The elevation gained after travelling 1.5 miles will be 3960ft.
Step-by-step explanation:
Angle of elevation = 30°
Distance travelled= 1.5 miles
1 mile = 5280 ft.
1.5 miles = 5280 x 1.5
= 7920 ft.
The height from the ground can be calculated by,
sin 30° = height / 7920
1/2 = height / 7920
Height = 7920/2
= 3960 ft.
The elevation gained after travelling 1.5 miles will be 3960ft.
Final answer:
To determine the elevation gain over 1.5 miles on a road with a 30° angle of elevation, the sine function reveals that the elevation gain is 0.5 * 1.5 miles * 5280 feet/mile, which calculates to approximately 3960 feet.
Explanation:
To calculate the elevation gain when traveling 1.5 miles on a road with a 30° angle of elevation, we can use trigonometric functions. Specifically, the sine function is useful, because it relates the angle of a right triangle to the ratio of the opposite side (elevation gain) over the hypotenuse (distance traveled).
The sine of a 30° angle is 1/2, and if the hypotenuse is 1.5 miles, we can find the length of the opposite side by multiplying:
sine(30°) = elevation gain / (1.5 miles)
0.5 = elevation gain / (1.5 miles * 5280 feet/mile)
elevation gain = 0.5 * 1.5 miles * 5280 feet/mile
elevation gain = 0.5 * 1.5 * 5280 feet
elevation gain ≈ 3960 feet
Therefore, you would gain approximately 3960 feet in elevation after traveling 1.5 miles on the road.
Solve x2 + 12x + 6 = 0 using the completing-the-square method.
Ox= 6 + V30
Ox= 6+ V30
Ox= 60 V6
Ox= 6 + V6
[tex] {x}^{2} + 12x + 6 = 0 \\ D = {12}^{2} - 4 \times 6 = 144 - 24 = 120 = \\ = (2 \sqrt{30} )^{2} \\ x_1= \frac{ - 12 + 2 \sqrt{30} }{2} = - 6 + \sqrt{30} \\ x_2= \frac{ - 12 - 2 \sqrt{30} }{2} = - 6 - \sqrt{30} [/tex]
But i don't see correct answer here
Ox= 6 + V30
Ox= 6+ V30
Ox= 60 V6
Ox= 6 + V6
or maybe i don't understend something
Solve.
{y=x−63x+2y=8
Use the substitution method.
Write your answer as a coordinate point (x,y).
Find the volume of this cylinder. Give your answer to one decimal place.
[tex]V = \pi r^{2} \times h[/tex]
[tex]r = 11 \div 2 = 5.5 \\ h = 14 \\ \pi = 3.14[/tex]
[tex]V = 3.14 \times 5.5 ^{2} \times 14 = 1,329.79[/tex]
Answer: V=1,329.8
Answer:
Step-by-step explanation:
Given
diameter (d) = 11 cm
Height(h) = 14 cm
first calculating the radius
radius = d/2 = 11/2 = 5.5 cm
Now
Volume of the cylinder
=[tex]\pi r^{2}h[/tex]
= 3.14 * (5.5)^2 * 14
= 1329.8 cm^3
Hope it will help
Which value is
equivalent to 2+12/2
A. 6
B. 7
C. 8
D. 12
Answer:
8
Step-by-step explanation:
I know its 8 because of using PEMDAS
well first in the equation you can divide and add so in PEMDAS diving comes before adding so 12/2=6 and 2+6=8
Explain the steps used to solve x - 2 = v ( x + 10) and check for extraneous solutions.
Answer:
x = 6
Step-by-step explanation:
Given
x - 2 = [tex]\sqrt{x+10}[/tex]
Square both sides to clear the radical
(x - 2)² = x + 10 ← expand left side using FOIL
x² - 4x + 4 = x + 10 ( subtract x + 10 from both sides )
x² - 5x - 6 = 0 ← in standard form
(x - 6)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 1 = 0 ⇒ x = - 1
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = - 1 : left side = - 1 - 2 = - 3
right side = [tex]\sqrt{-1+10}[/tex] = [tex]\sqrt{9}[/tex] = 3 ≠ - 3
---------------------------------------------------
x = 6 : left side = 6 - 2 = 4
right side = [tex]\sqrt{6+10}[/tex] = [tex]\sqrt{16}[/tex] = 4
----------------------------------------------
Thus x = 6 is the solution, x = - 1 is an extraneous solution
AngleFAE measures 72º. What other angle must measure
72°?
