Solve 9x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b

Answer:

5/8

Step-by-step explanation:

first plug in for x & y, then solve. you should get 5/8

2 -2 +5 +0 / 2 +3 +5 -2

5/8

Answer:

125/32

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The line x originates from the center of the circle and forms a perpendicular line with line RS, which means that the line is bisected.

That means that line RT is half of line RS, or 7.

Then we can use the Pythagorean Theorem to find the measure of x.

[tex]7^2+b^2=9^2[/tex]

[tex]49+b^2=81[/tex]

[tex]b^2=32[/tex]

b = √32

b ≈ 5.66

Answer:

5e^(3x+7)=21

e^(3x+7)=4.2

(3x+7)lne=ln4.2

lne=1

3x+7=1.435

3x= -5.565

x= -1.855

To solve the equation [tex]5e^{3x}+7=21[/tex], isolate the exponential term, take the natural logarithm of both sides, and then solve for x. This results in x ≈ 0.3362.

To solve the equation [tex]5e^{3x}+7=21[/tex], follow these steps:

First, isolate the exponential term by subtracting 7 from both sides:

[tex]5e^{3x} = 14[/tex]

Next, divide both sides of the equation by 5:

[tex]e^{3x} =\frac{14}{5}[/tex]

Now, take the natural logarithm (ln) of both sides:

[tex]ln(e^{3x}) = ln(\frac{14}{5})[/tex]

Since the natural logarithm and the exponential function are inverse operations, the left side simplifies to:

[tex]{3x} = ln(\frac{14}{5})[/tex]

Finally, solve for x by dividing by 3:

[tex]x =\frac{1}{3}\times ln(\frac{14}{5})[/tex]

Using a calculator, this results in:

x ≈ 0.3362

ANSWER

[tex]3= a( - 1 +6)( - 1 - 5)[/tex]

EXPLANATION

The equation of a parabola in factored form is

[tex]y = a(x + m)(x + n)[/tex]

where 'a' is the leading coefficient and 'm' and 'n' are the zeros.

From the question, the zeros of the parabola are 6 and −5.

This implies that,

[tex]m = 6 \: \: and \: \: n = - 5[/tex]

We plug in these zeros to get:

[tex]y= a(x +6)(x - 5)[/tex]

If (-1, 3) is a point on the graph of this parabola,then it must satisfy its equation.

We substitute x=-1 and y=3 to obtain:

[tex]3= a( - 1 +6)( - 1 - 5)[/tex]

The first choice is correct.

Final answer:

To rationalize the denominator and simplify the expression 6 / (5-3), multiply the numerator and denominator by 1/2. Then, simplify the expression to get 3/1 = 3.

Explanation:

To rationalize the denominator and simplify the expression 6 / (5-3), we can start by multiplying the numerator and denominator by a skillfully chosen factor. In this case, we can choose 1/2 as the factor.

The numerator becomes 6 * 1/2 = 3, and the denominator becomes (5-3) * 1/2 = 2/2 = 1.

Therefore, the simplified expression is 3/1 = 3.

Trapezoids and parallelograms both feature parallel sides, with a trapezoid having one pair and a parallelogram having two pairs. Parallelograms always have supplementary consecutive angles and congruent opposite sides, which is not necessarily the case for all trapezoids.

Trapezoids and parallelograms are related by the characteristic that they both have parallel sides. Specifically, a trapezoid has one pair of parallel sides known as the bases, whereas a parallelogram has two pairs of parallel sides.

Moreover, the consecutive angles in a parallelogram are supplementary, meaning that any two angles next to each other add up to 180 degrees. While trapezoids do not have this property for all four of their angles, the angles adjacent to the bases (the non-parallel sides) may also be supplementary, depending on the specific shape of the trapezoid.

It is important to note that while all parallelograms are quadrilaterals with opposite sides that are congruent and parallel, not all trapezoids share these properties. The key distinction between the two shapes lies in the number of parallel sides.

Additionally, comparing them with rhombuses, parallelograms can be rhombuses if all sides are congruent, but trapezoids cannot be rhombuses as they lack the two pairs of parallel sides.

