find the value of k so that the point A lies on the line given by the equation.
A(2,1), 3x+ky=8

The evaluated value of [tex]log_{7}30[/tex] is 1.748

Change of base formula is used to change the base of the logarithm. It is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm.

According to the change of base formula:

       [tex]log_{a}b = \frac{log_{x}b }{log_{x} a}[/tex]

where base x is considered base 10

According to the question, we have to find the value of [tex]log_{7} 30[/tex]

Thus applying change of base formula we get

    [tex]log_{7} 30 = \frac{log_{10} 30}{log_{10} 7}[/tex]

calculating the value of log from the calculator we get,

        [tex]log_{7} 30 = \frac{1.477}{0.845}[/tex]

        [tex]log_{7} 30 = 1.748[/tex]

Thus evaluated value of [tex]log_{7}30[/tex]  is 1.748

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Answer: 50 1/4

Step-by-step explanation:

Answer:

Step 1: 20

Step 2: 40

Step 3: 45

Step 4: 90

Step 5: 84

Step 6: 21

Step 7: 1

I did get 1 by following the steps.

The required solution of the system of equations are x=-6 and y=-10.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The system of equations are

-2x+2y=-8 and -3x+y=8

According to given question we have

Consider the first equation.

-2x+2y=-8

Taking  minus sign common  from both sides we get

-(2x-2y)=-8

2x-2y=8

Taking  2 common  from left sides,  we get

2(x-y)=8

Divide by 2 on both sides we get,

x-y= 4....(i)

-3x+y=8...(ii)

By adding 2 equation we get

-2x=12

x=-6

Put the value of x in Equation (i) we get

x-y= 4

-6-y=4

-y=4+6

y=-10

Therefore, the required solution of the system of equations are x=-6 and y=-10.

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Answer:

the first one is D. {3/2}

second one is C. {-10}

Step-by-step explanation:

hope this helps

Answer:

12.

Step-by-step explanation:

y /x = 6/8 = 3/4

y/x = 18/24 = 3/4

The relation is y = 3/4 x.

So, the missing value is 16 * 3/4

= 12.

Answer:

The length of UV is 10 units.

Step-by-step explanation:

It is given that the points T, U, V and W all lie on the same line segment, in that order, such that the ratio of TU:UV:VW is equal to 1:5:2.

Now, we need to calculate UW if TW = 32.

So, TU : UV : VW = 2 : 5 : 5

=> TW = 24

From the above conditions it can be observed that;

=> Ratio of TU = 2

=> Ratio of UV = 5

=> Ratio of VW = 5

Firstly, we have to sum up the total ratio that is;

=> Total = Ratio of TU + Ratio of UV + Ratio of VW

=> Total = 2 + 5 + 5

=> Total = 12

Now, we need to calculate the length of UV from which we get;

=> UV = 5/12 * 24

=> UV = 10

Therefore; length of UV is 10 units.

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In a quadrilateral with a perimeter of 120 inches, the longest of the four sides has length equal to 33 inches.

A quadrilateral is a two-dimensional figure that has 4 sides and 4 vertices. The perimeter of any two-dimensional figure is the sum of all its sides.

If the lengths of the four sides of a quadrilateral (in inches) are consecutive odd integers, we can express each side as:

x = length of side 1(odd integer)

x + 2 = length of side 2

x + 4 = length of side 3

x + 6 = length of side 4

If the perimeter of the quadrilateral is 120 inches, then the sum of the four sides is equal to 120 inches.

x + (x + 2) + (x + 4) + (x + 6) = 120

Simplifying and solving for x.

4x + 12 = 120

4x = 108

x = 27

Substitute the value of x on the expression for the length of the 4th side(longest side).

longest side = x + 6 = 27 + 6

longest side = 33 inches

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The solution is 6

Rewriting the given equation

√(4x + 1) - 5 = 0

Now, taking square of the equation to find the solution of equation -

(√(4x + 1))² = 5²

On squaring both sides we get the equation -

4x + 1 = 25

Shifting 1 to the Right Hand Side of the equation

4x = 25 - 1

Performing subtraction on Right Hand Side of the equation

4x = 24

Shifting 4 to the Right Hand Side of the equation as denominator

x = 24 ÷ 4

Performing division on Right Hand Side of the equation

x = 6

Thus, the solution is 6

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The correct question is - sqrt(4x+1)-5=0

