Answers
Answer: [tex]\sum^{24}_{n=1} (4n+5)[/tex]
Step-by-step explanation:
This is an arithmetic series with a common difference of 4, so we can immediately eliminate the two left-hand options.
To determine which of the two options on the right is correct, we can determine the first term of each sum expanded out.
For the top right, the first term is 4(0)+5=5, which does not match the first term of the given sequence.For the bottom right, the first term is 4(1)+5=9, which does match the first term of the given sequence.Related Questions
f(x) = x² + (k-6) x +9, k * 0. The roots of the equation f(x) = 0 are a and B. (a) Find, in terms of k, the value of (i) a² + ß² (ii) a² ß² Given that 9(a²+ B²) = 2a²p². find the value of k. (b) (c) Using your value of k, and without solving the equation f(x) = 0. form a quadratic equation, with integer coefficients, which has roots and 33² f ( x ) = x² + ( k - 6 ) x +9 , k * 0 . The roots of the equation f ( x ) = 0 are a and B. ( a ) Find , in terms of k , the value of ( i ) a² + ß² ( ii ) a² ß² Given that 9 ( a² + B² ) = 2a²p² . find the value of k . ( b ) ( c ) Using your value of k , and without solving the equation f ( x ) = 0 . form a quadratic equation , with integer coefficients , which has roots and 33²
Answers
(a) If [tex]\alpha[/tex] and [tex]\beta[/tex] are roots of [tex]f(x)[/tex], then we can factorize [tex]f[/tex] as
[tex]f(x) = x^2 + (k - 6) x + 9 = (x - \alpha) (x - \beta)[/tex]
Expand the right side and match up coefficients:
[tex]x^2 + (k-6) x + 9 = x^2 - (\alpha + \beta) x + \alpha \beta \implies \begin{cases} \alpha + \beta = -(k-6) \\ \alpha \beta = 9 \end{cases}[/tex]
Now, recall that [tex](x+y)^2 = x^2 + 2xy + y^2[/tex]. It follows that
[tex]\boxed{\alpha^2 + \beta^2} = (\alpha + \beta)^2 - 2\alpha\beta = (-(k-6))^2 - 2\times9 = \boxed{k^2 - 12k + 18}[/tex]
and
[tex]\boxed{\alpha^2\beta^2} = 9^2 = \boxed{81}[/tex]
(b) If [tex]9(\alpha^2+\beta^2) = 2\alpha^2\beta^2[/tex], then
[tex]9 (k^2 - 12k + 18) = 2\times81 \implies 9k^2 - 108k = 0 \implies 9k (k - 12) = 0[/tex]
Since [tex]k\neq0[/tex], it follows that [tex]\boxed{k=12}[/tex].
(c) The simplest quadratic expression with roots [tex]\frac1{\alpha^2}[/tex] and [tex]\frac1{\beta^2}[/tex] is
[tex]\left(x - \dfrac1{\alpha^2}\right) \left(x - \dfrac1{\beta^2}\right)[/tex]
which expands to
[tex]x^2 - \left(\dfrac1{\alpha^2} + \dfrac1{\beta^2}\right) x + \dfrac1{\alpha^2\beta^2}[/tex]
Reusing the identity from (a-i) and the result from part (b), we have
[tex]\left(\dfrac1\alpha + \dfrac1\beta\right)^2 = \dfrac1{\alpha^2} + \dfrac2{\alpha\beta} + \dfrac1{\beta^2} \\\\ \implies \dfrac1{\alpha^2} + \dfrac1{\beta^2} = \left(\dfrac{\alpha + \beta}{\alpha\beta}\right)^2 - \dfrac2{\alpha\beta} = \left(\dfrac{-(k-6)}9\right)^2 - \dfrac29 = \dfrac29[/tex]
We also know from part (a-ii) that [tex]\alpha^2\beta^2=81[/tex].
So, the simplest quadratic that fits the description is
[tex]x^2 - \dfrac29 x + \dfrac1{81}[/tex]
To get one with integer coefficients, we multiply the whole expression by 81 to get [tex]\boxed{81x^2 - 18x + 1}[/tex].
