Answer:
= 1/5
Step-by-step explanation:
The reciprocal number results from dividing the number 1 by the origial number, by example:
Original number: a
reciprocal number: 1/a
In this case:
original number: 5
reciprocal number: 1/5
Evaluate the integral. from 1 to 3 [ ✓ x2 + 9 dx
An integral in calculus is a mathematical concept that can be used to represent an area or an expanded version of an area. The basic components of calculus are integrals and derivatives is[tex]-1/2*(t^2/2+18ln(t)-81/(2t^2))+C\\[/tex].
The terms antiderivative and primal are additional terms for integral. Something that is essential is crucial or required. If you are an essential member of the team, it signifies that you are necessary for the team to work. To complete the whole, an essential component is required. The term "essential" is almost a synonym in this context.
The set of functions (the antiderivative) whose derivative is the integrand is represented by the integral, which is referred to as an indefinite integral. Calculus' fundamental theorem connects the assessment of definite integrals to that of indefinite integrals.
From 1 to 3:
[tex]sqrt(x^2+9)=t+x\\x=(9-t^2)/(2*t)\\anddx=-(t^2+9)/(2t^2)dt\\= 1/2int (t^2+9)^2/t^3dt\\= -1/2int (t+18/t+81/t^3)dt\\= -1/2*(t^2/2+18ln(t)-81/(2t^2))+C\\[/tex]
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Four friends drove from their homes in four different cities to a class reunion.Who drove the fastest?MarenSafiyaTomasCam
Tomas drove the fastest with the speed of 70 miles per hour.
What is speed?
The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
The formula for calculating speed is -
Speed = Distance / Time
Maren travels 60 miles in 1 hour.
Speed of Maren = 60/1
Speed of Maren = 60 miles per hour
Safiya travels 120 miles in 3 hour.
Speed of Safiya = 120/3
Speed of Safiya = 40 miles per hour
Tomas travels 84 miles in 1.2 hour.
Speed of Tomas = 84/1.2
Speed of Tomas = 70 miles per hour
Cam travels 75 miles in 1.5 hour.
Speed of Cam = 75/1.5
Speed of Cam = 50 miles per hour
Therefore, the fastest driver is Tomas.
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the probability of randomly picking out a paperback book from a bookshelf is 2 over 5. what are the odds in favor of choosing a paperback book? a.) 3:2 b.) 2:7 c.) 2:3 d.) 2:5
Therefore , selecting a paperback book has an odd favor of 2:5, this probability problem's solution indicates that.
What does the process of probability mean?Calculating the probability of an event happening or a declaration being true is the focus of the mathematical field of probability theory. A chance is just a number between 0 and 1, with 1 denoting certainty and 0 roughly indicating the likelihood of an event occurring. Probability is a mathematical expression of the likelihood or probability that because an event will take place. The percentage ranges of 0% to 100% as well as the numerals 0 and 1 can be used to describe probabilities. the percentage of times an event occurs in a perfect collection of equally likely alternatives, out of all possible outcomes.
Here,
Given The likelihood of selecting a paperback book at random from either a bookshelf is 2/5, as stated.
In order to determine whether picking a paperback book is more likely to be strange,
So, using the information provided, we observe it.
that the odd favor of picking a paperback book is 2:1.
Option D is the proper choice.
Since selecting a paperback book has an odd favor of 2:5, this probability problem's solution indicates that.
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Answer:
2:3
Step-by-step explanation:
find an equation of the tangent line to the given curve at the specified point. y = e^x /x , at the point (1, e)
An equation of the tangent line to the given curve at the specified point will be y = e(x - 1) + e.
Given the equation y = e^x /x and the point (1, e), the goal is to find an equation of the tangent line at this point.
To do this, we need to find the derivative of the equation at the point (1, e). Taking the derivative with respect to x gives us:
y' = (e^x * (1 - 1/x) - e^x/x^2) / x^2
Since we are looking for the derivative at the point (1, e), we can plug in x = 1 to get the derivative at this point:
y' = (e - e/1) / 1^2
y' = e
Therefore, the equation of the tangent line at the point (1, e) is y = e(x - 1) + e.
