Answer:
(-3, 8) is the solution
Step-by-step explanation:
The LCD of the first equation is (3)(4) = 12. Rewriting this equation, we get:
4x + 3y = 12
to which we add the second equation, obtaining:
4x + 3y = 12
2x - 3y = -30
-------------------
6x = -18
Dividing both sides by 6 yields x = -3
Substituting -3 for x in the first equation yields 4(-3) + 3y = 12, or
-12 + 3y = 12
Then 3y = 24 and y must be 8.
The solution to this system of linear equations is (-3, 8).
Which equation is in point slope form and is depicted by the line in the graph?
A.(y-3) = 3/5 (x-2)
B. (y-3) = -(3)/(5) (x+2)
C. (y-3)= 5/3 (x-2)
D. (y+3) = 5/3 (x+2)
The equation of line passing through (-2,3) and (3,0) will be (y - 3) = - 5/3 (x + 2). Then the correct option is B.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The graph is given below.
The equation of line passing through (-2,3) and (3,0) will be
The equation of line will be
(y - 3) = [(3 + 2) / (0 - 3)] (x + 2)
(y - 3) = - 5/3 (x + 2)
Then the correct option is B.
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ray and line segment difference
Answer:
A line segment is part of a line that has two endpoints and is finite in length. A ray is a line segment that extends indefinitely in one direction.
Step-by-step explanation:
hope it helps you and give me a brainliest
Answer:
A ray goes in one direction for forever, and also has an arrow.
A line segment is a segment, meaning that it has two end points and doesn't go on forever, it ends.
Step-by-step explanation:
Do the ordered pairs in the table represent a linear function?
Answer:
No.
Step-by-step explanation:
If you look at the y values, they do not have a constant rate of change. The numbers in the row for y: 3+1 is 4. 4+1 is 5. 5+7 is 12 .12+19 is 31. 31+ 37 is 68. So, as you can see, the rates at which each number changes are not constant. Therefore, the table does not represent a linear function.
Which equation is showed in the graph above
Answer: A
It has a negative gradient.
Hope this helps :))
P.s. Can you mark me as the brainliest? <3
Answer:
Step-by-step explanation:
Remark
You can read the y intercept right off the graph. Follow the y axis upwards until the line intercepts the y axis. I think you will find it is at 0,5
So far what you know is
y = mx + 5
Finding m is a little harder. I would use 6,0 and 0,5 as the two points that will define m.
Givens
x1 = 6
x2 = 0
y1 = 0
y2 = 5
Equation
m = (y2 - y1) / (x2 - x1) Put the givens into this equation.
Solution
m = (5 - 0) / (0 - 6)
m = 5/-6
m = - 5/6
Answer
The line is
y = -5/6 x + 5
what is true about this linear inequality
y>3/4-2
Inequalities help us to compare two unequal expressions. The statements that are correct are B, D, and E.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The complete question is:
Which statements are true about the linear inequality y >3/4 x – 2? Check all that apply.
-The slope of the line is –2.
-The graph of y >3/4 x – 2 is a dashed line.
-The area below the line is shaded.
-One solution to the inequality is (0, 0).
-The graph intercepts the y-axis at (0, –2)
-The slope of the line is 3/4. Thus, the first statement is false.
-The graph of y >3/4 x – 2 is a dashed line. The given statement is true.
-The area below the line is shaded. The statement is false.
-One solution to the inequality is (0, 0). The given statement is true.
-The graph intercepts the y-axis at (0, –2) The statement is true.
Hence, the statements that are correct are B, D, and E.
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help pls :) have a great day everyone plshelp me
The first step to solving almost any problem is to understand what the question is asking and what is given to us in order for us to solve for the question. In this problem, we are given a graph and asked two questions. One being what the coordinates of the vertex are and whether this parabola has a maximum or a minimum.
Let's define what a vertex, maximum, and minimums are.
Vertex ⇒ Vertex is the point at which it either reaches the maximum or minimum. This point can be easily defined as where the slope becomes flat.Maximum ⇒ Maximum occurs when the vertex is at the top and the lines go down in a negative-y-direction. Therefore with the vertex being at the top that would be considered a maximum as it's the largest point in the graph.Minimum ⇒ Minimum occurs when the vertex is at the bottom and the lines go up in a positive-y-direction. Therefore with the vertex being at the bottom that would be considered a minimum as it's the smallest point in the graph.Now, looking at our problem we can see that our vertex is at the bottom therefore it would classify as a minimum. Now that we know we have a minimum vertex, let us determine what the actual coordinates of the vertex are.
We can see that we travel -3 in the x direction and -5 in the y direction which means that the coordinate for our vertex is (-3, -5) where the first number represents the x-value and the second number represents the y-value.
