From the top of a 200 meters high building, the angle of depression to the bottom of a second building is 20 degrees. From the same point, the angle of elevation to the top of the second building is 10 degrees. Calculate the height of the second building to the nearest hundred meters.

The common ratio between the sum of a certain infinite geometric series is 2. the sum of the squares of all the terms is 3 is, - 1/9

Now, We can formulate;

⇒ { a/ 1-r} = 2

And, a²/ (1 - r²) = 5

⇒ 2a/ ( 1+r ) = 5

⇒ 2(2 - 2r)/ 1 + r = 5

⇒ 4 - 4r = 5 + 5r

⇒ 9r = - 1

⇒ r = - 1/9

Thus, The common ratio between the sum of a certain infinite geometric series is 2. the sum of the squares of all the terms is 3 is, - 1/9

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If the two angles are complementary, then their sum is 90 degrees.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

If the two angles are complementary, then their sum is 90 degrees.

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well, presumably the best deal is the cheaper one, so let's check how much is it for each

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 45.99}}{\left( \cfrac{15}{100} \right)45.99} ~~ \approx ~~ 6.90\hspace{5em}\underset{ Store~1 }{\stackrel{ 45.99~~ - ~~6.90 }{\approx\text{\LARGE 39.09}}}\checkmark \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em} \stackrel{\textit{20\% of 52.99}}{\left( \cfrac{20}{100} \right)52.99} ~~ \approx ~~ 10.60\hspace{4em}\underset{ Store~2 }{\stackrel{ 52.99~~ - ~~10.60 }{\approx\text{\LARGE 42.39}}}[/tex]

The statement that correctly describes the expression |x^3|+5 is 5 more than the absolute value of the cube of a number.

Given this expression: |x^3|+5

| | = This sign means Absolute value,

x^3 = x³ = x × x × x

Hence, the statement that correctly describes the expression |x^3|+5 is : 5 more than the absolute value of the cube of a number.

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The pineapple has 1097g more mass than the apples.

We have,

The difference between two values is the result of subtracting one value from the other.

In this case, we want to find the difference between the mass of the pineapple and the mass of the apples.

To do this, we subtract the mass of the apples from the mass of the pineapple.

The equation for this is:

Pineapple mass - Apple mass = Difference

Substituting the given values:

3547g - 2450g = 1097g

Therefore,

The pineapple has 1097g more mass than the apples.

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Thus the numbers that we are looking for are 8 and -6.

We would have to use a method in which we would call the  numbers that we want to find x and y.

We know that we have to solve the problem as a simultaneous equation so that we can be able to obtain the numbers that we seek.

If

xy = -48 ---(1)

x + y =2 --- (2)

y = -48/x ---(3)

Substitute (3) into (2)

x - 48/x = 2

x^2 - 48 = 2x

x^2 -2x - 48 = 0

x = 8 and x = -6

Thus;

8 + y = 2

y = -6

Or

-6 + y = 2

y = 8

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Missing parts:

What numbers multiply to -48 and add to 2 at the same time

The solutions for the inequality, in order from smallest to largest, are:

-7, -4, -2, 0, 0.9, 0.99, 0.999, 1

Here we have the inequality:

y ≤ 1

All the values that make the inequality true are the values equal or smaller than 1.

So we just need to list these in order from smaller to larger.

The correct order will be:

-7, -4, -2, 0, 0.9, 0.99, 0.999, 1

These are the solutions in order.

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The distinct orders of light bulbs are there if two light bulbs of the same color are considered identical = 4,620

Here, the total number of bulbs = 11

The number of red light bulbs = 3

The number of yellow light bulbs = 2

and the number of  pink light bulbs = 6

We know that the formula for the permutation with repetition is:

n! / (n1! × n2! x ... × nk!)

We use this formula to find the required number of light bulbs.

Here, two light bulbs of the same color are considered identical

We divide by 3! in order to adjust for overcounting, because we have 3 red light bulbs.

simmilarly for the 2 yellow light bulbs, we divide with 2!.

and for the 6 pink light bulbs, we divide by 6!

Thus, the total number of distinct orders of bulbs will be:

11! / (3! × 2! × 6!) = 4,620

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The requried measure of the angles is given as:

(1) ∠OLQ = 32, (2) ∠NQP = 38°, (3) ∠NLP = 38°, and (4) ∠NPL = 52°.

As shown in the figure,
(1) Following the property of angle subtended by an arc on the center of the circle and at a point on the circumference of a circle,
∠OLQ = ∠OQL = 64/2 = 32°.

(2)

Following the figure,
∠NQP = ∠LQP - ∠LQN
          = ∠LQP-[∠OQL+∠MQN]
          = 90 - [32+20]
          = 38°

Similarly,
∠NLP = 38°
∠NPL = 52°

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The volume of the solid figure is 75 ft³

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The volume of a figure is the amount of space it occupies in its three dimensional state.

