Answer:
y = 7 + 2√2, y = 7 - 2√2
Step-by-step explanation:
We need to solve for y to find the solutions of the quadratic equation:
3(y-7)^2 = 24
(y-7)^2 = 8
y-7 = ±√8 = ±√(4*2) = ±2√2
y = 7 + 2√2
y = 7 - 2√2
2√2 is the simplified radical form because 4 is the highest factor of 8 that is a perfect square.
Solve the following quadratic by
completing the square.
y = x^2 - 6x+7
Answer:
{3 - √2; 3 + √2}Step-by-step explanation:
GivenQuadratic function y = x² - 6x + 7Solving by completing the square x² - 6x + 7 = 0 Givenx² - 2*3x + 3² - 3² + 7 = 0 Add, subtract 3²(x - 3)² - 9 + 7 = 0 Simplify(x - 3)² - 2 = 0 Difference of squares(x - 3 + √2)(x - 3 - √2) = 0 Factorizex - 3 + √2 = 0 and x - 3 - √2 = 0 Solve each rootx = 3 - √2 and x = 3 + √2 AnswerAnswer:
[tex]x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}[/tex]
Step-by-step explanation:
Given quadratic equation:
[tex]y = x^2 - 6x+7[/tex]
To complete the square, begin by adding and subtracting the square of half the coefficient of the term in x:
[tex]\implies y = x^2 - 6x+\left(\dfrac{-6}{2}\right)^2-\left(\dfrac{-6}{2}\right)^2+7[/tex]
[tex]\implies y = x^2 - 6x+\left(-3\right)^2-\left(-3\right)^2+7[/tex]
[tex]\implies y = x^2 - 6x+9-9+7[/tex]
Factor the perfect square trinomial:
[tex]\implies y=(x-3)^2-9+7[/tex]
[tex]\implies y=(x-3)^2-2[/tex]
To solve the quadratic, set it to zero and solve for x:
[tex]\implies (x-3)^2-2=0[/tex]
[tex]\implies (x-3)^2-2+2=0+2[/tex]
[tex]\implies (x-3)^2=2[/tex]
[tex]\implies \sqrt{(x-3)^2}=\sqrt{2}[/tex]
[tex]\implies x-3= \pm\sqrt{2}[/tex]
[tex]\implies x-3+3= 3\pm\sqrt{2}[/tex]
[tex]\implies x= 3\pm\sqrt{2}[/tex]
Therefore, the solution to the given quadratic equation is:
[tex]x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}[/tex]
A bond is worth $100 and grows in value by 4 percent each year. Assuming this bond compounds quarterly, what is the value of the bond after 5 years?
Responses
$121.67
$122.02
$122.67
$120.00
Answer:it will be D
Step-by-step explanation: because $100 + 4%=$100.4
Select the correct answer.
What is the solution to the equation?
√x+2 = x
O A 1
O B.
O C. 1 and 4
O D. no solution
4
Answer:
x=4
Step-by-step explanation:
Square root of four equals 2 then +2 = 4
In a class of 29 students 9 play an instrument and 23 play a sport there are 5 students who play an instrument and also play a sport. What is the probability that a student plays an instrument given that they play a sport?
The probability for the given case is 5/23.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Given that,
Total number of students is 29.
The students who play instrument are 23.
Those who play a sport are 9.
And, those who play both are 5.
Given problem is the case of conditional probability which can be solved by Bayes's theorem as,
P(A|B) = P(A ∩ B) / P(B)
Suppose, A be the event the students play instrument.
B be the event the students play a sport.
And, A ∩ B is the event they play th both.
Then A|B implies the event when a student play instrument given he plays sport.
Apply the rule of probability in the equation for Bayes's theorem to get,
P(A|B) = (5/29) / (23/29)
= 5/23
Hence, the probability that a student plays an instrument given that they play a sport is 5/23.
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a specific pendulum has a period of t, given by the equation above. if the length of the string, l, is increased, the period will
If the length of the string, l, is increased, the period will; Increase
How to solve simple pendulum problems?The time period of a simple pendulum is given by the formula;
t = 2π√(l/g)
Where;
t is time period
l is length of the string
g is acceleration due to gravity.
We can see from the equation above that for simple pendulum, time period is directly proportional to length of the string; (t ∝ l ).
However, we see that the time period is inversely proportional to acceleration due to gravity ( t ∝ 1/g) .
Now, as we are told, If length(l) of the string is increased, then it means that the time period (t) of the pendulum will also increase.
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A player throws a basketball toward a hoop. The basketball follows a
parabolic path that can be modeled by the equation
y=125x² +2.08x + 4. The table models the parabolic path of another
basketball thrown from somewhere else on the court. If the center of the
hoop is at (12,11), will each ball pass through the hoop?