Answer:
(-3, -5)
Step-by-step explanation:
Here the vertex is also the minimum value; its x-coordinate is -3 and its y-coordinate is -5. Thus, the vertex is at (-3, -5). As stated above, this is the minimum value of the function.
Can someone pls help?
Answer:
D
Step-by-step explanation:
If you think of the x-axis as your horizontal line, you can see that there is more than one value for x for y=0.
For instance, (-2,0), (0,0), (0,2).
If 2a/4=b/4 and b≠0, what does 5b equal in terms of a?
A) 2a/15
B) 5a/6
C) 15/2a
D) 40a/3
Step-by-step explanation:
you must have made a typo here.
none of the answer options are correct for the given problem.
let me just show you what you told me, and how I can solve at least this :
2a/4 = b/4
this simply means (multiply both sides by 4) :
2a = b
so, 5b is then (multiplying both sides by 5) :
5×2a = 5b
10a = 5b
but again, "10a" is not among the offered answers.
so, I don't know if you made a mistake with the basic problem or with the answer options.
Which Graph Shows A System With One Solution?
Answer:I think it’s A
Step-by-step explanation:
because it intersects. Sorry if it’s wrong
Evaluate 4x² + 3x for x=6
Answer:
162
Step-by-step explanation:
Given algebraic expression:
4x² + 3xTo:
Evaluate this expression,with : x = 6Solution:
4x²+3xSimplify by plugging x = 6
4(6)²+3(6)4(36) + 18144 + 18162We can conclude:
By evaluating this expression by x = 6 , the answer will be 162.
Determine the scale of a map if the distance between 2 towns is 20km and the map distance is 5cm
The required ratio or scale will be 5cm o the map represent 20km on land
Ratio and scalingScaling is a way of enlarging or reducing the figure on an xy-plane. Given the conversion rate;
Given the following
distance between 2 towns is 20km
The distance on map is 5cm. The required ratio or scale will be 5cm o the map represent 20km on land
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3x + 12+ 9x - 72
Solve?
Answer:
12x - 60
Step-by-step explanation:
[tex]3x+12+9x-72\\=3x+9x+12-72\\=12x+12-72\\=12x-60[/tex]
Mike knows that (3,6.5) and (4,17.55) are points on the graph of an exponential function, g(x), and
he wants to find another point on the graph of this function.
First, he subtracts 6.5 from 17.55 to get 11.05.
Next, he adds 11.05 and 17.55 to get 28.6.
He states that (5,28.6) is a point on g(x).
Is he correct? Explain your reasoning.
Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect
How to determine if he is correct?The points are given as:
(3,6.5) and (4,17.55)
Calculate the rate of change using:
r = y4/y3
This means that:
r = 17.55/6.5
r = 2.7
So, the next point on the graph is:
Next point = 2.7 * y4
Substitute 17.55 for y4
Next point = 2.7 * 17.55
Evaluate
Next point = 47.39
This means that the next point on the graph is (5,47.99)
Hence, Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect
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Question 3 of 10
If P(x,y) is the point on the unit circle determined by real number ø, then tang
The tangent on the unit circle is y/x
How to determine the tangent value?The point on the unit circle is given as:
Point = (x,y)
By default
(cos(ø), sin(ø)) = (x,y)
This means that:
cos(ø) = x
sin(ø) = y
The tangent of an angle is:
tan(ø) = sin(ø)/cos(ø)
So, we have:
tan(ø) =y/x
Hence, the tangent on the unit circle is y/x
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The function f(x) is shown on the graph.
On a coordinate plane, a curved line with 3 arcs, labeled f of x, crosses the x-axis at (negative 2, 0), (negative 1, 0), (1, 0), and (3, 0), and the y-axis at (0, negative 6).
What is f(0)?
The value of f(0) in the function f(x) is -6
How to determine the value of f(0)?The coordinates are given as:
(-2, 0), (-1, 0), (1, 0), and (3, 0), and (0, -6)
To calculate f(0), we determine the function value when x =0
From the coordinate points, we have:
Point (0, -6)
This means that:
f(0) = -6
Hence, the value of f(0) is -6
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Answer:
Step-by-step explanation:
-2,1 or 3 only
In the figure below, which term best describes point X?
B
OA. Centroid
OB. Incenter
O C. Circumcenter
OD. Orthocenter
The term best describes point X is option A. Centroid.
What is the centroid of a triangle and its coordinates?The point of intersection of a triangle's medians is its centroid (the lines joining each vertex with the midpoint of the opposite side).
If the surface is plane triangle approximately and mass is uniformly distributed, then its center of mass will lie on the centroid of that triangle.
