Two buildings are 12m apart on the same horizontal level. From the top of the taller building, the angle of depression of the bottom of the shorter building is 48degrees and from the bottom, the angle of of elevation of the top of the shorter building is 36 degrees. Calculate the difference in the heights of the buildings

Answer:

b) 65.08

ii) 0.75

Step-by-step explanation:

x(Kg):                  62      63     64     65     66     67     68

Frequency(f):      1          5        11       15      10     6        2

           xf:           62       315    704    975  660  402    136

b) mean(X) = ∑xf/N = 3254/50 = 65.08

c) x - X :          -3.08    -2.08    -1.08    -0.08        0.92   1.92    2.92

   (x - X)²:        9.49     4.33      1.17       0.0064    0.85   3.69    8.53

ii) Standard deviation(S.D.):  √(∑(x - X)²/N = √(28.0664)/50 = √0.5613

 ∴ S.D.= 0.75

Answer:

$0.56, or 56¢.

Step-by-step explanation:

According to the picture, there are two dimes, two nickels, a penny, and a quarter.

A penny is worth $0.01.

A nickel is worth $0.05.

A dime is worth $0.10.

A quarter is worth $0.25.

2(0.1) + 2(0.05) + (0.01) + (0.25) = 0.2 + 0.1 + 0.01 + 0.25 = 0.3 + 0.26 = 0.56.

So, Vivian is using $0.56, or 56¢, to buy a toy. That's a cheap one!

Hope this helps!

Answer/Step-by-step Explanation:

Given, [tex]\frac{3}{4}*-4\frac{2}{9}[/tex]

Ivy solves this problem by writing each number as a fraction and then multiplies as shown below:

[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}* -\frac{38}{9} [/tex]

[tex] = \frac{3}{4}*-\frac{38}{9} = -\frac{3*38}{4*9} = -\frac{1*19}{2*3}[/tex]

[tex]= -\frac{19}{6}[/tex]

Fabian solves this problem by writing the mixed number as a sum and applies the distributive method of multiplication as shown below:

[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}(-4 + -\frac{2}{9}) [/tex]

[tex] = \frac{3}{4}*-4 + \frac{3}{4}*-\frac{2}{9} [/tex]

[tex] = -\frac{3}{1} + \frac{1}{2}*-\frac{1}{3} [/tex]

[tex] = -3 + (-\frac{1}{6}) [/tex]

[tex] = -3 - \frac{1}{6} = -3\frac{1}{6} [/tex]

Answer:

Option C and option E

Step-by-step explanation:

C.) 7,8,9,…

E.) 22

Natural numbers are also called counting numbers.

They begin from 1, 2, 3 to infinity.

Natural numbers are greater than zero (0)

They do not have decimal point in them.

They are positive integers, as such they do not have minus

Natural numbers can include commas when they are large like 3,000

Answer:

Step-by-step explanation:

I'm assuming you are trying to solve for x. I'm not sure, but that's what I figured out for the answer, so I'm gonna go with that. : )

We are looking for the value of x to make that statement true. It's going to take some trig manipulations, but if you are at this level of precalc, these identities should definitely NOT be new to you. We will begin by squaring both sides of that equation to get:

[tex]9sin^2(x)+3cos^2(x)=3[/tex]

From here we will factor out a 3 to get:

[tex]3(3sin^2x+cos^2x)=3[/tex] and then divide both sides by 3 to get:

[tex]3sin^2x+cos^2x=1[/tex]

Knowing the Pythagorean identity for the trig ratios, we will replace the sin-squared with what it is equal to in terms of cos-squared. If:

[tex]sin^2x+cos^2x=1[/tex], then

[tex]sin^2x=1-cos^2x[/tex]. Making that replacement gives us an equation with only one trig ratio in it, namely, cos:

[tex]3(1-cos^2x)+cos^2x=1[/tex] and distributing:

[tex]3-3cos^2x+cos^2x=1[/tex] which simplifies down to:

[tex]-2cos^2x=-2[/tex]. Divide both sides by -2 to get:

[tex]cos^2x=1[/tex]. When you take the square root of both sides you get:

[tex]cos(x)=1[/tex] and [tex]cos(x)=-1[/tex]. Here is where we will use the unit circle to see where the cos is 1 and where the cos is -1. You didn't give me an interval in which to work, so I am going to use from 0 degrees to 180. Within that interval, the cos is 1 at 0 degrees; within that interval, the cos is -1 at 180.

Now we need to plug those values into the original equation to see if they work. One of them may be extraneous. Plugging in 0 first:

3sin(0) + √3cos(0) = -√3. We need to see if this is true.

