A wire is tied from the top of one tower to the top of another. The angle of depression from the top
to the top of the taller tower to the top of the shorter tower is 37 degrees. If the wire is 100 feet long, find the
distance between the towers.

Answer:

Choice A.

Step.-by-step explanation:

y=√x

y=x² -1

Substituting the values in choice A:

1.2 = √1.5 = 1.2247     Approximately equal.

1.2 = (1.5)^2 - 1 = 1.25   Approximately equal.

Choice B.

-1.2 = √-1.5  which is imaginary so NOT this one.

Choice C

-1.2 = √1.5 = -1.2247

-1.2 = (1.5)^2 - 1 = 1.25  NO.

Choice D

We have the non real value √-1.5 again so NOT this one.

Answer: Option A

A.(1.5,1.2)

Step-by-step explanation:

We have the following system of equations

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

[tex]y=x^2 -1[/tex]

the solution of the system will be all points that satisfy both equations at the same time

For (1.5,1.2)

[tex]y=\sqrt{1.5}=1.2[/tex]

[tex]y=(1.5)^2 -1=1.2[/tex]

Both equations are satisfied

Note that we can discard options B and D because the domain of the equation [tex]y =\sqrt{x}[/tex] does not include the negative numbers.

We can discard option C because the range of the function [tex]y =\sqrt{x}[/tex] does not include the negative numbers.

Finally the answer is the option A

Answer:

5h -2

Step-by-step explanation:

(6h + 1) - (h+3)

= 6h + 1 - h -3

= 5h -2

6h +1 - h+3

Subtract like terms:

6h - h = 5h

1-3 = -2

The answer becomes 5h-2

The answer of -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] is 0.06237948089

Step-by-step explanation:

To solve this problem -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] we must start with

1. Solve this bracket [9 (-8.9 + 9/5) .01] at first

2. Multiply the answer of the bracket by 66.9

3. Multiply -3(8/9) and divide the answer by the product of the previous

   step

In [9 (-8.9 + 9/5) .01]

∵ (-8.9 + 9/5) = (-8.9 + 1.8) = -7.1

∴ [9 (-8.9 + 9/5) .01] = [9 (-7.1).01]

∵ 9(-7.1)(.01) = -0.639

∴ [9 (-8.9 + 9/5) .01] = -0.639

∵ 66.9 [-0.639] = -42.7491

∵ [tex]-3(\frac{8}{9})=\frac{-8}{3}[/tex]

∴ -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] = [tex]\frac{-8}{3}[/tex] ÷ -42.7491

∴ -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] = 0.06237948089

The answer of -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] is 0.06237948089

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Check the picture below.

Answer:

-13x^4+2x^3+8x^2-5x

Step-by-step explanation:

(3x^2-5x-7x^4)-(-2x^3+6x^4-5x^2)

= 3x^2-5x-7x^4+2x^3-6x^4+5x^2

= -13x^4+2x^3+8x^2-5x

Answer:

-x(13x³ - 2x² - 8x + 5)

Step-by-step explanation:

1. Distribute the negative to the numbers inside the parenthesis. Remember that two negatives multiplied will make a positive, and a negative and a positive will become a negative.

3x² - 5x - 7x^4 + 2x³ - 6x^4 +  5x²

2. Combine like terms. Remember that only numbers with the same number and exponents can be combined.

3x² - 5x - 7x^4 + 2x³ - 6x^4 +  5x²

                        ↓

   8x² - 5x - 7x^4 + 2x³ - 6x^4

                        ↓

        8x² - 5x - 13x^4 + 2x³

3. Rewrite the answer in descending order of powers.

-13x^4 + 2x³ + 8x² - 5x

4. Simplify The equation. The terms all have x in common, so we will take that out first. The smallest amount of x's any term has is one (-5x only has one x), so the most we can take out is one x. We will do this by lowering the power of every x by one.

x(-13x³ + 2x² + 8x - 5)

5. Since 13 and 5 are prime and do not go into 2 or 8 we will not be simplifying the coefficients. However, the last thing we can do is take out a negative.