To get the surface area:

Area of base = (6 ft * 2 ft) + (7 - 6)ft * 3 ft  = 15 ft²

Volume of figure = area of base * height = 15 ft² * 5 ft = 75 ft³

The volume of the figure is 75 ft³

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The percentage of boxes with green lamps is 60%, the correct option is C.

We are given that;

Number of boxes= 40

Green lamp boxes= 24

Now,

To calculate the percentage of boxes that contain green lamps, you need to divide the number of boxes with green lamps by the total number of boxes and then multiply by 100. This is according to the formula for finding a percentage of a number12.

=(24 / 40) x 100 = 60%

Therefore, by percentage the answer will be 60%.

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The surface area of the cylinder in terms of pi is:

S = pi*301 cm²

We know that for a cylinder of radius R and height H the surface area is:

S = pi*( 2RH + R²)

Here the height is 18 cm and the diameter is 14cm, then the radius is.

R = 14cm/2 = 7cm

Then the surface area will be:

S = pi*(2*7cm*18cm + (7cm)*7cm)

S = pi*301 cm²

That is the surface area in terms of pi.

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The range of the function f(x) = |x| + 5 include the following; B. R: {f(x) ∈ ℝ | f(x) ≥ 5}.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞} or -∞ ≤ x ≤ ∞.

Range = {5, ∞} or 5 ≤ f(x) ≤ ∞.

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Brenda's class left for the field trip at 10:16 A.M.

We have,

Let's break down the time of Brenda's class field trip:

50 minutes to drive to the museum

3 hours and 45 minutes (or 225 minutes) at the museum

56 minutes to drive back to school

Adding up all of these times, we get:

50 + 225 + 56 = 331 minutes

So the field trip took a total of 331 minutes.

If the class arrived back at school at 3:47 P.M., and we subtract 331 minutes from 3:47 P.M., we can determine the time they left for the field trip:

3:47 P.M. - 331 minutes

= 10:16 A.M.

Therefore,

Brenda's class left for the field trip at 10:16 A.M.

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Answer:

< - 1, 5 >

Step-by-step explanation:

a = < - 5, 2 >

b = < 4, 3 >

a + b

= < - 5, 2 > + < 4, 3 >

add corresponding elements

= < - 5 + 4, 2 + 3 >

= < - 1, 5 >

The number of scoops of birdseed Sarah puts in the feeder n = 2

Given data ,

Let the number of scoops of birdseed Sarah puts in the feeder be n

While utilizing a scoop that can contain 1/4 cup of birdseed, Sarah's bird feeder holds 1/2 cup of birdseed. We must divide the capacity of the bird feeder by the capacity of the scoop to determine how many scoops Sarah will add to the feeder.

On simplifying the equation , we get

1/2 ÷ 1/4 = n

n = 1/2 x 4/1

n = 4/2

n = 2 scoops

Hence , the equation is solved and n = 2

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Question 11 seems to have strange typos in it. Please double-check to make sure it has been typed correctly.

I'm not sure how to answer that one.

----------

I'll focus on Question 12.

The long division scratch work is shown in the image attachment below.

The answer to problem 12 is  x+9 remainder -7x-7

Please let me know if you have questions about any step of the polynomial long division process.

Answer:

The answer would be option A

Step-by-step explanation:

-14 times 8=-122

The value of the most expensive car loan that Cindy can afford is $13,712

We are given that;

Amount= $215

Percentage= 2.1%

PMT = 215 i = 0.021 / 12 = 0.00175 (the annual interest rate divided by 12 months) n = 6 × 12 = 72 (the number of months in 6 years)

Now,

The formula for the present value of an annuity is:

PV = PMT × (1 - 1/(1 + i)^n) / i

where:

PV = present value PMT = payment amount i = interest rate per period n = number of periods

Plugging these values into the formula, we get:

PV = 215 × (1 - 1/(1 + 0.00175)^72) / 0.00175 PV = 215 × (1 - 0.888) / 0.00175 PV = 215 × 0.112 / 0.00175 PV = 13,712

Therefore, by the percentage the answer will be $13,712.

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The relation between lengths of AB and BC are,

⇒  Lenght of AB and BC are different.

We have to given that;

Triangles ABD and BDC are given.

Here, All the angles of a triangle ABD are different from angles of BDC.

Hence, We get;

Both triangle ABD and BDC are congruent.

So, All the sides of ΔABD are different from the sides of different from ΔBDC.

Hence, Lenght of AB and BC are different.