The sin of 0 is 0; the cos of 0 is 1, so

0 + (√3)(1) = -√3?

The left side is √3, not -√3, so 0 doesn't work. Let's try 180 now, shall we?

3sin(180) + √3cos(180) = -√3. We need to see if this is true.

The sin of 180 is 0; the cos of 180 is -1, so

0 + (√3)(-1) = -√3?

The left side is -√3 and so is the right side, so

x = 180°

Answer:

The sum and product of zeroes are 1 and 1/4, respectively.

Step-by-step explanation:

To determine the zeroes of the quadratic polynomial, let equalize the polynomial to zero and solve in consequence:

[tex]16\cdot s^{2}-16\cdot s + 4 = 0[/tex]

By the General Quadratic Formula:

[tex]s_{1,2} = \frac{16\pm \sqrt{(-16)^{2}-4\cdot (16)\cdot (4)}}{2\cdot (16)}[/tex]

[tex]s_{1,2} = \frac{1}{2}[/tex]

Which means that zeroes are [tex]s_{1}=s_{2}=\frac{1}{2}[/tex].

The sum and product of zeroes are, respectively:

[tex]s_{1}+s_{2} =\frac{1}{2}+\frac{1}{2}[/tex]

[tex]s_{1}+s_{2} = 1[/tex]

[tex]s_{1}\cdot s_{2} = \left(\frac{1}{2} \right)^{2}[/tex]

[tex]s_{1}\cdot s_{2} = \frac{1}{4}[/tex]

The sum and product of zeroes are 1 and 1/4, respectively.

Answer:

D.

Step-by-step explanation:

From the given triangles above, there are just 2 triangles that look the same, that is ∆ABC and ∆XYZ.

∆ABC has two sides (AB and BC), and an included angle (angle B), which are equal to the two sides (YZ and YX) and the included angle (angle Y) of ∆XYZ as ∆ABC is a reflection of ∆XYZ.

Therefore, according to the SAS Theorem of congruency, ∆ABC is congruent to ∆XYZ.

Answer:

Rate of Change/Slope = -20

Equation: y= -20x +100

Step-by-step explanation:

A. We know the rate of change is also known as the slope.  If we used the slope formula to find the slope we can find the Rate of Change.

[tex]\frac{y2 - y1}{x2 - x1} = \frac{100-80}{1-2} = \frac{20}{-1} = -20[/tex]

B. Since we know the slope and 1 point on the graph we can substitute them in for 'b'

(0,100)

(100)=-20(0) + b

b = 100

Since we know the slope and the b value we can write the equation:\

y = -20x +100

The rate of change refers to the slope of the line, that is the change in y-axis per unit change in the value on the x-axis. Hence, the rate of change is :

Slope = - 100 / 5 = - 20

General form of a slope - intercept relation :

The intercept, c can be calculated thus:

100 = - 20(0) + c

100 = 0 + c

c = 100

Hence, the slope - intercept equation will be y = - 20x + 100

Learn more : https://brainly.com/question/18479471

Answer:

54

Step-by-step explanation:

To solve problems like this, always recall the "Two-Tangent theorem", which states that two tangents of a circle are congruent if they meet at an external point outside the circle.

The perimeter of the given triangle = IK + KM + MI

IK = IJ + JK = 13

KM = KL + LM = ?

MI = MN + NI ?

Let's find the length of each tangents.

NI = IJ = 5 (tangents from external point I)

JK = IK - IJ = 13 - 5 = 8

JK = KL = 8 (Tangents from external point K)

LM = MN = 14 (Tangents from external point M)

Thus,

IK = IJ + JK = 5 + 8 = 13

KM = KL + LM = 8 + 14 = 22

MI = MN + NI = 14 + 5 = 19

Perimeter = IK + KM + MI = 13 + 22 + 19 = 54

Answer:

[tex]\huge\boxed{\sf y = 2x -4}[/tex]

Step-by-step explanation:

The given equation is:

y = 2x + 3

Where Slope = m = 2 , Y-intercept = b = 3

Parallel lines have equal slopes

So, Slope of new line = m = 2

Now, Finding y-intercept:

Given Point = (x,y) = (1,-2)

So, x = 1 , y = -2

Putting m, x and y in standard form of equation to get b:

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

[tex]\sf -2 = (2)(1) + b\\-2 = 2 + b\\[/tex]

Subtracting 2 to both sides

[tex]\sf b = -2-2\\[/tex]

b = -4

So, the standard form og equation for the new line is :

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

[tex]\sf y = 2x -4[/tex]

