Help me with trig please, I don’t need an in-depth solution because I’m just checking my answers

To find the measure of angle X in right triangle XYZ, we can use the distance formula and an inverse trigonometric ratio. The angle can be determined by finding the slope of line XY and using it to calculate the tangent of the angle. Then, we can use the inverse tangent function to find the angle measure to the nearest tenth of a degree.

In right triangle XYZ with vertices X(2,2), Y(2,-2), and Z(7,-2), we want to find the measure of angle X. To do this, we first find the slope of line XY using the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using points X(2,2) and Y(2,-2), we have:

dXY = sqrt((2 - 2)^2 + (-2 - 2)^2) = sqrt(0 + 16) = 4

The slope of line XY can be found using the formula:

m = (y2 - y1) / (x2 - x1)

mXY = (-2 - 2) / (2 - 2) = -4 / 0 (undefined)

Since the slope is undefined, we know that line XY is vertical

learn more about right triangle . Therefore, angle X is a right angle (90 degrees).

Hence, the measure of angle X in right triangle XYZ is 90 degrees.

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Answer:

Step-by-step explanation:

\(2 . 4x =\\2 \times 4x\\\mathrm{Multiply\:the\:numbers:}\:2\times \:4=8\\\\= 8x\)

Answer:

B. 66

Step-by-step explanation:

idk how to explain it without repeating what it says in the answer

Answer:

The answer is:

B) 66 degrees

Step-by-step explanation:

Since the triangle is an isosceles triangle, angle C is the same as angle B.

57 + 57 = 114

Since you know two of the three angles, and you know that a triangle's angles must equal 180 degrees...

180 - 114 = 66

Angle A must equal 66 degrees for the triangle to equal 180 degrees.

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Answer:

He would have to collect 4 coins to get 80 points

Step-by-step explanation:

Can i get brainliest plz

The difference between the medians of the two data sets (Highlands and Lowlands) is 4 mm.

To analyze the dot plots and determine the difference between the medians of the two data sets (Highlands and Lowlands), we can visually examine the distribution and position of the dots.

The medians represent the middle values of each data set, so we need to identify the median values for both plots.

Looking at the dot plot for Highlands, the dots are concentrated between 8 and 24 mm of rainfall.

The dot plot for Lowlands shows a single dot located at 20 mm of rainfall.

The median for the Highlands data set can be estimated as the value that splits the dots evenly into two equal parts.

Since there are multiple dots between 8 and 24 mm, we can estimate the median to be around 16 mm.

On the other hand, the median for the Lowlands data set is simply the value represented by the single dot, which is 20 mm.

Now, to find the difference between the medians, we subtract the median of the Highlands from the median of the Lowlands:

Difference = Median of Lowlands - Median of Highlands

Difference = 20 mm - 16 mm

Difference = 4 mm.

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To display formulas, one way is to press the key combination [Ctrl]+[] (grave accent).

The key combination [Ctrl]+[] is used to display formulas.

This is a useful feature for checking and editing formulas without altering the calculated values.

By pressing [Ctrl]+[], users can easily view the underlying formulas and ensure their accuracy.

This key combination provides a convenient way to switch between the formula view and the results view, enabling efficient editing and troubleshooting of complex calculations.

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Answer:

Decrease of 4% ($4).

Step-by-step explanation:

Suppose the initial price was $100. An increase of 20% will make the price $120.

Now we decrease it 20% which brings it to 120 - 0.20 * 120

= 120 - 24

= $96.

So that's an overall decrease of $4 or 4%.

The initial entering basic variable is x₁, and the leaving basic variable is x₃.

To construct the complete first simplex tableau using the Big M method, we need to convert the given problem into standard form. We introduce slack, surplus, and artificial variables to transform the inequality and equality constraints into equations.

The given problem becomes:
Maximize Z = -2x₁ + x₂ - 4x₃ + 3x₄

subject to:
\(x₁ + x₂ + 3x₃ + 2x₄ + x₅ = 4\) (Equation 1)
\(x₁ - x₃ + x₄ - x₆ = -1\)(Equation 2)
\(2x₁ + x₂ + x₇ = 2\) (Equation 3)
\(x₁ + 2x₂ + x₃ + 2x₄ + x₈ = 2\) (Equation 4)

where x₅, x₆, x₇, x₈ are the introduced variables.

The initial entering basic variable is the one with the most negative coefficient in the objective function, which is x₁ in this case.

To identify the leaving basic variable, we consider the ratio of the right-hand side to the pivot column coefficient. The smallest positive ratio determines the leaving basic variable.

