The system of equations containing equations y = 5/2 x + 2 and 2y = 5 x + 4 will have infinitely many solutions.
What is system of equations?
A finite collection of equations for which we searched for the common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized. In everyday life, systems of equations are used to model problems when the unknown values can be represented by variables.
Given equations:
y = 5/2 x + 2
2y = 5 x + 4
We will use the substitution method, to get the values of x and y:
2 ( 5/2 x + 2 ) = 5 x + 4
5 x + 4 = 5 x + 4
0 · x = 0
x , y ∈ R
Therefore, this system of equations will have infinitely many solutions.
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Complete question
How many solutions does the following system of equations have?
y = 5/2x + 2,
2y = 5x + 4.
Laws of Exponents Solve and put your answers into the blue boxes (put the Exponent into the smaller one). If you are correct part of the mystery picture will be revealed. If you are incorrect the wrong color will appear! Once you have finished all the questions you have the option to highlight any mistakes.
8⁶ ÷ 8⁷ = (5²)⁹ =
9⁸ ÷ 9⁴ = (2⁶)² =
6⁵ · 6² = 2³ ⋅ 2² =
(7⁸)³ = 4⁵ ÷ 4³ =
(5⁶)⁴ = 5⁷ ÷ 5⁸ =
2⁶ · 2⁷ = 3⁵ ⋅ 3³ =
8⁴ · 8⁹ = (7⁵)⁶ =
9³ ÷ 9⁹ = 2² ÷ 2⁸ =
(5⁷)⁴ = 7⁹ ÷ 7⁴ =
9³ ÷ 9⁴ = 9⁴ ‧ 9⁴ =
Laws of Exponents Solve and put your answers into the blue boxes (put the Exponent into the smaller one). If you are correct part of the mystery picture will be revealed. If you are incorrect the wrong color will appear! Once you have finished all the questions you have the option to highlight any mistakes.
8⁶ ÷ 8⁷ = (5²)⁹ =
9⁸ ÷ 9⁴ = (2⁶)² =
6⁵ · 6² = 2³ ⋅ 2² =
(7⁸)³ = 4⁵ ÷ 4³ =
(5⁶)⁴ = 5⁷ ÷ 5⁸ =
2⁶ · 2⁷ = 3⁵ ⋅ 3³ =
8⁴ · 8⁹ = (7⁵)⁶ =
9³ ÷ 9⁹ = 2² ÷ 2⁸ =
(5⁷)⁴ = 7⁹ ÷ 7⁴ =
9³ ÷ 9⁴ = 9⁴ ‧ 9⁴ =
Answer:
1. 5¹⁸2. 2¹²3. 2⁶4. 4²5. 5¹ or 56. 3⁸7. 7³⁰8. 1/329. 7⁵10. 9⁸Find the value of x.answer choicesA. 70B. 65C. 30D. 40
ANSWER
[tex]70[/tex]EXPLANATION
In the given diagram;
The third angle on the triangle is calculated thus;
Let the third angle of the triangle be y;
[tex]\begin{gathered} y+15+20=180 \\ y=180-(15+20) \\ y=180-35 \\ y=145 \end{gathered}[/tex]Now, the inscribed angle and angle y are on a straight line
Let the inscribed angle be denoted by z, hence;
By sum of angles on a straight line
[tex]\begin{gathered} z+145=180 \\ z=180-145 \\ =35 \end{gathered}[/tex]Recall that intercepted arc is twice of inscribed angle, hence;
[tex]\begin{gathered} x=2z \\ =2\times35 \\ =70 \end{gathered}[/tex]Problem: The table shows expressions to represent the number of 8th grade students
enrolled in different electives. The number of students enrolled in Art and Music is equal
to the number of students enrolled in Band and Journalism. Write and solve an equation.
Then find the number of students enrolled in each elective.
Class
Band
Art
Music
Journalism
What are you trying to find out:
Workspace:
# of Students
2n
7n+6
4n-2
2(4n+6)
Total
Solution:
I
So, the number of students in Band, Art, Music and Journalism are 2n, 7n+6, 4n-2 and 2(4n+6) respectively.
