The sοlutiοns tο the equatiοn are x = 15 οr x = -2.
What is the equivalent expressiοn?Expressions that perform the same function despite their appearance are said to be equivalent. If two algebraic expressions are equivalent, then when the variable is set to the same value, they have the same value.
We must first simplify this equation by placing all the terms on one side of the equation in order to solve it.
Then we can factοr the denοminatοr and simplify further tο sοlve fοr x.
Starting with the given equatiοn:
\(7/(x-9) + 3x/(x+5) = (2x+1)/(x-9)\)
We can start by multiplying bοth sides by (x-9)(x+5) tο get rid οf the denοminatοrs:
\(7(x+5) + 3x(x-9) = (2x+1)(x+5)\)
Expanding the brackets and simplifying, we get:
\(7x + 35 + 3x^2 - 27x = 2x^2 + 11x + 5\)
Rearranging and simplifying further, we get:
\(x^2 - 13x - 30 = 0\)
Tο sοlve fοr x, we can factοr the left-hand side οf the equatiοn:
\((x - 15)(x + 2) = 0\)
Setting each factοr tο zerο and sοlving fοr x, we get:
x - 15 = 0 οr x + 2 = 0
Sο x = 15 οr x = -2.
Therefοre, the sοlutiοns tο the equatiοn are x = 15 οr x = -2.
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you have 26 dogs and 69 cats . what is your ratio of dogs to cats?
Answer:
Ratio is 26:69
Step-by-step explanation:
\({ \tt{dogs : cats = \frac{dogs}{cas} }} \\ \)
dogs → 26cats → 69\({ \tt{dogs : cats = \frac{26}{69} }} \\ \\ { \underline{ \tt{ \: dogs :cats = 26 : 69 \: }}}\)
Answer:
Step-by-step explanation:
dogs : Cats = 26 : 69
It is in the simplest form as they have no common terms.
The Diamond Rule says two factors, m and n, must multiply to get to the top number and add to get to the bottom number What are the possible values for m and n
-4 and -8
-2 and 16
4 and 8
-4 and 8
2 and 16
-2 and -16
Answer:
The answer for this should be A -4 and -8
Step-by-step explanation:
I'm also in k12
Answer
its 4 and 8 i took the quiz
Step-by-step explanation:
Classify 7/8 as either a whole number natural number an integer or rational number
Answer:
rational number
Step-by-step explanation:
a whole number is a non-negative integer, a natural number is a positive integer, an integer is any number that doesn't have decimal places and isn't a fraction. 7/8 isn't an integer so it isn't a whole or natural number. rational numbers can be written as fractions or are terminating decimals. 7/8 is a fraction so 7/8 is a rational number
Does the residual plot show that the line of best fit is appropriate for the data?
A residual plot alone does not provide a definitive answer about the appropriateness of the line of best fit. It should be used in conjunction with other diagnostic tools, such as examining the regression coefficients, goodness-of-fit measures (e.g., R-squared), and conducting hypothesis tests.
The residual plot is a graphical tool used to assess the appropriateness of the line of best fit or the regression model for the data. It helps to examine the distribution and patterns of the residuals, which are the differences between the observed data points and the predicted values from the regression model.
In a residual plot, the horizontal axis typically represents the independent variable or the predicted values, while the vertical axis represents the residuals. The residuals are plotted as points or dots, and their pattern can provide insights into the line of best fit.
To determine if the line of best fit is appropriate, you would generally look for the following characteristics in the residual plot:
Randomness: The residuals should appear randomly scattered around the horizontal axis. If there is a clear pattern or structure in the residuals, it suggests that the line of best fit is not capturing all the important information in the data.
Constant variance: The spread of the residuals should remain relatively constant across the range of predicted values. If the spread of the residuals systematically increases or decreases as the predicted values change, it indicates heteroscedasticity, which means the variability of the errors is not constant. This suggests that the line of best fit may not be appropriate for the data.
Zero mean: The residuals should have a mean value close to zero. If the residuals consistently deviate above or below zero, it suggests a systematic bias in the line of best fit.
