3
Find the value of a
in the equation,(3+4√3)(2-a√3)=-18+2√3
Given:
The equation is:
[tex]\left(3+4\sqrt{3}\right)\left(2-a\sqrt{3}\right)=-18+2\sqrt{3}[/tex]
To find:
The value of a.
Solution:
We have,
[tex]\left(3+4\sqrt{3}\right)\left(2-a\sqrt{3}\right)=-18+2\sqrt{3}[/tex]
On simplification, we get
[tex](3)(2)+(4\sqrt{3})(2)+(3)(-a\sqrt{3})+(4\sqrt{3})(-a\sqrt{3})=-18+2\sqrt{3}[/tex]
[tex]6+8\sqrt{3}-3a\sqrt{3}-4a(3)=-18+2\sqrt{3}[/tex]
[tex]6+8\sqrt{3}-3a\sqrt{3}-12a=-18+2\sqrt{3}[/tex]
[tex](6-12a)+(8-3a)\sqrt{3}=-18+2\sqrt{3}[/tex]
On comparing both sides, we get
[tex]6-12a=-18[/tex]
[tex]-12a=-18-6[/tex]
[tex]a=\dfrac{-24}{-12}[/tex]
[tex]a=2[/tex]
And,
[tex]8-3a=2[/tex]
[tex]-3a=2-8[/tex]
[tex]a=\dfrac{-6}{-3}[/tex]
[tex]a=2[/tex]
Therefore, the value of a is 2.
Help I need HELP FAST I give brainliest.
IGNORE THIS TEXT: Which graph shows this solution set? y is greater than negative 2 and y is less than or equal to 2Answer options with 5 optionsA.The graph shows a number line.Short description, The graph shows a number line.,Long description,A number line has negative 2 and positive 2. At negative 2 and positive 2, there are filled in circles. Between negative 2 and positive 2, the number line is shaded. B.The graph shows a number line.Short description, The graph shows a number line.,Long description,A number line has negative 2 and positive 2. At negative 2 and positive 2, there are open circles. Between negative 2 and positive 2, the number line is shaded. C.The graph shows a number line.Short description, The graph shows a number line.,Long description,A number line has negative 2 and positive 2. At negative 2, there is an open circle. At positive 2, there is a filled-in circle. Between negative 2 and positive 2, the number line is shaded. D.The graph shows a number line.Short description, The graph shows a number line.,Long description,A number line has negative 2 and positive 2. At negative 2, there is an open circle. At positive 2, there is a filled-in circle. The number line is shaded to the left of negative 2 and to the right of positive 2. E.The graph shows a number line.Short description, The graph shows a number line.,Long description,A number line has negative 2 and positive 2. At negative 2, there is filled in circle. At positive 2, there is an open circle. The number line is shaded to the left of negative 2 and to the right of positive 2.
Answer:
The answer choice would be C
Question 7 of 10
Identify the range of the function shown in the graph.
A. 1sys7
B. 1 sys 4
c. y21
D. All real numbers
helppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
perimeter is add up all the values on the sides
5+3+4=12
hope it helps :)
15 31/40 to the nearest whole number
Answer:
16
Step-by-step explanation:
Because the number is closer to 16, it can be rounded off to that. 15 31/40 is the same as 15.78. When the decimal is over .50 it is rounded up to the next whole number, but when it is under .50 it si rounded down to the nearest whole number. ex. since this one is over the .50, it's rounded up, but if it were 15.36 then it would be rounded down to 15. hope this helps :D
it takes 3 cups of flour to make 1 batch of cookies how many cups of flour will it take to make 6 batches of cookies
Answer:
6*3=18 cups
Step-by-step explanation:
3 cups of flour to make 1 batch
so to make 6 batches = 3*6 = 18
Tom and Susan park at different lots.
To see which lot is busier, they count the numbers of cars in the lots each day as they arrive.
Their data are shown in the box plots.
the questions to compare the variabilities of the data sets.
1. What is the interquartile range for Tom's data? Explain how you found the interquartile range.
Write your answer in the space below.
1
Answer:
Tom = 5
Susan = 3
Step-by-step explanation:
FROM THE BOXPLOT :
Tom's IQR :
IQR = Q3 - Q1
Q3 = third quartile (value at the endpoint of the box)
Q1 = 1st quartile (value at the beginning of the box)
IQR = 9 - 4
IQR = 5
SUSAN :
IQR = Q3 - Q1
Q3 = third quartile (value at the endpoint of the box)
Q1 = 1st quartile (value at the beginning of the box)
IQR = 8 - 5
IQR = 3
please help me out please
Answer:
DCB = 44 degree
Step-by-step explanation:
DAB (given = 100
(180-100 ) / 2 = 40
ADB = ABD = 40 degree (each)
ADC (given = 108
BDC = DBA = 108-40 = 68 degree;
(subtracting angle inscribed within another triangle)
Triangle DBC = 180- 68+68 = 180 - 136 = 44 degree
Find DCB We have found BDC and DBA by deducting ADB from ADC
to get BDC
Then we deduct BDC from ADC to get DCB
A training field is formed by joining a a rectangle and two semicircles, as shown below. The rectangle is 89 m long and 69 m wide. What is the length of a training track running around the field? (Use the value 3.14 for {pi symbol}, and do not round your answer. Be sure to include the correct unit in your answer.)
