To Find :
The area of triangle whose side are 4 yard, 14 yard and 17 yard.
Solution :
We will use Heron's formula to find area of the triangle.
So,
[tex]s = \dfrac{a+b+c}{2}\\\\s = \dfrac{4+14+17}{2}\\\\s = 17.5[/tex]
Now, heron's formula is :
[tex]A = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
Putting all given values in above equation :
[tex]A = \sqrt{17.5\times (17.5-4)\times(17.5-14)\times(17.5-17)}\\\\A = \sqrt{17.5\times 13.5\times 3.5\times 0.5}\\\\A = 20.33\ yard^2[/tex]
Hence, this is the required solution.
What is the equation of a line that is perpendicular to y = 2x + 4 and passes through the point (4, 6)? A. y=1/2x+4 B y=-1/2x+6 C y=-1/2x+4 D y=-1/2x+8
Answer:
y = -1/2x + 8
Step-by-step explanation:
y = -1/2x + b
6 = -1/2(4) + b
6 = -2 + b
8 = b
Subtract 6 2/5 - 1 1/4. Simplify the answer and write as a mixed number.
Answer:5 3/20
Step-by-step explanation:
6 8/20 0- 1 5/20= 5 3/20
Jello someone help is this correct answer
No links or files
Correct answer please
Answer:
c is the right answer
Step-by-step explanation:
Simplify the expression and choose the appropriate result.
3 (2+39)
Answer:
setup below, you'll have to do the final calculation
Step-by-step explanation:
first perform the operation in parenthesis
2+39= 41
then do the multiplication 3 x 41
in general do calculations in this order
1. Parenthesis
2. Multiplication
3. Division
4. Addition
5. Subtraction
working from left to right
24.8x45.67 plz help will mark Brainliest
Answer: 1132.616
lol-
Y=x2= is that a function?
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 16 % are pennies and 30 % are dimes. There are 2 more nickels than pennies. How much money does the bag contain?
In parallelogram ABCD, angle B is 75. Find the measure of angle D
Answer:
answer: 75
Hope that helps you!
a spinner has 8 sections 2 purple 2 yellow 3 blue and 1 red what is the probability of spinning and landing on a blue or purple section
Answer:
5/8 is the probability.
Step-by-step explanation:
1 point
What is the value of x? Round to the nearest tenths place
15 ft
13 ft
х
Answer:
7.5
Step-by-step explanation:
The values 15ft, 13ft and x are the sides of a right triangle;
According to pythagoras theorem;
15² = 13²+x²
x² = 15² - 13²
x² = 225 -169
x² = 56
x = √56
x = 7.48
Hence the value of x to the nearest tenth is 7.5 to the nearest tenth
Did anybody laugh when the ice skater fell down?
Answer:
okkkkkkk ty for he points
Step-by-step explanation:
Answer:
Ty
Step-by-step explanation:
the courthouse is the tallest building in the city. if it is 7 1/2 inches tall in the model, how tall is the actual building?
the scale of the model is 1 inch = 9 feet
Answer:67.6
Step-by-step explanation:
8 km
b
17 km
What is the length of the missing leg?
Please help me!! How do I do this?
Answer:
I think 12 * 12/ 60 = ?
12*12= 144
144/ 60= ?
Answer:
360°
Step-by-step explanation:
I think
1/2 base ×height
1/2×60×12
30×12
=360
The function ggg models the number of mosquitoes (in millions of mosquitoes) in a certain area as a function of rainfall (in centimeters) in that area. Which of these statements are true? Choose all answers that apply: Choose all answers that apply: (Choice A) A More rainfall relates to more mosquitoes as long as rainfall is less than 2\text{ cm}2 cm2, start text, space, c, m, end text. (Choice B) B More rainfall relates to more mosquitoes as long as rainfall is more than 2\text{ cm}2 cm2, start text, space, c, m, end text. (Choice C) C When there is no rainfall, there are about 111 million mosquitoes. (Choice D) D When there is no rainfall, there are about 222 million mosquitoes.
