There are no real numbers, actual solutions to the equation |x| = -5/8.
What does the term "absolute value" mean?Several mathematical disciplines, including calculus, algebra, geometry, and number theory, employ the absolute value function. By removing the sign from a number or changing a complicated expression into a simpler one, it is frequently used to simplify expressions and equations. The distance between two points in n-dimensional space, where n is any positive integer, is also defined using the absolute value function. The absolute value function is also employed in many mathematical applications, including physics, engineering, economics, and finance, where it is utilised to describe quantities that can only have non-negative values.
There are no actual solutions to the equation |x| = -5/8. This is because |x| can never be negative because the absolute value function always returns a non-negative number. It follows that |x| cannot be equal to the negative integer -5/8.
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1. Simply the answers
2. State domain in interval notation
When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated.
What is the substitute f(x) for x in the expression?Using the given functions, we have:
[tex]f(x) = x^2 + 3[/tex]
[tex]g(x) =[/tex] [tex]\sqrt{(x-4)}[/tex]
To find f(g(x)), we substitute g(x) for x in the expression for f(x):
[tex]f(g(x)) = (g(x))^2 + 3[/tex]
= ([tex]\sqrt{(x-4))^2 + 3}[/tex]
[tex]= (x-4) + 3[/tex]
[tex]= x - 1[/tex]
Therefore,[tex]f(g(x)) = x - 1.[/tex]
To find g(f(x)), we substitute f(x) for x in the expression for g(x):
[tex]g(f(x)) =[/tex] [tex]\sqrt{((f(x)) - 4)}[/tex]
= [tex]\sqrt{((x^2 + 3) - 4)}[/tex]
= [tex]\sqrt{(x^2 - 1)}[/tex]
= |x|[tex]\sqrt{(x^2 - 1)}[/tex]
Therefore, [tex]g(f(x)) =[/tex] |x| [tex]\sqrt{(x^2 - 1)}[/tex]
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To use the method of triangulation you need measurement from at least three locations
The given statement is false. The solution has been obtained by using the concept of triangulation.
What is triangulation?
Based on the principles of trigonometry, triangulation is a technique used to locate a fixed point. According to these principles, it is possible to compute the other two sides and angle of a triangle if just one side and two angles of the triangle are known.
We are given a statement that to use the method of triangulation you need measurement from at least three locations.
The statement is false because for this, we need only two points.
Hence, the given statement is false.
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Question: To use the method of triangulation, you need measurements from at least three other locations.
A.True
B.False
Which statement is true about the given expression 3x2 -11(2y+1)+4
Answer:
The given expression 3x2 -11(2y+1)+4 is a polynomial expression with two variables, x and y. It can be simplified by distributing the -11 to the terms inside the parentheses and combining like terms:
3x2 -11(2y+1)+4 = 3x2 -22y -11 +4
= 3x2 -22y -7
Therefore, the statement "the expression is a polynomial with two variables" is true, while the statements "the expression is in simplest form" and "the expression has a constant term of 11" are false.
Step-by-step explanation:
geometry question attached
The area of triangle PYR, obtained using the formula for the area of a triangle; A = (1/2)·a·b·sin(C), is about 87.85 square units
What is the formula for the area of a triangle that can be used to find the area of PYR?The area of a triangle is the product of half multiplied by the base length and the height of the triangle. The height of the triangle is the length of a side of the triangle multiplied by the sine of the included angle between two sides of the triangle.
The dimensions in the triangle indicates that we get;
Length of the side PQ = 36
Length of the side PR = 22
PQ = QM + MP (Segment addition postulate)
MQ ≅ MP (Definition of bisected segment PQ)
MQ = MP (Definition of congruent segments)
PQ = MP + MP (Substitution property)
PQ = 2 × MP
PQ = 36
36 = 2 × MP
2 × MP = 36
MP = 36/2 = 18
MP = 18
Length of the segment, MY = 8
The Pythagorean Theorem indicates that we get;
PY = √(18² + 8²) = 2·√(97)
∠MPY = arctan(8/18) ≈ 23.92°
Therefore; ∠YPR ≈ 23.92°
The area, A, of the triangle PYR can be obtained from the formula;
A = (1/2)·a·b·sin(C)
The area of the triangle PYR is therefore;
A ≈ (1/2) × (2·√(97)) × 22 × sin(23.92°) ≈ 87.85
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Use the long division to divide f(x) =b^4 + 3b^3-35b^2-46b+28 by d(x)= b+7 remember to show all your work cleary steps by steps and express your final answer in the from f(x)= q(x)d(x) +r(x)
The final function is f(x) = ( [tex]b^3-4b^2[/tex]+[tex]63b[/tex]-487b)(b+7)+3021.
