The formula for discriminant is:
discriminant = sqrt (b^2 – 4 a c)
Where,
a = 1
b = 4
c = -32
Therefore:
discriminant = sqrt (4^2 – 4 (1) (-32))
discriminant = sqrt 144
discriminant = 12
Since the discriminant is a positive real integer, then there are 2 unequal roots or 2 distinct real roots.
if ∠1 and ∠2 are complementary and m∠1= 17°, what is m∠2?
173 degrees
90 degrees
73 degrees
77 degrees
The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Check all that apply.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 24
x2 + (x + 2)2 = 100
Please help me quickly, I really need the help. I'll even mark brainiest if you do it correctly. I really need this and I need whoever does this to pay attention to the whole "Check all that apply". I'm adding the picture below.
The equation that can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex]
Given thatThe area of the right triangle shown is 24 square feet.
We have to determine
Which equations can be used to find the lengths of the legs of the triangle?
According to the question
From the given figure the base of the triangle is x.
And the height of the triangle is (x+2).
What is the area of a triangle?The area of the triangle is given by half the product of the height and base.
[tex]\rm Area = \dfrac{1}{2} \times base \times height\\ [/tex]
Substitute all the values in the formula;
[tex]\rm Area \ of \ right \ triangle= \dfrac{1}{2} \times base \times height\\ \\ \rm 24= \dfrac{1}{2} \times x \times (x+2)\\\\ \rm 0.5(x)(x + 2) = 24[/tex]
The equation can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex].
Hence, the equation can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex].
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Suppose i pick a jelly bean at random from a box containing two red and ten blue ones. i record the color and put the jelly bean back in the box. if i do this three times, what is the probability of getting a blue jelly bean each time? (round your answer to three decimal places.)
The city of Lakeside has a population of 22,000 people and is decreasing at a rate of 1.5% The population in 3 years would be
A)Approximately 21,000 people
B)None of the choices are correct
C)Approximately 20,000 people
D)Approximately 25,000 people
E)Approximately 19,000 people
Fiona decides to join a gym for a minimum of one month to train for a triathlon. The gym charges a joining fee of $100 and a monthly fee of $38. If x represents the number of months that Fiona is a member of the gym, the equation below can be used to determine C, her total membership fee for that duration of time: 100 + 38x = C Fiona has allocated a maximum of $328 to spend on her gym membership. Which number line shows the possible number of months that Fiona can be a member of the gym?
Answer:
x = 6
Step-by-step explanation:
Given : Fiona decides to join a gym :
A joining fee of $100
A monthly fee of $38
x represents the number of months.
Fiona has allocated a maximum of $328 to spend on her gym membership
Her total membership fee for that duration of time: 100 + 38x = C
Solution :
It is given that Fiona has allocated a maximum of $328 to spend
So, C = $328
Putting this value in equation 100 + 38x = C
⇒[tex]100+38x=328[/tex]
⇒[tex]38x=328-100[/tex]
⇒[tex]38x=228[/tex]
⇒[tex]x=\frac{228}{38}[/tex]
⇒[tex]x=6[/tex]
Thus, x = 6 is number line that shows the possible number of months that Fiona can be a member of the gym.
Apply the distributive property to factor out the greatest common factor. 45+75=
Which represents a quadratic function? f(x) = −8x3 − 16x2 − 4x f (x) = x 2 + 2x − 5 f(x) = + 1 f(x) = 0x2 − 9x + 7
Answer: The correct answer is [tex]f(x)=x^2+2x-5[/tex]
Step-by-step explanation:
A Quadratic equation is defined as the equation in which the highest power of the variable is 2. The general form of this equation represents:
[tex]ax^2+bx+c=0[/tex]
where, [tex]a\neq 0[/tex]
From the given options:
1. [tex]f(x)=-8x^3-16x^2-4x[/tex]: Here, the highest power of the variable is 3. Therefore, it is not a quadratic equation.
2. [tex]f(x)=x^2+2x-5[/tex]: Here, the highest power of the variable is 2. Therefore, it is a quadratic equation.
3. [tex]f(x)=+1[/tex]: Here, the highest power of the variable is 0. Therefore, it is not a quadratic equation.
4. [tex]f(x)=0x^2-9x+7[/tex]: Here, the highest power of the variable is 1. Therefore, it is not a quadratic equation.
Hence, the correct answer is [tex]f(x)=x^2+2x-5[/tex]
Which of the following triangles are right triangles? Check all that apply
A triangle with side lengths 4, 5, 6
A triangle with side lengths 6 inches, 8 inches, 10 inches
A triangle with side lengths 8, 15, 17
A triangle with side lengths 5, 12, 13
In this exercise we have to apply the Pythagorean theorem to know that it is possible to form a certain triangle, so we have:
A) No
B) Yes
C) Yes
D) Yes
Knowing that the Pythagorean theorem is given by:
[tex]a^2 = b^2 +c^2[/tex]
They are putting the values informed we have:
A) [tex]6^2 = 4^2 + 5^2[/tex]
B) [tex]10^2 = 6^2 + 8^2[/tex]
C) [tex]17^2=15^2+8^2[/tex]
D) [tex]13^2 = 12^2 + 5^2[/tex]
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Explain in terms of the unit circle and geometry why the trig identity cos2 x + sin2 x = 1 holds true for all values of x.
PLEASE I NEED HELP ASAP
We can imagine the given equation cos2 x + sin2 x = 1 to be in the form of the hypotenuse equation.
Where cos x and sin x is the base and height of the triangle and 1 is the hypotenuse.
Since 1 is the hypotenuse, it also indicates to the radius of the circle. Supposing that the center of the circle is at the origin, then at all values of x (at all values of the angle), the radius of the circle will always be the same which is equal to 1.
Therefore the equation cos2 x + sin2 x = 1 holds to be true for all values of x for a unit circle.
Why might algebra tiles not be a good tool to use to factor x2 + 18x + 80? Explain.
Algebra tiles are used to factorize a polynomial. The factorization of the given trinomial will be very difficult to perform using the algebra tiles due to the large number of tiles used.
The given quadratic polynomial or trinomial is [tex]x^2 + 18x + 80[/tex].
The algebra tiles required to solve the given trinomial are,
1 x-squared tile.18 x-tiles.80 unit tiles.So, the total number of times required will be 1+18+80 or 99 tiles.
Now, it will be very difficult to drag or arrange so many tiles on the board. Also, the space could be a problem in this case.
Therefore, the factorization of the given trinomial will be very difficult to perform using the algebra tiles due to a large number of tiles used.
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The function f(x) = –x2 + 16x – 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points
please help
Final answer:
The vertex of the profit function f(x) = -x^2 + 16x - 60 is (8, 4), meaning the maximum profit is $4 when 8 candles are sold. The x-intercepts are (6,0) and (10,0), indicating zero profit when either 6 or 10 candles are sold.
Explanation:
The function given is a quadratic equation of the form f(x) = ax2 + bx + c, where the constants are a = -1, b = 16, and c = -60. To find the vertex of the parabola, we can use the formula -b/(2a) for the x-coordinate of the vertex.
Calculate the x-coordinate of the vertex: x = -b/(2a) = -16/(2 * -1) = 8.
Substitute x = 8 into the original function to find the y-coordinate: f(8) = -(8)2 + 16(8) - 60 = -64 + 128 - 60 = 4.
The vertex is at the point (8, 4). In the context of the problem, this point represents the maximum daily profit of $4, which occurs when 8 candles are sold.
To determine the x-intercepts, we set f(x) to zero and solve for x, which represents the number of candles sold when the profit is zero.
Set the function equal to zero and solve for x: 0 = -x2 + 16x - 60.
Apply the quadratic formula x = [-b ± sqrt(b2 - 4ac)]/(2a) to find the x-intercepts. In this case, a = -1, b = 16, and c = -60.
Calculate the discriminant, sqrt(162 - 4(-1)(-60)) = sqrt(256 - 240) = sqrt(16) = 4.
Find the two x-intercepts: x = [16 ± 4]/(2 * -1) which yields x = 6 and x = 10.
