Suppose the ratio of Lev's age to Mina's age is $1 : 2$ and the ratio of Mina's age to Naomi's age is $3 : 4$. What is the ratio of Lev's age to Naomi's age? Give your answer in simplest form.
Answer:
3:8
Step-by-step explanation:
The ratio of Mina's age to Naomi's age is 3 : 4
Multiplying the above ratio by 2 = 6:8
The ratio of Lev's age to Mina's age is 1 : 2
Multiplying the above ratio by 3
= 3:6
Therefore, ratio of Lev's age to Naomi's age in simplest form.
= 3:8
Answer:
3:8
Step-by-step explanation:
Let L, M, and N stand for the three ages.
The given ratios tell us that
M = 2L
and
N = 4/3M.
Therefore,
N = 4/3 x 2L = 8/3L.
This means that Lev's and Naomi's ages are in the ratio 3:8.
PRACTISE NOW 11
Ex
15
Mr Lee drove from City P to City Q, which are 600 km apart. During his return journey,
his average speed was increased by 7 km/h and the time taken was 15 minutes less.
() 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.
(ii
) Solve the equation x² + 7x - 16 800 = 0, giving both your answers correct to
2 decimal places.
(iii) Find the time taken for the return journey.
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
50 PTS BRAINLIEST
Use Desmos to graph the following system of equations. Paste a link to your Desmos graph.
y = 2/3x-2
y = 2/3x+5
How many solutions does the graph have?
Answer:
it has 5 hopefully this helps you with work
Answer:
No solutionsStep-by-step explanation:
Given lines:
y = 2/3x-2 y = 2/3x+5These have same slopes of 2/3 and therefore are parallel, so no intersection. There is no solution if lines don't intersect.
The graph is attached as well to show lines are parallel.
what is the common difference of the arithmetic sequence 5,8,11,14?
Answer:
3
Step-by-step explanation:
8-5= 3
11-8= 3
14-11= 3
Answer:
common difference = difference between two consecutive number in a given series
hence,
8-5=3
common difference =3
2. Determine the value of each variable for parallelogram INDY has diagonals that intersec at P.1P=3x DP = 6x - 2 NP = 3y and YP=7x-2,
Answer:
x = 2/3 and y = 8/9
Step-by-step explanation:
If a parallelogram INDY has diagonals that intersects at P, then O bisects ID and YN
Hence IP = PD and NP = YP
Given
IP=3x
DP = 6x - 2
NP = 3y and
YP=7x-2,
Substitute
3x = 6x-2
3x-6x = -2
-3x = -2
x = 2/3
x = 0.67
Also NP = YP
3y = 7x-2
3y = 7(2/3) - 2
3y = 14/3 - 2
3y = 14-6/3
3y = 8/3
9y = 8
y = 8/9
Hence x = 2/3 and y = 8/9
Which graph shows a vertical translation of ƒ(x) up 5 units to give a new function g(x)?
I mist that one its not the first one
Step-by-step explanation:
Answer:
The correct answer is the last image...I just got it right on the quiz.
Step-by-step explanation:
PLS HELP I REALLY NEED IT RNNNNNN 20 POINTSSS
Which function matches the mapping shown?
A) f(x) = 2x
B) f(x) = 4x
C) f(x) = x4
D) f(x) = x + 4
Answer:
B.f(x)=4x
Step-by-step explanation:
Multiply x value by 4
How do I solve 2/3x-1=-3
An equation is different from an expression because it has...
Answer:
Because it bears an equal sign
Expressions don't have a definite solution to the problem.
how many significant figures are in 2856.110
♀️♀️♀️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
what is the minimum value of the parabola y = x^2 + 10 ?
A billiard ball is struck by a cue. It travels 100 cm before ricocheting off a rail and traveling another 100 cm into a corner pocket. The angle between the path as the ball approaches the rail and the path after it strikes the rail is 45 degrees. How far is the corner pocket from where the cue initially struck the ball?
Answer:
76.53 cm
Step-by-step explanation:
From the question, the triangle formed has 2 sides and an included angle ;
Angle, θ = C = 45°
We use cosine rule :
Taking the side to find as c
a = 100 ; b = 100
From cosine rule :
c = sqrt(a² + b² - 2abCosC)
c = sqrt(100² + 100² - 2(100*100)Cos45
c = sqrt(10000 + 10000 - 20000 * 0.7071067)
c = sqrt(20000 - 14142.135)
c = sqrt(5857.865)
c = 76.536690
c = 76.53 cm
What is the slope????
Answer:
-6
Step-by-step explanation:
is that quizzes join lol
solve : 3x - 3 = 2x
if you can show workings that would be great thank you !
Answer:
3
Step-by-step explanation:
3x-3=2x
3x-2x=3
x=3
Answer:
x=3
Step-by-step explanation:
3x - 3 = 2x
-3x -3x
-3 = -x
The x cannot be a negative so you divide both sides by -1 and then the answer becomes x=3
can someone help me find the slopes for all three problems this was due two days ago
:(
Two of the three representations have lines with the same slope. What is that slope?
