The number that should be added to complete the square of the expression 4x² - 8x is 1.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
To complete the square of the expression 4x² - 8x, add a constant term that will make it a perfect square trinomial.
First, factor out the coefficient of the x² term -
4x² - 8x = 4(x² - 2x)
Next, add a constant term that will make the expression inside the parentheses a perfect square.
To do this, take half of the coefficient of the x term and square it.
Half of -2 is -1, and (-1)^2 is 1.
So add 1 to the expression inside the parentheses to make it a perfect square -
4x² - 8x + 1 = 4(x² - 2x + 1)
Simplify this expression by factoring the trinomial inside the parentheses -
4x² - 8x + 1 = 4(x - 1)²
Therefore, the number is 1.
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May grave 1/5 of her property to her son and 1/3 to her daughter. what fraction of her left property is left
The fraction of May's property that is left is 7/15.
What is a fraction?A fraction is a value derived in such a way that it is a part of a given initial value. An example is one third of 12 is 4. In this case, 4 is a fraction of 12.
Considering the given question, we have;
let the total property of May be represented by 1, so that
fraction left after giving 1/5 to her son = 1 - 1/5
= (5 - 1)/ 5
= 4/ 5
The fraction left after giving 1/5 of her property to her son is 4/ 5.
So that;
the fraction left after she gave 1/3 to her daughter = 4/ 5 - 1/ 3
= (12 - 5)/ 15
= 7/ 15
Therefore, the fraction of her property left is 7/ 15.
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How do I do this? This is confusing..
The points are as selected on the graph.
How to select points on the graph?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
Since f(x) = -9. What this means is that the value of f(x) will always be -9 irrespective of the value of x. That is:
x f(x)
-2 -9
0 -9
2 -9
7 -9
9 -9
Check the attached image for the points on the graph
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HELPPPPP
i need the answer for this today
Answer:
Below
Step-by-step explanation:
The quations are both equal to 'y' so the equations are equal
5x-10 = -3x+ 14
8x = 24
x = 3 <====== use this value of 'x' in one of the equations to calculate y
y = 5x-10
y = 5(3)-10 = 5
The vertices of a rectangle are at (-4,2),(3,2),(3,-2), and (-4,-2). What is the length of the longer side of the rectangle?
The longer side of the rectangle is the side that connects the points (-4,2) and (3,2), which have the same y-coordinate, so it is a horizontal line.
The length of this side is the distance between the x-coordinates of these two points, which is:
3 - (-4) = 7
Therefore, the length of the longer side of the rectangle is 7 units.
During the course of your examination of the financial statements of Trojan Corporation for the year ended December 31, 2021, you come across several items needing further consideration. Currently, net income is $100,000. An insurance policy covering 12 months was purchased on October 1, 2021, for $24,000. The entire amount was debited to Prepaid Insurance and no adjusting entry was made for this item in 2021. During 2021, the company received a $4,000 cash advance from a customer for services to be performed in 2022. The $4,000 was incorrectly credited to Service Revenue. There were no supplies listed in the balance sheet under assets. However, you discover that supplies costing $2,750 were on hand at December 31, 2021. Trojan borrowed $70,000 from a local bank on September 1, 2021. Principal and interest at 9% will be paid on August 31, 2022. No accrual was made for interest in 2021.
Answer: $3,700 or $90,650
Step-by-step explanation:
Answer:
3,700
Step-by-step explanation:
i thibk thisisthay answer
true/false. problem 3-1a (static) determine accrual-basis and cash-basis revenues and expenses (lo3-1, 3-2) required: for each transaction, determine the amount of revenue or expense, if any, that is recorded under accrual-basis accounting and under cash-basis accounting in the current period.
Answer:
true
Step-by-step explanation:
cause I’ve done this before
A small-scale model of a submarine is being designed with the stabilizing wings and rudder to be added later. The fuselage is a cylinder of length 30 inches with a radius of 5 inches. The bow (front) is a semi sphere ( half of a sphere) that fits on one end of the cylinder. The stern (back) is a cone on the tail end that has a height of 6 inches. Calculate the volume and surface area of the new solid.
