The system of equations that satisfy the given problems is x + y = 52 and 50x + 75y = 2975, and the value of x = 15 and y= 37.
What is system of equations?A system of linear equations consists of two or more equations and looks for common answers.
1. Let us suppose small prints = x
Large prints = y
Total prints sold can be written as follows:
x + y = 52
The total cost of the prints can be written as follows:
50x + 75y = 2975
The system of equations is:
x + y = 52 . . . equation 1
50x + 75y = 2975 . . .equation 2
Using equation 1 we have:
x = 52 - y
Substituting the value of x in equation 2 we have:
50(52 - y) + 75y = 2975
2600 - 50y + 75y = 2975
25y = 2975 - 2600
25y = 375
y = 15
Now, substituting the value of y in equation 1 we have:
x + 15 = 52
x = 52 - 15
x = 37
Hence, the solution of the system of equations is y = 15 and x = 37.
2. Let us suppose the altitude = x.
The rising balloon can be thus written as:
40 +10x
The descending balloon can be written as:
165 - 15x
Solving the system of equations by substituting the value of x we get x= 5.
Hence, the altitude at which both the balloons are at the same height is 5m.
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Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded monthly, how much total will he have paid after 5 years?
$33,672.68
$34,157.04
$33,299.42
$34,710.88
$34,389.55
The requried, Mark will have paid a total of $34,389.55 after 5 years. The answer is option E, $34,389.55.
What is compound interest?Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
We can use the formula for compound interest to find the total amount Mark will have paid after 5 years:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
where A is the total amount paid, P is the principal (the original loan amount), r is the annual interest rate (as a decimal), n is the number of times per year the interest is compounded, and t is the time in years.
In this case, we have:
P = $25,690
r = 0.052 (5.2% expressed as a decimal)
n = 12 (compounded monthly)
t = 5
Substituting these values into the formula, we get:
[tex]A = $25,690(1 + 0.052/12)^{(12*5)}[/tex]
A = $34,389.55
Therefore, Mark will have paid a total of $34,389.55 after 5 years. The answer is closest to option E, $34,389.55.
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Solve each equation for both variables help please 15 points
Answer:
I hope this helps. Do let me know if you have any doubts and wish me luck I have my maths exams tomorrow!
Convert the degree measure to radians or the radian measure to degrees. Then find one positive angle and one negative angle that is coterminal with the given angle.
1. -560°
2. 170°
-560° in radian is -28π/9 radian and the positive and negative coterminals are 8π/9 and -10π/9 respectively.
170° in radian is 17π/18 radian and the positive and negative coterminals are 53π/18 and -19π/18 respectively
How to convert the degree measure of angle to radians?An angle can be converted from degree to radian by multiplying it by π/180.
1. -560°
-560° × π/180 = -28π/9 radian
2. 170°
170° × π/180 = 17π/18 radian
In general, if θ is any angle in radian, then θ + n(2π) is coterminal angle with θ, for all nonzero integer n.
coterminal of -28π/9:
positive: -28π/9 = -28π/9 + 2(2π) = 8π/9
negative: -28π/9 = -28π/9 + 2π = -10π/9
coterminal of 17π/18:
positive: 17π/18 = 17π/18 + 2π = 53π/18
negative: 17π/18 = 17π/18 - 2π = -19π/18
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LINKS WILL GET REPORTED PLS HELP CLICK TO SEE
Answer:
14
Step-by-step explanation: add all the x's and you get 14 that show's how many apples her clients ate last week
PLEASE HELP!!!!!!!!! With 9, 10 and 11
Answer:
9. 6.6
10. 6
11. 8.9
Step-by-step explanation:
Pythagorean theorem states that a^2 + b^2 = c^2 where a and b are legs, and c is the hypotenuse (the longest side of the triangle).
For the first one, you're given the leg (3.1 in) and the eg (5.8 in), so you can substitute those into the equation:
a^2 + b^2 = c^2
(3.1)^2 + (5.8)^2 = c^2
Then simplify
9.61 + 33.64 = c^2
43.25 = c^2
To isolate c, take the square root of both sides.