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Sarah has a loyalty card good for a 20% discount at her local grocery store. What would her total in dollars and cents be, after the discount and before tax, if the total cost of all the items she wants to buy is $39. 25? Round to the nearest cent
If Sarah has a 20% discount, her total cost after the discount in dollars and cents be 31.40.
Therefore the answer is $31.40
Sarah has a 20% discount, so the percentage of the cost she needs to pay is
100 - 20 = 80%.
To calculate the total cost after the discount, we need to multiply the original total cost by the percentage of the cost Sarah needs to pay:
= $39.25 x 0.8
= $31.40
So, after the discount, Sarah would pay $31.40 before tax.
To round it to the nearest cent we have $31.40 so the answer is 31.40
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The owner of a popular coffee shop believes that customers who drink espresso are less likely to use their own cup compared with customers who drink coffee. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all espresso purchases and 50 receipts from all coffee purchases. For espresso purchases, 15 receipts showed that the customer used their own cup. For coffee purchases, 24 receipts showed the customer used their own cup. Let pEspresso= the true proportion of customers who drink espresso and use their own cup and pCoffeee = the true proportion of customers who drink coffee and use their own cup. The P-value for this significance test is 0.033. Which of the following is the correct conclusion for this test of the hypotheses
The owner should reject the null hypothesis since 15 < 24. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.
The owner should reject the null hypothesis since 0.033 < 0.05. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.
The owner should fail to reject the null hypothesis since 15 < 24. There is not convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.
The owner should fail to reject the null hypothesis since 0.033 < 0.05. There is not convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup
Correct option is: b
The owner should reject the null hypothesis since 0.033 < 0.05. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.
This can e solved using the concept of null-hypothesis.
What is null-hypothesis?Using a single observable variable to compare two sets of observed data and measurable phenomena, the null hypothesis is a common statistical theory that contends that no statistical link and significance exists.
A hypothesis that a link of some sort exists between the variables is where scientists start their inquiry. The alternative, known as the null hypothesis, claims that there isn't any such link. Despite its uninteresting appearance, null hypothesis is a crucial component of research.
The correct hypotheses to test the owner's claim is as follows:
H0: pExpress - pCoffee = 0
Ha: pExpress - pCoffee < 0
Since p-value = 0.0330 < 0.05, we reject the null hypothesis.
Thus, the correct option for this hypothesis test is:
The owner should reject the null hypothesis since 0.033 < 0.05. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.
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Since 0.033 < 0.05, the owner should reject the null hypothesis. The genuine percentage of customers who drink espresso and bring their own cups is clearly lower than the true percentage of customers who drink coffee and bring their own cups.
What is the null hypothesis?The null hypothesis is a widely used statistical theory that asserts that no statistical relationship and significance exists when two sets of observed data and measurably occurring occurrences are compared.
Scientists begin their investigation with the presumption that there is some form of relationship between the factors. The alternative, often known as the null hypothesis, contends that such a connection doesn't exist. The null hypothesis, although appearing dull, is an essential part of the research.
The following are the proper assumptions to test the owner's assertion:
H0: pExpress - pCoffee = 0
Ha: pExpress - pCoffee < 0
Since p-value = 0.0330 < 0.05, we reject the null hypothesis.
Thus, the correct option for this hypothesis test is:
Since 0.033 < 0.05, the owner should reject the null hypothesis. There is strong proof that the actual percentage of consumers who order an espresso and bring their own cups is far lower than the actual percentage of customers who order coffee and bring their own cups.
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What are the solutions of x4 − 10x2 9 0?
The solutions are x = ±1.73, ±3.87.
Given equation: x4 − 10x2 + 9 = 0
Rewrite equation as (x2 - 9)(x2 + 1) = 0
Set each factor equal to 0 and solve for x
x2 - 9 = 0
⇒ x2 = 9
⇒ x = ±3.87
x2 + 1 = 0
⇒ x2 = -1 ⇒
x = ±1.73
The given equation is x4 − 10x2 + 9 = 0. This can be rewritten as (x2 - 9)(x2 + 1) = 0. By setting each factor equal to 0 and solving for x, we get x2 - 9 = 0 which implies x2 = 9 and x = ±3.87. Similarly, x2 + 1 = 0 implies x2 = -1 and x = ±1.73. Therefore, the solutions of x4 − 10x2 + 9 = 0 are x = ±1.73, ±3.87.
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your favorite restaurant has a promotion where you can win free food. you will roll 2 dice. the sum of the 2 dice will determine which prize you receive. 2-column table with 11 rows. column 1, outcome, entries 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. column 2, probability, entries startfraction 1 over 36 endfraction, startfraction 2 over 36 endfraction, startfraction 3 over 36 endfraction, startfraction 4 over 36 endfraction, startfraction 5 over 36 endfraction, startfraction 6 over 36 endfraction, startfraction 5 over 36 endfraction, startfraction 4 over 36 endfraction, startfraction 3 over 36 endfraction, startfraction 2 over 36 endfraction, startfraction 1 over 36 endfraction. which scenario uses the addition rule for mutually exclusive events? p(rolling a sum of 4) p(rolling a sum of 4 or rolling a sum of 5) p(rolling a sum of 12 or rolling a double 6) p(rolling a sum of 11 and rolling a sum of 12)
Answer: P(rolling a sum of 4 or rolling a sum of 5)
Step-by-step explanation: edge2023
The scenario that uses the addition rule for mutually exclusive events is:
p(rolling a sum of 4 or rolling a sum of 5) = p(rolling a sum of 4) + p(rolling a sum of 5)
This is because the events "rolling a sum of 4" and "rolling a sum of 5" are mutually exclusive, meaning that they cannot occur at the same time. Therefore, the probability of either event occurring is the sum of their individual probabilities.
The probability of rolling a sum of 4 is 3/36, and the probability of rolling a sum of 5 is 4/36. The addition rule states that the probability of rolling a sum of 4 or 5 is the sum of their individual probabilities: 3/36 + 4/36 = 7/36
The other scenarios do not use the addition rule for mutually exclusive events:
p(rolling a sum of 4) is a single event and does not involve a second event.
p(rolling a sum of 12 or rolling a double 6) although the two events are mutually exclusive, it's not the sum of their individual probabilities.
p(rolling a sum of 11 and rolling a sum of 12) these events are not mutually exclusive, they can happen at the same time, so it's not the sum of their individual probabilities.
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Solve each triangle using the Law of Cosines.
What do I put in the boxes?
1. The faculty members at McAdenville High School want to determine whether there are enough students to have a Winter Formal. Sixty-three of the 150 students surveyed said they would attend the Winter Formal. Construct and interpret a 99% confidence interval for p.
The 99% confidence interval is (0.3162, 0.5238). We are 99% confident the true proportion of students attending the Winter Formal is between 31.62% and 52.38%. The 99% confidence interval is (0.3162, 0.5238). There is a 99% chance that a randomly selected student who will attend the Winter Formal lies between 31.62% and 52.38%. The 99% confidence interval is (0.3162, 0.5238). Ninety-nine percent of all samples of this size will yield a confidence interval of (0.3162, 0.5238). The 99% confidence interval is (0.4762, 0.6838). We are 99% confident that the true proportion of students attending the Winter Formal is between 47.62% and 68.38%. The 99% confidence interval is (0.4762, 0.6838). Ninety-nine percent of all samples of this size will yield a confidence interval of (0.4762, 0.6838).
The first statement is correct. The 99% confidence interval is (0.3162, 0.5238). We are 99% confident the true proportion of students attending the Winter Formal is between 31.62% and 52.38%. However, the rest of the statements are incorrect.
"There is a 99% chance that a randomly selected student who will attend the Winter Formal lies between 31.62% and 52.38%." is incorrect, this statement is about a probability of a single student, but the confidence interval is about a probability of the whole population.
"Ninety-nine percent of all samples of this size will yield a confidence interval of (0.3162, 0.5238)." is correct, this statement is true, but it doesn't add any additional information.
"The 99% confidence interval is (0.4762, 0.6838)." is incorrect, this value is not the correct confidence interval.
"We are 99% confident that the true proportion of students attending the Winter Formal is between 47.62% and 68.38%." is incorrect, this statement is not true, as the confidence interval is not (0.4762, 0.6838) but (0.3162, 0.5238)
"Ninety-nine percent of all samples of this size will yield a confidence interval of (0.4762, 0.6838)." is incorrect, as this is not the correct confidence interval.