If a medium-scale model was required at 8x the scale of the small model, What is the overall length from back to the tip? What is the new surface area? What is the new Volume?
The Volume of Solid is 2,773.66 inch³ and Surface Area is
2,552.82 inch².
What is Surface Area?Surface area is the amount of space covering the outside of a three-dimensional shape.
Given:
Cylinder: Height = 30 inch, Radius = 5 inch
Semi sphere: radius = 5 inch
Cone: Height = 6 inch, radius = 5 inch, l= √r² + h² = 7.81 inch
Now, The Volume solid
= Volume of Semi sphere + Volume of Cylinder + Vol. of Cone
= 2/3 πr³ + πr²H + 1/3 πr²h
= πr² (2/3 r + H + 1/3 h)
= 3.14 x 5 x 5 (2/3(5) + 30 + 1/3 (6))
= 78.5 x ( 10/ 3 + 30 + 2)
= 2,773.66 inch³
Now, the Surface Area of Solid
= SA (Cylinder+ S. Sphere + Cone)
= πr²H + 2πr² + 1/3 πrl
= πr (rH + 2r + 1/3l)
= 3.14 x 5 (150 + 10 + 2.60)
= 2,552.82 inch²
Now, the model is increased by 8 times then the dimensions are:
Cylinder: Height = 240 inch, Radius = 40 inch
Semi sphere: radius = 40 inch
Cone: Height = 48 inch, radius = 40 inch, l= √r² + h² = 62.48 inch
and, Now, The Volume solid after dilation
= Volume of Semi sphere + Volume of Cylinder + Vol. of Cone
= 2/3 πr³ + πr²H + 1/3 πr²h
= πr² (2/3 r + H + 1/3 h)
= 3.14 x 40 x 40 (2/3(40) + 240 + 1/3 (48))
= 78.5 x ( 10/ 3 + 30 + 2)
= 1,420,117.33 inch³
Now, the Surface Area of Solid
= SA (Cylinder+ S. Sphere + Cone)
= πr²H + 2πr² + 1/3 πrl
= πr (rH + 2r + 1/3l)
= 3.14 x 5 (1200 + 80 + 20.82)
= 163, 382. 992 inch²
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What are the x-coordinates to the solutions of the system of equations:
x + y + 10 = 0
x ^ 2 + y - 2 = 0
A) x = - 4, -3
B) x= 4, 14
C) x= -3, 4
D) x= -3, -7
Answer:
C
Step-by-step explanation:
x + y + 10 = 0 ( subtract x + 10 from both sides )
y = - x - 10 → (1)
x² + y - 2 = 0 → (2)
substitute y = - x - 10 into (2)
x² - x - 10 - 2 = 0
x² - x - 12 = 0 ← in standard form
(x - 4)(x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 4 = 0 ⇒ x = 4
If you invest $9,500 per period for the following number of periods, how much would you have?
13 years at 10 percent.
50 years at 9 percent.
The accrued amounts are $32,796.58 and $706,396.44.
Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P (1+r/n[tex])^{rt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
(a) If you invest $9,500 per period for 13 years at 10 percent.
First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 9,500.00(1 + 0.1/1[tex])^{13}[/tex]
A = 9,500.00(1 + 0.1[tex])^{13}[/tex]
A = $32,796.58
(b). If you invest $9,500 per period for 50 years at 9 percent,
First, convert R as a percent to r as a decimal
r = R/100
r = 9/100
r = 0.09 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 9,500.00(1 + 0.09/1[tex])^{50}[/tex]
A = $706,396.44
Therefore, the amounts are$32,796.58 and $706,396.44.
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From a deck of regular playing cards, one card is chosen at
random. Find the probability the card is a diamond or a face card.
The probability that now the card is indeed a diamond or a face card is [tex]\frac{11}{26}[/tex].
