Use the Change of Base Formula to evaluate each expression.
log₂9

The point-slope equation of something like the line, with slope equal to 5/6 but instead passing through the point at(22 , 12), is:

(y - 12) = 5/6(x - 22).

A line's equation can be stated in three different ways:

The typical form of a line equation is ax + by = c, where a but rather b are the coefficients of variables x and y, respectively, as well as c is a constant if all possible values must be integers. In the meantime, the slope-intercept form is given by the formula y = mx + b, where m is the line's slope as well as b is the y-intercept. Given the slope m and a point on the line (x, y), we can formulate the equation using point-slope form, (y - y1) = m. (x - x1).

To build up the equation, use the point slope form and enter in the values.

(y - y1) = m(x - x1)

where;

m = 5/6

(x1 , y1) = (22 , 12)

(y - 12) = 5/6(x - 22)

In slope-intercept form, the equation of the line is:

(y - 12) = 5/6(x - 22)

y - 12 = 5/6 x - 110/6

y = 5/6 x - 19/3

In standard form, the equation of the line is:

y = 5/6 x - 19/3

5/6 x - y = 19/3

Multiplying both sides by 6,

5x - 6y = 38.

The point-slope equation of something like the line, with slope equal to 5/6 but instead passing through the point at(22 , 12), is:

(y - 12) = 5/6(x - 22).

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WAIT I THINK X = 3±i√31/4

Answer:

2x*-3x-5

* = squared

Step-by-step explanation:

step 1: distribute “x” to “2x+1”

-you now have the equation: 2x*+1x-4x-5

step 2: combine like terms (combine “1x” and “-4x”. that gets you “-3x”.)

-you now have the equation: 2x*-3x-5

step 3: you have no more like terms, your equation is solved.

final equation: 2x*-3x-5

Answer:

13/28 kg

Step-by-step explanation:

Convert to 28 in the denominator.

[tex]\frac17 \cdot (3+\frac14) = \frac37+ \frac{1}{28} = \frac{3\cdot4}{7\cdot4}+ \frac{1}{28} = \frac{12}{28}+ \frac{1}{28} = \frac{13}{28}[/tex]

Answer:

x = 22 1/3

Step-by-step explanation:

5x - 17 = 2x + 50

~Add 17 to both sides

5x = 2x + 67

~Subtract 2x to both sides

3x = 67

~Divide 3 to both sides

x = 22 1/3

Best of Luck!

The midpoint is located at (4,-0.5)

In the problem we are given that

E is located at (2,-1)

F is located at (6,0)

To find the midpoint, add the 2 X values together and divide by two, then do the same with the y values:

X = (2 + 6) /2= 8/2 = 4

Y = (-1+ 0)/2 = -1/2 = -0.5

The midpoint is located at (4,-0.5)

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All the roots of the polynomial 2x⁴+ x³-8x²- 4x = 0 are x = -2, x = -0.5, x = 0, x = 2 ( Option A ).

Given polynomial :

2x⁴+ x³-8x²- 4x = 0

The highest power of the polynomial is 4. This implies that this polynomial will have 4 roots or 4 zeroes.

There are numerous ways of finding roots or zeroes of a polynomial of any degree.

A root or zero of a polynomial is a solution or value of the variable which gives the value of the polynomial equal to 0.

Since this is a multiple choice based question, the easiest approach to this question is by eliminating options and finding the correct answer.

Option B and C get eliminated instantly because they have only three roots, however this is a polynomial of degree 4 and should have 4 roots.

For option A and C, we put x= -2, x = -0.5, x = 0, x = 2, and x = 0.5 in the given polynomial to check if the answer is equal to zero.

For x = -2, we get 2x⁴+ x³-8x²- 4x = 0

For x = 2, we get 2x⁴+ x³-8x²- 4x = 0

For x = 0, we get 2x⁴+ x³-8x²- 4x = 0

For x = -0.5, we get 2x⁴+ x³-8x²- 4x = 0

For x = 0.5, we get 2x⁴+ x³-8x²- 4x = -3.75

From this result, option C gets ruled out and all the values in option A check out as a root of the given polynomial.

