Anna's remaining marbles are worth 175 + 6k cents, where k is the worth of a large marble in cents.
Explanation:Here's a step-by-step solution: Anna initially had 5 small marbles that are worth 25 cents each and 8 large marbles that are worth k cents each. So, her total value in cents would be 5×25 + 8×k which equals 125 + 8k.
After trading 3 large marbles for 1 large marble and 6 small marbles, she now has 6 (8-3+1) large marbles and 11 (5 + 6) small marbles. The worth of her marbles now becomes 6×k (6 large marbles worth k cents each) + 275 (11 small marbles worth 25 cents each), totalling to 275 + 6k.
Anna then gives 4 small marbles to Henry. Now, she is left with 7 small marbles and 6 large marbles. Therefore, the worth of her remaining marbles in cents is 6k (6 large marbles worth k cents each) + 175 (7 small marbles worth 25 cents each), which on simplifying gives A + Bk = 175 + 6k.
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To find the value of the marbles Anna has left in terms of k, calculate the total value of the marbles started, subtract the value lost, and simplify the equation. The value of the marbles Anna has left is 275 cents + 10k cents.
Explanation:To find the value of the marbles Anna has left, we need to calculate the total value of the marbles she started with and then subtract the value lost through trading and giving marbles to Henry.
1. Total value of the small marbles: 5 small marbles x 25 cents each = 125 cents.
2. Total value of the large marbles: 8 large marbles x k cents each = 8k cents.
3. Value gained through trading: 3 large marbles - 1 large marble = 2 large marbles.
4. Value gained through trading (small marbles): 6 small marbles.
5. Value lost through giving marbles to Henry: 4 small marbles.
6. Value remaining: (125 cents + 8k cents) + (2 large marbles x k cents) + (6 small marbles x 25 cents) - (4 small marbles x 25 cents)
Simplifying the equation, we get: 125 cents + 8k cents + 2k cents + 150 cents - 100 cents = 275 cents + 10k cents. Therefore, the value of the marbles Anna has left, in terms of k, is A + Bk, where A = 275 and B = 10.
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56
There are 134 third-graders and 167 fourth-graders at the annual school and
family picnic. The number of students is 7 times the number of adults.
Each picnic table can seat 9 people. How many picnic tables will need to be
set up for the picnic?
Show your work.
total
301. Student
PRACTICE TEST 1
+63
64
i
n
63
third graders and
Answer:
39
Step-by-step explanation:
134 + 167 = 301
301/7=43
301+430= 344
344/9 = 38.2 so you would need 39 tables
2x2 + 14x- 4 = - x2 + 3x
first, lets solve by factoring:
Let's solve your equation step-by-step.
2x2+14x−4=−x2+3x
Step 1: Subtract -x^2+3x from both sides.
2x2+14x−4−(−x2+3x)=−x2+3x−(−x2+3x)
3x2+11x−4=0
Step 2: Factor left side of equation.
(3x−1)(x+4)=0
Step 3: Set factors equal to 0.
3x−1=0 or x+4=0
x=
1
3
or x=−4
we can also solve using the quadratic formula:
2x2+14x−4=−x2+3x
Step 1: Subtract -x^2+3x from both sides.
2x2+14x−4−(−x2+3x)=−x2+3x−(−x2+3x)
3x2+11x−4=0
Step 2: Use quadratic formula with a=3, b=11, c=-4.
x=
−b±√b2−4ac
2a
x=
−(11)±√(11)2−4(3)(−4)
2(3)
x=
−11±√169
6
x=
1
3
or x=−4
lastly, we can complete the square.
2x2+14x−4=−x2+3x
Step 1: Add x^2 to both sides.
2x2+14x−4+x2=−x2+3x+x2
3x2+14x−4=3x
Step 2: Subtract 3x from both sides.
3x2+14x−4−3x=3x−3x
3x2+11x−4=0
Step 3: Add 4 to both sides.
3x2+11x−4+4=0+4
3x2+11x=4
Step 4: Since the coefficient of 3x^2 is 3, divide both sides by 3.
3x2+11x
3
=
4
3
x2+
11
3
x=
4
3
Step 5: The coefficient of 11/3x is 11/3. Let b=11/3.
Then we need to add (b/2)^2=121/36 to both sides to complete the square.
Add 121/36 to both sides.
x2+
11
3
x+
121
36
=
4
3
+
121
36
x2+
11
3
x+
121
36
=
169
36
Step 6: Factor left side.
(x+
11
6
)2=
169
36
Step 7: Take square root.
x+
11
6
=±√
169
36
Step 8: Add (-11)/6 to both sides.
x+
11
6
+
−11
6
=
−11
6
±√
169
36
x=
−11
6
±√
169
36
x=
1
3
or x=−4
Answer:
x=
1
3
or x=−4
Final answer:
The equation [tex]2x^2 + 14x - 4 = -x^2 + 3x[/tex] is a quadratic equation, which can be solved by standard methods such as factoring, completing the square, or applying the quadratic formula and then validated by substituting the solutions back into the original equation.
Explanation:
To solve the quadratic equation, [tex]2x^2 + 14x - 4 = -x^2 + 3x[/tex], first combine like terms by getting all terms on one side of the equation, resulting in [tex]3x^2 + 11x - 4[/tex] = 0. This is a standardized quadratic equation [tex]ax^2[/tex] + bx + c = 0. To find the solutions for this equation, you can either factorize it, complete the square or use the quadratic formula, (-b ± √([tex]b^2[/tex] - 4ac)) / (2a). After finding the roots (values for x), verify them by plugging them back into the original equation to ensure they satisfy it.
Hassan used the iterative process to locate
0.15 on the number line,
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Which best describes Hassan's estimation?
Hassan is correct because 0.15 0.4.
Hassan is correct because the point is on the middle of the number line.
Hassan is incorrect because 0.15 is less than 0.4.
Hassan is incorrect because the point should be located between 0.1 and 0.2.
Answer: 3.
Hassan is incorrect because StartRoot 0.15 EndRoot is less than 0.4.
Step-by-step explanation:
Hassan used the iterative process to locate StartRoot 0.15 EndRoot on the number line.
A number line going from 0 to 0.9 in increments of 0.1. A point is between 0.4 and 0.5.
Which best describes Hassan’s estimation?
Hassan is correct because StartRoot 0.15 EndRoot almost-equals 0.4
Hassan is correct because the point is on the middle of the number line.
Hassan is incorrect because StartRoot 0.15 EndRoot is less than 0.4.
Hassan is incorrect because the point should be located between 0.1 and 0.2.
An athletics coach states that the distribution of player run times (in seconds) for a 100-meter dash is normally distributed with a mean equal to 13.00 and a standard deviation equal to 0.2 seconds. What percentage of players on the team run the 100-meter dash in 13.30 seconds or faster? (Round your answer to two decimal places.)
Answer:
6.68%
Step-by-step explanation:
First find the z-score:
z = (x − μ) / σ
z = (13.30 − 13.00) / 0.2
z = 1.50
Look the value up in a z-score table, or use a calculator.
P(z>1.50) = 1 − 0.9332
P(z>1.50) = 0.0668
6.68% of players on the team run the 100 meter dash in 13.30 seconds or faster.
Which statement correctly compares AB and FD?
AB and FD are the same length.
AB is longer than FD.
O
AB is shorter than FD
AB is shorter than or the same length as FD.
Answer:
AB is longer than FD.
Step-by-step explanation:
This is an SAS triangle problem.
According to the law of cosines,
c^2 = a^2 + b^2 - 2abcosC
In triangle ABC, a = BC, b = AC, and c = AB
In triangle FDE, a = DE, b = FE, and c = FD.
The only difference is that C is 72° in one triangle and 65° in the other.
We know that cos0° = 1 and cos 90° = 0, so cos72° < cos65°.
In triangle ABC, cosC is smaller, so you are subtracting a smaller number from a^2 + b^2.
c^2 is larger, so c is larger.
AB is longer than FD.
That makes sense because, as you widen the angle between your outstretched arms, the distance between your hands increases.
The statement which correctly compares AB and FD is AB is longer than FD.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
Given two triangles, ABC and DEF.
We have to find the relationship between the sides AB and FD.
Given that,
Sides AC and FE are congruent.
Sides BC and DE are congruent.
Included angles, ∠C = 72° and ∠E = 65°
The side opposite to larger angle will be larger.
So AB is longer than FD.
Hence AB is longer than FD.
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Find the slope of the line that contains the points (4,-3) and (-4,1). is it undefined?
[tex]\huge{\boxed{-\frac{1}{2}}}[/tex]
We can find the slope with [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are both points.
Plug in the values. [tex]\frac{1-(-3)}{-4-4}[/tex]
Simplify. [tex]\frac{1+3}{-4-4}[/tex]
Add/subtract. [tex]\frac{4}{-8}[/tex]
Simplify. [tex]\boxed{-\frac{1}{2}}[/tex]
Answer:
No.
The slope of the line is -1/2.
Step-by-step explanation:
I'll give you a hint, to solve slope of the line use [tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]\displaystyle \frac{1-(-3)}{(-4)-4}=\frac{4}{-8}=\frac{4\div4}{-8\div4}=\frac{1}{-2}=-\frac{1}{2}[/tex]
The slope of the line is -1/2, which is our answer.
I hope this helps!
Plz help!!!!!!!!!
Pre-calulus
Answer:
1
Step-by-step explanation:
We are to find the value of the following:
[tex] log _ 3 5 \times log _ { 2 5 } 9 [/tex]
[tex] \log _ { 3 } 5 \times \log _ { 2 5 } 9 =\dfrac{1}{\log_{5}3}\times\log_{25}9=\dfrac{1}{\log_{5}3}\times\log_{5^2}9=\dfrac{1}{\log_{5}3}\times\dfrac{1}{2}\log_{5}9[/tex]
[tex] \dfrac { 1 } { \log _ { 5 } 3 } \times \dfrac { 1 } { 2 } \log_ { 5 } 9 = \dfrac{1}{\log_{5}3}\cdot\dfrac{1}{2}\log_{5}3^2=\dfrac{1}{\log_{5}3}\cdot\dfrac{2}{2}\log_{5}3=\dfrac{1}{\log_{5}3}\cdot\log_{5}3=\dfrac{\log_{5}3}{\log_{5}3}=[/tex] 1
Answer:
The value is: 1
Step-by-step explanation:
Use the Change of base formula. This is:
[tex]log_a(x)=\frac{log_b(x)}{log_b(a)}[/tex]
Using base 10:
[tex]log_3(5)*log_{25}(9)=\frac{log(5)}{log(3)}*\frac{log(9)}{log(25)}[/tex]
We know that:
[tex]9=3^2\\25=5^2[/tex]
And according to the logarithms properties:
[tex]log(x)^n=nlog(x)[/tex]
Then, we can simplify the expression:
[tex]=\frac{log(5)}{log(3)}*\frac{log(3)^2}{log(5)^2}=\frac{log(5)}{log(3)}*\frac{2log(3)}{2log(5)}=\frac{log(5)}{log(3)}*\frac{log(3)}{log(5)}=\frac{log(5)*log(3)}{log(3)*log(5)}=1[/tex]
2. Find the distance between -18 and 8
using the ruler postulate.
Step-by-step explanation:
1 1-5 Measuring Segments Find the distance between two points using the Ruler Postulate Determine the length of a segment using the Segment Addition Postulate.
Answer:
26.
Step-by-step explanation:
We are asked to find the distance between -18 and 8 using the ruler postulate.
The ruler postulate states that the distance between two pints on a ruler is the absolute value of the difference between the numbers shown on ruler.
So the distance between -18 and 8 would be [tex]|-18-8|=|-26|=26[/tex].
Therefore, the distance between -18 and 8 is 26.
please help me with this math question
The ":" is actually a division, a fraction.
