The polynomial function with the given properties is:[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]
What do you mean by polynomial function?A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.
Since the polynomial has real coefficients and one of its zeros is complex, the complex conjugate of 4+ i, which is 4-i, must also be zero. So the three zeros of the polynomial are -1, 4+i and 4-i. To form a polynomial with these zeros, we start by writing the factors of the polynomial:
(x + 1) (x - 4 - i) (x - 4 + i)
We can simplify this expression by multiplying the factors:
[tex](x + 1) (x^2 - 8x + 17)[/tex]
Expanding this, we get:
[tex]x^3 - 7x^2+ 9x - 17[/tex]
Thus, the polynomial function with the given properties is:
[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]
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The polynomial function is p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16
What do you mean by polynomial function?A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.
If -1 is a zero of the polynomial function, then x+1 is a factor of the polynomial. Similarly, if 4+i is a zero, then 4-i is also a zero, because complex roots always occur in conjugate pairs. Therefore, (x+1) and (x - 4 - i)(x - 4 + i) = (x - 4)² + 1 are factors of the polynomial. We can then construct the polynomial function by multiplying these factors:
p(x) = A(x+1)(x - 4 - i)(x - 4 + i)
where A is a constant that we need to determine, and p(x) is the desired third-degree polynomial function.
To determine A, we can use the y-intercept given in the problem. The y-intercept is the value of p(0), so:
p(0) = A(0+1)(0 - 4 - i)(0 - 4 + i) = A(17+4i)
But we also know that p(0) = -17, so:
-17 = A(17+4i)
Solving for A:
A = -17/(17+4i) = (-17/5) + (68/5)i
Therefore, the polynomial function we seek is:
p(x) = [(-17/5) + (68/5)i](x+1)(x - 4 - i)(x - 4 + i)
Expanding the product and simplifying, we get:
p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16
This is a third-degree polynomial with only real coefficients, -1 and 4+i are two of the zeros, and the y-intercept is -17.
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Which equation is true?
An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the multiplication law of exponents for powers to each of the expressions, we have the following:
4 × n × n × n × n = 4n⁴
4 × n⁴ = 4n⁴
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A bicycle training wheel has a radius of 3 inches. The bicycle wheel has a radius of 10 inches. Approximately how much smaller, in square inches and rounded to the nearest hundredth, is the area of the training wheel than the area of the regular wheel?
The training wheel has an area approximately 286.34 square inches smaller than the regular wheel.
The area of a circle is given by the formula A = πr², where A is the area of the circle and r is the radius of the circle. Since we have the radii of both wheels, we can use this formula to find their respective areas.
The area of the training wheel is A₁ = π(3)² = 9π square inches.
The area of the regular wheel is A₂ = π(10)² = 100π square inches.
To find the difference in their areas, we can subtract A₁ from A₂:
A₂ - A₁ = 100π - 9π = 91π
So the difference in their areas is 91π square inches. To round to the nearest hundredth, we can use the approximation π ≈ 3.14:
91π ≈ 286.34 square inches
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Over what interval does f(x) = 2x
increase faster than g (X) =
¿x?
A. 1
B. x > 3
C.20
D. 1 > x > 21
If over what interval does f(x) = 2x increase faster than g (X): A. 1
What is over the interval?To determine over what interval f(x) = 2x increases faster than g(x) = x^2, we need to compare their derivatives. The derivative of f(x) is 2, which is a constant, and the derivative of g(x) is 2x. Therefore, f(x) increases at a constant rate of 2, while g(x) increases at a rate that depends on x.
To find the interval where f(x) increases faster than g(x), we need to find where the derivative of g(x) is less than 2. Setting 2x < 2 and solving for x, we get x < 1.
So, over the interval x < 1, f(x) = 2x increases faster than g(x) = x^2.
Therefore, the answer is A. 1.
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Choose the ordered pair that is a solution for this equation.
3x = 8 - y
A. (3, 1)
B. (2, 2)
C. (8, 0)
Answer:
B. (2, 2)
Step-by-step explanation:
(x, y)
3x = 8 - y
a) 3(3) = 8 - 1
9 = 8 - 1
9 = 7 False
b) 3(2) = 8 - 2
6 = 6 True
c) 3(8) = 8 - 0
24 = 8 False
1. Write a statistical question about each situation. a. vacation destinations b. books
a. Statistical question about vacation destinations: What percentage of people who traveled for vacation last year went to a beach destination?