For Equation 1:

\(Ratio = 4/1 \\= 4\)
For Equation 2:

\(Ratio = -1/(-1) \\= 1\)
For Equation 3:

\(Ratio = 2/2 \\= 1\)
For Equation 4:

\(Ratio = 2/1 \\= 2\)

The leaving basic variable is x₃ since it has the smallest positive ratio.

Constructing the complete first simplex tableau:

(Refer to the image attached below)

The initial entering basic variable is x₁, and the leaving basic variable is x₃.

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┌─────────────┬──────┬───────┬───────┬───────┬─────┬─────────────┐

│     BV      │  x₁  │   x₂  │   x₃  │   x₄  │  s₁ │      RHS    │

├─────────────┼──────┼───────┼───────┼───────┼─────┼─────────────┤

│      Z      │ -2   │   1   │  -4   │   3   │  0  │      0      │

├─────────────┼──────┼───────┼───────┼───────┼─────┼─────────────┤

│  -x₃ + x₄   │  1   │   0   │  -1   │   1   │  0  │     -12     │

├─────────────┼──────┼───────┼───────┼───────┼─────┼─────────────┤

│  2x₁ + x₂   │  2   │   1   │   0   │   0   │  0  │      2      │

├─────────────┼──────┼───────┼───────┼───────┼─────┼─────────────┤

│ x₁ + x₂ + x₃│ -1   │  -1   │   1   │   0   │  1  │      4      │

├─────────────┼──────┼───────┼───────┼───────┼─────┼─────────────┤

│ 2x₁ + 2x₂ + │ -2   │   2   │   1   │   2   │  0  │      2      │

│     x₃ + 2x₄ │      │       │       │       │     │             │

└─────────────┴──────┴───────┴───────┴───────┴─────┴─────────────┘

The initial entering basic variable is x₂, which has the highest coefficient in the objective row. The leaving basic variable is s₁, determined by selecting the row with the smallest positive ratio of the right-hand side (RHS) to the entering column's coefficient. In this case, the ratio for the third row (2/1) is the smallest, so s₁ leaves the basis.

To construct the complete first simplex tableau using the Big M method, we first rewrite the given problem into standard form by introducing slack, surplus, and artificial variables. We assign a large positive value (M) to each artificial variable in the objective row to penalize their inclusion in the optimal solution.

The first row represents the objective function, where the coefficients of the decision variables x₁, x₂, x₃, and x₄ are taken directly from the given problem. The artificial variable s₁ has a coefficient of 0 since it doesn't appear in the objective function.

The subsequent rows represent the constraints. Each row corresponds to one constraint, where the coefficients of the decision variables and the artificial variable are taken from the original problem. The right-hand side (RHS) values are also copied accordingly.

The initial entering basic variable is determined by selecting the most negative coefficient in the objective row, which is x₂ in this case. The leaving basic variable is determined by finding the smallest positive ratio of the RHS to the entering column's coefficient. The ratio for the third row (2/1) is the smallest, so s₁ leaves the basis.

The resulting tableau forms the basis for applying the simplex method to solve the linear programming problem iteratively.

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Answer:

A right 4 down 5

Step-by-step explanation:

counting the grid spaces from any point for example R and going to the point R' (R prime) will give you the translation

The characteristic equation is r^2 + 2r = 0. The solutions to the differential equation are r = 0 and r = -2. The differential equation is linear.

a) The characteristic equation for the given differential equation is r^2 + 2r = 0.

To obtain the characteristic equation, we replace each derivative term in the differential equation with the corresponding power of r. In this case, we have x^2x + 2x = 0. By factoring out an x from the equation, we get x(x + 2) = 0. This implies that either x = 0 or x + 2 = 0. Thus, the characteristic equation is r^2 + 2r = 0.

b) The solutions to the differential equation can be found by solving the characteristic equation. By factoring out r from r^2 + 2r = 0, we have r(r + 2) = 0. Therefore, the solutions are r = 0 and r = -2.

c) The given differential equation is linear. A differential equation is linear if the highest power of the dependent variable and its derivatives is 1. In this case, the highest power is 1, making it a linear differential equation.

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Answer:

1. 9-63x

2 7n+70

Step-by-step explanation:

Distribution means that you multiply what is inside the parentheses by what is on the outside.

1. 9(1-7x)

9 x 1 = 9

9 x -7x = -63x

1 can be rewritten as 9-63x

2. 7(n+10)

7 x n = 7n

7 x 10 = 70

2 can be rewritten as 7n+70

Answer:

ratio of girls to boys = 14:10 or 7:5 (simplified)

ratio of boys to class = 10:24 or 5:12 (simplified)

Step-by-step explanation:

Answer: The first is when we have what is called infinite solutions. This happens when all numbers are solutions. The equation 2x + 3 = x + x + 3 is an example of an equation that has an infinite number of solutions. ...

