663/3 = 21
21 is the middle number,
21+1 = 22
21-1 = 20
20 + 21 + 22 = 63
Our three consecutive integers can be represented as
X → first integer
X + 1 → second integer
X + 2 → third integer
If the sum of our three consecutive integers is 63, our equation will read...
X + X + 1 + X + 2 = 63
Now, we can simplify on the left. Once we simplify, our equation will now read
3x + 3 = 63
-3 -3 ← subtract 3 on both sides
3x = 60 ← divide both sides by 3
X = 20
Our three consecutive integers can be represented as
X → first integer = 20
X + 1 → second integer = 21
X + 2 → third integer = 22
Therefore, the three consecutive integers are 20, 21, and 22.
the number of science books checked out at the school library is directly proportional to the number of students in Physics class. If 42 books were checked out when 6 students were in physics class, how many books were checked out when 11 students were in the class. A. 66 books B. 47 books C. 53 books D. 77 books E. none of the above
Which of the following is the inverse of y=3^x
Please hurry
A. y= 1/3^x
B. y=log3x
C. y=(1/3)^x
D. y=log1/3x
Answer:
[tex]y=log_3x[/tex]
Step-by-step explanation:
We want to find the inverse of [tex]y=3^x[/tex].
We interchange [tex]x[/tex] and [tex]y[/tex] to obtain,
[tex]x=3^y[/tex].
We now make y the subject by taking logarithm of both sides to base 3 to get,
[tex]log_3x=log_33^y[/tex].
[tex]log_3x=y\:log_33[/tex].
[tex]\Rightarrow log_3x=y\:(1)[/tex].
[tex]\Rightarrow y=log_3x[/tex]
The correct answer is B.
What is the value of the digit 8 in Alaska's population
six sevenths 6/7
of an estate is to be divided among relatives. Of the remaining estate,
one fifth 1/5
goes to the American Cancer Society. What fraction of the estate goes to the American Cancer Society?
The fraction of the estate that goes to the American Cancer Society is
The American Cancer Society receives 1/35 of the total estate after it has been divided among relatives and other beneficiaries. This is determined by multiplying the fraction of the estate remaining (1/7) by the fraction of that remaining estate going to the Cancer Society (1/5).
Explanation:The question states that six-sevenths, or 6/7, of the estate has been divided among relatives, which leaves one-seventh, or 1/7, of the estate remaining. It is this remaining fraction that is further divided, with one fifth, or 1/5, going to the American Cancer Society. To determine the fraction of the total estate that this represents, we multiply these two fractions together: [tex]1/7 * 1/5 = 1/35.[/tex] Therefore, the American Cancer Society receives one-thirty-fifth of the total estate.
Learn more about Fraction multiplication here:https://brainly.com/question/10252019
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Which graph represents a reflection across the x-axis of g(x) = (3)x?
Answer:
the answer is B
Step-by-step explanation:
the curve starting at -4 all the way down.
Just did this on edge hope this helps :)
Over a 6 week period, the price of an MP3 player dropped steadily, from $82 to $34. What is the average weekly change in the price of the MP3 player over this period?
Arrange the values according to magnitude. What is the easiest way to tackle this?
A garden table and a bench cost $786 combined. The garden table costs $36 more than the bench. What is the cost of the bench?
Kate Alexander worked 40 hours last week. Her pay rate is $8.50 per hour. Assuming 7.65% social security withholding, how much should her employer withhold from her check for social security?
0.65
6.50
2.60
26.01
Which symbol correctly compares these fractions? 13 20 ___ 7 10
Answer:
[tex]\frac{13}{20} < \frac{7}{10}[/tex]
Step-by-step explanation:
[tex]\frac{13}{20} \ and \ \frac{7}{10}[/tex]
Now we compare both the fractions
To compare both the fractions, we make the denominators same
LCD is 20
To make the denominators same we multiply the denominator of second fraction by 2
[tex]\frac{7 \cdot 2}{10 \cdot 2}[/tex]
[tex]\frac{14}{20}[/tex]
[tex]\frac{13}{20}[/tex] and [tex]\frac{14}{20}[/tex]
13/20 is smaller than 14/20
[tex]\frac{13}{20} < \frac{14}{20}[/tex]
Your car is skidding to a stop from a high speed. you may want to review ( pages 112 - 114) . part a identify all forces acting on the object.
The forces acting on a car which is skidding to a stop are its weight due to gravity, a normal force coming from the ground, and the friction force due to the relative movement between the tires and the ground. Theoretically, we should also consider the friction force due to air viscosity, however practically we can neglect this force since it's contribution is very small in comparsion to the others (specially at low speeds).
