4.5 Is the answer required
Answer: 2
Step-by-step explanation: got it right :)
A student is running a 5 kilometer race. He runs 1 kilometer every 3 minutes. Select the function that describes his distance from the finish line after x minutes
The first one f(x) = -1/3x + 5
Answer:
f(x)=-1/3+5
Step-by-step explanation:
hope this helps
Write a complete two-column proof for the following information.
Given: AB = 3y - 1, BC = 7y, AC = 29
Prove: AB = 8
Answer:
The answer to your question is below
Step-by-step explanation:
Data
AB = 3y - 1
BC = 7y
AC = 29
Prove AB = 8
AB + BC = AC
3y - 1 + 7y = 29
10y -1 = 29
10y = 29 + 1
10y = 30
y = 30/10
y = 3
AB = 3y - 1
= 3(3) - 1
= 9 - 1
= 8
A shrew, the mammal with the fastest metabolism, has a mass of only 0.004 kg. What is its mass in grams? A. 0.4 g B. 0.04 g C. 4 g D. 0.000004 g
Answer:
C
Step-by-step explanation:1 kilogram = 1000 grams so if you multiply 0.004 times 1000 you get 4 grams
BD bisects ABC. m ABD=2y m DBC=5y-12. What is ABC?
In triangle ABC, BD bisects angle ABC into two parts with measures 2y and 5y-12. The measure of angle ABC is the sum of its parts, equating to 7y-12. Without additional information, the exact value of y and thus, the measure of angle ABC, cannot be determined.
Explanation:The given problem involves a geometrical concept related to triangles, specifically angle bisectors. In triangle ABC, BD is an angle bisector, dividing angle ABC into two angles with measures 2y for angle ABD and 5y-12 for angle DBC. To find the measure of the whole angle ABC, we need to understand that the angle bisector divides the angle into two parts, where their measures are equal to the sum of the parts' measures.
Given:
m ABD = 2ym DBC = 5y - 12Since BD is an angle bisector, the sum of the measures of angles ABD and DBC equals the measure of angle ABC. Thus, to find m ABC, we add the measures of angle ABD and angle DBC:
m ABC = m ABD + m DBC = 2y + (5y - 12) = 7y - 12
To solve for y, we note that additional information is required that is not provided in the question. However, the measure of angle ABC in terms of y is 7y - 12, showcasing the relationship between the angle and its bisector.
The set of valid inputs for a function is called the The letter a in parentheses above a horizontal line. _____ (a) , and the input variable x is called the The letter b in parentheses above a horizontal line. _____ (b) variable.
Answer:
(a) domain
(b) "argument," or "independent variable"
Step-by-step explanation:
You may want to refer to your notes for terminology related to functions. Different terms are used, depending on the context.
__
The set of valid inputs for a function is called the domain.
__
The input variable x is called the argument, or independent variable.
The set of valid inputs for a function is referred to as the domain, and the variable x is known as the independent variable in a function or an equation.
Explanation:The set of valid inputs for a function is called the domain (a), and the input variable x is called the independent variable (b).
In the context of the equation of a line, such as y = mx + b, the independent variable x is usually plotted on the horizontal axis. When you select a value for x, it is considered independent because it can be chosen freely, and then you solve the equation for y, which is the dependent variable because its value depends on the chosen x. An example would be setting x to a specific number to see what y would be, demonstrating how the equation represents a straight line on a graph with m representing the slope and b representing the y-intercept.
Two vectors A and B are added together to form a vector C. The relationship between the magnitudes of the vectors is given by a2 + b2 > c2. Which one of the following statements concerning these vectors is true?
The angle between the two vectors must be an obtuse angle, i.e, greater than 90 The two vectors must point in opposite directions
The two vectors must point in opposite directions
The two vectors must be parallel.
The angle between the two vectors must be an acute angle, l-e, less than 900.
Answer:
D.The angle between the two vectors must be an acute angle which is less than 90 degrees.
Step-by-step explanation:
We are given that two vectors A and B are added together to form a vector C.
The relationship between the magnitudes of the vectors is given by [tex]a^2+b^2 >c^2[/tex]
We have to find which statement is true about given vectors.
We know that if a triangle is an obtuse triangle then
[tex]c^2 >a^2+b^2[/tex]
If a triangle is an acute triangle then
[tex]a^2+b^2 >c^2[/tex]
If a triangle is right angle triangle then
[tex]c^2=a^2+b^2[/tex]
Therefore,the angle between the two vectors must be an acute angle which is less than 90 degrees.
Option D is true.
A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. What is the correct decision for a hypothesis test using α = .05?
Given : Sample size : n= 16
Degree of freedom = n-1=15
The obtained t-statistic value = 1.94
Since, The treatment is expected to increase scores and the sample mean shows an increase.
Let [tex]\mu_0[/tex] be the population mean before and [tex]\mu[/tex] denotes the population mean after the treatment.
then the related hypothesis will be :-
[tex]\text{Null hypothesis }H_0:\mu_0=\mu\\\\\text{Alternative hypothesis } H_1:\mu_0<\mu[/tex]
Since the alternative hypothesis is left-tailed, so the test is a left tailed test.
The critical value for [tex]\alpha=0.05[/tex]=1.753
Since, the obtained value (1.94) is greater than the critical value (1.753) so we reject the null hypothesis .
Therefore, we have enough evidence to support the alternative hypothesis.
Hence, we conclude that treatment may successful to increase scores and the sample mean shows an increase.
The distance from Los Angeles to Mumbai is 14,000 km. Flights take 22
hours, whilst the return flight from Mumbai to Los Angeles takes only 17
hours because of the direction of the prevailing wind. Assuming the
airplane would fly the same speed in both directions in still air, what is
the average wind velocity?
Answer:
about 93.6 km/h
Step-by-step explanation:
The speed westbound is ...
14000 km/(22 h) ≈ 636.364 km/h
The speed eastbound is ...
14000 km/(17 h) ≈ 823.529 km/h
The difference in speeds is twice the wind speed, so the wind speed is ...
(823.529 -636.364)/2 km/h ≈ 93.6 km/h
To find the wind velocity, first calculate the plane's average speed in still air by averaging its speeds in opposite directions. Then subtract the plane's speed against the wind from its speed in still air. The result is the wind velocity, which in this case is 93.59 km/h.
Explanation:To calculate the wind velocity, we will first need to find out the airplane's speed in still air. This can be calculated by getting the average of the two speeds in opposite directions. You see, when a plane flies from Los Angeles to Mumbai, it takes 22 hours, while the return flight from Mumbai to Los Angeles takes only 17 hours because of wind assistance. Here's how to work it out:
First, calculate the plane’s speed for both directions: For the LA to Mumbai direction it’s 14,000 km / 22 hours = 636.36 km/h, and for the Mumbai to LA direction it’s 14,000 km / 17 hours = 823.53 km/h.Now, get the average speed of the plane in still air. It would be the sum of these two speeds divided by two: (636.36 km/h + 823.53 km/h) / 2 = 729.95 km/h. This is the plane’s speed in an environment without wind.To find the wind velocity, subtract the plane's speed against the wind (LA to Mumbai direction) from the speed in still air. This gives us: 729.95 km/h - 636.36 km/h = 93.59 km/h. Therefore, the average wind velocity is 93.59 km/h.Learn more about Wind Velocity here:https://brainly.com/question/34068902
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Please help me out with this
Answer:
y = - 3x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (2, - 2) ← 2 points on the line
m = [tex]\frac{-2-4}{2-0}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3
Note the line crosses the y- axis at (0, 4) ⇒ c = 4
y = - 3x + 4 ← equation of line
Two symptoms are associated with a certain disease.
There is a 95% probability that at least one of the symptoms occurs;
in addition, the first symptom occurs with 50% probability, the second symptom occurs with 45% probability.
Based on these probability results, answer the following two questions
1) Are the two events "first symptom occurs" and "second symptom occurs" mutually exclusive (i.e. disjoint)?
2) Are the two events "first symptom occurs" and "second symptom occurs" independent?
For each question, clearly state YES or NO and provide a brief written explanation that includes the appropriate numerical support.
Answer:
Mutually exclusive, dependent events
Step-by-step explanation:
Two events A and B are mutually exclusive if [tex]P(A\cap B)=0[/tex]
Two events A and B are independent if [tex]P(A\cap B)=P(A)\cdot P(B)[/tex]
Remark: All mutually exclusive events are dependent.
Now,
A = the first symptom occurs
B = the second symptom occurs
[tex]P(A)=0.5\ (\text{or } 50\%)[/tex]
[tex]P(B)=0.45\ (\text{or } 45\%)[/tex]
[tex]P(A\cup B)=0.95 \ (\text{or }95\%)[/tex]
Use the rule
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\ \\0.95=0.5+0.45-P(A\cap B)\\ \\P(A\cap B)=0.5+0.45-0.95=0.95-0.95=0[/tex]
Thus, the events A and B are mutually exclusive (disjoint) and dependent (accordint to the remark)
Five friends a matinee movie spend $8 per ticket.They also purchase a small bag of popcorn each.If the friends pend a total of $62.50,how much does each bag of popcorn cost?
Five friends went to see a movie. Each person paid $5.
This is a total of $40.
$62.50 - $40 = $22.50.
We now have $22.50 to divide by 5 people.
So, $22.50/5 = $4.50.
Each person paid $4.50 for popcorn.
What is the measure of angle BAC?
ABCD is a square
30
45
60
90
Answer:
B:45 degrees.
Step-by-step explanation:
We are given that a square ABCD .
We have to find the measure of angle BAC.
We know that each angle of square is of 90 degrees.
We know that diagonal AC bisect the angle BAD.
Therefore, measure of angle BAC=Measure of angle CAD.
Measure of angle BAD=[tex]\frac{1}{2}\times 90=45^{\circ}[/tex]
Hence, the measure of angle BAC=45 degrees.
Answer:B:45 degrees.
Answer:
45
Step-by-step explanation:
A spyware is trying to break into a system by guessing its password. It does not give up until it tries 1 million different passwords. What is the probability that it will guess the password and break in if by rules, the password must consist of
(a) 6 different lower-case letters
(b) 6 different letters, some may be upper-case, and it is case-sensitive
(c) any 6 letters, upper- or lower-case, and it is case-sensitive
(d) any 6 characters including letters and digits
The probability of a spyware program breaking into a system depends on the complexity of the password rules. By calculating the total number of possible passwords based on given rules and comparing it to the number of guessing attempts (1,000,000), one can determine the probability for each scenario.
Explanation:The probability of a spyware program guessing a password correctly can be calculated by determining the total number of possible unique passwords and then seeing how many attempts the spyware has in comparison.
6 different lower-case letters: There are 26 possibilities for each character, and because the letters must be different, the total number of possibilities is 26 * 25 * 24 * 23 * 22 * 21. Since the spyware makes 1 million (1,000,000) attempts, the probability of guessing correctly is 1,000,000 / (26 * 25 * 24 * 23 * 22 * 21).6 different letters, case-sensitive: There are 52 possibilities for each character (26 lower-case + 26 upper-case), and since letters must be different, the total number of possibilities is 52 * 51 * 50 * 49 * 48 * 47. So the probability is 1,000,000 / (52 * 51 * 50 * 49 * 48 * 47).Case-sensitive combination of letters: Since letters can be the same and are case-sensitive, there are 52 possibilities for each character, for a total of 52^6 possible combinations. The probability is 1,000,000 / 52^6.Any 6 characters including letters and digits: There are 62 possibilities for each position (26 lower-case + 26 upper-case + 10 digits), giving us 62^6 possible combinations. The probability is 1,000,000 / 62^6.In all cases, the probability of the spyware breaking in is the quotient of the number of attempts made (1,000,000) and the total number of possible passwords for each scenario.
Slope and y intercept
Answer:
can you elaborate
Step-by-step explanation:
I think you're talking about the slope formula so I'll tell you that y=x+b
y2-y1/x2-x1 (x1,y1) is the first coordinate and (x2,y2) is the second coordinate
Answer:
Step-by-step explanation:
1 ) the slope formula for the line passes by : A(XA,YA) B(XB,YB)
the slope is : (YB - YA)/(XB -XA)
2) y intercept for the line when : x = 0
The equation A=p(1+r)^t can be used to calculate compound interest on a savings account. A = future balance, p = current balance, r = rate of interest, and t = time in years. If you deposit $2,000 at 10% each year, how much money will be in your account in 10 years(Round to the nearest dollar.)
A.
$2,200
B.
$4,000
C.
$4,318
D.
$5,187
To calculate the compound interest, the formula[tex]A=p(1+r)^t[/tex] is used with the principal amount of $2,000, an annual interest rate of 10%, and a time frame of 10 years. The correct calculation results in a future balance of $5,187, when rounded to the nearest dollar. The correct option is d.
The equation [tex]A=p(1+r)^t[/tex] is used to calculate the compound interest on a savings account. To find out how much money will be in the account after a certain number of years, we can follow these steps:
Identify the principal amount (p), which is the initial amount deposited. In this case, it's $2,000.Determine the annual interest rate (r), expressed as a decimal. For a 10% interest rate, r would be 0.10.Identify the time (t) in years that the money will be invested. Here, it is 10 years.Substitute these values into the formula: [tex]A = 2000(1 + 0.10)^{10[/tex]Calculate the future balance A.After performing the calculation, we get:
A =[tex]2000(1 + 0.10)^{10[/tex] = [tex]2000(1.10)^{10[/tex] = 2000 ×2.59374 = $5,187.48
Therefore, rounded to the nearest dollar, you will have $5,187 in your account after 10 years. The correct answer is D. $5,187.
Iran of paper contains 500 sheets of paper. Norm has 373 sheets of paper left from a team. Express the option of a rem Norm has as a fraction and as a decimal
Answer:
373/500 = 0.746
Step-by-step explanation:
373 out of 500 is represented by the fraction 373/500.
This value is easily converted to a decimal number by multiplying numerator and denominator by 2:
(373×2)/(500×2) = 746/1000 = 0.746
_____
You can also divide 373 by 500 using a calculator to get the decimal result.
A real estate office manages an apartment complex with 50 units. When the rent is $780 per month, all 50 units are occupied. However, when the rent is $825, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear (Note:The term demand refers to thenumber of occupied units.)
(a) Write a linear equation giving the demand x in terms of the rent p. (b) Linear extrapolation - Use a graphing utility to graph the demand equation and use the trace feature to predict the
number of units occupied when the rent is raised to $855. (c) Linear interpolation - Predict the number of units occupied when the rent is lowered to $795.
Answer:
A) The linear equation is [tex]x=\frac{-1}{15}p+102[/tex]
B) When the rent is raised to $855 the number of units occupied is 45.
C) When the rent is lowered to $795 the number of units occupied is 49.
Step-by-step explanation:
A) A linear equation for the demand is written as [tex]x=mp+p_{0}[/tex], where [tex]m[/tex] is the slope, [tex]x[/tex] is the number of occupied units, [tex]p[/tex] is the rent.
[tex]m[/tex] is calculated using the problem information. When the rent is [tex]p=$780[/tex] then [tex]x=50[/tex] and when the rent is [tex]p=$825[/tex] then [tex]x=47[/tex].
Using the slope equation we have:
[tex]m=\frac{50-47}{780-825}=\frac{-3}{45}=\frac{-1}{15}[/tex]
Thus the linear equation is:
[tex]x=\frac{-1}{15}p+p_{0}[/tex]
In order to calculate [tex]p_{0}[/tex] we use the problem information, When the rent is [tex]p=$780[/tex] then number of occupied units is [tex]x=50[/tex], thus:
[tex]50=\frac{-1}{15}780+p_{0} \\\\50=-52+p_{0} \\\\p_{0}=102 \\[/tex]
Finally, the linear equation is:
[tex]x=\frac{-1}{15}p+102[/tex]
B) The demand equation is plot in the attached file, the number of units occupied when the rent is raised to $855 is 45.
C) In order to predict the number of occupied units lets use the equation:
[tex]x=\frac{-1}{15}p+102[/tex]
where [tex]p=$795[/tex], then:
[tex]x=\frac{-1}{15}795+102\\ \\x=-53+102\\\\x=49[/tex]
Thus, when the rent is lowered to $795 the number of units occupied is 49.
Alex has 360 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Answer:
90 yd by 90 yd (square)8100 yd²Step-by-step explanation:
When the perimeter of the rectangle is 360 yd, the sum of the lengths of two adjacent sides is 180 yd. If x is the length of one side of the rectangle, then the adjacent side is (180-x). The area is the product of these lengths,
area = x(180 -x)
This describes a downward-opening parabola with zeros at x=0 and x=180. The vertex (maximum) of the parabola is halfway between, at x=90. The adjacent sides of the maximum-area rectangle are the same length: the rectangle is a square with sides 90 yards each.
The area is (90 yd)² = 8100 yd².
The maximum area is achieved when Alex uses the fencing to create a square. Dividing 360 yards by 4 gives each side a length of 90 yards. Thus, the maximum area that can be enclosed is 8100 square yards.
Explanation:Alex is attempting to maximize the area of a rectangular enclosure by manipulating the length and width dimensions. In this circumstance, the maximum area will be achieved when the rectangle is square. This is because for a fixed perimeter, in this case 360 yards, a square provides the largest possible area.
The rectangle will be square if all its sides are equal. Hence, to find the dimensions of the rectangle, divide the total length of the fencing by 4 (as a square has 4 equal sides), i.e., 360 yards/4 = 90 yards. Thus, the rectangle's dimensions will be 90 yards by 90 yards.
To find the maximum area, multiply the length by the width, i.e., 90 yards * 90 yards = 8100 square yards. Therefore, the maximum area that can be enclosed by the fencing is 8100 square yards.
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The heights of the adults in one town have a bell-shaped distribution with a mean of 67.5 inches and a standard deviation of 3.4 inches. Based on the empirical rule, what should you predict about the percentage of adults in the town whose heights are between 57.3 and 77.7 inches?
Answer:
The percentage is approximately 99.7%
Step-by-step explanation:
In order to understand this question you must understand the bell curve. (I would suggest googling a picture of the bell curve)
The mean of the bell curve is 67.5, meaning +1 standard deviation would be 70.9 (67.5+3.4). This would mean that 34% of the sample is between 67.5" and 70.9" (The bell curve % goes 34/14/2/.1 in that order)
When looking at the bell curve of this data, you would find that ±3 standard deviations gives you the range of 57.3" to 77.7". This would represent roughly (2+14+34+34+14+2)% of the sample. This excludes the .2% that are above or below 57.3" to 77.7". Therefore, the only answer that is close would be 99.7%
Using the empirical rule for a normal distribution, the calculation shows that approximately 99.7% of adults in town have heights between 57.3 and 77.7 inches.
Explanation:The heights of the adults in this town follow a bell-shaped distribution known as the normal distribution. This means that the values are symmetrically distributed around the mean, with most values close to the mean and fewer values farther away. The empirical rule states that approximately 68 percent of the data falls within one standard deviation of the mean, about 95 percent falls within two standard deviations, and about 99.7 percent falls within three standard deviations.
In this case, the mean is 67.5 inches and the standard deviation is 3.4 inches. Thus, one standard deviation away from the mean is a range from 67.5 - 3.4 = 64.1 inches to 67.5 + 3.4 = 70.9 inches. Two standard deviations away from the mean is a range from 64.1 - 3.4 = 60.7 inches to 70.9 + 3.4 = 74.3 inches. Three standard deviations away from the mean is a range from 60.7 - 3.4 = 57.3 inches to 74.3 + 3.4 = 77.7 inches.
Therefore, according to the empirical rule, we would predict that about 99.7 percent of adults in the town have heights between 57.3 and 77.7 inches.
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How many oranges are in a crate if the price of a crate of oranges is $1.60 and the price of oranges is $0.20 per pound and there are 3 oranges per pound?
The crate contains 24 oranges.
What is unitary method ?Unitary method is a mathematical technique for first finding the value of a single unit and then deriving the given units from it by multiplying with the single unit.
According to the given question a no. of oranges are in a crate which costs 1.60 dollars also given that per pound of orange costs 0.20 dollars.
∴ The crate contains (1.60/0.20) pounds of oranges which is
= 8 pounds of oranges.
Given 3 oranges are of 1 pound
∴ In 8 pounds of oranges pieces of oranges are (8×3) = 24 oranges.
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One street light flashed every 4 seconds Another street light flashes every 6 seconds If they both just flashed as the same movement how many seconds will it take before thwart flash at the same time again
Time for light A's Flash = 4 seconds
Time for light B's Flash = 6 seconds
Duration between the lights = 6-4=2
Duration to flash again = LCM of 6, 4
2/6,4
2/3,2
3/3,1
/1,1
2x2 x 3
4 x 3
= 12 seconds
Final answer:
The two street lights will flash together again after 12 seconds. This is determined by finding the least common multiple of the intervals at which each street light flashes (4 seconds and 6 seconds), which is 12 seconds.
Explanation:
The question you've posed is about finding the least common multiple (LCM) of two numbers, which in this case are the intervals at which two street lights flash: 4 seconds and 6 seconds. To determine when the street lights will flash together again, we must find the smallest time interval that is a multiple of both 4 and 6. The multiples of 4 are 4, 8, 12, 16, and so on. The multiples of 6 are 6, 12, 18, 24, and so on. The smallest multiple they have in common is 12 seconds.
To arrive at this answer, you can either list out the multiples as above or use a shortcut by calculating the LCM. Here's a step-by-step breakdown:
Write down the prime factors of each number: 4 = 2 x 2 and 6 = 2 x 3.
For each distinct prime factor, take the highest power present in the factorization of either number. Here, this gives us 22 (from 4) and 3 (from 6).
Multiply these together to get the LCM: 22 x 3 = 4 x 3 = 12.
Therefore, the two street lights will flash together again after 12 seconds.
Owen went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 500 mg of sodium and each frozen dinner has 650 mg of sodium. Owen purchased a total of 19 cans of soup and frozen dinners which collectively contain 11000 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.
Answer: 2 with the remainder of 200
Step-by-step explanation:
first you are going to times 19 cans by 500 mg of sodium and get 9,500
then you are going to subtract 11,000 by 9,500 and get 1,500
lastly you are going to take 1,500 and divide it by 650.
in the end you will get 2 with the remainder of 200.
Answer:
Owen bought [tex]9[/tex] cans of soup and [tex]10[/tex] cans of frozen dinners.
Step-by-step explanation:
We can solve this problem by writing the linear equation system that represents the situation.
Let be ''x'' the number of cans of soup purchased and ''y'' the number of frozen dinners purchased.
By reading the question we can write the following linear equation system :
[tex]x+y=19[/tex] (I)
[tex]x.(500)+y.(650)=11000[/tex] (II)
Working with the equation (I) we find that [tex]x=19-y[/tex] (III)
If we replace (III) in (II) :
[tex](19-y).(500)+y.(650)=11000[/tex]
[tex]9500-500y+650y=11000[/tex]
[tex]150y=1500[/tex]
[tex]y=10[/tex]
We find that Owen bought [tex]10[/tex] cans of frozen dinners.
If we replace the value of ''y'' in (I) :
[tex]x+10=19[/tex]
[tex]x=9[/tex]
We find that Owen bought [tex]9[/tex] cans of soup.
Complete the proof for the following conjecture.
Given: AC = BD
Prove: AB = CD
Statements Reasons
1. 1.
2. 2.
3. 3.
4. 4.
Please help!!!
Answer:
Statements Reasons
AC+CD=AD and AB+BD=AD Segment Addition Postulate
AC+CD=AB+BD Transitive/Substitution Property
AC=BD Given
BD+CD=AB+BD Substitution Property
CD=AB Subtraction Property
AB=CD Symmetric Property
Step-by-step explanation:
By segment addition postulate, we can say the following two equations:
AC+CD=AD and AB+BD=AD.
By either substitution/transitive property, you can say AC+CD=AB+BD.
You are given AC=BD, so we use substitution and write AC+CD=AB+AC.
After using subtraction property (subtracting both sides by AC), you obtain CD=AB.
By symmetric property, you may say AB=CD.
So let's write it into the 2 column-proof you have there:
Statements Reasons
AC+CD=AD and AB+BD=AD Segment Addition Postulate
AC+CD=AB+BD Transitive/Substitution Property
AC=BD Given
BD+CD=AB+BD Substitution Property
CD=AB Subtraction Property
AB=CD Symmetric Property
Properties/Postulates used:
Transitive property which says:
If a=b and b=c, then a=c.
Substitution property which says:
If a=b, then b can be substituted(replaced with) for a.
Subtraction property which says:
a=b implies a-c=b-c.
Segment Addition Postulate says:
If you break a segment into two smaller pieces then the measurement of that segment is equal to the sum of the smaller two segments' measurements.
Study the following distribution chart
Answer:
40 and 70
Step-by-step explanation:
The mode is the most occurring value in a data set. In this data set, the mode is 40 and 70 because
To make a greeting card, Bryce used 1/8 sheet of red paper, 3/8 sheet of green paper, and 7/8 sheet of white paper. How many sheets of paper did Bryce use?
Please help me out!!!!!!!!!!!!!!!!!!
Answer: true
Step-by-step explanation: x-values are not repeated
Answer:
True
Step-by-step explanation:
For a relation to be a function, each value of x in the domain maps to exactly one unique value of y in the range.
This is the case here, thus this is a function.
A checking account has the following balances:
1. Check register balance of $459.70
2. Bank statement balance of $562.43
3. Two outstanding checks of $76.40 and $29.83
4. Service charge of $3.50.
What is the true balance?
Answer:
The true balance is $562.43
Step-by-step explanation:
1. Check register balance of $459.70
2. Bank statement balance of $562.43
3. Two outstanding checks of $76.40 and $29.83
4. Service charge of $3.50.
The working is shown like -
Subtract the service charge from check register balance
[tex]459.70-3.50=456.20[/tex] dollars
Then add the outstanding checks to this
[tex]456.20+76.40+29.83=562.43[/tex] dollars
Hence, the true balance is $562.43.
Answer:
THIS ANSWER IS CORRECT!!
Step-by-step explanation:
What is the true balance?
$456.20
You have the Check registar balance which includes your outstanding checks. You minus the $3.50 fee to get the true balance.
A newborn calf weighs about 90 pounds. Each week, it's weight increases by 5%. a) If we were to graph this growth, would it be a linear or exponential function? b) How do you know? Support your answer.
Answer: exponential because it's a ratio :)
Step-by-step explanation:
Answer:
Exponential. Because of its cumulative nature (gain of weight) and its growth rate (5%).
Step-by-step explanation:
It's a growth graph given by an exponential function because every gain of weight is cumulative to the earlier week's. This function can be modeled this way since the rate of growth (5%) was given, which is added by 1 then plugged into the formula. [tex]y=90(1.05)^{t}[/tex] Besides, this model is identical to Interest Composite Rate, which follows the same basic structure, namely Cumulative Growth at a given rate.
Find (f + g)(x) and (f g)(x) for f(x) = 6x2 + 5 and g(x) = 7 – 5x.
A.
(f + g)(x) = 6x2 + 5x – 12
(f- g)(x) = 6x2 – 5x – 2
B.
(f + g)(x) = 6x2 – 5x + 12
(f- g)(x) = 6x2 + 5x – 2
C.
(f + g)(x) = 6x2 + 0x + 7
(f- g)(x) = 6x2 + 10x – 7
D.
(f + g)(x) = 6x2 + 5x – 2
(f- g)(x) = 6x2 – 5x + 12
Answer:
B. (f + g)(x) = 6x² – 5x + 12
(f- g)(x) = 6x² + 5x – 2
Step-by-step explanation:
1) (f +g)(x) = f(x) + g(x) = (6x² + 5) + (7 -5x) = 6x² -5x +12
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2) (f-g)(x) = f(x) -g(x) = (6x² + 5) - (7 -5x)
= 6x² +5 -7 +5x . . . the minus sign outside multiplies all the terms inside
= 6x² +5x -2
In this Mathematics problem, we are asked to add and subtract given functions f(x) and g(x). The sum results in (f+g)(x) = 6x^2 - 5x + 12 and the difference results in (f-g)(x) = 6x^2 + 5x - 2.
Explanation:The question is asking about finding the sum (f+g) and the difference (f-g) of two functions, f(x) and g(x). To answer this, we add (or subtract) the two given functions together.
For the function (f+g)(x), you simply add f(x) = 6x2 + 5 and g(x) = 7 - 5x together to get (f+g)(x) = 6x2 - 5x + 12. Thus, the sum of the two functions is 6x2 - 5x + 12.
Similarly, for the function (f-g)(x), we subtract g(x) from f(x) to get (f-g)(x) = 6x2 + 5x - 2. Thus, the difference of the two functions is 6x2 + 5x - 2.
So, the correct answer is B, (f+g)(x) = 6x2 - 5x + 12 and (f-g)(x) = 6x2 + 5x - 2.
Learn more about Function Addition and Subtraction here:https://brainly.com/question/33593405
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A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The sterilization tank contains 120 gal of a solution of 4% ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach should be 6% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?
Answer:
2.5 gal
Step-by-step explanation:
let be x = galons of solution to be drained and replace with bleach
so, we have to substract to the current solution of bleach 0.04*120, x gallons that have a concentration of 0.04 x
and also, we have to add the same gallons of bleach to the solution, that is x
and have to obtain a final concentration of 0.06*120
we can express the problem with the follow equation:
0.04*120 - 0.04*x + x = 0.06*120
solving the equation for x:
4.8+0.96*x=7.2
0.96*x=7.2-4.8
0.96*x=2.4
x =2.5 gallons