If the two functions be g(x) = x + 2 and h(x) = 3x - 3 then
(h - g)(x) = 2x - 5
(h + g)(x) = 4x - 1
(h . g)(1) = 3x² + 3x - 6
What is meant by expression ?A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: (Math Operator, Number/Variable, Math Operator) is an expression.
Mathematical expressions are built using the addition, subtraction, multiplication, and division operations.
Let the two functions be g(x) = x + 2 and h(x) = 3x - 3
(h - g)(x) = h(x) - g(x)
substitute the value expressions in the above equation, we get
= (3x - 3) - (x + 2)
= 2x - 5
(h + g)(x) = h(x) + g(x)
= (3x - 3) + (x + 2)
= 4x - 1
(h . g)(1) = h(1) . g(1)
= (3x - 3) . (x + 2)
= 3x² + 3x - 6
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Write the rational number 2.5 using quotients of the form p/q. Use the integers below.
-15 -6 -5 -2 2 5 6 15
The value of the number will be;
⇒ 5/2
What is Rational number?A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.
Given that;
The rational number is,
⇒ 2.5
Now,
Since, The rational number is,
⇒ 2.5
Hence, We get;
⇒ 2.5 = 25/10
= 5/2
Thus, The value of the number = 5/2
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A small country emits 120,000 kilotons of carbon dioxide per year. In a recent global
agreement, the country agreed to cut its carbon emissions by 3.4% per year for the
next 6 years. In the first year of the agreement, the country will keep its emissions at
120,000 kilotons and the emissions will decrease 3.4% in each successive year. How
many total kilotons of carbon dioxide would the country emit over the course of the 6
year period, to the nearest whole number?
The total carbon dioxide that the country would emit over the course of the 6 year period is 661,505 kilotons.
What is the total carbon dioxide that would be emitted?The formula that can be used to determine the emission each year is:
Emission in the first year x(1 - rate of decrease)^number of years
Emission in the first year = 120,000
Emission in the second year = 120,000 x (1 - 0.034)^1 = 115,920
Emission in the third year = 120,000 x (1 - 0.034)^2 = 111,978.72
Emission in the fourth year = 120,000 x (1 - 0.034)^3 = 108,171.44
Emission in the fifth year = 120,000 x (1 - 0.034)^4 = 104,493.61
Emission in the sixth year = 120,000 x (1 - 0.034)^5 = 100,940.83
Sum of emissions from the first year to the sixth year = 661,505
This illustrates the concept of exponential decrease.
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two students found the slope of the line shown. tavion used the points (-1,-3) and (0,-1) while jess used the points (3,5) and (0,-1). which of the following is a true statment
All the statements are true.
What is meant by slope of a line?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Why is the formula for slope?Y = mx + b, where m is the slope and b is the y-intercept, is the slope equation utilizing the equation of a line.
A. The triangles drawn between each pair of points are similar.
B. The ratio of y2-y1/x2-x1 will be the same for Tavion and Jess.
C. Both students should find a slope of .
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WILL SOMEONOE HELP ME WITH THIS SIMPLE GEOMETRY?
Answer:
Below
Step-by-step explanation:
If they are similar the ratios of their sides are similar
11 is similar to 43 as 8 is similar to OP
Set up a ratio of this statement:
11/43 = 8/OP then OP = 8 * 43/11 = 31.3 units
is this statistical, what is the total number of eggs in dozen?
Part A
ANALYZE Reece says that if you solve a system of equations using elimination by addition and the result is 0=2, then the solution of the system is (0,2). Select a counterexample to show that her statement is false.
A)
x+y = 1
-x-y = -1
B)
x+y=1
x-y=1
C)
x+y=1
-x-y=1
D)
x+y=-1
-x-y=-1
Part B
Justify your argument.
This system of equations has Select Choice
The counter example for the system of equation is given by x + y = 1 ,
-x - y = 1 has the result 0 = 2 but ( 0, 2 ) is not the solution of the equation. It proves statement is false.
As given in the question,
Form the given system of equations , using elimination method to get the solution of the equation which shows the result 0 = 2 is as follow:
a. x + y = 1
- x - y = -1
0 = 0
Not the required result.
b. x + y = 1
x - y = 1
2x = 2
Not a required result.
c. x + y = 1
- x - y = 1
0 = 2
Required result.
