The two positive numbers are 71 and 48
How to calculate for the two positive numbersWe shall apply algebra in finding the unknown numbers as follows;
Let us represent the two numbers with the letters x and y
so that;
x - y = 23...(1)
xy = 3408...(2)
from equation (1),
x = 23 + y {adding y to both sides}
putting the value 23 + y for x in equation (2) we get;
(23 + y)y = 3408 {by expansion}
23y + y² = 3408
y² + 23y - 3408 = 0 {we rearrange to get a quadratic equation}
we factorize as follows;
y² + 48y - 71y - 3408 = 0
y(y + 48) - 71(y + 48) = 0
(y + 48)(y - 71) = 0
so by factorization; y = -48 or y = 71
the numbers are positive hence we take y = 71
putting the value 71 for y in equation (2) we get;
x71 = 3408 {divide through by 71}
x = 3408/71
x = 48
Thus; 71 - 48 = 23 and 71 × 48 = 3408, and we can say that the two positive numbers are 71 and 23.
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"The question is on a test I have to do today! pls help me!
10. Which situation can be modeled by the equation y=m x+b ?
A. The number of butterflies (y) in a population doubles every month (x).
B. The time (y) it takes a car to travel 100 miles depends on the speed (x) of the car.
C. The volume (y) of a cylindrical tank with a height of 2 feet depends on the radius (x) of the tank.
D. The total income (y) of a worker who earns 8 dollars per hour depends on the number of hours (x) worked."
The situation that can be modeled by the linear function y = mx + b is given as follows:
D. The total income (y) of a worker who earns 8 dollars per hour depends on the number of hours (x) worked.
Which situations can be modeled by linear functions?Situations that can be modeled by linear functions are situations in which there is a constant change per unit interval.
The example in this problem is given by option D, as for each hour worked, the rate of change is given as follows:
8 dollars.
That is, for each hour worked, the total income of the worker increases by $8, hence the slope is of:
m = 8.
Then the intercept b represents the flat pay of the worker, which is how much the worker earns no matter the amount sold.
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I need help with this please help me
Answer:
67.38
Step-by-step explanation:
134.76/2 = 67.38
May I please have brainliest for this? Thank you!
If f(x)=2x-3 and g(x)= [tex]\sqrt{x} +7[/tex]
then find f(g(x))
The value of the function, f(g(x)), is f(g(x)) = 2√x + 11
Evaluating a functionFrom the question, we are to determine the value of the given function f(g(x))
From the given information,
The given functions are
f(x) = 2x - 3
and
g(x) = √x + 7
To determine f(g(x)), we will substitute the value of g(x) for x in f(x)
That is,
f(x) = 2x - 3
f(g(x)) = 2(√x + 7) - 3
Apply the distributive property
f(g(x)) = 2√x + 14 - 3
Simplify
f(g(x)) = 2√x + 11
Hence, the value of f(g(x)) is 2√x + 11
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a line that passes thru (-3,4) and is parallel to y=2
Parallel lines have the same slope.
y=2 is a horizontal line and has a slope of 0, so the line parallel to it must also be horizontal and have a slope of 0.
Horizontal lines always have the form " y = k " for some number k and every point on that line has a y-value of k.
In this case, if you want the line to go through the point (-3,4), then the equation will be " y = 4 ", since that's the y-value of the point on the line.
Answer:
y = 4
Step-by-step explanation:
A line with the equation y = a is a horizontal line that intercepts the y-axis at (0, a).
A line parallel to a horizontal line is another horizontal line.
If a horizontal line passes through point (p, q), then its equation is y = q, where q is the y-value of the point.
Therefore, the equation of a line that passes through (-3, 4) and is parallel to y = 2 is:
y = 4Please help my cousin needs help i appreciate your help!