Since the number of students enrolled in Art and Music is equal to the number of students enrolled in Band and Journalism, we have the equation
7n + 6 + (4n-2) = 2n + 2(4n+6).
We now expand the brackets :
7n + 6 + 4n - 2 = 2n + 8n + 12
-> 11n + 4 = 10n + 12
-> 11n + 4 - 10n - 12 = 0
-> n - 8 = 0
-> n = 8.
Therefore, the number of students that enrolled in :
Band : 2n = 16 students.
Art : 7n + 6 = 62 students.
Music : 4n - 2 = 30 students.
Journalism : 8n + 12 = 76 students.
76 = 16 = 62 + 30 = 92, satisfying the requirement.
rewrite y=(x+1)^2-3 in standard form
Answer:
y=x2+2x-2
Step-by-step explanation:
hope this work have a nice day
Multiply the Polynomials:
(2x+3) (-x+2y-4)
The result of multiplying the polynomials is (2x + 3) (-x + 2y - 4) = -2x² + 4xy - 11x + 6y - 12
How to multiply the polynomials?The polynomial expression is given as
(2x + 3) (-x + 2y - 4)
Expand the brackets in the above polynomial expression
So, we have
(2x + 3) (-x + 2y - 4) = 2x * (-x + 2y - 4) + 3 * (-x + 2y - 4)
Open the brackets in the above polynomial expression
So, we have
(2x + 3) (-x + 2y - 4) = -2x² + 4xy - 8x + -3x + 6y - 12
Evaluate the like terms in the above polynomial expression
So, we have
(2x + 3) (-x + 2y - 4) = -2x² + 4xy - 11x + 6y - 12
Hence, the solution is -2x² + 4xy - 11x + 6y - 12
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G.C.F for 42 and 19 I dont know what it is help.
Answer:
1
Step-by-step explanation:
Sketch a graph to match each description.
a. Increasing slowly at a constant
rate, then stagnating, then
decreasing rapidly at a constant rate
Let's sketch the graph.
Why do we need a graph?Graphs and charts are useful visual aids because they make information accessible and quick to understand. Therefore, it is not unexpected that print and electronic media frequently use graphs. When data is displayed as a graph rather than a table, it can often be easier to understand because the graph might show a pattern or comparison.
Given,
a. Increasing slowly at a constant rate,
b. stagnating, and
c. decreasing rapidly at a constant rate
See the image below which match all the description mentioned in question.
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my rectangular house is 30 feet by 40 feet. My goat Cassidy is outside on a 50-foot-long leash that is connected to a corner of my house. What is the area of the region in which Cassidy can roam?
Total area of the region in which the goat can roam is: 6283.2 ft² (nearest tenth)
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
The rectangular house is ABCD.
Given that rectangular house is 30 feet by 40 feet. Therefore, the goat Cassidy is outside on a 50-foot-long leash that is connected to a corner of my house.
Area of a circle = πr²
where r is the radius.
Therefore, Total area of the region in which the goat can roam is:
Area = 3/4πr² + 1/4πr² + 1/4πr²
Area = 3/4π(50)² + 1/4π(20)² + 1/4π(10)²
Area = 1875π + 100π + 25π
Area = 2000π = 6283.2 ft² (nearest tenth)
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BRAINLIEST!!! SOLVING LITERAL EQUATIONS!
Answer:
(1) x=BC (2) h=A+-πr^2 (3) ef+-ab (4) x=y+-3 (5) x=C+-B
2πr d A
Step-by-step explanation:
See above
Are the lines AB and CD perpendicular if the points defining the lines have coordinates of A(3,-2) B(6,13) C(-5,8) and D(5,6)? Justify your answer.
we find the slopes of the lines:
first line
[tex]\text{slope}=\frac{y2-y1}{x2-x1}=\frac{13-(-2)}{6-3}=\frac{13+2}{3}=\frac{15}{3}=5[/tex]second lline
[tex]\text{slope}=\frac{6-8}{5-(-5)}=-\frac{2}{5+5}=-\frac{2}{10}=-\frac{1}{5}[/tex]then, Two lines are perpendicular if & only if the product of their slopes equals -1, which is the case for 5 and -1/5.
answer: the lines are perpendicular
A boutique owner needs to sell $1,200 in clothing each week. This week, she is within $125 of her goal.
