Answer:
(i) The distance between B and C is approximately 552.9 m
(ii) ∠ACB is approximately 40.49°
(iii) The bearing of C from B is approximately 184.49°
(iv) The shortest distance from A to BC is approximately 331.155 m
Step-by-step explanation:
The given parameters are;
The length of segment AB = 370 m
The length of segment AC = 510 m
The bearing of B from A = 68°
The bearing of C from A = 144°
(i) From the bearing of B from A = 68° and the bearing of C from A = 144°, we have;
∠BAC = 144° - 68° = 76°
∠BAC = 76°
Let A represent ∠BAC, c represent segment AB, b represent segment AC, and a represent segment BC, by cosine rule, we have;
a² = b² + c² - 2·b·c·cos(A)
By substituting the known values, we get;
a² = 510² + 370² - 2 × 510 × 370 × cos(76°)
a² ≈ 397000 - 91301.3234 ≈ 305698.677
BC = a ≈ √(305,698.677) ≈ 552.9
The distance between B and C, BC ≈ 552.9 m
(ii) By sine rule, we have;
a/(sin(A) = b/(sin(B)) - c/(sin(C))
Therefore;
552.9/(sin (76°)) = 370/(sin(C))
sin(C) = 370/(552.9/(sin (76°))) ≈ 0.649321
C = arcsine(0.649321) ≈ 40.49°
∠C = ∠ACB ≈ 40.49°
(iii) Angle ∠B = ∠ABC = 180° - 76° - 40.49° ≈ 63.51°
The bearing of A from B = 360° - (180° - 68°) = 248°
Therefore, the bearing of C from B ≈ 248° - 63.51° ≈ 184.49°
(iv) The shortest distance from A to BC = 370 m × sin(63.51°) ≈ 331.155 m
Convert 60 inches to feet. There are 12 inches in a foot
Answer:
60/12= 5
5 feet
Answer:
5 feet
Step-by-step explanation:
Divide the length value (inches) by 12.
Two rectangles are similar. The
ratio of the length of rectangle A
to the length of rectangle B
is 1:4. If the length of rectangle
B is 14 meters, what is the
length of rectangle A?
1) Write an equation of a line that
is parallel to y = -5x + 2 and
passes through (-1, 4).
Answer:
y=-5x + 4
Step-by-step explanation:
Answer:
y=-5x-1
Step-by-step explanation:
It goes through the point (-1,4)
Ill give brainliest
Describe a situation where you might need to know the percent that something changed.
Answer:
Change: subtract old value from new value. Example: You had 5 books, but now have 7. The change is: 7−5 = 2. Percentage Change is all about comparing old to new values.
Step-by-step explanation:
hope this helps :)
Answer:
When finding the climate of an area
Step-by-step explanation:
Ex. Rainfall increased 30% since 2019 in florida (not true just an example)
How many solutions will this system of equations have??
Please explain your thinking
The number 1-50 are placed in a bag. What is the probability of selecting:
A) a number greater than 50______
B) multiple of 5________
C) a prime number _________
D) a composite number_______
A: 0
B: 10/50
C: 15/50
D: 34/50
Answers:
A) 0B) 1/5 = 0.2C) 3/10 = 0.3D) 17/25 = 0.68Nearly all of those answers involve a fraction form and an equivalent decimal form.
===========================================
Work Shown:
Part A
The largest number in the bag is 50, so we cannot select anything larger than that. The probability of getting something larger than 50 is 0% which converts to the decimal form 0
----------------------------
Part B
List out the multiples of 5 to get {5,10,15,20,25,30,35,40,45,50}
Note how 50/5 = 10, which shows there are 10 multiples listed above.
We have 10 items in that set out of 50 items in the set {1,2,3,...,49,50}. The probability of getting a multiple of 5 is 10/50 = 1/5. This converts to the decimal form 0.2
----------------------------
Part C
The prime numbers between 1 and 50 are:
{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47}
There are 15 items in that list out of 50 items in the bag, so 15/50 = (5*3)/(5*10) = 3/10 is the answer. Converting to decimal form gets us 3/10 = 0.3
----------------------------
Part D
There are 50 items in the bag and 15 primes. This means there are 50-15 = 35 composite items. Well this is close to the actual count. It turns out that the number "1" is not composite, and it's not prime either. So we really have 35-1 = 34 composite values.
We get 34/50 = (17*2)/(25*2) = 17/25 as the answer. That converts to 17/25 = 0.68
(-5,2) and (1,-2) what’s the rise/run?
Answer:
m= -2/3
Step-by-step explanation:
Use the slope formula to find the slope m .
Isabel finished her history assignment in 1/5 hours. Then she completed her math assignment in 1/2 hours. What was the total amount of time Isabel spent doing these two assignments?
