Answer + Step-by-step explanation:
an= 4(2)ⁿ⁻¹
First term (n = 1) :
a1= 4(2)¹⁻¹ = 4(2)⁰ = 4×(1) = 4
Second term (n = 2) :
a2= 4(2)²⁻¹ = 4(2)¹ = 4×(2) = 8
Third term (n = 3) :
a3= 4(2)³⁻¹ = 4(2)² = 4×(4) = 16
Fourth term (n = 4) :
a4= 4(2)⁴⁻¹ = 4(2)³ = 4×(8) = 32
ABC is a right angled triangle. If b=90 ac=96 c=30. What is ab?
Answer:
ab=48
Step-by-step explanation:
96/2=48
One side of a triangle is 10 feet long, the second side is 20 feet long. What is the
range of possible values for the third side of the triangle? Why?
The range for the length of the third side is it must be greater than 10 feet and less than 30 feet.
What is the condition for the sides of triangles?The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices.
The length of the third side had to be greater than the difference between the two given sides and less than the sum of the two given sides.
(20 – 10) < S <(20+ 10) ; 10< S < 30
Therefore, the range for the length of the third side is it must be greater than 10 feet and less than 30 feet.
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3. If the perimeter of an equilateral triangle is 36 ft, what is the length of one side?
O 18 ft
O 6 ft
12 ft
9 ft
Answer:
The length of one side is 12ft
Step-by-step explanation:
The triangle is equilateral so all the sides are the same length.
So you are simply going to divide 36ft by the 3 sides.
36ft/3 = 12ft
For the following exercises, determine whether the relation is a function.
1. {(a, b), (c, d), (e, d)}
Answer:
The given relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is a function.
Step-by-step explanation:
A relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is given.
It is required to determine whether the given relation is a function.
To determine whether the given function is a relation, identify the domain and range and then check whether the given relation is a function.
Step 1 of 1
The given relation is {(a, b),(c, d),(e, d)}.
The set of the first components of each ordered pair is called the domain.
From the relation, the domain is {a, c, e}.
The set of the second components of each ordered the range.
From the relation, the range is {b, d, d}.
The given relation is a function. But it is not a one-to-one function.
Which expression is the factorization of x2 + 10x + 21?
(x + 3)(x + 7)
(x + 4)(x + 6)
(x + 6)(x + 15)
(x + 7)(x + 14)\
Equation: x² + 10x + 21
Step 1: Find two numbers that can add up to 10 and be multiplied to 21. We have: 7 & 3, in the sense that 7+3=10, and 7×3=21. Replacing 10 with 7+3, the equation is now → x² + 7x + 3x + 21
Step 2: Get the new equation bracketed → (x² + 7x) (+3x + 21)
Step 3: Use 'x' in the equation. For the first part, we have 'x'. x² = x × x so, bring out one x out side the bracket, divide 7x by = 7 → x (x +7). Do the same for the second part by dividing 21 by 3 = 7, and then bringing out 3 from the bracket → 3 (x + 7).
Bringing everything together, we have: x(x+7) +3(x+7) → (x+3) (x+7)
Final answer:(x+3) (x+7)
Answer:
A. (x + 3)(x + 7)
Step-by-step explanation:
Got it correct… You’re welcome
Rationalize 5+2√3 / 7+4√3
Answer:
Answer is in the 2nd attachment
Step-by-step explanation:
the first attachment is the work done.
Identify all of the root(s) of g(x) = (x2 3x - 4)(x2 - 4x 29). -1 1 -4 4 2 5i 2 - 5i -2 10i -2 - 10i
The roots are (x + 1), (x - 4), (2 + 5i), and (2 - 5i).
g(x) = (x2 - 3x - 4)(x2 - 4x + 29)
Let us first consider x^2 - 3x - 4
By splitting the middle term
= x^2 + 1x - 4x - 4
= x(x + 1) - 4(x + 1)
= (x + 1)(x - 4)
Now let us consider x^2 - 4x + 29
First group the terms with variable on LHS and move the constant on the other side
x^2 - 4x = -29
Add 4 on both sides
x^2 - 4x + 4 = -29 + 4
x^2 - 4x + 4 = -25
It can be written as perfect squares
(x - 2)^2 = -25
We know that
i =√1
Take square root on both sides
x - 2 = ± 5i
x = 2 ± 5i
So we get,
x = 2 + 5i and x = 2 - 5i
g(x) = (x + 1)(x - 4)(2 + 5i)(2 - 5i)
A square root of a number is a price that, whilst extended by means of itself, offers variety. instance: four × four = 16, so a square root of 16 is four. The word that (−four) × (−four) = 16 too, so −four is likewise a square root of sixteen. The symbol is √ usually way the wonderful rectangular root. example: √36 = 6 (because 6 x 6 = 36).
