The number 5.78778778 is a rational number because it has a repeating decimal pattern that can be expressed as the fraction 573/99.
The number 5.78778778 is a rational number. Rational numbers are those that can be expressed as a fraction where both the numerator and the denominator are integers.
In this case, the number 5.78778778 has a repeating decimal pattern, which is a hallmark of rational numbers.
We can convert this repeating decimal into a fraction by setting it equal to a variable, say x, subtracting a shifted version of x to isolate the repeating part, and then solving for x to find its fractional equivalent.
If we perform this process, we can turn 5.78778778... into a fraction. For example:
→ Let x = 5.78778778...
→ Multiply both sides of the equation by 100 to shift the decimal two places: 100x = 578.78778778...
→ Subtract the original x from this new equation: (100x - x) = (578.78778778... - 5.78778778...)
→ This simplifies to 99x = 573
→ Divide both sides by 99 to solve for x: x = 573/99
→ This fraction represents the decimal number 5.78778778..., confirming it is rational.
Show that the statement is true. If GH has endpoints G(−2, 1) and H(4, −1), then the midpoint M of GH lies on the line y = −x + 1.
The midpoint M is ( , ). The midpoint does not lie or lies on the line y = −x + 1 since its coordinates satisfy or do not satisfy the equation.
The admission fee at a small fair is $1.50 for children and $4.00 for adults. on a certain day, 2200 people enter the fair and $5050 is collected. how many children and how many adults attended that day?
Please answer me this equation
Number like 10 100,1,000 and so on are called what
These numbers are called power of ten. A power of ten is 10 multiplied by itself the exponent number of times. For example:
We can write 10 as 10¹
100 as 10²
1000 as 10³
The exponent is equal to the number of zeros in the number like 100 has 2 zeros so the exponent is 2 and write it as 10²
How many, and what type of, solutions does 6x2−2x+7=0 have?
A.) 2 nonreal solutions
B.) 2 irrational solutions
C.)2 rational solutions
D.) 1 rational solution
Answer:
Nope! The answer is 2 Nonreal Solutions i took the test! :)
Step-by-step explanation:
The given quadratic equation will have 2 nonreal solutions. The correct option is A.
A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that the quadratic equation is 6x²−2x+7=0. The equation can be solved as below;-
6x²−2x + 7 = 0
The equation will have two non-real values for x. The correct option is A.
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Find three consecutive odd integers with a sum of -51 answer
If there are 30 red and 45 blue marbles in a jar with 200 marbles. what percent of the marbles are red
what number fills in the blank to complete the factorization of 3x+24?
Answer:
Complete factorization of 3x+24 is:
3(x+8)
Step-by-step explanation:
we have to completely factorize:
3x+24
Taking 3 common in the above expression
3(x+8)
This cannot be factorized further
Hence, complete factorization of 3x+24 is:
3(x+8)
Martha will be entering high school in a couple of years. Which steps should she take to ensure she has money to pay for college? Check all that apply. She should start or add to a college savings account so it can grow with deposits and earned interest. She should ask her parents if they have a college savings account set up for her. She should work to maintain high grades throughout school so she can qualify for scholarships. She should get involved in extracurricular activities like clubs and sports so she can discover what she enjoys and qualify for scholarships. She should fill out the FAFSA immediately so she does not miss grants or scholarships she qualifies for. She should ask all her friends and neighbors to contribute to her college savings account so it will grow faster.
Martha can ensure she has money to pay for college by starting or adding to a college savings account, maintaining high grades, getting involved in extracurricular activities, and filling out the FAFSA immediately.
Explanation:Martha can take the following steps to ensure she has money to pay for college:
Start or add to a college savings account: By saving money early, Martha can let it grow with deposits and earn interest.Work towards maintaining high grades: This will help her qualify for scholarships that can assist in paying for college.Get involved in extracurricular activities: Participating in clubs and sports can help Martha discover what she enjoys and also qualify her for scholarships.Fill out the FAFSA immediately: By submitting the FAFSA, Martha can ensure that she doesn't miss out on any grants or scholarships she may qualify for.
