The solution to the algebraic expression (2*3)*5 using a*b= a+b -2ab is; 68
How to solve Algebraic Expressions?Algebraic expressions are defined as the idea of expressing numbers using letters or alphabets without truly specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as a, b, c etc. These letters are usually referred to as variables.
We are given the format for the algebraic expression as;
a*b = a + b - 2ab
Thus, we can solve the expression (2*3)*5 as;
(2*3) = 2 + 3 - 2(2*3)
= -7
(-7 * 5) = -7 + 5 - 2(-7 * 5)
= -2 + 70
= 68
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,y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being
C(X,Y) is a statement that means a student X from the school is enrolled in class Y which is one of the classes offered by the school.
C(X,Y) is a statement that means a student X from the school is enrolled in class Y which is one of the classes offered by the school. The domain for X consists of all students in the school and the domain for Y consists of all classes being offered. To explain this statement further, firstly it should be noted that the statement is saying that a student (X) is enrolled in a class (Y). Secondly, the term “domain” refers to the set of all possible values that can be used for a given variable. In this case, the domain for X consists of all students in the school, while the domain for Y consists of all classes being offered at the school. Therefore, the statement C(X,y) is saying that a student from the school is enrolled in one of the classes offered by the school.
The complete question: Let C(X,Y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being
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Trina and Jessie went on a vacation to Hawaii. Trina went scuba diving and reached an elevation of -85.6 meters, which is below sea level. Jessie went hang-gliding and reached an altitude of 87.9 meters which is above sea level who is closer the the surface of the ocean
Answer:
Trina
Step-by-step explanation:
Trina is 85.6 below sea level
Jessie is 87.9 above
distance wise 85.6 is shorter
Special triangles
Find X and Y
The required values of x,y for the two triangles are (15√2,15√2) & (√10,2√5)
What is the Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c2.
Given here : Two special triangles
1) Clearly the given triangle is a right isosceles triangle as a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.
Thus x=y
Now using pythagoraes theorem we get
[tex]x^2+x^2=30^2\\2x^2=900\\x^2=450\\x=15\sqrt{2}[/tex]
Thus x=y=15√2
2) Again the given triangle is an isosceles triangle and thus x=√10
[tex]\sqrt{10}^2+\sqrt{10}^2 =y^2\\y^2=20\\y=2\sqrt{5}[/tex]
Hence, The required values of x,y for the two triangles are (15√2,15√2) & (√10,2√5)
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For merging two sorted lists of sizes m and n into a sorted list of size m+n, we required comparisons of
A O(m+n)
B O(m)
C O(n)
D O(logm + logn)
The merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons.
The merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons. This is because we must compare each element in both lists in order to sort them. So a total of m+n comparisons are required in the worst case scenario.
This can be visualized by using a formula: n + m = m+n. This formula can be used to calculate the total number of comparisons required.
For example, if m = 10 and n = 15, then 10 + 15 = 25. This means that 25 comparisons would be required in order to sort the two lists.
Thus, the merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons. This is because we must compare each element in both lists in order to sort them.
The merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons.
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Question 1 10 pts In Trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. The reference triangles always have a leg perpendicular to the [Select] , the hypotenuse is (Select] and O is the angle adjacent to the (Select] D Question 2 10 pts In Exploration 4.1.1 problem 3, which is the strongest answer on why the equation is or is not an identity? Is an identity because the equation was derived from the general quadratic equation so it always works. Is an identity because the equation always finds the zeros for a quadratic. Is not an identity because the equation sometimes results in complex solutions. Is not an identity because the equation only works for finding zeros for quadratics.
The equation is an identity because it always works to find the zeros of a quadratic equation regardless of the coefficients.
The equation in Exploration 4.1.1 problem 3 is an identity because it was derived from the general quadratic equation [tex](ax^2 + bx + c = 0)[/tex]. Therefore, it always works when given the coefficients of a quadratic equation. This is demonstrated by using the formula for the quadratic equation, which is [tex]x = (-b ±√(b^2 - 4ac))/2a[/tex]. Plugging in the coefficients of a quadratic equation, the result is always the zeros of the quadratic equation. For example, for the equation[tex]6x^2 - 4x + 3 = 0[/tex], the zeros are found by plugging in a = 6, b = -4, and c = 3 into the formula. This gives us[tex]x = (-(-4) ±√((-4)^2 - 4(6)(3))/2(6) = (4 ±√(16 - 72))/12 = (4 ±√(-56))/12 = (4 ±√(7i))/12[/tex]which corresponds to the two zeros of the equation,[tex]x = -2 ± 3i[/tex]. This demonstrates that the equation is an identity because it always works to find the zeros of a quadratic equation regardless of the coefficients.