Analyze : substitute x = 0 and y = 2 in any one equation
0 + 2 = 1
or -0 -2 = 1
Both the equations proves that statement is false.
d. x + y = -1
-x -y = -1
0 = -2
Not a required result.
Therefore, the system of equation of option c. x + y = 1 , -x - y = 1 has the result 0 = 2 and proves it is the false statement.
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Solve a system by elimination.
8x-2y=2
4x-y=2
Answer:
No solution.
Step-by-step explanation:
You would multiply -2 to the 2nd equation and you would get -8x+2y=-2 and you would add that to 8x-2y=2 and when you would add all of them would eliminate or cross each other out, showing no solution.
Find 4C – 3D. gradpoint help algebra 2
Answer:
-11 in top left, 5 in top right, -12 in bottom left, and -2 in bottom right.
Step-by-step explanation:
4C is the matrix C with all its elements multiplied by 4. Same logic applies for 3D. Then subtract each element of 3D from its counterpart of 4C which gives you the final answer. A big shortcut however if you have a TI-84 Plus Graphing Calculator is to use second x^-1 for matrices to edit the matrices and do matrix operations.
What is this as an algebraic expression for this:
12¾ less than the product of 7 and a number x
In the picture, I need help with #14.
Answer:
7x -(12¾)
Step-by-step explanation:
You want the algebraic expression for "12¾ less than the product of 7 and a number x".
TranslationThe product of 7 and x is represented as ...
7x
If you want 12¾ less than that, then you subtract 12¾.
7x -12¾ . . . . . . . the desired expression
__
Additional comment
A "product" is what we call the result of multiplication. The operation of multiplication can be indicated several ways. If there is no ambiguity, the most common way to show multiplication is to write the values next to each other without any symbol.
7x . . . . 7 times x
Sometimes, it is helpful to put the values in parentheses:
(7)(x)
A multiplication symbol can be used, if desired.
7·x
(7)×(x)
When showing multiplication using the symbol ×, care must be taken to differentiate it from the symbol x, especially if confusing these symbols will give a different result than desired. (Sometimes, when the symbol × is unavailable, an 'x' is used instead.)
Occasionally, you will see a dot on the baseline used as a multiplication symbol. Likewise, you may see a centered dot intended as a decimal point.
7.x . . . . . 7 times x
7·3x . . . . 7 and 3 tenths times x (maybe)
When different numbers are involved, the use of a baseline dot for multiplication, and a centered dot for a decimal point can be confusing.
7.3.x . . . . could be (7)(3)(x) or (7.3)(x)
7·3.x . . . . could be (7)(3)(x) or (7.3)(x)
In general, a notation should be chosen so as to reduce any ambiguity to a minimum and communicate in a way that the audience understands.
When a mixed number is involved, as above, it can be useful to enclose it in parentheses, so it is not confused with the product of an integer and a fraction. The font used to express the fraction can be chosen to help reduce the ambiguity.
a.) consider an n x n matrix A with the property that the row sums all equal the same number s. show that s is an eigenvalue of A. (hint: find an eigenvector)
b.) consider n x n matrix A with the property that the columns sums all equal th same number s. show that s is an eigenvalue of A.
s is an eigenvalue of A.
What is eigenvalue?Eigenvalues are a unique collection of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar component.
A =[tex]\left[\begin{array}{ccc}a_{11} &a_{12} &\\a_{21} &a_{22} &\\&\end{array}\right][/tex][tex]\left[\begin{array}{ccc}f1\\f2&\\\end{array}\right][/tex]
[tex]f_{1} = a_{11} + a_{12}[/tex]
[tex]f_{2} = a_{21} + a_{22}[/tex]
We see that if (A - sI) is unique, then s is an eigenvalue of A. ( I is the identity matrix). Keep in mind that if every column in A adds up to s, then the total of the resultant vector is zero when s is subtracted from one item.
We know that the image of a matrix is the span of its column vectors. Since all the column vectors are members of the above-mentioned subspace, the image of the transformation is contained in this subspace. Thus, the rank of our n x n matrix is less than n. Thus, (A - sI) is singular.
Thus, s is an eigenvalue of A.