The square root of 43.25 is 6.57647322, but they want you to round it to the nearest tenth, so round it to 6.6
For the second one, you're given one leg length and the hypotenuse.
8^2 + b^2 = 10^2
64 + b^2 = 100
To solve for b, subtract 64 from both sides
b^2 = 36
and take the square root of both sides
b = 6
For the last one, you're given a leg length and the hypotenuse
a^2 + 4.3^2 = 9.9^2
a^2 + 18.49 = 98.01
to isolate a, subtract 18.49 from both sides
a^2 = 79.52
then take the square root of both sides
a = 8.91739872 which rounds to 8.9
For brainliest and 50 points!!!
The statements in if-then form are given as follows:
If it is right-angled, then it is 90 degreesIf x=6, then x² = 36If two angles measure 180°, then they are supplementary If your body temperature is 103°, then you have a fever If is 6pm, then it is time for dinnerIf there is gas in the tank, then the car runs If there there are 12 eggs if the carton, then it is fullIf a car is leaking antifreeze, then it has a problemIf a dog is old, then you can't teach it new tricksIf a deer has white fur and pink eyes, then it is albino What is the value of an IF-Then Construct?If-Then statements are a sort of variable logic that allows the variable's output to be determined conditionally. All If-Then statements must specify the circumstances and actions that should occur when those criteria are fulfilled.
If-then arguments, also known as conditional arguments or hypothetical syllogisms, are deductive logic's workhorses. They are a loosely defined class of logical arguments with an if-then statement (a conditional) as a premise. The conventional form of the conditional is If P, Q follows.
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Which of the expressions below are equal to x2+2x−15? Select all that apply. A) x2+x−8+x−7 B) (x−3)(x+5) C) x(x+2+15) D) x2+x+x2+x−15
Answer:
A and B
Step-by-step explanation:
x2 + 2x − 15
A) x2 + x − 8 + x − 7
B) (x − 3)(x + 5)
suki has 54 rock songs 92 dance songs and 12 classical songs on her playlist what is the probability that the song will not be classical song
Answer:
The probability that the chosen song is not a classical song is 92.4%.
Step-by-step explanation:
Given that Suki has 54 rock songs, 92 dance songs and 12 classical songs on her playlist, to determine what is the probability that the chosen song will not be a classical song, the following calculation must be performed:
54 + 92 + 12 = 158
158 - 12 = 146
158 = 100
146 = X
146 x 100/158 = X
14600/158 = X
92.4 = X
Therefore, the probability that the chosen song is not a classical song is 92.4%.
Answer:
92.4
Step-by-step explanation:
Ubehebe Crater in Death Valley has a diameter of a little more than mile. If Latisha walks around its
rim at a rate of 2 miles per hour, about how long will it take her to walk all the way around the crater? Find your
answer to the nearest tenth. Use 3.14 for pi
On solving the provided question we can say that the it will 4 hrs to walk all the way around the crater, on doing the radius.
what is radius?The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle. Diameter
here,
D= 1
r = 1/2 = .5
A = 40
T = 40/10 4 hrs.
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A measurement of 50.8 centimeters is equivalent to how many inches? A. 25 B. 12 C.20 D. 10
Answer: C. 20
Step-by-step explanation:
1 inch is equal to 2.54 cm.
So we have to divide the amount of centimeters given by how many centimeters are in an inch to find how many inches.
50.8 ÷ 2.54 = 20
Hope this helps!!! :)
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
What is 31.83098862 to the nearest square inch ? Please help
Answer:
32
Step-by-step explanation:
The number to the right of the decimal is higher than 5, meaning you would round up.
6 10 14 18 22 26 30, what comes next in the series
Answer:
34
Step-by-step explanation:
add 4 each time
Answer:
34
Step-by-step explanation:
It is in a sequence.
