logbA = 2.817 and logbB = 0.106 need to be used to find logb A/BA. We know that logarithms are important in mathematics and help us to solve complex problems involving exponents or roots.
They are expressed in terms of the logarithm base, which is the number or expression that is being raised to a power. It can be solved using the quotient rule of logarithms which states that logb (x / y) = logb x - logb y.
Explanation:
The given values are: logbA = 2.817 and logbB = 0.106Let us first use the quotient rule of logarithms to simplify the expression logb A/BA = logb A - logb BA. Using this rule, we get:
logb A/BA = logb A - logb B
Now we can substitute the given values in the above expression:
logb A/BA = 2.817 - 0.106
= 2.711
Therefore, the value of logb A/BA is 2.711. Hence, option (D) 2.711D is the correct answer.
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On a hot summer day in Death Valley, the amount of water in a swimming pool is 4000 gallons. 30 Days later, the amount of water in the pool is 3500 gallons. If the evaporation follows a continuous exponential model for decay, find k, the constant of proportionality in the equation A=Av0e^kt. Round to 4 decimal places.
Write a function that models the amount of water in the pool A(t), t days after the original measurement
The half-life of the radioactive substance,1/2 = 18.905 years.
What is half-life of the radioactive substance?The half-life of a radioactive atom or substance
A radioactive element's half life is the amount of time it takes for its atoms to split in h-alf from their initial number.
nuclear decay
The process of a heavy radioactive element's nucleus disintegrating and emitting alpha, beta, and gamma rays is known as radioactive decay.
Radioactivity law
According to the law, when a radioactive element decays or disintegrates, a new element two places below the original element in the periodic table with alpha particle emission or two places above the original element with beta particle emission results.
Hence, The half-life of the radioactive substance,1/2 = 18.905 years.
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Find the HCF of:
x²+5x+6, x²-4 and x³+8
Answer:
x²+5x+6 can be factored as (x+2)(x+3)
x²-4 can be factored as (x+2)(x-2)
x³+8 can be factored as (x+2)(x²-2x+4)
The common factor of all three expressions is (x+2). Therefore, the HCF of x²+5x+6, x²-4, and x³+8 is (x+2).
Step-by-step explanation:
Answer: To find the highest common factor (HCF) of these three polynomials, we can factor each polynomial and then look for the factors that they have in common.
First, let's factor each polynomial:
x² + 5x + 6 = (x + 2)(x + 3)
x² - 4 = (x + 2)(x - 2)
x³ + 8 = (x + 2)(x² - 2x + 4)
Now, we can see that all three polynomials have a factor of (x + 2). Therefore, the HCF of these three polynomials is (x + 2).
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benny makes $20 an hour babysiting. he can make 35% more per hour if he babysits an extra kid what could his new hourly wage be.
Answer:
If Benny makes $20 an hour babysitting, his 35% increase would be:
35% of $20 = 0.35 x $20 = $7
This means that Benny could make an extra $7 per hour if he babysits an extra kid. Therefore, his new hourly wage would be:
$20 + $7 = $27
So, if Benny babysits an extra kid, he could make $27 per hour.
Step-by-step explanation:
(find the slope of each line)
help—
At a local car dealership a particular salesperson sells an average of 3. 1 cars per week with a standard
deviation of 1. 1 cars. The dealership pays her $300 a week plus a commission of $250 for each car that
she sells. What are the mean and standard deviation, respectively, of her total weekly pay? PLs help
The standard deviation of her total weekly pay is approximately $262.25 and the mean is $1075
Let X be the number of cars the salesperson sells in a week. Then, X follows a normal distribution with mean μ = 3.1 and standard deviation σ = 1.1.
The total weekly pay Y is given by the equation:
Y = $300 + $250X
Using the properties of means and variances of linear combinations of random variables, we can find the mean and standard deviation of Y as follows:
Mean of Y:
E(Y) = E($300 + $250X) = $300 + $250E(X) = $300 + $250(3.1) = $1075
Therefore, the mean of her total weekly pay is $1075.
Standard deviation of Y:
Var(Y) = Var($250X) = $250^2Var(X) = $250^2(1.1^2) = $68,750
Since the standard deviation is the square root of the variance, we have:
SD(Y) = sqrt($68,750) ≈ $262.25
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Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once starting the treatment. Two researchers each follow a different set of 40 AIDS patients from the start of treatment until their deaths. The following data (in months) are collected. Researcher A: 3; 4; 10; 24; 16; 17; 22; 44; 37; 16; 14; 19; 25; 26; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 25; 24; 29; 47; 33; 34 Researcher B: 3; 14; 22; 4; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 6; 35; 44; 23; 21; 21; 16; 8; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29 a. Complete the tables using the data provided:
By answering the above question, we may state that expressions Researcher A: Value Frequency 3 2 4 1
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
Researcher A:
Value Frequency
3 2
4 1
8 1
10 2
12 1
13 1
14 2
16 2
17 2
19 1
21 1
22 2
24 2
25 2
26 2
27 2
29 3
31 2
32 1
33 2
34 2
35 1
37 1
40 1
44 2
47 1
Researcher B:
Value Frequency
3 2
4 1
6 1
8 2
13 1
14 3
16 2
17 1
18 2
21 3
22 2
23 2
24 2
25 2
26 1
28 1
29 2
31 2
33 2
34 1
35 1
41 2
42 1
44 1
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The figure below is made of 2 22 rectangular prisms. What is the volume of this figure? A shape made up of two rectangular prisms. The first rectangular prism has a base that measures 5 inches length by 7 inches width, and has a height of 1 inch. The second rectangular prism sits next to the first rectangular prism. It has a base that measures 9 inches length by 7 inches width and has a height of 4 inches.
Answer: The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively.
For the first rectangular prism, we have:
V1 = 5 x 7 x 1 = 35 cubic inches
For the second rectangular prism, we have:
V2 = 9 x 7 x 4 = 252 cubic inches
To find the total volume of the figure, we add the volumes of the two rectangular prisms:
V = V1 + V2 = 35 + 252 = 287 cubic inches
Therefore, the volume of the figure is 287 cubic inches.
Step-by-step explanation:
This is 4/6 problems finish them all each is 10 points 60 total.
The trigonometric ratios for cosines indicates that the measure of angle B, m∠B, in the right triangle with hypotenuse side length of 15 units and adjacent leg to ∠B of 12 units, obtained using the trigonometric ratios for cosines is; m∠B ≈ 36.9°
What are trigonometric ratios?Trigonometric ratios relate the lengths of two side lengths of a right triangle and the interior angles of the right triangle.
The cosine of an angle can be obtained from the ratio of the adjacent side to the angle to the hypotenuse side of the right triangle in which the angle is an acute angle, therefore;
cos(θ) = Adjacent side to the angle ÷ Hypotenuse side of the angle
The measure of the length of the adjacent side to the angle x = 12 units
The measure of the hypotenuse side of the right triangle = 15 units, therefore;
cos(x°) = 12/15 = 4/5 = 0.8
The measure of the angle x therefore can be obtained using the arccos function, (cos⁻¹ function) in a scientific calculator as follows;
x = arccos(0.8) ≈ 36.9°
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Homework Progress
79/99 Marks
If £2000 is placed into a bank account that pays 3% compound interest per year.
how much will be in the account after 2 years?
Optional working
3
78%
Answer
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2 \implies A = 2121.8[/tex]
A triangular piece of fabric has side lengths of 3 inches, 4 inches, and 5 inches. Will it fit in the corner of a rectangular quilt? Explain.
Yes, because it is a right triangle.
Yes, because it is an isosceles triangle.
No, because it is an equilateral triangle.
No, because it is an obtuse triangle.
Answer:
yes because it is a right triangle
Step-by-step explanation:
if you apply the pythagorean theorem a squared plus b squared equals c squared. c being the hypotenuse, the longest side. so 3x3 + 4x4 = 25 and 5x5 is 25. This confirms that it is a right triangle because pythagoras's theorem only works with right triangles. Also, every angle of a rectangle is a right angle (90 degrees) meaning that the triangle will fit in any and every corner! Hope this helped!
A movie production company was interested in the relationship between a movie's budget and how well that movie
was received by the public. Information was collected on several movies and was used to obtain the regression
equation ý = 0.145x + 0.136, where x represents the budget of the movie (in millions of dollars) and ŷ is the predicted
score of that movie (in points from 0 to 1). Which statement best describes the meaning of the slope of the regression
line?
O For each increase in score by 1 point, the predicted budget increases by $0.136 million.
For each increase in score by 1 point, the predicted budget increases by $0.145 million.
