Answer: U = 600 m/s
Step-by-step explanation:
Given that an aeroplane covers a distance of 1500km in a certain time t at a certain speed U.
After increasing the speed by 100km/hr, that is, V = U + 100 it covers the same distance in a time which is half an hour less than the previous time. That is t2 = t - 0.5.
From the first statement
Speed = distance/ time
Distance = speed × time
1500 = Ut
Make t the subject of the formula
t = 1500/U ..... (1)
From the second statement
Distance = speed × time
1500 = (U + 100) × ( t - 0.5 )
Open the bracket
1500 = Ut - 0.5U + 100t - 50
Collect the like terms
1550 = Ut - 0.5U + 100t .... (2)
Substitutes equation 1 into 2
1550 = 1500U/U - 0.5U + 100(1500/U)
1550 = 1500 - 0.5U + 150000/U
1550 - 1500 = (150000 - 0.5U^2)/U
Cross multiply
50U = 150000 - 0.5U^2
0.5U^2 + 50U - 150000 = 0
Divide all by 0.5
U^2 + 100U - 300000 = 0
Using completing the square method
U^2 + 100U = 300000
U^2 + 100U + 50^2 = 300000 + 50^2
(U + 50)^2 = 302500
U + 50 = sqrt(302500)
U + 50 = +/-(550)
U = 50 + 550 or 50 - 550
U = 600 or - 500
Since U is of the same direction, it is
positive. Therefore, the previous speed of the aeroplane is 600 m/s
Answer:
500km/hr
Step-by-step explanation:
The formula for Speed (km/hr) = Distance / Time
Where S = Speed
D = Distance
T = Time
S = D/T
From the question, the aeroplane covered a distance of 1500 km
S = 1500/ T
ST = 1500
Time taken( T ) = 1500/S ......... Equation 1
We are told from the question that speed was increases by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time
This is expressed mathematically as:
The new speed =S + 100km/hr
The new Time taken = 1500/ S - 1/2....... Equation 2
Also since Time = Distance / Speed
The new Time taken also = 1500/ S + 100 ......... Equation 3
Step 1
We would simplify Equation 2:
Time = 1500/S - 1/2
Find the Lowest common multiple = 2
Time = (2 × 1500 - S )/ 2S
Time = 3000 - S / 2S ......... Equation 4
Step 2
Equate Equation 4 and 3 together since they are both equal to time taken
1500/ S + 100 = 3000 - S / 2S
We cross multiply
2S × 1500 = (S + 100) ( 3000 - S)
3000S = 3000S - S² + 300000 - 100S
3000S - 3000S + S² - 300000 + 100S = 0
S² + 100S - 300000 = 0
Step 3
We solve for S = Speed by using factorisation method.
S² + 100x - 300000 = 0
S² - 500S + 600S - 300000 = 0
(S² - 500S) + (600S - 300000) = 0
S(S - 500) + 600(S - 500) = 0
(S - 500) (S + 600) = 0
S - 500 = 0, S = 500
S + 600 = 0 , S = -600
Our answer cannot be in negative form, hence, the previous speed of the aeroplane = 500km/hr
what is the answer to -3x - 6+ (-1)
Answer:
-3x-7
Step-by-step explanation:
Answer:
-3x - 7
Step-by-step explanation:
the altitude of a right circular cone is 8cm and the radius of the base is 6cm what is its total surface area
Answer:
301.44 cm ^ 2
Step-by-step explanation:
We have that the total surface area of a cone would be the sum of the base area and the lateral surface area.
the area of the base, being a circle is pi * r ^ 2
the lateral area would come being the multiplication between the inclined height, the radius and the number pi, that is to say pi * r * l
the inclined height is calculated using the Pythagorean theorem, the legs being the radius and the altitude, thus:
l ^ 2 = 6 ^ 2 + 8 ^ 2
l ^ 2 = 100
l = 10
Therefore, we can replace:
A = 3.14 * 6 ^ 2 + 3.14 * 10 * 6
A = 301.44
It means that the total surface area is 301.44 cm ^ 2
Match each logarithm to its value
Answer:
D
C
B
A
Step-by-step explanation:
In the picture ⬆️
Llllllllllllllllllllll
Evaluate x ÷ y for x = 3 and y = 12. Your answer: A. 0.25 B. 4 C. 9 D. 36
Answer:
B or D
Step-by-step explanation:
best bet is B
Answer:4
Step-by-step explanation:
Two stacks of 23 quarters each are shown below. One stack forms a cylinder but the other stack does not form a cylinder.