What are probability and examples?The probability that any random event will occur is referred to as probability. This expression is used to calculate the likelihood that a given event will occur. When we fling a coin into the air, as an illustration. Probability: P(A) = f / N calculates the probability that an event will take place. Ratios and probability are related, but the former determines the latter. When calculating the likelihood of an event, it is necessary to know the probability of that event.
When we find the probability, we obtain:
A typical deck of cards contains 52 cards. There are 12 face cards, known as the Kings, Queens, and Jacks, because there are four suits. There are a total of 13 diamonds, of which 3 are previously counted face cards. Hence, there are 10 diamonds that are faceless.
So, total Diamond & face card =22
Probability =[tex]\frac{22}{52}[/tex]=[tex]\frac{11}{26}[/tex].
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Which statement BEST matches the image. Cannot be used more than once.
>
>
soda
soda
soda
A
↑
orange juice
A
orange juice
. A
1. Inefficient / Underutilization
2. Impossible / Unobtainable
3. Technological advances in
production
4. Efficient Production
Financial plan - The cost of a jug of squeezed orange is $2.00 and the cost of pop is $1.00. These information propose that Sharon is augmenting her utility from the given fixed spending plan
What is financial plan make sense of?A written financial program offers you a quantifiable objective to strive for. By monitoring your progress, you can eliminate doubt or uncertainty regarding your choices and make necessary adjustments to help you get past potential roadblocks.
Budgeting is the most crucial first step in financial planning. Making a budget is fairly simple; keeping one is more challenging! What matters is having the self-control to take the time as well as care to track and reconcile your spending in some way.
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The bakery uses 7 eggs to make a cake. If they have 380 eggs how many cakes can hey make?
Answer:
54.2 cakes
Step-by-step explanation:
divide 380 by 7 and you'll get 54.2 as your answer
Use the verticals line test to determine if y is a function of x in the graph
Which of the following statements is correct?
a) y is a function of x
B) y is not a function of x
Using the vertical line test we conclude that y is not a function of x.
How to use the vertical line test?When we have the graph of a relation, the vertical line test says that if we draw a vertical line over the graph and it intercepts the graph in more than one point, then the graph does not represent a function.
Here we have the graph of a circle, and there are multiple lines that intercept the graph twice (for example the line x = 0)
So we can conclude that this is not a function, thus, the correct option is A.
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Select the correct answer from each drop-down menu. Consider right triangle ABC. A triangle ABC has right angle at B is shown. Base AB has length labeled 40 units. Height BC has length labeled 9 units, and hypotenuse AC has length 41 units.
We know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse, then sin(A) = 9/41 and cos(A) = 40/41.
What are trigonometric ratios?
Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.
We can use the following trigonometric ratios:
sin(A) = opposite/hypotenuse
cos(A) = adjacent/hypotenuse
In this case, we know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse:
opposite = BC = 9 units
adjacent = AB = 40 units
hypotenuse = AC = 41 units
Using these values, we can calculate the sine and cosine of angle A:
sin(A) = opposite/hypotenuse = 9/41
cos(A) = adjacent/hypotenuse = 40/41
Therefore, we know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse, then sin(A) = 9/41 and cos(A) = 40/41.