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Select the correct answer.
Select the simplification that accurately explains the following statement.
3/7 = 73
O A.
100
B.
3
(71)² = 73.71.7371-1-1 = 78 = 7² = 7
(71)² = 78.73.7} = 7.73 = 3-1-7=1-7=7
3
C.
(7³)³ = 7³. 7³. 73 = 73 + } + ³ = 7³ = 7¹ = 7
D. (73)³ = 7³. 73. 73 = 7 · (++) = 7 ⋅ = 7 · 1 = 7
The simplification that represents ∛7=[tex]7^{1/3}[/tex] is [tex](7^{1/3} )^{3} =7^{1/3} .7^{1/3} .7^{1/3} =7^{1/3+1/3+1/3} =7^{1}=7[/tex]
How to simplify an expression?The simplification that accurately explains the statement ∛7 = [tex]7^{1/3}[/tex] is as follows;
Therefore, the simplification is as follows
[tex](7^{1/3} )^{3} =7^{1/3} .7^{1/3} .7^{1/3} =7^{1/3+1/3+1/3} =7^{1}=7[/tex]
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For the following exercises, find the x- and y-intercepts of the graphs of each function.
27. f(x) = −3| x − 2 | − 1
For the function f(x) = -3|x - 2| - 1, we have that:
The function has no x-intercepts.The y-intercept is of y = -7.What is the x-intercept of a function?The x-intercept of a function is the value of x when y = f(x) = 0, hence:
0 = -3|x - 2| - 1
-3|x - 2| = 1
|x - 2| = -1/3
The absolute value cannot be negative, hence the function has no x-intercepts.
What is the y-intercept of a function?The x-intercept of a function is the value of y = f(x) when x = 0, hence:
f(0) = -3|0 - 2| - 1 = -6 - 1 = -7.
The y-intercept is of y = -7.
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Enter the correct answer in the box.
What is the inverse of function f?
f(x)=-7x-4
Answer:
The inverse is -1/7(x+4)
Step-by-step explanation:
We have the function
y = -7x-4
To find the inverse, exchange x and y
x = -7y -4
Solve for y
Add 4 to each side
x+4 = -7y -4+4
x+4 = -7y
Divide each side by -7
-1/7(x+4) = -7y/-7
-1/7(x+4) = y
The inverse is -1/7(x+4)
Class A has 30 pupils and class B has 26 pupils.
Both classes sit the same maths test.
The mean score for class A is 70.
The mean score for both classes is 76.
What is the mean score (rounded to 2 DP) in the maths test for class B?
The mean score of class B is 82. 92
How to determine the mean scoreClass A = 30 pupils
Class B = 26 pupils
Mean score for class A = 70
Mean score of class B = unknown
Total mean score = 76
We have, [tex]\frac{(76 *( 30 + 26) - 70 *30) }{26}[/tex]
Then simply,
Calculate the sum or difference between the classes = [tex]\frac{76 * 56 - 70 * 30}{26}[/tex]
Calculate the product or quotient of the classes = [tex]\frac{4256 - 70 * 30}{26}[/tex]
= [tex]\frac{4256 - 2100}{26}[/tex]
= [tex]\frac{2156}{26}[/tex]
= [tex]\frac{1078}{13}[/tex]
= [tex]82. 92[/tex]
Thus, the mean score of class B is 82. 92
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mrs chapagain borrowed rs 9900 from a bank at the rate of 8% per annum. how much amount should she pay at the end of 2 years
Answer:
If compounding = rs 11547.36
If not compounding = rs 11484
Write the interval using interval notation to describe the set of values shown above.
Use "U" between the two intervals. Use "oo" (two lower case o's) for
∞.
