Answers
Answer:
For 1 it would be C for 2 It would be D
Step-by-step explanation:
ㅤㅤ [ SOLUTION ( 1 ) :- ]
ㅤ
In september, Dorothy sold ::
➸ 43 bracelets➸ 12 necklaces➸ For = $1105.25ㅤ
In october, Dorothy sold ::
➸ 74 bracelets➸ 51 necklaces➸ For = $2962.75ㅤ
Here ::
➸ Bracelets = b➸ Necklaces = nㅤ
So ::
\(\begin{gathered}\begin{gathered}\: \begin{gathered}\begin{gathered} \small{\underline{\boxed{\begin{array}{cc} \\ \: \orange{\frak{(C) \: 43b + 12n = 1105.25}} \\ \\ \orange{\frak{74b + 51n = 2962.75}}\\ \: \end{array}}}} \; \pmb{\bigstar}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\)
━━━━━━━━━━━━━━━━━━━━━━
ㅤㅤ [ SOLUTION ( 2 ) :- ]
ㅤ
Atq ::
\(\begin{gathered}\\:\longmapsto\quad\sf{a + c = 200\qquad\qquad\left\lgroup\begin{matrix}\sf{{eq}^{n}} \: (I) \end{matrix}\right\rgroup} \end{gathered}\)
\(\begin{gathered}\\:\longmapsto\quad\boxed{\sf{a = 200 - c}}\end{gathered}\)
\(\begin{gathered}\\:\longmapsto\quad\sf{8a + 6c = 1440\qquad\qquad\left\lgroup\begin{matrix}\sf{{eq}^{n}} \: (II) \end{matrix}\right\rgroup} \end{gathered}\)
ㅤ
Substituting the value of (a) in (II) ::
\(\begin{gathered} \\ \; \; \sf{:\longmapsto{8(200 - c) + 6c = 1440}} \\ \\ \end{gathered}\)
\(\begin{gathered} \\ \; \; \sf{:\longmapsto{1600 - 8c + 6c = 1440}} \\ \\ \end{gathered}\)
\(\begin{gathered} \\ \; \; \sf{:\longmapsto{1600 - 1440 = 8c - 6c}} \\ \\ \end{gathered}\)
\(\begin{gathered} \\ \; \; \sf{:\longmapsto{160 = 2c}} \\ \\ \end{gathered}\)
\(\begin{gathered} \\ \; \; \sf{:\longmapsto{\cancel{\dfrac{160}{2}} = c}} \\ \\ \end{gathered}\)
\(\begin{gathered}\\ \; \; :\longmapsto{\boxed{\orange{\frak{c = 80}}}} \; \pmb{\bigstar} \\ \\ \end{gathered}\)
Substituting the value of (c) in (II) ::
\(\begin{gathered} \\ \; \; \sf{:\longmapsto{a + 80 = 200}} \\ \\ \end{gathered}\)
\(\begin{gathered} \\ \; \; \sf{:\longmapsto{a = 200 - 80}} \\ \\ \end{gathered}\)
\(\begin{gathered}\\ \; \; :\longmapsto{\boxed{\orange{\frak{a = 120}}}} \; \pmb{\bigstar} \\ \\ \end{gathered}\)
∴ 120 Adult Tickets Were Sold
\(\bf{\pmb{\underline{\rule{170pt}{5pt}}}}\)
Related Questions
20=100(1/2)^t/214
find t
Answers
t= 428/5
Decimal form:
t= 85.6
Mixed form:
t= 85 3/5
The required value of t from the given expression is 496.86.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression
\(20=100(1/2)^{t/214}\\1/5 = [1/2]^{t /214}\\\)
taking log,
ln 1/5 = t /214 ln [1/2]
t = 214 ln 5 / ln [1/2]
t = 496.86
Thus, the required value of t from the given expression is 496.86.
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The sides of a triangle are 5, 12, and n. Write an inequality that expresses the interval of values that n may have. A. 5 < n < 12 B. 5 < n < 17 C. 7 < n < 17 D. 7 < n < 12
Answers
An inequality that expresses the interval of values that n may have is (B) \((5 < n < 17)\)
The sides of a triangle are 5, 12, and n.
To write an inequality that expresses the interval of values that n may have, we use the Triangle Inequality Theorem.
The Triangle Inequality 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.