Will the basketball that follows a parabolic path modeled by y=-.125x² +2.08x + 4 pass through the hoop?
yes
No
Will the other basketball, whose path is modeled by the table, pass through the
hoop?!
Yes
No
1. in this exercise you must substitute the value of of x = 12 in the equation of the parable given, if the result is 10 then the ball pass through the hoop
2. Y = (-.125)(12)^2+ (1.84)(12)+6 = -18+22.08+6 = 10.06≅10 , of this form it is demonstrated, that the ball pass through the hoop
solving linear equations with one variable
Answer:
I hope it will be helpful for you.
Della has 72 red beads and 32 blue beads. She would like to make bracelets for of beads. She does not want any beads left over. What is the maximum number her friends. She wants all the bracelets to have the same number of each colour bracelets she could make? How many beads of each colour would each bracelet have?
Answer:
8 bracelets can be made from given beads.
Step-by-step explanation:
To make similar bracelets using all the beads, we have to find the highest common factor of no of beads
Factors of 72 => 1, 2, 3, 4, 6, 8 , 9, 12, 18, 24, 36, 72
Factors of 32=> 1 , 2, 4 , 8 , 16 , 32
Observing this data, HCF of 72and 32 will be 8.
Therefore, total 8 bracelets can be made from given beads.
Find the scale factor. tell whether the dilation is a reduction or an enlargement. Then find the values of the variables.
1.
The dilation is an enlargement.The scale factor is of 3.The values of the variables are: x = 15, y = 18.2.
The dilation is a reduction.The scale factor is of 0.4167.The values of the variable is: x = 2.5.What is a dilation?A dilation occurs when each of the side lengths of an image are multiplied by a constant, which is called scale factor.
For item a, the scale factor is of:
12/4 = 3.
The scale factor is greater than 1, hence it represents an enlargement, and the missing values are found multiplying the equivalent sides by 3, hence:
x = 5 x 3 = 15.y = 6 x 3 = 18.For item b, the scale factor is of:
5/12 = 0.4167.
The scale factor is less than 1, hence it is a reduction, and the missing value is of:
x = 6 x 0.4167 = 2.5.
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The volume of a cube is 125 cubic inches.
What is the area of one face of the cube?
(Square Inches)
Answer:
The area of one face of the cube is 25 square inches.
Step-by-step explana
Which one of the following is discreate data
Number of people in a room is the discreate data .
What is meant by discrete data ?Data that only accepts specific values is referred to as discrete data or discrete values. This type of data, which can be counted and has a finite number of values, is frequently expressed as whole numbers or integers.
Information that only has a limited range of values is said to be discrete. These values don't have to be whole numbers (a child's shoe size might be 3.5 or a company's profit might be £3456.25), but they must be fixed values; a child's shoe size cannot be 3.72!
Discrete means "made up of individual, separate units" (not to be confused with "discreet," a completely different word that just so happens to sound similar). Discrete entities, such as logical statements and (obviously) integers, are the focus of discrete mathematics.
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Giuseppe’s buys supplies to make pizzas for $4. Operating expenses of the business are 110% of the cost and the profit made is 130% of cost. What is the regular selling price of each pizza?
The regular selling price of each pizza is $13.60.
Given that, Giuseppe’s buys supplies to make pizzas for $4.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
According to question,
Regular selling price = Cost price × (Operating expenses + Profit +1)
Cost price =$4
Operating expenses = 110% or 1.1
Profit = 130% or 1.3
Thus, regular selling price =$4 × (1.1 +1.3 +1)
Regular selling price =$4 × 3.4
Regular selling price = $13.60
Therefore, the regular selling price of each pizza is $13.60.
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Jason has 1/6 yard of craft wire for a jewelry project. He cuts the craft wire into 4 pieces of the same length. What is the length, in yards, of each piece of craft wire Jason cut?
Answer:
1/24 yd
Step-by-step explanation:
Since he cut the wire into 4 pieces of equal length, each piece is 1/4 the length of the original piece.
1/4 of 1/6 of a yd
1/4 × 1/6 yd = 1/24 yd
find a number which is 12 morethan its 3/4
Answer:
46
Step-by-step explanation:
What is 12 more than 34?
We are looking for a new number which is 12 more than 34.
We will get the new number by adding 12 to 34.
We write it down as:
34+12=46
And finally the solution for: What number is 12 more than 34?
is 46
i am once again asking for your intellectual support
Step-by-step explanation:
the first box is linear since when you add it to (x,y) it gives a straight line
Wiyot is earning money for a longboard by selling lemonade at the soccer fields. Being a precocious and poorly-supervised 12 year old, Wiyot has no transportation and decides to use water from a nearby river.
