Answer:
1) From the measure of 40°, you can write:
tan(40°) = 100/x, where x is the base from the building to the tower
⇒x=100/tan(40°) = 119,18 m
2) From the measure of 30°, you can write
tan(30°) = y / 119,18, where y is the height from the roof of Jill's building to the top of the tower.
Then, y = tan(30°) * 119,18 = 68,81 m
3) The height of Jill's building is 100 - 68,81 = 31,19 m
When the height of the tower is 100 meters, the height of Jill's apartment building is 31.19m
How to calculate the height?Let the base from the building to the Rowe be represented by x. Based on the information given, the value will be:
x = 100/tan 40°
x = 119.18m
The height can be represented as:
= 100 - [tan30° × 119.18]
= 100 - 68.81
= 31.19m
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4 + h ≤ 7 and h + 1 > 3 What is the value of the unknown number, h?
Answer:
2 < h <= 3
Step-by-step explanation:
4 + h <= 7
h <= 3 (subtract 4 on both side)
h + 1 > 3
h > 2 (subtract 1 on both side)
So, 2 < h <= 3
The distance from Parrot Point Airport to the Ivy Cliffs is 178 miles at and angle of 7.1 degrees northeast. There is a wind blowing southeast at 30 miles per hour. You want to make this trip in 2 hours by flying straight there. At what speed* and heading should you fly? * Round the speed to the nearest tenth of a mile per hour and angle to the nearest tenth of a degree. Where north is 0 degrees and positive is clockwise.
Answer:
The speed is 74.0 miles per hour and the angle is 65.1° north-east
Step-by-step explanation:
We resolve the distance moved by the wind and plane into horizontal and vertical components. The direction moved horizontally by the plane is 178sin7.1 = 22 miles.
Since the wind is moving south east, it is at 45 south of east or a bearing of 135.
Since the wind speed is 30 mph and it takes 2 hours to complete the trip, the horizontal distance moved by the wind is vtcos135 = 30 × 2cos45 = 42.43 miles
Also, the vertical displacement moved by the wind is vtsin135 = -30 × 2 sin45 = -42.43 miles
The displacement moved vertically by the plane is 178cos7.1 = 176.64 miles
The total horizontal displacement of the plane is 22 miles + 42.43 miles = 62.43 miles
The total vertical displacement of the plane is 176.64 miles - 42.43 miles = 134.21 miles
The resultant displacement is thus d = √(62.43² + 134.21²) = 148.02 miles
The direction of this displacement is thus
Ф = tan⁻¹(total vertical displacement/total horizontal displacement)
= tan⁻¹(134.21/62.43)
= tan⁻¹(2.1498)
= 65.05°
= 65.1° to the nearest tenth degree.
The speed is thus v = distance/ time = 148.02 miles/ 2 hours = 74.01 mph ≅ 74 mph. Since the direction of the displacement is the direction of the velocity, the velocity is thus 74 miles per hour at 65.1° north-east.
So the speed is 74.0 miles per hour and the angle is 65.1° north-east
A printer can print 12 pages in 9 seconds. What is the closest estimate of the number of pages it can print in one minute?
Answer:
80 pages
Step-by-step explanation:
Let's use a ratio to solve:
pages : seconds
12 : 9
4 : 3
[tex]p[/tex] : 60
It would seem that [tex]p[/tex] would equal 80. The printer can print 80 pages in 60 seconds or one minute.
WILL GIVE BRAILIEST! Find the mean of the data in the bar chart below. _________puppets
Answer: 2.5
Step-by-step explanation:
To find a mean, the average, we have to add everything together.
So we add 1 + 4 + 3 + 2, which is equal to 10. The next step to find the average is to divide by the total number of “things” which is the 4 puppeteers.
10/4 is 2.5
Help!!!!
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer.
Answer:
[tex]Slope (m) = -\frac{2}{3}[/tex]
Step-by-step explanation:
To find the slope of the line of the graph, pick any 2 points on the line as your coordinate pairs.
Thus, on the line, let's pick 2 points as our coordinate pairs at:
When x = -6, y = 5 => (-6, 5), and
When x = 3, y = -1 => (3, -1)
Let (-6, 5) be (x1, y1), and (3, -1) be (x2, y2)
[tex] Slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] Slope (m) = \frac{-1 - 5}{3 - (-6)} [/tex]
[tex] Slope (m) = \frac{-1 - 5}{3 + 6} [/tex]
[tex] Slope (m) = \frac{-6}{9} [/tex]
[tex]Slope (m) = -\frac{2}{3}[/tex]
How many different committees of 4 people can be chosen from a group of 21?
Answer:
There are 21 ways to choose the first person, 20 ways to choose the second, 19 ways for the third and 18 ways for the fourth so the answer is 21 * 20 * 19 * 18 = 143640.