So for this question, the inequality that expresses the interval of values that n may have is given as:\(5 + 12 > n12 + n > 5n + 5 > 12\)
Simplifying the above inequality: \(n > -7n > 7\)
The interval for n will be \([7,∞)\), where n has to be greater than 7.
Option D \((7 < n < 12\)) is not the correct answer.
Hence, the correct answer is option B\((5 < n < 17).\)
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LowStress Marketing Research designed a perceptual mapping study to compare several leading brands of soap for Bubbles O'Connor, product manager for Slippery Soap. Bubbles asked to see a sample question from the study and was shown the following format: Slipery Soap is a disinfectant soap: Neither Agree or Disagree, 4) Disagree, 5) Strongly Disagree. In addition, Bubbles saw the results from the regression analysis for soaps in the study which showed the following equation: Overall Preference -2.1 +2.3* Cleaning Ability+1.0* Cost+0.6 Disinfecting Ability. What would be the slope of the ideal vector?
Answers
The slope of the ideal vector, determined by examining the coefficients of the variables in the regression equation is:
Cleaning Ability: 2.3
Cost: 1.0
Disinfecting Ability: 0.6.
In this case, the regression equation is:
Overall Preference = -2.1 + 2.3 * Cleaning Ability + 1.0 * Cost + 0.6 * Disinfecting Ability
The coefficients of the variables represent the weights or importance assigned to each variable in determining the overall preference. Therefore, the slope of the ideal vector would be the coefficients of the variables in the regression equation.
Based on the given regression equation, the slope of the ideal vector would be:
Cleaning Ability: 2.3
Cost: 1.0
Disinfecting Ability: 0.6
These values indicate the relative importance or impact of each variable on the overall preference for Slippery Soap.
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Solve the system of equations -x+10y-2z=8. y-52=-4, 1+3x-y=0 via the SOR method using the starting point xo=0,yo=0.9,zo=1.1 tolerance=tol=0.05,a11=3,a22=10,a33=5and=0.9. [16 marks]
Answers
Three iterations are performed here to solve the system of equations using the Successive Over-Relaxation (SOR) method.
To solve the system of equations using the Successive Over-Relaxation (SOR) method, we need to iterate through the equations until convergence is achieved within the given tolerance.
The system of equations is:
- x + 10y - 2z = 8 (Equation 1)
y - 52 = -4 (Equation 2)
1 + 3x - y = 0 (Equation 3)
We start with the initial guesses:
x₀ = 0
y₀ = 0.9
z₀ = 1.1
Using the SOR method, the iteration formula is:
xₖ⁺¹ = (1 - ω)xₖ + (ω/a₁₁)(b₁ - a₁₂yₖ - a₁₃zₖ)
yₖ⁺¹ = (1 - ω)yₖ + (ω/a₂₂)(b₂ - a₂₁xₖ - a₂₃zₖ)
zₖ⁺¹ = (1 - ω)zₖ + (ω/a₃₃)(b₃ - a₃₁xₖ - a₃₂yₖ)
where ω is the relaxation factor, a₁₁, a₂₂, and a₃₃ are the diagonal elements of the coefficient matrix, b₁, b₂, and b₃ are the right-hand side values, and the subscripts k and k+1 represent the iteration steps.
Given:
tol = 0.05 (tolerance)
a₁₁ = 3
a₂₂ = 10
a₃₃ = 5
ω = 0.9
Let's proceed with the calculations using the SOR method:
Iteration 1:
x₁ = (1 - 0.9)(0) + (0.9/3)(8 - 10(0.9) - 2(1.1)) = 0.6
y₁ = (1 - 0.9)(0.9) + (0.9/10)(-4 - 3(0) - 5(1.1)) = 0.833
z₁ = (1 - 0.9)(1.1) + (0.9/5)(1 - 3(0) - 10(0.833)) = 1.035
Iteration 2:
x₂ = (1 - 0.9)(0.6) + (0.9/3)(8 - 10(0.833) - 2(1.035)) = 0.610
y₂ = (1 - 0.9)(0.833) + (0.9/10)(-4 - 3(0.6) - 5(1.035)) = 0.841
z₂ = (1 - 0.9)(1.035) + (0.9/5)(1 - 3(0.6) - 10(0.841)) = 1.012
Iteration 3:
x₃ = (1 - 0.9)(0.610) + (0.9/3)(8 - 10(0.841) - 2(1.012)) = 0.620
y₃ = (1 - 0.9)(0.841) + (0.9/10)(-4 - 3(0.610) - 5(1.012)) = 0.842
z₃ = (1 - 0.9)(
1.012) + (0.9/5)(1 - 3(0.610) - 10(0.842)) = 1.008
Continue these iterations until the solution converges within the given tolerance.
