What is 8/9 divided by 2/3?

The value of [tex]\log _{6}(36)[/tex] is 2.

Solution:

Given expression is [tex]\log _{6}(36)[/tex].

To evaluate the expression:

[tex]\log _{6}(36)[/tex]

36 can be written as 6².

       [tex]=\log _{6}\left(6^{2}\right)[/tex]

Using log rule: [tex]\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)[/tex]

       [tex]=2 \log _{6}(6)[/tex]

Using log rule: [tex]\log _{a}(a)=1[/tex] so that [tex]\log _{6}(6)=1[/tex]

       = 2(1)

       = 2

[tex]\log _{6}(36)=2[/tex]

Hence the value of [tex]\log _{6}(36)[/tex] is 2.

Final answer:

To find log₆ 36, we determine the exponent that 6 must be raised to to get 36. As 6 squared equals 36, the value of log base 6 of 36 is 2.

Explanation:

The question asks us to evaluate the logarithm of 36 with a base of 6, or, in mathematical terms, log base 6 of 36. We can solve this by recalling the definition of a logarithm, which is the power to which a base number must be raised to yield a given number. Since 6 squared is equal to 36 (6² = 36), the logarithm of 36 with a base of 6 is equal to 2.

The measure of arc EG = 16°.

Solution:

Given data:

m∠X = 47°  and m(ar FH = 110°)

To find the measure of arc EG:

We know that,

Angle formed by two intersecting secants outside the circle is equal to half of the difference between the intercepted arcs.

[tex]$m \angle X=\frac{1}{2}({arc} \ FH-{arc} \ EG)[/tex]

[tex]$47^{\circ}=\frac{1}{2}\left(110^\circ- {arc} \ EG}\right)[/tex]

Multiply by 2 on both sides.

94° = 110°  - arc EG

Subtract 110° from both sides.

-16° = -arc EG

Multiply -1 on both sides, we get

16° = arc EG

Switch the sides.

arc EG = 16°

The measure of arc EG = 16°.

Answer:

3.03143313302

Step-by-step explanation:

Answer:

3.03143313

Step-by-step explanation:

Answer:

x > 2

Step-by-step explanation:

7x +39 > 53

AND

16x + 15 > 31

7x > 14

AND

16x > 16

x > 2

AND

x > 1

And is intersection, which is x > 2

y = 75

Solution:

In a straight line, sum of the adjacent angles = 180°

80° + m∠DGF = 180°

Subtract 80° from both sides of the equation.

m∠DGF = 100°

Sum of all the interior angles in a quadrilateral = 360°

m∠DGF + m∠GFE + m∠FED + m∠EDG = 360°

100° + 120° + 65° + y° = 360°

285° + y° = 360°

Subtract 285° from both sides, we get

y° = 75°

Hence the value of y is 75.

Answer: equations 1,3,4 and 5 stated has solutions.

Step-by-step explanation:

From the question, (x + 5) + 5 = (x + 5) + 5

The equations that represent the situation are:

1. x + 5 = (5 − x) − 5 :which has one solution

2. x + 5 = (x + 5) − 5 : many solutions

3. x + 5 = (x + 5) − 5: no solution

4. x + 5 = (5 − x) − 5 : many solutions

5. (x + 5) + 5 = (x + 5) + 5: many solutions

Equation 2 has no solution. While the other equations have one and more than one solutions.

Answer:

x = 9

Step-by-step explanation:

you subtract 5 from 14 to get x alone with 9

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of the number x is 9.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The sum of a number x and 5 equals 14.

This can be written as,

x + 5 = 14

Subtract 5 on both sides.

x = 14 - 5

x = 9

Thus,

The value of the number x is 9.

Learn more about expressions here:

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The solution of the equation 4y − x + 9 = 0 and y = 6 − 2x will be (11/3, −4/3). Point (2, 3) is not the solution of the system.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The linear equations are given below.

