What is the solution of the system of equations? Show your work.
4x - 2y = 10
2x + y = -3

Answer:

tan30° = [tex]\frac{5}{12}[/tex]

Step-by-step explanation:

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{5}{12}[/tex]

Answer:

[tex]\dfrac{5}{12}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the values into the tan trigonometric ratio:

[tex]\implies \tan(30^{\circ})=\dfrac{5}{12}[/tex]

Answer:

this is your proper answer ...

Therefore , the solution of the given problem of trigonometry comes out to be Cos 2x = -0.760355.

The study of relationships among triangle angles and angles is known as trigonometry. Mathematical modeling is a fundamental idea in all of geometry because it can be used to reduce any straight-sided form to a collection of triangles. Amazingly complex connections exist between trigonometry and other areas of mathematics, particularly mathematics, real or complicated, infinite series, logarithms, and infinite series.

Here,

Given : Cosx = 9/26 (First quadrant)

To find : Cos2x

We use the formula:

=>Cos2x = 2Cos²x -1

=> Cos2x  = 2(9/26)² - 1

=> Cos 2x = -0.760355

Therefore , the solution of the given problem of trigonometry comes out to be Cos 2x = -0.760355.

To know more about trigonometry , visit

brainly.com/question/12068045

#SPJ1

Answer:

-------------------------------

The height h of the tree is opposite to 49° angle of a right triangle with the other leg:

Use tangent to find the value of h:

The height of the tree is 40 feet to the nearest foot.

How can the height of the tree be found?

It can be found using similar triangles.

Let's call the height of the tree "x".

Since the angle of elevation to the sun is 49°, we have two similar triangles:

Triangle 1: Sun - Naomi - Ground (illustration attached)

Triangle 2: Sun - Tree - Ground

The height of Naomi, 5 feet, is one of the corresponding sides in the two triangles, and the height of the tree, x feet, is the other. We know the ratio of their heights is 8:1, so:

x ÷ 5 = 8

Solving for x, we find that:

x = 40

So the height of the tree is 40 feet to the nearest foot.

To know more about similar triangle visit:

https://brainly.com/question/2644832

#SPJ1

Answer:100

Step-by-step explanation:

Answer:

I think Jacob wins the race

The given function will be represented by a straight line graph, as shown below in the attachment.

On a coordinate plane, functions can be graphed. To graph a function, first select several input values and compute the outputs. The x value is the independent variable, and the y value is the dependent variable. Plot the points and connect them with a line or a curve, depending on whether the function is linear or curvilinear.

Linear functions are written as y = mx + b, where m is the slope of the line and b is the y-intercept. A linear function's graph is a straight line that represents a constant rate of change between two variables. All other functions are curvilinear or non-linear.

Learn more about functions

https://brainly.com/question/9834848

#SPJ1

So we know that we need to add 15 to the double of this number. We know we need to add 15 since it says "15 more than" and we know we need to double/multiply the number by two since it says "twice a number"! We also know that this mystery number equals 5.

Therefore, we can set up our equation and solve! The variable x is used to represent the number we're looking for!

2x + 15 = 5

2x = -10

x = -5

So, your answer should be -5!

Pacquiao will have enough money (a future value of up to P7,000) to buy the gift if he deposits his money (P6,000) in an account paying 8 percent compounded semi-annually.

The future value is the compounded present value at an interest rate.

The future value can be determined using an online finance calculator, FV table, or FV formula.

N (# of periods) = 4 (2 years x 2)

I/Y (Interest per year) = 8%

PV (Present Value) = P6,000

PMT (Periodic Payment) = P0

Results:

Future Value (FV) = P7,019.15

Total Interest = P1,019.15

Thus, in 2 years' time, Pacquiao will have P7,019 enough to buy his mom a new bicycle.

Learn more about future values at https://brainly.com/question/24703884

#SPJ1

The answer to the above question is B. Multiply the first equation by -2 and add the second equation.

