Exact Form of the expression is mathematically given as
[tex]\sin \left(2 \arccos \left(\frac{1}{3}\right)\right)[/tex]
What is an expression?Generally, An expression is a combination of variables, numbers, operators, and/or functions that represent a value.
[tex]\sin \left(2 \arccos \left (\frac{1}{3}\right)\right)[/tex]
Evaluate[tex]$\arccos \left(\frac{1}{3}\right)$.[/tex]
sin (2 *1.23095941)
Multiply 2 by 1.23095941.
sin (2.46191883)
The result can be shown in multiple forms.
Exact Form:
[tex]\sin \left(2 \arccos \left(\frac{1}{3}\right)\right)[/tex]
Decimal Form:
0.62853936
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Question 2 of 10
Solve the inequality for x and identify the graph of its solution.
|x+3|< 2
Choose the answer that gives both the correct solution and the correct graph.
A. Solution: x < -5 or x>-1
411
O
-8 -7 -6 -5 -4 -3 -2 -1 0 12
B. Solution: x>-5 and x < -1
+
O11
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2
OC. Solution: x>-5 and x < -1
O
-8-7-6 -5 -4 -3 -2 -1 0 1 2
OD. Solution: x < 1 or x>5
O
-2 -1 0 1 2 3
3
4
O
5 6 7 8
The solution of the inequality |x+3| < 2 is -5 < x < -1.
And the graph is given in the image below.
The correct option is C.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
To solve the inequality |x+3| < 2, we need to consider two cases:
Case 1: x+3 ≥ 0
In this case, the inequality simplifies to x+3 < 2, which gives us x < -1.
Case 2: x+3 < 0
In this case, the inequality simplifies to -(x+3) < 2, which gives us -x-3 < 2, or -x < 5, or x > -5.
Combining the results from both cases, we get the solution:
-5 < x < -1
To graph the solution, we draw an open circle at x=-3
(since the absolute value is less than 2, not less than or equal to), and shade the region between -5 and -1.
Therefore, the solution is -5 < x < -1.
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Raj lent out Rs 65,000 for 3 years at 25% per annum and borrowed Rs 60,000 for 2 years at 15% per annum. How mach did he gain or lose?
Raj profited Rs 30,750 from lending and borrowing money.
Raj gained from lending out Rs 65,000 for 3 years at 25% per annum and lost from borrowing Rs 60,000 for 2 years at 15% per annum.
To find out how much he gained or lost, we need to calculate the interest earned from lending and the interest paid from borrowing and then find the difference between them.
Interest earned from lending = Principal x Rate x Time
= Rs 65,000 x 25% x 3
= Rs 48,750
Interest paid from borrowing = Principal x Rate x Time
= Rs 60,000 x 15% x 2
= Rs 18,000
Difference between interest earned and interest paid = Rs 48,750 - Rs 18,000
= Rs 30,750
Therefore, answer is +Rs. 30,750.
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k as the constant of variation for r varies directly as the square root of n and inversely as the square of y
The constant of variation k for this relationship is 4.
To find the constant of variation k for the given relationship, we can use the formula for direct and inverse variation:
k = (r * y^2) / √n
Where r is the variable that varies directly as the square root of n, and inversely as the square of y. To find the value of k, we can plug in the values of r, y, and n into the equation and solve for k.
For example, if r = 4, y = 2, and n = 16, we can plug these values into the equation to find k:
k = (4 * 2^2) / √16
k = (4 * 4) / 4
k = 16 / 4
k = 4
Therefore, the constant of variation k for this relationship is 4.
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Find the coordinates of the given vector with respect to the given basis β. (i) V=R2,β={(1,1),(1,−1)}, and v=(1,2). (ii) V=P2(R),β={1,1+x,1+x+x2}, and v=(x+1)2. (iii) V=span{sin(x),cos(x)},β={sin(x),cos(x)}, and v=sin(x+1).
The coordinates of v with respect to the basis β are (cos(1), sin(1)).
The coordinates of a vector with respect to a given basis can be found by expressing the vector as a linear combination of the basis vectors and finding the coefficients of the linear combination. These coefficients are the coordinates of the vector with respect to the given basis.
