For acute angles A and B it is known that sin A - 28/53 and tan B = 4/3. , , the value of cos(A+B) in simplest form is -15/53.
Describe Angles?In geometry, an angle is the measure of the amount of turn between two lines that intersect at a point, called the vertex of the angle. Angles are typically measured in degrees, but can also be measured in radians.
Angles can be classified based on their measures. An angle that measures less than 90 degrees is called an acute angle, while an angle that measures exactly 90 degrees is called a right angle. An angle that measures greater than 90 degrees but less than 180 degrees is called an obtuse angle, while an angle that measures exactly 180 degrees is called a straight angle. Finally, an angle that measures greater than 180 degrees but less than 360 degrees is called a reflex angle.
We can start by using the identity:
cos(A + B) = cos A cos B - sin A sin B
To find cos A and sin A, we can use the identity:
sin² A + cos² A = 1
sin A = √(1 - cos² A)
We are given sin A = 28/53, so we can solve for cos A:
sin² A + cos² A = 1
(28/53)² + cos² A = 1
cos² A = 1 - (28/53)²
cos A = ± √[(53/53)² - (28/53)²]
Since A is acute, we take the positive root:
cos A = √(1 - (28/53)²)
To find sin B and cos B, we can use the identity:
tan B = sin B / cos B
We are given tan B = 4/3, so we can solve for sin B and cos B using the Pythagorean identity:
sin² B + cos² B = 1
sin B = (4/3) cos B
(4/3)² cos² B + cos² B = 1
cos² B = 1 / ((4/3)² + 1)
cos B = √(1 / ((4/3)² + 1))
sin B = (4/3) cos B
Now we can substitute all of these values into the formula for cos(A + B):
cos(A + B) = cos A cos B - sin A sin B
cos(A + B) = √(1 - (28/53)²) √(1 / ((4/3)² + 1)) - (28/53) (4/3) √(1 / ((4/3)² + 1))
cos(A + B) = (√((53² - 28²) / 53²)) (√(9 / (16 + 9))) - (4/3) (28/53) (√(9 / (16 + 9)))
cos(A + B) = (45/53) (√(9/25)) - (112/265) (√(9/25))
cos(A + B) = (9/53) - (24/53)
cos(A + B) = -15/53
Therefore, cos(A + B) = -15/53.
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(x−a)xa3+(x−a)x−13a2+(x−a)x−23a+(x−a)31=(x−a)xx3
The solutions to the equation are x = a and x = a/2.
Equation calculation.
We can simplify the left-hand side of the equation using the common denominator of x^3:
(x-a)x/x^3 + (x-a)(-1)/(3a^2 x^3) + (x-a)(-2)/(3a x^3) + (x-a)(1)/(x^3)
= [(x-a)x^2 - (x-a)/(3a^2) - 2(x-a)/(3a) + (x-a)x]/x^3
= [(x^3 - a^3)/x^2 - (1/(3a^2))(x-a) - (2/(3a))(x-a)]/x
= [(x^2 + ax + a^2)(x-a)/(x^2 a^2) - (x-a)/(3a^2) - (2/3)(x-a)/a]/x
= (x^2 + ax + a^2)/(x^2 a^2) - 1/(3a^2) - 2/(3a)/x
= (3x^2 + 3ax + 3a^2 - x^2 a - ax^2 - a^3)/(3a^2 x^2)/x
= (2x^2 + 3ax + 3a^2 - ax^2 - a^3)/(3a^2 x^2)/x
= (x^2 + 3ax + 3a^2 - a^3)/(3a^2 x^2)/x
Now, we can see that the expression on the right-hand side is:
(x-a)/(x^3)
Multiplying both sides by x^3, we get:
(x-a)x = (x^2 + 3ax + 3a^2 - a^3)/3a^2
Multiplying both sides by 3a^2, we get:
(x-a)3a^2x = x^2 + 3ax + 3a^2 - a^3
Expanding (x-a)(3a^2)x, we get:
3a^2x^2 - 3a^3x = x^2 + 3ax + 3a^2 - a^3
Moving all terms to one side, we get:
2x^2 - 3ax + 2a^2 = 0
This is a quadratic equation, and we can solve for x using the quadratic formula:
x = [3a ± sqrt((9a^2 - 8a^2)/4)]/4
x = [3a ± a]/4
x = a or x = 2a/4 = a/2
Therefore, the solutions to the equation are x = a and x = a/2.
