The solution using correct step of substitution in the equation y=2x-1 4x+y=2 is x = 1/2 and y = 0
Simultaneous equationy = 2x - 1
4x + y = 2
Substitute the value of y in equation (1) into (2)4x + y = 2
4x + (2x - 1) = 2
4x + 2x - 1 = 2
6x - 1 = 2
6x = 2 + 1
6x = 3
x = 3/6
x = 1/2
substitute the value of x into equation (1)y = 2x - 1
y = 2(1/2) - 1
= 2/2 - 1
= 1 - 1
y = 0
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20 people show up to the party and robert decides to give them
Answer:
This question looks and sounds like a "personal opinion question" to me.so from my opinion Robert give them a Smack in their ases .
Hope this helps .
Good luck ✅.
AM and AN are tangent to circle C. If AM measures 2.5 cm, what is the measure of AN?
M
2.0 cm
O 5.0 cm
O 1.5 cm
2.5 cm
C
A
N
The measure of AN form the given figure is 2. 5cm. Option D
How to determine the length
It is important to note that if from one external point, two tangents are drawn to a circle then they have equal tangent segments.
We have that,
AM ≅ AN
so, if AM measures 2. 5cm
AN measures 2. 5cm
Thus, the measure of AN form the given figure is 2. 5cm. Option D
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(a) The coefficient of variation for males is _%
(b) The coefficient of variation for females is _%
(c) Compare the variability of grade point averages of males and females. Choose the correct answer below.
A.
The grade point averages of females and males have the same variation.
B.
The grade point averages of females and males do not vary.
C.
The grade point averages of males are more variable than females.
D.
The grade point averages of females are more variable than males.
The coefficients of variation shows that D. The grade point averages of females are more variable than males.
How to illustrate the information?From the complete information, the coefficients of variation for male is 21.3% and the coefficient of variation for female is 25.1%.
In this case, the coefficients of variation shows that the grade point averages of females are more variable than males.
In conclusion, the correct option is D.
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y = -2 f(3(x - 4)) - 1 Describe this transformation
The graph y = x^3 is compressed vertically by a factor of 1⁄2 , translated 4 units to the right, and translated 5 units upward.
Write the equation of the transformed function.
The equation of the transformed function is y = 1/2(x - 4)^3 + 5
How to describe the transformation?The parent function is given as:
y = x^3
When the function is vertically compressed by 1/2, the rule is:
(x, y) ⇒ (x, 1/2y)
So, we have
y = 1/2x^3
When translated 4 units right, we have:
y = 1/2(x - 4)^3
When translated 5 units up, we have:
y = 1/2(x - 4)^3 + 5
Hence, the equation of the transformed function is y = 1/2(x - 4)^3 + 5
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When we graph a line using slope and y-intercept, the first point that you graph is
ALWAYS on_____, and you use _____ to get to the next point.
Answer:
y=mx+b is the formula starting with b say it is 4 you put a dot on 4 on the y axis m is 1/2 you go up 1 right 2 on the 4 points then do the same on the next point you get then you get your line. hope this helps
The voyage of the Mayflower took 8 months and 11 days. Convert the time to days.
Answer:
If i did it correctly the answer should be 255 days
Step-by-step explanation:
please mark brainliest
Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
1. Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
3. Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
4. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.
5. Create a graph of the polynomial function you created in Question 4.
Part C
6. Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
The key features of the function g(x) = (x + 3)(x + 2)(x − 3) are; Maximum Point at g(x) = 6.065; Minimum Point at g(x) = -0.879; 2.593 is the point of inflection
How to identify the features of a Polynomial?1) The Fundamental Theorem of Algebra states that a polynomial of degree "n" has at most "n" number of complex roots.
Since Kelsey argues the function can have as many as three zeros only, then we can say that Kelsey is correct.
2) The g(x) function that I will choose is;
g(x) = (x + 3)(x + 2)(x − 3)
Expanding this gives us;
g(x) = x³ - x² - 4x + 4
To find the key features which are critical points (maximum, minimum, point of Inflection), we will differentiate g(x) with respect to x to get;
g'(x) = 3x² - 2x - 4 = 0
Using quadratic formula gives;
x = 1.535 and Minimum Point; x = -0.869
Thus;
g(1.535) = -0.879 minimum point
g(-0.869) = 6.065 maximum point
Thus;
Maximum Point occurs at g(x) = 6.065
Minimum Point occurs at g(x) = -0.879
g"(x) = 6x -2
At g"(x) = 0, we will have the point of inflection which is at;
x = 1/3
g(1/3) = 2.593 which is the point of inflection
3) The graph of the Polynomial of the function g(x) = (x + 3)(x + 2)(x − 3) is as attached.