-x(13x³ - 2x² - 8x + 5)

Answer:

you would divide the two numbers. 2 divided by 11 is 0.18

Answer:

0.181818182 or rounded is 0.18

Step-by-step explanation:

to turn any fraction into a decimal you always do numerator divided by denominator

Answer:

Simplification of [tex]-5-\sqrt{-44}[/tex] is:

[tex]-5-2i\sqrt{11}[/tex]

Step-by-step explanation:

We are given a expression:

[tex]-5-\sqrt{-44}[/tex]

We have to simplify the given expression.

We know that:

[tex]\sqrt{-1}=i[/tex]

[tex]-5-\sqrt{-44}\\\\=-5-\sqrt{-4\times 11}\\ \\=-5-\sqrt{-1\times 2^2\times 11}\\ \\=-5-2i\sqrt{11}[/tex]

Hence, simplification of [tex]-5-\sqrt{-44}[/tex] is:

[tex]-5-2i\sqrt{11}[/tex]

Answer:

Step-by-step explanation:

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

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

m - slope

b - y-intercept

========================================

Let

[tex]k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2[/tex]

========================================

We have the equation of a line in a general form (Ax + By + C = 0)

Convert it to the slope-intercept form:

[tex]4x+7y+3=0[/tex]             subtract 7y from both sides

[tex]4x+3=-7y[/tex]         divide both sides by (-7)

[tex]-\dfrac{4}{7}x-\dfrac{3}{7}=y\to m_1=-\dfrac{4}{7}[/tex]

Therefore

[tex]m_2=-\dfrac{1}{-\frac{4}{7}}=\dfrac{7}{4}[/tex]

We have the equation:

[tex]y=\dfrac{7}{4}x+b[/tex]

Put the coordinates of the point (-2, 1) to the equation, and solve for b :

[tex]1=\dfrac{7}{4}(-2)+b[/tex]

[tex]1=-\dfrac{7}{2}+b[/tex]     multiply both sides by 2

[tex]2=-7+2b[/tex]           add 7 to both sides

[tex]9=2b[/tex]            divide both sides by 2

[te]x\dfrac{9}{2}=b\to b=\dfrac{9}{2}[/tex]

Finally:

[tex]y=\dfrac{7}{4}x+\dfrac{9}{2}[/tex] - slope-intercept form

Convert to the general form:

[tex]y=\dfrac{7}{4}x+\dfrac{9}{2}[/tex]         multiply both sides by 4

[tex]4y=7x+18[/tex]      subtract 4y from both sides

[tex]0=7x-4y+18[/tex]

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{a^3b^{-4}}{a^2b^3a^{-5}}\implies \cfrac{a^3}{1}\cdot b^{-4}\cdot \cfrac{1}{a^2}\cdot \cfrac{1}{b^3}\cdot \cfrac{1}{a^{-5}}\implies a^3\cdot b^{-4}\cdot a^{-2}\cdot b^{-3}\cdot a^5 \\\\\\ a^3a^5a^{-2}b^{-4}b^{-3}\implies a^{3+5-2}b^{-4-3}\implies a^6b^{-7}[/tex]

Answer:

The value of f[ g(x) ] = 7x + 27

Step-by-step explanation:

It is given that, f( x ) = 7x + 13 and g( x ) = x + 2

To find the value of f(g(x))

g(x) = x + 2 and 7x + 13   (given)

Let g(x) = x + 2

f [ g(x) ] = 7(x + 2) + 13  [ substitute the value of g(x) in f(x) ]

 = 7x + 14 + 13

 = 7x + 27

Therefore the value of f[ g(x) ] = 7x + 27

Answer: y=-ax(x-500)(x-1000)^2

Step-by-step explanation:

The behavior of the x-intercept of a graph is given by the multiplicity of the zero

The required polynomial for the coaster is, y = -a·x·(x - 500)·(x - 1000)²

Reason:

The question relates to the introduction of characteristics to the graph of a polynomial through knowledge of the effect of parameters of a polynomial

Known parameter:

Parent function is, y = a·x·(x - 1000)

The polynomial crosses the x-axis when (x - 500) is a factor of the polynomial, therefore, we have;

y = a·x·(x - 500)·(x - 1000)

Given that the graph is to initially rise, the leading coefficient is negative, therefore, we have;

y = -a·x·(x - 500)·(x - 1000)

For the polynomial to come in smoothly to stop at y = 0, when x = 1,000 we have that a turning point of the polynomial will be located at x = 1,000, this is given by introduction of a bump on the x-axis at x = 1,000 with a factor of (x - 1,000)²

Therefore, the required polynomial is y = -a·x·(x - 500)·(x - 1000)²

The height of the above polynomial is progressively smaller as x tends towards 1,000, given that the factors, (x - 500), and (x - 1,000), becomes smaller.

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Answer:

f=31

Step-by-step explanation:

35-f=4

-35   -35

-f=-31

*-1  *-1

f=31

[tex]\large \textnormal{F=31}[/tex], is the correct answer.

[tex]\large \textnormal{First, subtract by 35 from both sides of the equation.}[/tex]

[tex]\displaystyle 35-f-35=4-35[/tex]

[tex]\large \textnormal{Solve.}[/tex]

[tex]\displaystyle -f=-31[/tex]

[tex]\large \textnormal{Then you divide by -1 from both sides of the equation.}[/tex]

[tex]\displaystyle \frac{-f}{-1}=\frac{-31}{-1}[/tex]

[tex]\large \textnormal{Solve to find the answer.}[/tex]

[tex]\displaystyle -31\div-1=31[/tex]

[tex]\large \boxed{f=31}\checkmark[/tex]

Hope this helps!

Answer:

x = -1255

Step-by-step explanation:

336+x/5=85

Subtract 336 from each side

336-336 +x/5=85-336

x/5 =-251

Multiply each side by 5

x/5 * 5 = -251 *5

x = -1255

Answer:

The graph has a minimum.

Step-by-step explanation:

The top answer choice would also be a genuine statement if that negative symbol was removed from outside the 4. Second, whenever A is positive, the parabola opens up with a minimum value.

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

No Solution

Brainliest Please :)

Answer:

6

Step-by-step explanation:

9^3 ÷2 the inverse is 9÷3×2 =9÷3=3×2=6 the answer is 6

Answer:

x = 12.25

Step-by-step explanation:

Given

x - 3(x - 7) = 4(x - 7) - 2x ← distribute parenthesis on both sides

x - 3x + 21 = 4x - 28 - 2x ← simplify both sides

- 2x + 21 = 2x - 28 ( subtract 2x from both sides )

- 4x + 21 = - 28 ( subtract 21 from both sides )

- 4x = - 49 ( divide both sides by - 4 )

x = [tex]\frac{49}{4}[/tex] = 12.25

Answer: x=12.25

Step-by-step explanation: First, multiply the numbers into the parentheses. You will get:

X -3x +21 = 4x -28 -2x

Combine like terms.

-2x +21 =2x -28

Isolate x by adding 2x to each side.

21 =4x -28

Add 28 to each side to get x by itself.

49=4x

Divide by 4.

X =12.25

Answer:

c. x = 6 only

Step-by-step explanation:

In order to calculate the zeros of f(x), we need to set it equal to zero and find the corresponding values of x.

[tex]x^{2}-12x+36=0[/tex]

Using the midterm breaking, we can split -12x into two such terms whose sum will be -12x and product will be 36x². These two terms are -6x and -6x

So, the above expression can be written as:

[tex]x^2-6x-6x+36=0\\\\ x(x-6)-6(x-6)=0\\\\ (x-6)(x-6)=0\\\\ (x-6)^{2}=0\\\\ x-6=0\\\\ x=6[/tex]

This means, the zero of f(x) occurs at x = 6 only.