It's important to note that a residual plot alone does not provide a definitive answer about the appropriateness of the line of best fit. It should be used in conjunction with other diagnostic tools, such as examining the regression coefficients, goodness-of-fit measures (e.g., R-squared), and conducting hypothesis tests.
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a pyramid has a surface area of 6400 square yards. if the new dimensions are 1/8 the original size, what is the surface area of the new pyramid
If the surface area of the original pyramid is 6400 square yards and the new dimensions are 1/8 of the original size, the surface area of the new pyramid will be 100 square yards.
Let's denote the original surface area of the pyramid as S1 and the new surface area as S2. We know that the new dimensions are 1/8 of the original size, which means the linear dimensions (height, base length, and base width) are also 1/8 of the original dimensions.
The surface area of a pyramid is given by the formula S = 2lw + lh + wh, where l, w, and h represent the base length, base width, and height, respectively.
Since the new dimensions are 1/8 of the original size, we can say that the new base length (l2), base width (w2), and height (h2) are equal to (1/8) * original base length (l1), (1/8) * original base width (w1), and (1/8) * original height (h1), respectively.
Therefore, the new surface area (S2) can be calculated as:
S2 = 2 * (1/8 * l1) * (1/8 * w1) + (1/8 * l1) * (1/8 * h1) + (1/8 * w1) * (1/8 * h1)
= 1/64 * (2l1w1 + l1h1 + w1h1)
Since we are given that S1 (the original surface area) is 6400 square yards, we can equate it to S2:
6400 = 1/64 * (2l1w1 + l1h1 + w1h1)
Simplifying the equation, we get:
2l1w1 + l1h1 + w1h1 = 6400 * 64
2l1w1 + l1h1 + w1h1 = 409600
Therefore, we can conclude that the surface area of the new pyramid (S2) is 100 square yards.
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Write equivalent fractions for
2/3
and
5/12
using the least common denominator.
The equivalent fractions for 2/3 is (3×2)/(3×3) = 6/9 and for 5/12 is (4×5)/(4×12) = 20/48.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
The equivalent fraction for 2/3 is (3×2)/(3×3) = 6/9.
The equivalent fraction for 5/12 is (4×5)/(4×12) = 20/48.
We have to multiply the same number to both the numerator and denominator to get equivalent fractions.
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Several bakeries in a town were asked the price for different amounts of donuts at their shop. The scatter plot with a line of best fit was created from the data gathered.
Part A: Estimate the correlation coefficient. Explain your reasoning for the given value. (4 points)
Part B: How many positive and negative residuals are there? Explain your reasoning. (3 points)
Part C: State the point with the largest absolute value residual and interpret the point in terms of the context of the data. (3 points)
Answer:
IT'S FREJARDDDDDD
Step-by-step explanation:
Determine the intercepts of the line
darwin's geometric ratio of increase pertains specifically to
Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.
In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.
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HELP!!! use the law of sines!
Answer:
21.28
Step-by-step explanation:
Hey There!
So the law of sines says
\(\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}\)
To solve for c we just plug in the values that are given to us
\(\frac{25}{sin38} =\frac{c}{sin31.6}\)
step 1 multiply each side by sin31.6
now we have
\(c=\frac{25sin31.6}{sin38} \\c=21.2773548\)
assuming that you have to round
if you're supposed to round to the nearest whole number then the answer is 21
if you're supposed to round to the nearest tenth then the answer is 21.3
if you're supposed to round to the nearest hundredth then the answer is 21.28
Complete the missing parts of the
table for the following function.
