Answer:
Simon's age is 18.
Step-by-step explanation:
Let Simons age be s and the age of each twin be t.
s + 2t = 48
s - t = 3
Subtract the second equation from the first:
s - s + 2t - (-t) = 45
2t + t = 45
3t = 45
t = 45/3 = 15.
Now we find Simon's age by plugging t = 15 in the second equation:
s - t = 3
s - 15 = 3
s = 3 + 15 = 18.
You are planning a three-day trip to Seattle, Washington, in October. Use the fact that on each day, it could either be
sunny or rainy, and that each day is equally likely to be sunny or rainy to answer the following question.
What is the probability that it rains all three days?
Suppose that the cost to ship an envelope is a function of its weight. For any
envelope up to 1 ounce, the charge is a stamp that costs $0.47. For an envelope over
1 ounce and up to 2 ounces, the charge is $0.68. Finally, for an envelope over 2
ounces and up to 3 ounces, the charge is $0.89. What are the practical domain and
range of this function?
The set of -values that are appropriate in the given situation is known as the practical domain. Solution: F (x) = 2 x is the function's formula.
What is a practical domain of a function?You are not accounting for or measuring any rainfall that occurred prior to the storm's onset, thus there is a total of 0 inches of precipitation at that time. Six and a half hours are spent in the storm.
Example :
Miami, Florida, experiences heavy rainfall due to a powerful hurricane. A 2 inch per hour downpour is occurring. In 6 and a half hours, the storm is over. The total amount of rain that has fallen throughout time should be modeled mathematically. The function is plotted. For this situation, identify the practical domain. The set of -values that are appropriate in the given situation is known as the practical domain.
Solution: Since there was no rain measured or included before the storm began, the function is as follows:
f(x)= 2x
There was 0 inches of rain at the moment the storm began. Six and a half hours are spent in the storm. f(6.5) = 2(6.5) = 13 inches of rain had been recorded at 6.5 hours, or so. It follows in words what the domain and range are:
Domain :
All real numbers between and including 0 and 6.5 hours.
Range :
All real numbers between and including 0 and 1.3 inches.
Domain and range can be expressed more easily with the help of some helpful notation, such as the following:
Domain { x∈R,0≤ x ≤ 6.5} [0,6.5]
Range { x∈R,0≤ x ≤ 6.13 [0,13].
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Select the correct answer. Consider the graph of f(x) given below. A curve labeled f of x declines through the points (negative 4, 7), (negative 3, 6), (negative 2, 5), (0, 3), (2, 1), (3, 0), (4, negative 1), (5, negative 2), (6, negative 3) and (7, negative 4) on the x y coordinate plane. The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)? A. g(x) = f(x) - 5 B. g(x) = f(x) - 2 C. g(x) = f(x - 5) D. g(x) = f(x + 2)
The functions could represent g(x) is C. g(x) = f(x - 5)
How to find the function?Using the general equation as Witten which can be used to find the y intercept of the line
g(x) = f(x) + b
The g(x) has intercept of y=-2,
Then the y-intercept of f(x) is at y=3
If we find the difference between both y-intercepts, we have
Recall that the y-intercept is the point where the graph intersects the y-axis
( -2 -3) = -5
This implies that the intercept of the line is -5
Then b=-5
Hence, g(x) = f(x - 5) is correct option for the function
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Please help me with 4 and 5!!!
Answer:
4. [tex]4^{x}[/tex] - [tex]2x^{2}[/tex] + 5x - 19
5. -[tex]4x^{3}[/tex] + [tex]x^{2}[/tex] - x - 5
Step-by-step explanation:
Find f - g
4. f(x) = 4^x - 7 and g(x) = 2x^2 - 5x + 12
f(x) - g(x) = 4^x - 7 - (2x^2 - 5x + 12)
distribute the -1 to 2x^2 - 5x + 12
4^x - 7 - 2x^2 + 5x - 12
combine like terms
4^x - 2x^2 + 5x - 19
5. f(x) = 3x - 8 and g(x) = 4x^3 - x^2 + 4x - 3
f(x) - g(x) = 3x - 8 - (4x^3 - x^2 + 4x - 3)
distribute the -1 to 4x^3 - x^2 + 4x - 3
3x - 8 - 4x^3 + x^2 - 4x + 3
combine like terms
-4x^3 + x^2 - x - 5
A microscope shows an image of an object that is 60 times the object's actual size. So, the
scale factor of the enlargement is 60. An insect has a body length of 5 millimeters. What is the
body length of the insect under the microscope?
