need help with this question. ​

Need Help With This Question.

Answers

Answer 1

We have this equation:

[tex]\log(x) + \log(x + 99) = 2[/tex]

First, combine both logarithms using the multiplication property and simplify the expression.

[tex]\log[x(x + 99)] = 2[/tex]

[tex]\log[ {x}^{2} + 99x ] = 2[/tex]

Now, use the definition of logarithm to transform the equation.

[tex] {10}^{2} = {x}^{2} + 99x[/tex]

[tex] {x}^{2} + 99x - 100 = 0[/tex]

Finally, use the quadratic formula to solve the equation.

[tex]x = \frac{ -99 ± \sqrt{ {99}^{2} - 4 \times 1 \times ( - 100)} }{2 \times 1} [/tex]

With this, we can say that the solution set is:

x = 1x = -100

We cannot choose x = -100 as a solution because we cannot have a negative logarithm. The only solution is x = 1.

Need Help With This Question.

Related Questions

If P= (-6,4) find Ry= -x (P)

Answers

The value of Ry= -x (P) is P' = (4, 6)

How to determine the transformation?

The point is given as:

P = (-6, 4)

The transformation Ry= -x (P) means tha:

(x, y) = (y, -x)

So, we have:

P' = (4, 6)

Hence, the value of Ry= -x (P) is P' = (4, 6)

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If x dozen eggs cost y dollars, what is the cost, C, of z dozen eggs?

Answers

Answer:

c=y×z

Step-by-step explanation:

the answer is this because z would be the number of dozens you have times y the cost of one by multiplying those together you will get the cost of the z dozens of eggs

The sum of three numbers 157. The third number is 7 less than the firstThe second number is 4 times the third What are the numbers?

Answers

Step-by-step explanation:

Let the first number be = x

Let the second number be = 4x -28

Let the third = x-7

x + 4x+ x -28 - 7

6x - 35

6x -35 = 157

6x = 157 +35

6x = 192

x = 32

therefore, x = 32, the second x = 4(32) -28

728 - 28

x = 100

third x = 32 - 7

x = 25.

b. Miguel tiene 104 canicas grandes, 117
medianas y 130 pequeñas. Si quiere
repartirlas en grupos iguales con la
mayor cantidad de cada tipo de cani-
cas, ¿cuántos grupos podrá formar?
¿Cuántas canicas de cada tipo habrá
en cada grupo?

Answers

Considerando la definición de divisor común mayor:

si Miguel quiere repartir las canicas en grupos iguales con la mayor cantidad de cada tipo tendrá 13 grupos.en cada grupo habrá 8 canicas grandes, 9 canicas medianas y 10 canicas pequeñas.

Definición de divisor

Los divisores de un número natural son los números naturales que lo pueden dividir, resultando de cociente otro número natural y de resto 0. Ser divisor es lo recíproco a ser múltiplo.

En otras palabras, un número es divisor de otro si está contenido una cantidad entera de veces. Por lo tanto, al dividir el número por el divisor el cociente debe resultar un número entero (que no sea un número decimal) y el residuo o resto de la división sea 0.

Divisor común mayor

Se denomina máximo común divisor al mayor número que divide exactamente a dos o más números a la vez.

En otras palabras, el divisor común mayor es el mayor de los divisores que tienen en común dos o más números.

Para calcular el divisor común mayor se debe realizar los siguientes pasos:

Descomponer cada número en factores primos.Después, señalar los factores comunes (números primos que aparecen en todos los números).A continuación, en cada uno de los comunes, escoger el factor con menor exponente (factor que aparece la menor cantidad de veces).Por ultimo, multiplicar los factores elegidos.

Cantidad de grupos

Para calcular la cantidad de grupos se debe calcular el divisor común mayor. Para ello, en primer lugar se descomponen los números:

104= 2×2×2×13= 2³×13117= 3×3×13= 3²×13130= 2×5×13

El factor común a todos los números es el número 13. Esto indica que si Miguel quiere repartir las canicas en grupos iguales con la mayor cantidad de cada tipo tendrá 13 grupos.

Cantidad de canicas de cada tipo en cada grupo

Para esto se deberá dividir la cantidad de cada tipo de canica por la cantidad de grupos formados, que en este caso es 13. Esto es:

104 canicas grandes÷ 13 grupos= 8 canicas grandes117 canicas medianas÷ 13 grupos= 9 canicas medianas130 canicas pequeñas÷ 13 grupos= 10 canicas pequeñas

Finalmente, en cada grupo habrá 8 canicas grandes, 9 canicas medianas y 10 canicas pequeñas.