I NEED HELP QUICK like very quick
Answer:
2.5 or 2 1/2
Step-by-step explanation:
i caculated do order of operations
If the lengths of the legs of a right triangle are 3 and 10, what is the length of the hypotenuse?
Answer:
a = √109 or 10.44Step-by-step explanation:
To find the hypotenuse we use Pythagoras theorem which is given by
a² = b² + c²
where a is the hypotenuse
So we have
a² = 10² + 3²
a² = 100 + 9
a² = 109
a = √109 or 10.44Hope this helps you
Answer:
10.4
Step-by-step explanation:
Help please!!!!!!!!!!
Answer:
H. 1/9.
Step-by-step explanation:
The area of a circle is calculated by solving for π[tex]r^2[/tex].
The smallest circle has an area of π[tex]1^2[/tex] = π * 1 = π.
The middle ring will then have an area of π[tex]2^2[/tex] - π = π * 4 - π = 4π - π = 3π.
The largest ring will then have an area of π[tex]3^{2}[/tex] - π[tex]2^{2}[/tex] = 9π - 4π = 5π.
5π + 3π + π = 9π
So, the probability of hitting the innermost circle will be π / 9π = 1 / 9.
Your answer is H. 1/9.
Hope this helps!
HELP ME PLZ! I will not accept non sense answers. BRAINLIEST will be given to the person who gets it correct with full solutions.
[tex]A = 1500(1.00167)^{12t}[/tex]
=================================
Explanation:
You could use the formula
[tex]A = P(1+\frac{r}{n})^{nt}[/tex]
to plug in P = 1500, r = 0.02 and n = 12 to get the answer above. This is the compound interest formula. The interest rate r is divided into n = 12 to account for monthly compounding. The original exponent t turns into 12t. So for instance, if t = 2 years go by, then 12*t = 12*2 = 24 months have gone by.
AB is tangent to circle D. Find the value of x.
Answer:
c 15
Step-by-step explanation:
Tangent AB is tangent to circle D at point A. The angle made by a tangent to a circle and a radius of the circle at the point of tangency is a right angle. That means that angle is a right angle, and triangle ABD is a right triangle.
We can use the Pythagoren theorem.
a^2 + b^2 = c^2
x^2 + 20^2 = (x + 10)^2
x^2 + 400 = (x + 10)(x + 10)
x^2 + 400 = x^2 + 10x + 10x + 100
400 = 20x + 100
20x = 300
x = 15
Drag the tiles to the correct boxes. Not all tiles will be used. Consider the following function: f(x) = -3/4x+9. Place the steps for finding f^-1(x) in the correct order.
Answer:
The steps include:
1. y = –3/4x + 9
2. x = –3/4y + 9
3. x – 9 = –3/4y
4. –4/3(x – 9) = y
5. y = –4/3x + 12
6. f¯¹(x) = –4/3x + 12
Step-by-step explanation:
f(x) = –3/4x + 9
The inverse, f¯¹(x) of the above expression can be obtained as follow:
f(x) = –3/4x + 9
Let y = f(x)
y = –3/4x + 9
Interchange x and y
x = –3/4y + 9
Making y the subject of the expression, we have:
x = –3/4y + 9
Rearrange
x – 9 = –3/4y
Cross multiply
4(x – 9) = –3y
Divide both side by –3
–4/3(x – 9) = y
Clear bracket
y = –4/3x + 12
Replace y with f¯¹(x)
f¯¹(x) = –4/3x + 12
Therefore, the steps include:
1. y = –3/4x + 9
2. x = –3/4y + 9
3. x – 9 = –3/4y
4. –4/3(x – 9) = y
5. y = –4/3x + 12
6. f¯¹(x) = –4/3x + 12
Answer:
1. y = –3/4x + 9
2. x = –3/4y + 9
3. x – 9 = –3/4y
4. –4/3(x – 9) = y
5. y = –4/3x + 12
6. f¯¹(x) = –4/3x + 12
Step-by-step explanation:
f(x) = –3/4x + 9
The inverse, f¯¹(x) of the above expression can be obtained as follow:
f(x) = –3/4x + 9
Let y = f(x)
y = –3/4x + 9
Interchange x and y
x = –3/4y + 9
Making y the subject of the expression, we have:
x = –3/4y + 9
Rearrange
x – 9 = –3/4y
Cross multiply
4(x – 9) = –3y
Divide both side by –3
–4/3(x – 9) = y
Clear bracket
y = –4/3x + 12
Replace y with f¯¹(x)
f¯¹(x) = –4/3x + 12
Therefore, the steps include:
1. y = –3/4x + 9
2. x = –3/4y + 9
3. x – 9 = –3/4y
4. –4/3(x – 9) = y
5. y = –4/3x + 12
6. f¯¹(x) = –4/3x + 12
Step-by-step explanation:
what is known as terms of ratio
Answer: The mathematics terms of ratio are the indicates many times one number contains to the another number.
