Given that x² - 6x + 1 = (x-a)² - b for all values of x, (i) find the value of a and the value of b.
Answer:
(x-3)^2 - 8, so a is 3 and b is 8
Step-by-step explanation:
use completing the square
hope this works :)
k/3+16 algebraic expression
Answer: -48
Step-by-step explanation:
k/3 + 16
find the roots by factoring
which leads to -48
k/3 + 16
To add or subtract expressions, expand them so their denominators are the same. Multiply 16 by 3/3.
k/3 + 16 × 3/3
Since k/3 and 16 × 3/3 have the same denominator, we join their numerators to add them.
k + 16 × 3/3
We perform the multiplications in k+16×3.
k + 48/3
See more about algebraic expressions at:https://brainly.com/question/24548997
How do i do this? This is all due tomorrow
1.2 because you take 2 congruent sides of each shape and divide the larger one by the small one. in this example you could do
8.4÷7
36.6÷30.5
19.2÷16
they all give you 1.2
At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path. The bicyclist heading north is riding 8 km/hour faster then the bicyclist heading south. At 11:00, they are 40 km apart. Find the two bicyclists' rates.
Answer:a
Step-by-step explanation:its a
The sum of three consecutive odd integers is 153. What is the value of the largest of the integers?
Help me pls
the value of largest integer when the sum of 3 consecutive odd integers is 153 is 53.
We know that odd consecutive numbers means the difference between the numbers will be 2
So, let the first odd number be x
Second number will be = x + 2
Third number will be = x + 2 + 2 = x + 4
Now, we are given that, the sum of these odd integers is 153
So, we get the equation as:
x + x + 2 + x + 4 = 153
3 x + 6 = 153
3 x = 153 - 6
3 x = 147
x = 147 / 3
x = 49
Largest integer = x + 4 = 49 + 4 = 53
Therefore, we get that, the value of largest integer when the sum of 3 consecutive odd integers is 153 is 53.
Learn more about integers here:
https://brainly.com/question/17695139
#SPJ9
Sydney measured a line to be 3.8 inches long. If the actual length of the line is 3.6
inches, then what was the percent error of the measurement, to the nearest tenth of a
percent?
Answer:
5.5%
Step-by-step explanation:
If JK = 3x, KL = 8, and JL = 5x, what is JK?
The value of JK is 12
How to determine the valueFrom the diagram shown, we can see that;
Line JL = 5xLine JK = 3xLine KL = 8But line JL is the line with JK and KL as the line segments and K the midpoint between J and K
This can be represented as;
JK + KL = JL
substitute the values into the equation, we have;
3x + 8 = 5x
collect like terms
3x - 5x = -8
subtract like terms
-2x = -8
makes 'x' the subject of formula
x = -8/-2
x = 4
But JK = 3x = 3(4) = 12
Thus, the value of JK is 12
Learn more about line segments here:
https://brainly.com/question/2437195
#SPJ1
Order the following numbers from greatest to least: 7.321, 7.3, 7.065, 7.65
answer:
7.65, 7.321, 7.3, 7.065
explanation:
on a number line, these numbers would be in order as shown above from right to left (decreasing value)
Answer:The order for the given decimal numbers, from the greatest to the least, is: D. 7.65, 7.321, 7.3, 7.065.
Step-by-step explanation:
Order the following numbers from greatest to least: 7.321, 7.3, 7.065, 7.65
7.065, 7.3, 7.321, 7.65
7.3, 7.321, 7.065, 7.65
7.321, 7.3, 7.65, 7.065
this is correct--> 7.65, 7.321, 7.3, 7.065
-1 5/6 • 6 1/2
Please help I have a math test soon I don’t know how do this
Answer:
-143/12 or -11 11/12
Step-by-step explanation:
Convert each to improper fraction and multiply straight across (numerator times numerator, denominator times denominator)
-1 5/6 x 6 1/2
= -11/6 x 13/2
= -143/12
Answer:
-143/12 as a fraction and 11.916666666... (six repeating) as a decimal
Step-by-step explanation:
Turn into improper fractions.