Answer:

D

Step-by-step explanation:

Given

2x² + 3x - 7 = x² + 5x + 39

Subtract x² + 5x + 39 from both sides

x² - 2x - 46 = 0 ← in standard form

with a = 1, b = - 2, c = - 46

Solve for x using the quadratic formula

x = (- (- 2) ±[tex]\sqrt{(-2)^2-(4(1)(-46)}[/tex] ) / 2

  = ( 2 ± [tex]\sqrt{4+184}[/tex] ) / 2

  = ( 2 ± [tex]\sqrt{188}[/tex] ) / 2

  = ( 2 ± 2[tex]\sqrt{47}[/tex] ) / 2

  = 1 ± [tex]\sqrt{47}[/tex]

Answer:

Roger works 30 hours and his brother works 50 hours

Step-by-step explanation:

Let

x ---->the number of hours Roger works in a month

y ---->the number of hours his brother works in a month

step 1

Find out how much they earn per hour

5,400-3,240=$2,160 -----> amount earned by 20 hours of work

$2,160/20=$108 per hour

step 2

Find out how many hours each brother works in a month

Roger

108*x=3,240

x=3,240/108=30 hours

His brother

y=x+20

y=30+20=50 hours

Answer:

i dont know

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

2 x 6 = 12/2 = 6

Answer:

A = 6 units ^2

Step-by-step explanation:

The area of a triangle is found by

A = 1/2 bh  where b is the length of the base and h is the height

A = 1/2 (6) *2

A = 6 units ^2

Answer:I believe your answer should be C: 23/15

Step-by-step explanation:

So you add 11/15 and 12/15 since the common denominator is already 15 you only need to add the numerator which is 11 and 12 and 11+12= 23 thus you get 23/15

Answer:

29 red marbles

Step-by-step explanation:

Call R the number of red marbles and B the number of black marbles.

According to the second sentence, R = 2B + 3.

According to the third sentence, R + B = 42.

Now we have 2 equations, 2 unknowns. Sub the first into the second since it already has R isolated:

2B + 3 + B = 42

3B = 39

B = 13

Now sub this into either of the original equations (I'll use the first):

R = 2(13) + 3

R = 29

If we divide both sides by -2, we have

[tex]bx-5 = -8 \iff bx = -3 \iff x = -\dfrac{3}{b}[/tex]

So, if you choose b=3, you have x = -3/3=-1

a)

       The value of x in terms of b is:

                [tex]x=\dfrac{-3}{b}[/tex]

b)

         The value of x when b is 3 is:

                      [tex]x=-1[/tex]

We are given a equation in terms of x and b as follows:

           [tex]-2(bx-5)=16-----------(1)[/tex]

a)

Now on simplifying the equation i.e. we solve for x i.e. we find the value of x in terms of b as follows:

On dividing both side of the equation by -2 we get:

[tex]bx-5=-8[/tex]

Now on adding both side by 5 we get:

[tex]bx=-8+5\\\\\\bx=-3[/tex]

Now, on dividing both side of the equation by b we get:

          [tex]x=\dfrac{-3}{b}------------(2)[/tex]

b)

when b=3 in equation (2) we have:

              [tex]x=\dfrac{-3}{3}\\\\\\x=-1[/tex]

Final answer:

To solve the equation 4x = 8x - 1, isolate the variable x by subtracting 4x from both sides, then add 1 to both sides, and finally divide both sides by 4. The solution is x = 1/4.

Explanation:

To solve the equation 4x = 8x - 1, we need to isolate the variable x. We can do this by subtracting 4x from both sides of the equation:

4x - 4x = 8x - 4x - 1

0 = 4x - 1

Next, we can add 1 to both sides of the equation:

1 = 4x - 1 + 1

1 = 4x

Finally, we can divide both sides of the equation by 4 to solve for x:

1/4 = 4x/4

x = 1/4

The solution to the equation 4x = 8x - 1 is x = 1/4. We solve the equation by isolating x through standard algebraic steps. Checking our solution, we substitute it back into the original equation and confirm it is correct by verifying the equality.

The equation given by the student is 4x = 8x − 1. To find the value of x, we need to solve the equation. We start by subtracting 4x from both sides of the equation to get 0 = 4x − 1. We then add 1 to both sides which gives us 1 = 4x. Finally, we divide both sides by 4 to isolate x, which results in x = 1/4. This is the solution to the equation.

As a check, substituting x = 1/4 back into the original equation yields 4(1/4) = 8(1/4) − 1, simplifying to 1 = 2 − 1, which is a true statement and confirms our solution is correct.

Using the same technique, we can also solve different algebraic equations or systems of equations by manipulating the equations algebraically before substituting numerical values. This is illustrated in the given set of equations where variables are systematically eliminated until we end up with a single variable.

Therefore the by solving the equation 4x = 8x - 1 we get x = 1/4

Answer: Eight percent.

Step-by-step explanation: In order to find this, we have to use the probability formula, which is:

The Event We Are Looking For/All of the Events.

In this case, plugging the numbers into the formula we get

May(1)/All the months in the year, including May (12).

Diving this, our answer will be 0.08333..., or rounded up to 0.8

However, since we are only looking for one specific event, we can take the number 100, and divide it by all the events. 12/100 is 8.333..., or rounded to 8.

Final answer:

The chance that a person randomly selected off the street was born in May is about 8%, assuming birth rates are evenly distributed throughout the year.