What is a qualitative and quantitative data?Data that is descriptive but not numerical is considered qualitative data. It is frequently used to describe the qualities or traits of things, people, or occasions. Qualitative data examples include hues, textures, tastes, and perspectives.
On the other hand, quantitative data are numerical data that can be measured and statistically analysed. It is frequently used to describe numbers or amounts of different things. Measurements like height, weight, temperature, and test results are examples of quantitative data.
a. Statistical question about vacation destinations: What percentage of people who traveled for vacation last year went to a beach destination?
b. Statistical question about books: What is the average number of books read per month by individuals who report reading as a favorite hobby?
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5. Patty starts at the bottom of a Ferris wheel with a radius of 8 m. The Ferris wheel rotates so Patty is now at the top. Arlene is on a merry-go-round with a radius of 6 m. The merry-go-round moves two- thirds of the way around its axle. Who travels farther? How much farther to the nearest tenth of a metre ?
Answer is down below!
Step-by-step explanation:
This is of the form h = a + b cos ct, where: a = 40 m. This is the height of the axle of the Ferris wheel. b = -30 m. The magnitude of this number is the radius of the wheel.
A particle moves in the xy plane so that at any time
,
x=3sint
and
.y=t-4cost+1
What is the vertical component of the particle's location when it's horizontal component is 2?
Responses
y = -1.05
y = -1.05
y = -2.25
y = -2.25
y = -1.25
y = -1.25
y = 0.73
The vertical component of the particle's location, when its horizontal component is 2, is:
y = -1.25
How to solveTo find the vertical component of the particle's location when its horizontal component is 2, we need to first find the value of t when x = 2.
Given the equation:
x = 3sin(t)
Substitute x with 2:
2 = 3sin(t)
Now, isolate t by dividing both sides by 3:
sin(t) = 2/3
Take the inverse sine (arcsin) of both sides:
t = arcsin(2/3)
Now, plug the value of t back into the y equation:
y = t - 4cos(t) + 1
y = arcsin(2/3) - 4cos(arcsin(2/3)) + 1
Using a calculator to find the approximate value of y, we get:
y ≈ -1.25
Therefore, the vertical component of the particle's location when its horizontal component is 2 is:
y = -1.25
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Hannon Company makes swimsuits and sells these suits directly to retailers. Although
Hannon has a variety of suits, it does not make the All-Body suit used by highly skilled
swimmers. The market research department believes that a strong market exists for thistype of suit. The department indicates that the All-Body suit would sell for approximately $100. Given its experience, Hannon believes the All-Body suit would have the following manufacturing costs
Direct materials $ 25
Direct labor 30
Manufacturing overhead 45
Total costs $100
Instructions
(a) Assume that Hannon uses cost-plus pricing, setting the selling price 20% above its
costs. (1) What would be the price charged for the All-Body swimsuit? (2) Under what
circumstances might Hannon consider manufacturing the All-Body swimsuit given this approach?
(b) Assume that Hannon uses target costing. What is the price that Hannon would charge the retailer for the All-Body swimsuit?
(c) What is the highest acceptable manufacturing cost Hannon would be willing to incur to produce the All-Body swimsuit, if it desired a profit of $20 per unit? (Assume target costing.)
Hannon's maximum allowable production cost for the All-Body swimsuit is $80 if it wants to make a profit of $20 per unit.
Given data ,
a)
Using cost-plus pricing, the selling price is set 20% above the costs.
Selling price=Costs+(Costs x Markup)
Selling price=$100 + ($100x0.20)
Selling price=$100+$20
On simplifying the equation , we get
Selling price=$120
The price charged for the All-Body swimsuit would be$120.
Hannon might consider manufacturing the All-Body swimsuit under the cost-plus pricing approach if the market demand is strong enough to justify the selling price of $120 and if Hannon can efficiently produce and sell the swimsuit to generate profits.
(b)
Using target costing, the price charged by Hannon to the retailer is determined by subtracting the desired profit per unit from the target selling price.
Target selling price=$100 (given)
Desired profit per unit=$20 (given)
Price charged to retailer=Target selling price - Desired profit per unit
Price charged to retailer=$100-$20
On simplifying the equation , we get
Price charged to retailer=$80
The price that Hannon would charge the retailer for the All-Body swimsuit under target costing is$80.
(c)
To determine the highest acceptable manufacturing cost for the All-Body swimsuit under target costing, we subtract the desired profit per unit from the target selling price.
Target selling price=$100 (given)
Desired profit per unit=$20 (given)
Highest acceptable manufacturing cost=Target selling price-Desired profit per unit
Highest acceptable manufacturing cost=$100-$20
Highest acceptable manufacturing cost=$80
Hannon would be ready to spend up to $80 in manufacturing costs to develop the All-Body swimsuit if it wanted to make $20 each unit.
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A coordinator will select five songs from a list of 11 songs to compose in events, musical entertainment lineup. How many different lineups are possible?
There are 462 different possible lineups of 5 songs that can be composed from the given list of 11 songs.
How to determine the number of different musical entertainment ?We need to use the idea of combinations to figure out how many different lineups of musical entertainment can be made. A way to select objects from a larger set without regard to their order is called a combination.
In this problem, we have to choose five songs from an 11-song list. We would like to know how many different ways there are for us to select five songs from the eleven that are available, where the order of the songs in the lineup is irrelevant. We can use the combination formula to solve this.:
n choose k = n! / (k! * (n - k)!)
where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial, which is the product of all positive integers up to and including that number.
In this case, we have 11 songs to choose from and we want to choose 5 songs. So we can plug these values into the formula:
11 choose 5 = 11! / (5! * (11 - 5)!)
= (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1)
= 11,880 / 120
= 462
Consequently, there are 462 unique potential setups of 5 tunes that can be created from the given rundown of 11 melodies.
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Expand and simplify 3(6y+5) — 2(4y — 1) pleaseee lots of points for answering
Answer:
10y + 17
Step-by-step explanation:
1) (given): 3(6y+5) — 2(4y — 1)
2) (distributive property): 18y + 15 - 8y + 2
3) (combine like terms): 10y + 17
Find the volume of the figure. For calculations involving , give both the exact value and an approximation to the nearest hundredth of a unit. Let d = 10 and h = 18.
________ ft3 ≈ _________ft3
Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.
Explain about the shape of cylinder:A cylinder is three-dimensional. It's not a flat thing. There are parallel circular bases in this shape. These bases have a curved face affixed to them. A cylinder in this instance has three faces. Along both end of a curved face, which rounds back to the face's origin, are two spherical bases.
Given that-
diameter d = 10 ftRadius r = 10/2 = 5 ftHeight h = 18 ftVolume of cylinder = πr²h
Volume of cylinder = 3.14 *5²*18
Volume of cylinder = 3.14*25*18
Volume of cylinder = 1413 ft³
Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.
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Compare and contrast the primary differences between the Job costing and
Process costing by completing the following table:
Job Costing Process Costing
Most suitable manufacturing environment
Cost object used for accumulating costs
Primary document for tracking costs
Manufacturing cost categories
Flow of costs through accounts
We can compare and contrast the primary differences between the Job costing and Process costing processes as follows:
Job costing process:
Most suitable manufacturing environmentManufacturing cost categoriesPrimary document for tracking costsProcess costing:
Cost object used for accumulating costsFlow of costs through accountsHow to classify the cost typesWe can classify the cost types by understanding their usage in the accounting industry. Process costing is used for calculating the costs for mass-produced materials while job costing is used for calculating the cost for customized products.
Process costing is used for accumulating costs and to ascertain the flow of costs through accounts. Job costing is the main document for tracking costs.
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Laurel's W-2 form reported total Medicare wages as $100,750. She contributed $30 per weekly paycheck to her FSA and $75 per weekly paycheck to her retirement plan. She received a 1099 form from her bank for her savings account interest in the amount of $690 and a 1099 form from an employer that she did some consulting work for in the amount of $2,600. What is Laurel's taxable income?
If Laurel received a 1099 form from her bank for her savings account interest in the amount of $690 and a 1099 form from an employer that she did some consulting work for in the amount of $2,600, then Laurel's taxable income is calculated as $98,580.
What is taxable income?Taxable income refers to the base upon which an income tax system imposes tax.
We deduct the following;
Wages reported on W-2 = $100,750
Interest income reported on 1099= $690
Consulting income reported on 1099= $2,600
Therefore, her total income = $100,750 + $690 + $2,600 = $104,040
Laurel's allowable deductions include:
FSA contributions: $30 per week x 52 weeks = $1,560
Retirement plan contributions: $75 per week x 52 weeks = $3,900
Total deductions = $1,560 + $3,900 = $5,460
Laurel's taxable income is found as
= Total income - Total deductions
= $104,040 - $5,460
= $98,580
In conclusion, Laurel's taxable income is $98,580.
