Answer:
2 - √3Step-by-step explanation:
If the polynomial is degree 2, then it has 2, 1 or 0 zeros.
If the polynomial is degree 2 and the zeros are 2 irrational numbers, then they are in the form a + b√c and a - b√c.
Therefore if one of the zero is 2 + √3, then the other zero is 2 - √3.
The probability that Ashley drives faster than the speed limit (event A) is 0.34, and the probability that he gets a speeding ticket (event B) is 0.22. The probability that he drives faster than the speed limit, given that he has gotten a speeding ticket, is 1. Are events A and B dependent or independent? A. dependent B. independent C. insufficient data D. depends on the other events in the sample space
The correct answer between all
the choices given is the first choice or letter A. I am hoping that this answer
Answer: Option 'A' is correct
Step-by-step explanation:
Since we have given that
A be the event that Ashley drives faster than the speed limit.
P(A)=0.34
B be the event that he gets a speeding ticket.
P(B)=0.22
Probability that he drives faster than the speed limit, given that he has gotten a speeding ticket i.e.
P(A|B)=1
but for A and B to be independent ,
P(A).P(B)= P(A and B)
0.34×0.22=0.0748
but,
[tex]P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}\\\\1=\dfrac{P(A\cap B)}{0.22}\\\\0.22=P(A\cap B)[/tex]
So, P(A∩B) does not satisfy the condition.
Hence, A and B are not independent events.
Option 'A' is correct as they are dependent events.
Without graphing predict weather the function y= (1/2)x shows exponential growth or decay. Justify your predictions
Answer:
The base of the exponential function is 0.5 which is between 0 and 1 and thus this is an exponential decay function.
Step-by-step explanation:
Exponential equations are usually in the form;
[tex]y=ab^{x}[/tex]
where;
a is the initial value, that is the value of y when x is 0,
b is the growth or decay factor and also the base of the exponential function
If b>1, then it is an exponential growth function and the values of y keep getting bigger.
if 0<b<1, then it is an exponential decay function and the y values keep getting smaller as x increases.
In the function given;
[tex]y=(\frac{1}{2})^{x}[/tex]
The base of the exponential function is 0.5 which is between 0 and 1 and thus this is an exponential decay function.
In order to justify our prediction, we can simply obtain the graph of the function and check on how x and y vary.
From the attachment below we can see that the values of y become increasingly smaller as the values of x increases in magnitude which justifies our predictions.
The function y = [tex](1/2)^x[/tex] represents an exponential decay because the base (1/2) is a fraction less than 1.
The function y = [tex](1/2)^x[/tex] represents an exponential decay model because it is in the form y = [tex]a^x[/tex] where a is a fraction between 0 and 1 (0 < a < 1).
An exponential decay function describes a situation where the quantity decreases over time, and the rate of decrease slows down as the quantity gets smaller.
In contrast, if a were greater than 1, it would represent exponential growth, indicating that the quantity increases over time, and the rate of increase accelerates as the quantity grows larger.
So, since (1/2) is less than 1, the function shows exponential decay.
Subtract 7x2 + 4x - 9 from 5x2 + 10x - 5. Express the result as a trinomial in descending
degree order.
Answer:
2x^2-6x-4
Step-by-step explanation:
(7x2 + 4x - 9)
-(5x2 + 10x - 5)
=
7x^2-5x^2=2x^2
4x-10x=-6x
-9-(-5)=-4
thus, your answer is 2x^2-6x-4
PLEASE HELP!!!!
Which statement about the function below is true? f(x) = x3 + 3x2 - 9x- 27 = (x-3)(x + 3)(x + 3)?
The root -3 has a multiplicity of 1.
The root -3 has a multiplicity of 2.
The root 3 has a multiplicity of 2.
The root 3 has a multiplicity of 3.