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Whats the correct answer answer asap
gym help
when doing any weighted exercises that involve using all or little of my body weight do i count my body weight and the added weight as my “actual weight lifted”? for example i weigh 150lbs and let’s say i did a single rep of weighted overhand chin ups with a single 20lbs weight wrapped around me and i wanted to track how much “actual weight” i just lifted would i write down and track just the 20lbs or my body weight 150lbs plus the weight 20lbs?
You should write down and track only the 20lbs weight during your weighted exercise while ignoring your body weight.
What is actual weight?Actual weight is also referred to as gross weight and it can be defined as the exact (original) weight of an object, as measured using an appropriate weighing scale.
This ultimately implies that, you would write down and track only the 20lbs weight during your weighted exercise such as a single rep of weighted overhand chin ups.
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Which of the following is not in the domain of tan(x)? Select all correct answers.
The Domain and Range of tan(x) are mathematically given as
Domain [tex]:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}[/tex]
Range: all Real numbers
What is The Domain and Range of tan(x)?All real numbers are in the domain of the function "y=tan (x)," with the exception of the value "[tex]\pi/2+\pi n[/tex]" for all integers n, which is the case when cos(x) = 0.
It follows that "[tex]\frac{-3 \pi }{2}[/tex]" is not in the domain of "tan (x)" among the possible values.
In conclusion,
Domain [tex]:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}[/tex]
Range: all Real numbers
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Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
V = r²h
Write the formula to calculate the height, h.
Answer:
Cone: h = [tex]3\frac{V}{\pi r^{2} }[/tex]
Cylinder: h = [tex]\frac{V}{\pi r^{2} }[/tex]
Step-by-step explanation:
- the formula you described is not the formula for the volume of a cone as it is V = [tex]\pi rx^{2} \frac{h}{3}[/tex]
- to find the height you simply rearrange the formula, so the formula to calculate the height of the cone is:
- h = [tex]3\frac{V}{\pi r^{2} }[/tex]
- based on the formula you described, it is closer to a cylinder and the formula for the volume of a cylinder is: V = [tex]\pi r^{2} h[/tex]
- once again, to find the height you simply rearrange the formula, so the formula to calculate the height of the cone is:
- h = [tex]\frac{V}{\pi r^{2} }[/tex]
hope this helps :)
Suppose the theoretical probability of winning a prize at a carnival game is 0.18. Based on this probability how many more customers would you have expected to win a prize
Answer:
Could you please provide more context to the problem
Step-by-step explanation:
There is not much context provided for us on this problem, but you can set the decimal to a percentage: 18% of customers win a prize. Now to properly solve this question we need to know either the number of people or the percentage of kids and adults.
You are planning a trip to Bermuda but have heard stories of people getting "lost" in the area that forms what is known as the Bermuda Triangle. You are
curious just how big the area that forms the triangle actually is and decide to investigate. You discover that one side length of the triangle is 900 miles and
another sides is 930 miles and the angle between them is 56 degrees. What is the area that the plane can fly and be in the zone known as the Bermuda
Triangle? Round your answer to the nearest mile.
The area that the plane can fly and be in the zone known as the Bermuda is; 346952 mile²
How to use the area rule to find the area of a triangle?The area rule states that the area of any triangle is equal to half the product of the lengths of the two sides of the triangle multiplied by the sine of the angle included by the two sides.
Now, from the question, we are give;
Side 1 = 900 miles
Side 2 = 930 miles
Angle between two sides = 56°.
Thus, by the area rule we have;
Area = (1/2) * 900 * 930 * sin 56°
Area = 346952 mile²
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The plane 15x − 12y + 20z = 60 is represented by which graph below? Notice the z-axis.
Answer:
b
Step-by-step explanation:
I did it
giving brainliest :)
Answer:
The last one - 256 people
What is the equation of the function represented by this graph?
Answer:
[tex]\displaystyle g(x) = -(x + 2)(x - 4)[/tex]
Step-by-step explanation:
First, look at the graph to determine whether it opens down or up, which in this case is down, so you insert a negative in front of the expression. Next, locate your x-intercepts [zeros (where the graph insects the x-axis)]. You will see that the graph intersects [tex]\displaystyle [-2, 0][/tex] and [tex]\displaystyle [4, 0],[/tex] so what you do is insert the zeros' OPPOCITES into the equation because according to the vertex equation, [tex]\displaystyle y = A[x - h]^2 + k,[/tex] that negative in front of [tex]\displaystyle h[/tex] gives you the OPPOCITE outcome, so be careful.