Answer:

Vertex=(-3,6) and Y intercept is 15/(0,15)

The estimate of the product is reasonable

The product expression is given as

759 x 68

As an estimate, we have

759 - 760

68 = 70

So, we have:

759 x 68 = 760 * 70

Evaluate the product

759 x 68 = 53200

For the actual product, we have

759 x 68 = 51612

The estimate and the actual product both approximate to 50000

Hence, the estimate of the product is reasonable

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Answer:

[tex] \sqrt[5]{x } = - 2 = - 35[/tex]

The statement that explains whether Juliana is correct is A. She is correct because she can multiply 6 and 10 by any number to form an equivalent ratio.

From the information, it should be noted that

Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6:10.

It should be noted that she is correct because she can multiply 6 and 10 by any number to form an equivalent ratio.

An example is (6 × 2)/(10 × 2) = 12/20

It should be noted that 6/10 is equivalent to 12/20.

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The values of x that will make x² = 9 are positive 3 and negative 3.

A quadratic equation is an algebraic equation that has highest degree of 2, therefore, it also has two roots or we can say it has two solutions.

We know sign distributions that negative distributed to a negative is positive and positive distributed to a positive also results in positive.

∴ 9 can be obtained by either multiplying (-3)(-3) or (3)(3).

So, the value of x that will make x² = 9 is

x = ± √9

x = ± 3.

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A full cycle, if the pendulum is 10 cm, is 0.6 seconds long. A full cycle, if the pendulum is 20 cm, is 0.9 seconds long. A pendulum that takes 2 seconds for one full cycle is 100 cm long.

Given,

The time t in seconds for a swinging pendulum to complete one full cycle is given by the function t as,

t = 0.2 √I

Here, l is the length of the pendulum in centimeters.

For the first part, two lengths are given for the pendulum is given

We can obtain the value of t by substituting the value of l

This implies,

For l =  10 cm

t =  0.2 √10 = 0.632 = 0.6 seconds

For l =  20 cm

t =  0.2 √20 = 0.894 = 0.9 seconds

For the second part, time is given

We can obtain the value of l by substituting the value of t

This implies,

For t = 2 seconds

l = t² / (0.2)² = t² / 0.04 = 2² / 0.04 = 4 / 0.04 = 100 cm

Therefore, A full cycle is 0.6 seconds long if the pendulum is 10 cm long, 0.9 seconds long if the pendulum is 20 cm long, and 100 cm long if the pendulum takes 2 seconds to complete one full cycle.

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Based on the given parameters, the value of the polynomial function f(8) is -4

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

The polynomial function is given as

Polynomial = f(x)

Also, we have the following statement

a remainder of -4 when divided by x-8

To start with, we set the divisor to 0

So, we have

x - 8 = 0

Add 8 to both sides of the equation

So, we have

x = 8

Express as a function

f(x) = f(8)

Set the equation to the remainder

So, we have

f(x) = f(8) = -4

Hence, the value of the polynomial function f(8) is -4

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The value of x for log (5-2 x)=0 is 2.

It is established that the exponential equation x = ay and the logarithmic function y = logax are equal. Only when x = ay, a > 0, and a 1 do y and logax coincide. The base-a logarithmic function is what it is known as. Think about what it means for the exponential function to be inversed: x = ay.

Given,

log (5-2 x)=0

It can be expressed as -

5 - 2x = 10⁰

= 5 - 2x = 1

= x = 2

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The margin of error is 3.083 min

Margin of Error: The margin of error is the range of error permitted around the sample statistic in order to estimate the population parameter. The margin of error indicates the size of the confidence interval. The breadth of the confidence interval increases with the margin of error.

Sample size, n=24

Sample mean, ¯x=31.5 min

Sample standard deviation, s=7.3 min

Confidence level, c=95%

=0.95

From the given information we can calculate the below-required quantities,

Significance level, α=1−c=1−0.95=0.05

Degrees of freedom, DOF=n−1

=24−1

=23

Now from the t-distribution table,

The value of t (α2, DOF) is,

t (0.025,23) = 2.069  

Hence the margin of error will be,

MOE= t (α2, DOF) × s/√ n

=2.069×7.3/√24

=3.083 min

i. The upper limit of the confidence interval will be,

UL=¯x + MOE=31.5+3.083=34.583

The lower limit of the confidence interval will be,

LL=¯x−MOE

=31.5−3.083

=28.417

Hence, the 95% confidence interval is (28.417,34.583)

(28.417,34.583)

The answer is 28.417,34.583

ii. The required answer is MOE=3.083 min

ii. We have found the 95% confidence interval for the population mean to be (28.417,34.583). This means with 95 % confidence; it can be said that the population mean commute time is between the bounds of the confidence interval.