Complete question:
Two stacks of 23 quarters each are shown below. One stack forms a cylinder but the other stack does not form a cylinder.
Use Cavelieri’s principle to explain why the volumes of these two stacks of quarters are equal.
Answer:
In this image, we have 2 stacks, whereby one stack forms a cylinder and the other stack doesn't form a cylinder.
We are required to use Cavelieri’s principle to explain why the volumes of the two stacks of quarters are equal.
Cavelieri’s principle states that the volume of two solid figures will be equal if both figures have equal height, the distance from their respective base is equal and their corresponding cross section are of the same area.
Here, we can see that the quater of each stack have the same base area. Since, both quaters have the same base area, there will be no difference in the area of the cross section of both stacks.
The volume of these 2 stacks of quarters will be equal because both stacks have have the same height of 23 quaters.
A machine is programmed to make a horizontal cut along
the x-axis, trimming the sides of the satellite dish. What is
the resulting width of the satellite dish, in feet?
Answer:12ft
Step-by-step explanation:
As per linear equation, the resulting width of the satellite dish is 12 feet.
What is a linear equation?A linear equation is an equation that may contain one or multiple variable with the highest power of the variable is 1.
The width of the satellite dish extended along with the x-axis from (- 6, 0) to (6, 0).
Therefore, the width of the satellite dish is
= (6 + 6) feet
= 12 feet
Therefore, the width is 12 feet.
Learn more about a linear equation here: https://brainly.com/question/16908943
#SPJ3
please help me i really need help i dont understand
write an inequality for the folowing statement :
The sum of triple a number x and eight is atleast a number y.
Inequality : ___________
Cupcakes cost $2.00 each. Ballons cost $1.25 each. Her bill was no less than $25.00.Write an inequality that could be used to find n, the greatest possible number of cupcakes, and m, the greatest possible number of ballons , she bought. Inequality:____________
Answer:
Step-by-step explanation:
First problem: 3x + 8 ≥ y
Second problem: Represent the number of cupcakes with n and that of balloons by m. Then ($2/cupcake)(n) + ($1.25/balloon)(m) ≥ $25
Solve this equation 3x-1/5-2/9x=124/5 , simply by combining like terms, Which terms can be combined? Isolate the variable term by adding this value to both sides of the equation?
Answer:
x=9
Step-by-step explanation:
x in (-oo:+oo)
3*x-((2/9)*x)-(1/5) = 124/5 // - 124/5
3*x-((2/9)*x)-(1/5)-(124/5) = 0
3*x+(-2/9)*x-1/5-124/5 = 0
25/9*x-25 = 0 // + 25
25/9*x = 25 // : 25/9
x = 25/25/9
x = 9
Answer:
1/5
Step-by-step explanation:
i got it right
what is the slope of the linear relationship shown in this table?
Answer:
-1/2
Step-by-step explanation:
Slope is change in x over change in y
so..
2-(-4)
over
-1-11
so...
-6/12 or -1/2
how do you figure out what is a trinomial?
Answer:
To factor trinomals in the form of x^2+bx+c, you have to find 2 integers, r and s, whose product is c, and whose sum is b. You have to rewrite the trinomial as x^2+rx+sx+c and then using the grouping and distribution of property to factor the polynomial. The result of the factors will be (x+r) and (x+s)
Step-by-step explanation:
Can someone help with this question?
Answer:
1. 5
2. -3
3. -4
4. 0
Step-by-step explanation:
Substitute the value of x in the equation with each of the x's given in the table.
Example:
When x = -1
y = -1^2 - 4 x -1 = 1 - 4 = -3
When x = 4
y = 4^2 - 4 x 4 = 16 - 16 = 0
Please add brainiest
What value of b with cause the system to have an infinite number of solutions?
