The base is 5 and the exponential is 2. This can be written in expanded form as 5 multiplied by 5, which is equal to 25. In standard form, this can be written as 52, which is shorthand for the same calculation.
Base: 5
Exponent: 2
Expanded form: 5 x 5
Standard form: 52
An exponential expression is a mathematical expression that uses the operation of exponentiation. In this expression, one number, known as the base, is raised to the power of another number called the exponent. To write an exponential expression, choose a number between 0 and 10 for the base and another number between 0 and 10, different from the base, for the exponent. Then, write the exponential expression in expanded form and standard form. For example, if the base is 5 and the exponent is 2, then the expression can be written in expanded form as 5 multiplied by 5, which is equal to 25. In standard form, this can be written as 52, which is shorthand for the same calculation. This expression can be used to represent any number or calculation that can be written in exponential form.
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For each pair of triangles below, decide whether or not they are similar. If they are similar, write the similarity
statement (
ABC
. . .) and the similarity property (
SSS SAS , ,
etc. ) that proves it. If they are not similar,
write “not ” and explain why. NOTE: Pictures are likely not drawn to scale!
a) The triangles are not similar, as they have different angle measures.
b) The triangles are similar by the SAS theorem.
c) The triangles are similar by the SSS theorem.
What are similar triangles?Similar triangles are triangle that share these following two features:
Congruent angle measures.Proportional side lengths.For item a, we have that the angle measures are given as follows:
49º, 38º and 180 - (49 + 38) = 93º.92º, 49º and 39º.Different angle measures, hence not similar.
For item b, we have that the side lengths are proportional, as:
13.2/6 = 15.4/7
As the angle between these two sides has the same measure of 90º, the SAS theorem proves that these two triangles are congruent.
For item c, the side lengths are proportional, as:
9.9/3 = 3.3.13.2/4 = 3.316.5/5 = 3.3.Hence the triangles are similar by the SSS theorem.
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The ubfield of pychology are related to each other becaue they hare a common goal, which i
Each of psychology's subfields or subtypes takes a unique approach to considering issues and topics. Despite the fact that they each have their unique areas of interest, they all strive to understand and research human mind and behavior.
Psychology's subfields are always expanding and changing due to the wide variety of human behavior. Many schools and universities offer courses and degree programs in some of these subfields, which have established themselves as popular subjects of study.
Each category of psychology denotes a distinct field of research centered on a certain subject. Psychologists frequently choose to focus their careers on one of these.
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Your car's gas mileage is an average of 25 miles per gallon. Let g represent the number of gallons of gas you need to put in your car such that
g (m)=where m is the number of miles you drove. The total cost of filling your car's gas tank is C(x) where C is cost in dollars and x is the number
of gallons purchased.
What does the expression C (g (m)) represent?
The expression C(g(m)) represents the total cost of filling the car's gas tank based on the number of miles driven.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
It is given that the car's gas mileage is 25 miles per gallon, then the number of gallons of gas needed to fill the car's tank can be found by dividing the number of miles driven by the gas mileage.
The expression for this is g(m) = m / 25 where m is the number of miles driven.
The total cost of filling the car's gas tank is represented by the expression C(x) where C is the cost in dollars and x is the number of gallons purchased.
So when g(m) is substituted into C(x), C(g(m)) is obtained which represents the total cost of filling the car's gas tank based on the number of miles driven.
Therefore, this expression is the cost of filling the gas tank given the number of miles driven.
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Tell whether the ordered pairs are a solution of the system of linear inequalities
Pair 1: (-3, -1)
Pair 2: (1, 0.5)
The solution of the system of linear inequalities is the intersection of both graphs and the coordinates of the intersection are neither at pair 1 nor at pair 2.
What is linear inequality?According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).
Given the graph for a system of linear inequalities,
the shaded region for the inequalities is below the dashed line,
for the solution of the system of linear inequalities,
the point where both the pair of lines intersect is the solution of the equations,
the equation for a dashed line from the graph is y < - x - 2
and the equation for the second line is y ≤ x/2 + 5
from the graph, the intersection point does not lie on any of the given pairs.
Hence the solution of the system of linear inequalities neither at Pair 1 nor at Pair 2
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Write a polynomial function f of leat degree that ha a leading coefficient of 1 and the given zero −2, 3, 6
A polynomial function of least degree with a leading coefficient of 1 and zeroes at -2, 3, 6 is given by: "f(x) = (x + 2)(x - 3)(x - 6) = x^3 - x^2 - 9x - 12)".
