The trinomial "10[tex]x^2[/tex] + 7x - 12" is factored by finding two numbers that multiply to -120 and add up to 7, which are 15 and -8. Split the middle term, group, and factor by grouping to get (2x + 3)(5x - 4), which is option A.
Explanation:To factor the trinomial "10x2 + 7x − 12" completely, you want to find two binomials that, when multiplied together, will give you the original trinomial. To do this, you will need two numbers that multiply to give you the product of the coefficient of the x2 term (which is 10) and the constant term (which is −12), which equals −120, and also add up to the coefficient of the x term (which is 7).
The two numbers that meet these criteria are 15 and −8, since (15)(−8) = −120 and 15 + (−8) = 7. Next, split the middle term of the trinomial using these two numbers:
10x2 + 15x − 8x − 12
Now, group the terms:
(10x2 + 15x) − (8x + 12)
Factor out the greatest common factor from each group:
5x(2x + 3) − 4(2x + 3)
Finally, factor out the common binomial factor:
(2x + 3)(5x − 4)
Therefore, the correct factorization of the trinomial 10x2 + 7x − 12 is (2x + 3)(5x − 4), which corresponds to option A.
For what value of a does (1/9)^a+1 = 81^a+1 x 27^2-a?
Answer:
-4
Step-by-step explanation:
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What is the sum of the polynomials?
A. 10x^2 - 9
B. 11x^2 - x - 9
C. 11x^2 + x - 1
D. 12x^2 - 1
Use double angle to rewrite 12sinxcosx
To rewrite 12sinxcosx using the double angle formula, multiply by (1/2) and use the formula for sin(2x) to obtain the answer of 12sin(2x).
Explanation:To rewrite 12sin(x)cos(x) using the double angle formula, we need to know the formula for sin(2x) and cos(2x). The double angle formula for sine is sin(2x) = 2sin(x)cos(x), and for cosine it is cos(2x) = cos^2(x) - sin^2(x). Let's use these formulas to rewrite the expression:
12sin(x)cos(x) = 12 * (1/2) * 2sin(x)cos(x), since 1/2 is the value of cos^2(x) - sin^2(x).12 * (1/2) * 2sin(x)cos(x) = 6 * 2sin(x)cos(x).6 * 2sin(x)cos(x) = 12sin(2x). This is our final answer, using the double angle formula to rewrite the original expression.Learn more about double angle formula here:https://brainly.com/question/34830073
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Final answer:
The expression 12sinxcosx can be rewritten as 6sin(2x) by using the double angle formula for sine.
Explanation:
The expression 12sinxcosx can be rewritten using the double angle formula for sine, which is sin(2a) = 2sina ⋅ cosa. By comparing this to the given expression, we can see that it is in the form of the right-hand side of the double angle formula, where a is equivalent to x. Therefore, the expression can be rewritten as 6sin(2x). Such double angle formulae are available for other trigonometric ratios as well.
Mr. Hart is hanging a picture on a wall. the picture frame has a length of 13 inches and a width of 9 inches. how much wall space will the picture need?
To determine the wall space needed for Mr. Hart's picture, calculate the area of the rectangle formed by the picture's dimensions: length (13 inches) times width (9 inches), resulting in 117 square inches of wall space.
The student's question about Mr. Hart hanging a picture on a wall involves calculating the wall space the picture will occupy. This is essentially a question about finding the area of a rectangle. To find the area, one must multiply the length by the width of the rectangle. In this case, the length of the picture frame is 13 inches and the width is 9 inches. The calculation will be:
Area = Length × Width
Area = 13 inches × 9 inches
Area = 117 square inches
Therefore, the picture will need 117 square inches of wall space.
Is the mean value theorem for integrals the same as the mean value thoerem for derivatives?
Answer:
a^2 + b^2 =C^2
Step-by-step explanation:
A piggy bank contains the same number of quarters, nickels, and dimes. the coins total $4.40. how many of each type of coin does the piggy bank contain?
Answer: 11 of each type
Step-by-step explanation:
divide and simplify completely. 8x-8/x^2-1 * x + 1 / 6x^2 - 12x / 24 / x^2 - 4
A 32 / x(x + 2)(x - 2)^2
B x + 2 / 18x
C 32(x + 1) / x(x + 2)(x - 2)^2
D (x + 2)(x + 1) / 18x(x - 1)
You’re baking a circular cake for a party. Your cake can be any size you want. What will the radius of your cake be and how many slices will you be able to cut?
14. the number of deer spotted in a nature preserve each day over a two week period is listed below. 32 27 15 12 42 35 46 29 38 18 40 38 32 34
which frequency table represents the data ?
A. deer
10-19
20-29
30-39
40-49
frequency
3
3
5
4
B. Deer
10-19
20-29
30-39
40-49
frequency
3
2
5
4
c. deer
10-19
20-29
30-39
40-49
frequency
4
1
7
2
d. deer
10-19
20-29
30-39
40-49
frequency
3
2
6
3
Using Frequency table, Option: (d) is correct.
What is Frequency?Frequency refers to "the number of times an event or values occurs".
According to the question,
The number of deer spotted in preserve is
32,27,15,1,42,35,46,29,38,18,40,38,32,34
The number deer appear in the interval 10 - 19 is 3
The number deer appear in the interval 20 - 29 is 2
The number deer appear in the interval 30 - 39 is 6
The number deer appear in the interval 40 - 49 is 3
From the above data, we can form frequency table
Deer 10 - 19 20 - 29 30 - 39 40 - 49
Frequency 3 2 6 3
Hence, the answer is Option: (d)
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PLEASE HELP. evaluate the radical 3√1000
42) According to the 2000 Census the population of Canton was 7,720. Holly Spring's population was 3,200. Canton's population increases at a rate of 80 people a year and Holly Spring's population increases by 120 people a year. Which equation may be used to determine the number of years before the populations are equal?
A fair coin is tossed three time sin succession. the set of equally likely outcomes is {hhh,hht,hth,thh,htt,tht,tth,ttt}. find the probabilty of getting exactly zero tails
Sara loves to go hiking this weekend she hiked 3 miles on Monday 4 miles on Tuesdays and 3 miles on Thursday .last week Sara hiked 8 miles. How many more miles did Sara hike this week than last week
Answer:
2 miles
Step-by-step explanation:
Sara loves to go hiking.
She hiked 3 miles on Monday 4 miles on Tuesdays and 3 miles on Thursday.
Last week Sara hiked 8 miles
This week sara hiked = Monday + Tuesday + Thursday
= 3 + 4 + 3
= 10 miles
Last week hiked = 8 miles
Difference in two week hiked by Sarah = 10 - 8
= 2 miles
So, Sarah hike 2 miles more than last week.
What is the interquartile range of this data? 6 7 8 9 Box-and whisker plot titled Temperatures in Celsius ranging from 12 to 48 with the five number summary from left to right 18, 25, 28, 33, and 42
What is the interquartile range of this data? 6 7 8 9 Box-and whisker plot titled Temperatures in Celsius ranging from 12 to 48 with the five number summary from left to right 18, 25, 28, 33, and 42
Solution:
The problem is not clear.
But, considering data set is:
18,25,28,33,42
So, if we consider the data set, Interquartile Range is the difference of Quartile3-Quartile1
IQR=Q3-Q1
To find, Q1 and Q3. Let us find the median, or, Q2 first.
Median is the middle term of the data set.
So, Median, Q2=28
Q1 is the median of first half of the data set. That is, 18,25,28
So, Lower Quartile, Q1=25
Q3 is the median of second half of data set. That is, 28, 33,42
So, Upper Quartile, Q3=33
IQR=Q3-Q1
=33-25=8
Answer: IQR=8
If we consider data set: 6,7,8,9
Median, Q2=[tex] \frac{(7+8)}{2}=\frac{15}{2} [/tex]=7.5
Lower Quartile, Q1=6.25
Upper Quartile, Q2=8.75
IQR=Q3-Q1=8.75-6.25=2.5
IQR=2.5
A students is taking a 5-question
a. True
b. False quiz and guesses at each question. find the probability that the student will get all questions correct. find the probability that the student will get no questions correct.
help please, i don't understand it!!!!
In a study of 38% of adults questioned reported that their health was excellent. a researcher wishes to study the health of people living close to a nuclear power plant. find the probability that when 11 adults are randomly selected, at most 3 are in excellent health
The probability that when 12 adults are randomly selected, 3 or fewer are in excellent health is 0.947.
To find the probability that when 12 adults are randomly selected, 3 or fewer are in excellent health, we can use the binomial distribution formula.
The formula for the probability of getting exactly k successes in n trials, with a probability of success p, is:
P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))
In this case, n = 12, k = 3, and p = 0.38 (as 38% of adults reported excellent health).