(-6/6 + -5/6) = -11/6
2/2 + 2/2 +2/2 + 2/2 +2/2 + 2/2 + 1/2 = 13/2
-11/6 times 13/2
-11 times 13 = -143
6 times 2 = 12
-143/12 = 11.916666666... (six repeating)
which expression simplifies to 41? choose all that apply! question 14 options: 10 2³ ∙ 4 - 1 10 2³ ∙ (4 - 1) (10 2³) ∙ 4 - 1 10 (2³ ∙ 4) - 1
The expressions that simplifies to 41 are:
a) 10 + 2³ * 4 - 1
d) 10 + (2³ * 4) - 1
Information about the problem:
a) 10 + 2³ * 4 - 1
b) 10 + 2³ * (4 - 1)
c) (10 + 2³) * 4 - 1
d) 10 + (2³ * 4) - 1
We solve the equations respecting the level of hierarchy:
First the operations in parentheses, then brackets and finally braces.Of the arithmetic operations, first the multiplication and divisions and then the additions and subtractions.a) 10 + 2³ * 4 - 1
10 + 8*4 - 1
10 + 32 - 1
42 - 1
41 (it applies)
b) 10 + 2³ * (4 - 1)
10 + 8 * (3)
10 + 24
34 (it doesn't applies)
c) (10 + 2³) * 4 - 1
(10 + 8) * 4 - 1
18*4 - 1
72 - 1
71 (it doesn't applies)
d) 10 + (2³ * 4) - 1
10 + (8*4) - 1
10 + 32 -1
42 - 1
41 (it applies)
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
Learn more about algebraic operations at: brainly.com/question/3927786
#SPJ4
Sophia need to earn at least 1,800 each month to cover her living expenses.what is the minimum amount she needs to sell in order to earn at least 1,800 if she earn a 10.75commission on everything she sells?round to the nearest dollar
In a condition where Sophia needs to earn at least $1800 as a part of her living expenses, she will need to sell goods worth at least $16,745 if she earns 10.75% commission on everything she sells.
What is the significance of living expenses?
Living expenses of an individual can be referred to or considered as the amount of expenditure made by a person for living for a predefined period of time. The living expenses also include the spending towards the necessities of an individual.
In the condition given above, the provided information can be used in order to find out about the living expenses as,
Living Expenses = Sales x Commission
1800 = Sales x 10.75%
Sales = 1800 / 10.75%
Sales = $16,744.12
Therefore, the significance regarding the living expenses has been aforementioned.
Learn more about living expenses here:
https://brainly.com/question/21276082
#SPJ4
The community college theater department sold three kinds of tickets to its latest play production. The adult tickets sold for $15, the student tickets for $10 and the child tickets for $8. The theater department was thrilled to have sold 250 tickets and brought in $2,825 in one night. The number of student tickets sold is twice the number of adult tickets sold. How many of each type did the department sell?
Using a system of equations, the amounts of each ticket sold are given as follows:
Adult: 75.Student: 150.Child: 25.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: number of adult tickets sold.Variable y: number of student tickets sold.Variable z: number of child tickets sold.The theater sold 250 tickets, hence:
x + y + z = 250.
The theater brought in $2,825, hence, considering the value of each ticket:
15x + 10y + 8z = 2825.
The number of student tickets sold is twice the number of adult tickets sold, hence:
y = 2x.
Replacing in the first two equations:
3x + z = 250.35x + 8z = 2825.Multiplying the first equation by -8 and adding with the second, we have that:
11x = 825
x = 825/11
x = 75.
Then:
y = 2x = 2(75) = 150.z = 250 - 3x = 250 - 3(75) = 25.The amounts of each ticket sold are given as follows:
Adult: 75.Student: 150.Child: 25.More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
If 1/2 cup of soup equals 120 milliliters, then how many milliliters are in 3 1/4 cups of soup?
If 1/2 cup of soup equals 120 milliliters, then there are 780 milliliters in
3 1/4 cups of soup.
A milliliter is a metric unit that is abbreviated as ml and is used to measure volumes for liquid and gas states. It is usually used to measure smaller volumes of liquids as it is equal to 1/1000 of a liter.
We can find the milliliters in 3 1/4 cups of soup as follows:
1/2 cup of soup = 120 milliliters
As 1/2 = 0.5
We can rewrite it as:
0.5 cup of soup = 120 milliliters
3 1/4 cups = 3.25 cups
Consider milliliters in 3 1/4 cups = x
Therefore,
0.5 cup = 120 ml
3.25 cups= x
Cross multiply to find x,
0.5 x = 120x3.25
0.5 x = 390
x= 390/0.5 = 780 milliliters
Hence it is found that 3 1/4 cups of soup is equal to 780 milliliters.
To learn more about milliliters, click here:
https://brainly.com/question/9282738
#SPJ4
sixteen slices of pizza are distributed in a society of four people so that one person receives eight slices, the second person receives six slices, the third receives two, and the last receives no pizza. if no person wants to give up the pizza he or she has but they all agree that the fair outcome would be the one where each person gets four slices, then could be improved at the expense of .
