Given:
The expressions are
[tex]-6a^2b^{-1}[/tex]
[tex]\dfrac{5}{y^{-3}}[/tex]
To find:
The simplified form of each expression.
Solution:
We have,
[tex]-6a^2b^{-1}[/tex]
[tex]=-6a^2(\dfrac{1}{b})[/tex] [tex][\because x^{-n}=\dfrac{1}{x^n}][/tex]
[tex]=-\dfrac{6a^2}{b}[/tex]
Therefore, the simplified form of [tex]-6a^2b^{-1}[/tex] is [tex]-\dfrac{6a^2}{b}[/tex].
We have,
[tex]\dfrac{5}{y^{-3}}[/tex]
[tex]=\dfrac{5}{\dfrac{1}{y^3}}[/tex] [tex][\because x^{-n}=\dfrac{1}{x^n}][/tex]
[tex]=5\times \dfrac{y^3}{1}[/tex]
[tex]=5y^3[/tex]
Therefore, the simplified form of [tex]\dfrac{5}{y^{-3}}[/tex] is [tex]5y^3[/tex].
Which is the factored form of 6x^3 + 8?
For Sunday brunch, Alisha is making a recipe that requires 8cups of milk. She has 3 quarts of milk. Does she have enough for the recipe?
Answer:
Step-by-step explanation:
She does have enough
Amir’s average math score for the first 4 tests of the school year is 88 Which equation can be used to calculate what Amir’s average must be on the next two tests so that his overall average is 90
Answer:
Equation that can be used = [tex]\frac{4(88)+2x}{6} = 90[/tex]
Step-by-step explanation:
Given that:
Amir's average on four tests = 88
Let,
x be the score on one test
For two tests = 2x
Sum of all scores = Average of four tests + Score of two tests
Sum of all scores = 4(88) + 2x
Total number of tests = 6
Overall average needed = 90
Now,
[tex]Average = \frac{Sum\ of\ quantities}{Number\ of\ quantities}\\90 = \frac{4(88)+2x}{6}\\\\\frac{4(88)+2x}{6} = 90[/tex]
Hence,
Equation that can be used = [tex]\frac{4(88)+2x}{6} = 90[/tex]
what kind of angles are 2 and 6
Answer:
A. corresponding
Step-by-step explanation:
Corresponding angles are angles that lie on top of two parallel lines.
Alternate interior angles are angles that lie on two sides of parallel lines and are mostly located with one angle up and one angle down.
Same side interior angles are angles within two parallel lines.
Answer:
corresponding angles
Step-by-step explanation:
∠ 2 and ∠ 6 are corresponding angles because each is in the same position ( upper right- hand corner ) in its group of 4 angles.
Name five fractions whose values are between 1/2and
7/8
Answer:
9/16 10/16 11/16 12/16 13/16
Step-by-step explanation:
On a field trip, there are 3 chaperones for every 20 students. There are 92 people on the trip. Answer these questions. If you get stuck, consider using a tape diagram.
How many chaperones are there?
Answer:
14
Step-by-step explanation:
20 times four is 80 so we already have 12 chaperones because there are 3 chaperones for every 20 students.
20 divided by 3 is 6.6
We cannot have .6 of a chaperone so we round up to 7
And since 7 can only go into 20 two times
That means there are two more chaperones
2+12 is 14
There are 14 chaperones for the 92 students
(Hope this helps and hope im right)
Answer:
80(students)
12(chaperons)
Step-by-step explanation:
since total of 92 people in the trip including student and chaperon,add groups of 23 to become 92 or use this equation:
(20+3)×y=92
23y=92
y=92/23
y=4
therefore,
20×4=80(students)
3×4=12(chaperons)
Due today please help!
Pls help and take your time cuz if I get this wrong I fail WILL MARK BRAINIEST
target sells 24 bottles of water for $3 and 36 bottles of water for $4 which is the better buy and by how much?
A 24 bottles for $3 by 1.5 ¢ per bottle
B 24 bottles for $3 by 70 ¢ per bottle
C 24 bottles for $3 by 75 ¢ per bottle
D 36 bottles for $4 by 1.4 ¢ per bottle
x
Equivalent ratios
ord
Select two ratios that are equivalent to 4: 18.
Please I need help ............
Answer:
Dileah is correct
Step-by-step explanation:
6 is greater than 5 but yet its 6/5 and makes it an improper fraction. Its an enlargement
Answer:
Delilah
Step-by-step explanation:
It is an enlargement since the x and y values was multiplied by a number greater than 1.
Find the measure of angle A.
75°
x + 53
+68
Answer:
Step-by-step explanaton:
Factor the expression 4x + 32. Explain each step you
take in the process.
Answer:
4x + 32 = 4x + 4.8 = || 4. (x + 8) ||
Step-by-step explanation:
HELP ASAP PLEASE
Kristen Lynn sells college textbooks on commission. She gets 4% on the first
$5000 of sales, 8% on the next $5000 of sales, and 12% on sales over
$10,000. In July of 1997 Kristen's sales total was $13,500.