Answer:
x = - 3 with multiplicity 2
Step-by-step explanation:
f(x) = (x - 3)(x + 3)(x + 3) = (x - 3)(x + 3)²
Equating each factor to zero and solving for x
x - 3 = 0 ⇒ x = 3 with multiplicity 1
x + 3 = 0 ⇒ x = - 3
x + 3 = 0 ⇒ x = -3
Thus x = - 3 has multiplicity of 2
The fact that the factor is squared gives the multiplicity
(x + 3)³ has root - 3 of multiplicity 3
The perimeter of an equilateral triangle is 51 feet.what is the length of one of its side?explain your work
Hello!
The answer is: 17 ft.
Explanation:
To find this out, just divide the perimeter, and the amount of sides in a triangle, which is 3. This will only work with equilateral triangles because an equilateral triangle has all three sides the same length. Anyway, divide 51 and 3. (51 / 3 = 17) Just to make sure, you can add three 17's together, 17 + 17 + 17 = 51, the perimeter.
I hope this helped! ~Q
The length of one of side of Equilateral Triangle is 17 feet, whose perimeter is 51 feet.
What is perimeter of equilateral triangle?
An equilateral triangle's perimeter is the sum of its three sides. P = 3a.
'a' is the side of equilateral triangle.
Given that:
Perimeter of Equilateral Triangle = 51 feet
where 'a' is the side of equilateral Triangle.
As we know that all side of equilateral triangle are equal.
So, its all sides measure 'a'.
Perimeter = a +a +a
51= 3a
a= 51/3
a=17 feet.
Hence, the side of equilateral triangle measures 17 feet.
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Mr. Harmin is sitting in his office on the third floor of a building. He is at an elevation of 30 feet in relation to street level. Mr. Ehrig is in the parking garage at an elevation of –35 feet, and Mrs. White is in the parking garage at an elevation of –25 feet in relation to street level.
Which statements are true? Check all that apply.
A) Mr. Harmin is closest to street level.
B) Mr. Ehrig is at the lowest elevation.
C) Mrs. White is closest to street level.
D) Mr. Harmin is closer to street level than Mrs. White.
E) Mrs. White is at the highest elevation.
Answer:
B and C are true.
The statement (B) Mr. Ehrig is at the lowest elevation, and statement (C) Mrs. White is closest to street level are correct.
What is elevation?The distance up or down a specified point of comparison, most often a reference spherical geometry, a mathematical model of the Earth's sea level as an equipotential gravitational surface, determines a physical location's elevation.
We have:
Mr. Harmin is sitting in his office on the third floor of a building.
He is at an elevation of 30 feet in relation to street level.
Mr. Ehrig is in the parking garage at an elevation of –35 feet, and Mrs. White is in the parking garage at an elevation of –25 feet in relation to street level.
From the above data we can say Mr. Ehrig is at the lowest elevation which is -35 and Mrs. White is closest to street level which is 25 feet
Thus, the statement (B) Mr. Ehrig is at the lowest elevation, and statement (C) Mrs. White is closest to street level are correct.
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If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = -16t^2 + 6t +4. Round your answer to the nearest hundredth.
Answer:
t = 0.722 seconds
Step-by-step explanation:
Given in the question that an equation
h = -16t² + 6t + 4
here h is the height
t is the time
To solve this question we need to substitute height with zero because at ground level height is zero
h = 00 = -16t² + 6t + 4
a = -16
b = 6
c = 4
Formula to use
t = -b±√(b²-4ac) / 2a
Plug values in the formula
t = -6 ± √36-4(-16)(4) / 2(-16)
t = 6±2√73 / 32
t = 6+2√73 / 32 or t = 6-2√73 / 32
t = 0.722 or t = -0.347
since time can't be in negative so we reject t = -0.347
Tina raised the number 3 to a power and then added 19 to the result .She obtained the sum 100. To what power did she raise 3 ?
Answer:
3^4, she raised it to the 4th power
Step-by-step explanation:
3^x+19=100
-19
3^x=81
We can make a table now to find what power of three = 81
Powers of three table
3^1=3 3^2=9 3^3=27 3^4=81
The power she raised the number to is 4.
What is equationThis is a mathematic expression or statement often used to represent word problems.
To solve this question, we need to write an equation to represent this problem.
[tex]3^x + 19 = 100\\ [/tex]
The equation above represents the problem.
Let's solve for x
[tex]3^x + 19 = 100\\ [/tex]
collect like terms
[tex]3^x = 100 - 19\\ 3^x = 81\\ [/tex]
[tex]3^x = 81\\ x = 4[/tex]
What we did above is that how many power are we going to raise 3 to give us 81 and the answer is 4 times.
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Which model best fits the set of data shown on this graph?
A. quadratic model
B. quartic model
C. linear model
D. cubic model
Answer:
C
Step-by-step explanation:
Quadratic model is shaped like a "U", or a parabola
Quartic model is shaped like a "W", highest degree is 4 (x^4).
Linear model is a line.
Cubic model is x^3, shaped like a curvy snake.
Looking at the graph, it clearly shows a line. So, linear model is the answer.
C is the correct answer.
Simplify square root 72 minus 3 times square root 12 plus square root of 192
A. 6 square root 2 plus 2 square root 3
B. 12 square root 2 plus 2
C. 14 square root 2
D. 8 square root 3 minus square root 1
Step-by-step explanation:
hope it helps you!!!!!!!
Answer: Option 'A' is correct.
Step-by-step explanation:
Since we have given that
√72-3×√12+√192
As we have
[tex]\sqrt{72}=6\sqrt{2}[/tex]
[tex]\sqrt{12}=6\sqrt{2}[/tex]
[tex]\sqrt{192}=8\sqrt{3}[/tex]
So, our equation becomes
[tex]6\sqrt{2}-3\times 2\sqrt{3}+8\sqrt{3}\\\\=6\sqrt{2}-6\sqrt{3}+8\sqrt{3}\\\\=6\sqrt{2}+2\sqrt{3}[/tex]
Hence, Option 'A' is correct.
PLEASE HELP: The mass of a ball is 128 g. It has a density of 0.5 g/cm³. What is the volume of the ball? Show your work and place a box around your answer. Optional Bonus point: what is the radius of the ball?
Answer:
Part 1) The volume of the ball is 256 cm³
Part 2) The radius of the ball is 3.94 cm
Step-by-step explanation:
Part 1) we know that
The density is equal to divide the mass by the volume
D=m/V
Solve for the volume
The volume is equal to divide the mass by the density
V=m/D
In this problem we have
m=128 g
D=0.5 g/cm³
substitute
V=128/0.5=256 cm³
Part 2) what is the radius of the ball?
we know that
The volume of the sphere (ball) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]V=256\ cm^{3}[/tex]
assume
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]256=\frac{4}{3}(3.14)r^{3}[/tex]
[tex]768=(12.56)r^{3}[/tex]
[tex]r^{3}=768/(12.56)[/tex]
[tex]r=3.94\ cm[/tex]
Convert the function into standard form. Show your work. y-2=-3(x+4)^2
Answer:
y = -3x² - 24 x + 50
Step-by-step explanation:
y - 2 = - 3(x+4)²
y - 2 = -3(x²+8x+16)
y - 2 = -3x² -24x +48
y = -3x² - 24 x + 50
ANSWER
The standard form is
.
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
EXPLANATION
The given function is
[tex]y - 2 = - 3(x + 4)^{2} [/tex]
The standard form is given by
[tex]y =a {x}^{2} + bx + c[/tex]
We expand to obtain:
[tex]y - 2 = - 3( {x}^{2} + 8x + 16)[/tex]
We expand the parenthesis to obtain:
[tex]y - 2 = - 3 {x}^{2} - 24x - 48[/tex]
Group the similar terms to obtain:
[tex]y = - 3 {x}^{2} - 24x - 48 + 2[/tex]
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
The standard form is
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
Seiki is planning her workout at her gym. She wants to spend more than 40 minutes exercising. Her workout plan includes 20 minutes lifting weights and the rest of the time on three different cardio machines. She wants to spend the same amount of time on each cardio machine. How many minutes should Seiki spend on each cardio machine?
