Answer:
Plane speed = 40 m/s.
Wind speed = 300 m/s.
Step-by-step explanation:
Let the speed of the plane = Y
And the speed of the wind = X
If the plane then travel 340 miles per hour with the wind, that means the plane and the wind are moving in the same direction. Therefore,
X + Y = 340 ..... ( 1 )
Also, 260 miles per hour against the wind. That is, the plane is moving opposite to the direction of the wind. Therefore,
X - Y = 260 ..... ( 2 )
Solve the two equations simultaneously by addition. That will eliminate Y
X + Y = 340
X - Y = 260
2X = 600
X = 600/2
X = 300 m/s
Substitutes X in equation (1)
300 + Y = 340
Make Y the subject of formula by collecting the like terms
Y = 340 - 300
Y = 40 m/s
Therefore, the speed of the plane is 40 m/s. While the speed of the wind is 300 m/s.
question 9: consecutive angles in a parallelogram are___ A: cute B: congruent C: parallel D: Supplementary E: Convex
Answer:
Consecutive angles in a parallelogram are, D supplementary.
Step-by-step explanation:
Consecutive angles in a parallelogram will always sum to 180 degrees.
Answer:
Supplementary
Step-by-step explanation:
Correct answer in Ap3x. Just took the quiz.
Which equation represents a line parallel to the line shown on the graph? On a coordinate plane, a line goes through (negative 6, 0) and (negative 8, 6). y = 3 x minus 7 y = negative 3 x + 3 y = one-third x + StartFraction 7 Over 9 EndFraction y = negative one-third x + 12
Answer:
[tex]\boxed{ \mathrm{y = \ negative \ 3 x + 3}}[/tex]
Step-by-step explanation:
The coordinates are (-6,0) and (-8,6)
Finding slope of the line
Slope = [tex]\frac{rise}{run} = \frac{y2-y1}{x2-x1}[/tex]
Slope = [tex]\frac{6-0}{-8+6}[/tex]
Slope =[tex]\frac{6}{-2}[/tex]
Slope = -3
Parallel lines have equal slopes.
So, the line which is parallel to this line is y = negative 3 x + 3
Answer:
[tex]\boxed{ \mathrm{y = \ negative \ 3 x + 3}}[/tex]
Step-by-step explanation:
The coordinates are given (-6, 0) and (-8, 6)
Find slope of the line.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{6-0}{-8--6}[/tex]
[tex]m=\frac{6}{-2}[/tex]
[tex]m=-3[/tex]
Parralel lines have same slope.
y = mx + b
m = -3
What is the volume of the following rectangular prism?
Answer:
Step-by-step explanation:
The formula is V= w h l
So it’s be V= 16 1/4 x 1/2
V= 16.25 x .50
V= 8.125
V=8
(1 mark)
13.
The time to finish a certain work decreases as the number of worker increases
in number. What kind of proportion is illustrated in the situation?
Answer:
Inverse proportion
Step-by-step explanation:
Inverse proportion: in this type of relation, two quantities proportion such that one decreases and other increases or vice-versa.
So, in the given question when the number of workers increases, time is taken for certain work decreases.
So, Inverse proportion is the correct answer.
Which expression can be used to find the surface area of the following square pyramid?
Answer:
Step-by-step explanation:
The slant height of one side of this pyramid is 5, and the base of this side is 4. Thus, the area of one slant side is (1/2)(5)(4) = 10 units^2.
There are 4 such sides. Thus, the total slant surface area is 4(10 units^2), or 40 units^2.
If you also want to include the base area, the total would be
40 units^2 + 16 units^2 = 56 units^2.
Match the number with its opposite.
Answer:
3.2 matches with (A) -3.3
-2.3 matches with (C) 2.3
-1.5 matches with (B) 1.5
5.1 matches with (D) -5.1
Rose is making necklaces. She needs 7 sapphires and 6 rubies to make one necklace. Complete the double number line diagram to show the numbers of rubies and sapphires Rose needs to make 1 , 2 3 and 4 necklaces.