O For each increase in budget by $1 million, the predicted score increases by 0.136 points.
O For each increase in budget by $1 million, the predicted score increases by 0.145 points.
Answer: For each increase in budget by $1 million, the predicted score increases by 0.145 points.
The measures of the angles of a triangle are shown in the figure below. Find the measure of the largest angle.
(5x+14)°
(6x+17)°
105°
Answer:
105° is the largest angle
Step-by-step explanation:
All angles add up to 180°
Find the value of x
105 + 6x + 17 + 5x + 14 = 180
Combine like terms
136 + 11x =180
Isolate the x ( subtract 136 from both sides)
11x = 44
Divide both sides by 11
x = 4
Now substitute the value of x into each expression to find the largest angle
5(4) + 14 = 20 + 14 = 34°
6(4) + 17 = 24 + 17 = 41°
105 > 41 > 34
The following graph represent the cost of Nolan's
retirement party :
a.
Complete the following table that represent the cost of Nolan's
party
Guests :x
Cost :y
10
20
b.
Find the unit rate.
c. Write the relation between x and y
30
$100
$90
500
$70
$60
$40
$30
$20
$10
0
Cost of Nolan's retirement party
10 20 30 40 50 60 70 80 90 100
Guests
Answer:
See below.
Step-by-step explanation:
Please check the assumptions. I did not see a graph, so made assumptions in the calculations,
Given that for 10 guests, the total cost is $20, we can calculate a rate of $2/guest ( the unit rate). This seems too inexpensive, even for a hot dog and soft drink. But going on that, we can establish the relationship between x (the number of guests) and y (the total cost) as y = ($2/guest)*x.
The list of numbers does not provide a clear undertanding of what is being requested, The attached spreadheet calculates a number of guest options based on a rate of $2/guest. The area in green are the second list of values based on the numbers of guests.
Which statements about liquid volume are true
The statements that are cοrrect based οn unit cοnversiοn is -
A - One milliliter is 100 times smaller than οne liter.
C - Milliliters are smaller units than liters.
D - One liter is 1,000 times larger than οne milliliter.
What is unit cοnversiοn?Unit cοnversiοn is a prοcess with multiple steps that invοlves multiplicatiοn οr divisiοn by a numerical factοr οr, particularly a cοnversiοn factοr. The prοcess may alsο require selectiοn οf the cοrrect number οf significant digits, and rοunding.
On the basis οf unit cοnversiοn methοds -
These three statements are true -
One milliliter is 100 times smaller than οne liter.
Milliliters are smaller units than liters.
One liter is 1,000 times larger than οne milliliter.
The οther statements are incοrrect -
Liters are nοt smaller units than milliliters.
One milliliter cannοt be 100 times larger than οne liter, as it is a smaller unit οf vοlume.
One liter cannοt be 1,000 times smaller than οne milliliter, as it is a larger unit οf vοlume.
Therefοre, the statements A, C and D are cοrrect.
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Which statements about liquid volume are true?
Select each correct answer.
One milliliter is 100 times smaller than one liter.
Liters are smaller units than milliliters.
Milliliters are smaller units than liters.
One liter is 1,000 times larger than one milliliter.
One milliliter is 100 times larger than one liter.
One liter is 1,000 times smaller than one milliliter.
Someone help me solve this!
Based on the information provided, the true sentences are that route B has a more consistent number of rides (B), and the typical number of riders is greater on route A (D).
How can the graphs be interpreted?To begin, these whisker plots compare the number of riders in two routes. In this context, the graph shows the median for route A is 40 and for the route, B is 35, which means the "typical number of riders is greater on route" (option D). Besides this, it can be observed that the number of riders varies more for route A than for route B, which makes B to be true.
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If the degree of a polynomial function is odd and the leading coefficient is negative, then the end behavior of the function is
The end behavior of a polynomial function is to decrease without bound as x approaches negative infinity, and to increase without bound as x approaches positive infinity.
If the degree of a polynomial function is odd and the leading coefficient is negative, then the end behavior of the function is as follows:
As x approaches negative infinity, the value of the function decreases without bound.
As x approaches positive infinity, the value of the function increases without bound.
To understand why this is the case, consider a polynomial function of the form:
f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0
where n is odd and a_n < 0.
As x approaches negative infinity, the dominant term in the polynomial is a_n x^n, and since n is odd and a_n is negative, the value of the dominant term approaches negative infinity as x approaches negative infinity.
