The solution to the equation 3(4x-10) = 2(3x-30) is x = -5.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
Let's solve for x:
3(4x - 10) = 2(3x - 30)
First, we can simplify both sides by distributing the coefficients:
12x - 30 = 6x - 60
Next, we'll move all the x terms to one side of the equation and the constants to the other side:
12x - 6x = -60 + 30
Simplifying further:
6x = -30
Finally, we can solve for x by dividing both sides by 6:
x = -5
Therefore, the solution to the equation 3(4x-10) = 2(3x-30) is x = -5.
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Match the terms to their definition.
1 .
the number that is repeated as a factor in an exponential expression
exponent
2 .
the smaller number in an exponential expression; tells how many times a factor is repeated
base
The proper pairing is as follows:
(1) The factor in an exponential equation that is repeated: Base
(2) The smaller number indicates the number of times a factor is repeated in an exponential expression: Exponent
What are exponent and base?Exponentiation is a mathematical process that involves the base b and the exponent or power n.
It is represented as bn and is pronounced as "b to the n."
The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0.
The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
The correct matching will be as follows:
(1) The number that is repeated as a factor in an exponential expression: Base
(2) The smaller number in an exponential expression; tells how many times a factor is repeated: Exponent
Therefore, the proper pairing is as follows:
(1) The factor in an exponential equation that is repeated: Base
(2) The smaller number indicates the number of times a factor is repeated in an exponential expression: Exponent
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y = 4x y = -x + 3 what is one way you can use substitution to see if arabelle is correct
The solution to the equation is (3/5, 12/5)
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
y = 4x
y = -x + 3
substitute the known values in the above equation, so, we have the following representation
4x = -x + 3
Evaluate the like terms
5x = 3
So, we have
x = 3/5
This gives
y = 4 * 3/5
Evaluate
y = 12/5
Hence, the solution is (3/5, 12/5)
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Malik received a$300 gift card from his grandparents and is using it only to pay for his karate lessons, which cost $30 per month.
Write a function that describes the amount, d, in dollars, on the card after t months in both general and factored form.
Answer:
(General function) d(t) = 300 - 30t(Factored version) d(t) = 30(10 - t)Step-by-step explanation:
The amount in dollars is represented by d, and the amount of months is represented by the letter t. Using this, you can construct an equation using the given values in the form of f(x) = a - b(c). This equation represents the decrease in Malik's income after one month.
Hope this helps! :)
If you were to graph the information provided in the table, what would be the labels for the x- and y-axes?
Answer:
The answer is right there, the left of the graph "number of burritos" is the x-axis, the y axis is the "cost"
Step-by-step explanation:
Show that the function is 1/n.
A Thermometer with an arbitrary scale of equal divisons register -10 celsius at the ice point and +110 celsius at the steam point. Compute :
A. The centigrade temperature corresponding to 20 celsius on this thermometer
B. The Fahrenheit temperature corresponding to a reading of 45 celsius on this thermometer
Answer:
Step-by-step explanation:
The range (ice to steam) of a Celsius thermometer = 100 C.
The range of the given thermometer = 10 + 110 = 120 degrees.
So, 1 degree C ≡ 1.2 degrees on the given thermometer.
A. So, 20 degrees C ≡ 24 on given thermometer and the reading will be 24 - 10 = 14.
Emily earns $11.15 an hour at the movie theater. She earns $0.7
more an hour than Azzata who works at Chick-fil-A. How much does
Azzata earn an hour?
Using Subtraction, Azzata earns $ 10.45 an hour.
To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.
Any subtraction problem has three components: the minuend, which is the part you start with; the subtrahend, which is the part being subtracted; and the difference, which is the part that is left over.
Emily earns $11.15 an hour at the movie theater.
She earns $0.7 more an hour than Azzata
Azzata earns -
⇒ $11.15 - $ 0.7
⇒ $ 10.45
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Ayden owns a food truck that sells tacos and burritos. He only has enough supplies to make 120 tacos or burritos. He sells each taco for $3-75 and each burrito for $6.25.
