Will mark brainliest.. There are 3 questions related to the problem in the first picture. please help thanks.
Factor completely.
15x^2y^2-3x^3y+75x^4
5.1 Pull out like factors :
75x4 + 3x3y + 15x2y2 = 3x2 • (25x2 + xy + 5y2)
5.2 Factoring 25x2 + xy + 5y2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
The factorized form of the algebraic expression 15x²y² - 3x³y + 75x⁴ is 3x²(5y² - xy + 15x²).
What is the factorization of algebraic expressions?Factorization of algebraic expressions is a process to break the expression and show it as a product of two or more smaller expressions by grouping and taking the greatest common factor out of the groups.
How to solve the question?In the question, we have been asked to factor the expression 15x²y² - 3x³y + 75x⁴ completely.
We know that factorization is the process of breaking the expression into smaller expressions.
We first try to find the greatest common factor among the three terms provided in the expression.
First, we will go with the numerical part.
We have 15, -3, and 75.
The greatest common factor for these three is 3.
No, we will go with the variable part.
We have x²y², x³y, and x⁴.
The greatest common factor for these three is x².
Thus, the greatest common factor for the expression is 3x²
.
Taking 3x² common throughout, we get:
3x²(5y² - xy + 15x²), which is the required factored form.
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Quick!!!Geoffrey buys 48 shares of Ignyta, Inc. (RXDX) at $6.15 each, and his broker charges him a commission of $81. How much did Geoffrey pay for his stock?A.$376.20
B.$295.20
C.$450.30
D.$219.60
Solve these simultaneous equations:
5x+2y=24 and 4x+3y=10
To solve the simultaneous equations 5x+2y=24 and 4x+3y=10, we use the elimination method, leading to a solution of x = 7.43 and y = -6.575.
To solve the simultaneous equations 5x+2y=24 and 4x+3y=10, we can use the method of elimination or substitution. Here, we will solve it using the elimination method.
Multiply the first equation by 3 and the second equation by 2 to make the coefficients of y equal in magnitude. This gives us 15x + 6y = 72 and 8x + 6y = 20.
Subtract the second new equation from the first to eliminate y. This gives 7x = 52.
Divide by 7 to solve for x, which gives x = 52 / 7 or x = 7.43 (approximately).
Substitute x = 7.43 back into one of the original equations to solve for y. Using the first equation, 5(7.43) + 2y = 24, we get 2y = 24 - 37.15, which simplifies to 2y = -13.15, and finally y = -6.575.
Therefore, the solution to the simultaneous equations is x = 7.43 and y = -6.575.
What is the area of the composite figure whose vertices have the following coordinates?
(−4, 3) , (2, 3) , (4, −1) , (0, −3) , (−2, −1)
Answer:
30 square units
Step-by-step explanation:
There are several ways to determine the area of the figure from its coordinates. A straightforward method is to plot the coordinates on a graph and decompose the resulting figure into simple shapes whose area formulas are known
Area from simpler shapesA plot reveals the figure to be a parallelogram with a base length 6 and a height of 4, together with a triangle of base 6 and height 2.
The area of the parallelogram is given by the formula ...
A = bh
The area of the triangle is given by the formula ...
A = 1/2bh
In each case, 'b' represents the base of the figure, and 'h' represents its height.
Parallelogram area
A = bh = (6)(4) = 24
Triangle area
A = 1/2bh = 1/2(6)(2) = 6
Total area
The composite area will be the sum of the parallelogram and triangle areas:
A = 24 +6 = 30 . . . . square units
The area of the composite figure is 30 square units.
__
Area from coordinatesThe area can also be figured directly from the coordinates. The formula for that can be written ...
[tex]\displaystyle A=\dfrac{1}{2}\left|\sum_{k=1}^n (x_k(y_{k+1}-y_{k-1}))\right|\qquad\text{where $y_0=y_n$ and $y_{n+1}=y_1$}[/tex]
Using this formula, we find the area to be ...
A = 1/2|(-4(3-(-1)) +2(-1-3) +4(-3-3) +0(-1-(-1)) -2(3-(-3))|
= 1/2|-16 -8 -24 +0 -12| = 1/2|-60| = 30
The area of the figure is 30 square units.
How to write a fraction with a numerator of 12 and a denominator of 13
SHIFT 2: 18 25 56 42 29 38 54 47 35 30. SHIFT 2: 23 19 50 49 67 34 30 59 40 33. SHIFT 3: 19 22 24 40 45 29 33 29 39 59. SHIFT 4: 21 23 25 40 35 19 70 40 22 23. The summary statistics for all of the workers at a steel factory are shown. Four sample groups were taken from each of the four shifts. For which sample group is the mean closest to the population mean?
In the problem · N = 1, N must be _____. the additive inverse of the multiplicative inverse of the additive identity the multiplicative identity NEXT
The value N as shown in the question must be the multiplicative identity.
Multiplicative identityThe term multiplicative identity refers to that with which a number is multiplied and the result remains that number. Multiplying a number by its multiplicative identity returns the same value.
Therefore, the the problem, we can see that the value N as shown in the question must be the multiplicative identity.
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Answer: the multiplicative inverse of 3/4
Step-by-step explanation: its right :)
During a construction project, heavy rain filled construction cones with water. The diameter of a cone is 12 in. and the height is 27 in.
What is the volume of the water that filled one cone?
Enter your answer as a decimal in the box. Use 3.14 for pi.
Is this right???? Can someone please help?
Lauren is shopping and finds 6 bracelets, 2 pairs of earrings, and 3 necklaces that she likes. How many ways can Lauren select 4 pieces of jewelry to buy?
There are 330 ways can Lauren select 4 pieces of jewelry to buy.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Lauren is shopping and finds 6 bracelets, 2 pairs of earrings, and 3 necklaces that she likes.
Now, We have;
Total number of jewelry = 6 + 2 + 3 = 11
Hence, Number of ways can Lauren select 4 pieces of jewelry to buy is,
⇒ ¹¹C₄
⇒ 330
Thus, There are 330 ways can Lauren select 4 pieces of jewelry to buy.
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Eudora ran from her home to her secret laboratory at an average speed of 12\text{ km/h}12 km/h12, space, k, m, slash, h. she then took one of her jetpacks and flew to her school at an average speed of 76\text{ km/h}76 km/h76, space, k, m, slash, h. eudora traveled a total distance of 120120120 kilometers, and the entire trip took 222 hours. how long did eudora spend running, and how long did she spend flying using her jetpack? eudora ran for hours and flew for hours using her jetpack.
Eudora ran 0.5 hours and flew 1.5 hours using her jetpack.
Given that, Eudora ran from her home to her secret laboratory at an average speed of 12 km/h.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let x = the time she ran (in hours) and y = the time she flew (in hours).
Remember that distance traveled is simply the rate times the time. So she traveled 12x kilometers by running and 76y kilometers by flying.
The total time is simply the running time plus the flying time: x + y = 2.
The total distance is simply the running distance plus the flying distance: 12x + 76y = 120
If you solve the time equation for x, you get: y = 2 - x.
This allows you to substitute 2 - x into the distance equation for y.
12x + 76(2 - x) = 120
12x + 152 - 76x = 120
152 - 64x = 120
-64x = -32
x = 0.5
Using the result, we can find y.
y = 2 - 0.5 = 1.5
Therefore, Eudora ran 0.5 hours and flew 1.5 hours using her jetpack.
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a game is played where 26 tiles are in a bag. each tile has a different letter of the alphabet on it. if you draw 5 letters what is the probability of the letters being m-u-s-i-c in order if there is no replacement?
The probability of drawing the letters M-U-S-I-C in order from a bag of 26 tiles without replacement is approximately 0.000207.
Explanation:The probability of drawing the letters M-U-S-I-C in order from a bag of 26 tiles without replacement can be calculated as follows:
First, we need to determine the total number of ways to draw 5 tiles from 26, which is represented by the combination formula: C(26,5) = 26! / (5! * (26-5)!).Next, we need to determine the number of ways to draw the letters M-U-S-I-C in order. Since there is only 1 M, 1 U, 1 S, 1 I, and 1 C in the bag, the number of ways to draw these 5 letters in order is 1.Finally, we divide the number of ways to draw the letters M-U-S-I-C in order by the total number of ways to draw 5 tiles from 26 to get the probability: P = 1 / C(26,5).Using a calculator or computer program, the probability can be calculated to approximately 0.000207.
Final answer:
The probability of drawing the letters 'M-U-S-I-C' in order from a bag of 26 alphabetic tiles without replacement is calculated by multiplying the individual probabilities of drawing each letter consecutively, starting with 1/26 and decreasing with each draw.
Explanation:
The question involves calculating the probability of drawing a specific sequence of letters from a bag containing all the letters of the alphabet without replacement. Here's how to calculate it step by step:
The probability of drawing the letter 'M' first is 1/26 since there are 26 letters and only one 'M'.
After drawing 'M', the probability of drawing 'U' is 1/25 because there are now 25 letters remaining.
Following this pattern, the probability of then drawing 'S' is 1/24, 'I' is 1/23, and 'C' is 1/22.
To find the combined probability of drawing 'M-U-S-I-C' in that order, multiply these probabilities together: (1/26) * (1/25) * (1/24) * (1/23) * (1/22).
The final calculation gives us the probability of the sequence occurring without any tiles being replaced.
At school athletic events you can buy 3 drinks and 2 hot dogs for $4.80 or you can buy 1 drink and 1 hot dog for $2.00. How much does 1 hot dog cost?
Suppose the probability that a randomly selected man, aged 55-59, will die of cancer during the course of the year is startfraction 300 over 100 comma 000 endfraction 300 100,000. how would you find the probability that at least 1 man out of 1,000 of this age will die of cancer during the course of the year?
Final answer:
To assess the likelihood of at least one cancer death among 1,000 men, calculate the probability none die and subtract from one. The actuarially fair premiums for men with and without family cancer history are different, but when combined for the whole group, there's a risk of adverse selection affecting the company.
Explanation:
To find the probability that at least one man out of 1,000 aged 55-59 will die of cancer in a year, given that the probability for any one man is 300/100,000, we first find the probability that no man dies of cancer and then subtract this from 1 (the certainty). The probability that a randomly chosen man will not die from cancer in the year is 1 - 300/100,000 = 99,700/100,000.
The probability that all 1,000 men do not die of cancer is (99,700/100,000)^1,000. Subtracting this from 1 gives us the probability that at least one man out of 1,000 will die of cancer in the year:
1 - (99,700/100,000)^1,000
For the life insurance question, to calculate the actuarially fair premium for each group, we use the probability of death and expected payout. For the group with family history (20% of 1,000 men), the probability is 1/50, and for the group without (80% of 1,000 men), it's 1/200. Thus, the premiums would be:
Group with history: (1/50) * $100,000 = $2,000Group without history: (1/200) * $100,000 = $500An actuarially fair premium for the group as a whole requires weighted averaging:
Premium whole group = (20% * $2,000) + (80% * $500) = $400 + $400 = $800
If the company charges this combined premium, it faces adverse selection; higher-risk individuals are more likely to purchase insurance, driving costs up.
Miss Watson runs a distance of 200 meters in 25 seconds. Workout the average speed of Mrs Watson in meters per second.
At a family cookout, each guest gets an equal amount of hot dogs.there are 10 guests and 32 hot dogs. how many hot dogs will be leftover
I WANT DIAGRAM
A vertical tower subtends a right angle on the top of 10m high flagstaff.if distance between them is 20m,find the height of the tower
James needs to clock a minimum of 9 hours per day at work. The data set records his daily work hours, which vary between 9 hours and 12 hours, for a certain number of days.