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Need helping solving this problem
The cost of the burger and the cost of an order of fries to Lynn would be :
Cost of burgher - $3.00Cost of fries - $ 1. 60How to find the cost ?From the problem, we know that Lynn spent $20.00 and purchased 4 hamburgers and 5 orders of fries. Similarly, we know that Ricardo spent $41.20 and purchased 10 hamburgers and 7 orders of fries, which gives us the equations:
4h + 5f = 20
10h + 7f = 41.20
Using substitution, we can express h in form of f to be :
4h + 5f = 20
4 [ ( 3 f + 1. 20 ) / 2] + 5 f = 20
6 f + 2 . 40 + 5 f = 20
11 f = 17. 60
f = $ 1. 60
We can then find the cost of hamburgers using the first equation :
4h + 5f = 20
4h + 5 ( 1. 60 ) = 20
4h + 8 = 20
4h = 12
h = $ 3
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The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y < −2x + 10 y < 1 over 2x − 2 coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3 I B A F Question 7(Multiple Choice Worth 1 points) (05.06 MC) A class trip to a ski resort has been planned for your senior trip. The mountain only allows skiing when the temperature is between −10 degrees and 35 degrees. There is room for 38 people on your trip. Write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip. −10 < x < 35 and 0 < y ≤ 38 x < 35 and y > −10 0 < x ≤ 38 and −10 < y < 35 x > −10 and y < 35 Question 8(Multiple Choice Worth 1 points) (05.06 MC) A company dyes two sizes of rugs. A small rug requires 2 hours for dyeing, and a medium-size rug requires 3 hours for dyeing. The dyers need to make at least 15 rugs, and they must do it in less than 60 hours. Let x equal small rugs and y equal medium rugs. Which of the following inequalities can be paired with x + y ≥ 15 to create a system that represents this situation? 2x + 3y < 60 3x + 2y < 60 2x + 3y > 60 3x + 2y > 60 Question 9(Multiple Choice Worth 1 points) (05.06 MC) Solve the following systems of inequalities and select the correct graph: 2x − y < 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB. a dashed line g of x rising left to right that is shaded below and a dashed line f of x that is falling left to right that is shaded above a dashed line f of x rising left to right that is shaded above and a dashed line that is falling g of x left to right that is shaded above a dashed line
The point that is a solution to the system of inequalities y < −2x + 10 and y < 1/2x − 2 is point E at (4, -2). This is because point E satisfies both inequalities.
When we plug in the x and y values of point E into the first inequality, we get -2 < -2(4) + 10, which simplifies to -2 < 2, which is true.
When we plug in the x and y values of point E into the second inequality, we get -2 < 1/2(4) - 2, which simplifies to -2 < 0, which is also true. Therefore, point E is a solution to the system of inequalities.
For question 7, the correct answer is −10 < x < 35 and 0 < y ≤ 38. This is because the temperature must be between -10 and 35 degrees, and there must be between 0 and 38 people on the trip.
For question 8, the correct answer is 2x + 3y < 60. This is because a small rug requires 2 hours for dyeing and a medium-size rug requires 3 hours for dyeing, and the total time must be less than 60 hours.
For question 9, the correct answer is the graph with a dashed line f of x rising left to right that is shaded above and a dashed line that is falling g of x left to right that is shaded above.
This is because the solution to the system of inequalities is the area where both inequalities are true, which is the area where they have shading in common. In this case, it is the area above both dashed lines.
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use the multiplier method to increase £258 by 43%
Answer:
43% * 258 = 110.94 (£110.94 is 43% of £258) 258 + 110.94 = 368.94
Step-by-step explanation:
let $pqr$ be an equilateral triangle, centered at $o.$ a point $x$ is chosen at random inside the triangle. find the probability that $x$ is closer to $o$ than to any of the vertices. (in other words, find the probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$)
The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,
⇒ 1/3
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
Let $pqr$ be an equilateral triangle, centered at $o$ a point $x$ is chosen at random inside the triangle.
Hence, The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,
⇒ 1/3
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Which best describes the rate at which Mandy used up her bags of dog food?
OA. 6 bags per day
OB. 2/3 bags per day
OC. 4 bags per day
OD. 3/2 bags per day
The rate at which Mandy used up her bags of dog food is 2/3 bags per day
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Slope = change in y /change in x
Here, Slope = change in bags of food/ /change in days
form the graph = 4/6 = 4 bags per 6 days
4/6 simplifies to 2/3
=> 2/3 bags per day
The rate at which Mandy used up her bags of dog food is 2/3 bags per day
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HELP PLEASE!!!!!!
Square ABCD is graphed in the xy- plane with origin O. A transformation maps ABCD onto A'B'C'D'.
In the following table, consider the congruence statement listed in each row together with the type of transformation listed in each column.
Select each cell for which the congruence statement must be true for the type of transformation.
