The median of the solutions to the equation 3x³ + 5x² − 6x − 10 = 0 is -√2. The correct answer is A.
To find the median of the solutions to the equation 3x³ + 5x² − 6x − 10 = 0, first find the solutions of the equation and then find the middle value of those solutions.
Group the terms and factor out (3x + 5).
(3x³ + 5x²) + (-6x − 10) = 0
(3x + 5)(x²) + (3x + 5)(-2) = 0
(3x + 5)(x² - 2) = 0
Factor (x² - 2).
(3x + 5)(x + √2)(x - √2) = 0
So the solutions of the equation are x = -5/3, x = -√2, and x = √2.
To find the median of these solutions, we need to order them from least to greatest:
-5/3 < -√2 < √2
The median of these solutions is -√2.
Therefore, the correct answer is (A) -√2.
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when flying on an air plane the weight limit for carry on luggage is 30 pounds there are approximately 453.6 grams in 1 pound which measurement is closet to the weight of the checked luggage in grams
Answer:
Step-by-step explanation:
30x453.6=13608 grams
How to express a two logarithm into a single logarithm
Answer:
There are different methods to express a two logarithm into a single logarithm, depending on the specific form of the logarithms involved. Here are some examples:
Logarithms with the same base:
If you have two logarithms with the same base, you can use the following logarithmic identity:
log_a(x) + log_a(y) = log_a(xy)
Using this identity, you can express a sum or difference of logarithms with the same base as a single logarithm:
Example 1: log_2(3) + log_2(5) = log_2(3*5) = log_2(15)
Example 2: log_5(7) - log_5(2) = log_5(7/2)
Logarithms with different bases:
If you have two logarithms with different bases, you can use the following change of base formula to express them with a common base:
log_a(x) = log_b(x) / log_b(a)
Using this formula, you can rewrite a logarithm with a base a as a logarithm with a base b:
Example 1: log_2(7) = log_10(7) / log_10(2)
Example 2: log_5(2) = log_2(2) / log_2(5)
Once you have expressed both logarithms with the same base, you can apply the logarithmic identity from method 1 to simplify them into a single logarithm.
23
b. Complete the double number line diagram that represents the situation.
Photos
0
0
Minutes!
:: 1
7
2
4
:: 4
:: 6
1
#15
21
8
3
28
:: 9
80
#20
# 10
35
12
:: 14
PLEASE HELP I NEEEDA LIKE FINISH IT RN HELP
Answer:
10mins for 35 photos
Step-by-step explanation:
If it takes 8mins to produce 28photos, that is ratio 1:3.5
For 7 photos, divide by 3.5, that is 2mins
For 4mins, multiply by 3.5, that will be 14photos
For 21 photos, divide by 3.5, that will be 6 mins
Use the commutative or associative property to simplify the expression. (1)/(13)(13y)
The simplified expression of (1)/(13)(13y) is 169y.
To simplify the expression (1)/(13)(13y) using the commutative or associative property, we can rearrange the terms and group them together.
Using the commutative property, we can rearrange the terms so that the two 13's are next to each other:
(1)(13)(13y) = (13)(13y)(1)
Now, using the associative property, we can group the two 13's together and simplify:
(13)(13y)(1) = (13*13)(y)(1) = (169)(y)(1)
Finally, we can simplify further by multiplying the 169 and 1 together:
(169)(y)(1) = (169y)(1) = 169y
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What is the solution to this equation?
9 ^x- 1 = 2
O A. 1
O B. 2
O C.
1/2
OD. -1/2
The solution to this equation 9ˣ - 1 = 2 is 1/2.
The correct option is A.
What is an equation?
Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
An equation:
9ˣ - 1 = 2
Simplifying,
9ˣ = 3
3²ˣ = 3
Comparing, we get,
2x = 1
x = 1/2
Therefore, the solution is x = 1/2.
what is the ratio of 2:35
Answer:
2:35
Step-by-step explanation:
In Exercises 11-14|, use a matrix equation to solve the system of linear equations. \( 11\left\{\begin{array}{r}x+2 y=3 \\ 2 x+6 y=5\end{array}\right. \)
x = 4/3 and y = 2/3
To solve this system of linear equations using a matrix equation, we first need to construct a matrix by writing the coefficients of the variables and the constants from the equation in a rectangular array.