Therefore, we get all the roots of the polynomial 2x⁴+ x³-8x²- 4x = 0 as x = -2, x = -0.5, x = 0, x = 2

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Option A, 65 + |−5| = 70°, 65° is the farthest from 0°

Here, we are given that.

The average temperature in the mountains is 65° in April.

The average temperature in that same spot is −5° in December.

Thus, the difference in the temperature will be-

65 - (-5)

= 65 + 5

= 70°

Therefore, this location is 70° warmer in April than in December.

Now, their distance from 0 will be-

|65 - 0| = 65

as distance cannot be negative, we look at only the absolute difference.

Similarly |-5 -0| = 5

Thus, we see that 65° is the farthest from 0°.

Hence, option A, 65 + |−5| = 70°, 65° is the farthest from 0°, is the correct answer.

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The meaning of the 2 in the expression 3t + 2c is the weight of each car

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

3t + 2c

From the question we have the following parameters:

This means that the weight of each car is 2

Hence, the meaning of the 2 in the expression 3t + 2c is the weight of each car

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There will be more than a percentage of 33 % of households that have an interfaith marriage from 2017 onwards.

In this problem we find a linear equation that models the percentage of households with an interfaith marriage in time. The expression indicates that the percentage increases uniformly in time. Herein we must look up for the year, from which the percentage is at least 33 % greater. Then:

I = (1 / 4) · x + 23

(1 + 33 / 100) · 23 = (1 / 4) · x + 23

30.59 = (1 / 4) · x + 23

(1 / 4) · x = 7.59

x = 30.36

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Answer:

6 minutes

Step-by-step explanation:

No. of pages printed in 4 minutes = 72

No. of pages printed in 1 minute   = 72/4 = 18

Remaining pages to be printed    = 177 - 72 = 105

Time taken to print 105 pages = 105/18 = 5.83 minutes

Rounded off to the nearest whole number ⇒ 6 minutes

Answer:

- 67

Step-by-step explanation:

note that + (-) = -

- 56 - 8 + (- 3)

= - 64 - 3

= - 67

To solve this problem, you need to use PEMDAS.

Parentheses, exponents, multiplication, division, addition, and subtraction.

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

In the end, your answer would be -67.

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

Hopefully I understood your question correctly!

Have a great day and God bless! :)

Answer:

1 3/10

Step-by-step explanation:

The area of each card is 80.05cm^2, and the edge of each card is 8.95cm.

Priti chose a green coloured square paper of 20.5cm, since its a square the length and breadth of the card are equal

l = b

Recall the area of a square is

A = l^2

A = (20.5)^2

A= 20.5 × 20.5

A= 400.25cm^2

Since the paper is to be used for 5 cards, therefore the is divided in 5 equal cards. The are area of each card will be

A = A/5

A = 400.25/5

A = 80.05cm^2

The edge of each card is the side of the each card which can either be the length or the breadth since all the sides are equal for a square.

Recall that

A = l^2

Since the Area of each card is 80.05cm^2. Therefore,

80.05 = l^2

Finding the square root of both sides

(80.05)^1/2 = (l^2)^1/2

l = 8.947cm

Approximate l to 2 decimal place

l = 8.95cm

Therefore, the edge of each card is 8.95cm

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Jeffery will obtain $54 as interest on $4,500.00

If Jeffery originally invested $4,500.00.

Then, 1.2% interest on 4,500.00 will be:

Therefore, Jeffery will obtain $54 as interest on $4,500.00.

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The expression can be simplified through division of the exponential (power).

In the given expression, if the powers have the same base, we can actually divide the power.  In order to carry out the division of the exponential (power), we can subtract their exponential.

In the general form, a-m=1/am

As there are two different base terms x and y in the numerator and denominator, we will subtract the powers of x terms and powers of y terms.

