Answer:
The solutions are B. -4 and C. -5
Step-by-step explanation:
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
For [tex]\mathrm{}\quad a=3,\:b=27,\:c=60:\quad x_{1,\:2}=\frac{-27\pm \sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}[/tex]
[tex]x_1=\frac{-27+\sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}\\\\x_1=\frac{-27+\sqrt{9}}{2\cdot \:3}\\\\x_1=\frac{-27+3}{2\cdot \:3}\\\\x_1=\frac{-24}{6} = -4[/tex]
[tex]x_2=\frac{-27-\sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}\\\\x_2=\frac{-27-\sqrt{9}}{2\cdot \:3}\\\\x_2=\frac{-27-3}{2\cdot \:3}\\\\x_2=-\frac{30}{6} = -5[/tex]
Simplify the rational expression. state any excluded values. 4x - 4/ x - 1
Answer:
1 and 4 i believe
Step-by-step explanation:
What is the volume of a pyramid with slant height 17 feet and square base with edges of 16 feet?
The volume of the pyramid is 1280 cubic feet.
To find the volume of a pyramid, we can use the formula:
Volume = (1/3) * Base Area * Height
Given that the pyramid has a square base with edges of 16 feet, the base area (A) is calculated as:
[tex]Base Area (A) = side^2\\A = 16^2 = 256 square feet[/tex]
The height of the pyramid can be found using the Pythagorean theorem. The height, slant height, and half the length of a side form a right triangle. The half length of a side is 16/2 = 8 feet. The slant height is 17 feet. So, using the Pythagorean theorem:
[tex]Height^2 + (Half side length)^2 = Slant height^2\\Height^2 + 8^2 = 17^2\\Height^2 + 64 = 289\\Height^2 = 289 - 64\\Height^2 = 225\\Height = \sqrt{225}\\Height = 15 feet\\[/tex]
Now that we have the base area (A = 256 square feet) and the height (h = 15 feet), we can find the volume:
Volume = (1/3) * 256 * 15
Volume = (1/3) * 3840
Volume = 1280 cubic feet
Therefore, the volume of the pyramid is 1280 cubic feet.
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A fair dice is rolled 5 times in sequence. what is the probability that you will get exactly the same number for all 5 rollings
Add (13a + 5b) + (a + 5b - 3)
Parallel lines r and s are cut by two transversals, parallel lines t and u.
Which angles are alternate exterior angles with angle 11?
Answer:
The alternate exterior angles with angle 11 are angle 13 and angle 5.
Step-by-step explanation:
Two angles are called Alternate exterior angles if
1. They are on the exterior side of parallel lines and
2. Lie on the opposite sides of the transversal line.
It is given that
[tex]r\parallel s[/tex] and [tex]t\parallel u[/tex]
From the figure it is noticed that the angle 13 and angle 5 are on the exterior side of parallel lines and they lie on the opposite sides of the transversal line.
Therefore alternate exterior angles with angle 11 are angle 13 and angle 5.
Answer:
The alternate exterior angles with angle 11 are angle 13 and angle 5.
Step-by-step explanation:
The sum of the measures of two angles of a scalene triangle is calculated, and the result is the same as the measure of one of the external angles of a triangle. Which pair of angle measures was calculated?
The Exterior Angle Theorem establishes that the measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle.
so
the answer is the option
A. the remote interior angles
For parametric equations x= a cos t and y= b sin t, describe how the values of a and b determine which conic section will be traced
In mathematics, a conic section is
a curve obtained as the intersection of the surface of
a cone with a plane. The four types of conic section are
the hyperbola, the parabola, the circumference and the ellipse.
For the problem we have this parametric
equation:
(1) [tex]\left\{{{x=acost}\atop{y=bsint}}\right[/tex]
From geometry, we know that we can express a
circumference in terms of parameters like this:
(2) [tex]\left \{ {{x=rcost} \atop {y=rsint}}\right[/tex]
being r the radius of the circumference.
On the other hands, we know that a ellipse can
be expressed in terms of parameters like this:
(3) [tex]\left \{ {{x=acost} \atop {y=bsint}}\right[/tex]
Therefore, we will have three answers that are
the cases for the values a and b, namely.
Case 1:
Circumference
To the case of a circumference, the more simple
ordinary equation is given by:
(4) [tex]x^{2} + y^{2} = r^{2}[/tex]
Substituting (1) into (4):
[tex]a^{2}cos^{2}t+b^{2}cos^{2}t=r^{2}[/tex]
But because of the equation (2), necessarily:
[tex]a = b = r[/tex]
Case 2: Ellipse
(focal axis matches the x-axis)
In this case, the simple ordinary equation is
given by:
(5) [tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex]
being a and b semi-major axis and semi-minor
axis respectively.