So, the probability that 3 or fewer adults are in excellent health can be calculated as follows:
P(X <= 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Let's calculate each term:
P(X = 0) = (12 choose 0) * (0.38^0) * (0.62^12) = 0.190P(X = 1) = (12 choose 1) * (0.38^1) * (0.62^11) = 0.342P(X = 2) = (12 choose 2) * (0.38^2) * (0.62^10) = 0.269P(X = 3) = (12 choose 3) * (0.38^3) * (0.62^9) = 0.146Adding up these probabilities:
P(X <= 3) = 0.190 + 0.342 + 0.269 + 0.146 = 0.947
Rounded to three decimal places, the probability that when 12 adults are randomly selected, 3 or fewer are in excellent health is 0.947.
The probable question may be:
In a study, 38% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 12 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 12 adults are randomly selected, 3 or fewer are in excellent health. Round to three decimal places.
The real number 8.09 belongs to which set of numbers??
A-natural numbers
B-integers
C-irrational numbers
D-rational numbers
Draw a box plot for the data:
135, 149, 156, 112, 134, 141, 154, 116, 134, 156
The solution is: The box plot is attached.
What is median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
We first order the data from least to greatest:
112, 116, 134, 134, 135, 141, 149, 154, 156, 156
We find the median (middle value). There are 10 data values, which puts the median between 135 and 141:
(135+141)/2 = 276/2 = 138
The Upper Quartile (UQ) is the median of the upper half of data, cut by the median. This is 154.
The Lower Quartile (LQ) is the median of the lower half of data, cut by the median. This is 134.
The middle line of the box is drawn at the median, 138. The left side of the box is at the LQ, 134. The right side of the box is at the UQ, 154. There is a whisker drawn from the right side to the highest value, 156. There is a whisker drawn from the left side to the smallest value, 112.
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How many solutions are there for the system of equations shown on the graph?
No solution
One solution
Two solutions
Infinitely many solutions
Answer:
D. Infinitely many solutions
Step-by-step explanation:
We have been given an image of two lines on coordinate plane. We are asked to find the number of solutions for our given lines.
Upon looking at our given graph, we can see that both lines are same. Since both lines coincide, therefore, each point on the line will be solution of our given lines.
Therefore, our given lines will have infinitely many solutions and option D is the correct choice.
triston is baking specity bread for the school bake sale. she has 10 1/2 cups of flour. the recipe for 1 loaf of bread calls for 2 1/3 cups of flour. How many whole loaves of bread can she make.
Triston can make 4 whole loaves of bread using her 10 1/2 cups of flour. This was determined by dividing the total flour available by the flour required per loaf. Fractional or partial loaves are not counted.
To determine how many whole loaves of bread Triston can make, we need to perform a simple division of the total amount of flour by the amount required for one loaf.
First, let's convert the mixed numbers to improper fractions:
10 1/2 cups of flour = 21/2 cups of flour2 1/3 cups of flour = 7/3 cups of flourNext, we will divide the total flour by the flour needed per loaf:
(21/2) ÷ (7/3) = (21/2) × (3/7) = (21 × 3) / (2 × 7) = 63/14 = 4.5 loaves
Since we can only make whole loaves, Triston can make 4 whole loaves of bread.
In the circle below, radius mn = 1.4 m and mlmn = 52°. determine the length of arc ln. round your answer to the nearest tenth and use π = 3.14.
Answer:
1.27 is the answer
Step-by-step explanation:
Find the value of x.
The polygons are similar, but not necessarily drawn to scale.
Answer:
[tex]x=10 units[/tex]
Step-by-step explanation:
Given: The polygons ABCD and JKLM are similar.
To find: The value of x.
Solution: Since, the given polygons are similar, therefore using the similarity condition, we have
[tex]\frac{AD}{JM}=\frac{CD}{LM}[/tex]
Substituting the given values, we get
[tex]\frac{12}{40}=\frac{3}{x}[/tex]
On cross multiplying, we get
[tex]\frac{3\times40}{12}=x[/tex]
[tex]x=10 units[/tex]
Therefore, the value of x is 10 units.
Simplify the expression below. 6n2 - 5n2 + 7n2
What is 6.8 rounded to the nearest ones place?
The slope of BY is -1/5, and BYllJE
What is the slope of JE?
-5
-1/5
1/5
5
The diameter of Jupiter is 88,000 miles This is about 11.1 times the diameter of Earth What is the diameter of the earth
Calculate cos theta where theta is the angle between u and v
Which of the following is equivalent to C(16, 4)?
answer choices:
12!
C(16, 12)
C(15, 3)
Answer- C(16,12)
C(n,r) = n! / r!* (n-r)!
So,
C(16,4) = 16!/ 4! * 12!
C(16,12) = !6!/ 12! * 4!
On a map, the distance between two cities is 2.4 inches. the two cities are actually 768 miles apart. on this same map, what would be the distance between two cities in miles that are 4.8 inches apart on the map?