The x-intercepts (6,0) and (10,0) indicate the number of candles sold at which the profit would be zero, specifically at 6 and at 10 candles sold.
Simplify the expression. Type your answer in the blank.
-
The surface area of a sphere
324 square centimeters. What is volume in cubic centimeters, of the sphere? Express your answer in terms of pi
The surface area of the sphere is SA = 324π cm².
Calculate the surface area of the sphere by using the formula: SA = 4πr².
To find the value of r, substitute SA = 324π in the above formula.
324π = 4πr²
81 = r²
r = ± 9.
The measurements of the sphere cannot be expressed in negative sign.
The radius of the sphere is r = 9 cm.
Calculate the surface area of the sphere by using the formula: V = (4/3)πr³.
Substitute r = 9 in the above formula
V = (4/3)π 9³ = 972π cm³.
Meike earned $1565 in tips while working a summer job at a coffee shop. She wants to use this money to take a trip to Europe next summer. If she places the money in an account which pays 6.5% compounded continuously, how much money will she have in nine months?
Given the equation 5x + 23 = − 2x − 12, which order of operations completely solves for x?
a.Subtract 5x, then subtract 23, lastly divide by −7
b. Subtract 2x, then add −23, lastly divide by 7
c.Add 5x, then subtract 12, lastly divide by 7
d. Add 2x, then subtract 23, lastly divide by 7
(02.03 MC)
The figure shows two triangles on a coordinate grid:
What set of transformations is performed on triangle ABC to form triangle A'B'C'?
A.. A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units down
B. A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin
C. A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right
D. A translation 5 units to the right, followed by a 270-degree counterclockwise rotation about the origin
3+-1/1/3 the first half is 3+-1 the second half is 1/3
The GCD(a, b) = 6, the LCM(a, b)=180. Find the least possible value of a+b.
True or False...
P^2+2pq+q^2= 1
Answer:
defiantly a false!!
Step-by-step explanation:
(02.05 MC)
Triangle ABC is transformed to obtain triangle A′B′C′:
Which statement is correct for Triangle ABC. and Triangle A prime B prime C prime.?
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 6. and then rotating it about the origin by 90 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 180 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 90 degrees
Triangle ABC is similar to triangle A prime B prime C prime. because triangle A prime B prime C prime. is obtained by dilating Triangle ABC.by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees
PLEASE HELP ASAP!!! A talent competition on television had five elimination rounds. After each elimination, only one-third of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition: x 1 2 3 4 5 f(x) 243 81 27 9 3 Compute the average rate of change of f(x) from x = 1 to x = 4 and describe what it represents.
A) −78 contestants per round, and it represents the number of contestants who will reach the final round
B)−234 contestants per round, and it represents the number of contestants who will reach the final round
C)−234 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round
D) −78 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round
Answer:
D
Step-by-step explanation:
Given the following data
x 1 2 3 4 5
f(x) 243 81 27 9 3
The rate of change between the second and the first points is computed as
(f(x2) - f(x1))/(x2 -x1) = (81 - 243)/(2-1) = -162
Analogously, between 3rd and 2nd points and between 4th and 3rd points:
27 - 81 = -54
9 - 27 = -18
Therefore, the average rate of change is (-162 -54 -18)/3 = -78 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round .
Take 2y 2 - 3y - 5 from y 3 - 6y 2 + 5y. Select the correct answer. y3 - 2y2 + 3y + 5, y3 - 4y2 + 2y - 5, y3 - 4y2 + 2y + 5, y3 - 8y2 + 8y + 5.
Answer:
[tex]y^3 - 8y^2 + 8y+5)[/tex]
Step-by-step explanation:
Take [tex]2y^2 - 3y - 5[/tex] from [tex]y^3 - 6y^2 + 5y[/tex]
Subtract [tex]2y^2 - 3y - 5[/tex] from [tex]y^3 - 6y^2 + 5y[/tex]
[tex]y^3 - 6y^2 + 5y-(2y^2 - 3y - 5)[/tex]
Multiply negative sign inside the parenthesis
[tex]y^3 - 6y^2 + 5y- 2y^2 + 3y +5[/tex]
Combine like terms
[tex]y^3 - 8y^2 + 8y+5[/tex]
Answer:
Step-by-step explanation: y3 - 8y2 + 8y + 5 (Take 2y 2 - 3y - 5 from y 3 - 6y 2 + 5y. Select the correct answer.)
