Final answer:
To create a system of linear equations with the solution (-3, 9), we need to construct two equations that intersect at this point, for example, y = -3x + 18 and y = 2x + 15.
Explanation:
To write a system of linear equations with the solution (-3, 9), we can create two separate equations that intersect at this point. Using the equation provided, y = 9 + 3x, we can see that the point (-3, 9) satisfies this equation since plugging in x = -3 gives us y = 9 + 3(-3) = 9 - 9 = 0, which is incorrect. We must correct the mistake and ensure that the solution (-3, 9) satisfies both equations in our system.
A correct form of the first equation would be y = -3x + 9 (not y = 9 + 3x as provided), since plugging x = -3 yields y = -3(-3) + 9 = 9 + 9 = 18, which is also incorrect. Therefore, we need to be careful in constructing our equations.
Let's construct two new equations correctly:
First, we start with the equation y = -3x + 18, which does satisfy the condition when x = -3 and y = 9. Next, we can create a different equation with the same solution. For instance, if we want another equation, we might use the slope-intercept form, y = mx + b. We can choose a different slope (m), for example, m = 2, and find b such that when x = -3, y = 9:
y = mx + b
9 = 2(-3) + b
9 = -6 + b
b = 15
So, the second equation is y = 2x + 15. The system of linear equations with the solution (-3, 9) is:
1. y = -3x + 18
2. y = 2x + 15
What is m∠D ?
Enter your answer in the box. __°
Answer
Find out the m∠D .
To proof
In Δ ABE
∠EAB + ∠ABE + ∠AEB = 180 °
(By using the angle sum property of a triangle.)
As given and shown in the diagram
∠EAB = 14° , ∠ABE = 45 °
Put in the above equation
14° + 45° + ∠AEB = 180 °
∠AEB = 180 °- 59°
∠AEB = 121 °
∠AEB = ∠DEC = 121°
(by using the vertical opposite angles property)
Now in ΔCED
∠DEC + ∠EDC + ∠ECD = 180 °
(Angle sum property of a triangle)
(as given ∠DEC = 121° ,∠ECD = 27° shown in the diagram )
∠EDC = 180 ° - 27 ° - 121 °
∠EDC = 32°
therefore
∠ D = 32 °
Hence proved
Can you write a linear inequality whose solution contains only points with positive x-values and y-values? why or why not?
Yes, a linear inequality can be written whose solution contains only points with positive x-values and y-values.
Explanation:A linear inequality is a mathematical statement that expresses a relationship between two linear expressions using inequality symbols (>, <, ≥, or ≤). It describes a region of values that satisfy the inequality, often represented on a coordinate plane as a shaded area.
Yes, a linear inequality can be written whose solution contains only points with positive x-values and y-values. One example of such an inequality is y > 0. This inequality represents all the points above the x-axis in the coordinate plane, where both x-values and y-values are positive.
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Evaluate the expression below when x = -1.
2x2 − 5
x + 9
-7
8
-3
8
-1
8
-1
Answer:
-3/8
Step-by-step explanation:
plato
Factor polynomial 2x^2-11x+15
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▹ Answer
(2x - 5) * (x - 3)
▹ Step-by-Step Explanation
2x² - 11x + 15
Rewrite:
2x² - 5x - 6x + 15
Factor:
x(2x - 5) - 6x + 15
x(2x - 5) - 3(2x - 5)
Factor:
(2x - 5) * (x - 3)
Hope this helps!
CloutAnswers ❁
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The cost of a movie ticket is $5. it costs a group of friends $105 to go to the movies. which equation describes the number of people that went to the movies?
The equation that describes the number of people that went to the movies could be 5x = 105
What is a solution to a system of equations?For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs,
So solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)
Given; The cost of a movie ticket is $5. it costs a group of friends $105 to go to the movies.
Each ticket cost is $5,
The tickets were $105.
So, multiplied 5 x 105 = 525.
Let x be the number of people that went to the movies.
So, 105 / 5 = x = 21
OR
5x = 105
Therefore, the equation that describes the number of people that went to the movies could be 5x = 105
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A particle's position is r⃗ =(ct2−2dt3)i^+(2ct2−dt3)j^,
where c and d are positive constants. Find expressions for times t > 0 when the particle is moving in the x-direction.
Find an equation of the line that satisfies the given conditions. through (−5, −13); perpendicular to the line passing through (−2, −1) and (2, −3)
There are 3 in. of snow on the ground when it begins to snow 0.5 in. /h.
Which linear equation represents the total depth of the snow, in inches, after x hours?
A. y=0.5x
B. 3+y=0.5x
C. y=0.5x+3
D. x=0.5y
Answer:
c. i took the test
Step-by-step explanation:
The required linear equation y = 0.5x + 3 represents the total depth of the snow, in inches, after x hours which is the correct answer would be option (C).
What exactly is a linear equation?A linear equation is one in which the greatest power of the variable is always one.
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
We have been given that there is 3 in. of snow on the ground when it begins to snow 0.5 in. /h.
Let the total depth of the snow, in inches, after x hours
As per the given information, translate the phrase into an algebraic form:
y = 0.5x + 3
Here y represents the total depth of the snow.
Therefore, the correct answer would be option (C).
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What is the common term for the set of all points with x- coordinate zero?
A. X axis
B. Y axis
C. Coordinate plane
D. Origin
2(x+3) + 6 = 3x - 9 written in word form? HELP!!!
Which equation is related to the equation shown? x + 3 = 12
a. x = 12 + 3
b. x = 12 ÷ 3
c. x = 12 − 3
d. x = 12 • 3 open study?
The line segments are translated 2 units to the left to form J′K′ and M′N′. Which statement describes J′K′ and M′N′?
Answer:
Step-by-step explanation:
the line segments J'K' and M'N' do not intersect and are the same distance apart as JK and MN.
Write an inequality for the given statement: The sum of y and 20 is more than 50.
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~
We know that we will be using the greater than symbol...
By know this we can assume that the start of the problem looks like this:
> 50
This is because the answer of said question MUST be greater than 50...
We also know that the question states "the sum of y and 20"
So... that will look like this:
y + 20
We also know that it says "the sum of y and 20 is more than 50", so we set that up like this:
y + 20 > 50
So the inequality for this is: y + 20 > 50
Chad bought 8 pounds of strawberries for $25.25. What is the cost, c, of 1 pound of strawberries?
A parabola has vertex (2, 3) and contains the point (0, 0). find an equation that represents this parabola.
The required equation is y = (-3/4)(x - 2)² + 3 that represents given parabola.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c.
The parabola equation into the vertex form:
(y-k) = a(x-h)²
Where (h,k) are the x and y-coordinates of the vertex.
The parabola has vertex (2, 3) which is given in the question
Here h = 2,and k = 3
Substitute the values of h = 2 and k = 3 in the above equation
y - 3 = a(x - 2)²
y = a(x - 2)² + 3
If the parabola contains the point (0, 0)
Substitute the point (0, 0) in the above equation
0 = a((-2)² + 3
4a = -3
a = -3/4
Thus, the equation becomes y = (-3/4)(x - 2)² + 3
Hence, the required equation is y = (-3/4)(x - 2)² + 3 that represents given parabola.
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I need Help with 9??
A box has dimensions of 17 inches long 1.3 feet wide and 8 inches high what is the volume of the box the formula of the volumes is v=l•w•h
Can someone help me with 11? I’m confused on how to solve for the rest of the problem. I don’t know how to get rid of the 3
10 more than the quotient of a number and 8 is at least 12
Five times a number is equal to the number increased by 12
The required expression is [tex]5n = n+ 12[/tex] and the unknown number is [tex]3[/tex]
Let the unknown number be "n"
Five times the number is expressed as 5nThe number increased by 12 is expressed as n + 12Equating both expressions will give:
[tex]5n = n + 12[/tex]
Solve for n:
[tex]5n - n = 12\\4n = 12\\n = 12/4\\n = 3[/tex]
Hence the required expression is [tex]5n = n+ 12[/tex] and the unknown number is [tex]3[/tex]
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The product of some negative number and 3 less than twice that number is 209. find the number
***PLEASE HELP*** ***50 POINTS***
Construct a system of two linear equations where (−2, 3) is a solution to the first equation but not to the second equation, and where (5, −2) is the solution to your system.
You need to write the equations of your system and graph them on the same graph.
