Answer:
A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are coefficients and x is the variable.
The roots of a quadratic equation are the values of x that make the equation equal to zero.
Given that the roots of the quadratic equation are (3+√5) and (3-√5), we can set the quadratic equation equal to zero and substitute the roots for x:
ax^2 + bx + c = 0
(x - (3+√5))(x - (3-√5)) = 0
(x - 3 - √5)(x - 3 + √5) = 0
(x - 3 - √5)(x - 3 + √5) = (x-3)^2 - (√5)^2 = (x-3)^2 - 5 = 0
x^2 - 6x + 9 - 5 = 0
x^2 - 6x + 4 = 0
So the quadratic equation whose roots are (3+√5) and (3-√5) is x^2 - 6x + 4 = 0
Step-by-step explanation:
A student, lives within walking distance of 6 restaurants. unbeknownst to her, she has exactly 1 friend at 3 of the restaurants, she has 2 friends at 2 of the restaurants, and she has no friends at one of the restaurants. suppose that this accounts for all of her friends. supposing that she chooses a restaurant at random, what is the probability she will have at least one friend at the restaurant
The probability she will have at least one friend at the restaurant is 1/3.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
From the given information the total number of friends (F) is 3 and the total number of restaurants N(R) is 6.
Therefore,
The likelihood that she will be accompanied by at least one friend to the restaurant is,
P(F) = N(F)/N(R).
P(F) = 3/6.
P(F) = 1/3.
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if f(x) = 5 - 3x and g(x)= 4x + 1, determine the value of x such that f(x) = g(x)
help pls
If f(x) = 5 - 3x and g(x)= 4x + 1, then the value of x such that f(x) = g(x) is, x 4/7
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
Two functions, f(x) = 5 - 3x and g(x)= 4x + 1,
The value of x, for which f(x) = g(x)
Now, equating both the functions
⇒ 5 - 3x = 4x + 1
⇒ 4 = 7x
⇒ x = 4/7
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the perimeter of a rectangle is 34 centimenters the length is two more than twice the width. write and solve a system of linear equations to find the width of the rectanlge.
The linear equation that can be used to find the width of the rectangle is 34 = 6w, and w = 5.67cm
What is linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.
The length of the rectangle is twice the width. Therefore, l = 2w
The perimeter of a rectangle is expressed as : P = 2(l+w)
l = 2w
P= 2(2w + w)
P = 6w
34 = 6w
therefore the equation that can be used to find the width of the rectangle is 34 = 6w
and the value of w = 34/6 = 5.67cm
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find the amount of empty space within a cylinder containing three solid spheres, where each sphere has a radius of 3 cm. (volume of a sphere
Ves = 169.56 cm³ is the amount of empty space within a cylinder containing three solid spheres, where each sphere has a radius of 3 cm.
Let call Vc volume of cylinder
If the cylinder has to contain three spheres of radius 3 cm the height of the
cylinder is 3 * 2 * 3 = 18 cm ( we have three diameters )
The radius of the base of the cylinder is 3 cm
And Vc = π*r²*h ⇒ Vc = (3,14) * 9 * 18 ⇒ Vc = 508.68 cm³
On the other hand we have Vs (volume of one sphere)
Vs = 4/3 * π * r³ ⇒ Vs = 4/3 * 3,14 * (3)³ ⇒ Vs = 113,04 cm³
as we have 3 spheres the total volume is 3 * 113.04
Vts = (total volume of spheres) = 339,12 cm³
The empty space withing the cylinder is the difference between Vc and Vts
Ves ( volume of empty space ) = Vc - Vts = 508.68 - 339,12
Ves = 169.56 cm³
Ves = 169.56 cm³ is the amount of empty space within a cylinder containing three solid spheres, where each sphere has a radius of 3 cm.
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Identify or mark the missing side or angle that would make the triangle ABC congruent to triangle PDF by AAS
The missing sides or angles that make the triangle ABC congruent to PDF by SAS are AC and PF, ∠A and ∠P and ∠B and ∠D
What are congruent triangles?If all three corresponding sides and all three corresponding angles are equal for two triangles, they are said to be congruent. The corresponding sides and angles of two triangles must be equal for them to be considered congruent.
The triangles are congruent by AAS if two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle (angle angle side). Hence, the missing side or the angle that makes the triangle ABC congruent to triangle PDF are as follows:AC ≅ PF∠A ≅ ∠P∠B ≅ ∠D
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a teacher would like to estimate the mean amount of time it takes for students taking this statistics class to complete this multiple-choice assessment item. to do so, she selects a random sample of 50 students enrolled in this statistics class and records the amount of time (in minutes) it takes them to complete this question. the standard error of the mean is 0.27 minutes. what is the interpretation of the standard error of the mean?