Answer:
B
Step-by-step explanation:
If the rectangle below is enlarged by a scale factor of 1.8, what will be the perimeter of the new rectangle? 39.4 units 43.2 units 45.6 units 48.2 units
Answer:
43.2 units
Step-by-step explanation:
On this problem you would just find the perimeter which is 2(l+w) and that is 24 units and after you do that you would just have to multiply the perimeter 24 times 1.8 which would leave you with and answer of 43.2 units.
Answer:
New length = 3.5 x 8 = 28 cm
New width = 3.5 x 6 = 21 cm
Step-by-step explanation:
Perimeter = 2(28) + 2(21) = 56 + 42 = 98 cm
Area = 28 x 21 = 588 square cm
The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. The sum of the base angles is 140°. a. Find the length of the diagonal. b. Find the length of the shorter base. Round your answers to the nearest hundredth. show work please!
Answer:
Step-by-step explanation:
as the non parallel sides are equal and it is a trapezoid.∴ base angles are equal.each base angle=1/2×140=70°let the foot of perpendicular from end of shorter side is at distance x from nearest end of longer side.[tex]\frac{x}{7}=cos ~70\\x=7 \times cos~70 \approx 2.394\\2x \approx 4.788 \approx 4.79\\[/tex]shorter side=22-4.79=17.21 ftto find diagonal use cos formula[tex]cos ~70=\frac{22^2+7^2-d^2}{2*22*7} \\308 cos~70=484+49-d^2\\d=\sqrt{533-308~cos~70} \approx~20.68\\where ~d~is~diagonal.[/tex]d=20.68 fta. The length of the diagonal is approximately 15.74 feet.
b. The length of the shorter base is approximately 27.77 feet.
a. To find the length of the diagonal (d), we can use the given information and the formulas mentioned. Let's substitute the values into the formula:
h = (7/2) * tan(140°)
h ≈ (7/2) * (-1.376381920471173)
h ≈ -4.796335681196056
Now, substitute the values into the formula for the diagonal:
[tex]d = \sqrt{(22 - x)^2 + [(7/2) * tan(140\°)]^2}\\\\d = \sqrt{(22 - 7)^2 + [(-4.796335681196056)]^2}\\\\d = \sqrt{15^2 + 23.011228900189124}\\\\d = \sqrt{225 + 23.011228900189124}\\\\d = \sqrt{248.011228900189124}\\\\d = 15.74[/tex]
Therefore, the length of the diagonal is approximately 15.74 feet.
b. To find the length of the shorter base (b), we can use the given information and the law of cosines:
[tex]b^2 = 7^2 + 22^2 - 2 * 7 * 22 * cos(140\°)\\\\b^2 = 49 + 484 - 2 * 7 * 22 * cos(140\°)\\\\b^2 = 533 - 308 * cos(140\°)\\\\b^2 = 533 - 308 * (-0.766044443118978)\\\\b^2 = 533 + 236.924\\\\b^2 = 769.924\\\\b = 27.77[/tex]
Therefore, the length of the shorter base is approximately 27.77 feet (rounded to the nearest hundredth).
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An insurance company is considering implementing a plan based on mileage. The current plan, Plan A, charges a flat rate of $235.90 per month. Plan B charges a flat rate of $160.30 per month plus an additional $0.07 per mile driven the previous month. Using the inequality below, find the number of miles, x, where the cost of Plan B is less than the cost of Plan A. $160.30 + $0.07x < $235.90 A. x < 529 B. x < 5,660 C. x < 1,080 D. x < 2,160
Answer:
plan A
Step-by-step explanation:
Right isosceles triangles are constructed on the sides of a 3−4−5 right triangle, as shown. A capital letter represents the area of each triangle. What is [tex]\frac{X+Y}{Z}[/tex]
Answer:
1
Step-by-step explanation:
because the triangles are isosceles, that means that the area of Z is 5x5x1/2, which equals 12.5
the area of X is 4.5
the area of y is 8
(8+4.5)/(12.5) = 1
Write an equation and solve it to answer each question:
A pile of 55 coins, consisting of nickels and dimes, is worth $3.90. find the number of each.
