The solution of the system of equations y = 2x - 3.5 and x - 2y = -14 is (7, 10.5).
In the given question, we have to solve the solution to the system of equations
y = 2x - 3.5..................(1)
x - 2y = -14...............(2)
Now putting the value of y from the equation 1 in the equation 2.
x - 2(2x - 3.5) = -14
Now simplifying the expression using the distributive property
x - 4x + 7 = -14
-3x + 7 = -14
Subtract 7 on both side, we get
-3x = -21
Divide by -3 on both side, we get
x = 7
Now putting the value of x in the equation 1,
y = 2(7) - 3.5
y = 14 - 3.5
y = 10.5
Hence, the solution to the system of equations y = 2x - 3.5 and x - 2y = -14 is (7, 10.5).
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The complete question is:
What is the solution to the system of equations y = 2x - 3.5 and x - 2y = -14?
Is X 0 A zero of/p x )= x²?.
The value x = 0 is zero of function p(x) = x²
Consider given function p(x) = x²
We know that from the definition of zeros of function, the zeros of a function are nothing but the values of the variable of the function that makes the function value equal to 0.
To find the zeros of function p(x), we need to equate p(x) to zero then solve it for x.
Here we need to check whether x = 0 is zero of function p(x)
If for x = 0, p(x) = 0 then x = 0 is zero of function p(x).
Substitute x = 0 in given function p(x)
⇒ p(x) = x²
⇒ p(0) = 0²
⇒ p(0) = 0
Thus x = 0 is a zero of given function.
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The complete question is:
Is x = 0 a zero of p(x)=x² ?
What is the inverse of 8?.
The inverse of 8 is 1/8.
The multiplicative inverse of a number for any n is simply 1/n. It is denoted as:
1/x (or) x⁻¹
It is also called the reciprocal of a number and 1 is called the multiplicative identity.
The reciprocal of a number obtained is such that when it is multiplied by the original number, the value equals identity 1.
There are a few steps to find the inverse of a number:
Write the number as the denominator of a fraction that has 1 as a numerator to find the reciprocal of an integer. Place a decimal number as the denominator of a fraction with 1 as the numerator, then divide to calculate the reciprocal of a decimal.Reverse the placement of the numerator and denominator for the reciprocal of a fraction.To know more about the inverse of a number:
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can somebody explain how the answer to this math problem is this?
answer is actually 0(<)x(<)2 but why?
The volume and value of x is x>9.
How to solve for x?Since x represents the width, it clearly must be greater than zero since a box must have each dimension be positive which makes the lower bound. The question is whether (17-2x) and (4-2x) represent the other 2 dimensions or not.
If so, then (4-2x) must also be greater than zero which makes the possible range of x as 0<x<1.5
If not, then in addition to the above range, values of x such that both 4-2x and 17-2 evaluate to negative still result in a positive volume.
Therefore, additional values of x are x>9.
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GOVERNMENT The Texa State Legilature i compried of tate enator and
tate repreentative. There i a greater number of repreentative than enator. The um of the number of repreentative and the number of enator i 181. The
difference of the number of repreentative and number of enator i 119. A. Write a ytem of equation to find the number of tate repreentative, r,
and enator,. B. How many enator and how many repreentative make up the Texa State
Legilature?
The system of equations is: r + s = 181 and r - s = 119. There are 31 state senators and 150 state representatives in the Texas State Legislature.
A. Let "r" be the number of state representatives and "s" be the number of state senators. We know from the problem that:
r + s = 181 (the sum of the number of representatives and senators is 181)
r - s = 119 (the difference of the number of representatives and senators is 119)
So the system of equations is:
r + s = 181
r - s = 119
B. To solve this system of equations, you can use the first equation to solve for one of the variables in terms of the other. Let's solve for "r" in terms of "s":
r = 181 - s
Now we can substitute this expression for "r" into the second equation:
(181 - s) - s = 119
Simplifying, we get:
181 - 2s = 119
2s = 62
s = 31
So there are 31 state senators in the Texas State Legislature. To find the number of representatives, we can use the first equation and substitute in the value of "s" that we just found:
r + 31 = 181
r = 150
So there are 150 state representatives in the Texas State Legislature.
Therefore, The system of equations is: r + s = 181 and r - s = 119. There are 31 state senators and 150 state representatives in the Texas State Legislature.
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the function y = f(x) is a NOT one-to-one. which equation could represent f(x)?
a) x^2 + y^2 = 16
b) 3x - 5y = 12
c) 1/y = x-4
d) none of the above
The equation 3x - 5y = 12 could be used to represent the function y = f(x), which is NOT one-to-one.
What is Function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given that function f(x) is not one-to-one
That means the given equation will have only one solution for the one value of x,
Since Quadratic equations have two values at the one value of x that means option a would not satisfy
option c also makes an exponential graph which means it also has more than one value at x
Since Option (b ) 3x - 5y = 12 has a linear function and linear functions do not have more than one value at a value of x
Therefore, the function y = f(x) is NOT one-to-one, the equation could represent f(x) as 3x - 5y = 12.
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what is a number that goes into a greater number with no remainders called?
The dividend is influenced by both the quotient and the divisor when the remainder is zero.
What is division with no remainder called?Any integer that divides a different number is the divisor. A factor, on the other hand, is a divisor that completely divides a number and leaves no remainder. Therefore, all factors are also divisors of a number. But not every divisor will also be a factor. The factors of 20 in the aforementioned case are 4 and 5.
We are left with a value after division if a number (dividend) cannot be divided entirely by another number (divisor). The term "remainder" refers to this amount.
When the remainder is zero, the dividend is affected by both the quotient and the divisor. When the remainder does not equal zero, neither the quotient nor the divisor are dividend factors.
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A rocket is launched upwards by physics students record a tight as a function of the time since it was launched. The rocket reaches a peak height of 112 feet at a time of 2.48 seconds. The rocket then falls and hits the ground 5.12 seconds after it was launched. find a model for the height of the rocket h(t) in vertex form. Round your value of a to the nearest tenth.
The height of the rocket 45.161 km.
How is the height in vertex form determined?
By adding a and b to h=-b2a, you may determine h, the x-coordinate of the vertex.
Determine k, the vertex's y-coordinate, by calculating k=f(h)=f(b2a).
According to the graph, the velocity first increases for 20 seconds before declining for 120 seconds before changing course.
Thus, it was at its highest peak at t=120 seconds.
Therefore, all that is left to do is figure out the triangle OAB's area at its highest point. This is 2 base + perpendicular = 2 120 * 1000 * 60 km.
The rocket reaches a peak height of 112 feet at a time of 2.48 seconds. The rocket then falls and hits the ground 5.12 seconds after it was launched.
According to the graph, the velocity first increases for 20 seconds before declining for 112 seconds before changing course.
Thus, it was at its highest peak at t = 112
2.48 seconds.
Therefore, all that is left to do is figure out the triangle OAB's area at its highest point. This is 2 base + perpendicular = 112 * 1000 /2.48 = 45.161 km.
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What are complex expressions?.
Complex numbers are those whose representation is given by the notation a+ib, where a, b are real numbers and I is a made-up expressions called a "iota." I'm equal to (-1).
If complex numbers are required to answer an equation, it is considered complex. Complex numbers are made up of both imaginary and real parts. This is how it is stated: The letters A and B in the preceding equation both represent numerical values. A complex number is something like 4+3i.
In order to attain vague goals that cannot be met through conventional actions, complex issue solving is a collection of self-regulated psychological processes and activities. It takes a variety of tactics and inventive knowledge combinations.
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Timothy found a new coat on sale. The original price was $80. It is on
sale for 25% off. What is the sale price of the coat? Help asap
True or False: Segment GT is congruent to segment PD.
GT Y
-10
B M
+$|||$||$
-5
0
PD W
|$|||||
5
10
"Segment GT is congruent to segment PD on the number line." this statement is True.
What is a number line?
A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.
The number line is used to represent the coordinates G, T, Y, B, M, P, D, W.
The point of G is -10 and the point of T is -9.
To get the measurement subtract G from T -
= -9 - (-10)
= -9 + 10
= 1
The point of P is 5 and the point of D is 6.
To get the measurement subtract P from D -
= 6 - 5
= 1
The measurement of GT and PD both is 1.
Therefore, segment GD is congruent to segment PD on the number line.
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An airplane leaves a runway heading due east then turns 35 degrees to the right as shown in the figure. How much more will the airplane have to turn to be heading due south?