Transposition preserves eigenvalues (this is actually a profound statement, in a way). If A has columns adding to s, then A^T has rows adding to s. Let v be the column vector of 1's.
A^T * v = s * v.
Thus, s is an eigenvalue of A^T
Thus, s is an eigenvalue of A.
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A 4-sided polygon is classified as a quadrilateral.
True
False
Answer:
TRUEEEEEEEEEEEEEEEEEE
Step-by-step explanation:
write an equation for the line, in point-slope form, that passes through the following points (5,-5) (-1,-1)
Answer:
[tex]y+5=-\frac{2}{3}(x-5)[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{-1-(-5)}{-1-5}=-\frac{2}{3}[/tex].
Using the point [tex](5,-5)[/tex], the equation is [tex]y+5=-\frac{2}{3}(x-5)[/tex].
50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! PLEASE HELP
Which scatterplot(s) show a positive linear association between the variables?
A.
Table A only
B.
Neither table
C.
Table B only
D.
Both tables
Answer:
Step-by-step explanation:
I'd say c.) table b only. Because it's a straight line which I think is positive but i'm not sure about the association between the variables part. If wrong I'm sorry.
Polynomial using Remainder Theorem and Factor Theorem checking using synthetic division.
x^4 - x^3 - 3x^2+ 4x + 2 ÷ (x + 2)
Answer: 2 / (x + 2)
Message: If this was helpful, let me know by giving me a thanks! :)
Given F (0, 2) and G (2,6), if point S lies 1/3 of the way along FG, closer to F than to G, find the coordinates of S. Leave your answer in fraction form.
The coordinates of S(x₁, y₁)=(3/2 , 5) if F(0, 2) and G(2,6) and the lines divided in the ratio 1:3
What is a section formula?Finding the ratio by which a line segment is divided by a point internally or externally in coordinate geometry is done using the Section formula. The centroid, incenter, and ex center of a triangle are determined using it. Finding systems' centers of mass, equilibrium locations, etc. are all done using this method in physics. Finding the ratio by which a line segment is divided by a point internally or externally in coordinate geometry is done using the Section formula. The centroid, incenter, and ex center of a triangle are determined using it.
Given,
F(0, 2) and G(2, 6)
And also given that the points S lies on the way along FG then:
The lines divides the ratio,
1:3= m:n
Here we have to find the coordinates of S, we get:
S(x₁, y₁)=((mx₁+n x₂)/(m+ n), (my₁+n y₂)/(m+ n))
=((1(0)+3(2))/4 , (1(2)+3(6))/4)
=(6/4 , 20/4)
=(3/2 , 5)
S(x₁, y₁)=(3/2 , 5)
Therefore, the coordinates of S(x₁, y₁)=(3/2 , 5).
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Answer:
S(2/3, 10/3)----------------------------------
Given
Points F(0, 2) and G(2,6).We need to find the point S(x, y) which makes FS = 1/3 FG.
Each coordinate of S is at 1/3 FG distance from F.
Find values of x and y:
x = 0 + 1/3(2 - 0) = 0 + 2/3 = 2/3y = 2 + 1/3(6 - 2) = 2 + 4/3 = 10/3So the point S is at (2/3, 10/3).
The speed of sound in ocean water is 1,500 m/sec. If scientist use
sonar to determine the depth of the ocean and find it takes 20 seconds
for the sound wave to return to the ship, how deep is the ocean at that
point?
O15,000 meters
O 3,000 meters
O 30,000 meters
O 1,500 meters
Speed
1500 m/sec
Time 20 seconds
Given speed and time, you can calculate distance.
Distance = Time * Speed
Distance = 1500 * 20
Distance = 15000 * 2
Distance travelled by the sonar = 30,000 meters
Since its bouncing off the ocean floor and returning, divide by 2 to find one way distance.
Depth 15,000 meters
Hope this helps :)
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- Jeron
Andrea rode her bike to the beach! After zero minutes, how far do you think Andrea traveled? She constantly rode her bike 6 miles per hour. Fill in the table below. How long would it take Andrea to travel 60 1/4 miles?
What equation is equivalent?