Write an absolute value equation to represent the scenario. (2 points)
A.
|x + 1,200| = 125
B.
|x - 1,200| = 125
C.
|x + 125| = 1,200
D.
|x - 125| = 1,200
Answer:
B. |x - 1,200| = 125
Step-by-step explanation:
You want an absolute value equation to represent the fact that a boutique owner is within $125 of reaching her goal of selling $1200 each week.
DifferenceThe equation will represent that the positive difference between sales (x) and the goal (1200) is equal to 125:
|x -1200| = 125 . . . . . . . . matches choice B
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How much will you be charged for buying 0.85 yards of fabric if the fabric costs $7.86 per yard
Answer: 6.68 dollar
Step-by-step explanation:
Since you are charged 7.86 per yard, you multiply that by the amount you would buy. 0.85*7.86 is 6.681. But since you can't spend 0.001, you round to the nearest hundreths, 6.68.
An auto mechanic converts a metric part to 0.473 in. The part comes only in fractional sized given to the nearest 64th of an inch. What would be the closest size?
Answer:
30/64 inches.
Explanation:
The size of the converted metric part = 0.473 in.
Now, we know that:
[tex]\frac{1}{64}=0.015625[/tex]Therefore:
[tex]\frac{0.473}{0.015625}=30.272\approx30[/tex]Thus, we have that:
[tex]0.473\approx\frac{30}{64}\text{ inch}[/tex]To the nearest 64th of an inch, the closest size will be 30/64 inches.
S(13, 7) and T(-2, -7)what’s the midpoint
Answer:
(5.5,0)
Step-by-step explanation:
You average the x's and the y's.
x:
[tex]\frac{13-2}{2}[/tex] = [tex]\frac{11}{2}[/tex] = 5.5
y:
[tex]\frac{7-7}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0
2,5X+10=15
Solve please
Answer:
x = 2
Step-by-step explanation:
assuming you mean
2.5x + 10 = 15 ( subtract 10 from both sides )
2.5x = 5 ( divide both sides by 2.5 )
x = 2
If you can solve this I will give you 100 points!
3x+1
Answer:
The 3x + 1 Conjecture asserts that, starting from any positive integer n, repeated iteration of this function eventually produces the value 1.
the 3X + 1 problem has appeared in various forms. It is one of the most infamous unsolved puzzles in the word. Prizes have been offered for its solution for more than forty years, but no one has completely and successfully solved it
Step-by-step explanation:
The 3x+1 problem concerns an iterated function and the question of whether it always reaches 1 when starting from any positive integer. It is also known as the Collatz problem or the hailstone problem
Answer:
Step-by-step explanation:
3x+1=0 /-1
3x=-1 /:3
x=-1:3
If you mean:
y = 3x+1 or f(x) = 3x+1
determine the equation of the ellipse with center (2,2), focus (2,0), and vertex (2,5).multiple choices
Given:
The ellipse has center (2,2), focus (2,0), and vertex (2,5).
The equation of elllipse is given as,
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]a is the distance between vertex and center.
[tex]\begin{gathered} a=\sqrt[]{(2-2)^2+(5-2)^2} \\ a=\sqrt[]{3^2}=3 \end{gathered}[/tex]c is distance between focus and center.
[tex]\begin{gathered} c=\sqrt[]{(2-2)^2+(0-2)^2} \\ c=\sqrt[]{4} \\ c=2 \end{gathered}[/tex]It gives,
[tex]\begin{gathered} c^2=a^2-b^2 \\ 2^2=a^2-b^2 \\ b^2=9-4 \\ b^2=5 \\ b=\pm\sqrt[]{5} \\ b=\sqrt[]{5}\ldots\ldots\text{ Since b is distance and it should be positive} \end{gathered}[/tex]So, the equation of the ellipse is,
[tex]\begin{gathered} \frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}^{}=1 \\ \frac{(x-2)^2}{(\sqrt[]{5})^2^{}}+\frac{(y-2)^2}{3^2}=1 \\ \frac{(x-2)^2}{5^{}}+\frac{(y-2)^2}{9^{}}=1 \end{gathered}[/tex]Answer: option b)
Tom has a new set of golf clubs. Using a club 8, the ball travels an average distance of 100 meters. Using a club 7, the ball travels an average distance of 108 meters. Using a club 6, the ball travels an average distance of 114 meters. How far will the ball go if Tom uses a club 5?