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If r and s represent two numbers, write the following:
53a. Twice the sum of the two numbers
53b. 5% of the difference between the two numbers

Answers

Answer:

hope it helps. good day .in case of any question please ask.

Find the value of 1 + 3 +5+ ... + 125

Answers

Answer:

3906

Step-by-step explanation:

(125-1):2+1=63

63x(125+1):2=3906

Which measures are true for the quilt piece? select three options. a = 60° x = 3 in. the perimeter of the rhombus is 16 inches. the measure of the greater interior angle of the rhombus is 90°. the length of the longer diagonal is approximately 7 inches.

Answers

The measures that are true for the quilt piece include:

a=. = 60°The perimeter of the rhombus is 16 inches.The length of the longer diagonal is 7 inches.

How to depict the information?

The value of a will be:

= 90° - 30°

= 60°

The perimeter will be:

= 4 × 4

= 16 inches.

The length of the diagonal will be:

= 2 × 3.46

= 6.92 = 7

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Please help answering this question

Answers

Answer:

DF = 3

Step-by-step explanation:

BC = DF

Which mean D is (0,2) and F is (3,2)

Here, this is clear that y-intercept is 2

DF = D(x) + F(x) = 0 +3 = 3

Find the
quotient for 12 2/5 / 1/4

Answers

[tex]12 \frac{2}{5}=\frac{62}{5}\\\\\frac{62/5}{1/4}=4\left(\frac{62}{5} \right)=\frac{248}{5}=\boxed{49 \frac{3}{5}}[/tex]

11) Gretchen purchased a dress that originally cost $89.99. It was marked down 30% off. What was the cost of the
dress?
O a.) $65.99
Ob.) $63.99
Oc.) $62.99
Od.) $64.99

Answers

Answer is c. $62.99
Step by step
89.99 x 70% = x
89.99 x .70 = 62.99
Hint: If the dress was 30% off, it’s cost is 70%

You can also do this in two steps
89.99 x 30% = discount of $27.
Then
89.99 - $27 = $62.99



Least common multiple of 10,20 35

Answers

Answer: 140

Step-by-step explanation:

What is the value of In e^4?
0 0
O 1
02
04

Answers

Answer:

4

Step-by-step explanation:

[tex]In(e^4)[/tex] =  [tex]4In(e)[/tex]
          = 4 x 1
          = 4

The value of the expression ln([tex]e^4[/tex]) is 4.

Option D is the correct answer.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The natural logarithm (ln) is the inverse function of the exponential function,

[tex]e^x[/tex].

ln([tex]e^4[/tex]) = 4,

since ln([tex]e^4[/tex]) "undoes" the exponentiation of [tex]e^4[/tex].

So the value of ln([tex]e^4[/tex]) is 4.

Thus,

The value of the expression ln([tex]e^4[/tex]) is 4.

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What is 8/9 divided by 2/3

Answers

Use it the way I solved in the picture you will understand much better

¿What are Equivalent Fractions?
50 points​

Answers

Answer:

Step-by-step explanation:

Equivalent fractions represent the same value, even though they look different. For example, if you have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake.

Numeric Example= [tex]\frac{2}{2} =\frac{1}{1}[/tex]

[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]

Equivalent Fractions have the same value, even though they look different.

Example :-

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt \dfrac{1}{2} = \dfrac{2}{4} = \dfrac{4}{8} }[/tex]

¿Why are they the same?

Because when you multiply or divide the numerator and denominator by the same amount, the fraction does NOT change.

Remember that :-

Remember that :- The multiplication and division that you apply in the numerator to e must repeat in the denominator.

That's why the fractions are really the same.

Watch the process ;

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \boxed{ \tt \frac{1}{2} = \frac{2}{4} = \frac{4}{8} }[/tex]

That's multiplying

(Image 1)

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \tt\dfrac{18}{36} = \dfrac{6}{12 } = \dfrac{1}{2} }[/tex]

That's Division

(Image 2)

I hope I've helped : )

Help please
This diagram shows the measurements of a yard.
What is the area of the yard?
Enter your answer in the box.