Explanation:

The question, "What is the chance that a person randomly selected off the street was born in May?" is one that pertains to the subject of probability in Mathematics. Since there are typically 12 equally likely months that a person could be born in, and assuming there is no significant variation in birth rates by month, the chance that someone chosen at random off the street was born in May is 1 out of 12 months.

Thus, to calculate the probability, you would divide 1 by 12, which equals approximately 0.0833. To express this as a percentage, we multiply by 100, yielding an 8.33% chance. Therefore, the closest answer among the provided options is 8%.

A geometric object which is defined as the set of all points in a plane that are equidistant from two (2) points is: D. Line.

A line can be defined as a geometric object which comprises the set of all points in a plane that are all equidistant from two (2) points.

This ultimately implies that, a line is a one-dimensional geometric object that is straight and forms the shortest distance between two (2) points because it extends endlessly in both directions.

Read more on line here: https://brainly.com/question/1655368

Answer:

a line

Step-by-step explanation:

Answer:

x = 25

Step-by-step explanation:

The 2 given angles form a straight angle and are supplementary, that is

2x + 2 + 5x + 3 = 180

7x + 5 = 180 ( subtract 5 from both sides )

7x = 175 ( divide both sides by 7 )

x = 25

Answer:

A. x^2 + y^2 = 36

Step-by-step explanation:

The equation of a circle is usually written in the form

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

The center is at the origin so (h,k) = (0,0) and  the radius is 6 so r=6

x^2 + y^2 = 6^2

or x^2 +y^2 = 36

Answer:

A. [tex]x^2+y^2=36[/tex]

Step-by-step explanation:

An equation of a circle form is: [tex](x-h)^2+(y-k)^2=r^2[/tex]

Details:

[tex](h, k)[/tex] is the center of a circle, [tex]r[/tex] which means radius.

The origin is the center of the circle. [tex](h,k)=(0,0)[/tex] and the radius is [tex]6[/tex] so that means [tex]r=6[/tex]. [tex]x^2+y^2=6^2[/tex], and or [tex]x^2+y^2=36[/tex].

Note: I hope this helps anyone. Sorry about the wait for another answer but should help you and others in the meantime. And if you could please give either me, or the other person brainliest.

And enjoy the rest of your day. :)

[tex]0-(6+4i)=0-6-4i=-6-4i[/tex]

The additive inverse of the complex number 6+4i is -6-4i because it negates both the real and imaginary parts, resulting in a sum of zero when added to the original number.

The additive inverse of a complex number is a number that, when added to the original number, yields a sum of zero. For the complex number 6+4i, its additive inverse is found by changing the sign of both the real and the imaginary parts. Therefore, the additive inverse of 6+4i is -6-4i.

Answer:

10

Step-by-step explanation:

Range=big-small=34-16=18

Interquartile range=big number in box-small number in box= 29-21=8

The different between the two is 18-8=10

Answer:

The difference of range and interquartile range is 10.

Step-by-step explanation:

Consider the provided information.

From the box plot we can identify:

The lowest value is 16

The first quartile is 21

The 2nd quartile or median is 26

The 3rd quartile is 29

The highest value is 34

Range is the difference of the highest value and lowest value of the data set.

Range = 34 - 16 = 18

Interquartile range is the difference of the 3rd quartile from the 1st quartile.

IQR: 29 - 21 = 8

Thus, the difference of range and interquartile range is:

18 - 8 = 10

Hence, the difference of range and interquartile range is 10.

The deviation from 80 of about 16 is normal.

So the lowest is usually 80 - 16 = 64 and the highest is 80 + 16 = 96

But now we have a "deviation" that is 2 standard deviations above the mean score.

So 80 + 16 + 16 = 112 is this score.

Hope this helps.

r3t40

Final answer:

To calculate the score that is 2 standard deviations above the mean of 80 with a standard deviation of 16, you add 2 times the standard deviation to the mean, resulting in a score of 112.

Explanation:

To find the score that is 2 standard deviations above the mean on a test with a mean of 80 and a standard deviation of 16, we use the formula:

Score = Mean + (Number of Standard Deviations × Standard Deviation)

So, plugging in the numbers we get:

Score = 80 + (2 × 16)

Score = 80 + 32

Score = 112

The desired score is therefore 112, which is 2 standard deviations above the mean of 80.