Further explanationBy making the free body diagram of the car, we can observe 3 things:
The car has a certain mass, therefor due to the effect of gravity, it will have certain weight pointing towards the ground. It is important to remember that the weight always points downwards, even if the car would be on an inclined plane.Even though weight pulls the car down, the floor excerts a force over the car upward which keeps it in place. This is called the normal force and it is always perpendicular to the ground.Due to the roughness of the tires and the concrete, there will be a friction force do the relative movement between them. This friction force always goes in the opposite direction in which the car is moving (so if the car is heading to the right, the friction force aims towards the left, thus slowing it down).As a reference you can check the attached image, which shows how the forces would be in case the car would brake on a horizontal street. In case the car would be slowing on a floor which is not horizontal, like on a hill, the forces would have different directions.
Learn moreForces acting on a body: https://brainly.com/question/4230804Difference between kinetic and static friction: https://brainly.com/question/1714663Newton's second law: https://brainly.com/question/254316KeywordsForces, acceleration, friction
Out of 106 total sophomores, there were forty-eight boys who received either an a, b, or c on their first math test. out of the twenty-eight total a’s, sixteen girls received a’s. out of the total fifty-four b’s, thirty girls received b’s. twelve boys received a c out of the twenty-four total c’s on the test. which two-way table represents this information
The two-way table that represents this information correctly is: Table B.
What is a Two-Way Table?A two-way table is used to demonstrate the frequencies for two variables collated from a single group. Rows and columns are used to represent information. The pieces of information stated above are well represented by chart B.
For instance, in the horizontal row, the total number of boys that had a, b, and c was shown to be 48. This means that there were forty-eight boys who received either an a, b, or c on their first test.
Learn more about two-way tables here:
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Jessica earned $13.50 babysitting one night. After babysitting the next day, she had a total of $31.75. How much did she earn babysitting the next day? Equation: 13.50 + x = 31.75
what is the complete factorization of the polynomial below. x^3-3x^2+x-3
Answer:
(x-3)(x+i)(x-i)
Step-by-step explanation:
[tex]x^3-3x^2+x-3[/tex]
We apply grouping method
We group first two terms and last two terms
[tex](x^3-3x^2)+(x-3)[/tex]
Take out GCF x^2 from first group. Also take out 1 from second group
[tex]x^2(x-3)+1(x-3)[/tex]
[tex](x-3) (x^2+1)[/tex]
Now we factor x^2 + 1
We use difference of square formula
a^2 - b^2 = (a+b)(a-b)
x^1 + 1 can be written as [tex]x^2 - (-1)[/tex], the value of -1 is i^2
[tex]x^2 +1 = x^2 -(-1) = x^2 - i^2[/tex]
x^2 - i^2 = (x+i)(x-i)
Final answer is (x-3)(x+i)(x-i)
The complete factorization of the polynomial x^3 - 3x^2 + x - 3 is (x - 3)(x^2 + 1). The process involves grouping and factoring out common terms.
The question asks for the complete factorization of the polynomial x^3 - 3x^2 + x - 3. To factor this polynomial, we are looking for factors of the lowest possible order that will multiply together to give us the original polynomial. Let's first look for a common factor in all the terms. In this case, there isn't a common factor except for 1, so we move on to finding factors through other means such as grouping.
We can attempt to group terms to facilitate the factoring process:
First, consider the polynomial in two parts (x^3 - 3x^2) and (x - 3).Within the first group (x^3 - 3x^2), we can factor out an x^2, which gives us x^2(x - 3).The second group is already in the form (x - 3), mirroring the (x - 3) factor we found in the first group.We then combine these to get the full expression x^2(x - 3) + (x - 3).Next, we can factor out the common (x - 3) term from both groups, obtaining (x - 3)(x^2 + 1).The polynomial x^3 - 3x^2 + x - 3 can now be expressed as the product of (x - 3) and (x^2 + 1). This represents the polynomial in its factored form using real coefficients.
Round 8473227 to the nearest 100000
Rodrigo is starting his own part time business. He plans to earn $25 per hour. He has the following expenses each month, $750 for overhead, $110 for phone and fax and $75 for materials. a. Write an equality that describes the number of hours h he must work to earn a profit of $625. b. How many hours should he have worked to earn a profit of at least $625?
The equality that describes the number of hours h he must work to earn a profit of $625 is h = 62.4 hours and The inequality that describes the number of hours h he must work to earn a profit of atleast $625 is [tex]\rm h \geq 62.4\;hours[/tex] and this can be determine by using arithmetic operations.
Given :
Rodrigo plans to earn $25 per hour.Total expenses each month - $750 for overhead, $110 for phne and fax and $75 for materials.a). Let the total number of hours be 'h'. The equality that describes the number of hours Rodrigo needs to work to earn a profit of $625 is given by:
25h - (750 + 110 + 75) = 625
25h = 1560
h = 62.4 hours
b). Then the inequality that describes the number of hours Rodrigo needs to work to earn a profit of atleast $625. is given by:
[tex]\rm 25h -(750+110+75)\geq 625[/tex]
[tex]\rm 25h - 935 \geq 625[/tex]
[tex]\rm 25h \geq 625+935[/tex]
[tex]\rm 25h \geq 1560[/tex]
[tex]\rm h \geq 62.4\; hours[/tex]
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Jordan and Manuel are on the track and field team at school.running around the track one day, Jordan ran 444m and Manuel ran 777 m. They both ran an even number of times around the track. How far is the track
Answer:
The track is 111 m
Step-by-step explanation:
The easiest way to calculate the meters in the track is to find the Greatest Common Divisor (GCD). This method is used to find the largest number to exactly divide both numbers 444 and 777, which are the meters both guys ran. The resulting number will give us the longest distance the track could have.