If all agree that the fair outcome would be the one where each person gets four slices, then could be improved at the expense of each person equally.
In mathematics, it deals with numbers of operations according to the statements.
Here,
If all agree, that each of one should get an equal number of slices, then it can be concluded that each of them should pay an equal amount for the 4 pizzas.
Thus, if all agree that the fair outcome would be the one where each person gets four slices, then could be improved at the expense of each person equally.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ4
Calculate the density of a piece of
wood with a mass of 80g and a
volume of 90cm³
Answer:
0.89 g/cm³
Step-by-step explanation:
used the formula d=M/V
M is mass which is = 80g
V is volume which is = 90cm³
d = 80/90
d = 0.89 g/cm³
Marie has 2 boxes for numbered ping
pong balls, labeled A and B, as shown
in the figure above. Box A is for ping
pong balls that are multiples of 2 and
box B is for ping pong balls that are
multiples of 7. If Marie were to move
all the balls that could go in either one
of these boxes into a third box, which
best describes the ping pong balls this
third box would have?
A) Multiples of 2
B) Multiples of 7
C) Multiples of 14
D) Multiples of 42
Answer:
multiples of 14
Step-by-step explanation:
we multiply 7×2
Order numbers from least to greatest: 4 3/4, -2 1/2, -8/3, 9/2
Answer:
-8/3 < -2 1/2 < 9/2 < 4 3/4
Step-by-step explanation:
-2.667 < -2.5 < 4.5 < 4.75
If 65% of a number is 39 and 35% of the same number is 21, find 100% of that number.
Answer:
60
Step-by-step explanation:
divide 39 by 65%,
you will get
39 / ( 65/ 100)
= 39 * (100/65)
= 39 * (20 /13)
= 3*20
= 60
A party will have hexagonal tables placed together with space for one person on each open side:
n
12
a. Complete this table showing the number of people P (n) who can sit at n tables.
If n =12 then there are 50 person who can sit .
Hexagonal - In geometry, a hexagon is a closed two-dimensional six-sided polygon. It is made up of six line segments and six vertices that form six internal angles. The sum of all the internal angles of a hexagon is 720°.
Each table seats 4 people, which can be represented with n,plus two more people at either end of the set of tables. The table is hexagonal and so can seat 6 people. So, the given equation defines this situation.
The number of people who can sit at the tables increases by 4 each time a table is added
P=4n+2
the given equation to find the number of tables n.
P=4n+2
Where P = person
and n= no of tables .
given that
n=12
put value of n in equation to find the no. of person .
P = 4(12) +2
P = 48 +2
P = 50.
Hence,in this given seating arrangement 50 person can sit on 12 tables. .
To learn more about Seating arrangements
Visit - https://brainly.com/question/28412833
#SPJ9
–5x – 10 = 2 – (x + 4)
Please help me step by step
Thanks!
Answer:
x = -2
Step-by-step explanation:
Solve for x:
-5 x - 10 = -(x + 4) + 2
-(x + 4) = -x - 4:
-5 x - 10 = (-x - 4) + 2
Grouping like terms, -x - 4 + 2 = -x + (2 - 4):
-5 x - 10 = (-x + (2 - 4))
2 - 4 = -2:
-5 x - 10 = -x + -2
Add x to both sides:
x - 5 x - 10 = (x - x) - 2
x - x = 0:
x - 5 x - 10 = -2
Grouping like terms, x - 5 x - 10 = (-5 x + x) - 10:
((-5 x + x) - 10) = -2
x - 5 x = -4 x:
-4 x - 10 = -2
Add 10 to both sides:
(10 - 10) - 4 x = 10 - 2
10 - 10 = 0:
-4 x = 10 - 2
10 - 2 = 8:
-4 x = 8
Divide both sides of -4 x = 8 by -4:
(-4 x)/(-4) = 8/(-4)
(-4)/(-4) = 1:
x = 8/(-4)
The gcd of 8 and -4 is 4, so 8/(-4) = (4×2)/(4 (-1)) = 4/4×2/(-1) = 2/(-1):
x = 2/(-1)
Multiply numerator and denominator of 2/(-1) by -1:
Answer: x = -2
Answer:
Step-by-step explanation:
Distribute:
-5x - 10 = 2 - (x + 4)
-5x-10=2-x-4
x = -2
3x+2=2x+13 all divided by 3
Answer:
x = 11Step-by-step explanation:
following the clarification in the comment
3x+2=2x+13 all divided by 3 (both side)
(3x + 2)/3 = (2x + 13)/3
3x + 2 = 2x + 13
x = 13 - 2
x = 11
--------------------
check
(3 * 11 + 2)/3 = 2 * 11 + 13)/3
3 * 11 + 2 = 2 * 11 + 13
35 = 35
the answer is good
Need a good explanation. Struggling with derivative basics.