Business is booming! He sells 33 lemonades on the first day, and 6 additional lemonades each day as the summer heats up. How many TOTAL cups of giardia-laced lemonade will Wiyot have sold by the time his parents get a call from county health officials on day 8?
________
The cups of giardia-laced lemonade that Wiyot will have sold by the time his parents get a call from county health officials on day 8 is 75 cups.
How to calculate the value?From the information, Wiyot sells 33 lemonades on the first day, and 6 additional lemonades each day as the summer heats up.
This is an arithmetic sequence and will be expressed as:
= a + (n - 1)d
a = first term = 33
d = common difference = 6
n = 8
This will be:
= a + (n - 1)d
= 33 + (8 - 1)6
= 33 + (7 × 6)
= 33 + 42
= 75
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The following figure is made of 1 triangle and 1 rectangle.
A
Figure
Triangle A
Rectangle B
Whole figure
9
B
5
Find the area of each part of the figure and the whole figure.
6
Area (square units)
The area of triangle A, rectangle B and the whole figure are 12, 54 and 66 square units respectively.
What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel.
Area of rectangle: The area of a rectangle is the product of its length 'a' and width or breadth 'b'. So, Area of Rectangle = (a × b) square units.
What is triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Area of triangle: The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.
Here we have a diagram PQRTS comprising the triangle PQT and rectangle QRTS.
Given: PS = 9 units & QR = 5 units
⇒ PT = 4 units, RS = QT= 6 units
The area of ΔPQT= M = 1/2*b*h = 1/2*PT*QT
⇒ M= 1/2*4*6=12 square units
⇒ M = 12 square units
Now, the area of rectangle QRTS = N = l*b = QT*TS = 6*9 = 54 square units
⇒ N = 54 square units
Now, the area of whole diagram = area of triangle A + area of rectangle B
⇒ M + N = (12 + 54)square units = 66 square units.
⇒ Area of whole figure = 66 square units.
Therefore, the area of triangle A, rectangle B and the whole figure were found to be 12, 54 and 66 square units respectively.
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How can i Graph y= -3x + 9
Answer:
Step-by-step explanation:
-3x -9 graph negative -3 then graph 9 add them together to get negative 12
Determine whether the following quadratic function has a maximum of a minimum value. Then find the maximum or minimum value and where it occurs.
F(x)=-3x²+18x+3
Select the correct choice below and fill in the answer boxes to complete of
(Simplify your answers.)
The function has a maximum value of ___at x=____.
The function has a minimum value of ___at x= ___.
The function has a maximum value of 30 at x = 3
How to determine if the quadratic function has a maximum or minimum?From the question, we have the following equation that can be used in our computation:
F(x) = -3x²+18x+3
This can be expressed properly as
F(x) = -3x² + 18x + 3
A quadratic function is represented as
F(x) = ax² + bx + 3
By comparison, we have
a = -3
For a quadratic function to have a maximum value, the value of a must be less than 0
This means that the function has a maximum value because -3 is less than 0
Solving further, we have
F(x) = -3x² + 18x + 3
Differentiate and set to 0
-6x + 18 = 0
So, we have
x = 3
Substitute x = 3 in F(x)
F(3) = -3(3)² + 18(3) + 3
Evaluate
F(3) = 30
This represents the maximum value
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Russ deposits $4,500 in a one year CD at
4.3% interest, compounded daily. What is
his APY to the nearest hundredth of a
percent?
The annual percentage yield (APY) of Russ is 4.39 %
What is Annual Percentage Yield?
The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest.
Given data ,
Deposit amount of Russ = $ 4500
Interest rate R = 4.3 %
And it is given that the interest rate is compounded daily , so
Interest rate R = 4.3 % / 365
= 0.043 / 365
= 0.0001178
Now , The annual percentage yield (APY) is calculated as
The interest amount = 4500 x ( 1 + 0.0001178 )³⁶⁵
= 4500 x ( 1.0001178 )³⁶⁵
= 4500 x 1.04393211
= 4697.694
≈ 4697.69
Therefore , the interest will be
= 4697.69 - 4500
= $ 197.69
Now , the annual percentage yield (APY) is given by
= Interest / Deposit
= 197.69 / 4500
= 0.0439
≈ 4.39 %
Hence , annual percentage yield (APY) of Russ is 4.39 %
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SOLVE AND GRAPH THE INEQUALITY X + 8 > 0
x>-8
look at the image below for the graph answer.
Question content area top
Part 1
Find the coordinates of the image.
Ry=−2(P)
The image is enter your response here. (Type an ordered pair.)
