Which of the following is correctly written in Standard Form?

The solution to the system of linear equations is x = 10 and y = 22.

To solve this system of linear equations, we can use the substitution method.

First, we want to isolate one of the variables in either equation. Let's start with equation 1:

3x - 2y = 14

Add 2y to both sides to isolate x:

3x = 14 + 2y

Divide both sides by 3 to solve for x:

x = (14 + 2y) / 3

Now, substitute this expression for x into equation 2:

5x + y = 32

5(14 + 2y) / 3 + y = 32

Simplify:

70 + 10y + y = 32

Combine like terms:

11y = -38

Divide both sides by 11 to solve for y:

y = -38 / 11

y = -3.45454545...

Now, substitute -3.45454545... for y in the expression for x:

x = (14 + 2(-3.45454545...)) / 3

x = (14 - 6.9090909...) / 3

x = 7.09090909... / 3

x = 2.36363636...

x = 2.4 (rounded to nearest tenth)

Now that we have both x and y, the solution to the system of linear equations is x = 2.4 and y = -3.5.

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The equivalent expression would be; function G(t) = 86,400•3^t

What is a function in simple definition?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

The number of views on a viral video can be modeled by the function

G(t) = 2500(5) 2-4.

we have to find out an equivalent function of the form G(t) = ab.

Here, we want to make a transformation

From what we have;

G(t) = 2500(5)^(t - 4)

From indices, we know that;

x^(a + b) = x^a•x^b

Thus, we have it that;

G(t) = 2500•3^t•3^2

G(t) = (9 * 9600) * 3^t

G(t) = 86,400•3^t

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The answer to the given question is  x = -2, x = 2. The given problem can be solved by the following steps :

Step 1: Rewrite the equation in standard form: x2 + 7x - 4 = 0

Step 2: Find the factors of the coefficient of x and the constant term: -4 = -2 x -2, 7 = 7

Step 3: Set up the factors to solve the equation: (x + 2)(x - 2) = 0

Step 4: Solve each factor: x + 2 = 0, x - 2 = 0

Step 5: Find the solutions: x = -2, x = 2

Therefore, the final answer is x = -2, x = 2.

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Answer:

15

Step-by-step explanation:

5 X 10 = 50

170 / 50 = 3 sets  = 15

Answer:

2.5

Step-by-step explanation:

just divide 50 by 20

Answer:

2.35 + 0.55 × 15 = 10.6

Therefore, she can go 10.6 miles.

Answer:

10.6

Step-by-step explanation:

2.35 + 0.55 x 15 = 10.6

Answer: 3150

Step-by-step explanation:

V = lwh

V = 25 x 7 x 18

V = 3150

Complementary angles add to 90 degrees. This means that 65 + x = 90, so x = 90 - 65 = 25.

The area of circle A to the area of circle B ratio is 100: 64, and the ratio of e: f is 13: 10.

The area of the circle is equal to the multiplication of the square of the circle's radius and π.

A = πr²

where 'r' is the radius

Circumference of circle A × 0.8 = circumference of circle B

So, taking r as the radius of A,

2πr =  circumference of circle A

2πr × 0.8 = circumference of circle B

So the radius of B is r × 0.8.

Now we can substitute that in the area equations :

Area of A = π×r²

Area of B = π × (r × 0.8)² = π × r² × 0.64

The circumferences of the A to B ratio is

Circumference of A : Circumference of B = (2 × π × r)/(2 × π × r × 0.8)

= 1: 0.8 = 100: 80,

The areas of circle A to circle B ratio is

Area of A : Area of B = (π × r²)/(π × r² × 0.64) = 1: 0.64 = 100: 64

e² = f² × 1.69

69% larger shows that f² is the 100% to which we must add 69% to obtain e². 100% + 69% Equals 169%, obtaining a factor of 1.69.

We have this equation:

e² = f² × 1.69

Apply the square root on both sides.

e = f × √(1.69) = f × 1.3

e/f = 1.3 = 1.3/1 = 13/10

the ratio e:f = 13: 10

Thus, the ratio of circle A's area to circle B's area is 100: 64 and the ratio of e: f is 13: 10.

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9514 1404 393

Answer:

  x ≈ 4.2

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(72°) = b/x = 13/x

  x = 13/tan(72°) ≈ 4.223956

Rounded to the nearest tenth, x ≈ 4.2.

The value of exponent x, if [tex]$\sqrt[\text X]{81} = 3[/tex], is 4, in the given equation.