A
True
False
P
Given the diagram as marked.
True or False: P is on the angle bisector of A
Answers
Answer:
False
Step-by-step explanation:
P is not necessarily on the angle bisector of angle A.
Attached is an example of a carefully constructed shape (so that it's easy to see the measurements):
Angle A measures 45° (again, for convenience)Point P is 4 units to the right of and 3 units above point A.Point P forms a right angle with two congruent line segments, each of which terminate on the rays extending from Point A, forming angle A.The lower point is 8 units to the right of point A; the upper point is 7 units to the right of and 7 units above point A.The length of the two line segments is 5 units, and thus they are congruent.Visually, point P is not on the angle bisector of angle A.
While having two adjacent congruent segments is necessary for P to be on the bisector of angle A, it is not sufficient. The segments on the rays from A to the end of those segments would also need to be a pair of congruent adjacent sides (forming a kite). For a kite, the diagonal from the point between one pair of adjacent congruent sides to the point between the other pair of adjacent congruent sides does form an angle bisector with both angles.
3x - [2 +3 (2-x) = S-(3-X)
Answers
Consider the function shown on the graph.
Answers
Answer:
C.) y = 3(x - 3)(x - 7)
For the function:
x intercept: (3, 0), (7, 0)vertex point: (5, -12)point: (8, 15)Writing equation:
y = a(x - h)² + k
15 = a(8 - 5)² - 12
15 = 9a - 12
9a = 15 + 12
9a = 27
a = 3
So the equation is:
y = 3(x - 5)² - 12
y = 3(x² - 10x + 25) - 12
y = 3x² - 30x + 63
y = 3(x - 3)(x - 7)
If the volume of the pyramid is 192 yd³; and the area of the base is 64 yd², what is the height measured in yards?
Answers
Answer:
177
Step-by-step explanation:
Find the value of x.
Answers
Answer:
7x-1 + 2x-1 =7 ..... given
9x-2 = 7
9x = 9
x = 1
Step-by-step explanation:
This is the answer of the above condition.
Please mark as BRAINLIEST and THANK ME.
A cake recipe requires 4 and one-half cups of flour to make 1 cake. How many cakes can be made by a baker who has 16 cups of flour?
Answers
Answer:
3 cakes
Step-by-step explanation:
just flow by the formula then ignore the remainder and take the whole number which is 3 then that becomes your answer good day.
urgent algebra 2 help please
Answers
Answer:
y = 4x - 5
Step-by-step explanation:
y = mx + b
By putting above values in equation (i)
-1 = 4 (1) + b
-1 = 4 + b
-5 = b
b = -5
y = 4x - 5
Helppp needed plx as fast as u can
Answers
Answer:
The answer is either 30 degrees or 36 degrees.
You need a protractor to measure it.
Most probably, the answer is 30 degrees.
BUT PLEASE MEASURE THE ANGLE WITH A PROTRACTOR!
Answer:
d. 60°
Step-by-step explanation:
Since the clock is a full circle, it has a degree span of 360°.
∴ every 5-min interval on the clock
= 360° ÷ 12 five min intervals
= 30°
∴ acute angle formed by clock in figure
= two 5-min intervals
= 60°
Which pairs of angles are congruent?
Answers
Answer:
b) angles 1 and 4 are congruent.
Hope it helps!
an airplane that is flying at an altitude of 30 000 ft is beginning to descend at a rate of 1000 feet per minute. a helicopter is beginning its trip, starting at an altitude of zero feet. the helicopter ascends more slowly than the airplane, going up at a rate of 500 feet per minute. after how many minutes will the airplane and the helicopter be at the same altitude
Answers
Based on the altitudes of both the airplane and the helicopter, the number of minutes until they are at the same altitude is 20 minutes.
When will the airplane and helicopter be at the same altitude?Assuming the minute both will be on the same altitude is x, the altitude that the airplane would be at that point is:
= 30,000 - 1,000x
The helicopter's altitude would be:
= 0 + 500x
Putting them together gives:
30,000 - 1,000x = 500x
30,000 = 1,500x
x = 30,000 / 1,500
= 20 minutes
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A tank weighs 5.6kg when it 1/4 filled with water.If it weighs 10.4kg when it is full ,what will be it's weight when it is empty.