Explain how your graph shows that your system satisfies the 2 required conditions.
see attached picture:
A segment with endpoint M Left parenthesis 5 comma 9 right parenthesis and N Left parenthesis 4 comma 3 right parenthesis is rotated 270°. What are the coordinates of M prime and N prime?
The correct answer is : M prime (9,-5) and N prime (3,-4)
A right triangle has exterior angles at each of its acute angles with measures in te ratio 13:14. find the measures o the two acute angles of the right triangle.
if a right triangle has side lengths x + 9, x + 2, x + 10 is the hypotenuse, find the value of x
To determine the value of x for the right triangle, we applied the Pythagorean theorem to the side lengths and solved the resulting quadratic equation, revealing x to be -1.
Explanation:To find the value of x for the side lengths of a right triangle with side lengths x + 9, x + 2, and x + 10 as the hypotenuse, we use the Pythagorean theorem, which states that in a right triangle, a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the two other sides.
Here's the step by step solution:
Write the Pythagorean theorem with the given side lengths: (x + 2)² + (x + 9)² = (x + 10)².Expand the squares: x² + 4x + 4 + x² + 18x + 81 = x² + 20x + 100.Combine like terms and move all terms to one side: x² + 22x + 85 = 0.Solve the quadratic equation, which yields x = -1 or x = -85. However, since side lengths cannot be negative, the only logical value of x is -1.
Final answer:
To find the value of x in a right triangle with sides x + 9, x + 2, and hypotenuse x + 10, the Pythagorean theorem is used. After applying the theorem, we simplify and solve the resulting quadratic equation, which gives us a positive value of x = 3.
Explanation:
The student is asking how to find the value of x in a right triangle with sides x + 9, x + 2, and x + 10, where x + 10 is the hypotenuse. To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².
For this particular triangle:
Identify the legs and the hypotenuse of the triangle: Leg 1 is x + 9, Leg 2 is x + 2, and the Hypotenuse is x + 10.Apply the Pythagorean theorem: (x + 9)² + (x + 2)² = (x + 10)².Simplify and solve for x. Expand the squares: x² + 18x + 81 + x² + 4x + 4 = x² + 20x + 100.Combine like terms and move all terms to one side of the equation:(2x² + 22x + 85) - (x² + 20x + 100) = 0x² + 2x - 15 = 0Factor the quadratic equation: (x + 5)(x - 3) = 0Find the possible values for x: x = -5 or x = 3. Since a side length can't be negative, the value for x must be 3.Therefore, the value of x is 3.
Which would hold more water a teaspoon or a milliliter?
How many 3 digit positive integers are odd and do not contain the digit 5?
The length of a rectangle is twice its width. if the area of the rectangle is 162 m2 , find its perimeter.
The width of the rectangle is 9m and the length is 18m. The perimeter of the rectangle is 54m.
Explanation:Let's assume the width of the rectangle as 'w'. According to the given information, the length would be twice the width, so the length can be represented as '2w'.
The formula for the area of a rectangle is length multiplied by width, which can be written as 'A = lw', where 'A' is the area. By substituting the given area value of 162m2, the equation becomes '162 = 2w * w'.
Solving this equation, we get 'w = 9m' which represents the width. The length can be found by doubling the width, so the length is '2 * 9m = 18m'.
The perimeter of a rectangle can be calculated using the formula 'P = 2(l + w)', where 'P' is the perimeter, 'l' is the length, and 'w' is the width. Plugging in the values, the perimeter of the rectangle is 'P = 2(18m + 9m) = 54m'.
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Which of the following does not have a measure of 40 degrees?
∠AOX
∠DOA
∠COA
Answer:
the correct answer is C) COA
Look at the diagram. If RS= 8y + 4, ST = 4y + 8, and RT = 36, find the value of y.
Answer:
(A) y=2
Step-by-step explanation:
It is given that [tex]RS=8y+4[/tex], [tex]ST=4y+8[/tex]and [tex]RT = 36,[/tex] then
According to the figure given, we have
[tex]RT=RS+ST[/tex]
[tex]36=8y+4+4y+8[/tex]
[tex]36=12y+12[/tex]
[tex]24=12y[/tex]
[tex]y=\frac{24}{12}[/tex]
[tex]y=2[/tex]
Thus, the value of y will be 2.
Hence, option A is correct.