The coordinates of the image are -2P
How to determine the coordinates of the image?From the question, we have the following parameters that can be used in our computation:
Ry = -2(P)
To calculate the coordinate of the image, we simply open the bracket
So, we have
Ry = -2(P)
Solving further, the equation can be represented as
Ry = -2 * P
Evaluate the product
So, we have the following representation
Ry = -2P
Hence, the image has an coordinate or ordered pair of -2P
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The tech group built a go cart with 10in diameter
wheels. This cart must travel 20 FEET to complete the
race. How many rotations will be required to travel this
distance?
The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 20 feet will be 7.64.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The longest line which can be drawn inside the circle will be the diameter.
The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation.
Distance traveled in one rotation = Perimeter of the wheel.
⇒ 2π(5) = 31.42 inches
The number of rotations = (20×12)/31.42 = 7.63
Hence "The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 20 feet will be 7.64".
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9
Evaluar la siguiente ecuación: *
(2 puntos)
y= 2x + 8, cuando x = 1
Respuesta: 10
Solución paso a paso:
Si x es 1, eso significa que el x en la ecuación es 1. Entonces, cambiamos la x por 1, entonces nos quedamos con:
y = 2(1) + 8
Si evalúas esto, te quedas con 10.
What is Consumidores secundarios?
Consumidores secundarios are organisms in an ecosystem that feed on primary consumers, which in turn feed on producers.
They occupy the second trophic level in a food chain or food web.
How many quarters and dimes do you need to make $1.45?
Answer:
.25 * 5 = 1.25
.1 * 2 = . 2
1.45
Step-by-step explanation:
10 points!
Write a compound inequality to
represent a budget to spend
between $5 and $25 at
Starbucks in a month.
The required compound inequality is given as 5 < x < 25.
Given that,
To determine a compound inequality to represent a budget to spend between $5 and $25 at Starbucks in a month.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let x be the amount to be spend at Starbucks in a month,
According to the question,
X should not be less than 5 and should not be greater than 25,
So X > 5 and x < 25
Compounding the above inequalities,
5 < x < 25
Thus, the required compound inequality is given as 5 < x < 25.
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Write 64 % as a decimal and as a simplified fraction.
O 6.4 and 64/100
O 0.64 and 64/100
O 6400 and 6400/1
0.64 and 16/25
Answer:
b. 0.64 and 64/100
Step-by-step explanation:
hope this helps!!
Answer: B.) 0.64 and 64/100
Step-by-step explanation:
A percentage is x/100
For example, 4% = 4/100.
So 64% = 64/100
64/100 = 0.64
Multi-Step Problem You are choosing between two electricity providers. The Zap Electric Company charges $0.06 per kilowatt hour plus a $6.55 monthly service fee. The Bolt Electric Company charges $0. 12 per kilowatt hour plus a $2.83 monthly service fee. a. Let r represent the number of kilowatt hours you use in one month, and let y represent the total cost of your electric service. Write the two equations representing the cost of each company's service for one month.
The total cost for Bolt Electric Company and Zap Electric Company are y = 0.12r + 2.83 and y = 0.06r + 6.55 respectively
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let r represent the number of kilowatt hours you use in one month, and let y represent the total cost of your electric service.
The Bolt Electric Company charges $0. 12 per kilowatt hour plus a $2.83 monthly service fee. Hence:
y = 0.12r + 2.83
The Zap Electric Company charges $0.06 per kilowatt hour plus a $6.55 monthly service fee. Hence:
y = 0.06r + 6.55
The cost is y = 0.06r + 6.55 and y = 0.12r + 2.83
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A farmer with 350 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? What are the dimensions of the enclosed area?
The width, labeled x in the figure, is ____
(Type an integer or decimal rounded to the nearest tenth as needed.)
The length, labeled 350-2 x in the figure, is ____
(Type an integer or decimal rounded to the nearest tenth as needed.)
The largest area that can be enclosed is _______
(Type an integer or decimal rounded to the nearest tenth as needed.)
The solution to the questions are:
The width, labelled x in the figure is 87.5 metersThe length, labelled 350-2 x in the figure, is 175 metersThe largest area that can be enclosed is 15312.5 square metersHow to determine the width and the length of the rectangle?From the question, we have the following parameters that can be used in our computation:
Length = 350 - 2x
Width = x
The area of a rectangle is the product of its dimensions
So, we have
Area = Length x Width
Substitute the known values in the above equation, so, we have the following representation
A = (350 - 2x) * x
Evaluate
A = 350x - 2x²
Differentiate and set to 0
350 - 4x = 0
So, we have
4x = 350
Divide by 4
x = 87.5
Recall that
Length = 350 - 2x
So, we have
Length = 350 - 2 x 87.5
Evaluate
Length = 175
The area is then calculated as
Area = Length x Width
So, we have
Area = 175 x 87.5
Evaluate
Area = 15312.5 square meters
Hence, the area is 15312.5 square meters
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