Answer:
Because the plane is flying due east, it has to turn 90º to face south, before it turns the extra 35.31º to fly towards the airport. 90° + 35.31° = 125.31º It actually turns through the exterior angle of the triangle :
Step-by-step explanation:
hope this helps B)
Answer:
55°
Step-by-step explanation:
You want to know the additional angle a plane must turn through to be going south after it took off going east, then turned right 35°.
BearingThe initial bearing angle was 90° (straight east). After turning right 35°, the airplane now has a heading of (90+35)° = 125°. To be going south (180°), the bearing must increase by ...
180° -125° = 55°
The airplane will have to turn 55° more to be heading due south.
Your family has decided to put a rectangular patio in your backyard, similar to the shape of your backyard. Your backyard has a length of 45 feet and a width of 20 feet. The length of your new patio is 18 feet. Find the perimeters of your backyard and of the patio.
The perimeter of your new patio is 52.
Given that,
In order to match the shape of your backyard, your family has decided to build a rectangular patio there. The dimensions of your backyard are 20 feet wide by 45 feet long. Your new patio measures 18 feet in length.
To find : The perimeters of your backyard and of the patio.
The dimensions of the yard are length 45 and width 20.
The patio is going to have the same shape, only smaller.
The length of the patio is 18 feet.
The ratio of the length of the patio to the length of the yard is 18/45.
Since the patio and the yard are to have the same shape, then that same ratio of 18/45, applied to the width of 20, gives you a patio width of 18/45* 20 = 8
Therefore, The perimeter of your new patio is 2 * (18 + 8) = 2 * 26 = 52.
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I need to find the foci of this equation to answer my problem!
Correct option is A, The foci of the hyperbola is (0,±√17).
A hyperbola is a plane curve that is produced by a point that is moving so that the difference between the distances from two fixed points is constant. It is created when a double right circular cone intersects with a plane that cuts through both ends of the cone.
The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.
Given the equation of hyperbola is [tex]\frac{y^2}{12} - \frac{x^2}{5} = 1[/tex]
In this equation,
a² = 12
b² = 5
Using the relation c² = a² + b²
c = √(12 + 5)
c = √ 17
As, the hyperbola is vertical,
The value of foci will be (0,±√17)
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The circumference of circle C is 60 cm. What is the length of AB (in red)?
Help please
Answer:the a would be 10
and the b would be 6
Step-by-step explanation:
A non-regular octagon has seven interior angle measures of: 103, 175, 155, 158, 169, 157,
55. What is the sum of all interior angles and what is the measure of the eighth interior
angle?
Sum of Interior Angles =
Eighth interior Angle =
Answer:
Sum of Interior Angles = (8-2) * 180 = 1080 degrees
Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees
Step-by-step explanation:
The sum of the interior angles in a polygon can be found using the formula (n-2)*180, where n is the number of sides in the polygon.
In the case of an octagon (8 sides), the sum of the interior angles is (8-2)*180 = 1080 degrees.
The measure of the eighth interior angle can be found by subtracting the sum of the known interior angle measures from the total sum of the interior angles.
So,
Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees
In short,
Sum of Interior Angles = (8-2) * 180 = 1080 degrees
Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees
A careless university student leaves her iclicker device behind with probability 1/4 each time she attends a class. She sets out with her iclicker device to attend 5 different classes (each class is in a different lecture theatre).
The probability of forgetting iClicker device in each class = 1/4 = 0.25 = p
The probability of remembering iClicker device in each class = 1-p = 0.75
(a) Given that she is sure she has the iClicker device after leaving the first class.
The probability that she left it in second class = 1(0.25) = 0.25
The probability that she left it in third class = 1(0.75)(0.25) = 0.1875
The probability that she left it in fourth class = 1(0.75)(0.75)(0.25) = 0.1406
The probability that she left it in fifth class = 1(0.75)(0.75)(0.75)(0.25) = 0.1055
The total probability that she left iClicker given that she is sure she has the iClicker device after leaving the first class is:
0.25 + 0.1875 + 0.1406 + 0.1055 = 0.6836
Given that she is sure she has the iClicker device after leaving the first class, the probability that she left it in the 5th class is:
0.1055/0.6836 = 0.154
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Which is the best estimate for the mass of a bicycle?
Answer:
1 kilogram
Step-by-step explanation:
Show how to add the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator
(Quickly, and will give brainliest i to the best described one.)
Adding the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator exists 5/24.
What is meant by fractions?A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.
Let the fractions be 1/8 and 1/12
8 = 2 × 4
12 = 3 × 4
By using LCM, we get
[tex]$2 \times 3 \times 4=24 \quad\{L C M\}$[/tex]
= 1/8 + 1/12
simplifying the equation, we get
[tex]$=\frac{1 \times 3}{8 \times 3}+\frac{1 \times 2}{12 \times 2}$[/tex]
= 3/24 + 2/24
= 5/24
Therefore, adding the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator exists 5/24.
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Is 36 a prime factor?.
No, 36 is not a prime number. Because the number 36 is divisible by 1, 2, 3, 4, 6, 9, 12, 18, 36.
A prime number is a natural number more than 1 that has no positive divisors aside from 1 and itself. Prime numbers have several important properties and applications in mathematics, such as the fundamental theorem of arithmetic, which states that every positive integer can be written as a unique product of primes. They are also used in number theory, cryptography, and coding theory.
In addition, prime numbers are of interest in studying patterns and properties in the distribution of numbers, such as the distribution of twin primes and Mersenne primes. They play a crucial role in number theory, which is a branch of mathematics that studies the properties of integers. Prime numbers are infinite in number, and it is an open question whether there are infinitely many prime pairs or twin primes, which are pairs of prime numbers that differ by 2.
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please view the image and answer the questions.
Step 1: The greatest common factor (GCF) in this equation is x^3. So we can factor it out:
y = x^3(x - 343)
What does a math equation mean?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Step 2: We can not take root of a³ and b as there is no square term in the equation.
Step 3:
a= x^3
b= - 343
Step 4: Plugging in a and b into the original equation, we get
y = x^3(x - 343)
This is the simplified form of the equation.
So, the equation is a polynomial equation of degree 4, with the leading coefficient a = x^3 and the constant term b = -343, and it can be written as y = a(x-b) which is y = x^3(x-343)
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Michelle's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 48 sodas in all, 25% of which were regular. How many regular sodas did the diner serve?
The number of regular sodas served is 12.
How many regular sodas was served?Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. Percentage is a measure of frequency.
Number of regular sodas served = percentage of regular sodas served x number of sodas served
= 25% x 48
= 25/100 x 48 = 12
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What is triangle class 6?.
Answer:
The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side.
Step-by-step explanation:
On 800 km trip Ryan’s family travelled at 90 km/h for the first 600km and 100 km/h for the remainder of the journey. If they had travelled 90 km/h for the entire journey how much longer would the trip have taken
Answer:
Choose whichever format you want to give the answer
[tex]\boxed{\dfrac{2}{9} \textrm{ hour}}[/tex]
[tex]\boxed{0.2222 \textrm{ hour}}[/tex]
[tex]\boxed{13.3333 \textrm{ minutes}}[/tex]
Step-by-step explanation:
[tex]\sf{Travel\: time = \dfrac{Distance}{Speed}}[/tex]
The time taken to travel the first 600 km
[tex]= \dfrac{600}{90} = \dfrac{20}{3}\; \sf{hours}[/tex]
This leaves 200 km which was travelled at a speed of 100 km/hr
Time taken for this stretch = 200/100 = 2 hours
If the entire trip were driven at 90 km/h, it would take the same time as the first case. Therefore we only need to be concerned about the last 200km
If the last 200km were traveled at 90 km/h instead of 100 km/h, time taken
[tex]=\dfrac{200}{90} = \dfrac{20}{9}\\\\[/tex]
The difference in time then would be:
[tex]=\dfrac{20}{9} - 2\\\\\\= \dfrac{20}{9} - \dfrac{18}{9}\\\\=\dfrac{2}{9}\; hour[/tex]
= 0.22 hour in decimal
= 13.33 minutes
Need help before the deadline tonight
Answer:
25°
Step-by-step explanation:
Please see the attached document for how I set up this problem. I used the law/theorem of alternate interior angles to solve for the missing angle we're looking for, and knowing that a straight line will also have an angle measure of 180 degrees. We can also check the answer we arrive at by adding up all the angles that we have and seeing if they add up to 360 degrees, just as all the angles in a four-sided shape would.