I am joyous to assist you at any time.
Which expression is equivalent to (2x²y) ³?
O 2x¹y4
2x¹2y3
8x¹ y
O 8x¹2y³
Answer: [tex]8x^6 y^3[/tex]
Step-by-step explanation:
See attached image.
The expression which is equivalent to (2x²y)³ is 8x⁶y³
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (2x²y)³
Two times of x square times of y whole to the power of three
We have to find the equivalent expression of the given expression.
Equivalent expressions are expressions that work the same even though they look different.
We have a property that [tex](a^m)^n=a^m^n[/tex]
So (2x²y)³ = 2³x⁶y³
=8x⁶y³
Hence, the expression which is equivalent to (2x²y)³ is 8x⁶y³
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Joy is going to a sub shop for a sandwich. At the restaurant, she can choose either a roll (R), bread (B), or a wrap (W). There are two meat choices, ham (H) and turkey (T), and 2 kinds of cheese, Swiss (S) and American (A). Before she goes, Joy wants to make a list of her choices. If she chooses one item from each selection, which will be part of her list?
Answer:
so their are three kinds of breed 2 kinds of meet and 2 kinds of cheese here the list
roll, ham,swiss
roll, turkey,american
roll,ham,american
roll, turkey,swiss
bread, ham,swiss
bread, turkey,american
bread,ham,american
bread, turkey,swiss
wrap, ham,swiss
wrap, turkey,american
wrap,ham,american
wrap, turkey,swiss
Hope This Helps!!!
QUESTION IS DOWN BELOW!
Answer:
The ratio of the widths is 3:16, the ratio of the volumes is 27:4096, and the ratio of the surface areas is 9:256.
Step-by-step explanation:
In Geometry, you'll learn that when the scale factor of similar figures is a:b, then the ratio of the perimeter is a:b, the ratio of the area is a*a:b*b and the ratio of volume is a*a*a:b*b*b.
A line passes through the point (-2, 8) and has a slope of-5/2.
Write an equation in slope-intercept form for this line.
Answer:
[tex]y = -\frac{5}{2} x + 3[/tex]
Step-by-step explanation:
We are given that a line passes through (-2, 8) and has a slope of -5/2.
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.
Since we are already given the slope of this line, we can immediately plug it into the equation.
Replace m with -5/2.
[tex]y = -\frac{5}{2} x+ b[/tex]
Now we need to find b.
As the equation passes through the point (-2, 8), we can use its values to help solve for b.
Substitute -2 as x and 8 as y.
[tex]8 = -\frac{5}{2} (-2) +b[/tex]
Multiply.
8 = 5 + b
Subtract 5 from both sides.
3 = b
Replace b with 3 in the equation.
[tex]y = -\frac{5}{2} x + 3[/tex]
Topic: finding the equation of the line (slope-intercept form)
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Sarah will ship packages for anyone. She charges $6 for her services and then $2.75 per item. How much would she charge to ship 8 items
Consider a convex hexagon in which all pairs of opposite sides are parallel. Prove that if one pair of opposite sides have equal length, then the other two pairs of opposite sides also have equal length.
A pair of the opposite sides of a hexagon has equal length and this is proved below.
How to illustrate the hexagon?It should be noted that a hexagon is a polygon that has six sides.
In this case, it has 6 sides.
The total angles will be:
= (n - 2) × 180
= (6 - 2) × 180
= 720°
Each angle will hence be:
= 720°/6
= 120°
Each angle are equal and this illustrates that the parallel sides are equal.
A diagram is attached to illustrate the pair of parallel sides.
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set x is made up of the possible ways five students, represented by a, B, C, D, and E, can be formed into groups of three. Says y is made up of the possible ways five students can be formed into groups of three if student a must be in all possible groups. which statements about the situation are true
The true statement about the set include:
Set X has 10 possible groupings. X Y Set Y = {ABC, ABD, ABE, ACD, ACE, ADE} There are three ways to form a group if persons A and C must be in it.How to illustrate the information?If set X is made up of the possible ways five students, represented by A, B, C, D, and E, can be formed into groups of three, then the set X consists of such triples {ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE}.