Step-by-step explanation:Terms of ratio may be specified both constitution number or value to the equal correspond to the equal ratio.
"a to b"
"a:b"
There are Sixteen and eight apples and lemon in the table of fruit the ratio(that is 16:8 to the equivalent the ratio 8:4).
a:b=(a+b):a or ratio is equivalently a:b=(1+b/a):1.
The number in a terms ratio quantities of both numbers are to be positive
Solve for x. Write both solutions, separated by a
comma.
7x2 - 4x - 3=0
Answer:
x = - 3/7 or x = 1Step-by-step explanation:
7x² - 4x - 3 = 0
Rewrite - 4x as a difference
That's
7x² - 7x + 3x - 3 = 0
Factorize the expression
7x( x - 1) + 3 ( x - 1) = 0
(7x + 3)( x - 1 ) = 0
7x + 3 = 0 x - 1 = 0
7x = - 3 x = 1
x = -3/7
The solutions are
x = - 3/7 or x = 1
Hope this helps you
A cylinder shaped storage tank has a radius of (x+5) metres and a height of x metres. Determine the dimensions (round to two decimal places) of the tank if the volume is about 192 cubic metres.
Answer:
Radius = 6.46 meters
Height = 1.46 meters
Step-by-step explanation:
The volume of a cylinder = πr²h
In the above question, we were given
r = (x + 5) meters
h = x meters
Volume = 192 cubic meters
Hence,
192 = π × (x + 5)² × x
192 = π × (x² + 10x + 25) × x
192 = π × (x³ + 10x² + 25x)
Divide both sides by π
192/π = x³ + 10x² + 25x
61.115498147 = x³ + 10x² + 25x
x³ + 10x² + 25x - 61.12
This Quadratic equation is a polynomial
x = 1.46119
From the above:
Radius = (x + 5)meters
Radius = 1.46119 + 5 = 6.46119 meters
Approximately to 2 decimal places = 6.46 meters
Height = x meters
Height = 1.46119 meters
Approximately to 2 decimal places = 1.46 meters
Starting from an airport, an airplane flies 290 miles east and then 290 miles northwest. How far, in miles, from the airport is the plane? (Round your answer to the nearest mile.)
Answer:
The airplane is 222 miles far from the airport.
Step-by-step explanation:
After a careful reading of the statement, distances can be described in a vectorial way. A vector is represented by a magnitude and direction. That is:
Airplane flies 290 miles (east) (290 km with an angle of 0º)
[tex]\vec r_{A} = (290\,mi)\cdot i[/tex]
Airplane flies 290 miles (northwest) (290 km with and angle of 135º)
[tex]\vec r_{B} = [(290\,mi)\cdot \cos 135^{\circ}]\cdot i + [(290\,mi)\cdot \sin 135^{\circ}]\cdot j[/tex]
The resultant vector is equal to the sum of the two vectors:
[tex]\vec r_{C} = \vec r_{A} + \vec r_{B}[/tex]
[tex]\vec r_{C} = \{(290\,mi) + \left[(290\,mi)\cdot \cos 135^{\circ}\right]\}\cdot i + \left[(290\,mi)\cdot \sin 135^{\circ}\right]\cdot j[/tex]
[tex]\vec r_{C} = (84.939\,mi)\cdot i + (205.061\,mi)\cdot j[/tex]
The magnitude of the final distance of the airplane from the airport is obtained by the Pythagorean Theorem:
[tex]\|\vec r_{C}\|=\sqrt{(84.939\,mi)^{2}+(205.061\,mi)^{2}}[/tex]
[tex]\|\vec r_{C}\| = 221.956\,mi[/tex]
The airplane is 222 miles far from the airport.
A hair color manufacturer performed a survey which was normally distributed. They found that the average age at which a person's hair starts turning gray is 32 years, with a standard deviation of 4 years. Which of the following graphs displays the normal distribution of the average age at which a person's hair starts turning gray?
W.
X.
Y.
Z.
Answer: X
Step-by-step explanation:
g(x)= √x+3 help plsss
Answer:
All real values of x such that x ≥-3
Step-by-step explanation:
g(x) = sqrt(x+3)
A sqrt must be greater than or equal to zero
sqrt (x+3) ≥ 0
Square each side
x+3≥ 0
Subtract 3 from each side
x ≥-3
The restrictions on x are x ≥-3
That means the domain is x ≥-3
All real values of x such that x ≥-3
Answer:
[tex]\boxed{\mathrm{B}}[/tex]
Step-by-step explanation:
[tex]g(x)=\sqrt{x+3}[/tex]
A square root must have a value of greater than or equal to 0.