According to the Factor Theorem, k is a zero of a given polynomial function f (x), if and only if (x - k) is a factor of the given polynomial function f(x).
Since -2,3 and 6 are zeros to be given of f (x), so
you need to put -2,3 and 6 in (x - k)
such as
f (x) = { (x - k) (x - k) (x - k) }
= { (x - (-2) (x - 3) (x - 6) }
= {(x+2) (x-3)(x-6) }
= {( x^3 - x^2 - 9x - 12) }
'f(x) = { (x^3 - x^2 - 9x - 12) }' is the required polynomial function.
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36. Business A jeweler plans to produce a ring made of silver and gold. The price of
gold is about $25 per gram. The price of silver is approximately $.40 per gram. She
considers the following in deciding how much gold and silver to use in the ring.
The total mass must be more than 10 g but less than 20 g.
•The ring must contain at least 2 g of gold.
The total cost of the gold and silver must be less than $90.
a. Write and graph the inequalities that describe this situation.
b. For one solution, find the mass of the ring and the cost of the gold and silver.
The border line is so much shaded below the inequality symbol (shown in purple).
what is inequality ?A relationship among two expresses or values that is neither equal in mathematics is referred to by the term inequality. Thus, unequal results from imbalance. In arithmetic, an inequality explains the links between two non-equal numbers. Egality nor disparities are not the same. Were using the not equal symbol most usually when two values are just not equal (). Values of any size can be contrast using a variety of discrepancies. By changing the two sides till only the variables are left, many straightforward inequalities can be solved. However, a variety of factors support injustice: Both sides' negative values are split or added. Change the left and the right.
given
Gold costs $25 a gram, therefore y grams would cost $25. Because silver costs $0.40 per gram, x grams will cost you $0.0040. If the entire cost of the ring must be less than $90, then 25y+0.40x90, making the cost of the ring (25y+0.40x) dollars. For y, resolve this inequality: 25+0.40<90/25−0.40+90
Take 0.40 off of both sides.
<−0.016+3.6
25y+0.40x y900.40x+900.016x+3.6 = 25y+0.40x y900.40x+903.6
Remove 0.40x from both sides.
Add 25 to both sides.
The boundary line is therefore defined as =0.016+3.6 y=0.016x+3.6, which has a y-intercept of 3.6 and a slope of 0.016 0.016.
The border line is so much shaded below the inequality symbol (shown in purple).
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Is rectangle DABC the result of a dilation of rectangle HEFG with a center of dilation at the origin? Why or why not?
Yes, because both figures are rectangles and all rectangles are similar.
What is rectangles?A rectangle is a four-sided polygon with four right angles. It is one of the most common shapes in both two-dimensional and three-dimensional geometry and can be found in everyday objects such as windows, doors, and tables. Rectangles are also found in nature, like rivers, beaches, and mountains. The area of a rectangle is the product of its length and width, while the perimeter is the sum of its four sides. Rectangles are also special cases of other shapes such as squares and parallelograms, as they are the same shape but with different lengths of sides.
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m+1/m-1 -m-1/m+1 + 4m/m^2 +1
The expression can be simplified to:
(m^2 + 1 - m^2 - 2m + m^2 + 2m + 1) / (m^2 + 1) + 4m / (m^2 + 1)
= (4m) / (m^2 + 1)
So the final simplified form of the expression is (4m) / (m^2 + 1)
What are the 9 types of solution with example?.
9 types of solution are gas in gas, liquid in liquid, solid in liquid, solid in solid, gas in liquid, liquid in gas, solid in gas, gas in solid and supercritical fluid.
There are many different types of solutions, but here are 9 common types with examples:
Gas in gas: air (a mixture of gases)
Liquid in liquid: oil and vinegar salad dressing
Solid in liquid: sugar in water
Solid in solid: alloy of gold and silver
Gas in liquid: carbonated water
Liquid in gas: fog (water droplets in air)
Solid in gas: smoke (solid particles in air)
Gas in solid: a gas bubble in a solid piece of plastic
Supercritical fluid: carbon dioxide in a supercritical state (above its critical temperature and pressure)
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What is the boundary line for the linear inequality 2x 3y 6?.
A point (x1, y1) is said to satisfy the inequality ax + by ≤ c if a(x1) + b(y1) ≤ c. The graph of a linear inequality is the set of all points in the plane which satisfy the inequality.
Now, the given equation is 2x + 3y ≥ 6
We can find multiple points (x, y) that satisfy the given inequality. For now, we can take the point (1,2).
To check if (1,2) satisfies the inequality, put x = 1, y = 2 in the inequality.
2 + 6 ≥ 6
8 ≥ 6, which is true.
This line cuts the plane in half. One half contains all points (x, y) with 2x + 3y > 6 and the other half contains all points with 2x + 3y < 6.
To find which half is which, we need only check one point on one side of the line. (if the line does not cut through (0, 0), we can check that point easily.) In this case we find that 2(0) + 3(0) < 6.
Therefore the solution to the inequality 2x + 3y ≥ 6 is the half plane not containing (0, 0) shaded below. We can also represent it with arrows as in the diagram on the right.
Since the region includes the points along the line 2x + 3y = 6, we draw a
solid line. We use a dotted line when we want to indicate strict inequality as in the solution set to 2x + 3y > 6 shown in the diagram.
Thus, this is the boundary line for the given inequality.
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How do you describe the nature of the roots of a quadratic equation if b2 4ac 0?.
If the discriminant b² - 4ac = 0 for a quadratic equation ax² + bx + c = 0, it means that the nature of roots of the equation has one real and identical (repeated) root.
When the discriminant is equal to zero, the square root of the discriminant will be zero, and the equation will have one solution for x, regardless of the values of a, b and c.
This can be observed in the quadratic formula, where the square root of the discriminant is used to determine the solutions of x. In this case the equation will be reduced to:
x = -b/2a
It's also possible to observe this by factoring the equation, in this case the equation can be factored as (x - r)^2 = 0, where r is the common root. This means that the graph of the equation will touch the x-axis only once.
In summary, when the discriminant b² - 4ac = 0, the roots of the quadratic equation are real and identical (repeated).
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2. The table shows values that represent a function. x –2 –3 6 7 5 y 4 2 1 3 4 Part I: Write values that represent the inverse of the function represented in the table above.
The values that represent the inverse of the function which is represented in the table above include the following:
x 4 2 1 3 4
y -2 -3 6 7 5
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should interchange (swap) both the input value (x-value) and output value (y-value). This ultimately implies that, the inverse relation of any function has its input value (x-value) and output value (y-value) interchanged (swapped) as follows;
x y
4 -2
2 -3
1 6
3 7
4 5
In conclusion, we can logically deduce that the above inverse relation is not a function because the same input value (4) appears more than once with different output values (-2 and 5).
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-(5/6)?
A:-6/5
B:5/6
C:6/5
Answer: -5/6, none of your choices
Step-by-step explanation:
-(5/6) = -5/6
None of your choices
Samantha and Phil share some money in the ratio 3:5.
Phil receives £235.
Calculate how much money was shared.
Please help
If Phil received £235 in the ratio 3:5, we can use this information to find out how much money was shared in total.
We know that the ratio of Samantha's share to Phil's share is 3:5.
This means that for every 3 parts of the total money that Samantha gets, Phil gets 5 parts.
We can use this information to set up a proportion:
(Samantha's share) / (Phil's share) = (3) / (5)
We know that Phil's share is £235, so we can substitute that into the proportion:
(Samantha's share) / (235) = (3) / (5)
To find the total amount of money shared, we can cross-multiply and divide:
Samantha's share = (3/5) * 235
Samantha's share = 141
To find the total amount of money shared, we can add the amount Samantha received to the amount Phil received:
141 + 235 = £376
Therefore, £376 was shared in total.
may i please get a step-by-step I need for my finals? it would be super helpful.[tex]Solve |h+3|<5. Write the solution set using set-builder notation.[/tex]
The solution for the absolute function is h < 2.
What is an absolute function?The variable in the absolute value bars makes up an essential algebraic function known as the absolute value function. The most widely used version of the absolute value function is f(x) = |x|, where a = 1 and h = k = 0. The general form of this function is f(x) = a |x - h| + k.
When we extend the absolute value function f(x) = |x|, we can write it as x if x 0 and -x if x 0 since the range of this function, f(x) = |x|, is always non-negative.
The function will be solved as,
| h + 3 | < 5
h + 3 < 5
h < 5 - 3
h < 2
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What is the common factor of each term in the expression 2b 1 5b?
Answer:
the common factor is b since it is divisible by both 2b and 5b
Step-by-step explanation:
Janice ha a coin collection that began with 26 coin. Since then, he ha been adding to her collection at a rate of 5 coin every 3 month
The equation that relates the number of coins, y, in Janice's collection x months since she started adding to her collection is y = 26 + 5/3 x In the context of this problem, the y-intercept is the initial number of coins that Janice had in her collection while the slope is the rate at which Janice is adding to her collection which is 5/3.