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Use the slope of 5/3 and the point (−3, –4) to graph the line
The equation of the line is 3y-5x=3 and the graph is attached.
Geometrically speaking, a line is a one-dimensional figure because it has length but no width. A group of points can be extended endlessly in opposing directions to form a line. Two points in a two-dimensional plane determine it. There are, however, additional ways to formulate the equation of a line in a two-dimensional coordinate system. The three most popular methods are the point-slope form, slope-intercept form, and general or standard form of the equation of a line. As its name suggests, the point-slope form combines a line point and a straight-line slope. The equations of infinite lines with a particular slope can be expressed, however when we specify that the line passes through a particular point, we get a singularity.
the equation of a line is
y-y'=m(x-x')
[tex]y+4=\frac{5}{3}(x+3)\\\\3y+12=5x+15\\3y-5x=3[/tex]
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The total for which two pet sales is 731
Answer: 363+368=731
Step-by-step explanation:
please help me i really need it please
Answer: First one (top left)
Step-by-step explanation:
Answer:
One in the top left corner
Hope this helps!
Step-by-step explanation:
i need help asap i have to finish
Answer: (D) 12 to 4
Step-by-step explanation:
First, we will find the number of people waiting in line for each activity.
➜ Bumper cars is 12
➜ Slingshot is 4
Next, we will create our ratio. This is asking for Bumper cars to Slingshot, so Bumper cars is first with Slingshot second.
➜ 12 to 4
Fond the sum 2/5 + 3/6
To add 2/5 and 3/6, we need to find a common denominator for the two fractions. The smallest number that both 5 and 6 divide into evenly is 30. So, we can convert the two fractions to have a denominator of 30:
2/5 = 12/30 3/6 = 15/30
Now, we can add the two fractions by simply adding their numerators (since they have the same denominator):
12/30 + 15/30 = 27/30
We can simplify the fraction by reducing it to the lowest terms. Both the numerator and denominator have 3 as a factor, so we can divide them both by 3:
27/30 = (3 x 9) / (3 x 10) = 9/10
Therefore, the sum 2/5 + 3/6 is equal to 9/10.
A camera's normal price is $460. Buying it duty free reduces the price by 25%. Find the actual selling price of the camera.
The actual selling price of the camera after the 25% discount is $345.
What is selling price?The amount received by the buyer is the selling price of a product or service. Although the seller sets the price, a number of variables affect how the seller arrives at that particular figure. Depending on the seller's discretion, different customers may pay different prices for the same good or service.
If the normal price of the camera is $460, a 25% reduction in price would be:
25% of $460 = 0.25 x $460 = $115
This means the reduction in price when buying the camera duty-free is $115.
So the actual selling price of the camera after the discount is:
$460 - $115 = $345
Therefore, the actual selling price of the camera after the 25% discount is $345.
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Cual es el valor de x ? 5 ( x - 56 ) = -3 ( x + 2 ) + 1
Answer:
Step-by-step explanation:
[tex]\frac{275}{8}=34,375[/tex]
10 men can complete a job in 14 days, How long will it take 4 men to finish the same Job if they work at the same rate?
Keisha is playing a game using a wheel divided into 8 equal sectors, as shown in the diagram below. Each time the spinner lands on blue, she will win a prize.
If Keisha spins this wheel twice, what is the probability that she will win a prize on both spins?
show all steps
Answer:
4/64
Step-by-step explanation:
The spinner is independent (the total won't be effected)
we know there is 2 whites with 8 coloured option.
we want the probability of getting two whites.
2/8 x 2/8 = 4/64
there is 3 ways to work out probability, fraction, decimal and percentage (i'd personally say fraction is the most easiest)
PLEASE HELP!!! MIDDLE SCHOOL MATH!!!!!!!!!!!!!!!!!!!!!
Which of the following represent angle measures in the figure shown? select all that apply
PLEASE LOOK AT PICTURE BELOW!!!!!! MUST SHOW WORK!!!!!!!!!!!!!!