A.
B.
C.
or
D.
Step-by-step explanation:
-3x+3x-(b÷2)=-3
0-(b÷2)=-3
-(b÷2)=-3
b=-2×-3=+6
=> b=6
This is a compound event problem. (Check the videos from this week's assignments.).
You roll a fair six-sided die and spin a spinner. What is the probability that the die shows a 4 and the spinner lands on yellow?
Fraction
Decimal (provide the first 5 decimal numbers)
Percent % (Round to the nearest tenth.)
Answer:
1/12
Step-by-step explanation:
The desired probability is the product of the probabilities of two independent events. The probability of obtaining a 4 on the fair 6-sided die is 1/6 (one out of 6) and that of the spinner's coming to rest on Yellow is 2/4, or 1/2.
Calculate the probability of this joint event as follows: (1/6)(1/2) = 1/12
The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached the
spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s?
Answer:
[tex]s = \frac{3}{10}m[/tex]
I hope this helps!
Answer: s=3/10m
Step-by-step explanation:
I took the math test in Edgenuity.
Hope this helps!
Anyone know the Answer asap
Answer:
39/10
Step-by-step explanation:
Answer:
39/10
Step-by-step explanation:
happy to help u:)
can you do this for me 3x+y=10, 2x^2+y^2=19
Answer:
1 , 29/11
Step-by-step explanation:
3x+y = 10 ....(1)
2x² +y² = 19 ....(2)
3x+y= 10
y = 10-3x
substituting the value of y in 2nd equation
2x² + y² = 19
2x² + (10-3x)² = 19
2x² + 100 + 9x² - 60x -19 = 0
11x² - 60x +81 = 0
11x² - 33x - 27x + 81 = 0
11x( x-3) - 27(x-3) = 0
(x-3)(11x-27) = 0
x = 3, 27/11
substituting x value on first equation
x= 3 x= 27/11
y= 10-3(3) y= 10 - 81/11
= 10-9 = (110-81)/11
= 1 = 29/11
Hope it helps...
^9 belongs to what family of real numbers?
Answer:
Rational number
Step-by-step explanation:
Rational numbers repeat and terminate. The square root of 9 is 3, and 3 is a whole number as well as a number that terminates, which makes it a rational number
If this trapezoid is moved through the translation (x+3,y-2), what will be the coordinates of be?
Answer:
C'(1, 2 )
Step-by-step explanation:
The translation (x + 3, y - 2 ) means add 3 to the original x- coordinate and subtract 2 from the original y- coordinate, thus
C(- 2, 4 ) → C'(- 2 + 3, 4 - 2 ) → C'(1, 2 )
Would someone help me with this?
Answer:
A,E
Step-by-step explanation:
A The minimum number of pages read was 24. The smallest number is the dot on the left side which is at 24
E The mean is the middle line in the box, this is at 48
*I WILL MARK YOU BRAINLIEST!!!!*
Answer:
The answer would be -9 and -3 which would be B and D
Step-by-step explanation:
Suppose statement p is true but statement q is false. Which of these compound statements are true? Check all that apply. p ∧ q p ∨ q p → q q → p p ↔ q q ↔ p
Answer:
p ∨ q → True
(q → p) → True
Step-by-step explanation:
If the truth value of the statement p is 'True' and truth value of statement q is 'False',
p ∧ q → False [Conjunction of both the statements will be true only when both the statements are True]
p ∨ q → True [Disjunction of two statements will be false only when both the statements are false]
(p → q) → False
(q → p) → True [Implication of both the statements is false only when p is true and q is false otherwise true]
(p ↔ q) → False [Bi-conditional statements are true if and only when both the statements are true]
(q ↔ p) → False
Answer:
Your answer would be answer two and four.
Can someone please help me to finish this up and I don’t know
Answer:
This is an enlargement.
Step-by-step explanation:
This is an enlargement.
A reduction would be smaller
A rotation would be changing the angle and a reflection would be a mirror image
Onsider the enlargement of the triangle with a scale factor of 8 2 triangles have corresponding side lengths of 8 centimeters and 64 centimeters. Side A corresponds with a side with length of 2 centimeters. Side A = 2(8) = 16 cm. What is the length of side B?
Answer: Incomplete question
Step-by-step explanation: The question does not provide a diagram, and that makes it difficult to determine which side is labelled as B. Nevertheless I will give you clues to help you answer your question by explaining this topic which is SIMILAR TRIANGLES.
When you have been given two triangles with a scale factor, the scale factor is an important part of answering the question eventually.
Consider a triangle which I shall call triangle 1, with sides abc and another triangle ABC, which I shall call triangle 2. The scale factor is 8, which means triangle 1 can be enlarged into a similar triangle by simply multiplying any corresponding side by 8. Hence, if in triangle abc, you have a side that measures 8 centimetres, the corresponding side in triangle ABC would be 8 times 8 which equals 64 centimetres.
The question states that side A corresponds with a side measuring length 2 centimetres. That means side A is derived as 2 times 8 which equals 16 centimetres, as explained above (and as shown in the question). Therefore side B which is yet unknown shall also be the corresponding side in triangle 1 multiplied by 8.
Since the corresponding side was not stated, I shall assume for the sake of explanation that the corresponding side is 10 centimetres. That means, side B would now be derived as 10 times 8 which equals 80 centimetres.
These can be expressed mathematically as follows;
If A = 16, a = 2 and b = 10 then B would be calculated as follows;
A/a = B/b
16/2 = B/10
By cross multiplication, you now have
16 * 10 = 2 * B
160/2 = B
80 = B
Following these steps along with the explanations, the length of side B can be derived if the value of its corresponding side is given or a diagram is provided.
Answer:
its 40 because the dude above is an but face (sorry) (not sorry u suk)
Step-by-step explanation:
welcum
Simplify (5 + 1)^2- (11 +32) divided by 4
Answer:
-7/4
Step-by-step explanation:
((5 + 1)^2- (11 +32))/ 4=(36-43)/4= -7/4
Answer:
31
Step-by-step explanation:
The point-slope from of a line that has a slope of -2 and passes through the point (5,-2)
Step-by-step explanation:
y + 2. = -2(x - 5)
y + 2 = -2x + 10.
y = -2x + 8
A punter kicks a football into the air with an initial velocity of 84 feet per second. The equation
[tex] {16}t^{2} + 84[/tex]
gives the height of the ball after t seconds.
What is the maximum height of the football.
Answer:
84feetStep-by-step explanation:
Given the height of the ball modelled by the equation h(t)=16t²+84 after t secs. At the maximum height, the velocity of the ball is zero.
Velocity V is the change of rate of displacement.
V = dh/dt = 32t
0 = 32t
t = 0secs
at t = 0;
h(0) = 16(0)²+84
h(0) = 84feet
This shows that the maximum height of the ball is 84feet
Determine the number of solutions for the quadratic function f(x) = -x^2 + 3x - 9.
Answer:
0
Step-by-step explanation:
Rewrite the equation as x^2-3x+9=0
find the determinant.
D = b^2-4ac = (-3)^2-4*1*9 <0
no solution
difference in the abscissa of points A (4,3) and B (-7,2)
Answer:
The difference is 11 units
Step-by-step explanation:
When we talk of the abscissa, we are referring to the x-axis.
So what this question is asking us is the difference between the values of the x-axis
At point A, the value is 4 while at point B, the value here is -7
So the difference between this two would be 4-(-7) = 4 + 7 = 11 units
Solve for x X+10y=1550
Answer:
X=1550-10y
Step-by-step explanation:
X+10y=1550
Subtract 10y from each side
X+10y- 10y=1550-10y
X=1550-10y
Answer:
[tex]x = 1550 - 10y[/tex]
Step-by-step explanation:
[tex]x + 10y = 1550 \\ x + 10y - 10y = 1550 - 10y \\ x = 1550 - 10y[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What’s the sum of -30 and 29
Answer:
The answer of -1.
Step-by-step explanation:
You have to add both numbers together :
[tex] - 30 + 29 \\ = - 1[/tex]
[tex] - 30 + 29 \\ = - 1 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
