Answer:
x = - [tex]\frac{1}{2}[/tex], x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given
x² - x - [tex]\frac{3}{4}[/tex] = 0
Multiply through by 4 to clear the fraction
4x² - 4x - 3 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 3 = - 12 and sum = - 4
The factors are + 2 and - 6
Use these factors to split the x- term
4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(2x - 3) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
The solutions are x = 3 and x = -7.
To solve the quadratic equation, we first need to bring it to the standard form of ax2 + bx + c = 0. In the example given, we have the equation x2 + 4x - 21 = 0, where a = 1, b = 4, and c = -21. To find the solutions for x, we will use the quadratic formula, which is x = (-b ± √(b2 - 4ac)) / (2a).
Substituting the values of a, b, and c into the quadratic formula, we get:
x = (-(4) ± √((4)2 - 4(1)(-21))) / (2(1))
x = (-4 ± √(16 + 84)) / 2
x = (-4 ± √100) / 2
x = (-4 ± 10) / 2
Which gives us two solutions:
x = (6 / 2) = 3
x = (-14 / 2) = -7
Therefore, the solutions to the quadratic equation x2 + 4x - 21 = 0 are x = 3 and x = -7.
10. Sue has a boat that would go 9 miles per hour in still water. She travels downstream for a
certain distance and then back upstream to where she stared. Sue notices that it takes her 4
hours to travel upstream against the river, and only 2 hours to travel downstream with the
river. The rivers speed is r miles per hour. Write and Solve for r.
Answer:
The speed of the river is 3 miles per hour.Step-by-step explanation:
In downstream, the speed of the boat will be (9 + r) miles per hour and in upstream the speed of the boat will be (9 - r) miles per hour.
Ratio of the speed in downstream to the speed in upstream is (9 + r):(9 - r).
Hence, the ratio of the time taken by the boat to cover the distance in downstream to upstream is (9 - r):(9 + r).
[tex]\frac{9 - r}{9 + r} = \frac{2}{4} \\18 - 2r = 9 + r\\3r = 9\\r = 3[/tex]
Lesledi has a box that is 36cm wide, 24cm high, and 20cm deep. She wants to fill the box with packages that are 12cm wide, 6cm high, and 4cm deep.
What's the greatest number of packages Lesledi can put in the box without it overflowing?
Answer:
The answer is 3
Step-by-step explanation:
36÷12=3, which is the lowest number on either side of the boxes
Lesledi can put a maximum of 60 packages in the box without it overflowing.
What is Unitary Method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
The maximum number of 12cm wide packages that can fit in the 36cm width of the box is
= 36 ÷ 12
= 3
and, The maximum number of 6cm high packages that can fit in the 24cm height of the box is
= 24 ÷ 6
= 4
and, The maximum number of 4cm deep packages that can fit in the 20cm depth of the box is
= 20 ÷ 4
= 5
Therefore, the maximum number of packages that can fit in the box is:
= 3 x 4 x 5
= 60
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Here is a math question I need help with, offering 20 points for full answer.
Answer: 8 sqrt7
Step-by-step explanation:
Emma has $3.15 worth of dimes and quarters. She has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Emma has.
Answer:
Emma has 14 pennies and 7 quarters
When, Emma has $3.15 worth of dimes and quarters and she has twice as many dimes as quarters. Then, Emma has 14 dimes and 7 quarters.
To solve this, we set up two equations based on the given information. Let the number of quarters be q and the number of dimes be d.
From the information given:
Emma has twice as many dimes as quarters (d = 2q).The total value of the dimes and quarters is $3.15.The value equation can be written as 0.10d + 0.25q = 3.15 (since dimes are worth $0.10 and quarters $0.25).
Substituting the first equation into the second gives: 0.10(2q) + 0.25q = 3.15, which simplifies to 0.45q = 3.15.
Dividing both sides by 0.45 gives us q = 7. Since the number of dimes is twice the number of quarters, d = 2 x 7 = 14.
Therefore, Emma has 14 dimes and 7 quarters.
What is the value of the expression (-8/9)*(-2/3) multiplied by (-4 1/2)
Answer:
-8/3
Step-by-step explanation:
-4 1/2=-9/2
(-8/9)(-2/3)=16/27
(16/27)(-9/2)=-144/54
-8/3
preliminary sample of 100 labourers was selected from a population of 5000 labourers by simple random sampling. It was found that 40 of the selected labourers opt for a new incentive scheme. How large a sample must be selected to have a precision of ± 5% with 95% confidence ?
Answer:
[tex]n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79[/tex]
n=369
Step-by-step explanation:
1) Notation and definitions
[tex]X=40[/tex] number of the selected labourers opt for a new incentive scheme.
[tex]n=100[/tex] random sample taken
[tex]\hat p=\frac{40}{100}=0.4[/tex] estimated proportion of the selected labourers opt for a new incentive scheme.
[tex]p[/tex] true population proportion of the selected labourers opt for a new incentive scheme.
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]
2) Solution tot he problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79[/tex]
And rounded up we have that n=369
The size of the sample that must be selected to have a precision of ± 5% with 95% confidence is 369
How to find the margin of error of sample proportion?For large enough sample, let the population proportion of a quantity be denoted by random variable [tex]p[/tex]
Then, we get:
[tex]p \sim N(\hat{p}, \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})[/tex]
where
[tex]\hat{p}[/tex] = estimated (mean value) proportion of that quantity, andn = size of sample drawn.It is visible that as we increase the value of n, the standard deviation decreases, therefore, forcing the values of population proportion to be closer to the estimated proportion.
Margin of error is the distance between the mean and one of the end point of the confidence interval(assuming its equal on both the sides of the mean). The margin of error with level of significance [tex]\alpha[/tex] is calculated as:
[tex]MOE = Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
where
[tex]Z_{\alpha/2}[/tex]
is the critical value of the test statistic for level of significance [tex]\alpha[/tex]
For the considered case, we have following facts:
Size of the preliminary sample = 100The precision needed = Margin of error = 5% =0.05Confidence level = 95%Count of labors in sample who opt for a new incentive scheme = 40Thus, if we denote p = proportion of labors opting for a new incentive scheme in the considered population, then,
[tex]\hat{p} = 40/100 = 0.4[/tex] (estimate from the sample about the proportion of such labors who opt for new incentive scheme to the total count of labors of the sample).
For 95% confidence interval, level of significance is 100% - 95% = 5% = 0.05
At this level of significance, the critical value of Z is ±1.96
Let the needed sample size be 'n', then:
[tex]MOE = Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\0.05= \pm 1.96 \sqrt{\dfrac{0.4(1-04)}{n}}\\\\n = \dfrac{0.4 \times 0.6}{(0.05/1.96)^2} \approx 369[/tex]
Thus, the size of the sample that must be selected to have a precision of ± 5% with 95% confidence is 369
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Fenyang got 6 rabbits to raise on his farm. From the following month forward, the rabbit population
doubled every month.
Let g(n) be the number of rabbits in Fenyang's farm in the nth month since he got the rabbits.
g is a sequence. What kind of sequence is it?
a-arithmetic sequence
b-geometric sequence
Complete the recursive formula for g(n).
g(1)=_________
g(n)=g(n-1) _______
NEED HELP NOW!
Answer:
g is a geometric sequence.
g(1) = 6
g(n) = g(n-1)*2
Step-by-step explanation:
A geometric sequence is one in which each next term is found by multiplying the previous term by a constant number.
In our case the rabbit population doubles each month, therefore we are multiplying the population of the previous month by 2 to get the population of the next month. Thus g(n) is a geometric sequence.
The sequence described is a geometric sequence with a ratio of doubling each month. The recursive formula for the sequence is g(1) = 6 and g(n) = 2*g(n-1).
Explanation:The sequence described is a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio. In this case, that ratio is 2 because the rabbit population doubles every month.
When providing the recursive formula for the function g(n), the first term, g(1), would be 6, as that is the number of rabbits Fenyang started with. For any other term in the sequence, g(n), it would be twice the previous term, g(n-1). So, the complete recursive formula for the sequence would be:
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The surface area of the rectangular prism can be found using the expression 6x exponent 3 + 4x exponent 2 + 12x. if the value of x is 3, what is the surface area, in square centimeters of the prism?