Continue by adding 4 each time
too dice are tossed simultaneously, what is the
probability that
the sum of their squares is more than 7
Answer: 5/13
Step-by-step explanation:
36 possible outcomes
the highest the sum can be is 12
so 8, 9, 10, 11, and 12 are all options
2+6, 4+4, 3+5, 5+3, 6+2 - for 8
3+6, 4+5, 5+4, 6+3 - for 9
4+6, 5+5, 6+4 - for 10
5+6, 6+5 - for 11
6+6 - for 12
total - 15/36 or 5/13
Directions: Find the area of each shaded region. Assume that all angles that appear to
be right angles are right angles.
Answer:
#1
10*3.7/2 = 18.5 m² (both the triangle and rectangle have same base and height)#2
3.14*6² - 2² = 109.04 m²#3
4.1*8.2/2 = 16.81 cm² (the square is half the rectangle)#4
18² - 3.14*9² = 69.66 dm²#5
It's not clear what is shaded. Giving all options
1. Rectangle in the middle:
4*3.4 = 13.6 m²2. Two semicircles:
3.14*2² = 12.56 m²3. Total area:
13.6 + 12.56 = 26.16 m²look at pic 10 pts will mark brainilest shsh
Answer:
D
Step-by-step explanation:
Divide and multiply
:)
Answer:
it d
Step-by-step explanation:
In Exercises 7-8, find the domain of the function.
7. f(x) = x-5/x + 2
8. h(x) = 4x²
On solving the provided question, we can say that - the value of the function is = x-5/x + 2 => x= 2 => -3/4
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
x-5/x + 2
x= 2
-3/4
ans also 4x² = 4 *2*2 = 16
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One angle is a right angle
Answer:
an angle with 90 degree is a right angle
helppp...........................math
Homework help!
y=2x + 10
whats the initial amount?
whats the growth/decay factor or slope?
Answer:
10
2
Step-by-step explanation:
if x=0 => y = 2(0)+10= 10
y = mx + c
m = slope factor
=> y = 2x + 10
so, slope factor = 2
Which of the following statements is TRUE based on the information given?
If you can’t see, my apologies, but you can zoom in so you can see the answer choices!
DO NOT ANSWER IF YOU DO NOT KNOW THE ANSWER! Whoever answers correctly will get Brainliest! :)
Answer:
B
Step-by-step explanation:
The sum of the angle 1, 2 and 3 is 180 degrees , so B is the correct answer, because 70 + 110 = 180
Answer:
b
Step-by-step explanation:
I REALLY NEED HELP WITH PLINK A PLUNK
Therefore ,We can see that in equation 1 plunk yields the most lorgs at 30. So the plunk coin is the most valuable.
Describe equation.A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 5x - 5 = 25 is an equation. We can find that the variable x has a value of 6 by resolving this equation.
Here,
we need to convert everything to the same unit in order to establish a legitimate comparison when comparing units like inches, feet, and yards. Therefore, we would have to convert everything, for example, to inches. For these five coins, the same concept holds true. Either lorgs, sinds, plunks, harps, or dalts must be used for everything (pick one of those five).
It's equivalent to attempting to change a dollar amount into cents (for example, $1.37 becomes 137 cents). The alternative is to think about it as 1 dollar = 100 cents, 1 quarter = 25 cents, 1 dime = 10 cents, and so on.
The procedures in the various parts below are designed to convert all coinage to lorgs, which will serve as our base unit. Trial and error led me to the conclusion that the lorg coin had the lowest worth, thus I'm striving to obtain everything in lorgs.
The four equations provided are
4 lorgs to a sind
5 dalts x 2 plunks
2 harps from 5 sinds.
3 harps equal 1 plunk.
In that order, I'll refer to them as equations (1) through (4).
One sind equals four logs (1)
5 sinds = 20 lorgs; add 5 to both sides.
2 harps = 20 lorgs; in the equation, swap out "5 sinds" with "2 harps" (3)
1 harp = 10 lorgs; multiply both sides by 2, then write this as an equation (5)
Equation: 1 plunk = 30 lorgs (6)
Each of those equations enables us to determine the lorg value of the coins sind, dalt, harp, and plunk.