Answer:
Step-by-step explanation:
3rd times the charm. Someone please help me.
What is 9876 times 567
Answer:
5599692
Step-by-step explanation:
Simply do the multiplication out, then you should get the answer:
5599692
Answer:5599692
Step-by-step explanation:
just multy and you will get it
POSSIBLE POINTS: 33.33
Tyler can complete his Algebra Il project in 2.5 hours, but if he works with Luke they can finish in 1.5 hours. How long would it take Luke to finish the
project on his own?
10×-50
---------- =13
5
Answer:
I think it's -500 = 135
Step-by-step explanation:
multiply 10 and -50 to get -500
Figure ABCD is a rectangle. Find the value of x.
X= [?]
the answer is
x=2
qwertyuioplkjhgfdsazxcvbnmzxcvbnmasdfghjkgfwertyuytrewertyujhgfdsdefgbhgvftcdrxsxdrcftvgyvftcx4f
The magnitude and direction of two vectors are shown in the diagram. What is the magnitude of their sum?
Answer:
2√5
Step-by-step explanation:
Using the formula for calculating resultant
R = √Fx + Fy
\sum Fx = -2sin 45 + 4 cos 45
\sum Fx = 2cos45
\sum Fx = 2(1/√2)
\sum Fx = 2/√2
Similarly;
\sum Fy = 2 cos 45 + 4 sin45
\sum Fx = 2(1/√2) + 4(1/√2)
\sum Fx = 6/√2
Magnitude = √(2/√2)²+6/√2)²
Magnitude = √4/2 + 36/2
Magnitude = √2+18
Magnitude = √20
Magnitude = 2√5
Hence the magnitude of their sum is 2√5
Answer:
2√5
Step-by-step explanation:
Izzy's Frozen Treats sells both frozen yogurt and frozen custard by the ounce. Last week, Marco noticed that a 3-ounce cup of frozen yogurt cost less than a 3-ounce cup of frozen custard. Marco has $5 to spend at Izzy's Frozen Treats today. Which can he buy more of, frozen yogurt or frozen custard?
A)frozen yogurt
B)frozen custard
plz show the work i really need help and this is Compare rates: word problems
Answer:
A. Frozen yogurt
Step-by-step explanation:
The frozen yogurt costs less than the frozen custard, even though you get the same amount (3 ounces)
No matter how much money Marco has, he would be able to buy more of the frozen yogurt because it has a cheaper unit rate.
So, the answer is A, frozen yogurt
evaluate 2-(-4) +(-and) where Y = 7.
Answer:
2-4=4+7=11 so that is the answer begginer
The 25 students in Mr. Martinez’s class vote on their favorite farm animal. 40% like pigs. How many students like pigs?
Answer:
10
Step-by-step explanation:
Find the value of x.
.
10
7
Answer:
X = 12.21
Step-by-step explanation:
Since this is a right triangle, use the formula A^2 + B^2 = C^2 and plug in appropriate values.
(10)^2 + (7)^2 = C^2
100 + 49 = C^2
149 = C^2
12.2065 = C
Rounded to two decimal places, this makes X equal to 12.21.
The required value of x is 12.21 for the given right triangle.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
Since this is a right triangle, use the formula A² + B² = C² and substitute appropriate values.
(10)² + (7)² = x²
100 + 49 = x²
149 = x²
x = √149
x = 12.2066
Rounded to two decimal places,
x = 12.21
Therefore, the required value of x is 12.21.
Learn more about Pythagoras's theorem here:
brainly.com/question/343682
#SPJ2
URGENT HELP NEEDED SO PLS HELP
Answer:
1. 18π
2. 39.27cm
3. 4[tex]x^{5}[/tex][tex]z^{8}[/tex]
Please help me with this
Answer:
True
Step-by-step explanation:
Cuz if u substitute (3,-3/2) it would work
Y = 1/2x - 3
-3/2 = 1/2(3)-3
-3/2 = 1.5 - 3
-3/2 = -1.5
& -3/2 is -1.5 as a decimal lol
please help :(
how do you know you have a direct variation in the relationship between two quantities?
Fill in the missing number in this newspaper report:
Houses cost £100 000 one year ago
They now cost £
This is a 25% increase
How much does it now cost ?
Answer:
£125000
Step-by-step explanation:
Original cost of house = £100 000
Percent increase = 25%
Increase in price = 25% of 100,000
Increase in price = 0.25 * 100,000
Increase in price = 25000
New cost = original cost + Increment
New cost = 100,000 + 25,000
New cost = 125,000
Hence it now cost £125000
The perimeter of a triangle is 19 units. The second side is four units longer than the first side and the third side is three times the length of the first side. What are the lengths of the sides?
Answer:
First: 3 units Second: 7 units Third: 9 units
Step-by-step explanation:
19=x+(x+4)+3x
19=5x+4
15=5x
x=3
first side is 3 units
3+4=7
second side is 7 units
3*3=9
third side is 9 units