Answer:
f(x) = 2^x
Step-by-step explanation:
13. The Cyclone Coaster has 16
cars. Some of them hold 2
passengers and some hold 3
passengers. If there is room for
36 people altogether, how many
cars hold 3 passengers?
Answer:
Four cars that can hold 3 passengers
Step-by-step explanation:
The number of cars on the Cyclone Coaster = 16 cars
The number of passengers some cars hold = 2 passengers
The number of passengers the other cars hold = 3 passengers
The number of people altogether the Cyclone Coaster has room for = 36 people
Let x represent the number of cars that can hold 3 passengers, and let y represent the number of cars that can hold 2 passengers, we have;
3·x + 2·y = 36...(1)
x + y = 16...(2)
The value of x can be found by making y the subject of equation (1) and equation (2) and equating both values of y given in x as follows;
The value of y from equation (1) is, y₁ = (36 - 3·x)/2 = 18 - 3·x/2
∴ y₁ = 18 - 3·x/2
The value of y from equation (2) is, y₂ = 16 - x
Equating both y values, to find the coordinates of the common point to both equations, gives;
At the common point y₁ = y₂
By the substitution property of equality
∴ 18 - 3·x/2 = 16 - x
3·x/2 - x = 18 - 16 = 2
x/2 = 2
∴ x = 4
The number of cars that can hold 3 passengers, x = 4
(From y₂ = 16 - x, we have
y₁ = y₂ = 16 - 4 = 12
y = 1
The number of cars that can hold 2 passengers, y = 12).
Please help me expand theses and then help me factorise these brackets
Answer:
-9xy+16x
Step-by-step explanation:
x(y-2) +3x(6-y) -7xy
Distribute
xy -2x +18x-3xy -7xy
Combine like terms
-9xy+16x
Answer:
-9xy+16x
Step-by-step explanation:
x(y-2)+3x(6-y)-7xy
xy-2x+18x-3xy-7xy
xy-3xy-7xy-2x+18x
-9xy+16x
which of the following is a result of shiftinga circle with equation (×-2)+(y-3)^2= 25 to the left 2 unit ?
Answer:
x^2+(y-1)^2=25
Step-by-step explanation:
eqn of circle : (x-h)^2+(y-k)^2=r^2
center of circle = (h,k)
hence, the center of the current circle is (2,3)
moving 2 units to the left would make the center (0,1)
the radius would remain the same (5) , hence the new eqn would be
(x-0)^2+(y-1)^2=25
x^2+(y-1)^2=25
the LCM of 30 , 45,90
Answer:
540 is the answer
Step-by-step explanation:
hope u liked!
find the value of x in the triangle.
Answer:
The answer is 36°.
Hope it helps.
Step-by-step explanation:
• • •
please can someone help me?
Answer:
∠ 3 = 90°
Step-by-step explanation:
∠ 3 and ∠ 4 are adjacent angles on a straight line and sum to 180° , then
∠ 3 + ∠ 4 = 180°
∠ 3 + 90° = 180° ( subtract 90° from both sides )
∠ 3 = 90°
A game decreased in price by
2
3
. After the reduction it was priced at £17. What was the original price of the game?
Answer:
51
Step-by-step explanation:
which answer is correct
Answer:
a+b+c +90+90 = 540
Step-by-step explanation:
A five sided figure has interior angles that add to 540
a+b+c +90+90 = 540
The diameter of the circle above is 18 cm. What is the circumference of the circle? (Use = 3.14.)
Answer:
56.57
Step-by-step explanation:
See attached photo for steps
EDIT: I forgot to add 3.14, I am so sorry
Answer:
56.52
Step-by-step explanation:
Amanda teaches the art of quilling to 4 students. These students each teach the art of quilling to 4 other students. This process continues through 3 more generations.
4x4=16 16x3=48 so I think the answer is 48
(x-3).(x+3)-(x+5).(x-1)
25) A father is twice as old as his son. The sum oth of the ages is 99 years. Find their ages.
Answer:
If the son’s age is x, the father’s age is 2x.
If the son’s age is x, the father’s age is 2x.Ten years ago:
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 52
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 52
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 24
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 242x = 48
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 242x = 48So the son’s age is 24 and the father’s is 48. Ten years ago, they were 14 and 38, which adds up to 52.
Hope this answer helps you..!!.
.
Select this answer as the BRAINLIEST4.
Which point is NOT part of the solution of the inequality y < (3x + 1?
(-4, 12)
(0,0)
(2, -9)
(3, 15)
Answer: The non solutions of the inequality are A and D.