(i) In the first case, we have V=R2, β={(1,1),(1,−1)}, and v=(1,2). We can express v as a linear combination of the basis vectors as follows:
v = a(1,1) + b(1,-1) = (a+b, a-b)
Equating the coordinates, we get:
a+b = 1
a-b = 2
Solving for a and b, we get a=3/2 and b=-1/2. Therefore, the coordinates of v with respect to the basis β are (3/2, -1/2).
(ii) In the second case, we have V=P2(R), β={1,1+x,1+x+x2}, and v=(x+1)2. We can express v as a linear combination of the basis vectors as follows:
v = a(1) + b(1+x) + c(1+x+x2) = a + (b+c)x + cx2
Equating the coefficients, we get:
a = 1
b+c = 2
c = 1
Solving for a, b, and c, we get a=1, b=1, and c=1. Therefore, the coordinates of v with respect to the basis β are (1, 1, 1).
(iii) In the third case, we have V=span{sin(x),cos(x)}, β={sin(x),cos(x)}, and v=sin(x+1). Using the trigonometric identity sin(x+1) = sin(x)cos(1) + cos(x)sin(1), we can express v as a linear combination of the basis vectors as follows:
v = a(sin(x)) + b(cos(x)) = (a)sin(x) + (b)cos(x)
Equating the coefficients, we get:
a = cos(1)
b = sin(1)
Therefore, the coordinates of v with respect to the basis β are (cos(1), sin(1)).
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The ratio of 1 Bertha to form 1 Florence is 12:20 if there are 120 pupils in Florence calculate how many pupils are in Bertha
There are 72 pupils in bertha if the ratio of 1 Bertha to form 1 Florence is 12:20 if there are 120 pupils in Florence.
The problem can be solved by using the concept of ratios and inverse ratios. It involves setting up a proportion based on the given ratio and using algebra to solve for the unknown quantity.
If the ratio of Bertha to Florence is 12:20, then the ratio of Florence to Bertha is 20:12 (inverse ratio).
Let the number of pupils in Bertha be x. Then, the number of pupils in Florence would be:
20/12 * x = 120
Simplifying:
x = 120 * 12/20
x = 72
Therefore, there are 72 pupils in Bertha.
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PLS HELP 30 POINTS I REALLY NEED HELP RN
Answer:
Bears: 12
Tigers: 5
Step-by-step explanation:
9:15
the common factor of 9 and 15 is 3. so we divide both sides by 3.
3:5
12:20
This diagram is a genetic map that shows the relative positions of four alleles
along a chromosome.
Chromosome
H
G
k
p
Which two alleles have the highest probability of being inherited together?
A. G and K
B. H and K
C. G and P
D. H and P
The two alleles that have the highest probability of being inherited together are A. G and k.
Why would certain alleles have a greater probability of being inherited together?Alleles that are physically close to each other on a chromosome have a higher probability of being inherited together, a phenomenon known as linkage. The closer two alleles are to each other on a chromosome, the less likely it is that they will be separated by a recombination event during meiosis.
The degree of linkage between two alleles is determined by their relative physical distance on the chromosome. The closer two alleles are, the higher the probability that they will be inherited together.
G and k are the closest alleles to each other on the genetic map and so have a higher probability of being inherited together.
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in Chicago, the temperature was 3 degrees. By 5am, it had dropped 15 degrees. What was the temperature at 5am?
Andrew Albring purchases an inflatable shark for $12.99, 8 gallons of chlorine at $1.99 each, 2 gallons of
algaecide at $7.99 each, 1 thermometer for $12.99, and 2 sets of fins at $22.99 each. If the sales tax rate
is 7.5%, what is the total purchase price?
A)$63.37
B)$86.94
C)$111.13
D)$111.65
Option D is correct, the total purchase price is $111.65.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Lets find the price of each item
Inflatable shark: $12.99
8 gallons of chlorine at $1.99 each: 8 x $1.99 = $15.92
2 gallons of algaecide at $7.99 each: 2 x $7.99 = $15.98
1 thermometer for $12.99: $12.99
2 sets of fins at $22.99 each: 2 x $22.99 = $45.98
Now add the costs of all the items:
$12.99 + $15.92 + $15.98 + $12.99 + $45.98 = $103.86
we multiply the total cost by the tax rate to find the sales tax.
$103.86 x 0.075 = $7.79
Finally, we add the sales tax to the total cost to get the final purchase price:
$103.86 + $7.79 = $111.65
Therefore, the total purchase price is $111.65.Option D is correct.
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1. Interpret the effect size (hp2) for your ANOVA results.
a. Remember, for ANOVAs, SPSS reports a partial-eta squared which has a slightly different interpretation than Cohen’s d or correlations.
possible medication to treat high blood pressure. They decide it would be best to have 3 groups of randomly selected male participants: • One group (n=5) will be given a high dose of HyBlox: • One group (n=5) will be given a low dose of HyBlox: • One group (n=5) will be given a placebo sugar pill. They measure participants' blood pressures on a continuous scale. Participants are blind to condition and don't know which pill they've been given. The experimenters hypothesize that the participants given the highest level of HyBlox will have the lowest mean blood pressure level, the low dose HyBlox will have the second-lowest mean blood pressure level, and that the placebo group will have the highest mean blood pressure level. QUESTIONS: 1. Is this study within-subjects, between-subjects, or mixed? 2. What are the independent and dependent variables?
ANOVA results
1. This study is a between-subjects design.
2. The independent variable is the type of medication given and the dependent variable is the participants' blood pressure levels.
The effect size (hp2) for the ANOVA results is a measure of the strength of the relationship between the independent variable (type of medication) and the dependent variable (blood pressure levels).
A larger effect size indicates a stronger relationship between the two variables. It is important to remember that SPSS reports a partial-eta squared, which has a slightly different interpretation than Cohen's d or correlations.
Partial-eta squared is the proportion of the total variance in the dependent variable that is explained by the independent variable, after controlling for other factors. A partial-eta squared of .01 is considered a small effect, .06 is considered a medium effect, and .14 is considered a large effect.
Hence,
1. This study is a between-subjects design because each participant is only assigned to one group and is only exposed to one level of the independent variable.
2. The independent variable is the type of medication given (high dose HyBlox, low dose HyBlox, or placebo) and the dependent variable is the participants' blood pressure levels.
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The path of a ball thrown from a cliff is modelled by the quadratic function h(t)=-4.9(t-1)^2+35.
From what height is the hall thrown?
Range of the function?
How long does it take for the ball to land?
Answer:
2 hours
Step-by-step explanation:
shhsjdnd
dididjd
djdjdjdj
How many solutions does this equation have? -7t-6=-7t no solution one solution infinitely many solutions
The equation -7t-6=-7t has no solution.
Because when we try to isolate the variable t on one side of the equation, we end up with an equation that is not true.
Here's how we can do this:
-7t-6=-7t
First, we can add 7t to both sides of the equation:
-6=0
This equation is not true, so there are no values of t that will make this equation true. Therefore, the equation has no solution.
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Please help! Will mark brainliest!
Different triangles with the same areas include:
Right angle triangle: base = 6, height = 4
Acute triangle: base = 8, height = 3
Obtuse triangle: base = 16, height = 1.5
How to create triangles with the same areas?To create a right angle triangle, an acute triangle, and an obtuse triangle that all have the same area, we can use the following dimensions:
Right triangle: base = 6, height = 4
Acute triangle: base = 8, height = 3
Obtuse triangle: base = 16, height = 1.5
We can calculate the area of each triangle using the formula A = 1/2 (base x height):
Right triangle: A = 1/2 (6 x 4) = 12
Acute triangle: A = 1/2 (8 x 3) = 12
Obtuse triangle: A = 1/2 (16 x 1.5) = 12
Therefore, we can see that all three triangles have the same area, which is 12 square units. We know this because they all have the same base-to-height ratios, which means they have the same "steepness" or "slope". This means that the area of each triangle is proportional to its base and height, and since they all have the same ratio of base to height, they will all have the same area.
