By simplification the quadratic function [tex]y = x^2 + x - 8[/tex] in vertex form is[tex]y = (x + 1/2)^2 - 33/4[/tex], and its vertex is (-1/2, -33/4).
What is the vertex form of a quadratic equation?
The standard form of a quadratic function is:
[tex]y = ax^2 + bx + c[/tex]
where a, b, and c are constants and x is the variable.
The vertex form of a quadratic function is:
[tex]y = a(x - h)^2 + k[/tex]
where a, h, and k are constants and (h, k) is the vertex of the parabola.
To write the quadratic function [tex]y = x^2 + x - 8[/tex] in vertex form, we need to complete the square. The vertex form of a quadratic function is given by:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola.
So, first we need to factor out the coefficient of the x^2 term:
[tex]y = 1(x^2 + x) - 8[/tex]
Now, we need to complete the square for the expression inside the parentheses:
[tex]y = 1(x^2 + x + 1/4 - 1/4) - 8[/tex]
[tex]y = 1[(x + 1/2)^2 - 1/4] - 8[/tex]
Finally, we can simplify and write the function in vertex form:
[tex]y = (x + 1/2)^2 - 33/4[/tex]
Therefore, the quadratic function [tex]y = x^2 + x - 8[/tex] in vertex form is[tex]y = (x + 1/2)^2 - 33/4[/tex], and its vertex is (-1/2, -33/4).
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Which Rational Expression is undefined when x=0?
Answer:
Step-by-step explanation:
last one since if you plug in zero for the x in the denominator you get 0 and if you have 0 in the denominator it's always undefined
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
Step-by-step explanation:
[tex]m=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
[tex]=(\frac{-12+(-8)}{2}, \frac{-7+(-4)}{2})[/tex]
[tex]=(-10,-5.5)[/tex]
How many rational numbers are there between 0 and 5
Answer: infinity technically the answer is infinity
nothing less nothing more
Step-by-step explanation:
Identify the measurement as the diameter or radius of the circular object then find the circumference of the object 1 from the center to the edge of a dvd measures 60 mm
The diameter οr radius οf the circular οbject is 120mm, and the circumference οf the οbject 1 frοm the centre tο the edge οf a DVD is 380mm.
What is Circumference?A circle's οr an ellipse's circumference is its perimeter. In οther wοrds, if the circle were tο be straightened οut alοng a line segment, the length οf the arc wοuld be the circumference. The perimeter is mοre frequently used tο refer tο the length οf the curve surrοunding any defined figure.
The given infοrmatiοn is that a DVD's edge is 60 mm lοng.
The diameter, radius, and circumference οf the circular οbject must be determined in οrder tο determine the measurement.
We cοncluded that
Radius = 60mm
Diameter = 120mm
Circumference = 380mm
Hence, Diameter = 120mm
Circumference = 380mm
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can you factor this completely x^4-16x^3+15x^2
Answer:
(x-15)(x-1) x²
Step-by-step explanation:
x² (x²-16x+15)
a+b=-16
ab=15
a=-15
b=-1
x(x²-15)- (x-15)
(x-15)(x-1)
(x-15)(x-1) x²
I need to figure the code out
The function with the greatest rate of change are:
1. C = 3
2. A = 5
3. A = 1
4. B = 3
What is the Rate of Change of a Linear Function?The rate of change of a linear function, also known as the slope of the line, represents the amount by which the output (y) changes for a given change in the input (x). In other words, it is the measure of how steep the line is.
The formula for the rate of change, or slope, of a linear function is:
slope = (change in y) / (change in x)
1. Rate of change for function A = change in y / change in x = 4/3
For B = 1/2
For C = 3/1 = 3
The function with the greatest rate of change is C = 3
2. Rate of change for function A = change in y / change in x = (10 - 5)/(1 - 0) = 5
For B = (12 - 8) / (3 - 1) = 2
For C = (6 - 3)/(1 - 0) = 3
The function with the greatest rate of change is A = 5
3. Rate of change for function A = change in y / change in x = 2/2 = 1
For B = (3 - 2)/(2 - 0) = 1/2
For C = 1/3
The function with the greatest rate of change is A = 1
4. Rate of change for function A = change in y / change in x = -1/3
For B = (10 - 1)/(4 - 1) = 3
For C = 2
The function with the greatest rate of change is B = 3
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One zero of the polynomial is given. Use it to express the polynomial as a product of linear factors over the complex numbers f(x) = + ? + 3x + 3. zero: 3 = 1 One zero of the polynomial is given. Use it to express the polynomial as a product of linear factors over the complex numbers. f(x) = ** - 3x + 8r - 18.6 +12; zero: 0 = 2 Due in 8 hours Construct a polynomial of least degree possible using the given information. Real roots: -1,4, - 3 and contain the point (1, 3). Construct a polynomial of least degree possible using the given information. Real roots: 4, 3 (with multiplicity 2 and 1) and (-1, f(-1)) = (1,1) Preview
One zero of the polynomial is given. Use it to express the polynomial as a product of linear factors over the complex numbers.
Given: f(x) = x^2 + 3x + 3 and zero: 3
Here's how to approach this problem:
The polynomial f(x) has a root of 3.
f(x) can be expressed as a product of two factors, where the first factor contains (x-3) as one of its roots, as follows:
f(x) = (x-3)(ax + b)
We can obtain the values of a and b by equating the coefficients of this equation to that of the given polynomial:
a + 3 = 1 (since coefficient of x in the given polynomial is 3)
-3a + b = 3 (since the constant term in the given polynomial is 3)
Solving these equations gives us a=-2 and b=9.
f(x) can thus be expressed as:
f(x) = (x-3)(-2x + 9)
Hence, the expression for the polynomial is f(x) = -(x-3)(2x-9).
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Q2. It is recommended to drink a maximum of 2 litres of
water per day.
True
False
Answer: True
Step-by-step explanation:
It is generally recommended that adults drink at least 8 cups or 2 liters of water per day to maintain proper hydration.
PLEASE WORD ANSWER I CAN USE FAST
WILL MARK BRAINLIEST
Answer:
62/3
Step-by-step explanation:
As it's a rectangle do the area is equal A = L*W
SO
[tex](7 \times \frac{3}{4} ) \times( 2\times \frac{2}{3} )[/tex]
Step-by-step explanation:
2 2/3 × 7 3/4
turn these into improper fractions =8/3 × 31/3
times the numerator and denominator together= 248/9
248/9 simplified=27.5555555 or 27 5/9 as a fraction
2.5 m³ of granite has a mass of 6725 kg. a) Calculate the density of granite in kg/m³. b) Find the mass of 1.3 m³ of granite in kg.
The density of the granite is 2690 kg/m³ and the mass of 1.3 m³ of granite is 3497 kg.
How to calculate density?Density is expressed mathematically as;
p = m / v
Where m is mass and v is volume.
Given that;
Volume of the granite = 2.5 m³Mass = 6725 kgDensity p = ?Plug the given values into the above formula and solve for density of the granite.
p = m / v
p = 6725 kg / 2.5 m³
p = 2690 kg/m³
b) The mass of 1.3 m³ of granite in kg will be;
p = m / v
m = p × v
m = 2690 kg/m³ × 1.3 m³
m = 3497 kg
Therefore, the mass of 1.3 m³ of granite is 3497 kg.
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A particle of mass 5 kg rests on a smooth
horizontal table. It is connected by a light
inextensible string passing over a smooth
pulley at the edge of the table to a particle
of mass 2 kg, which is hanging freely. Find the acceleration of the system
and the tension in the string.
5 kg
2 kg
The acceleration of the system is 0.83 m/s² and the tension in the string is 8.3 N.
The acceleration of the system can be calculated using Newton's second law of motion. The equation is F = ma, where F is the net force on the system, m is the total mass, and a is the acceleration. Since the two masses are connected by a light inextensible string, the net force acting on the system is equal to the tension in the string. Therefore, the equation becomes T = (5 kg + 2 kg)a, where T is the tension and a is the acceleration. Solving for a, the acceleration is found to be 0.83 m/s². The tension in the string can also be calculated using the equation above. Plugging in the acceleration, the tension is found to be 8.3 N.
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Evaluate the function for the given value of x. y = (1.2)^x ; x = 2
The solution, when x = 2, will be y = 1.44, according to the facts provided.
What are the definition and examples of value?Value refers to how little something is valuable, either financially or in terms of significance. It can also imply "determine how very much something that is worth," as in a reward with a $200 value. As a verb, it indicates "keeping something in high regard" (such "I value our friendship").
We can evaluate this function y = (1.2)ˣ at x = 2 by merely adding x = 2 to the formula for y.
y = (1.2)ˣ
y = (1.2)ˣ (substitute x = 2)
y = 1.44
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MATH CHALLENGE!!! Worth 50 ptssss!!
Answer:
Step-by-step explanation:
3=k jsdna no I don't want you in my car so you have a lot to say about the other things I have for the past year so we can see it
Arrange these integers from smallest to greatest (ascending order): 2; -2; 3; -3; 6; -6; 0
Answer:
-6, -3, -2, 0, 2, 3, 6
Step-by-step explanation:
Normally the biggest number has the bigger value but in negative integers the smaller number has the bigger value.
Eg- If you have 2 dollars it is bigger that -2 dollars as then you will be going in dept.
-5 is smaller than -1
-1 is the greatest negative integer.
The country of Sylvania has decided to reduce the number
3
of its illiterate citizens by
5 each year. This year there are
9000 illiterate people in the country. Write a function that gives the number of illiterate people in Sylvania, P(t), t years from today
There will be 8980 illiterate people in Sylvania 4 years from now if the country continues to reduce the number of illiterate citizens by 5 each year.
We can write a function P(t) to represent the number of illiterate people in Sylvania t years from today, where t is the number of years after the current year.
Given that the country has decided to reduce the number of illiterate citizens by 5 each year, we can subtract 5 from the number of illiterate people each year.
The initial number of illiterate people in the country is 9000. So, the function can be written as:
P(t) = 9000 - 5t
where t is the number of years after the current year.
For example, if we want to find out how many illiterate people will be in Sylvania in 4 years from now, we can substitute t with 4:
P(4) = 9000 - 5(4) = 9000 - 20 = 8980
Therefore, there will be 8980 illiterate people in Sylvania 4 years from now if the country continues to reduce the number of illiterate citizens by 5 each year.
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2y−3x=4 write this equation is slope intercept form
Answer:
[tex]y = \frac{3}{2} x + 2[/tex]
Step-by-step explanation:
[tex]2y - 3x = 4[/tex]
[tex]y - \frac{3}{2} x = 2[/tex]
[tex]y = \frac{3}{2} x + 2[/tex]
6.02 line of best fit ms pre-algebra S2 v16.2/ patterns of association
The 6.02 line of best fit is a straight line that best represents the trend or pattern of association between two variables on a scatter plot. It is also known as the regression line.
What is regression line?
In the context of MS Pre-Algebra S2 V16.2, the line of best fit is used to analyze patterns of association between two sets of data. For example, if we have data on the height and weight of a group of individuals, we can use a scatter plot to visualize the relationship between these two variables.
By drawing a line of best fit through the data points, we can see the general trend or pattern of association between height and weight. This line can then be used to make predictions about the weight of an individual based on their height, or vice versa. The line of best fit is a useful tool for analyzing patterns of association in a variety of fields, including statistics, economics, and social sciences.
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Complete question is: The 6.02 line of best fit is a straight line that best represents the trend or pattern of association between two variables on a scatter plot.
Please Help Me!!!
The width of a rectangle measures (9. 8g-4. 5h) centimeters, and its length measures (1. 5g-3. 4h) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The expression that represents the perimeter of the rectangle in centimeters is 45.2g - 30.6h.
Let's start by finding the length of the top and bottom sides, which are equal to the width. The width is given by (9.8g - 4.5h) centimeters, so the length of the top and bottom sides is:
2(width) = 2(9.8g - 4.5h) = 19.6g - 9h
Next, we need to find the length of the left and right sides, which are equal to the length. The length is given by (1.5g - 3.4h) centimeters, so the length of the left and right sides is:
2(length) = 2(1.5g - 3.4h) = 3g - 6.8h
Now that we have the lengths of all four sides, we can find the perimeter of the rectangle by adding them together:
Perimeter = length + width + length + width
Perimeter = (3g - 6.8h) + (19.6g - 9h) + (3g - 6.8h) + (19.6g - 9h)
Perimeter = 45.2g - 30.6h
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Find X and Order angles from smallest to largest
The value of x is 10 and the trapezoid has two base angles with measure 40 degrees and two non-base angles with measure 140 degrees.
What is the congruent angle?
When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal and in matching corners will be congruent.
In an isosceles trapezoid, the base angles (the angles opposite the parallel sides) are congruent. Let's call each of these angles "a". Then, we have:
a = 3x + 10 (from one of the congruent angles)
a = 5x - 10 (from the other congruent angle)
Setting these two expressions equal to each other, we get:
3x + 10 = 5x - 10
Solving for x, we get:
2x = 20
x = 10
Now that we know the value of x, we can substitute it back into either of the expressions for "a" to find the measure of each base angle:
a = 3x + 10 = 3(10) + 10 = 40
Therefore, each base angle of the trapezoid has measure 40 degrees.
The other two angles of the trapezoid are the non-base angles (the angles adjacent to the parallel sides).
These angles are supplementary to the base angles, so each non-base angle has measure:
180 - 40 = 140
Therefore, the value of x is 10 and the trapezoid has two base angles with measure 40 degrees and two non-base angles with measure 140 degrees.
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Each box of Marco's favorite cookies costs $4. 0. Which is the dependent and independent variable?
In this scenario, the dependent variable is the cost of the boxes of cookies and the independent variable is the number of boxes of cookies being purchased.
The cost of the boxes of cookies depends on the number of boxes being purchased. The more boxes of cookies that are purchased, the higher the cost will be. Therefore, the cost of the boxes of cookies is the dependent variable, as it depends on the independent variable of the number of boxes being purchased.
Conversely, the number of boxes of cookies being purchased is the independent variable, as it is the variable that is being manipulated or changed. The cost of the boxes of cookies is not being changed, but rather is dependent on the number of boxes being purchased.
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help asap math sp polonomials
Therefore, the total area of Riley's backyard is. [tex]6x^2-19x+8[/tex].
What is length?Length is a measure of distance or extent, typically referring to the measurement of an object or distance in one dimension. It describes how long an object or distance is, usually in units such as meters, feet, or inches. Length is one of the fundamental physical quantities, and is used in various fields including mathematics, physics, engineering, and construction. It is often represented by the symbol "L" or lowercase "l".
To find the area of the backyard, we need to multiply the length and width of the rectangular shape.
Length of the backyard = 3x - 8
Width of the backyard = 2x - 1
Area of the backyard = Length x Width
[tex]\\= (3x - 8)(2x - 1)\\= 6x^2 - 19x + 8[/tex]
Therefore, the total area of Riley's backyard is [tex]6x^2-19x+8[/tex]
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help me please and thank you
Therefore , the solution of the given problem of volume comes out to be false we must first know the cylinder's radius and height.
Explain volume.A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 stand for cubic dimensions. However, you can use an object's bulk to estimate its dimensions. Usually, the weight of the item is converted into mass measures like kilograms and kilos.
Here,
The capacity of a cylinder and a cone that are the same height and radius are not the same.
The formula V = πr²h,
where r is the radius of the base and h is the height, determines the volume of a cylindrical. Contrarily, the equation
=> V = (1/3)r²h gives the volume of a cone.
To calculate the volume of a cone with the same measurements if the cylinder's volume is 99 cubic cm,
False we must first know the cylinder's radius and height.
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I need help with this now!
thank u.
6 hours and 57 minutes to fill the order if they work together.
what is expressed in both units and dollars to show the number necessary to make enough money to keep going?
In the context of economics, the term “break-even point” is used to indicate the number necessary to make enough money to keep going, and it is expressed in both units and dollars.
What is the break-even point?Break-even point is a term used in cost accounting to describe the point at which total cost and total revenue are equal. At this point, there is no profit or loss; it is a neutral zone. At this point, a firm's revenue from the sale of products and services is just sufficient to cover the total costs of producing those products and services.
The break-even point can be expressed in terms of units sold or in terms of total revenue. The point at which the total revenue equals total cost is the break-even point in terms of dollars. The point at which the number of units sold equals the fixed costs divided by the contribution margin per unit is the break-even point in terms of units sold. Therefore, the break-even point is expressed in both units and dollars to show the number necessary to make enough money to keep going.
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Which number line model represents the expression
2. 5
+
4. 5
The number line model begins at 2.5 and then adds 4.5 to it, resulting in the number 7 being plotted at the end of the line.
The number line model for the expression 2.5 + 4.5 is shown below. The equation for this expression is 2.5 + 4.5 = 7. This number line model illustrates this expression by starting at the number 2.5 and then adding 4.5 to it, which results in the number 7 being plotted at the end of the line. This is represented by the arrow extending from 2.5 to 7. Starting at 2.5, the arrow first passes through 3, then 4, then 5, then 6, before finally reaching 7. This is the result of adding 4.5 to 2.5, which is shown on the number line model.The expression 2.5 + 4.5 can also be written mathematically as 2.5 + 4.5 = 7. This equation is read as "2.5 plus 4.5 equals 7," and it is a statement that the sum of 2.5 and 4.5 is equal to 7. The number line model of this expression illustrates this mathematical equation by showing how 2.5 plus 4.5 equals 7. The number line model begins at 2.5 and then adds 4.5 to it, resulting in the number 7 being plotted at the end of the line.
|-----|-----|-----|-----|-----|-----|
0 1 2 3 4 5 6
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Which number line model represents the expression 2.5 + 4.5?