Answer:
Assuming that Seiki wants to be as close to 40 minutes are possible (to the nearest minute), She would want to spend 7 minutes on each of the 3 cardio machines
Step-by-step explanation:
With Seiki wanting to spend at least 40 minutes exercising and spending 20 minutes lifting weights, she needs to spend at least 20 more minutes on her cardio. If we are looking for a number that is divisible by 3, that would mean that she would spend 21 minutes exercising.
Seiki should spend at least 10 minutes on each cardio machine after her 20-minute weightlifting session to meet continuous exercise and weekly cumulative goals, therefore surpassing her minimum of 40 minutes of exercise and aligning with health recommendations.
Time Allocation For Cardio Machines
Seiki wants to spend more than 40 minutes exercising, with 20 minutes devoted to lifting weights and the rest on three different cardio machines. To calculate the time she should spend on each cardio machine, we first deduct the weightlifting time from the total minimum exercise time.
This leaves us with more than 20 minutes for cardio (40 minutes total - 20 minutes of weights = 20+ minutes for cardio).
Since she wants to spend the same amount of time on each machine, we divide the remaining time by three. Let's assume Seiki decides on the minimum of 21 minutes for cardio to exceed the 40 minutes total.
So, 21 minutes divided by three cardio machines equals seven minutes per machine.
However, to align with the recommendations for sessions to be continuous for 10 minutes or more and the goal of a cumulative total of 150-300 minutes from at least three days a week, Seiki should aim for at least 10 minutes on each machine.
This would translate to at least a total of 30 minutes on cardio machines, bringing her workout to a minimum of 50 minutes (20 minutes of weights + 30 minutes of cardio).
Remember, these calculations are based on the minimum requirements, and Seiki can adjust her workout duration on the cardio machines to suit her fitness goals and available time.
doug decided to guess on the last three multiple choice questions on his science test. if each question had four choices, how many ways can he answer the question
There are 64 possible
Answer:
12
Step-by-step explanation:
3 questions times 4 answers equals 12 possible choices,
(4+4+4)
The slope of the line whose equation is 3y + 2x = 1 is: A.)-2/3 B.)-3/2 C.)1/3
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 3y + 2x = 1 into this form
Subtract 2x from both sides
3y = - 2x + 1 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{1}{3}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex] → A
By rearranging the equation 3y + 2x = 1 into slope-intercept form, y = mx + b, we find that the slope of the line is -2/3. The correct answer is A.) -2/3.
The slope of the line whose equation is 3y + 2x = 1 is found by solving for y to get the line into slope-intercept form, which is y = mx + b, where m represents the slope.
First, subtract 2x from both sides of the equation: 3y = -2x + 1.Next, divide each term by 3 to solve for y: y = (-2/3)x + 1/3.Now that the equation is in slope-intercept form, we can see that the slope m is -2/3. Therefore, the correct answer is A.) -2/3.
Solve the following equation. Then place the correct number in the box provided. Leave answer in terms of a mixed number. 7x - 2 < 10
Answer:
[tex]\huge \boxed{x<\frac{12}{7}}[/tex]
Step-by-step explanation:
First thing you do is add by 2 from both sides of equation.
[tex]\displaystyle 7x-2+2<10+2[/tex]
Simplify.
[tex]\displaystyle 10+2=12[/tex]
[tex]\displaystyle 7x<12[/tex]
Divide by 7 from both sides of equation.
[tex]\displaystyle \frac{7x}{7}<\frac{12}{7}[/tex]
Simplify, to find the answer.
[tex]\displaystyle\huge\boxed{ x<\frac{12}{7}}[/tex], which is our answer.
The inequation 7x - 2 < 10 is x < 12/7.
What are inequalities and it's types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The inequation 7x - 2 < 10 is,
7x < 12.
x < 12/7.
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Write 0.6 as a fraction.
A) 1 3
B) 2 3
C) 3 7
D) 3 9
Answer:
All of them are wrong, the answer is 3/5
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
0.6 = 6 / 10 = 3 / 5
Given: NQ is an altitude of △MNP
Prove: Sinm/m = Sinp/p
PLEASE HELP ASAP any answers appreciated I am completely stuck on this
Answer:
Statement: Reason:
ΔNQM and ΔNQP are right triangle Definition of a right triangle
SinM = h/p and SinP = h/m Definition of sine ratio
p sin M = m sin P Substitution property of equality
p sin M / pm = msinP / pm Division property of equality.
Which transformation(s) can be used to map one triangle onto the other? reflection only translation only dilation, then translation rotation, then translation rotation then dilation
Answer:
reflection only
rotation, then translation
Step-by-step explanation:reflection only rotation, then translation
Answer:
Transformation which can be used for mapping of one triangle to another are;
Only translationRotation then dilation.Step-by-step explanation:
Given information:
We need to map one triangle to another ;
Hence, for mapping of one triangle to another,
The transformation which can be used from the given options are;
Only translationRotation then dilation.For more information visit;
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Math question,, ^-^ will give brainiest answer!
Answer:
I think its C im not sure but thats what i got
Sorry If its wrong
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The inscribed angle ∠CAD is half the central angle ∠CBD. Therefore:
35° = 1/2 ∠CBD
∠CBD = 70°
The area of a sector is:
A = (θ/360) πr²
Since r = 10:
A = (70/360) π(10)²
A = 7000π/360
A = 175π/9
Answer is B.
PLZZZZZ HELP!!!
The graph shows two lines, A and B.
Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer. (5 points)
Part B: What is the solution to the equations of lines A and B? Explain your answer. (5 points)
Answer:
Part A: 1 solution
Part B: x = 3, y = 4
Step-by-step explanation:
Lines A & B intersect one time, meaning there is only one pair of x and y values that will make the two equations equalThey intersect at x = 3, and y = 4What is the solution to the equation 1 / 4 x = 5?
x = 4 / 5
x = 5 / 4
x = 20
x = 1
Answer:
The solution to the equation 1/4 x = 5 is '' x = 20''
Step-by-step explanation:
you take ''1/4'' and multiply it by ''20'' and the answer you'll get is ''5''
The solution to the equation 1 / 4 x = 5 is found by isolating x. After multiplying both sides of the equation by 4, you find that x = 20.
Explanation:The solution to your equation, 1 / 4 x = 5, can be found using the principles of algebra. This equation is asking us 'What value of x can I multiply by 1/4 to equal 5?'
The best way to find the solution is to isolate x on one side of the equation. In this case, you'll start by multiplying both sides of the equation by 4. Now your equation looks like this:
1/4 x * 4 = 5 * 4
Simplifying the equation, you'll get:
x = 20
Therefore, you can see that the solution to the equation 1/4 x = 5 is x = 20.
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Which line is a graph of the equation: -2x + 5y=10
Answer:
Step-by-step explanation: first, find y by itself by adding 2x to the other side then diving by the 5y to get y=2/5x +2! Rise 2, run 5 from your start at positive 2 on the graph and you should get line a!!!
The graph of the equation -2x + 5y = 10 has a positive slope of 2/5 and a y-intercept of 2. None of the provided options accurately describe the graph of the equation, as they indicate incorrect y-intercept values and describe the slope incorrectly.
Explanation:To find which line is a graph of the equation -2x + 5y = 10, we need to identify the slope and the y-intercept of the line. To do this, we should rearrange the equation into slope-intercept form, which is y = mx + b where m is the slope and b is the y-intercept.
Rearranging the equation, we get:
5y = 2x + 10
y = (2/5)x + 2
The slope is the coefficient of x, which is 2/5, and the y-intercept is the constant term, which is 2. The line has a positive slope, and based on the slope-intercept form, it rises on the graph as the x-value increases. Therefore, option d with a positive slope and a y-intercept of 50 must have a typo since our y-intercept is 2. The correct interpretation would be that the line gradually moves upward on the graph as the x-value increases, thanks to its positive slope.
