The expression which represents the area of the triangle : [tex]2x^{2}-16x+24[/tex].
Length of base = B = 2x - 12
Height = H = Length of base + 8
= 2x - 12 + 8
= 2x - 4
Area = [tex]\frac{1}{2}(B)(H)[/tex]
= [tex]\frac{1}{2}(2x-12)(2x-4)[/tex]
= [tex]\frac{4}{2}(x-6)(x-2)[/tex]
= [tex]2(x^{2} -8x+12)[/tex]
= [tex]2x^{2}-16x+24[/tex]
Hence, the expression is [tex]2x^{2}-16x+24[/tex].
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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
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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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.
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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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
62 hours is what percent of 3 days?
62 hours is 86% percent of 3 days
What is percentage and how to calculate it?
Percentage is the ratio in which the denominator is 100. To calculate the percentage we multiply the obtained value by 100.
We are given 62 hours and 3 days
Now 1 day has 24 hours
Hence 3 days will have 3*24 = 72 hours
Now To find the percentage we first have to find the ratio of 62 and 72
And to do that we divide 62 by 72
we get 62/72 = 0.86
To get the percentage we multiply this value by 100
0.86 * 100= 86%
Hence, 62 is 86% of 3 days
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select the correct y- intercept to write the equation of the line with slope-2/3 that passes through the point (-6,5).
Answer:
[tex]y=-\frac{2}{3}x+1.[/tex]
Step-by-step explanation:
1. common form of slope-interception form is:
y=(slope)*x-interception;
Then
[tex]2. \ y=-\frac{2}{3} x+interception;[/tex]
3. in order to calculate the 'interception' is it needed to substitute the given coordinates into this non-completed equation:
[tex]5=-\frac{2}{3} *(-6)+interception; \\interception=1;[/tex]
4. finally, the required equation is:
[tex]y=-\frac{2}{3} x+1.[/tex]
solving linear equations with one variable
Answer:
I hope it will be helpful for you.
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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George made 50% of the money Alex made at the lemonade stand. If George made $125.00, how much did Alex make?
(PLEASE HELP!)
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:
Find x and y. Give reasons to justify your solution.
The angles will be x = 8° and y = 21°
given information:
∠AOB = 180°
∠EOG = 90°
∠EOF and ∠FOG are complementary angles. Complementary angles are those whose sum is equal to 90° and it is given to us in the question.
∠EOG = ∠EOF + ∠FOG
90° = 27° + 3y
90 - 27 = 3y
63 / 3 = y
y = 21°
Similarly ∠AOE , ∠AOG and ∠GOB are supplementary to each other. Supplementary angles are those whose sum is equal to 180°
∠AOB = ∠AOE + ∠AOG + ∠GOB
180° = x + 90° + 8x + 18°
180 - 90 - 18 = 9x
9x = 72
x = 72 / 9
x = 8°
Hence we can clearly say that x = 8° and y = 21°
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Arthur is a ride-hailing driver. He spent $500 on bottled water during the year. He personally consumed $20 of the water he purchased, but the remaining $480 was consumed by riders. How much is Arthur's Schedule C (Form 1040) deduction for refreshments?
The amount of money to represent Arthur's Schedule C (Form 1040) deduction for refreshments is: C. $480.
What are the types of tax?In Economics, there are different types of tax which are levied on individuals (employees) or business firms by the government, and these include the following:
Sales taxProperty taxFederal income taxWhat is a Form 1040?A Form 1040 was formally referred to as U.S. Individual Income Tax Return or Schedule C and it can be defined as an internal revenue service (IRS) tax form which is used by taxpayers in the United States of America, to file their annual income tax return.
In this scenario, Arthur's deduction for refreshments should be recorded as $480 in the Schedule C (Form 1040).
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Complete Question:
Arthur is a ride-hailing driver. He spent $500 on bottled water during the year. He personally consumed $20 of the water he purchased, but the remaining $480 was consumed by riders. How much is Arthur's Schedule C (Form 1040) deduction for refreshments?
$0
$240
$480
$500
A patient is administered 310cm^3 of a saline and water solution that is labeled as 9% saline. Find the amount of each ingredient the patient will receive. Round to the nearest tenth of a cubic centimeter.
The amount of saline and water in the solution is given as 27.9 cm³ and 282.1 cm³ respectively.
Given,
A patient is administered 310cm^3 of a saline and water solution that is labeled as 9% saline.
What is saline solution?
Salt and water are combined to make saline. Because of its salt content (0.9% saline), which is comparable to that of tears, blood, and other bodily fluids, a normal saline solution is known as normal. Isotonic solution is another name for it.
Here,
Amount of saline = 0.09 × 310 = 27.9
Amount of water = 310 - 27.9 = 282.1
Thus, the amount of saline and water in the solution is given as 27.9 cm³ and 282.1 cm³ respectively.
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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
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
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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graph the inequality of -3x-4y<8
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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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
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.
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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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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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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How do you find the endpoint of a confidence interval on a TI 84?
This is the way to find the endpoint if a confidence interval in the TI calculator:
First, select the T Interval. Press Stat, then select TESTS from the list.Step 2: Complete the required fields. The following details will be requested by the calculator:Step 3: Analyze the outcomes. The 95% confidence interval for the population mean will appear after you hit ENTER.What is the confidence interval?An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.
A confidence interval is used to calculate an estimate for an unknown population parameter. Specifically, to provide an interval so that any value of the parameter falling inside the range is a credible value, and values falling outside the interval are implausible
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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
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
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]
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