The ball go 118 m if Tom uses a club 5
Define Arithmetic series?An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant d.
Given,
Using a club 8, the ball travels an average distance of 100 m.
Using a club 7, the ball travels an average distance of 108 m.
Using a club 6, the ball travels an average distance of 114 m.
club 8 → 100 m
club 7 → 108 m (100 + 8)
club 6 → 114 m (108 + 6)
club 5 → 118 m (114 + 4)
The distance is reducing by 2. so we find the series of sequence difference of 2 i.e, 8, 6, 4 and so on
Therefore, the ball go 118 m if Tom uses a club 5.
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I need help with #4, I don't get it.
Answer: Dilation, scale factor of 2.
Step-by-step explanation: The scale factor would be the number we multiply the 4 by 6 rectangle to get the 8 by 12 rectangle print.
Since we start with a rectangle with a length of 6 and a width of 4, and the measurements are changed to 8 and 12, we know the scale factor is 2. The scale factor is two because 4 • 2 is 8, and 6 • 2 is 12. Out of the transformations, (reflection, rotation, translation, dilation) the only one that includes a scale factor would be dilation. We also know it’s a dilation since the print is getting larger, and the pre image and image are not the same.
for f(x)3x+10x and g(x) 2x-4 find (f-g)(x)
Answer:
11x+4
Step-by-step explanation:
To do this, we can substitute 3x+10x for f(x) and 2x-4 for g(x), and we get 13x-(2x-4). By distributing the negative to 2x-4, we just swap the signs, and get 13x-2x+4, which equals 11x+4
Also, is there supposed to be an exponent on the first f(x)? I'm not sure because I haven't seen the real problem.
(Otherwise it would just be f=13x.) Maybe try being a little more clear when asking a question :)
Please let me know if you need more help or explanation on another problem!
A rectangle has length 3x + 4 and width 2x - 1. What is the perimeter of the rectangle?
Responses
A 10x + 610x + 6
B 10x + 1010x + 10
C 5x + 35x + 3
D 6x² + 5x - 4
Answer:
I believe the answer is 10x + 6
Step-by-step explanation:
well we know that the same length and width of a rectangle is twice . this means that you can multiply the length and width by 2 to get the perimeter and add them . so by foiling you will have 2(3x+4) + 2(2x-1). you can solve this and simplify it to get 6x + 8 + 4x - 2 . simplify this more to get 10x + 6.
I'm a little confused because I do not see an answer on your question that says 10x + 6 . can you add a diagram, formatting, or more context if I am wrong?
Solve for g.
r= 3g+ 3w
The equation is solved below.
What is an equation?
A mathematical equation is a calculation that uses the identical sign to represent the equivalency of two variables. The definitions of the word equation and its cognates in various languages might vary slightly. For instance, in French, an equation is defined as having one or more variables, but in English, the equation would be any well-formed solution that comprises two variables linked by the assignment operator. Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unidentified variables are considered as the parameters for which the equation must be calculated, and the unknown perfect blend of shades that fulfill the equivalence are known as the equation's answers. Equations come in two varieties: assumptions and conditioned equations.
Given equation
r=3g + 3w
or, 3g = r - 3w
or, g = (r - 3w)/3
or, g = r/3 - w
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What is the probability of rolling a number less than 4 on a number cube labeled 1 through 6?