Let us simplify the x terms,

x¹/₂÷x³/₄=x(1/2)-(3/4)  

Solving the powers,(½)–(¾)=(2/4)–(¾)=(2-3)/4=-1/4

x¹/₂÷ x³/₄=x(1/2)-(3/4)= x-1/4  

Let us simplify the y terms,

y⁻¹/₃÷y¹/₂= y(⁻¹/₃)-(¹/₂)

Solving the powers, (-1/3)-(1/2)=(-2/6)-(3/6)=-5/6

y⁻¹/₃÷y¹/₂= y(⁻¹/₃)-(¹/₂)=y-5/6

Putting the terms together gives us,

x-1/4 *y-5/6

It can be expressed as a fraction as a-m=1/am

x-1/4 *y-5/6=1/x1/4y5/6

Hence, x¹/₂ y⁻¹/₃ / x³/₄ y¹/₂= x-1/4 *y-5/6=1/x1/4y5/6

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Answer: No

Step-by-step explanation:

It is already in its simplest form, but the decimal for it would be 0.53.

Answer: 8/15 can`t be simplified

Step-by-step explanation:

[tex]\displaystyle\\\frac{8}{15} =\\\\\frac{2*4}{3*5} \\\\Hence,\\\\ 8/15\ can`t\ be\ simplified[/tex]

If Jim has to run faster than 80% of adult then he need to run with speed 5.89 mph.

A Normal Distribution is defined as the distribution where the random variable values are distributed symmetrically.

In the Question it is given  that

mean (μ) = 5.3                                                   ...(i)

standard deviation (σ) = 0.7                             ...(ii)

and Jim runs faster than 80% of adult men,

and the group follows a normal distribution.

For Normal Distribution

Jim runs faster than 80% of adult men, is represented by

P(x<z)=0.80

z=φ(0.80)

z=0.842    ( from z table )                                  ...(iii)

we know that

[tex]z=\frac{x-\mu}{\sigma}[/tex]                                         ...(iv)

Substituting the values of (i),(ii) and (iii)  in (iv) we get

[tex]0.842=\frac{x-5.3}{0.7} \\ \\ x-5.3=0.842*0.7\\ \\ x-5.3=0.5894[/tex]

[tex]x=0.5894+5.3\\x=5.8894[/tex]

x≅5.89

Therefore , if Jim has to run faster than 80% of adult then he need to run with speed 5.89 mph.

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Answer:

x=−4y+9

Step-by-step explanation:

Let's solve for x.

x+4y=9

Step 1: Add -4y to both sides.

x+4y+−4y=9+−4y

x=−4y+9

Answer:

x = 9 - 4y

Step-by-step explanation:

Answer:

7 and 1/3

O___O

Answer:

x = 9

A(lol,brainly wont let me post this)F = 19

Step-by-step explanation:

see image. Since F is the midpoint, both halves of the segment must have the same measure.

If AhalfF is 2x+1, then the other half of AD must also be 2x+1.

We were given the length of the whole thing as well, so we can set up an equation to solve. See image.

[tex] \large \bf \implies{x = 24 \degree \: and \: y = 15 \degree}[/tex]

[tex] \bf \longrightarrow(6x - 7 ) \degree+ (3x - 29) \degree = 180 \degree \\\bf \longrightarrow (9x - 36) \degree = 180 \degree \\\bf \longrightarrow 9x = 180 \degree + 36 \degree \\\bf \longrightarrow 9x = 216 \degree \\\bf \longrightarrow x = \frac{ \cancel{216} \degree}{ \cancel{9} } \\\bf \longrightarrow \boxed{ \bold{ x = 24 \degree}}[/tex]

[tex] \red{ \rule{7cm}{0cm}}[/tex]

[tex]\bf \longrightarrow(8y + 17) \degree = (6x - 7) \degree[Vertical \: angles] \\\bf \longrightarrow 8y = 6 \times 24 - 7 - 17 \\ \bf \longrightarrow8y = 144 - 24 \\\bf \longrightarrow 8y = 120 \\\bf \longrightarrow y = \frac{ \cancel{120}}{ \cancel{8} } \\\bf \longrightarrow \boxed{ \bold{y = 15 \degree}}[/tex]

Answer:

-4 is the coefficient to the variable [tex]f[/tex].