Step-by-step explanation:
martin is filling his bathtub, but he left the drain partially open. martin knows that it takes 8 minutes to fill his 40 gallon tub. the equation v = 2.5t represents the volume, v , of water that drains out of the tub in t minutes. if martin leaves the water on, will the tub ever overflow ?
please someone help
Answer:
Yes, it will overflow after 16 minutes..
Step-by-step explanation:
The tub fills at a rate of 5 gallons every minute, but it drains at a rate of 2.5 gallons every minute. This means that it fills twice as fast as it drains, so it would take 16 minutes for the tub to overflow. If you subtract the rate of draining from the rate of filling then the net rate of water going up is 2.5 gallons a minute.
Which of the following is a solution of y + x < -5?
(-2, -3)
(-4, -2)
(-3, -2)
(-1, -3)
The answer is (-4, -2)
-2 + -4 < -5
-6 < -5
Hope this helps!
Answer:
(- 4, - 2 )
Step-by-step explanation:
Substitute the coordinate value into the left side of the inequality and compare the value obtained to the right side
(- 2 , - 3 )
- 3 - 2 = - 5 = - 5 ← not a solution
(- 4, - 2 )
- 2 - 4 = - 6 < - 5 ← solution
(- 3, - 2 )
- 2 - 3 = - 5 ← not a solution
(- 1, - 3 )
- 3 - 1 = - 4 > - 5 ← not a solution
A group of rowdy teenagers near a wind turbine decide to place a pair of
pink shorts on the tip of one blade. They notice that the shorts are at its
maximum height of 16 metres at t = 10 s and its minimum height of 2 metres at
t = 25 s.
a) Determine the equation of the sinusoidal function that describes
the height of the shorts in terms of time.
b) Determine the height of the shorts at exactly t = 10 minutes, to
the nearest tenth of a metre.
Answer:
a) Sinusoidal functions are y = a sin [b(x-h)] + k (or)
y = a cos [b(x-h)] + k
Where a is amplitude a= (max-min)/2=(16-2)/2=7
period p= 2π/b
b=2π/30
Horizontal transformation to 10 units right h=10
k= (max+min)/2=(16+2)/2=9
h = 7 cos [π/15(t-10)]+ 9
b) t=10min=600 sec
substitue in the above equation
h=5.5m
A man drove his car a distance of 260 miles in 4 hours. If continuing at this rate how many miles will he travel in 8 miles
Answer:
520
Step-by-step explanation:
260/4=520/8
Method 1: Cross Multiply
Method 2: Find GCF
Solve for a. a+|-23+6|=-32
Plz help
Answer:
a = -49
Step-by-step explanation:
a+|-23+6|=-32
Simplify the absolute value term
a+|-17|=-32
a+17=-32
Subtract 17 from each side
a +17-17 = -32-17
a = -49
Answer:
a = −49
Step-by-step explanation:
a + ∣ − 17∣ = −32
a + 17 = −32
a = −32 − 17
Simplify.
-32 - 17 to -49.
Find x.
A. 6√6
B. 18
C. 9√2
D. 24√3
Answer:
C
Step-by-step explanation:
Indicate in standard form the equation of the line through the given points, writing the answer in the equation box below.
K(6, 4), L(-6, 4)
9514 1404 393
Answer:
y = 4
Step-by-step explanation:
The given points are on the horizontal line ...
y = 4
This is the standard-form equation of that line.
Bob is hired by Company A and is given an annual salary of $35 000 with a 10% raise
after 1 year. Sam is hired by Company B and is paid $3842.42 per month with a 5% raise
after 1 year. Determine the difference of salary after 1 year.
Step-by-step explanation:
Bob's salary : $35000 per year plus 10% after one year
100% = 35000
1% = 100%/100 = 35000/100 = $350
10% = 10×1% = 10×350 = $3500
so in total, his salary will be $35000+$3500 = $38500 after one year.
Sam's salary : $3842.42 per month plus 5% after one year.
100% = $3842.42 per month. but to make it comparable to Bob's salary, we need to calculate the annual salary.
so, 100% 12×3842.42 = $46109.04
1% = 100%/100 = 46109.04/100 = $461.09
5% = 5×1% = 5×461.09 = $2305.45
so, in total, his salary will be $46109.04+$2305.45 = $
Based on the markings of the two triangles, what statement could be made about ΔABC and ΔA′B′C′? Question 1 options: A) The corresponding pairs of sides and angles of ΔABC and ΔA′B′C′ aren't congruent. B) ΔABC and ΔA′B′C′ are congruent. C) ΔABC and ΔA′B′C′ are irregular polygons. D) ΔABC and ΔA′B′C′ aBased on the markings of the two triangles, what statement could be made about ΔABC and ΔA′B′C′? Question 1 options: A) The corresponding pairs of sides and angles of ΔABC and ΔA′B′C′ aren't congruent. B) ΔABC and ΔA′B′C′ are congruent. C) ΔABC and ΔA′B′C′ are irregular polygons. D) ΔABC and ΔA′B′C′ are similar but not congruent.re similar but not congruent.
