Answer:
Option A) [tex]\frac{1}{x^2y^2}[/tex] is correct.
Therefore the simplified given expression [tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^2}[/tex]
Step-by-step explanation:
Given expression is [tex]\frac{x^0y^{-3}}{x^2y^{-1}}[/tex]
To simplify the given expression:
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}[/tex]
Above expression can be written as
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{(1)y^{-3}}{x^2y^{-1}}[/tex]
(since [tex]x^0=1[/tex] ,anything variable to the power "0' is 1)
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{y^{-3}}{x^2y^{-1}}[/tex]
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^{-1}y^3}[/tex] (since [tex]a^{-m}=\frac{1}{a^m}[/tex] )
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^{-1+3}}[/tex] (using the property [tex]a^m+a^n=a^{m+n}[/tex])
[tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^2}[/tex]
Therefore [tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^2}[/tex]
Therefore Option A) [tex]\frac{1}{x^2y^2}[/tex] is correct.
Therefore the simplified given expression [tex]\frac{x^0y^{-3}}{x^2y^{-1}}=\frac{1}{x^2y^2}[/tex]
How to solve -7-8(6x+5)
Answer: -47 - 48x
Step-by-step explanation: When you first take a look at this problem, it's tempting to want to subtract -7 - 8 to get -15 and then distribute the -15 through the parentheses.
You wouldn't want to subtract however before you distribute because the distributive property is a form of multiplication and remember from your order of operations that multiplication comes before subtraction.
So the first thing you want to do here is distribute and change the minus sign in front of the -8 to plus a negative 8 so that you know you are distributing a -8 through your parentheses.
So we have -7 + -8 times 6x which is -42x + -8 times 5 which is -40.
Now we have -7 + -48x + -40.
Now just combine your like terms. -7 + -40 is -47 and plus a negative 48x can be written as -48x so we have -47 - 48x.
So your answer is just -47 - 48x.
The Saxena family plans to install a light to illuminate part of their rectangular yard. Nikki and Dylan each proposed a
different spot to place the light. The proposed placements and the lit area that each produces are shown below.
Nikki's Proposed Placement
Light
27.5 ft
Dylan's Proposed Placement
Light
16.5 ft
38
38 ft
Lit area
Lit Area
60
60 ft
How do Nikki's and Dylan's proposals compare? Check all that apply.
Nikki's proposed placement will light a greater area than Dylan's placement
Dylan's proposed placement will light a greater area than Nikki's placement.
Both proposed placements will light the same sized area.
Answer
THE REAL ANSWER IS c and f
Step-by-step explanation:
I just finished and they are the only 2 and I got it right
Nikki's and Dylan's Both proposed placements will light the same sized area.
Area of triangleThe area of a triangle is defined as the total space that is enclosed by the three sides of the triangle.The area of a triangle can be determined using the formula below,A = 1/2 × b × h.
How to solve this problem?The steps are as follow:
From the question, of the base and height of Nikki's and Dylan's proposed placements are the same which is 60 and 38ft respectively.The area that would be covered by both of them would be,A= 1/2×60×38
A= 30×38
A = 1,140ft.
So, Nikki's and Dylan's Both proposed placements will light the same sized area.
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Factor completely 6x^2 − 11x − 10.
(6x + 2)(x − 5)
(6x − 2)(x + 5)
(3x + 2)(2x − 5)
(3x − 2)(2x + 5)
Answer:
(3x+2)(2x-5)
Step-by-step explanation:
you can use process of elimination on this one just distribute the equations:
3x(2x-5)+2(2x-5)
6x^2-15x+4x-10 <------ Combine like terms
6x^2-11x-10
Final answer:
Factor completely [tex]6x^2[/tex] - 11x - 10 to find the equivalent binomials involves finding two numbers that multiply to -60 and add to -11. In this case, the numbers are -15 and +4, and using factor by grouping, the correct factorization is (3x + 2)(2x - 5).
Explanation:
When asked to factor the expression [tex]6x^2[/tex] − 11x − 10 completely, we're looking for two binomial expressions that multiply together to produce the original quadratic equation. To do this, we seek two numbers that multiply to give [tex]6x^2[/tex] times -10 (which is -[tex]60x^2[/tex]) and add to give -11x. Factoring is a method to express an equation as a product of its factors.
Let's find two such numbers: -15 and +4. These numbers give a product of -60 and a sum of -11, which fits our criteria. Now we replace the middle term (-11x) with -15x+4x to use factor by grouping.
