Answer:
The rate at which the distance between them is changing at 2:00 p.m. is approximately 1.92 km/h
Step-by-step explanation:
At noon the location of Lan = 300 km north of Makenna
Lan's direction = South
Lan's speed = 60 km/h
Makenna's direction and speed = West at 75 km/h
The distance Lan has traveled at 2:00 PM = 2 h × 60 km/h = 120 km
The distance north between Lan and Makenna at 2:00 p.m = 300 km - 120 km = 180 km
The distance West Makenna has traveled at 2:00 p.m. = 2 h × 75 km/h = 150 km
Let 's' represent the distance between them, let 'y' represent the Lan's position north of Makenna at 2:00 p.m., and let 'x' represent Makenna's position west from Lan at 2:00 p.m.
By Pythagoras' theorem, we have;
s² = x² + y²
The distance between them at 2:00 p.m. s = √(180² + 150²) = 30·√61
ds²/dt = dx²/dt + dy²/dt
2·s·ds/dt = 2·x·dx/dt + 2·y·dy/dt
2×30·√61 × ds/dt = 2×150×75 + 2×180×(-60) = 900
ds/dt = 900/(2×30·√61) ≈ 1.92
The rate at which the distance between them is changing at 2:00 p.m. ds/dt ≈ 1.92 km/h
Find xy if x + y=3, x^2 + y^2 = 5
Answer:
mark me
Step-by-step explanation:
x+y=3
x=3-y
putting the value of x
in this
x²+y²=5
(3-y) ²+y²=5
9-6y+y²+y²=5
2y²-6y+9-5=0
2y²-6y+4=0
2y²-4y-2y+4=0
2y(y-2)-2(y-2)=0
(2y-2) (y-2) =0
2y-2=0 or y-2=0
y=1 or y=2
so x=2 or 1
so x×y=2×1 or 1×2=2
I HOPE THIS WILL HELP YOU MARK ME BRAINLIEST
Beth will you help Andy with his algebra?
which punctuation mark is missing in the sentence?
A),
B)!
C)´
D)-
Answer:
A)
Step-by-step explanation:
mark me brainliest plzzzzzzz
PLEASE HELP!! WILL GIVE BRAINLIEST!!
Answer:
Step-by-step explanation:
2100000 × (1.06)³= sorry I don't have a calculator but type that in.
The power 3 is for the years 2012 and 2015 as there is a 3 year gap. Hope that helps
Mrs. Smith paid $125 to have her hair colored and cut. If she tips her hairdresser 15% of her bill, how much was the tip? (pls include the steps)
Answer:
$18.75
Step-by-step explanation:
15% = 15/100
125 × 15/100
=1875/100
=18.75
Solve for X. Not drawn to scale
Answer:
[tex]x=4.02[/tex]
Step-by-step explanation:
The given triangle is a right triangle, this is indicated by the box around one of the angles, signifying that the angle is a (90) degree angle. Therefore, to solve this problem one must use trigonometric ratios. These ratios are used to describe the relationship between an angle and the sides in a right triangle.
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\[/tex]
Bear in mind, the names of the sides of the triangle are relative to the angle that one uses to describe it in the triangle. Therefore the (opposite) and (adjacent) sides will change depending on the angle one chooses to look at it from.
In this case, one is given the length of the side opposite the given angle. One is asked to find the measure of the side adjacent to the angle. Therefore, it would make the most sense to use the tangent (tan) ratio.
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
Substitute,
[tex]tan(20)=\frac{9}{x}[/tex]
Manipulate the equation such that it is solved for (x),
[tex]x=\frac{9}{tan(20)}[/tex]
Solve,
[tex]x=4.02[/tex]
The watermelon that weighed 12 pounds cost $5.76 what was the cost per ounce of the watermelon? A. $0.48  B. $0.36 C. $0.03 D. $0.02
Answer:
the answer is A. 0.48 $
Step-by-step explanation:
the price of ounce of the watermelon is :
[tex] \frac{5.76}{12} = 0.48 \: [/tex]
Find x. Round your answer to the nearest tenth of a degree.
Answer:
60.9º
Step-by-step explanation:
tan = opp/adj
tanX = 45/25
X = arctan 45/25
use calculator
X = 60.945395900922855
Rounded
60.9º
Can someone help
Me solve the rest of this please
Answer:
Step-by-step explanation:
Find the area of each figure
Answer:
92
Step-by-step explanation:
this figure can be "split" into 3 sub-figures.
one rectangle in the middle, one triangle to the right, and one triangle on top.
these areas we can calculate very easily. and then we simply sum up all 3 of them and we have the answer.
it is clear, the area of a rectangle is length×width.
and the area of triangle is baseline×height/2.
where in a right-angled triangle one of the sides next to the 90 degree angle is the baseline and the other is the height.
the rectangle
R = 10×6 = 60
the triangle to the right
T1 = (14-10)×6/2 = 12
the triangle on the top
T2 = 10×(10-6)/2 = 20
so, the total area is
60+12+20 = 92
The area of the given figure is 92.