Answer:
Step-by-step explanation:
5000 at 4% =200 (5000*0.04)
5000 at 8% = 400 (5000*0.08)
3,500 at 12% = 420 (3500*0.12)
200+400+420 = 1020
Her commission is 1,020 dollars :)
convert 11/8 and 5/9 to decimals
Solve x^2- 2x - 4 = 0
Answer:
[tex]\displaystyle x= 1\pm \sqrt{5}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Step-by-step explanation:
Step 1: Define
x² - 2x - 4 = 0
Step 2: Identify Variables
a = 1
b = -2
c = -4
Step 3: Solve for x
Substitute [QF]: [tex]\displaystyle x=\frac{2\pm\sqrt{(-2)^2-4(1)(-4)} }{2(1)}[/tex]Exponents: [tex]\displaystyle x=\frac{2\pm\sqrt{4-4(1)(-4)} }{2(1)}[/tex]Multiply: [tex]\displaystyle x=\frac{2\pm\sqrt{4+16} }{2}[/tex]Add: [tex]\displaystyle x=\frac{2\pm\sqrt{20} }{2}[/tex]Simplify: [tex]\displaystyle x=\frac{2\pm 2\sqrt{5} }{2}[/tex]Factor: [tex]\displaystyle x=\frac{2(1\pm \sqrt{5}) }{2}[/tex]Divide: [tex]\displaystyle x= 1\pm \sqrt{5}[/tex]Answer:
yes
Step-by-step explanation:
What is the value of 12⁰?
Answer:
1
Step-by-step explanation:
Anything to the power of zero is = 1
Answer: the answer is 1
Step-by-step explanation:
Find the value of x in a triangle 68 27
help with the question above I have NO IDEA
Answer:
I would say not a function but im not 100% sure, i would go with not a function. Tell me if im wrong.
Step-by-step explanation:
2. Two teachers, Mr. Donahue and Mrs. Ortiz, decide to buy mechanical pencils and rulers for their classrooms. Mrs. Ortiz buys 50 mechanical pencils and 30 rulers for $55. Mr. Donahue buys 30 of each for $45. What was the price per mechanical pencil? What was the price per ruler?
a. Fill in the equation for the cost of Mrs. Ortiz's purchase. Let x represent the cost of a pencil and y represent the cost of a ruler.
______ = ______ x + ______ y
b. Fill in the equation for the cost of Mr. Donahue's purchase. Let x represent the cost of a pencil and y represent the cost of a ruler.
______ = ______ x + ______ y
c. Circle the best method for solving the system:
Graphing Substitution Elimination
d. Solve the system using the method you chose.
A mechanical pencil costs ______ and a ruler costs _______.
e. Check your answer:
Answer:
Step-by-step explanation:
a. Fill in the equation for the cost of Mrs. Ortiz's purchase. Let x represent the cost of a pencil and y represent the cost of a ruler.
__$55__ = __50__ x + __30_ y
b. Fill in the equation for the cost of Mr. Donahue's purchase. Let x represent the cost of a pencil and y represent the cost of a ruler.
__$45__ = __30__ x + __30__ y
c. Circle the best method for solving the system:
Elimination
d. Solve the system using the method you chose.
55 =50x+30y
-1(45) =(30x+30y)-1 = -45=-30x-30y
55 =50x+30y
+ -45=-30x-30y
10=20x
(1/20)10=20x(1/20)
0.50=x
3(55) =(50x+30y )3 = 165=150x+90y
-5(45) =(30x+30y)-5 = -225=-150x-150y
165 =150x+90y
+ -225=-150x-150y
-60=-60y
(1/-60)-60=-60y(1/-60)
1=y
A mechanical pencil costs _$0.50__ and a ruler costs __$1.00__.
e. Check your answer:
$55=50x+30y $45=30x+30y
$55=50(0.5)+30(1) $45=30(0.5)+30(1)
$55=25+30 $45=15+30
$55=$55 $45=$45
A mechanical pencil costs $0.50 and a ruler costs $1.00.
What is meant by cost?In calculus, a cost function is a mathematical formula used to determine how much it will cost to produce a certain number of units. The total cost formula is used to calculate the total cost by combining the variable and fixed costs of providing goods. Total cost = (average fixed cost x average variable cost) x number of units produced. A unit price is defined as a price expressed as a quantity of one, such as $25 per ticket or $0.89 per can. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio.The current answer as follows:
a. Fill in the blanks to calculate Mrs. Ortiz's purchase price. Let x denote the price of a pencil and y the price of a ruler.
$55 = 50x + 30y
b.Fill in the blanks with the cost of Mr. Donahue's purchase. Let x represent the cost of a pencil and y represent the cost of a ruler.