Answer:
234 cm²
Step-by-step explanation:
Given expression to represent the surface area of the rectangular prism is [tex]6x^{3} +4x^{2} +12x[/tex]
The given value of x is 3.
Now, finding value of expression by sustituting value of "x" as given.
Surface area of the rectangular prism = [tex]6x^{3} +4x^{2} +12x[/tex]
Surface area of the rectangular prism= [tex]6\times 3^{3} +4\times 3^{2} +12\times 3[/tex]
∴ Surface area of the rectangular prism= [tex]6\times 27+ 4\times 9+ 12\times 3[/tex]
Surface area of the rectangular prism= [tex]162+36+36= 234\ cm^{2}[/tex]
∴ Surface area of the rectangular prism= 234 cm²
After dividing a piece of wood into four equal sections,each section is 4 in.long.How long was the piece of wood I started with
I'm going to out on a limb and say 16 in.
4 pieces * 4 in. = 16
quick! can someone please explain 9 1/6 - 8 5/6 ??
The 9 at the side on the fraction represents one full 6/6
So by taking one out, it will give the top number an extra 6.
What is the quotient of 3227/555? What is the repetend?
Answer:
A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating (i.e. all except finitely many digits are zero). For example, the decimal representation of
1
/
3
becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e. 0.333.... A more complicated example is
3227
/
555
, whose decimal becomes periodic at the second digit following the decimal point and then repeats the sequence "144" forever, i.e. 5.8144144144.... At present, there is no single universally accepted notation or phrasing for repeating decimals.
The infinitely repeated digit sequence is called the repetend or reptend. If the repetend is a zero, this decimal representation is called a terminating decimal rather than a repeating decimal, since the zeros can be omitted and the decimal terminates before these zeros.[1] Every terminating decimal representation can be written as a decimal fraction, a fraction whose divisor is a power of 10 (e.g. 1.585 =
1585
/
1000
); it may also be written as a ratio of the form
k
/
2n5m
(e.g. 1.585 =
317
/
2352
). However, every number with a terminating decimal representation also trivially has a second, alternative representation as a repeating decimal whose repetend is the digit 9. This is obtained by decreasing the final (rightmost) non-zero digit by one and appending a repetend of 9. 1.000... = 0.999... and 1.585000... = 1.584999... are two examples of this. (This type of repeating decimal can be obtained by long division if one uses a modified form of the usual division algorithm.[2])
Step-by-step explanation:
The sum of the digits of a two-digit number is 11. If we interchange the digits then the new number formed is 45 less than the original. Find the original number.
Answer:
38
Step-by-step explanation:
the value of the number is 10*y (y is the tens digit) + x = 10x( now x is the tens digit) + y +45
9x+45=9y
x+5=y
x+y=11
x=11-y
x-11=-y
y=11-x
x+5=11-x
2x=6
x=3
y=8
original number is 38
What is the value of tan a ? 24/7 24/25 7/25 or 7/24
Answer:
24/7
Step-by-step explanation:
tan(A)=BC/AC
in the right angle triangle as shown in figure we can see
tan(A)=BC/AC
tan(A)=perpedicular /base
perpendicular is just opposite of Angle(A) that is BC and base is AC
so tan(A)=BC/AC
Find the interest earned in an account with 3,600 invested at 3 1/2% simple interest for 5 years at
Answer:
Total Interest earned is $630.
Step-by-step explanation:
Principal = $3,600
Time = 5 Years
Interest Rate = 3 1/2% = 7/2% = 3.5%
Interest = Principal x Time x Interest Rate
Interest = $3,600 x 5 x 0.035
Interest = $630
Please help me with this question I need to eat when im dOne with ThiS!!!!
Answer: Ham 1 3/4 is your answer
Step-by-step explanation: you just divide them all
$14.50 divided by 1 3/4 =$8.28
$26.25 divided by 2 1/2 =$10.5
$5.50 divided by 3/8 =$14.66
47. What is the 12th term of the geometric sequence?
3,6, 12, 24, ...
A) 6144
B) 3072
C) 1526
D) 36
Answer:
A
Step-by-step explanation:
The rule is 2x.
So 3,6,12,24,48,96,192,384,768,1536,3072,6144,12288,....
The question asked for the 12th term so 6144.
Answer:
The answer to this is:
A. 6144
Step-by-step explanation:
3,6,12,24,48,96,192,384,768,1536,3072,6144 all you have to do is multiply the last number by 2.
:
CHCK Farms raises hens and roosters. They have enough space to raise at most 300
300
birds per year. Each hen eats 80
80
pounds of food per year, and each rooster eats 60
60
pounds of food per year. The business can only afford 20,000
20
,
000
pounds of food per year. The graph below shows the solution set of a system of linear inequalities that represents this situation.
Answer:
The number of hens is 100 and the number of roosters is 200.
Step-by-step explanation:
Let the number of hens be x and the number of roosters be y
then the total number of hens and roosters, is 300
so,
[tex]x+y \leq 300[/tex]----------------------------(1)
Also the hen eats 80 pounds of food per year and roosters eats 60 pounds of food per year,
[tex]80x+60y \leq 20000[/tex]----------------(2)
To solve the equations , multilpy eq(1) by 80
[tex]80x +80y \leq 24000[/tex]------------------(3)
Subracting (2) from (3)
[tex]20y \leq 4000[/tex]
[tex]y \leq 200[/tex]
substituting y in eq(1) we get
[tex]x+200 \leq300[/tex]
[tex]x \leq300 - 200[/tex]
x = 100
write an equation of a line that is parallel to the line containing the points (0,-7) and (5,12)
For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have the following points through which the line passes:
[tex](x_ {1}, y_ {1}) :( 0, -7)\\(x_ {2}, y_ {2}) :( 5,12)[/tex]
Thus, the slope of the line is:
[tex]m = \frac {y- {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {12 - (- 7)} {5-0} = \frac {12 + 7 } {5} = \frac {19} {5}[/tex]
By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will be of the form:
[tex]y = \frac {19} {5}x + b[/tex]
Answer:
[tex]y = \frac {19} {5}x + b[/tex]
I
-72
–54
-36
y
25
13
1
What is the y-intercept of the line?
Answer:
-23
Step-by-step explanation:
As I increases by 18, y decreases by 12. From the last value in the table, I needs to increase by 2·18 for it to become zero. Hence the y-intercept will be 2·12 less than the last value in the table:
1 - 2·12 = -23 . . . the y-intercept
Answer:
-23
I hope this helped you and i hope you have a good day.
If the point (-6, 10) lies on the graph of y=f(x) then which of the following points must lie on the graph of y=1/2f(x)?
Answer:
(-6,5)
Step-by-step explanation:
we have
y=f(x) ----> the parent function
y=1/2f(x) ---> the new y-value will be 1/2 times the original value
The rule of the transformation of f(x) to 1/2f(x) is
(x,y) -----> (x,y/2)
substitute the given value
(-6,10) ------> (-6,10/2)
(-6,10) ------> (-6,5)
21. Alcohol's effect on the circulatory system can lead to
A. O heat loss
B. O a feeling of warmth
C. O Both A and B
Line A is perpendicular to line B. Which statement about lines A and B is true
Answer:
Product of slope will be -1.
Step-by-step explanation:
We know that slope of the line describes its orientation , where tangent of the angle made by the line with the x axis will be the slope of the line .
Since here , We are given that line A and B are perpendicular to each other ,
If one line makes the angle a with x axis then other will make -(90-a) ,
So product of slope of the given lines will be , tan(a).tan-(90-a) = -1.
Now , sum of slopes can't be zero as they are not equal in magnitude
And , also slope are not equal as orientation of the lines are different.
Option A is the correct answer. Product of slopes of the lines will be -1.
Answer: Product of slope will be -1.
Step-by-step explanation:
For i = √−1 , what is the sum (7 + i) + (−8 + 9i ) ? √ is the square root symbol.
A) −1 + 12i
B) −1 − 6i
C) 15 + 12i
D) 15 − 6i
Question is incomplete, complete question is given below;
For i = √−1 , what is the sum (7 + 3i) + (−8 + 9i ) ? √ is the square root symbol.
Answer:
A) −1 + 12i
Step-by-step explanation:
Given,
[tex]i = \sqrt{-1 }[/tex]
We have to find the sum of[tex](7+3i)+(-8+9i)[/tex].
Solution,
Firstly we Substitute the the value of 'i' in given expression.
[tex](7 + 3\sqrt{-1}) + (-8 + 9\sqrt{-1} )[/tex]
On combining the like terms, we get;
[tex]7+(-8)+3\sqrt{-1}+9\sqrt{-1}[/tex]
On we use the addition property of equality and get;
[tex]-1+12\sqrt{-1}[/tex]
Since [tex]\sqrt{-1}[/tex] = i
Then we can say that;
[tex]-1+12\sqrt{-1}[/tex] = [tex]-1+12i[/tex]
Hence The sum of [tex](7+3i)+(-8+9i)[/tex] is [tex]-1+12i[/tex].
A jet left Paris at the same time as a
passenger plane. The planes flew in
opposite directions. The passenger plane
flew at a speed of 450 mph. After 11 hours
they were 9460 mi. apart. How fast did the
jet fly?
Answer:
The speed of the jet is 410 mph.
Step-by-step explanation:
The jet and the passenger plane flew in opposite directions.
Given that the passenger plane flew at a speed of 450 mph, then after 11 hours, the passenger plane will fly (450 × 11) = 4950 miles.
Again, given that after 11 hours the passenger plane and the jet are 9460 miles apart.
Therefore, in 11 hours the jet flew (9460 - 4950) = 4510 miles.
Hence, the speed of the jet is [tex]\frac{4510}{11} = 410[/tex] mph. (Answer)
Final answer:
The jet flew at a speed of 410 mph. This was calculated by first determining the distance covered by the passenger plane (at 450 mph for 11 hours) and then subtracting this from the total separation distance of 9460 miles to find the distance covered by the jet.
Explanation:
To determine how fast the jet flew, we need to consider the total distance covered by both planes after 11 hours when they are 9460 miles apart. Given that the passenger plane flew at a speed of 450 mph, we can calculate the distance it covered and then subtract this from the total separation distance to find how much distance the jet covered. Since they traveled in opposite directions, their speeds add up to account for the total separation distance.
First, calculate the distance covered by the passenger plane:
Distance = Speed × Time
Distance for passenger plane = 450 mph × 11 hours = 4950 miles
Now, subtract the passenger plane's distance from the total distance to find the distance covered by the jet:
Distance for jet = Total distance - Distance for passenger plane
Distance for jet = 9460 miles - 4950 miles = 4510 miles
Finally, calculate the speed of the jet:
Speed of jet = Distance for jet / Time
Speed of jet = 4510 miles / 11 hours = 410 mph
28. Emily is buying some graduation pictures. She pays $25 for the sitting and $15 for each
sheet of pictures she buys. (make a table if it helps)
a. How much does she pay for 5 sheets of pictures?
b. How much does she pay for "x" sheets?
c. How many sheets can she buy for $145?!
a. She pays $100 for 5 sheets
b. 25+15x dollars for x sheets
c. 8 sheets
Step-by-step explanation:
Given
Sitting cost = $25
Per sheet picture cost = $15
Let p be the number of sheets of pictures
Then the cost can be written as a function of p
[tex]c(p) = 25+15p[/tex]
Now,
a. How much does she pay for 5 sheets of pictures?!
Putting p = 5 in the function
[tex]c(5) = 25 + 15(5)\\= 25+75\\=100[/tex]
She will pay $100 for 5 sheets of pictures
b. How much does she pay for "x" sheets?
Putting x in place of p
[tex]c(x) = 25+15x[/tex]
c. How many sheets can she buy for $145?
We know the cost now, we have to find p so,
[tex]145 = 25+15p\\145-25 = 25+15p-25\\120 = 15p[/tex]
Dividing both sides by 15
[tex]\frac{15p}{15} = \frac{120}{15}\\p = 8[/tex]
Hence,
She can buy 8 sheets for $145
Keywords: Linear equation, Algebraic functions
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A torch and a battery cost £2.50 altogether.
The torch costs £1.50 more than the battery.
What fraction of the total price is the torch?
Give your answer in its simplest form.
Answer:
3/5
Step-by-step explanation:
Dunno?
Write a sentence about a real-life situation that matches the equation |-29|=29.
Answer:
an object is 29cm away from the mirror how far is the image from the mirror. if the distance of object from mirror = distance of image from mirror
answer in absolute value
Final answer:
A real-life situation that matches the equation |-29|=29 could be measuring the distance between two opposite points on a number line.
Explanation:
A real-life situation that matches the equation |-29|=29 could be measuring the distance between two opposite points on a number line. For example, suppose you have a number line with -29 on one end and 29 on the other end. The absolute value of -29 is 29, which represents the distance between the two points.
Given: ∆ABC, AB = 12, AC = 17 Area ∆ABC = 65 Find: BC, m∠A, m∠B, m∠C
Answer:
BC = 10.89, ∠A = 39.59°, ∠B = 95.80°, ∠C = 44.61°
BC = 27.34, ∠A = 140.41°, ∠B = 23.35°, ∠C = 16.24°
Step-by-step explanation:
Using the area formula to find angle A, we get ...
Area = (1/2)bc·sin(A)
65 = (1/2)(12)(17)sin(A)
sin(A) = 65/102 . . . . divide by the coefficient of the sine term
A = arcsin(65/102) = 39.59° or 180°-39.59° = 140.41°
Then from the law of cosines*, ...
BC² = AB² +AC² -2·AB·AC·cos(A) = 12² +17² ±2·12·17·cos(39.59°)
BC² = 433 ± 314.426
BC = √118.574 or √747.426
BC = 10.89 or 27.34
___
For A = 39.59° and BC = 10.89, the remaining angles are ...
sin(C)/AB = sin(A)/BC
C = arcsin(12·(65/102)/10.89) = arcsin(.7023) = 44.61°
B = 180° -39.59° -44.61° = 95.80°
__
For A = 140.41° and BC = 27.34, the remaining angles are ...
sin(C) = AB·sin(A)/BC = 12(65/102)/27.34
C = arcsin(0.2797) = 16.24°
B = 180° -140.41° -16.24° = 23.35°
__
In summary, the solutions are ...
BC = 10.89, ∠A = 39.59°, ∠B = 95.80°, ∠C = 44.61°
BC = 27.34, ∠A = 140.41°, ∠B = 23.35°, ∠C = 16.24°
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* For a given value of 0 < (x=sin(α)) < 1, there are two possible positive angles: α = arcsin(x) and 180°-α. In the Law of Cosines formula, these different angles result in cos(α) and cos(180°-α) = -cos(α).
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The solution process is the same for the remaining sides and angles, once you recognize that the initial value of sin(A)=65/102 can have two different angles as its solution.
Which statement is true about the equations -3x + 4y = 12
The system of the equations has exactly one solution at (-8, 3).
The system of the equations has exactly one solution at (-4, 3).
The system of the equations has no solution; the two lines are parallel.
The system of the equations has an infinite number of solutions represented by either equation.
Answer:
D)
Step-by-step explanation:
A tree is 212
1
2
feet tall. How tall will it be in 3 years if it grows 14
1
4
foot each year?
Which method will NOT give the correct number of feet?
Answer: The incorrect choice is the one in the bottom left.
Step-by-step explanation: This is because you have to multiply the 1/4 by 3 then add it on to the 2 1/4. Hope this helped
Final answer:
The current height of the tree is 212 feet, and it grows 141 feet each year. Over 3 years, the tree will grow 4¼ feet, reaching a height of 216¼ feet. Incorrect arithmetic or unit conversion could lead to an error in calculating the tree's future height.
Explanation:
The question involves calculating the future height of a tree given its current height and its annual growth rate. The tree is currently 212 feet tall and grows 141 foot each year. After 3 years, we would expect the tree to have grown an additional 3 years × 141 feet per year = 3 × 141 feet = 4 1/4 feet. Adding this to the initial height, the tree will be 212 + 4 1/4 = 216 1/4feet tall after 3 years. To determine which method will not give the correct number of feet, students need to ensure they correctly apply arithmetic operations and unit conversion if necessary.
To measure the height of a tree, one can use a measuring tape. Trees can be measured in feet or yards, and methods can vary depending on the desired level of accuracy and the tools available. For example, measuring directly with a tape or using a mathematical model based on the tree's shadow or geometric properties are valid approaches.