You have to Answer like this:
If there are x nickels, then the equation is______
The number of nickels is_____
the number of dimes is______
Answer:
there are 25 nickels and 30 dimes
I need a quick response! Please help!
A park ranger sees a fire from an observation deck 120 feet high. The fire is at an angle of
depression 2.5 degrees. How far is the fire from base of the observation deck ?
Answer: 2748.5 feet
Step-by-step explanation:
Given that the
Height h = 120 feet.
angle of depression = 2.5 degrees
The angle of depression is equal to the angle of elevation.
The base of the observation deck will be achieved by using trigonometry ratio.
Tan Ø = opposite/ adjacent
Opposite = height = 120 feet
Adjacent = base = ?
Substitutes the given parameters into the trigonometry ratio.
Tan 2.5 = 120 / adjacent
Adjacent = 120 / tan 2.5
Adjacent = 2748.452
Therefore, the base of the observation deck is 2748.5 feet
Write a word phrase that represents x + 5.
Answer:
5 added to a number, x.
Step-by-step explanation:
I phrased it like other ones I saw before so... :) (Also if you ask someone to write it, I'm sure they'd get x+5)
Answer:5 added to a number, x
Step-by-step explanation:
The graph below represents which systems of inequalities?
A. Y> 2x+3
y>+3
B. Y<2x+3
y
C. Y<3x+2
y<-x+2
D Y> - 2x+ 3
y>x+3
Answer:
y ≤ x + 3
y ≤ -2x + 3
Step-by-step explanation:
Graph attached shows two solid lines having equal y-intercepts as 3 units.
Since one line passes through two points (0, 3) and (-3, 0),
Slope of this line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{3-0}{0+3}[/tex]
= 1
Let the equation of the this line is,
y = mx + b
where m = slope of the line
b = y-intercept
Therefore, equation of the line having slope = 1 and y-intercept = 3 units,
y = 1.x + 3
y = x + 3
Since, shaded region shown is on the left of the line y = x + 3
Therefore, y ≤ x + 3 will be the inequality with shaded area in green.
Slope of the second line passing through (0, 3) and (1.5, 0)
m' = [tex]\frac{3-0}{0-1.5}[/tex]
= -2
Therefore, equation of the second line will be,
y = (-2)x + 3
y = -2x + 3
Since shade area (In yellow) is below the given solid line, equation of the inequality will be,
y ≤ -2x + 3
The formula for calculating simple interest is I = prt. Which is the equivalent equation solved for r? StartFraction I Over p t EndFraction = r StartFraction p t Over I EndFraction = r I minus p t = r I + p t = r
Answer: r = I/pt
Step-by-step explanation:
Interest divided by the principal × time gives the rate. It's usually expressed as a percentage per year.
The equivalent equation for r is r=I/pt which is option a.
What is equation?Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.
How to find equation?We have been given an equation I=prt and we have to find the equivalent equation which is solved for r.
I=prt
In this p is principal, r is rate of interest and t is time period.
Divide both sides by pt.
I/pt=prt/pt
I/pt=r
Hence the equation equivalent to I=prt is r=I/pt which is option a.
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Hurry!!
State the domain of the glven relation.
Answer:
x ≤ -1
Step-by-step explanation:
What is the inverse of the function f(x)=-\dfrac{1}{2}(x+3)f(x)=− 2 1 (x+3)f, left parenthesis, x, right parenthesis, equals, minus, start fraction, 1, divided by, 2, end fraction, left parenthesis, x, plus, 3, right parenthesis
Answer:
The inverse of the function is
-2x-3
Step-by-step explanation:
The inverse of the function f(x) = -\dfrac{1}{2}(x+3) is f(x)⁻¹ = -2x - 3
What is the inverse of a function?The inverse of a function is a function that gives us the actual value for which the desired function has a given result.
