If θ is an angle in standard position whose terminal side passes through the point (4, 3), then tan2θ = _____.



3/2


24/7


7/24


21/32

Triangle proportionality theorem is used for finding the length of the missing side of the triangle .

For example , let's take a question to solve.

We have to find the value of x, in the given dig.

If DEbar || BCbar , then AD/DB = AE/EC

The lines QR¯¯¯¯¯  and  ST¯¯¯¯¯ are parallel.

Therefore, by the Triangle Proportionality Theorem,

PS/QS=PT/RT

Substitute the values and solve for x .

6/2=9/x

Cross multiply.

6x=18

Divide both sides by 6 .

6x/6=18/6x=3

The value of x is 3 .

Therefore , the missing side of the triangle is 3

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Answer:

The 5 in 8523 is 10x greater than the 5 in 9852.

Step-by-step explanation:

Note the place value of the two number's digit 5:

8523: Hundreds place value.

9852: Tens place value.

10 x 10 = 100 ∴ The 5 in 8523 (hundreds place value) is 10x greater than the 5 in 9852 (tens place value).

~

The sum of the monthly payments is $2880 and the fee charged for the layaway is $280.

They sell a $2,600 stereo system on a nine-month layaway plan.

The monthly payment is $320.

The sum of the monthly payments can be calculated as follows:

sum of monthly payment = 320 × 9

sum of monthly payment = $2880

Therefore, the fee charged for the layaway plan can be calculated as follows:

fee charged for the layaway = 2880 - 2600

fee charged for the layaway = $280

Therefore,

sum of monthly payments = $2880

Fee charged for the layaway =  $280.

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Answer:

y+3= -4x

Step-by-step explanation:

general equation is (y-y1) = m(x-x1)

m=rise/run=  -4/1 (is negative because looking from left to right on the graph it goes downward)

pick any point on the line to put in. the equation for example (0,-3)

y+3= -4x

Answer:

The surface area of the similar prism is 56 square inches

Step-by-step explanation:

Given surface area of prism, A = 224 square inches

The total surface area of a triangular prism = 2 x Area of triangle + ph

Area of triangle = ¹/₂bh

Where;

b is the base of the prism

h is the height of the prism

p is the perimeter of lateral surfaces

Area of prism involves the product of the dimensions, if the new dimensions is 1/4 the original dimensions;

Product of original dimensions = 224 square inches

1/4 of the product of original dimensions = 1/4 x 224 square inches

= 56 square inches

The surface area of the similar prism = 56 square inches

Thus, the surface area of the similar prism is 56 square inches

Step-by-step explanation:

4×4×4=64

so the forth cube number is 64

Answer:

23.6 m

Step-by-step explanation:

In a right-angled triangle, a ² + b ² = c ²

b² = 10² - 8.8²

100 - 77.44

b = 4.75

perimeter = 4.75 + 8.8 + 10 = 23.55 = 23.6 m to nearest tenth

Answer:

The answer is 23.5m to 1 d.p

Step-by-step explanation:

c²=a²+b²

b²=c²-a²

b²=10²-8.8²

b²=100-77.44

b²=22.56

√b²=√22.56

b=4.7m

Perimeter =a+b+c

P=8.8+4.7+10

P=23.5

P=23.5m to 1 d.p

The area of the shape that the robot painted is 10 square units.

To calculate the area of the shape that the robot painted, we can use the method of triangulation. By connecting consecutive points in the list, we can form a series of triangles. The sum of the areas of these triangles will give us the total area of the shape.

The points provided are: (1, 1), (-1, 3), (-3, 3), (-3, 1), and (-2, -2).

Connecting these points, we can form four triangles: (0, 0), (1, 1), (-1, 3); (0, 0), (-1, 3), (-3, 3); (0, 0), (-3, 3), (-3, 1); (0, 0), (-3, 1), (-2, -2).

Calculating the area of each triangle using the formula for the area of a triangle (base multiplied by height divided by 2), we find the areas to be: 1.5, 3, 2.5, and 3 respectively.

Summing up these areas, we get 1.5 + 3 + 2.5 + 3 = 10 square units.

Therefore, the area of the shape that the robot painted is 10 square units.

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Answer:

a = 3

Step-by-step explanation:

since the parabola passes through (7, 27 ) then te coordinates of the point make the equation true.

substitute x = 7 and y = 27 into the equation and solve for a

27 = a(7 + 2)(7 - 6) = a(9)(1) = 9a ( divide both sides by 9 )

3 = a

Answer:

b must be positive

Step-by-step explanation:

if a is less than -1

that means to get smaller numbers

b needs to be positive

so that when a is multiplied by b you would have

numbers that are more negative

Answer:

b > 1

Step-by-step explanation:

Given:

Substituting a = -1 into ab < a

⇒ (-1)b < -1  

⇒ -b < -1

⇒ b > 1

If a < -1 then a is negative.  If ab < a then ab is also negative.  

In order for ab to be negative (when a is negative) b must be positive.

For ab < a then b > 1.

Proof

If b = 0.5 and a = -1.5 then ab = -0.75

As -0.75 > -1.5 then ab > a so this cannot be true.

If b = 1.5 and a = -1.5 then ab = -2.25

As -2.25 < -1.5 then ab < a so this is true.

Therefore b > 1

The age of the twins is 13 years old.

These are equations that consists of unknown variables and equations.

Let the age of Johnson twins be x

Let the age of their older sister be y

If the Johnson twins were born six years after their older sister, then;

x = y + 6

If this year, the product of the three siblings ages is exactly 3166 more than the sum of their ages, then;

xy = x+y+3166

Substitute the first equation into the second

x * x * (x+6) = x + x + (x+6) + 3166

x² * (x+6) = 3x + 3172

x³ + 6x² = 3x + 3172

x³ + 6x² - 3x - 3172 = 0

x = 13

Therefore the age of the twins is 13 years old.

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Answer:

44.80

Step-By-Step Explanation:

Ap3x

The BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

BMI stands for Body Mass Index.

It's a measure of body fat based on height and weight that applies to both adult men and women.

BMI is an easy-to-perform screening tool for body fat levels that can help identify individuals who have health risks linked with excess body fatness.

It's important to keep in mind that the BMI measurement should not be used as a diagnostic tool for health conditions and is only one component in an overall evaluation of a person's health status.

Using the formula below, we can calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall: BMI = (weight in pounds / (height in inches x height in inches)) x 703

First, we need to convert the height into inches:5 feet 4 inches = 64 inches

Next, we plug the values into the formula and solve for the BMI:

BMI = (118 / (64 x 64)) x 703BMI = (118 / 4,096) x 703BMI = 0.0288 x 703BMI = 20.2464

Therefore, the BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

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Answer:

Explanation:

Let's refer to 1st the handle as A and the 2nd handle

The average measures the expected value of a determined variable. Shows the "most likelly observation" of said distribution.

The median is a measure of center values that divides the sample in exact halves. When the distribution of the variable of interest is irregular or doesn't follow a determined pattern, it allows you to determine a basic distribution of the values.

The mode is the value or values with the most observed absolute frequency, this is, the value or values that are most repeated.

Examples

"Per capita earnings in New yourk City"

For this variable you could use the mode as a value of center tendency so that you will be able to determine the most frequent incomes or the mean, that will allow you to determine or predict the expected earnings.

23. "Number of times people change jobs during their carrers"

This variable doesn't have a determined distribution, meaning, there is not a natural variation in it, people changes jobs when the oportunity comes but it is relativelly random.

The best measure of center tendency for this variable will be the Median.

25. "The individual weights of oranges in a 5-pound bag"

The weight is characteristic that can be cassified as a continuous variable, these kind of variables have often a normal distribution or tend to it. The best measure of center for any continuous variable is the Mean.

The area of WXYZ is g square meters.

Based on the information given, we have the equation AB = 2CY, which implies that the length of AB is twice the length of CY. However, the dimensions of the sides of the quadrilateral WXYZ are not provided, and there is no direct relationship mentioned between AB and WXYZ. Therefore, we cannot determine the exact area of WXYZ based on the given information.

The given area of ABCD is g square meters, but the shape and dimensions of ABCD are also unspecified. Without further details, we cannot establish any specific geometric properties or relationships within the figure. As a result, we cannot accurately calculate the area of WXYZ.

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Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

6 or -1

Step-by-step explanation:

6=a^2-5a

=a^2-5a-6

(a-6)(a+1)

a=6, -1

Answer:

Option C is correct

Step-by-step explanation:

Here,

3/10, 6/7 and 4/5 are proper fraction because the numerator is smaller than denominator.

But,

10/3 is the example of improper fraction

Thus, The answer is 10/3

The correct option is D. 1/4 of the distance from A to B.

D. 1/4 of distance from A to B.

The potential energy of a spring varies with the displacement of the object from its equilibrium position. At the equilibrium position, the potential energy is at a minimum, and the kinetic energy is at its maximum. As the object moves away from the equilibrium position, the potential energy increases and the kinetic energy decreases until the object reaches the maximum displacement point, where the potential energy is at a maximum and the kinetic energy is at a minimum.

In the case of a vertical spring, the equilibrium position is the midpoint between the two extreme points, A and B. At this point, the object has zero potential energy and maximum kinetic energy. As the object moves away from the equilibrium position towards point A, its potential energy increases and its kinetic energy decreases until it reaches point A, where the potential energy is at a maximum and the kinetic energy is at a minimum. Therefore, the object is located at point A when the kinetic energy is at a minimum.