Angle BFD
Angle DEA
Angle EDF
Angle FBE
Answer: FBE
Step-by-step explanation:
EDGE
I need to know if the following pairs of expressions are equivalent!
10a - 7a and 5a + 2a - 4a
9 - 4y and 4y - 9
6 + s and 6s
2c + 6c + 9 - c - 4 and 7c + 5
Answer:
Step-by-step explanation:
1) 10a - 7a = 3a {10a & 7a are like terms. So we can subtract}
5a + 2a - 4a = 7a - 4a = 3a {5a, 2a, 4a are like tems}
So, 10a - 7a and 5a + 2a - 4a are equivalent expressions
2) 9 - 4y and 4y - 9 are not equivalent
3) 6 + s means 6 is added to s
6s means 6 is multiplied by s.
6 + s and 6s are not equivalent expressions
4) 2c + 6c +9 - c - 4 = 2c + 6c - c + 9 - 4
= 8c - c + 5
= 7c + 5
7c + 5
2c + 6c +9 - c - 4 and 7c + 5 are equivalent expressions
Solve for x.
х/5= 20
0. 25
4
10
100
Answer:
100
Step-by-step explanation:
x = 5 × 20 = 100
.........................
Jeremy's scores for the first 20 times he played the card game, Clubs and Swords, are listed. 50, 199, 246, 356, 89,
210, 391, 325, 273, 260, 100, 172, 123, 167, 194, 172, 23, 426, 75,239
Complete the Frequency Table to display Jeremy's scores.
Score
Frequency
0-100
_________
Answer:
Score: 0 - 100
Frequency: 5
Score: 100 - 200
Frequency: 6
Score: 200 - 300
Frequency: 5
Score: 300 - 400
Frequency: 3
Score: 400 - 500
Frequency: 1
(I NEED HELP ASAP) plz
Given:
The two angles A and B are vertical angles.
The measure of ∠A is x and the measure of ∠B is 5x - 20.
We need to determine the measure of ∠A.
Value of x:
Since, the angles A and B are vertical angles and the vertical angles are always congruent.
Thus, we have;
[tex]\angle A=\angle B[/tex]
Substituting the values, we have;
[tex]x=5x-8 0[/tex]
[tex]0=4x-80[/tex]
Adding both sides of the equation by 80, we have;
[tex]80=4x[/tex]
[tex]20=x[/tex]
Thus, the value of x is 20.
Measure of ∠A:
The measure of ∠A can be determined by substituting x = 20 in the measure of angle A.
Thus, we get;
[tex]\angle A=20^{\circ}[/tex]
Thus, the measure of ∠A is 20°
If triangle ABC is similar to DEF, what is the measure of angle F?
Answer:43
Step-by-step explanation:118+15+x=180
x=43
Answer:
Angle F is 47°
Step-by-step explanation:
The measure of all the angles on a triangle is 180°, so you subtract the 2 given angles (A and B) to find the 3rd angle (C). That third angle is equal to the corresponding angle (F) on the similar triangle (DEF).
Can someone please help
I’ll give brainliest
Answer:
2. a) 0.80a + 1.25c =i
b) 4 x 0.80 = 3.2
2 x 1.25 = 2.5
3.2 + 2.5 = 5.7
4. a) 30
b) 9
c) 50
d) 22.4
Use the drop-down menu to complete the statement.
Based on the data in the line graph, you can predict
there will likely be
-fewer
-more
-the same number of
In December compared to October
Answer: fewer
Step-by-step explanation: The data has a positive trend, then a negative. And using common sense, since when do people go to the pool in December unless indoors, even then it is rare. Some questions require common sense too BTW.
what is the experimental probability of rolling a number less than 4?
Answer:
50%
Step-by-step explanation:
In dice, there are 6 numbers, and less than 4 is 1, 2, or 3. 3/6=50%
PLEASE HELP!!! 50 POINTS AWARDED!!
Answer:
answers below
Step-by-step explanation:
1. no
2. yes
3. no
4. yes
5. no
6. yes
7. no
8. no
9. no
10. no
11. no
12. yes
Answer:
Below.
Step-by-step explanation:
1. No because there is a one-to-many relation in the diagram ( 8 maps to 3 and also to 4.
2. Yes. It is a one-to-one mapping.
3. Yes. It consists of on-to-one and many to one mapping.
4. No. Because it fails the vertical line test.
5. No. As number 4.
6. Yes . this passes the vertical line test.
7. Yes.
8. No. Input 1 maps to output 4 and output 7.
9. Yes.
10. No. Because of the (3, 7) and the (3, 6).
11. No , because 1 maps to 8, 2 and 7.
12. Yes.
What is the surface area of the prism in square inches?