y = ()*
X-2 -1
0 1 2 3
y 36 [?] 1 1
1
216
Answer:
Remember the property:
a^-1 = (1/a)^1
and:
(a/b)^n = (a^n)/(b^n)
A table for a function like:
\(\left[\begin{array}{ccc}x&f(x)\\&\\&\\&\\&\end{array}\right]\)
Is just completed as:
\(\left[\begin{array}{ccc}x&f(x)\\x_1&f(x_1)\\x_2&f(x_2)\\x_3&f(x_3)\\x_4&f(x_4)\end{array}\right]\)
So, here we have:
y = f(x) = (1/6)^x
To complete the table, we need to find:
f(-1)
and
f(2)
So let's find these two values:
f(-1) = (1/6)^-1 = (6/1)^1 = 6
and the other value is:
f(2) = (1/6)^2 = 1/36
Then the complete table is:
\(\left[\begin{array}{ccc}x&f(x)\\-2&36\\-1&6\\0&1\\1&1/6\\2&1/36\\1&1/216\end{array}\right]\)
The ratio of Chris, Gary and John age is 1:3:3
respectively. If the total of their ages is 56, how old is
Chris?
Answer:
Chris is 8 years old
Step-by-step explanation:
If you add the ratio together, it becomes 7
Divide 56/7 -> 8
1*8=8
Chris is 8
Answer:
8
Step-by-step explanation:
If we say the there ages is x
it would be x+3x+3x=56
and lets say the x=8
then 8+24+24
That would mean Chris should be 8.
I think it would.
Problema de capacidades Una empresa aceitera ha envasado 3000 litros de aceite en 1200 botellas de dos y de cinco litros. ¿Cuántas botellas de cada clase se han utilizado?
Answer:
Hay 200 botellas de 5 litros y 1000 botellas de 2 litros.
Step-by-step explanation:
Un sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones de primer grado, en el cual se relacionan dos o más incógnitas.
Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema.
En este caso, las variables a calcular son:
x= cantidad de botellas de 2 litros.y= cantidad de botellas de 5 litros.Una empresa aceitera ha envasado 3000 litros de aceite en 1200 botellas de dos y de cinco litros. Entonces es posible plantear el siguiente sistema de ecuaciones:
\(\left \{ {{2*x+5*y=3000} \atop {x+y=1200}} \right.\)
Existen varios métodos para resolver un sistema de ecuaciones. Resolviendo por el método de sustitución, que consiste en despejar o aislar una de las incógnitas y sustituir su expresión en la otra ecuación, despejas x de la segunda ecuación:
x= 1200 - y
Sustituyendo la expresión en la primer ecuación:
2*(1200 - y) + 5*y=3000
Resolviendo se obtiene:
2*1200 - 2*y + 5*y= 3000
2400 +3*y= 3000
3*y= 3000 - 2400
3*y= 600
y= 600÷3
y= 200
Reemplazando en la expresión x= 1200 - y:
x= 1200 - y
x=1200 -200
x= 1000
Hay 200 botellas de 5 litros y 1000 botellas de 2 litros.
Tray weighs 142 pounds .Multiply his weight on Earth by 0.92 to find his weight on the planet Saturn. What is the difference between Tray´s weight on earth and his weight on Saturn
Answer:
There is a 11.36 pounds difference between Tray's weight on Earth and on Saturn
Step-by-step explanation:
142 × .92 = 130.64
142-130.64= 11.36
Which is Greater, negative 2 and 2 fifths or negative 2 and 1 forth?
Answer:
-2 and 1/4
Step-by-step explanation:
1/4 is equal to 0.25
2/5 is equal to 0.40
Because it is negative, 1/4 is considered greater.
Need an answer in less than 5 minutes pls!
Find the length of the hypotenuse. Round your answer to the nearest tenth.
A.) 89 units
B.) 13 units
C.) 3.6 units
D.) 9.4 units
Answer:
9.4
Step-by-step explanation:
a2+b2=c2
8^2 + 5^2 = c2
64 + 25 = 89
square root of 89 = 9.4
An airplane is preparing to land at an airport. It is 53100 feet above the ground and is descending at the rate of 3300 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2600 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be? Use pencil and paper. Use two other methods to solve the problem. Explain which methods are easier to use and which are more difficult to use for the situation.
A different farmer has a flock of 100 chickens
that is producing 55 eggs at 20 weeks past
maturity. He wants to calculate the percent
error of this amount compared to that
predicted by the line of best fit. What is the
percent error? Round to the nearest whole
percent and ignore the percent sign when
entering your answer.
The percent error is approximately 7%.