Answers

Answer:

Step-by-step explanation:

we can break up the figure into 2 rectangles by extending the 8m side downward until it meets the bottom (see image)

Area of this rectangle = 10 * 2 =20 sq meters

Area of the other rectangle = 8 *2 = 16 sq meters

Total area = 36 sq meters

what is the common ratio of 3,1,1/3,1/9?

Answers

Answer:

mine was D

Step-by-step explanation:

mine was D unless its diffrent

Question
You want to find the area of the front of a house, whose shape is a triangle on top of a rectangle with
a width of 8. The triangle's height is 7 and the rectangle's height is 10. What is the total area of the
front of the house? Do not include units in your answer.

Answers

Answer:

108

Step-by-step explanation:

if the width of the rectangle is 8, and the triangle is on the width of the rectangle, then the base of the rectangle is 8. the height is 7, so we use the formula area = height * base / 2 to find that the area of the triangular portion is 28. then, we find the area of the rectangle by doing 10 * 8(height * width) for a value of 80. the total area of the front of the house is 28 + 80: 108.

Cheryl invested $1000 on Monday.Each day after that the stock increased 1% of its original value.On Wednesday she was charged an administrative fee of $10. Graph the value of the stock account at the end of each day

Answers

The value of the stock account at the end of each day is  mathematically given as

x=1010$.

What is the value of the stock account at the end of each day?

Generally, The price of the stock would have climbed by 1000 points, which is equal to 0.1 times 1000, or 10 dollars.

Therefore, the price of the stock would be 1010 dollars plus 10 dollars, which is 1020 dollars.

In conclusion, Cheryl was required to pay a ten dollar administrative fee, and this cost would be deducted from the stock price.

Following this logic, the price of the stock would be

x=1020-10

x=1010$.

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Find the height of a triangle with an area (A) of 42 square inches and
base (b) of 7 inches. Use the formula for the area of a triangle,

588 inches
147 inches
3 inches
12 inches

Answers

Answer:

147

Step-by-step explanation:

start by multiplying 42 and 7=294

now divide that by 1/2 =147

2.5.2 project performance task:trade show booth

Answers

The booth space and the product brochures are less than $3000 hence the equation of inequality will be  B + P ≤ $ 3000.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Let the booth space be B and the product brochures be P.

Then the equation of inequality will be  

B + P ≤ $ 3000

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Complete question:

2.5.2 Project: A Trade Show Booth

The Scenario: Your manager has asked you to help plan your company's participation at a local trade show. You have $3000 to spend on the booth space and product brochures. Use what you know about solving inequalities to prepare the inequality that meets the budget.

how can -6 divide by 4 x=12 be solved in one step

Answers

Here are the solving steps for the problem.

   Given:

[tex]\displaystyle \frac{-6}{4x}=12[/tex]

    [1] Multiply both sides of the equation by 4x:

[tex]\displaystyle 4x(\frac{-6}{4x})=(12)4x[/tex]

-6 = 48x

    [2] Divide both sides of the equation by 48:

[tex]\displaystyle \frac{-6}{48} = \frac{48x}{48}[/tex]

[tex]\displaystyle x=-\frac{1}{8}[/tex]

I am not sure how to solve the equation in one step, so here is it in two steps. My apologies.

Answer:

[tex] - \frac{1}{8} [/tex]

Step-by-step explanation:

The Algebraic Equation -6 divide by 4x = 12 can be stated mathematically as :

[tex] \frac{ - 6}{4x} = 12 \\ \\ cross \: multiplying \\ \\ 4x \: \times 12 = - 6 \\ \\ 48x = - 6 \\ dividing \: bothsides \: by \: 48 \\ \frac{48x}{48} = \frac{ - 6}{48} \\ \\ x = - \frac{1}{8} [/tex]

Drag each equation to the correct location on the table. Determine which equations will result in extraneous solutions.

Answers

Answer:

extraneous: 2, 5, 7

not: 1, 3, 4, 6, 8

Step-by-step explanation:

ones that have root of an even number and equal a negative are extraneous

Does anyone know the answer to this?