Since the spring is ideal and massless, the potential energy is proportional to the square of the displacement from the equilibrium position. The kinetic energy is proportional to the square of the velocity of the object. At point A, the velocity of the object is zero, and hence the kinetic energy is at a minimum. Therefore, the object is located at point A when the kinetic energy is a minimum.

The distance from A to B is divided into four equal parts, and the object is located at the first quarter point from A to B, which is 1/4 of the distance from A to B. Therefore, the correct option is D. 1/4 of the distance from A to B.

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The graph shows the  inequality x² ≤ 16

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

Inequalities are often used to describe conditions or constraints in real-world problems.

You will notice that the values represented in the graph ranges from -4 to 4. Thus, solving x² ≤ 16 will produce these values. That is:

x² ≤ 16

x ≤ ±√16

x ≤ ±4

x ≤ -4 or x ≤ 4

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When the beam of light emerges into the air after passing through the entire stack, it makes an angle of approximately 29.4° with the normal.

We need to apply Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction for two different media.

Step 1: Calculate the angle of refraction in the first material using Snell's Law.
n1 * sin(i1) = n2 * sin(r1)
1 * sin(60°) = 1.20 * sin(r1)
sin(r1) = 0.5/1.20
r1 ≈ 25.4°

Step 2: Repeat the process for the remaining materials, using the previous angle of refraction as the new angle of incidence. Calculate the final angle of refraction in the last material.

For the second material:
1.20 * sin(25.4°) = 1.40 * sin(r2)
r2 ≈ 21.4°

For the third material:
1.40 * sin(21.4°) = 1.32 * sin(r3)
r3 ≈ 22.9°

For the fourth material:
1.32 * sin(22.9°) = 1.28 * sin(r4)
r4 ≈ 23.3°

Step 3: Calculate the angle of emergence in air.
1.28 * sin(23.3°) = 1 * sin(e)
e ≈ 29.4°

When the beam of light emerges into the air after passing through the entire stack, it makes an angle of approximately 29.4° with the normal.

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Answer:

A

Step-by-step explanation:

just did this it was right on my test

Answer:

5(x+3)-9x+4

5x+15-9x+4

-4x+19

Answer is B

Step-by-step explanation:

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Who ever is reading this:

I love u.

U matter.

The world needs u

hang in there ik it may be bad but u deserve the world <3

ur beautiful no matter ur shape, size, color, gender.. anything

don't give up i need u to live.

i wish i could take everyones problems so yall wouldn't have to have em but i cant so just know ily and if anyone needs to talk u can talk to me

Pls pass this on. Everyone deserves to know this. ♥️♥️

just copy and paste its not hard pls this could save someones life

The square of a binomial, the value of the constant \(c\) should be equal to half the coefficient of the linear term squared, which in this case is \(c = \left(\frac{22}{2}\right)^2 = 121\). Therefore, the constant that needs to be filled in is 121.

To express the quadratic expression \(x^2 + 22x + c\) as the square of a binomial, we need to find a binomial of the form \((x + a)^2\) that expands to \(x^2 + 22x + c\). Expanding \((x + a)^2\) gives \(x^2 + 2ax + a^2\). Comparing the coefficients of the expanded binomial and the given quadratic expression, we can equate the linear terms to find \(2ax = 22x\), which gives \(a = 11\). Substituting this value of \(a\) back into the expanded binomial, we have \(x^2 + 22x + 121\). Therefore, the constant that needs to be filled in is 121.

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Answer: 18a+42b-6

Step-by-step explanation:

Simplifying means combining like terms

so 36a and -18a can simplify  to 18a

and the rest you can't simplify so

18a+42b-6

Answer:

Volume = 315 cm³

Step-by-step explanation:

Volume = Length × Width × Height

→ Substitute in the values

Volume = 6 cm × 3.5 cm × 15 cm

→ Simplify

Volume = 315 cm³

Hi there.

Glad to see you using Brainly!

Equation:

a^2-b^2c^2

Then, multiply the terms with equal exponents.

(We can do this by multiplying their bases)

After:

a^2 - (b c)^2

Now, using a^2 - b^2 = (a-b)(a+b) we factor.

Therefore, after using that we get:

(a-bc) x (a+bc)

Therefore, our solution is

(a - bc) x (a+bc)

Thanks for using Brainly!

- Tutor John

Answer:

\( {a}^{2} - {b}^{2} {c}^{2} = (a - bc)(a + bc) \)

Answer:

Sorry, I don't think that's enough money. A marble countertop alone costs thousands of dollars, and kitchen renovations usually cost anywhere from $10,000 to $40,000. (I watch a lot of HGTV.) I think you do have enough money to buy some paint and do the walls/shelves, or perhaps buy some new decor, but you don't have enough money for a kitchen renovation.