Answer:
55°90°145°Step-by-step explanation:
For the 90°/right angle part, we can subtract 35° from 90° to get the degree of that area.
90° - 35° = 55°
We can check off the "55°" box
----------------------------------------------
Now, for the other half of the straight angle including the right angle, we can subtract 90° from 180°.
Getting 90°
We can check off the "90°" box
-------------------------------------------------
To find the degree of the "(7x + 5°)" -- assuming that that angle is vertical to the "other" -- we can make an equation of
⇒ 7x + 5° = 90° + 55°
Solve:
Add together 90 and 55 which is 145°
New equation:
7x + 5° = 145°
Subtract 5° from both sides, getting the equation
7x = 140°
Isolate x by dividing both sides by 7
x = 20°
Substitute what we have for x into the equation "7x + 5°"
7(20°) + 5
= 145°
We can check off the "145°" box
------------------------------------------
All the boxes checked off:
55°90°145°Hopefully this helps! -- mark me brainliest if you want ofc
Need help! (For 50 points)
Answer:
168°------------------------------
Supplementary angles add up to 180°:
m∠A + m∠B = 180°Substitute and solve for x:
x - 9 + 7x + 21 = 1808x + 12 = 1808x = 168x = 21Find the measure of ∠B:
m∠B = (7*21 + 21)° = 168°The net shown represents a square pyramid. 20 ft 32 ft • Determine the area, in square feet, of one triangular face of the square pyramid • Determine the total surface area, in square feet, of the square pyramid.
The total surface area must be calculated by adding the areas of all five faces, the four triangular faces, and the square base.
What is a square pyramid known as?The term "square pyramid" refers to a three-dimensional geometric form with a square base and four triangular faces or sides that meet at a single point (known as a vertex). Because it has five faces, it is referred to as a pentahedron.
Given :
Let s represent the square base's side length and h represent the slant height of each triangle face. The area of a single triangle is then determined by:
A = (1/2) * s * h
The areas of all five face the four triangular faces and the square base must be added up in order to determine the overall surface area of the pyramid.
The overall surface area is: since the square base has a simple area of s2.
When we replace A with the expression, we obtain:
We require further details regarding the pyramid in order to determine the values of s and h.
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In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Hudson sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
80 visitors purchased no costume.
32 visitors purchased exactly one costume.
3 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase more than one costume as a percent to the nearest whole number.
The probability that the next person will purchase more than one costume as a percent to the nearest whole number is 3%
.Out of the total 80 + 32 + 3 = 115 visitors, 80 did not purchase any costumes and 32 purchased exactly one costume. This means that the remaining 3 visitors purchased more than one costume.
Therefore, the probability that the next person will purchase more than one costume is 3/115, which is approximately 0.0261.
To express this as a percentage to the nearest whole number, we need to multiply by 100 and round to the nearest integer. Thus, the answer is:
0.0261 × 100 ≈ 3%
Therefore, the probability that the next person will purchase more than one costume is approximately 3%.
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(b) During a housing boom the price of houses increased over an 18 month period. A house that cost 240000 at the start of the period had a sale value of 276000 at the end of the period. What was the average rate of change in the price per month?
After answering the presented question, we can conclude that As a result, the average monthly rate of change in price during the housing bubble was $2,000.
What is average rate?The term "average rate" can have different meanings depending on the context in which it is used. In general, it refers to the amount of change that occurs over a certain period of time, divided by the length of that time period. Here are a few examples of how the term might be used in different fields.
The average monthly rate of change in price can be estimated by dividing the total price change by the number of months:
(final price - beginning price) / number of months = average rate of change
The beginning price was $240,000, the final price was $276,000, and the time duration was 18 months in this example. Hence, using these data, we can calculate the average rate of change as:
(276000 - 240000) / 18 = 36000 / 18 = 2000 Average rate of change
As a result, the average monthly rate of change in price during the housing bubble was $2,000.
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how do i plug 3x^2 - 13x + 4 = 0 into a calculator?
the question is asking to factor and solve
Answer:
x=1/3
≈ 0.333333333
x=4
Step-by-step explanation:
Uma pessoa decide fazer uma reforma na sala de
sua casa e, para não provocar problemas estruturais,
resolve analisar a planta da construção primeiro. Ela
nota que a planta da casa está em uma escala de 1:200
e mostra que a área da sala é de 21 cm².