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Dalton flies a plane against a headwind for 4661 miles. The return trip with the wind took 20 hours less time. If the wind speed is 10 mph, how fast does Dalton fly the plane when there is no wind?
Dalton flies the plane at a speed of 251 mph when there is no wind.
To solve this proble,m we can use the formula for distance, which is distance = speed × time. We can also use the fact that the speed of the plane with the wind is the sum of the speed of the plane without the wind and the wind speed, and the speed of the plane against the wind is the difference between the speed of the plane without the wind and the wind speed.
Let x be the speed of the plane without the wind, and t be the time it takes for the return trip with the wind. Then we can write the following equations:
4661 = (x - 10) × (t + 20) (1) for the trip against the wind
4661 = (x + 10) × t (2) for the return trip with the wind
Multiplying equation (2) by (t + 20) and subtracting equation (1) from it, we get:
4661t + 93220 = 4661t + 20x^2 + 200x - 200x - 200
20x^2 = 93220
x^2 = 4661
x = 251
Therefore, Dalton flies the plane at a speed of 251 mph when there is no wind.
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RADICALS Solving an equation usir Solve x^(3)=-13 where x is a rea Simplify your answer as much a
To solve the equation x^(3) = -13, we need to take the cube root of both sides of the equation. The cube root of x^(3) is x, and the cube root of -13 is -2.3513 (rounded to 4 decimal places). Therefore, the solution to the equation is x = -2.3513.
Here are the steps to solve the equation:
1. Start with the equation x^(3) = -13
2. Take the cube root of both sides of the equation: (x^(3))^(1/3) = (-13)^(1/3)
3. Simplify the left side of the equation: x = (-13)^(1/3)
4. Calculate the cube root of -13: x = -2.3513 (rounded to 4 decimal places)
So the solution to the equation is x = -2.3513.
Note: The original question had some typos and irrelevant parts, so I ignored those and focused on the main equation to solve.
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Four coins are tossed. a. Give an example of a simple event. b. Give an example of a joint event. c. What is the complement of getting a tail on the fourth coin? d. What does the sample space consist of? a. Give an example of a simple event. Which of the following is a simple event? A. Getting a tail on all coins B. Getting a tail on no coins C. Getting a head on the third coin and a head on the fourth coin D. Getting a tail on the fourth coin b. Give an example of a joint event. Which of the following is a joint event? A. Not getting a head on the second coin B. Getting a head or a tail on the first coin C. Getting a head on the first coin and a tail on the third coin D. Not getting a tail on the fourth coin c. What is the complement of getting a tail on the fourth coin? Which of the following is the complement of getting a tail on the fourth coin? A. Getting a head on the fourth coin B. Getting a tail on the fourth coin and a head on all others c. Getting a head on all coins
d. Getting a head on the fourth coin and a tail on all others d. What does the sample space consist of? Which of the following identifies the sample space for the four flipped coins? A. Not getting a head on all coins B. Getting a tail on any of the coins c. Getting a tail on one coin and a head on all others
D. Getting a head or a tail on any of the four coins
The sample space includes the following outcomes: HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT.
a. A simple event is an event that has only one possible outcome. An example of a simple event is getting a head on the third coin. This is represented by option C: "Getting a head on the third coin and a head on the fourth coin."
b. A joint event is an event that involves two or more simple events happening at the same time. An example of a joint event is getting a head on the first coin and a tail on the third coin. This is represented by option C: "Getting a head on the first coin and a tail on the third coin."
c. The complement of getting a tail on the fourth coin is getting a head on the fourth coin. This is represented by option A: "Getting a head on the fourth coin."
d. The sample space consists of all possible outcomes of the four flipped coins. This is represented by option D: "Getting a head or a tail on any of the four coins." The sample space includes the following outcomes: HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT.
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Algebraically, the point (1, -5) satisfies the first inequality, but it does not satisfy the second inequality because -5 is not greater than -5. Graphically, the point (1, -5) lies in the shaded area of the first inequality but lies on the dashed line of the second inequality, which is not inclusive. Therefore (1, -5) is not a solution to the given system of inequalities.
Since it only resolves one of the two inequalities, (1, -5) cannot be a solution to the given system of inequalities.
How are coordinates determined?
We must check that the point (1, -5) fulfils both inequalities in order to determine if it is a solution to the system of inequalities.
y > -6x - 11 is the first inequality. Inputting x = 1 and y = -5 results in:
[tex]-5 > -6(1) (1) - 11 \s-5 > -6 - 11 \s-5 > -17[/tex]
The first inequality is satisfied at the position (1, -5) since -5 is greater than -17.
y - x - 5 is the second inequality. Inputting x = 1 and y = -5 results in:
[tex]-5 ≥ -(1) (1) - 5 \s-5 ≥ -6[/tex]
The point (1, -5) does not satisfy the second inequality since -5 is not greater than -6.
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Find A if: a. 5A−|[1 0], [2 3]|=3A−|[5 2] ,[ 6 1]| b. 3A−[2],[1]=5A−2[3],[0]
The solutions for A if 5A−|[1 0], [2 3]|=3A−|[5 2] ,[ 6 1]| is 5 and for equation 3A−[2],[1]=5A−2[3],[0] is 2.
To find A in the given equations, we need to use the properties of matrices and solve for A.
For equation a:
5A−|[1 0], [2 3]|=3A−|[5 2], [6 1]|
First, we need to find the determinants of the matrices. The determinant of a 2x2 matrix is found by multiplying the elements on the main diagonal and subtracting the product of the elements on the other diagonal.
So, |[1 0], [2 3]| = (1*3) - (0*2) = 3
And, |[5 2], [6 1]| = (5*1) - (2*6) = -7
Now we can substitute these values back into the equation and solve for A.
5A - 3 = 3A - (-7)
5A - 3 = 3A + 7
2A = 10
A = 5
For equation b:
3A−[2],[1]=5A−2[3],[0]
First, we need to find the determinant of the matrix [2],[1]. The determinant of a 1x1 matrix is simply the value of the single element.
So, |[2],[1]| = 2
Now we can substitute this value back into the equation and solve for A.
3A - 2 = 5A - 2(3)
3A - 2 = 5A - 6
2A = 4
A = 2
Therefore, the solutions for A are 5 for equation a and for equation b the value A is 2
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A cone has a volume of 1959. 36 cubic feet and a radius of 12 feet. What is its height?
The height of the cone is approximately 13.5 feet.
The volume of a cone is given by the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height.
In this problem, we are given the volume of the cone, which is 1959.36 cubic feet, and the radius, which is 12 feet. We need to find the height, h.
We can start by plugging in the given values into the formula for volume:
1959.36 = (1/3)π(12)²h
Simplifying, we get:
1959.36 = 144πh
To solve for h, we need to isolate it on one side of the equation. We can do this by dividing both sides by 144π:
h = 1959.36 / (144π)
Using a calculator to evaluate this expression, we get:
h ≈ 13.5
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Using the quotient and reciprocal identities again, simplify the left side. \[ \begin{aligned} \frac{\sec x+\tan x \csc x}{\csc x} & =\frac{\sec x+\sec x}{\csc x} \\ & =\frac{2 \sec x}{\csc x} \end{al
The simplified form of the left side of the equation is $2 \tan x$.
The left side of the equation can be simplified using the quotient and reciprocal identities. The quotient identity states that $\tan x = \frac{\sin x}{\cos x}$ and the reciprocal identity states that $\sec x = \frac{1}{\cos x}$ and $\csc x = \frac{1}{\sin x}$. By substituting these identities into the equation, we can simplify the left side:
\[ \begin{aligned} \frac{\sec x+\tan x \csc x}{\csc x} & =\frac{\frac{1}{\cos x}+\frac{\sin x}{\cos x} \cdot \frac{1}{\sin x}}{\frac{1}{\sin x}} \\ & =\frac{\frac{1}{\cos x}+\frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2 \cdot \frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2}{\cos x} \cdot \frac{\sin x}{1} \\ & =\frac{2 \sin x}{\cos x} \\ & =2 \tan x \end{aligned} \]
Therefore, the simplified form of the left side of the equation is $2 \tan x$.