The steps Martha should take to ensure she has money to pay for college are as follows:
1. She should start or add to a college savings account so it can grow with deposits and earned interest. This is a proactive step that allows the money to benefit from compound interest over time.
2. She should ask her parents if they have a college savings account set up for her. It's important to know if there are existing funds that can be used for her education.
3. She should work to maintain high grades throughout school so she can qualify for scholarships. Many scholarships are merit-based, and good grades are often a key criterion.
4. She should get involved in extracurricular activities like clubs and sports so she can discover what she enjoys and qualify for scholarships. Participation in these activities can make her a well-rounded candidate for scholarships that value leadership and community involvement.
5. She should fill out the FAFSA (Free Application for Federal Student Aid) when she is eligible, which is typically during her senior year of high school. This form is crucial for accessing federal grants, loans, and work-study opportunities, as well as some state and college-specific aid.
6. While asking friends and neighbors to contribute to her college savings account could potentially help the account grow faster, it is not a conventional or reliable method for funding college education. Therefore, it is not a primary step she should take.
In summary, Martha should focus on saving money, exploring existing savings, maintaining good grades, engaging in extracurricular activities, and preparing to fill out the FAFSA. These steps will help her secure funding for college through savings, scholarships, and financial aid.
Lucy is thinking of a number. the number is greater than two hundred twenty-five. her number is less than 2hundred, 2 tens,7 ones. what is lucy number? howq do i solve this
Keiko runs 10 miles in 75 minutes. at the same rate, how many miles would she run in 69 minutes?
The sum of two even numbers is even. the sum of 6 and another number is even. what conjecture can you make about the other number?
Answer: We can say that the other number is even since the sum of two even numbers is even.
The required conjecture is given as the other number must be an even number.
What is an even number?An even number is defined as a number that is a multiple of 2 is called even number, such as 2, 4, 6, 12, and so on.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
here,
The sum of two even numbers is even. Following the statement,
If the sum of 6 and another number is even, that another number must be even to get the sum of 6 and another number to be even, while 6 it self is an even number.
Thus, the required conjecture is given as the other number must be an even number.
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In combining like terms when adding or subtracting do you add the exponents together
Answer: If adding exponents, they have to the same value or same coefficient.
For example:
1) 2x^2+2x^2= 4x^2
Solve the triangle. A = 46°, a = 31, b = 27
To solve the given triangle with A = 46°, a = 31, and b = 27, we use the Law of Sines to first find angle B, then use the sum of angles to find angle C, and finally, use the Law of Sines again to find side c.
Explanation:To solve the triangle with the given information A = 46°, a = 31, and b = 27, we need to use the Law of Sines or the Law of Cosines. Since we have one angle and the side opposite to it (a = 31), as well as another side (b = 27), we first need to find angle B using the Law of Sines:
\frac{\sin(A)}{a} = \frac{\sin(B)}{b}
By solving for sin(B), we get:
\sin(B) = \frac{\sin(46°) * 27}{31}
Next, we calculate the value of sin(B) and then angle B. After that, we can find angle C by using the fact that the sum of angles in a triangle is 180°:
A + B + C = 180°
Once we have angle C, we can use the Law of Sines again to find side c:
\frac{\sin(C)}{c} = \frac{\sin(A)}{a}
By rearranging and solving for c, we get:
c = \frac{\sin(C) * a}{\sin(A)}
This process will give us the lengths of all sides and the measurements of all angles, thus solving the triangle.
Point M is the midpoint of LN. LM = 7x - 12 and MN = 3x + 16. Find LM.
The sum of three consecutive even integers is less than 84. find the set of these three integers with the greatest sum.