Original equation: [tex]6x^2[/tex] − 11x − 10
Rewritten with new terms: [tex]6x^2[/tex] − 15x + 4x − 10
Factor by grouping: ([tex]6x^2[/tex] − 15x) + (4x − 10)
Factor out common terms: 3x(2x − 5) + 2(2x − 5)
Factor out the common binomial: (2x − 5)(3x + 2)
The completely factored form of the quadratic equation is (3x + 2)(2x − 5).
An amusement park charges an admission fee of 40 dollars per person. The cost, C (In dollars), of admission for a group of p people is give by the following
C=40p
What is the cost of admission for a group of 3 people
Cost of admission for a group of 3 people is $ 120
Solution:
Given that amusement park charges an admission fee of 40 dollars per person
The cost, C (In dollars), of admission for a group of p people is give by the following expression:
C = 40p
Here "p" denotes the number of people
To find: cost of admission for a group of 3 people
For a group of 3 people, p = 3
Substituting p = 3 in given cost formula, we get the cost of admission for a group of 3 people
[tex]c = 40p\\\\c = 40(3) = 120[/tex]
Thus cost of admission for a group of 3 people is $ 120
15. At a school fair, 70% of the people are under 16 years old. One of the people
teachers. If there are 21 teachers at the fait, how many people are there at the air
Answer:
210 people.
Step-by-step explanation:
Here is the correct question: At a school fair, 70% of the people are under 16 years old. One third of the people remaining are teachers. If there are 21 teachers at the fair, how many people are there at the fair?
Now, solving to find total number people in the fair.
Lets assume total number of people in the fair is "x".
As given, there is 70% of total number of people are under 16 year old.
∴ People under 16 year old= [tex]70\% of x= \frac{7x}{10}[/tex]
Next, finding the number of remaining people.
∴ Number of remaining people= [tex]x-\frac{7x}{10} = x-0.7x[/tex]
Number of remaining people is 0.3x
As given, One third of the people remaining are teachers.
∴ Number of teachers= [tex]\frac{1}{3} \times 0.3x= 0.1x[/tex]
As given there are 21 teachers at the fair.
⇒ [tex]0.1x= 21\ teachers[/tex]
∴ x= [tex]\frac{21}{0.1} = 210[/tex]
Hence, total number of people in the fair are 210.
A student measures the temperature of boiling water a number of times. If the
boiling point of water is 212 degrees, which of his measurements is the most
accurate?
A: 205.46 degrees F
B: 212.1 degrees F
C: 210 degrees F
D: 213.15 degrees F
The most accurate measurement of the boiling point of water is option B: 212.1 degrees F.
Explanation:The most accurate measurement of the boiling point of water is option B: 212.1 degrees F.
When measuring the temperature of boiling water, it is important to consider the accuracy and precision of the measuring instrument. The given options range between 205.46 and 213.15 degrees F, but the boiling point of water is widely accepted to be 212 degrees F at standard atmospheric pressure.
Therefore, the measurement closest to this accepted value is the most accurate, which is option B: 212.1 degrees F.
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Answer:
G. 17.3
solution:
CAN SOMEONE HELP ME FIND THE DISTANCE..
The angle of elevation from point C to point A is [tex]32^{\circ}[/tex]
Solution:
Given that we have to find the angle of elevation from point C to Point A
Given in figure that, angle A = [tex]58^{\circ}[/tex]
Given is a right angled triangle ABC where angle B = [tex]90^{\circ}[/tex]
We have to find angle C
The angle sum property of a triangle states that the angles of a triangle always add up to 180°
Therefore, in given triangle ABC
angle A + angle B + angle C = 180
[tex]58^{\circ} + 90^{\circ} + C = 180^{\circ}[/tex]
[tex]148^{\circ} + C = 180^{\circ}\\\\C = 180^{\circ} - 148^{\circ}\\\\C = 32^{\circ}[/tex]
Therefore angle C = [tex]32^{\circ}[/tex]
Find the value of x when a = 7/2, h = 10, k = 15, If
Answer:
9
Step-by-step explanation:
x= hk/ (k+h)(a-2)
10*15 (15+10) (7/2-2)= 9
please help 56 POINTS
If the sum of a number and five is doubled, the results is one less than the number.find the number
The number is -11.
Step-by-step explanation:
Let,
the number be x.
According to given statement;
Sum of a number and five is doubled;
2(x+5)
is equals to one less than the number
= x-1
Combining both the sides and forming an equation
2(x+5)=x-1
[tex]2x+10=x-1\\2x-x=-1-10\\x=-11\\[/tex]
The number is -11.
Keywords: addition, subtraction
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what is the solution set of -9x greater than 27
Answer:
x<-3
Step-by-step explanation:
-9x>27
x>27/-9
x>-3
Find the value of x and y.
Answer:
Step-by-step explanation:
CD and AB are parallel; DB transverse
∠D + ∠B = 180 {co interior angles}
112 + 27 + y = 180
139 + y = 180
y = 180 - 139
y = 41
In ΔABC,
49 + x + y = 180 ( sum of all angles of triangle}
49 + x + 41 = 180
90 + x = 180
x = 180 - 90
x = 90
Match the real-world problem to its constant of proportionality.
$4.16 for 4 pounds of bananas
$16.48 for 8 pounds of potatoes
$18.36 for 2 pizzas
2 cups of flour to make 36 cookies
9.18,1.04,18,2.06
Real word problem ⇒ constant of proportionality
$4.16 for 4 pounds of bananas ⇒ 1.04
$16.48 for 8 pounds of potatoes ⇒ 2.06
$18.36 for 2 pizzas ⇒ 9.18
2 cups of flour to make 36 cookies ⇒ 18
Solution:
A proportional relationship is one in which two quantities vary directly with each other.
We say the variable y varies directly as x,
if for x ∝ y
then, x = y k
Where "k" is called constant of proportionality
[tex]k = \frac{x}{y}[/tex]
$4.16 for 4 pounds of bananas
x = 4.16 and y = 4
[tex]k = \frac{4.16}{4} = 1.04[/tex]
Thus constant of proportionality is 1.04
$16.48 for 8 pounds of potatoes
x = 16.48 and y = 8
[tex]k = \frac{16.48}{8} = 2.06[/tex]
Thus constant of proportionality is 2.06
$18.36 for 2 pizzas
x = 18.36 and y = 2
[tex]k = \frac{18.36}{2} = 9.18[/tex]
Thus constant of proportionality is 9.18
2 cups of flour to make 36 cookies
x = 36 and y = 2
[tex]k = \frac{36}{2} = 18[/tex]
Thus constant of proportionality is 18
you want to save $5,000 for future family vacation. if the bank pays 4.3% compounded monthly for 3 years, then how much will you need to invest to reach your vacation goal?
Answer:
The principal amount invested is $4395.93 .
Step-by-step explanation:
Given as :
The Amount that saved for future = A = $5,000
The bank applied rate of interest = r = 4.3% compounded monthly
The time period of loan = t = 3 years
Let the principal amount invested = $p
Now, From monthly Compound Interest method
Amount = principal × [tex](1+\dfrac{\textrm rate}{12\times 100})^{12\times time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{12\times 100})^{12\times t}[/tex]
Or, $5000 = p × [tex](1+\dfrac{\textrm 4.3}{12\times 100})^{12\times 3}[/tex]
Or, $5000 = p × [tex](1.003583)^{36}[/tex]
Or, $5000 = p × 1.137414
∴ p = [tex]\dfrac{5000}{1.137414}[/tex]
i.e p = $4395.93
So, The principal amount invested = p = $4395.93
Hence, The principal amount invested is $4395.93 . Answer
Avery’s water bottle holds 300 milliliters. Dashawn’s container holds 3/4 as much water how much do both containers hold?
Answer: Avery's bottle holds 300 milliliters. If Dashawn's container holds 3/4 as much, then his container can hold 225 milliliters. Added together, both containers can hold 525.
Step-by-step explanation: 3/4 of 300 is 225. 300 + 225 = 525.
dose y= -3 have a negative slope
Answer:
no because it is just a straight line. a dot is plotted at (0,-3) and a straight line is horizontal.
Can someone help me solve this question I can't seem to manage it
Answer:
LA=6 WA=4 LB=6 WB=2
Step-by-step explanation:
Its a square so the sides are 6cm. 2:1 ratio means A is 6*4=24 cm while B is 6*2=12cm.
Sarah and George wanted to buy some sweets so they decided to buy brownies and banana bread Sarah bought four boxes of brownies and six loaves of banana bread George bought five boxes of brownies and three loaves of banana bread is Sarah spent $44 and George spent $37 determine how much the cost is for a box of brownies and a loaf of banana bread
Answer:
Cost of a box of brownies = $5
Cost of a loaf of banana bread = $4
Step-by-step explanation:
Let, x= box of brownies.
y=loaf of banana bread.
Now,
Sarah bought 4 boxes of brownies and 6 loaves of banana at $44, after expressing this in equation form we get:-
[tex]4x+6y=44[/tex] --------------------------(equation 1)
And George bought 5 boxes of brownies and 3 loaves of banana at $37, after expressing this in equation form we get:-
[tex]5x+3y=37[/tex] --------------------------(equation 2)
Now,
[tex]4x+6y=44[/tex]
[tex]4x=44-6y[/tex]
[tex]x=\frac{44-6y}{4}[/tex]
[tex]x=11-\frac{6}{4}y[/tex]
[tex]x=11-\frac{3}{2}y[/tex]------------------(equation 3)
Now substituting equation 3 in equation 2 we get,
[tex]5x+3y=37[/tex]
[tex]5(11-\frac{3}{2}y)+3y=37[/tex]
[tex]55-(\frac{15}{2}\times y) +3y=37[/tex]
[tex]55-37=(\frac{15}{2}\times y)-3y[/tex]
[tex]18=7.5y-3y[/tex]
[tex]18=4.5y[/tex]
[tex]y=4[/tex] ----------------------------------(Equation 4)
Now putting value of y from equation 4 in equation 3
i.e. [tex]x=11-\frac{3}{2}y[/tex]
[tex]x=11-\frac{3\times 4}{2}[/tex]
[tex]x=11-6[/tex]
[tex]x=5[/tex]
Therefore the cost of a box of brownies = $5
the cost of a loaf of banana bread = $4
What is the probability of spinning these two spinners and having each one land
on a 3? Write the probability as a decimal.
Answer:
The probabilities are 0.4 and 0.6 respectively.
Step-by-step explanation:
We are given two spinning wheels with numbers on it and we have to find the probability of getting 3.
In the first wheel, there are 5 slots and the numbers are 3, 3, 2, 5 and 4.
So the probability of getting 3 =[tex]\frac{number of 3's}{total number of slots}[/tex]
= [tex]\frac{2}{5}[/tex]
= 0.4
In the second spinner there are three 3's and total of 5 slots.
So probability of getting 3 = [tex]\frac{number of 3's}{total number of slots}[/tex]
= [tex]\frac{3}{5}[/tex]
= 0.6
Hence the probabilities are 0.4 and 0.6 respectively.
WILL GIVE BRAINLIST
Fill in the blank with a number to make the expression a perfect square.
w² - 6w + ___
Answer:
9 should be added to the expression to make it a perfect square
Step-by-step explanation:
Given expression:
[tex]w^2-6w+_-[/tex]
To fill in the missing term such that the expression becomes a perfect square.
Solution:
In order to make the expression a perfect square we will use completing the square method.
We have : [tex]w^2-6w[/tex]
By complete the square method we will add the square of the quotient of the co-efficient of the middle term which is [tex]-6w[/tex] and 2.
The co-efficient of middle term = -6
Thus the number to be added will be = [tex](\frac{-6}{2})^2=(-3)^2=9[/tex]
Thus, on adding 9 the expression will become:
[tex]w^2-6w+9[/tex] which is a perfect square of the binomial [tex](w-3)[/tex]
This can be shown as:
[tex](w-3)^2=w^2-6w+9[/tex]
Thus, we add 9 to the expression to make it a perfect square.
Answer:
9
Step-by-step explanation:
Given: [tex]w^{2} -6w+[/tex]
Finding the number to make expression a perfect square.
From the expression we can see that coefficient of variable is 1 and -6.
Now, lets take a= 1 and b= -6 and finding c .
∴ c= [tex]\frac{b^{2} }{4a}[/tex]
Subtituting the value of a and b.
⇒ c= [tex]\frac{-6^{2} }{4\times 1} = \frac{36}{4}[/tex] (∵ [tex]-6\times -6= 36[/tex])
∴ c= 9
Next putting the value in the expression.
[tex]w^{2} -6w+9[/tex]
= [tex](w-3)(w-3)[/tex]
= [tex](w-3)^{2}[/tex]
Hence, 9 is a number to make the expression a perfect square.
BRAINIAC IN LAW OF SINES?? Ill give brainlest and extra points
Answer:
[tex]x \approx 31.8[/tex]
Step-by-step explanation:
[tex]\frac{\sin(75)}{22}=\frac{\sin(x)}{12}[/tex]
Cross multiply:
[tex]\sin(75) \cdot 12=\sin(x)\cdot 22[/tex]
Divide both sides by 22:
[tex]\frac{\sin(75) \cdot 12}{22}=\sin(x)[/tex]
Take [tex]\sin^{-1}( )[/tex] of both sides:
[tex]\sin^{-1}(\frac{\sin(75) \cdot 12}{22}=x[/tex]
Put left hand side into a calculator now:
[tex]31.7941 \approx x[/tex]
To the nearest tenth that is: [tex]x \approx 31.8[/tex]
Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 8 cm/min. How fast is the area of the pool increasing when the radius is 13 cm?
Answer:
The area of the pool increasing at the rate of 653.12[tex]cm^2/min[/tex] when the radius is 13 cm
Step-by-step explanation:
Given:
radius of the pool increases at a rate of 8 cm/min
To Find:
How fast is the area of the pool increasing when the radius is 13 cm ?
Solution:
we are given with the circular pool
hence the area of the circular pool =
A =[tex]\pi r^2[/tex]-----------------------------(1)
The area of the pool os increasing at the rate of 8 cm/min, meaning that the arae of the pool is changing with respect to time t
so differentiating eq (1) with respect to t , we have
[tex]\frac{d A}{d t}=\pi \cdot 2 r \cdot \frac{d r}{d t}[/tex]
we have to find [tex]\frac{d A}{d t}[/tex] with [tex]\frac{d r}{d t}[/tex] = 8 cm/min and r = 13cm
substituting the values
[tex]\frac{d A}{d t}=\pi \cdot 2 (13) \cdot 8[/tex]
[tex]\frac{d A}{d t}=\pi \cdot 26 \cdot 8[/tex]
[tex]\frac{d A}{d t}=\pi \cdot 208[/tex]
[tex]\frac{d A}{d t}= 208 \pi[/tex]
[tex]\frac{d A}{d t}=653.12[/tex]
Answer:
208pi cm^2/min
Step-by-step explanation:Take the derivative of the formula for Area and substitute the values
Given that AD and BC are parallel, find the value of x.
Answer:
Therefore the value of x is 15.
Step-by-step explanation:
Given:
AD || BC
m∠ B = (9x + 15)°
m∠ A = (3x - 15)°
To Find:
x = ?
Solution:
AD || BC ...............Given
If two lines are parallel and sum of the interior angles are supplementary.
i.e m∠ B and m∠ A are interior between Parallel lines.
∴ [tex]\angle B + \angle C =180\\[/tex]
Substituting the given values we get
∴ [tex](9x + 15)+( 3x - 15)=180\\12x=180\\\\x=\frac{180}{12} \\\\\therefore x =15[/tex]
Therefore the value of x is 15.
Write the definition of midpoint, provide a supporting figure
Step-by-step explanation: Using the diagram shown which I have provided in the image attached, the definition of a midpoint states that M is the midpoint of segment LN, then segment LN ≅ to MN.
The definition of a midpoint can also be stated the other way around. using the diagram shown, if segment LN ≅ to segment MN, then M is the midpoint of segment LN.
We can use hash marks in the figure to show that are 2 segments are congruent.
if 10,000 bacteria are present initially and the number of bacteria doubles in 5 hours, how many bacteria will there be in 24 hours?
Answer:
20,000
Step-by-step explanation:
-5(4m - 2) = -2/3 + 6m).
Answer:
m=16/39
Step-by-step explanation:
-5(4m-2)=-2/3+6m
-20m+10=-2/3+6m
-20m-6m=-2/3-10
-26m=-2/3-30/3
-26m=-32/3
26m=32/3
m=(32/3)/26
m=(32/3)(1/26)
m=32/78
m=16/39
What is the slope? Help me please I really am stuck on this
can anyone help to find the answer to this:
17x - 2x/3
Answer:
49x
Step-by-step explanation:
what interval contains a positive solution to the equation 0.2x^2-0.8x=1.6
Step-by-step explanation:
0.2x² − 0.8x = 1.6
Multiply both sides by 5.
x² − 4x = 8
Complete the square by adding 4 to both sides.
x² − 4x + 4 = 12
(x − 2)² = 12
x − 2 = ±√12
x = 2 ± √12
The positive solution is x = 2 + √12 ≈ 5.46.