The matrix for the given equations will be:
Now, we can solve the system by multiplying the inverse of the matrix of coefficients with the matrix of constants. To find the inverse of the matrix, we can use the following equation:
where |A| is the determinant of the matrix, and adj(A) is the adjoint of the matrix.
We can use this equation to find the inverse of the matrix, which is:
We can then multiply this inverse by the matrix of constants to get the solution for the system:
Therefore, the solution for the system is x = 4/3 and y = 2/3.
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Work the problem using the three-step method. Show your work.
The sum of three consecutive integers is 18. Find the integers.
WRITER
Answer:
5,6 and 7.
Step-by-step explanation:
I am not sure what the three step method is, but here is how I solved it.
Consecutive integers means integers in a row. For example, 5,6 7 are consecutive integers or -4,-3,-2 are consecutive integers.
Integers are all the whole numbers (0,1,2,3...) and their opposites (..., -3, -2, -1) 1/2 or -.23 are not integers.
Let x = the first number
Let x + 1 = the second number
Let x + 2 = the third number
x + (x + 1) + (x + 2) = 18 I do not need the parentheses, but I want you to see that the first number, plus the second number, plus the third number equals 18.
x + x + 1 + x + 2 = 18 Combine like terms
3x + 3 = 18 Subtract 3 from both sides of the equation
3x + 3 - 3 = 18 - 3
3x = 15 Divide both sides by 3
[tex]\frac{3x}{3}[/tex] = [tex]\frac{15}{3}[/tex]
x = 5
The first number is 5. The second number is 6 and the last number is 7.
Check:
5 + 6 + 7 = 18
18 =18 Checks.
Helping in the name of Jesus.
Use an appropriate infinite series method about x = 0 to find two solutions of the given differential equation. (Enter the first four nonzero terms for each linearly independent solution, if there are fewer than four nonzero terms then enter all terms. In each case, the first term has been provided for you. )
3xy" y+y=0
Y₁ = 1 -
12 = x2/3
The two linearly independent solutions are y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + … and y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...
We can use the power series method to find the two solutions of the given differential equation:
Let y = ∑anxn be a power series solution. Then, we have:
y' = ∑nanxn-1
y'' = ∑nan(n-1)xn-2
Substituting these into the differential equation and equating coefficients of like powers of x, we get:
3x∑nan(n-1)xn-1 + ∑anxn = 0
Simplifying, we obtain:
∑[3nan(n-1) + an-1]xn = 0
Since x ≠ 0, the coefficients of like powers of x must be zero. This gives us the recurrence relation:
an = -an-1/(3n(n-1)), n ≥ 1
Using this recurrence relation and the initial condition y(0) = 1, we can find the power series solution:
y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + ...
To find a second linearly independent solution, we can use the method of reduction of order. Let y₂(x) = v(x)y₁(x). Then, we have:
y₂' = v'y₁ + vy₁'
y₂'' = v''y₁ + 2v'y₁' + vy₁''
Substituting these into the differential equation and simplifying, we get:
v''y1x + (2v'y1' + vy1'')x + 3vy1 = 0
Since y₁(x) is a solution, we have:
y₁'' + (1/3x)y₁ = 0
Multiplying by y1 and integrating, we obtain:
(y₁')² + y₁²/3 = C
where C is a constant of integration. Using the initial condition y₂(0) = 0, we can find the second solution:
y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...
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Use a calculator to find the trigonometric value to 4 decimal places. sin 14° = __________
The trigonometric value of sin 14° to 4 decimal places is sin 14° = 0.241.
Step 1: Enter the value of 14 into the calculatorStep 2: Press the sin button on the calculatorStep 3: The calculator will display the value of sin 14°Step 4: Round the value to 4 decimal places
The value of sin 14° to 4 decimal places is 0.2419.
An angle is the measure that determines two straight lines, which when joined together create a point of origin, which is called the vertex of the angle.
The unit of measurement associated with angles is degrees.
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For each relationship described, type an equation using the variables y and z to create an identity. a. addition and subtraction: b. multiplication and division: (when y 0 or when z = 0)
Step-by-step explanation:
addition and subtraction:
y + z - z = y
b. multiplication and division:
When y ≠ 0:
yz / y = z
When z ≠ 0:
y / z * z = y
Find the values of x and y
. Write your answer in
simplest form.
X
45°
X =
y =
y
16
&
Answer:
X: 45° Y:16°
Step-by-step explanation:
by help of teacher
Find the measure of pkt
Answer:
32°
Step-by-step explanation:
You want the measure of the smaller angle of the linear pair marked (3g+23) and (7g+127).
Linear pairThe angles of a linear pair total 180°, so we have ...
(3g +23) +(7g +127) = 180
10g = 30 . . . . . . . . . subtract 150
g = 3 . . . . . . . . . divide by 10
The smaller angle is ...
∠PKT = (3·3 +23)°
∠PKT = 32°
Three friends, Martin, Tyreese, and Braydon, are collecting donations to help in their community's clean-up initiative. Their total contribution goal is represented by the expression 7x2 − 4xy + 8. The friends have already collected the following amounts:
Martin: 5xy + 16
Tyreese: x2
Braydon: 4x2 − 7
Which expression represents the amount of money the friends still need to collect to meet their goal?
2x2 − 9xy − 1
2x2 + xy + 17
5x2 + 5xy + 9
12x2 + xy + 17
2x2 - 9xy - 1 is the expression for how much money the buddies still need to gather to reach their objective.
What exactly is a phrase?A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities.
The total of what they have already raised towards the overall fundraising target.
The total contribution goal is given as: 7x² - 4xy + 8
The amount Martin has already collected is: 5xy + 16
The amount Tyreese has already collected is: x²
The amount Braydon has already collected is: 4x² - 7
Adding the amounts already collected:
= (5xy + 16) + x² + (4x² - 7)
= 5xy + x² + 4x² + 16 - 7
= 5xy + 5x² + 9
By deducting the total of the contributions from the overall contribution target:
= (7x² - 4xy + 8) - (5xy + 5x² + 9)
= 2x² - 9xy - 1
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Answer: A
Step-by-step explanation: i wish other people would just put the letter, but here ya go c:
extra points for help (dont guess please)
The exponential functions y=1.2ˣ shows exponential growth and y=0.71ˣ shows exponential decay.
What exactly are exponential functions?
Exponential functions are functions that involve a variable exponent. They are of the form f(x) = aˣ, where "a" is a positive constant base and "x" is the variable exponent.
Exponential functions exhibit rapid growth or decay, depending on the value of "a" and the sign of "x". For example, if "a" is greater than 1, the function grows rapidly as "x" increases, while if "a" is between 0 and 1, the function decays rapidly as "x" increases.
Now,
As stated above that for exponential function y=aˣ
when a>1 it shows exponential growth
and when a<1 it shows decay.
hence,
The exponential functions y=1.2ˣ shows exponential growth and y=0.71ˣ shows exponential decay.
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Calculate the interest earned when $46 230 is invested for 9 years at 7.8% p.a., with interest compounded twice a year.
Given:
What is the interest earned when $46,230 is invested for 9 years at 7.8% p.a?
To find:
The interest
Solution:
[tex]interest = \frac{p \times r \times t}{100} [/tex]let the interest be x. [tex]x = \frac{46230 \times 9 \times 7.8}{100} [/tex][tex]x = 32456.46[/tex]But the interest is compounded twice a year so, [tex]32456.46 \times 2 \times 9[/tex][tex] = 64912.92 \times 9[/tex][tex] = 584216.28[/tex]therefore, the final answer is 584,216.28the form Q+bar (D) where the degree of R is less than the degree of (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4)
In this expression, Q+bar (D) is a polynomial, and we are asked to compare the degree of R with that of the polynomial (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4).