Qual é a área real da sala, em m²?
A 19
B 38
C42
D 84
E168
Sea=4x⁵-x³+7 y b(x)=2x⁵+x²
Al dividir a entrar b podemos encontrar polinomios únicos, conciente de que y resuido r que satisfacen la ecuación
Donde de r(x) es menor que el grado de b(c)
Cuál es la conciente de que (x)
Y el resuido de r(x)
En resumen, al dividir Sea=4x⁵-x³+7 entre b(x)=2x⁵+x², obtenemos un cociente de 2x³-x² y un residuo de -2x²+7.
Para encontrar los cocientes y el residuo al dividir Sea=4x⁵-x³+7 entre b(x)=2x⁵+x², debemos realizar la división larga de polinomios. El procedimiento es similar a la división larga de números enteros:
2x³ -x² +0x +0
---------------------------------
2x⁵ | 4x⁵ +0x⁴ -x³ +0x² +0x +7
4x⁵ +0x⁴
-------------
0x⁴ -x³
0x⁴ +0x³
-------------
-x³ +0x²
-x³ +0x²
-------------
0x² +0x
0x² +0x
------------
7
2x⁵ +x²
--------
-2x² +7
Por lo tanto, el cociente de la división es 2x³-x², y el residuo es -2x²+7. Es importante notar que el grado del residuo (grado 2) es menor que el grado del divisor b(x) (grado 5), como se requiere en la definición de la división de polinomios.
La respuesta a la pregunta "cuál es la conciente de que (x)" no es clara, ya que no está claro lo que se está pidiendo. Podría ser una pregunta incompleta o una cuestión mal redactada.
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( Need Help Please and thank you! )
Answer:
( x - 5 )
Hope this helps!
Step-by-step explanation:
[tex]2x^{2} -7x-15[/tex] can factor into ( 2x + 3 ) ( x - 5 ).
( 2x + 3 ) ( x - 5 ) = ( cross multiply ) : [tex]2x^{2} -10x + 3x - 15[/tex] = [tex]2x^{2} -7x-15[/tex].
At a dog show, the mean weight of the Norfolk Terriers is
11.5 pounds with a MAD of 2. The mean weight of the
Cairn Terriers is 13 pounds with a MAD of 1.8. Express the
difference in mean weights as a multiple of the MAD for
both dog breeds. Show your work.
Answer:
Step-by-step explanation:
To express the difference in mean weights as a multiple of the MAD for both dog breeds, we can use the formula:
(difference in means) / (mean absolute deviation)
Let's plug in the values given in the problem:
(difference in means) = 13 - 11.5 = 1.5
(mean absolute deviation) = 2 + 1.8 / 2 = 1.9 (taking the average of the two MADs)
Now we can calculate:
(difference in means) / (mean absolute deviation) = 1.5 / 1.9 ≈ 0.7895
Therefore, the difference in mean weights between the two breeds is approximately 0.7895 times the average MAD for both breeds.
y^2-16/4y-16/y+4/16y is
Answer: 4y^2y-80+y^2/4y
Step-by-step explanation:
whats 2+2? i rlly need to know
Answer:
4
Step-by-step explanation:
2+2 = 4
The answer is 2+2 = 4.
A TV cable company has 9600 subscribers who are each paying $36 per month. It can get 160 more subscribers for each $0.50 decrease in the monthly fee. What rate will yield maximum revenue, and what will this revenue be?
The function has the maximum revenue of $348,480 with the increasing rate of $33.
Explain about the maxima of function:The highest and smallest values of a function, respectively, can either be found inside a specific range or distributed throughout the entire domain. They are also sometimes referred to collectively as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, accordingly.
Given data:
We are aware that monthly subscription fees are $36.The corporation can increase its subscription count for a $0.50 drop.We also know that the business has 9600 subscribers and has the capacity to add 160 more.The overall revenue is thus:
y = (36 - 0.50x)(9600 + 160x)
Differentiate with respect to x.
y ' = (-0.50)(9600 + 160x) + 160(36 - 0.50x)
y' = -4800 - 80x + 5760 - 80x
y' = 960 - 160x
To find x, put y' = 0
960 - 160x = 0
x = 960/160 = 6 (critical point)
Function is decreasing in interval - [6, +∞)
Increasing Function in interval - (-∞, 6]
Thus, the function has the maximum value at x = 6.
maximum revenue f(6):
f(6) = (36 - 0.50x)(9600 + 160x)
f(6) = (36 - 0.50(6))(9600 + 160(6))
f(6) = $348,480
Rate : 36 - 0.50(6) = $33
The function has the maximum revenue of $348,480 with the increasing rate of $33.
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Cost of Production Report
Bavarian Chocolate Company processes chocolate into candy bars. The process begins by placing direct materials (raw chocolate, milk, and sugar) into the Blending Department. All materials are placed into production at the beginning of the blending process. After blending, the milk chocolate is then transferred to the Molding Department, where the milk chocolate is formed into candy bars. The following is a partial work in process account of the Blending Department at October 31:
ACCOUNT Work in Process—Blending Department ACCOUNT NO.
Date Item Debit Credit Balance
Debit Balance
Credit
October 1 Bal., 2,300 units, 3/5 completed 46,368
31 Direct materials, 26,000 units 429,000 475,368
31 Direct labor 100,560 575,928
31 Factory overhead 48,480 624,408
31 Goods transferred, 25,700 units ?
31 Bal., ? units, 1/5 completed ?
Required:
1. Prepare a cost of production report, and identify the missing amounts for Work in Process—Blending Department. If an amount is zero enter "0". If required, round your cost per equivalent unit answers to the nearest cent.
Bavarian Chocolate Company
Cost of Production Report—Blending Department
For the Month Ended March 31
The missing amounts for Work in Process - Blending Department are: 25,700 units, and $70,944 for direct materials.
Cost of Production Report
Bavarian Chocolate Company processes chocolate into candy bars.
The process begins by placing direct materials (raw chocolate, milk, and sugar) into the Blending Department.
All materials are placed into production at the beginning of the blending process.
After blending, the milk chocolate is then transferred to the Molding Department, where the milk chocolate is formed into candy bars.
The following is a partial work in process account of the Blending Department at October 31:
ACCOUNT Work in Process—Blending Department ACCOUNT NO.
Date Item Debit Credit Balance
Debit Balance
Credit
October 1 Bal., 2,300 units, 3/5 completed 46,368
31 Direct materials, 26,000 units 429,000 475,368
31 Direct labor 100,560 575,928
31 Factory overhead 48,480 624,408
31 Goods transferred, 25,700 units.
1. Prepare a cost of production report, and identify the missing amounts for Work in Process—Blending Department. If an amount is zero enter "0". If required, round your cost per equivalent unit answers to the nearest cent.
Bavarian Chocolate Company
Cost of Production Report—Blending Department
For the Month Ended March 31
Bavarian Chocolate Company
Cost of Production Report—Blending Department
For the Month Ended October 31
Equivalent Units Schedule
Direct Materials Conversion Costs
Units to be accounted for:
Work in process, October 1 (3/5 completed) 2,300 2,300
Units started in October 26,000 26,000
Total units to be accounted for 28,300 28,300
Units accounted for:
Goods transferred to the Molding Department (25,700 units × 100%) 25,700 25,700
Work in process, October 31 (1/5 completed):
Total units accounted for:
Costs to be accounted for:
Direct materials cost $429,000
Direct labor cost $100,560
Factory overhead cost $48,480
Total costs to be accounted for $578,040
Costs accounted for:
Direct materials cost (26,000 units × $15 per unit) $390,000
Direct labor cost (2,300 units × $44 per unit) 101,200
Factory overhead cost (2,300 units × $21.12 per unit) 48,576
Total costs accounted for $539,776
Cost per Equivalent Unit:
Direct materials cost ($429,000 ÷ 28,300 units) $15.16
Direct labor cost ($100,560 ÷ 2,300 units) $43.74
Factory overhead cost ($48,480 ÷ 2,300 units) $21.12
Total cost per equivalent unit $80.02
Work in Process—Blending Department
Direct Materials Conversion Costs Total
Balance, October 1 $27,820 $18,548 $46,368
Current costs $352,380 $222,548 $574,928
Total cost $380,200 $241,096 $621,296
Less: Goods transferred to the Molding Department (25,700 units × $80.02 per unit) (2) $2,048 $2,048
Balance, October 31 (2) $378,152 (2) $239,048 (2) $617,200
(1) Equivalent units of direct materials and conversion costs have been calculated based on the weighted-average method.
(2) The missing amounts for Work in Process—Blending Department are:
Units, October 31: 2,600 units (28,300 total units – 25,700 transferred units).
Direct Materials, October 31: $352,380 (current costs) - $390,000 (costs accounted for) = -$37,620 (overallocated)
Conversion Costs, October 31: $222,548 (current costs) - $241,096 (costs accounted for) = -$18,548 (overallocated).
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Mailani saves some money in a box under her bed. She deposits an additional amount into a savings account where it earns interest compounded annually. This situation can be modeled by the function . Which statement is true? Select all that apply.
The correct statements are:
Mailani saves $200 in a box under her bed.The y-intercept of the function is (0, 700).Explanation:
The function f(x) represents the total amount of money that Mailani has saved after x years. The first term 500 represents the initial amount she saved in the box under her bed, and the second term (1+0.04)^x represents the amount she deposited into the savings account, which earns an interest rate of 4% compounded annually. The third term +200 represents the additional amount she deposited every year into the savings account.
The range of the function is y>=500, since the initial amount saved is 500, and the function is increasing with time.The y-intercept of the function is (0, 700), not (0, 200), because the initial amount saved in the box is 500, and the additional amount deposited into the savings account is 200 per year, so after 0 years, the total saved amount is 500+200=700.The function does not have an asymptote at y=200. An asymptote is a line that a graph approaches but never touches. In this case, the function is increasing with time, so it does not approach any line as x gets larger.Learn more about asymptote here brainly.com/question/4084552
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Full question:
Mailani saves some money in a box under her bed. She deposits an additional amount into a savings account where it earns interest compounded annually. . This situation can be modeled by the function
[tex]f(x)= 500(1+0.04)^x+200[/tex]
Which statements are true? Select all that apply.
The range of the function is y>=0Mailani saves $200 in a box under her bed.The y-intercept of the function is (0, 200).The function has an asymptote at y = 200.5. Counting problems, leave answers as expressions, e.g., 10 npr 4, 8 nCr 3 or 35 [5 pts each part]
a) A club elects a steering committee of 5. Among these 5, a chair and secretary are chosen. How many different sets of committees (including officer selection) are possible if club has 15 members? Officers are not the same as the non-officer members, so this is hybrid permutation/combination problem.
b) At an event that drew 100 people where each attendee gets one raffle ticket, there are 6 raffle prizes worth $200, $100, $50, $25, $25, $25. How many different raffle ticket winner selections are possible? Be careful, the $25 prizes are equivalent, so this is hybrid permutation and combination problem.
c)If repeats are allowed but a code cannot begin with 0, how many six-digit PIN codes can be made?
Answer:
Step-by-step explanation:
a) The steering committee of 5 can be chosen from 15 members in 15 nCr 5 ways. Once the committee is chosen, the chair can be selected in 5 ways and the secretary can be selected in 4 ways (since the chair cannot also be the secretary). Therefore, the total number of different sets of committees (including officer selection) is:
15 nCr 5 * 5 * 4 = 3,003,600
b) Each of the 6 raffle prizes can be awarded to any of the 100 people, so there are 100 choices for the first prize, 99 choices for the second prize, and so on, down to 95 choices for the sixth prize. However, since the three $25 prizes are equivalent, we need to divide by 3! to account for the ways in which the $25 prizes can be arranged. Therefore, the total number of different raffle ticket winner selections is:
(100 * 99 * 98 * 97 * 96 * 95) / (3!) = 903,450,240,000
c) Since repeats are allowed and the code cannot begin with 0, there are 9 choices for the first digit and 10 choices for each of the remaining digits. Therefore, the total number of six-digit PIN codes that can be made is:
9 * 10^5 = 9,000,000
pls help this is due in 20 mins
The quadratic function's equation, when given the numbers in the table, can be found to be f(x) = x^2 - 5x + 6.
