The correct answer is option is a) x^4 – 6x^2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 , e) 6x^4 = -x^2 + 5.
How do you write a quadratic form?
A quadratic equation can be expressed using the formula au^2+bu+c=0. where u is a mathematical expression. In each case, the leading term's exponent is equal to the middle term's exponent multiplied by two.
What is quadratic standard form?
Standard form refers to the quadratic function f(x) = a(x - h)2 + k, where an is not equal to zero. The graph opens either upward or downward depending on the value of a. The vertex is the point, while the line of symmetry is the vertical line x = h.
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A ship is tied to a dock with a rope
length 10 m. At low tide, the rope is
stretched tight, forming an angle of 45⁰ with the horizontal. At high tide, the stretched rope makes an angle of 30° with the horizontal. How much closer to the dock, horizontally, is the ship at low tide than at high tide?
1 meter and 59 centimeters.
Describe the hypotenuse.The longest side in a right triangle is called the hypotenuse. In other terms, the hypotenuse is the side that faces the right angle.
theorem of Pythagoras
[tex]a^{2} +b^{2} = c^{2}[/tex]
A is a right triangle's side.
B is the right triangle's side.
c = hypotenuse
Think of a right triangle where the height and distance are the legs and the hypotenuse is the rope.
We are aware that:
cos(45°) =x/10
cos(30°) =y/10,
where x represents the distance between the ship and the dock at low tides and y represents the distance during high tides.
We are searching for the y-x distance difference (since it will be farther away during high tides).
Using the previous equations:
x=cos(45°) and y=cos(30°)
Hence:
y - x = 10(cos(30°) - cos(45°))
Hence, the exact value of the distance is 10(cos30° - cos45°)
Using a calculator, this is approximately 1.59 meters.
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If four times my age is
increased by 20, the result is 80.
How old am I?
Use the unique factorization for the integers' theorem (Section 4.3) and the definition of logarithm to prove that log3 (7) is irrational.
It is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.
Explain the term unique factorization theorem?Every integer bigger than 1 is either a prime number by itself or the result of a singular combination of prime numbers, based on the fundamental theorem of arithmetic (FTA), Often known as the unique factorization theorem or even the unique-prime-factorization theorem.If a contradiction is rational, then log3(7) = a/b for some a,b∈R .
In which, b≠0 will be true.
As a result, 7 = 3ᵃ/ᵇ according to the definition of logarithms.
7 = 1*7 is unique according to the unique factorization theorem.
Thus, it is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.
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What is the perimeter of ? Show your work.
If the length of the side PR is 7 feet. Then the perimeter of the triangle ΔPQR will be 17 feet.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The perimeter of the triangle is determined by adding together all of its sides.
The triangles ΔPQR and ΔSTU are congruent triangles. Then we have
PR = SU
3y - 2 = y + 4
3y - y = 2 + 4
2y = 6
y = 3
Then the value of the side PR is given as,
PR = 3(3) - 2
PR = 9 - 2
PR = 7 feet
Then the perimeter of the triangle ΔPQR is calculated as,
P = 4 + 6 + 7
P = 17 feet
If the length of the side PR is 7 feet. Then the perimeter of the triangle ΔPQR will be 17 feet.
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Which of the following groups of numbers are all prime numbers?
O A. 3, 11, 23, 31
OB. 7, 17, 29, 49X
OC. 2, 3, 5, 9%
O D. 2, 5, 15, 196
Answer:
O A. 3, 11, 23, 21
OB. 7, 17, 29
OC. 2, 3, 5
OD. 2, 5
Step-by-step explanation:
While catching tadpoles, you and your friend decide to have a competition. After m minutes, you have (5m + 7) tadpoles and your friend has (3m+ 18) tadpoles. Select any expressions that could represent the total number of tadpoles that you and your friend can catch.
Answer:
TOTAL NUMBER OF TADPOLES = (5m + 7) + (3m+ 18)
Step-by-step explanation:
They ask you "elect any expressions that could represent the total number of tadpoles that you and your friend can catch."
then you need the SUM of both.
TOTAL NUMBER OF TADPOLES = (5m + 7) + (3m+ 18)
A worker will waterproof 4 commercial roofs if he spends 1 1/4 of waterproofing for each roof.
How many liters does he need to do the job?
If you already had 2 1/4 liters, then how much waterproofing do you need?
is fractions with procedure
-First question:
To calculate the number of liters, the number of roofs must be multiplied by the amount of waterproofing used for each roof.
To multiply the fractions, transform the mixed fractions to improper:
[tex]\begin{gathered} \sf1 \frac{1}{4} \times 4 = \\ \\ \sf \frac{4 \times 1 + 1}{4} \times \frac{4}{1} = \\ \\ \sf \frac{4 + 1}{4} \times \frac{4}{1} = \\ \\ \sf\frac{5}{4} \times \frac{4}{1} = \\ \\ \sf \frac {5 \times 4}{4 \times 1} = \\ \\ \boxed{ \sf \frac{ \red{20}}{ \red4}} = \sf \blue5\end{gathered}[/tex]
So you need five liters of waterproofing to get the job done.
-Second question:
To calculate the number of liters; It must be subtracted from the number of liters you need in total, which you already had or had:
[tex]\begin{gathered} \sf5 - 2 \frac{1}{4} = \\ \\ \sf \frac{5}{1} - \frac{4 \times 2 + 1}{4} = \\ \\ \sf\frac {5}{1} - \frac{8 + 1}{4} = \\ \\ \sf \frac{5}{1} - \frac{9}{4} = \\ \\ \sf\frac{4 \div 1 \times 5 - 4 \div 4 \times 9}{4} = \\ \\ \sf \frac{20 - 9}{4} = \\ \\ \boxed{ \sf \frac{11}{4}} = \boxed{ \sf \blue2 \: \: \blue{\sf\frac{3 }{4} }}\end{gathered}[/tex]
So, you need two whole and three quarter liters of waterproofing.
For the following word problems, first write a system of equations then solve for full marks.
3. The perimeter of a rectangle is 64 cm. Twice the width is 4 cm more than the length.
Find the dimensions of the rectangle.
The length of rectangle is 20cm and width is 12cm.
Let the length is x cm and width is y cm.
then perimeter 2(x+y) =64 cm
=> x+y = 64/2 = 32
=> x + y = 32 .............(1)
and according to question twice the width is 4cm more than length so,
2y = x + 4
=> 2y -x = 4 .............(2)
now we add these two equation to find the value of x and y.
3y = 36
=> y = 12
now put the value of y on any equation to find value of x ,
x +12 = 32
=> x = 32 -12 = 20
so, the length of rectangle is 20cm and width is 12cm.
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Convert 3 pints into liters. Round your answer to the nearest hundredth
Answer:
1.42 liters is the correct answer
In an assembly of athletes from three sports, six athletes are from the BASKETBALL team labeled 1,2,3,4,5,6, five athletes are from the SWIM team labeled 1,2,3,4,5, and four athletes are from the HOCKEY team labeled 1,2,3,4. If an athlete is randomly chosen, what is the probability that the athlete is SWIM and EVEN?
The probability that the card is between four and eight (inclusive) or is a club is 4/13.
What is Probability?Probability helps us to know the chances of an event occurring.
The number of cards can be written as,
The number of cards between 4 and 8 is 3 {4,5,6,7,8}.
Number of club cards = 13
Number of cards between 4 and 8 from heart, spades, and diamonds = 15
Now, the probability that the card is between four and eight (inclusive) or is a club is,
Probability = desired outcomes / total number of outcomes possible
= (Number of club cards+ Number of cards between 4 and 8)/(Total number of cards)
= (13+15)/(52)
= 28/52
= 4/13
Hence, the probability that the card is between four and eight (inclusive) or is a club is 4/13.
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The perimeter of a square is 56. Express the length of a diagonal of the square in simplest radical form.?
The length of the diagonal of a square with a perimeter of 56 is 14√2.
What is a diagonal?A diagonal is the longest line that divides a plane shape into two equal parts.
To calculate the length of the diagonal of the square, first we need to find the length of the square using the perimeter formula.
Formula:
P = 4a............ Equation 1Where:
P = Perimeter of the squarea = Length of the squareFrom the question,
Given:
P = 56Substitute the value into equation 1 and solve for a
56 = 4aa = 56/4a = 14Finally to find the length of the diagonal of the square, we use the formula below
d = √(2a²)................... Equation 2Where:
d = Lenght of the diagonal of the squarea = Length of the square = 14Substitute into equation 2
d = √(2×14²)d = 14√2Hence, the length of the diagonal is 14√2.
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Answer:
qfewwqeffwqfefewqwqreg
Step-by-step explanation:
Tami rolled a die 20 times. 14 times it landed on an even number; 6 times it landed on an odd number. How does the experimental and theoretical probability compare, for rolling an odd number?
A)
The theoretical probability is higher.
B)
The experimental probability is higher.
C)
The experimental and theoretical probability are equal.
The answer is the Theoretical probability is higher than the Experimental probability.
Experimental and Theoretical Probabilities:Experimental probability:
The basis for experimental probability is what actually happens. It is dependent on the outcomes of several tests or experiments.
It is calculated by repeatedly recreating the event, recording the outcomes, and then converting the outcomes into a ratio or decimals.
Experimental probability = No of times event occurs/ No of trials
Theoretical Probability:
Theoretical probability is derived from a theory or what is predicted to occur. It is based on information and math.
It is determined by dividing the total number of outcomes by the proportion of favorable results. Either convert it to decimal form or leave it as a ratio or fraction.
Theoretical probability = No of favorable outcomes/ No of outcomes
Here we have
Tami rolled a die 20 times
14 times it landed on an even number;
6 times it landed on an odd number.
The die rolled for an odd number
As we a die will have 6 faces
Number of odd numbers = 3 [i.e 1, 3, 5 ]
Number of even numbers = 3 [ i.e 2, 4, 6 ]
⇒ Theoretical probability = 3/ 6 × 100 = 50%
The die is rolled 20 times, 6 times it landed on an odd number.
⇒ Experimental probability = 6 / 20 = 30%
As we can see,
The theoretical probability is higher than the Experimental probability.
Therefore,
The answer is the Theoretical probability is higher than the Experimental probability.
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4+2p=10( 5 3 p−2) i really need help ASAP!!
Answer:
p=24/528
Step-by-step explanation:
4+2p=10(53p-2)
4+2p=530p-20
24+2p=530p
24=528p
24/528=p
In circle R, RS= 15 and the length of ST =6pi Find angleSRT
Step-by-step explanation:
you can find it by using the arc formula?
2. Table 1 shows the number of pupils attending a motivation camp.
Two pupils from the group are required to take part in a show.
a) If a pupil is chosen at random from school A and another one from school B, calculate the probability that both are girls.
b) If two pupils are chosen at random from the group of boys, calculate the probability that both are from the same school.
a) The probability that both are girls is of: 21/150.
b) The probability that both are from the same school is of: 0.7333 = 73.33%.
How to obtain the probabilities?The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.
For item a, the outcomes are given as follows:
One girl from school A -> 7/15 probability.One girl from school B -> 3/10 probability.Hence the probability that both are girls is of:
p = 7/15 x 3/10 = 21/150.
The probability that the two boys are from the same school can be given by these two cases:
School A: 8/15 x 7/14.School B: 7/10 x 6/9.Then the probability is of:
p = 8/15 x 7/14 + 7/10 x 6/9 = 0.7333 = 73.33%.
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PLS answer this i need it asap
Answer:
b
step by step explanation
A truck enters a highway driving 60 mph. A car enters the highway at the same place 6 minutes later and drives 73 mph in the same direction. From the time the car enters the highway, how long will
it take the car to pass the truck?
Answer:
27.7 min
Step-by-step explanation:
In 6 minutes the truck will be 6 miles ahead of the car....
the car is going 13 mph faster and will cover this 6 miles in
6 mi / 13 mi/hr = .4615 hr =27.7 min
If 20% of a number is 40, find 2% of that number.