Answer:
B: y=2/3-5x
Step-by-step explanation:
15x+3y=2
-15x. -15x
3y=2-15x
/3 /3. /3
y=2/3-5x
so B is the correct answer
hopes this helps please mark brainliest
Answer:
D
Step-by-step explanation:
Based on the information provided, it appears that the correct answer would be option D: y=2 - 15x. This can be determined by solving the given equation for y by isolating the y-term on one side of the equation. To do this, you can subtract 15x from both sides of the equation, resulting in y = 2 - 15x.
Here is the complete process for solving the equation:
Begin by subtracting 15x from both sides of the equation:
15x + 3y = 2
-15x -15x
This simplifies to:
3y = 2 - 15x
Now, divide both sides by 3 to isolate the y-term:
3y/3 = (2 - 15x)/3
This simplifies to:
y = 2/3 - 15x/3
Finally, since 3 is a common factor, we can simplify the right side of the equation further by dividing both the numerator and the denominator by 3:
y = 2/3 - 15x/3
y = (2/3) / (3/3) - (15x/3) / (3/3)
y = (2/3) / 1 - (15x/3) / 1
y = 2/3 - 15x/3
y = 2/3 - 5x
Therefore, the equivalent equation is y = 2/3 - 5x, which is option D.
A teacher conducted an experiment to see if she was more likely to call on boys or girls in class. One day she recorded the number of times she called on boys in class and the number of times she called on girls in class. She found that out of 30 questions she asked, she called on girls 23 times.
To see if the results were typical, she ran 50 simulations and created a dotplot showing the number of times a girl was called on out of 30 questions. Were her results typical for that one day? Explain.
Responses
A Her results were not typical. She should have called on females fewer than 10 times since most of the data is centered around 10. Her results were not typical. She should have called on females fewer than 10 times since most of the data is centered around 10.
B Cannot be determined. You can not use a simulation to see if experimental results are typical. Cannot be determined. You can not use a simulation to see if experimental results are typical.
C Her results were not typical. Her results were on the high end. Based on the mean of the data, she should have called on females around 16 times.Her results were not typical. Her results were on the high end. Based on the mean of the data, she should have called on females around 16 times.
D Her results were typical. Most of the data on the dot plot falls between 17 and 28, and 23 lies right in the middle.
From the explanations, we can say that for the research experiment;
A Her results were not typical. She should have called on females fewer than 10 times since most of the data is centered around 10.
How to Interpret Research Experiment?Since the teacher is conduction the experiment to see if she was more likely to call on boys or girls in class, it means that there may have been some bias in the research.
The reason for the purposed bias comes from the she is also a female. However, it is not only just about genders only but which student was closer and as such if the teacher is female it’s more likely for a female student to be closer to her eye view whereas the boys may be in the back as usual and so 23 shows a typical expectation.
Now, looking at the options, we can say that the correct one is certainly.
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What expression is equivalent to -2/5
Answer:
2/-5
Step-by-step explanation:
one angle the triangle measures 10° Greater the smallest angle and the third angle measures 10° less than twice the smallest angle find the measurement of the three angles
The measure of three angles of triangle are 45°, 55° and 80°.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Let the smallest angle of triangle be x.
One angle the triangle measures 10° greater the smallest angle, that is x+10°
The third angle measures 10° less than twice the smallest angle.
The third angle is 2x-10°
Now, x+2x-10°x+10°=180°
⇒ 4x=180°
⇒ x=45°
So, 2x-10°=80° and x+10°=55°
Therefore, the measure of three angles of triangle are 45°, 55° and 80°.
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A company manufactures small refrigerators. The total cost to manufacture 57 refrigerators is $6665. The total costs to manufacture 180 refrigerators is $18965. Assume that total cost, C, is linearly related to the number of refrigerators, x, the company manufactures and includes a fixed cost and a cost per refrigerator.
1.The total cost to manufacture 145 refrigerators is $
2.The fixed costs are $
3.The cost to produce each additional refrigerator is $
the cost of 145 refrigerators is $16954.82 and fixed cost rate per refrigerator is $116.92
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
A company manufactures small refrigerators. The total cost to manufacture 57 refrigerators is $6665.
manufacture 1 refrigerator is $6665/57 = $116.92
So to make 145 refrigerators the money will spent is $116.92*145= $16954.82
The fixed cost arte per refrigerator is $116.92
Hencve the cost of 145 refrigerators is $16954.82 and the fixed cost rate per refrigerator is $116.92
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30-60-90 triangle question is in the image
Answer:
it is easy 56 and 45 and 567
245 as a reduced fraction
The reduced fraction of 0.245 is 49/200.