30 millimeters
300 millimeters
300 centimeters
3,000 millimeters
If the body of insect has length of 5m, then in microscope of a scale factor of 60, it will become 300 millimetres
What is scale factor?Scale factor is a multiplying entity that falls between (0, infinity). Depending on the scale factor, an original figure may be increased or decreased.
Imagine that you have two circles that are visually identical. Even though both circles are described as identical, this does not guarantee equality. Their radii might differ. The one figure would be the scaled version of the other one.
Scale factors and the ideas of ratio and proportion go hand in hand. In ratio and proportion, we multiply or divide a given quantity to create a new one.
If the scale factor is 60
Then body length of insect under the microscope is
5 × 60
= 300 millimetres
Thus, If the body of insect has length of 5m, then in microscope of a scale factor of 60, it will become 300 millimetres
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Are all triangles 180 degrees?.
Answer:
Every triangle has interior angles that add up tp 180°
Step-by-step explanation:
What is the initial value of the function?
Answer:
In math, the initial value of a function means that it is the y-intercept of the function. For instance, if the function is f(x)=2x+3 f (x) = 2x + 3 , the y intercept, (initial value) is 3 . This value is graphed on the y axis.
Step-by-step explanation:
Answer:
In math, an initial value of a function means that it is the y-intercept of the function. Knowing the y-intercept will help in graph functions. For instance, if the function is f(x)=2x+3 f ( x ) = 2 x + 3 , the y intercept, (initial value) is 3 . This value is graphed on the y axis.
Step-by-step explanation:
How do you show a solution to a system of inequalities?.
The ordered pair that is a solution to all system inequalities is the linear inequality's solution, and the linear inequality's graph is the system's solution graph.
Shade the half-plane that satisfies the inequality and graph one line at a time in the same coordinate plane.
How can one tell if an inequality system has a solution?The system does not have a solution when two inequalities have parallel lines and the shaded areas do not overlap (i.e., the opposite areas are shaded). As a result, neither of the inequalities can be proven true at any given coordinate point.
How can you tell if a system has a fix?Solution to a System of Linear Equations To determine whether a point is a solution to a system, we will either look for the point of intersection of two lines on a graph or look for the point's algebraic location on both lines.
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how far above the ground is the ladder
The length from the point the ladder touche the wall from the ground 13 feet approximately to the nearest whole number derived using the Pythagoras rule
What is the Pythagoras ruleThe Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We shall represent the length of the from the wall where the ladder touches the wall to the ground with the letter x, such that by Pythagoras rule we evaluate for the hypotenuse as follows;
14² = x² + 5²
196 = x² - 25
x² = 196 - 25 {subtract 25 from both sides}
x² = 171
x = √171 {take square root of both sides}
x = 13.08
Therefore, the ladder is 13 feet approximately to the nearest whole number from the ground to where it touches the wall using the Pythagoras rule
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Please reduce each fraction and give the variable values to make the solution work.
Answer:
10
Step-by-step explanation:
hi
Complete the following:
Write an exponential expreion: chooe a number between 0 and 10 to be the bae and another number between 0 and 10, different from the bae, to be the exponent. Label the bae and the exponent. Then write the exponential expreion in expanded form and tandard form. Eay
The base is 5 and the exponential is 2. This can be written in expanded form as 5 multiplied by 5, which is equal to 25. In standard form, this can be written as 52, which is shorthand for the same calculation.