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The complete question is : " A nation has five types of coins: sinds, dalts, lorgs, harps, and plunks.1 sind = 4 lorgs ,2 plunks = 5 dalts ,5 sinds = 2 harps , 1 plunk = 3 harps Which coin is the most valuable? a) sindb) daltc) harpd) plunk"
jane used $68 more than two fifths of her last paycheck to purchase a new surfboard. If the surfboard cost $289, find the amount of her paycheck.
Answer: Let x be the amount of Jane's paycheck.
We know that:
surfboard cost = $289
and jane used $68 more than two fifths of her last paycheck to purchase a new surfboard.
So we can set an equation as:
surfboard cost = 2/5 x + $68
289 = 2/5 x + 68
Now we can substitute the known value in the above equation:
289 = 2/5 x + 68
221 = 2/5 x
x = (2215) / 2 = 115 = 55
So the amount of her paycheck is $55.
Therefore, jane's last paycheck was $55.
Step-by-step explanation:
write the slope intercept form of the equation of the line through (2,1) and (4,5)
Answer:
[tex]y=2x-3[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where the two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (2,1) and (4,5)
[tex]m=\frac{5-1}{4-2}\\m=\frac{4}{2}\\m=2[/tex]
Therefore, the slope of the line is 2. Plug this into [tex]y=mx+b[/tex] :
[tex]y=2x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=2x+b[/tex]
Plug in one of the given points and isolate b
[tex]1=2(2)+b\\1=4+b[/tex]
Subtract both sides by 4
[tex]1-4=4+b-4\\-3=b[/tex]
Therefore, the y-intercept of the line is -3. Plug this into [tex]y=2x+b[/tex]:
[tex]y=2x-3[/tex]
I hope this helps!
Answer:
y=2x-3Step-by-step explanation:
Slope formula:
[tex]\sf{\dfrac{Y_2-Y_1}{X_2-X_1}[/tex]
y2=5
y1=1
x2=4
x1=2
Solve.
5-1/4-2
Subtract.
5-1=4
4-2=2
Divide.
4/2=2
The slope is 2.
You have to solve with slope-intercept form.
[tex]\sf{y=mx+b}[/tex]
m represents the slope.
b represents the y-intercept.
y-intercept is -3.
[tex]\sf{\boxed{y=2x-3}[/tex]
So, the correct answer is y=2x-3.
8th-grade mathematics
Answer:
1072.33 cm^3
Step-by-step explanation:
formula
(2/3)*pi*(r)^3
A giant satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the surface for the dish and are reflected to the focus, where the receiver is located. The satellite dish has a diameter of 300 feet and. depth of 44 feet. How far from the base of the dish should the receiver be placed? Round your answer to the nearest foot.
The answer of given parabola question is 6.125ft.
The definition of a parabola?a curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a fixed point is equal to its distance from a fixed line.
x² = 4py
x=radius which can be found by dividing d=14ft by half
x = d/2 = 11/2 = 7ft
y=2ft is the depth
p is the vertex of the parabola
finding p;p = x²/4y
p = 7²/4×2
p=6.125ft
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Please answer these question(s)! It has to do with math statistics. I will give you brainliest and thanks!
Answer:
2
Step-by-step explanation:
Count how many edges use that vertex as an endpoint. In this case B and E.
write 4/27 as the product of a prime raised to a power
Answer:
write 4/27 as the product of a prime raised to a power
The sum of 9 and y is at most 27
Answer:
9 + y > 28
Step-by-step explanation:
Answer:
9 + y ≤ 27
Hope this helps!
if you need to know the y value, then y ≤ 18
Hope this helps!
each minute your heart pumps 1.5 gallons of blood around your body. How many pints of blood will your heart pump in a day? PLEASE HELP ME
Answer:
So there are 60 minutes in an hour, and since there are 24 hours in a day you will multiply 60 by 24:
60 * 24 = 1440.
That multiplied by 1.5 is 2160, so that would be your answer.
Step-by-step explanation:
Hope it helps! =D