Similarly, as x approaches positive infinity, the dominant term in the polynomial is again a_n x^n, but this time the value of the dominant term approaches negative infinity as x approaches positive infinity.
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Which of the following is not an attribute of a right pyramid?
Triangular faces
Triangular base
1 apex
8 edges
Answer:
Triangular base
Step-by-step explanation:
It possesses all attributes except from triangular base
Find the surface area of the cube shown below?
The surface area οf the cube with sides οf 25 cm is 3750 square centimeters.
What is Surface Area?Surface area is the measure οf the tοtal area that the surface οf a three-dimensiοnal οbject οccupies, including all οf its faces, sides, and curves. It is οften expressed in square units such as square meters οr square feet, and is an impοrtant parameter fοr determining prοperties such as heat transfer, frictiοn, and οptical prοperties οf an οbject.
The surface area οf a cube with sides οf length "a" can be fοund by using the fοrmula:
Surface area[tex]= 6a^2[/tex]
Substituting the given value οf "a" intο the fοrmula, we get:
Surface area [tex]= 6(25 cm)^2[/tex]
Surface area[tex]= 6(625 cm^2)[/tex]
Surface area [tex]= 3750 cm^2[/tex]
Therefοre, the surface area οf the cube with sides οf 25 cm is 3750 square centimeters.
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The question was incomplete, the complete question is mentioned here:
Find the surface area of the cube with side 25cm?
Fill in the table so that every row and every column sums to zero.
Answer:
Step-by-step explanation:
wheres the table
Diego applied to x colleges. If Nikki applied to 3 times as many colleges as Diego did, how many colleges did Nikki apply to?
3
x + 3
3x
3x + 3
Nikki applied to 3x colleges.
To determine the number of colleges Nikki applied to, we need to multiply the number of colleges Diego applied to by 3. Hence, the answer is represented by the mathematical expression 3x.
Explanation:In this problem, 'x' represents the number of colleges Diego applied to. Nikki, on the other hand, applied to 3 times as many colleges as Diego did.
So, to find out the total number of colleges Nikki applied to, we multiply the number of colleges Diego applied to ('x') by 3.
Hence, the correct mathematical expression for the number of colleges Nikki applied to would be 3x.
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PLEASE HELP ASAP !!!!!!!!!!!!!
The length of the x is 9 units.
Describe Triangle?Triangles can be classified based on the lengths of their sides and the sizes of their angles. The three most common types of triangles are equilateral, isosceles, and scalene. In an equilateral triangle, all sides and angles are equal. In an isosceles triangle, two sides and two angles are equal. In a scalene triangle, all three sides and angles are different.
Let's call the two sides of the triangle that the median divides into 9 and 10 "a" and "b", respectively. Then, we can use the formula for the length of a median in a triangle:
median = 1/2 * √(2a² + 2b² - c²)
where c is the length of the third side of the triangle. However, we don't know the length of the third side, so we need to find it. We can use the fact that the median divides the third side into two equal parts:
c/2 = (a + b)/2
c = a + b
Now we can substitute this into the formula for the length of the median:
x = 1/2 * √(2a² + 2b² - (a + b)²)
Simplifying:
x = 1/2 * √(2a² + 2b² - a² - 2ab - b²)
x = 1/2 * √(a² + 2ab + b²)
x = 1/2 * √((a + b)²)
x = 1/2 * (a + b)
x = 1/2 * (9 + 10)
x = 9
So the length of the median is 9 units.
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For a measurement project in math class, students measured the lengths of their pinky fingers. Alex's measured 2 inches long. Jerimiah's pinky finger was (7)/(4) inches long. Whose finger is longer? Draw a number line to help prove your answer.
Jerimiah's finger is longer. A number line can be drawn from 0 to 8 inches with 2 inches marked for Alex's finger and 7/4 inches marked for Jerimiah's finger. Since 7/4 is greater than 2, Jerimiah's finger is longer.
To prove that Jerimiah's finger is longer than Alex's, we can use a number line. On this number line, we start with 0 inches at one end and 8 inches at the other. We mark 2 inches for Alex's finger and 7/4 inches for Jerimiah's finger. Since 7/4 inches is greater than 2 inches, Jerimiah's finger is longer than Alex's. To further prove this, we can convert the fraction 7/4 into a decimal. 7/4 = 1.75, which is greater than 2. Therefore, Jerimiah's finger is longer than Alex's.
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A certain radioactive material is decaying at a rate proportional to the amount present. If a sample of 50 grams of the material was present initially and after 2 hours the sample lost 10% of its mass, find: An expression for the mass of the material remaining at any time t. The mass of the material after 4 hours. The half-life of the material.
The Half-Life of the material is 13.86 hours. The mass of the material remaining at any time t can be expressed as:
M(t) = 50e^(-0.05t), where t is measured in hours.
The amount of time needed for a number (of material) to decrease to half of its original value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long steady atoms last.
The mass of the material after 4 hours is M(4) = 50e^(-0.2) ≈ 31.4 grams. The half-life of the material can be found by solving for when M(t) = 25 grams:
t = ln(2)/0.05 ≈ 13.86 hours.
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The following data represent a random sample of the number of shares of a pharmaceutical company's stock traded for 20 days in 2000. Use a normal probability plot to asses whether the sample data could have come from a population that is normally distributed. Start 4 By 5 Matrix 1st Row 1st Column 4. 78 2nd Column 9. 7 3rd Column 11. 2 4st Column 8. 32 5st Column 14. 64 2nd Row 1st Column 6. 09 2nd Column 10. 49 3rd Column 9. 74 4st Column 12. 9 5st Column 14. 05 3rd Row 1st Column 5. 04 2nd Column 9. 34 3rd Column 12. 39 4st Column 7. 55 5st Column 28. 34 4st Row 1st Column 8. 51 2nd Column 10. 94 3rd Column 5. 08 4st Column 8. 04 5st Column 11. 68 EndMatrix 4. 78 9. 7 11. 2 8. 32 14. 64 6. 09 10. 49 9. 74 12. 9 14. 05 05. 04 09. 34 12. 39 7. 55 28. 34 8. 51 10. 94 5. 08 08. 04 11. 68
we can tentatively conclude that the data is reasonably well-approximated by a normal distribution, but further analysis may be needed to confirm this conclusion.
To create a normal probability plot, we need to first sort the data in ascending order and then calculate the corresponding z-scores for each observation based on the normal distribution. We can then plot the observed z-scores against the expected z-scores on a normal distribution.
Here is the sorted data:
5.04 5.08 6.09 7.55 8.04 8.32 8.51 9.34 9.7 9.74
10.49 10.94 11.2 11.68 12.39 12.9 14.05 14.64 28.34
And here are the corresponding z-scores calculated based on the normal distribution:
diff
-1.77 -1.74 -1.53 -1.17 -1.04 -0.96 -0.90 -0.72 -0.67 -0.65
-0.41 -0.29 -0.24 -0.17 0.06 0.21 0.48 0.65 3.09
The plot appears to be fairly linear, which suggests that the data could have come from a population that is normally distributed. However, there are a few points that deviate slightly from the line, particularly the two extreme points on the right-hand side. This suggests that there may be some skewness or outliers in the data that are causing deviations from normality.
Overall, we can tentatively conclude that the data is reasonably well-approximated by a normal distribution, but further analysis may be needed to confirm this conclusion.
the complete question is :
"The following data represent a random sample of the number of shares of a pharmaceutical company's stock traded for 20 days in 2000. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.
4.78 9.7 11.2 8.32 14.64
6.09 10.49 9.74 12.9 14.05
5.04 9.34 12.39 7.55 28.34
8.51 10.94 5.08 8.04 11.68
Please create a normal probability plot and interpret your findings."
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can anyone help me please
The interval of the expression x ≤ 3 and x ≥ -3 is (-3, 3).
How to graph equations?To graph a linear equation with one variable, first solve the problem, then find the answer on the axis (number line), and place a point there. We have seen that graphs often provide information that the original equation would not have shown. The graphs of one-variable linear equations do not provide much, if any, information, but they provide as a basis for graphs with greater dimensions.
The given inequality is x ≤ 3 and x ≥ -3.
Since, the signs are less than and equal to and more than and equal to we use solid dots to represent the number 3 and -3 on the number line.
Also, the expression requires all the numbers between 3 and -3. Thus, the interval is:
(-3, 3).
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This composite figure is created by placing a sector of a circle on a triangle. What is the area of this
composite figure? Use 3.14 for . Round to the nearest hundredth. Show your work
As a result, the answer to the following question, When we round to the area nearest hundredth, we get: 42.84 square units in total.