Ayden must sell no less than $530 worth of tacos and burritos each day. Also, he can sell at most 70 burritos. If a represents the number of tacos sold and y represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
see below for a graph
(x, y) = (50, 60) . . . . one possible solution
Step-by-step explanation:
You want inequalities, their graph, and one possible solution to match the Ayden food truck scenario: a total of 120 tacos (x) or burritos (y) can be sold, with that total including at most 70 burritos. At $3.75 per taco and $6.25 per burrito, revenue must be at least $530.
InequalitiesAn inequality can be written for each constraint:
total number of tacos and burritos: x + y ≤ 120
minimum revenue: 3.75x +6.25y ≥ 530
maximum burritos: y ≤ 70
GraphThese are graphed in the attachment. The point (x, y) = (50, 60) represents one possible solution: 50 tacos and 60 burritos sold for $562.50.
PLEASE HELP!!
if 90° < 0 <180° and csc0 = 3, then cot0=
the value of cot∅ will be -2√2.
What is trigonometric function?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
Given csc∅ = 3
This is given in 2nd qudrant (90° < 0 <180°).
Sin∅ = 1/3
cos∅ = √1-(1/3)² = -√ (8/9)
cot∅ = cos∅/Sin∅ = -2√2
Hence the value of cot∅ will be -2√2.
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Use the number line below, where RS=6y+3, ST=4y+8, and RT=61.
a. What is the value of y?
b. Find RS and ST.
Using the number line below, where RS=6y+3, ST=4y+8, and RT=61, the value of y was found to be 4.
what is line segments ?An area of a line that can connect two points is known as a line segment. A and B, the ends of this line segment, both have fixed lengths. The separation between endpoints A and B is the length of this line segment. An area or portion of a line with two endpoints is known as a line segment. A line segment has a set length as opposed to a line. Both metric measurements, such as millimeters and centimeters, as well as conventional units, such as feet or inches, can be used to measure the length of a line segment. The length of one line segment in comparison to the other when there are two can be determined just by glancing at them. The line segment CD is longer than AB, as can be seen.
given
ST = 2y + 9 RS = 7y + 3
RT = 14y - 8
S lies between R and T, hence we can deduce that:
RS plus ST = RT
Therefore, we can swap out the equations for each of the segments above to obtain:
We can now solve this for y; to do so, let's move all the phrases that begin with y to the left.
14y -7y - 2y = 3 + 9 + 8\s(14 - 7 - 2) (14 - 7 - 2)
*y = 20
5*y = 20
y = 20/5 = 4\
y = 4
The value of y was determined to be 4.
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Write Short note on variations ?
Using the concept of statistics, We are aware about population, sample and data, Variations refers to different forms of same thing.
What is statistics?Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to describe, understand, and make inferences about data sets, and to make predictions and decisions based on that data. Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to describe, understand, and make inferences about data sets, and to make predictions and decisions based on that data.
What do you mean by population and sample?In statistics, a population is the entire group of individuals or objects that have some common characteristic or that we are interested in studying. For example, the population of a country would be all its citizens, or the population of a certain species of animal would be all the individuals of that species. A sample is a smaller group of individuals or objects selected from the population in order to study or make inferences about the population as a whole.
Variation refers to the degree to which data points in a set differ from one another. In statistics, variation is used to describe the spread or dispersion of a set of data, and is an important aspect of describing and understanding the data. Variation can be measured using different statistical measures such as range, variance, and standard deviation.
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Jacqueline, Kimberly, and Julia collect mechanical pencils. Kimberly owns two less than three times the number of mechanical pencils Jacqueline owns. Julia owns three less mechanical pencils than Jacqueline. Together, the three collectors own a total of 100 mechanical pencils. How many mechanical pencils does Kimberly own?
Kimberley owns 55 pencils.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given: Kimberly owns two less than three times the number of mechanical pencils Jacqueline owns. Julia owns three less mechanical pencils than Jacqueline. Together, the three collectors own a total of 100 mechanical pencils. Let Jacqueline own x pencils then Kimberley owns 3x-2 and Julia owns x-3
Thus 3x-2+ x-3+x=100
5x=95
x=19
Hence, Kimberley owns 55 pencils.
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Which answer describes the graph of the system of equations?
The point of intersection is (0, 4).
The point of intersection is (4, 0).
The lines are parallel.
The lines coincide.