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You missed an A in your art course by only 8 points. Your point total for the course was 415. How many points were possible in the course? (Assume that you needed 90% of the course total for an A.)
The total possible points in the course is approximately 470.
HOW CAN WE SOLVE AN EQUATION?Let's assume that the total possible points in the course is "x".
Since you needed 90% of the course total for an A, that means you needed to earn 90% of "x" to get an A. This is equivalent to 0.90x.
You missed an A by only 8 points, so your actual earned points must be 90% of "x" minus 8. This can be expressed as 0.90x - 8.
Given that your actual earned points for the course is 415, we can set up an equation:
0.90x - 8 = 415
Now, we can solve for "x" to determine the total possible points in the course:
0.90x = 415 + 8
0.90x = 423
x = 423 / 0.90
x ≈ 470
So, the total possible points in the course is approximately 470.
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The ratio of apples to pears at a farm stand is 5:3. What is the percentage of the fruit to apples?
Solve for b and c. Select BOTH correct answers. Responses c = 8 c = 8 b = 4√3 b = 4√3 b = 8 b = 8 c = 4√3 c = 4√3
The values of b and c include the following:
c = 8
b = 4√3
How to determine the length of b?In order to determine the length of b, we would apply the law of tangent because the given side lengths represent the adjacent side and opposite side of a right-angled triangle.
Tan(θ) = Opp/Adj
Where:
Adj represents the adjacent side of a right-angled triangle.Opp represents the opposite side of a right-angled triangle.θ represents the angle.Therefore, we have the following tangent trigonometric function:
Tan(θ) = Opp/Adj
Tan(30°) = 4/b
√3/3 = 4/b.
b = 4√3
From Pythagorean Theorem, the length of c is given by;
c² = (4√3)² + 4²
c² = 48 + 16
c = √64
c = 8
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A ship leaves a port with a bearing of S80°E and a speed of 15 knots. After 1 hour, the ship turns 90° towards the North with the same speed in 2 hours. What is the bearing to the ship from the port (due North)? How far is the ship from the port now?
The bearing of B from P is N24.65°E (or S24.65°W), and the ship is approximately 33.54 nautical miles from the port.
Since the ship travels at a constant speed, we can use the formula:
distance = speed × time
For the first hour, the ship travels at a bearing of S80°E, which is equivalent to a bearing of N10°E. Therefore, the ship travels 15 nautical miles in a direction N10°E. This gives us:
PA = distance = speed × time = 15 × 1 = 15 nautical miles
After the first hour, the ship turns 90° towards the North. This means that the ship is now heading due East. Therefore, for the next 2 hours, the ship travels 15 × 2 = 30 nautical miles in an easterly direction. This gives us:
AB = distance = speed × time = 15 × 2 = 30 nautical miles
Now, we can use the Pythagorean theorem to find the value of y:
y² = x² + (AB)²
y² = 15² + 30²
y² = 225 + 900
y² = 1125
y ≈ 33.54 nautical miles
To find the bearing of B from P, we can use trigonometry. The bearing is the angle between the line PA and due North. Let θ be this angle. Then we have:
tan(θ) = x / y
θ = tan^-1(x / y)
Using the values we have found, we get:
tan(θ) = 15 / 33.54
θ ≈ 24.65°
Therefore, the bearing of B from P is N24.65°E (or S24.65°W), and the ship is approximately 33.54 nautical miles from the port.
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and area of the original figure to
of the reduced figure using the
3
6
Which statements are true about the comparison
between the two figures? Check all that apply.
The scale factor is 2.
The scale factor is
2
The perimeter of the model is the product of the
scale factor and the perimeter of the original
rectangle.
The area of the reduced figure is half the area of
the original figure.
The area of the reduced figure is
area of the original figure.
(94
times the
The scale factοr is οne-half. The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle. The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure
What is the scale factοr?The ratiο between cοmparable measurements οf an οbject and a representatiοn οf that οbject is knοwn as a scale factοr in mathematics.
Here,
We have tο cοmpare the perimeter and area οf the οriginal figure tο the perimeter and area οf the reduced figure using the scale factοr.
The ratiο οf the length οf the οriginal rectangle tο that οf the reduced rectangle is 6 tο 3 οr a factοr οf 1/2.