How to calculate percent error in chicken egg production?
To calculate the percent error, you first need to calculate the predicted amount of eggs for 20 weeks past maturity based on the line of best fit. Then, you can calculate the difference between the predicted amount and the actual amount produced by the farmer's flock, and divide it by the predicted amount. Finally, you can multiply the result by 100 to get the percent error.
For example, let's say the line of best fit predicts that a flock of chickens at 20 weeks past maturity should produce 60 eggs. However, the farmer's flock only produced 55 eggs.
To calculate the percent error, you would first find the difference between the predicted amount and the actual amount:
60 - 55 = 5
Then, you would divide that difference by the predicted amount:
5 / 60 = 0.0833
Finally, you would multiply that result by 100 to get the percent error:
0.0833 x 100 = 8.33%
So the percent error in this case would be 8% (rounded to the nearest whole percent).
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BRAINLIEST One T-shirt is sold for every 5 people who attend a concert.
What is the ratio of people to T-shirts sold?
differentiate between the Markov analysis and replacement chart and when it is appropriate to use either approach?
Markov analysis is used for analyzing the performance and reliability of complex systems, while replacement charts are used for optimizing the replacement timing of deteriorating assets.
Markov Analysis:
Markov analysis is a probabilistic model that is used to predict the future state of a system based on its current state.
It involves the use of Markov chains to model the transitions between different states of a system over time.
Markov analysis is commonly used when the equipment or system under consideration can be in multiple states with varying probabilities of transition.
It is suitable for analyzing systems that have a continuous or non-repairable nature, such as complex machinery, infrastructure, or systems with multiple failure modes.
The primary objective of Markov analysis is to assess the reliability, availability, and performance of the system and make decisions regarding maintenance, replacement, or repair strategies.
Replacement Chart:
A replacement chart, also known as a replacement model or replacement policy, is a decision-making tool used to determine the optimal time to replace a piece of equipment or system.
It involves comparing the costs associated with continuing to use the existing equipment (including maintenance and repair costs) with the costs of replacing it.
The replacement chart provides a visual representation of the costs over time and helps identify the point at which replacement becomes more cost-effective than continued use.
Replacement charts are commonly used for assets that are subject to wear and tear, aging, or deterioration over time, such as vehicles, machinery, or equipment with a defined lifespan.
The primary objective of a replacement chart is to minimize costs associated with the asset's life cycle by optimizing the replacement timing.
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please helpppppppppppppp
Answer:
it is d because a budget is when u set an amount to spend. there for you be safe in a sertint amount.
This data set represents the number of cups of coffee sold in a café between 8 a.m. and 10 a.m. every day for 14 days.
Answer:
The answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6
Step-by-step explanation:
Numbers in order:
4,5,6,6,7,8,9,9,10,10,12,12,14,15
List into two equal parts:
4,5,6,6,7,8,9 and 9,10,10,12,12,14,15
Find middle numbers:
4,5,6,6,7,8,9 and 9,10,10,12,12,14,15
Lower quartile: 6
Upper quartile: 12
Thus the answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6
26) In triangle ABC, if AB-BC and B
= 70°, ZA will be: *
O a. 70°
O b. 110°
O c. 55°
O d. 130°
Answer:
55degrees
Step-by-step explanation:
Let the other angles of the triangle are x, x degrees. Since the sum of angles in a triangle is 180degrees, hence;
<A + <B+ <C = 180
x + 70 + x = 180
2x+70 = 180
2x = 180 - 70
2x = 110
x = 110/2
x = 55
SInce <A is equal to x, hence <A is 55degrees
five positive consecutive integers starting with a have average b. what is the average of 5 consecutive integers that start with b?
The average of 5 consecutive numbers starting from b is a+4.
Average of 5 numbers starting from a :
Avg = (a+a+1+a+2+a+3+a+4)/5
Avg = a+2
=> b = a+2
Average of 5 numbers starting form b :
Avg = (b+b+1+b+2+b+3+b+4)/5
Avg = b+2
Substituting b = a+2
Avg = (a+2) + 2
Avg = a+4
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Please please please help me I need a 80 to pass
Answer:
fb=7 units
Step-by-step explanation:
Answer:
If they’re both equal to each other in length and both pentagons, then I think the answer is 7 units.
