We can actually deduce here that the following that is characterized by drawing the boundaries of legislative districts in bizarre or unusual ways to favor one party is: A. Gerrymandering.
What is gerrymandering?Gerrymandering is actually known to be characterized by the practice of setting electoral district boundaries in order to favour some specific political interest in some legislative bodies and district.
Gerrymandering usually leads to the creation of convoluted districts rather than compact areas. The gerrymandering is seen in the United States.
The word "gerrymandering" was actually coined when Massachusetts's redistricting maps of 1812 was reviewed by Governor Elbridge Gerry. This was done when it was noted that one of the districts resembled a salamander.
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100 POINTS:
Can someone convert the following to standard form? (Shown work is not required but appreciated"
1. The function f(x) = (x+5)(x-9) in standard form is x²-4x-45.
2. The function f(x) = (x+4)² in standard form is x²+8x+16.
3. The function f(x) = (x+2)²-25 in standard form is x²+4x-21.
4. The function f(x) = 4(x-2)² in standard form is 4x²-16x+16.
5. The function f(x) = 6(2x+1)² in standard form is 24x²+24x+6.
6. The function f(x) = 3(x+4)(x-5) in standard form is 3x²-3x-60.
7. The function f(x) = (x+10)²-100 in standard form is x²+20x.
8. The function f(x) = 9-(x+1)² in standard form is -x²-2x-8.
9. The function f(x) = 2(x+5)²+10 in standard form is 2x²+20x+60.
What is the standard form?
A linear equation can also be written in standard form, slope intercept form, and point slope form.
The formula for standard form is Ax+By=C.
The first function is y = f(x) = (x+5)(x-9).
Simplifying the equation -
f(x) = (x+5)(x-9)
x(x-9)+5(x-9)
x²-9x+5x-45
x²-4x-45
Therefore, the standard form is x²-4x-45.
The second function is y = f(x) = (x+4)².
Simplifying the equation -
f(x) = (x+4)²
Follow the formula - (a+b)² = (a²+2ab+b²)
(x)²+2(x)(4)+(4)²
x²+8x+16
Therefore, the standard form is x²+8x+16.
The third function is y = f(x) = (x+2)²-25.
Simplifying the equation -
f(x) = (x+2)²-25
Follow the formula - (a+b)² = (a²+2ab+b²)
[(x)²+2(x)(2)+(2)²]-25
x²+4x+4-25
x²+4x-21
Therefore, the standard form is x²+4x-21.
The fourth function is y = f(x) = 4(x-2)².
Simplifying the equation -
f(x) = 4(x-2)²
Follow the formula - (a-b)² = (a²-2ab+b²)
4[(x)²-2(x)(2)+(2)²]
4[x²-4x+4]
4x²-16x+16
Therefore, the standard form is 4x²-16x+16.
The fifth function is y = f(x) = 6(2x+1)².
Simplifying the equation -
f(x) = 6(2x+1)²
Follow the formula - (a+b)² = (a²+2ab+b²)
6[(2x)²+2(2x)(1)+(1)²]
6[4x²+4x+1]
24x²+24x+6
Therefore, the standard form is 24x²+24x+6.
The sixth function is y = f(x) = 3(x+4)(x-5).
Simplifying the equation -
f(x) = 3(x+4)(x-5)
3[x(x-5)+4(x-5)]
3[x²-5x+4x-20]
3[x²-x-20]
3x²-3x-60
Therefore, the standard form is 3x²-3x-60.
The seventh function is y = f(x) = (x+10)²-100.
Simplifying the equation -
f(x) = (x+10)²-100
Follow the formula - (a+b)² = (a²+2ab+b²)
[(x)²+2(x)(10)+(10)²]-100
x²+20x+100-100
x²+20x
Therefore, the standard form is x²+20x.
The eighth function is y = f(x) = 9-(x+1)².
Simplifying the equation -
f(x) = 9-(x+1)²
Follow the formula - (a+b)² = (a²+2ab+b²)
9-[(x)²+2(x)(1)+(1)²]
9-x²-2x-1
-x²-2x-8
Therefore, the standard form is -x²-2x-8.
The ninth function is y = f(x) = 2(x+5)²+10.
Simplifying the equation -
f(x) = 2(x+5)²+10
Follow the formula - (a+b)² = (a²+2ab+b²)
2[(x)²+2(x)(5)+(5)²]+10
2[x²+10x+25]+10
2x²+20x+50+10
2x²+20x+60
Therefore, the standard form is 2x²+20x+60.
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what does -2/3 slope look like on a graph
On solving the provided question, we can say that the provided slope is -2/3 equation of line 2x + 3y -7 = 0
what is slope?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
the provided slope is -2/3
let us assume x1 = 2 and y1 = 1
equation of line =>
y-1 = -2/3(x-2)
y-1 = -2x/3 + 4/3
3y-3 = -2x + 4
2x + 3y -7 = 0
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What is the formula for finding the sides of a triangle?
Therefore , the solution of the given problem of trigonometry comes out to be we can find the sides of triangle by trigonometry ratios.
What does trigonometry mean?The area of mathematics known as trigonometry explores the correlation between square side length and As a result of the combination of astronomy and geometry studies, the field initially emerged inside the Nineteenth century, most likely there in third century BC. Precise methods of mathematics cover a number of geometric equations and possible applications to calculations.
Here,
To find the all sides of a triangle
By using trigonometry ,
We can:
Apply the law of sines or trigonometry to find the right triangle side lengths: a = c × sin(α) or
a = c × cos(β)
b = c × sin(β) or
b = c × cos(α)
Therefore , the solution of the given problem of trigonometry comes out to be we can find the sides of triangle by trigonometry ratios.
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The length of a rectangle is 4yd longer than its width. If the perimeter of the rectangle is 40yd , find its area.
The area of rectangle is found to be 117 sq. yd.
Define the term perimeter of the rectangle?If you simply know the width and height, you can easily search all four sides, since two of them are equal to each of the height as well as the width. Add the results after dividing the height and breadth by two.Let the length of rectangle be L:
The, the width is W + 4 = L
Perimeter = 2(length + width)
P = 2(L + B)
P = 2(W + 4 + W)
P = 2(2W + 4)
40 = 4W + 4
4W =36
W = 9
The, L = 9 + 4 = 13 yd.
Area = length * width
Area = 9*13
Area = 117
Thus, the area of rectangle is found to be 117 sq. yd.
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Answer:
Step-by-step explanation:
What is perimeter of a Rectangle:The perimeter of a rectangle is the total circumference of the rectangle.
Perimeter=2(Length + breadth)
Perimeter=40yd
Length=x+4 and breadth=x
40=2(x+x+4);
40=4x+8;
4x=32 and x=8yd
So, length=12yd and breadth=8yd.
Area = length*breadth
So Area = 12*8= 96ydsq
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Which of the following is the equation of the circle with center C and a point P on the circle, as shown in the graph?
(x – 4)2 + (y + 5)2 = 10
(x + 2)2 + (y – 3)2 = 10
(x – 2)2 + (y + 3)2 = 100
(x + 4)2 + (y – 5)2 = 100
The equation of the circle center, C(2, -3), with the point on the circle, P(-4, 5), is the option;
(x - 2)² + (y + 3)² = 100What is the standard form of the equation of a circle?The standard form of the equation of a circle is presented as follows;
(x - h)² + (y - k)² = r²
Where;
(h, k) = The coordinates of the center of the circle
r = The length of the radius of the circle
The location of the specified center of the circle, C = (2, -3)
The location of the point P = (-4, 5)
The radius of the circle found using the distance formula used for finding the distance between two points is therefore;
r = √((-4 - 2)² + (5 - (-3))²) = √((-6)² + (8)²) = 10
The radius of the circle, r = 10
Therefore;
The center of the circle, (h, k) = (2, -3)
The equation of the circle = (x - 2)² + (y - (-3))² = 10²
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What is the coefficient of X²Y in the product 7x² 5y X² 3y?
The coefficient of x²y in the product ( 7x²-5y) ( x²+3y) is 16.
The coefficient of x²y in the product (7x²-5y) (x²+3y) is the numerical factor that is multiplied to x²y when the two polynomials (7x²-5y) and (x²+3y) are multiplied together.
To find the coefficient of x²y in the product, you can use the distributive property of multiplication over addition, also called the FOIL method, which states that to multiply two binomials, you must multiply the first term of the first binomial by the first term of the second binomial, the first term of the first binomial by the second term of the second binomial, the second term of the first binomial by the first term of the second binomial, and the second term of the first binomial by the second term of the second binomial.
The product of (7x²-5y) (x²+3y) can be expanded as follows:
(7x²-5y) (x²+3y) = 7x²x² + 7x²3y -5yx² -5y3y
=7x⁴ + 21x²y -5x²y - 15y²
= 7x⁴ + 16x²y - 15y²
So, the coefficient of x²y in the product ( 7x²-5y) ( x²+3y) is 16.
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1. What is the expression for the perimeter of the entire gardening area based on Lisa’s measurements?
The expression for the perimeter of the gardening area is 10x+16
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.
The perimeter of the garden will be the sum of all the sides of the garden.
left side = x+3+x = 2x+3
right side = x+3x+x =2x+3
top side = x+3+x+3+x = 3x+6
bottom side = 3x+6
therefore this shot the garden as a rectangular shape.
The perimeter of a rectangle = 2(L+B)
= 2((2x+3)+3x+6)
= 2( 5x+8)
therefore the expression that best represents the perimeter of the garden is 10x+16
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Give a algebra equation to represent this pattern
The equation m = 4w + 3 shows the number of days in January.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A pattern shown in the image.
Let m is the number of days in a month.
And w represents the number of days in the weeks.
So, algebraic equation,
m = 4w + 3.
Therefore, the equation is m = 4w + 3.
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what is 200000x 20456
The EYE company spends $4,000,000 to refurbish its prescription-sunglasses factory. Each pair of sunglasses sells for $99. Labor and materials cost $30 per pair and marketing cost another $19 per pair. How many pairs of sunglasses, s, will the company need to sell so that it makes a profit?
The number of pair of sunglasses that the company needs to sell in order to make profit is 80,000.
What is Break-even Point?In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even". There is no net loss or gain, and one has "broken even," despite the fact that opportunity costs were incurred and capital got the risk-adjusted, expected return.
In order to make profit the organization needs to be at breakeven. Therefore, firstly they need to make profit that is equal to the refurbish cost.
The Profit on per pair of glass = Selling price per pair - Labor and material cost per pair - marketing cost per pair
The Profit on per pair of glass = $99 - $30 - $19
The Profit on per pair of glass = $50
Now, the breakeven point can be found as,
Break even quantity = Refurbish Cost / Profit on a pair of sunglasses
= $4,000,000 / $50
= 80,000
Hence, the company needs to sell 80,000 pair of sunglasses.
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HELP THIS IS DUE TOMORROW!!!!
Since the fourth quarter of 2014, the flash storage capacity of smartphones has grown by approximately 12 gigabytes a year. The average flash storage in 2014 was 15.9 gigabytes.
a. Write an equation to represent this situation , defining both variables .
b . Assuming the trend continues , write a one - varia equation that can be used to find the average f storage capacity of smartphones in 2025 .
C. Solve your equation from Part B.
D. Interpret the solution
Answer:
A. c = 15.9 + 12(y - 2014)
B. c = 15.9 + 12(2025 - 2014)
C. 147.9 gigabytes
D. Unsure what you meant
Step-by-step explanation:
A. In this equation, 'c' represents the flash storage capacity in year 'y' and '15.9' is the flash storage capacity in year 2014. '12' represents the yearly increase in storage and '(y-2014)' represents how many years have passed from 2014.
B.To find the average flash storage capacity of smartphones in 2025, we can use the equation:
c = 15.9 + 12(y - 2014)
We can substitute 'y' with 2025 in the above equation to find the average flash storage capacity of smartphones in 2025
C.
c = 15.9 + 12(2025 - 2014)
c = 15.9 + 12(11)
c = 15.9 + 132
c = 147.9 gigabytes
how could you use a 1/4 cup measuring cup to to measure
the water
Answer:
Step-by-step explanation:
1 you would pour the water in the cup and see what dash it lands on
let's say you pour the water and it lands on the 1/8 mark it would be one 1/8
Hope this help if not sorry
PERSEVERE ABCD is a parallelogram with side lengths as indicated in the given figure. The perimeter of ABCD is 22. Find AB.
The value of side AB is 6 units for parallelogram ABCD with perimeter is 22 units.
What is an equation?An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic
Parallelogram is a quadrilateral (four angles and sides) in which opposite sides are equal and parallel.
From the diagram:
AB = DC (opposite sides are equal)
2y + 1 = 4 - 4w
2y + 4w = 3 (1)
AD = BC (opposite sides are equal)
3x - 2 = x - w + 1
2x + w = 3 (2)
The perimeter of ABCD is 22:
2(AB + AD) = Perimeter
2(2y + 1 + 3 - 4w) = 22
2(2y - 4w + 4) = 22
4y - 8w + 8 = 22
4y - 8w = 14 (3)
From the three equations:
w = -0.5, x = 1.75, y = 2.5
AB = 2y + 1 = 2(2.5) + 1 = 6 units
The value of side AB is 6 units
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The sum of Lisa's age and Myra's age is 40. In 10 years, Lisa will be 3
times as old as Myra. How old is each person now?
Answer:
Lisa: 35Myra: 5Step-by-step explanation:
You want Lisa's and Myra's ages if the sum of their ages is 40 and in 10 years, Lisa will be 3 times as old as Myra.
10 years henceThe current sum of their ages is 40. In 10 years, 10 will be added to each of their ages, so the sum will be 60.
At that time Lisa's age is 3 times Myra's age, so will be 3/(3+1) = 3/4 of the total.
Lisa's age in 10 years = (3/4)(60) = 45
Lisa is 35 now, and Myra is 5 now.
__
Additional comment
We could write some equations, but we find a mental solution based on ratios to be quick and easy. Here is a solution using equations:
L + M = 40
(L +10) = 3(M +10) . . . . . . age relation in 10 years
(40 -M) +10 = 3M +30 . . . . substitute for L
20 = 4M . . . . . . . . . add M-30
M = 5; L = 40-M = 35
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What is the function of for loop explain with example?
For loop is a type of looping structure that is used in programming to repeat a sequence of codes until a certain condition is met.
What is function?In mathematics, a function is a relation between a set of inputs and a set of outputs, such that each input is related to exactly one output. Functions are often represented as mathematical expressions, or as a graph or table. The input to a function is known as the argument, while the output is known as the value. Functions are used to describe physical phenomena, and to model relationships between different variables.
It is commonly used to go through each element in an array or a list without having to write the same code multiple times. For example:
// Initialize array
int arr[] = {1, 2, 3, 4, 5};
// For loop to print out each element in the array
for (int i = 0; i < 5; i++) {
System.out.println(arr[i]);
}
In this example, the for loop will print out each element of the array until it reaches the condition that i is less than 5, which is the length of the array.
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LOTS OF POINTS PLEASE HELP
Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table:
Student Amber Ben Carter
Description Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function. Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day. Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares f(x) = 3(4)x
Day Number of Shares
0 2
1 6
2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.
Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
A graph of each of the exponential equation is shown in the image attached below.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = ab^x
Where:
a represents the initial value or y-intercept.x represents time.b represents the rate of change.Since Amber shared her photo with 3 people who continued to share it, an exponential function that models the situation is given by:
f(x) = 3(4)^x
Similarly, Ben's post was shared with 2 friends and each of them shared it with 3 more every day, tripling the number of shares every day, an exponential function that models the situation is given by:
g(x) = 2(3)^x
Lastly, an exponential function that represents the spread of Carter's social media post is given by:
h(x) = 10(2)^x
In this scenario, we would use an online graphing calculator to graph each function as shown in the image attached below.
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They continued to share it, so the number of shares increases every day, as shown by the function.
Social Media Post Shares f(x) = 3(4)x
Day Number of Shares
0 2
1 6
2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.
PLEASE HELP
Select all the right angles.
Which equations are equivalent to Negative one-fourth (x) + three-fourths = 12 Select all that apply. (StartFraction negative 4 x over 1 EndFraction + three-fourths = 12 Negative 1 (StartFraction x over 4 EndFraction) + three-fourths = 12 StartFraction negative x + 3 over 4 EndFraction = 12 One-fourth (x + 3) = 12 (StartFraction negative x over 4 EndFraction + three-fourths = 12
The equations which are equivalent to -1/4(x) + 3/4 = 12 are -1(x/4) + 3/4 = 12 and -x/4 +3/4 = 12. Choose the 2nd and 5th options
How determine which equations are equivalent?Equivalent equations are equations that work the same way even though they look different
The given equation is -1/4(x) + 3/4 = 12 which can simplified as:
-1/4(x) + 3/4 = 12
(-x + 3)/4 = 12
Compare with options:
1. 4x/1 + 3/4 = 12
4x/1 + 3/4 = 12
This is not equivalent
2. -1(x/4) + 3/4 = 12
-1(x/4) + 3/4 = 12
-x/4 + 3/4 = 12
(-x + 3)/4 = 12
This is equivalent
3. -(x+3)/4 = 12
-(x+3)/4 = 12
This is not equivalent
4. 1/4(x+3) = 12
1/4(x+3) = 12
This is not equivalent
5. -x/4 +3/4 = 12
-x/4 +3/4 = 12
(-x+3)/4 = 12
This is equivalent
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Answer:it’s b and d
Step-by-step explanation:
What 2 numbers multiply to get 0 and add to get 7
Answer:
There is no such set of two numbers that multiply to get 0 and add to get 7. Since any number multiplied by 0 is 0, it is impossible for two numbers to multiply to 0 and add to 7 as adding two numbers that multiply to 0 will always result in zero.
Answer:
Step-by-step explanation:
the numbers are 0 and 7 itself.
Multiply : 0*7 = 0
Add : 0+7 = 7
A cuba diver tart at ea level and travel to a poition that i a little lower than −18
-
18
feet. Ue the drop-down menu to complete the tatement about the cuba diver' poition
As per the given statement, the scuba diver's position means the distance he traveled is below 18 feet at the sea level.
Here we have given that a scuba diver starts at sea level and travels to a position that is a little lower than -18 feet.
Now, we need to find the scuba diver's position means the distance he traveled.
While we consider that the scuba driver travelled on -18 feet.
Here the negative term is defined that the the traveler goes on the bottom level.
Therefore, here we said that the person is going to below the sea level.
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What is the 4 sequence in math?
The four types of Sequence are Arithmetic Sequence , Geometric sequence , Harmonic Sequence and Fibonacci Sequence .
What is a Sequence ?
The Sequence is defined as an arrangement of objects or a set of numbers in a particular order which are followed by some rule .
The Four Types of Sequences are :
(i) Arithmetic Sequence : It is defined as a type of sequence in which every term of the series is created by adding or subtracting a fixed number to preceding number .
(ii) Geometric Sequence : It is defined as a type of sequence in which every term is obtained by multiplying or dividing a fixed number with the preceding number .
(iii) Harmonic Sequence : It is defined as a type of sequence in which the reciprocals of the terms follows the Arithmetic Progression .
(iv) Fibonacci Sequence : It is defined as a type of sequence in which every element is obtained by adding the two preceding elements and the sequence starts with 0 and 1 .
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The weights and heights of six mathematics students are given in the following table: Weight (in pounds)
165 123 212 175 165 147
Height (in centimeters)
172 157 183 178 163 167
State whether weight is a function of height for the six students and explain.
a. Yes, height is a function of weight because two students weigh 165 pounds but have different heights.
b. No, height is not a function of weight because two students weigh 165 pounds but have different heights.
c. Yes, weight is a function of height because for each value of height there is one corresponding value of weight.
d. No, weight is not a function of height because there is not enough data to determine a function.
The input variable is "Height," while the output variable is "Weight."
Explain about the independent variable?A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, could be an independent variable.
The cause is the independent variable. Its value is unaffected by the other study variables. Effect is the dependent variable. Changes in the independent variable affect its value.
When doing an experiment, the independent variable is what you alter, and the dependent variable is what changes as a result of that change. This is an easy way to conceive of independent and dependent variables. The independent variable can alternatively be viewed as the cause, and the dependent variable as the result.
The input and output variables are "Height" and "Weight," respectively.
Detailed explanation:
"Weight and height are related"
As we all know, the independent variable in a function of the form y=f(x) is x, and the dependent variable is y.
In other words, after substituting the values of "x," we are getting the values of the quantity "y."
As a result, we can infer from the assertion that,
We are getting the values of "Weight" after substituting the values of "Height."
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What are the 4 coordinates of a graph?
The four coordinate plane quadrants don't have names but are simply known as the first quadrant, second quadrant, third quadrant, and fourth quadrant
example of coordinate
Take into account that the midpoint in between the points (x1,y1) and (x,2y,2) is given by:
xo = (x1 + x2)/2
yo = (y1 + y2)/2
in this case you have
(x1,y1) = (4,-4)
(xo,yo) = (6,-1)
by using the expression for xo and yo, you can find the values of the coordinate of point B, as follow:
xo = (x1 + x2)/2
2xo = x1 + x2
x2 = 2xo - x1
x2 = 2(6) - 4
x2 = 8
yo = (y1 + y2)/2
2yo = y1 + y2
y2 = 2yo - y1
y2 = 2(-1) - (-4)
y2 = 2
Hence, the coordinates of point B is
(xo,yo) = (8,2)
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Which statement is true about the function f(x)=4x-4
Answer: The statement that is true about the function f(x)=4x-4 is:
It is a linear function, as it is a straight line in the form of y=mx+b where m is 4 and b is -4
The y-intercept of this line is -4, which means when x=0, y=-4
The slope of this line is 4, which means for every 1 unit increase in x, y increases by 4 units
The domain of this function is all real numbers and the range is all real numbers except -4
The equation of the line is y = 4x - 4
The graph of this function is a line with a slope of 4 and y-intercept of -4.
Step-by-step explanation:
The equation for line d is 4x + 2y = 18. Line c is perpendicular to line d and intersects line d
at the point (1,7).
Write the equation for line c in slope-intercept form.
Give an example of a quartic trinomial.
Give an example of a quintic polynomial.
Answer:
quartic trinomial : 3x4 – 2x3 + x2 + 8, a4 + 1, and m3n + m2n2 + mn.
quintic polynomial: x5 – x3 + x, y5 + y4 + y3 + y2 + y + 1, and 42a3b2.
Step-by-step explanation:
Quartic Polynomial
A polynomial of degree 4.
Examples: 3x4 – 2x3 + x2 + 8, a4 + 1, and m3n + m2n2 + mn.
a quintic function is defined by a polynomial of degree five.
Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional local maximum and one additional local minimum.
The quartic trinomial having a degree of 4 and the quintic polynomial having a degree of 5.
Quartic Trinomial:
A quartic trinomial is a polynomial expression of degree four that consists of three terms.
The general form of a quartic trinomial is:
[tex]ax^4 + bx^2 + c[/tex]
Example:
Let's consider the quartic trinomial:
[tex]2x^4 - 5x^2 + 3[/tex]
In this example, the term "[tex]2x^4[/tex]" is the highest degree term (degree 4), the term "-[tex]5x^2[/tex]" is the second highest degree term (degree 2), and the constant term "3" has no variable.
So, the quartic trinomial has three terms.
Quintic Polynomial:
A quintic polynomial is a polynomial expression of degree five that may contain multiple terms.
The general form of a quintic polynomial is:
[tex]ax^5 + bx^4 + cx^3 + dx^2 + ex + f[/tex]
Example:
Let's consider the quintic polynomial:
[tex]3x^5 - 2x^4 + 4x^3 + x^2 - 7x + 2[/tex]
In this example, the term "[tex]3x^5[/tex]" is the highest degree term (degree 5), the term "-[tex]2x^4[/tex]" is the second highest degree term (degree 4), and so on. The quintic polynomial has six terms, including the constant term "2".
Hence the quartic trinomial having a degree of 4 and the quintic polynomial having a degree of 5.
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Which among the following are solution of the equation 2x+3y=8a) x=0,y=5b) x=3,y=2c) x=-5,y=6d) x=-1,y=-2
(C) x=-5, y=6 is the solution of the equation 2x+3y=8
To find out which among the following options are solutions of the equation 2x+3y=8, we can substitute the values of x and y in the equation and see if it holds true or not.
a) x=0, y=5 : 2(0) + 3(5) = 0 + 15 = 15 != 8
b) x=3, y=2 : 2(3) + 3(2) = 6 + 6 = 12 != 8
c) x=-5, y=6 : 2(-5) + 3(6) = -10 + 18 = 8 = 8
d) x=-1, y=-2 : 2(-1) + 3(-2) = -2 + -6 = -8 != 8
so the value of left hand side and right hand side of a), b) ,d) is not equals to each other and hence they won't be the equation solution .
So the correct answer is (c) x=-5, y=6
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A 8 foot ramp leads from the ground to the tailgate of a truck and forms a 35° angle with the the ground. Find the height of the tailgate from the ground
The height of the tailgate (from the ground), holding the 8 ft ramp inclined at 35° with the ground, found using trigonometric ratios is about 4.59 ft
What are trigonometric ratios?A trigonometric ratio (trig ratio) specifies the relationship between an angle in a right triangle and two sides of the right triangle.
The length of the ramp = 8 ft
The angle the ramp forms with the ground = 35°
The ramp leads from the ground to the tailgate of the truck
The height of the tailgate from the ground can therefore be found using trigonometric ratios as follows;
The trigonometric ratio for the sine of an angle, θ, using SOH CAH TOA therefore is; sin(θ) = Opposite side
Where;
θ = 35°
The opposite side to the angle θ = Height of the tailgate from the ground = h
The hypotenuse side of the right triangle formed by the ramp = The length of the ramp = 8 ft. We get;
sin(35°) = (Height of the tailgate from ground, )/(Length of the ramp)
Therefore;
sin(35°) = h/8
h/8 = sin(35°)
h = 8 × sin(35°) ≈ 4.59
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Answer:
See explanation below.
Step-by-step explanation:
2.3p – 10.1 = 6.5p – 4 – 0.01p?
2.3p -6.5p + 0.01p= – 4 + 10.1
-4.19p = 6.1 [Combine like terms and moved from one side to the other]
p = -1.456
Select two options.
The options seem to run together. Where does one equation stop and the other begin?
Are these the equation options?
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p
– 400 – p 23p – 101 = 65p – 40
– p 2.3p – 14.1 = 6.4p – 4
These don't look correct. Please review the derivation of p=-1.456 and find the option(s) that provide the same result.
This relationship can also be shown in a table. Complete the equation that represents the relationship between n and w.
An equation that represents the relationship between n and w is w = 10n + 8.
How to write the required equation?Mathematically, the slope-intercept form of a line can be represented by using this linear equation:
y = mx + c
Where:
m represents the slope.c represents the y-intercept.x and y are the data points.Next, we would determine the slope of the data points in this table (see attachment) as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (78 - 68)/(7 - 6)
Slope, m = 10/1
Slope, m = 10.
At point (6, 68), an equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - 68 = 10(x - 6)
y - 68 = 10x - 60
y = 10x - 60 + 68
y = 10x + 8 ≡ w = 10n + 8.
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