In conclusion, the faculty members at McAdenville High School can be 99% confident that the true proportion of students who will attend the Winter Formal is between 31.62% and 52.38%.
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Which expression is equivalent to StartFraction b Superscript negative 2 Baseline OvWhich expression is equivalent to (StartFraction (2 a Superscript negative 3 Baseline b Superscript 4 Baseline) squared Over (3 a Superscript 5 Baseline b) Superscript negative 2 Baseline EndFraction) Superscript negative 1
On solving the provided question, we can say that the value of the expression will be as - [tex]1/ ( 36a^4b^{10} )[/tex]
what is expression?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
here,
the expression is -
[ [tex][( 2a{-3}b^4)^2 / (3a^5b){-2}]^{-1}[/tex] ]
[tex][( 1 /2a{-3}b^4)^2 (3a^5b){2}]^{-1}[/tex]
[tex]1/ ( 36a^4b^{10} )[/tex]
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What are types of solutions?
There are three main types of solutions found in mathematics for a given problem or equation: No solution, Unique solution, and Infinitely many solutions.
Solutions in mathematics are a set of values that can be assigned to the variables of an equation or a system of equations so that it holds true. In other words, it is a set of values that satisfies the equation or system of equations.
Types of solutions:
No solution: In this situation, there is no set of values that can be assigned to the variables of an equation or system of equations so that it holds true.
Unique solution: In this situation, there is only one set of values that can be assigned to the variables of an equation or system of equations so that it holds true.
Infinitely many solutions: In this situation, there are infinitely many sets of values that can be assigned to the variables of an equation or system of equations so that it holds true. This situation arises when the given equation is not independent.
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The sizes of seven of the exterior angles of an octagon are 42˚, 110˚, 13˚, 67˚, 55˚, 11˚ and 53˚. Work out the size of each of the eight interior angles.
The eight interior angle based on the information given will be 728°.
How to calculate the angle?From the information, the sizes of seven of the exterior angles of an octagon are 42˚, 110˚, 13˚, 67˚, 55˚, 11˚ and 53˚ and.we.wany to eork out the size of each of the eight interior angles
In this case, it should be noted the octagon has with sides. This will be Illustrated as:
= (n - 2) × 180
= (8 - 2) × 180
= 1080
The eight interior angle will be:
= 1080 - (42 + 110 + 13 + 67 + 55 + 11 + 54)
= 1080 - 352
= 728
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A student is assessing the correlation between the average number of hours of internet browsing and the average score on a math test. The table below shows the data:
Number of hours of internet browsing
(x) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Score on math test
(y) 95 94 93 92 91 90 89 88 87 86
Part A: Is there any correlation between the average number of hours of internet browsing and the average score on the math test? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What do the slope and y-intercept of the plot indicate? (3 points)
1. There is a correlation that exists between the average number of hours of internet browsing and the average score on the math test.
2. The function that best fits the data is: Y = f(X)
3. The slope and the intercept tells us that a student would be at their best in a test if they spent 0 hours browsing.
How to find the correlation in the data set1. The correlation that exists in this data set tells us that as a person spends more time on the computer, they would spend less time on their test preparation. This would eventually affect their score.
When the student did not browse the internet, they had their highest score in math. As they started to spend more time on the internet, the score started to drop.
2. The function is given as
math test score Y = function of X: hours spent browsing the internet
this is written mathematically as:
Y = f(X)
3. The Y intercept is at the point where the student spent 0 hours browsing. this is the point where they did their best in this test. This tells us that if a student spent 0 hours on the internet, they would do their best in the test.
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Last summer, there were 888 houses for sale in Neil's town. The other 37 houses in the town were not for sale. What percentage of the houses in Neil's town were for sale last summer?
Answer:
96% of the houses were up for sale.
Step-by-step explanation:
Total number of houses
888 = 37 = 925
888 / 925 = .96
You change a decimal into a percent by multiplying by 100%
.96 x 100% = 96%
Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.25 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?
4 jars
5 jars
10 jars
Answer: I'm pretty sure there was suppose to be a 4th option that is not included here, none of these are correct, Lorraine can fill 8 jars.
Step-by-step explanation: First, we need to convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.
Then we divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.
⚠️Please verify inthe comments if there was indeed a 4th option⚠️
Answer:
8
Step-by-step explanation:
convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.
Then divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.
A company models its net income, in thousands of dollars, with the function f(x) = 9x2 – 54x – 144, where x is the number of units of its product sold. How many units of its product does the company need to sell in order for the net income to equal $0?
The quantity of units that the company needs to sell in order for the net income to equal $0 would be = 8.
How to calculate the quantity of units using quadratic equations?The net income of the company in thousands of dollars is represented with the function;
f(x) = 9x2 – 54x – 144,
It can be simplified as follows:
f(x) = 9(x² - 6x - 16)
Then:
f(x) = 9[(x + 2)(x - 8)]
It has a net income equals to 0 when:
f(x) = 0, hence:
x + 2 = 0 -> x = -2.
x - 8 = 0 -> x = 8.
The positive value and not a negative shows that there are amount of products sold which should be = 8.
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Circle O shown below has a radius of 30 inches. To the nearest tenth of an inch,
determine the length of the arc, x, subtended by an angle of 1.8 radians.
30 inches
0=1.8 rad
Answer:
To the nearest tenth of an inch, the length of the arc is 54.0 inches
Step-by-step explanation:
To determine the length of the arc, x, we need to use the formula for arc length, which is:
arc length = radius * angle (in radians)
Therefore,
arc length = 30 inches * 1.8 radians = 54 inches
76 pencils come in a box. If 4 teachers share 3 boxes equally, how many pencils does each teacher
receive?
Answer:
The total number of pencils is 76 x 3 = 228 pencils
If each teacher receives an equal amount of pencils, we can divide the total number of pencils by the number of teachers to find how many pencils each teacher receives:
228 pencils / 4 teachers = 57 pencils/teacher
Each teacher receives 57 pencils.
Is 1 a factor of all number?
1 is a factor of every whole number. Every whole number can be evenly divided by 1, so 1 is a factor of every whole number.
1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.
1 is the greatest factor of itself and the smallest factor of any other number.
There are some properties of factors one:
Every whole number is the product of 1 and itself so, each number is a factor of itself.
Every number is a factor of zero and 1 is the smallest factor of every number, and multiple and the greatest factor of a multiple is the multiple itself.
Every number other than 1 has at least two factors, namely the number itself and 1.
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jake sold 28 tickets to the school fair, and jeanne sold 21 tickets. what is the ratio,in simplest form
The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne in the simplest form, will be 4:3
The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 28:21.
To simplify this ratio, we can divide both numbers by their greatest common factor (GCF). The GCF of 28 and 21 is 7.
So, the simplified ratio is 28/7: 21/7 = 4:3
So the ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 4:3 in simplest form.
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State the domain of A. (Assume the length of the rectangle is longer than its width. Enter your answer in interval notation) 14. 0/2 points Previous Answers CalcETS 1.1.058. Find a formula for the described function. A rectangle has area 36 m2 Express the perimeter of the rectangle as a function of the length L of one of its sides PIL) = || State the domain of P. (Assume the length of the rectangle is larger than its width. Enter your answer using interval notation.) Submit Answer 15. 0/2 points Previous Answers CalcET8 1.1.061. Find a formula for the described function. An open rectangular box with volume 3 m has a square base Express the surface area SA of the box as a function of the length of SA 26 Xma State the domain of SA. (Enter your answer in interval notation.)
Previous question
The answer is CalcETS 1.1.058.
What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel. Since, a rectangle is a 2-D shape, it is characterized by two dimensions, length, and width. Length is the longer side of the rectangle and width is the shorter side.In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
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The Total number of cherries on a plate, in a cup, and in a bowl is 780. The plate contains 145 cherries. The number of cherries in the bowl is 4 times the total number of cherries on the plate and in the cup. How many cherries are in the cup?
Triangle FGHFGH is formed by connecting the midpoints of the side of triangle CDECDE. The lengths of the sides of triangle CDECDE are shown. What is the length of \overline{FH} FH
The length of the side overline(FH) when Triangle FGH is formed by connecting the midpoints of the side of triangle CDE is 5.
This problem can be solved using the Median Line theorem. The Median Theorem states that the medians of a triangle intersect at a point called the centroid which is two-thirds of the distance from the vertices to the midpoint of the opposite sides. This is what we will use to solve the given problem.
From the problem, we can conclude that points H and F are the midpoints of the sides CE and CD respectively. Hence, line HF is the median line of the triangle CDE. So, the length of the line HF/FH is going to be -
= (1/2)*ED
= 5
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Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. x g(x) 0 2 5 4 10 6 The slope of f(x) is greater than the slope of g(x). The slope of f(x) is less than the slope of g(x). The slope of f(x) is equal to the slope of g(x). The slope of g(x) is undefined.
The slope of a line f(x) exceeds the slope of a line g. (x). As a result, option A is the right response.
What is the slope of a line's equation?A line's slope or gradient is a number that defines both its direction and its steepness. The slope may be calculated using the following formula: slope = (y2-y1)/ (x2-x1). The coordinate points on the equation of line g(x) are (0, 2), (5, 4) and (10, 6) while the coordinate points on the equation of line f(x) are (3, 1) and (0, -1).
The slope of the line g(x) is now (4-2)/(5-0) =2/5.
The slope of a line f(x) is (-1)/. (0-3)
=2/3
The slope of a line f(x) exceeds the slope of a line g. (x). As a result, option A is the right response.
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3x +5y=-25
Y=-3 over 5 x + 3
The slope-intercept form of the given equation is y = -3/5x - 5
Writing equations in slope-intercept formFrom the question, we are to write the given equation in the slope-intercept form
From the given information,
The given equation is
3x + 5y = -25
The general form for the slope-intercept form of the equation of a line is
y = mx + b
Where m is the slope
and b is the y-intercept
Writing the equation in the slope-intercept form of a line
3x + 5y = -25
5y = -3x - 25
Divide through by 5
5y/5 = -3/5x - 25/5
y = -3/5x - 5
The equation is y = -3/5x - 5
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26 over 100 in simplest form
Find the solutions of the given equation.
25x² +64 = 289
O A. x =
-√√3, √3
OB.
x =
-9,9
OC.
x = -3, 3
O D. x = -3√3, 3√/3
The solution of the given equation is x = -3,3. Hence option C is the correct option.
What is a quadratic equation?
A quadratic equation is any equation in algebra that can be rearranged in a standard form where x represents an unknown value and a, b, and c represent known numbers, with a ≠ 0.
The number of solutions of a quadratic equation is 2. The degree of a quadratic equation is also 2.
Given equation is
25x² +64 = 289
Subtract 64 from both sides of the equation:
25x² +64 -64 = 289 -64
25x² = 225
Divide both sides by 25:
25x²/25 = 225/25
x² = 9
Take square root on both sides:
√x² = √9
x = ±3.
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two arithmetic sequences and both begin with and have common differences of absolute value , with sequence increasing and sequence decreasing. what is the absolute value of the difference between the st term of sequence and the st term of sequence ?
The difference between the 51st term of a and the 51st term of b is 1000.
the nth term of an arithmetic series is given by [tex]a_{n}= a_{0}+(n-1)*d[/tex]
where [tex]a_{0}[/tex] is the first term of the arithmetic series, [tex]a_{n}[/tex] is the nth term of the series and d is the common difference
Given that,
[tex]a_{0}=b_{0}=30[/tex]
Common difference of both series that have absolute value = 10
common difference of series a is 10 as this series is increasing
similarly, the common difference of series b is -10 as it is decreasing
Putting the values in the above equation we get:
[tex]a_{51}= a_{0}+(n-1)*d\\[/tex]
=> 30 + (51-1)*10
=> 30 + 500 = 530
Thus, the value of [tex]a_{51}[/tex] is 530.
[tex]b_{51}= b_{0}+(n-1)*d\\[/tex]
=> 30 + (51-1)*-10
=> 30 -500 = -470
Thus, the value of [tex]b_{51}[/tex] is -470.
so we have to find the value of [tex]a_{51}-b_{51}[/tex] which is 530 - (-470) =530 +470 =1000
Therefore, The difference between the 51st term of a and the 51st term of b is 1000.
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