W will be 15.84.
What is an equation?The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 has the two expressions 3x + 5 and 14 that are separated by the 'equal' sign.
We know that w divided by 1.1 minus 3.9 equals 10.5
That will be W/1.1 - 3.9 = 10.5
W/1.1 = 10.5 + 3.9
W/1.1 = 14.4
W = 14.4* 1.1
W = 15.84
W will thus equal 15.84.
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Please do this I have to turn it in to pass
Answer:
I've solved all of the above for you :)
Step-by-step explanation:
3q² + 7 = 55
3q² = + 7 - 7 = 55 - 7
3q² = 48
3q²/3 = 48/3
q² = 12
q = 2√3
√p - 4 = - 5
p - 4 = (-5)²
p - 4 + 4 = 25 + 4
p = 29
5√a/2 = 40
5√a/2 × 2 = 40 × 2
5√a = 80
5√a/5 = 80/5
√a = 16
a = 256
c³ - 4 = 23
c³ - 4 + 4 = 23 + 4
c³ = 27
c = 3
(k + 3)² = 4
k² + 6k + 9 = 4
k² + 6k + 9 - 4 = 0
k² + 6k + 5 = 0
k² + k + 5k + 5 = 0
k(k + 1) + 5(k + 1) = 0
(k + 5) (k + 1) = 0
k = (-5) or (-1)
√s + 4 = 6
s + 4 = (6)²
s + 4 - 4 = 36 - 4
s = 32
(√f - 5) = (√7 - f)
(√f - 5)² = (√7 - f)²
f - 5 = 7 - f
f - 5 + 5 + f = 7 + 5 - f + f
2f/2 = 12/2
f = 6
∛j + 9 = 0
∛j + 9 - 9 = -9
∛j = (-9)
j = (-9)³
j = (-729)
b² - 1 = 24
b² - 1 + 1 = 24 + 1
b² = 25
√b² = √25
b = 5
13 = (w - 2)² + 5
13 = w² - 4w + 4 + 5
13 - 9 = w² - 4w
w² - 4w = 4
w² - 4w - 4 = 0
w² - 2w - 2w - 4 = 0
w(w - 2) - 2(w - 2) = 0
(w - 2) (w - 2) = 0
w = 2 or 2
12 = 4√2x + 1
12/4 = 4√2x + 1/4
3 = √2x + 1
√2x + 1 = 3
2x + 1 = 9
2x + 1 - 1 = 9 - 1
2x/2 = 8/2
x = 4
(g + 1)³ = (-8)
g³ + 1³ + 3g(g + 1) = (-8)
g³ + 1 + 3g² + 3g = (-8)
g³ + 3g² + 3g = (-8) - 1
g³ + 3g² + 3g = -9
g³ + 3g² + 3g + 9 = 0
g = (-3)
∜(5m + 1) = 4
[∜(5m + 1)]⁴ = (4)⁴
5m + 1 = 256
5m + 1 - 1 = 256 - 1
5m/5 = 255/5
m = 51
∛(y³ - 19) = 2
(y³ - 19) = (2)³
y³ - 19 = 8
y³ - 19 + 19 = 8 + 19
y³ = 27
y = 3
Are the two expressions x-5 and x-5 equivalent? Give evidence to support your yes or no answer.
Remember, for expressions to be equivalent, they must have the same value for all values of the input
variable, x.
The expressions x - 5 and x - 5 gives the equal value for the different values of x, therefore expressions are equivalent.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expressions are,
x - 5 and x - 5
To determine the expressions are equivalent,
Since, in the both, the expression x is a variable, and 5 is an integer,
Therefore, for the values of x the value of expression should be equal.
Substitute x = 0,
x - 5 = 0 - 5 = - 5
And
x - 5 = 0 - 5 = - 5
Substitute x = 1
x - 5 = 1 - 5 = - 4
and
x - 5 = 1 - 5 = - 4
Since, for the different values of x the values of expressions are equal.
Hence, expression x - 5 and x - 5 are equivalent.
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tell how you can use the structure of mathematics to complete the task
Answer: It is crucial for students to look for and make use of a structure because this practice requires them to reason about the underlying mathematical structure and unity of mathematics ideas.
a building has a height of 250 in length of 160 m on a scale drawing of the building the height is 50 cm what is the length of the building on the scale drawing a centimeters
The required length of the building is given as 32 cm.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
The height of the building is 250 meters, the length of the building is 160m, and on the drawing, the height of the building is 50 cm,
Scale factor = height on drawing / original height
Scale factor = 50 / 250
Scale factor = 1/5
Now,
Length in drawing = scale factor × original length,
length in drawing = 1 / 5 × 160
= 31
Thus, the length of the building as of the scale factor 1/5 is given as 31 cm.
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What is the length of side AB? please help
top I think he or she is right
The length of the AB in the given right triangle is √3/6
Given that, a right triangle with the base measure 6 units and an acute angle 30°,
We need to find the measure of side AB,
So, we will use the concept of trigonometric ratios,
Tan 30° = AB / AC
Tan 30° = AB / 6
1 / √3 = AB / 6
AB = √3/6
Hence the length of the AB in the given right triangle is √3/6
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The graph shows the proportional relationship between the number of gems collected and the number of levels that has been completed in a video game.
Determine the constant of proportionality for the relationship.
The constant of proportionality for the relationship is 70.
From the given graph (2, 140), (4, 280), (6, 420), (8, 560) and (10, 700).
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
From the graph we can see it is direct proportion.
Here, y∝x
⇒ y=kx
⇒ k=y/x
⇒ k=140/2
⇒ k=70
Hence, the constant of proportionality for the relationship is 70.
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Help Please! This is 6th grade k12
Answer:Put a one under the five then sop he last faction and start multiplying
Step-by-step explanation:
Melvin and Sylvia are married with no children, and they're filing their federal income tax return. Melvin had a gross income of $44,500 last year, while Sylvia had a gross income of $51,200, and they plan to use the standard deduction. They're trying to decide whether to file their return jointly or separately, so they want to calculate how much less they would pay in federal income taxes if they filed jointly rather than separately. part 2
Answer: 3702
Step-by-step explanation: from plato
John paid $280 for a new mountain bicycle to sell in his shop. He wants to price it so that he can offer a 30% discount but still make 10% of the price he paid for it. At what price should the bike be marked?
By using the concept of discount, it can be calculated that
The bike should be marked at $440
What is discount?
Sometimes during sale, the items are sold at a reduced price from the original price of the item. The difference between the reduced price and the original price of the item is called discount.
Price paid by John for a new mountain bike = $280
Markup price = [tex]\frac{10}{100} \times 280[/tex] = $28
Price after markup = $(280 + 28) - $308
Let the marked price be $x
Rate of discount = 30%
Discount = [tex]\frac{30}{100}\times x[/tex]
Price after discount = [tex]x - \frac{30}{100}\times x[/tex]
= [tex]\frac{100x - 30x}{100}[/tex]
= [tex]\frac{70}{100}x[/tex]
By the problem,
[tex]\frac{70}{100}x = 308\\x = \frac{308 \times 100}{70}\\[/tex]
x = $440
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A sample of 38 observations is selected from one population with a population standard deviation of 3.0. The sample mean is 100.5. A sample of 50 observations is selected from a second population with a population standard deviation of 5.2. The sample mean is 98.8. Conduct the following test of hypothesis using the 0.02 significance level.
P value?
A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
What is the hypotheses in research?A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.Hypotheses are used to support scientific research and create breakthroughs in knowledge. These brief statements are what form the basis of entire research experiments. Thus, a flaw in the formulation of a hypothesis may cause a flaw in the design of an entire experiment.a. two-tailed test
b. reject H0 if Z>1.96 or Z<-1.96
c. Z = 1.73
d. we have failed to reject the null hypothesis
e. P-value = 0.0418
We will use a Z test to resolve this, an it will be a two-tailed test because the hypothesis statements are not indicating a specific direction for the significant difference (H0 : μ1 = μ2 ; H1 : μ1 ≠ μ2), this also means that the significanclevel will be divided between the both tails (2.5% en each tail for the rejection regions). See attached drawing for reference.We need to find our critical value:
Zα/2 = Z(0.05/2) = 0.025
If we look for 0.025 in a Z table we will find that the critical value is 1.96 to the right, and by symmetry -1.96 to the left. So our decision rule will be to reject H0 if Z>1.96 or Z<-1.96The Z test will be done using the next equation:
Z = (x⁻1 - x⁻2) - (μ1 - μ2) / √( σ²1/n1 + σ²2/n2
Because we are testing the null hypothesis we know that μ1 - μ2 must be zero if they are supposed to be equal (H0 : μ1 = μ2), so we calculate as follows:Z = (100.5 - 98.8) - (0) / √( (3.4)²/38 + (5.8)²/51 = 1.7/0.9817 = 1.73
Z<1.96, therefore we have failed to reject the null hypothesis
The P-value for this test would be represented by the probability of Z being greater than 1.73, so we can look for it in any Z table, finding that its value is 0.0418, and because P-value>0.025 we again confirm that we don't have evidence statistically significant to reject the null hypothesis
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Suppose your gross monthly income is $6,500 and your current monthly payments are $525. If the
bank will allow you to pay up to 38% of your gross monthly income (less current monthly payments)
for a monthly house payment, what is the maximum loan you can obtain if the rate for a 25-year
mortgage is 8.65%?
The maximum loan you can obtain if the rate for a 25-year mortgage is 8.65% is $298,853.76
How to find monthly payment?A monthly payment can be calculated as;
Monthly payment = (Monthly income - payment)(percentage payment)
38% of your gross monthly income is
0.38 × $6,500 = $2470
If you're already spending $525 on monthly payments, the amount the bank says you can afford for a mortgage loan;
Then
$2470-525= $1945
The amortization formula can be used to find the corresponding loan value.
A = P(r/25)/(1 -(1 +r/25)^(-25t))
where A is the monthly payment on a loan of P at interest rate of r for time t years.
Filling in the known values, we have ;
1945= P(.0525/25)/(1 -(1 +.0525/25)^(-12·30))
≈ 0.00515636808·P
Then the maximum loan can obtain is
P = $1945/0.00515636
P ≈ $298,853.76
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A person works at a vegetable farm and a paddy field. He earns Rs 200/- per hour from
vegetable farm and Rs 250/- per hour from paddy field. Last week, he worked for both jobs for a total of 30 hours, and earned a total of Rs 6900/-. How long did the person work at the vegetable farm last week, and how long did he work at the paddy field.. ?
Answer:
He worked 26 hours at the vegetable farm and 4 hours at the paddy field.
Step-by-step explanation:
Let us take the working hour at a vegetable farm be x and at paddy field be y
He worked for both jobs for a total of 30 hours.
So,
x + y = 30 ...(1)
He earns Rs 200/- per hour from vegetable farm and Rs 250/- per hour from paddy field, total of Rs 6900.
So,
200x + 250y = 6900
2x + 5y = 138 ...(2)
From equation 1 we get,
x = 30 - y
Put the value of x = 30 - y in equation 2 we get,
2x + 5y = 138
2(30 - y) + 5y = 138
60 - 2y + 5y = 138
60 + 3y = 138
3y = 138 - 60
3y = 78
y = 26
Now, put the value of y in equation 1 we get,
x + y = 30
x + 26 = 30
x + 26 - 26 = 30 - 26
x = 4
Thus, He worked 26 hours at the vegetable farm and 4 hours at the paddy field.
Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x)=(x²-64)^{1/11} on the domain [-8,9]
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The absolute maximum is , which occurs at x= (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.)
B. There is no absolute maximum.
The absolute maximum is 1.29, which occurs at x= 9
What is absolute extrema?
An absolute extremum of a perform in an exceedingly given interval is that the purpose at that a most or minimum worth of the perform is obtained. Frequently, the interval given is that the function's domain, and therefore the absolute extremum is that the purpose admire the most or minimum worth of the complete perform.
Main body:
Given =
f(x) = [tex](x^{2} -64)^{1/11[/tex]
f' (x) = derivative of function f(x)
f'(x) = 1/11[tex](x^{2} -64)^{-10/11[/tex] . 2x
= [tex]2 \frac{x}{11}[/tex][tex](x^{2} -64)^{-10/11[/tex]
putting f'(x) = 0
2x/11 [tex](x^{2} -64)^{-10/11[/tex] = 0
[tex](x^{2} -64)^{-10/11[/tex] = 0
[tex]x^{2} -64[/tex] = 0
x² = 64
x = ±8
We are given interval [-8,9].
Hence, calculating f(x) at -8, 8, 9.
f(-8) = 0
f(8) = 0
f(9) = [tex]17^{1/11}[/tex]
= 1.29
Hence, absolute maximum value is 1.29 at x=9.
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Miguel drove his car 315 miles, which was 7 inches on his road map. Which equation represents the actual miles traveled, m, relative to the distance shown on the map, d.
m=d/45
m=45xd
d=45xm
d=45/m
The equation representing the actual miles traveled, m, relative to the distance shown on the map, d is m = 45 × d, so option B is correct.
What is the equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.
Given:
The distance travelled = 315 miles,
The distance on the map = 7 inches,
Calculate the equation represents the actual miles traveled,
Actual distance = The distance traveled / The distance on the map × The distance on the map
m = 315 / 7 × d
m = 45 × d
Therefore, the equation representing the actual miles traveled, m, relative to the distance shown on the map, d is m = 45 × d.
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Is 5/6 greater than 10/12
Answer:
Step-by-step explanation:
Clearly, it can be seen that 10/12 represents the largest fraction. Hence 5/6 (which is equivalent to 10/12) is larger than 2/3 or 3/4.
Answer: no they are equal either simplified to 5/6 or decimal 0.83 repeating decimal.
Step-by-step explanation:
Write a function g whose graph is a horizontal shrink by a factor of 1/3
of the graph of f. F(x)=2|x+3|-2
Answer:
g(x) = 6|x + 1| - 2-----------------------------------------
Given:
Function f(x) = 2|x + 3| - 2Find a function g which is a horizontal shrink by a factor of 1/3 of f(x).
Horizontal shrink by a factor of k is:
g(x) = f(x/k)Apply this to the given function:
g(x) = f(x : 1/3) = f(3x) = 2|3x + 3| - 2 = 6|x + 1| - 2Question content area top Part 1 A motorboat is capable of traveling at a speed of 10 miles per hour in still water. On a particular day, it took 15 minutes longer to travel a distance of 6 miles upstream than it took to travel the same distance downstream. What was the rate of current in the stream on that day? PLEASE HURRY
We can determine the stream's current velocity by solving a set of equations, which gives us S is 2 mi/h.
Calculate the stream's current flow rate on that particular day?The total speed of a motorboat traveling downstream is equal to the speed of the boat in still water plus the speed of the stream, whereas the total speed of a motorboat traveling upstream is equal to the speed of the stream minus one.
Therefore, the speed upstream is: (14 mi/h - S)
The speed downstream is (14 mph + S), where S is the stream's current flow rate.
We can construct the equations below after we know that it takes 15 minutes longer to walk 12 miles downstream:
14 mph plus speed (S) times the time (T minus 15 minutes) equals 12 miles.
In order to solve this, one of the variables in one of the equations needs to be isolated. I'll isolate T in the first equation:
T = (12 miles)/(14 miles per hour Plus S)
By substituting it in the other equation, we will obtain the following value: (14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi.
Taking only the favorable outcome, we obtain:
S = (24 - 25)/(-0.5) = 2 mph
2 mi/hr is the stream's current velocity.
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The classroom outside bag had 5 frisbees in it. If 25% of the outside toys are frisbees, then how many total toys are in the bag?
Answer: 15, not including the frisbees. (The answer would be 20 if the frisbees were in there)
Step-by-step explanation: 25% is equivalent to 1/4, and 5 is equal to 1/4. The simplest way to solve this is to multiply 5 by 4, and you'll get 20. Then subtract 5 (the frisbees) and you'll get 15. (Sorry if that doesn't make much sense haha) Hope this helps!!
16
22
34
52
76
?
Select one:
a.
106
b.
137
c.
89
d.
105
Answer:
106
Step-by-step explanation:
The pattern goes +6, +12, +18, etc
Thus, the final term is simply +30.
76+30 = 106
Hope it helps :) and let me know if you want me to elaborate.
Select the correct answer. What happens if the correlation coefficient equals 0? A. There is a strong negative linear relationship between x and y. B. There is not a linear relationship between x and y. C. There is a strong positive linear relationship between x and y. D. There is a weak negative linear relationship between x and y. Reset Next
By the Definition of a Correlation Coefficient,
x and y do not have a linear relationship.
Option B is the correct answer.
What Is the Definition of a Correlation Coefficient?The correlation coefficient describes the movement of one variable in relation to another. A positive correlation indicates that the two are moving in the same direction, with 1 denoting a perfect positive correlation. A value of -1 indicates a perfect negative, or inverse, correlation, while a value of zero indicates that no linear correlation exists.
What does a correlation between 0 and +1 mean?The number's value indicates the strength of the relationship: r = 0 indicates that there is no correlation. r = 1 indicates that there is a perfect positive correlation. r = -1 shows a perfect negative correlation.
According to the question, If the correlation coefficient is zero, there is no linear relationship.
If the correlation coefficient is zero, the relationship between x and y is not linear. Another possible relationship (such as an exponential or quadratic) could exist, but this is dependent on the scatter plot provided.
By the Definition of a Correlation Coefficient,
Option B is the correct answer.
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By the Definition of a Correlation Coefficient, X and Y do not have a linear relationship. Option B is the correct answer.
What Is the Definition of a Correlation Coefficient?The correlation coefficient describes the movement of one variable in relation to another. A positive correlation indicates that the two are moving in the same direction, with 1 denoting a perfect positive correlation. A value of -1 indicates a perfect negative, or inverse, correlation, while a value of zero indicates that no linear correlation exists.
What does a correlation between 0 and +1 mean?The number's value indicates the strength of the relationship: r = 0 indicates that there is no correlation. r = 1 indicates that there is a perfect positive correlation. r = -1 shows a perfect negative correlation.
According to the question, If the correlation coefficient is zero, there is no linear relationship.
If the correlation coefficient is zero, the relationship between x and y is not linear. Another possible relationship (such as an exponential or quadratic) could exist, but this is dependent on the scatter plot provided.
By the Definition of a Correlation Coefficient,
Option B is the correct answer.
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if you roll die, what is the probability of rolling a numbe rless than 4 or rolling an odd number
The probability of rolling an odd number or a number less than 4 is 2/3.
What is probability?
The degree to which something is likely; the probability that something will occur or will be the case.
Here, we have
Given
A single die is rolled.
Sample space = {1, 2, 3, 4, 5, 6}
Let P(A) be the probability of getting an odd number, where A = {1, 3, 5}
Let P(B) be the probability of getting a number less than 4,
where B = {1,2,3}
A ⋂ B ={1, 3}
P(A) = 3/6 = 1/2
P(B) = 3/6 = 1/2
P(A ⋂ B) = 2/6 = 1/3
Let P be the required probability of getting an odd number or a number less than 4
P = P( A ⋃ B ) = P(A) + P(B) - P(A ⋂ B)
P( A ⋃ B ) = 1/2 + 1/2 - 1/3
P( A ⋃ B ) = 1 - 1/3
P( A ⋃ B ) = 2/3
Hence, the probability of rolling an odd number or a number less than 4 is 2/3.
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HELPPP PLEASE ASPPP!!!!!!
Examine the graph below. Calculate the slope.
Slope of line is 1/2.
What is slope?
In arithmetic, the slope or gradient of a line is a range that describes each the direction and therefore the gradient of the road.
Main body:
to find the slope from a graph , we need to fix two co-ordinates at slope for axis
let point at x be = (40,40)
let point y = (80,60)
Formula for slope ,
m = y₂-y₁/x₂-x₁
m = 60-40/80-40
m = 20/40
m = 1/2
hence , slope of line is 1/2.
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7.) Given the following triangle, what is the value of x and the value of y ?
Answer: x = 36; y = 36
Step-by-step explanation:
This is an isosceles triangle, so the 2 "bottom" angles are equal:
2x = 72
x = 72/2 = 36
sum of interior angles = 180
180 - 72 - 72 = 36
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
205, 201, 197, ...
Find the 35th term.
The first three terms of a sequence are given, so the 35th term is: [tex]a_n = 69[/tex]
What is sequence?A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts. A sequence is a list of elements that has been arranged in a certain way.
An ordered list of numbers is a sequence. The three dots indicate that the established pattern should go forward. A phrase is used to describe each number in the series. The first word in the order 1, 3, 5, 7, 9,... is 1, the second is 3, the third is 5, and so on.
The first three terms are : 205, 201, 197, .......
The general term through the pattern is:
[tex]a_n = - 4n+209[/tex]
or, [tex]a_n = - 4(35)+209[/tex]
here, n = 35
or, [tex]a_n = 69[/tex]
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bus company uses a grid to locate bus stops. The bus station is at (3, 4). The point (7, 6) represents the first bus stop. The location of each stop after that is determined using the same relationships as those between the coordinates of the bus station and the first bus stop. A coordinate plane is titled Which point represents the fourth bus stop? A. (11, 8) B. (13, 12) C. (15, 10) D. (19, 12) 7 / 7 6 of 7 Answered
Answer:
I think that's 11,8
Step-by-step explanation:
Hope its right
Hassan is cooking some rice the recipe says he needs 450 grams of rice for 6 people how many kilograms or rice would he need for 18 people?
Answer:
450 g = 6 people
? kg = 18 people
450 x 18 = 8100
8100 = 6x
8100/6 = 6x/6
x = 3150 kg of rice is needed for 18 people.
estimate the difference between 3,894,256 and 756,533 by rounding each number to the nearest thousand. 4,561,000 3,137,000 3,138,000 3,139,000
The difference between 3894256 and 756533 by rounding each number to the nearest thousand is 3138000
The first number = 3894256
The second number = 756533
To find the difference between the numbers we have to use the subtraction
Difference between 3894256 and 756533 = 3894256 - 756533
Subtract the numbers
= 3137723
Rounding of a number is write the numbers to the nearest place values like tens, hundreds and thousand etc.
Here, the number is 3137723 and we have to round the number to nearest thousand
Round to nearest thousand = 3137000
Therefore, the result nearest to the thousand is 3138000
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Find the area of the triangle below.
Be sure to include the correct unit in your answer.
10yd
4yd
7yd
The area of the triangle below 8 yards
What is triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Triangles are three-sided shapes. The many kinds of triangles go by various names. The size of the angles and the length of the sides determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.7-15=8
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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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Write the expression x2 - 6x-2 in the form (x + a)² + b
Answer:
(x - 3)² - 11--------------------------
GivenExpression x² - 6x - 2.Convert this to vertex form by completing the square.
Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:
x² - 6x - 2 = x² - 2*3*x + 3² - 3² - 2 = (x - 3)² - 9 - 2 = (x - 3)² - 11Answer:
[tex](x-3)^2-11[/tex]
Step-by-step explanation:
Given quadratic expression:
[tex]x^2-6x-2[/tex]
To write the given expression in the form (x + a)² + b, complete the square.
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies x^2-6x+\left(\dfrac{-6}{2}\right)^2-2-\left(\dfrac{-6}{2}\right)^2[/tex]
Simplify:
[tex]\implies x^2-6x+\left(-3\right)^2-2-\left(-3\right)^2[/tex]
[tex]\implies x^2-6x+9-2-9[/tex]
The first three terms x² - 6x + 9 form a perfect square trinomial.
A perfect square trinomial can be written as the square of a binomial.
Factor the perfect square trinomial:
[tex]\implies(x-3)^2-2-9[/tex]
Simplify:
[tex]\implies(x-3)^2-11[/tex]
Therefore, the given expression written in the form (x + a)² + b is:
[tex]\boxed{(x-3)^2-11}[/tex]