9, 15, 3√35 as a classified triangle
A triangle with sides lengths 9, 15, and 3√35 would be classified as a scalene triangle.
What are the types of triangle?In Geometry, there are five (5) major types of triangle based on the length of their sides (side lengths) and angles, and these include the following;
Equilateral triangleScalene triangleIsosceles triangleObtuse triangleRight-angled triangleWhat is a scalene angle?In Mathematics and Geometry, a scalene triangle can be defined as a type of triangle that has all of its three (3) sides and interior angles different in length and size respectively.
Since the given side lengths 9, 15, and 3√35 units are all different, we can logically deduce that they would form a scalene triangle.
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A company's circular logo, printed on a poster, has a radius of 1.25 feet and an area of about 5 square feet. The logo is being scaled up so it can be painted on a billboard. The equation k = √ A/5
shows the scale factor, k, that is needed to achieve an area A. A graph
of the equation is shown.
The company has 240 square feet worth of paint. If they want to use all their paint,
approximately what scale factor should they apply to the logo, and what will the dilated
logo's radius be?
The radius οf the dilated lοgο will be apprοximately 8.66 feet.
What is the scale factοr?The scale factοr is a number that represents the ratiο οf the cοrrespοnding side lengths οf twο similar figures. It can be used tο enlarge οr reduce the size οf a figure by a certain percentage οr factοr.
The area οf the lοgο is given as 5 square feet, and the radius οf the lοgο is 1.25 feet.
Therefοre, we can find the scale factοr as fοllοws:
k = √(A/5) = √(240/5) = √48 ≈ 6.93
Sο the scale factοr is apprοximately 6.93. Tο find the radius οf the dilated lοgο, we multiply the οriginal radius by the scale factοr:
r' = kr = 6.93(1.25) = 8.66
Hence, the radius οf the dilated lοgο will be apprοximately 8.66 feet.
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Function g is the result of these transformations on the parent sine function: vertical stretch by a factor of 3 horizontal shift left units vertical shift down 4 units Substitute the values of A, C, and D to complete the equation modeling function g
The equation modeling function g after the given transformations on the parent sine function is:
g of (x) = A x sine(C(x minus D))+k
where A is the vertical stretch factor, C is the reciprocal of the horizontal stretch factor, D is the horizontal shift, and k is the vertical shift.
Substituting the given values, we get:
g of (x) = 3*sine((1/1)(x+1))+(-4)
Simplifying further, we get:
g of (x) = 3*sine of (x+1)-4
Therefore, the equation modeling function g is g of (x) = 3*sine(x+1)-4 after the given transformations on the parent sine function.
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A rectangular prism. A is an edge, B is a vertex, and C is a face.
Label the highlighted parts of this prism.
A is
.
B is
.
C is
The volume of the rectangular prism can be calculated by using the formula V = lwh, where l is the length, w is the width, and h is the height.
The volume of a rectangular prism can be calculated by the formula V = lwh, where l is the length, w is the width, and h is the height. To calculate the volume of a rectangular prism, first measure the length, width, and height of the prism. Then, plug these measurements into the formula V = lwh and solve for V.
For example, if the length of the prism is 6 cm, the width is 5 cm, and the height is 4 cm, the volume can be calculated by plugging these values into the formula. V = 6 x 5 x 4 = 120 cm3. This means that the volume of this rectangular prism is 120 cm3.
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Complete question:
What are the labels for the highlighted parts of a rectangular prism: A, B, and C?
Answer:
A. is an edge
B. a vertex
C. a face
Step-by-step explanation:
I have this same question now and got this. If you need more proof then look at attachment.
Base on the given data uploaded, 1. Will you conclude that people can bargain price down when purchasing a house at 5% level of significance? 2. Will you conclude that the 3-bedroom houses is cheaper than 4-bedroom houses?
To know whether people can bargain the price down when purchasing a house at a 5% level of significance, we need to put a hypothesis test. The null hypothesis would be that people cannot bargain the price down
To determine whether 3-bedroom houses are cheaper than 4-bedroom houses, we would again give out a hypothesis test. The null hypothesis would be that there is no difference in price between 3-bedroom and 4-bedroom houses.
but the other hypothesis would be that 3-bedroom houses are cheaper than 4-bedroom houses. If the p-value is less than 0.05, we can reject the null hypothesis and say that 3-bedroom houses are more cheaper than 4-bedroom houses.
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