Given that a an b are variables of the
parametrization, and a and b are variables of the ellipse as well, to avoid
confusion we will modify the equation (5) like this:
(6) [tex]\frac{x^{2}}{a'^{2}}+\frac{y^{2}}{b'^{2}}=1[/tex]
So, substituting (2) into (6):
[tex]\frac{a^{2}cos^{2}t}{a'^{2}}+\frac{b^{2}cos^{2}t}{b'^{2}}=1[/tex]
Necessarily:
[tex]a=a'[/tex] and [tex]b=b'[/tex]
and given that the focal axis matches the
x-axis, then:
[tex]a>b[/tex]
Case 3: Ellipse
(focal axis matches the y-axis)
In this case, applying the same previous
reasoning, the simple ordinary equation is given by:
(7) [tex]\frac{x^{2} }{b'^{2}}+\frac{y^{2}}{a'^{2}}=1[/tex]
being a' and b' semi-major axis and semi-minor
axis respectively.
So, substituting (2) into (7):
[tex]\frac{a^{2}cos^{2}t}{b'^{2}}+\frac{b^{2}cos^{2}t}{a'^{2}}=1[/tex]
Necessarily:
[tex]a = b'[/tex] and [tex]b = a'[/tex]
and given that the focal axis matches the y-axis, then:
[tex]a<b[/tex]
Finally, the conclusions are:
1. If [tex]a = b[/tex] then a circumference will be traced. (See Figure 1)
2. If [tex]a>b[/tex] then a ellipse will be traced with focal axis matching the x-axis. (See Figure 2)
3. If [tex]a<b[/tex] then a ellipse will be traced with focal axis matching the y-axis. (See Figure 3)
How the values of a and b determine which conic section will be traced was discussed thoroughly.
What is a conic section?A conic section is a curve obtained as the intersection of the surface of a cone with a plane.
The given parametric equations are:
[tex]x=acos t[/tex]
[tex]\frac{x}{a} =cost[/tex]....(1)
[tex]y=bsint[/tex]
[tex]\frac{y}{b} =sint[/tex]....(2)
Adding the squares of (1) and (2)
[tex](\frac{x}{a} )^2+(\frac{y}{b} )^2=cos^{2} t + sin^{2} t[/tex]
We know [tex]cos^{2} t + sin^{2} t=1[/tex]
So, [tex]\frac{x^{2} }{a^{2} } +\frac{y^2}{b^2} =1[/tex]........(3)
If [tex]a=b[/tex], (3) will be reduced into:
[tex]x^{2} +y^{2} =a^{2}[/tex] representing a circle.
If [tex]a > b[/tex], (3) will represent an ellipse with the length of the major axis > length of the minor axis.
if [tex]a < b,[/tex] (3) will represent an ellipse with the length of the major axis < length of the minor axis.
Thus, How the values of a and b determine which conic section will be traced was discussed thoroughly.
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Find the surface area 4cm 5cm 6cm 13cm
Roman saves $500 each year in account earning interest at an account earning interest at an annual rate of 4% compounded annually.How much interest will the account earn at the end of each of the first 3 years?
The vertex angle of an isosceles triangle is 20° less than the sum of the base angles. Which system of equations can be used to find the measure of the vertex and base angles?
A)
v + 2b = 180; 2b - 20 = v
B)
v + 2b = 180; 2b + 20 = v
C)
v - 2b = 180; v + 2b = -20
D)
v - 2b = 180; -2b - 20 = v
The answer to the above question can be explained as under -
We know that, the sum of angles of triangle is 180°.
So, vertex angle plus base angles are equal are equal to 180°.
Let the vertex angle be represented by "v" and base angles be represented by "b".
Thus, v + b + b = 180°
So, v + 2b = 180°
Next, the question says, the vertex angle is 20° less than the sum of base angles.
Thus, 2b - 20° = v
Thus, we can conclude that the correct option is A) v + 2b = 180°, 2b - 20° = v
The correct system of equations for an isosceles triangle where the vertex angle is 20 degrees less than the sum of the base angles is v + 2b = 180 for the sum of the angles, and 2b - 20 = v for the relationship between the base angles and the vertex angle. Option A is correct.
The correct system of equations to find the measure of the vertex and base angles of an isosceles triangle, where the vertex angle is 20° less than the sum of the base angles, is given by option A. The two equations can be described as follows:
The sum of the angles in a triangle is 180°, leading to the equation: v + 2b = 180.The vertex angle v is 20° less than the sum of the base angles, giving us the equation: 2b - 20 = v.To solve for the angles, you would substitute the expression for v from the second equation into the first and then solve for b, which represents the measure of each base angle. Once you have b, you can find v by substituting b back into the second equation.
which of the points satisfy the linear inequality graphed here?
a) (0,0)
b) (10,0)
c) (-10,0)
d) (10,10)
Mary is walking 3 miles per hour jerry starts jogging at a rate of 4 miles per hour after marry has been walking for 15 minuets jerry jogs 2 miles as Mary continues walking and they both stop at the same time
T (2,10) is the midpoint of CD. The coordinates of D are (2,13). What are the coordinates of C?