Answers
Answer:
4 kg
Step-by-step explanation:
so 1.6 * 4 is 6.4 so you just double check if you want
4 + 1.6 which is 1/4 of 6.4 will be 5.6 (matches with the question)
4 + (1.6*4) (indicates it's full) = 10.4( also Matches with the question)
there is another way by setting up an equation. let me know in comments if you want to see it that way
If tank weighs 5.6kg when it 1/4 filled with water. If it weighs 10.4kg when it is full , then weight when it is empty is 0.93kg
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A tank weighs 5.6kg when it 1/4 filled with water
Tank weighs 10.4kg when it is full
We need to find the weight when it is empty.
Let weight of the tank “x” and the weight of the water in the full tank “y”.
From the problem statements, we deduce the following equations:
x + y/4 = 5.6kg => x = 5.6kg - y/4
x + y = 10.4kg => y = 10.5kg - x
y = 10.5kg - (5.6kg - y/4)
3y/4 = 4.9
Thus y = 6.53kg; x = 0.93kg
Hence, weight of the tank when it is empty is 0.93kg.
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A table lamp emits light in the shape of a hyperbola. If the hyperbola is modeled by the equation 25x2 – 144y2 + 3,600 = 0, which of the following equations represents the boundaries of the light?
y equals five twelfths x and y equals negative five twelfths x
y equals twelve fifths x and y equals negative twelve fifths x
y equals five thirteenths x and y equals negative five thirteenths x
y equals thirteen fifths times x and y equals negative thirteen fifths times x
Answers
Answer:
(a) y = 5/12x and y = -5/12x
Step-by-step explanation:
Given the equation of a hyperbola 25x² – 144y² + 3,600 = 0, you want the equations of the asymptotes.
Standard formDividing by 3600 and doing a little rearrangement, we have ...
(y/5)² -(x/12)² = 1 . . . . . standard form equation of a hyperbola
AsymptotesThe equation of the asymptotes is ...
(y/5)² -(x/12)² = 0
Solving for y gives ...
(y/5)² = (x/12)²
y/5 = ±x/12 . . . . . . take the square root
y = ±5/12·x . . . . . . . matches the first choice
__
Additional comment
The equation of a hyperbola with vertices on the y-axis is often written as ...
y²/a² -x²/b² = 1
We have written it in the above form to better show the scale factors applied to x and y.
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A bronze statue weighs 2400 N and has a base that is 4 m by ½ m. What is the pressure the statue exerts on the floor?
Answers
The pressure by the statue exerted on the floor will be 1200 N per square meter.
What is pressure?
The term pressure is defined as the force per unit area.
The formula is igven below.
P = F /A
A bronze statue weighs 2400 N and has a base that is 4 m by ½ m.
Then the base area will be
A = 4 x 1/2
A = 2 square meters
Then the pressure will be
P = 2400 / 2
P = 1200 N per square meter.
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How do you write 16/25 as a percentage?
Answers
Answer:
64%
Step-by-step explanation:
Convert 16/25 to Percentage by Converting to Decimal
With this method, we first need to divide the numerator by the denominator:
16 ÷ 25 = 0.64
Once we have the fraction in a decimal format, the answer is then multiplied by 100 to get the correct percentage:
0.64 × 100 = 64%
We can see that this gives us the exact same answer as the first method: 16/25 as a percentage is 64%.
Note, the final percentage is rounded to 2 decimal places to make the answer simple to read and understand.
Explain the order in which to simplify the following and then simplify it.
Answers
Answer:
16 x^14 / y^16
Step-by-step explanation:
Remember ' PEDMAS '
Parentheses
Exponents
Division
Multiplication
Addition
Subtraction
so do the stuff inside the parentheses to get
y^8 ^-2
4x^7
Now do the exponents ( the -2 one)
y^-16
4^-2 x^-14 then simplify
16 x^14 / y^16
There are 15 players on a volleyball team. Only 6 players can be on the court for a game. How many different groups of players of 6 players can the coach make, if the position does not matter? 720 810 5,005 3,603,600
Answers
The no. of different groups of players of 6 players , if the position does not matter is given by 5005 ,Option C is the right answer.
What is Combination ?Combination is a method of selection of items from a set of distinct objects , when the position doesn't matter .
It is given that
Total number of players = 15 = n
No. of players to be selected = 6 = r
The no. of different groups of players of 6 players , if the position does not matter is given by
[tex]\rm ^nC_r = \dfrac{n!}{r! (n-r)!}[/tex]
So
[tex]\rm ^{15}C_6 = \dfrac{15!}{6! (15-6)!}\\\\\rm ^{15}C_6 = \dfrac{15!}{6! (9)!}\\\\\\^{15}C_6 = \dfrac{15 * 14 * 13* 12 * 11 * 10 }{6 *5* 4 * 3 * 2*1}\\\\ ^{15}C_6 = 5005\\[/tex]
Therefore , The no. of different groups of players of 6 players , if the position does not matter is given by 5005
Option C is the right answer.
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Solve 22x = 5.3 by graphing.
a x ≈ 0.3
b x ≈ 0.7
c x ≈ 1.2
d x ≈ 0.4
Answers
The solution is x ≈ 0.3 , Option A is the right Answer.
What is an Equation ?An Equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
To find the value of
22x = 5.3
A graph has to be plotted for the line
From the graph it can be clearly seen the point at which the line intersect x axis is x = 0.24 , which is approx equal to 0.3.
Therefore the solution is x ≈ 0.3 ,
Option A is the right Answer.
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Need help please answer!!!
Answers
It can be modeled by an exponential function because each time x increases by 1, f(x) is multiplied by 4.
This means the base of the exponential function is 4, and since f(x)=3 when x=0, [tex]f(x)=3(4)^{x}[/tex]
Which algebraic expression is equivalent to the expression below
5(4x + 5) - 17
A.
20x + 9
B.
5x + 9
C.
20x + 42
D.
20x + 8
Answers
Answer:
20x + 8
Step-by-step explanation:
5*4x + 5*5 -17
20x +25 -17
20x + 8
Solve x: 30 pts if u can figure it out and the first one that sounds right gets brainiest answer
3x+99x=1188
Is this even possible to work out????
Please dont just type random letters Bec then there’s just no point of u being on here.. and ur wasting ur time! So please think about it
Answers
Answer:
x = 99
Step-by-step explanation:
3x + 99x = 12x
12x = 1188 divide 1188 ÷ 12
x = 99
You can round it if allowed to 11.6
Reason
First combine like terms
3x + 99x = 1188
102x = 1188
Now solve for x
Divide both sides by 102
X = 11.6470588
Write 31/8 as a mixed number.
Reward: Mark as brainlist.
Answers
Answer:
[tex]3 \frac{7}{8}[/tex]
Step-by-step explanation:
(correct answers only)
A sailfish is swimming after a herring in a straight line at 11.8 m/s and begins to accelerate at 6.39 m/s². How long does it take for the sailfish to reach the herring if it is 55.0 m away?
(unit=s)
Answers
According to second equation of kinematics
s=ut+1/2at²55=11.8t+1/2(6.39)t²110=23.6t+6.39t²6.39t²+23.6t-110=0Take positive value
t=2.7sAnswer:
2.7 s (1 d.p.)
Step-by-step explanation:
Use the Constant Acceleration Equations where:
s = displacement in metersu = initial speed in m/sv = final speed in m/sa = acceleration in m/s²t = time in s (seconds)Given:
s = 55 mu = 11.8 m/sa = 6.39 m/s²[tex]\begin{aligned}\text{Using }s & =ut+\dfrac{1}{2}at^2\\\implies 55 & =11.8t+\dfrac{1}{2}(6.39)t^2\end{aligned}[/tex]
Rearrange the equation to equal zero:
[tex]\implies 3.195t^2+11.8t-55=0[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Use the quadratic equation to solve for t:
[tex]\implies a=3.195, \quad b=11.8, \quad c=-55[/tex]
[tex]\implies t=\dfrac{-11.8 \pm \sqrt{11.8^2-4(3.195)(-55)} }{2(3.195)}[/tex]
[tex]\implies t=2.694780675, -6.388051411[/tex]
As time is positive:
[tex]\implies t=2.694780675... \:\text{s}[/tex]
[tex]\implies t=2.7 \: \text{s (1 d.p.)}[/tex]
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38. How much does Mike Carson earn every
day?
