after a 60% reduction, you purchase a new soft drink machine on sale for $200. what was the original price of the soft drink
your answer is 740 {:
Step-by-step explanation:
let x be the original price
then we write our equation
x-60%x=200 (x=100%x)
100%x-60%x=200
40%x=200
(40/100)x=200
x=(200*100)/40
x=20000/40=500
so the original price was $500
A plane travels 800 metres along the runway before taking off at an angle of 10∘
.It travels a further 1 000 metres at this angle as seen in the figure. Work out the distance of the plane from its starting point. Give your answer to 2 decimal places.
I hope this step by step explanation helps.
A plane travels 800 meters along the runway before taking off, then the distance travelled from the starting point will be equal to 1793.24 meters.
What is Velocity?Velocity is the rate at which a moving object's direction changes as perceived from a certain vantage point and measured by a particular unit of time. Kinematics, the area of special relativity that investigates how bodies move, starts with the fundamental idea of speed.
In order to be explained, the scientific vector quantity known as velocity needs to have both a magnitude and a direction.
As per the given data in the question,
Distance travelled by plane = 800 meters
Use the equation,
a² = b² + c² -2bc cos A
d² = 800² + 1000² - (2 × 800 × 1000 × cos 170°)
d² = 1640000 - 1600000(cos 170°)
d² = 3215692.405
d = 1793.24
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Plz I am really stuck on this question, your time is appreciated.
Answer: 0.05
Step-by-step explanation:
1) Re-arrange the formula given to find the rate (r)
I = Prt
becomes r = I / Pt
Now we add in the values we know
P = 3000, t = 3 years, I = 450
r = 450 / ( 3000 × 3 )
r = 0.05 or 5% / year
Which is the equation of the line that passes through (-2,2) and (4,-5)
Answer:
here you go
Step-by-step explanation:
Algebra questions and answers. Write an equation of the line that passes through (4,5) and is parallel to the line defined by 4x+y=-2. Write the answer in slope-intercept form (if possible) and in standard form (Ax+By=C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.
The scale drawing car length is 3 cm. If the scale is 1 cm:4 ft, what is the actual car length?
O 16 feet
0 10 feet
12 feet
ОО
0 4 feet
4a-b=10 . 2a + 3b=12
Answer:
a = 3
b = 2
Step-by-step explanation:
Solve 4a - b = 10 for b:
[tex]4a - b = 10[/tex] [tex]4a - b - 4a = 10 - 4a[/tex] (Subtract 4a from both sides)[tex]-b = -4a +10[/tex] [tex]\frac{-b}{-1} = \frac{-4a+10}{-1}[/tex] (Divide both sides by -1)[tex]b = 4a - 10[/tex]Substitute 4a - 10 for b in 2a + 3b = 12
[tex]2a + 3b = 12[/tex] [tex]2a + 3(4a-10)=12[/tex] [tex]2a + 12a -30 = 12[/tex] (Simplifying)[tex]14a - 30 = 12[/tex] (Simplifying[tex]14a - 30 + 30 = 12 + 30[/tex] (Add 30 to both sides)[tex]14a = 42[/tex] [tex]\frac{14a}{14} = \frac{42}{14}[/tex] (Divide both sides by 14)[tex]a = 3[/tex]Substitute 3 for a in b = 4a - 10
[tex]b = 4a - 10[/tex] [tex]b = 4(3) - 10[/tex] [tex]b = 12 - 10[/tex] [tex]b = 2[/tex]Therefore, a = 3 and b = 2.
Plz help me I just need the answer
Name the property illustrated.