There are various techniques used to find the GCD. One of the is to find all divisors of both numbers and then look for the biggest one they have in common.
D 444 = { 1, 2, 3, 4, 6, 12, 37, 74, 111, 148, 222, 444 }
D 777 = { 1, 3, 7, 21, 37, 111, 259, 777 }
As we can see, the only divisors they have in common are 1, 3 ,37 and 111. The greatest of them is 111 ----> GCD(444,777) = 111.
This means the track has 111 m.
(Actually, the track could have been as long as any of the other common divisors, but it wouldn't have been realistic for the track to be 1, 3 or 37 meters).
All of the following are true statements except _____. |56| = 56 -|56| = 56 |-56| = 56 -|56| = -56
Nick can read 3 pages in 1 minute. Write the ordered pairs (number of minutes, number of pages read) for Nick reading 0,1,2,and 3 minutes.
Danika is making necklaces.she has 512 silver beads and 278 blue.About how many more silver than beads does Danika have?
Answer:
234 more silver beads.
Step-by-step explanation:
We have been given that Danika is making necklaces. She has 512 silver beads and 278 blue.
To find the number of silver beads is how much more than blue beads, we will subtract number of blue beads from silver beads.
[tex]\text{Number of more silver beads}=512-278[/tex]
[tex]\text{Number of more silver beads}=234[/tex]
Therefore, Danika has 234 more silver beads than blue beds.
Simplify. −3i √-40
Enter your answer, in simplest radical form, in the box.
HURRY!
i have the answer here
6√10
-3i√-40
-3i^2√40
^
4 * 10
2*2 5*2
-3i^2√2*2*2*5
-6i^2√10
-6(-1)=6
6√10
☺
How do you rename 5400 as hundred
To receive a C grade, a student must average more than 77 but less than or equal to 85 . If Ethan received a C in the course and had five grades of 78 , 79 76 , 64 , and 85 before taking the final exam, what were the possible grades for his final if there were 100 points possible?
Factor 3x^3-24x^2+36x
Dr. Black is standing 15 feet from a streetlamp. The lamp is making his shadow 8 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the street lamp 50 degrees. To the nearest foot, the streetlamp is about
For football tryouts, 12 coaches and 42 players will split into groups. Each group will have the same numbers of coaches and players. What is the greatest number of groups that can be formed?
gratest common factor for 12 and 42 is 6
so 6 groups can be formed
12/6 = 2
42/6 = 7
6 groups with 2 coaches and 7 palers
Put these decimals in order from least to greatest.
7.0,0.07,0.7,0.077
Solve the problem. Round to the nearest cent.
Stan’s savings account has a balance of $1986. After 23 years, what will the amount of interest be at 4% compounded annually?
a.
$2908.93
c.
$2913.93
b.
$2899.93
d.
$794.40
1986*1.04^(23) = 4894.93
4894.93-1986 = 2908.93
Answer is A
Answer:
a. $2908.93
Step-by-step explanation:
We have been given that Stan’s savings account has a balance of $1986. The amount of interest be at 4% compounded annually.
To find the final amount after 23 years we will use compound interest formula.
[tex]A=P(1+\frac{r}{n})^{nT}[/tex], where,
A = Final amount,
P= Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest in compounded per year,
t = Time in years.
Let us convert our given rate in decimal form.
[tex]4\%=\frac{4}{100}=0.04[/tex]
Upon substituting our given values in above formula we will get,
[tex]A=\$1986(1+\frac{0.04}{1})^{1*23}[/tex]
[tex]A=\$1986(1+0.04)^{23}[/tex]
[tex]A=\$1986(1.04)^{23}[/tex]
[tex]A=\$1986*2.4647155431651442[/tex]
[tex]A=\$4894.9250687259763812[/tex]
To find the amount of interest we will subtract principal amount from final amount.
[tex]\text{Amount of interest}=\$4894.9250687259763812-\$1986[/tex]
[tex]\text{Amount of interest}=\$2908.925068725976\approx 2908.93[/tex]
Therefore, the amount of interest after 23 years will be $2908.93 and option a is the correct choice.
A washer and dryer cost $815 combined. The washer cost $85 less than the dryer. What is the cost of the dryer?
a triangle has two sides that are 2 inches and 12 inches what could be the length of the third side of the triangle
Answer:18
Step-by-step explanation:6+12>x
18>x