This figure contained 3 sub-figures.
One rectangle in the middle, one triangle to the right, and one triangle on top.
The area of these areas we can calculate very easily. and then we ad all 3 of them and we have the answer.
What is the area of a rectangle?The area of a rectangle is,
[tex]A=length\times width.[/tex]
What is the area of triangle?The area of triangle is
[tex]A^*= \frac{1}{2} \times base\times height[/tex]
Where in a right-angled triangle one of the sides next to the 90 degree angle is the baseline and the other is the height.
The area of rectangle
[tex]R =l\times w \\R=10\times 6 \\R= 60[/tex]
The triangle to the right
[tex]T_1 = (14-10)\times 6/2 = 12[/tex]
The triangle on the top
[tex]T_2 = 10\times (10-6)/2 = 20[/tex]
Therefore, the total area is,
60+12+20 = 92
Therefore the area of the given figure is 92.
To learn more about the area visit:
https://brainly.com/question/3948796
The ratio of color papers to white paper is 3:8. If there are 48 white papers how many color papers are there
Answer: 18 color papers
Step-by-step explanation:
The ratio of color paper to white paper is 3:8 which means that for every 3 color papers there should be 8 white papers.
If there are 48 white papers therefore, you need to use direct proportion to solve for the color papers:
3 : 8
x 48
8x = 144
x = 144 / 8
x = 18 color papers
HELP ME I'LL MARK AS BRAINEST PLZ HELP ME!!! (=0)
Answer:
9/10 x 4/5 = 36/50 simplified = 18/25 is your area
PLEASE HELP WILL GIVE BRAINLIEST
Answer:
8/23. Sana po makatulong
Evaluate the expression 33.15/n n=1.5
Answer:
22.1
Step-by-step explanation:
33.15/n
33.15/1.5
= 22.1
HELP ME OUT PLEASE....
please help a girl out
Answer:
[tex]r=\frac{7±3\sqrt{5} }{2}[/tex]
Ignore the A before the ±. It wouldn't let me type it correctly.
Step-by-step explanation:
2r² + 7r - 1 = 3r²
2r² + 7r - 1 - 3r² = 0
- r² + 7r - 1 = 0
- (r² - 7r + 1) = 0
- (r² - 7r + 1) ÷ - 1 = 0 ÷ - 1
r² - 7r + 1 = 0
[tex]r=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
Ignore the A before the ±. It wouldn't let me type it correctly.
r² - 7r + 1 = 0
a = 1
b = - 7
c = 1
[tex]r=\frac{-(-7)±\sqrt{(-7)^{2}-4((1)(1)) } }{2(1)}[/tex]
[tex]r=\frac{-(-7)±\sqrt{49-4((1)(1)) } }{2(1)}[/tex]
[tex]r=\frac{-(-7)±\sqrt{49-4 } }{2(1)}[/tex]
[tex]r=\frac{-(-7)±\sqrt{45 } }{2(1)}[/tex]
[tex]r=\frac{-(-7)±\sqrt{(3)(3)(5) } }{2(1)}[/tex]
[tex]r=\frac{7±(\sqrt{3 } )(\sqrt{3})(\sqrt{5}) }{2(1)}[/tex]
[tex]r=\frac{7±3\sqrt{5} }{2}[/tex]
Two separate equations
[tex]r=\frac{7+3\sqrt{5} }{2}[/tex]
[tex]r=\frac{7-3\sqrt{5} }{2}[/tex]
You are examining your choices of banks to open a new checking account. Potential costs include monthly maintenance fees, statement copy fees, and ___________.
Answer:
overdraft fees is your answer
Step-by-step explanation:
rhombus wxyz with vertices w(1 0) x(4,-1) y(5,-4) and z(2,-3)
Answer:
W 2,3
X 5,3
Y 1,2
Z 8,4
Step-by-step explanation:
The coordinates of the Rhombus after the dilation is W' ( 3 , 0 ) , X' ( 12 , -3 ) , Y' ( 15 , -12 ) and Z' ( 6 , -9 )
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.