Hence, none of the provided options describe the graph of the equation -2x + 5y = 10 accurately because the y-intercept should be 2, not 50, and the slope is positive. Keep in mind that a positive slope results in an upward, not a downward, trend as x increases.
which graph represents y= square root x?
[tex]y=\sqrt{x}[/tex] is the square root function. The graph of this function has been attached below. As you can see, this is in fact a function it passes the Vertical Line Test for Functions that establishes that if a vertical line intersects a graph at most one point, then this is a function. From the square root function we know:
The domain of the function is the set of all nonnegative real numbers. The range of the function is the set of all nonnegative real numbers. The origin [tex](0,0)[/tex] is an intercept of the graph. The graph increases on the interval [tex](0, \infty)[/tex].Answer:
b on edge
Step-by-step explanation:
suppose the radius of a circle is 8 units. what is its circumference
Answer:
[tex]\large\boxed{C=16\pi\approx50.24}[/tex]
Step-by-step explanation:
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
r - radius
We have r = 8. Substitute:
[tex]C=2\pi(8)=16\pi[/tex]
[tex]\pi\approx3.14\to C\approx(16)(3.14)=50.24[/tex]
Answer:
50.24 units
Step-by-step explanation:
Hope this helps!
What is the answer pls?
:) Hope this answers your question :)
Factor 8X squared + 10x + 2
Answer:
2(4x + 1)(x + 1)
Step-by-step explanation:
Given
8x² + 10x + 2 ← factor out 2 from each term
= 2(4x² + 5x + 1)
To factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × 1 = 4 and sum = + 5
The factors are + 1 and + 4
Use these factors to split the x - term
4x² + x + 4x + 1 ( factor the first/second and third/fourth terms )
= x(4x + 1) + 1 (4x + 1) ← factor out (4x + 1)
= (4x + 1)(x + 1), thus
4x² + 5x + 1 = (4x + 1)(x + 1) and
8x² + 10x + 2 = 2(4x + 1)(x + 1) ← in factored form
What is the area of the base of a cylinder with a volume of 174π in.3 and a height of 12 inches? 1. Apply the formula for the volume of a cylinder: V = Bh 2. Substitute the known measures into the formula: 174π = B(12) 3. Apply the division property of equality: 174π 12 = B 12 12 The area of the base of the cyclinder is π in.2.
ANSWER
The area of the base is 14.5π in²
EXPLANATION
The volume of a cylinder is given by
[tex]Volume =base\:area \times height[/tex]
Or
V=Bh
It was given that the volume of the cylinder is 174π in³.
The height was given as 12 inches.
We substitute to get,
174π=12B
Divide both sides by 12 to get:
B=14.5π in²
Hence the area of the base is 14.5π in²
Answer:
14.5
Step-by-step explanation:
Destiny has one round window that is 20 inches in diameter. What is the circumference and area of the window?
Answer:
The Circumference is 62.80, The Area is 100 inches squared
Step-by-step explanation:
Diameter is 20 so the Radius is half of thats.
D=20 In
R=10 in
Circumference is diameter multipied by pi
so you multiply 20 by 3.14 and you get 62.80 inches
To Find Area you have to multiply the radius times it self. so 10×10 whoch equals 100.
so the area is 100 inches squared.
All regular polygon:
A. Have four sides
B.Have an even number of sides
C.are symmetrical
D.are the same size
C. Are simmetrical
ExplanationA. is false because only quadrilaterals have 4 sides
B. is false because polygons like equilateral triangle and regular pentagon have an odd number of sides
D. A polygon doesn't have an unique size. It changes every time, cause we can decide its size
Answer: The answer is C. are symmetrical.
Step-by-step explanation: There is a line of symmetry, which is a line where one half of the polygon is a mirror image of the other side. This means that even if a polygon has 5 sides, for example, then it would still be symmetrical.