The interpretation of the standard error of the mean is the amount of time it takes for students taking this statistics class to complete this multiple-choice assessment item would vary by 0.27 minutes.
What Is the Standard Error Of The Mean?The population mean's likelihood to differ from a sample mean is indicated by the standard error of the mean, or simply standard error. It reveals how much the sample mean would change if a study were to be repeated with fresh samples drawn from a single population.The sample mean duration of time required to complete this question would normally deviate from the population mean by roughly 0.27 minutes if we randomly sampled a large number of students enrolled in this statistics course.
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Whats 10, -5, 3, 16, -1, 0, 1 in order from least to greatest ?
The lightbulb in my kitchen has blown. I checked the prices of bulbs online, which one should I buy and why? I have my kitchen light on for 5 hours a day every day for a year. The energy company charges me 12p per kWh (kilowatt hour) How much would it cost to run a normal vs energy efficient bulb for a year?
Depending on the comparable model, Energy Star appliances will save you 10% to 50% of the energy used;
Does utilising less energy cost less money?Energy efficiency helps homes and companies save money on their monthly energy bills by minimising energy consumption. In the long run, energy-efficient items often end up saving you money even though they initially cost more to purchase than other solutions.Depending on the comparable model, Energy Star appliances will save you 10% to 50% of the energy used; if you are replacing an older appliance, the savings will be much more. The Environmental Protection Agency and the Department of Energy together run a programme called Energy Star.To learn more about energy cost refer to:
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Using an energy efficient bulb will result in a significant cost saving over the long term.
Does utilising less energy cost less money?
A normal incandescent bulb uses 60W of power and lasts around 1000 hours, while a LED bulb uses around 8-12W of power and can last up to 25,000 hours.
So if you use the light 5 hours a day, 365 days a year, a 60W incandescent bulb will consume 11.25 kWh per year and cost you approximately £1.35 per year to run. In contrast, a 8W LED bulb will consume approximately 0.6 kWh per year, costing you approximately £0.072 per year to run.
Therefore, using an energy efficient bulb will result in a significant cost saving over the long term.
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The length of a picture is 2 more than the width. There is a frame of uniform width around the picture that is 3 inches wide. If the area of everything is 224 in 2 , find the dimensions of the picture.
Width = 8 inch
Length = 10 inch
This can be solved using rectangular area formula.
What is rectangular area?The area a rectangle takes up inside its four sides or limits is known as the area of the rectangle. A rectangle's sides determine how much space it has. The product of the rectangle's length and width is essentially the area formula.
By multiplying the rectangle's length by its breadth, we may get its area.
length of the picture = l inch
width of the picture = w inch
given that, length of a picture is 2 more than the width.
so, l = w + 2
There is a frame of uniform width around the picture that is 3 inches wide, now length becomes: l = w + 2 + 3
l = w + 5
and the width becomes: w = w + 3
the area of everything is 224 inch²
l × w = 224 inch²
or, (w + 5) × (w + 3) = 224 inch²
or, w² + 8w + 15 = 224
or, (w + 19) (w - 8) = 0
or, w = 8, -19
Width never be negative so w = 8 inch
Now, length = w + 2
l = 8 + 2
l = 10 inch
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The dimensions of the picture are 10 × 8 in if the area of everything is 224 in².
What is a rectangular area?The area a rectangle takes up inside its four sides or limits is known as the area of the rectangle. A rectangle's sides determine how much space it has. The product of the rectangle's length and width is essentially the area formula.
By multiplying the rectangle's length by its breadth, we may get its area.
Length of the picture = l inch
Width of the picture = w inch
Given that, the length of a picture is 2 more than the width.
So, l = w + 2
There is a frame of uniform width around the picture that is 3 inches wide, now length becomes: l = w + 2 + 3
l = w + 5
The width becomes: w = w + 3
The area of everything is 224 inch².
l × w = 224 inch²
(w + 5) × (w + 3) = 224 inch²
w² + 8w + 15 = 224
(w + 19) (w - 8) = 0
w = 8, -19
Width never be negative so w = 8 inch
Now, length = w + 2
l = 8 + 2
l = 10 inch
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Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Question 14
[tex]\frac{\sin x}{26}=\frac{\sin 49^{\circ}}{25}\\\\\sin x=\frac{26\sin 49^{\circ}}{25}\\\\x \approx 51.7^{\circ}, 128.3^{\circ}[/tex]
Both of these values satisfy the angle sum of a triangle.
Question 16
[tex]\frac{\sin x}{8}=\frac{\sin 105^{\circ}}{11}\\\\\sin x=\frac{8 \sin 105^{\circ}}{11}\\\\x \approx 44.6^{\circ}, 135.4^{\circ}[/tex]
However, the second case exceeds the angle sum of a triangle, so [tex]x \approx 44.6^{\circ}[/tex].
from the beginning of the second trimester a pregnant woman needs approximately an additional how many calories a day? responses 100 100 300 300 800 800 1,000
From the beginning of the second trimester a pregnant woman needs approximately an additional 300 calories a day.
Second Trimester:
Pregnancy helps you think about pregnancy because the changes you and your baby are going through fall into three broad categories: early, mid, and late. Metaphase, represents the 13th to 26th week. For many women, one of the best things about this trimester is when the nausea starts to subside.
I have had personal experiences with this, as to the fact I have 3 siblings and I have helped raise them. 300 calories are just the right amount for the mother and the growing baby. If she ate more than that, she would gain much more baby weight.
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Using a metric ruler with 1 mm divisions, you find the sides of a rectangular piece of plywood as 3.7 cm and 4.85 cm. To the correct number of significant figures, the area should be expressed as _____. A. 17,95 cm2 B. 17,945 cm2 C. 18 cm2 D. 17,9 cm2
On solving the provide question, we can say that the correct number of significant figures, the area should be expressed as 5 cm and 10 dm and 2500 mm and 750 cm
what is significant figures?The number of significant digits in a value—often a measurement—contributes to the accuracy of the value. From the first non-zero digit, begin counting the important digits. To the right of the last non-zero decimal place, all zeros are acceptable. For instance, the number 0.0079800 has five significant digits. When they come from the measurement, any zeros to the right of the final non-zero digit are important. equivalently rounds an integer to 3 significant digits and 3 decimal places. Start counting at the first non-zero digit and go up to three. After that, remove the final digit. Add zeros to the last two numbers to the right of the decimal point.
he sides of a rectangular piece of plywood as = 3.7 cm and 4.85 cm
the correct number of significant figures, the area should be expressed as
1. 5 cm
2. 10 dm
3. 2500 mm
4. 750 cm
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If f(1)=8 and f(n)=f(n-1)+3 then find the value of f(6)
Answer:
f(6)=23
Step-by-step explanation:
f(n)=f(n-1)+3
f(1) becomes f(1-1)+3
f(1-1)+3 = 8
f(0) +3=8
f(0) = 5
=
f(2) = f(2-1)+3
f(2) = f(1)+3
f(2) = 8+3
f(2) = 11
f(3) = f(3-1)+3
f(3) = f(2) + 3
f(3) = 11+3
F(3) = 14
We can see that the sequence adds three to each prior value:
x Result
0 5
1 8
2 11
3 14
4 17
5 20
6 23
f(6) = 23
Write the equation of the circle centered at (6, 2) with radius 1. Fully simplify the equation.
Answer:
[tex]x^2-12x+y^2-4y+39=0[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Given:
center = (6, 2)radius = 1Substitute the given values into the equation of a circle formula:
[tex]\implies (x-6)^2+(y-2)^2=1^2[/tex]
Simplify by expanding:
[tex]\implies (x-6)(x-6)+(y-2)(y-2)=1[/tex]
[tex]\implies x^2-12x+36+y^2-4y+4=1[/tex]
[tex]\implies x^2-12x+y^2-4y+39=0[/tex]
The graph h shows the height, in meters, of a rocket t seconds after it was launched
a) H0 = 15 m, is the initial height, the height of the rocket at time 0 s.
b) D = [0,5]
c) R = [0,35]
What is a domain?The set of inputs that a function will accept is known as the domain of the function in mathematics. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Here, we have
a) H0 is the initial height. It means the height of the rocket at time 0 s.
This value is 15 m.
b) The domain is all values of t between 0 and 5 seconds.
D = [0,5]
c) The range is all values of height from 0 to 35 meters.
R = [0,35]
Hence, a) H0 = 15 m, is the initial height, the height of the rocket at time 0 s.
b) D = [0,5]
c) R = [0,35]
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Complete question is: The graph H shows the height, in meters, of a rocket 1 seconds after it was launched.
a. Find H0). What does this value
represent?
b. Describe the domain of this function.
c. Describe the range of this function.
Answer:
Step-by-step explanation:
.
Complete. 64 yd = in.
Answer: 2304
Step-by-step explanation: 64 x 36 = 2304
Answer:
2,304 in.