Answer:
4
Step-by-step explanation:
20% = 40
10% = 20
100% = 200
200 * .02 = 4
The value of 2% of that number is,
⇒ 4
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
20% of a number is 40.
Let the number = x
Hence, We get;
⇒ 20% of x = 40
⇒ 20/100 × x = 40
⇒ 1/5 × x = 40
⇒ x = 200
Thus, The value of 2% of that number is,
⇒ 2% of 200
⇒ 2/100 x 200
⇒ 4
Thus, The value of 2% of that number is,
⇒ 4
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PLEASE HELP!
Research two different movie production companies. For each company, collect data on a categorial variable and a quantitative variable for comparison purposes. For example, you could determine the genre of the last 20 movies produced, the length of the most
recent 30 movies, the amount of money earned by the 50 highest grossing movies of all time, etc.
Display the categorical data that you collected from each of the two individuals in a side-by-side bar graph, segmented bar graph, or mosaic plot.
Nominal and ordinal categorical variables are the two different types.
What are the 2 types of categorical variables explain and give examples each?Nominal and ordinal categorical variables are the two different types.A nominal variable's categories do not naturally have an inherent order.For instance, gender is a categorical variable that has two categories (male and female), neither of which have any inherent ordering.The ordering of an ordinal variable is obvious.Any variable where the data indicate amounts is referred to be a quantitative variable.Any variable where the data represent groupings is referred to as a categorical variable.This comprises categories (like where people placed in a race), rankings (like cereal brands), and binary results.To learn more about categorical variables refer
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Solve the following inequality:
r/2+15>45
Answer: r > 30
Step-by-step explanation:
The chances of finding a rare card in a pack of trading cards can be represented with the equation y equals one twenty-second times x, where y represents the number of rare trading cards and x represents the number of packs of trading cards. Determine how many rare trading cards you would find if you bought 110 packs of trading cards.
2,420
22
5
one over 22
You will find 5 rare trading cards if you bought 110 packs of trading cards
How to determine the number of rare trading cards?
Given that:
The chances of finding a rare card in a pack of trading cards can be represented with the equation y equals one twenty-second times x.
Thus, we can the equation as:
y = (1/22)x
To determine the number of rare trading cards if you bought 110 packs of trading cards, substitute x = 110 into the equation:
y = 1/22 × 110
y = 5
Therefore, you will find 5 rare trading cards if you bought 110 packs of trading cards
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Answer:
Step-by-step explanation:
y = the number of rare trading cards found
x = the number of packs of trading cards
1/22 = the probability of finding a rare card per pack
Equation
y = 1/22(x)
y = 1/22(110)
y = 110/22
y = 5
There is a chance of finding 5 rare cards in 110 packs of trading cards.
Poison Ivy received a total piecework paycheck of $465.47. She receives 89 cents per unit produced. How many units did she produce?
There are 523 units did she produced.
What is paycheck?
Traditionally, an employer would issue a paper document known as a paycheck—also spelled pay cheque, pay check, or pay cheque—to pay an employee for services rendered.
Businesses pay their employees for their work through paychecks. Bi-weekly and semi-monthly delivery schedules are the most typical ones, though this can change depending on the employer's preferences and any applicable state laws and regulations.
Given that:
Piecework pay = $465.47
Price per unit = 89 cents = $0.89
Number of units=$x
Let,
Total piecework pay = Price per unit x number of items sold
$465.47 = 0.89 x x
x = 523
Hence, there are 523 units did she produced.
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How many boards 6 5/6 in wide will cover floor 205 in wide
By using fraction, it can be calculated that
30 boards are required to cover a floor of width 205 inches wide
What is fraction?
Suppose there is a collection and a part of collection has to be taken.
The part which is taken is called fraction. In other words part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
This is a word problem on fraction
Width of each board = [tex]6\frac{5}{6}[/tex] inches = [tex]\frac{41}{6}[/tex] inches.
Total width of floor = 205 inches.
Number of boards required = [tex]205 \div \frac{41}{6}[/tex] = [tex]205 \times \frac{6}{41}[/tex] = 30
30 boards are required
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You are considering taking out a loan of $8,000.00 that will be paid back over 8 years with quarterly payments of $320.19. If the interest rate is 6.3% compounded quarterly, what would the remaining balance be immediately after the fourteenth payment?