Sumita is following this recipe to make flapjacks.
Sumita uses 125 g of oats.
How many flapjacks is Sumita making?
Recipe: Makes 8 flapjacks
225 g margarine
150 g sugar
125 mL syrup
250 g oats
25 g sultanas
Answer:
20 flapjacks is the answer.
Cherries are $2.00/ pound what is the constant of proportionality
Answer:
$2 price per pound
2 is the constant of proportionality
Step-by-step explanation:
Price of Cherries = $2 per pound
what is the constant of proportionality
If y = total cost of buying x pounds of Cherries at $2 per pound
The equation below represent the situation
y = $2 * x
y = 2x
The constant of proportionality is 2
That is, the $2 price per pound
Jacob is practicing the 100 meter dash. the data show his times in seconds.
14, 13, 13.5, 16, 14, 15.5, 14.5
which box plot shows the distribution of the data?
12
+
12
13
13
14
time (s)
14
time (s)
15
15
16
16
12
12
13
13
14
time (s)
14
time (s)
15
15
16
16
The set's interquartile range is 2 seconds for the values 14, 13, 13.5, 16, 14, 15.5, and 14.5.
The interquartile range (IQR) represents the second and third quartiles of your data collection (IQR). The spread of the middle half of a data set is provided by the interquartile range, whereas the spread of the complete data set is provided by the range.
Due to it,
Jacob competes in the 100-meter dash.
the information displaying time in seconds,
14, 13, 13.5, 16, 14, 15.5. 14.5
Find the median of the provided set first before calculating the interquartile range.
Data should be arranged from lower to higher values,
13, 13.5, 14, 14, 14.5, 15.5, 16.
The data's median is 14
13, 13.5, and 14 for the set's lower half.
The set's upper half equals 14.5, 15.5, and 16.
Q1 = Lower half's middle period, or 13.5
Q2 = Upper half's middle period, or 15.5
The IQR is 15.5 to 13.5, or 2 seconds.
The set's necessary interquartile range is 2 seconds.
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b) The monthly income of A is double than that of B and the monthly income of B is treble than that of C. If the total income of three persons is Rs 80,000, find monthly income of each of person.
Answer:
A = Rs 48,000
B = Rs 24,000
C = R2 8,000
Step-by-step explanation:
To solve this problem, create and solve a system of linear equations using the given information.
From the given information:
If the monthly income of A is double than that of B, then A = 2B.If the monthly income of B is treble than that of C, then B = 3C.If the total income of three persons is Rs 80,000, then A + B + C = 80000.Therefore, the system of linear equations is:
\(\begin{cases}A=2B\\B=3C\\A+B+C=80000\end{cases}\)
Substitute the second equation into the first to create and equation for A in terms of C:
\(\begin{aligned}A &= 2B\\&=2(3C)\\&=6C\end{aligned}\)
Substitute this and the second equation into the third equation and solve for C:
\(\begin{aligned}A+B+C&=80000\\6C+3C+C&=80000\\10C&=80000\\C&=8000\end{aligned}\)
Now that we have found the monthly income of person C, substitute this value into the expressions for A and B to calculate the monthly incomes of persons A and B:
\(\begin{aligned}A &=6C\\&=6(8000)\\&=48000\end{aligned}\)
\(\begin{aligned}B &=3C\\&=3(8000)\\&=24000\end{aligned}\)
Therefore, the monthly income of each person is:
A = Rs 48,000B = Rs 24,000C = R2 8,000Write the equation of the line with a slope of 3 and passes through the point (0,5).
Answer can be in either slope-intercept
form or point-slope
form
Answer:
y=3x+5
Step-by-step explanation:
y-y1=m(x-x1)
y-5=3(x-0)
y-5=3(x)
y-5=3x
y=3x+5
Note that the slope intercept form is y=mx+b where m=slope and b=y-intercept.
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