Answer:
The answer is 252 square inches
How do you write this number using words?
274,075
Answer:
two hundred seventy four thousand seventy-five
Answer: Step-by-step explanation: 274,075 written in words is:
Two Hundred Seventy Four Thousand Seventy-Five
Find the area of the semicircle.
Given:
Given that the radius of the semicircle is 4 units.
We need to determine the area of the semicircle.
Area of the semicircle:
The area of the semicircle can be determined using the formula,
[tex]A=\frac{\pi r^2}{2}[/tex]
Substituting π = 3.14 and r = 4, we get;
[tex]A=\frac{3.14 \times (4)^2}{2}[/tex]
Simplifying, we get;
[tex]A=\frac{3.14 \times 16}{2}[/tex]
Multiplying, we get;
[tex]A=\frac{50.24}{2}[/tex]
Dividing, we get;
[tex]A=25.12[/tex]
Thus, the area of the semicircle is 25.12 square units.
Describe the transformations of the quadratic function
Answer:
B
Step-by-step explanation:
[tex]x_0 = \frac{ - b}{2a} = 0 \\ y_0 = {0}^{2} + 3 = 3[/tex]
the 6th term of an arithmetic progression is 35 and the 13th term is 77. find the 20th term
20th term= 119
Step-by-step explanation:
Let the first term of AP be a
and common difference be d
nth term is given by,
= a+(n-1)d
6th term = 35
a+(6-1)d= 35
a+5d=35 -----------------(i)
13th term = 77
a+12d= 77----------------(ii)
Now, equation (ii) - (i)
a+12d-(a+5d)= 77-35
a+12d-a-5d= 42
7d=42
d=6
Now, from equation (i)
a= 35-5d= 35-5(6)= 35-30 = 5
20th term= a+19d= 5+19(6)= 119
In an arithmetic progression, the difference between any two successive terms is constant. By using this rule and the term numbers and values given, we can determine that the 20th term of the arithmetic progression is 119.
Explanation:We have two pairs of term number and term value in the arithmetic progression (AP), which are (6, 35) and (13, 77). In an arithmetic progression, the difference between any two successive terms is constant, known as the common difference.
We can calculate the common difference (d) as (77-35)/(13-6) = 42/7 = 6.
Next, we find the first term (a) using the formula for the nth term of an AP, which is a = An - (n-1)*d. Using 6th term values, a = 35 - (6-1)*6 = 5.
Finally, we find the 20th term (A20) using the formula An = a + (n-1)*d. This gives us A20 = 5 + (20-1)*6 = 119.
So, the 20th term of this arithmetic progression is 119.
Learn more about Arithmetic Progression here:https://brainly.com/question/35697112
#SPJ3
PLZ ANSWER QUICK-MATH TRIG
In ΔFGH, the measure of ∠H=90°, the measure of ∠F=18°, and HF = 9.2 feet. Find the length of FG to the nearest tenth of a foot.
Answer:
FG = 9.7ft
Step-by-step explanation:
Find the diagram in the attachment.
The diagram is a right angled triangle since one of its angle is 90°
Using SOH CAH TOA to calculate the length FG which is the hypotenuse.
According to SOH
Sin∠G = Opposite/Hypotenuse
To get the ∠G,
∠F+∠H+∠G = 180°
18°+90°+∠G = 180°
∠G = 180°-108°
∠G = 72°
Sin72° = 9.2/FG
FG = 9.2/sin72°
FG = 9.67feet
FG = 9.7ft (to the nearest tenth of a foot)
Answer:9.7
Step-by-step explanation:
Cos 18= 9.2/X
Cross multiple
Divided each side by 18
9.2/cos18
why in math is X first (X,Y) but we graph Y first.
Answer:
You can graph it doing either first, trick question
Step-by-step explanation:
Answer:
The order in which you write x- and y-coordinates in an ordered pair is very important. The x-coordinate always comes first, followed by the y-coordinate.
Step-by-step explanation:
1,000 divided by 1/4?
Step-by-step explanation:
[tex] \frac{1000}{ \frac{1}{4} } [/tex]
Doing reciprocal we get
= 1000 * 4
= 4000
Hope it will help you.
