The correct statements regarding the quadratic function x² - 6x + 2 are given as follows:
The graph of the quadratic equation has a minimum value.The solutions are: x = 0.35 and x = 5.64.The extreme value is at the point (3,-7).How to analyze the quadratic function?The quadratic function in the context of this problem is given as follows:
y = x² - 6x + 2.
The coefficients are given as follows:
a = 1, b = -6, c = 2.
As a > 0, the function is a concave up quadratic function, hence it has a minimum value.
Using a calculator with the given coefficients, we have that:
The solutions are: x = 0.35 and x = 5.64.The vertex is: (3, -7).Missing InformationThe function is:
y = x² - 6x + 2.
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Find the area of the circle. Use pie = 3.14.
A calculator displays 6E6. How do you write 6E6 in standard form
6E6 is a number written in scientific notation, which means that it represents 6 times 10 raised to the power of 6. To write this number in standard form, we need to evaluate the exponent and write the number in expanded form.
6E6 = 6 x 10^6
Evaluating the exponent 6 means multiplying 6 by 10 six times:
6 x 10^6 = 6 x 10 x 10 x 10 x 10 x 10 x 10
Simplifying the expression, we get:
6 x 10^6 = 6,000,000
Therefore, 6E6 in standard form is 6,000,000.
can someone help me with this??
10. At an exotic food store, a sign states that three pounds of
octopus costs $24. The owner tells you that the pricing of octopus
is a linear function based upon the weight in pounds.
a) Write a linear function to model the relationship between the
cost, c, of octopus and the weight, w, in pounds.
B) Explain the meaning of the slope of your equation as it relates to this problem.
The linear equation is solved and slope is m = (24 - b) / 3 = 8
Given data ,
a)
To write a linear function that models the relationship between the cost, c, of octopus and the weight, w, in pounds, we need to determine the equation of a line in slope-intercept form, y = mx + b, where y represents the cost of octopus (c) and x represents the weight in pounds (w).
We are given that three pounds of octopus costs $24. This gives us a point on the line, which is (3, 24). Using this point, we can find the slope (m) of the line.
Let's use the slope formula:
m = (y2 - y1) / (x2 - x1)
Taking (3, 24) as our first point, and choosing another arbitrary point on the line, let's say (0, b), we can substitute the coordinates into the slope formula:
m = (24 - b) / (3 - 0)
Since the slope is constant for the linear function, we can set this expression equal to m:
m = (24 - b) / 3
Now, we have the slope (m) in terms of b. To find the value of b, we can substitute the coordinates of the known point (3, 24) into the slope-intercept form:
24 = m * 3 + b
Substituting the expression for m:
24 = [(24 - b) / 3] * 3 + b
Simplifying:
24 = 24 - b + b
24 = 24
Since the equation is true for any value of b, we can choose any value for b. Let's choose b = 0 for simplicity.
Plugging in the values of m = (24 - b) / 3 and b = 0, we have:
m = (24 - 0) / 3
m = 24 / 3
m = 8
Therefore, the slope of the linear function is 8
b)
The meaning of the slope in this context is that for each additional pound of octopus purchased, the cost increases by $8. This means that the cost of octopus is increasing at a constant rate of $8 per pound. The positive slope indicates that as the weight of the octopus increases, the cost also increases.
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The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Answer:
The range of the function is all real numbers less than or equal to 9.
Step-by-step explanation:
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
have a great day and thx for your inquiry :)
George has opened a new store and he is monitoring its success closely.
He has found that this store’s revenue each month can be modeled by r(x)=x2+6x+10 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars.
He has also found that his expenses each month can be modeled by c(x)=x2−4x+5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars.
What does (r−c)(4) mean about George's new store?
Responses
The new store will have a profit of $2300 after its fourth month in business.
The new store will have a profit of $2300 after its fourth month in business.
The new store will sell 4500 items in its fourth month in business.
The new store will sell 4500 items in its fourth month in business.
The new store will sell 2300 items in its fourth month in business.
The new store will sell 2300 items in its fourth month in business.
The new store will have a profit of $4500 after its fourth month in business.
Fourth month in business, George's new store will have a profit of $4500. The option "The new store will have a profit of $4500 after its fourth month in business" is the correct response.
To determine the meaning of (r - c)(4) for George's new store, we need to evaluate the expression (r - c) at x = 4.
Given that r(x) represents the store's revenue and c(x) represents the store's expenses, (r - c)(4) represents the difference between the revenue and expenses of the store after four months.
Substituting x = 4 into the expressions for revenue and expenses, we get:
r(4) = (4)^2 + 6(4) + 10 = 16 + 24 + 10 = 50
c(4) = (4)^2 - 4(4) + 5 = 16 - 16 + 5 = 5
Thus, (r - c)(4) = r(4) - c(4) = 50 - 5 = 45.
Therefore, (r - c)(4) means that after its fourth month in business, George's new store will have a profit of $4500 (since r(x) and c(x) are measured in hundreds of dollars).
The option "The new store will have a profit of $4500 after its fourth month in business" is the correct response.
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help pls, will give brainliest
Find the perimeter of the figure. Simplify your answer.
The perimeter of the figure is 9k² + 13k - 8
Finding the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
The figure
The perimeter of the figure is the sum of the side lengths
Using the above as a guide, we have the following:
Perimeter = -k + k² - 2 + 2k² + 5k + 2 + k² - 2 - k + 5k² + 10k - 6
When the expression is evaluated, we have
Perimeter = 9k² + 13k - 8
Hence, the perimeter of the figure is 9k² + 13k - 8
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What is the image of (-8, 6) after a reflection over the line y = -x?
The image of the point after a reflection over the line y = -x is (-6, 8)
Calculating the image of the point after a reflection over the line y = -x?From the question, we have the following parameters that can be used in our computation:
Point = (-8, 6)
Transformation rule
A reflection over the line y = -x
The rule of a reflection over the line y = -x is
(x, y) = (-y, -x)
Using the above as a guide, we have the following:
Image = (-6, 8)
Hence the image of the point after a reflection over the line y = -x is (-6, 8)
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A central angle in a circle with a diameter of 9 meters measures radians. 7/18 Find the length
of the arc intercepted by this angle.
To find the length of an arc intercepted by a central angle in a circle, we need to use the formula:
Arc Length = (Angle in radians) * (Radius)
In this case, the circle has a diameter of 9 meters, which means the radius is half of the diameter, so the radius is 4.5 meters.
The central angle measures radians, which we need to convert to radians. To convert a fraction to radians, we divide the numerator by the denominator and multiply by π (pi).
Radians = (7/18) * π
Now we can calculate the length of the arc:
Arc Length = (7/18) * π * 4.5
Simplifying this expression, we can calculate the approximate length of the arc.
It's important to note that the length of the arc is proportional to the measure of the central angle and the radius of the circle. The larger the central angle or the radius, the longer the arc.
In this case, the length of the arc will be determined by the specific value of the central angle in radians and the radius of the circle.
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simplify. (write each expression without using the absolute value symbol.)
1.|x+3| if x > 5
2. |x+3| if x>2
1.
If x > 5, then the absolute value on |x+3| isn't actually doing anything.
|x+3| = x+3 (without the absolute value) since x+3 is positive for x > 5.
2.
If x > 2, then the absolute value on |x+3| again isn't actually doing anything.
|x+3| = x+3 (without the absolute value) since x+3 is positive for x > 2.
You'd have to be dealing with x-values less than -3 for the absolute value to impact the calculation. Only for x < -3 would "x+3" not be positive and only then does the absolute value change the result.
Determine the value of f (2) for the function. Please help!
The value of f (2) for the function is,
⇒ f (2) = undefined
We have to given that;
The function is defined as;
⇒ f (x) = { x³ + 18x² + 99x + 162 ; x ≤ - 3
= { (3x - 6) / (x³ - 7x + 6) ; - 3 < x ≤ 2
= { √(x² - 4) ; x > 2
Hence, We can see that;
At x = 2;
Function is defined as;
⇒ f (x) = (3x - 6) / (x³ - 7x + 6)
Plug x = 2;
⇒ f (2) = (3 × 2 - 6) / (2³ - 7×2 + 6)
⇒ f (2) = (6 - 6) / (8 - 14 + 6)
⇒ f (2) = 0 / 0
⇒ f (2) = undefined
Thus, The value of f (2) for the function is,
⇒ f (2) = undefined
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The total mass of a trolley and some watermelons is 27 kg.
The total mass of the same trolley and some mangoes is 11 kg.
The mass of the watermelons was thrice the mass of the mangoes.
Answer:
Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.
Step-by-step explanation:
Let's assign variables to the masses involved to solve the problem systematically.
Let's say:
Mass of the trolley = T kg
Mass of the mangoes = M kg
Mass of the watermelons = W kg
According to the given information:
The total mass of the trolley and mangoes is 11 kg:
T + M = 11 -- Equation (1)
The mass of the watermelons is three times the mass of the mangoes:
W = 3M -- Equation (2)
Now, we can use these equations to find the values of T, M, and W.
From Equation (2), we can express M in terms of W:
M = W / 3
Substitute this value of M into Equation (1):
T + W / 3 = 11
Multiply through by 3 to eliminate the fraction:
3T + W = 33 -- Equation (3)
Now, we have a system of two equations (Equation 2 and Equation 3) with two unknowns (T and W). We can solve this system to find the values.
Since we don't have a specific value for any variable, we can express the solution in terms of the variables.
Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.
Write the standard equation of the circle with center (-5,12) that passes through the point (-9,15)
The standard equation of the circle with center (-5,12) that passes through the point (-9,15) is (x + 5 )² + (y - 12)² = 25.
What is the equation of the circle?The standard form equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)² = r²
Given that; the center is (-5, 12) and a point on the circle is (-9, 15).
First, we determine the radius, we can use the distance formula between the center and the point on the circle:
[tex]r = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \\\\r = \sqrt{(-9 - (-5))^2+(15 - 12)^2} \\\\r = \sqrt{(-9 + 5)^2+(15 - 12)^2} \\\\r = \sqrt{(-4)^2+(3)^2} \\\\r = \sqrt{16+9} \\\\r = \sqrt{25} \\\\r = 5[/tex]
Now, center: (-5, 12)
h = -5
k = 12
and r = 5
Plug these into the equation above:
(x - h)² + (y - k)² = r²
(x - (-5) )² + (y - 12)² = 5²
Simplify
(x + 5 )² + (y - 12)² = 25
Therefore, the equation of the circle is (x + 5 )² + (y - 12)² = 25.
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The slope of the line parallel to the line y = 10 - 8x.
A. 10
B. -8x
C. -8
D. 8
Answer:
The correct answer is C.
Step-by-step explanation:
you use y = mx +b
Craig has a building block in the shape of a rectangular pyramid. A net of which is shown below.
If a measures 16 cm, b measures 8 cm, and d measures 17 cm, what is the surface area of the rectangular pyramid?
A terrain in the form of an isosceles trapezoid has the measurements that appear in the figure:
The owner of the land placed a sign in which she wishes to specify the area of the land. Knowing that the height of the trapezoid is 8.7 m, I help complete the sign.
According to the information, we can infer that the sign should read: "Area of land: 178.35 square meters."
How to find the area of the trapezoid?To find the area of the trapezoid, we need to use the formula:
Area = (b1 + b2) / 2 * hwhere,
b1 and b2 = lengths of the parallel basesh = height of the trapezoidFrom the figure, we can see that:
b1 = 25 mb2 = 16 mSubstituting these values into the formula, we get:
Area = (25 + 16) / 2 * 8.7Area = 20.5 * 8.7Area = 178.35 square metersLearn more about figures in: https://brainly.com/question/30740690
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3. Create your own piecewise function with at least two functions. Explain, using complete
sentences, the steps for graphing the function. Graph the function by hand or using a
graphing software of your choice (remember to submit the graph).
Mary gave her brother 1/4 of her plums and her sister 1/3. Mary remained with 20 plums. how many plums Mary had before sharing?
What is the surface area of a cone that has a height of 10 centimeters
and has a diameter of 5 centimeters?
Answer:
266.9cm
Step-by-step explanation:
there's no explanation.
Answer:
52.334
Step-by-step explanation:
3.14[phi] x 5 cm =15.70 x 10 [height] = 157.0 x 1/3 = 52.334
cone = phi x d x height x1/3
this is the volume btw
Find the area of each paralleogram or rhombus
The area of the given parallelogram is 12 yd².
Given that a parallelogram of base 2 yds and height 6 yds,
We need to find the area of the parallelogram,
A parallelogram is a quadrilateral in which the opposite sides are parallel and equal. Parallelograms are classified into three main types: square, rectangle, and rhombus, and each of them has its own unique properties.
A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.
So, the area of a parallelogram = base × height
so the area of the given parallelogram = 6 × 2 = 12 yd²
Hence the area of the given parallelogram is 12 yd².
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Help please I have to answer these questions using the graph.
The values of the points on the graph of the concentration of the drug in the bloodstream, indicates;
1 a. 24 mg/L
b. Increases; [0, 2]
Decreasing; [2, 20
c. The drug is at the maximum concentration at t = 2 hours
The maximum concentration is 64 mg/L
d. 8 hours
e. The concentration after 1 week is minute
The concentration after 1 month is more reduced than the concentration after 1 week.
f. The concentration of the drug for the first 20 hours increases in the first 2 hours, then decreases and approaches the x-axis as the x-value increases.
What is the graph of a function?A graph is a visual display of the ordered pair of a function on the coordinate plane.
1. The graph in the question specifies the concentration of the drug in the bloodstream after t hours in mg/L
a. The graph indicates that the concentration after 8 hours is 24 mg/L
b. The interval over which the concentration increases is; [0, 2)
The interval over which the concentration decreases is; (2, 20]
c. The graph indicates that the drug is at its maximum concentration when the time t = 2 hours
The maximum concentration, based on the peak of the graph is 64 mg/L
d. The concentration of the drug is 16 mg/L at t = 10 hours, therefore, the time it takes the concentration to decrease to 16 mg/L from the peak therefore is; 10 hours - 2 hours = 8 hours
e. The shape of the graph indicates that the concentration of the drug in the bloodstream continuously decreases after the first two hours, therefore, the concentration after a week will be approximately 0
The concentration after 1 month will trace amounts
f. The concentration of the drug in the bloodstream over the first 20 hours indicates that concentration increases within the first 2 hours, and decreases rapidly in the next 8 hours, such that after 20 hours, the concentration in the blood is less than 4 mg/L
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Given A(2, 4), what are the coordinates of A′ for the dilation with scale factor 1.5 and center at the origin?
The coordinates of A′ for the dilation with a scale factor of 1.5 and center at the origin are (3, 6).
To find the coordinates of A′, we need to apply the dilation formula:
A′ = (1.5)(A - O) + O
Where O is the center of dilation, which in this case is the origin (0, 0).
Substituting the values we have:
A′ = (1.5)(2, 4 - 0, 0) + (0, 0)
A′ = (3, 6) + (0, 0)
A′ = (3, 6)
Therefore, the coordinates of A′ for the dilation with scale factor 1.5 and center at the origin are (3, 6).
To find the coordinates of A' for the dilation with a scale factor of 1.5 and center at the origin, follow these steps:
1. Identify the given point A(2, 4) and the scale factor 1.5.
2. The center of dilation is at the origin (0, 0).
3. Multiply the x-coordinate of point A by the scale factor: 2 * 1.5 = 3.
4. Multiply the y-coordinate of point A by the scale factor: 4 * 1.5 = 6.
5. The coordinates of A' after dilation are (3, 6).
So, the coordinates of A′ for the dilation with a scale factor of 1.5 and center at the origin are (3, 6).
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PLS HELP Triangle LMN has vertices at L(−1, 5), M(−1, 0), N(−2, 5). Determine the vertices of image L′M′N′ if the preimage is rotated 180° counterclockwise about the origin.
L′(5, 1), M′(0, 1), N′(5, 2)
L′(−1, −5), M′(−1, 0), N′(−2, −5)
L′(−5, −1), M′(0, −1), N′(−5, −2).
L′(1, −5), M′(1, 0), N′(2, −5)
The coordinates of the triangle after transformation are:
L′(1, −5), M′(1, 0), N′(2, −5)
What are the coordinates after transformation?There are different methods of transformation such as:
Translation
Rotation
Reflection
Dilation
Now, a rotation of 180 degrees counterclockwise about the origin is equivalent to the coordinate transformation given as (x, y) → ( −x, −y) . Meanwhile, a rotation of 270 degrees counterclockwise about the origin is equivalent to the coordinate transformation (x, y) → ( y, -x) .
Applying the rule for rotation of 180 degrees counterclockwise to the coordinates L(−1, 5), M(−1, 0), N(−2, 5) gives us:
L'(1, -5), M'(1, 0), N'(2, -5)
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Plan the media elements that you will use in your presentation. Think about what types of media
elements, such as charts or diagrams, could be used to support your ideas.
Provide at least three
media examples in the table below.
Media Type
Media Use
Important Idea to Communicate
Zane is in charge of equipment at Putter Around Fun Center. He opens a huge new box of golf
balls that just arrived. The golf balls are assorted colors that are mixed throughout the box.
Zane has no idea how many of each color are in the box, so he randomly picks 30 balls out of
the box. He picks 8 yellow, 3 red, 5 orange, 6 green, and 8 pink golf balls.