The transformation from ABCD onto A'B'C'D' is a rigid transformation.
How to determine the congruent statementsFrom the question, we have the following parameters that can be used in our computation:
A transformation maps ABCD onto A'B'C'D'
In order for a transformation to map square ABCD onto square A'B'C'D', certain congruence statements must be true.
The corresponding sides of ABCD and A'B'C'D' must have the same length i.e. AB = A'B', BC = B'C', CD = C'D', and DA = D'A'.
The corresponding angles of ABCD and A'B'C'D' must have the same measure i.e angle A = angle A', angle B = angle B', angle C = angle C', and angle D = angle D'.
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Mark would like to buy a new guitar that costs $169.00. Mark has saved $55 and receives an allowance of $12 a week. Choose the equation that represents how many weeks, w , it will take for Mark to save enough money to buy the guitar. Responses
With a weekly budget of $12, Mark will need to save money for 9 weeks, 5 days in order to purchase the guitar.
what is equation ?The value is said to be in its simplified form when divided through its smallest equivalent fraction. How to find the most basic form. Find common factors in the denominator and numerators. Verify a minority integer t verify if it qualifies like a prime number. A statement comprising two rotational symmetry and an equal sign in the middle is called an equation in mathematics. The general form of almost any equation contains the degrees of all variables in descending order. The conventional form of something like a linear equation is an x + b = 0. The general form of a mathematical expression with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as identities or conditional solutions. An identity holds true irrespective of the value given to the variables.
given
let the week be x
equation = $55 + 12x = $169.00
55 + 12x = 169
12x = 169 - 55
12x = 114
x = 9.5
With a weekly budget of $12, Mark will need to save money for 9 weeks, 5 days in order to purchase the guitar.
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Solve for l if V = 120 w = 5 and h = 4
Answer:
The value of l is 48. The formula to calculate volume (V) is V = l * w * h, so we can rearrange the equation to solve for l, or l = V/(w * h). In this case, l = 120/(5 * 4) = 48.
Answer:
125
Step-by-step explanation:
w
Just need help with this question..
Graph appears to intersect the X axis in between 20 and 22 and algebraically the estimate of zero is 21.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Given a linear function which represents the profit of Bethany, y after x hours of dog walking.
(a) From the graph, we have to estimate the zero.
The graph seems to intersect the X axis in between 20 and 22, approximately 21.
(b) To solve this algebraically, we have the profit function,
y = 23x - 480
When y = 0,
23x - 480 = 0
23x = 480
x = 20.87 ≈ 21
Hence the graphical method gives the same estimate as the algebraic method.
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Precision Engineering Factory consumes 12,500 units of a component in every three- month period. The ordering, receiving and handling costs are TZS 3 per order while the trucking costs are TZS 12 per order. Further details are as follows: deterioration and obsolescence cost TZS 0.04 per unit per year, interest cost, TZs 0.06 per unit per year, storage cost TZS 1,000 per year for 50.000 units, a) Calculate the total cost of matenal (ignore decimals and show working clearly).
If Precision Engineering Factory consumes 12,500 units of a component in every three- month period. the total cost of material is TZS 6,060 per year.
How to find the total cost of material?The annual demand for the material can be calculated as follows:
Annual demand = (12,500 units/3 months) x (4 quarters/year) = 50,000 units/year
Ordering cost = TZS 3 per order
Number of orders = (50,000 units/year) / (12,500 units/order) = 4 orders/year
Ordering cost per year = (4 orders/year) x (TZS 3/order) = TZS 12/year
Trucking cost = TZS 12 per order
Trucking cost per year = (4 orders/year) x (TZS 12/order) = TZS 48/year
Deterioration and obsolescence cost = TZS 0.04 per unit per year
Deterioration and obsolescence cost per year = (50,000 units/year) x (TZS 0.04/unit/year) = TZS 2,000/year
Interest cost = TZS 0.06 per unit per year
Interest cost per year = (50,000 units/year) x (TZS 0.06/unit/year) = TZS 3,000/year
Storage cost = TZS 1,000 per year for 50,000 units
Storage cost per unit per year = (TZS 1,000/year) / (50,000 units) = TZS 0.02/unit/year
Storage cost per year = (50,000 units/year) x (TZS 0.02/unit/year) = TZS 1,000/year
Total cost of material = Ordering cost + Trucking cost + Deterioration and obsolescence cost + Interest cost + Storage cost
Total cost of material = TZS 12/year + TZS 48/year + TZS 2,000/year + TZS 3,000/year + TZS 1,000/year
Total cost of material = TZS 6,060/year
Therefore, the total cost of material is TZS 6,060 per year.