What is the greatest common factor (GCF)?
A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. Since four is the largest, we refer to the GCF of 12, 20, and 24 as four. Frequently, GCF is used to identify common denominators.
We have,
0.245
Write 0.245 as
0.245 / 1
Multiply both the numerator and denominator by 10 for each digit after the decimal point.
0.245/1
= 0.245 x 1000 / 1 x 1000
= 245 / 1000
In order to reduce the fraction find the Greatest Common Factor (GCF) for 245 and 1000. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 245 are: 1 5 7 35 49 245
The factors of 1000 are: 1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000
The Greatest Common Factor (GCF) for both 245 and 1000 is: 5
Now to reduce the fraction we divide both the numerator and denominator by the GCF value.
245/ 1000
= 245 ÷ 5 /1000 ÷ 5
= 49 / 200
The decimal part is: 0.245 = 245/1000
Full simple fraction breakdown: 245/1000
= 49/200
Hence, the reduced fraction of 0.245 is 49/200.
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A 80 kg patient needs a medication X in the amount of 0.25 mg/kg/day. The medication comes in a liquid solution of 50 mg for every 10 ml. How many ml of this solution will this patient need in a day?
The 4ml of this solution, this patient will need in a day.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that 80 kg patient needs a medication X in the amount of 0.25 mg/kg/day.
The medication comes in a liquid solution of 50 mg for every 10 ml therefore,
0.25 x 80 = 20mg/day
50/10 = 5mg/ml
Then the patient need in a day;
20/5= 4ml
Theefore, The solution, this patient will need in a day is 4 ml.
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Which of the following proves these triangles are congruent
A. ASA
B. Not enough information
C. AAS
Answer:
not enough information
Using the information in the Box-and-Whisker plot below, what is the 2nd Quartile?
A. 5
B. 12.5
C. 20
D. 27.5
The answer would be (C) 20.
Answer:
The 2nd quartile, also known as the median, is the middle value of a dataset, or the value that separates the lower half of the data from the upper half. In a box-and-whisker plot, the 2nd quartile is represented by the line in the middle of the box.
In the given box-and-whisker plot, the 2nd quartile is 12.5, which is the middle value of the data set. This can be determined by looking at the scale on the x-axis and finding the value that is in the middle of the box.
Option B, 12.5, is the correct answer.
Step-by-step explanation:
FluffytopFluffytopFluffytopFluffytop
Answer:
continue the streak:)
Step-by-step explanation:
fluffytopfluffytopfluffytopfluffytopfluffytopfluffytopfluffytopfluffytopfluffytop
hoped this helped:)
brainliest for the brains lol
Determine the measure of angles #1-#20 in the following figure.
Line AB is parallel to Line CD.
Line EF is parallel to Line GH.
Angle #5 = 63⁰
Angle #8 = 80⁰
The measure of all the angles from 1 to 20 is obtained from the concepts related to transversal lines.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
Given, AB || CD and EF || GH.
m∠5 = 63° and m∠8 = 80°.
Now from all the concepts of vertically opposite angles are equal,
pair of alternate angles are equal, the sum of all the sides of interior angles in a triangle is 180°, pair of linear angles is 180°, measure of an exterior angle in a triangle is the sum of two opposite interior angles we obtain that,
m∠1 = 37°, m∠2 = 63°, m∠3 = 80°, m∠4 = 37°, m∠5 = 63°, m∠6 = 80°,
m∠7 = 100°, m∠11, = 63°, m∠12 = 80°, m∠13 = 47°. m∠14 = 63°, m∠15 = 80°,
m∠16 = 47°, m∠17 = 110°, m∠18 = 70°, m∠19 = 110°, m∠20 = 70°.
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you buy a shirt that is on sale for 30% off. the original price is $22.40. your friend wants to know the sale price of the shirt. how can your friend find the sale price?
The sale price of the shirt can be found by calculating 30% of the original price, which in this case would be $22.40 x 0.30 = $6.72. Thus, the sale price of the shirt would be $22.40 - $6.72 = $15.68.