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The  inequality given that the function f is increasing over it s domain

f(x²-2)<f (7x-8), Df =  (-∞,2) is: x ∈ (-∞,1) U (6,2).

We know the  values of x within the domain by setting the intersection points of the two functions f(x2-2) and f(7x-8).

f (x²-2) = f (7x-8)

So,

x²-2 = 7x-8

Simplify and find x

x² - 7x + 6 = 0

(x - 1)(x - 6) = 0

x = 1 or x = 6

The domain (-,2) is divided into the intervals (-,1), (1,6), and (6,2). Now let assess the interval endpoints because f is rising:

For x < 1:

x² - 2 < 7x - 8

x² - 7x + 6 < 0

(x - 1)(x - 6) < 0

For 1 < x < 6:

x² - 2 < 7x - 8

x² - 7x + 6 < 0

(x - 1)(x - 6) > 0

For x > 6:

x² - 2 < 7x - 8

x² - 7x + 6 < 0

(x - 1)(x - 6) < 0

Since f is rising across its domain the inequality f(x2-2) f(7x-8) has the following solution: x ∈ (-∞,1) U (6,2).

Therefore the inequality is  x ∈ (-∞,1) U (6,2).

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Answer:

80%

Step-by-step explanation:

After all the trade he got 50 stickers

40 Big

10 small

50 stickers is 100%

40B stickers is ??

WE multiply 40 by 100 then divide by 50

so 80%

The result of -3u + 5v is the vector (12, -34).

Let's start by defining the two given vectors u and v:

u = (1, 3)

v = (3, -5)

To find the dot product of two vectors, we need to multiply their corresponding components and then add up the results. The formula for the dot product of two vectors can be written as:

u · v = u₁v₁ + u₂v₂ + ... + uₙvₙ

where u₁ and v₁ are the first components of vectors u and v, u₂ and v₂ are the second components, and so on up to un and vₙ, which are the nth components.

Using this formula, we can find the dot product of u and v as follows:

u · v = (1)(3) + (3)(-5)

= 3 - 15

= -12

So, the dot product of vectors u and v is -12.

Next, we need to calculate -3u + 5v. To do this, we need to multiply each component of vector u by -3 and add it to the corresponding component of vector v multiplied by 5. We can write this as follows:

-3u + 5v = (-3)(u₁, u₂) + (5)(v₁, v₂)

= (-3)(1, 3) + (5)(3, -5)

= (-3, -9) + (15, -25)

= (12, -34)

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Length of board should Jessica buy is 4.4 feets.

Step-by-step explanation:

Height of the ramp =

Distance of the porch from the ground = x

Inclination of the ramp,θ = 35°

In triangle ABC,

AB =

AC = x

θ = 35°

According trigonometric ratios:

Length of board should Jessica buy is 4.4 feets.

Answer:

how many or how much or what is the amount

Step-by-step explanation:

quantity means

the amount or number of a material or immaterial thing not usually estimated by spatial measurement.

if I were to ask you " How many apples are in that bag" Im basically asking what is the quantity of apples in that bag. So, in scatter plots it's asking you, how many points are on this graph of scatter points

The Venn diagram for (D ⋃ E) ⋃ F will be the ovarlapped region of D,E and F.

To represent the sets D, E, and F in the Venn diagram, we first construct three overlapping circles. Then, beginning with the innermost operation and moving outward, we shade the regions corresponding to the set operations in the expression.

We shade the area where the circles for D and E overlap because the equation (D ⋃ E)  denotes the union of the sets D and E. All the elements in D, E, or both are represented by this area.

The union of (D ⋃ E) with F is the next step. This indicates that we darken the area where the circle for F crosses over into the area that we shaded earlier. All the components found in sets D, E, F, or any combination of these sets are represented in this region.

The final Venn diagram should include three overlapping circles, with (D ⋃ E) ⋃ F shaded in the area where all three circles overlap.

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Victoria's statement that her running speed is faster an elephant's does not make sense because it is based on the comparison of unlike units of measurement.

Elephant's running speed = 100 yards in 20 seconds

= 5 yards per second (100 ÷ 20)

1 yard = 3 feet

5 yards = 15 feet (5 x 3)

The elephant's running speed = 15 feet per second.

Victoria's running speed = 60 feet in 10 seconds

= 6 feet per second (60  ÷ 10)

Thus, we conclude that the elephant's running speed is 15 feet per second, while Victoria does 6 feet per second, making her claim untrue.

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Answer:proving that EFGH is a square: points E,F,G,H

separate the sides of the square ABCD into two lines. if AE=BF=CG=DH then

AH=DG=EB=FC and it shows that if we connect the points E,F,G,H to each other with line we will have a square

HAE~EBF~FCG

Answer:

correct answer is D

Step-by-step explanation: