Answer: We can simplify the expression by using the identity for the tangent of half an angle:
tan(x/2) = sin(x) / (1 + cos(x))
where x is the angle in radians. We can use this identity by setting x = 56° since 2*28°= 56°.
So, we have:
sin(28°) / (1 + cos(28°)) = tan(56°/2)
We know that 56°/2 = 28°, so we have:
tan(28°)
Therefore, the expression simplifies to a single trigonometric function:
tan(28°)
Step-by-step explanation:
Which expressions are equivalent to the one below? Check all that apply. 21^x/3^x
The only equivalent expression is option (a) [tex]7^x[/tex].
What is expression ?
An expression in mathematics is a group of symbols that represent a statistical correlation or quantity, such as integers, variables, and operators. It may contain exponents, logarithms, and trigonometric functions in addition to mathematical operations like addition, multiplication, multiplication, and division. It may also contain constants, variables, and functions. Expressions can be used in a variety of subjects, including mathematics, calculus, geometry, and statistics, to represent mathematical models, resolve equations, and carry out calculations.
To find equivalent expressions for[tex]21^x/3^x[/tex], we can try to simplify the expression using exponent rules.
21 can be factored as 7*3, so we can write:
[tex]21^x/3^x = (7 × 3)^x/3^x = 7^x × 3^x/3^x = 7^x[/tex]
Therefore, we can see that option (a) 7^x is equivalent to the given expression.
To check the other options:
b) [tex](7/3)^x[/tex] = [tex](7^x)/(3^x)[/tex] which is not equivalent to the given expression.
c) [tex]3^(2x+1)[/tex] can be written as [tex]3^(2x)[/tex] × [tex]3^1[/tex] = [tex](3^2)^x[/tex] × 3 = [tex]9^x[/tex] × 3 which is not equivalent to the given expression.
d) [tex]7^(x-1)[/tex] can be written as [tex]7^x/7[/tex] which is not equivalent to the given expression.
e) [tex](3/7)^x[/tex] is not equivalent to the given expression.
Therefore, the only equivalent expression is option (a) [tex]7^x[/tex].
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The complete question is:
Which expressions are equivalent to [tex]21^x/3^x[/tex]? Check all that apply.
a) [tex]7^x[/tex]
b) [tex](7/3)^x[/tex]
c) [tex]3^(2x+1)[/tex]
d) [tex]7^(x-1)[/tex]
e) [tex](3/7)^x[/tex]
how will the product change if one number is increase by a factor of 12 and the other is decreased by a factor of 4
Using factors, we can conclude that the new product will be 48 time more than the old product.
Define factors?In mathematics, the factor of a number is a divisor of the inputted integer that entirely divides it, leaving no residue. We can use a variety of techniques, including the division method and the multiplication method, to identify a number's components.
Let the product be P.
Let the numbers be a and b.
Now,
P = a × b
According to the question.
Let a is increased by a factor of 12 and b by 4:
P = 12a × 4b
P = 48 × a × b
Hence, we can conclude that the product will increase by a factor of 48.
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127.6÷10 to the power of 5
im not sure if that is how you type it
Answer:
338262.124
Step-by-step explanation:
127.6/10 = 12.76 (depending on how many zero is how much you'll move the decimal to the left)
12.76^5 = 338262.124 because it's 12.76x12.76x12.76x12.76x12.76
-(x+5)³ + 2 = 1
im supposed to be solving cubic equations but im stuck plez help
Answer: X= -4
Step-by-step explanation:
1/5 of a large wall was covered in red paint, 1/10 in blue paint, and 1/4 in green paint. What
percentage of the whole wall is covered in paint (of any colour)?
19%
32%
55%
50%
68%
Answer:
55% of the whole wall is covered in paint of any color.
Step-by-step explanation:
To determine what percentage of the wall is covered in paint, we need to add the fractions of the wall covered by each color of paint and then convert the result into a percentage.
Red paint: 1/5
Blue paint: 1/10
Green paint: 1/4
First, we need to find a common denominator, which is the least common multiple (LCM) of the denominators 5, 10, and 4. The LCM of 5, 10, and 4 is 20. Now, we can convert the fractions to equivalent fractions with a denominator of 20:
Red paint: (1/5) * (4/4) = 4/20
Blue paint: (1/10) * (2/2) = 2/20
Green paint: (1/4) * (5/5) = 5/20
Now, add the fractions:
Total paint coverage = 4/20 + 2/20 + 5/20 = (4 + 2 + 5)/20 = 11/20
To convert this fraction to a percentage, we can divide 11 by 20 and multiply the result by 100:
(11/20) * 100 = 0.55 * 100 = 55%
Thus, 55% of the whole wall is covered in paint of any color.
please solve this fast
Answer:
34
Step-by-step explanation:
5+5+2=12
12+6+3=21
21+8+5=34
Answer:45
Step-by-step explanation:
5+5(8)=45
why am i wasting my time in school?