The area of the softball field is 4732 yd²
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given is a field with side measurements,
To find the area will we divide the field into a trapezium and a triangle,
Area of trapezium = (sum of parallel sides)x height/2
Area of triangle = 1/2xbasexheight
Area of trapezium = (104+52)x26/2 = 2028 yd²
Area of triangle = 2704 yd²
Area of the field = 2704 + 2028 = 4732 yd²
Hence, The area of the softball field is 4732 yd²
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32x = 3(5x−8) is equivalent to the equation 3(2x) = 3(5x − 8).
True
False
Answer: False
Step-by-step explanation:
This is because when u simplify 32x = 3(5x−8), it is 32x = 15x - 24
When u simplify 3(2x) = 3(5x − 8), you will get 6x = 15x - 24
How do you solve #18?
Find the value of X.
Answer:
x = 3
Step-by-step explanation:
Notice the markings in the lower two angles of the triangle. We are dealing with Angle Bisectors.
Angle Bisectors of a triangle intersect at the Incenter, which is Equidistant from the sides of the triangle (given by the perpendicular symbols).
Therefore, 2x = x+3 => x = 3
Will give brainliest. urgent, 100 points
a) Yes , the variable y varies directly with x
b) The constant of variation is k = 1/3
c) The function rule is given by the equation y = x/3
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be A
Now , the values of x are in set P = { 57 , 63 , 66 }
The values of y are in the set Q = { 19 , 21 , 22 }
a)
From the data set of P and Q , we can see that when the value of y increase the value of x also increases
Therefore , the value of variable y varies directly with x
And , y ∝ x
b)
The value of variable y varies directly with x
And , y ∝ x
So , y = kx
Substituting the value for x and y from the data set , we get
The equation will be
y = kx
19 = 57k
Divide by 57 on both sides of the equation , we get
k = 19 / 57
k = 1/3
Therefore , the constant of variation k is 1/3
c)
The function rule is given by the equation
y = kx
Substituting the value for k in the equation , we get
y = ( 1/3 ) x
y = x/3
Hence ,
a) Yes , the variable y varies directly with x
b) The constant of variation is k = 1/3
c) The function rule is given by the equation y = x/3
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Answer:
its six hundred men
Step-by-step explanation:
its Six hundred men, six hundred men under my command
With only one goal in mind
Make it back alive to our homeland
Six hundred men, six hundred miles of open sea
But the problem's not the distance
It's what lies in between
And Ithaca's waiting Ithaca's waiting
My kingdom is waiting The kingdom is waiting
Penelope's waiting for me
So full speed ahead, full speed ahead
Im having trouble with my homework and im not sure how to do this question could someone please explain?
line u has an equation of y+6=3/2(x–6). Line v is perpendicular to line u and passes through (2,–1). What is the equation of line v?
what is the missing lengths for the problems?
Answer:
≈5.6
Step-by-step explanation:
Use ratios: 4/3 = 7.5/x
3 times 7.5 then divide by 4 to get 5.6
Let me know if this helped you out!
i need helpp please tell me what is the perimeter of the rectangle, in units, if b= 2 1/2??
1.The perimeter of a rectangle is found by adding up the length of all four sides. Since the two long sides are 12 cm, and the two shorter sides are 7 cm the perimeter can be found by:
The perimeter is 38 cm.
2.To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width). Multiply both the height and width by two and add the results.
hope this helps
Find the value of x.
Answer:
x = 10
Step-by-step explanation:
we see that the two triangle are equivalent and therefore the two angles degrees are the same
set them equal to each other
5x - 11 = 8x - 41
then solve
add 41 to both sides
5x + 30 = 8x
subtract 5x to both sides
30 = 3x
swap them
3x = 30
divide all by 3
x = 10
thats your answer
Ann is 10 years older than Bob. Ten years ago, Ann was twice as the old as Bob. How old is Ann now? How old is Bob now?
It doesn't seem like there is enough information to solve the scenario.
The biggest part we are missing to properly solve this would be:
We are missing the current age of Ann.cone a is 10 centimeters high and its base has a diameter of 4 centimeters. Cone B is twice as tall with a hight of 20 centimeters and a diameter of 4 centimeters. Cone C is the same height as cone A, 10 centimeters, but the diameter of its base is 8 centimeters. Which cone has the greatest volume?