The degree of a polynomial is determined by the highest power of the variable. The highest power of c in (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4) is 3, so this polynomial has a degree of 3.
To compare it to the degree of R, we need to know the highest power of R in our expression. If the degree of R is less than the degree of (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4), then the expression Q+bar (D) will have a degree of 3.
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NEED HELP DUE FRIDAY!!!!!!!!!!!
Find cos(A), sin(A), and tan(A) for triangle ABC.
Answer:
It’s a right triangle
Step-by-step explanation:
15 squared plus 8 squared equals 17 squared which 289=289
Graph the inequality y+4<-2(x-4) on the set of axes below
Answer:
y < 2x + 4
Step-by-step explanation:
y+4<-2(x-4)
y + 4 < -2x +8
y < 2x + 4
point (s) possible Find the LCD (least common denominator ) of the set of fractions. Do not combine the fractions; only find the LCD. (7)/(20) and (9)/(40)
The answer are LCD (least common denominator) of the set of fractions (7)/(20) and (9)/(40) is 40.
Here is a step-by-step explanation on how to find the LCD:
1. Find the multiples of each denominator.
- Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200...
- Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400...
2. Compare the multiples of each denominator and find the smallest number that appears in both lists.
- The smallest number that appears in both lists is 40.
3. The smallest number that appears in both lists is the LCD.
- Therefore, the LCD of the set of fractions (7)/(20) and (9)/(40) is 40.
So the answer to the question "Find the LCD (least common denominator) of the set of fractions. Do not combine the fractions; only find the LCD. (7)/(20) and (9)/(40)" is 40.
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In Exercises \( 1-8, W \) is a subset of \( R^{2} \) consisting of vectors of the form \[ \mathbf{x}=\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right] \] In each case determine whether \( W \)
Yes
Yes, \( W \) is a subset of \( R^{2} \) since it consists of vectors of the form
\[ \mathbf{x}=\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right] \]. Therefore, for Exercises \( 1-8 \), the answer is yes.
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Ina makes cakes in a pan shaped like a rectangular prism. The base of the pan is an 8-inch by 12-inch rectangle, and the volume of the pan is 288 cubic inches. Find the surface area of a cheesecake baked in this pan
Answer:
312 square inches
Step-by-step explanation:
To find the surface area of a cake baked in a rectangular pan with an 8-inch by 12-inch base and a volume of 288 cubic inches, we need to find the dimensions of the pan. We can do this by dividing the volume by the area of the base, which gives us the height of the pan. Once we know the height, we can use the dimensions of the base and the height to find the surface area of the cake.
On a certain day, the temperature of the pool was 76°F at 10 A.M. and 91°F at 1 P.M. If the temperature rose at a constant rate from 10 A.M. to 1P.M. on that day, what was the temperature at 11 A.M.? a. 79°F d. 89°F b. 81°F e. 90°F c. 86°F
The correct answer is b. 81°F.
On a certain day, the temperature of the pool rose at a constant rate from 76°F at 10 A.M. to 91°F at 1 P.M. To find the temperature at 11 A.M., we need to find the rate of change in temperature and then use it to calculate the temperature at 11 A.M.
The rate of change in temperature can be found by dividing the difference in temperature by the difference in time:
Rate of change = (91°F - 76°F) / (1 P.M. - 10 A.M.) = 15°F / 3 hours = 5°F per hour
Now, we can use this rate of change to find the temperature at 11 A.M.:
Temperature at 11 A.M. = 76°F + (5°F per hour)(1 hour) = 81°F
Therefore, the correct answer is b. 81°F.
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Mrs.may mixed 4 gal of red paint with every 6 gal of blue paint in order to make purple paint. which ratio of gallons of red paint to gallons of blue pint will make the same shade of purple paint?
Answer: 20 gallons of red paint and 30 gallons blue paint
Step-by-step explanation:
Please note that for 1 pound of bananas the cost is
$0.63/lb
(according to the US Bureau of Labor Statistics.) In 1939 , the cost of bananas was
14%
lower. Pam buys 5 pounds of bananas for children at the camp she works for. What would these bananas have cost in 1939?