$45 = 30x + 30y
c. Circle the best method for solving the system:
Elimination
d. Solve the system using the method you chose.
55 = 50x + 30y - 1(45) = (30x + 30y) - 1 = -45 = -30x - 30y
55 = 50x + 30y + -45 = -30x - 30y
10 = 20x
(1/20)10 = 20x (1/20)
0.50 = x
3(55) = (50x + 30y )3 = 165 = 150x + 90y
-5 (45) = (30x + 30y) - 5 = -225 = -150x - 150y
165 = 150x + 90y + -225 = -150x - 150y
-60 = -60y
(1/-60) -60 = -60y (1/-60)
1 = y
A mechanical pencil costs $0.50 and a ruler costs $1.00.
To learn more about cost, refer to:
https://brainly.com/question/25109150
#SPJ2
What is the equation in standard form using integers y+4=3/4(x+7)
What’s the area and perimeter
Answer:
Step-by-step explanation:
1. ✔️Using Pythagorean Theorem, thus the missing length, x, would be:
x² = 19² - 17² = 72
x = √72
x = 8.5 (nearest tenth)
✔️Area = ½*b*h
b = 17
h = 8.5
Area = ½*17*8.5 = 72.25 units²
✔️Perimeter = 19 + 17 + 8.5 = 44.5 units
2. ✔️Using Pythagorean Theorem, thus the missing length, x, would be:
x² = 5² + 13² = 194
x = √194
x = 13.9 (nearest tenth)
✔️Area = ½*b*h
b = 13
h = 5
Area = ½*13*5 = 32.5 units²
✔️Perimeter = 13 + 5 + 13.9 = 31.9 unit
3. ✔️Using Pythagorean Theorem, thus the missing length, x, would be:
x² = 20² - 10² = 300
x = √300
x = 17.3 (nearest tenth)
✔️Area = ½*b*h
b = 17.3
h = 10
Area = ½*17.3*10 = 86.5 units²
✔️Perimeter = 17.3 + 10 + 20 = 47.3 unit
4. ✔️Using Pythagorean Theorem, thus the missing length, x, would be:
x² = 5² + 14² = 221
x = √221
x = 14.9 (nearest tenth)
✔️Area = ½*b*h
b = 14
h = 5
Area = ½*14*5 = 35 units²
✔️Perimeter = 14.9 + 14 + 5 = 33.9 unit
Find the value of x and fill in the table below.
a man buys a washing machine who price VAT(value added tax) is birr 175.its VAT is charged at 15% how much did the man actually pay?
Answer:
He actually paid a sum of $201.25
Step-by-step explanation:
We simply add the vat value to the cost of the machine
Mathematically, that’s (
175 + 15% of 175
= 175 + (15/100 * 175)
= 175 + 26.25
= $201.25
B^10/B^2=B^5 True or false
Answer:
True
Step-by-step explanation:
how many 3/5s are in 4/3s
Answer:
how does this question make any sense
4/3s is 1 and 1/3
figure out how many 3/5ths go into that
Step-by-step explanation:
Answer:
This dont make sense
Step-by-step explanation:
HELP LOTS OF POINTS AND BRAINLIEST
Find each probability for one roll of a number cube:
12. P(4) 13. P(odd)
Answer:
12. P(4) = 1/6
13. P(odd) = 3/6 = 1/2
Step-by-step explanation:
hope this helps, pls mark brainliest :D
Nhich relationships could have a negative correlation? Select three options.
Number of hours on video games and test scores
Speed of a car and minimum stopping distance
average running speed and total race time
adult's head circumference and age
outside temperature and amount of a heating bill
Answer:
A,C,E
Step-by-step explanation:
Just took teh Semester Exam for Math, got the answer correct
Sry im 2 days late lol
Answer:
ITS A,C,E
Step-by-step explanation:
just did a exam lol
Solve the inequality 2.5d+11.4<-1.3d solve the inequality
Answer:
d < -3
Step-by-step explanation:
2.5d+11.4<-1.3d
3.8d+11.4<0
3.8d<-11.4
d < -3
Just isolate and solve for x and remember, what you do to one side, you must do to the other.
Hope this helps!
Answer:
[tex]d < -3[/tex]
Step-by-step explanation:
Move the constant to the right-hand side and change its sign:
[tex]2.5d < - 1.3d - 11.4[/tex]
Move the variable to the left-hand side and change its signs:
[tex]2.5d + 1.3d < 11.4[/tex]
Collect like terms:
[tex]3.8d < - 11.4[/tex]
Divide both sides of the inequality by 3.8:
[tex]3.8 \div - 11.4 = - 3[/tex]
Therefore, the answer is d < -3.
David made $216 for 12 hours of work. At the same rate, how many hours would he have to work to make $306?
Answer:
17 hours
Step-by-step explanation:
216/12 = $18 per hour
306/18 = 17 hours.
Hope this helps! :)
Answer:
Is 17 hours the correct