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it takes 12 builders 7 days to build 2 houses. how long will it take 15 builders to build the same amount of houses. write your answer in days and hours.
To solve this problem, we can use the formula for work rate:
Work rate = (Number of workers) × (Time taken) / (Number of houses built)
We can plug in the given values to find the work rate for the 12 builders:
Work rate = (12 builders) × (7 days) / (2 houses) = 42 builder-days / house
Now we can use this work rate to find the time taken for 15 builders to build the same amount of houses:
42 builder-days / house = (15 builders) × (Time taken) / (2 houses)
Solving for Time taken, we get:
Time taken = (42 builder-days / house) × (2 houses) / (15 builders) = 5.6 days
Therefore, it will take 15 builders 5.6 days to build the same amount of houses.
To convert this to days and hours, we can multiply the decimal part of the answer by 24 (since there are 24 hours in a day):
0.6 days × 24 hours/day = 14.4 hours
So the final answer is 5 days and 14.4 hours, or 5 days and 14 hours and 24 minutes.
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I need some help please
Answer:
Step-by-step explanation:
so first you add 3 by 4 and see if it is greater than six and then that's your answer.
Write an equation for the description. A number x increase by 16 is 124
The equation for the description for given number is x + 16 = 124
"A number x increases by 16" means that we start with a certain number, which we don't know yet, and then add 16 to it. So, we can represent this as:
x + 16
The next part of the description tells us that the result of this addition is 124. So, we can set up an equation by equating this expression to 124, like this:
x + 16 = 124
This is the equation that represents the given description. To find the value of x, we can solve for it by subtracting 16 from both sides of the equation:
x = 124 - 16
x = 108
So, the value of x that satisfies the given description is 108.
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Given x1 = x2 – x1(x1^2 + x2^2 -1) and x2 = -x1 - x2(x1^2 + x2^2 -1) as state dr do equations. Polar coordinates are r and tetha. Please prove that dr/dt = -r(r^2 -1) and dtetha/dt= -1. Then explain why r=1 is a stable limit cycle.
To solve this problem, we'll start by finding the polar coordinates r and θ in terms of x1 and x2. We have r^2 = x1^2 + x2^2, tan(θ) = x2/x1.
Taking the derivative of x1 with respect to time t, we have: dx1/dt = dx2/dt - 2x1(dx1^2 + x2^2 - 1) - x1^2(2x1dx1 + 2x2dx2)
Similarly, the derivative of x2 with respect to t is: dx2/dt = -dx1/dt -2x2(dx1^2 +x2^2 -1) - x2^2(2x1dx1 + 2x2dx2) Using the chain rule, we can write: dr/dt = (x1dx1 + x2dx2)/r dθ/dt = (1/r^2)(x2dx1 - x1dx2)
Substituting dx1/dt and dx2/dt in these equations and simplifying, we get: dr/dt = -r(r^2 -1) dθ/dt = -1 Now, to prove that r=1 is a stable limit cycle, we can use the method of linearization.
This involves finding the Jacobian matrix at the equilibrium point r=1, θ=0: Jacobian = [[-3 -1], [-1 -3]] Taking the eigenvalues of this matrix, we get -4 and -2.
Since both eigenvalues are negative, we conclude that the equilibrium point corresponds to a stable limit cycle at r=1, θ=0. In summary, we have shown that the differential equations for dr/dt and dθ/dt are -r(r^2 -1) and -1, respectively. We have also demonstrated that r=1 is a stable limit cycle.
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what is 36/12÷ one whole
Answer:
12/36 ÷ 2/2 = 6/18
12/36 ÷ 3/3 = 4/12
12/36 ÷ 4/4 = 3/9
All of these equations are equal to one another since they are all being divided by a whole, they are all just being expressed differently.
I hope this helped & Good Luck <3 !!!
Answer:
12/36 ÷ 1 = 0.0333333.......
Step-by-step explanation:
36/12 ÷ 1 =3
12 divided by 36 gives 0.333...... and the result divided by 1 gives the same answer. The same process applies to 36 divided by 12, which gives 3. The result which is three is divided by 1 which gives the same three.
NB: Any number divided by 1 is still the same number. Example: 1200/1 = 1200
Hope it helps.
Please help I’ll give brainliest!!
25-9x² can be expressed in factor form as (5+3x)(5-3x)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 25-9x²
We have to factor it completely
We have an identity that a²-b²=(a+b)(a-b)
25-9x² can be written as 5²-(3x)²
Now apply the identity
(5+3x)(5-3x)
Hence, 25-9x² can be expressed in factor form as (5+3x)(5-3x)
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The sides of a triangle have lengths 2, 6, and 7. What kind of triangle is it?
Answer:
Scalene triangle
Step-by-step explanation:
To determine the type of triangle, we need to compare the lengths of the sides to each other.
If all three sides have the same length, it's an equilateral triangle.
If two sides have the same length and the third is different, it's an isosceles triangle.
If all three sides have different lengths, it's a scalene triangle.
Using the lengths given, we see that all three sides have different lengths, so this is a scalene triangle.
Answer:
an obtuse triangle.
Step-by-step explanation:
To determine the type of triangle with sides of lengths 2, 6, and 7, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we can check whether this condition holds for the three sides of lengths 2, 6, and 7:
2 + 6 > 7 (True)
6 + 7 > 2 (True)
2 + 7 > 6 (True)
Since all three inequalities are true, the given lengths of 2, 6, and 7 form a valid triangle.
To determine the type of triangle, we can use the lengths of the sides and the Pythagorean theorem or trigonometric functions. For this triangle, we can use the Pythagorean theorem to find that the longest side (7) is opposite the largest angle, which is greater than 90 degrees. Therefore, this triangle is an obtuse triangle.
Find the mark down rate for dress which was originally tagged at Php 5,220 but is now being sold at Php 4,900.
The mark down rate for the dress originally tagged at Php 5,220 but now being sold at Php 4,900 is 6.13%.
To calculate the mark down rate, use the formula:
Mark down rate = (Original Price - Discounted Price) / Original Price
Plugging in the numbers:
Mark down rate = (5,220 - 4,900) / 5,220 = 0.0613
To convert to a percentage, multiply 0.062 by 100 and you will get 6.13%.
Therefore, the mark down rate for the dress is 6.13%.
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How long will it take $3,000 to grow to $20,000 if it is invested at 4% compounded monthly? years (Round to the nearest tenth of a year.) If $8000 is invested at 8% compounded continuously, what is the amount 8 years?
If $8000 is invested at 8% compounded continuously, the amount 8 years is $12,904.95.
To find out how long it will take $3,000 to grow to $20,000 if it is invested at 4% compounded monthly, we can use the formula A=P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values, we get:
20,000=3,000(1+0.04/12)^(12t)
Dividing both sides by 3,000, we get:
6.66667=(1+0.04/12)^(12t)
Taking the natural logarithm of both sides, we get:
ln(6.66667)=12t*ln(1+0.04/12)
Solving for t, we get:
t=ln(6.66667)/(12*ln(1+0.04/12))
t=41.2 years
So it will take approximately 41.2 years for $3,000 to grow to $20,000 if it is invested at 4% compounded monthly.
To find out the amount of $8,000 invested at 8% compounded continuously for 8 years, we can use the formula A=Pe^(rt), where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the number of years. Plugging in the given values, we get:
A=8,000e^⁰ ⁶⁴
A=12,904.95
So the amount of $8,000 invested at 8% compounded continuously for 8 years is $12,904.95.
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Determine the solution to each linear system by using the substitution method
2x+3y=34
y=5x
(2, 10)
(2, -6)
(-3, 5)
(4, 3)
put y = 5x in equation 1 :
2x + 3 (5x) = 34
2x + 15x = 34
17x = 34
x = 2
Now put x = 2 in any of the two equation to get
y :
y = 5x
y = 5 × 2
y = 10
