor.  Add 3 to both sides so you have a value of 25 on the left side.

x^2+10x+25=34  Next, factor the left side.

(x+5)^2=34  

The solutions to this equation are not rational, you could use the quadratic formula to find the exact answer or put the equation into a graphing calculator to find approximate solutions.

Answer:

A.

f(x+1)=5/2f(x) with f(1)=3/2

Step-by-step explanation:

So we are looking for a recursive form of

[tex]f(x)=\frac{3}{2}(\frac{5}{2})^{x-1}[/tex].

This is the explicit form of a geometric sequence where [tex]r=5/2[/tex] and [tex]a_1=\frac{3}{2}[/tex].

The general form of an explicit equation for a geometric sequence is

[tex]a_1(r)^{n-1} \text{ where } a_1 \text{ is the first term and } r \text{ is the common ratio}[/tex].

The recursive form of that sequence is:

[tex]a_{n+1}=ra_n \text{ where you give the first term value for } a_1[/tex].

So we have r=5/2 here so the answer is A.

f(x+1)=5/2f(x) with f(1)=3/2

By the way all this says is term is equal to 5/2 times previous term.

Answer:

A

Step-by-step explanation:

Edge 2021

Answer:

I know it has nothing to do with Christianity, so C and D are wrong. It's either A or B, but I'm more with the A. But I'm not sure so...

Answer:

(3/8) ^2

Step-by-step explanation:

P ( male history teacher) = Number males/ total

                                         = 3/8

Assuming nothing changes in year two

P ( male history teacher year two) = Number males/ total

                                         = 3/8

P( male, male) = 3/8 * 3/8 = (3/8) ^2

(3/8)^2 would be your answer.

Since there are 3 male and 5 female, that means there are 3/8 male and 5/8 female. We are talking about male and how many times it would happen in 2 years, so (3/8)^2 would be your answer.

Answer:

on plato the answer is B, it reads the same as the answer c does on this example. Please make sure that you read the answers and match them up with the correct one on your side.

Step-by-step explanation:

Using the information provided, Michael's height changes from above to below the platform every 40 seconds for the second roller coaster. However, without more concrete information regarding the first roller coaster, a definitive answer for that cannot be provided.

The topic in discussion here is the modeling of Michael's height changes on two different roller coasters using functions and graphs. Given the question, we can observe that the second roller coaster's height variations follow a pattern corresponding to a trigonometric function, changing from 0, to 50, to 100, and so forth, then repeating. From this pattern, we can infer that Michael's height on the second roller coaster oscillates from a positive value (above the platform) to a negative value (below the platform) and back every 40 seconds since the value of g(t) changes from positive to negative (or vice versa) at each 40-second interval.

However, without the details of the first roller coaster's function or graph, we cannot accurately determine how often Michael's height on the first coaster changes from positive to negative. Therefore, based on the given information, we cannot definitively choose between the provided answer options.

https://brainly.com/question/5449909

#SPJ3

Notice that both sides of the equation have a similar form. If we ignore angle functions we end up with,

[tex]A+A\cdot B=B+B\cdot A[/tex]

That is true if condition [tex]A=B[/tex] is met.

Otherwise it is false.

Hope this helps.

r3t40

Answer:

Choose something close to (1.8,2.6)

Choice A

Step-by-step explanation:

Without the graph provided, I would prefer to do this algebraically.

y=2x-1

y=-1/4x+3

Since both are solved for y, I'm going to replace the first y with what the second y equals.

-1/4x+3=2x-1

I don't really like to deal with fractions quite yet so I'm going to multiply both sides by 4.

-1x+12=8x-4

I'm going to add 1x on both sides.

     12=9x-4

I'm going to add 4 on both sides.

     16=9x

I'm going to divide both sides by 9

    16/9=x

This is the same as saying x=16/9.

Now to find y, just choose one of the equations and replace x with 16/9.

y=2x-1

y=2(16/9)-1

y=32/9-1

y=32/9-9/9

y=(32-9)/9

y=23/9

So the exact solution is (16/9,23/9).

Round these numbers to the nearest tenths you get:

(1.8, 2.6) .

To get this I just typed into my calculator 16 divided by 9 and 23 divided by 9

16 divided by 9 gave me 1.777777777777777777777777777

23 divided by 9 gave me 2.5555555555555555555555555

So choose something close to (1.8, 2.6).

So your ordered pair (1.75,2.5) is pretty close to that so choice A.

Answer:

1) 396

2) 20 1/2

3) 26.6

4) 8x + 56

5) 66 + 6x

6) 8x + 8

Step-by-step explanation:

* Lets explain how to solve the product mentally

# Remember the distributive property can help you to find the product

  mentally the distributive property ⇒ a(b + c) = ab + ac

- Lets solve them

1)

- In 9 × 44 we can write 44 as (40 + 4)

∴ 9 × 44 = 9(40 + 4)

∵ 9(40 + 4) = 9 × 40 + 9 × 4

- Now lets multiply 9 by 40 and 9 by 4

∵ 9(40) = 360

∵ 9(4) = 36

∴ 9 × 40 + 9 × 4 = 360 + 36 = 396

∴ 9 × 44 = 396

2)

- In 4 × 5 1/8 we can write 5 1/8 as (5 + 1/8)

∴ 4 × 5 1/8 = 4(5 + 1/8)

∵ 4(5 + 1/8) = 4 × 5 + 4 × 1/8

- Now lets multiply 4 by 5 and 4 by 1/8

∵ 4(5) = 20

∵ 4(1/8) = 1/2

∴ 4 × 5 + 4 × 1/8 = 20 + 1/2 = 20 1/2

∴ 4 × 5 1/8 = 20 1/2

3)

- In 7 × 3.8 we can write 3.8 as (3 + 0.8)

∴ 7 × 3.8 = 7(3 + 0.8)

∵ 7(3 + 0.8) = 7 × 3 + 7 × 0.8

- Now lets multiply 7 by 3 and 7 by 0.8

∵ 7(3) = 21

∵ 7(0.8) = 5.6

∴ 7 × 3 + 7 × 0.8 = 21 + 5.6 = 26.6

∴ 7 × 3.8 = 26.6

- The distributive property ⇒ a(b + c) = ab + ac

4)

- In 8(x + 7) we will multiply 8 by x and 8 by 7 and add them

∵ 8 × x = 8x

∵ 8 × 7 = 56

∴ 8(x + 7) = 8x + 56

5)

- In 6(11 + x) we will multiply 6 by 11 and 6 by x and add them

∵ 6 × 11 = 66

∵ 6 × x = 6x

∴ 6(11 + x) = 66 + 6x

6)

- In 8(x + 1) we will multiply 8 by x and 8 by 1 and add them

∵ 8 × x = 8x

∵ 8 × 1 = 8

∴ 8(x + 1) = 8x + 8

Answer:

The answer is -1

Step-by-step explanation:

f(x) = 2x³ + x² - 3x - 1  

f(1) = 2(1)³ + (1)² - 3(1) - 1

f(1)= 2 + 1 - 3 - 1

f(1)=3-3-1

f(1)=0-1

f(1)= -1

Thus the answer is -1 ....

Answer:

-1

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = 5x + 4 ( subtract 4 from both sides )

y - 4 = 5x ( divide both sides by 5 )

[tex]\frac{y-4}{5}[/tex] = x

Change y back into terms of x

[tex]f^{-1}[/tex] (x) = [tex]\frac{x-4}{5}[/tex]

Answer:

[tex]\theta=\frac{\pi}{3}, \frac{5\pi}{3}[/tex].

Step-by-step explanation:

[tex]2\cos(\theta)+2=3[/tex]

Subtract 2 on both sides:

[tex]2\cos(\theta)=3-2[/tex]

Simplify:

[tex]2\cos(\theta)=1[/tex]

Divide both sides by 2:

[tex]\cos(\theta)=\frac{1}{2}[/tex]

Now let's refer to the unit circle... When is the x-coordinate, 1/2?

There are 2 places this happens on [0,2pi].

One is in the first quadrant and the other in the fourth quadrant.

It is at [tex]\theta=\frac{\pi}{3}, \frac{5\pi}{3}[/tex].

Answer:

50

Step-by-step explanation:

20 / (2/5)

To divide by a fraction, multiply by the reciprocal.

20 × (5/2)

50

He can feed 50 cats.

50 cats

20 pounds is 100/5 pounds when written with a denominator of 5. Then you divide 100 by 2 and get 50.

Answer:

cross multiplication

Step-by-step explanation: