An equivalent expression of x² - 8x + 5 is (x - 4)² - 11
To convert this quadratic expression x² - 8x + 5 into the form (x - a)² - b we will use completing the square method.
Comparing expression x² - 8x + 5 with ax² + bx + c we get,
a = 1, b = -8 and c = 5
First we find the value of the expression (b/2a)² is:
(b/2a)²
= [-8/(2 × 1)]²
= (-8/2)²
= (-4)²
= 16
Now, we add and subtract the value of the term (b/2a)² in the expression x² - 8x + 5
So the expression x² - 8x + 5 becomes,
x² - 8x + 5
= x² - 8x + 5 + 16 - 16
= x² - 8x + 16 + 5 - 16 ......(commutative property of addition)
= (x - 4)² - 11 ......(since (x - 4)² = x² - 8x + 16)
Therefore, the required expression is: (x - 4)² - 11
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1 plus the product of 2 and m
Answer:
1+(2×m)
Step-by-step explanation:
We can break the problem down and find the keywords.
1 plus the product of 2 and m
plus=+
product=×
1+(2×m)
What does it mean when it says solve a system algebraically
Answer:
The system of equations are solved by eliminating a variable and solving for the remaining variable. Add the two equations together to eliminate the y, then solve for x.
why can i not type anything
now I can but pleas read the image and elp
Answer:
Step-by-step explanation: have u tried turning off and back on again
gianna has $760 to spend at a bicycle store for some new gear and biking outfits.assume all prices listed include tax she buys a new bicycle for $356.46 she buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72 she plans to spend some of all of the money she has left to buy new biking outfits for $45.35 each
Answer:
she can buy 2 outfits
Step-by-step explanation:
i grow 2 cupcakes every 8 hours for 24 hours
how many cupcakes grow?
At the end of 24 hours, 48 cupcakes will have grown. Every 8 hours, two cupcakes are grown, so after 24 hours, 24 sets of two cupcakes have been grown. Therefore, 48 cupcakes have grown.
At the end of 24 hours, 48 cupcakes will have grown. This is because every 8 hours, two cupcakes are grown. After 24 hours, 24 sets of two cupcakes have been grown. This means that in the 24 hours, two cupcakes were grown a total of 24 times. When this total is multiplied by two, it results in 48 cupcakes being grown. Therefore, after 24 hours, 48 cupcakes have grown. It is important to note that this is only the number of cupcakes that have grown in the 24 hour period, and not the total number of cupcakes. This number includes any cupcakes that were already present at the beginning of the 24 hour period, so the total number of cupcakes at the end of the 24 hour period could be higher than 48.
1. Calculate the number of sets of cupcakes grown in 24 hours: 24 hours divided by 8 hours = 3 sets
2. Calculate the number of cupcakes grown in 24 hours: 3 sets multiplied by 2 cupcakes = 6 cupcakes
3. Calculate the total number of cupcakes grown in 24 hours: 6 cupcakes multiplied by 4 sets = 24 cupcakes
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The tables show the number of necklaces made and the number of beads used. Which table shows a proportional relationship?
Select one:
Number of Necklaces 2 4 6 8
Number of Beads 20 40 60 80
Number of Necklaces 2 4 6 8
Number of Beads 10 15 20 25
Number of Necklaces 2 4 6 8
Number of Beads 14 21 28 35
Number of Necklaces 2 4 6 8
Number of Beads 15 20 25 30
HELP ME!!!!!!
The table shows a proportional relationship is:
Number of Necklaces 2 4 6 8
Number of Beads 20 40 60 80
As per the data given:
The tables show the number of necklaces made and the number of beads used.
Number of Necklaces 2 4 6 8
Number of Beads 20 40 60 80
From the table:
2 : 20 = 1 : 10
4 : 40 = 1 : 10
6 : 60 = 1 : 10
8 : 80 = 1 : 10
As there is a common ratio between each value there will be a proportional relationship
Number of Necklaces 2 4 6 8
Number of Beads 10 15 20 25
From the table:
2 : 10 = 1 : 5
4 : 15
6 : 20 = 3 : 10
8 : 25
As there is no common ratio between each value there will not be any proportional relationship
Number of Necklaces 2 4 6 8
Number of Beads 14 21 28 35
From the table:
2 : 14 = 1 : 7
4 : 21
6 : 28 = 3 : 14
8 : 35
As there is no common ratio between each value there will not be any proportional relationship
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Find the period, the equation of the midline, and amplitude of the function y = 6 sin 4x.
The period of the function is 1.57 s.
The amplitude of the function is 6.
The equation of the midline, y = 6 sin 4x + 0.
What is the period and amplitude of the sine function?
The general form of a sinusoidal function is y = A sin(Bx - C) + D,
where:
A is the amplitudeB determines the period, as T = 2π/BC is the phase shift (how much the graph is shifted horizontally)D is the vertical shift (how much the graph is shifted vertically)For the given function y = 6 sin 4x, we can see that:
A = 6 (the amplitude is the absolute value of the coefficient of the sine function)
B = 4 (the coefficient of x inside the sine function determines the period)
C = 0 (there is no horizontal shift)
D = 0 (there is no vertical shift, so the midline is the x-axis)
Therefore, the period T is given by:
T = 2π/B = 2π/4 = π/2 = 1.57 s
The midline is the x-axis, so its equation is y = 0.
The amplitude is A = 6.
Therefore, we can write the equation of the function in the general form as:
y = 6 sin 4x + 0
or
y = 6 sin(4x)
Note that since the midline is the x-axis and there is no vertical shift, the sine function will oscillate between -6 and 6.
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A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20 pounds of phosphoric acid, 30 pounds of nitrogen, and 5 pounds of potash. Each cubic yard of mix B contains 10 pounds of phosphoric acid,30 pounds of nitrogen, and 10 pounds of potash. The minimum monthly requirements are 400 pounds of phosphoric acid,960 pounds of nitrogen, and 210 pounds of potash. If mix A costs $25 per cubic yard and mix B costs $35 per cubic yard, how many cubic yards of each mix should the farmer blend to meet the minimum monthly requirements at a minimum cost? What is this cost? If mix A costs $25 per cubic yard and mix B costs $35 per cubic yard, the farmer should blend_____ yd3 of mix A and_____ yd3 of mix B to meet the minimum monthly requirements at a minimum cost. the cost is $_____
The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.
Let X be the amount of mix A (in pounds), and Y be the amount of mix B.
The constraints are
20X + 10Y >= 400
10X + 30Y >= 960
5X + 10Y >= 210
X >= 0, Y >= 10.
The objective function to minimize is F(X, Y) = 20X+40Y.
In the equivalent form, the constraints are
2X + 1Y >= 40
X+ Y >= 33
X+2Y >= 42
The feasibility area is the infinite area in the first quadrant which lies ABOVE each of the following straight lines :
A red (which represents the constraint (1'));
The green (which represents the constraint (2')),
A blue (which represents the constraint (3')).
Plot 2X + 1Y = 40 (const. (1'), red);
X+Y = 33 (const. (2'), green)
X+2Y = 42 (const. (3'), blue)
The four corner points of the area are:
P1 = (0,40), P2 = (7,26), P3 = (24,9), P4 = (42,0)
As per the Linear Programming method, we can calculate and compare the values at these 4 points.
These values of P1, P2, P3,P4 are:
P1: F(0,40) = 0 + 40*40 = 1600
P2: F(7,26) = 20*7+40*26 = 1180
P3: F(24,9) = 20*24+40*9 = 840
P4: F(42,0) = 20*42+0 = 840.
By comparing the numbers, any value of (X, Y) that lies on the segment [P3, P4] satisfies the minimum requirements.
The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.
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An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 8.
Event B: The sum is an even number.
Write your answers as fractions.
Answer:
Step-by-step explanation:
There are 6 possible outcomes for each of the two rolls, so there are 6 x 6 = 36 possible outcomes for the sum of two rolls.
Event A: The sum is greater than 8.
There are five possible ways to achieve a sum greater than 8: (3, 6), (4, 5), (4, 6), (5, 4), and (6, 3). Each of these outcomes has a probability of 1/36. Therefore, the probability of event A is:
P(A) = 5/36
Event B: The sum is an even number.
There are three possible ways to achieve an even sum: (1, 1), (2, 2), and (3, 3). Each of these outcomes has a probability of 1/36. There are also three possible ways to achieve a sum of 4: (1, 3), (2, 2), and (3, 1). Each of these outcomes has a probability of 1/36. Similarly, there are three possible ways to achieve a sum of 6, 8, 10, and 12. Therefore, the probability of event B is:
P(B) = (3 + 3 + 3 + 3 + 3 + 3)/36
P(B) = 18/36
P(B) = 1/2
Therefore, the probability of event A is 5/36 and the probability of event B is 1/2.