−x + 4y = −9        ...1

y = −2x + 6         ...2

From equations 1 and 2, then we have

−x + 4(−2x + 6) = −9

−x − 8x + 24 = −9

−9x + 24 = −9

9x = 24 + 9

9x = 33

x = 11 / 3

Then the value of the variable 'y' is calculated as,

y = −2(11/3) + 6

y = −22/3 + 6

y = −4/3

The arrangement of the situation 4y − x + 9 = 0 and y = 6 − 2x will be (11/3, −4/3). Point (2, 3) isn't the arrangement of the framework.

More about the solution of the equation link is given below.

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The point (2, 3) does not satisfy either of the given equations, −x + 4y = −9 and y = −2x + 6. Therefore, it is not a solution to the system of equations.

To determine if the point (2, 3) is a solution to the system of equations consisting of −x + 4y = −9 and y = −2x + 6, we need to check whether the point satisfies both equations.

Let's substitute the values into the first equation:
−(2) + 4(3) = −8 + 12 = 4, which does not equal −9. Therefore, the point does not satisfy the first equation.

For the second equation:
−2(2) + 6 = −4 + 6 = 2, which does not equal 3. Hence, the point does not satisfy the second equation either.

Since the point (2, 3) does not satisfy either equation, it is not a solution to the system of equations.

To find out how much money your friend spent at the clothing store, set up a proportion using the information given. Your friend spent $20 at the clothing store.

To find out how much money your friend spent at the clothing store, we can set up a proportion using the information given. Let's let x represent the total amount your friend spent.

Since your friend paid $17 for a shirt, and that amount was 85% of the total amount spent, we can set up the equation:

17/x = 85/100

Cross multiplying, we get:

100 * 17 = 85 * x

1700 = 85x

To solve for x, we divide both sides of the equation by 85:

x = 1700 / 85 = 20

Therefore, your friend spent $20 at the clothing store.

Answer: 900

Step-by-step explanation:

Answer:

900

Step-by-step explanation:

Answer: its c

Step-by-step explanation:

Answer:

Your total earning for the week is $260

Step-by-step explanation:

You earn a salary of $200 weekly, which is constant. Then there is 3% commission on sales you make weekly too.

So it you make $2000, your commission is

3/100 × 2000 = $60

So your total earning for the week is constant income (salary) + commission, which is

$200 +$60 = $260

Explanation of identifying the percentage, base, and part of the base in an income scenario.

The total earning is $ 200 + 3% of $2000  

                                     = $ 200 + 60 = $260

The question: Identify the percentage, base, and part of the base in the given scenario.

Percentage: 3%

Base: Total sales made in the week, which is $2000

Part of the base: The commission earned, which is 3% of $2000

Answer:68

Step-by-step explanation:

Area of triangle=1/2×base×height

1632=1/2×48×h

1632×2=48×h

3264=48×h

3264/48=h

68=h

Final answer:

To find the height of a triangle with an area of 1,632 square inches and a base of 48 inches, we use the formula A = (base × height) / 2. Solving for height gives us a result of 68 inches.

Explanation:

To calculate the height of a triangle when its area and base length are known, we use the formula for the area of a triangle: A = (base × height) / 2. Given that the area of the triangular banner is 1,632 square inches and the base length is 48 inches, we can set up the equation:

1,632 = (48 × height) / 2

Multiplying both sides of the equation by 2 to get rid of the denominator:

3,264 = 48 × height

Next, divide both sides by 48 to isolate the height:

height = 3,264 / 48

height = 68 inches

Therefore, the height of the triangular banner is 68 inches.