The ratiο οf the width οf the οriginal rectangle tο that οf the reduced rectangle is 2 tο 1, οr, again, a factοr οf 1/2. Sο, because this ratiο οf 1/2 is cοnstant, we knοw the tοtal scale factοr is 1/2, making B cοrrect.
16 ×(1/2) = 8, which means that the perimeter οf the scale-factοred, reduced rectangle is "the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle". Sο, C is cοrrect.
Hence, The scale factοr is οne-half.
The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle.
The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure.
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Assume that you are the president of your company and paid a year-end bonus according to the amount of net income earned during the year. When prices are rising, would you choose a FIFO or weighted average cost flow assumption? Explain, using an example to support your answer. Would your choice be the same if prices were falling?
If prices are rising, I would choose to use the FIFO (first-in, first-out) cost flow assumption. This is because under FIFO, the earliest inventory items purchased are assumed to be sold first, leaving the more recently purchased, and therefore higher-priced, items in inventory. As a result, the cost of goods sold (COGS) will be based on the lower, earlier purchase prices, resulting in higher net income and, therefore, a higher year-end bonus.
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The rule for the pattern is add one column. What are the next three terms? (3 points) An image of a pattern. Term one has six dots, term two has eight dots, and term three has ten dots. a 15, 20, 25 b 12, 14, 16 c 8, 10, 15 d 6, 8, 10
Answer:
b 12, 14, 16
Step-by-step explanation:
You want the next three terms of a sequence that starts 6, 8, 10, ....
RuleThe rule seems to be "add 2." If we continue to add 2 to each term, we find the next terms to be ...
10 +2 = 12
12 +2 = 14
14 +2 = 16
The next 3 terms are 12, 14, 16.
__
Additional comment
Without the figure, the idea of "add one column" is meaningless. Since answers are in terms of dot counts, it would be more meaningful to describe the pattern in terms of what happens to the dot count.
Use an array model on graph paper to solve and explain your solution to – Candy comes in 3 1/2pound bags. At a recent party, those attending ate 2 1/4 bags of candy. How many pounds of candy did they eat? Your solution should be in simplest form.
those attending the party ate 4 1/2 pounds of candy in total.
How to solve the question?
To solve this problem using an array model on graph paper, we can draw a rectangular array with 2 1/4 rows and 3 1/2 columns. Each cell in the array represents a 1/4 pound of candy. The total number of cells in the array will give us the total amount of candy eaten.
To start, we can divide each row into four equal parts to represent 1/4 pound of candy. We can also divide each column into two equal parts to represent 1/2 pound of candy. Then, we can shade in the cells that represent the amount of candy eaten.
Starting with the first row, we shade in two full rows and an additional half row, representing 2 1/2 bags of candy. Then, in the second row, we shade in two full columns and an additional half column, representing 2 1/4 bags of candy.
When we count the total number of shaded cells in the array, we see that there are 18 cells shaded. Each cell represents 1/4 pound of candy, so we can multiply 18 by 1/4 to get the total amount of candy eaten:
18 * 1/4 = 4 1/2 pounds
Therefore, those attending the party ate 4 1/2 pounds of candy in total.
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Find the measure of the angle
The angle turns through 5/8 of the circle
The angle mesure of 5/8 of the circle is _°
An architect creates a blueprint using a scale of 1 inch = 3.5 ft. If the actual
length of a patio is 21 feet, how long will the patio's length appear in the
blueprint?
O 6 inches
O 7 inches
O 17.5 inches
O 73.5 inches
6 inches will be the length of the patio.
According to the scale, 1 inch on the plan corresponds to 3.5 feet in real life.
We must convert the patio's real length of 21 feet to inches using the scale in order to determine how long it would look on the blueprint:
3.5 feet to one inch
21 feet in x inches
If we cross-multiply, we obtain:
1 inch/3.5 feet * 21 feet
= x inches
= 6 inches.
As a result, the length of the patio will be indicated on the blueprint as 6 inches.
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In which data set is the mean equal to the median?
Answer: PSD
Step-by-step explanation: perfectly symmetrical distribution
Select the values that make the inequality v ≥ 3 true.
(Numbers written in order from least to greatest going across.)
Answer:
The inequality v ≥ 3 can be satisfied by any number greater than or equal to 3, such as 4, 5, 6.7 etc. The smallest value that will make the inequality true is 3 itself. As long as the number chosen for v is greater than or equal to three then it will satisfy the given equation and make it true.