(10 + 1) + 9 = 10 + (1 + 9)
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{PROPERTIES of MATH (of addition)}}\\\\\large\bullet\boxed{\mathsf{\ Commutative \ property: \boxed{\bf x + y = y + x}}}\\\bullet\boxed{\mathsf{\ Identity\ property: \boxed{\bf x + y = x}}}\\\bullet\boxed{\ \mathsf{Associative\ property: \boxed{\bf (x + y) + z = z + (x + y)}}}\\\bullet\boxed{\ \mathsf{Distributive\ property: \boxed{\bf x(y + z) = x\times y + x\times z}}}[/tex]
[tex]\large\boxed{\mathsf{(10 + 1) + 9 = 10 + (1 + 9)}}\\\\\\\large\boxed{\mathsf{(10 + 1) + 9}}\\\large\boxed{\mathsf{= 10 + 1 + 9}}\\\large\boxed{\mathsf{= 11 + 9}}\\\large\boxed{= \mathsf{20}}\\\\\large\boxed{\mathsf{10 + (1 + 9)}}\\\large\boxed{\mathsf{= 10 + 1 + 9}}\\\large\boxed{\mathsf{= 11 + 9}}\\\large\boxed{= \mathsf{20}}\\\\\\\\\huge\boxed{\mathsf{20 = 20}}\huge\checkmark[/tex]
[tex]\huge\boxed{\mathsf{Based\ on\ the\ information\ we \ have\ above\ your}}\\\huge\boxed{\mathsf{answer \ is: \underline{\underline{\bf Associative \ Property}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
3x - 5 < -14 or 2x - 1 > 7 for x
Answer:
see below
Step-by-step explanation:
x < -3 for the first equation
x > 4 for the second equation
Write an equation of the parabola that passes through the points (-1,4), (0,1), and (2,7)
y = _____
Answer:
y = -6x^2 + 15x -5
Step-by-step explanation:
equation step 1 for parabola
y2-y1 /x2-x1
= 1 - 4 / 0 - - 1
= -3 / 1
y = -3
We try again different points
y2-y1 / x2-x1
= 7 - 1 / 2 - 0
= 6 / 2
y = 3
we can see that one side is descending and 1 side is ascending
The start of the parabola is 0,1 as x = 0 and crosses the line.
we try again
y2-y1 /x2-x1
7-1 / 2-0
= 6 / 2
y = 3
You should know that a parabola is determined by 3 points, so unless your points happen to be collinear, they will determine a parabola. A straight forward, if not always the easiest way would be to take the general equation
y = ax^2 + bx + c
plug in each point, eg.y = y1 and x = x1 eg) y = y2 and x = y2 eg) y = y3 x=x3
Top equation re-used last see at end.
4 = a(-1)^2 + b(-1 ) + c = a+b+c=4
1 = a(0)^2 +b(0) + c = c =1
7 = a(2)^2 + b(2) + c = 4a+2b=7
a= -1-0 = -1 b = -1-0 = -1 and 4-1 = 3
-a +-b = 3
2nd set of equations
4a-0a = 4a
2b-0b = 2b
7-1 = 6
4a +2b=6 and previous
-a +-b = 3 here we can multiply by -2 to get 2b equality to 1st equation
2a + 2b = -6
4a + 2b = 6
2a = -12
2a = -12 / 2
a = -6
plug a
4(-6) + 2b = 6
-24 + 2b = 6
2b = 6 +24
2b = 30
b = 15
then put a + b+ c into top equation
(-6) + (15) + c = 4
9 + 0 = 4
9 -9 = 4 -9 cancel
c = -5
Then put into first equation as c and complete equation
To find that;
y = -6x^2 + 15x -5 = is our equation of the parabola.
This is how to solve your two linear equations in three unknowns.
The equation of parabola passing through (-1, 4), (0, 1), and (2, 7) is y = 2x² - x + 1.
To find equation of parabola that passes through the given points, we use the general-form of quadratic equation: y = ax² + bx + c.
Since we have three points, we substitute the coordinates of each point into the equation to create a system of equations. Solve for a, b, and c:
Substitute (-1, 4), We get,
4 = a(-1)² + b(-1) + c,
4 = a - b + c,
Next, Substitute (0, 1):
1 = a(0)² + b(0) + c
1 = c
Next, Substitute (2, 7):
7 = a(2)² + b(2) + c
7 = 4a + 2b + c
Now, we have a system of equations:
a - b + c = 4 ...equation(1)
c = 1 ...equation(2)
4a + 2b + c = 7 ...equation(3)
From equation(2), we know that c = 1. Substituting this into equation(1) and 3, we get,
a - b + 1 = 4
4a + 2b + 1 = 7
Solve equation(1) for a - b:
We get, a - b = 3,
Solve equation(3) for 4a + 2b:
4a + 2b = 6
Now we have a system-of-equations as :
a - b = 3
4a + 2b = 6
Solving the system for "a" and "b", We get,
a = 2; b = -1
Now we can write the equation of the parabola:
y = ax² + bx + c ⇒ y = 2x² - x + 1,
Therefore, the required equation of parabola is y = 2x² - x + 1.