Given data ,
Let the coordinates of the rhombus be represented as WXYZ
where W' ( 1 , 0 ) , X ( 4 , -1 ) , Y ( 5 , -4 ) and Z ( 2 , -3 )
Now , the dilation scale factor is k = 3 centered at origin
So , result of this transformation is an image with the same shape as the original
The coordinates of the dilated figure is W'X'Y'Z'
where W' ( 3 , 0 ) , X' ( 12 , -3 ) , Y' ( 15 , -12 ) and Z' ( 6 , -9 )
Hence , the dilation is solved
To learn more about dilation click :
https://brainly.com/question/13176891
#SPJ2
can you guys help please
What is the volume of the pyramid? Show all work.
3. What is the value of x?
A.36
B.32
C.12
D.28
Oooooooioooooooooooo
Answer:
b
Step-by-step explanation:
How do I solve this?
Find the value of x. Show work
Answer:
b) 8
Step-by-step explanation:
6x+(5x+2)=90
11x+2=90
11x=88
x=8
:)
ZAED = 137°. What is AEB?
A А.
D
UJ
с
Answer:
AEB =43
Step-by-step explanation:
The two angles form a straight line so they add to 180 degrees
AED + AEB = 180
137+AEB = 180
AEB = 180-137
AEB =43
Answer:
[tex]\text{B. }43^{\circ}[/tex]
Step-by-step explanation:
Angles [tex]\angle AED[/tex] and [tex]\angle AEB[/tex] are supplementary, meaning they add up to 180 degrees, because they form one side of a line.
Thus, we have:
[tex]\angle AED+\angle AEB=180,\\137+\angle AEB=180,\\\angle AEB=\boxed{43^{\circ}}[/tex]
Help with my mathhhhh
Answer:
See the image below for the answer:)
Step-by-step explanation:
A research center project involved a survey of 846 internet users. It provided a variety of statistics on internet users. (a) The sample survey showed that 94% of respondents said the internet has been a good thing for them personally. Develop a 95% confidence interval for the proportion of respondents who say the internet has been a good thing for them personally. (Round your answers to four decimal places.) 0.9239 Incorrect: Your answer is incorrect. to 0.9561 Incorrect: Your answer is incorrect. (b) The sample survey showed that 67% of internet users said the internet has generally strengthened their relationship with family and friends. Develop a 95% confidence interval for the proportion of respondents who say the internet has strengthened their relationship with family and friends. (Round your answers to four decimal places.) 0.6385 Incorrect: Your answer is incorrect. to 0.7015 Incorrect: Your answer is incorrect.
Answer:
(a) (0.9240, 0.956)
(b) (0.6383, 0.7017)
Step-by-step explanation:
The number of internet users involved in the survey, n = 846
The percentage of the respondents that said the internet has been good thing for them personally, [tex]\hat p[/tex] = 94%
(a) The confidence interval of a percentage is given as follows;
[tex]CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
The z-value for 95% confidence interval = 1.96
We get;
[tex]CI=0.94\pm 1.96\times \sqrt{\dfrac{0.94 \times (1-0.94)}{846}} \approx 0.94 \pm 1.6003 \times 10^{-2}[/tex]
CI = 0.9240 ≤ [tex]\hat p[/tex] ≤ 0.956 = (0.9240, 0.956)
(b) The percentage of the internet users that said the internet has directly strengthened their relationship with their families, [tex]\hat p[/tex] = 67% = 0.67
The 95% confidence interval is therefore;
[tex]CI=0.67\pm 1.96\times \sqrt{\dfrac{0.67 \times (1-0.67)}{846}} \approx 0.67 \pm 3.1686\times 10^{-2}[/tex]
From which we have;
CI = 0.6383 ≤ [tex]\hat p[/tex] ≤ 0.7017 = (0.6383, 0.7017)
Simplify the expression: 16x - (3x + 9) + 17
Step-by-step explanation:
16x -(3x + 9) + 17
16x -3x -9 +17
13x + 8
can someone pls pls help me ?
5 number summary? Please help this is confusing and please do step by step
new community center. How I Find the prime factorization of the number 24
Answer:
2*2*2*3
or
2^3 * 3
Step-by-step explanation:
24 = 4*6
But 4 and 6 aren't prime
24 = 4*6 = (2*2) * (2*3)
All these numbers are prime
24 = 2*2*2*3 or with exponents = 2^3 * 3
Explain how to check if two or more ratios are a proportion
Answer:
¿Cómo comprobar que las razones son proporcionales? ,5
Step-by-step explanation:
Para comprobar si dos o más razones son proporcionales se aplica la propiedad fundamental de las proporciones. 1 * 4 = 1 2 2 4 4 = 4 1 2 3 6 1 * 6 = 6 = 6 = = ? ? 1 2 0,5 1 = Así se concluye que las tres razones son proporcionales. 1 * 1 = 1 = 1 1ra forma. 2 * 2 2 * 3 ? 2 * 0,5