If the triangle has its vertices as [tex](x_1, y_1), (x_2, y_2) , \: (x_3, y_3)[/tex]then the coordinates of the centroid of that triangle is given by:
[tex](x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)[/tex]
The term best describes point X is option A. Centroid.
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The function f(x) is shown in this graph.
--5-
The function g(x) = -6x + 3.
Compare the slopes and y-intercepts.
OA. Both the slopes and the y-intercepts are the same.
OB. The slopes are the same but the y-intercepts are different.
C. Both the slopes and the y-intercepts are different.
OD. The slopes are different but the y-intercepts are the same.
f(x)
(0,3)
Both the slopes and the y-intercepts are different. Option C is the correct answer.
What is Straight Line?A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity.
Here, slope intercept form of given equation:
y = mx + c ............(i)
where, m is slope of line and c is y-intercept.
Given equation of line;
g(x) = y = -6x + 3
On comparing this with equation (i), we get
m = -6 and c = 3
Thus, Both the slopes and the y-intercepts are different. Option C is the correct answer.
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The bouncy kat toys are manufactured using a layering process. the plastic is
added to the ball one layer at a time, with the radius of each ball increasing at a
rate of 0. 1 inch per second. we have been unable to correctly manage the volume
of plastic flowing into the machine. assuming the machine produces 100 toys at a
time, what is the appropriate flow rate of the plastic (in cubic inches per second)
when the radius of each toy is 0. 5 inch? what should the average flow rate of the
plastic be over each 10-second production cycle?
The flow rate to produce the balls is 12.5in/s and 1.25in/s
a. The rate flow to produce the ballsThe number of toys = 100
The increase in radius = 1inch/sec
5 toys are going to increase by 0.5 radius
The rate flow to produce the balls
5x100 = 500
Rate flow = 500 x 0.5³ / 5
= 12.5inch/s
b. New productionTime = 10 seconds x 5 = 50 seconds
radius = 0.5 inches
Flow rate = 50 * 0.5³/5*10
= 1.25 inches/s
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The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length
of a side of the regular hexagon.
A triangle is a three-edged polygon with three vertices. The length of a side of the regular hexagon is √24 inches.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.
Given the perimeter of the equilateral triangle is 36 inches, therefore, the length of the side of the equilateral triangle is 12 inches. Now, the area of the equilateral triangle is,
Area of the equilateral triangle = (√3)/4 a²
= (√3)/4 × (12)²
= (36√3) inches²
Since the area of the equilateral triangle is equal to the area of the hexagon , therefore we can write,
Area of equilateral triangle = Area of Hexagon
(36√3) = (3√3)/2× a²
a² = 24
a = √24 inches
Hence, the length of a side of the regular hexagon is √24 inches.
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Using the expansion of (1-(x/2))^8 and a suitable value of x, evaluate 0.996^8 to 5 d p
Answer:
4j8rd⁸8xud4 ex fiiu8rftsuf
(3x-4y)^2-(3x-4y)(3x+4y)
Answer:
[tex]-24xy + 32y^2[/tex]
Step-by-step explanation:
Hello!
We can use the special binomial product formulas:
[tex](a + b)^2 = a^2 + 2ab + b^2[/tex][tex](a + b)(a - b) = a^2 - b^2[/tex]Simplify[tex](3x - 4y)^2 - (3x - 4y)(3x + 4y)[/tex][tex](9x^2-24xy+16y^2) - (9x^2 - 16y^2)[/tex][tex]9x^2 - 9x^2 - 24xy + 16y^2 + 16y^2[/tex][tex]-24xy + 32y^2[/tex]The simplified form is [tex]-24xy + 32y^2[/tex]
someone help please
Answer:
I think 40.
Step-by-step explanation:
The graph of f(x) = StartRoot x EndRoot is reflected across the x-axis and then across the y-axis to create the graph of function g(x). Which statements about the functions f(x) and g(x) are true? Check all that apply.
The functions have the same range.
The functions have the same domains.
The only value that is in the domains of both functions is 0.
There are no values that are in the ranges of both functions.
The domain of g(x) is all values greater than or equal to 0.
The range of g(x) is all values less than or equal to 0.
The only value that is in the domains of both functions is 0. The range of g(x) is all values less than or equal to 0. Then the correct options are C and F.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The graph of f(x) = √x is reflected across the x-axis and then across the y-axis to create the graph of function g(x).
Then the function g(x) will be
g(x) = -√(-x)
The domain of the f(x) and g(x) will be [0, ∞) and (-∞, 0] respectively.
The range of g(x) will be (-∞, 0].
The only value that is in the domains of both functions is 0.
The range of g(x) is all values less than or equal to 0.
Then the correct options are C and F.