[tex]\sqrt{x+3}\geq 0[/tex]
Square both sides.
[tex]x+3\geq 0[/tex]
Subtract 3 from both sides.
[tex]x\geq -3[/tex]
Explain why 7 x 9 x 11 x 13 + 13 is a composite number.
Answer:
7 x 9 x 11 x 13 + 13 is a composite number because the answer is a positive number which is 9022.
7 x 9 x 11 x 13 + 13 is a positive integer that can be formed by multiplying small positive numbers which are 7, 9, 11 and 13. Equivalently, 9022 is a positive integer that has at least one divisor other than 1 and itself. For example, 9022 can be divided by 2. 9022 is exactly a number but it is not a prime number.
I hope you will understand my explanation!
Find the missing side. Round your answer to the nearest tenth.
Answer:
44.8
Step-by-step explanation:
cos α = adjacent leg/hypotenuse
cos 48° = 30/x
x = 30/(cos 48°) = 44.8
Help me pLEASSSSE ! do it step by step so I can see how y'all do it.
Answer:
5
Step-by-step explanation:
Since y equals 200 + 10x and y also equals 5x, then
200 + 10x = 50x
Subtract 10x from both sides.
200 = 40x
Divide both sides by 40.
5 = x
Answer: He must sell 5 sculptures.
For the following systems of equations, match each diagram on the left with its solution on the right.
Answer:
1. (2,1)
2. (6,-1)
3.(-2,3)
Answer:
1. (2,1)
2. (6,-1)
3. (-2,3)
Step-by-step explanation:
Each of the answer is consistent system because the lines intersect at one point, which is one solution.
please i need help look at picture
Answer:
84
Step-by-step explanation:
Surface area is the combined area of the 2 dimensional planes.
6 × 5 + 3 × 4 × 1/2 × 2 + 6 × 3 + 4 × 6
30 + 12 + 18 + 24
= 84
The surface area is 84 square centimeters.
need help a s a p HURRYYYYY
Step-by-step explanation:
v= 4/3πr³
4/3×314/100×8×8×8
•
= 2,143.573
To decrease a number by 40%, what do we multiply by???
Answer:
Step-by-step explanation:
to decrease a number by 40% i would do
100% = number you got
50% divide by 2
10%= dived 100% number by 10 then take the 10% away from the 50% to get 40%
then take the 40% away from the 100%
hope this helps :)
A piece of string 8 inches long is cut into two pieces, one of which is of length x inches. If this piece is made into the circumference of a circle, and the other piece is made into the circumference of a square, then the combined area of the circle and square, as a function of x, is:
Answer:
2πr + 4a = 8
Step-by-step explanation:
En un rectangulo el ancho es menor en 5cm al largo . si el P= 38cm calcule su area
Answer:
84cm²
Step-by-step explanation:
Perímetro de un rectángulo = 2L + 2W
Representemos la longitud del rectángulo = L
En la pregunta anterior se nos dijo que el ancho del rectángulo = es menor que 5 en la longitud
Por lo tanto, ancho del rectángulo = L - 5
Perímetro del rectángulo = 38 cm
Por lo tanto
38 = 2 (L) + 2 (L - 5)
38 = 2L + 2L - 10
38 + 10 = 4L
48 = 4L
L = 48/4
L = 12 cm
La longitud del rectángulo = 12 cm
Como L = 12, encontramos el ancho
Ancho = L - 5
= 12 cm - 5 cm
= 7 cm
El ancho del rectángulo = 7 cm
En la pregunta nos pidieron encontrar el área del rectángulo.
Área del rectángulo = Largo × Ancho
Área del rectángulo = 12 cm × 7 cm
Área del rectángulo = 84cm²
For what values of x is x2 + 2x = 24 true?
–6 and –4
–4 and 6
4 and –6
6 and 4
Answer:
Option C
x²+ 2x -24=0
x²+6x-4x-24= 0
x(x+6) -4(x+6) = 0
(x+6)(x-4) = 0
x= -6 and 4
Therefore, for x = 4 and -6 , the above given equation is true.
Lines m and n are parallel. Which of the other 5 named angles have a measure of 110°?
Which of these are true?
Answer:
<2, <5
Step-by-step explanation:
<2 is a vertical angle so it is equal to 110
<5 is a corresponding angle and since the lines are parallel it is also equal to 110
52.85 rounded to the nearest tenth
Answer: 52.9
Step-by-step explanation:
The value 5 is rounded up.
Hope it helps <3
Answer:
52.9
Step-by-step explanation:
round up using the last number. since its 5, you round up