Answer:

C

Step-by-step explanation:

Answer:c

Step-by-step explanation:

Answer:

[tex]\frac{sin(45^o)}{7}=\frac{sin(40^o)}{b}[/tex]

Step-by-step explanation:

The correct question is

In a triangle ABC, m∠A=45°, m∠B 40°, and a=7. which equation should you solve to find b?

we know that

Applying the law of sines

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}[/tex]

substitute the given values

[tex]\frac{sin(45^o)}{7}=\frac{sin(40^o)}{b}[/tex]

solve for b

[tex]b=(7)sin(40^o)/sin(45^o)[/tex]

[tex]b=6.4\ units[/tex]

Answer:

Sin45/7 = sin40/b

Step-by-step explanation:

:D

Answer:

The correct answer is A. 1.5

Step-by-step explanation:

This is the information given to us to answer the question correctly:

Week                        1  2  3  4  5  6

Numbers of Books 2  3  1  2  0  1

**************************************************

Assuming that these six weeks are representative of his reading  habits, what is the average number of books does Anthony read per week?

Let's calculate the average number of books, this way:

Average number of books Anthony reads per week = (2 + 3 + 1 + 2 + 0 + 1)/6

Average number of books Anthony reads per week = 9/6

Average number of books Anthony reads per week = 1.5

The correct answer is A. 1.5

Answer:

hi there! i can help you out! i don't want you to get a zero on your report card!!

Step-by-step explanation:

so, on the x-axis, which is all the numbers through 1-10 and there are the patient's number. so for ex, the first question says patient 1 : 3 hours right??

so the hours are the y-axis and you can label them 2,4,6,8 because skip counting by twos are probably the easiest! so for the first question, you would line a dot up on top of 1 and go up and you see 2 and 4 right, cuz you just labeled it... do go between 2 and 4 which is 3 and place the dot there...

and keep doing the same things with other ones too...

another ex! so on the second question, it says patient 2 : 7 hours so place the dot on top of the 2 and go up untill you see 6 and 8 and place the dot beween them!

Sorry but I forgot about Mean Median And Mode! Sorry I would hate to see you get a zero!

Answer: D. one equilateral triangle

explanation: Means, triangle is equilateral. If angle between , two sides having measure 5 cm , is not 60 degree, then the triangle will be always Isosceles. we will sine rule to find remaining measurements. In this case,also ,triangle is equilateral

Answer: one equilateral triangle

Step-by-step explanation:

Answer:

Step-by-step explanation:

I don't have a picture so I'll visually describe it. You start at the point (0,9) because 9 is the y intercept. Now that you have your first point, to get the next point, move up one and 2 to the right. Now, you're at the point (2,10). Continue going up one and 2 to the right until you get to the end of the graph. Then, go back to the point (0,9). This time, go the opposite way. Go one down, and two to the left. Now, you should be at the point (-2,8). Continue going down one, two left until once again, you run out of room on the graph. Then, use a ruler or freehand draw a line connecting your points. Add arrows on the ends on the line. Hope this helped!

Answer:

F(X) = 5 or -6

Step-by-step explanation:

F(X)  = [tex]x^{2} +x-30[/tex]

Using the Formula

[tex]-b[/tex]±[tex]\frac{\sqrt{b^{2} -4ac } }{2a}[/tex]

Where a = coefficient of [tex]x^{2}[/tex] i. e 1

b = coefficient of [tex]x[/tex] i. e 1

And c = 30

imputing the values, we have

[tex]-1[/tex] ± [tex]\frac{\sqrt{1^{2} - 4 X 1 X 30} }{2 X 1}[/tex]

[tex]-1[/tex] ± [tex]\frac{\sqrt{121} }{2}[/tex]

[tex]-1+\frac{11}{2}[/tex] OR [tex]-1-\frac{11}{2}[/tex]

Therefore, F(X) is either 5 or -6

Answer:

The answer is D: 5

Step-by-step explanation:

5 x 5 = 25 - 4 = 21 and 3 x 5 = 15 + 6 = 21

Answer: 5

Step-by-step explanation: Here, we want to determine which number can be replaced for the variable in this problem so the statement holds true.

5 would be the only number in this set that can work. Let's test it out.

We can do this by simply plugging in 5 for x. If the statement holds true when 5 is plugged in for x, then 5 is a solution.

Plugging in 5 for x, we have 5(5) - 4 = 3(5) + 6.

Simplifying, we have 25 - 4 = 15 + 6 or 21 = 21 which is a true statement.

So 5 is a solution.