How to find the quadratic function's equation ?We are given a table of values and need to find the quadratic function in standard form: f(x) = ax^2 + bx + c. Let's use the points (-6, 72), (-4, 42), and (-3, 30).
For point (-6, 72):
72 = a(-6)^2 + b(-6) + c
For point (-4, 42):
42 = a(-4)^2 + b(-4) + c
For point (-3, 30):
30 = a(-3)^2 + b(-3) + c
Let's use the elimination method.
1 - 3) 42 = 27a - 3b
2 - 3) 12 = 7a - b
b = 7a - 12
Substitute this expression for b into the first equation:
42 = 27a - 3(7a - 12)
42 = 27a - 21a + 36
6 = 6a
a = 1
Now that we know a = 1, let's find b:
b = 7(1) - 12
b = -5
Finally, let's find c by substituting a and b into any of the original equations. We'll use the first one:
72 = 36(1) - 6(-5) + c
72 = 36 + 30 + c
6 = c
So, the quadratic function in standard form is:
f(x) = x^2 - 5x + 6
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The foci for the hyperbola (x-1)^2/25 - (y+3)^2/9=1 are (1 + square root 34, -3) and (1 - square root 34, -3)
A. True
B. False
The assertion is accurate. This mean option that is selected should be true
The formula c = √(a 2 + b 2), where a and b are the lengths of the semi-major and semi-minor axes, respectively, yields the foci of a hyperbola.
What exactly is hyperbola?. A hyperbola is a particular kind of conic section that resembles two slightly mirrored parabolic curves. It is described as the collection of all points in a plane where the difference between the locations of two fixed points (referred to as foci) is always constant.
Each of the two branches of a hyperbola resembles a parabola. In relation to the hyperbola's centre, the branches are symmetric. The semi-major axis is the distance between the centre and each vertex, whereas the semi-minor axis is the distance between the centre and each terminal of the transverse axis.
When a² = 25 and b² = 9,
the hyperbola (x-1)2/25 - (y+3)2/9=1 can be calculated.
In light of this, c = √(25 + 9) = √ (34).
The hyperbola's center is located at (1, -3).
The foci are at (1 + √(34), -3) and (1 - √(34), -3), respectively.
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Estimate each project draw a diagram if necessary 2/3 x 26
Each product of the fractions are
Part1. =17.33
Part2.= 0.73
Part3.=45.93
Define multiplicationMultiplication is a mathematical operation that involves combining two or more numbers to obtain a product or result. Multiplication is a fundamental arithmetic operation that is used in a wide range of mathematical applications, from simple calculations such as calculating the area of a rectangle, to more complex problems in algebra, geometry, and calculus.
Part1.⅔×26
Multiplying 2 and 26, we get
52/3
Now, dividing it with3, we get
17.33
Part2.⅞×5/6
Multiplying 7 and 5 and 8 and 6, we get
35/48
Now, dividing 35 and 48, we get
.73
Part3.5 ⅕× 8 ×⅚
Solving the improper fractions;
26/5×53/6
Multiplying 26 and 53 and 5 and 6, we get
1378/30
Now, dividing 35 and 48, we get
45.93.
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if log x of y=2 and xy=27 find the values of x and y
When we enter x = 3 into the first equation, we obtain: y = 2 log 3 y = 32 y = 9 .Hence, x=3 and y=9.
how can we describe logarithm ?A log is a mathematical function used to calculate how many times the base, or initial value, must be increased by itself to produce the target value. In other terms, a logarithm is an exponent's negative action.
The base-10 logarithm is the most widely used type of logarithm, though there are other types as well. Some many mathematical and scientific tasks include the usage of logarithms, such as estimating the pH of a solution, gauging the volume of sound, and estimating population growth rates.
given
As we are aware that log x of y = 2, x2 = y.
We also understand that xy = 27.
When we change y in the second equation to x2, we obtain:
[tex]xx^{2} =7^{2} \\x^{3} = 27\\[/tex]
x = 3
When we enter x = 3 into the first equation, we obtain: y = 2 log 3 y = 32 y = 9 .Hence, x=3 and y=9.
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