Work Shown:
x = length
x-2 = width
area = length*width
area = x(x-2)
x(x-2) = 168
x^2-2x = 168
x^2-2x-168 = 0
Plug a = 1, b = -2, c = -168 into the quadratic formula.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-168)}}{2(1)}\\\\x = \frac{2\pm\sqrt{676}}{2}\\\\x = \frac{2\pm26}{2}\\\\x = \frac{2+26}{2} \ \text{ or } \ x = \frac{2-26}{2}\\\\x = \frac{28}{2} \ \text{ or } \ x = \frac{-24}{2}\\\\x = 14 \ \text{ or } \ x = -12\\\\[/tex]
Ignore x = -12 since we cannot have a negative length.
The only practical solution is x = 14.
If x = 14, then x-2 = 14-2 = 12
The rectangular mirror is 14 inches by 12 inches
Check: area = length*width = 14*12 = 168
The answers are confirmed.
find the 6th term of the geometric sequence whose common ratio 1/3 and whose first term is 4
Answer:
a6 = 4/243
Step-by-step explanation:
We can represent the geometric sequence with [tex]a_n=4(\frac{1}{3})^{n-1}[/tex], so the 6th term would be [tex]a_6=4(\frac{1}{3})^{6-1}=\frac{4}{243}[/tex].
A circular table has a diameter of 3 feet. What is the circumference of the table to the nearest tenth? (Use 3.14 for π) Remember the formula for circumference of a circle is C=πd
The circumference of the table is 9.42 feet
What is circumference?The circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.
For a example a circular ball with diameter 7 cm will have a circumference of 44cm
The circumference of a circle is expressed as:
C = πd
C = 3.14 ×3
C = 9.42 feet
Therefore the circumference of the table is 9.42 feet.
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Provide the missing reasons for the proof.
Given: C = E
Prove ABC ~ DBE
By AAA similarity, triangles are proved similar.
Similariy of Triangles:Two triangles are similar if they have an equivalent number of corresponding sides and corresponding angles. Objects with multiple identically shaped but differently sized figures are known as similar figures.
In the given triangles ABC and triangle DBE,
it is given that,
/C = /E
Now in the given triangles,
/C = /E .......(given)
/B = /B ........(vertically opposite angles)
/A = /D .........(if two angles of a given pair of triangles
are equal, then third angle will also be equal)
Therefore, by AAA similarity, triangles
ABC ~ DBE.
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In 1997 the World Resources Institute estimated the world's proven oil reserves to be 1,000 billion barrels and the ultimately recoverable reserves to be 2,000 billion barrels..
Year Consumption(million barrels per day
1997 74
At the 1997 rate of consumption about how long will the estimated 2,000 billion barrels of oil last?
The proved oil reserves in the globe were projected to be 1,000 billion barrels by the World Resources Institute in 1997, while the eventually recoverable reserves were predicted to be 2,000 billion barrels. 75 years old
The World Resources Institute (WRI) has offices abroad in Brazil, China, India, Indonesia, Mexico, and the United States. The organization's goal is to advance human health and wellbeing, economic opportunity, and environmental sustainability. WRI collaborates with regional and federal governments, private businesses, publicly traded firms, and other non-profit organizations to provide services addressing challenges such as the global climate change, sustainable markets, ecosystem protection, and environmentally conscious governance. Since the first of October 2008, WRI has maintained a Charity Navigator rating of 4 out of 4.
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How has the heart transformed with just one transformation? dilation rotation translation reflection
The transformation done on the heart as shown in the figure was rotation.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.
Rotation is the flipping of a figure about a fixed point. Rotation is a rigid transformation because it preserves the shape and size of the figure.
The transformation done on the heart shown was rotation.
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need help with this math problem, problem shown below. show work
The slope of line q can be found using the proportion JN/MN = KP/LP. Therefore, option D is the correct answer.
From the give graph,
In triangle LPK,
Slope = KP/LP
In triangle MNJ
Slope = JN/MN
Therefore, option D is the correct answer.
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Stefan sells Jin a bicycle for $173 and a helmet for $19. The total cost for Jim is 160% of what Stefan spent originally to buy the bike and helmet. How much did Stephan spend originally. How much money did he make by selling the bicycle and helmet to him
Answer:
120$ 60$
Step-by-step explanation:
The total cost 161+19=180
180X150%=180×1.5
= = 120
150%=15, the rule of multiplication
" Stefan spend originally $120. 180-120=60
He make $60 by selling the bicycle and helmet to Jin.
Please help me quick!!!
Answer:
7 and 45
Step-by-step explanation:
First one is 7
Second one is 45
Rule is y = 5x
Answer:
the x (input ) is by 8
Step-by-step explanation:
rule by 5
What does outliers mean in math?
An outlier is a mathematical value in a set of data which is quite distinguishing from the other values.
Its more like outliers are values uncommonly far from the middle. Mostly, outliers have a significant impact on mean, but not on the median, or mode.
Hence making the outliers are crucial in their influence on the mean.
we can say that the outlier is a data point that lies outside the entire pattern in a distribution.
They are mostly shown as dots and its known that the whiskers are required to change. Whiskers stretch out to the farthest point in the data set that isn't an outlier.
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About what percent of x values lie between the mean and three standard deviations. hint: (empirical rule)
about 31%
about 27%
about 50%
about 40%
Previous
correct answer gets brainliest
Answer:
The answer is A
Step-by-step explanation:
Help please I am struggling to answer
Answer:
angle 1 is 24 degrees, and angle 2 is 66
Step-by-step explanation:
;)
What is the area of ΔABC such that b = 26 centimeters, c = 16 centimeters, and measure of angle A equals 25 degrees?
203. 013 centimeters2
189. 333 centimeters2
87. 905 centimeters2
29. 647 centimeters2
The area of ΔABC is 87.905 centimeters². The correct answer is C.
The area of ΔABC can be calculated using the formula A = (1/2)bc sin A, where b and c are the lengths of two sides and A is the measure of the angle between them.
Given that b = 26 centimeters, c = 16 centimeters, and measure of angle A equals 25 degrees, we can plug these values into the formula and calculate the area:
A = (1/2)(26)(16) sin 25
A = (1/2)(416) sin 25
A = 208 sin 25
A = 87.905 centimeters²
Therefore, the area of ΔABC is 87.905 centimeters2. The correct answer is option C. 87. 905 centimeters².
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a rectangular picture is 9 inches wide and 12 inches long. the picture has a frame of uniform width. if the combined area of picture and frame is 180 in^2, what is the width of the frame?
The width of the frame will be 6 inches.
What is an area?The area of the rectangle is defined as the space occupied by the rectangle in two dimensional space.
Given that a rectangular picture is 9 inches wide and 12 inches long. the picture has a frame of uniform width. if the combined area of picture and frame is 180 in².
The area of the picture is calculated as:-
Area = L x W
Area = 12 x 9
Area = 108 square inches
The remaining area of the frame is,
Area = 180 - 108
Area = 72 square inches.
The width of the ram is calculated as:-
Area = L x W
72 = 12 x W
W = 72 / 12
W = 6 inches
Therefore, the frame will have a width of 6 inches.
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what does 5 halves equal?
Answer: 2.5 or 2 1/2
Step-by-step explanation:
One way: 1/2 x 5 = 5/2
5/2 = 2 1/2 = 2.5
Another way: 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 5/2 = 2 1/2 = 2.5
solve the inequality
x/4 + 1 <6
Answer:
x > 20 is the answer.
Good luck.
Chloe trota todas las mañanas. Su ruta diaria es de 3.5 millas de largo.
a) ¿Qué distancia habrá corrido Chloe después de 30 días?
b) Escribe una expresión para la distancia total que Chloe ha corrido después d días.
Algien que me ayude porfaa
a) Chloe will run 105 miles in 30 days.
b) the expression total miles he ran in d days is 3.5d.
What's Expression?Mathematical expressions correspond of at least two figures or variables, at least one computation operation, and a statement. It's possible to multiply, divide, add, or abate with this fine operation. An expression's structure is as follows Expression( Math Operator, Number/ Variable, Math Operator)
Given:
Chloe daily route is 3.5 miles long.
So, in 30 days Chloe will run
= 30 x 3.5
= 105 miles.
b) the expression for total distance Chloe has run after d days.
= 3.5 x d
=3.5d
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The question attached here is in other Language whose translation is:
Chloe jogs every morning. His daily route is 3.5 miles long.
a) How far will Chloe have run after 30 days?
b) Write an expression for the total distance Chloe has run after d days.
An airplane flew with the wind for 2. 5 hours and returned the same distance against the wind in 3. 5 hours. If the cruising speed of the plane was a constant 360 mph in air, how fast was the wind blowing? (Hint: If the wind speed is r miles per hour, then the plane travels at (360- + r) mph with the wind and at (360 - r) mph against the wind
The speed of the wind is 60 mph.
Determine the speedLet's denote the speed of the wind as r. When the plane is flying with the wind, its speed is (360 + r) mph, and when it's flying against the wind, its speed is (360 - r) mph.
According to the question, the plane flew the same distance with and against the wind, so we can set up an equation:
2.5(360 + r) = 3.5(360 - r)
Expanding the equation, we get:
900 + 2.5r = 1260 - 3.5r
Simplifying and rearranging the terms, we get:
6r = 360
Dividing both sides of the equation by 6, we get:
r = 60
Therefore, the speed of the wind is 60 mph.
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What is the formula for percentage error in physics?
The formula for percentage error in physics is:
% error = (|experimental value - accepted value| / accepted value) x 100%
In this formula, the experimental value is the measured value obtained from an experiment, the accepted value is the true or theoretical value, and the absolute value of the difference between them represents the error. Dividing this error by the accepted value and multiplying by 100% gives the percentage error.
The percentage error is used to assess the accuracy of experimental measurements and to determine the degree of deviation between the experimental and accepted values. The lower the percentage error, the more accurate the measurement is considered to be.
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A reading specialist wanted to estimate the mean word length, in number of letters, for an elementary school history textbook. The specialist took repeated random samples of size 100 words and estimated the mean and standard deviation of the sampling distribution to be 4.9 letters and 0.15 letter, respectively.Based on the estimates for the sampling distribution, which of the following provides the best estimates of the population parameters?A)Mean 4.9 letters and standard deviation 0.015 letter B)Mean 4.9 letters and standard deviation 0.15 letter C)Mean 4.9 letters and standard deviation 1.5 letters D)Mean 0.49 letter and standard deviation 0.15 letter E)Mean 49 letters and standard deviation 15 letters
Mean 4.9 letters and standard deviation 1.5 letters are best estimates of the population parameters . So, the correct option is (C)
The estimated mean of the sampling distribution is 4.9 letters, which is a good estimate of the population mean word length. The estimated standard deviation of the sampling distribution is 0.15 letter, which is the standard error of the mean.
The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size. Since the sample size is 100 and the standard error is 0.15 letter, we can estimate the population standard deviation as follows:
population standard deviation = standard error x sqrt(sample size)
= 0.15 x sqrt(100)
= 1.5 letters
Therefore, the best estimates of the population parameters are:
Mean = 4.9 letters (same as the estimated mean of the sampling distribution)
Standard deviation = 1.5 letters
So, the correct option is (C) Mean 4.9 letters and standard deviation 1.5 letters.
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Angela has $15 to spend at the store. She will buy p pencils and n notebooks. Pencils cost $0.50 each, and notebooks cost $1.75 each. Angela will buy at least 5 notebooks. Which system of inequalities represents Angela’s situation?
Answer: I think it's P.E.M.D.A.S
Step-by-step explanation:
What is the main theme in Fahrenheit 451?
The main theme of Fahrenheit 451, a novel written by Ray Bradbury, is the dangers of censorship, conformity, and the importance of preserving knowledge and free thought.
The novel is set in a dystopian society in which books are banned and "firemen" are responsible for burning any that are found. The protagonist, Guy Montag, is a fireman who begins to question his job and the society he lives in, eventually leading him to join a group of rebels who memorize books in order to preserve their contents. Bradbury uses the story to warn against the dangers of censorship, mindless conformity, and the loss of intellectual curiosity, emphasizing the need for critical thinking, individuality, and the preservation of knowledge.
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. Write an equivalent expression to 8k - (5 + 2k) without parentheses.
Then simplify.
8k - (5 + 2k) =8k__5__2k
= 8k __2k__5
=__k__5
The equivalent expression to 8k - (5 + 2k) is 6k-5.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 8k-(5+2k)
Eight times k minus five plus two times of k.
We need to find the equivalent expression to the given expression.
K is the variable in the expression.
Equivalent expressions are expressions that work the same even though they look different.
Apply distributive property
8k-5-2k
Add the like terms
6k-5
Hence, 6k - 5 is the equivalent expression of 8k-(5+2k).
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How many 39 euros to $100?
There are 2.19, 39 euros in $100.
To determine how many 39 euros are equivalent to $100, you need to know the current exchange rate between euros and US dollars. The exchange rate varies constantly, so it's important to use the most up-to-date rate.
As of the time of writing, the exchange rate is 1 euro = 1.17 US dollars. This means that for every euro, you get 1.17 US dollars.
To determine how many 39 euros are equivalent to $100, you can use the following formula:
39 euros * (1.17 US dollars/1 euro) = X US dollars
Simplifying the equation gives:
45.63 US dollars = X US dollars
So, 39 euros are equivalent to 45.63 US dollars. To determine how many 39 euros are equivalent to $100, you can use the following formula:
$100 / (1.17 US dollars/1 euro) = X euros
Simplifying the equation gives:
85.47 euros = X euros
So, 85.47 euros are equivalent to $100. Therefore, you would need approximately 85.47/39 = 2.19 sets of 39 euros to reach $100.
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The population of a city has been increasing by 2% annually. In 2000, the population was 2000. Predict the population of the city in 2020.
we can predict that the population of the city in 2020 will be approximately 2931 (rounded to the nearest whole number).
What is percentage ?
A percentage is a way of expressing a number as a fraction of 100. The symbol for percentage is "%". For example, 50% means 50 out of 100 or 0.5 as a decimal.
Percentages are commonly used to represent proportions, rates, and changes in quantities. They can be used to compare quantities of different sizes, or to express how much one quantity has changed relative to another quantity.
According to the question:
To predict the population of the city in 2020, we can use the formula:
P = P₀(1 + r)ᵗ
where:
P₀ = the initial population (in 2000) = 2000
r = the annual growth rate as a decimal = 0.02
t = the number of years since the initial population = 20 (since we want to predict the population in 2020, which is 20 years after 2000)
Substituting these values into the formula, we get:
P = 2000(1 + 0.02)²⁰
Using a calculator, we can simplify this to:
P ≈ 2930.63
Therefore, we can predict that the population of the city in 2020 will be approximately 2931 (rounded to the nearest whole number).
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Find the perimeter of △CBH if △CBH~△FEH, ADEG is a parallelogram, CH=7, FH=10, FE=11, and EH=6. Express your answer as a decimal, if necessary.
The perimeter of triangle ΔCBH found using the relationship between similar triangles, ΔCBH, and ΔFEH is 18.9
What are similar triangles?Similar triangles are triangles that have the same shape and interior angles and between which the ratio of their corresponding sides are equivalent.
The specified parameters are;
The triangles ΔCBH and ΔFEH are similar, ΔCBH ~ ΔFEH
The alternate interior angles theorem indicates that we get;
∠BCH is congruent to ∠EFH and ∠CBH is congruent to ∠FEH
Vertical angles theorem, indicates that we get;
∠CHB ≅ ∠FHE
The ratio of the corresponding sides formed between similar triangles are equivalent, therefore, we get;
CH/FH = BH/EH
7/10 = BH/6
BH = 6 × (7/10) = 4.2
BH = 4.2
CH/FH = BC/EF
7/10 = BC/11
BC = 11 × 7/10 = 7.7
BC = 7.7
The perimeter of the triangle ΔCBH = BC + BH + CH
Therefore, the perimeter of ΔCBH = 7.7 + 4.2 + 7 = 18.9
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Find an equation for the nth term where the first term in the sequence is a1
The equation of the nth term is a(n) = 2-8n
What is Arithmetic sequence?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.
The common difference = -14-(-6) = -14 +6 = -8
The first term is a1
The nth term of an arithmetic sequence =
a(n )= a1+(n-1)d
a(n) = a1+(n-1)-8
a(n )= a1-8n+8
if a1 = -6
a(n) = -6-8n +8
a(n) = 2-8n
therefore the nth term of the sequence is 2-8n
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Pls help i need help i don’t understand this question very well
The value of the angle x in the parallel lines is 70 degrees.
How to find the angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, let's find x in the lines.
Sum of angles in a triangle is 180 degrees.
Hence,
∠KDP = 180 - 70 - 60
∠KDP = 50 degrees
∠BDC = ∠KDP = 50 degrees(vertically opposite angles)
∠DBC = 180 - 50 - 60
∠DBC = 70 degrees
∠DBC = x = 70 degrees(corresponding angles)
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Can someone Help please
since the triangles are equivalent we can set both the equations with an equal sign
2x-15=x+15
solve for x
2x-x=15+15
x=30
plug in x into 2x-15 to get an angle of triangle ABC
2(30)-15
x=45
then to get the last angle of triangle ABC we do
180-(90+45)
= 45
to get the other triangle's (DFE) angles we plug in x again
into
x+15
45+15= 60
to get the last angle we do
180-(90+60)
= 30
What is forty-seven and seven tenths minus twenty-three and nineteen hundredths? and give an answer as a decimal(step by step pls)
Forty-seven and seven tenths minus twenty-three and nineteen-hundredths is equal to twenty-four and fifty-one hundredths, or 24.51 as a decimal.
To find the difference between forty-seven and seven tenths (47.7) and twenty-three and nineteen hundredths (23.19), we can simply subtract the two numbers using the standard subtraction method for decimals. Here are the steps:
1. Line up the decimals:
47.70
-23.19
2. Subtract the hundredths place: 0 - 9 = -9. Since we can't have a negative number in the hundredth place, we need to borrow 1 from the tenths place. So, 10 - 9 = 1.
3. Subtract the tenths place: 6 (after borrowing) - 1 = 5.
4. Subtract the ones place: 7 - 3 = 4.
5. Subtract the tens place: 4 - 2 = 2.
So, the final answer is 24.51.
Therefore, forty-seven and seven tenths minus twenty-three and nineteen-hundredths is equal to twenty-four and fifty-one hundredths, or 24.51 as a decimal.
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