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Which supplementary angles can prove
that lines L and M are parallel?
A. 5 and 6
B. 3 and 8
C. 2 and 4
Answer: 3 and 8
Step-by-step explanation:
5 and 6 only apply to line M, 2 and 4 only apply to line M, while 3 and 8 apply to both.
ic.
f
8. EXERCISE Del Ray can run 20 1/2 miles in
2 1/4 hours. How many miles per hour can
he run?
(rounded) 9 miles OR 9 1/10 miles
what number is not a common denominator of 2/4 and 3/8
The diagram shows a square.
(7x + 3)cm (5x + 8) cm
Find the length of the side of the square.
Answer:
x = 5/2cm
Step-by-step explanation:
Because this is a square and each side is equal to each other in length, we can say:
7x + 3 = 5x + 8
We can start rearranging this equation to collect like terms:
7x = 5x + 8 - 3
7x = 5x + 5
7x - 5x = 5
2x = 5
x = 5/2
We can test this out by substituting our new found value for x into the original equation:
7 * (5/2) + 3 = 5 * (5/2) + 8
(35/2) + 3 = (25/2) + 8
I'm going to change the integers (3 and 8) to fractions so the arithmetic is easier, as they'll all have the same denominator.
(35/2) + (6/2) = (25/2) + (16/2)
(41/2) = (41/2)
So as you can see above, with x = 5/2, both sides are equal.
You don't need to put the fractions in brackets; I just do that to make it look a little less messy.
Also, I've only included the units (cm) in the answer. I don't like using units when doing calculations, but your teacher may ask you to perform the calculations using the units throughout.
How do I do this please help
Sorry that this is long, but hopefully this has the answers and explanations you are looking for. Have a nice day!
1a: P' (0, 1) Q' (9, 7)
First, we will look at point P. It is at (-7, -2). If we move it up three and right 7, we will do (-7 +7, -2 +3) which gives us (0, 1). We do the same for Q, (2, 4) -> (2+7, 4 +3) = (9, 7)
2a: This transformation represents the point being moved down 5 units and to the right 2 units. X is left/right and it's being moved positive two, hence right 2. Y is up/down, and it's being moved negative 5, hence down 5.
2b: (4, -3) (not 100% sure on this one)
The wording slightly confused me, but if it's talking about having point A be apart of 2a, here is what we do:
(2, 2) -> (2 + 2, 2 - 5) -> (4, -3)
3a: (x - 26, y + 17)
So (in the y) -13 becomes 4, so it moves 17 units up. For the x, -2 becomes -28, so it is moved 26 units down. This becomes x - 26 and y + 17, which is written correctly above.
3b: A. AP and A'P' have different locations
For a translation shape, size, and direction doesn't change, just where it's at (location).
Answers?..............
Ricky's heartbeat is 70 beat per minute. How many days have elapsed if his
heart beat a total of 504,000?
The number of days passed to have an accumulated heartbeat of 504,000 is the ratio of the total heartbeat and the number of beat per minute ; Hence, the number of days is 5 days
Heart beat rate per minute = 70 beats Total number of beats = 504,000Number of heartbeats per day = 70 × (24 × 60) = 100,800 beats
Number of days = (504,000) ÷ (100,800) = 5days
Therefore, the Number of days elapsed is 5 days.
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100 Points
3. In the image below, the m
Answer:
yo can someone answere this i need it to
Step-by-step explanation:
Solve for x: 7x-3/2 = -2/3
Hence, the value of x ix 5/21.
★ Solution (1) :-[tex]\sf \leadsto \dfrac{7x - 3}{2} = \dfrac{-2}{3}[/tex]
[tex]\sf \leadsto 3(7x - 3) = -2(2)[/tex]
[tex]\sf \leadsto 21x - 9 = -4[/tex]
[tex]\sf \leadsto 21x = -4 + 9[/tex]
[tex]\sf \leadsto 21x = 5[/tex]
[tex]\sf \leadsto x = \dfrac{5}{21}[/tex]
Answer:
5/42
Step-by-step explanation:
7x - 3/2 = -2/3 (Take -3/2 to the other side so it becomes +3/2)
7x = -2/3 +3/2 (Add the two fractions)
7x = 5/6 (7 is taken to the other side so 5/6 ÷ 7)
x = 5/42
The points (0, 3) and (1, 9) fall on a particular line. What is its equation in slope-intercept form?
Answer:
y = 6x + 3
Step-by-step explanation:
y2 - y1 / x2 - x1
9 - 3 / 1 - 0
6/1
= 6
y = 6x + b
3 = 6(0) + b
3 = 0 + b
3 = b
Answer:
y = 6x+3
Step-by-step explanation:
[tex]\frac{y2-y1}{x2-x1}\\\\= \frac{9-3}{1-0}\\\\= \frac{6}{1}\\\\= 6[/tex]
Hence, the slope is 6.
Substituting the slope value to the equation 'y=mx+c',
y = 6x +c
Substituting (0,3):
3 = 0 + c
c = 3
Hence,
y = 6x + 3
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plz help with this problem
Answer:
d=30°
e=117°
f=66°
Answer:
E: 117
D: 30
F: 33
Step-by-step explanation:
360-117-117-30-30=66
66 divide by 2 = 33
12 workers build a wall in 10hours. How long do 5 workers build a wall
Answer:
24 hours
Step-by-step explanation:
If 12 workers take 10 hours to build a wall, assuming they build at the same rate, it would take one worker 120 hours to build a wall.
By this logic, it would take 120/5 or 24 hours for 5 workers to build a wall
The number of hours 5 men take with the same rate of 12 workers taking 10 hours will be 24 hours.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
The number of hours 1 person take to build the wall = 12 x 10 = 120 hour
Number of men = 5
The number of 5 men will take as 120/5 = 24 hour
Hence "The number of hours 5 men take with the same rate of 12 workers taking 10 hours will be 24 hours".
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How many variable terms are in the expression 3x3y + 5xz − 4y + x − z + 9?
(Input a numeric value only.)
Answer:
3
Step-by-step explanation:
there are only x y and z used in the expression no matter how many times they multiply.
How do you Factor out greatest common factor of 30x³y³z²+12x²y²z³-18x⁵y⁶z ?
Step-by-step explanation:
30x³y³z²+12x²y²z³-18x⁵y⁶z
6x²y²z(5xyz+2z²-3x³y⁴).
hope this helps you.
Johnathan needs 3 5/8 yards of blue material and 6 3/4 yards of red material How many yards does Johnathan need in all?
Answer:D) 10 3/8
Step-by-step explanation:
Have a wonderful rest of ur day!!
Mrs. Alejandro places four cards on the board. Which does not represent the same distance?
A. 36 yards
B. 432 feet
C. 1296 inches
D. 108 feet
Answer:
B. 432 feet
Step-by-step explanation:
36 yards * 3 = 108 feet
108 feet * 12 = 1296 inches
Scale the numerator and the denominator down by a factor of 4 (divide) to write a fraction equivalent to 8/56. (i really need help with this)
8/56 = ??
Answer:
2/14
Step-by-step explanation:
when you scale the numerator and denominator down by 4, you just divide both of them by 4. So since 8 divided by 4 is 2 and 56 divided by 4 is 14, the answer is 2/14
Can you solve this? I'm terrible at math
The thermometer currently reads 36°C. In the evening, the temperature drops 4°C every hour. What will the thermometer read after 3 hours?
Answer:
This thermometer shows a temperature of -6 degrees Celsius. If the temperature rises a few degrees and gets very close to 0 degrees without reaching it,
Step-by-step explanation:
hope this helps have a great day :)
One of the greatest assets of a secretary is often his/her ability on the keyboard of a computer. Mrs. Garcia has been recognized as the Most Outstanding Typist at a prestigious firm because of her outstanding typing speed. The table below displays data collected from her most recent evaluation.
Write an equation to represent the total number of words, y, that Mrs. Garcia can type in x minutes_________
If Mrs. Garcia maintains a constant speed consistent with the results above, how many words will she type in 49 minutes?_______
Answer:
y = 70x3,430Step-by-step explanation:
The table shows that Mrs. Garcia types 70 words in the first minute and 70 additional words in each additional minute.
That is, in x minues, Mrs. Garcia types 70x words:
y = 70x . . . . words Mrs Garcia can type in x minutes
__
When x=49, the number of words Mrs. Garcia is expected to type is ...
y = 70×49 = 3,430
She will type 3,430 words in 49 minutes.