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Answer:
C AND F
Step-by-step explanation:
Edge 2023
Hi please help!!
Given the following function:
f(x)=2x^2
fill the table with coordinates that work for this function.
x y
(5 empty columns going down)
The table of values of the function y = 2x^2 is:
x 0 1 2 3 4
y 0 2 8 18 32
How to complete the table?The equation of the function is given as:
y = 2x^2
When x= 0, we have
y = 2 * 0^2 = 0
When x= 1, we have
y = 2 * 1^2 = 2
When x= 2, we have
y = 2 * 2^2 = 8
When x= 3, we have
y = 2 * 3^2 = 18
When x= 4, we have
y = 2 * 4^2 = 32
So, the table of values is:
x 0 1 2 3 4
y 0 2 8 18 32
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help i need answers fast now
Do you know the answer to this
Answer:
[tex] 4x^2y\sqrt[4]{3y} [/tex]
Step-by-step explanation:
[tex] \sqrt[4]{768x^8y^5} = [/tex]
[tex] = \sqrt[4]{256 \times 3(x^2)^4y^4y} [/tex]
[tex] = \sqrt[4]{4^4 \times 3(x^2)^4y^4y} [/tex]
[tex] = 4x^2y\sqrt[4]{3y} [/tex]
The circumference of a circle is 9 pi m. What is the area, in square meters? Express your answer in terms of pi
Answer:
The circumference of a circle = 2πr = 9π inches
Or, 2πr = 9π
Or, r = 9/2
Or, r = 4.5 inches
The area of a circle = πr²
Or, The area of a circle = π×4.5×4.5
Or, The area of a circle = 20.25π square inches
Step-by-step explanation:
wright the follwing in decimlal form:3/4
Answer:
3/4 in decimal form is 0.75.
Step-by-step explanation:
I hope this helps! :)
Answer:
0.75
Step-by-step explanation:
3/4 is expressed as 0.75 in the decimal form.
to make a fraction into a decimal you just divide the numerator by the
denominator.
and the numerator is the part of a fraction that is above the line
denominator is at the bottom
so 3 / 4 = 0.75
3/4 in decimal form is 0.75
Hope This Helped
Consider the functions below.
f(x) = x² - 6x - 27
g(x) = x - 9
Please help me thanks!
Problem 1
Any pair of equilateral triangles are always similar triangles. We can use the SSS (side side side) similarity theorem to prove this. One triangle is an enlarged copy of the other, or a shrunken reduced copy.
The rectangle is NOT similar to the square. They are different shapes. Similar figures are figures that are the same shape, but different sizes.
==========================================================
Problem 2
horizontal/vertical = horizontal/vertical
24/x = 6/5
24*5 = 6x
120 = 6x
x = 120/6
x = 20
Answer: The flagpole is 20 ft high (about 2 stories tall)
==========================================================
Problem 3
The formula to use is [tex]z = \sqrt{x*y}[/tex]
z = geometric mean of x and y
We multiply the numbers and take the square root. This only works for two values at a time. The geometric mean of three numbers will involve the cube root. Four numbers involves the 4th root, and so on.
Geometric mean of 6 and 10 is sqrt(60) = 7.74597 approximatelyGeometric mean of 2 and 32 is 8 exactlyGeometric mean of 2 and 8 is 4 exactlyGeometric mean of 7 and 9 is sqrt(63) = 7.93725 approximately==========================================================
Problem 4
For each figure, the y is the altitude and can be determined using the geometric mean formula.
Figure on the left: y = sqrt(2*6) = sqrt(12) = 3.4641Figure on the right: y = sqrt(6*14) = sqrt(84) = 9.1652The decimal values are approximate.
==========================================================
Problem 5
For 45-45-90 triangles, we divide the hypotenuse over sqrt(2) to find the leg length.
For the first triangle in the first row, we have y = 18/sqrt(2) = 9*sqrt(2) after rationalizing the denominator. Multiply top and bottom by sqrt(2).
Take this process in reverse to determine the hypotenuse if you know the leg length. This explains why the hypotenuse is 3.2*sqrt(2) for the second triangle in the first row.
-------------------
For 30-60-90 triangles, we go from the short leg x to the hypotenuse 2x.
Double the short leg to get the hypotenuse.
2x = 36
x = 36/2
x = 18
This is for the first triangle in the bottom row.
For the other triangle in this bottom row, we have a long leg of 4*sqrt(3). This must mean the short leg is exactly 4 units long. Therefore, the hypotenuse is 2*4 = 8 units long.
-------------------
Summary:Top row, first column: y = 9*sqrt(2)Top row, second column: y = 3.2*sqrt(2)Bottom row, first column: x = 18Bottom row, second column: y = 8