Find f(x) and g(x) so the function can be expressed as y = f(g(x)). There may be more than one possible decomposition.
y = (x^3 + 1)^2
How many even numbers can be formed from the digits 1,2,3,4,5?
If i was born in 2002 how old will i be in 2130
Which function grows at the fastest rate for increasing values of x?
p(x)=5x3+3
f(x)=8x2−3x
h(x)=2x
g(x)=19x
The function which has the fastest rate for increasing values of x are:
[tex]p(x)=5x^3+3[/tex]
Step-by-step explanation:We are given four polynomial functions as:
[tex]p(x)=5x^3+3\\\\\\ f(x)=8x^2-3x\\\\\\h(x)=2x\\\\\\g(x)=19x[/tex]
Now as we know that if the degree of the polynomial increases the function becomes more extreme i.e. it increases very quickly with the increasing value of x.
Hence, among the given options the function which has the fastest rate of increase is:
[tex]p(x)=5x^3+3[/tex]
( Since, it's degree is 3 which is highest as compared to the other polynomials (one of degree 2 and 2 of degree 1) )
24 divided by 2 find the qoutient
24/2 = 12
the quotient is 12
Answer: So your answer is 12 for 24 divided by 2 which gives you 12 I hope this helps
Step-by-step explanation:
24 divided by 2 = 12
12 times 2= 24
Or 2 times 12 = 24
Find the rectangular coordinates of the point that has polar coordinates , 4, −3π/4
Jermaine’s father owes $6,300 in interest at the end of a 60-month car loan at a 7% simple annual interest rate. What was the original loan amount?
Answer:
$18,000
Step-by-step explanation:
It is given that the interest amount $6,300
We will calculate the principal amount.
So we use the formula
I = prt
P = Principal amount
r = rate of interest 7% ( 0.07 )
t = time in years 60 months ( [tex]\frac{60}{12}[/tex] years )
6,300 = P × 0.07 × [tex]\frac{60}{12}[/tex]
6,300 = P × 0.07 × 5
6,300 = 0.35P
[tex]\frac{6,300}{0.35}[/tex] = P
P = $18000
The original loan amount was $18,000.
If P is the midpoint of ST, SP = x + 4, and ST = 4x, determine the length of ST
Answer:
ST = 16.
Step-by-step explanation:
Given : P is the midpoint of ST, SP = x + 4, and ST = 4x,
To find : Determine the length of ST.
Solution : We have given P is mid point of ST.
It mean P divide the ST in to two equal parts .
So, SP = PT .
We can say
ST = 2 SP .
Plug the given values SP = x + 4, and ST = 4x,
4x = 2 ( x +4).
4x = 2x + 8.
On subtracting both sides by 2x
4x -2x = 8.
2x = 8
On dividing both sides by 2
x = 4.
ST = 4 * 4 = 16.
Therefore, ST = 16.
In how many ways can 15 identical math books be distributed among 6 students?
Which is a pair of vertical angles ?
The pair of angles that are vertical are <TRS and <VRW.
Determining vertical anglesTo calculate vertical angles, take the following actions:
Recognize the intersecting lines: Vertical angles are created when two lines cross.
Find the common vertex: The point where the two lines join is the common vertex for vertical angles.
Recognize the pairs of opposite angles: Two pairs of opposite angles cross the intersection point to generate vertical angles.
Hence the pair of angles that are vertical are <TRS and <VRW.
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Round to the nearest hundredth what is the positive solution to the quadratic equation 0 = 2x^2 + 3x -8
Answer: the guy above is right for anyone looking at this and was sceptical
Step-by-step explanation:
Find (f•g)(x)=x^2-7x+12 and g(x)=3/x^2-16
Which statements are true regarding the diagram
Answer:
A. AngleGNH and AngleHNJ are complementary.
C.AngleKNL and AngleLNM are complementary.
D.mAngleHNK + mAngleKNL = 180°
Step-by-step explanation:
What is the surface area of this cone ?