Answer:
Because you are spending your time doing other things
Step-by-step explanation:
most of the time people waste time in school because they are busy doing other things and they probably don't think school is important.
a way to stop wasting time in school is to pay attention more in class and start developing a desire to learn.
:) i hope this helps lol
Answer:
For more opportunities to go to college, graduating college gets you a degree, the better degree the better job opportunities, the better job opportunities the more money earned. Your in school for money, the best end goal.
Triangle ABC aid dilated by a scale factor of 3. Which is an algebraic representation of the dilation?
Answer:
[tex](3x, 3y)[/tex]
Step-by-step explanation:
The scale factor is 3 so you multiply 3 by the (x,y) to get (3x,3y) as the scale factor
PLS HELP ASP!!!
The state of Colorado is 4 centimeters long and 2 centimeters wide on a map. A cartographer wants to use a scale factor of 3.5 to enlarge the map. What is the area of the enlarged map?
98 cm2
42 cm2
28 cm2
8 cm2
Answer: 98 cm²
Step-by-step explanation:
When a cartographer enlarges a map with a scale factor, both the length and the width are multiplied by the scale factor. In this case, the scale factor is 3.5.
Original dimensions of Colorado on the map:
Length: 4 cm
Width: 2 cm
Enlarged dimensions using the scale factor of 3.5:
Length: 4 cm × 3.5 = 14 cm
Width: 2 cm × 3.5 = 7 cm
To find the area of the enlarged map, multiply the enlarged length and width:
Area = Length × Width
Area = 14 cm × 7 cm
Area = 98 cm²
The area of the enlarged map is 98 cm².
In X8, Erin had the following capital gains (losses) from the sale of her investments: $2,600 LTCG, $24,400 STCG, ($9,600) LTCL, and ($15,600) STCL. What is the amount and nature of Erin's capital gains and losses?
Erin's capital gains are the sum of her long-term capital gains (LTCG) and short-term capital gains (STCG), which is $2,600 + $24,400 = $27,000.
Erin's capital losses are the sum of her long-term capital losses (LTCL) and short-term capital losses (STCL), which is ($9,600) + ($15,600) = ($25,200).
Since Erin's capital gains exceed her capital losses, she has a net capital gain of $27,000 - $25,200 = $1,800.
The nature of Erin's capital gains and losses are as follows:
LTCG: long-term capital gain, meaning the asset was held for more than one year before it was sold.STCG: short-term capital gain, meaning the asset was held for one year or less before it was sold.LTCL: long-term capital loss, meaning the asset was held for more than one year before it was sold.STCL: short-term capital loss, meaning the asset was held for one year or less before it was sold.Paul hits a baseball straight up in the air. The baseball is hit with an initial velocity of 70 ft/s when it is 3.5 ft off the ground. What quadratic function mods the height h of the ball after t seconds in flight?
The quadratic function that models the height h of the ball after t seconds in flight is h(t) = -16t² + 70t + 3.5
Describe Quadratic Function?A quadratic function is a type of function in algebra that involves a variable raised to the power of 2, or squared. The general form of a quadratic function is:
f(x) = ax² + bx + c
where f(x) represents the output of the function for a given input x, a, b, and c are constants that determine the shape and position of the function, and x is the input variable.
The graph of a quadratic function is a parabola, which is a curved shape that opens upwards if the coefficient a is positive, and downwards if the coefficient a is negative. The vertex of the parabola is the point at which the function reaches its minimum or maximum value, depending on the direction of the opening of the parabola. The x-coordinate of the vertex is given by:
x = -b/2a
The height h of the ball after t seconds in flight can be modeled by the quadratic function:
h(t) = -16t² + vt + s
where v is the initial velocity of the ball, s is the initial height of the ball, and -16 is the acceleration due to gravity in feet per second squared.
In this case, we know that the ball is hit with an initial velocity of 70 ft/s and is 3.5 ft off the ground, so we can substitute these values into the equation:
h(t) = -16t² + 70t + 3.5
Therefore, the quadratic function that models the height h of the ball after t seconds in flight is:
h(t) = -16t² + 70t + 3.5
Note that this function is only valid until the ball reaches its maximum height and starts falling back down to the ground.
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(Need help please and thank you!) :)
Step-by-step explanation:
In order to find the f(x) or y value, you have to replace x with the given one in the table:
x = -1,
[tex]y = \sqrt[3]{ - 1 - 7} = \sqrt[3]{ - 8} = - 2[/tex]
.
x = 6,
[tex]y = \sqrt[3]{ 6 - 7} = \sqrt[3]{ - 1} = - 1[/tex]
.
x = 7,
[tex]y = \sqrt[3]{7 - 7} = \sqrt[3]{0} = 0 [/tex]
.
x = 8,
[tex]y = \sqrt[3]{8 - 7} = \sqrt[3]{1} = 1 [/tex]
.
x = 15,
[tex]y = \sqrt[3]{15 - 7} = \sqrt[3]{8} = 2[/tex]
Also, the correct graph is in the 2nd photo, where the root is (7; 0)
Quadrilateral ABCD is translated 5 units up. What are the coordinates of
quadrilateral A'B'C'D?
A
D
A(-5, 5)
D(-5, 1)
B' Y
G
C₁
8(-1,5)
C(1, 2)
OA. A'(-5, 0), B'(-1,0), C'(-1, -3),
D'(-5,-4)
OB. A'(-5, 10), B'(-1, 10), C'(-1,7),
D'(-5, 6)
C. A'(-10, 10), B'(-6, 10), C'(-6, 7),
D'(-10, 6)
D. A'(-10, 5), B'(-6, 5), C'(-6, 2),
D'(-10, 1)
Answer:
it should be B but I could be wrong
Step-by-step explanation:
B
Alexa claims she can use counting
by 8 to find the fifth multiple of. Is Alexa correct? Explain.
Answer:
Yes, Alexa is correct.
Step-by-step explanation:
Counting by 8 means adding 8 repeatedly. The first multiple of 8 is 8 (1 x 8), the second multiple is 16 (2 x 8), the third multiple is 24 (3 x 8), the fourth multiple is 32 (4 x 8), and the fifth multiple is 40 (5 x 8). So, by counting by 8 five times, Alexa can find the fifth multiple of 8 which is 40.
Solve the problem in the picture please!
The answer choices are
A) 5
B) 2
C) 200
D) 100
Find the expression for both A: (x+4) (2x - 1)
Answer:
2x^2+8x-4
Step-by-step explanation:
4 1/5 -5/3 subtract
how do i do this eqation
Answer:
38/15
Step-by-step explanation:
4 1/5 - 5/3
4 1/5 = 21/5
21/5 - 5/3 = 63/15 - 25/15 = 38/15
So, the answer is 38/15
Describe the transformations that would map the graph
of f(x) = x^2 + 1 to the graph of g(x) = (x − 3)^2 − 2.
The graph of [tex]g(x)[/tex] is the result of taking the graph of [tex]f(x)\\[/tex], shifting it right three units and down two units.
The federal government has developed the body mass index (bmi) to determine ideal weights. a person's bmi is directly proportional to his or her weight in pounds and inversely proportional to the square of his or her height in inches. (a bmi of 19 to 25 corresponds to a healthy weight.) a 6-foot-tall person weighing 177 lb has bmi 24. find the bmi (to the nearest whole number) of a person whose weight is 176 lb and whose height is 77 in.
The BMI of a person whose weight is 176 lb and whose height is 77 inches is 21.
First, let's use the given information to find the constant of proportionality in the BMI formula:
BMI = k × (weight in pounds) / (height in inches)²
When the 6-foot-tall person weighing 177 lb has a BMI of 24, we can plug in the values and solve for k:
24 = k ₓ 177 / (72²)
k = 24 ₓ (72²) / 177
k ≈ 9.94
Now we can use this value of k to find the BMI of the person whose weight is 176 lb and whose height is 77 in:
BMI ≈ 21
BMI = 9.94 ₓ 176 / (77²)
Therefore, the BMI (to the nearest whole number) of the person is 21, which falls within the healthy weight range of 19 to 25.
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6+r=2r+3 how to solve this
Answer:
soln
6+r =2r+3
6-3=2r-r
3=r
ans r=3Given RP = 22, RA = 6, and PQ is tangent to .R at Q, find PQ.
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{22}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{PQ} \end{cases} \\\\\\ PQ=\sqrt{ 22^2 - 6^2}\implies PQ=\sqrt{ 484 - 36 } \implies PQ=\sqrt{ 448 }\implies PQ\approx 21.17[/tex]
Tom has $160,000 in his retirement account. It is earning an APR of 4.57%. What would be the monthly yield on the account for a 30-year period?
The monthly interest yield on Tom's retirement account for a 30-year period would be $637.71.
Assuming that the interest is compounded monthly, the monthly yield on Tom's retirement account with an APR of 4.57% for a 30-year period can be calculated using the formula:
Monthly Yield = (Principal × Monthly Interest Rate) ÷ (1 - (1 + Monthly Interest Rate[tex])^{(-Number of Months)}[/tex]
Here, Principal = $160,000
APR = 4.57%,
Number of Months = 30 years ÷ 12 months/year = 360 months.