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here the given function f(x)=[tex]b^4 + 3b^3-35b^2-46b+28[/tex] and d(x)=b+7.
Now using long division then,
=> [tex]b^3-4b^2[/tex]+[tex]63b[/tex]-487b
[tex]\\b+7)\overline{b^4 + 3b^3-35b^2-46b+28 }\\\\[/tex]
(-) [tex]{b^4+7b^3}[/tex]
[tex]\overline{-4b^3+35b^2+46b-28}[/tex]
(-) [tex]-4b^3-28b^2[/tex]
[tex]\overline{63b^2-46b+28}[/tex]
(-) [tex]63b^2+441b[/tex]
[tex]\overline{-487b-28}[/tex]
(-) [tex]\underline {-487b-3049}[/tex]
3021
Quotient q(x) = [tex]b^3-4b^2[/tex]+[tex]63b[/tex]-487b
Remainder r(x) = 3021
Hence the final function is f(x) = ( [tex]b^3-4b^2[/tex]+[tex]63b[/tex]-487b)(b+7)+3021.
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If X is a discrete uniform random variable ranging from 0 to 12 find
The calculated value of probability, P(X≥10) is option b) 0.1666
What is probability?Probability refers to possibility. The subject of this mathematical discipline is the occurrence of random events. An event is occur by a chance.
Since the given distribution is uniform, the percentage of data set lying between any two consecutive values of X is given by:
[tex]= \frac{100\ \% }{Maximum \ possible\ X - minimum\ possible\ X}[/tex]
[tex]= \frac{100\ \%}{(12\ -\ 0)}[/tex]
[tex]= \frac{100\ \%}{12}[/tex]
[tex]= 8.33\ \%[/tex]
The probability of X having a value that is greater than or equal to 10 i.e.
P(X≥10) is given by:
[tex]= (12- 10) * Percentage \ of data set \ lying\ between \ any two \ values \ of\ x[/tex]
[tex]=2*8.33\%[/tex]
[tex]=16.66\%[/tex]
[tex]=0.1666[/tex]
The calculated value of probability, P(X≥10) is 0.1666.
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On Monday, the worker drove a total of 134 work-related and personal miles. She received $32.13 for the work-related miles she drove on Monday. what percent of her total miles driven were work-related on Monday
Answer:
Step-by-step explanation:
If the worker drove a total of 134 miles on Monday, and received $32.13 for the work-related miles, then we can assume that the work-related miles pay rate is constant, and calculate the total pay for all the miles:
Total pay for all miles = Total miles * Pay rate per mile
Since the worker received $32.13 for the work-related miles, and we assume a constant pay rate, we can find the pay rate per mile:
Pay rate per mile = Total pay for all miles / Total miles
= $32.13 / Total work-related miles
Now we can use this pay rate per mile to calculate the percentage of work-related miles:
Percentage of work-related miles = (Pay for work-related miles / Pay rate per mile) / Total miles * 100
Plugging in the given values, we get:
Percentage of work-related miles = (32.13 / (134 - 32.13)) / (134) * 100
= 0.2874 * 100
= 28.74%
Therefore, approximately 28.74% of the worker's total miles driven on Monday were work-related.
determine the length of a plot of land 16 m wide and whose area is 336 m².
Answer:
21
Step-by-step explanation:
The equation to find the area of a space is length x width. Divide the total area by the width to find the length.
determine the total amount of money that was utilized on fuel in june 2022.
The Consumer Price Index (CPI) for All Urban Consumers grew by 9.1%. The all items index rose 9.1%, the largest annual increase since the year that ended in November 1981.
What is Consumer Price Index?A consumer price index can be defined as a measure of a market basket of goods and services that households have purchased at a weighted average price. The measured CPI fluctuates(differs) to reflect changes in prices over time.
The CPI is one of the most widely(popularly) used indicators of inflation and deflation.
