Write the expression as a single logarithm.


4logby + 3logbx

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The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)

From the question, we have the following expression that can be used in our computation:

–3(2x – 5) < 5(2 – x)

Divide bot sides of the inequality by -1

So, we have the following representation

3(2x – 5) > -5(2 – x)

Next, we open the brackets

This gives

6x – 15 > -10 + 5x

Hence, the representation is 6x – 15 > -10 + 5x

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Complete question

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

(a) 6x – 15 > -10 + 5x

(b) 6x – 15 < -10 + 5x

(c) 3(2x – 5) > -5(2 – x)

(d) 3(2x – 5) < -5(2 – x)

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

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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Answer:

C)   1/3

Step-by-step explanation:

3 = 3/1

3/1  x  1/3  = 3/3  = 1

Answer:

A is your answer

Step-by-step explanation:

Answer:

8²+16²=x²

Step-by-step explanation:

because h²=base²+perpendicular ²

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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The answer is 1.57! I hope this helps you!

Answer:

x=78

Step-by-step explanation:

x+x+24=180

2x+24=180

2x=156

x=78

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:

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

Answer:

15

Step-by-step explanation:

5 X 10 = 50

170 / 50 = 3 sets  = 15

According to fraction and ratio, second dog is 3/2 feet long.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

First dog is 5 feet long.

then,

5 feet is equal to 4/5 of the second dog's length.

multiply both sides by 5/4.

5/4 x 5 feet is the second dog's length.

The second dog is 25/4 feet long.

The second dog is 6(1/4) feet long.

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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

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 solution of the given function cosx - √(3 - 3cos³x) = 0 is C. 30° + 360° n, 330° + 360°n

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are given the function as;

cosx - √(3 - 3cos³x) = 0

cosx = √(3 - 3cos³x)

Taking square root on both sides.

cos ²x = √(3 - 3cos³x) ²

cos ²x = (3 - 3cos³x)

For solving for x in

cos ²x = (3 - 3cos³x)

cos ²x = 3 (1 - cos³x)

(1 - cos³x) = cos ²x/3

x= π/6 + 2πn

or

x=11π/6 + 2πn

where n is an integer.

30° + 360° n, 330° + 360°n

The correct answer is C.

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Answer:

1200

Step-by-step explanation:

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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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:

Step-by-step explanation:

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

Answer:

4

Step-by-step explanation:

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:

I think no 3

if wrong correct me please

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Answer: 3150

Step-by-step explanation:

V = lwh

V = 25 x 7 x 18

V = 3150

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.

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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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