The set X totally contains 10 elements.
There are three ways to form a group if persons A and C must be in it. This statement is true and these groups are ABC, ACD, ACE.
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Let v = leftanglebracket 3, negative 2 rightanglebracket. what is the approximate direction angle of v?
The approximate direction angle of v is 326°
Definition of Direction Angle
A vector's direction angle is the angle formed by the positive x-axis and the vector v. The arctangent of the ratio between the vertical and horizontal components of the vector, v=xi+yj, can be used to determine the direction angle, θ.
What is the direction angle of v?
Let θ be the direction angle of v or the angle mad by v with the horizontal line.
It is given that,
[tex]v = < 3, -2 >[/tex]
We know that,
θ = tan⁻¹([tex]\frac{y}{x}[/tex])
Here, we have y = -2 and x = 3. Hence, we get,
∴ θ = tan⁻¹[tex](\frac{-2}{3})[/tex]
⇒θ = tan⁻¹(0.66)
Hence the direction angle of v = 360 - tan⁻¹(0.66)
≈ 326°
Thus, the approximate direction angle of v is 326°.
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0. In 1996 Jabu decides to invest in the Stock Exchange. He buys 1200 shares in a company at R6.75 per share. How much did he pay for the shares?
Answer:
[tex]1200\times6.75=R8100[/tex]
6 in.
10 in.
15 in.
V = [?] in.³
area of base
Volume of Prism B.h
Answer:
300
Step-by-step explanation:
A pyramid with a triangle-shaped base whose three triangular faces meet at the ap/ex. The triangular pyramid formula included both the volume and surface area of the pyramid. The triangular pyramid volume formula calculates the base area and the height whereas the surface area of the triangular pyramid calculates the base area, perimeter,, and slant height. Formulas for volume and surface area of the triangular pyramid are given below that are used in the triangular pyramid formula:
Volume= 1/3 × Base area × Height
Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your
finding to state whether or not the given r represents a significant linear correlation. Use a significance level of
0.05.
r = 0.543, n = 25
A) Critical values: r = +0.487, no significant linear correlation
B) Critical values: r = +0.396, no significant linear correlation
C) Critical values: r = +0.487, significant linear correlation
D) Critical values: r = +0.396, significant linear correlation
The critical value of r is mathematically given as r = +0.487, with no significant linear correlation. Option A.
What are the critical values of r?
Question Parameters
r = -0.868
n = 5
df = 5 - 2
df = 3
[tex]\alpha / 2 =0.025[/tex]
Critical values [tex]r= \pm 0.878[/tex]
Generally, there exists no linear correlation between the Critical values
as r=0.878
In conclusion, Critical values: r = +0.487, no significant linear correlation
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The graph of the function f(x)=log7(x) is stretched vertically by a factor of 4, shifted to the left by 5 units, and shifted down by 3 units.
The resulting function after all transformations have been carried out is; 4log7(x+5) + 2.
Which function results from all the Transformations?The transformations which ensued on the function given are as follows;
Stretched vertically by a factor of 4; Hence, we have; 4f(x) = 4log7(x).
Shifted to the left by 5 units; 4f(x) = 4log7(x +5).
Shifted down by 2 units; 4f(x) +2 = 4log7(x+5) + 2.
On this note, it follows that the resulting function upon all the Transformations is; = 4log7(x+5) + 2.
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Estimate the following quantities without using a calculator. Then find a more precise result, using a calculator if necessary. Discuss whether the approximation technique worked.
The approximate value of 63000 x 200 will be 12600000.
What is multiplication?
In mathematics, multiplication is defined as the sum of the numbers to the other number given. Like if 2 is multiplied by 3 then the multiplication will be the sum of the two-three times.
Given expression is 63000 x 200 so here we need to calculate the sum of the 63000 to 200 times.
E = 63000 x 200
E = 12600000
Therefore the approximate value of 63000 x 200 will be 12600000.
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Simplify the following expression, and combine like terms: 15x²y - 4(-2xy² - 9xy) + 12xy² - 8xy - 9x
Answer:
15x^2y+20xy^2+28xy-9x
Step-by-step explanation:
15x²y - 4(-2xy² - 9xy) + 12xy² - 8xy - 9x
First distribute the -4 to all the terms in the parentheses
15x²y +8xy² + 36xy + 12xy² - 8xy - 9x
Now combine like terms
15x²y +8xy² + 12xy² + 36xy - 8xy - 9x
15x^2y+20xy^2+28xy-9x