{9, 9.5, 10, 10.5, 10.5, 11, 11, 11.5, 11.5, 11.5, 12, 12}.
The median number of hours James worked is 10 11 12 13 . The skew of the distribution is negative positive zero zero with symmetry .
The area of a rectangular television screen is 3456 in^2. The width of that screen is 24 inches longer than the length. What is a quadratic equation the represents the area of the screen? What are the dimensions of the screen?
Final Answer:
Quadratic equation: [tex]\( x^2 + 24x - 3456 = 0 \)[/tex]
Dimensions: Length = 48 inches, Width = 72 inches
Explanation:
To find the quadratic equation representing the area of the screen, we first need to express the area as a product of its length (L) and width (W). Given that the width is 24 inches longer than the length, we can represent the width as [tex]\( L + 24 \)[/tex]. Thus, the equation becomes [tex]\( L \times (L + 24) = 3456 \)[/tex], which simplifies to the quadratic equation [tex]\( x^2 + 24x - 3456 = 0 \)[/tex], where x represents the length of the screen. Solving this equation yields the length x as 48 inches. Substituting this value back into [tex]\( L + 24 \)[/tex] gives the width as 72 inches. Therefore, the dimensions of the screen are 48 inches by 72 inches.
What is the simplest form of this binomial expression?
a4 − b4
Answer:
[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]
Step-by-step explanation:
The given expression is
[tex]a^{4}-b^{4}[/tex]
This expression is the difference of two perfect squares, and their square roots are
[tex]\sqrt{a^{4}} =a^{2}\\ \sqrt{b^{4}} =b^{2}[/tex]
Now, the difference of two perfect squares can be factored as
[tex]x^{2} -y^{2}=(x+y)(x-y)[/tex]
So, if we apply this rule, the result would be
[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]
Therefore, the simplest form of the binomial expression is
[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]
Answer and work in images
Peter has 6 sweaters, 4 pairs of jeans, and 3 pairs of shoes. how many different outfits can peter make using one sweater, one pair of jeans, and one pair of shoes?
Find the perimeter of the shaded figure
Perimeter of the given figure is 38 units.
Perimeter is the measure of the boundary of any figure. It measures the total length around the outside of a shape. Generally it is calculated as the sum of all sides of the figure.
Name the figure as ACDEFGHB, image attached below:
Perimeter of the given figure,P = Sum of all its sides.
P= AC+CD+DE+EF+FG+GH+HB+AB...........................1
AC=7 units
CD=2 units
DE=2 units
EF=6 units
FG=2 units
GH=2 units
HB=7 units
AB=10 units
On substituting values in 1
P=7+2+2+6+2+2+7+10
P=38 units.
Thus, perimeter is 38 units.
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Find the area of the figure.
When csc(theta) sin(theta) is simplified, what is the result?
The result of cosecθsinθ is 1.
What is Trigonometric functions?
Trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.
⇒ cosecθsinθ
∵sinθ = 1/cosecθ
⇒ cosecθ(1/cosecθ)
⇒ 1
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WILL GIVE BRAINIEST IF CORRECT (20 PTS)
A survey asked 10 boys and 10 girls how many text messages they sent the previous day. The number of texts are given in the line plots.
Select from the drop-down menus to complete each statement.
The data set with the greater range is __________The median ___________
Blank 1: a. the boys, b. the girls, c. neither as the range is the same
Blank 2: a. its the same for both sets of dats, b. its greater for the boys, c. its greater for the girls.
Matt and ming are selling fruit for a school fundraiser.customers can buy small boxes of oranges and large boxes of oranges. matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of 203. ming for a total of 203. ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of 220. find the cost of one small box of oranges and one large box of oranges
Based on the graphic, which three-dimensional figure has the greatest volume?
Answer:
all three have the same volume
Step-by-step explanation:
Cavalieri's principle states that if the areas of the cross sections of two solids are equal, and the height of the two solids are equal, then the volumes of the two solids are equal.
Im really confused can someone help me
How will buying auto insurance help you?