So part a is therefore,
[tex]\dfrac{w}{100}=\dfrac{12}{25}[/tex]
Here we use cross multiplication,
[tex]\dfrac{a}{b}=\dfrac{c}{d}\Longleftrightarrow ad=bc[/tex]
And we have,
[tex]
25w=12\cdot100 \\
w=\dfrac{12\cdot100}{25}=\dfrac{1200}{25}=\boxed{48}
[/tex]
Now part b.
First convert 2m to cm. 1m = 100cm therefore 2m is 200cm.
Now we have simplified to,
[tex]\dfrac{180}{200}=\dfrac{1.8}{2}=\dfrac{\dfrac{18}{10}}{2}=\dfrac{\dfrac{9}{5}}{2}=\boxed{\dfrac{9}{10}=9:10}
[/tex]
Hope this helps.
r3t40
Look at the diagram below. If JM = LM, then angles JKM are congruent.- From Apex
True or False
Answer:
The answer to this question is True
Answer: true
Step-by-step explanation:
Write the domain and range of the function using interval notation.
Answer:
Domain [-5,3)
Range [0,2]
Step-by-step explanation:
Domain is where the function exists for the x's.
The graph starts at x=-5 and ends at x=3. The graph includes what happened at x=-5 but not at x=3. Since there are no breaks in the graph, the graph exists for x values bigger that or equal to -5 but less than 3.
The domain is [-5,3) in interval notation.
Range is very similar except it is for the y values. So the graph starts at y=0 and stops at y=2. It includes something happening at both and there are no breaks between y=0 and y=2.
The range in interval notation is [0,2].
The values are (x = -5) and (x = 3). But the graph includes what happened at (x = -5) but not (x = 3), therefore, the domain is [-5,0). The values are (y = 0) and (y = 2) and the graph includes what happened at (y = 0) and (y = 2), therefore, the range is [0,2].
Domain is nothing but the value of x in the equation (y = f(x)) and range is nothing but the value of y in the equation (y = f(x)).
So, from the given graph there are two values of 'x' at which the graph of the function gets started and ends.
The values are (x = -5) and (x = 3). But the graph includes what happened at (x = -5) but not (x = 3). Therefore, the domain of the given graph is:
[tex]x\; \epsilon\;[-5,3)[/tex]
Similarly, there are two values of 'y' at which the graph of the function gets started and ends.
The values are (y = 0) and (y = 2) and the graph includes what happened at (y = 0) and (y = 2). Therefore, the range of the given graph is:
[tex]y\; \epsilon\;[0,2][/tex]
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Figure ABCD is transformed to figure , as shown: Which of the following sequences of transformations is used to obtain figure from figure A'B'C'D?
You need a picture deficiencies did that for 20 characters
Which of the following sets of points are ALL on the line:
2x + 2y = 8
A(-2,2)
(-1,3)
(3,-1)
B(4,0)
(-2,4)
(3,0)
C(2,-2)
(3,-1)
(0,4)
D(1,3)
(2, 2)
(3, 1)
Answer:
(1, 3)
(2, 2)
(3, 1)
Step-by-step explanation:
Substitute x and y with the numbers given
2(1) + 2(3) = 8
2(2) + 2(2) = 8
2(3) + 2(1) = 8
Answer
(1, 3)
(2, 2)
(3, 1)
There needs to be work shown
Tonya wrote the equation below which solves for x.
x=150-6y
Which equation is equivalent to Tonya’s equation?
Answer:
x+6y=150
Step-by-step explanation:
If you add 6y to both sides of the equation, it becomes this, making it equal.
Answer:
x+6y = 150 (B)
Step-by-step explanation:
Given the equation x = 150-6y
The equation is also equivalent to
x+6y = 150.
This is gotten simply by taking -6y to the other side of the equation but note that if a function or constant is crossing an 'equal to' sign in an equation, it changes the sign. Considering this equation, -6y changed to +6y upon crossing the equal to sign to give is x+6y = 150 which is the required answer.
p (a) =0.60, p(b) = 0.25, and p(a and b) =0.15 what is p(a or b) ?
a.) 0.40
b.) 0.85
c.) 0.70
d.) 0.75
Answer:
C is the correct option
Step-by-step explanation:
To find the probability of P(a or b) we will use the formula:
P(a or b)= P(a)+ P(b) - P(a-b)
Now put the given values in the formula:
P(a or b)= 0.60+0.25-0.15
P(a or b)=0.85 - 0.15
P(a or b)= 0.70
Thus the correct option is C....
Answer: Option C
[tex]P (A\ or\ B) = 0.70[/tex]
Step-by-step explanation:
If A and B are events that are not mutually exciting, then it is true that:
[tex]P (A\ or\ B) = P (A) + P (B) - P (A\ and\ B)[/tex]
In this case we know [tex]P(A)[/tex], [tex]P(B)[/tex] and we also know [tex]P (A\ and\ B)[/tex]
[tex]P(A)=0.60[/tex]
[tex]P(B) = 0.25[/tex]
[tex]P(A\ and\ B)=0.15[/tex]
Therefore we have that:
[tex]P (A\ or\ B) = 0.60 + 0.25 - 0.15[/tex]
[tex]P (A\ or\ B) = 0.60 + 0.1[/tex]
[tex]P (A\ or\ B) = 0.70[/tex]
write the equation of the lines that passes through the points (-3, -2) and (0, -3)
Answer:
[tex]-\frac{1}{3}[/tex]
Step-by-step explanation:
To find the slope of a line using two points, employ the use of the slope formula.
[tex]\frac{y_{2}-y_{1}}{x_{2}- x_{1}}[/tex]
Your y1 term is -2, your y2 term is -3.
Your x1 term is -3, your x2 term is 0.
[tex]\frac{-3-(-2)}{0-(-3)} \\\\\\\frac{-3+2}{0+3} \\\\\frac{-1}{3} \\[/tex]
Which of the following polynomials has a remainder of -11 when divided by x+1? A. −2x3+4x2+3x−2 B. 3x3+6x−2 C. x3−2x2−4x+1 D. 4x3+2x2+5
Answer:
B. 3x3+6x−2
Step-by-step explanation:
When you divide 3x3+6x−2 by x+1 we get a remainder of -11.
6 friends are going to sit together in a rollercoaster that has 6 seats. In how many different arrangements can they sit?
Answer:
36
Step-by-step explanation:
I think it may be 36. I did 6×6, but I'm not fully positive
There are 720 different arrangements in which the 6 friends can sit in the 6 seats of the rollercoaster.
To calculate the number of different arrangements in which the 6 friends can sit in the 6 seats of the rollercoaster, we can use the concept of permutations.
Since each friend occupies one seat and no two friends can occupy the same seat, we have 6 choices for the first seat, 5 choices for the second seat, 4 choices for the third seat, and so on until 1 choice for the last seat.
So, the total number of arrangements is the product of these choices:
[tex]\[ 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]
Suppose that you want to design a cylinder with the same volume as a given cylinder, but you want to use a different radius and height. In general
terms, how can you changer and h to produce the same wolume for both cylinders?
volume of a cylinder = pi×r^2×h
Answer:
I can increase r and decrease h, or I can decrease r and increase h.
Step-by-step explanation:
answer given in edmentum
please help. its an emergency!!!!
Answer:
The equation x+3=9 is true if and only if x=6.
Not enough information.
Step-by-step explanation:
We are looking for a if and only if statement for a bioconditional.
There is only one such choice:
The equation x+3=9 is true if and only if x=6.
We only know information about the triangle's angles, and nothing about their sides. AAA (angle-angle-angle) is not enough information to conclude congruence. It is enough for proving it to be similar.
based only on the information given in the diagram which congruence theorems or postulates could be given as reason why ABC=DEF
Answer:
HL
SAS
SSS
Step-by-step explanation:
Since these are right triangles, and you have the two hypotenuses are congruent to each other and two legs that are also congruent to each other, then HL can be applied.
For HA to work we must have been given something else about one of those angle (besides the 90 degree one).
Since you have two corresponding sides that are congruent, then the 90 degree angles in both are congruent, and then the sides right after that 90 degree angle are also congruent to each other, so SAS can be applied.
We can't use AAS. We only know something about one angle per each triangle due to the markers.
LA? Needed another angle besides the 90 degree one.
All three corresponding sides are congruent. The markers tell us this. So we can apply SSS.
Answer:
HL
SAS
SSS
Step-by-step explanation:
What is the sum of the lengths of the two trails?
The correct option is B.
The sum of the lengths of the diagonals in the given parallelogram is 12 miles. This value was derived by first identifying the values of the segments in relation to 'y', calculating for 'y', then using the property of the parallelogram where the diagonals bisect each other.
Explanation:To solve for this geometry problem involving a parallelogram, we need to equate the given values and solve for 'y'. The values given stipulate that DE = EB; therefore, we get:
y+2 = 3y-4
y-3y = -4-2
-2y = -6
y = 3
Solving for y, we obtain y = 3.
Next is to solve AE, which is given as CE = AE and substituting the calculated value of y, we get:
AE = 2y - 3 = 2(3) - 3 = 3 miles.
In this parallelogram, it is a property that the diagonals bisect each other. Hence, DE = EB, and AE = EC. Therefore, AC equals 2 * AE = 2 * 3 miles = 6 miles.
Similarly, DB equals 2 * DE = 2 * 3 miles = 6 miles.
Thus, the sum of the lengths of the two trails, AC and BD, is 6 miles + 6 miles = 12 miles.
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The complete question is given below:
The parallelogram shown represents a map of the boundaries of a natural preserve. Walking trails run from points A to C and from points B to D. The measurements shown represent miles.
What is the sum of the lengths of the two trails?
A. 6 miles
B. 12 miles
C. 16 miles
D. 36 miles
Helena uses a free online account to store digital photos and videos. She uploads 650 photo and video files from her phone to the account. The average size of each photo is 4 megabytes and the average size of each video is 9 megabytes. The total upload size was 2,925 megabytes. Which system of equations can be used to determine the number of photo files, p, and the number of video files, v, Helena uploaded from her phone?
p + v = 650 and 4v + 9p = 2,925
p = 650 – v and 4p + 9v = 2,925
4v = 650 – 9p and 13(p + v) = 2,925
9v + 4p = 650 and v + p = 2,925
Answer:
p = 650 – v and 4p + 9v = 2,925 , Its B
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Answer:
b
Step-by-step explanation:
There are 200 counters in a bag.
50 of them are taken out and have a dab of white paint placed on them.
These 50 marked counters are now put back in the bag which is given
a good shake to ensure even distribution of the marked counters.
80 counters are now taken out of the bag.
About how many of them would you expect to be marked with a
dab of white paint?
Out of those 80 counters, 20 counters may have a white dab on them.
Given to usTotal number of counters in the bag = 200
counters that have a white dab = 50
counters that are now taken out of the bag = 80
Let's first take the ratio of counters that have a white dab to the total number of counters in the bag.
The ratio of bag[tex]\rm{=\dfrac{counters\ that\ have\ a\ white\ dab}{Total\ number\ of\ counters\ in\ the\ bag}[/tex]
[tex]=\dfrac{50}{200} = \dfrac{1}{4} = 0.25[/tex]
Therefore, the ratio of counters that have a white dab to the total number of counters in the bag is 0.25.
80 countersAs the bag is given a good shake to ensure even distribution of the marked counters.
Those 80 counters will follow the same ratio of the bag, so, the number of tokens with white dab will be,
Number of tokens taken out x ratio of the bag
= 80 x 0.25
= 20
Hence, out of those 80 counters, 20 counters may have a white dab on them.
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Solve and graph the absolute value inequality: |2x + 4| > 14.
number line with open circles on negative 9 and 5, shading going in the opposite directions.
number line with open circles on negative 9 and 5, shading in between.
number line with closed circles on negative 9 and 5, shading going in the opposite directions.
a number line with open circles on negative 5 and 5, shading going in the opposite directions.
Answer:
"number line with open circles on negative 9 and 5, shading going in the opposite directions."
