Answer:
5
Step-by-step explanation:
2x²y³ + 4y³ = 149 + 3x²
[tex] 2x^2y^3 - 3x^2 = 149 - 4y^3 [/tex]
[tex] x^2(2y^3 - 3) = 149 - 4y^3 [/tex]
[tex] x^2 = \dfrac{149 - 4y^3}{2y^3 - 3} [/tex]
[tex] x = \pm \sqrt{\dfrac{149 - 4y^3}{2y^3 - 3}} [/tex]
Try y = 1
[tex]x = \pm \sqrt{\dfrac{149 - 4(1)}{2(1)^3 - 3}} = \pm \sqrt{-145} = i\sqrt{145}[/tex]
For y = 1, x is imaginary.
Try y = 2
[tex] x = \pm \sqrt{\dfrac{149 - 4(2)^3}{2(2)^3 - 3}} = \pm \sqrt{9} = \pm 3[/tex]
Since x and y are positive integers, ignore x = -3.
When x = 3, y = 2.
x + y = 3 + 2 = 5
The value of x + y is 5.
What is Polynomial?Polynomials are expressions which consist of variables, constants, coefficients and exponents.
We have the equation,
2x²y³ + 4y³ = 149 + 3x²
2x²y³ - 3x² = 149 - 4y³
x² (2y³ - 3) = 149 - 4y³
x² = (149 - 4y³) / (2y³ - 3)
x = √[(149 - 4y³) / (2y³ - 3)]
Now, we have to find two positive integers.
We can use trial and error method here.
Trial putting y = 1.
x = √[(149 - 4 × 1³) / (2 × 1³ - 3)]
= √[145 / (-1)]
= √(-145)
There is no real root for √(-145). So y = 1 is not applicable.
Trial putting y = 2.
x = √[(149 - 4 × 2³) / (2 × 2³ - 3)]
= √[117 / 13]
= √(9)
= ± 3
But we need positive integers. So we ignore -3.
So x = 3 and y = 2 ⇒ x + y = 5
Hence x + y = 5.
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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
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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Find the value of x.
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.
If f(x) = x², and
g(x) = x1, then
f(g(x)) = ?
will give brainliest answer !!
Answer: 1, -2, 1
Step-by-step explanation:
[tex]f(g(x))=f(x-1)=(x-1)^{2}=x^{2}-2x+1[/tex]
Consider the function shown on the graph.
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)
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.
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).
The following excerpt comes from the International Bottled Water Association
"In 2012, total U.S. bottled water consumption increased to 9.67 billion gallons, up from 9.1 billion gallons in 2011. In fact, 2012's consumption growth was the strongest it has been in five years. In addition,
per-capita consumption is up 5.3 percent in 2012, with every person in America drinking an average of 30.8 gallons of bottled water last year. Bottled water increased in absolute volume more than any other
beverage category in the U.S. Bottled water sales increased by 6.7 percent in 2012, and now total $11.8 billion."
(i) Estimate the per capita consumption from 2011 from data in the statement. Express your answer rounded correctly to the nearest tenth of a gallon.
Using proportions, the estimate of the per capita consumption from 2011 is of 29.2 gallons.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
From the data, the 2012 consumption was 5.3% percent higher than in 2011, that is 105.3% of 1.053x. This consumption was of 30.8 gallons, hence:
1.053x = 30.8.
x = 30.8/1.053
x = 29.2.
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Y=-1/3x+2
A.
B.
C.
D.
Answer:
C
Step-by-step explanation:
The slope is -1/3, so it will go down and to the right. Down 1, to the right 3 (rise over run!)
The y intercept is 2.
Find the area of a circle with a diameter of 10 ft. ( = 3.14)
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
Write 31/8 as a mixed number.
Reward: Mark as brainlist.
Answer:
[tex]3 \frac{7}{8}[/tex]
Step-by-step explanation:
urgent algebra 2 help please
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
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?
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.
3x - [2 +3 (2-x) = S-(3-X)
Need help please answer!!!
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
Answer:
20x + 8
Step-by-step explanation:
5*4x + 5*5 -17
20x +25 -17
20x + 8
the equation of lime 1 is 3x-2y=5, and the equation of lime 2 is x+2y=7. What is the point of intersection of the two lines?
To find the point of intersection for two lines, we can use substitution to solve for the coordinates.
Solving the QuestionWe're given:
[tex]3x-2y=5[/tex][tex]x+2y=7[/tex]With these two equations, we can:
First isolate x in the second equationUse substitution to input in second equation into the first and solve for yUse the y-coordinate to find the corresponding x-coordinate using substitutionIsolate x in the second equation:
[tex]x+2y=7\\x =7-2y[/tex]
Substitute the second equation into the first:
[tex]3x-2y=5\\3(7-2y)-2y=5\\21-6y-2y=5\\21-8y=5\\21-8y=5[/tex]
Solve for y:
[tex]21-6y-2y=5\\21-8y=5\\-8y=-16\\y=2[/tex]
Solve for x:
[tex]x+2y=7\\x+2(2)=7\\x+4=7\\x=3[/tex]
AnswerThe point of intersection of the lines is (3,2).
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
Answer:
x = 99
Step-by-step explanation:
3x + 99x = 12x
12x = 1188 divide 1188 ÷ 12
x = 99
Explain the order in which to simplify the following and then simplify it.
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
A
True
False
P
Given the diagram as marked.
True or False: P is on the angle bisector of A
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.
Solve 22x = 5.3 by graphing.
a x ≈ 0.3
b x ≈ 0.7
c x ≈ 1.2
d x ≈ 0.4
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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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%
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
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.
<95141404393>
what is 2/3 x 6/7 answer
Answer:
4/7
Step-by-step explanation:
2/3 × 6
7
4/7
and bro that's really it
How do you write 16/25 as a percentage?
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.
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
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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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?
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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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!
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
(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)
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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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
(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 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.
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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Helppp needed plx as fast as u can
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°