Gabriel invested $23,000 in an account paying an interest rate of 11% compounded daily. Ava invested $23,000 in an account paying an interest rate of 0% compounded continuously. After 8 years, how much more money would Gabriel have in his account than Ava, to the nearest dollar?
Gabriel would have $45,985.67 more than Ava in his account. This is because Gabriel's account is compounded daily, meaning that his interest would be compounded 365 times a year, while Ava's account is compounded continuously,
What is compounded ?Compounding is the process of combining two or more elements to create a new, more complex product. In finance, compounding refers to the interest earned on an investment that is reinvested and earns additional interest. This cycle continues, allowing the principal to grow exponentially over time. The effective rate of return is greater than the stated interest rate.
The calculation for Gabriel's account is: 23,000 * (1.11^(365*8)) = $69,985.67. The calculation for Ava's account is: 23,000 * e^(0*8) = $24,000. The difference between the two is $45,985.67.
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Answer:997
Step-by-step explanation:
1059 divided by 2.2, please show work
A temple has 14 cylindrical pillars made of concrete. If the radius of base of each pillar is 20 cm and height is 5 m,how much concrete is required to make the pillars?Find it
The volume of the 14 cylindrical pillars made of concrete is 8.8 m³
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The volume of a cylinder is:
Volume = π * radius² * height
A temple has 14 cylindrical pillars made of concrete. If the radius of base of each pillar is 20 cm and height is 5 m.
Radius = 20 cm = 0.2 m
Volume of each cylindrical pillar = π * 0.2² * 5 = 0.628 m³
Volume of 14 cylindrical pillar = 14 * 0.628 m³ = 8.8 m³
The volume of the pillars is 8.8 m³
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Rocks are sometimes used along coasts
to prevent erosion. If a rock needs to
weigh 2,000 lb in order not to be shifted by
waves, how big (what volume) does it need
to be? You are using basalt, which has a
typical density of 3200 lb/in³.
Volume =
If a rock needs to weigh 2,000 lb in order not to be shifted by waves, the volume of this basalt rock is equal to 0.625 in³.
What is density?In Science, the density of a chemical substance such as lead can be calculated by using this formula:
Density = M/V
Where:
M represents the mass of a chemical substance or physical object.V represents the volume of a physical substance or object.Making volume the subject of formula, we have the following:
Volume = Mass/Density
Volume = 2,000/3,200
Volume = 0.625 in³.
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What is the measurement of
what is the measurement of
IMAGE BELOW PEASE HELP ASAP
The angles m∠w and m∠y are supplementary angles and their measures are 50° and 130° respectively.
How to evaluate for the unknown anglesIf two angles add up to 180°, they are considered supplementary angles, we can observe that the positions of the angles formed by the transversal cutting the parallel lines makes the two angles on a straight line which are supplementary so;
4x + 6 + 12x - 2 = 180
16x + 4 = 180°
16x = 180 - 4 {subtract 4 from both sides}
16x = 176
x = 176/16 {divide through by 16}
x = 11.
m∠w = 4(11) + 6 = 50°
m∠y = 12(11) - 2 = 130°
Therefore, the supplementary angles m∠w and m∠y have their measures as 50° and 130° respectively.
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Use the equation to answer the question.
-(t+2) = -31 +23
What value of t makes the equation true? Enter the answer in the box.
Answer:
t = 6
Step-by-step explanation:
-(t+2) = -31 +23
Solve for t.
Combine like terms on the right.
-(t+2) = -8
Divide each side by -1.
t+2 = 8
Subtract 2 from each side.
t+2-2 = 8-2
t = 6
Point A of a triangle ABC is at (3,2). If triangle ABC is reflected about the x-axis, what are the new coordinates of A?
The new coordinates of A would be (3, -2)
Answer:
A prime = (3,-2)
x=3
y=-2
c. How does the estimated value compare to the actual value
from the table when x is 2.3?
d. How does the estimated value compare to the actual value
from the table when x is 3?
(c) When x is 2.3, the predicted value is 0.02 less than the actual value first from database (d). When x is 3 and the predicted value is compared to the actual figure from the table, the residual is -1.27.
What would be an estimate?For instance, rounding these values with two decimal places to one nearest tenth (3.4 + 5.5) would result in an approximate reply of 8.9. The estimated result would be 9, but they might potentially be increased to the next full number (3 + 6). The correct response is 8.91.
(c). Nearly 6.2 Minus 6.18 = 0.02 separates the projected result from the actual value. As a result, there is hardly any change. The residual is thus 0.02
(d). Y Equals 4.47 whenever x = 3 because 2.45 × 3 + 11.82. Since the true value is 3.2 and the anticipated value is 4.47, the differences between the two is 1.27. The residual is thus 1.27.
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Simplify 3sin²θ−3.
simplify
Answer:
- 3cos²Θ
Step-by-step explanation:
using the identity
sin²Θ + cos²Θ = 1 , then
sin²Θ = 1 - cos²Θ
given
3sin²Θ - 3
= 3(1 - cos²Θ) - 3
= 3 - 3cos²Θ - 3
= - 3cos²Θ
What is the volume of the shape below?
A circle is drawn. Two points are marked outside the circle such that only 3 tangents can be drawn to the circle using these two points.
Which of the following is true based on the above information?
A) All 3 tangents are equal in length.
B) Both the points lie on one of the tangents.
C) The tangents and the circle have two common points in total.
D) (such a situation is not possible as with 2 points, there will be 4 tangents to the circle)
Answer:
D) (such a situation is not possible as with 2 points, there will be 4 tangents to the circle)
A maintenance worker needs to wax a restaurant floor shaped like the image shown.
If the wax cost $1.38 a square foot, how much will the wax cost to cover the floor?
(A six-sided figure. There is a horizontal base of 35 feet then another horizontal base below it of 20 feet. The longest side is to the right and is 40 feet. The top is 30 feet. There is a perpendicular from the vertex of the top to the first base of 35 that is labeled 15 feet.)
Based on the total area of the floor, the cost to cover the floor is $1569.75.
What is the area of the floor?The area of the floor is calculated as follows:
Area of floor = Area of the trapezium + Area of rectangle
Area of the trapezium = (a + b)/ * h
a = 30 - 20 ft or 10 ft
b = 35 ft
h = 15 ft
Area of the trapezium = (10 + 35)/2 * 15
Area of the trapezium = 337.5 ft²
Area of rectangle = 40 * 20
Area of rectangle = 800 ft²
Area of floor = 800 ft² + 337.5 ft² or 1137.5 ft²
The cost to cover the floor = 1137.5 * $1.38
The cost to cover the floor = $1569.75
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A. B. C. D. 1 2 Steps For Sally b = 11 For Sally m = 2(11) + 4 For Mike b = 22 4 For Mike m = 2(22+4) In which step did Mike make an error? 3 Mike's Work Step 1 Step 2 Step 3 Step 4
In Step 3, Mike made an error. He incorrectly calculated his value for m by multiplying 2 by 22 instead of 2 by (22 + 4). The correct equation should have been m = 2(22 + 4).
Which step did Mike make an error?Sally's formula for calculating b is correct:
b = 11
Sally's formula for calculating m is also correct:
m = 2(11) + 4 = 26
Mike's formula for calculating b is correct:
b = 22
However, Mike's formula for calculating m is incorrect. Instead of using the formula m = 2(b + 4), he used the formula m = 2(22 + 4), which gives him a value of 50 instead of the correct value of 50.
Therefore, Mike made a mistake in Step 3. He computed his answer for m erroneously by multiplying 2 by 22 rather than 2 by (22 + 4). The proper formula would have been m = 2(22 + 4).
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Sue has a bag of 18 sweets.
5 of the sweets are blue
7 of the sweets are red
6 of the sweets are green
Sue takes at random a sweet from the bag.
Write down the probability that Sue
(i) takes a red sweet,
(ii) does not take a green sweet
(ii) takes a yellow sweet
Answer:
(i) 38.9%
(ii) 33.3%
(iii) 0%
Step-by-step explanation:
The total number of sweets is 18. The probability of picking a color can be determined by dividing the number of each color by the total:
Blue: 5/18 or 27.8%
Red: 7/17 or 38.9%
Green: 6/18 or 33.3%
Yellow: 0/18 or 00.0%
Totals 18/18 100%
Note that the question askes for Yellow sweets, but there are none.
for three years a local coffee shop rewards program offered 1 point for every whole dollar spent and an additional 5 points for each purchase suppose the shop changes the points offered to an additional 8 points for each purchase and 1 point for every whole dollar spent write two step rules f(x) and g(x) that model each rewards program
On solving the provided question, we can say that The function that can be made are f(x)= INT (x) + 5 and g(x)= INT (x) + 8
Describe function.Quantities and their variations, equations and related structures, shapes and their placements, and locations where they can be found are all included in the study of mathematics.
The relationship between a group of inputs, each of which has a related output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Every function has a domain and a codomain, often known as a scope. F is typically used to denote functions (x).
An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
The function that can be made are -
Let x = dollar spent
coffee shop rewards program offered 1 point for every whole dollar spent and an additional 5 points for each purchase
⇒ f(x)= INT (x) + 5
the shop changes the points offered to an additional 8 points for each purchase and 1 point for every whole dollar spent
⇒ g(x)= INT (x) + 8
The graph of g will be a vertical translation and 3 units up from the graph of f.
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2.discuss the differences between divergence and curl of function. can the divergence and curl be defined for a scalar function?
Divergence and curl are two important concepts in vector calculus. They are used to describe the behaviour of vector fields, which are functions that assign a vector to each point in space.
Divergence is a scalar function that describes the extent to which a vector field is spreading or contracting at a given point. If the vector field is spreading, the divergence at that point is positive; if it is contracting, the divergence is negative.
If the vector field is unchanged in size, the divergence is zero. The formula for the divergence of a vector field is given by the dot product of the gradient of the field with the unit normal vector at a point.
Curl, on the other hand, is a vector function that describes the rotational aspect of a vector field. It is defined as the cross-product of the del operator and the field. Curl measures the rate at which the vectors in a field are rotating about a point. If the curl is zero, the field is said to be irrotational. If the curl is non-zero, the field is said to be rotational.
Divergence and curl cannot be defined for a scalar function because a scalar function assigns a single scalar value to each point in space, while divergence and curl describe the behaviour of vector fields.
A scalar function has no direction or rotational component, so there is no way to describe the spreading or contracting behaviour or the rotational behaviour of the function.
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Please help I’m so bad at math I don’t understand
Answer:
f(-4) = -18
Step-by-step explanation:
So we have f(x) and we have f(-4). The X is where the -4 is so that means x = -4.
Since we know that, we plug it into the equation. Everywhere we see an X
So instead of 5(x) + 2, it will be 5(-4)+2.
5 times -4 is -20, which makes it -20 + 2
-20 + 2 = -18. Giving us our answer
Answer:
[tex]-18[/tex]
Step-by-step explanation:
f is a function of x. f depends on x. For every value of x, a certain value of f(x) is obtained.
This question requires us to determine the value of f(x) for x = [tex]-4[/tex]:
Substitute x = [tex]-4[/tex] into the provided function:
[tex]f(-4) = 5(-4) +2[/tex]
= [tex]-20 + 2[/tex]
= [tex]-18[/tex]
Amanda uses 1/3 of a cup of milk each time she makes a batch of pancakes. How many batches can she make if she only has 11/12 of a cup of milk left?
What are the leading coefficient and degree of the polynomial?
18 + 9w^2 - w^3 - w
Answer:
The leading coefficient is -1. The degree of the polynomial is cubic.
Step-by-step explanation:
The leading coefficient is the number in front of the variable showcasing the biggest exponent. The degree of the polynomial is considered by looking at the biggest exponent, and identifying which one it is. In this case, it's a cubic polynomial.
Part A
Create a random triangle, ΔABC. Measure and record its angles.
The triangle that's created has angles of 90°, 45° and 45°.
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
The triangle is attached.
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Which figure has the same area as the parallelogram? pls answer i need this tonight. 32.2 is at the bottom and 20.5 is on the left side
The area of the parallelogram that has a width of 32.2 units and a height of 12.6 units will be 405.72 square units.
What is the area of the parallelogram?Let H be the height and W be the width of the parallelogram. Then the area of the parallelogram will be given as,
Area of the parallelogram = H × W square units
The width of the parallelogram is 32.2 units and the height of the parallelogram is 12.6 units. Then the area of the parallelogram is given as,
A = 32.2 x 12.6
A = 405.72 square units
The area of the parallelogram that has a width of 32.2 units and a height of 12.6 units will be 405.72 square units.
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