Answer:

y = 2x - 4

Step-by-step explanation:

the problem is called (slope-intercept form)

the equation of the line is y = mx + b

the equation of a line is given as y = 2x + 3

slope = 2

b = y-intercept is where the line crosses the y-axis = 3

so point (x1, y1)  = (1, -2)

by using the equation.

y = mx + b

-2 = 2 (1) + b

-2 -2 = b

therefore b = -4

writing the new equation using the slope intercept form

y = mx + b  would be y = 2x + 4

so the equation parallel to the equation y = 2x + 3 is y = 2x - 4

Answer:

Addition property of Equality

Step-by-step explanation:

Adding same quantity to both sides of equation is called addition property of equality

Answer:

e. cannot be determined

Step-by-step explanation:

m = 1/2( x + x + 10) = 1/2(2x + 10) = x + 5

n = 1/2(x² + x + 10) =

m/n = (x+5)/(1/2(x² + x + 10))

Not enough information

Answer:The number of days it will grow to be 18.5 cm tall is 17 days.

Step-by-step explanation:

To find how many days it will grow until it reaches 18.5 centimeters, first find the difference of the new height by the old height.

So= 18.5-10= 8.5cm

8.5 is the centimeters it needs to grow to be 18.5 cm tall.

Then, divide it by the number of centimeters it will grow in one day, which is 0.5, to find the days it grew 8.5 cm.

So= 8.5÷0.5= 17

I hope this helps! Ask me if you're confused.

Answer: it would be 40/2 or 20, but im not sure.

Step-by-step explanation: so what I did was: 100 1/4 - 60 1/2: 100 - 60 = 40 and then I subtracted 1-1 which is 0 then 4-2 which is 2, and got 40/2 or just simplify which will be equal to 20

Answer:

12.5 percent; 2/16; 1/8

Step-by-step explanation:

Peter and Mary make up 2 of the clubs members, so the probability that they are chosen is 2/16. This simplifies to 1/8, and in decimal form is .125. Therefore, the percentage form of the probability they are chosen is 12.5 percent.

Answer:

slope = 1

Step-by-step explanation:

midpoint of (2, 4) and (0, -2)

(2 + 0)/2 = 1 and (4 + -2)/2 = 1

(1, 1)

midpoint of (5, 1) and (1, 5)

(5 + 1)/2 = 3 and (1 + 5)/2 = 3

(3, 3)

slope = (3-1)/(3-1) = 2/2 = 1

Answer:

30.9 cm²

Step-by-step explanation:

To find the surface area of this figure, we find the area of the base and the 3 identical sides.

The base is split into two identical right triangles. Let's find the area of one and multiply by two.

Half of 3: 1.5

[tex]1.5\cdot2.6=3.9\\3.9\div2=1.95[/tex]

There are two right triangles:

[tex]1.95\cdot2=3.9[/tex]

The area of one of the sides will be the same thing, except the height is 6.

[tex]1.5\cdot6=9\\9\div2=4.5\\4.5\cdot2=9[/tex]

There are 3 sides identical to this one:

[tex]9\cdot3=27[/tex].

Add 27 and 3.9:

[tex]27+3.9=30.9[/tex]

Hope this helped!

Answer:

30.9 square centimeters

Step-by-step explanation:

3 * 1/2(3)(6) + 1/2(3)(2.6) = 30.9

Answer:

[tex]\boxed{\mathrm{view \ explanation}}[/tex]

Step-by-step explanation:

The difference of two cubes formula is given as:

[tex]a^3-b^3 =(a-b)(a^2 +ab+b^2)[/tex]

Step-by-step explanation:

[tex] {(a - b)}^{3} = {(a - b)}^{2} (a - b)[/tex]

[tex] {a}^{3} - 3{a}^{2} b + 3a {b}^{2} - {b}^{3} = {(a - b)}^{2} (a - b)[/tex]

[tex] {a}^{3} - {b}^{3} + 3ab(a - b)= {(a - b)}^{2} (a - b)[/tex]

[tex] {a}^{3} - {b}^{3}= {(a - b)}^{2} (a - b) + 3ab(a - b)[/tex]

[tex] {a}^{3} - {b}^{3} = (a - b)(( {a}^{2} - 2ab + {b}^{2} ) - 3ab)[/tex]

[tex] {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]

Answer:

Recorrera 495 km con 11 galones de gasolina

Y necesitara 14.44 galones para recorrer 650 km

Step-by-step explanation:

k          g                                                                  k             g

90         2                                                                 90           2

x            11                                                                650         x

=(11 x 90)/2                                                              =(650x2)/90

=990/2                                                                    =1300/90

=495 km                                                                 =14.44

[tex] \Large{ \boxed{ \rm{ \red{Refer \: to \: the \: attachment}}}}[/tex]

➤ Like Here, AB = BC and AD = CD

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Answer:

16b^5

Step-by-step explanation:

8b^2×2b^3

= 16b^2+3

= 16b^5

Answer:

D)16b5

Step-by-step explanation:

8b2×2b3

= 16b2+3

= 16b5

Answer:

What we need to do is simply multiply the values in both columns e.g 4 * 3/36 = 12/36

Please check explanation for complete answer

Step-by-step explanation:

Here, we are concerned about filling the empty columns of the table.