Answer:

3) circumference = 15.7 m

                 Area   = 19.625 m²

Step-by-step explanation:

3) First find the diameter of the circle, using Pythagorean theorem.

We are using Pythagorean theorem to find the diameter as the given triangle is right angle triangle.

Hypotenuse² = base² + altitude²

                       = 3² + 4²

                       = 9 + 16

                        = 25

Hypotenuse    = √25

                   d  = 5 m

Circumference of circle = πd

                                       = 3.14 * 5

                                       = 15.7 m

r = 5 ÷2 = 2.5 m

Area of circle = πr²

                       = 3.14 * 2.5 *2.5

                       = 19.625 m²

The statement that "the tribe is the οldest sοciοpοlitical type; the tribe predates the state" is a widely accepted view in anthrοpοlοgy and archaeοlοgy.

It suggests that human sοcieties evοlved frοm smaller, kinship-based grοups knοwn as tribes befοre transitiοning tο larger, centralized fοrms οf pοlitical οrganizatiοn knοwn as states.

Tribes are characterized by a clοse-knit sοcial structure based οn kinship ties, with members sharing cοmmοn ancestry and οften living in smaller, decentralized cοmmunities. Tribal sοcieties typically have egalitarian sοcial structures, with leadership based οn kinship οr achieved status rather than fοrmal hierarchical systems.

As human sοcieties evοlved, sοme tribes eventually develοped intο states, which are characterized by centralized pοlitical authοrity, fοrmal legal systems, and defined territοrial bοundaries. States οften have mοre cοmplex sοcial hierarchies, specialized institutiοns, and a mοnοpοly οn the use οf fοrce.

The transitiοn frοm tribes tο states is believed tο have οccurred gradually οver thοusands οf years, as human pοpulatiοns grew and interactiοns between grοups increased. The emergence οf agriculture, surplus prοductiοn, and the need fοr larger-scale gοvernance are οften cited as factοrs cοntributing tο the develοpment οf states.

While the specific timeline and prοcesses οf this transitiοn are still subjects οf οngοing research and debate, it is generally accepted that tribal sοcieties predate the develοpment οf states in human histοry.

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Mark and Don have 18  and 92 marbles respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

Let the number of marbles Mark has be x.

According to the question,

Don has (5x+2) marbles.

Total number of marbles=110

Thus, the required equation is:

x+5x+2=110

6x=108

x=108/6

x=18

Mark has 18 marbles.

Don has (5*18+2)=92 marbles.

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The total amount of fencing they need = 38x + 10.

Perimeter for the rectangular fencing of the home = 160 yards

Perimeter for the square fencing of the pool = 40 yards

Perimeter of a rectangle = 2(length + width)

Perimeter of a square = 4(side length).

Perimeter for the rectangular fencing of the home = 2(3 + 10x + 2 + 5x) = 2(15x + 5) = 30x + 10

Perimeter for the square fencing of the pool = 4(2x) = 8x

The total amount of fencing they need = 30x + 10 + 8x = 38x + 10.

If x = 5, then:

Perimeter for the rectangular fencing of the home = 30x + 10 = 30(5) + 10 = 160 yards

Perimeter for the square fencing of the pool = 4(2x) = 8x = 8(5) = 40 yards.

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Answer:

38
160
40

Step-by-step explanation:

The solution is:

x ≥ 6

Work/explanation:

To solve this inequality, I should isolate x.

First I add 23 on each side

\(\multimap\phantom{333}\bf{3x\geqslant-5+23}\)

\(\multimap\phantom{333}\bf{3x\geqslant18}\)

Divide each side by 3

\(\multimap\phantom{333}\bf{x\geqslant6}\)

Answer:

2 2/4

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Rate of Changes:

\(\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{y_2-y_1}{x_2-x_1}}\)

Pick two values of x and y from the given table:

Therefore:

\(\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{5-13}{1-(-1)}}\\\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{-8}{1+1}}\\\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{-8}{2}}\\\displaystyle \large{\dfrac{\Delta y}{\Delta x}=-4}\)

Therefore, rate of change is -4

The value of y in the given figure is 108°.

The angles formed by a transversal line on the same side and position of the line, if lines are parallel then the corresponding angle are congruent.

Given is a figure, where two line AB and CD are being intersected by a transversal FE,

Let FE intersects AB and CD at P and O, respectively, (refer to the figure attached)

Since, AB ║ CD

Therefore, ∠ FPB  ≅ ∠ POD by the definition of corresponding angles,

2x+16 = 3x-12

x = 28

∠ POD = 28×3-12 = 72°

∠ POD and ∠ EOD are forming linear pair and therefore are supplementary,

∠ POD + y = 180°

72° + y =180°

y = 180°-72°

y = 108°

Hence, y = 108°

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Answer:

1/2

Step-by-step explanation:

2, 3, and 5 are the prime numbers. Therefore, it would be 3/6 or 1/2 chance she rolls a prime number.