Answer:
B) ΔABC and ΔA′B′C′ are congruent.
Step-by-step explanation:
Given
See attachment for [tex]\triangle ABC[/tex] and [tex]\triangle A'B'C'[/tex]
Required
Determine the relationship between both triangles
The single line on all sides of both triangles implies that the sides of the triangles are equal
i.e.
[tex]\triangle ABC \cong \triangle A'B'C'[/tex] --- sides
Similarly, the same mark on the three angles of both triangles means that the angles of the both triangles are equal
i.e.
[tex]\triangle ABC \cong \triangle A'B'C'[/tex] --- angles
Hence, both triangles are congruent
Answer:
B) ΔABC and ΔA′B′C′ are congruent.
Step-by-step explanation:
find the value of x in the diagram below
Answer:
70
Step-by-step explanation:
In a trapezoid lines are parallel, so corresponding angle sum = 180
X+X+40 = 180
2x + 40 = 180
2x = 180-40
2x = 140
X = 140/2
X = 70
Answered by Gauthmath
Number 13 I don’t get it
===========================================
Explanation:
The two equations given to us are
ab = 3ab^2 = 18Divide the second equation over the first equation and that would lead to b = 6
Notice how the 'a' terms divide to 1 and go away, i.e. cancel out.
The b terms divide to (b^2)/b = b
The right hand side values divide to 18/3 = 6
So that's how we end up with b = 6
-------------------------
Now if b = 6, then we can say,
ab = 3
a*6 = 3
a = 3/6
a = 1/2
Or we could say
ab^2 = 18
a*6^2 = 18
a*36 = 18
a = 18/36
a = 1/2
Help me pls asappp with Pythagorean theorem
please help geometry!!
Answer:
A' (-5, 5)
B' (20, 0)
C' (5, -15)
Step-by-step explanation:
Multiply each coordinate by 5, and your result is given above.
Answer:
Step-by-step explanation:
A fruit stand has to decide what to charge for their produce. They decide to charge \$5.30$5.30dollar sign, 5, point, 30 for 111 apple and 111 orange. They also plan to charge \$14$14dollar sign, 14 for 222 apples and 222 oranges. We put this information into a system of linear equations. Can we find a unique price for an apple and an orange?
Answer:
a + b = 5.30
a + b = 7
No
Step-by-step explanation:
Expressing the information as system of linear equation :
Let apples = a, oranges = b
If $5.30 is charged for one apple and one orange, then we have ;
a + b = 5.30 - - - (1)
If $14 is charged for 2 apples and 2 oranges, then we have ;
2a + 2b = 14 - - - - (2)
a + b = 7
Since both equations gives varying combined cost for equal amount of the fruit, then a unique cost cannot be obtained for each fruit from the systems of equation using simultaneous equation process.
From (1)
a = 5.30 - b
Put a = 5.30 - b in (2)
2(5.30 - b) + 2b = 14
10.6 - 2b + 2b = 14
10.6 = 14 - - - - - (variables cancels out).
Answer:No the System has no solution
Step-by-step explanation:
Wilma worked 38 hours 52 minutes last week. She earns $25.15 per hour. What is wilma's pay for this work period? Round your answer to the nearest hundredth
Answer:
$968.78
Step-by-step explanation:
multiply worked hours by her pay per hour
38.52×$25.15=
38.52×$25.15=$968.778
then you round it to the nearest hundredth
since the thousandth is greater than 5 the 8 will round the 7 to an 8
giving you $968.78
Answer: $977.50
Step-by-step explanation:
(38)(25.15)=955.70
(52)(25.15)/60=21.80
955.70 + 21.80 = 977.50
Draw the parabola's axis of symmetry.
solve for x.
solve for x.
solve for x.
Answer:
x = 10
Step-by-step explanation:
7(x+1+7)=6(x+5+6)
or, 7(x+8)=6(x+11)
or, 7x+56=6x+66
or, 7x-6x=66-56
or, x=10
Answered by GAUTHMATH