Step-by-step explanation:
The values that make the inequality v ≥ -3 make true are -3, -2.99, -2.9, and 0.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have the inequality v ≥ -3.
Here the inequality shows that the value is equal to greater than -3.
1. -11 < -3.
2. -8 < -3
3. -6 < -3
4. -4< -3
5. -3.1< 3
6. -3.01 < -3
7. -3.001 < -3
8. -3 = -3
9. -2.999 > -3
10. -2.99 > -3
11. -2.9 > -3
12. 0 > -3
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trish is breaking ground for a rose garden inher backyard. the garden will be a square with a side length of 7 meters. what will be the area of the rose garden?
Answer:
the area is 49m² this because for area you have to mutiple
Step-by-step explanation:
7×7=49
Which equation can pair with x - y = -2 to create a consistent and dependent system?
6x + 2y = 15
O-3x + 3y = 6
O-8x-3y = 2
O4x - 4y = 6
To create a consistent and dependent system with the equation x - y = -2, we need to find another equation that has the same solution as this equation.
We can manipulate the equation x - y = -2 to get y = x + 2.
Which equation can pair with x - y = -2 to create a consistent and dependent system?Now, we can substitute y = x + 2 into each of the given equations to see which one creates a dependent system:
6x + 2y = 15 becomes 6x + 2(x + 2) = 15, which simplifies to 8x = 11. This equation has no solution, so it does not pair with x - y = -2 to create a dependent system.
-3x + 3y = 6 becomes -3x + 3(x + 2) = 6, which simplifies to 0 = 0. This equation has infinitely many solutions and pairs with x - y = -2 to create a dependent system.
-8x - 3y = 2 becomes -8x - 3(x + 2) = 2, which simplifies to -11x = -8. This equation has a unique solution, so it does not pair with x - y = -2 to create a dependent system.
4x - 4y = 6 becomes 4x - 4(x + 2) = 6, which simplifies to -4 = 6. This equation has no solution, so it does not pair with x - y = -2 to create a dependent system.
Therefore, the equation -3x + 3y = 6 can pair with x - y = -2 to create a consistent and dependent system.
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A force of 350 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 10 centimeters to 40 centimeters?
The work done in stretching the spring from 10 cm to 40 cm is 10,837.5 J.
The work done in stretching a spring is given by the formula:
W = (1/2)k[tex]x^{2}[/tex]
where W is the work done, k is the spring constant, and x is the displacement of the spring from its original position.
To find the spring constant k, we can use the given information:
F = kx
where F is the force applied to the spring. Rearranging this equation, we get:
k = F/x
Substituting the given values, we get:
k = 350 N / 30 cm = 11.67 N/cm
Now, we can find the work done in stretching the spring from 10 cm to 40 cm:
W = (1/2)k([tex](x_{2})^{2} -(x_{1} )^{2}[/tex])
where [tex]x_{1}[/tex] is the initial displacement of the spring (10 cm) and [tex]x_{2}[/tex] is the final displacement (40 cm).
Substituting the values, we get:
W = (1/2) * 11.67 N/cm * ([tex](40 cm)^{2} - (10 cm)^{2}[/tex])
W = (1/2) * 11.67 N/cm * (1600 [tex]cm^{2}[/tex] - 100 [tex]cm^{2}[/tex])
W = (1/2) * 11.67 N/cm * 1500 [tex]cm^{2}[/tex]
W = 10,837.5 joules (J)
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Use a net to find the surface area of the prism.
A. 426 m2
B. 213 m2
C. 306 m2
D. 336 m2
The surface area of the prism is 426 m²
What is surface area of cuboid?A cuboid is a rectangular prism. And has all the properties related to a prism. The general formula for the surface area of a cuboid is ;
SA = 2B + ph
We can use net formula to find the surface area of a cuboid.
surface area of a cuboid is expressed as;
SA = 2( lb+lh +bh)
l = 12m , b = 5m and h = 9m
lb = 12×5 = 60m²
lh = 12 × 9 = 108m²
bh = 5×9 = 45m²
SA = 2(60+108+45)
= 2(213)
= 426 m²
therefore the surface area of the cuboid is 426m²
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Stacy invests $55,000 into an account at 2.3% interest compounded monthly. Find the total value of the investment after 4 years.
In the formula, A is the amount after interest, P is the principal, r is interest rate in decimals, n is the amount of times the interest is compounded per year, and t is the amount of years.