The necessary preprocessor directive to enable the use of functions like sqrt and sin

#include <math.h>

Generally, A preprocessor directive is a command that is processed by the preprocessor in a programming language before the actual compilation of the source code begins.

Preprocessor directives are used to give instructions to the preprocessor, which is a program that performs text substitution on

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Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^

The dimensions of a scale drawing of a rectangular flag that is 40 centimeters by 72 centimeters using the scale 1:8 is 4 cm by 7.2 cm. Option C.

This is because a 1:8 scale means that for every actual unit of length, the corresponding length on the scale drawing is 8 times smaller.

Therefore, in order to find the dimensions of the scaled drawing of the flag, we must divide the actual dimensions (40 cm by 72 cm) by 8. The result is 4 cm by 7.2 cm.

It is important to make sure that you use the correct scale when attempting to determine the dimensions of a scaled drawing. If you use a different scale than the one intended, your result will be incorrect.

For example, if you use a 1:4 scale instead of a 1:8 scale, you will end up with a scaled drawing that has dimensions of 20 cm by 36 cm, which is double the correct answer.

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In ICD-10-CM, only two code categories are used to report infectious arthropathies: M00 and M01.

The codes in these categories are used to describe the variety of arthropathies that can be caused by various bacterial, viral, fungal, and other infectious agents.

The M00 code group includes pyogenic arthritis, osteomyelitis, and other non-tuberculous infections of joints and bones. The M01 code category includes other types of arthritis and arthropathies caused by bacteria, viruses, fungi, and parasites, as well as other infectious agents.

Infectious arthropathies are diseases that cause joint inflammation and pain as a result of infection with a variety of infectious agents, such as bacteria, viruses, fungi, and parasites. Symptoms vary depending on the type of infection, but they usually include pain, swelling, redness, stiffness, and limited mobility.

The diagnosis of infectious arthropathies usually involves a combination of physical examination, laboratory testing, and imaging studies. Treatment usually involves antibiotics or antiviral medications, as well as pain management and physical therapy.

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Answer:

x = 12.48

Step-by-step explanation:

Simplifying

12(x + -13) = 13(12 + -1x)

Reorder the terms:

12(-13 + x) = 13(12 + -1x)

(-13 * 12 + x * 12) = 13(12 + -1x)

(-156 + 12x) = 13(12 + -1x)

-156 + 12x = (12 * 13 + -1x * 13)

-156 + 12x = (156 + -13x)

Solving

-156 + 12x = 156 + -13x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13x' to each side of the equation.

-156 + 12x + 13x = 156 + -13x + 13x

Combine like terms: 12x + 13x = 25x

-156 + 25x = 156 + -13x + 13x

Combine like terms: -13x + 13x = 0

-156 + 25x = 156 + 0

-156 + 25x = 156

Add '156' to each side of the equation.

-156 + 156 + 25x = 156 + 156

Combine like terms: -156 + 156 = 0

0 + 25x = 156 + 156

25x = 156 + 156

Combine like terms: 156 + 156 = 312

25x = 312

Divide each side by '25'.

x = 12.48

Simplifying

x = 12.48

Answer:

x=72±2180313=72±21803√13

Step-by-step explanation:

Answer:

1/4x - 4 = 3/4x - 15

-1/2x - 4 = -15

-1/2x = -11

x = 22

Answer:

10.67 degree.

Step-by-step explanation:

Note:
The angle between two lines can be found using their direction cosines. The formula is:

\(\boxed{\tt cos\: \theta = \frac{a * b}{||a|| * ||b||}}\)

where:

In this case, the direction cosines of the two lines are proportional to 1, 2, 3 and 3, 4, 5.

So, we can write the direction cosines as follows:

a = (1, 2, 3)

b = (3, 4, 5)

The magnitudes of a and b are:

\(\tt ||a|| = \sqrt{1^2 + 2^2 + 3^2} = \sqrt{13}\)

\(\tt ||b|| = \sqrt{3^2 + 4^2 + 5^2}= 5\sqrt{2}\)

Now, we can find the angle between the two lines using the formula above:

\(\tt cos \: \theta = \frac{1 * 3 + 2 * 4 + 3 * 5}{\sqrt{13} * 5\sqrt{2} }=\frac{13\sqrt{7}}{35}\)

The angle theta can be found using the arc cos function or inverse cos function.

\(\tt \theta =cos^{-1}(\frac{13\sqrt{7}}{35})=10.67\)

Therefore, the angle between the two lines is 10.67 degree.