What we want to do here is simply straightforward. All we need to do is to

multiply the values of x by the values of P(x) in each of the individual rows.

Also recall, we do not need to reduce the fractions.

So we have;

2. 3 * 2/36 = 6/36

3. 4 * 3/36 = 12/36

4. 5 * 4/36 = 20/36

5. 6 * 5/36 = 30/36

6. 7 * 6/36 = 42/36

7. 8 * 5/36 = 40/36

8. 9 * 4/36 = 36/36

9. 10 * 3/36 = 30/36

10. 11 * 2/36 = 22/36

11. 12 * 1/36 = 12/36

Answer:

  0, 1, or 2 real solutions

Step-by-step explanation:

Including complex and repeated solutions, a polynomial with real coefficients, and of degree n, always has n solutions.

If you're only concerned about real solutions, a 2nd degree equation in one variable may have 0, 1, or 2 real solutions. Here are some examples.

Answer:

a

Step-by-step explanation:

1:cancel out any answers with equal to since the line is dotted

2:pick any two points of your choice and work out the gradient

3:use the gradient a point on the line and an anonymous point (x,y) to get equation of a line

4:then choose a point (0,0) and substitute x with 0 in the equation to get y (in this case it's -1) which is less than 0 hope it helps

The inequality that is graphed on the coordinate plane is y ≤ [tex]x^{2}[/tex].

The graph of this inequality is a parabola that is facing downwards. The parabola opens downwards because the inequality symbol is less than or equal to (≤). The vertex of the parabola is at the point (0, 0).

The parabola intersects the x-axis at the points (-1, 1) and (1, 1). This means that the values of x that satisfy the inequality are all the values that are less than or equal to 1.

The parabola does not touch the x-axis at any other points, so the values of x that do not satisfy the inequality are all the values that are greater than 1.

Here is a graph of the inequality y ≤ [tex]x^{2}[/tex]:

parabola that is facing downwards and intersects the x-axis at (-1, 1) and (1, 1)Opens in a new window

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parabola that is facing downwards and intersects the x-axis at (-1, 1) and (1, 1)

The other inequalities that are shown in the answer choices are not graphed correctly. The inequality y ≥ [tex]x^{2}[/tex] is graphed as a parabola that is facing upwards. The inequality y = [tex]x^{2}[/tex] is graphed as a line that is not a parabola. The inequality y > [tex]x^{2}[/tex] is not graphed at all.

Therefore, the only inequality that is graphed correctly is y ≤ [tex]x^{2}[/tex].

Learn more about inequality here: brainly.com/question/20383699

#SPJ2

Answer:

[tex]\frac{x^{3} }{4y^{5} }[/tex]

Step-by-step explanation:

Simplifica la expresión

Answer:

y- intercept = - 39

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 12x + 2 ← is in slope- intercept form

with slope m = 12

Parallel lines have equal slopes, thus

y = mx + c ← is the partial equation

To find c substitute (4, 9) into the partial equation

9 = 48 + c ⇒ c = 9 - 48 = - 39 ← y- intercept

Answer:

y-intercept = -39

Step-by-step explanation:

if two lines are parallel it means they have the same gradient so we compare the equation given to the default equation of a line

y=mx+c

y=12x+2

comparing we have the gradient m=12 now finding the equation of the line parallel to the given line we use

y-y1=m(x-x1)

y1=9 and x1=4

y-9=12(x-4)

y-9=12x-48

y=2x-48+9

y=2x-39

comparing to the default equation of a line y=mx+c where c is the y-intercept

therefore the y-intercept is -39

Answer: 4t - 3 < 12

Step-by-step explanation:

Answer:

Complementary effect

Step-by-step explanation:

Answer:

6 = n

Step-by-step explanation:

-3=n/2-6

Add 6 to each side

-3+6 = n/2 -6+6

3 = n/2

Multiply each side by 2

3*2 = n/2 *2

6 = n

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▹ Answer

n = 6

▹ Step-by-Step Explanation

-3 = n/2 - 6

Multiply both sides by 2:

-6 = n - 12

Rearrange the terms:

-n -6 = -12

Calculate:

-n = -6

Change the signs:

n = 6

Hope this helps!

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