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Jabari needs a new refrigerator for his home. He finds one he likes for $780. If he borrows the amount at 7% interest, how much does Jabari owe if he plans to pay off the loan in 25 weeks?
The total amount that he will owe after the loan period of 25 weeks is; $806.25
How to calculate the Simple Interest?The formula to calculate simple interest is;
I = PRT/100
Where;
P is principal
R is rate
T is time
We are given;
P = $780
R = 7%
T = 25 weeks = 25/52 years
Thus;
I = (780 * 7 * 25/52)/100
I = $26.25
Total payoff = $780 + $26.25
= $806.25
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what is a pythagorean tripe using Euclids rule?
A Pythagorean triple using Euclid's rule is (3, 4, 5).
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Given:
Pythagorean triples consist of the three positive numbers a, b, and c, where a²+b² = c².
The symbols for these triples are (a, b, c).
Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.
The example of triplets is (3,4,5).
Therefore, the example of triplets is (3,4,5).
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Suppose that the demand and price for a certain model of a youth wristwatch are related by � = � ( � ) = 16 − 1.25 � p=D(q)=16−1.25q, where � p is the price (in dollars) and � q is the quantity demanded (in hundreds). Find the price at each level of demand
the price at each level of demand can be calculated by p = D(q) = 28 - 2.25q.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given, Given a function that defines the price for a certain model of a youth wristwatch is related by p = D(q) = 28 - 2.25q.
Thus,
A) The demand function is p = 28 - 2.25q.
When demand q is 0,
price is p = 28 - 2.25*0 = $28
B) When demand q is 400,
price is p = 28 - 2.25*4 = $19.
C) When the price is 10,
we have 10 = 28 - 2.25q or 2.25q = 18.
This gives q = 800 or 8 in hundreds
D) Graph of the demand function will have a vertical intercept of 28 (When q = 0, the value of p is 28) and a horizontal intercept of 12.44.
Here the first graph in part A is correct because it fits the intercepts
E) Supply function is p = 1.25q.
When the price is 0,
the quantity supplied is 0.
F) When the price is 17,
quantity supplied is 17 = 1.25q or q* = 13.6 of 1360 in hundreds
G) The vertical intercept is 0.
The graph will be similar to the one in option A because it matches both demand and supply equations.
H) Equilibrium occurs when demand and supply are equal
28 - 2.25q = 1.25q
28 = 3.5q
q* = 28/3.5 = 8 or 800 watches
price is p = 1.25*8 = $10.
therefore, the price at each level of demand is solved above.
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Complete question:
Let x be a number. Increasing x by twenty percent yields that same result as decreasing the product of four and x by five. What is x?
Possible Answers:
O 25/7
O 25/14
O 50/7
O 25/19
O 100/19
If x must be a number. The same outcome is obtained by increasing x by 20% as well as by decreasing that product of four with x by 5. x has the value of 25/14.
Explain about the inequalities of the equation?According to the issue, if we decreased that product of four with x by five, we would obtain the same result as increasing x by 20%. Finding equations for these two scenarios will allow us to set them equal and then solve for x.Let's look up an expression for raising x by 20%. This might be shown as x + 20%. x = x + 0.2x = 1.2x = 6x/5.
Let's come up with a formula to reduce that product of four with x by five. The first step is to determine the 4x, or the product of 4 and x.Then, since we need to reduce this by 5, we must remove 5 from 4x, which is equal to 4x - 5.The two expressions must now be set to be equal to each other.
6x/5 = 4x - 5
Add 6x/5 to both sides and subtract. To make 4x and 6x/5 have a similar denominator, we can rephrase 4x as 20x/5.
0 = 20x/5 - 6x/5 - 5 = 14x/5 - 5
0 = 14x/5 - 5
We can now increase both sides by five.
5 = 14x/5
Now that we have the reciprocal of 14/5, 5/14, we may multiply either sides by this number.
5(5/14) = (14x/5)(5/14) = x
25/14 = x
Thus, the solution is 25/14.
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A triangle has sides with lengths 8, 15, and 17.
a. Verify this is a Pythagorean triple.
Type your response in the space below.
b. Approximate the acute angles in this triangle. Round each angle to the nearest degree.
Type the answers in the boxes below.
The values 8, 15 and 17 is a Pythagorean triple and therefore a right angle triangle.
What is Pythagoras TripleA Pythagorean triple is a set of three positive integers, a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right-angled triangle, where c is the hypotenuse.
In this problem, we can we can check if the values are for a right angle triangle.
Assuming this is a right angle triangle which obeys Pythagoras theorem, the longest side will be the hypothenuse.
c = hypothenuse = 17a = leg = 15b = 8c² = a² + b²
17² = 15² + 8²
289 = 225 + 64
289 = 289
From the calculation above, the values of is a Pythagorean triple.
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a father is 7 times older than his son and his son is 24 years younger than his father how old is each now
The father age is now 168 years old and the son is now 24 years old.
Father's age = 7 times the son's age
7x = (Father's age) - (son's age)
7x = 168 - 24
7x = 144
x = 144/7
x = 24
Therefore, the father is 168 years old and the son is 24 years old.
The father is currently 168 years old and the son is 24 years old. This is because the father is seven times older than his son and 24 years older than his son.
The complete question is :
A father is seven times older than his son and his son is 24 years younger than his father. How old is each now?
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Help meeeee please
If the speed of a car, in miles per hour, is square root 20L
, where L is the length, in feet, of its skid mark, what was the speed of a car with skid mark 100 feet? Round your answer to one decimal place.
The speed of the car was _____ mph.
The speed of the car is 0.8 miles per hour when the skid mark is 100 feet.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, The speed of a car in miles per hour is √(20)L, Where 'L' is the length in feet of its skid mark.
We know, 1 mile is equal to 5280 feet.
So, The speed of the car is √(20)×(L/5280) miles.
Therefore, The speed of the car when the skid mark is 100 feet is,
= √(20)×(100/5280) miles.
= √20×0.019 miles.
= 0.8 miles per hour.
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Identify the lateral area and the surface area of a right rectangular prism with a 12 cm by 10 cm base and a height of 16 cm.
Options:
L = 352 cm2 ; S = 944 cm2
L = 704 cm2 ; S = 944 cm2
L = 704 cm2 ; S = 824 cm2
L = 352 cm2 ; S = 824 cm2
The answer is [tex]L = 624 cm^2; S = 944 cm^2[/tex] where L is the lateral area and S is the surface area of a right rectangular prism.
The lateral area of a right rectangular prism is given by the formula:
[tex]L = 2(lw + bh)[/tex]
where l and b are the length and width of the base, and h is the height of the prism.
The surface area is given by the formula:
[tex]S = 2(lb + bh + lh)[/tex]
For the given prism with a base of 12 cm by 10 cm and a height of 16 cm, the lateral area is:
[tex]L = 2((12 cm)(10 cm) + (12 cm)(16 cm)) \\= 2(120 cm^2 + 192 cm^2)\\= 2(312 cm^2)\\= 624 cm^2.[/tex]
The surface area is:
[tex]S = 2((12 cm)(10 cm) + (10 cm)(16 cm) + (12 cm)(16 cm))\\ = 2(120 cm^2 + 160 cm^2 + 192 cm^2) \\ = 2(472 cm^2) \\ = 944 cm^2.[/tex]
So the answer is [tex]L = 624 cm^2[/tex] ; [tex]S = 944 cm^2[/tex] .
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Answer:
The correct answer is L=704 cm^2 ; S-944 cm^2
Step-by-step explanation:
p=2l+2w
P=2(12)+2(10)=24+20=44cm
L=(44)(16)=704 cm^2
So the lateral area is 704 cm^2
B=(12)(10)=120cm^2
S=704+2(120)=704+240=944cm^2
So the surface area is 944 cm^2
pleasee help im crying so hard i don’t understand
The required solution of the given simultaneous equations y = 1/5x + 6 and 4x + 5y = 5 is (-5, 5).
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Given equation,
y = 1/5x + 6,
4x + 5y = 5
Graph the given equation on the coordinate plane,
As we can see both lines intersect each other at (-5, 5), which is the solution of the system of the equation given.
Thus, the required solution of the given simultaneous equations y = 1/5x + 6 and 4x + 5y = 5 is (-5, 5).
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During a scuba dive, Lainey descended to a point 22 feet below the ocean surface. She continued her descent at a rate of 22 feet per minute. Enter an inequality you could solve to find the number of minutes she can continue to descend if she does not want to reach a point more than 93 feet below the ocean surface. Use t to represent the variable for the minutes Lainey can continue to descend.
Lainey cannot descend for more than 3 minutes.
What is Inequality?Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.
Given:
We know that she first descends 22 feet, and then she descends at a rate of 22 feet per minute. Basically, we have 22 feet which have to me summed with 22x, which expresses the ratio per minute, where x is minutes, and these terms cannot be more than 93 feet, so there are equal or less than 93 feet.
The expression would be
22 + 22x ≤ 93
If we solve this, we have,
22 + 22x ≤ 93
22x ≤ 93 - 22
22x ≤ 71
x ≤ [tex]\frac{71}{22}[/tex]
Therefore, She cannot descent for more than 3 minutes.
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What kind of angle is this
Answer:
SAS
Step-by-step explanation:
What is the area of the triangle?
Write your answer as a fraction or as a whole or mixed number.
2 height
3 2/3 base
Answer: 3 2/3
Step-by-step explanation:
Remeber that the formula is A=(b*h)/2
2 times 3 2/3 = 7 1/3
7 1/3 halved is 3 2/3
Therefore, the answer is 3 2/3
98. A Jenae gets paid every two weeks. If she got paid on January 25, which was the previous pay date?
Answer: Jan 11
Step-by-step explanation:
You subtract two weeks (14 days) from Jan 25.
25-14=11
The last pay day was January 11.
Help I don’t know this someone please tell me how to solve it
The formula for V0 from the expression given will be V0 = V1 - at
How to show the formulaIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, the formula for V0 will be found thus:
a = V1 - V0 / t
Cross Multiply
at = V1 - V0
Subtract V1 from both sides
-V0 = at - V1
V0 = V1 - at
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a random sample of 50 students at a large high school resulted in a 95 percent confidence interval for the mean number of hours of sleep per day of (6.73, 7.67). which of the following statements best summarizes the meaning of this confidence interval?
There is a 95% chance that the true mean number of hours of sleep per day for all students in the school falls within this range
To calculate the 95% confidence interval for the mean number of hours of sleep per day of a random sample of 50 students from a large high school, you would need to follow these steps:
Calculate the mean of the sample by adding up all the hours of sleep reported and dividing by the sample size (n).
Calculate the standard deviation (σ) of the sample by taking the square root of the sum of squares of the differences between the sample values and the mean divided by n1.
Calculate the standard error (SE) by dividing the standard deviation by the square root of n.
Calculate the margin of error (ME) by multiplying the standard error by the critical value of 1. 96.
Calculate the confidence interval by adding and subtracting the margin of error from the mean. This will give you the lower and upper bounds of the confidence interval.
Therefore, the 95% confidence interval for the mean number of hours of sleep per day of a random sample of 50 students from a large high school is (6. 73, 7. 67). This means that there is a 95% chance that the true mean number of hours of sleep per day for all students in the school falls within this range
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Find the area of this trapezoid: 5 ft 19 ft 25 ft 4 ft 5 ft
Answer:
47500
Step-by-step explanation:
5 x 19=95
95 x 25=2375
2375 x 4=9500
9500 x 5= 47500
hope this is correct :)
Suppose you are working at a burger place where the burgers can be made with any of the following: cheese, lettuce, tomato, pickles, onions, mayo, catsup, and mustard. You have a picky clientele: They all want everything on their burgers, but they wish to specify the order of the placement of the items! How many different types of burgers with
There would be 40,320 different types of burgers.
Solution
If each burger must have all of the ingredients listed (cheese, lettuce, tomato, pickles, onions, mayo, catsup, and mustard), and the order of the ingredients is important, then the number of different types of burgers would be 8! (8 factorial), which is the number of permutations of 8 items.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
So there would be 40,320 different types of burgers that can be made with all of the ingredients and the order of placement is important.
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Help with thissss pleaseeeeeeeeeee
Answer:
X < 4
Step-by-step explanation:
3rd one.
Can you please help me answer these math questions. These are domain questions.
The domain of each function is given as follows:
11. All real values except x = -2 and x = 4.
12. All real values except x = -1 and x = 1.
13. All real values except x = -2.
What is the domain of a function?The domain of a function is the set that contains all the possible input values for the function.
The functions in this problem are rational functions, meaning that all the values of x that make the denominator zero are excluded from the domain.
Then the excluded values are obtained as follows:
11. x² - 4 = 0 -> x = -2 and x = 2.
12. x² - 1 = 0 -> x = -1 and x = 1.
13. x + 2 = 0 -> x = -2.
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Can you help please on this
Answer:
5
Step-by-step explanation:
-3x-2(5x-7)=-12
Solve for x
Answer:
x=2
Step-by-step explanation:
-3x-2(5x-7)=-12
-3x-10x+14=-12
-13x=-26
x=2
Angela belongs to a baking
club. She pays a one-time
membership fee and then.
receives baking recipes and
supplies at a discounted rate.
After receiving 4 recipes,
Angela had spent $85. After
receiving 10 recipes, she had
spent $160. Write an equation
to represent this situation.
Please help.
The equation to represent the situation is y = 12.5x + 35
How use equation to represent a situation?Angela belongs to a baking club. After receiving 4 recipes, Angela had spent $85. After receiving 10 recipes, she had spent $160.
The situation represent a linear equation. Therefore, the equation to represent the situation is as follows;
Using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore,
using (4, 85) and (10, 160)
slope = m = 160 - 85 / 10 - 4
m = 75 / 6
m = 12.5
Therefore, let's find y-intercept using (10, 160)
160 = 12.5(10) + b
160 - 125 = b
b = 35
Hence, the equation is y = 12.5x + 35
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the organizers of a conference want to survey attendees about the registration fee. which of the following best describes a random sample of attendees?
Option C. A random sample of attendees would be a group of attendees selected in a systematic and unbiased manner, such that each attendee has an equal chance of being selected to participate in the survey.
This ensures that the opinions represented in the survey are representative of the opinions of the entire attendee population. For example, the organizers could randomly select every 10th attendee, or they could use a random number generator to select a certain number of attendees. The important thing is that the selection process is not influenced by any extraneous factors and is done in a way that ensures each attendee has an equal chance of being selected.
Finally, it is also important to ensure that the survey questions are clear, unbiased, and relevant to the topic being studied. This will help ensure that the responses obtained are meaningful and accurately reflect the opinions of the attendees.
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The organizers of a conference want to survey attendees about the registration fee. Which of the following best describes a random sample of attendees?
A. The organizers form groups of 20 attendees based on the day the attendees registered. Then, the organizers randomly choose 4 groups and select all of the attendees in these groups.
B. The organizers select the first 80 attendees who register for the conference because these attendees are easily accessible.
C. The organizers assign each attendee a different number. Using a random number table, the organizers draw 80 of those numbers at random. Then, organizers select the attendees assigned to the drawn numbers. Every set of 80 attendees is equally likely to be drawn using the random number table.
Solving inequalities #5
25 points!!
Answer:
x ≥ 1
Step-by-step explanation:
The filled in circle means the inequality includes 1
Hope this helped!
The following inequalities form a system.
y is greater than or equal to two-thirds times x plus 1
y is less than negative one-fourth times x plus 2
Which ordered pair is included in the solution to this system?
A (−6, 3.5)
B (−6, −3)
C (−4, 3)
D (−4, 4)
Answer:
Option B)
Step-by-step explanation:
The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.
What is inequality?
A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given phrase,
y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1
y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2
Substitute, point (−6, −3)
-3 ≥ (2/3)(-6) + 1
-3 ≥ -3
Substitute in second inequality,
-3 < (-1/4)(-6) + 2
-3 < 7/2
Hence "The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality".
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