A. $89.33
B $76.80
C. $27.00
D. $9.60
39. Mike Carson takes home approximately
what percent of his gross pay?
A. 33%
B. 50%
C. 75%
D, 90%
40. Approximately what percent of total
carnings is deducted for city and state
withholding tax?
A. 3%
B. 10%
C. 15%
D. 25%
Answers
1.the answer is B
2.the answer is A
3.the answer is C
Find the area of a circle with a diameter of 10 ft. ( = 3.14)
Answers
Answer:
78.5 ft² or25πStep-by-step explanation:
Find the area of a circle with a diameter of 10 ft.
Area of a Circle
A = π × r²
r = diameter : 2
10 : 2 = 5 ft (radius)
A = π × 5²
A = 3.14 * 25
A = 78.5 ft²
what is 2/3 x 6/7 answer
Answers
Answer:
4/7
Step-by-step explanation:
2/3 × 6
7
4/7
and bro that's really it
If f(x) = x², and
g(x) = x1, then
f(g(x)) = ?
will give brainliest answer !!
Answers
Answer: 1, -2, 1
Step-by-step explanation:
[tex]f(g(x))=f(x-1)=(x-1)^{2}=x^{2}-2x+1[/tex]
10 points need help finding area
Answers
Answer:
8 un^2
Step-by-step explanation:
to find this answer you must find the area of the rectangle and then the triangle
the rectangles area is
2 * 3 = 6 un^2
the traingle is
2 * 2 * 1/2 = 2 un^2
now you add them
6 + 2 = 8 un^2
15
16
Matt had 1 pound of dog food in a bag.
He fed his puppy pound of the food.
How much dog food is left in the bag?
Give your answer in simplest form.
pound
WOOF!
Answers
Step-by-step explanation:
1/2 represents every fraction, where the denominator (bottom part) is twice the numerator (top part).
like 4/8 or 6/12 or 128/256 or ...
what do we need in the denominator to calculate with 15/16 ?
the same : 16.
and what is half of 16 ? 8.
so, we need the 1/2 based on 16th = 8/16.
so, the dog ate 8/16 (1/2) of the original 15/16.
what was left was
15/16 - 8/16 = 7/16 pound
IMPORTANT, PLEASE HELP QUICKLY! 40 POINTSS
Answer the following questions given that Angles A and B are the acute
angles found in a right triangle.
1. If tan (A) = 3/4, then tan (B) equals?
2. If tan (B) = 2/7, then tan (A) equals?
3. Based on the information in #2, which angle would be bigger, A or B?
Use a diagram to help justify your answers.
Answers
Answer:
[tex]\sf 1. \quad \tan(B)=\dfrac{4}{3}[/tex]
[tex]\sf 2. \quad \tan(A)=\dfrac{7}{2}[/tex]
[tex]\sf 3. \quad \angle A[/tex]
Step-by-step explanation:
Acute angle: an angle less than 90°
Tan trigonometric ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleQuestion 1
Refer to the first attached diagram.
If tan(A) = 3/4 then the side opposite ∠A is 3 units, and the side adjacent ∠A is 4 units.
Therefore:
[tex]\implies \sf \tan(B)=\dfrac{4}{3}[/tex]
Question 2
Refer to the second attached diagram.
If tan(B) = 2/7 then the side opposite ∠B is ,and the side adjacent ∠B is 7.
Therefore:
[tex]\implies \sf \tan(A)=\dfrac{7}{2}[/tex]
Question 3Angle A would be bigger (see second attachment).