The angle of KLM is 50 degrees. The opposite angle, MJK, is also 50 degrees. JKL and LMJ have the same angle of 130 degrees. When we add this together, we reach 360 degrees, letting us know our answer is correct.
Where do we use range () function give an example?.
The set of potential output values of a function is often referenced by the range () function.
A built-in Python function called range() can be used to produce a series of numbers. The range() function's parameters can be supplied by the user if they want to generate a series of numbers given the starting and ending values.
It can be used to generate a list of numbers or to iterate over a series of numbers in for loops.
For example, range(5) will generate a sequence of numbers from 0 to 4, and range(2, 5) will generate a sequence of numbers from 2 to 4.
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Pam worked as sale clerk is paid a basic rate of $3.75 during the rush Christmas Season.she works 6 hours overtime on Friday at time and quarter 8 hours overtime on Saturday at time and a half and 5 hours overtime on Sunday at double time..a)calculate Pam overtime wage for that week .b)Pam works a basic week of 40 hours calculate her basic wage.c)hence determine Pam gross wage for that week during Christmas
a) Pam overtime wage for that week is 110.625
b) Pam works a basic week of 40 hours her basic wage is 150.
c) Pam gross wage for that week during Christmas 114.375.
What is Basic wages?
An employee may not legally sell their labor for less than the minimum wage, which is the lowest compensation a business may pay their staff. By the turn of the 20th century, minimum wage laws were in place in the majority of nations.
What is Gross wages?
The total of the base salary, overtime compensation, commissions, bonuses, and other regular cash payments is referred to as the monthly gross wage. It does not include employer CPF contributions, bonuses, stock options, other lump sum payments, or payments-in-kind. It is prior to deducting employee CPF contributions and personal income tax.
Given that;
a)Calculation for Pam overtime wage for that week ;
So, 25% of 3.75 = 0.9375
and add it to 3.75.
then 0.9375 + 3.75 = 4.6875
Since she worked 6 hours at that new wage,
then 6 x 4.6875 = 28.125
Now for 50% of 3.75 =1.875
and add it to 3.75
then 1.875 + 3.75 = 5.625
Since she worked 8 hours at that new wage,
then 8 x 5.625 = 45
She works double time, which means she receives two times her regular pay.
Since she worked five hours at the wage, double her basic wage by two and then by five.
then 2 x 3.75 x 5 = 37.5
So, Pam overtime wage for that week is ;
28.125 + 45 + 37.5 = 110.625
b) Pam works a basic week of 40 hours her basic wage is ;
40 x 3.75 = 150
c) Pam gross wage for that week during Christmas is ;
total wages + overtime wages
⇒110.625 + 3.75 = 114.375
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A circular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet. What is the approximate area of the path alone? Use 3.14 for π
Answer:
200.96
Step-by-step explanation:
Pi(8 to the power of 2)
14 seats in 2 rows =
seats in 1 row
Answer: 7 seats in each row.
Step-by-step explanation:
14 / 2 = 7 seats in each row.
A chemist is using 389 milliliters of a solution of acid and water. If 18.6% of the solution is acid, how many milliliters of acid are there?
Step-by-step explanation:
for questions about % always find out first what 100% or what 1% are.
everything else can be calculated out of these 2 numbers.
in our case here
100% = 389 ml
1% = 100%/100 = 389/100 = 3.89 ml
18.6% = 18.6×1% = 18.6 × 3.89 = 72.354 ml
so, there are 72.354 ml of acid in the solution.
FYI
as you can see, we can combine both steps into one and do any of the following
18.6% = 18.6 × 100%/100 = 18.6 × 389/100 =
= (18.6/100) × 389 = 0.186 × 389
Classify this triangle by its sides and angles.
A.) right and scalene
B.) acute and scalene
C.) right and equilateral
D.) acute and equilateral
Answer:
acute and scalene, remember:
Isoceles: An isosceles triangle is a triangle with two sides of equal length. The two equal sides are called legs and the third side is called the base.
Scalene: A scalene triangle is a triangle with all sides of different lengths. None of its angles are congruent.
Equilateral: An equilateral triangle is a triangle with all three sides of equal length. All three angles are congruent and measure 60 degrees.