The cone that has the greatest volume is cone C
How to determine the cone that has the greatest volume?The given parameters in the question are
Cone A
Height = 10 cm
Diameter = 4 cm
Cone B
Height = 20 cm
Diameter = 4 cm
Cone C
Height = 10 cm
Diameter = 8 cm
The volume of a cone can be calculated using the following volume equation
Volume of a cone = 1/3π(d/2)²h
Where
h = height of the cone
r = radius of the cone
d = diameter of the cone
Using the above equations, we have the following computations
Volume of a cone A = 1/3π * (4/2)² * 10
Volume of a cone A = 40/3π
Volume of a cone B = 1/3π * (4/2)² * 20
Volume of a cone B = 80/3π
Volume of a cone C = 1/3π * (8/2)² * 10
Volume of a cone C = 160/3π
We can see that 160/3π is greater than 40/3π and 80/3π
Hence, cone C has the highest volume
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The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $4400, which was to be divided equally among the members going. Prior to the trip, 15 members decided not to go. If the cost per person increased by $66, how many people went on the expedition?
25 persons went on the expedition as the total cost was $4400.
What is a quadratic equation?A quadratic equation in algebra is any equation that can be written in standard form as where x stands for an unknown value and a, b, and c are known quantities. The assumption is that a > 0; equations with a = 0 are thought to be degenerate because they become linear or even simpler.
x denotes number of people
y denotes cost per person
Total cost =$4400
y = 4400 / x
15 members made the decision not to travel before the trip. The price per person went up by $66.
y +66 =4400 / (x -15)
(y +66) (x -15) = 4400
(4400/x +66)(x -15) = 4400
4400 -66000/x +66x -990 =4400
- 66000/x +66x=990
(- 66000 + 66x²) =990x
66x² - 990x - 66000 =0
x²-15x-1000=0
x =40 and x =-25 are the results of applying the quadratic formula to this quadratic equation. There is only sense in the positive x.
x- 15 =40-15=25 persons participated in the mission.
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This article says short sleepers (fewer than 6 hours) are four times more likely to catch a cold than longer sleepers (over 7 hours). The article says "The researchers then sequestered 164 volunteers in a hotel, administered the cold virus via nasal drops and monitored them for a week." Without further info, what is potentially misleading?
The use of volunteer sampling means that the result of the survey is potentially misleading.
What is volunteer sampling?Volunteer sampling is a sampling technique in which each participant in the sample opts to join the research, as is the case for this problem, as each participant opted to join in the project to compare their cold lengths.
The drawback of this type of sampling is that it should contain lots of participants that share similar characteristics, such as desiring to weight/diet, and this may influence their recovery to cold. The participants also may lie, which can cause misleading results to the study.
Options to remove misleading conclusions is to use a different type of sampling, such as stratified sampling, as groups of people that are either short or long sleepers are compared to reach a conclusion.
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Solve the system of linear equations by graphing. y = 3/4x-4 y= -1/2x+11
Taking into account the definition of a system of linear equations, the solution of the linear equation is (12,5).
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
This caseIn this case, the system of equations to be solved is
y = 3/4x-4
y= -1/2x+11
There are several methods to solve a system of equations, it is decided to solve it using the graphical method. This method consists of representing the graphs associated with the equations of the system to deduce its solution. The solution of the system is the point of intersection between the graphs since the coordinates of said point satisfy both equations.
In this case, graphing both equations, it is obtained that the point of intersection, and therefore the solution, is (12,5).
The graph of the system of equations is attached.
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How does
modifying the input or the output of a linear e
function rule transform its graph?
Answer:
Step-by-step explanation:
Adding a constant k to the output of a linear function translates the graph vertically by k units. If k < 0 k<0 k<0, then the translation is downwards and if k > 0 k>0 k>0. Adding a constant k to the input of the function translates the graph horizontally by k k k units.
In exercises 11-14, solve the system of nonlinear equations using the graph.
Answer:
No solution------------------------------
We see two graphs on the opposite sides of the x-axis.
There is no intersection, so no common points. It means there is no solution.
A car advertisement states that a certain car can accelerate from rest to 72 km/h in 12.5 seconds.
Initially the car is at rest, so the initial velocity is ______
m/s.
The car speeds up to 72 km/h which is equivalent to _______
m/s. Find the car’s average acceleration.
The acceleration of the car is _______
m/s2
The initial velocity is 0 m/sec
The car speed up to 72km/h which is equivalent to 36m/sec
The acceleration of the car is 2.88 m/sec².
What is acceleration?Acceleration is the rate of change of the velocity of an object with respect to time. Vector quantities are accelerations. Acceleration = (Final Velocity - Initial Velocity)/ Time taken
Given that car can accelerate from rest to 72km/h in 12.5 seconds. Therefore, we can write:
Initial Velocity = 0 m/sec
Final Velocity = 72 km/hr = 72×(0.50) m/sec = 36m/sec
Time taken = 12.5 second
Now, the car’s acceleration in m/s can be written as,
Acceleration = (Final Velocity - Initial Velocity)/ Time taken
(36 m/sec - 0 m/sec)/12.5 seconds
= 2.88 m/sec²
Hence, the car’s acceleration in m/s is 2.88 m/sec².
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Two cars start moving from the same point. One travels south at 56 km/h and the other travels west at 42 km/h. At what rate (in km/h) is the distance between the cars increasing three hours later?
The distance between the cars increasing three hours later rate (in km/h) is 70km/h.
What do you mean by distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
According to the given question,
We have given information:
Two cars start moving from the same point. One travels south at 56 km/h and the other travels west at 42 km/h.
Now, we will calculate the distance between the cars increasing three hours later,
S² + W² = D²
where S is the southbound car,
W is the westbound car,
D is the distance,
2 * S dS/dt + 2 W dW/dt = 2 D dD/dt
S dS/dt + W dW/dt = D dD/dt
In 3 hours,
S=3*56 = 168 and W = 3*42 = 126
and D = [tex]\sqrt{(168)^{2}+ (126)^{2}}[/tex] = 210
168 * 56 + 126 * 42 = 210 * dD/dt
(168 * 56 + 126 * 42) / 210 = dD/dt
dD/dt = (9408+5292)/210
dD/dt = 14700/210 = 70
Therefore, the distance between the cars increasing three hours later rate (in km/h) is 70km/h.
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The product of a number and 3 is twice the sum of that number and 5
The number that the product and 3 is twice the sum of that number and 5 is 10.
How to find the number?The product of a number and 3 is twice the sum of that number and 5.
Therefore,
let
x = the number
Hence,
3 × x = 2(x + 5)
3x = 2(x + 5)
3x = 2x + 10
subtract 2x from both sides of the equation
3x = 2x + 10
3x - 2x = 2x - 2x + 10
x = 10
Therefore, the number is 10.
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Anything helps! Thanks you :)
Define a variable and write an equation for each real-world problem. (Examples 1-4) 1. The Marriott Rivercenter in San Antonio, Texas has a main roof height of 441 feet. With the additional height of antennas, the structure is 546 feet tall. What is the height of the antennas?
The height of antennas added to the main roof of the Marriott Rivercenter in San Antonio is 105 feet.
Explain the term variable of the equation?A symbol (often a letter) used in mathematics to represent an unknowable numerical value in an expression or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.For the stated question-
Height of the main roof of Texas = 441 feet.
Height along with additional height of antennas = 546 feet.
Then,
Height of antennas = Total height - height of main roof.
Height of antennas = 546 feet - 441 feet
Height of antennas = 105 feet.
Thus, the height of the antennas added to the main roof of the Marriott Rivercenter in San Antonio is 105 feet.
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A vending machine has a total of 41 chocolate bars and bags of pretzels The number of chocolate bars is one less than twice the number of bags of pretzels. How many chocolate bars are in the vending machine?
The number of chocolate bars that are in the vending machine are; 27 bars
How to solve algebra word problems?We are told that the total number of chocolate bars and bags of pretzels in the vending machine is 41.
Let the number of bags of pretzels be x.
Now, we are told that number of chocolate bars is one less than twice the number of bags of pretzels. Thus;
Number of chocolate bars = 2x - 1
Thus, we can develop the algebraic expression as;
x + 2x - 1 = 41
3x - 1 = 41
3x = 42
x = 42/3
x = 14
Number of chocolate bars = 2(14) - 1 = 27 bars
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When Hudson runs the 400 meter dash, his finishing times are normally distributed with a mean on 70 seconds and a standard deviation of 2 seconds. If Hudson were to run 22 practice trials of the 400 meter dash, how many of those trials would be between 71 and 73 seconds, to the nearest whole number?
The required number of trials is between 71 and 73 second is 5 trials.
Given that,
Hudson runs the 400-meter dash, his finishing times are normally distributed with a mean of 70 seconds and a standard deviation of 2 seconds. If Hudson were to run 22 practice trials of the 400-meter dash,
Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
let x be the time,
According to the question,
z = x - 70 / 2 then Z ≈ N(0, 1)
71 < x < 73
71 - 70 / 2 < z < 73 - 70 / 2
1 / 2 < Z < 3/2
P[1/2 < Z < 3/2] = 0.9332- 0.691
= 0.2417
Now,
Required trials = 22 [0.2417] = 5.3174
Thus, the required number of trials is between 71 and 73 second is 5 trials.
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Convert 8 ounces into grams. Round your
answer to the nearest whole number.
*Note: you must use these exact conversion factors to
get this question right.
Answer:
227
Step-by-step explanation:
I think
PLEASE TELL ME WHERE TO PUT IT AND IF IT SHOULD BE FILLED IN OR NOT
Answer:
Step-by-step explanation:
5x≥15
/5. /5
x≥3
On the number line we put a filled dot since it is both equal to and greater then at 3 and make it point to the right since it is greater it has to go up
Hopes this helps please mark brainliest
Answer:
Choose the bottom right ray and put it at 3.
Step-by-step explanation:
Brainliest, please!What is the prime factorization of 16807 1680716807? Enter your answer as a product of prime numbers, like 2 × 3 2×32, times, 3, or as a single prime number, like 17 1717.
The Prime Factorization of 16807 are:7, 7, 7, 7, 7. This implies 7 raise to power 5.
What is prime factorization?The term "Prime Factorization" refers to determining which prime numbers multiply together to produce the original number.
The process of writing all numbers as a product of primes is known as prime factorization. As an example, suppose we have the number 20. We can divide this into two categories. "Well, that's 2 time 2 times 5," we can say. Also, 5 is a prime number.
In this case 16807 will be:
16807 ÷ 7 = 2401
2401 ÷ 7 = 343
343 ÷ 7 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
Again, all the prime numbers you used to divide above are the Prime Factors of 16807. Thus, the Prime Factors of 16807 are:7, 7, 7, 7, 7.
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An object was launched from the top of a hill with an upward vertical velocity of 170 feet per second. The height of the object can be
modeled by the function h(t) = -16t2 + 170t + 100, where t represents the number of seconds after the launch. Assume the object landed on the ground at sea level. Use technology to find the answer.
The object was __ feet in the air 9 seconds after it was launched.
The object was 334 feet in the air 9 seconds after it was launched.
The height of an object launched from the top of a hill can be modeled by the function h(t) = -16t² + 170t + 100, where t represents the number of seconds after the launch.
This function gives the height of the object in feet at any time t after the launch.
To find the height of the object 9 seconds after it was launched,
Substitute 9 for t in the function h(t) to calculate the height of the object at that time. This gives us the equation :
⇒ h(9) = -16(9)² + 170(9) + 100
⇒ h(9) = -16(81) + 1530 + 100
⇒ h(9) = -1296 + 1530 + 100
⇒ h(9) = 334 feet.
Therefore, 9 seconds after being launched, the object had reached a height of 334 feet.
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