Answer:
(Choice A) A More rainfall relates to more mosquitoes, as long as rainfall is less than 2 cm²
Step-by-step explanation:
The given function for the number of mosquitoes, (by analysis of the options) is, g(x) = 4·x - x²
Where;
x = The amount of rainfall
g(x) = The number of mosquitoes in millions
The given function can be expressed as follows;
g(x) = 4·x - x² + 0
The maximum point is given by g'(x) = d(4·x - x²)/dx = 4 - 2·x = 0
At the maximum (turning point), we have;
4 - 2·x = 0
4 = 2·x
x = 4/2 = 2
The level of rainfall that gives the maximum number of mosquitoes is, x = 2 cm²
The number of mosquitoes increases from zero rainfall up to the maximum number of 4 million mosquitoes at 2 cm² rainfall and then decreases to zero as the rainfall increases further more than 2 cm², as shown in the attached graph of the function g(x) that models the number of mosquitoes created with MS Excel
Therefore, the true statement is (Choice A) more rainfall relates to more mosquitoes, as long as (the level of) rainfall is less than (the maximum) 2 cm².
The CSU Tropical Meteorology Project team predicts 17 named storms during the Atlantic hurricane season. Of those, researchers expect eight to become hurricanes and four to reach major hurricane strength (Saffir/Simpson category 3-4-5) with sustained winds of 111 miles per hour or more.
What is the predicted probability that out of the 17 named storms will actually produce hurricanes? _________
Answer:
the answer is 1 5/12
Write an equation based off this trigonometric graph.
Answer(s):
[tex]\displaystyle y = 4cos\:(2x - \frac{\pi}{2}) - 1 \\ y = 4sin\:2x - 1[/tex]
Explanation:
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4cos\:2x - 1,[/tex] in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex] to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex] which means the C-term will be positive, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.[/tex] So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2cos\:(2x - \frac{\pi}{2}) - 1.[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-\frac{\pi}{4}, -5],[/tex] from there to [tex]\displaystyle [\frac{3}{4}\pi, -5],[/tex] they are obviously [tex]\displaystyle \pi\:units[/tex] apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = -1,[/tex] in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
David can run at a consistent rate of 8.2 miles per hour. If he has 3 and a half hours to
run, how far will he run if he runs at that rate?
Answer:
David can run 28.7 miles in 3.5 hours.
Step-by-step explanation:
8.2mph × 3.5hours = 28.7miles
good luck, i hope this helps :)
9 books are to be bought by a student. Some cost $6 and the remainder cost $3 each. if the total amount spent was $39, how many of each are bought?
Please explain your answer.
Answer:
four nine dollar books
Step-by-step explanation:
36 divivded by 9
PLEASEEEEE HELPPPPPPPP
Answer:
142.5
Step-by-step explanation:
It is 142.5 because when finding area you have to do base x height our base here is 15 and are height is 9.5 so now that we know are base and height we just multiply! so 15 × 9.5 = 142.5 Hope this helps!
Find the area of the figure
Answer:
A = 76.912Step-by-step explanation:
Area of triangle with angle of 30°:
[tex]A_1=\frac12\cdot 5^2\cdot\sin(30^o)=\dfrac{25}4=6.25[/tex]
Area of triangle with angle of 50°:
[tex]A_2=\frac12\cdot 5^2\cdot\sin(50^o)=\dfrac{25}2\cdot0.766=9.575[/tex]
Area of the rest of the figure:
[tex]A_3=\dfrac{(360-30-50)^o}{360^o}\cdot\pi\cdot5^2=\dfrac79\cdot\pi\cdot25 =61.087[/tex]
Therefore:
[tex]A=A_1+A_2+A_3=6.25+9.575+61.087=76.912[/tex]
How to write an equation in point -slope form for each line
A 25 foot ladder is placed against a building at a point 21 feet from the ground find the distance from the base of the building to the base of the ladder
Answer:
The distance from the base of the building to the base of the ladder is 13.56 feet.
Step-by-step explanation:
This can be solved using Pythagorus theorem.