Part A
The equation for the number of coins, y, in Janice's collection x months since she started adding to her collection is the total amount of coins she has and can be expressed as
y = 26 + 5/3 x
where y is the total number of coins, and x is the number of months.
Part B
The y-intercept of the equation is the point where the line of the equation crosses the y-axis. In this case, the y-intercept is the point (0,26) which means that when x = 0, the number of coins in Janice's collection is 26. This is the initial number of coins that Janice had in her collection before she started adding to it.
The slope of the equation is the rate of change of the dependent variable (y) with respect to the independent variable (x). In this case, the slope of the equation is 5/3, which means that for every 3 months that pass, the number of coins in Janice's collection increases by 5. So the slope is the rate at which Janice is adding to her collection.
The problem seems incomplete. It must have been
"Janice has a coin collection that began with 26 coins. Since then, she has been adding to her collection at a rate of 5 coins every 3 months. Part A Write an equation that relates the number of coins, y, in Janice's collection x months since she started adding to her collection. Part B In the context of this problem, interpret and explain the y-intercept and slope of the graph of the equation."
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The scatter plot shows the relationship between the average number of nightly customers and the number of months since a restaurant opened. The equation represents the linear model for this data. Y = 5x + 120 what does the number 120 in the equation mean in this context?.
The number 120 symbolizes the restaurant that has been open for 120 months.
Use Slope-intercept form
The equation of the straight line is provided by:
y =mx+ b
m stands the slope of the line
b stands for the initial value or y-intercept.
As per the information:
The scatter plot displays the association between the average number of nightly consumers and the number of months since a restaurant opened.
The equation describes the linear standard for these details
y = 5x + 120
Where,
y denotes the number of months since a restaurant opened and,
x denotes the average number of nightly customers.
We have to discover the number 120 in the equation indicate in this context.
On analogizing provided equation with we have;
m=5
b= 120
means y(0) = 120
and
Thus, The number 120 symbolizes the restaurant that has been open for 120 months.
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Three forces with magnitudes of 80 pounds, 95 pounds, and 125 pounds act on an object at angles of 30°, 45°, and 120°, respectively, with the x-axis. Find the direction and magnitude of the resultant of these forces. (Round your answers to one decimal place.)
To find the direction and magnitude of the resultant of these three forces, we can use the law of cosines and the law of sines.
First, we need to resolve each force into its x and y components using trigonometry.
F1x = 80 * cos(30) = 69.28
F1y = 80 * sin(30) = 40
F2x = 95 * cos(45) = 67.08
F2y = 95 * sin(45) = 67.08
F3x = 125 * cos(120) = -62.5
F3y = 125 * sin(120) = -106.6
Then we can find the x and y components of the resultant force by adding the x and y components of each force respectively.
Rx = F1x + F2x + F3x = 69.28 + 67.08 - 62.5 = 74.86
Ry = F1y + F2y + F3y = 40 + 67.08 - 106.6 = 0.48
Finally, using these values we can use the law of cosines to find the magnitude of the resultant force:
R = sqrt(Rx^2 + Ry^2) = sqrt(74.86^2 + 0.48^2) = sqrt(5633.79) = 75.24
And we can use the law of sines to find the direction of the resultant force:
theta = atan2(Ry, Rx) = atan2(0.48, 74.86) = 0.01
Therefore, the magnitude of the resultant force is 75.24 pounds and the direction of the resultant force is 0.01 degrees.
What is the solution to the system?.
A collection of values for a variable that simultaneously fulfil each equation is the solution to a system of equations.
A set of two linear equations with two variables is a system of linear equations.
1. Examine the two algebraic methods of substitution and elimination for solving systems of linear equations.
2. Visualize systems of linear equations to better grasp when they have a single solution, none at all, or an unlimited number of solutions.
3. Examine algebraic techniques for determining the quantity of solutions for systems involving two linear equations.
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Can anyone please help me w this question?
Answer:
the picture is blurry I can not see the question to help you!
5. What is the missing number?
5,600 ÷
= 80
6. Kenji needs to make 525 storage
boxes for a move that is 72 days
away. If he wants to make about the
same number of boxes each day,
about how many boxes should he
make each day? Find compatible
numbers to estimate.
5. 70
6. not sure sorry :/
What is the product of two mixed fractions?.
The Product of two mixed fractions is always greater than 1.
Now, According to the question;
1. Convert the mixed number into an improper fraction.
2: Multiply the numerators of the fraction and multiply the denominators of the fraction.
3: Convert it into simplified form if required.