Step-by-step explanation:
I attached a pic of my work.
3^5 x 10 ^5 x 35 divided by 5^7 x 6^5
step by step explantion pls
ty ig
Answer:84652646.4
Step-by-step explanation:
Identify or mark the missing side or angle that would make the triangle ABC congruent to triangle PDF by SAS
The missing sides or angles that makes the triangle ABC congruent to PDF by SAS are AB and PD, BC and DF and ∠B and ∠D
What are congruent triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal .
In other words, two triangles are congruent when the corresponding sides and angles are equal.
Hence, let's find the missing side of angle that makes the triangle ABC congruent to triangle PDF by SAS.
Hence,
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent by SAS.
Therefore, the missing sides are as follows:
AB ≅ PD
BC ≅ DF
∠B ≅ ∠D
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a lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left- handers. the typical size of classes that meet there is 188, and we can assume that about 13% of students are left-handed. a) show that a binomial model is appropriate to use. then find the probability that a right-handed student in one of these classes is forced to use a lefty arm tablet. b) solve this problem again using the normal model. first show that a normal model is appropriate to use.
The probability of a right-handed student being forced to use a left-handed arm tablet is 0.085 or 8.5% using either the binomial or normal model.
A binomial model is appropriate to use for this problem since there are two possible outcomes (left or right-handed) and the probability of each outcome is independent of the other. The probability of a right-handed student being forced to use a left-handed arm tablet is calculated by subtracting the number of left-handed arm tablets (30) from the total number of students in the class (188) and dividing that by the total number of arm tablets (200). This yields a probability of 0.085 or 8.5%.
Using the normal model, the probability of a right-handed student being forced to use a left-handed arm tablet can also be calculated. This model is appropriate since there are a large number of students (188) and the probability of a student being right or left-handed is close to the population average (13%). The probability can be calculated by subtracting the number of left-handed arm tablets (30) from the total number of students in the class (188) and dividing that by the total number of arm tablets (200). This yields a probability of 0.085 or 8.5%.
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Give an example of an in nite collection of open sets in R2 whose inter- section is not open (in the standard topology).
A point on the real line with the conventional topology is a frequent example of this.
In that topology, a point a ∈ R is not an open point; rather, it is the intersection of open intervals.
{a} = ∩ (a - [tex]\frac{1}{n}[/tex] , a + [tex]\frac{1}{n}[/tex] ) { for n=1 to ∞ }
What is Open Set?
The fundamental building blocks of topology are open sets. The open sets have a natural description in the well-known context of a metric space, which can be conceptualized as a generalization of an open interval on the real number line. In the same manner that an interval's endpoints are not contained within the interval, an open set is logically defined as a set that does not contain its border.
Therefore our suitable example will be a point in the real line.
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(02.04 LC)
What is the equation of the following graph in vertex form?
Courtesy of Texas Instruments
Oy=(x-1)²
Oy=(x-1)²+1
Oy=(x + 1)²-1
(0, 1)
first off let's take a looksie at the picture above, hmmm the vertex is at (-1 , 0) and it has another point at (0 , 1) ok hmmm
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-1\\ k=0\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=0\\ y=1 \end{cases}[/tex]
[tex]1=a(~~0-(-1)~~)^2 + 0\implies 1=a(1)^2\implies 1=a \\\\\\ y=1(~~x-(-1)~~)^2 + 0\implies {\Large \begin{array}{llll} y=(x+1)^2 \end{array}}[/tex]
Simplify: Negative two and one-third minus negative ten and one-sixth(5 points)
Negative twelve and one-half
Twelve and one-half
Seven and five-sixths
Negative seven and five-sixths
After simplification, we can express the given expression as "Negative twelve and one-half."
Option (B) is correct.
What is a simplification in mathematics?
In mathematics, simplification refers to the process of making an expression or equation simpler or easier to understand or work with. This can involve combining like terms, removing unnecessary terms or factors, or rearranging the order of the terms.
To simplify the expression: Negative two and one-third minus negative ten and one-sixth, we will convert the mixed numbers to fractions and then perform the subtraction.
First, we convert the mixed numbers to fractions:
Negative two and one-third = -2 + (1/3) = -2 + 1/3
Negative ten and one-sixth = -10 + (1/6) = -10 + 1/6
Then we perform the subtraction:
(-2 + 1/3) - (-10 + 1/6) = -2 -10 + 1/3 - 1/6 = -12 + 2/6 + 1/6 = -12 + 3/6 = -12 + 1/2
So the simplified expression is Negative twelve and one-half.
Hence, after simplification, we can express the given expression as "Negative twelve and one-half."
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A handyman wants to build a fence round a garden in the shape of a triangle. He plans to use a 6-ft-longpiece of fencing and a 7-ft-long piece of fencing. What could be the length of the third piece of fencing?
Answer:
1 < x < 13
Step-by-step explanation:
The longest leg of a triangle must be less than the sum of the shorter legs.
c < a + b
If the third piece is the longest leg, then:
x < 6 + 7
x < 13
If the 7-ft piece is the longest leg, then:
7 < 6 + x
x > 1
Therefore, the third leg is between 1 ft and 13 ft.
Fill in the missing amounts.
Answer:
Mar Apr May
Receipts $1,155 $1,250 $
Expenses $1,100 $990 $900
Net Cash Flow $55 $ $45
Cumulative Balance $ $315 $360
Identify the cross-section shown.
triangle
hexagon
circle
octagon
Answer: hexagon
Step-by-step explanation: it has six sides !!
Does someone mind helping me with this problem? Thank you!
Answer:
x = 5
y = 8
Step-by-step explanation:
2x + y = 18
y = 4x - 12
First, let's find the value of x:Since y = 4x - 12, we can replace the y in the first equation with 4x - 12.2x + 4x - 12 = 18
Add like terms.6x - 12 = 18
Add 12 to both sides of the equation to isolate x.6x = 30
Divide both sides by 6.x = 5
Now onto the value of y:2x + y = 18
We know x = 5 from the previous work so we can replace x with 6 in the equation.2*5 + y = 18
Multiply.10 + y = 18
Isolate y.y = 8
consider a qubit to be in the state . what is the state of the qubit after the spin projection along the x-axis measurement outcome is found to be 1?
The state of the qubit after the spin projection along the x-axis in graph measurement outcome is found to be 1 is |1⟩.
The original state of the qubit is given as |ψ⟩ = a|0⟩ + b|1⟩.
After a spin projection along the x-axis measurement, if the outcome is 1, then the state of the qubit after the measurement is |1⟩. This can be expressed as |1⟩ = a|0⟩ + b|1⟩.
Therefore, the state of the qubit after the spin projection along the x-axis measurement outcome is found to be 1 is |1⟩.
The state of the qubit after the spin projection along the x-axis measurement outcome is found to be 1 is |1⟩.
The state of the qubit before the spin projection along the x-axis measurement was given as |ψ⟩ = a|0⟩ + b|1⟩, where a and b are complex numbers such that |a|2 + |b|2 = 1. After the spin projection along the x-axis measurement, if the outcome was 1, then the state of the qubit after the measurement is |1⟩ = a|0⟩ + b|1⟩, which is the state of the qubit after the spin projection along the x-axis graph measurement outcome is found to be 1.
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I'm doing mathematical that I have never learned
Answer: 6
Step-by-step explanation:
Cancel out the GCF (4)
Multiply the numbers in parenthesis (9x3)
Cancel out GCF (3 and 27)
9-3=6
Answer: 6
Step-by-step explanation:
Given Equation: 1/3*(9/4*12)-3
To solve this equation, you will need to do so according to PEMDAS.
First, you must solve the equation in the parenthesis.
1/3*(9/4*12)-3
= 1/3*(27)-3
Next, do the multiplication.
1/3*(27)-3
=9-3
Finally, subtract the values.
9-3
=6
Answer: 6
−11 + |−5| − |−15| help
The expression −11 + |−5| − |−15| containing modulus sign is solved to get -21
What are absolute values?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
A number can never have a negative absolute value.
How to solve the absolute value equationThe equation is written in the form below
= −11 + |−5| − |−15|
removing the absolute value sign
= −11 + 5 − 15
performing the mathematical operations (addition and subtraction)
= -11 - 10
= -21
The absolute value equation was solved to get -10
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a) Work out 38% of 124
b) Work out 138% of 124
Give each of your answers as a decimal.
A) 38% of 124 is 46.32 (as a decimal)
B) 138% of 124 is 171.12 (as a decimal)
What is the decimal form?
The decimal form of a number is a way of expressing that number as a decimal (base 10) number. A decimal number is made up of a whole number part and a fractional part, separated by a decimal point.
A) To work out 38% of 124, we can use the following formula:
(percentage/100) * value = result
So, in this case:
(38/100) * 124 = 0.38 * 124 = 46.32
So, 38% of 124 is 46.32 (as a decimal)
B) To work out 138% of 124, we can use the same formula:
(138/100) * 124 = 1.38 * 124 = 171.12
So, 138% of 124 is 171.12 (as a decimal)
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