I have no clue this queshtion seems pretty hard.
R.
A circle has a diameter of 6 inches.
Show your work to find the following (use
3.14 for pi):
A) Area of the circle
B) Circumference of the circle
FIND THE VALUES FOR ANGLES A, B, C,
CuOUL/CYPLAIN YOUR
Answer: A IS CORRECT
Step-by-step explanation:
Josie makes fruit punch by mixing fruit juice and lemonade in the ratio 1:3
She needs to make 28 litres of punch for a party,
How much of each ingredient does she need?
Fruit juice = 7 litres Lemonade = 21 litres [4]
During the party Josie decides to make some more.
She has 3 litres of fruit juice left and plenty of lemonade,
How much extra punch can she make?
litres
To make the second batch of punch go further Josie
adds 3 more litres of lemonade,
What is the ratio of fruit juice to
lemonade in the second batch?
Mrs. Shiroff charges $97 for materials for each bookcase she builds.
She also charges $30 for each hour she works building them. It takes
Mrs. Shiroff 90 hours to build 9 bookcases. How much will she charge?
Isaiah’s vegetable garden is `15` feet long by `5` feet wide.
He plans to increase the width and length of his garden and put a fence around it.
He writes this expression for the total amount of fencing:
(x+15) + (x+5) + (x+15) + (x+5)
Describe what `x` represents in this situation.
Answer:
Step-by-step explanation:
x is the quantity by which the original measurements of the garden is increased. For example: the original width is 5 ft and x is the amount by which this is increased.
x here is the added value in the width and length of his garden to increase the fencing.
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.
Given that, Isaiah’s vegetable garden is 15 feet long by 5 feet wide.
He wants to increase the width and length of his garden and put a fence around it.
He writes an expression for the same, we need to find what is x here,
(x+15) + (x+5) + (x+15) + (x+5) is giving the perimeter of the farm after increasing the width and length of his garden,
So, simply we can say that, x here is the extra length and width.
The farmer added x to each width and the length to increase his fencing,
So, his new dimension will be = x+15 and x+5
So, the perimeter = 2(x+15+x+5)
Here, the perimeter is fencing =
= 2(x+15+x+5)
= x+15+x+5+x+15+x+5
Hence, x here is the added value in the width and length of his garden to increase the fencing.
Learn more about perimeter, click;
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Consider the salt shaker shown.
5 cm
cm
What is the volume of the salt shaker, including the top? Round your answer to the nearest hundredth.
Volume of Salt Shaker =
Answer:
Volume of salt shaker = 42.4 cm³ (Approx.)
Step-by-step explanation:
Given:
Height of salt shaker = 5 cm
Diameter of salt shaker = 3 cm
Find:
Volume of salt shaker
Computation:
Radius of salt shaker = Diameter of salt shaker / 2
Radius of salt shaker = 3 / 2
Radius of salt shaker = 1.5 cm
Volume of salt shaker = Volume of cylinder + Volume of Hemisphere
Volume of salt shaker = πr²h + (2/3)πr³
Volume of salt shaker = (3.14)(1.5)²(5) + (2/3)(3.14)(1.5)³
Volume of salt shaker = (3.14)(2.25)(5) + (0.667)(3.14)(3.375)
Volume of salt shaker = 35.325 + 7.068
Volume of salt shaker = 42.4 cm³ (Approx.)
Which measurement is closest to the area of the sign in square inches
Option C. The area ≈ 706.86
A ranger spots a forest fire while on a 30-meter observation tower. The angle of depression from the tower to the fire is 14°. To the nearest meter, how far is the fire from the base of the tower?
a. 7 meters
b. 4 meters
c. 124 meters
d. 120 meters
The fire from the base of the tower is at 120 m and Option D is the correct answer.
What is Angle of Depression ?The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards at an object is known as an angle of depression.
The formula is
[tex]\rm sin\;\theta = y/z\\\\\\cos\; \theta = x/z\\\\\\tan\; \theta = y/x[/tex]
where x is the distance between the point of the ground and the object , horizontally,
y is the perpendicular distance between the surface to the object
and z is the measure of line of sight
[tex]\rm \theta[/tex] is the angle of depression = 14°
It is given in the question that y= 30 m
x= ?
To determine we will substitute the value
[tex]\rm tan\; \theta = y/x\\\\\\tan \;14^{o} = 30/ x\\\\\\0.25 = 30/x\\\\\\\x= 30/0.25\\\\\\x= 120 m\\[/tex]
Therefore the fire from the base of the tower is at 120 m and Option D is the correct answer.
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I have a math problem.
Oranges cost 2.50 cents
How much did James pay for 8296 oranges
•ω• Hewo fren!
☆☆●◉✿Answer:✿◉●☆☆
20740
☆☆●◉✿Step-by-step explanation:✿◉●☆☆
Since the oranges cost 2.50 cents each then the ratio would be 2.50 cents to 1 orange, 2.5:1. James is buying 8296 oranges so we would have to multiply the ratio by 8296 since the oranges increased. 1 × 8296 = 8296.
2.5 × 8296 = 20740. James paid 20740 dollars for 8296 oranges. (20740:8296 would be the ratio.)
HOPE I HELPED! ∧∧
→⇒brainliest please? ∑(OΔO )♥♥︎
{WHY SO MANY ORANGES ono}
How many solutions exist for the given equation?
1/2(x + 12) = 4x - 1
zero
one
two
O infinitely many
Answer: X = 2
Step-by-step explanation:
Step 1: Simplify both sides of the equation!
Step 2: Subtract 4x from both sides.
Step 3: Subtract 6 from both sides.
Step 4: Multiply both sides by 2/(-7).
What is the sum of the first 47 terms of the sequence? -215, -201, -187, -173, ...
Answer:
5029
Step-by-step explanation:
There is a common difference between consecutive terms, that is
d = - 201 - (- 215) = - 187 - (- 201) = - 173 - (- 187) = 14
This indicates the sequence is arithmetic with sum to n term
= [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = - 215 and d = 14 , then
= [ (2 × - 215) + (46 × 14) ]
= 23.5 (- 430 + 644)
= 23.5 × 214
= 5029
SOMEONE PLEASE HELP ASAP!!
-missing angle-
What do I do?!
Answer:
156°
Step-by-step explanation:
2x + 4 + 24 = 180
2x + 28 = 180
2x = 180 - 28
2x = 152
x = 152 / 2
x = 76
The missing angle
= 2x + 4
= 2 ( 76 ) + 4
= 152 + 4
= 156°
Which events are mutually exclusive?
Answer:
2.option is the correct answer
Which of the following gives the number of petals of the rose curve r=6cos 20 ?
(A) 1 (B)2 (C) 4 (D) 6
(E) 12
please include work
assalam o aalaikum
Step-by-step explanation:
1. At the Blue Jays game, Steven Matz (height = 1.2m) throws a baseball(140g) straight in
the air with 95N of force for 30cm.
1. What is the speed of the ball 2.4 m above the ground?
2. What is the maximum height of the ball (assuming no air resistance)?
Two squares were used to form a figure. The side length of each square is shown.
8 m
What is the area of the part of the figure that is NOT shaded?
F 80 m2
G 16 m
H8 m2
J 48 m²
Answer:
i think the area if shadded region is 16m
A recipe for pancakes requires 3/4 cup of oil. If Mr. Darcy wants to triple the recipe, how much oil will he need?
Answer:
2.25, or 2 1/4 or 9/4.
Step-by-step explanation:
3/4 times 3 = 9/4
When factored completely, the expression p4 - 81 is equivalent to ....
1. (p2+9)(p2-9)
2. (p2-9)(p2-9)
3. (p2+9)(p+3)(p-3)
4. (p+3)(p-3)(p+3)(p-3)
If 8 people can be seated at a dinner table, how many tables are required to seat 72 people?
Answer:
9
Step-by-step explanation:
Given that ,
8 people can be seated at a dinner table.This is the case of direct proportion where , when quantity increases , the other also increases. Here we can use unitary method.
=> 8 people can sit on 1 table
=> 1 person can sit of 1/8
=> 72 people can sit on 1/8 * 72 = 9 tables
Hence 9 tables is the required answer.find the degree measure of angle HRP?
Cooper Bank Ballpark charges 87 per ticket (t) and $3 to park. Good Foods
Ballpark charges $6 per ticket, and $10 to park. At how many tickets will the
total cost (c) be the same?
Answer:
13.33
Step-by-step explanation:
let p be park.
[tex]t+p = c\\\\t_{2}(x) + p_{2} = c[/tex]
[tex]\\(87)+(3) = 90\\\\(6)x+(10) = 90[/tex]
(6)x needs to make up 80 to get the total cost(c)
80/6 = 13.33
so x should be 13.33
why is solar power a renewable energy source
Answer:
Solar energy is a renewable resource, meaning it won't ever run out or be in short supply. ... Solar energy reaches us via the sun's rays, while fossil fuels come from ancient carbon-rich remains on earth. So, as long as the sun is shining, solar energy will be around.
Step-by-step explanation:
Use the graphs below to help you answer the question.
Which is the best approximation to a solution of the equation ln x = x - 2
- 2
1
2
3
Answer:
Here we can not see the graph, so I will upload a new graph for this case.
To solve the equation:
Ln(x) = x - 2
We can first graph the equations:
y = Ln(x)
y = x - 2
And find the point where these graphs intersect.
In the graph we can see two intersects.
One (the first one) is near the point ( 0.15, -1.85)
And the other intersection is near the point (3.14, 1.14)
Then two possible values of x that are solutions of:
ln(x) = x - 2
are:
x = 0.15
x = 3.14