Choose the polynomial that is written in standard form. (1 point)
−3x5y2 + 4x3y + 10x2
−8xy2 + 4x4y2 + 3x3
x4y2 + 4x3y5 + 10x4
x6y2 + 4x3y8 + 10x7
Answer:
[tex]-3x^5y^2+4x^3y+10x^2[/tex]
Step-by-step explanation:
A polynomial in two variables is in standard form if its monomial from left to right are arrangerd in descending order. We say that a monomial [tex]x^ay^b[/tex] is greater than a monomial [tex]x^{a^{\prime}}y^{b^{\prime}}[/tex] if [tex]a+b > a^{\prime} + b^{\prime}[/tex] or [tex]a+b=a^{\prime}+b^{\prime} \quad \text{and} \quad (a,b)>(a^{\prime},b^{\prime}})[/tex] in the alphabetical order.
For example
[tex]x^2y>xy \quad \text{since} \quad 2+1>1+1 \\\\x^2y>xy^2 \quad \text{since} \quad 2+1=1+2 \quad \text{and} \quad 2>1[/tex]
The polynomial [tex]-3x^5y^2+4x^3y+10x^2[/tex] is in standard form, since [tex]x^5y^2 > x^3y >x^2[/tex]. On the other hand, the polynomial [tex]-8xy^2+4x^4y^2+3x^3[/tex] is not in standard form since [tex]x^4y^2>xy^2.[/tex]
How do you find a scale factor?
Can Someone Please Help Me Factor (x^(2)+6x+58)
Sandra can type 180 words in 3 minutes. At this rate, how many words can she type in 5 minutes?
_____MInutes
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I will give brainliest.
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)? y + 5 = x + 2 y − 2 = x − 5 y − 5 = −(x − 2) y + 2 = −(x + 5)
Answer:
You are requested to kindly provide the equation of line to which our to be found line is perpendicular.
Step-by-step explanation:
We are learning polynomials in algebra one. Can anyone help explain trinomials like- n^3 - 5n^2 - 50n
How do you find the x intercept, y intercept, and M
***WILL GIVE MEDAL TO WHOEVER HELPS***
Question:
Sherri has 23 pieces of jewelry to sell. She sells the bracelets for $2 and the necklaces for $3, and earns a total of $55. If the bracelets are represented by x and the necklaces are represented by y, which of the following systems of equations can be used to calculate the number of bracelets and necklaces sold?
Answer choices:
x + y = 23, 3x + 2y = 55
x + y = 55, 3x + 2y = 23
x + y = 23, 2x + 3y = 55
x + y = 55, 2x + 3y = 23,
What equation results from completing the square and then factoring x^2-12x=58
The correct answer is (x - 6)2 = 94
Answer:
A for me
Step-by-step explanation:
Express the ratio of a's to n's in the word banana, in simplest form.
The ratio of A's to N's in the word BANANA is 2:1. This means that there are twice as many A's as there are N's in the word. Therefore, the correct answer is D: 2:1.
To find the ratio of A's to N's in the word BANANA, we need to count the number of A's and N's in the word.
1. Count the occurrences of A and N:
In the word BANANA, there are 3 A's and 1 N.
2. Express the ratio:
The ratio of A's to N's is 3:1.
3. Simplify the ratio:
To simplify the ratio, we can divide both parts by their greatest common divisor (GCD), which is 1 in this case, because 3 and 1 have no common divisor other than 1.
[tex]\[ \text{Ratio} = \frac{3}{1} = 3:1 \][/tex]
4. Check the given options:
Now, let's compare the simplified ratio 3:1 with the given options.
A. 2:3 - This doesn't match the simplified ratio.
B. 3:2 - This doesn't match the simplified ratio.
C. 1:2 - This doesn't match the simplified ratio.
D. 2:1 - This matches the simplified ratio.
Therefore, the correct answer is D: 2:1.
The ratio of A's to N's in the word BANANA is 2:1. This means that there are twice as many A's as there are N's in the word.
The complete question is:
Express the ratio of A's to N's in the word BANANA, in simplest form.
A: 2:3
B: 3:2
C: 1:2
D: 2:1
Please help asap!!! 16 points ):
Convert 4 miles to feet.
20,210 feet
21,000 feet
21,120 feet
22,000 feet
If it takes bottling machine to fill 150 bottles per minute, how many minutes will it take the machine to bottle 4500 bottles
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
V(t)=24,500(0.95^t)
Find the initial value of the car and the value after 13 years.
Round answers to the nearest dollar as necessary.
The value after 13 years will be 12576.9 dollars if the dollar value v(t) of a certain car model that is t years old is represented by the exponential function.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
It is given that:
The dollar value v(t) of a certain car model that is t years old is given by the exponential function.
[tex]\rm V(t)=24,500(0.95^t)[/tex]
The initial value plug t = 0 in the above function:
V(0) = $24500
Plug t = 13 years in the above exponential function
[tex]\rm V(13)=24,500(0.95^1^3)[/tex]
After calculating, we get:
V(13) = 12576.88
V(13) = 12576.9 dollars
Thus, the value after 13 years will be 12576.9 dollars if the dollar value v(t) of a certain car model that is t years old is represented by the exponential function.
Learn more about the exponential function here:
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Molly can either take her lunch or buy it at school. It cost $1.95 to buy lunch. If she wants to spend no more than $30 each month, how many lunches can she buy at most?
Final answer:
Molly can purchase a maximum of 15 school lunches per month with a budget of $30, considering each lunch costs $1.95.
Explanation:
The question asks how many school lunches Molly can buy if each lunch costs $1.95 and she wants to spend no more than $30 each month. To find out how many lunches Molly can buy, we divide her monthly budget by the cost of one lunch.
So, we perform the calculation: $30 ÷ $1.95 ≈ 15.38. Since Molly cannot buy a fraction of a lunch, we round down to the nearest whole number, which means Molly can buy 15 lunches at most in a month without exceeding her budget.
the sum of two fractions is three times their difference.six times the smaller fraction exceeds the larger fraction by 3/2.find the fractions
PLEASE HELP ME ASAP
PLEASE
A jar made of 3/16-inch-thick glass has an inside radius of 3.00 inches and a total height of 6.00 inches (including the bottom thickness of glass). The glass has a density of 165 lb/ft3. The jar is placed in water with a density of 62.5 lb/ft3.
Assume the jar sits upright in the water without tipping over. How far will the empty jar sink into the water?
What is the volume of the glass shell of the jar? Precision 0.00
What is the weight of the jar? Precision 0.00
What is the weight of water the empty jar will displace? Precision 0.00
What is the volume of water the empty jar will displace? Precision 0.00
How far will the empty jar sink?
The volume of the glass shell of the jar is 0.0136 ft³ and its weight is 2.24 lbs. The weight and volume of the water it will displace amounts to 2.24 lbs and 0.036 ft³ respectively. Consequently, the jar will sink approximately 2.2 inches into the water.
Explanation:To begin, the volume of the glass shell of the jar will first need to be established. Given that the thickness of the glass is 3/16 inches, the outer radius of the jar is 3 inches + 3/16 inches = 3.1875 inches. To get the volume, utilise the formula for the volume of a cylinder, which is πr²h. Thus, with measurements converted to feet for the calculations (1 inch = 0.08333 foot), we have an external volume of π(0.265625 ft)² * 0.5 ft = 0.1118 ft³ and an internal volume of π(0.25 ft)² * 0.5 ft = 0.0982 ft³. Hence, the volume of glass is 0.1118 ft³ - 0.0982 ft³ = 0.0136 ft³
Next, the weight of the jar is determined by the formula mass = volume * density, so mass = 0.0136 ft³ * 165 lb/ft³ = 2.24 lbs.
To ascertain the weight of water the jar will displace, we consider the principle of buoyancy, which suggests that an object will displace a volume of fluid with a weight equal to its own weight. Thus, the weight of the water displaced is 2.24 lbs.
Then, the volume of this water is found with the formula volume = weight/density -> volume = 2.24 lbs / 62.5 lb/ft³ = 0.036 ft³.
Lastly, considering the jar will sink until the weight of the water being moved equals the weight of the jar. The volume of the water displaced equates to the submerged volume of the jar. Its depth in feet is then the volume divided by the cross-sectional area of the jar (internal radius), so the distance the jar sinks is roughly 0.036 ft³ / π(0.25 ft)² = 0.18 ft -> convert to inches = 2.2 inches.