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when the sum of the first ten terms of an arithmetic progression is four times the sum of the first five terms, the ratio of the first term to the common difference is:
Answers
The ratio of the first term to the common difference is 1 is to 1 (1:1).
Let's say the first term of the arithmetic progression is 'a' and the common difference is 'd'.
Then the sum of the first five terms will be,
S5 = a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 5a + 10d
And the sum of the first ten terms will be,
S10 = a + (a + d) + (a + 2d)+ ... + (a + 9d)
=10a + 45d
We have been given that sum of the first 10 terms is equal to four times the sum of the first 5 terms, i.e
S10 = 4S5
Substituting the expressions for S5 and S10 in terms of a and d, we get,
10a + 45d = 4(5a + 10d)
Simplifying this equation, we get,
10a + 45d = 20a + 40d
10d = 10a
d = a
So the ratio of the first term to the common difference is 1:1 or 1/1.
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1 2/3 yards of chain cost 9.00.
How much money for 1 yard
Answers
Alright nevermind, imma delete this answer.
Answer: $5.40
Step-by-step explanation:
1 and 2/3 yards costs $9
5/3 yards costs $9 <--- changes 1 and 2/3 to improper
5 * 1/3 yards costs $9 <---- 5/3 = 5 * 1/3
1/3 yard costs $9/5 = $1.80 <--- divides the ratio by 5
1 yard costs $1.80 * 3 = $5.40
variables Review find r if 2r+10=22
Answers
EXPLANATION
If the equation is 2r+10=22
Subtracting -10 to both sides:
2r = 22 - 10
Subtracting numbers:
2r = 12
Dividing both sides by 2:
r = 12/2
Simplifying:
r=6
The answer is r=6
Answer with proof pls
Answers
Rounding to the nearest tenth, the volume of the sphere is 1767.1 cubic inches.
What do you mean by the volume of sphere?The volume of a sphere refers to the amount of space occupied by a sphere in three-dimensional space. It is a measure of the total amount of space inside the sphere. The formula for finding the volume of a sphere is V = (4/3)πr³, where V is the volume, π is pi (approximately equal to 3.14), and r is the radius of the sphere.
In the given question,
The diameter of the sphere is 15 inches, which means the radius is half of the diameter, so:
radius = 15in / 2 = 7.5in
Using the formula for the volume of a sphere, we get:
volume = (4/3) * pi * radius^3
volume = (4/3) * 3.14159 * (7.5in)^3
volume ≈ 1767.15 cubic inches
Therefore, the volume of the sphere with 15in diameter is approximately 1767.15 cubic inches, rounded to the nearest tenth.
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Which recursively defined function has a first term equal to 10 and a common difference of 4?
Answers
The recursively defined function has a first term equal to 10 and a common difference of 4 is f(n) = 6 + 4n.
When a recursive procedure gets repeated, it's called recursion. A recursive is a type of function or expression stating some conception or property of one or further variables, which is specified by a procedure that yields values or cases of that function by constantly applying a given relation or routine operation to known values of the function.
We have first term = a = 10
And the common difference of d = 4
We have the formula for the t terms of a as 10 and d as 4
f(n) = a + (n - 1)d
f(n) = 10 + (n-1) x 4
f(n) = 10 + 4n - 4
f(n) = 6 + 4n
So, the defined function is f(n) = 6 + 4n.
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The amount of time a certain brand of light bulb lasts is normally distributed with a
mean of 1500 hours and a standard deviation of 45 hours. Out of 625 freshly installed
light bulbs in a new large building, how many would be expected to last between 1390
hours and 1620 hours, to the nearest whole number?
Answers
We can anticipate that, rounded to the closest whole number, 618 light bulbs will last between 1390 and 1620 hours.
We can calculate the z-scores for each of these values using the following formula to determine the approximate number of light bulbs that will last between 1390 and 1620 hours:
Where x is the supplied value, is the mean, and is the standard deviation, z = (x - ) /.
Z = (1390 - 1500) / 45 = -2.44 for 1390 hours.
Z = (1620 - 1500) / 45 = 2.67 for 1620 hours.