There must be several solutions for which the lines of the equation coincide for an equation system to be a dependent consistent system. D is the right answer.
What is a System of equations?The lines of the equations must be parallel to one another for a system of equations to have no meaningful solution.
Consistent Method
First, Dependent Consistent System
There must be several solutions for which the lines of the equation coincide for an equation system to be a dependent consistent system.2. Independent Consistency SystemA system of equations must have a single unique solution for which the equation's lines must intersect at a certain location in order to qualify as an Independent Consistent System.It is clear that the lines coincide if the graph of the given system of equations is drawn as shown below. Therefore, choice D is the right one.The complete question is,
Which answer describes the graph of the system of equations?
{y=4-x
{2y=8-2x
A) the point of intersection is (0,4)
B) the point of intersection is (4,0)
C) the lines are parallel
D) the lines coincide
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Answer:
d (the line coincide)
Step-by-step explanation:
we all need help
in 1986 one of the first video games, the Nintendo, sold for $180. Similar to many items, its value depreciated over time.
The depreciated value in 1990 will be $146.6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that in 1986 one of the first video games, the Nintendo sold for $180. The depreciation rate per year is 5%.
The price after 1990 will be calculated as,
Price = 180 x ( 0.95 )⁵
Price = $146.6
The complete question is given below.
In 1986 one of the first video games, the Nintendo sold for $180. The depreciation rate per year is 5%. What is the cost at the end of 1990.
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Noah is 1.35 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 31.55 meters. He stands 26.2 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
3.64 meters
Step-by-step explanation:
To find the height of the tree to the nearest hundredth of a meter, you can use the principle of similar triangles.
First, we can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the height of the tree, the distance between the base of the tree and the point where the shadows meet, and the length of the shadow of the tree.
c = √(a² + b²)
c = √(h² + 26.2²)
Next, we can use the similar triangles to establish a ratio between the length of the shadow and the height of the tree and the length of the shadow and the distance from the tree.
shadow tree / height tree = shadow person / height person
31.55 / h = 31.55 / 26.2
Now, we can cross-multiply and divide to solve for h
h = 31.55 * 1.35 / 26.2
h = 3.64 meters
We can round it up to the nearest hundredth of a meter:
h = 3.64 meters
Therefore, the height of the tree is 3.64 meters to the nearest hundredth of a meter.
Which number makes the equation true?
Answer:
7/28 = 1/4
This is because:
7/28 = 0.25
0.25 = 1/4
Step-by-step explanation:
Hope it helps! =D
Answer:
a) 7
Step-by-step explanation:
Given problem,
→ [ ] ÷ 28 = 1/4
Let us assume that,
→ missing number = x
Forming the equation,
→ x ÷ 28 = 1/4
→ x = (1/4) × 28
→ x = 28/4
→ [ x = 7 ]
Hence, the answer is 7.
Write 3 numbers that are divisible by 2,
5, and 10.
Answer:A number is divisible by 2 if it ends in 2, 4, 6, 8 or 0. A number is divisible by 5 if it ends in 5 or 0. A number is divisible by 10 if it ends in a 0.Apr 8, 2018
The _____ describes the average distance of distribution values from the mean.
A.standard deviation
B.arithmetic average
C.mean
D.mode
E.median
Graph -3x2+12y2=84 . What Are The Domain And Range?
The domain and range of the given graph function is R.
The equation -3x^2 + 12y^2 = 84 represents an ellipse in the coordinate plane. The standard form of an ellipse is (x^2/a^2) + (y^2/b^2) = 1, where a and b are the lengths of the semi-major and semi-minor axis, respectively.
To put the given equation in standard form, we need to divide both sides by 84, and divide the x^2 and y^2 by the square of their respective coefficient:
(-3/84)x^2 + (12/84)y^2 = 1
This gives us x^2/ (84/-3)^2 + y^2/ (84/12)^2 = 1
Which gives us x^2/28 + y^2/7 = 1
This means that the semi-major axis has a length of 2sqrt(7) and the semi-minor axis has a length of sqrt(7).
The domain of this function is all real numbers, because the x values can take any real value.
The range of this function is also all real numbers, because the y values can take any real value, within the boundaries of the ellipse.