Exponent is the process of expressing large numbers as powers, according to the definition. Accordingly, the exponent describes the number of times a number has been multiplied by itself. Using 6 as an example, multiply it by itself four times, or 6×6×6×6. 6⁴ can be used to represent this. In this case, the base is 6 and the exponent is 4. You can interpret this as 6 raised to the power of 4.

Exponents are represented by the symbol. The word "carrot" refers to this symbol (). 4 raised to a power of two, for instance, can be expressed as 4^2 or 4². Thus, 4^2 = 4 × 4 = 16. A few exponent-based numerical expressions are represented in the table below.

The value of x, if [tex]$\sqrt[\text X]{81} = 3[/tex]

3 × 3 = 9

9 × 3 = 27

27 × 3 = 81

Thus, The value of x, if [tex]$\sqrt[\text X]{81} = 3[/tex], is 4.

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Answer:

C)   1/3

Step-by-step explanation:

3 = 3/1

3/1  x  1/3  = 3/3  = 1

Answer:

Step-by-step explanation:

formula 0.5 x base x height

Answer:

Remember the formula a^2+b^2=c^2

Step-by-step explanation:

This can be used on right triangles. Now your a and b represent the legs of a triangle and the c represents the hypotenuse(the longest side). If you had a leg that was 2 inches and a second leg that was 4 inches you would plug it into the equation so...

2^2+4^2=c^2

Now evaluate

2^2=4

4^4=16

so

4+16=c

20=c

Now take the square root of 20 which is approximately 4.47 or leave it as square root of 20

If you had one leg and a hypotenuse then plug in and solve like any other equation.

Hope this helps!

Answer:

x = 16/9

Step-by-step explanation:

9x -16 = 0

9x = 16

x = 16/9

Let's check

9(16/9) -16 = 0

144/9 - 16 = 0

16 - 16 = 0

0 = 0

So, x = 16/9 is correct!

Answer:

Step-by-step explanation:

9x = 16

x = 16/9

Answer:

1/2

Step-by-step explanation:

Answer:

2/3 + 1/6 + 2/8

=(2×8+1×4+2×3)/24

=(16+4+6)/24

=26/24

=13/12

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Answer:

x=8

Step-by-step explanation:

Add up the angles to 90 because angle GHI and angle IHJ should add up to 90°

3x+66=90

-66=-66

Solve for x.

3x = 24

3 = 3

x =8

Hope this helps.

Answer:

Step-by-step explanation:

y = [tex]\sqrt{x+4}[/tex] + 5

Step-by-step explanation:

For Pythagoras' Theorem to be valid, the triangle must be a right-angled one.

The formula is:

c^2 = a^2 + b^2

Where c is the longest side. While a,b are the side lengths.

Using the above formula and the measurements given in the question, we can find the value of x.

By Pythagoras' Theorem,

26^2 = (5x)^2 + (12x)^2

676 = 25x^2 + 144x^2

169x^2 = 676

x^2 = 676 ÷ 169

x^2 = 4

x = 2

Answer:

5. x = 25.6

6. x = 11.0

7. x = 41.8°

8. x = 64.2°

9. x = 12.8°

10. x = 51.3°

Step-by-step explanation:

Let's find the x value for each triangle.

For point 5      

We have:

x: is the opposite cathetus to 52°  

20: is the adjacent cathetus to 52°  

52°: is the angle

We can find "x" with the following trigonometric function:

[tex] tan(52) = \frac{x}{20} [/tex]

[tex] x = tan(52)*20 = 25.6 [/tex]

For point 6      

We have:

x: is the hypotenuse  

5: is the opposite cathetus to the given angle  

27°: is the angle

To find "x" we need to use the trigonometric function:

[tex] sin(27) = \frac{5}{x} [/tex]

[tex]x = \frac{5}{sin(27)} = 11.0[/tex]

For point 7

We know:

x°: is the angle

6: is the hypotenuse

4: is the opposite cathetus to x°

Hence, x is:

[tex] sin(x) = \frac{4}{6} [/tex]

[tex] x = sin^{-1}(\frac{4}{6}) = 41.8 [/tex]

For point 8    

We have:

x°: is the angle

14: is the adjacent cathetus to x°

29: is the opposite cathetus to x°

To calculate "x" we need to use the trigonometric function tan(x):

[tex] tan(x) = \frac{29}{14} [/tex]