A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
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Colton would like to bike 200 miles. Let
h be the number of hours it will take
Colton to bike this distance. Solve a
proportion for h. Round to the nearest
tenth of an hour.
Answer:
Hmmm, I do not know, but thanks for asking!
Step-by-step explanation:
...
Answer:
11.11 hours
Step-by-step explanation:
Average Bike Speed on Flat Terrain: 18 mph
So Colton can travel 200 miles in 200 / 18 = 11.11 hours
What is the inverse function of f/x )= 3x?.
The inverse of y = 3x is f⁻¹(x) = 1/3x.
The inverse is a function or an operation which reverses the order of operation of another function or an operation”.
There are a few steps to find the inverse of a number:
Write the number as the denominator of a fraction that has 1 as a numerator to find the reciprocal of an integer.Place a decimal number as the denominator of a fraction with 1 as the numerator, then divide to calculate the reciprocal of a decimal.Reverse the placement of the numerator and denominator for the reciprocal of a fraction.We will be using the concept of inverse function to solve this.
Given that, y=3x
Let f(x) =y=3x
Switch x and y
x=3y
Express y in terms of x.
y = 1/3x
From the definition of the inverse function. f(x)=y⇒x=f⁻¹(y)
⇒ f⁻¹(y)=1/3x
Thus, the inverse of y = 3x is f⁻¹(x)=1/3x.
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Draw a model to compare 1/3 and 3/5
3/5 is greater than 1/3
What is the fraction?
A fraction is a way of representing a number that is not a whole number. It consists of two parts: a numerator and a denominator. The numerator represents the number of equal parts of a whole, and the denominator represents the total number of parts in the whole.
One way to compare the fractions 1/3 and 3/5 is to find a common denominator between them. In this case, the least common multiple of 3 and 5 is 15. So, you can convert 1/3 to 5/15 and 3/5 to 9/15. Now, you can compare the two fractions by looking at their numerators: 5 and 9. Since 9 is greater than 5, you can say that 3/5 is greater than 1/3.
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What is the solution of the equation 2x y 5 and 3x 2y 4?.
On solving the linear equations 2x + y = 5 and 3x - 2y = 4 we get x = 2 and y = 1.
Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.
The set of equations given are linear equations that can be solved simultaneously to find the values of variables x and y.
2x + y = 5------->(1)
3x - 2y = 4------->(2)
Multiply equation (1) by 2 and add to equation (2)
4x + 2y = 10
3x - 2y = 4
7x + 0 = 14
7x = 14
x = 2
Substituting x = 2 in (1) we get
2(2) + y = 5
y = 5 - 4 = 1
y = 1
Therefore on solving the system of linear equations simultaneously the values of x and y obtained are 2 and 1 respectively.
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You invest $1,000 into your retirement account. Your money earns 12% per year (in other words, your money grows 12% per year). What exponential function below represents this situation?
Answer:
Option 3 [tex]f(x) = 1,000 x (1.12)^{x}[/tex]
Step-by-step explanation:
10. Given that∢DAB and∢DCB are right angles and m∢ABD = 42°, what is the measure of ACB? (show work)
If ∡DAB and ∡DCB are right angles and m∡ABD = 42°, then the measure of arc ACB is 264°.
What is an arc?
An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve's arc is a component.
The angles ∡DAB and ∡DCB are right angles.
The measure of ∡ABD = 42°
It can be seen that ∠ABD is inscribed angle of arc AD, so the measure of arc AD is two times the measure of ∠ABD.
AD = 42° × 2 = 84°
It can also be seen that segment DB is diameter of given circle as inscribed angle of diameter is a right angle.
Since segment DB is diameter of given circle, so measure of arc DCB would be equal to half the measure of 360 degrees.
DAB = 360°/2
DAB = 180°
ACB = AD + DCB
ACB = 84° + 180°
ACB = 264°
Therefore, the measure of arc ACB is 264°.
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if tan 0 =-3/4 and 0 is in quadrant IV, what is cos 20 & tan 20
Using Trigonometric ratios, Tan(20 ) = -24/7 and cos(20) = 7/25
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
It can be simpler to use a calculator when necessary. (See under)
The reference angle will be less than 45° since the magnitude of the tangent is less than 1. If the angle is less than 90 degrees when doubled, it will remain in the fourth quadrant, where the tangent is negative and the cosine is positive.
Additionally, you can use the identities.
cos(2) is equal to (1 - tan()2)/(1 + tan()2).
cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)
cos(2θ) = 7/25
Tan(2)=2tan()/(1 -tan(2)2) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)
tan(2θ) = -24/7
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