Step-by-step explanation:
Your inequality doesn't include an equal sign so there will be no closed holes. It will only be open holes.
|u|>14 means that the number u has to be greater than 14 or less than -14. These numbers I describe just now all have a distance greater than 14 from 0.
So |u|>14 implies u>14 or u<-14.
But we are solving |2x+4|>14 so this implies we have 2x+4>14 or 2x+4<-14.
2x+4>14
Subtract 4 on both sides:
2x >10
Divide both sides by 2:
x >5
2x+4<-14
Subtract 4 on both sides:
2x <-18
Divide both sides by 2:
x <-9
So our solution is x>5 or x<-9.
Graphing!
~~~~~~~O O~~~~~~~~
-----------(-9)---------------------------------(5)---------------
So we shaded to the right of 5 because our inequality says x is bigger than 5.
We shaded to the left of -9 because our inequality says x is less than -9.
I really need help with this
Answer:
[tex]\frac{1}{x^2y^6}[/tex]
Step-by-step explanation:
We are given [tex](xy^3)^2 \cdot (xy^3)^{-4}[/tex]
First rule I'm going to use is [tex](m^rn^p)^s=m^{r \cdot s}n^{p \cdot s}[/tex].
This gives us:
[tex](xy^3)^2 \cdot (xy^3)^{-4}[/tex] is
[tex](x^2y^6) \cdot (x^{-4}y^{-12})[/tex].
Now pair up the bases that are the same:
[tex](x^2x^{-4}) \cdot (y^6y^{-12})[/tex].
Add the exponents when multiplying if the bases are the same:
[tex]x^{-2} \cdot y^{-6}[/tex]
Now usually teachers don't like negative exponents.
To get rid of the negative exponents just take the reciprocal:
[tex]\frac{1}{x^2} \cdot \frac{1}{y^6}[/tex]
[tex]\frac{1}{x^2y^6}[/tex]
Which of the following inequalities matches the graph?
[tex]x > - 3[/tex]
[tex]x < - 3[/tex]
[tex]y > - 3[/tex]
[tex]y < - 3[/tex]
which one is it 1,2,3,or 4 one
Answer:
y < -3Step-by-step explanation:
<, > - dotted line
≤, ≥ - solid line
x ≤ a or x < a - the region below the horizontal line x = a
x ≥ a or x > a - the region above the horizontal line x = a
y ≤ a or y < a - the region on the left side of the vertical line y = a
y ≥ a or y > a - the region to the right of the vertical line y = a
=========================================
We have dotted line (<, >).
The vertical line (y).
The region on the left side of the vertical dotted line y = -3
You are a real estate agent. For every house you sell you earn 3.8% commission. This month you sold 2 houses that had a combined total of $560,950. How much commission will you earn?
Answer:
$ 134,628
Step-by-step explanation:
1. make 3.8 into a percent round decimal to the right 2 times
2.multiply the total with the percent
3.solve
4.take answer and subtracted from the total
5.solve
6. subtract the number you got from the first solution problem from the last problen solution
7.solve
Answer: $21,316.1
Step-by-step explanation:
Given : For every house you sell you earn 3.8% commission.
Which can be written as 0.038.
This month you sold 2 houses that had a combined total of $560,950
Then, the amount of commission you will earn is given by :-
[tex]\$560,950\times0.038=\$21,316.1[/tex]
Therefore, the you will earn $21,316.1 as commission.
The length of a rectangle is (3x - 5) inches, and its width is 2x inches. Find the area of the rectangle.
Answer:
6x^2 - 10x inches ^2
Step-by-step explanation:
The area of a rectangle is
A = l*w
= (3x-5) * (2x)
= 6x^2 - 10x
Answer:
The area of the rectangle is 6x^2(squared)-10x
Step-by-step explanation:
To find the area of rectangles, you must multiply the length by the width. The formst for this is A=LxW. When you substitute each part of the equation in, it becomes 2x(3x-5). When you have parentheses, distribute the number on the outside to each number(or variable) on the inside. First, multiply 2x by 3x. This leaves you with 6x^2(squared). Then, multiply the 2x by the -5. This leaves you with -10x. Combine each part to get 6x^2(squared)-10x. :)