Answer:

TRUE

Step-by-step explanation:

Answer:

My blue dot is the y-intercept.

My red dot is my x-intercept.

Please look at the graph.

Step-by-step explanation:

I can show you my graph and mark it where the x-intercepts and y-intercepts are.

Let's begin.

We have y=2/3 x+4.

Compare this to the slope-intercept form, y=mx+b where m is the slope and b is the y-intercept.

You should see that m=2/3 and b=4.

This means the slope is 2/3 and the y-intercept is 4.

Don't forget slope means rise/run.

So once we graph 4 (plot a point) on the y-axis, then we will use our slope to get to one more point.  The slope here tells us to rise 2 and run 3.

Now sometimes our graph is not accurate when drawing by hand so there is a way without graphing that you can find the x- and y-intercepts.

The x-intercept is when the y-coordinate is 0.

The y-intercept is when the x-coordinate is 0.

So to find the x-intercept, I'm going to set y to 0 and solve for x. Like so,

0=2/3 x +4

Subtract 4 on both sides:

-4=2/3 x

Multiply both sides by the reciprocal of 2/3 which is 3/2:

3/2 (-4)=x

Simplify:

-12/2=x

Simplify:

-6=x

Symmetric Property:

x=-6

So the x-intercept is (-6,0).

I actually already have the y-intercept since my equation is in y=mx+b (slope-intercept form).  But if it wasn't you could just set x to 0 and solve for y. Like so:

y=2/3 (0)+4

y=0+4

y=4

The y-intercept is (0,4).

Let's go to our graph now.

Answer:

After I had submitted my answer it gave me this answer

Step-by-step explanation:

Final answer:

To find the liters for 5 cups of water, divide 5 by 4.22, according to the conversion rate obtained from the given table.

Explanation:

To calculate the number of liters used if Saloman used 5 cups of water, we need to determine how many cups are in a liter. According to the unit conversion provided, 1 liter is equivalent to approximately 4.22 cups. To find the number of liters from the number of cups, we should divide the total cups by the number of cups per liter. Therefore, to find the liters for 5 cups, we divide 5 by 4.22.

The calculation is: 5 cups ÷ 4.22 cups/liter = number of liters.

Answer:

Total distance mouse traveled in 3 hours = [tex]\frac{3}{24}[/tex] of a mile

The mouse traveled the same distance in each hour. So in order to find the distance covered in 1 hour we have to divide the distance covered in 3 hours by 3. This will give us the distance that the mouse traveled in one hour.

So, the distance traveled in one hour will be = [tex]\frac{3}{24} \div 3 = \frac{3}{24} \times \frac{1}{3} =\frac{1}{24}[/tex] of a mile

The error which Matt made was that he divided only the denominator of the expression by 3, this probably was a calculation error.

Correct conclusion will be: Mouse travel 1/24 of a mile each hour

Answer:

Matt should have divided 3 by 3, not 24 by 3. (C.)

Step-by-step explanation:

since its a whole number you do not divide it at all.

Also:

Answer:

(12,1.625)

Step-by-step explanation:

According to the given statement:

Cost of gas per gallon = $6

Cost of diesel per gallon = $8

Cost of x gallon gas  = 6x

Cost of y gallon diesel = 8y

You have at most $85 to spend on fuel

Therefore the equation we get is:

6x+8y≤85

You must purchase at least 12 gallons of gas for your car

x≥12

Plot the graph and you get possible solutions:

(12,1.625)..

Step-by-step explanation:

Six less than five times a number is at least thirty- four

n - number

a)

5n - 6 ≥ 34           add 6 to both sides

5n ≥ 40           divide both sides by 5

n ≥ 8

b) in the attachment

c) n ∈ [8, ∞)

For this case we must subtract:

[tex]2- \frac {5} {8} =\\\frac {8 * 2-5} {8} =\\\frac {16-5} {8} =\\\frac {11} {8}[/tex]

Thus, you have [tex]\frac {11} {8}[/tex]of string, after you have cut[tex]\frac {5} {8}[/tex] of it.

