The negative and zero exponents of the given exponents will be 3 x¹⁵y²⁰ × x⁻³y⁻⁵z⁰.
What is the law of indices?Index (indices) in Maths is the power or exponent which is raised to a number or a variable.
The mathematics of power or exponent of any number is called indices.
For example 5³ = 5²5 here we break 5³ into 5² and 5 so it is called the law of indices.
Another example could be 7² = 7³/7 here we divide to obtain power 2.
As per the given,
36 x¹⁵y²⁰/ 12 x³y⁵ = [(36/12) (x¹⁵y²⁰)/(x³y⁵)]
36 x¹⁵y²⁰/ 12 x³y⁵ = 3x¹⁵y²⁰ × x⁻³y⁻⁵z⁰
Hence "The negative and zero exponents of the given exponents will be 3 x¹⁵y²⁰ × x⁻³y⁻⁵z⁰".
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When loaded with bricks, a lorry has a mass of 11600 kg. If the mass of the bricks is three times that of the empty lorry, find the mass of the bricks.
Answer:
8700kg
Step-by-step explanation:
b = mass of bricks
l = mass of lorry
b+l = total mass = 11600kg
b = 3l ==> l = b/3
substitute: b + b/3 = 11600
multiply every term by 3 to get rid of denominator: 3b + b = 34800
simplify and solve: 4b = 34800 ==> b = 8700
check: l = 8700/3 = 2900
2900 + 8700 = 11600? YES
The length of a rectangle is 8 inches more than it’s width. It’s area is 308 square inches. The length is?
Answer:38.5
Step-by-step explanation:
308/8 =38.5
Answer: 8ft
Step-by-step explanation:
the length of the room is 8fr
Solve the system of linear equations by substitution.
5x + 2y = 9
-0.5x - y = 7.5
Answer:
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{5x+2y=9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \atop {-0.5x-y=7.5\ \ \ \ \ \ \ \ |\cdot2}} \right. \\\\\\\left \{ {{5x+2y=9} \atop {-x-2y=15}} \right. \\+\\--------\\4x=24\ \ \Rightarrow\ x=24:4\Rightarrow\ x=6\\\\y=-0.5x-7.5=-0.5\cdot6-7.5=-3-7.5=-10.5\\\\\boxed{(x;y)=(6;-10.5)}[/tex]
Leila's vegetable garden has an area of 400 ft. It is the shape of a rectangle with a length of 40 ft and a width of She has decided to expand the garden to make room for several new varieties of lettuce. The new garden will be a larger rectangle. She plans on making the new length 2 times the current length and the new' width 4 times the current width.
(a) Fill in the blanks to describe the size of Leila's new garden.
___ ft x ___ ft = ___ ft²
(b) How will the expansion change the area of the garden?
The area of the new garden will be _____ times the area of the current garden.
(c) Leila's friend Keiko also wants to expand her rectangular garden. Keiko wants her new garden to be a rectangle that has 20 times the area of her current garden. She goes to Leila for advice. Fill in the blank so that Leila's advice to Keiko is correct.
Make the new length 5 times the current length, and make the new width _____times the current width.
The answers of all the blanks are as:
a) 3200ft².
b) 8 times.
c) 100ft.
What is the area of the rectangle?
When calculating a rectangle's area, we multiply the length by the width of the rectangle.
we have,
length = 40ft
width = 10ft
Leila's vegetable garden has an area of 400 ft.
a)
new length = 40 * 2 =80ft
new width = 10 * 4 = 40ft
Therefore, this describes the size of Leila's new garden :
= 80 * 40 = 3200ft²
b)
3200 / 400 = 8
The expansion changes the area of the garden:
The area of the new garden will be 8 times the area of the current garden.
c)
Leila's friend Keiko wants to expand her rectangular garden by 20 times the area of her current garden:
400 * 20 = 8000ft²
Keiko's garden length would be 5 times the current length:
40 * 5 = 80ft
and the new width would be the current width :
new width of Keiko's garden = 8000 / 80 = 100ft.
Hence, the answers of all the blanks are as:
a) 3200ft².
b) 8 times.
c) 100ft.
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Four consecutive even integers have a sum of 332. What is the least of these integer
Answer: 80
Step-by-step explanation:
set the 4 numbers to be x,x+2,x+4,x+6
They add up to 332 so the equation would be
x+(x+2)+(x+4)+(x+6)=332
4x=320
x=80
the rest of the numbers are 82,84,86
smallest is 80
Find the solution of the system of equations.
4x - y = -1
-4x-6y=-34
Answer:
Step-by-step explanation:
4x-3y=11. 2 (2x-7y=22).=> 4x-14y=44. 4x-3y=11....................1. 4x-14y=44. 11y= -33. y= -3. then,putting it in 1. 4x-3 (-3)=11.
Solve for x and the missing measures given QS = 34 and TS = 3x + 2
Answer:
x = 5
TS = 17
QT = 17
Step-by-step explanation:
The tick marks show us that line segment QT is equal to TS.
QS = QT + TS and QT and TS are the same length
34 = 2(3x + 2) Distribute the 2
34 = 6x + 4 Subtract 4 from both sides
30 = 6x Divide both sides by 6
5 = x
Substitute in 5 for x
3x + 2
3(5) + 2
15 + 2 = 17
TS is 17
QT is 17
Old Navy had $940 worth of orders for shirts. The prices for the shirts were categorized by style: $10 for tank tops, $14 for graphic tees, and $22 for polos. The number of polos ordered was one more than half the number of graphic tees, and the number of graphic tees ordered was eight less than twice the number of tank tops. Determine the number of each type of shirt ordered.
The number of each type of shirt ordered are as follows;
number of graphic tees = 29number of tanks tops = 19number of polos = 15How to find the number of each type of shirt ordered?Old Navy had $940 worth of orders for shirts.
The prices for the shirts were categorized by style: $10 for tank tops, $14 for graphic tees, and $22 for polos.
The number of polos ordered was one more than half the number of graphic tees, and the number of graphic tees ordered was eight less than twice the number of tank tops.
let
x = number of graphic tees
Hence,
number of polos = 1 + 1 / 2 x
Number of tank tops = 1 / 2 x + 4
Therefore, the total
14x + 10(1 / 2 x + 4) + 22(1 + 1 / 2 x) = 940
14x + 5x + 40 + 22 + 11x = 940
30x + 62 = 940
30x = 878
x = 29.266667
x = 29
number of polos = 1 + 1 / 2 (29) ≈ 15
Number of tank tops = 1 / 2 (29) + 4 ≈ 19
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A recipe called for the ratio of sugar to flour to be 7 : 3. If you used 63 ounces of sugar, how many ounces of flour would you need to use? Solve by using equivalent fractions.
_________________ounces of flour (write just the number)
Correct answer is:
27
Answer:
There would be 27 ounces of flour
Step-by-step explanation:
The ratio is 7:3 for sugar to flour.
I divided the 63 ounces of sugar by 7 to earn 9
Now, I multiplied 9 by 3 to get 27
Now thee ratio is 63:27
If you divide 7 and 3 you will get 2.3 repeating
If you divide 63 and 27 you will also get 2.3 repeating
Hope that makes sense! ;)
17. Write 2 numbers that are less than -1000?
Answer: -1001, -1002
Step-by-step explanation:
Solve w=1/2x^2y for x
Answer : x= [tex]\sqrt{2wy}[/tex]/ y
Step-by-step explanation:
Alan purchased three types of pipe for a plumbing job: foot of PVC pipe, foot of copper pipe, and 2 feet of cast iron
pipe. How many total feet of pipe did he purchase? (Simplify your answer and state it as a mixed number.)
O2 feet
Answer: 4 feet of pipe
Step-by-step explanation:
1(f)+1(f)+(2(f)=4(f)
f=feet
Solve one and three-fourths times two-fourths equals blank.
fourteen-sixteenths
fifteen-sixteenths
one and one-sixteenth
one and two-sixteenths
Answer:
fourteen-sixteenths or seven eights = 7/8 or 14/16
Step-by-step explanation:
What angles are linear pairs? Check all that apply.
Answer:
show the choices please.
Step-by-step explanation:
PLEASE HELP ASAP!!!! FULL ANSWER ONLY!!!
A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The quadratic function h = − 16 t^2 + 84 t + 72 models the ball's height above the ground, h , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball? ____________ feet
b) How many seconds does it take until the ball hits the ground? ____________ seconds
The time taken by the ball to hit the ground is 9 seconds in quadratic equation .
What does quartic equation mean?
A fourth-degree equation, also known as a quartic equation, is one that reduces a quartic polynomial to zero and has the formula: where a 0. A quartic function's derivative is a cubic function.
a) The maximum height of the ball can be obtained by differentiating the given quadratic function, h = -16t² + 136t + 72.
Differentiating both sides.
δh/δt = -32t + 136
-32t + 136 = 0
or, t = 136/32 = 4.5.
To check whether the value of h is maximum/minimum at t = 4.5, we differentiate
δh/δt = -32t + 136
δh/δt = -32
which is < 0, which that implies, h is maximum at t = 4.5.
the maximum height, by putting in t = 4.5, in the equation, to get:
h = -16(4.5)² + 136(4.5) + 72,
or, h = -16(20.25) + 612 + 72,
or, h = -324 + 684 = 360
Therefore, The maximum height of the ball is 360 feet.
b) the quadratic function h = -16t² + 136t + 72, as the height of the ball at the ground is 0.
Therefore, it can be written as:
0 = -16t² + 136t + 72.
or, 16t² - 136t - 72 = 0.
Solving this using the quadratic equation, we get
t = - ( -136)± √(-136)² - 4( 16 ) ( -72)/2 * 16
t = 136 ± √18496 + 4608/32
t = 136 ± √23104/32
t = 136 ± 52/32
Therefore, either t = (136+152)/32 = 9,
or, t (136 - 152)/32 = -0.5.
Since t represents time, we won't take the negative value, and hence t = 9.
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Dr. Hill charges $30 for a tutoring session, plus $0.25 per problem.
Write an equation to represent the problem.
Then, determine how many problems he helped with if he charged $47.75
Factor the expression.
- 20a-35
The positive GCF of -20a and -35 is 5. Complete each equation with an expression or integer factor.
5x -4a=-20a
5× - 7 = - 35
The expression with 5 factored out is
Answer:
5(-4a -7) = -20a -35
Step-by-step explanation:
HELP ME OUT OMG THANKS
Answer: r = 12
Step-by-step explanation:
11 - 23 = 12
YOUR SO WELCOME!!! :D
two packages of cookies cost $9.50. How much do seven packages cost?Try using a proportion to solve or finding unit rate?
Answer:
$33.25
Step-by-step explanation:
Two packages cost $9.50
Divide $9.50 by two get the cost for one package
$4.75 per package
$4.75 * 7 to get the cost for 7 packages
$33.25
A pillar of height 222 ft casts a shadow of 348 ft long.
Find the measure of the angle of elevation of the sun.
Using tangent of the angle, the angle of elevation is 32.5 degrees
Angle of ElevationThe angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
In this problem, we have to use the tangent of the angle since we know the opposite and adjacent sides
opposite side = 222adjacent side = 348Tan θ = opposite / adjacent
tanθ = 222 / 348
tan θ = 0.6379
θ = tan⁻¹(0.6379)
θ = 32.5°
The angle of elevation is 32.5 degrees
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Which ordered pairs in the form (x, y) are solutions to the equation
7x−5y=28?
Select each correct answer.
Responses
(7, 9)
Begin ordered pair 7 comma 9 end ordered pair
(4, 10)
Begin ordered pair4 comma 10 end ordered pair
(−1, −7)
Begin ordered pair negative 1 comma negative 7 end ordered pair
(−6, −14)
The ordered pair (-1, -7) is the solution to the equation 7x - 5y = 28.
Define solutions of linear equations.The collection of variable values in linear equations that yields all feasible solutions is referred to as the solution of a linear equation. In order to describe real-world issues, linear equations contain unknown values in the form of one or more variables. The collection of values for each variable in a system of linear equations is referred to as the solution set.
Consider the equation,
7x - 5y = 28
Now put the values from options, the pair values at which LHS = RHS that will be the solution to the equation.
Put x = 77, y = 9 in the equation
7(7) -5(9)
= 49 - 45
= 4
This is not a solution.
Put x =4, y= 10
7(4) - 5(10)= 28 - 50
= -32
This is not a solution.
Put x= -1, y = -7
7(-1) - 5 (-7)
= -7 + 35
= 28
So, this is the solution to the equation as LHS = RHS
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Answer:
C. the ordered pair (1.5, 10)
Step-by-step explanation:
The microwave oven uses only 1000 watts of electricity. Does this allow you to have both the microwave oven and the toaster plugged into the circuit at the same time? Explain your reasoning.
Suppose that the function h is defined, for all real numbers, as follows.
According to the query that the function h is established, h(-3) = -1/2, h(2) = 4, and h(4) = -4/1 for all real integers.
What are the different kinds of functions?An statement, rule, or law in mathematics that establishes the link between an independent variable and a predictor variables (the dependent variable). Equations may be found all around arithmetic, and they are essential for building physical connections in the sciences. A mappings between A and B will only be a function if every member in set A only has end and only 1 photo in set B. Where A & B even be two separate sets.
Briefing:Have used the top form of h(x) for x = variables -3 and 4 (which deviate from 2):
[tex]\begin{aligned}& h(x)=-\frac{1}{2} x^2+4 \\& h(-3)=-\frac{1}{2}(-3)^2+4=-\frac{9}{2}+4=-\frac{9}{2}+\frac{4}{2}=-\frac{1}{2} \\& h(4)=-\frac{1}{2}(4)^2+4=-\frac{16}{2}+4=-\frac{16}{2}+\frac{4}{1}=-\frac{4}{1}\end{aligned}[/tex]
Alternatively, h(2) must be defined explicitly as stated in the function's second description (specific for when x equals 2). Thus, h(2) equals 4.
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Solve for y. y ≥ 10 y ≥ -10 y ≤ -10 y ≤ 10
The solution for y in the inequality is (a) y ≥ 10
How to determine the solution for x?From the question, we have the following inequality expression that can be used in our computation:
42≤4.2y
Rewrite the expression properly
So, we have the following representation
42 ≤ 4.2y
Divide both sides of the inequality by 4.2
So, we have
42/4.2 ≤ 4.2y/4.2
Evaluate the quotients
So, we have the following representation
10 ≤ y
Rewrite the expression as
y ≥ 10
Hence, the solution is y ≥ 10
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Possible question
Solve for y. 42≤4.2y
y ≥ 10 y ≥ -10 y ≤ -10 y ≤ 10
What is the distance between point p and q
- P(-5,7) Q(6,7)
The distance between the two points P(-5, 7) and Q(6, 7) is 11 units.
What is the distance formula?The distance formula between two points (x₁, y₁) and (x₂, y₂) is,
D = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].
Two points are given P(-5, 7) and Q(6, 7).
∴ D = [tex]\sqrt{(6 + 5)^2 + (7 - 7)^2[/tex].
D = [tex]\sqrt{(11)^2[/tex].
D = 11 units.
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Could anyone help? I have to turn this in tomorrow!
Answer:
Step-by-step explanation:
5 is D
6 is also D
In a certain board game, players spin a spinner to determine how many spaces they advance. The odds in favor of advancing five spaces are 3/10. Find the probability of advancing five spaces.
(b)Ravi has a box of candies with different flavors. He will randomly choose one piece of candy. The probability that he chooses a strawberry-flavored piece is 6/19. What are the odds against him choosing a strawberry-flavored piece?
The probability of advancing five spaces is 3/13 and the odds against is 13 : 6
How to determine the probability and the odds?The board game
From the question, we have the odds to be
Odds in favour = 3/10
This can be rewritten as
Odds in favour = 3 : 10
For an odd represented as a : b, the probability is
Probability = a/a + b
Using the above as a guide, we have
Probability = 3/13
The box of candies
From the question, we have the probability to be
Probability = 6/19
For a probability represented as a/b, the odds against is
Odds = b - a : a
Using the above as a guide, we have
Odds = 19 - 6: 6
Evaluate
Odds = 13 : 6
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use the parallax formula to complete the following statements correctly.
A star with a parallax angle of 0.1 arcsecond is ___ away from us:
A star with a parallax angle of 0.01 arcsecond is ___ away from us:
A star with a parallax angle of 0.001 arcsecond is _____ away from us.
A star with a parallax angle of 0.0001 arcsecond is ____ away from us.
The distance between us and a star with a parallax angle of 0.1 arcsecond is 3.26 light years.
The distance between us and a star with a parallax angle of 0.01 arcsecond is 326 light years.
The distance between us and a star with a parallax angle of 0.001 arcsecond is 3260 light years.
The distance between us and a star with a parallax angle of 0.0001 arcsecond is 32600 light years.
How do you determine distances?The distance at which an object has a parallax of 1 arcsecond is known as a parsec. 3.26 light years are about how far this is.
The length of one parsec is 3.26 light years.
One arcsecond is equal to one parsec, which is equal to 3.26 light years.
We determine the other provided arcseconds based on this comparison.
3.26 light years make up a parsec.
0.1 arcsecond = 10 parsec
= 10 * 3.26 light years
= 32.6 light years
0.01 arcsecond = 100 parsec
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help meee please for a lot of points it gotta be to answer choices
Answer:
B and D
Step-by-step explanation: I got it right
"Test I. Encircle the letter that corresponds your answer. 2 points each
1. How many solutions do you get when you solve by completing the square?
a. 1
b. 2
c. 3
d. 4
2. When completing the square, what do you do if your x squared term has a coefficient?
a. Divide both sides by this coefficient
c. Multiply both sides by this coefficient
b. Nothing
d. Move it to the other side
3. Find the value of b in the quadratic equation 2x²=-5 x+7
a. 2
b. 5
c. -7
d. -5
4. Which of the following mathematical statements is not a quadratic equation?
a. 2 r²-3r-5=0
c. 3t²+7t-2=0
b. 7h+12=h²
d. s²=-8s-15
5. It is a polynomial equation of degree two that can be written in the form ax²+bx+c=0, where a, b, and c are real numbers and a≠ 0.
a. Linear Equation
b. Linear Inequality
c. Quadratic Equation
d. Quadratic Inequality)
"
The solutions using completing the square of quadratic equations are;
1) B: 2
2) A: Divide both sides by this coefficient
3) B: 5
4) All are quadratic equations
5) C. Quadratic Equation
How to solve quadratic equations by completing the square?1) Completing the square is basically a method for solving quadratic equations. Now, quadratic equations are second degree polynomials and as such have 2 roots. Thus, the solutions are 2.
2) Usually when using the method of completing the square, we are also trying to get rid of the coefficient attached to x squared and as such if we notice x squared has a coefficient, we will divide both sides by this coefficient.
3) The general form of quadratic equation is;
y = ax² + bx + c
Thus, we have;
2x² + 5x - 7 = 0
Thus, b = 5
4) They are all quadratic equations.
5) The correct one here is Quadratic Equation
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