Base: 5
Exponent: 2
Expanded form: 5 x 5
Standard form: 52
An exponential expression is a mathematical expression that uses the operation of exponentiation. In this expression, one number, known as the base, is raised to the power of another number called the exponent. To write an exponential expression, choose a number between 0 and 10 for the base and another number between 0 and 10, different from the base, for the exponent. Then, write the exponential expression in expanded form and standard form. For example, if the base is 5 and the exponent is 2, then the expression can be written in expanded form as 5 multiplied by 5, which is equal to 25. In standard form, this can be written as 52, which is shorthand for the same calculation. This expression can be used to represent any number or calculation that can be written in exponential form.
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What is the formula of a parabola with the vertex at 2/3 and focus at 0 3 )?.
The formula of a parabola with the vertex at (2,3) and focus at (0,3) is (y - 3)² = 8(x - 2)
The term vertex in math is known as a special point of a mathematical object, and is usually a location where two or more lines or edges meet.
Here we have given the value of a parabola with the vertex at (2,3) and focus at (0,3).
As we all know that the general form of the vertex is written as,
=> (y − k)² = 4a(x − h) for horizontal parabola
Here we have given that Vertex (2,3) and focus (0,3)
Then it can be easily noticed that focus and vertex lie on the same horizontal line y = 3
Which defined that the axis of symmetry is a horizontal line and also here the focus lies to the right of the vertex so the parabola will open up rightward.
Then the vertex equation is written as,
=> a = 2 - 0 = 2
=> (y - 3)² = (4 x 2) (x - 2)
=> (y - 3)² = 8(x - 2)
Complete Question:
What is the formula of a parabola with the vertex at (2,3) and the focus at (0,3)?
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QUICK PLEASE I REALLY NEED HELP !!!
The transformation will map ΔABC onto image ΔA'B'C' is, a reflection in the line y = x. So Option C is correct
What is a triangle?In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°
If anyone of the triangle is 90° then it is called as right angle triangle
Given that,
Two triangles,
First, ΔABC
Whose coordinates are A(1,3), B(1, 6), C(4, 6)
Second, ΔA'B'C'
Whose coordinates are A'(3, 1), B'(6, 1), C'(6, 4)
There is only one transformation is possible,
Which is a reflection in the line y = x
Because, the distance of the points will be equal from the line y = x
In comparison of corresponding points
Hence, the transformation is a reflection in the line y = x
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Can you complete the equation how many fifths are equivalent to 6/10 this is just for fun
The number of 5ths in the fraction, 6/10 are 3, or there are 3 1/5s in 6/10
A fraction is a representation of a part of a whole. A fraction consists of a number (the numerator) known as the dividend, being divided by another number, (the denominator), also known as the divisor, arranged one over the other.
The expression of a fifth is 1/5
The number of fifths in 6/10 can be obtained by dividing 6/10 by 1/5 as follows;
6/10 ÷ 1/5 = 3
The number of fifths in 6/10 are 3 fifths
The number of fifths in 6/10 can also be obtained by simplifying the fraction, 6/10 as follows;
6/10 = (2 × 3)/(2 × 5) = (2/2) × (3/5)
2/2 = 1, therefore;
6/10 = 1 × 3/5 = 3/5
3/5 = 3 × 1/5
Therefore;
6/10 = 3/5 = 3 × 1/5
6/10 = 3 × 1/5
3 × 1/5 = 6/10
There are three 1/5s (fifths) in 6/10
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What is the slope of y =- 5x?.
The slope of the line y = -5x is -5
The slope of the LineThe slope of a line is a measure of its steepness or incline. It is calculated as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. Mathematically, it is represented as "m" in the equation y = mx + b, where "m" is the slope, "x" and "y" are the coordinates of a point on the line, and "b" is the y-intercept.
If the slope is positive, the line rises as it moves from left to right. If the slope is negative, the line falls as it moves from left to right. If the slope is zero, the line is horizontal. If the slope is undefined, the line is vertical.According to the question,
The slope of a line in the equation y = mx + b, where m is the slope of the line and b is the y-intercept, is the coefficient of x.
In the equation y = -5x, the slope of the line is -5.
The slope of a line represents the steepness or the "slant" of the line. It is the ratio of the change in y to the change in x. In the equation y = -5x, the slope of the line is negative, which means that the line is slanting downwards as we move from left to right on the graph. The absolute value of the slope gives the steepness of the line, in this case, the line is steep because the absolute value of -5 is 5.
A negative slope indicates that the line is decreasing and for every 1 unit increase in the x-axis, the y-value will decrease by 5 units. Conversely, for every 1 unit decrease in the x-axis, the y-value will increase by 5 units.
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How do you find the missing length of a triangle using sine?.
To find the missing length of a triangle using sine it is essential to know at least one side's length
One needs to know the lengths of at least one side and one angle of the triangle in order to use the sine function to get the missing length. In a right triangle, the sine function describes the relationship between the hypotenuse's length and the side length that is opposite the angle.
There are certain steps as to how the sine function determines a triangle's missing length. These steps are -
Firstly, the Sin(angle) which is equal to the opposite/hypotenuse is the sine formula to be written out.Next, it is required to choose the side whose length is known and the angle that it naturally forms.The missing side can be found by substituting the known values into the formula.Read more about triangles on:
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У саду ростуть 500 дерев. Яблуні становлять 24% всіх
дерев, груші — 115 % кількості яблунь, вишні - 5/6 кількості
груш, а решта дерев-сливи.
Скільки сливових де-
рев росте в саду?
В саду росте 500 дерев, з яких 24% є яблуні, що дає 120 яблунь. Груші становлять 115% кількості яблунь, тобто 135 груш. Вишні становлять 5/6 кількості груш, тобто 112,5 вишні. Решта дерев - сливи становлять 500 - 120 - 135 - 112.5 = 142.5 сливових дерев.
[tex]\it \dfrac{24}{100}\cdot500=24\cdot5=120\ apples\ trees\\ \\ \\ \dfrac{115}{100}\cdot120=\dfrac{115\cdot12}{10}=\dfrac{1380}{10}=138\ \ pears\ trees\\ \\ \\ \dfrac{5}{6}\cdot138=\dfrac{5\cdot138}{5}=\dfrac{690}{6}=115\ cherries\ trees\\ \\ \\ 500-(120+138+115)=500-373=127\ plums\ trees[/tex]
–3m = –786
10 POINTS AND BRILLIANTEST
Answer: I think it’s m= 262
Step-by-step explanation:
Answer:
m = 262
Step-by-step explanation:
Now we have to,
→ find the required value of m.
The equation is,
→ -3m = -786
Then the value of m will be,
→ -3m = -786
→ m = (-786)/(-3)
→ m = 786/3
→ [ m = 262 ]
Hence, the value of m is 262.
On a map, tony stark's house and spiderman's house are 3.5 inches apart. The map legend says that each inch represents four miles. How far apart are their houses?
Answer:14
Step-by-step explanation: This question is asked oddly but I believe it's still 14
3.5 x 4 = 14
Latoya bought a new rack for her CD collection. She has 977 CDs. Each row of the rack holds 12 CDs. How many rows can she fill? Write the answer as a mixed number
Latoya can fill 81 5/12 rows for her CD collection
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
According to the data problem,
Total CDs= 977Row capacity = 12 CDs/rackNumber of row = ?Calculating how many rows can she fill, we get:
Number of row = Total CDs / Row capacity
Number of row = 977 /12
Number of row = 81 5/12
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Brooke has 3 more dresses than Sarah. Which 2-variable equation shows how many dresses Brooke owns?
B = 3 + S
Where:
B = Brooke's number of dresses S = Sarah's number of dressesIn this equation, B stands for Brooke's number of dresses and S stands for Sarah's number of dresses. The equation states that Brooke's number of dresses is three more than Sarah's number of dresses, so if we know how many dresses Sarah has, we can calculate how many dresses Brooke owns.