We may calculate the area under the curve between these z-scores using a calculator or a normal distribution table.
The region displays the percentage of lightbulbs that are anticipated to fall inside this range.
Expected number = 0.9886 \(\times\) 625 = 617.875.
The region displays the percentage of lightbulbs that are anticipated to fall inside this range.
The area between -2.44 and 2.67 is approximately 0.9886, according to the table or calculator.
We multiply this fraction by the total number of light bulbs to determine the number of bulbs.
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how many different license plates are available if the license plate pattern consists of 4 letters followed by 3 digits? assume all letters are uppercase and the digits are 0,1,2,...,9.duplicates are okay.
Answers
The total number of different license plates available is the product of the number of arrangements of letters and digits, which is $456,976 \times 1,000 = 456,976,000$.
To determine the number of different license plates available if the pattern consists of 4 letters followed by 3 digits, we need to calculate the total number of possible arrangements of letters and digits.
There are 26 letters in the alphabet, and we can choose any of them for the first letter, any of them for the second letter, and so on. For the first letter, there are 26 choices, and for the second letter, there are also 26 choices. We have 4 letters in total, so the total number of arrangements of letters is $26 \times 26 \times 26 \times 26 = 456,976$.
For the three digits that follow the letters, we have 10 choices for each digit. So the total number of arrangements of digits is $10 \times 10 \times 10 = 1,000$.
Therefore, the total number of different license plates available is the product of the number of arrangements of letters and digits, which is $456,976 \times 1,000 = 456,976,000$. So, there are 456,976,000 different license plates available with the given pattern.
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The Pyramid of the Sun in Mexico is a square pyramid. The base edge is approximately 220 meters, and the height is approximately 70 meters.
What is the approximate surface area of the sides of the pyramid to the nearest thousand square meters?
Answers
The surface area of the square pyramid will be 105768.98 square meters.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of anybody is called the surface area.
Given that:-
The base edge is approximately 220 metersThe height is approximately 70 metersThe surface area of the pyramid will be:-
\(SA\ = \ a^2+2a\sqrt{\dfrac{a^2}{4}+h^2}}\)
SA = 48400 + 440 √17000
SA = 48400 + 57368
SA = 105768.98 square meters
Therefore the surface area of the square pyramid will be 105768.98 square meters.
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NEED QUICKThe sum of x and 3 is the same as the 5 less than 3x. Find x
Answers
Let's begin by identifying key information given to us:
\(\begin{gathered} x+3=3x-5 \\ \text{Put like terms together, we have:} \\ \text{Subtract ''x'' from both sides, we have:} \\ x-x+3=3x-x-5 \\ 3=2x-5 \\ Add\text{ ''5'' to both sides, we have:} \\ 3+5=2x-5+5 \\ 8=2x\Rightarrow2x=8 \\ 2x=8 \\ \frac{2}{2}x=\frac{8}{2} \\ x=4 \end{gathered}\)Brady has been
approved for a home loan on a property he has under contract. The purchase
price is $150,000, and he is required to have $5,250 as a down payment. Which
of the following loan types is Brady most likely getting?
a. Conventional loan
b. ARM loan
c. FHA loan
d. VA loan
e. Fixed loan
Answers
The type of loan that Brady most likely getting is option (a) conventional loan
Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.
ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.
VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.
Therefore, the correct option is (a) Conventional loan
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Find and reduce -4/7 x 2/3
What is the answer to this?
Answers
Answer:
-8/21
Step-by-step explanation:
in class. Graph the following linear,
values to create a picture. The first equation is graphed for you.
Remember:
y = mx + b is the equation of a line
y = # is the equation of a horizontal line
x = # is the equation of a vertical line
y = a/x - hl+ k is an absolute value equation which has a V-shape
y = a (x = h)² + k is a quadratic equation which has a U-shape
Starting point
(-1,-12)
(-19,-)
Equation
y = 2x - 10
y=-3x + 12 +11
y=-(x-16)² - 11
y = 12
y = -10
y=-x+15
y =
y = -15
y = 2x - 12
y=x+5
1
2
y = -6
y = 8
y = −(x − 7)² + 12
y=-15
and quadratic equations between the given x or y-
(x+7)² - 13
y = 10
y = 11
y=-12
y = 12
y = |x-11| + 10
y = 3(x - 2)² - 15
y = 10
x = -5
x = 1
x = 4
x = 11
x = -11
x= -13
y = 3x - 3
y = 8
(14,
(1,
(-19,
(3,
(-13,
(0,
(3,
(-9,
(2,
(-5,
(5,
(-4,
(-5,
(6,
(-3,
(-5,
(9,
(2,
(-2,
L
(
C
)
)
70
J
-)
(-4,
(1,_
)
LLL LL
,8)
8)
9)
8)
-15)
______-15)
J
Ending point
(2,-6)
(-5, ID)
(18,
(3,
HERN V PRANJONSHME
(-11,
2/3/23
177
C
(
r
(0,.
)
)
-
-)
(-)
)
LLL
12)
12)
11)
10)
-10)
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(-3,
(3,_______
Answers
Which number line and equation show how to find the distance from 2 to 5?
Answers
Nancy wrote the expression 3x-12 to represent the relationship in the table of values.use operations to write two equivalent expressions.
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given the expression
3x-12
1)
Writing the expression in an equivalent form
3x-12
Factor out common term 3
3x-12 = 3(x-4)
Thus, 3(x-4) is equivalent to 3x-12.
2)
Writing the expression in an equivalent form
3x-12
Multiply the expression by 2/2
\(3x-12\:=\frac{2}{2}\:\times \:\left[3x-12\right]\)
Therefore, \(\frac{2}{2}\:\times \:\left[3x-12\right]\) is equivalent to 3x-12.
The __________ shows the number of data items with values less than or equal to the upper class limit of each class.
Answers
Answer: Cumulative frequency distribution
Step-by-step explanation: Not entirely sure but I believe you are looking for this definition based on the question. Hope this helps :)
The exam will have true/false and short answer questions.
points each, and the true/false questions are worth two points each. There will be 50 questions we
total of 150 points. How many of each type of question are on the exam?
Answers
Answer:
there could be multiple of either
Step-by-step explanation:
A first number is four more than seven time a second. The sum of the number is 92. Find the number.
Answers
Answer:
11
81
Step-by-step explanation:
x = 7y + 4
x + y = 92
Solve for x in the second equation
x = 92 - y
92 - y = x
Equate the 2 xs
92 - y = 7y + 4 Add y to both sides
92 = 7y+y + 4 Combine
92 = 8y + 4 Subtract 4 from both sides
88 = 8y Divide by 8
88/8 = y
y = 11
===========
x = 7y + 4
x = 77 +4
x = 81
A flange is to be machined at a diameter of 6.77 cm ± 0.01 cm. The process standard deviation is 0.005 cm. What is the process capability ratio? A. 0.67. B. 1.01. C. 0.87. D. 0,34.
Answers
The process capability ratio is approximately 0.67 (option A).
To calculate the process capability ratio, we need to use the following formula:
Process Capability Ratio = (Upper Specification Limit - Lower Specification Limit) / (6 * Process Standard Deviation)
Given the following values:
Upper Specification Limit = Diameter + Tolerance = 6.77 cm + 0.01 cm = 6.78 cm
Lower Specification Limit = Diameter - Tolerance = 6.77 cm - 0.01 cm = 6.76 cm
Process Standard Deviation = 0.005 cm
Plugging these values into the formula, we have:
Process Capability Ratio = (6.78 cm - 6.76 cm) / (6 * 0.005 cm)
Process Capability Ratio = 0.02 cm / 0.03 cm
Process Capability Ratio ≈ 0.67
Therefore, the process capability ratio is approximately 0.67. The correct answer is A) 0.67.
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The overtime rate of pay which is one and a half times the basic rate of
$300 per hour is
0 $1500
O $700
O $450
O $1300
Answers
Answer:
$450
Step-by-step explanation:
To calculate one and a half times, you can multiply $300 by 1.5, which comes out to $450
The table represents the function f(x).
4
0
1
f(x) -4 -3
-
x
If gtx)= 4√ 8, which statement is true?
OA. The y-intercept of g(x) is less than the y-intercept of f(x).
OB. The y-intercept of g(x) is equal to the y-intercept of f(x).
OC. The x-intercept of g(x) is equal to the x-intercept of f(x).
OD. The x-intercept of gtx) is greater than the x-intercept of f(x).
42
96
-1
16
Answers
Answer:I don’t Knowt Try To Answer it yourself
Step-by-step explanation:
What’s the answer ?