If we convert to a mixed number we have to:

[tex]\frac {11} {8} = 1 \frac {3} {8}[/tex]

Answer:

He has [tex]1 \frac {3} {8}[/tex] of string.

Answer:

f(x) = x

Step-by-step explanation:

f(x) = x is of the form y = mx + b.

y = mx + b is the slope-intercept form of the equation of a line, so its graph is a line.

f(x) = x^2 has a variable to the second power, so its graph is a parabola, and not a line.

f(x) = |x| has an absolute value, so its graph is shaped like a V. It is not a line.

Answer:

X     Y

1       5

4/5   4

2/5   2

Step-by-step explanation:

y=5x

We we know y we need to solve for x

X Y

  5

  4

  2

Let y =5

5 = 5x

Divide by 5

5/5 =5x/5

1=x

Let y =4

4 = 5x

Divide by 5

4/5 =5x/5

4/5=x

Let y =2

2 = 5x

Divide by 5

2/5 =5x/5

2/5=x

X     Y

1       5

4/5   4

2/5   2

Answer:

x=0.8 if y=4, x=0.4 if y=2

Step-by-step explanation:

Rearrange the equation to get:

5x= 4 and

5x= 2

Divide equations by 5 to get:

x=0.8

x=0.4

Answer:

Step-by-step explanation:

write this expression : f(x) = a(x-h)²+k

when  the axis of symmetry is the line  : x =h and the vertex A(h,k)

y=2x²+4x-3

y = 2(x²+2x - 3/2)

y=2((x²+2x+1) -1 -3/2)

y = 2((x+1)² - 5/2)

y = 2(x+1)² -5.....vertex form      x= -1 the axis of symmetry  and A(-1,-5)the vertex

Answer:

The equation of the axis of symmetry is x = -1.

The  coordinates of the vertex are (-1, -5).

Step-by-step explanation:

y = 2x^2 + 4x - 3

y = 2(x^2 + 2x) - 3

y = 2[ (x + 1)^2 - 1] - 3

y = 2(x + 1)^2  - 5.

The equation of the axis of symmetry is x = -1.

The  coordinates of the vertex are (-1, -5)

Answer:

2

Step-by-step explanation:

Angela has a marbles.

Brian has twice as many as Angela, so Brain has 2a.

Caden has three times as many as Brain, so Caden has 3(2a)=6a.

Daryl has five times the number of marbles as Caden, so Daryl has 5(6a)=30a.

We are given that these 4 people together have 78 marbles.

Angela's + Brain's + Caden's + Daryl's =78

  a          +    2a      +   6a        + 30a      =78

Combine the like terms:

39a=78

Divide both sides by 39:

  a=78/39

   a=2

Answer:

C. 52 cm

Step-by-step explanation:

A full circle has a degree measure of 360 degrees.

Minor arc DE is intercepted by a central angle of 120 degrees.

120 degrees is 1/3 of 360 degrees, so the length of minor arc DE is 1/3 of the circumference of the circle.

length of minor arc DE = (120/360) * 2 * pi * r

length of minor arc DE = (1/3) * 2 * 3.14 * 25 cm

length of minor arc DE = 52.3333... cm

Answer:

the correct answer is 52.

Step-by-step explanation:

I just got it correct.

Answer:

C:  Two dimensions

Step-by-step explanation:

Yes:  a plane has two dimensions; think of a plane as being defined by the x- and y-axes, which intersect at a point in the plane.

A plane have two dimensions.

A plane is a flat, two-dimensional surface that prolongs infinitely far. A plane is a two-dimensional analogue that could consist of a point, a line and three-dimensional space.

A plane is a flat, two-dimensional surface that extends indefinitely. It has two dimensions because every point in the plane can be described by a linear combination of two independent vectors.

Hence, a plane have two dimensions.

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