[tex] x = tan^{-1}(\frac{29}{14}) = 64.2 [/tex]

For point 9    

We have:

x°: is the angle

54: is the hypotenuse

12: is the opposite cathetus to x°

We can use sin(x) to solve for x:

[tex] sin(x) = \frac{12}{54} [/tex]

[tex] x = sin^{-1}(\frac{12}{54}) = 12.8 [/tex]

For point 10  

We have:

x°: is the angle

40: is the hypotenuse

25: is the adjacent cathetus to x°

We need to use cos(x) to solve for x:

[tex] cos(x) = \frac{25}{40} [/tex]  

[tex] x = cos^{-1}(\frac{25}{40}) = 51.3 [/tex]

I hope it helps you!

To solve the given questions, either of the trigonometric functions; sine, cosine and tangent of an angle has to be applied appropriately to either of the questions. The answers to the questions are:

5. x = 25.60

6. x = 11.00

7. x = [tex]41.8^{o}[/tex]

8. x = [tex]64.2^{o}[/tex]

9. x = [tex]12.8^{o}[/tex]

10. x = [tex]51.3^{o}[/tex]

The questions given are right angled triangles which requires the application of trigonometric functions appropriately. A right angle triangle is one that has one of its angles to be [tex]90^{o}[/tex].

So, each of the questions can be solved as follows:

5. Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan 52 = [tex]\frac{x}{20}[/tex]

⇒  x = Tan 52 * 20

       = 25.5988

x = 25.60

6. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin 27 = [tex]\frac{5}{x}[/tex]

⇒ x = [tex]\frac{5}{Sin 27}[/tex]

       = 11.0134

x = 11.00

7. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin x = [tex]\frac{4}{6}[/tex]

        = 0.66667

x = [tex]Sin^{-1}[/tex] 0.66667

  = [tex]41.8^{o}[/tex]

x = [tex]41.8^{o}[/tex]

8. Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan x = [tex]\frac{29}{14}[/tex]

          = 2.0714

x = [tex]Tan^{-1}[/tex] 2.0714

  = [tex]64.2^{o}[/tex]

x = [tex]64.2^{o}[/tex]

9. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin x = [tex]\frac{12}{54}[/tex]

        = 0.22222

x = [tex]Sin^{-1}[/tex] 0.22222

  = [tex]12.8^{o}[/tex]

x = [tex]12.8^{o}[/tex]

10. Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Cos x = [tex]\frac{25}{40}[/tex]

         = 0.625

x = [tex]Cos^{-1}[/tex] 0.625

  = [tex]51.3^{o}[/tex]

x = [tex]51.3^{o}[/tex]

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Draw a line and locate the origin '0', mark the positive numbers on the right and the negative number on the left of '0' at an equal distance.

A number line is a horizontal straight line in which the integers are placed in equal intervals. All the numbers can be represented in a number line. This line can be extended indefinitely at both ends. 

A number line is a graphical representation of numbers on a straight line. It is used for comparing and ordering numbers. It can be used for representing any real number that includes every whole number and natural number.

Draw a line and locate the point ‘0’. This point is known as the origin. If the given number is positive, draw it on the right side of the origin. If it is a negative number, draw it on the left side of zero. Divide each unit into the values equal to the denominator of the given fraction.

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Answer:

A is your answer

Step-by-step explanation:

Answer:

8²+16²=x²

Step-by-step explanation:

because h²=base²+perpendicular ²

After the taxes and rent, the remaining amount in his gross pay is $5,700

The term gross income is defined as also known as gross pay when it’s on a paycheck is an individual’s total earnings before taxes or other deductions.

Here we have given that Rene makes $38,000 per year and pays about 35% of his gross monthly income in federal and state taxes.

And as we all know that If you live in a metropolitan city, your HRA is equivalent to 50% of your basic salary.

Therefore, the remaining amount in his hand is calculated as,

=> $38000 - [35% of income + 50% of income]

Here the 35% of income is

=> 38000 x 35/100

=> 380 x 35

=> 13300

Similarly, the 50 percent of the income is

=> 38000 x 50/100

=> 380 x 50

=> 19000

Then the remaining amount is calculated by apply the values on it, then we get,

=> $38000 - [$13300 + $19000]

=> $3800 - $32300

=> $5700

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Answer:

21/5

Step-by-step explanation:

cross multiply

21=5x

flip

5x= 21

divide both sides

Answer:

1200

Step-by-step explanation:

Answer:

4

Step-by-step explanation: