The simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]
Complete questionSimplify the expression: (x³ + (-y)³) / (x - y)
Do not include parentheses in your answer.
How to simplify the expression?The expression is given as:
[tex]\frac{x^3 + (-y)^3}{(x - y}[/tex]
Open the inner bracket
[tex]\frac{x^3 -y^3}{(x - y}[/tex]
Apply the difference of two cubes to the numerator
[tex]\frac{(x-y)(x^2+xy+y^2)}{(x - y}[/tex]
Cancel out the common factors
[tex]x^2+xy+y^2[/tex]
Hence, the simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]
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whats the answer? :(
Answer:
D) 8[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
5[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex] = 8[tex]\frac{1}{2}[/tex]
Study each of the growing geometrical patterns. Then do the following for each pattern. (I) Give a verbal description of how the pattern is growing. (ii)Set up a table of values.(III) Write down a numerical description for each pattern (you must relate the number of the frame to the number of figures in the frame). (IV) For each pattern, write down a formula that can be used to calculate the number of building blocks in any term. (v) Write down the value of the 10th frame. Use your formula to determine how many building blocks there are in the 100th frame of each growing pattern. M M Δ Δ Δ 2 (6) (6) (8) [40]
A description of how the pattern is growing is that the pattern is growing by the addition of two blocks every time.
How to illustrate the pattern?A numerical description of the pattern is:
1 - 2 blocks.
2 - 4 blocks.
3 - 6 blocks
4 - 8 blocks.
The formula that can be used to calculate the number if building blocks in any term will be 2n. For example, the number of blocks for the 5th term will be:
= 2n = 2 × 5 = 10
The value for the 10th frame will be:
= 2n
= 2 × 10 = 20
The value for the 100th frame will be:
= 2n
= 2 × 100 = 200
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What is the volume of the complex figure
The volume of the given figure is 104 m³.
We need to find the volume of the given figure.
What is volume?Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Divide the given figure into two convenient cuboids. That is one with dimensions length=4 m, breadth=4 m and height=3 m. Another with length=4 m, breadth=7 m and height=2 m.
We know that, the volume of cuboid =l×b×h cubic units.
Now, the volume of cuboid=4×4×3=48 m³ and the volume of another
cuboid=4×7×2=56 m³.
The volume of the given figure=48+56=104 m³.
Therefore, the volume of the given figure is 104 m³.
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Given the data set (4,85),(7,92),(14,110), which of the following equation best represents a line of best fit
Given the graph, find the initial value of the domain [ ___, 2].
Answer:
Looks to me like it should be -2
What is the value of the expression
(12+x) +
4+x
when X= 4 and y=-8?
OA) 4
OB)
OC)
OD 10
Step-by-step explanation:
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The value of the expression x
4
−8x
3
+18x
2
−8x+2, when x=2+
3
, is:
Medium
Solution
verified
Verified by Toppr
Correct option is B)
Let f(x)=x
4
−8x
3
+18x
2
−8x+2
Substituting x=2+
3
, we get
f(2+
3
)=(2+
3
)
4
−8(2+
3
)
3
+18(2+
3
)
2
−8(2+
3
)+2
=(2+
3
)
2
((2+
3
)
2
+18)−8(2+
3
)((2+
3
)
2
+1)+2
=(7+4
3
)(4
3
+25)−8(2+
3
)(8+4
3
)+2
=175+48−128−96+2
=1
Hence, option B is correct.
Someone explain the equation
Answer:
An equation connects two expressions with an equal sign. It shows that the two expressions are equal to each other, like 5 = 5, or for variables, 5x = 2x, which means that x = 0.
Brainliest, please :)
Answer:
An equation is a problem consist sting of many numbers mostly division or mulitiplication
Step-by-step explanation:
PLEASEEE HELPPP!!
Using the sheet music example above, please name the parts:
________________________
________________________
What is this LINE of music called? ________________________
When both of these staves are connected with this symbol, what is this called? ________________________
Please name all 3 things inside of the box: ___________________________________
_________________________
The line of music is refered to as the bracket
What is music?It should be noted that music simply means a vocal or instrumental sounds that are combined to produce beauty of harmony and expression if emotions.
When When both of these staves are connected with this symbol, it's called a brace.
Lastly, the things inside the box are voice, piano, and guitar.
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how do i work this out?
She has 45% of the original amount left
Ratio and proportionsFractions are written as a ratio of two integers
Given the following
Initial amount. = ∈4000
Amount given to her sister = 1/4 * 4000 = 1000
Amount given to her brother = 40% of 3000 = 1200
Amount left = 4000 - (1000+1200)
Amount left = ∈1800
Determine the percentage left
x * 4000 = 1800
x = 1800/4000
x = 0.45
x = 45%
Hence she has 45% of the original amount left
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The points (2,3) and (5,9) are on the line. What is the equation of the line
The equation of the line is y = 3x +3 .
What is a Straight Line Equation ?A straight line equation is that can be represented by y = mx +c , where m is the slope and c is the intercept on y axis.
The points given are (2,3) and (5,9)
m = (9-3)/(5-2) = 3
m = 3
Therefore the equation becomes
y = 3x +c
Te equation is given by
(y-y₁) = m(x-x₁)
y-3 = 3(x - 2)
y-3 = 3x -6
y = 3x +3
Therefore the equation of the line is y = 3x +3 .
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If y = 2x-3, then which of the following ordered pairs lies on the graph?
O (-3,0)
O (1,-1)
O (5,4)
Plug in the points and see if they satisfy the equation.
y = 2x - 3
(1, -1)
-1 = 2(1) - 3
-1 = 2 - 3
-1 = -1
So (1, -1) satisfies the equation.
(-3, 0)
0 = 2(-3) - 3
0 = -6 - 3
0 = -9
So (-3, 0) does not satisfy the equation.
(5, 4)
4 = 2(5) - 3
4 = 10 - 3
4 = 7
So (5, 4) does not satisfy the equation.
Therefore your answer is (1, -1).
Answer:
the answer is 5,4
Step 1: Choose the lowest common denominator.
02 03 04 05 06 08 010 012
3/4
50/80
O
Find the sum: -and
The expression written in equivalent form with a
common denominator is
The sum is
The expression written in equivalent form with a common denominator is -1/6
Adding fractionsFractions are written as ratio of two integers. For instance a/b is a fraction.
Given the sum of the fractions shown;
-3/4 and 5/8
Sum = -3/4 + 5/8
Sum = 5/8 - 3/4
Sum = 5-6/8
Sum = -1/8
Hence the sum of the given fraction -1/3 and 5/8 is -1/6
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Emma bought 1305 bags of carrot for 16910 dollars. Find the unit rate in terms of bags per dollar.
Answer: $12.96
Given:
1305 bags of carrots purchased
Total cost = $16,910
Step-by-step explanation:
To find the unit cost, divide 16910 by 1305 to find the cost of one bag of carrots:
[tex]\frac{16910}{1305} = 12.96[/tex] (rounded to nearest hundredth)
Solve the inequality graphically. 3^-8 > 6^-8
a. x < 1
b. x > 1
c. x > 0
d. x < 0
THE ANSWER IS -> b. x > 1
hope it helps
thanks
Answer: c. x>0
Step-by-step explanation:
Help is needed with this math problem!
Answer:
expression for (g + h)([tex]x\\[/tex]) = [tex]2x[/tex] + [tex]3x^2\\[/tex] and for (g - h)([tex]x[/tex]) = [tex]2x[/tex] - [tex]3x^2[/tex]
value of (g .h)(2) = 24
Step-by-step explanation:
function operations: Functions with overlapping domains can be added, subtracted, multiplied and divided. If f(x) and g(x) are two functions, then for all x in the domain of both functions we can find the sum, difference, product and quotient
given :
g([tex]x[/tex]) = [tex]2x[/tex]
h([tex]x[/tex]) = [tex]3x^2[/tex]
we know that ;
(g + h)([tex]x[/tex]) = g([tex]x[/tex]) + h([tex]x[/tex])
= [tex]2x[/tex] + [tex]3x^2[/tex]
similarly;
(g - h)([tex]x[/tex]) = g([tex]x[/tex]) - h([tex]x[/tex])
= [tex]2x[/tex] - [tex]3x^2[/tex]
now,
(g . h)([tex]x[/tex]) = 2([tex]3x^2\\[/tex])
= 6[tex]x^2\\[/tex]
for (g .h)(2) = 6([tex]2^2[/tex])
= 6 × 4
= 24
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A school bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s^2. How much time does it take to travel 95.1 m?
The school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have:
A school bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
From the second equation of motion:
[tex]\rm s = u + \dfrac{1}{2}at^2[/tex]
We have given:
s = 95.1 m
u = 26.8 m/s
a = 4.73 m/s²
[tex]\rm 95.1 = 26.8 + \dfrac{1}{2}(4.73)t^2[/tex]
The above equation is a quadratic equation:
After simplification:
[tex]\rm \dfrac{4.73}{2}t^2=68.3[/tex]
[tex]\rm t^2=28.879[/tex]
t = 5.373 seconds ≈ 5.34 seconds
Thus, the school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
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The function f(x)=5(x−1) is shown on the coordinate plane.
Select from the drop-down menus to correctly describe the end behavior of f(x).
As x decreases without bound, the graph of f(x) ______
1. approaches y=0
2. increases without bond
3. decreases without bond
As x increases without bound, the graph of f(x) ______
1. approaches y=0
2. increases without bond
3. decreases without bond
As x decreases without bound, the graph of f(x) approaches y = 0
As x increases without bound, the graph of f(x) increases without bound
What is Function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
f(x)=5^(x−1)
When x -> -∞
[tex]lim_{ x- > -\infty.[/tex] f(x)= 5 ^(x-1) = 0
When x -> ∞
[tex]lim_{ x- > \infty.[/tex] f(x)= 5 ^(x-1) = ∞
Hence,
As x decreases without bound, the graph of f(x) approaches y = 0
As x increases without bound, the graph of f(x) increases without bound
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Mrs. Avery is going to randomly select one student from her class to read a poem out loud. There are 151515 boys and 131313 girls in her class.
What is \text{P(boy})P(boy)start text, P, left parenthesis, b, o, y, end text, right parenthesis?
If necessary, round your answer to 222 decimal places.
The probability that a boy is selected is 0.5357 or 53.57%
What is the probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
P(boy) is asking for the probability that a boy will be chosen to read a poem out loud. Since there are 15 boys, we can get the probability by dividing this by the total number of students.
This is because out of all the students, there is an equal possibility that each of the 15 boys will be chosen.
P = ( 15 ) / ( 15+13)
P = 15 / 28
P = 0.5357
Therefore the probability that a boy is selected is 0.5357 or 53.57%
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Answer:
53.57%
Step-by-step explanation:
If the domain (or pre-image) is (-4, -2), (5, 9), (-6, 2) and the range (or image) is
(-2, 4), (9,-5), (2, 6), what rotation was applied?
Answer: 90 degrees clockwise
This is equivalent to 270 degrees counterclockwise
The rule for either rotation is [tex](x,y) \to (y,-x)[/tex]
The x and y coordinates swap places, and the new second coordinate flips from positive to negative (or vice versa).
The diagram below shows an example of this for the point (-4,-2) rotating to (-2, 4). The center of the rotation is the origin (0,0).
There are 60 students studying Sciences (Biology, Chemistry or Physics). 7 students study Biology, Chemistry and Physics. 12 students study Biology and Chemistry. 15 students study Biology and Physics. 20 students study Chemistry and Physics. 35 students study Biology. 32 students study Physics. B Complete the Venn diagram. E P C There are 60 students studying Sciences ( Biology , Chemistry or Physics ) . 7 students study Biology , Chemistry and Physics . 12 students study Biology and Chemistry . 15 students study Biology and Physics . 20 students study Chemistry and Physics . 35 students study Biology . 32 students study Physics . B Complete the Venn diagram . E P C
Answer:
8 in the box.
Step-by-step explanation:
As, it is given that 35 students study Biology.
So, in Biology circle,
15+7+5+x=35
27+x=35
x=35-27
x=8
David throws a ball up in the air. The graph below shows the height of the ball hh in feet after tt seconds. What is the ball’s greatest height?
HELP ASAP!
The greatest height is 9 feet.
What is projectile?
A projectile is any object thrown into space upon which the only acting force is gravity.
As, from the graph we can see that
The highest point the ball reaches shown by the coordinates (0.75, 9)
As, the maximum height is shown by y- axis(vertical axis).
Hence, the greatest height is 9 feet.
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Consider the following hypothesis test: 0 : 12 a : 12 HH A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.32. a. Compute the value of the test statistic. b. Use the t distribution table to compute a range for the p-value. c. At a = 0.05, what is your conclusion? d. What is the rejection rule using the critical value? What is your conclusion?
a) The test statistic is given as t = [tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315
b) The pa value will be P = P( t₂₄ > 2.315 ) = 0.015
c) If we compare the p-value and the significance level is given we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance
What is a null hypothesis?In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
X= represents the sample mean
s = represent the sample standard deviation
n = 25 sample size
[tex]\mu_o[/tex] = 12 represent the value that we want to test
[tex]\alpha[/tex] = 0.05 represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p-value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 12, the system of hypothesis would be:
Null hypothesis: ≤ 12
Alternative hypothesis: > 12
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better to apply a t-test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\dfrac{X-\mu_o}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to a specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315
P-value:-
The first step is calculate the degrees of freedom, on this case:
df = n - 1 =25 - 1 = 2
Since is a one side right tailed test the p value would be:
[tex]p_v[/tex] = P( t₂₄ > 2.315 ) = 0.015
Conclusion
If we compare the p-value and the significance level is given [tex]\alpha[/tex]= 0.05 we see that [tex]p_v < \alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance.
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Based on the circle graph,how many pounds of milk and eggs does the average American consume each year?PLEASE EXPLAIN IMAGE IS PROVIDED
E.300
F.368
G.460
H.552
About 492 pounds of milk and egg were consumed each year
Pie charts and percentagesGiven the following parameters from the chart
Total consumption = 1640 pounds per person
The percentage of milk and egg = 100 -(38 + 10 + 10 +8 + 4)
The percentage of milk and egg = 30%
Determine the amount consumed each year
Amount of milk and egg consumed = 30% of 1640
Amount of milk and egg consumed = 492 pounds
Hence about 492 pounds of milk and egg were consumed each year
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what is π x 5
please tell me the answer as quick
what is the fraction 2500 of 3600
Answer:
25/36
Step-by-step explanation:
put 2500 over 3600 and you get 2500/3600 but you can simplify to get 25/36 but removing the 0's
A rental car agency charges $230 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $415?
The number of miles you can travel in one week for $415 is
Answer:
740 miles
Step-by-step explanation:
$415-$230=$185
$185÷0.25 per miles =740 miles
a skyscraper casts a shadow 200 feet long. If the angle of elevation of the sun is 38 degrees, then the height of the skyscraper is approximately__.
A. 173.34 feet
B. 156.26 feet
C. 300 feet
D. There is not enough information.
If you receive a 15% MARKUP on an item costing $60.00, how much money do you pay in total?
Answer:
The total money we have to pay is $69.
Step-by-step explanation:
MARKUP is the amount added to the cost price.
MARKUP formula = 100*profit / cost
Cost of the item = $60.00
put the value in the formula
15 = 100*profit/60
profit = 60 × 15 ÷ 100 = 9
the total money is cost + profit
which is 60 + 9 = $69.
So the total money we have to pay is $69.
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Olympic Enterprises has the following inventory data: Assuming average cost, what is the cost of goods sold for the June 14 sale?
Assuming average cost of $55.5, the cost of goods sold by Olympic Enterprises for the June 14 sale is equal to $444.
How to calculate cost of goods?In Financial accounting, the cost of goods sold for a business firm can be calculated by multiplying the total quantity of goods by an average cost. Mathematically, this is given by:
Cost of goods = quantity × average cost
Note: We would assume an average cost of $55.5.
Substituting the parameters into the formula, we have:
Cost of goods sold = 8 × 55.5
Cost of goods sold = $444.
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You buy a CD for $9000 that earns $172.92 in interest every 2 months. What is the
annual yield on your investment?
Answer:
$4,000.343
Step-by-step explanation:
Divided the months of the year and caculate the intrest.