A. (2, 16)
B. (2, 20)
C. (2, 11.5)
D. (2, 7)
what is 3√27x^9
3x^6
3x^3
9x^3
9x^6
The value of the expression ∛27x⁹ is 9x³.
The given expression is ∛27x⁹.
Cube root of twenty seven times of x power nine.
We can split the terms inside the cube root.
27=3×3×3
∛x⁹ = x³
Now let us plug in the above expression.
= 3√3³ × x⁹
= 3√3³ × √ x⁹
= 3 × 3 × x³
= 9x³.
Hence, the value of the expression ∛27x⁹ is 9x³.
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A cube has a side length of 120 cm, what is its volume in cubic meters? (100 cm = 1 m)
The value of volume of cube is,
⇒ V = 1.728 meter³
What is mean by Cuboid?A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.
Given that;
A cube has a side length of 120 cm.
Since, We know that;
1 m = 100 cm
Hence,
120 cm = 120 / 100 m
= 1.2 m
So, Volume of cube is,
⇒ V = side³
⇒ V = 1.2³
⇒ V = 1.728 meter³
Thus, volume of cube is,
⇒ V = 1.728 meter³
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how do you do 27?????
A number is chosen at random from 1 to 10. find the probabilty of not selecting a multiple of 3
A solid oblique pyramid has a square base with an edge length of 2 cm. Angle BAC measures 45°.What is the volume of the pyramid?2.4 cm33.6 cm34.8 cm37.2 cm3
Answer:4.8cm^3
Step-by-step explanation:I got it right on edge.
fatima wants to find the value of sin theta, given cot theta equals 4/7. which identity would be best for fatima to use?
Answer:
D edge
Step-by-step explanation:
help! I will give thanks!
how many terms are in the arithmetic sequence shown below?
15, 7, -1, -9...,-225
Final answer:
To determine the number of terms in the given arithmetic sequence, we calculate the common difference and apply the formula for the nth term. With a common difference of -8 and an nth term of -225, we find that there are 31 terms in the sequence.
Explanation:
To find out how many terms are in the arithmetic sequence 15, 7, -1, -9,..., -225, we need to determine the common difference and use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
In this sequence, the common difference d is 7 - 15 = -8. Now we use the formula with an = -225, a1 = 15, and d = -8 to find n.
Plugging these values into the formula, we get:
-225 = 15 + (n - 1)(-8)
-225 = 15 - 8n + 8
-225 = 23 - 8n
-248 = -8n
n = 31
Therefore, there are 31 terms in the arithmetic sequence.
On average, Carson spends $2 of his $20 monthly allowance on library fines. What percent of his allowance is spent on library fines?
My coin collection had 27 coins. They are only quarters and half-dollars. If its worth $10.50. How many are there of each coin?
PLEASE SHOW WORK
simplify the problem sqrt 245c^5
Answer: the answer above is pretty much right, the answe is B
Will give brainliest! Which are simplified forms of the expression sec^2theta sin2theta
Which is the second answer? I already got the first one
Answer:
C) 2 tan θ
E) [tex]\frac{sin2[theta]}{cos^2[theta]}[/tex] (it wouldn't let me do the actual θ symbol)
Step-by-step explanation:
This is essentially what the other person said, but in a better format.
If you buy a computer directly from the manufacturer for $ 2,469 and agree to repay it in 48 equal installments at 2.1 % interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
Final answer:
The monthly payments would be approximately $61.02 and the total interest paid would be approximately -$764.04.
Explanation:
To calculate the monthly payments, you can use the formula for the monthly payment on a loan:
P = (r * PV) / (1 - (1 + r)^-n)
Where:
P is the monthly paymentr is the monthly interest ratePV is the present value or the loan amountn is the total number of paymentsUsing the given values, we can calculate:
P = (0.021 * 2469) / (1 - (1 + 0.021)^-48)
P ≈ $61.02
Therefore, the monthly payments would be approximately $61.02.
To calculate the total interest paid, you can multiply the monthly payment by the total number of payments and subtract the loan amount:
Total Interest = (P * n) - PV
Total Interest ≈ ($61.02 * 48) - $2469
Total Interest ≈ $1704.96 - $2469
Total Interest ≈ -$764.04
Therefore, the total interest paid would be approximately -$764.04. This negative value indicates that you will pay back less than the initial loan amount.
David, Egil and Frances share money in the ratio 2:7:9. David gets £25. Work out how much Egil and Frances get.
Please help. Needed for tomorrow.
Find the variable of each pair
What is grater 9km or 145cm
9km is greater than 145cm due to the conversion factor between kilometers and centimeters.
9km is greater than 145cm because when comparing the two, you need to ensure they are in the same unit. To compare, convert km to cm, 9km = 9,000,000cm. So, 9,000,000cm is greater than 145cm.
Jack runs 3 miles in 27 minutes. at this constant rate how long will it take him to run 10 miles answer