The width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches. What are the length and width of the rectangle? A. length = 20 inches, width = 17 inches B. length = 17 inches, width = 14 inches C. length = 10 inches, width = 7 inches D. length = 34 inches, width = 10 inches
To find the length and width of a rectangle given its area and the relationship between its dimensions, set up and solve an equation by following the step-by-step process.
Explanation:Given: The width of a rectangle is 3 inches less than its length and the area is 340 square inches.
To solve: Let the length be 'x' inches, then the width is 'x - 3' inches. Set up the equation 'x(x - 3) = 340', solve for 'x' to find the length and width.
Step-by-step:
Express the area as a product of the length and width: 'x(x - 3) = 340'.Expand and rearrange the equation: 'x^2 - 3x - 340 = 0'.Factor the quadratic equation: '(x + 17)(x - 20) = 0'.Solve for 'x': 'x = -17' or 'x = 20'. Since length cannot be negative, the length is 20 inches.Calculate the width: '20 - 3 = 17 inches'.Solve the equation x^16 – 2x^15 – x^14 + 4x^13 – x^12 – 2x^11 + x^10 = 0 in the real number system.
a) x = 0 with multiplicity 10, x = –1 with multiplicity 4, x = 1 with multiplicity 2
b) x = 0 with multiplicity 10, x = –1 with multiplicity 3, x = 1 with multiplicity 3
c) x = 0 with multiplicity 10, x = –1 with multiplicity 2, x = 1 with multiplicity 4
d) x = –1 with multiplicity 2, x = 1 with multiplicity 4
Answer:
C:x = 0 with multiplicity 10, x = –1 with multiplicity 2, x = 1 with multiplicity 4
Consider a game in which a coin will be flipped three times. for each heads you will be paid $100. assume that the coin comes up heads with probability 4/5.
If a student scored 82 points on a test where the mean score was 78.2 and the standard deviation was 6.7. the student's z score is .
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24 cubic units what is the height of the cylinder
the answer is c.6 i just took the test.
how can you be able to find an area
The cost for a pack of 4 padlocks is $17.60 . Find the unit price in dollars per padlock. If necessary, round your answer to the nearest cent.
Answer:
18.00
Step-by-step explanation:
60+40=100
True or False 68oz < 4lb 6oz
Answer:true!!!
Step-by-step explanation:
Two years ago Carol's living expenses were $ 1200 $ 1200 per month. This year the same items cost Carol $ 1400 $ 1400 per month. What was the annual inflation rate for the past two years?
The population of a small town decreased from 983 to 901. What is the percent decrease, to the nearest tenth of a percent?
The population of the small town percent decreased by approximately 8.4%.
To find the percent decrease in the population of the small town, we can use the formula for percent decrease:
Percent Decrease = [(Initial Value - Final Value) / Initial Value] * 100
Given that the initial population was 983 and the final population was 901, we can plug these values into the formula:
Percent Decrease = [(983 - 901) / 983] * 100
Now, calculate the numerator:
Percent Decrease = [82 / 983] * 100
Divide and multiply:
Percent Decrease = 0.0835 * 100
Now, calculate the percent decrease to the nearest tenth of a percent:
Percent Decrease ≈ 8.4%
So, the population of the small town decreased by approximately 8.4%.
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How do you solve 7(2-j)-5??
which of the following is the graph of the rational function? y=x^2+2x-8/x^2-9
A chord of a circle is a line segment connecting any point on the circle to the center of the circle.
Answer:
FALSE
Step-by-step explanation:
A chord of a circle is a line segment that connects two points on the circle.
Answer:
FALSE
Step-by-step explanation:
Sylvia is going to pick out a souvenir hat while she is on vacation. She knows the price of the hat will increase by 5% when she pays sales tax. She writes the expression h + 0.05h to find the total amount she will pay for the hat if it costs h dollars. Jin correctly writes another expression, 1.05h, that will also find the the total amount Sylvia will pay for the hat if it costs h dollars. Use the drop-down menus to explain what each part of Sylvia's and Jin's expressions mean.
Answer:
Step-by-step explanation:
Answer and step-by-step explanation:
Sylvia's expression is h+0.05h.
The variable h represents the cost of the hat.
0.05 represents the 5% sales tax; 5% = 5/100 = 0.05.
0.05h represents the amount of tax paid on the hat. To find a percent of a number, we multiply the decimal form of the percent by the original amount.
The total cost is given by h+0.05h.
Jin's expression is 1.05h.
The variable h represents the cost of the hat.
1.05 represents 100% of the cost of the hat plus the additional 5% tax; 100+5 = 105%; 105% = 105/100 = 1.05.
Together the total cost is given by 1.05h.
Two secant segments intersect outside a circle as shown. What is the value of x?
what is the greatest common factor (gcf) of the numerator and denominator in the rational expression below? 7x+14/2x^2+x-6
a. -6
b. 7
c. x+2
d. 2x-3
Final answer:
The greatest common factor (GCF) of the numerator and denominator in the rational expression (7x+14)/(2x²+x-6) is x+2. Thus, option C is correct.
Explanation:
To find the greatest common factor (GCF) of the numerator and denominator of the given rational expression (7x+14)/(2x²+x-6), we need to factor both the numerator and the denominator separately.
For the numerator 7x+14, we can factor out a 7:
7x + 14 = 7(x + 2)
For the denominator 2x² + x - 6, we need to factor it as a quadratic expression. This can be done by finding two numbers that multiply to give -12 (the product of the coefficient of x² and the constant term) and add up to 1 (the coefficient of x). These numbers are 3 and -4, so the denominator can be factored as:
2x² + x - 6 = (2x - 3)(x + 2)
Now we can see that the common factor between the numerator and the denominator is x + 2. Therefore, the GCF is x + 2, which corresponds to option (c).
Which statements about the opposite of −12 are true? Select each correct answer. −12 and its opposite are on located on the same side of zero on a number line. The opposite of the opposite of −12 is −12 . The opposite of −12 is −112 . −12 and its opposite are located the same distance from zero on a number line.
there's more than 1 answer
The true statements about the opposite of -12 are that the opposite of the opposite of -12 is -12 and -12 and its opposite are located the same distance from zero on a number line. The opposite of -12 is +12.
Explanation:In mathematics, the opposite of a number is also called its additive inverse, which is the number that, when added to the original number, will result in zero. −12 and its opposite, +12, are indeed located on opposite sides of zero on a number line, not on the same side. The second statement is true, the opposite of the opposite of −12 is indeed −12. The third statement is incorrect, the opposite of −12 is +12, not −112. The fourth statement is also true, −12 and its opposite are both 12 units away from zero on a number line, so they're at the same distance from zero.
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if f(x) = 5x^3-2 and g(x)= 2x+1, find (f+g) (x).
The expression for (f + g)(x) is [tex]\rm 5x^3+2x-1[/tex] and this can be determined by using the arithmetic operations and the given data.
Given :
[tex]\rm f(x) = 5x^3-2[/tex][tex]\rm g(x) = 2x + 1[/tex]The following steps can be used in order to determine the value of (f + g)(x):
Step 1 - Write the given functions.
[tex]\rm f(x) = 5x^3-2[/tex] --- (1)
[tex]\rm g(x) = 2x + 1[/tex] --- (2)
Step 2 - Now, to determine the value of (f + g)(x), add both function f(x) and g(x).
f(x) + g(x) = (f + g)(x)
Step 3 - Substitute the value of f(x) and g(x) in the above expression.
[tex]\rm (f + g)(x) = 5x^3-2+2x+1[/tex]
Step 4 - Simplify the above expression.
[tex]\rm (f + g)(x) = 5x^3+2x-1[/tex]
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From the sample space sequals={1, 2, 3, 4,..., 15} a single number is to be selected at random. given event a, that the selected number is even, and event b, that the selected number is a multiple of 4, find p(upper a vertial line upper ba∣b).
The probability of randomly selecting an even number given that the number is a multiple of 4, or p(A|B), is 1.
Explanation:The question is asking for the conditional probability p(A|B), meaning the probability of event A (number is even) given that event B (number is a multiple of 4) has already occurred. In this sample space, there are 8 even numbers {2, 4, 6, 8, 10, 12, 14, 16} and 4 multiples of 4 {4, 8, 12, 16}. Therefore, the probability of picking an even number out of the ones that are multiples of 4 is as follows:
First, determine the probability of event A within event B by dividing the number of favorable outcomes (even numbers and multiples of 4) by the total outcomes of event B. In this case, all multiples of 4 are even numbers, so there are 4 favorable outcomes.
Calculating p(A|B): Number of instances where A and B occur together / Number of instances where B occurs = 4 / 4 = 1
Therefore, the probability of randomly selecting an even number given that the number is a multiple of 4, p(A|B), is 1.
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EXPERTS/ACE/GENIUSES HELP PLZ!!:)
( only #2 )
Explain as well!! Best answer will get brainlist... but make ur answer short and sweet plz.
(a) Volume of 1st cup = (1/3)pi *(4/2)^2 * 8 = 32/3 pi in^3
scoops = (2000/3)pi / ( 32/3) pi = 2000/32 = 62.5 = 63
(b) Volume of 2nd cup = (1/3)pi *(8/2)^2 * 8 = 128/3 pi in^3
scoops = (2000/3)pi / ( 128/3) pi = 2000/128 = 15.625 = 16
Ming says that 0.24 > 14 because 0.24 = 24. Which best explains Ming's error?
Answer:
Ming says that 0.24 > 14
1
4
because 0.24 = 24
2
4
. Which best explains Ming's error?
Step-by-step explanation:
A right triangle has legs that are 15 feet and 25 feet long. What is the length of the hypotenuse? Enter your answer as a decimal in the box. Round your answer to the nearest hundredth.
Diameter of a cylindrical tank is 9 feet and the height of a tank is 25 feet. Find the approximate volume of the cylindrical tank to the nearest hundredth place
C. 1,589.63 cubic feet
D. 2,325.26 cubic feet
E. 6,358.50 cubic feet
F. 3,489.27 cubic feet.
Solve the following word problem. A man travels from Town X to Town Y at an average rate of 50 mph and returns at an average rate of 40 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 45 mph. What is the distance from Town X to Town Y?
______ miles
Distance from Town X to Town Y = 100 miles
Distance = Speed x Time
Speed while going = 50 mph , Speed while returning = 40 mph
Let the time taken while going = t hours
So, the time taken while returning = t + 0.5 hours
Distance while going = Distance while coming backSo, 50 t = 40 ( t + 0.5)
50 t = 40x + 20
50 t - 40 t = 10x = 20
10 t = 20
t = 20 / 10 = 2
Hence, distance = 50 t = 40 ( t + 0.5 )
= 50 x 2 ; or 40 x 2.5 = 100
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The distance from Town X to Town Y is 180 miles. This is determined by setting up and solving an equation based on the given speeds and time difference.
Explanation:The subject of this question is Mathematics, specifically it is a problem in a genre called distance, speed, time problems. Let's denote the distance from Town X to Town Y as 'd' miles. The man covers this distance twice - once going and once coming back. The time he takes to travel from X to Y is d/50 and to travel back from Y to X is d/40.
So, the actual total time he spends travelling is (d/50 + d/40) hours. If he made the round trip at an average speed of 45 mph, he would take (2d/45) hours (distance = speed x time). Given that the actual journey took a 1/2 hour longer than this, we can create the following equation:
(d/50 + d/40) = 2d/45 + 1/2.
Solving this equation for 'd', we get d = 180 miles. So, the answer is that the distance from Town X to Town Y is 180 miles.
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The volume of a rectangular prism is (x3-3x2+5x-3), and the area of its base is (x -2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
To find the height of the rectangular prism, divide the volume by the area of the base.
Explanation:To find the height of the rectangular prism, we need to divide the volume by the area of the base. The formula for the volume of a rectangular prism is V = lwh, where l, w, and h represent the length, width, and height, respectively. The formula for the area of the base is A = lw.
In this case, the volume is given as (x3-3x2+5x-3) and the area of the base is (x -2). So, we need to divide the volume by the area of the base, which gives us:
(x3-3x2+5x-3)/(x -2).
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IF YOU ANSWER WITHOUT A PROPER ANSWER AND YOU JUST WANT POINTS YOUR ANSWER WILL BE REPORTED! 99 POINT QUESTION! So I want a full explanation, best answer gets to be the brainliest. How much is 457 - (-54) + 7700 * 325 = ? I feel generous today so I'm making this 99 points. Btw, this is my first question asked here on brainly.
The game called lotto sponsored by the louisiana lottery commission pays its largest prize when a contestant matches all 4 of the 41 possible numbers. assume there are 41 ping-pong balls each with a single number between 1 and 41. any number appears only once, and the winning balls are selected without replacement.
a. the commission reports that the probability of matching all the numbers are 1 in 101,270. what is this in terms of probability
Final answer:
The reported probability of 1 in 101,270 for matching all four lotto numbers is equivalent to a decimal probability of approximately 0.00000987.
Explanation:
The Louisiana Lottery Commission's lotto game entails participants matching all 4 numbers out of a pool of 41. The reported probability of achieving this feat is 1 in 101,270. To express this probability, we utilize the ratio of successful outcomes to total possible outcomes. Consequently, the probability of matching all four numbers is 1/101,270, equivalent to approximately 0.00000987 in decimal form. This minute probability underscores the challenging nature of the lotto game, highlighting the rarity of successfully predicting and matching the specified set of numbers within the given range.
Which graph correctly solves the system of equations below? x2 + y2 = 25 y = x + 1
Use the graph to find the local minimum and the local maximum for the given function.
In the interval [-3, 0] the local minimum is -16 and In the interval [0, 3], the local maximum is 4 and local minimum is -3.
What is Local Maxima and Local Minima?
The local maxima and minima are the input values for which the function gives the maximum and minimum output values respectively. The y - coordinate of local maxima is called local maximum and that of local minima is called as local minimum.
Given is a graph of a function.
In the graph the local maximum is the y - coordinate that has maximum value at any specific input. Similarly, local maximum is the y - coordinate that has minimum value at any specific input.
PART A
In the interval [-3, 0], the local minimum is -16
PART B
In the interval [0, 3], the local maximum is 4 and local minimum is -3.
Therefore, in the interval [-3, 0] the local minimum is -16 and In the interval [0, 3], the local maximum is 4 and local minimum is -3.
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There are 100 books in the library. There are non-fiction and fiction books. Write the fraction of the books that are fiction.