A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."

Given,

[tex]2x - 2y = 24\\4x + 7y=-40\-4x +4y = -96\\4x+7y = -40\\11y = -136\\y = -136/11[/tex]

The answer to the above question is B. Multiply the first equation by -2 and add the second equation.

To know more about equation visit:

brainly.com/question/649785

#SPJ1

ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.

There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra. This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.

X now has 300 mg of sodium in it.

[tex]x = 300[/tex]

Y also has 450 mg of sodium in it.

[tex]y = 450[/tex]

Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.

Let the number of frozen dinners be "b," and the number of soup cans be "a."

ax + by = 6000

a(300) + b(450) = 6000 .

Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation

[tex]a + 5 = b \\a(300) + (a + 5)(450) = 6000\\300a + 450a = 6000 - 2250\\ 750a = 3750\\ a = 3750/750\\ a = 5\\5 + 5 = b\\ b = 10[/tex]

To know more about equation visit:

brainly.com/question/649785

#SPJ1

Answer:

Step-by-step explanation:

distance = [tex]\sqrt{(-5/2+1/2)^{2} +(9/4+3/4)^{2} }=\sqrt{13}[/tex]=3.61

Answer:

dddd

Step-by-step explanation:

The maximum number of zeros is 2, and the x-intercepts are -9, 9.

The x-intercept is where the graph crosses the x-axis.

Here, we have,

The function is given as:

y=(x+9)(x-9)^2

The above function can be rewritten as:

y=(x+9)(x-9)(x-9)

The x-intercept is the point where the graph crosses the x-axis

To determine the x-intercepts, we remove the common factors

So, we have:

y=(x+9)(x-9)

Equate to 0

(x+9)(x-9)=0

Split

(x+9)=0 and, (x-9)=0

Solve for x

x=9 & x=-9

So, the maximum number of zeros is 2, and the x-intercepts are -9, 9.

Read more about zeros and intercepts at:

brainly.com/question/15526500

#SPJ1

The domain of the function whose graph shown in diagram is x ≤ 1.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

The domain of the function whose graph shown in diagram is x ≤ 1 as the value of x is less than 1.

To learn more about domain of a function visit:

brainly.com/question/13113489

#SPJ1

On solving the provided question, we can say that  on matching the expressions are 100X 14 = 1400 and 14(10) = 140 and 361 . 100 = 36100 and 100(361) = 36100

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

so, on matching the expressions are

100X 14 = 1400

14(10) = 140

361 . 100 = 36100

100(361) = 36100

To know more about expressions visit :-

https://brainly.com/question/14083225

#SPJ1

Answer: Her total earnings would be $28+$54=$82.

Step-by-step explanation:

Lori's base salary is calculated by multiplying her hourly rate by the number of hours she works. If Lori works 4 hours on a Tuesday and earns $7/hr, her base salary would be 4*$7=$28.

Lori's tips are calculated as 18% of her food sales. If Lori has $300 of food sales on a Tuesday, her tips would be 18%*$300=$54.

Lori's total earnings for the day would be the sum of her base salary and her tips. In this case, her total earnings would be $28+$54=$82.

Answer shown in bold

The non-bolded values to the left are not to be typed in the answer box. They're present to keep track of the values. In other words, you'll type "40" without quotes into the first box, then "19" without quotes in the second box, and so on.

========================================================

Explanations:

Let me know if you have any questions.

1. The length of the altitude is 15 units.

2. The perimeter of trapezoid ABCD is 132 units.

An altitude is the vertical height of a given object from the sea level. This is majorly a height reached by an object to the sea level as a reference.

The perimeter of a trapezoid is the sum of all its sides.

From the question;

1. To determine AE,

DE = (DG - EF)/ 2

     = (22 - 6)/ 2          (since AB = EF = 6)

     = 8

DE = 8 units

The altitude AE can be determined by applying the Pythagorean theorem to triangle ADE. So that;

/hyp/^2 = /opp/^2 + /adj/^2

AD^2 = DE^" + AE^2

17^2 = 8^2 + AE^2

289 = 64 + AE^2

AE^2 = 225

AE = 15

Thus the length of the altitude is 15 units.

2. To determine the perimeter of the trapezoid, we have;

AE = (AD - EF)/ 2

     = (58 - 16)/ 2           (since BC = EF = 16)

     = 21

AE = 21 units

So that from triangle ABE, applying the Pythagorean theorem to determine the value of AB, we have;

/hyp/^2 = /opp/^2 + /adj/^2

AB^2 = BE^2 + AE^2

         = 20^2 + 21^2

AB = 841^1/2

AB = 29

Perimeter of the trapezoid = 29 + 16 + 29 + 58

                       = 132 units

Thus, the perimeter of the trapezoid is 132 units.

Learn more about the perimeter of a trapezoid at https://brainly.com/question/25967620

#SPJ1

The distance that the minute hand moves in 50 minutes, given that it started at 7 minutes, is 258 degrees.

A rotatation around the clock by the minute hand, is a full 360 degrees as it begins at 12 and ends at 12 .

If a minute hand is at 7 minutes, then it means that the degrees moved is:

= 7 / 60  x 360

= 42 degrees

At 50 minutes, the degrees moved is :

= 50 / 60 x 360

= 300 degrees

Seeing as the minute hand started at 7 minutes, the distance moved is :

= 300 - 42

= 258 degrees

Find out more on minute hand at https://brainly.com/question/17106527

#SPJ1

Answer: 3/-2

Step-by-step explanation:

3/-2 and -3/2 mean the same thing and give same result if we divide the numerator by denominator.

hope that helps...

Answer:

Step-by-step explanation:

Answer: 10:9, 10/9, 10 to 9.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]N^{2} =49[/tex]

To solve take the square root of 49.

[tex]\sqrt{49}[/tex] = 7

Option c which is 7

Answer:

they are intersecting.. so, there's one solution. the ordered pair is (-1,4).

Answer:

Step-by-step explanation:

That is not possible.

Answer:

Step-by-step explanation:

9.0 × 10-10 I think.....

Based on the principles of kinetic theory, the speed of sound in matter is determined by the mean free paths of the molecules that make up the matter and the properties of the material itself.

Velocity is the speed at which an object moves or changes position over a period of time. It is usually measured in units such as meters/second, miles/hour, kilometers/hour. It is an important factor in the movement of objects and the movement of sound, light and other forms of energy. Speed ​​is also an important factor in transport safety, as it affects how long it takes a vehicle to stop and how far it must travel to stop safely.

Predict the ranking of sound speeds for four different materials.

Steel, 25°C air, 50°C air and water. Use the theory of motion of matter to protect your predictions.

Therefore, the speed of sound varies greatly depending on the material. Below is the ranking of the speed of sound for the four substances listed. From fastest to slowest:

1. 25°C Air: The speed of sound in warm air at 25°C is the fastest of the four substances, and because air is made up of both light and heavy molecules, it can travel quickly. The speed of sound in warm air at 25 °C is about 343 m/s.

2. 50°C air: The speed of sound in air at 50°C is slower than in air at 25°C. This is because molecules in warm air spread out more and move more slowly. The speed of sound in air at 50 °C is approximately 331 m/s.

3. Water: Water molecules are denser and move slower, so the speed of sound in water is slower than in air. The speed of sound in water is approximately 1,482 m/s.

4. Steel: The speed of sound in steel is the slowest of the four substances. This is because steel is composed of heavier molecules that move slower than those in air and water.

Overall, the order of sound velocities for the four materials is air at 25°C, air at 50°C, water, and steel. This classification is based on the principle of kinetics that the speed of sound in a material is determined by the mean free paths of the molecules that make up the material and the properties of the material itself.

To know more about force click-

https://brainly.com/question/1675020

#SPJ1