The cost of 5 pounds of bananas in 1939 would have been $2.709.
According to the US Bureau of Labor Statistics, the cost of 1 pound of bananas is $0.63/lb. In 1939, the cost of bananas was 14% lower. Therefore, to find the cost of bananas in 1939, we need to calculate 14% of $0.63/lb and then subtract it from $0.63/lb.
Calculate 14% of $0.63/lb
0.14 * $0.63/lb = $0.0882/lb
Subtract $0.0882/lb from $0.63/lb to get the cost of bananas in 1939
$0.63/lb - $0.0882/lb = $0.5418/lb
Multiply the cost of bananas in 1939 by the number of pounds Pam buys
$0.5418/lb * 5 lb = $2.709
Therefore, the cost of 5 pounds of bananas in 1939 would have been $2.709.
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Practice and Problem S Subtract using the vertical form. 1. (5g^(2)+6g-10)-(2g^(2)+2g+9)
(5g^(2)+6g-10)-(2g^(2)+2g+9) = 3g^(2) + 4g - 19
To subtract the two polynomials, we will use the vertical form. This means that we will line up the like terms and subtract them.
Step 1: Line up the like terms in the vertical form.
5g^(2) + 6g - 10
- (2g^(2) + 2g + 9)
Step 2: Distribute the negative sign to each term in the second polynomial.
5g^(2) + 6g - 10
- 2g^(2) - 2g - 9
Step 3: Subtract the like terms.
5g^(2) - 2g^(2) = 3g^(2)
6g - 2g = 4g
-10 - 9 = -19
Step 4: Write the final answer.
3g^(2) + 4g - 19
Therefore, the answer is 3g^(2) + 4g - 19.
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e) Solve: f(x) = g(x) for x = [-240°; 240°]
Answer:
218.88
Step-by-step explanation:
The surface area of a rectangular prism is 250 cm 2. If its height is 10 centimeters, and its width is 5 centimeters, what is its volume?
The volume of the rectangular prism whose surface area is 250 cm square is 250cubic centimeters.
The surface area of a rectanular prism is calculates by the formula
= 2( length*width + length*height + width*height ) square units
Let the length of the given prism be l centimeters.
Given, width is 5 centimeters and height is 10 centimeters of the rectangular prism.
The surface area of the rectangular prism is 250 cm square.
Thus by the above formula,
250 = 2 ( l*5 + l*10 +10*5)
⇒250 = 2 (15*l +50)
⇒ 250= 30*l + 100
⇒ 150 = 30*l
⇒l = 150/30 = 5 (centimeters)
Thus the volume of the given rectangular prism is calculated as
= ( length*width*height) cubic units
= (5*5*10) cubic centimeters
= 250 cubic centimeters
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Find the minimum and maximum of P=4x+2y subject to 3x+5y>=20 3x+y<=16 -2x+y<=2 x>=0,y>=0
The minimum of P is 16 and the maximum of P is 24.
Calculating the value of P for these points, we get:
P(2,6) = 4*2 + 2*6 = 20
P(0,8) = 4*0 + 2*8 = 16
P(4,2) = 4*4 + 2*2 = 24
P(3,3) = 4*3 + 2*3 = 18
Therefore, the minimum of P is 16 and the maximum of P is 24.
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Designing an Addition A 40-ft-wide house has a roof with a
6-12 pitch (the roof rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will have a 3-12 pitch to its roof. Find the lengths of AB and BC in the accompanying figure.
We can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.
What is sine formula in trigonometry?Sine formula is used to calculate the sine angle of a right-angled triangle which is the ratio of the opposite side and the hypotenuse.
Given is that a 40-ft-wide house has a roof with a 6-12 pitch (the roof
rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will
have a 3-12 pitch to its roof.
We can write the measure of length AB as -
AB = 6 + √(9 + 296)
AB = 6 + 17.46
AB = 23.46 ft
We can write the measure of length BC as -
BC = 6 + 1/4 x 12
BC = 6 + 3
BC = 9 ft
Therefore, we can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.
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