So, the domain and range of the function -3x^2 + 12y^2 = 84 is all real numbers.
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Solve algebraically for c:
|3/2c - 10| - 9 ≤ - 1
explanation please
Therefore, using an algebraic method, c = 1/12 in the equation |3/2c - 10| - 9 - 1 is the value of c.
what is equation ?Using the equal symbol (=) to indicate equivalence, a mathematical equation is a formula that joins two statements. An equation in algebra is a statement of mathematics proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign places the variables 3x + 5 and 14 apart. The relationship between two sentences on either side of a letter is described by a mathematical formula. A single variable, which also serves as the symbol, is frequently present. like in 2x - 4 = 2, for instance.
given
|3/2c - 10| - 9 ≤ - 1
3/2c-10 -9 = -1
3/2c - 19 = -1
3/2c = 18
36c = 3
c = 1/12
Therefore, using an algebraic method, c = 1/12 in the equation |3/2c - 10| - 9 - 1 is the value of c.
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f(x)=2x-3, find f(-4)
Answer:
f(- 4) = - 11
Step-by-step explanation:
substitute x = - 4 into f(x) , that is
f(- 4) = 2(- 4) - 3 = - 8 - 3 = - 11
Answer:
f(-4)=-11
Step-by-step explanation:
f(x)=2x-3
Let x=-4
f(-4)=2(-4)-3
= -8-3
= -11
The graph at the right illustrates the rate at which Dave and Joe are saving money.
a. Estimate the solution to the system.
b. Explain what this means in the context of
the saving money scenario.
This problem can be solved using a system of equations.
What is the system of equations?
A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and graphical solutions are possible for these equations. The point of intersection of two lines represents the system of equations' solution.
Line 1
Taking two points on this line (0,300) and (4,450)
Equation of line y = mx+c
m = [tex]\frac{450 - 300}{4 - 0}[/tex] = 37.5
y = 37.5x + c
Substituting (0,300) in the above equation
300 = 37.5 * 0 + c
c = 300
Line equation y = 37.5x + 300
Line 2
Taking two points on this line (0,400) and (5,500)
m = [tex]\frac{500 - 400}{5 - 0}[/tex] = 20
y = 20x + c
Substituting (0,400) in the above equation
400 = 250* 0 + c
c = 400
Line equation y = 20x + 400
a) The solution of the system is when both lines coincide
37.5 x + 300 = 20x + 400
17.5 x = 100
x = 5.7
y = 20 * 5.7 + 400 = 514
Therefore the solution of the system is ( 5.7 , 514)
b) In terms of saving money scenario. This means that Dave and Joe have the same amount of savings at this point.
Therefore these are the solutions to the above system of equations.
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The original price of a toaster is $20.00. If Horace uses a coupon and the price is decreased 10%, what is the price Horace will pay?
Answer:
18 dollars
Step-by-step explanation:
The easiest way of calculating discount is, in this case, to multiply the normal price $20 by 10 then divide it by one hundred. So, the discount is equal to $2. To calculate the sales price, simply deduct the discount of $2 from the original price $20 then get $18 as the sales price.
Higher Order Thinking Lauren has a stamp collection. She gives Kristen 12 stamps and Ethan 15 stamps. Lauren has 22 stamps left. How many stamps did she have at the start?
Answer: 49 Stamps
Step-by-step explanation:
If Lauren gave Kristen and Ethan 12 stamps and 15 stamps respectively, that means that she gave them a total of 27 stamps. This leaves her with 22 stamps left. In order to find the number of stamps she had at the start, add the stamps she gave away to the stamps she had left at the end. So,
15 stamps + 12 stamps + 22 stamps = 49 stamps total at the start
Lauren had 49 stamps in the beginning. Since she gives Kristen 12 stamps, and Ethan 15 stamps, we can add both amounts to assume the total number of stamps she gave away. 15+12=27, so she gave away 27 stamps. Lauren was left with 22 stamps. We can add 22 to 27 to find out how many stamps she had in all. 27+22=49. Therefore, we can come to the conclusion that Lauren had 49 stamps at the start.