The remaining balance would be $___________. (Round to 2 decimal places.)
Answer:
78.8
Step-by-step explanation:
What is 2 3/2 equal to?
Answer:
(a) √8
Step-by-step explanation:
You want to know the radical equivalent to 2^(3/2).
IndicesThe relationship of indices to radicals is ...
[tex]\large{\sqrt[n]{a^m}}={a^{\frac{m}{n}}[/tex]
ApplicationThe given expression can be rewritten as ...
[tex]2^{\frac{3}{2}}=\sqrt[2]{2^3}=\boxed{\sqrt[2]{8}}[/tex]
__
Additional comment
When the index of the radical is 2, it is usually left off. The radical can be simplified by removing the perfect square factor.
[tex]\sqrt[2]{8}=\sqrt{8}=2\sqrt{2}[/tex]
7 people equally share 1/2 a pan of macaroni and cheese how much of the whole pan each person get
Answer:
1/14
Step-by-step explanation:
If 7 people equally share 1/2 a pan of macaroni and cheese, each person will get 1/2 / 7 = 1/14 of the pan.
To find the fraction of the pan that each person gets in terms of the whole pan, we can multiply the fraction 1/14 by the denominator of the fraction representing the whole pan. If the whole pan is represented by 1 pan, the fraction representing each person's share would be 1/14 * 1 = 1/14 of a pan.
So, each person would get 1/14 of a pan of macaroni and cheese.
Answer: 1/14
Step-by-step explanation:
1/2 / 7 = 1/14≅ 0.07142857
Solve for x:
4(x-5)
8
= 9y
X =
= [?]y + []
Enter
Simplify Tan A + Cot A
Tan A + Cot A = 2 Cosec 2A.
It is a simple TRIGNOMETRY question, which is directly based on their formulas.
In this question we have one side of formula either LHS or RHS and we have to find other,
Tan A + Cot A
we know Tan A = sin A /Cos A and Cot A = cos A / sin A
So by putting this in place of Tan A + Cot A we get,
⇒ (sin A / cos A) + (cos A / sin A)
⇒ (sin∧2 A + cos∧2 A) / cos A sin A
⇒1/ cos A sin A
⇒2/2cos A sin A
⇒ 2/Sin 2A
⇒ 2 Cosec 2A
Hence, the question is simplified.
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What is the measure of angle x? (5 points)
A pair of parallel lines is cut by a transversal. An exterior angle on the left of the transversal is labeled as 45 degrees. An interior angle on the right of the transversal, which is not vertically opposite to the 45 degree angle, is labeled as x.
Question 2 options:
1)
45 degrees
2)
90 degrees
3)
135 degrees
4)
140 degrees
Answer:
idek
Step-by-step explanation:
Please help me I really need it
Answer:
a) 4(8019) +3s ≥ 70000
b) yes
Step-by-step explanation:
Diego has walked an average of 8019 steps per day for 4 days and wants to walk 70000 steps in a week. You want an inequality for the average number of steps per day that Diego must walk for the last 3 days of the week, and you want to know if 12642 is a solution.
a) InequalityThe inequality will express the relationship between the steps walked and the goal. Let s represent the average number of steps walked each day for the last 3 days of the week.
The total number of steps walked in the first 4 days is the average per day times the number of days: 4(8019). The total number of steps walked in the last 3 days is the average per day times the number of days: 3s.
The total for the week is the sum of these. We want that to exceed 70000:
4(8019) +3s ≥ 70000 . . . . . . . the desired inequality
b) SolutionSolving for s, we find ...
3s ≥ 7000 -4(8019)
3s ≥ 37924 . . . . . . . . . subtract 32076
s ≥ 12641 1/3 . . . . . . . . divide by 3
The offered number, 12642, is greater than 12641 1/3, so is a solution.
Diego will meet his goal if he averages 12642 steps per day for the last 3 days of the week.
__
Additional comment
If Diego's 3-day average is 12462, he will have walked 70002 steps for the week, a number that is more than 70000.