Answer:
1/3
Step-by-step explanation:
just took the quiz
The graph shows the proportional relationship between grams of protein and cups of milk. a. What is the constant of proportionality for the relationship between grams of protein and cups of milk? b. What does the point (0,0) mean in this situation? c. What does the point (4, 32) mean in this situation? Protein (grams)
a. The constant of proportionality for the relationship is: k = 8.
b. 0 cups of milk will give 0 grams of protein
c. 2 grams of protein are in 4 cups of milk.
How to Find the Constant of Proportionality of a Relationship?To find the constant of proportionality (k) use any point on the graph, (x, y), and find k = y/x.
a. Using a point on the given graph, (1, 8):
The constant of proportionality, k = y/x = 8/1
The constant of proportionality, k = 8
b. (0, 0), in the situation means that 0 cups of milk will provide 0 grams of protein. This is also the point of origin.
c. In this situation, what the point (4, 32) means is that 32 grams of protein are in 4 cups of milk.
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Jack works as a math tutor. He charged a flat rate of $50 per group per class. He spends $6
for each student' s material.
(a)
y=1
Using variables x to represent the number of students in a group and y to represent the
amount he can make out of each class, write the linear function.
Answer: yo what?
Step-by-step explanation:
Given: c || d, <1 = <7
Prove: a || b
(PLEASE HELP IM REFERRING TO QUESTION 5 ON THE IMAGE)
Prove that a || b
What is Angles?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given,
c || d
<1 = <7
We have to prove a || b
∠1 = ∠5 corresponding angles of lines a and b
∠1 = ∠4 are alternate interior angles of lines a and b
∠5 = ∠7 corresponding angles of lines a and b
∠3 = ∠7 corresponding angles of lines a and b
Therefore, a || b by converse corresponding angle theorem
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There are 198,714 people living in Belleville. What is the number of people rounded to the nearest ten thousand?What digit is in the ten thousands place?Which place is used to decide which way to round the ten thousands place?What is the digit in this place?Should you round the number in the ten thousands place up or down?What happens when you round up a 9?What do you do when the value of a place is 10 or more?What is the value of the ten thousands place when the number is rounded to the nearest tenthousand?What is 198,714 rounded to the nearest ten thousand?What is 302,895 rounded to the nearest thousand?What is 7,142 rounded to the nearest ten?Round 24,793 to the nearest hundred.?
198714 to the nearest ten thousand:
[tex]198714\approx200000[/tex]The digit in the ten thousands place is:
[tex]9[/tex]Which place is used to decide which way to round the ten thousands place:
The second place from the left
--------------------------------
302895 to the nearest thousand:
[tex]303000[/tex]7142 to the nearest ten:
[tex]7140[/tex]24793 to the nearest hundred:
[tex]24800[/tex]which one is the right answer
The slope of the line for Carlo's plot represents The average change in the number of hot cocoas sold for every additional degree of the day's high temperature.
How to determine the interpretation of the slope of the line for Carlo's plotInformation given in the question include
A plot the number of hot cocoas he sold relative to the day's high temperature and then draw the line of best fit
The data is plotted as a linear function
What is linear function ?
A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the change of the output values to the input values
the output is hot cocoa soldthe input is high temperature in degree FahrenheitThis matches with option B
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"Complete the table" can i get some help with this pls and ty
Here is the completed table:
Feet 3 6 9 18 21
Yard 1 2 3 6 7
How to complete the table?The mathematical operations that would be used to solve this question are multiplication and division. Multiplication is the process that is used to determine the product of two or more numbers. Division is the process of determining the quotient of two or more numbers.
The first step is to determine the unit of conversion of yards to feet and feet to yards.
Unit of conversion of yards to feet = 9 / 3 = 3
Unit of conversion of feet to yards = 3/9 = 1/3
This means that: 1 yard = 3 feet
1 feet = 1/3 yards
3 feet = 3/3 = 1 yard
6 feet = 6 / 3 = 2 yard
6 yard = 6 x 3 = 18 feet
7 yard = 7 x 3 = 21 feet
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find the area of the circle
Answer:
i got 12.56
Step-by-step explanation:
hope this helped :P
Answer:
12.56
Step-by-step explanation:
2*2*π= 4π. You use 3.14 for π. Then you multiply 2*2*3.14, which is 12.56 inches^2