Answers
if f(x) = 3*2ˣ + 2 is vertically stretched by a factor of 2, then the new function g(x) is 6*2ˣ + 4.
What is the new function g(x)?
To vertically stretch the function f(x) by a factor of 2, we need to multiply the entire function by 2.
This will stretch the function vertically, making it twice as tall as before.
Therefore, if f(x) = 3*2ˣ + 2 is vertically stretched by a factor of 2, then the new function g(x) is:
g(x) = 2*f(x)
g(x) = 2*(3*2ˣ + 2)
g(x) = 6*2ˣ + 4
So the new function g(x) is 6*2ˣ + 4.
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1. checking account balance $740,000; certificate of deposit $1,120,000; cash advance to subsidiary of $784,000; utility deposit paid to gas company $144. cash balance $enter cash balance in dollars
Answers
The cash balance is $1,076,144.
The cash balance is the sum of the checking account balance, certificate of deposit, and utility deposit, minus the cash advance to the subsidiary.
The balances for the checking account and certificate of deposit are given as $740,000 and $1,120,000 respectively. The balance for the cash advance to the subsidiary is $784,000, and the utility deposit paid to the gas company is $144. However, the question does not provide any information about the current balance in the cash account.
Cash balance = ($740,000 + $1,120,000 + $144) - $784,000
Cash balance = $1,860,144 - $784,000
Cash balance = $1,076,144
Therefore, The cash balance is $1,076,144.
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use the 2 yellow points to write the equation in slope intercept form
Answers
In Euclidean geometry, any three points not on the same line can lie on how many planes?
Answers
Step-by-step explanation:
the question is phrased incorrectly.
the "can" is the problem.
they "can" lie on 3 different planes, even if they are on the same line.
but what 3 points always do in 3-dimensional geometry : they define 1 plane, if they are not on the same line.
it is the minimum of needed information to define a plane : 3 points not on the same line. because they create a triangle, which is a 2- dimensional shape representing its own plane in a 3- dimensional world.
similar to 2-dimensional and 3- dimensional geometry, any 2 points (if they are not identical on the same dot) define 1 line.
Use a sum-to-product formula to show the following. Sin(55°) sin(5°) = sin(65°) use a sum-to-product formula for sine and simplify
Answers
sin(55°) + sin(5°) = sin(65°) using a sum-to-product formula for sine
We can use the sum-to-product formula for sine to show that sin(55°) + sin(5°) = sin(65°). The formula is:
sin A + sin B = 2 sin[(A + B)/2] cos[(A - B)/2]
Substituting A = 55° and B = 5°, we get:
sin(55°) + sin(5°) = 2 sin[(55° + 5°)/2] cos[(55° - 5°)/2]
Simplifying, we get:
sin(55°) + sin(5°) = 2 sin(30°) cos(25°)
We know that sin(30°) = 1/2 and cos(25°) = sin(90° - 25°), so we can substitute these into the expression:
sin(55°) + sin(5°) = sin(90° - 25°)
We also know that sin(90° - 25°) = sin(65°), so we can substitute this into the expression:
sin(55°) + sin(5°) = sin(65°)
Therefore, sin(55°) + sin(5°) = sin(65°) using a sum-to-product formula for sine.
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Given question is incomplete, the complete question is below
Show that sin(55°) + sin(5°) = sin(65°)
use a sum-to-product formula for sine and simplify
Find the real or imaginary solutions of 2x^2 + 3 = 4x by factoring.
Show steps (*30 pts)
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The real or imaginary solutions of 2x² + 3 = 4x by factoring is x1 = (2 - √2) / 2 and x2 = (2 + √2) / 2
Equation
2x² + 3 = 4x
Rearrange to form a quadratic equation2x² + 3 - 4x = 0
2x² - 4x + 3 = 0
Factoring to find real or imaginary solution∆ = (-4)² - (4 × 2 × 3)
= 16 - 24
∆ = 8
√∆ = √8
= 2√2
x1 = -(-4) - 2√2 / (2 × 2)
or
x2 = -(-4) + 2√2 / (2 × 2)
x1 = 4 - 2√2 / 4
or
x2 = 4 + 2√2 / 4
x1 = (2 - √2) / 2
or
x2 = (2 + √2) / 2
Therefore, the real or imaginary solutions of 2x² + 3 = 4x by factoring is x1 = (2 - √2) / 2 and x2 = (2 + √2) / 2
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