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Answer:

[tex]\frac{3}{22}[/tex]

Step-by-step explanation:

To multiply fractions, just multiply the numerators (tops) times each other and the denominators (bottoms) times each other:

[tex]\frac{-1}{4}[/tex] x [tex]\frac{-6}{11}[/tex] = [tex]\frac{6}{44}[/tex]

Now all we have to do is to simplify.  In this case, just find the largest number that goes evenly into the numerator and the denominator: it is 2.  Divide numerator and denominator by 2 to get the final answer: [tex]\frac{3}{22}[/tex]

Answer:

the answer will be (-1, -6.5)

Step-by-step explanation:

The midpoint formula is [tex](\frac{x^1 + x^2}{2} , \frac{y^1 + y^2}{2} )[/tex]

so you would do [tex](\frac{2 - 4)}{2} , \frac{-9-4}{2} )[/tex] , the only reason it is subtracting is that a positive and a negative make a negative so you might as well subtract, either way, if you insert the equation by doing 2 + (-4) you will get the same thing

then you would just do the math and get your answer

Hope this helps :)

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -4 +2}{2}~~~ ,~~~ \cfrac{ -4 -9}{2} \right) \implies \left(\cfrac{ -2 }{2}~~~ ,~~~ \cfrac{ -13 }{2} \right)\implies \left(-1~~,~~-6\frac{1}{2} \right)[/tex]

The first five terms of the sequence area s follows:

4, 6 , 8 , 10, 12

Each term of the sequence is 2 more than the previous term.

The third term is 8.

The sequence is an arithmetic sequence base on the difference.

Using arithmetic sequence formula,

aₙ = a + (n - 1)d

where

Therefore, let's used the third term to find the first term.

8 = a + 2d

8 = a + 2(2)

8 = a + 4

a = 8 - 4

a = 4

Therefore, the first term of the sequence is 4.

Hence, the first five terms of the sequence area s follows:

4, 6 , 8 , 10, 12

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Answer:

3.5 in decimal form or 3 1/5

Step-by-step explanation:

Answer:

= - 1 1/6

Step-by-step explanation:

1 1/2 - 2 1/3

= 1 2/6 - 2 3/6

= 8/6 - 15/6

= - 7/6

= - 1 1/6

Answer:

The answer is 7

Step-by-step explanation:

The formula you would use is A=bxh

So you would just plug it in

3.5 x 2 which gives you 7

Hope this helps:)

A real coefficient quadratic equation cannot have one real root and one imaginary root.

Therefore, a real coefficient quadratic equation cannot have one real root and one imaginary root.

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Answer:

x+21/2.

Step-by-step explanation:

3/4(3x+6)-1/4(5x-24).

=9x/4-5x/4+9/2+6.

=x+21/2

The given  logarithmic expression statement is false. Because log₄7- log ₄3 = log₄(7/3).

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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Answer:first do the exponents thats equal to 9 then times -2 is -16+7 is -11

hope that helps

Step-by-step explanation:

Answer:

-11.

Step-by-step explanation:

7+(-2)•3^2

= 7 - 2*9

= 7 - 18

= -11.

After solving, the factors of equation x²-5x+6 are:

So,

Given the equation: x²-5x+6

Then,

Factors are: (x-3) and (x-2)

Therefore, after solving, the factors of equation x²-5x+6 are:

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The steps for constructing the bisector of an angle by using a ruler and compasses are as follows:

Step 1:

Take a compass and place its point on the angle's vertex Q.

Step 2:

Adjust the compass to the medium wide setting. The exact width is not important.

Step 3:

Without changing the compasses' width, draw an arc across each leg of the angle.

Step 4:

Now, place the compass on the point where one arc crosses a leg and draw the arc in the interior of the angle.

Step 5:

Without changing the compass setting repeat for the other leg so that the two arcs cross.

Step 6:

Now by using a ruler draw a line from the vertex to the point where the arcs cross.

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