Based on the data, what is the probability of choosing a red golf ball?
Write your answer as a fraction.
The probability of choosing a red golf ball as a fraction would be = 1/10.
How to calculate the probability of choosing a red ball at random?To calculate the probability of choosing a red ball at random, the formula that should be used is given below.
That is;
Probability = possible outcome/sample space
Total number of yellow balls= 8
Total number of red ball= 3
Total number of orange balls = 5
Total number of green balls = 6
Total number of pink balls = 8
possible outcome = 3 balls(red)
Sample space = 8+3+5+6+8= 30 balls
Then probability= 3/30 = 1/10
Therefore, when a ball is selected at random the probability that Zane would pick a red ball out of all the golf coloured balls would be= 1/10.
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Find out Monomials and Binomials from the following algebraic expressions:
**+9x²+7x-35, ln x, - 3x3 + 2x, x, x³, √x, 18x14x + 14,7x-1, 1
Sin (x), x³-5, e*, (x + 4)², - 3n+2y + 2x + 1, √x +y, 3-x.
Monomials are algebraic expressions that consist of a single term, whereas binomials consist of two terms.A binomial is an algebraic expression that consists of two terms.
Monomials are algebraic expressions that consist of a single term, whereas binomials consist of two terms.A binomial is an algebraic expression that consists of two terms. These terms can be added or subtracted, and they may contain variables, constants, and exponents. Binomials are commonly used in algebra to represent equations, formulas, and functions.
Monomials:
- 9x²
- 7x
- ln x
- -3x³
- 2x
- x
- x³
- √x
- 18x14x
- √x
- 7x-1
- 1
- Sin (x)
- x³
- e*
- √x +y
- 3-x
Binomials:
- 18x14x + 14
- (x + 4)²
- - 3n+2y + 2x + 1
- x³-5
Here are the monomials and binomials from the given algebraic expressions:
Monomials:
- ln x
- x
- x³
- √x
- 1
- Sin(x)
- e*
- 3-x
Binomials:
- +9x²+7x-35
- -3x³ + 2x
- 18x¹⁴x + 14
- 7x-1
- x³-5
- (x + 4)²
- -3n+2y + 2x + 1
- √x + y
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For ∆RST, RS=3ft, ST=6ft, and m∠R=29°. What are m∠T and m∠S
To find the measures of angles T and S, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
m∠R + m∠S + m∠T = 180°
We know that m∠R = 29°, and we can use the Law of Cosines to find the measure of angle S:
cos(m∠S) = (6^2 + 3^2 - x^2) / (2 * 6 * 3) = 0.9167
m∠S = cos^-1(0.9167) = 23.6°
Now we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle T:
m∠T = 180° - m∠R - m∠S = 180° - 29° - 23.6° = 127.4°
Therefore, m∠T is 127.4° and m∠S is 23.6°.
mm m mm Answer:
Step-by-step explanation:
mnnmnmn
Anita has invited her friends to her birthday party. Guess the number of friends she has invited
given the following clues:
•
They are more than the number of days in September.
The sum of their digits is 10.
The difference in their digits is 2.
They are less than 5 dozen.
Heys guys...please help me out on this. Also please provide the working too.
Answer:
f(x) = x^2
f'(x) = 2x, so f'(1.8) = 2(1.8) = 3.6
B is the correct answer.
The value of the function , f'(1.8) = 3.6. option B
What is a function?A function can simply be defined as an expression, a law or a rule that is used to represent the relationship between two variables in an equation.
These variables are listed as;
Dependent variableThe independent variablesFrom the information given, we have that;
The function , f(x) is represented as x²
This is written as;
f(x) = x²
Find the derivative of the function, we get;
f'(x) = 2x
Now, substitute the value of x as 1.8 in the function, we have that;
f'(1.8) = 2(1.8)
expand the bracket, we have that;
f'(1.8) = 3.6
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Help pleaseee!! I will give brainlist
The length FE in the circle is 6 units
The arc AE has a measure of 64 degrees
Calculating the length FEFrom the question, we have the following parameters that can be used in our computation:
The circle
Given that the lengths from the center to either chords are equal
This means that
FE = 6 units
Calculating the measure of arc AEFor the other circle, we have
BC = 58 degrees
AB = ED
The arc AE is calculated as
AE = 180 - BC - ED
Where
AB = ED = BC = 58 degrees
So, we have
AE = 180 - 58 - 58
Evaluate
AE = 64
Hence, the arc AE is 64 degrees
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