[tex]Annual\ CPI = \frac{Value\ of Basket\ in \ Current \Year}{Value\ of Basket\ in \ Prior\ Year} *100[/tex]
[tex]Inflation\ Rate = \frac{New \ CPI - Prior\ CPI}{Prior\ CPI} *100[/tex]
It is one of the most used methods for measuring inflation and reveals the state and trajectory of the economy.
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Algebra 1 please help
An exponential function is a function in which the independent variable x appears as an exponent.
a is the y-intercept.
b is the rate of change.
The function is exponential growth when b > 1.
The function is exponential growth when b < 1.
y-intercept is the initial value of the function when x is equal to 0.
Asymptote is the line that the function approaches but does not cross.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = ab^x
Where:
a represents the base value or y-intercept.x represents time.b represents the rate of change.What is an asymptote?In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch or cross.
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Can someone explain me how to do this task please? Thank you
12) the common multiples of 3 and 5 up to 50 are: 15, 30, 45.
13) the common multiples of 4 and 6 up to 50 are: 12, 24, 36, 48.
14) the common multiples of 3 and 7 up to 50 are: 12, 42.
15) the equivalent fraction of 3/4 is 6/8
16) the equivalent fraction of 2/3 is 4/6
17) the equivalent fraction of 4/5 is 8/10
18) In its simplest form, 4/12 is 1/3
19) In its simplest form, 6/10 is 3/5
20) In its simplest form, 4/8 is 1/2.
What is the justification for the above response?12) To find the common multiples of 3 and 5 up to 50, we can simply list the multiples of 15 (which is the least common multiple of 3 and 5) that are less than or equal to 50.
Multiples of 15: 15, 30, 45
Therefore, the common multiples of 3 and 5 up to 50 are:
15, 30, 45
13)
To find the common multiples of 4 and 6 up to 50, we can again find the least common multiple of 4 and 6, which is 12, and list its multiples that are less than or equal to 50.
Multiples of 12: 12, 24, 36, 48
Therefore, the common multiples of 4 and 6 up to 50 are:
12, 24, 36, 48
14)
To find the common multiples of 3 and 7 up to 50, we can again find the least common multiple of 3 and 7, which is 21, and list its multiples that are less than or equal to 50.
Multiples of 21: 21, 42
Therefore, the common multiples of 3 and 7 up to 50 are:
21, 42
15)
To write an equivalent fraction of 3/4, we can multiply or divide both the numerator and denominator of 3/4 by the same non-zero number. This will give us a fraction that has the same value as 3/4 but with a different numerator and denominator.
For example, if we multiply both the numerator and denominator of 3/4 by 2, we get:
3/4 * 2/2 = 6/8
Therefore, an equivalent fraction of 3/4 is 6/8.
replicating this logic for 16 and 17, we have:
16) the equivalent fraction of 2/3 is 4/6 and
17) the equivalent fraction of 4/5 is 8/10
18) to get the simplest form of 4/12, we can divide the numerator and denominator by 4 to get
(4/4)/(12/4)
= 1/3
replicate this logic for 19 and 20, and we get:
19) In its simplest form, 6/10 is 3/5
20) In its simplest form, 4/8 is 1/2.
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A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1534 and the standard deviation was 310. The test scores of four students selected at random are 1940, 1280, 2260, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual.
The first student Z-score= 1.31, the second student= -0.82, the third student = 2.35, the fourth student = -0.37. None of these scores are unusual.
Describe Z-score?In statistics, a Z-score (also known as a standard score) is a measure of how many standard deviations a data point is from the mean of a population or sample. The Z-score is calculated by subtracting the mean from the data point and then dividing by the standard deviation.
A Z-score of 0 indicates that the data point is equal to the mean, while positive Z-scores indicate that the data point is above the mean and negative Z-scores indicate that the data point is below the mean.
Z-scores are often used in statistics to standardize data so that it can be compared across different populations or samples. Z-scores can also be used to identify outliers, which are data points that are unusually far from the mean and may skew the analysis of the data.
To find the z-score for each student, we use the formula:
z = (x - μ) / σ
where x is the student's score, μ is the mean test score, and σ is the standard deviation.
For the first student with a score of 1940:
z = (1940 - 1534) / 310
z = 1.31
For the second student with a score of 1280:
z = (1280 - 1534) / 310
z = -0.82
For the third student with a score of 2260:
z = (2260 - 1534) / 310
z = 2.35
For the fourth student with a score of 1420:
z = (1420 - 1534) / 310
z = -0.37
To determine if any of these values are unusual, we can use the rule of thumb that considers any z-score greater than 3 or less than -3 to be unusual.
None of the z-scores calculated above are greater than 3 or less than -3, so we can conclude that none of these scores are unusual.
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The diameter of a circle is 33 cm. Find its area to the nearest whole number.
Answer:
Step-by-step explanation:
The answer is not 855.3^2cm
Megan used her bike to go to a friend's house, 10 miles away from her house, and then jogged for 8 miles with her friend. The jogging time was one hour longer than her bike ride, and her biking speed was 4 times the jogging speed. Find the speed of Megan on the bike and while jogging, in mph.
Megan's biking speed was 6.4 mph and her jogging speed was 1.6 mph
What is variable ?A variable is a quantity that may change within the context of a mathematical problem.
Let's use the following variables to represent the unknown speed :
v_bike: Megan's biking speed, in miles per hour (mph)v_jog: Megan's jogging speed, in mphWe know that Megan biked for a certain amount of time, and then jogged for one hour longer. Let's use the variable t to represent Megan's biking time, in hours. Then her jogging time is t + 1 hour.
We can use the formula:
distance = rate x time
To create two equations based on the given information.
For the biking distance of 10 miles, we have:
10 = v_bike * t
For the jogging distance of 8 miles, we have:
8 = v_jog * (t + 1)
We also know that Megan's biking speed was 4 times her jogging speed, so we have:
v_bike = 4 * v_jog
We can substitute this equation into the first equation to get:
10 = 4 * v_jog * t
Simplifying this equation, we get:
t = 2.5 * v_jog
We can substitute this equation into the second equation to get:
8 = v_jog * (2.5 * v_jog + 1)
Simplifying this equation, we get:
8 = 2.5 * v_jog^2 + v_jog
Rearranging the terms, we get:
2.5 * v_jog^2 + v_jog - 8 = 0
We can solve this quadratic equation using the quadratic formula:
v_jog = (-1 ± sqrt(1 + 4 * 2.5 * 8)) / (2 * 2.5)v_jog = (-1 ± sqrt(81)) / 5v_jog = (-1 ± 9) / 5v_jog = 1.6 mph (ignoring the negative solution)Finally, we can use the equation v_bike = 4 * v_jog to find Megan's biking speed:
v_bike = 4 * 1.6 mph = 6.4 mph
Therefore, Megan's biking speed was 6.4 mph and her jogging speed was 1.6 mph
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Which statement is in-correct
The statement "The Poisson distribution is always skewed right" is incorrect. Option A
What is Poisson distribution?The Poisson distribution is a discrete probability distribution that is used to model the probability of a given number of events occurring in a fixed interval of time or space, assuming that the events occur independently and at a constant rate.
The key features of the Poisson distribution include:
The distribution is discrete, meaning that it only takes on integer values.The distribution is defined by a single parameter, lambda (λ), which represents the expected number of events that will occur in the interval.The distribution is skewed right, with a long tail on the right-hand side.The mean and variance of the distribution are both equal to λ.The statement "The Poisson distribution is always skewed right" is incorrect.
The Poisson distribution can be skewed left, right, or approximately symmetric depending on the value of its parameter lambda. If lambda is small, the distribution will be skewed right. If lambda is large, the distribution will be approximately symmetric.
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HURRY I WILL GIVE BRAINLIEST TO WHO ANSWERS FIRST
Raymond was riding a zip-cable from the top of a viewing post. The cable is 55 yards long. The viewing post is 44 yards high and forms a right angle with the ground, as shown in the picture below.
Given this information, how far is the bottom of the cable from the base of the viewing post?
Answer: i am pretty sure it is 33
Step-by-step explanation:
Classify the events as independent or not independent. Events A and B where P(A) = 0.7, P(B) = 0.8, and P(A and B) = 0.56
The given events A and B are two independent events.
Independent and Non-independent events:In probability, independent events are those events where the occurrence of one event does not affect the probability of the other event occurring.
On the other hand, non-independent events are those events where the occurrence of one event affects the probability of the other event occurring.
If A and B are two independent events then
P(A and B) = P(A) * P(B)Here we have
A and B are two events
where P(A) = 0.7, P(B) = 0.8, and P(A and B) = 0.56
Using the above formula,
=> P(A and B) = (0.7) (0.8) = 0.56
=> P(A and B) = 0.56
From the data, P(A and B) = 0.56
Therefore,
The given events A and B are two independent events.
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Which of the following represent dividing 72 by 6?
a. 72 ÷ 6
b. 7/2
c. 6÷72
d. 7/2
a and d
a and c
b and c
Cb and d
Answer:
Step-by-step explanation:
The answer to your question is a.
A parallelogram has a height of 5 units. One side of the parallelogram is AB⎯⎯⎯⎯⎯. The parallelogram has no right angles.
Draw the parallelogram using the Polygon tool.
Each segment of the grid represents 1 unit.
Keyboard Instructions
Initial graph state
The horizontal axis goes from 1.5 to 12.5 with ticks spaced every 1 unit(s).
The vertical axis goes from 1.5 to 12.5 with ticks spaced every 1 unit(s).
Point with coordinates (2, 3) labelled: A.
Point with coordinates (8, 3) labelled: B.
Parallelogram, In Euclidean geometry, a parallelogram is a simple quadrilateral with two(2) pairs of parallel sides.
What is Parallelogram?A parallelogram is a geometric object with sides that are parallel to one another in two(2) dimensions. It is a form of a polygon with four(4) sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length.
A Quadrilateral is a closed shape and a type of polygon that has four sides, four(4) vertices and four angles. It is formed by joining(connecting) four non-collinear points. The sum of the interior angles of quadrilaterals(4 sides) is always equal to 360 degrees.
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An insurance company offers renters insurance to customers in a certain area. Suppose they charge $ 40 $40dollar sign, 40 for a given plan. Based on historical data, there is a 1 11 in 500 500500 probability that a customer with this plan makes a claim, and in those cases, the average payout from the insurance company to the customer was $ 5 , 000 $5,000dollar sign, 5, comma, 000. Here is a table that summarizes the possible outcomes from the company's perspective: Event Payout Net gain ( X ) (X)left parenthesis, X, right parenthesis Claim $ 5 , 000 $5,000dollar sign, 5, comma, 000 − $ 4 , 960 −$4,960minus, dollar sign, 4, comma, 960 No claim $ 0 $0dollar sign, 0 $ 40 $40dollar sign, 40 Let X XX represent the company's net gain from one of these plans. Calculate the expected net gain E ( X ) E(X)E, left parenthesis, X, right parenthesis. E ( X ) = E(X)=E, left parenthesis, X, right parenthesis, equals dollars
An insurance company's anticipated total profit from a single of these policies is $0.08.
What does the term "insurance" mean?Describe insurance. Insurance is a tool for risk management. You acquire security against unforeseen financial losses when you purchase insurance. If something terrible occurs to you, the insurance company compensates you or someone else of your choosing.
The expected net gain can be calculated as:
E(X) = P(Claim) × Net gain (Claim) + P(No claim) × Net gain (No claim)
P(Claim) = 1/500
P(No claim) = 1 - P(Claim) = 499/500
Net gain (Claim) = -$4960 + $5000 = $40
Net gain (No claim) = $40 - $40 = $0
Therefore,
E(X) = (1/500) × $40 + (499/500) × $0
E(X) = $0.08
So the expected net gain for the insurance company from one of these plans is $0.08.
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Answer:
30 dollars
Step-by-step explanation:
Khan Academy
PLEASE HELP ME I NEED THIS FAST TO PASS!!
Answer:-225
Step-by-step explanation:The arithmetic series is given by:
a1 = -1, d=-2, n = 15
where a1 is the first term, d is the common difference, and n is the number of terms.
To evaluate this series, we can use the formula for the sum of an arithmetic series:
Sn = n/2 * [2a1 + (n-1)d]
where Sn is the sum of the first n terms.
Substituting the given values, we get:
S15 = 15/2 * [2(-1) + (15-1)(-2)]
= 15/2 * [-2 - 28]
= 15/2 * (-30)
= -225
Therefore, the sum of the first 15 terms of the arithmetic series with a1 = -1, d=-2 is -225.
Given the function of(x) = 2√x +√x³, find f'(3). Express your answer as a
single fraction in simplest radical form.
Answer:
Here is the answer for the following question:
Cuantos minutos tardará en llenarse un depósito de 10.080 litros de capacidad si recibe agua por 3 grifos diferentes que arrojan 60 litros, 70 litros, 80 litros cada minuto?
Answer:
El tanque tardará aproximadamente 48 minutos en llenarse.
Step-by-step explanation:
Podemos encontrar la tasa de llenado del depósito sumando las tasas de flujo de los tres grifos:
Tasa de llenado = 60 + 70 + 80 = 210 litros/minuto
Luego, podemos usar la fórmula:
Tiempo = Volumen / Tasa de llenado
Donde el volumen es 10.080 litros y la tasa de llenado es 210 litros/minuto. Sustituyendo estos valores, obtenemos:
Tiempo = 10.080 / 210 ≈ 48 minutos
Por lo tanto, tardará alrededor de 48 minutos en llenarse el depósito de capacidad 10.080 litros si recibe agua por tres grifos diferentes que arrojan 60 litros, 70 litros, 80 litros cada minuto.
¡Espero que esto ayude! Lo siento si no es así. ¡Si necesitas más ayuda, pregúntame! :]
|a-b|-|c+d| if a=-5, b=4. c=1, d=-3
please help soon!
Answer:-7
Step-by-step explanation:
|-5 - 4| = -9
|1 + -3|= -2
|-9 - -2| = -7
Answer:
Step-by-step explanation:
[tex]|a-b|-|c+d|=|-5-4|-|1+(-3)|=|-9|-|-2|=9-2=7[/tex]
Absolute value is just the distance from 0 and therefore is always positive.
li
People can pick strawberries on a farm.
The pay for the strawberries they pick.
Brian picks 4 ½ kg of strawberries.
He pays a total of £15.75.
Sue wants 500 grams of strawberries.
Brian says she can buy them from him for the same price he paid.
How much should Sue pay Brian for 500 grams of strawberries?
Answer:
Question 10
Not yet answered
Marked out of 1.00
Robert packs potatoes into bags.
He then packs bags into boxes to sell to shops.
Robert has these orders.
P Flag question
Browns
25 hoxes
Brian will receive £[tex]1.75[/tex] from Sue buying [tex]500[/tex] grams of berries.
What is grams vs. kg?The metric measure for a tiny amount of mass and weight is the gram (g). It weighs the same as one milliliter (or one cubic centimeter) of water. 1,000 grams make to one kilogram (kg). One liter liquid water weighs exactly one kilogram (kg).
How should I weigh a gram?Using a scale is the most accurate technique to measure in grams. Kitchen spoons and cups, for example, offer an approximate approximation. Moreover, always have a conversion tool or chart on available so you can estimate grams without a scale.
Brian paid a total of £[tex]15.75[/tex] for [tex]4\frac{1}{2}[/tex] kg of strawberries. To find out the price per gram, we can divide the total cost by the total weight:
Price per gram [tex]=[/tex]Total cost / Total weight
Total weight of strawberries [tex]= 4.5 kg = 4500 grams[/tex]
Price per gram [tex]=[/tex] £[tex]15.75 / 4500[/tex] grams
Price per gram [tex]=[/tex] £[tex]0.0035[/tex] per gram
So, Brian paid £[tex]0.0035[/tex] for every gram of strawberries he picked.
Cost of [tex]500[/tex] grams [tex]=[/tex] [tex]500 grams *[/tex] £[tex]0.0035/gram[/tex]
Cost of [tex]500[/tex] grams [tex]=[/tex] £[tex]1.75[/tex]
Therefore, Sue should pay Brian £[tex]1.75[/tex] for [tex]500[/tex] grams of strawberries.
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In ΔSTU, \overline{SU}
SU
is extended through point U to point V, \text{m}\angle STU = (3x+14)^{\circ}m∠STU=(3x+14)
∘
, \text{m}\angle UST = (2x+12)^{\circ}m∠UST=(2x+12)
∘
, and \text{m}\angle TUV = (7x+6)^{\circ}m∠TUV=(7x+6)
∘
. What is the value of x?x?