Learn more about Buoyancy here:https://brainly.com/question/36883204
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The width of Zorn’s patio is labeled in the diagram below. If the perimeter of the patio is (30x + 26) feet, what is the length of the patio?
The following is an idealized equation representing the world population of Leatherback turtles, where t represents time in years since 1970.
f(t) = 50,000(.92)^t
How would you determine the population in the year 2000?
Is this a growth or a decay function?
How can you tell a growth or decay function just by looking at it?
Please help me asap!!!
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Let the function f be defined by f(x) = (x - 1)(x + 7). Which of the following is an equivalent form of f in which the minimum value of f appears as either a coefficient or a constant?
A. f(x) = x^2 - 7
B. f(x) = x^2 + 6x - 7
C. f(x) = (x + 3)^2 - 16
D. f(x) = (x - 3)^2 - 20
Andy is trying to determine the correlation between the number of math homework assignments he completes and his test score. Which is the BEST estimate for the correlation coefficient of the data? A) r = 1.5 B) r = 0.5 C) r = 0.96 D) r = −0.90
Answer:
Option C
Step-by-step explanation:
It is really obvious that whenever the number of homework assignments he completes increases, his knowledge in the subject increases. This will increase automatically his test score in Maths.
Thus we can expect a perfect linear association between number of assignments done and his test score.
The correlation coefficient which is a measure of linear association between two variables always lies between -1 and +1.
Hence Option a cannot be correct since the value is greater than 1.
b) r=0.5 gives a positive but not very strong association. This is wrong as there is a strong association between the two variables
c) r=0.96 seems to be a correct answer as the positive and near to 1 r value confirms the linear strong positive association between the two variables.
D) r =-0.90 is wrong since there cannot be a negative association.
So only option right is option C
Jensen wants to hang a mirror in his boat and put a frame around it. The mirror and frame must have an area of 19.75 square feet. The mirror is 4 feet wide and 5 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (2 points)
2x2 + 6x − 19.25 = 0
3x2 + 5x − 19.25 = 0
4x2 + 18x + 0.25 = 0
4x2 + 18x + 20 = 0
If x and y are positive integers, what is the value of x + y ? x+y=15 xy=6
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Answer:
b is correct
Step-by-step explanation:
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Answer:
2
Step-by-step explanation:
In your math class there are 15 boys and 21 girls. 12 of the boys and 15 of the girls are freshmen. if you randomly choose a student in your class, what is the probability that you'll choose a girl or a freshman?
Final answer:
The probability of randomly choosing a girl or a freshman from the class is 0.916 or 91.6%. This is calculated by considering the total number of girls and freshmen in the class, while avoiding double-counting freshman girls in the calculation.
Explanation:
To calculate the probability that a randomly chosen student from the class is either a girl or a freshman, we need to consider the total number of students in the class, as well as the number of girls and the number of freshmen. The class consists of 15 boys and 21 girls, totaling 36 students. Out of these, 12 boys are freshmen and 15 girls are freshmen, but we must avoid double-counting the girls who are also freshmen.
First, we calculate the total number of freshmen: 12 boys + 15 girls = 27 freshmen. Next, we calculate the probability of picking a girl: 21 girls / 36 total students = 0.583 (to three decimal places). We then calculate the probability of picking a freshman: 27 freshmen / 36 total students = 0.750. However, since the freshmen include both boys and girls, we must subtract the probability of picking a freshman girl to avoid double-counting: 15 girls who are freshmen / 36 total students = 0.417.
Finally, we add the probability of picking a girl and the probability of picking a freshman, and subtract the probability of picking a freshman girl to obtain the inclusive probability: 0.583 (girl) + 0.750 (freshman) - 0.417 (freshman girl) = 0.916.
Therefore, the probability that a randomly chosen student is either a girl or a freshman is 0.916, or 91.6%.
Taylor is competing in a 30 km race. She has already run 12.35 km through a park and swam 3.75 km. She will bike the rest of the way. Round each distance to the nearest km. About how far does Taylor need to bike to finish the race? A. about 12 km B. about 13 km C. about 14 km D. about 23 km
Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.