The given function is:
[tex]\mathbf{ f(x)=-\dfrac{1}{2}(x+3)}[/tex]
To find the inverse, we need to follow the following steps
replace the role of f(x) by y;[tex]\mathbf{ y=-\dfrac{(x+3)}{2}}[/tex]
Swap x and y variables[tex]\mathbf{ x=-\dfrac{(y+3)}{2}}[/tex]
Solve for y;2x = - (y + 3)
2x = -y - 3
y = -2x - 3
Writing back in inverse notation, we have:
f(x)⁻¹ = -2x - 3
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Right isosceles triangles are constructed on the sides of a3−4−5 right triangle, as shown. A capital letter represents the area of each triangle. What is X+Y /z
Answer:
(X + Y)/Z = 1
Step-by-step explanation:
Given the leg sides of the isosceles right triangles as 4, 5, and 3, we have
Length of the other leg sides of the isosceles triangle = Length of the given leg side sizes
Therefore, the respective height and base of each right angled isosceles triangle are equal which gives the areas as follows;
Z = 1/2*5*5 = 12.5 unit²
Y = 1/2*4*4 = 8 unit²
X = 1/2*3*3 = 4.5 unit²
W = 1/2*4*3 = 6 unit²
(X + Y)/Z = (4.5 + 8)/12.5 = 12.5/12.5 = 1.
What is the length of AB?
A. 18
B. 48
C. 6
D. 9
Answer:
D
Step-by-step explanation:
Since AC is 18
Midpoint is B
Therefore AB is 18÷2=9.
Hope this helps.
The length of AB shown in the circle is 9.
Hence option D is correct.
In the given circle
The Centre of the circle is o
Length of chord AC = 18
Since we know that,
The line segment connecting any two locations on a circle's circumference is known as the chord of the circle. It should be emphasized that the diameter is the circle's longest chord, which runs through its centre.
And we can see that,
B is the midpoint of the chord AC of the circle
Therefore The length of AB is just half of chord AC
Therefore,
AB = AC/2
And it is given that AC = 18
Therefore,
AB = 18/2
Hence,
AB = 9
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Select the correct answer from each drop-down menu. At a business conference, there were 10 social workers, 16 doctors, 5 lawyers, and 2 journalists. If a person is picked at random from the entire group, it is to be/likely/unlikey/niether. be a lawyer, and it is to be a doctor.
Answer:
If a person is picked at random from the entire group, it is
unlikely
to be a lawyer, and it is.....
Unlikely was right but likely was wrong
Step-by-step explanation:
I honestly don't know the answer and that the person above me makes no sense.
he said "If a person is picked at random from the entire group, it is
unlikely
to be a lawyer, and it is.....
Unlikely was right but likely was wrong
WHAT IS THE ANSWER TO THE DOCTOR PART???
What is the midpoint of the segment below?
(3,5)
(-6,-6)
A. (-1.5, -0.5)
B. (0,0)
C. (1.5, 0.5)
D. (0.5, -0.5)
Answer:
The answer is option A.
( - 1.5 , - 0.5)Step-by-step explanation:
Midpoint of a line is given by
[tex] (\frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )[/tex]
Where ( x1 , y1 ) and ( x2 , y2) are the points
Midpoint of (3 , 5) and ( - 6 , - 6) is
[tex]( \frac{3 - 6}{2} , \: \frac{5 - 6}{2} )= ( - \frac{3}{2} , \: - \frac{1}{2} )[/tex]
We have the final answer as
( - 1.5 , - 0.5)
Hope this helps you.
Answer:
A. (-1.5, -0.5)Step-by-step explanation:
[tex](3,5), (-6,-6)\\Midpoint = [\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} ]\\x_1 = 3\\y_1=5\\x_2 =-6\\y_2 = -6\\\\Midpoint = [\frac{3+(-6)}{2} , \frac{5+(-6)}{2} ]\\Midpoint = [ \frac{3-6}{2} , \frac{5-6}{2} ]\\\\Midpoint = [-\frac{3}{2} ,-1/2]\\\\Midpoint = [ -1.5 , -0.5][/tex]
WILL MARK BRAINLIEST Beth has a graph to represent her distance when she runs 5 miles per hour. What would the point (2, 10) mean on her graph? Explain what this graph might look like.