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g bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.truefalse
True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.
What are error bars?A confidence intervals bar chart (shown as red lines)
In graphs, error bars are used to graphically show data variability and to denote error or uncertainty in reported measurements. They provide a basic indication of a measurement's accuracy or, alternatively, how far the true (error-free) value may deviate from the reported value. The standard deviation of uncertainty, the standard error, or a specific confidence range (such a 95% interval) are frequently represented as error bars. Due to the fact that these values are not the same, the measure chosen needs to be specified clearly in the graph or supporting text.
According to the definition the statement is true.
True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.
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This problem refers to triangle ABC. If B = 150°, C = 20°, and c = 21 inches, find b. (Round your answer to the nearest whole number.)
b = ? in
Answer:
Step-by-step explanation:
To solve for b, we can use the law of sines, which states that in any triangle ABC:
a/sin(A) = b/sin(B) = c/sin(C)
Here, we are given B = 150°, C = 20°, and c = 21 inches. We can solve for the remaining angle A by using the fact that the angles of a triangle add up to 180°:
A + B + C = 180°
A = 180° - B - C
A = 180° - 150° - 20°
A = 10°
Now we can use the law of sines to solve for b:
a/sin(A) = b/sin(B)
a = c * sin(A)/sin(C) = 21 * sin(10°)/sin(20°)
b = a * sin(B)/sin(A) = 21 * sin(10°)/sin(20°) * sin(150°)/sin(10°)
b = 21 * sin(150°)/sin(20°)
Using a calculator, we get:
b ≈ 41 inches (rounded to the nearest whole number)
Therefore, the length of side b is approximately 41 inches.
a rectangle below has an area 84 cm saquered, what is half of the rectangle area?
2 Select the correct answer. A circle with radius 5 and center A. The coordinates of the center of the circle are (-3, 12). What is the general form of the equation of the given circle with center A? A. x2 + y2 + 6x − 24y − 25 = 0 B. x2 + y2 − 6x + 24y + 128 = 0 C. x2 + y2 + 6x – 24y + 128 = 0 D. x2 + y2 + 6x − 24y + 148 = 0 Reset Next
The correct equation is D. x2 + y2 + 6x − 24y + 148 = 0.
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
This equation is the general form of a circle with center A and radius 5. The equation can be derived from the coordinates of the center A and the radius of the circle. The center of the circle is located at (-3, 12). To get the equation, first calculate the distance between the center A and a point on the circumference of the circle, which is the radius of the circle, 5. Then, use the Pythagorean theorem to calculate the equation of the circle: x2 + y2 + 6x – 24y + 148 = 0.
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What is the value of x?
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Answer:
x = 54
Step-by-step explanation:
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Calculus please help
f(x) is discontinuous.
Since LHS ≠ RHS ≠ f(x).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
here, we have,
We have,
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
Now,
A x = 1
LHS of f(x) = lim f((h - 1)) = (h - 1 - 1) = 0 -2 = -2
RHS of f(x) = lim f(h + 1) = (2(h + 1) - 1) = 2h + 2 - 1 = 0 + 1
f(1) = x + 1 = 1 + 1 = 2
We see that,
LHS ≠ RHS ≠ f(x)
So,
f(x) is not continuous, it is discontinuous.
Thus,
f(x) is discontinuous.
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The complete question.
Show that the following functions are continuous or discontinuous at x = 1.
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
