Answer:
i. x² + 7x - 16800 = 0 ii. x = 126.16 km/h or -133.16 km/h iii. 5.01 h
Step-by-step explanation:
i. If he drove at an average speed of x km/h on his journey from City P to City Q formulate an equation in x and show that it reduces to x2 + 7x – 16 800 = 0.
For the first journey from City P to City Q, with Mr Lee moving at an average speed of x km/h, he reaches there in time, t and covers the distance, d = 600 km
So, xt = 600 (1)
On his return journey from City Q to CIty P, his average speed increases by 7 km/h, so it is (x + 7)km/h and his time is 15 minutes less than his first journey. 15 min = 15/60 h = 0.25 h, we have that his time for the journey is (t - 0.25) h. Since the distance covered is the same d = 600 km,
We have (x + 7)(t - 0.25) = 600 (2)
Expanding the brackets, we have
xt - 0.25x + 7t - 0.25(7) = 600
xt - 0.25x + 7t - 1.75 = 600
From (1) t = 600/x and xt = 600
Substituting these into the equation, we have
600 - 0.25x + 7(600/x) - 1.75 = 600
simplifying
-0.25x + 4200/x - 1.75 = 600 - 600
-0.25x + 4200/x - 1.75 = 0
multiplying through by x, we have
-0.25x² + 4200 - 1.75x = 0
dividing through by -0.25, we have
-0.25x²/-0.25 + 4200/-0.25 - 1.75x/-0.25 = 0
x² - 16800 + 7x = 0
re-arranging, we have
x² + 7x - 16800 = 0
ii. Solve the equation x² + 7x - 16 800 = 0, giving both your answers correct to 2 decimal places.
Using the quadratic formula, we solve x² + 7x - 16800 = 0 for x
So, [tex]x = \frac{-7 +/-\sqrt{7^{2} - 4 X 1 X -16800} }{2 X 1}\\x = \frac{-7 +/-\sqrt{49 + 67200} }{2} \\x = \frac{-7 +/-\sqrt{67249} }{2} \\x = \frac{-7 +/- 259.32}{2} \\x = \frac{-7 + 259.32}{2} or x = \frac{-7 - 259.32}{2} \\x = 252.32/2 or x= -266.32/2\\x = 126.16 km/hor x = -133.16 km/h[/tex]
So, x = 126.16 km/h or -133.16 km/h
iii. Find the time taken for the return journey
The time taken for the return journey is t' = t + 0.25. Now. t = 600/x
Since x cannot be negative, we use x = 126.16 km/h.
So, t = 600/x = 600/126.16 = 4.76 h
t' = t + 0.25
t' = 4.76 + 0.25
t' = 5.01 h
What is the slope of (-1,-2) and (5,-3)
Answer:
M = -1/6
Step-by-step explanation:
I need number 7!plz help
Answer:
x-4,y-3
Step-by-step explanation:
left = negative , down = negative
When salt and water are combined, they form a salt or saline solution. How much ml of water must be added to 150 mL of an 80% saline solution to produce a 30% saline solution?
Answer:
We must add 400 ml of water.
Step-by-step explanation:
We can use the following equation:
[tex]C_{i}V_{i}=C_{f}V_{f}[/tex]
Where:
C(i) is the initial concentration of the solution (80%)C(f) is the final concentration of the solution (30%)V(i) is the initial volume (150 ml)V(f) is the final volumeNow, we just need to solve the equation for V(f).
[tex]V_{f}=\frac{C_{i}V_{i}}{C_{f}}[/tex]
[tex]V_{f}=\frac{80*150}{30}[/tex]
[tex]V_{f}=400\: ml[/tex]
Therefore, we must add 400 ml of water.
I hope it helps you!
A coffee can in the shape of a cylinder has a Volume of V = 67.57 in. Find the forumla that gives the radius of the coffee can, r, in terms of the volume V and height h. If the height is 7.5 inches, what is the radius of the coffee can?
Answer:
r = sq rt [v/(h x Pi)]
r = 1.69
Step-by-step explanation:
v=h x Pi x r^2
r^2 = v/(h x Pi)
r = sq rt [v/(h x Pi)]
r = sq rt [67.57 / (7.5 x 3.14)]
r = sq rt 2.8692
r = 1.69
Dennis needs to fix a leaky roof on his house but does not own a ladder. He thinks that a 25-foot ladder will be
long enough to reach the roof, but he needs to be sure before he spends the money to buy one. He chooses a
point P on the ground where he can visually align the roof of his car with the edge of the house roof. Help Dennis
determine if a 25-foot ladder will be long enough for him to safely reach his roof.