What is area?An area is the size of a surface area. The surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a form or flat layer. The area of an item is the entire amount of space occupied by its planar (2-D) surface or form. Using a pencil, draw a square on a sheet of paper. A two-dimensional character. The area of a form on paper is the amount of space it occupies. Assume that the square is made up of smaller unit squares.
The formula for a sector's area is:
Sector area = (central angle/360) x pi x radius2
When we plug in the values we know, we get:
Sector area = (60/360) x 3.14 x 62
Sector area = 18.84 square units
Triangle area = (base x height)/2
When we plug in the values we know, we get:
Triangle area = (8 x 6)/2 Triangle area = 24 square units
Total area Equals sector area + triangle area
18.84 + 24 = total area
42.84 square units in total
When we round to the nearest hundredth, we get:
42.84 square units in total.
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a number decreased by 16 is -26. Find the number number
The value of the required number is - 10
Finding the unknown number:To find the unknown number represent the number with a variable 'x' and form a linear equation according to the condition given in the problem.
Solve the resultant equation for the value variable 'x' by adding or subtracting the same number on both sides.
Here we have
A number decreased by 16 and the result was -26.
Let 'x' be the number
According to the given data,
=> x - 16 = - 26
Add 16 on both sides
=> x - 16 + 16 = - 26 + 16
=> x = - 10
Hence,
The value of the required number is - 10
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solve the quadratics attached using at least two different methods (factoring, completing the square or the quadratic formula)
[tex]m^2+7m+10\\\\n^2\:+9n+18\\\\\\p^2-6p+8[/tex]
Method 1: Factoring
m^2 + 7m + 10
We need to find two numbers that multiply to 10 and add up to 7. These numbers are 2 and 5.
m^2 + 2m + 5m + 10
(m + 2)(m + 5)
n^2 + 9n + 18
We need to find two numbers that multiply to 18 and add up to 9. These numbers are 3 and 6.
n^2 + 3n + 6n + 18
(n + 3)(n + 6)
p^2 - 6p + 8
We need to find two numbers that multiply to 8 and add up to -6. There are no such numbers, so we cannot factor this quadratic.
Method 2: Quadratic Formula
m^2 + 7m + 10
a = 1, b = 7, c = 10
m = (-b ± sqrt(b^2 - 4ac)) / 2a
m = (-7 ± sqrt(7^2 - 4(1)(10))) / 2(1)
m = (-7 ± sqrt(9)) / 2
m = -5 or -2
n^2 + 9n + 18
a = 1, b = 9, c = 18
n = (-b ± sqrt(b^2 - 4ac)) / 2a
n = (-9 ± sqrt(9^2 - 4(1)(18))) / 2(1)
n = (-9 ± sqrt(9)) / 2
n = -3 or -6
p^2 - 6p + 8
a = 1, b = -6, c = 8
p = (-b ± sqrt(b^2 - 4ac)) / 2a
p = (6 ± sqrt(6^2 - 4(1)(8))) / 2(1)
p = (6 ± sqrt(16)) / 2
p = 2 or 4
Therefore, the solutions to the quadratics are:
m^2 + 7m + 10 = (m + 2)(m + 5) or m = -5 or -2
n^2 + 9n + 18 = (n + 3)(n + 6) or n = -3 or -6
p^2 - 6p + 8 = (p - 2)(p - 4) or p = 2 or 4
Write 27^2/9^4 as a power of 3
Answer: We can simplify 27 as 3^3 and 9 as 3^2. Then, we have:
27^2/9^4 = (3^3)^2/(3^2)^4
Using the power of a power rule, we can simplify:
= 3^(3x2)/(3^2x4)
= 3^6/3^8
Using the quotient rule, we can subtract the exponents:
= 3^(6-8)
= 3^-2
Therefore, 27^2/9^4 can be expressed as 3^-2 in terms of a power of 3.
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Use the triangle below to write the given ratios.
In the given triangle the value of the ratios are Sin (P) = 5/13. tan (T) = 12 /5. cos (T) = 5/13.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to determine each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.
Using the trigonometric identities we can write the ratios as follows:
Sin (P) = Opposite side to P / Hypotenuse= 5/13
tan (T) = Opposite side to T / Adjacent side to T = 12 /5
cos (T) = adjacent side to T / Hypotenuse = 5/13.
Learn more about tangent function here:
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