Answer:
Ok so you have to find how much it goes up at a time. So the first one is 1,5. Then multiply both by 5 to get 5,25. That is your answer then. The graph will have 5 on the bottom and 25 on the side.
Step-by-step explanation:
1. George want to score at least a 90% on his math tests this quarter. So far his test scores are 88, 97 and
80. What does George need to score on his last test to average at least 90%?
Define variable:
Equation:
Solution:
check my work please! it’s number 1 :)
Answer:
Yes you are correct.
Step-by-step explanation:
The best way to check theese types of questions is go back in plug in X with your answer so 88+97+80+90(which is x)=360 then divide by 4 and get 90! So yes you are correct good job!
Isabella filled her pool with water at a constant rate. The table compares the remaining volume of water left to fill the pool (in liters) and the time since Isabella started filling the pool (in minutes).
Time (m) Remaining Volume (L)
4 148
6 112
8 76
What is the size of her pool?
Answer:
It was kinda hard to really understand your question but as of all the information that I received the answer is 220 liters
Step-by-step explanation:
is 5 rational or irrational
Answer:Rational
Step-by-step explanation:
Every integer is a rational number, since each integer n can be written in the form n/1.
Answer:
Rational
................
Complete the point-slope equation of the line through (1,3) (5,1) y-3=?
Answer:
[tex]\huge\boxed{y-3=-\frac{1}{2}(x-1)}[/tex]
Step-by-step explanation:
Point-slope is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]m-\text{This represents the slope.}\\\\(x_1,y_1)-\text{This represents the point used in the equation.}[/tex]
Our goal:We have to complete the point-slope equation of the line through (1,3) (5,1).
--------------------------------------------------------
We have a incomplete equation of the line.
[tex]y-3=m(x-x_1)[/tex]
We need to find the slope of the line, and the value of [tex]x_1[/tex].
--------------------------------------------------------
Finding 'x1':It seems that the value of 3 was used to be [tex]y_1[/tex]. This means that the point [tex](1,3)[/tex] was used for the equation. This means that [tex]x_1[/tex] would have to be 1.
Finding Slope:Slope is rise over run.
[tex]m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (1,3) and (5,1).
[tex]m=\frac{1-3}{5-1}=\frac{-2}{4}=\frac{-1}{2}=\boxed{-\frac{1}{2}}[/tex]
The slope is one-half.
--------------------------------------------------------
We now have enough information to complete the point-slope equation.
[tex]{\left \{ {{x_1=1} \atop {m=-\frac{1}{2} }} \right.}\\\\y-3=m(x-x_1)\rightarrow\boxed{y-3=-\frac{1}{2}(x-1)}[/tex]
Our final equation is:
[tex]y-3=-\frac{1}{2}(x-1)[/tex]
Which of the following relations is not a function? x y 0 1 1 4 -1 4 x y 0 2 1 3 1 -3 x y 0 -2 1 -3 -2 5 x y 0 -2 1 -2 2 -2
Answer:
-1 4 x y
Step-by-step explanation:
Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2).
Answer:
(-6,6), (0,12), (4,8)
Step-by-step explanation:
To dilate an object, we need to multiply the x and y values by the given scale factor.
In this case the scale factor is 2 --> 2(x, y)
Before-> After dilation
2(-3,3) = (-6,6)
2(0,6) = (0,12)
2(2,4) = (4,8)
Please leave a 'thanks' if this helps!
There are 20 players on a soccer team. From them, a captain and an alternate captain have to be chosen. How many possibilities are there?
Answer:
190 possibilities.
Step-by-step explanation:
The problem is called 20 choose 2, given by the formula for combinations
C(20,2) = 20! / (2! (20-2)!) = 190
alternatively, we can reason it this way:
there are 20 choices to choose a captain and 19 choices for an alternate captain for a total of 380 ways.
However, there are 20 choices to choose an alternate captain and 19 choices for a captain for a total of 380 ways.
Since we are essentially double counting every choice of the posts, we need to divide 380 by 2 to get 190 ways.