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Designing a Room
Jeff is an interior designer. He is designing a floor plan for a
rectangular bedroom. On his floor plan, 1 cm represents 1 ft.
window
261
(=2πr
13"
3.6
A. Draw a floor plan for a rectangular bedroom. Include at least
four pieces of furniture. Include at least one circular piece of
furniture.
door
B. Calculate the side lengths of each piece of furniture in metric
and imperial measures so the customer has a choice of which
system to use. Label these on your diagram.
C. Label the diameter and the circumference of the circular piece
of furniture.
D. Which piece of furniture has the greatest perimeter?
On solving the provided question we can say that - The answer to the question is that all real numbers or domain (−∞,∞)
What is Domain?The range of values that may be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while employing a value for x to that end, then the selected x-value is said to belong to the domain of f.
The answer to the question is that all real numbers or (−∞,∞)
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On solving the provided question, we can say that Area of rectangular bedroom = 12 X 3.6 = 43.2 cm sq.
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
here,
dimension of rectangular bedroom
L = 12
W = 3.6
Area of rectangular bedroom = 12 X 3.6 = 43.2 cm sq.
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Mindy and Troy combined ate 999 pieces of the wedding cake. Mindy ate 333 pieces of cake and Troy had \dfrac14
4
1
start fraction, 1, divided by, 4, end fraction of the total cake.
The expression is 3 + c/4 = 9 and the total pieces of care are 24.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator).
Given total cake eaten by mindy and troy = 9 pieces
Mindy ate = 3 pieces of cake
Troy = had ¼ of the total cake.
let there be c pieces of cake,
troy ate = c/4
Let Mindy ate be a and troy ate be b
a + b = 9
and a = 3, b = x/4
3 + c/4 = 9
c = 6 * 4
c = 24
Hence the equation is 3 + c/4 = 9 and there are 24 pieces of cake.
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the correct question is ,
Mindy and Troy combined 9 pieces of the wedding cake .Mindy ate three pieces of cake and Troy had 1/4 of the total cake
write an equation to determine how many pieces of cake (c) there were in total
For which interval is the function constant?
(−∞,−6)
(2,∞)
(−6,0)
(0,2)
The function is constant in the interval (-6 to 0).
The correct option is (C).
What is a Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
If the value of one of the variables does not alter the value of the other, the function is said to be constant.
As we can see, the function is constant in the range from x=-6 to 0, because the value of y in the function does not change as the value of x changes (-6 to 0).
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1. Give the number 78.07526 correct to
a. 1 decimal place
b. 2 decimal places
c. 3 decimal places
Answer:
Step-by-step explanation:
When the digit in the thousands place is < 5, the thousandths place and following digits are replace by 0.
2. When the digit in the thousands place is = or > 5, the digit in the hundredths places is increased by 1 and the following digits become 0.
Use the graph to evaluate the function below for specific inputs and outputs.
Inputs and outputs are 3,-2.One point can be used to represent each set of input and output values on a graph.
Inputs and outputs are graphical in what way?One point can be used to represent each set of input and output values on a graph. The vertical axis is used to measure output values, whereas the horizontal axis is used to measure input values. On each axis, a scale that is consistent and can hold all the necessary points is drawn.
The C language provides input and output functions for carrying out the most typical operations. Three fundamental tasks are performed in every C program: taking input data, processing that data, and producing output. Data that is accepted is considered input, and data that is presented is considered output.
According to question:-
At x=-4, g(x) equals 6.
g(x)= -2 x=3
kindly examine the g(x) graph.
the value of y is equal to 6 for x=-4.
with x = 3, the value of y Equals -2.
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For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 81 N acts on a certain object, the acceleration of the object is 9m/2 . If the acceleration of the object becomes ms/2, what is the force?
If the acceleration of the object becomes 3 m/s^2, the force is equal to 27 Newton.
What is a direct proportion?Mathematically, a direct proportion can be represented the following mathematical expression:
y = kx
Where:
y represents the force.x represents the acceleration.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 81/9
Constant of proportionality (k) = 9.
For the force when the acceleration of the object becomes 3 m/s^2, we have:
y = kx
y = 9(3)
y = 27 Newton.
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Complete Question:
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 81 N acts on a certain object, the acceleration of the object is 9 m/s^2. If the acceleration of the object becomes 3 m/s^2, what is the force?