Answer:

Step-by-step explanation:

how many touch downs did the team get?

A bar graph represents the points scored by a football team for each touchdown scored.

The graph that represents this situation is a bar graph. The x-axis represents the number of touchdowns scored and the y-axis represents the number of points scored. Each bar on the graph represents a different number of touchdowns scored, and the height of the bar represents the number of points scored for that number of touchdowns. For example, if the team scores 2 touchdowns, the corresponding bar on the graph would have a height of 12 (2 touchdowns * 6 points per touchdown).

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Answer:

  w = 300 +12.32v

Step-by-step explanation:

Calista's wages are ...

  wages = (straight time earnings) + (overtime pay)

  = $300 + (overtime hours)·(overtime pay per hour)

  = $300 + (v)($12.32)

Using the symbols required by the problem statement, we have ...

  w = 300 + 12.32v

Answer:

A=800πcm²

Step-by-step explanation:

Knowing that the area of a circular sector is:

[tex]A_{cs}=\frac{\pi\alpha r^{2}}{360}[/tex]

where α is the sweep angle and r in the radio (according to the graph),

then

A=(45° π 80²)/360° = 800πcm²

Final answer:

The area swept by the door is 10π cm and the area of the sector is 200π cm².

Explanation:

To find the area swept by the door, we can first find the length of the arc created by the door when it opens. The arc length formula is given by:

Arc length = r × θ

Where r is the radius (half the width of the door) and θ is the angle through which the door opens. In this case, the radius is 40 centimeters (half of 80 centimeters) and the angle is 45 degrees.

So, the arc length = 40 cm × (45 degrees) = 40π/4 cm = 10π cm

The swept area can be approximated by treating it as a sector of a circle with radius 40 cm and central angle 45 degrees. The area of the sector is given by:

Area = (θ/360) × π × r²

Where θ is the central angle and r is the radius. Substituting the values, we get:

Area = (45/360) × π × (40 cm)² = 1/8 × π × 1600 cm² = 200π cm²

Answer:

Step-by-step explanation:

Given that

3+2(2p+4t)

Let open the bracket first

3+ 2×2p + 2×4t

3+4p+8t

This is the equivalent of the expression.

The equivalent expression for 3+2(2p+4t) is given by performing the operations according to the mathematical rules of order of operations. First, apply the distributive property to get 4p + 8t. Then, the expression become 3 + 4p + 8t.

The student is looking to simplify and find the equivalent mathematical expression for: 3 + 2(2p + 4t).

First, you should apply the distributive property of operations, which means you multiply the number outside the parenthesis with each term inside the parenthesis. So, 2(2p + 4t) becomes 4p + 8t.

Next, add the 3 to the simplified expression 4p + 8t. The final equivalent expression will be 3 + 4p + 8t.

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Answer:

⅓

Step-by-step explanation:

Less than 3: 1 or 2

2/6 = 1/3

Answer:

Step-by-step explanation:

x/2=3.5

x=3.5*2

x=7

Answer:

Step-by-step explanation:

14/8

Answer:

Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:

                                             [tex]y=\frac{-8}{5}x-3[/tex]  

Step-by-step explanation:

Given the point (-5, 5)

slope = m = -8/5

Using the slope intercept form:  

[tex]y=mx+b[/tex]

Plugging point (-5, 5) and slope = m = -8/5 in the slope intercept form to find the y-intercept 'b'.

[tex]5=\frac{-8}{5}\left(-5\right)+b[/tex]

[tex]\mathrm{Switch\:sides}[/tex]

[tex]\frac{-8}{5}\left(-5\right)+b=5[/tex]

[tex]8+b=5[/tex]

[tex]8+b-8=5-8[/tex]

[tex]b=-3[/tex]

so the equation of the line will be:

[tex]y=mx+b[/tex]

plugging m = -8/5 and b = -3 in slope intercept form

[tex]y=\frac{-8}{5}x-3[/tex]      

Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:

                                             [tex]y=\frac{-8}{5}x-3[/tex]