The interval on the number line is (-∞, 2) U [3, ∞)
How to determine the interval?From the number line, we have the following inequalities
x < 2 and x ≥ 3
In inequalities, < and > are represented by brackets i.e. ( and )
While ≤ and ≥ are represented by square brackets i.e. [ and ]
So, we have:
x < 2 and x ≥ 3 = 2) and [3
The intervals must be closed and opened with infinity symbols.
So, we have:
x < 2 and x ≥ 3 = (-∞, 2) and [3, ∞)
Replace and with U
x < 2 and x ≥ 3 = (-∞, 2) U [3, ∞)
Hence, the interval on the number line is (-∞, 2) U [3, ∞)
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How many real solutions does this system of equations have? x² + y² = 25 and x-3y=15
[tex]x - 3y = 15 \\ x = 15 + 3y[/tex]
[tex](15 + 3y) {}^{2} + y {}^{2} = 25[/tex]
[tex]225 + 90y + 9y {}^{2} + y {}^{2} = 25[/tex]
[tex]10y {}^{2} + 90y + 200 = 0[/tex]
[tex]y {}^{2} + 9y + 20 = 0[/tex]
[tex](y + 4)(y + 5) = 0[/tex]
[tex]y = - 4 \: \: \: \: \: \: y = - 5[/tex]
[tex]for \: y= - 4 \\ x = 15 + 3( - 4) = 15 - 12 = 3[/tex]
[tex]for \: y = - 5 \\ x = 15 + 3( - 5) = 15 - 15 = 0[/tex]
Write an equation for the graph below in terms of x
I really need help asap! ty!
The length of AL in the triangle is 12cm.
How to calculate the value?From the information given, angle C = 90° and BAC is given as 2ABC.
In this case, the length of angle BC is given as 24cm. Therefore, the length of AL will be:
= 24/2
= 12..
Therefore, AL = 12cm
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Find the area in square centimeters of the composite, shape shown
below. Enter only a number as your answer.
A
11 cm
B
E
13 cm
18 cm
D
7 cm
C
The area of the composite shape is 136 square cm
Area of a composite functionThe area of the composite function is expressed as;
Area = area of triangle + area of rectangle
Area of the composite shape = (1/2* 4 * 5) + (7*18)
Area of the composite shape = 10 + 126
Area of the composite shape = 136 square cm
Hence the area of the composite shape is 136 square cm
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On a coordinate plane, quadrilateral J K L M with diagonals is shown. Point J is at (4, 5), point K is at (5, 1), point L is at (1, 2), and point M is at (1, 5).
Which statement proves that quadrilateral JKLM is a kite?
∠M is a right angle and MK bisects ∠LMJ.
LM = JM = 3 and JK = LK = StartRoot 17 EndRoot.
MK intersects LJ at its midpoint.
The slope of MK is –1 and the slope of LJ is 1.
The statement that proves that that quadrilateral JKLM is a kite is: (Option B) which indicates that:
LM = MJ = 3; a
JK = KL = √17
What is the explanation for the above?We know the following:
J = (4,5)
K = (5,1)
L = (1,2)
M = (1, 5)
What is the proof?We must commence by computing the length of the sides of the quadrilateral using:
D = [tex]\sqrt{((x1-x2)^{2} + (y1 -y2)^{2} }[/tex]
JK = [tex]\sqrt{(4-5)^{2} + (5-1)^{2} }[/tex]
= [tex]\sqrt{17}[/tex]
KL = [tex]\sqrt{(5-1)^{2} + (1-2)^{2} }[/tex]
= [tex]\sqrt{17}[/tex]
LM = [tex]\sqrt{(1-1)^{2} + (5-5)^{2} }[/tex]
= [tex]\sqrt{9}[/tex]
= 3
MJ = [tex]\sqrt{(1-4)^{2} + (5-5)^{2} }[/tex]
= [tex]\sqrt{9}[/tex]
= 3
From the above, it is clear that
LM = MJ = 3; and
JK = KL = [tex]\sqrt{17}[/tex]
QED
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Answer: B
Step-by-step explanation:
GIVING BRAINLIEST TO THE BEST ANSWER! Choose the proportion to use to solve side LM.
A. 9/13.5 = x/11
B. 9/11 = 13.5/x
C. 9/13.5 = x/21
D. 9/11 = x/21
(the / represents fractions)
The equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM
Similarity theorem of triangleIn order to find the measure of LM, we will take the ratio of the sides of the similar triangles.