5 IS THE DERIVATIVE OF k(x)= 5x at x=10
WHAT ARE DERIVATIVES ?The rate at which a function alters in relation to a variable is known as a derivative in mathematics. Problems involving calculus and differential equations need the use of derivatives.
CALCULATIONf(x)=5x
∴f'(10)=f(10+h)−f(10)h
=5(10+h)−5(10)
= h→0/h
=[tex]\lim_{h\to 0}[/tex]5h/h
=[tex]\lim_{h\to 0}[/tex]5
=5.
LEARN MORE ABOUT DERIVATIVES HERE :
brainly.com/question/28395522
#SPJ4
Given −47.01 × 6.2, find the product.
−291.462
−282.02
−37.608
29.1462
Step-by-step explanation:
-282.02 its korrect now
Can someone please help mee (20 points
brainliest!!!)
what multiplication equation can you use to find 5 divided by 1/3
The multiplication equation to find 5 divided by 1/3 is 5 x 3 = 15.
What is division?The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.
At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another.
Unlike the other basic operations, when dividing natural numbers there is sometimes a remainder that will not go evenly into the dividend.
Division has two parts dividend and divisor.
Division is not commutative, meaning that a / b is not always equal to b / a.
Division is also not, in general, associative.
Division is traditionally considered as left-associative.
Division is right-distributive over addition and subtraction.
Division is shown in algebra and science by placing the dividend over the divisor with a horizontal line, also called a fraction bar, between them. For example, "a divided by b" can written as:
a/b
Now it is given that,
5 divided by 1/3
This can be expressed as,
5 divided by 1/3 = 5 ÷ 1/3
Since to convert the division of fraction into multiplication, we reciprocate the fraction
So, applying division we get,
5 ÷ 1/3 = 5 x 3
So, the multiplication equation is,
5 x 3
Now multiplying 5 and 3 we get,
5 x 3 = 15
this is the required multiplication equation of 5 divided by 1/3.
Thus, the multiplication equation to find 5 divided by 1/3 is 5 x 3 = 15.
To learn more about Division :
brainly.com/question/28032495
#SPJ1
2000, 200, 20, 2, ... what 3 numbers come next pls help
Answer:
2, 20, 200, 2,000, 20,000, 200,000
Answer: 0.2, 0.02 0.002
Miles driven
120
300
380
480
Gas Use
20
24
33
39
Gallons of
gasoline used
If the car always uses the same amount of gasoline each mile, how many gallons of gasoline would be needed to
travel 480 miles?
6
15
18
2
Answer:
the answer is 70,007
Step-by-step explanation:
again the answer is 102,002
Answer:
Step-by-step explanation:
70007
Evaluate the expression when m = 7 and n = 23.
63
n
M
Answer:
If it is M x N then it is 161.
If it is 63 x M x N then it is 10,143.
W-2 The diameter of a circle is 4 units.
What is the radius of the circle?
I don't understand but it's due today help
Answer:
2 units
Step-by-step explanation:
radius = diameter/2 -> r = 4/2 = 2 units
(05.03)bev has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. calculate the area of the polygon. be sure to show all your work and explain your answer. six-sided polygon that includes two isosceles right triangles, one with height and base of 15 feet, the other height and base of 4 feet, and one rectangle measuring 25 feet by 4 feet.
The area of the six-sided polygon = 220.5 square ft.
Given that the six-sided polygon consists of two isosceles triangles and a rectangle. So the total area to be cut will be equal to the sum of areas of the triangles and the rectangle.
First triangle has base = 15 ft and height = 15 ft
Area of a 1st triangle = 1/2 x base x height
= 1/2 x 15 x 15
= 112.5 square feet
Second triangle has base = 4 ft and height = 4 ft
Area of the 2nd triangle = 1/2 x base x height
= 1/2 x 4 x 4
= 8 square ft
The rectangle has length = 25 ft and width = 4 ft
Area of the rectangle = length x width
= 25 x 4
= 100 square ft
So the total area of the six-sided polygon = 112.5 + 8 + 100
= 220.5 square ft.
Learn more about area of polygons at https://brainly.com/question/8409681
#SPJ4