For example, if Sarah owns 6 dresses, then Brooke owns 9 dresses (6 + 3).The equation B = 3 + S shows that Brooke has three more dresses than Sarah. Knowing Sarah's number of dresses allows us to calculate Brooke's number of dresses by adding three.
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How do you do algebraic expressions Grade 6?.
One can solve basic algebraic expressions by following these steps.
In grade 6, students typically learn to solve basic algebraic expressions by following these steps:
Identify the variable and the coefficient (number in front of the variable) in the expression.
Use the order of operations (PEMDAS) to simplify any arithmetic within the expression.
Use the distributive property to combine like terms.
Isolate the variable on one side of the equation by using inverse operations (such as adding or subtracting the same value from both sides, or dividing or multiplying both sides by the same non-zero value).
Substitute in a value for the variable to find the numerical value of the expression.
It's good to practice with a lot of examples and check the solutions and ask for help if needed.
Example:
Solve for x: 3x + 2 = 12
variable is x, coefficient is 3
nothing to simplify
nothing to combine
subtract 2 from both sides: 3x = 10
divide both sides by 3: x = 10/3 or 3.3333
x = 3.3333
It's important to note that solving algebraic expressions can become more complex as the student progresses, but the basic steps remain the same.
Thus, One can solve basic algebraic expressions by following these steps.
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On a scale drawing, 1 2 1 2 inch = 1 foot. A rectangular room measures 6 inches by 11 inches on the drawing. What is the area of the actual room?
The requried area of the actual room is given as 264 foot².
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
As given in the question,
1/2 inch = 1 foot
1 inch = 2 foot
Now,
A rectangular room measures 6 inches by 11 inches on the drawing.
= 6 inch × 11 inch
= 6 (2 foot) × 11 (2 foot)
= 12 × 22 foot²
= 264 foot²
Thus, the requried area of the actual room is given as 264 foot².
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What is the slope and y-intercept of y =- 9?.
The slope and y-intercept of y=-9 is 0 and (0,-9).
Linear equations can be written in the form y=mx+b, where:y is a y coordinate on the line m is the slope of the line.A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
Change y=9 in the slope-intercept form: y=mx+c, where m is the slope of the line and c is the y-intercept, y=0(x)+(-9),
Comparing the equation y=0(x)+9 with the equation y=mx+c, we get that m=0. It is a horizontal line. The slope = 0.
The line cuts the y-axis at the point (0,-9), The y-intercept is at the point (0,-9)
Hence, the slope and y intercept is 0 and (0,-9).
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evaluate the function for x=5:f(x)= 2x-4/3
Answer: 26/3
Step-by-step explanation:
[tex]f(x) = 2x - \frac{4}{3} \\f(5) = 2(5) - \frac{4}{3} \\f(5) = 10 - \frac{4}{3} \\f(5) = \frac{30}{3} - \frac{4}{3} \\f(5) = \frac{26}{3}[/tex]
In this question we need to evaluate the function f(x) = (2x-4)/3 for the question to be solved with perfect answer.
Evaluating a function means:
Replaces or substitutes each variable with the specified number or expression.
Now, according to question we have to replace x with number 5 so we can get the desired solution.
First evaluate by replacing and substituting the function for variable x with number 5 which is x=5. Hence by replacing the given number gives us the following equation
f (5) = (2*5-4)/3
Now, simplifying
f (5) = (10-4)/3
f (5) = (6)/3
f (5) = 2
Hence, the correct answer for this is 2.
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How do you solve a system of equations by 8th grade?.
There are different methods to solve a system of equations, but some common ones that are typically taught in 8th grade are graphing, substitution and elimination.
Graphing: This method involves plotting each equation on a coordinate plane and then finding the point of intersection, which represents the solution of the system.