A store's cost for a stereo was $27. The markup was 75%. A customer purchased it on sale at 40% off the markup price. What was the purchase price of the stereo
16% of what number is 17 ?
Step-by-step explanation:
To find out what 16% of 17 is, we create a cross multiply equation
16/100=17/x
Cross multiply
(16 * x = 16x)
(100 * 17 = 1700)
16x = 1700
1700/16 = 106.25
How many possible 10-digit phone numbers with the area code 617 are there? (any decimal digit can be the digit of a phone number. For instance the number 617−000−0000 is a possible phone number)
Answer:
10,000,000
This is the answer because you have to do 10^7 because 3 of ten dights are filled so you have seven dights remaining. And yeah, i already checked it in my homework thingy fir RSM cuz I had the same problem. So yeah. I hope everyone who sees this has a lovely and beautiful day.
Quote of the day is: Everyone Suffers. Thats the truth. You have you pain and I have mine. But in your life, you pain will come to an end. Don't waste good opportunities and don't be afraid to hide yourself of how you look, or act, or your race and sexuality. Think of it like this, if your pain is a dark tunnel, you are so close to the end you can almost touch the light, so keep moving!
-Me
Hope everyone has a great day and an amazing life ahead
Find the length of the diameter of a sphere with a surface area of 452.39^2 ft.
surface area = 4*pi*r^2
using 3.14 for pi
452.39 = 4*3.14*r^2=
452.39=12.56* r^2
r^2 = 452.39/12.56 = 36.0
sqrt(36) = 6= r
diameter = 2r = 6*2= 12
diameter = 12 feet
The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12).
The equation of the parabola is y =
x2 +
x +
.
The equation of the parabola with a vertex at (-2, -20) and a y-intercept at (0, -12) is y = 2x^2 + 8x - 12.
Explanation:To find the equation of the parabola, we can use the vertex form of a parabola's equation, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola, and 'a' is a coefficient that determines the parabola's width and direction. Since we have the vertex (-2, -20) and the y-intercept (0, -12), we can plug in these values to solve for 'a':
y = a(x - (-2))^2 - 20
Using the y-intercept:
-12 = a(0 - (-2))^2 - 20
-12 = 4a - 20
8 = 4a
a = 2
The equation of the parabola is therefore:
y = 2(x + 2)^2 - 20
Expanding the equation:
y = 2(x^2 + 4x + 4) - 20
y = 2x^2 + 8x + 8 - 20
y = 2x^2 + 8x - 12
The final quadratic equation of the parabola is:
y = 2x^2 + 8x - 12
Identify the value of y
24^2 = 18 * (18 +y)
576 = 324+18y
252 =18y
y = 252/18 =14
y = 14
The value of y is 14.
What is a circle?'A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant'
According to the given problem,
We know,
⇒ 18 ( 18 + y ) = 24²
⇒ 324 + 18y = 576
⇒ 18y = 576 - 324
⇒ 18y = 252
⇒ y = 252/18
⇒ y = 14
Hence, we can conclude, the value of y is 14.
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If (-3)^-5 =1/x, what is the value of x?
Read the following statement: If two angles are acute, their sum is never a straight line. The hypothesis of the statement is:
their sum is never a straight line.
two angles are acute.
If two angles are acute they are straight lines.
None of the choices are correct.
The correct option is (3).
What is acute angle?An acute angle is defined as an angle that measures less than 90 degrees that is measure between 0° to 90°.
Given that if two angles are acute, their sum is never a straight line.
The hypothesis of this would be the one which would satisfy the opposite of the given statement
1) their sum is never a straight line which is Incorrect.
2) two angles are acute which is incorrect because this is given.
3) If two angles are acute they are straight lines which is right.
Hence, the correct option is (3).
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