[tex]f[/tex] is, as said one line before, a variable.

Answer: -4 is a coefficient, and f is a variable.

Step-by-step explanation: I hope this helps.

Answer:

The resultant expression is 48 + 30 = 6 (8 + 5) = 6 (13) = 78.

Step-by-step explanation:

It is given that the GCF of 48 and 30 to write the sum of the two numbers as the product of their GCF and another sum.

Now,

The largest number that can divide two numbers is known as the GCF. The formula for 48 plus 30 is as follows;

=> 48 + 30

=> 6 (8 + 5)

=> 6 (13)

=> 78

Here, the numbers are given as 48 and 30 so, the expression is;

=> 48 + 30

And their GCF is 6 so, we get;

=> 48 + 30 = 6 × 8 + 6 × 5

=> 48 + 30 = 6 (8 + 5)

=> 48 + 30 = 6 (13)

=> 48 + 30 = 78

Therefore, the resultant expression is 48 + 30 = 6 (8 + 5) = 6 (13) = 78.

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Answer:

5x + 7

Step-by-step explanation:

8x + 8 + 2x + 7 = 10x + 15

15x + 22 - (10x + 15) = 5x + 7

There is no Real number whose square is −16.

If

a∈R then a2≥0. So there is no real square root of −16

If i is the imaginary unit, then i

i^2=-1

and we find that:

(4i)2=2⋅i2=16⋅−1=-16

So 4i is a square root of −16.

(−4i)2=(−4)2i2=16⋅−1=−16

So, −4i is a square root of −16√−16=i√16=4i

There is no Real number whose square is −16.

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We need to know about percentage to solve the problem. The price of the pair of pants after discount but before tax is $19.8

Percentage of a number gives us a certain part of the quantity, suppose we say that 20% of 100 then we have 20. It can be defined as a given part in every hundred. In this question we know that the store Feng goes to buy a pair of pants offers 40% discount, which means that Feng can save 40% of the price of the pants. The original price on tag is given as $33, we have to find what 40% of $33 is and then subtract that amount from $33 to get the price of the pair of pants after discount but before tax.

Discount=[tex]\frac{40}{100}[/tex]x33=132/10=13.2

The price of the pants after discount =$(33-13.2)=$19.8

Therefore we found that the price of the pair of pants after discount but before tax is $19.8

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Answer:

y = 4x

Step-by-step explanation:

it's on the orgin and I got it right

Answer:

y = 4x - 9

Explanation:

slope intercept form:

In the given equation y = 4x - 7, the slope is 4 and y-intercept is -7.

If the equation's are parallel to each other, the slopes are same. [tex]\sf m_1 = m_2[/tex]

So the slope for equation which passes through (3, 3) will be 4.

Equation:

[tex]\sf y - y_1 = m(x - x_1)[/tex]

[tex]\rightarrow y - 3 = 4(x - 3)[/tex]

[tex]\rightarrow y - 3 = 4x - 12[/tex]

[tex]\rightarrow y = 4x - 12+3[/tex]

[tex]\rightarrow y = 4x - 9[/tex]

This is an expression testing the knowledge on indices. Solve the like terms and apply the index rule: a^m÷ a^n = a^m-n.

x²/₃ y⁻¹/₄ / x¹/₂ y⁻¹/₂

x²/₃ y⁻¹/₄ ÷ (x¹/₂ y⁻¹/₂)

x²/₃÷ (x¹/₂) . y⁻¹/₄ ÷ (y⁻¹/₂)

x^(2/3-1/2)y^(-1/4--1/2)

x^1/6.y^1/4

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The point that is on the interior of angle CAB is Point E.

A point that is in the interior of an angle or shape is on that is not on the angle, line or shape, and is instead within the shape itself.

Points A, B, and C are all on the line and so are not interior. Point B is outside the shape formed and so is not in the interior.

Point E is not on the line and it is inside the shape formed so it is in the interior.

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