Write your answer as a fraction in simplest form.
Answer:70/100 or 7/10
Step-by-step explanation:
one hour is 60 mins
1/5 of an hour is 12 mins
1/2 of an hour is 30
30 + 12 = 42
42/60 simplified is 7/10
PLEASE PLEASE HELP I STG IVE BEEN ASKING THE SAME QUESTIONS FOR SO LONG AND NOONES ANSWERING ITS DUE SOON im just gonna fail tbh
Answer:
3) 5/2
Step-by-step explanation:
5x - 2y = 20
(First, put it in slope intercept form: y = mx + b).
5x - 2y - 5x = 20 - 5x --> Subtracted 5x on both sides of the equation
- 2y = -5x + 20 --> Simplified
-2y/-2 = (-5x + 20)/-2 --> Divided by -2 on both sides
y = 2.5x - 10 --> Simplified
Since formula is, y = mx + b, then:
m (slope): 2.5
b (y-intercept): -10
Therefore, the answer is 3) 5/2
Hope this helped! <3
Let's solve for y.
5x − 2y = 20
Step 1: Add -5x to both sides.
5x−2y+−5x=20+−5x
−2y=−5x+20
Step 2: Divide both sides by -2.
−2y/−2 = −5x + 20/−2
y = 5/2x − 10
Answer:
y = 5/2x − 10
Slope = x, therefore, the slope = 5/2.
Solve for x and find AB
Solve for y and find BX
9514 1404 393
Answer:
x = 7; AB = 30y = 5; BX = 25Step-by-step explanation:
Opposite sides of a parallelogram are the same length.
AB = CD
5x -5 = 3x +9
2x = 14
x = 7
AB = 5(7) -5)
AB = 30
__
The diagonals of a parallelogram are bisected by each other.
XB = XD
7y -10 = 5y
2y = 10
y = 5
BX = 7(5) -10
BX = 25
Three hundred cars drove over a bridge in 23 minutes. At that rate, how
many cars would drive over the bridge in 138 minutes?
Answer:
1800
Step-by-step explanation:
300 cars in 23 minutes so 300/25 = how many cars each minute
that equals 13.04347....
so on your calculator multiply that by 138 which gives you 1800 cars
Answer:
138/23×300=1800cars drove over the bridge
Step-by-step explanation:
What number should go in the box? 34816=▢+4000+800+10+6
Answer:
30,000 number should go in the box
Answer:
30000.
Step-by-step explanation:
34816=▢+4000+800+10+6
34816 = ▢ + 4816
▢ = 34816 - 4816
= 30000
Find the measure of the missing angle.
Answer:
Hi
U should do like this
90-51=39...
Answer: 39 degrees
Step-by-step explanation:
Right angle is 90 degrees so 51 plus a will equal 90
A is 39 degrees
HELP!!! NEED ANSWER ASAP!
Answer:
Yeah he's right...
Step-by-step explanation:
Can you guys help meh pls
Which statement about the dilation of these triangles is true?
The scale factor is
The scale factor is 2
The scale factor is 3.
The scale factor is 4.
Answer
when 2 triangle scales are similar the ration reduces and become a scale factor
Answer:
The scale factor is 2
Step-by-step explanation:
Jasmine sold half of her Barbie doll Collection
and then bought 9 dolls. She now has 13 dolls.
Barbie dolls did she begin with?
How many
simplify 3 to the 2nd power + 1 x 2
Which Pixar characters do you think were the hardest to bring to the screen, and why?
Please answer!! I added a screenshot
Answer:
S + 2.5S + (2.5S - 3.3)
Step-by-step explanation:
To get the perimeter of ANY shape, simply add up all the sides.
Can someone plz help me with the red #6 the graph is on the screen plz anyone fast ☹️
I NEED HELP PLEASE I DON’T WANT TO FAIL PLEASE PLEASE HELP ME
plss
s
s
ss
s
d
d
d
d
d
d
d
d
d
d
s
s
s
Answer:
$6,600
Step-by-step explanation:
231/0.035= 6,600
Help I will mark brainliestttt
Answer:
11 or more
Step-by-step explanation:
55-40=15
160/15=10.666
11 or more
Giving 5 stars and brainlist to whoever answers this correct!!!!
The table shows the number of animals in the most popular exhibit at the zoo.
Flamingo - 12
Crocodile - 4
Elephants - 3
Monkeys - 11
If an animal is selected at random to be fed in front of an audience, which expression can be used to determine the probability the animal will NOT be an elephant?
A. 1/10
B. 9/10
C. 3/10
D. 3/3
Answer:
its A because it can't be B or D obviously, and since there are the least amount of elephants, its gonna be the one will less of a percentage. So its A.
Step-by-step explanation:
jabsbabsbavvsbabs
2 sides of a triangle have measures of 5 inches and 11 inches which measure could be the length of the third side
Answer:
the third side must be greater than 6 but less than 16
Step-by-step explanation:
use triangle inequality theorem - 3 scenarios (one of which is discounted because it produces a negative and a side of a triangle cannot be negative)
5 + 11 > 3rd side (n) n < 16
5 + n > 11 n > 6
11 + n > 5; n > -6 discounted
Find the value of x.
Answer:
81 degrees
Step-by-step explanation:
Step-by-step explanation:
Here,
X+128+100+51=360
X+279=360
X=360-279
:.x=81
use the quotient rule to find the derrivatives of 3/x^2
With full process
Answer:
[tex]\displaystyle \frac{d}{dx} \Big [ \frac{3}{x^2} \Big ]=-\frac{6}{x^3}[/tex]
Step-by-step explanation:
We can use either the Power Rule or the Quotient Rule to find the derivative of 3/x².
Power Rule: [tex]\displaystyle \frac{d}{dx}[ x^n] = nx^n^-^1[/tex]Rewrite [tex]\displaystyle \frac{3}{x^2}[/tex] as [tex]\displaystyle 3\cdot \frac{1}{x^2}[/tex] which is equivalent to [tex]3\cdot x^-^2[/tex].
Now we can apply the power rule to 3x⁻². Subtract 1 from the exponent and multiply the coefficient by -2.
3(-2)x⁻³ = -6x⁻³This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex].
Quotient Rule: [tex]\displaystyle \frac{d}{dx} \Big [ \frac{f(x)}{g(x)} \Big ]=\frac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}[/tex]Substituting 3 for f(x) and x² for g(x), we get:
[tex]\displaystyle \frac{(x^2)(0)-(3)(2x)}{(x^2)^2}[/tex]Simplify.
[tex]\displaystyle \frac{-6x}{x^4}[/tex]Using exponent rules, we can rewrite this as:
[tex]-6x^1^-^4 = -6x^-^3[/tex]This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex], which is the same as what we got using the product rule.
Answer:
[tex]\displaystyle \frac{d}{d x}\left[\frac{3}{x^2}\right] = -\frac{6}{x^{3}}[/tex].
Step-by-step explanation:
Let [tex]f(x)[/tex] and [tex]g(x)[/tex] denote two functions of [tex]x[/tex]. Assume that [tex]g(x) \ne 0[/tex]. The quotient rule states that:
[tex]\displaystyle \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right] = \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2}[/tex].
In this question:
The numerator of the fraction is [tex]f(x) = 3[/tex] (a constant function.)The denominator of the fraction is [tex]g(x) = x^{2}[/tex].Find [tex]{f}^{\prime}(x)[/tex] and [tex]{g}^{\prime}(x)[/tex].
Notice that the value of [tex]f(x)[/tex] is constantly [tex]3[/tex] regardless of the value of [tex]x[/tex]. By the constant rule, [tex]{f}^{\prime}(x) = 0[/tex].
For [tex]{g}^{\prime}(x)[/tex], consider the power rule:
if [tex]m[/tex] represents a rational number (such as [tex]2[/tex],) then by the power rule, [tex]\displaystyle \frac{d}{d x}\left[{x}^{m}\right] = m\, {x}^{m-1}[/tex].
Apply this rule to find [tex]{g}^{\prime}(x)[/tex].
[tex]\begin{aligned}{g}^{\prime}(x) &= \frac{d}{d x} \left[x^{2}\right] \\ &= 2\, x^{2 - 1} \\ &= 2\, x\end{aligned}[/tex].
Substitute [tex]f(x) = 3[/tex], [tex]{f}^{\prime}(x) = 0[/tex], [tex]g(x) = x^{2}[/tex], and [tex]{g}^{\prime}(x) = 2\, x[/tex] into the quotient rule expression to find [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right][/tex]:
[tex]\begin{aligned}&\; \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] \quad \genfrac{}{}{0em}{}{\leftarrow f(x) = 3}{\leftarrow g(x) = {x}^{2}} \\ =&\; \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right]\\ =&\; \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2} \\ =& \; \frac{0 \, x^2 - 3\, (2\, x)}{\left({x}^{2}\right)} \\ =&\; -\frac{6}{x^{3}}\end{aligned}[/tex].
Therefore, [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] = -\frac{6}{x^{3}}[/tex].
Simplify the following by combining like terms: 10 + 7r+b-4r*
10+ 3r
O 10 + 3r + b
O 13r + b
Simplify the expression:
4+4+7d
Answer:
8+7d
Step-by-step explanation:
So forest you combine like terms
4+4=8
There are no longer any like terms so your finished product is 8+7d