Answer: 15 ft 9 in
Step-by-step explanation:
The division of fraction 9/14 by 15/2 in simplest form is 3/70 by dividing both the numerator and the denominator by the GCD
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. In this case, the reciprocal of 15/2 is 2/15. Therefore, we can rewrite the division as multiplication:
(9/14) * (2/15)
Next, we can multiply the numerators together and the denominators together:
(9 * 2) / (14 * 15)
Simplifying further, we get:
18 / 210
To simplify the fraction, we can find the greatest common divisor (GCD) of the numerator and the denominator, which is 6 in this case. Dividing both the numerator and the denominator by the GCD, we get:
18 ÷ 6 / 210 ÷ 6
This simplifies to:
3 / 35
Therefore, the division of 9/14 by 15/2 in simplest form is 3/70.
In summary, to divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Then, we simplify the resulting fraction by finding the GCD of the numerator and the denominator and dividing both by the GCD. Applying these steps to the given fractions, we obtain the simplified form of 3/70.
Learn more about fraction division here:
https://brainly.com/question/20725043
#SPJ6
i have no clue what im doing.. please help
Answer:
2
Step-by-step explanation:
If triangles are similar (like shape ratios are exactly the same), then, 21 ÷ 3 = 7. Now you know the ratio to apply. So, side with the length of 14 s/b divided by that ratio of 7, that is, 14 ÷ 7 = 2
BE NICE AND SOLVE PLS
Answer:
BC=FE=5
BC=5
BA=DE=11
angle A= angle D=27
Can someone plzzz help ASAP
Answer:
x = 7 √3 km
Step-by-step explanation:
Here, we want to get the value of x
As we can see, we have a right angled triangle with hypotenuse 14 km
we can use the Pythagoras’ theorem to get the value of x
Mathematically, the square of the hypotenuse equals the sum of the squares of the two other sides
Thus,
14^2 = x^2 + 7^2
x^2 = 196-49
x^2 = 147
x = 7 √3 km
Find 27.1% of 208. Round to the nearest tenth.
Answer:
56.4 is your answer
Correct me if I'm wrong.
Answer:
56.368
Step-by-step explanation:
what is 115.7 rouned the ones place
Answer:
brainliest please
Step-by-step explanation:
116
What is the difference of the polynomials?
(–2x3y2 + 4x2y3 – 3xy4) – (6x4y – 5x2y3 – y5)
–6x4y – 2x3y2 + 9x2y3 – 3xy4 + y5
–6x4y – 2x3y2 – x2y3 – 3xy4 – y5
–6x4y + 3x3y2 + 4x2y3 – 3xy4 + y5
–6x4y – 7x3y2 + 4x2y3 – 3xy4 – y5
Answer:
The first
Step-by-step explanation:
The difference of the given polynomials is - 6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵.
The given polynomials
(-2x³y² + 4x²y³ - 3xy⁴) - (6x⁴y - 5x²y³ - y⁵)
The difference in the given polynomialsThe difference in the given polynomials is calculated as follows;
(-2x³y² + 4x²y³ - 3xy⁴) - (6x⁴y - 5x²y³ - y⁵)
open the brackets;
-2x³y² + 4x²y³ - 3xy⁴ - 6x⁴y + 5x²y³ + y⁵
add similar terms together;
- 6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵
Thus, the difference of the given polynomials is - 6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵.
Learn more about difference between polynomials here: https://brainly.com/question/2833285
Please help I’ll give you brainleast and thanks
Answer:
i got 49
i think its correct
Step-by-step explanation:
HELP ASAP IM IN A LIVE LESSON
Answer: 70 Degrees
Step-by-step explanation:
65+45=110
180-110=70 degrees
so..my teacher NEEDS work from us so please don't put a random answer i need the work for that. thanks
Answer:
Original Equation: s + 3 1/2 = 8 1/2
Subtract 3/12 from both sides: s + 3 1/2 - 3 1/2 = 8 1/2 - 3 1/2
Simplify: s = 5
So, A is the correct answer.
Let me know if this helps!
Marcos debe pintar 5/9 de la cubierta de un velero. Al acabar el día ha pintado 21/36 . ¿Ha conseguido cumplir su objetivo? ¿Ha pintado más? ¿Ha pintado menos?
Answer:
a) Have you managed to meet your goal?
Yes
b) Have you painted more? Have you painted less?
You have painted more.
Step-by-step explanation:
Marcos should paint 5/9 of the deck of a sailboat.
At the end of the day he painted 21/36.
Reducing this to the simplest form = 21/36
Dividing Numerator and Denominator by 3
= 7/12
Finding the difference between both fractions
= 7/12 - 5/9
The Lowest Common Denominator = 36
= 21 - 20/36
= 1/36
Therefore:
a) Have you managed to meet your goal?
Yes
b) Have you painted more? Have you painted less?