If the length of the ladder is taken as the hypotenuse and the distance from the building as the base of the triangle then the altitude can be found out by using
c²= a²+b²
Where c is the hypotenuse and b is the base and a is the altitude
Putting the values
25²= a²+ 21²
a²= 25²-21²
a²= 625-441
a²= 184
a= √184= 13.56 feet
The distance from the base of the building to the base of the ladder is 13.56 feet
(Don't answer if unsure) If the triangle rotated 360 degrees to the right, where would the plotted points be? (Coordinates are (-8,2) (-8,8) (-4,2)
Answer:
Step-by-step explanation:
A correct answer can only be obtained from a complete question.
A rotation is not always about the origin, but in the absence of information, this will be assumed.
Rotating to the right is assumed to mean rotated from the second towards the first quadrant about the origin.
Rotating any shape about the origin by 360° will always return to the original (starting) position, so the final coordinates will be (-8,2) (-8,8) (-4,2).
Consider a triangle ABC like the one below. Suppose that a = 47, b = 59, and A = 37" (The figure is not drawn to scale.) Solve the triangle,
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or",
Answer:
B = 49.1°
C = 93.9°
c = 77.9
Step-by-step explanation:
Given:
a = 47, b = 59, and A = 37°
Required:
B, C, and c
Solution:
✔️To find B, apply the law of sines:
[tex] \frac{sin(A)}{a} = \frac{sin(B)}{b} [/tex]
Plug in the values
[tex] \frac{sin(37)}{47} = \frac{sin(B)}{59} [/tex]
Cross multiply
[tex] 47*sin(B) = sin(37)*59 [/tex]
Divide both sides by 47
[tex] \frac{47*sin(B)}{47} = \frac{sin(37)*59}{47} [/tex]
[tex] sin(B) = 0.7555 [/tex]
[tex] B = sin^{-1}(0.7555) [/tex]
[tex] B = sin^{-1}(0.7555) [/tex]
B = 49.0690779° ≈ 49.1° (nearest tenth)
✔️C = 180° - (A + B) (sum of triangle)
C = 180° - (37° + 49.1°)
C = 93.9°
✔️To find c, apply the law of sines:
[tex] \frac{sin(B)}{b} = \frac{sin(C)}{c} [/tex]
Plug in the values
[tex] \frac{sin(49.1)}{59} = \frac{sin(93.9)}{c} [/tex]
Cross multiply
[tex] c*sin(49.1) = sin(93.9)*59 [/tex]
Divide both sides by sin(49.1)
[tex] c = \frac{sin(93.9)*59}{sin(49.1)} [/tex]
c = 77.8766982
c ≈ 77.9 (nearest tenth)
Armando took his dog, Tasha, to the vet. Tasha was placed on the scale and weighed 45.72 pounds. The veterinarian told Armando that Tasha’s breed should weigh no more than Thirty-six and one-half pounds. Armando calculated about how much weight Tasha should lose to be under the breed’s maximum weight. 45.72 rounds to 45 rounds to 37 45 – 37 = 8 pounds Which statements are true about Armando’s calculations? Check all that apply. Armando should have added 37 to 45. Armando should have rounded 45.72 to 45.5. Armando should not have rounded Thirty-six and one-half to 37. Armando should have calculated that the difference between 45 and 37 is 7. Armando’s last step should have shown 45.5 Minus thirty-six and one-half = 9.
Answer: 17 pounds
Step-by-step explanation:
I invest $1,000 at 5% interest that compounds annually. How much will I have in 5 years?
Answer:
$250....................
F/R/E/E P/O/I/N/T/S
Answer:
tysm!!
Step-by-step explanation:
[tex]have[/tex] [tex]a[/tex] [tex]great[/tex] [tex]day[/tex] [tex]:)[/tex]
AAAAAAA THANK YOU :D
pls and thanks Solve the equation 4(c-3) = 8 what is the value of c
Answer: C=5
Hope this helps!
please answer quickk
Answer:
t + 25 = 26
t = 26 - 25
t = 1
I hope it's helps you