First, we need to convert the APR to a monthly interest rate by dividing it by 12:
Monthly Interest Rate = 4.57% × 12
Monthly Interest Rate = 0.3808%
Monthly Yield = (160000 × 0.3808%) ÷ (1 - (1 + 0.3808%[tex])^{-360}[/tex]
Monthly Yield = $637.71
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Screenshot, I WILL GIVE 20 POINTS AND BRAINLIST!!!!
Answer:
0.7 = 0.70, so 0.17 < 0.70
A multiple-choice test question has six possible choices.
a) If you randomly select one of the choices, what is the probability that you select the correct choice?
b) If you randomly select one of the choices, what is the probability that you select an incorrect choice?
c) If you can eliminate three of the six choices and randomly select one of the remaining choices, what is th
probability that you select the correct choice?
d) If you can eliminate three of the six choices and randomly select one of the remaining choices, what is the
probability that you select an incorrect choice?
a) P(correct) =
b) P(incorrect)
113
(Type an integer or a simplified fraction.)
6
-
(Type an integer or a simplified fraction.)
5
The probabilities that select an incorrect choice are
a) P(correct) = 1/6 b) P(incorrect) = 5/6 c) P(correct) = 1/3 d) P(incorrect) = 2/3.
What is probability?
Probability is a measure of the likelihood or chance that a particular event will occur. It is a way of quantifying uncertainty, and is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain.
What are events in probability?
In probability, an event refers to an outcome or a set of outcomes of a random experiment or a process. A random experiment is an experiment or a process that has multiple possible outcomes, and the outcome of the experiment is uncertain or unpredictable.
According to given information:a) The probability of selecting the correct choice from six possible choices is 1 out of 6, or 1/6, since there is only one correct answer among the six options.
b) The probability of selecting an incorrect choice from six possible choices is 5 out of 6, or 5/6, since there are five incorrect answers among the six options.
c) If three choices can be eliminated, then there are only three options left, with one correct answer among them. Therefore, the probability of selecting the correct choice from the remaining options is 1 out of 3, or 1/3.
d) Similarly, if three choices can be eliminated, then there are three options left, with two incorrect answers among them. Therefore, the probability of selecting an incorrect choice from the remaining options is 2 out of 3, or 2/3.
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Calculate the area of the shape below
Answer:
Step-by-step explanation:
Area of rectangle+area of triangle
hope the picture helps
What is the solution to x^3+4x^2 >x+4?
Answer:
Step-by-step explanation:
it’s equals 0 I think
PLS HELP :))
The property taxes on a house were $1265
. What was the tax rate if the house was valued at $115,000
? Follow the problem-solving process and round your answer to the nearest hundredth of a percent, if necessary.
The tax rate of a house valued at $115,000 with a property tax of $1265 is 110%. or $110 per $1,000 of property value.
What is property tax?The property tax is the levy imposed on the assessed value of the property of an individual or corporation.
Property tax is usually levied as a percentage of the assessed value.
Data and Calculations:Property tax = $1265
House value - $115,000
Tax rate = 110% [tex](\$1265\div\$115000 \times 100)[/tex]
Thus, the tax rate of a house valued at $115,000 with a property tax of $115,000 is 110%. or $110 per $1,000 of property value.
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Which statement best reflects how the cultural setting influences
Sigismondo's attitude in the excerpt from "The City Lost in the Snow"?
A
B
C
D
The competition between snow shovelers makes Sigismondo
excited to prove himself to Marcovaldo.
The fast-paced urban environment explains why workers like
Sigismondo must keep the city moving.
The scarcity of jobs makes Sigismondo appreciate the temporary
employment the snow provides.
The industrialization of the city leads Sigismondo to feel ambitious
about his future opportunities.
In the excerpt from "The City Lost in the Snow," the statement that best reflects how the cultural setting influences Sigismondo's attitude is: C.
The scarcity of jobs makes Sigismondo appreciate the temporary employment the snow provides. T
his statement reflects the importance of the cultural setting, as it shows that Sigismondo values the opportunity to work and earn money, even if it's temporary, due to the scarcity of jobs in the city.
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x^2-6x-16 when factored is
Answer: (x+2)(x-8)
Step-by-step explanation:
x^2-6x-16
x^2-8x+2x-16
x(x-8)+2(x-8)
(x+2)(x-8)
Here is another riddle:
-The sum of two numbers is less than 2
-If we subtract the second number from the first, the difference is greater than 1
The riddle can be represented by a system of inequalities. Write a inequality for each statement.
Name a possible (ordered pair) solution to the riddle.