You have painted more.
What is the solution of the system? Use elimination.
5x-6y=-32
3x+6y=48
Answer:
x=2 y=7
Step-by-step explanation:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Ali receives a 4% commission for all his sales. His sales for January were $15,000. What was the commission amount he earned for the month of January?
Answer:
$600
Step-by-step explanation:
Convert the 4% commission into a decimal, which is 0.04.Multiply the sales ($15,000) by the commission as a decimal (0.04). This is $600, which is the answer.Please Help Me!!!
Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home.
Andre wrote the inequality 3x + 10 ≤ 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality.
Solve Andre’s inequality and explain what the solution means.
Answer:
6 small cranes
Step-by-step explanation:
3x + 10 is less than or equal to 30
3 is the minutes for the small cranes
X is the amount of small cranes
10 is the minutes for the large crane
30 is the total time limit
first, subtract 10 from 30, which gives you 20 so
3x is less than or equal to 20.
to figure this out, divide 20 by 3, which gives you 6 with a remainder of two minutes.
Andre can make 6 small cranes.
Does anyone under stand this one ??
Answer:
its c i belive'
Step-by-step explanation:
-2(-5x - 10) + 30 = -110
Answer:
your answer will be x=−16
Step-by-step explanation:
Simplify −2(−5x−10)+30
10x+50=−110
10x=−160
Divide each term by 10
and simplify.
x=−16
I hope this helps ^_^
What is the area of triangle ABC? a \large 6\sqrt{3} square units b \large 18\sqrt{3} square units c \large 36\sqrt{3} square units d \large 72\sqrt{3} square units
question isn't clear but I believe you are asking for the area of triangle ABC given sides a, b, c
We use the example question:
Find the area (in square units) of the triangle described.
a = 49mm, b = 33mm, c = 18mm
Answer and explanation:
We apply Heron's formula to solve the area of a triangle given the sides of the triangle a, b, c
A= √s(s-a)(s-b)(s-c)
Where A = area of triangle in square units
s= semiperimeter(a+b+c/2) of a triangle
a, b, c= lengths of the sides of the triangle
Therefore area of triangle =√50(50-49)(50-33)(50-18)
= √27200
=164.92mm²
can someone please help its due soon.ill give brainliest!
Step-by-step explanation:
LINE K is linear equation
y = mx + b
m = delta y/ delta x
= 6/3
= 2
b = y-intercept (at x = 0, y = 0)
y = 2x
What is the value of x?
answer: 12
Step-by-step explanation:
Olivia is thinking of a number. she says, "my number is odd. It is a factor of 30 and a multiple of 3" There are two numbers she is thinking of, what are those numbers?
I need some help on this question! I will mark you if you answer.
Answer:
definitely 145
Step-by-step explanation:
It is 145 degrees I hope this helps :)
1. 6x - 29 = 115
2. 3y - 1 = 29
3. 4z - 32 = 36
find x, y, and z
Answer:
x = 24 , y = 10, z = 17
Step-by-step explanation:
Given
6x - 29 = 115
6x = 115 + 29
6x = 144
x = 144 / 6
x = 24
3y - 1 = 29
3y = 29 + 1
3y = 30
y = 30 / 3
y = 10
4z - 32 = 36
4z = 36 + 32
4z = 68
z = 68 / 4
z = 17
Hope it will help :)
-29=9-6k-2k - 1please do the work, i’ll mark as brainliest
Answer:
k = 37/8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
-29 = 9 - 6k - 2k - 1
Step 2: Solve for k
Combine like terms: -29 = 8 - 8k[Subtraction Property of Equality] Subtract 8 on both sides: -37 = -8k[Division Property of Equality] Divide -8 on both sides: 37/8 = kRewrite/Rearrange: k = 37/8Step 3: Check
Plug in k into the original equation to verify it's a solution.
Substitute in k: -29 = 9 - 6(37/8) - 2(37/8) - 1Multiply: -29 = 9 - 111/4 - 37/4 - 1Subtract: -29 = -75/4 - 37/4 - 1Subtract: -29 = -28 - 1Subtract: -29 = -29Here we see that -29 does indeed equal -29.
∴ k = 37/8 is the solution to the equation.
Sarah has 30 oranges an 48 plums . What is the ratio of oranges to plums
Answer:
30:48
Step-by-step explanation:
because there are 30 oranges and 48 plums. I got this by putting oranges in front of plums to get the ratio of 30:48
For Problem 10, simplify the expressions using properties of operations. 10. (t - 1) – (-7t+2)
Answer:
8t-3
Step-by-step explanation:
(t-1)-(-7t+2)
t-1+7t-2
t+7t-1-2
8t-1-2
8t-3
10x -20 plus 7x plus 4 equals 180 what is x