Using the equation as shown
DF/EF = LK/LM
DF/LK = EF/LM
Substitute the measure of the sides
9/13.5 = 14/LM
Hence the equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM
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What are the domain and range of the exponential function below?
F(x) = 4x + 3
A. Domain: All real numbers Range: All real numbers greater than 0
B. Domain: All real numbers greater than 0 Range: All real numbers greater than 3
C. Domain: All real numbers greater than 0 Range: All real numbers greater than 0
D. Domain: All real numbers Range: All real numbers greater than 3
The domain and the range of the function are all set of real numbers
How to determine the domain and the range?The function is given as:
f(x) = 4x + 3
The above function is a linear function
Linear functions have a domain and a range of all set of real numbers
Hence, the domain and the range of the function are all set of real numbers
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please help me find the solution
Answer:
22
Step-by-step explanation:
BD bisects <ABC, this means the half-line divided the angle into two equal parts.
If m<ABC is equal to 44 then m<ABD is
44/2 = 22
The difference of two complementary angles is 48. Find the measures of the two angles.
The smaller angle is
Submit Question
and the larger angle is
B
The larger angle is 55 deg at the larger angle.
We have to know which angles are called Complementary Angles...
if we add two angles and the total will be equal to 90 deg
let's say one angle is x and another angle is y
as they are complementary angles from the definition we can write the equation x + y = 90
one angle is 20 deg more than another one so from the above condition we write x = 20 + y
Substitute the value of x in the first eaquation we get, 20 + y + y = 90
Then, 20 + 2y = 90
subtracting 20 from both sides,
2y = 90-20 = 70
dividing both sides by 2,
2y/ 2 = 70 / 2
y = 35
So we got one angle is 35 deg
another angle is 35 + 20 = 55 deg.
Our answer is 55 deg the larger angle.
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Susan's calculator has a key that replaces the number displayed with its cube. If a² is displayed, how many times must Susan press the " cubing" key to display a number that is greater than 10^9?
Please explain it step-by-step! Also, I will give you a brainlist!!
If we want to replace a input and display an output greater than 10⁹ in Susan's calculator, then we want at least 3 consecutive operations.
How to determine a power by a "cubing" key
In accordance with the statement, Susan's calculator performs the following operation by pressing the "cubing" key:
x → x³
If we need to display a number that is greater than 10⁹, then we need to press the "cubing" key as many as needed. By algebra we have the following property for a power:
[tex](x^{m})^{n} = x^{m\cdot n}[/tex] (1)
Since we have a "cubing" key and we are supposed to make consecutive operation, we derive the following operation:
x → [tex]x^{3^{i}}[/tex], where i is the number of consecutive "cubing" operations.
If we want to replace a input and display an output greater than 10⁹ in Susan's calculator, then we want at least 3 consecutive operations.
Remark
The statement presents typing mistakes, correct form is shown below:
Susan's calculator has a key that replaces the number displayed with its cube. If a³, is displayed, how many time must Susan press the "cubing" key to display a number that is greater than 10⁹.
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The area of a rectangular pool is (x 2 + 17x + 72) square meters. There is a 3-meter-wide concrete
walkway around the pool. Write expressions to represent the dimensions of the outside border of the
walkway. (Lesson 8.1)
Step-by-step explanation:
the area is
(x² + 17x + 72) m²
it is the result of the usual
length × width
calculation.
length = x + g
width = x + h
length × width = x² + gx + hx + ab = x² + (g+h)x + gh =
= x² + 17x + 72
g + h = 17
gh = 72
just by looking at it that gives us 9 and 8 as g and h.
FYI - formally to calculate them we can say
g = 17 - h
(17 - h)h = 72
17h - h² = 72
h² - 17h + 72 = 0
the solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = h
a = 1
b = -17
c = 72
h = (17 ± sqrt(17² - 4×1×72))/(2×1) =
= (17 ± sqrt(289 - 288))/2 = (17 ± 1)/2
h1 = (17 + 1)/2 = 18/2 = 9
h2 = (17 - 1)/2 = 16/2 = 8
as we can see
g = 17 - h
if we say h = 9, then g = 8.
if we say h = 8, then g = 9.
so, these are our solutions.
we simply pick that length is longer than width, so, g = 9, h = 8.
the area including the walkway is then
(length + 3)(width + 3) =
= (x + 9 + 3)(x + 8 + 3) = (x + 12)(x + 11) m²
and the dimensions incl. the walkway are
length = x + 9 + 3 = x + 12
width = x + 8 + 3 = x + 11
Determine whether you would use the Law of Sines or the Law of Cosines to solve each triangle. Do not solve the triangle.