Step-by-step explanation:

y = 2/27 x² − 4/3 x

a) The leading coefficient (the coefficient of the x² term) is positive, so that means the parabola points up.  So the vertex is at the bottom of the parabola, making it a minimum.

b) For a parabola y = ax² + bx + c, the x coordinate of the vertex can be found at x = -b / (2a).  Here, a = 2/27 and b = -4/3.

x = -(-4/3) / (2 × 2/27)

x = (4/3) / (4/27)

x = (4/3) × (27/4)

x = 9

c) To find the y coordinate of the vertex, we simply evaluate the function at x=9:

y = 2/27 x² − 4/3 x

y = 2/27 (9)² − 4/3 (9)

y = 6 − 12

y = -6

d) The ordered pair is (9, -6).  This means that at the lowest point of the dish, the dish is 6 inches deep.  Also, since the dish is symmetrical, and the lowest point is 9 inches from the end, then the total width is double that, or 18 inches.

The vertex of the function is a minimum point. The x and y-coordinates of the vertex are 27 and -54 respectively, representing the deepest point in the dish where signals are concentrated.

a) The vertex of a parabolic function y = ax^2 + bx + c is a maximum point if 'a' is negative and a minimum point if 'a' is positive. In this case, we have a = 2/27, which is positive, so the vertex of the function is a minimum point.

b) The x-coordinate of the vertex can be found using the formula -b/2a. For the quadratic function y = 2/27x^2 - 4/3x, b = -4/3, and a = 2/27. So the x-coordinate of the vertex is -(-4/3)/(2*2/27) = 27.

c) The y-coordinate of the vertex can be obtained by substituting the x-coordinate of the vertex into the equation. Therefore, y = 2/27*(27)^2 - 4/3*27 = -54

d) So the vertex, as an ordered pair (x, y), is (27, -54). The vertex represents the shallowest point in the parabola, which in the case of a satellite dish, equates to the deepest point of the dish, where signals are most concentrated or focused.

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Answer:

22

Step-by-step explanation:

substitute:

5(7) - 3(8) + 11=0

35 - 24 + 11 = 0

=22

[tex]

5\times7-3\times8+11= \\

35-24+11= \\

11+11=22

[/tex]

Hope this helps.

r3t40

Answer:

0.14

Step-by-step explanation:

Fourteen of the 100  digital video recorders​ (DVRs) in an inventory are known to be defective. It means that the probability that a randomly selected item is defective is: [tex]\frac{14}{100} = 0.14[/tex].

Answer:

No solution

Step-by-step explanation:

x + 2/3 = 2/3 + x - 1/4

x = x - 1/4

0 ≠ -1/4

Answer:

  5x^2 + 9x + 15.

Step-by-step explanation:

There is no term in x so we add  one (0x).

            5x^2 + 9x + 15  <------------Quotient.

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

3x - 5 )  15x^3 + 2x^2 + 0 x  - 75

            15x^3 - 25x^2

           --------------------

                         27x^2 + 0x

                         27x^2 - 45x

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

                                      45x - 75

                                       45x - 75

                                         ..........

Answer:

283cm³

Step-by-step explanation:

The linear scale factor= Height of larger/Height of smaller cylinder.

=8cm/4cm=2

VOLUME scale factor = linear scale factor³

=2³=8

Therefore we divide the volume of the larger cylinder by  the volume scale factor.

volume of small cylinder=2264cm³÷8

=283cm³

Answer: first option.

Step-by-step explanation:

 You know that the height of the smaller cylinder is 4 cm and the height of the  larger cylinder is 8 cm, then you can find the volume ratio. This  is:

[tex]Volume\ ratio=(\frac{4\ cm}{8\ cm})^3\\\\Volume\ ratio=\frac{1}{8}[/tex]

Knowing that the volume of the larger cylinder is 2,264 cubic centimeters, you need to multiply it by the volume ratio to find the volume of the smaller cylinder.

Therefore:

[tex]V_{smaller}=\frac{1}{8}(2264\ cm^3)\\\\V_{smaller}=283\ cm^3[/tex]

Answer:

B.) -19

Step-by-step explanation:

-37 + n = -56

Add 37 to each side

-37 +37+ n = -56+37

n = -19

Answer: b) -19

Step-by-step explanation:

-37 + n=-56

use inverse operations and subtract -56 by 37 to get your answer

Answer:

Option D) 15 3/4 cups

Step-by-step explanation:

we know that

using proportion

Let

x ----> the cups of flour needed

[tex]4\frac{1}{2}=\frac{4*2+1}{2}=\frac{9}{2}\ cups\ flour[/tex]

[tex]\frac{(9/2)}{2}=\frac{x}{7} \\ \\x=(9/2)*7/2\\ \\x=63/4\ cups\ flour[/tex]

convert to mixed number

[tex]63/4\ cups=15.75=15\frac{3}{4}\ cups[/tex]

Answer:

200

Step-by-step explanation:

Of means multiply and is means equals

30% * W = 60

Change to decimal form

.30 * W = 60

Divide each side by .30

.30W /.30 = 60/.30

W = 200