The value of x from the calculation is given as 10
How to solve for the value of xWe have ∠TUV = ∠STU + ∠UST
(7x+6) = (3x+14) + (2x+12)
open the bracket
7x+6 = 3x+14 + 2x+12
take the like terms
7x + 6 = 3x + 2x + 14 + 12
7x + 6 = 5x + 26
7x - 5x = 26 - 6
2x = 20
Divide through the equation that we have by 2 to get the value of x
2x / 2 = 20 / 2
x = 10
Hence the value of x is given as 10
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determine whether f (x) x^2-2x-3/x^2+3x+2 has any holes. if it does, give coordinates
Answer:
hole at (- 1, - 4 )
Step-by-step explanation:
If f(x) has terms that cancel , on the numerator/ denominator then a discontinuity corresponding to that factor is removable and there is a hole.
f(x) = [tex]\frac{x^2-2x-3}{x^2+3x+2}[/tex] ← factor numerator and denominator
= [tex]\frac{(x-3)(x+1)}{(x+2)(x+1)}[/tex] ← cancel (x + 1) on numerator/ denominator
= [tex]\frac{x-3}{x+2}[/tex]
this indicates that x + 1 = 0 ( or x = - 1) is a removable discontinuity and the graph has a hole in it.
substitute x = - 1 into the remaining f(x) for y- coordinate of hole
f(- 1) = [tex]\frac{-1-3}{-1+2}[/tex] = [tex]\frac{-4}{1}[/tex] = - 4
coordinates of hole are (- 1, - 4 )
Answer:
Yes, this function has one hole
This occurs at [tex](-1, -4)[/tex]
Step-by-step explanation:
Definition of hole
A hole on a rational function represents the fact that the function approaches the point, but is not actually defined on that precise x value.
Given function
[tex]f(x) = \dfrac{x^2-2x\:-3}{x^2+\:3x\:+\:2}\\[/tex]
Factor the numerator:
[tex]x^2 - 2x - 3 = (x+1)(x - 3)[/tex]
Factor the denominator:
[tex]x^2+\:3x\:+\:2 = (x + 1)(x + 2)[/tex]
Hence
[tex]\begin{aligned}f(x) & = \dfrac{x^2-2x\:-3}{x^2+\:3x\:+\:2}\\\\& = \dfrac{ (x+1)(x - 3)}{(x + 1)(x + 2)}\\\\ &= \dfrac{x - 3}{x+2} \end{aligned}[/tex]
The common factor is [tex](x + 1)[/tex]
Set this = 0 to find the hole:
[tex]x + 1 = 0 = > x = -1[/tex]
So at[tex]x = -1[/tex] there is a hole.
Substitute this value of x in the factored function to get the y value for the hole
We have
[tex]f(x) = \dfrac{x - 3}{x+2}[/tex]
[tex]\begin{aligned}f(2) &= \dfrac{-1 - 3}{-1 + 2}\\& = \dfrac{-4}{1}\\&= -4\end{aligned}[/tex]
So the hole occurs at [tex](-1, -4)[/tex]
A triangle has the measures of two of its interior angles 48° and 65°, the third interior angle is unknown. What is the value of the exterior angle corresponding to the interior angle whose value is unknown?
a) 123°
b) 131°
c) 113°
d) 128°
e) 118°
Answer:
c) 113°
Step-by-step explanation:
Exterior angle is equal to the sum or the "remote" interior angles, that is the two angles that are not just next to the exterior angle. See image.
So the answer, quickly:
exterior angle
= 65° + 48°
= 113°
This is why:
(skip if you don't care)
The three angles in a triangle add up to 180° But also, a linear pair of angles also add up to 180°
So
x + 65° + 48° = 180°
x + y = 180°
y = 65° + 48°
See image.
Simplify:
2
(
3
x
)
+
(
x
+
10
)
2(3x)+(x+10)
Answer:
7x+10
Step-by-step explanation:
2x(3x)+1x(x+10)
6x+1x+10
7x+10
If m/P = (4x - 1)° and m/R = (12x - 27), find mQPS.
The arc angle QPS is 258 degrees.
How to find the angles of a cyclic quadrilateral?A cyclic quadrilateral is a four sided shape(quadrilateral) that can be inscribed into a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.
The opposite angles of a cyclic quadrilateral have a total of. 180 ° . In other words, the opposite angles of a cyclic quadrilateral is supplementary angles.
Therefore,
m∠P = 4x - 1
m∠R = 12x - 27
Hence,
4x - 1 + 12x - 27 = 180
16x - 28 = 180
16x = 180 + 28
16x = 208
x = 208 / 16
x = 13
m∠R = 12(13) - 27
m∠R = 156 - 27
m∠R = 129 degrees
Therefore,
m∠R = 1 / 2 (QPS)
129 = 1 / 2 × x
x = 129 ×2
x = 258 degrees
Hence,
mQPS = 258 degrees
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