Answer:
4000
Step-by-step explanation:
If you divide by a fraction, you get the reciprocal of the fraction, and multiply by it
The reciprocal of 1/4 is 4
1000 * 4 is 4000
y = 5/6x + 2 . y = -5/6x + 9 These lines are...
a. parallel
b. perpendicular
c. intersecting
Answer:
intersecting
Step-by-step explanation:
parallel lines have the same slope
perpendicular lines have slopes that are negative reciprocals
73.7 is 55% of what number?
a. 134
b. 40.5
c. 74.6
d. 0.134
46 is what percent of 65? (Round your answer to the nearest tenth of a percent).
a. 141.3%
b. 70.7%
c. 70.8%
d. 141%
Answer:
a.) Let the total number be : x
∴(73.7÷x) ×100 = 55%
∴x= (73.7×100) ÷ 55
=> 7370÷55
∴x=134
Thus, Option-A.
----------------------------------------------------
b.) Let the percentage be : x
∴x= (46÷65) ×100
∴x= (0.707) × 100
∴x=70.7%
Thus, Option-B.
MARK AS BRAINLIEST.
Jana determined that she is approximately 1.013 10-3 miles tall. How many places, and in
which direction, must you move the decimal to determine her height in standard notation?
An electrician charges $40 per hour for service calls up to eight hours, but increases this rate by 50% for additional hours. The electrician will not work more than twelve hours per service call and also charges a $25 trip charge. The graph provides a visual for customers. If the electrician doubles the normal hourly rate, and still increases the rate by 50% for additional hours, how will the graph change? A) The y-intercept will be (0, 50), the slopes of the line segments will 40 and 60, and the range will be [50, 1170]. B) The y-intercept will be (0, 25), the slopes of the line segments will 80 and 120, and the range will be [25 1170]. C) The y-intercept will be (0, 50), the slopes of the line segments will 80 and 120, and the range will be [50, 1145]. D) The y-intercept will be (0, 25), the slopes of the line segments will 80 and 120, and the range will be [25, 1145].
Answer:
Actually the Answer is B
Step-by-step explanation:
The reason, cause I just chose C and got the answer wrong. Here’s further proof.
Answer: it’s D
Step-by-step explanation: got it wrong and it’s D
How do I complete a square
Eg solve the equation x(squared) + 4x - 7 = 0
By completing the square
Step-by-step explanation:
[tex]{x}^{2} + 4x - 7 = 0[/tex]
Take -7 to the other side making it +7
Half the coefficient of x and square it
[tex] \frac{1}{2} \times 4 = 2[/tex]
Square the answer
[tex]{2}^{2} = 4[/tex]
Join your answers
[
[tex](x + 2) - 4 = 7[/tex]
Take -4 to the other side making it +4
[tex](x + 2) = 7 + 4 \\
(x + 2) = 11
[/tex]
Square root both sides
[tex] \sqrt{x + 2}= \sqrt{11} [/tex]
[tex]x + 2 = \sqrt{11} [/tex]
Take +2 to the other side
[tex]x = - 2 \ + or - \sqrt{11} [/tex]
[tex]x = - 2 + \sqrt{11} [/tex]
or
[tex]x = - 2 - \sqrt{11} [/tex]
This can be your answering surd form if required or in decimals
The function f(x) = 2(x - 3)^2 + 9 is graphed in the coordinate plane. Which of the following are true? Select all that apply. *
The graph of the parabola opens downward.
The vertex of the graph is (-3,9).
The axis of symmetry of the graph is x = 3.
The y-intercept of the graph is 9.
The minimum of the function is 9.
Answer:
-The minimum of the function is 9
-The axis of symmetry of the graph is x=0
Step-by-step explanation:
You are looking at the top of a building and thinking it would be great to make a zipline from the top to your current location. You measure the angle of elevation as 37 degrees and you are 123 feet from the base of the building . How long a zipline is needed if you are 6 feet tall ? Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a foot.
The length of the zipline for the building which you are looking at needed to be 154.01 feet.
What is a trigonometric function?The domain input value for the six basic trigonometric operations is the angle of a right triangle, and the result is a range of numbers.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.
Given the situation making a right-angle triangle with an angle of 37° and a base is 123 feet.
By trigonometric function
cos37° = 123/zipline
zipline = 123/cos37°
zipline = 154.01 feet
Hence, the zipline which is needed is 154.01 feet.
For more information about the trigonometric function,
brainly.com/question/1143565
#SPJ5