A triangle is a three-edged polygon with three vertices. Only the law of Sine can be applied to solve the triangle.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The sum of all three angles can be written as,
118° + 22° + x = 180°
x = 40°
For the sine rule to be applicable, two angles and a side or an angle and two sides are needed. Therefore, the law of Sine can be applied to solve the triangle.
For the cosine rule to be applicable, two sides and an angle between them is needed to be known, hence, the law of cosine can not be applied.
Hence, Only the law of Sine can be applied to solve the triangle.
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1. Annie and her friends are playing a game called Doubles. In the game, a player
rolls two number cubes at the same time. The outcome of each roll is the sum of the
two number cubes. Extra points are scored for rolling doubles the same number
on both number cubes.
-
Part A: Complete this table to show the sample space for each roll in the game. (6
points)
HELP ASAP WILL GIVE BRAINLIEST!!!!
The sample space is a combination of these two dice as we have shown in the attachment
Die A = {1,2,3,4,5,6}Die b = {1,2,3,4,5,6}What is sample space?This is the defined to be the set of all of the possible outcomes that can exist or be possible in a random experiment.
The question has two dice. These dice are made up of numbers from 1 to 6 each.
Die A = {1,2,3,4,5,6}
Die b = {1,2,3,4,5,6}
The sample space would be pairs of two of these two dices. The total number in the sample space would be 36.
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104, 137, 154, 131, x; mean= 130
Hello!
The mean is the average of the terms.
⇒ Mean = Sum of terms / Number of terms
⇒ 130 = 104 + 137 + 154 + 131 + x / 5
⇒ x + 526 = 650
⇒ x = 124
∴ The missing number is 124.
Find sin 0
a. 8/15
b. 15/8
c. 15/17
D 8/17
Answer:
C
Step-by-step explanation:
first you need to memorize
SOH CAH TOA
IT means
Sine =opposite/hipotenuse
Cosine = adjecent/hipotenuse
tangent = opposite/adjecent
in this case, we need to find sine
so it's SOH
opposite of theta Θ is 15
and it's hipotenuse , we don't know yet. so need to find it by using Pythagorean theorem
let it be x
x =√ 15²+ 8²
=√ 225+ 64
=√289
= 17
so the answer is 15/17
Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
Answer:
10
Step-by-step explanation:
2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.
The total number of legs in the room would be 10.
How to identify how many legs are on the floor of the room?From the given information, it can be inferred that none of the legs of the animals is on the floor of the room.
It is given that 2 dogs, 4 horses, 1 giraffe, and a duck are lying on the bed. 3 chickens are flying over a chair.
The legs of the bed and the chair do.
So we can say that the chair and the bed each have four legs.
so that would be two more legs.
In total we have:
4 + 4 + 2 = 10.
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Help me to solve this question
Answer:
[tex]\left \{ {{\theta_1=\frac{\pi }{4} } \atop {\theta_2=\frac{3\pi }{4} }} \right. .[/tex]
Step-by-step explanation:
[tex]2*cos^2\theta-1=0\ \ \ \ (0^0\leq \theta\leq 360^0)\ \ \ \ \ \theta=?\\2*cos^2\theta-(sin^2\theta+cos^2\theta)=0\\2*cos^2\theta-sin^2\theta-cos^2\theta=0\\cos^2\theta-sin^2\theta=0\\cos2\theta=0\\0^0\leq \theta\leq 360^0\ \ \ \ \Rightarrow\\\left \{ {{2\theta=\frac{\pi }{2}\ |:2 } \atop {2\theta=\frac{3\pi }{2}\ |:2 }} \right. \ \ \ \ \left \{ {{\theta_1=\frac{\pi }{4} } \atop {\theta_2=\frac{3\pi }{4} }} \right. .[/tex]
Good luck and have a nice day!