Substitution: This method involves solving one equation for one of the variables and then substituting that expression into the other equation. This will give you an equation with only one variable, which you can then solve.
Elimination: This method involves adding or subtracting the equations in such a way that one of the variables is eliminated. This will give you an equation with only one variable, which you can then solve.
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0.4 how it come
[tex]10 \div 10[/tex]
We need to remove the decimal and multiply and divide by 10, resulting in 0.4/1 x 10/10 = 4/104/10. This can be further reduced to 2/5, so 0.4 as a fraction is 4/10 or 2/5.
What is fraction?A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fraction" which means 'to break'. The Egyptians, being the earliest civilization to study fractions, used fractions to resolve their mathematical problems, which included the division of food, supplies, and the absence of a bullion currency.
In Ancient Rome, fractions were only written using words to describe a part of the whole. In India, the fractions were first written with one number above another (numerator and denominator), but without a line. It was the Arabs only, who added the line which is used to separate the numerator and the denominator.
First, we need to remove the decimal.
For that, we multiply and divide by 10 as there is only one digit after the decimal.
We get, 0.4/1 x 10/10 = 4/10
4/10 can further be reduced to 2/5
Hence, we can say that 0.4 as a fraction is 4/10 or 2/5.
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What is the inverse of the logarithmic function f/x log9 X?.
The inverse of the logarithmic function f(x) = log9x is f^-1(x) = 9^x.
The inverse of a function is a new function that "undoes" the original function. For a logarithmic function, such as f(x) = log9x, the inverse is an exponential function.
To find the inverse of f(x) = log9x, you can follow these steps:
Switch the roles of x and y in the original function to make y the subject of the formula.
log9x = y
Replace the logarithm function with its inverse function, the exponential function.
9^y = x
Switch x and y back to their original roles in the equation.
x = 9^y
It's worth noting that for this logarithmic function, the domain of the function is x > 0 and the range is y > 0, and the inverse function will have its domain as y > 0 and range as x > 0. Also, the base of the logarithm 9, is a positive real number, different than 1, this ensures that the logarithm function is defined for all x > 0, for b = 1 it would not be defined for x = 1.
So the inverse of the logarithmic function f(x) = log9x is f^-1(x) = 9^x
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How is a complex number expressed?.
Complex numbers are those expressed as a+ib, where a, b are real numbers and I is a fictitious number called a "iota." I is equal to (-1).
A complex equation is one that needs complex numbers to be solved. Complex numbers are those that have both real and fictitious components. It is spelled out as follows: Both the letters A and B in the previous equation stand for numerical values. 4+3i is an example of a complicated number.
Complex issue solving is a set of self-regulated psychological processes and activities that are used to achieve ill-defined goals that cannot be accomplished through typical behaviors. Numerous strategies and creative knowledge combinations are needed.
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Last football season the starting quarterback of a professional football team completed just 55% of his attempted passes. The owner of this team has given the quarterback the ultimatum that he must improve his completion percentage during the off season or he will be fired. The owner plans to use a random sample of 50 passing attempts at the end of spring training to test the hypotheses where p represents the true proportion of passes this quarterback can complete after training during the off season. If the owner wants to minimize the chance of firing the quarterback when he really has improved, should he use a significance level of 0. 01 or 0. 10
The owner should use a significance level of 0.10 to minimize the chance of firing the quarterback when he has improved.
The owner should use a significance level of 0.10, not 0.01 when evaluating the quarterback's performance. The significance level is the probability of making a type I error, which is rejecting the null hypothesis when it is true. A lower significance level (e.g. 0.01) means that the owner is setting more stringent criteria for accepting the null hypothesis, and therefore is more likely to reject it and potentially fire the quarterback, even if he has improved.
On the other hand, a higher significance level (e.g. 0.10) means that the owner is setting less stringent criteria, and therefore is less likely to reject the null hypothesis and fire the quarterback if he has improved. In this case, the owner wants to minimize the chance of firing the quarterback when he has improved, so it is better to use a higher significance level of 0.10.
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