Answers

1) m∠1 = 62°, lines t and l intersect (given)

2) ∠1 and ∠4 are vertical angles (intersecting lines form vertical angles)

3) ∠1 and ∠4 are congruent (vertical angles are congruent)

4) m∠1 = m∠4 (congruent angles have equal measure)

5) 62° = m∠4 (substitution)

6) m∠4 = 62° (symmetric property of equality)

Drag each tile to the correct box. The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below. A graph represents the water level to fill the tank on Y-axis per time on X-axis. Segments A, B, and C fill the tank from 10 to 60, 60 to 80, and 80 to 110 centimeters in the first 2, next 4, and last 3 minutes. Place the segments in the correct order from the least to the greatest rate of increase in the water level. B A C

Answers

The least to greatest slope, the segments are B, C, and A.

We have given that,

The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below.

A graph represents the water level to fill the tank on Y-axis per time on X-axis.

The rate of increase of water level is indicated by the slope of the segment. The slope is the ratio of rise to run, and is related to the angle the segment makes with the +x axis.

Segments that have more rise for the same run have greater slope. Segments that make a larger reference angle with the +x axis have a larger slope.

Here, segment B has the least slope, followed by C, then A, which has the largest slope.

In order, the least to greatest slope, the segments are B, C, and A.

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Answer: bca

Step-by-step explanation:

B C A

What is the explicit formula for this sequence? -7, -3, 1, 5, ...

Answers

Hello,

What is the explicit formula for this sequence? -7, -3, 1, 5, ... ?

Aₙ₊₁ = Aₙ + 4 and A₀ = -7

⇒ Aₙ = A₀ + nr = -7 + 4n

Question 1- Whats the derivative of: A) f(x)= 4 cos(x) + ln(x+1)
B) f(x)= sec(x) X tg(x)

Answers

The derivatives for this problem are given as follows:

a) [tex]f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}[/tex]

b) [tex]f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}[/tex].

What is the derivative of the sum?

The derivative of the sum is the sum of the derivatives.

In this problem, the function is:

[tex]f(x) = 4\cos{x} + \ln{(x + 1)}[/tex]

Using a derivative table for the derivatives of the cosine and the ln, the derivative of the function is:

[tex]f^{\prime}(x) = (4\cos{x})^{\prime} + (\ln{(x + 1)})^{\prime}[/tex]

[tex]f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}[/tex]

What is the product rule?

The derivative of the product is given as follows:

[tex](f(x) \times g(x))^{\prime} = f^{\prime}(x)g(x) + g^{\prime}(x)f(x)[/tex]

In this problem, we have that:

[tex]f(x) = \sec{x}, f^{\prime}(x) = \sec{x}\tan{x}[/tex].[tex]g(x) = \tan{x}, f^{\prime}(x) = \sec^2{x}[/tex].

Hence the derivative is:

[tex]f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}[/tex].

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solve for the pattern 7, 11, 2, 18, -7, ?

Answers

Answer:

7, 11, 2, 18, -7, 25

Please help!! Having a hard time with this! Bob can buy individual songs for $1.00 to download, or an entire album costs $10.00 to download. He can spend no more than a total of $60. He wants to buy at least three albums, and no more than 35 individual songs.


The following system of inequalities represents this situation, where x is the number of individual songs and y is the number of albums.


x + 10y ≤ 60

x ≤ 35

y ≥ 3


Which yellow shaded region corresponds to Bob’s possible choices?

Answers

Answer:

second one listed

Step-by-step explanation:

second one given--he can buy between 3 and 6 albums; and 0 to 30 songs

(if he were to buy exactly 3 albums, he could not buy more than 30 songs; which is why that portion of the graph is not shaded)

(shaded = possible)

hope this helps!

How can we develop a margin of error through the use of simulation models for random sampling

Answers

When using simulation models for random sampling, we can develop the margin of error by multiplying the critical value by the standard error.

What is the margin or error?

This is a measure of the error that we get when we use a random sampling model.

It can be found by the formula:

= Critical value x Standard error

If using a z-test, the critical value would be z and the standard error would be (σ / √n). The margin or error would therefore be:

= z (σ / √n)

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assuming that the series will continue in the same pattern the next number in the series 3,5,11,29... is

Answers

Notice that

5 - 3 = 2

11 - 5 = 6

29 - 11 = 18

and these differences form a geometric sequence,

{2, 6, 18, ...} = {2×3⁰, 2×3, 2×3², ...}

so a reasonable guess for the next number in the sequence might be 2×3³ = 54.

The sequence might be 2×3^3^3 = 54.

We notice that 5 - 3 = 2

11 - 5 = 6

29 - 11 = 18

and these differences form a geometric sequence,

What is the geometric sequence?

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.

{2, 6, 18, ...} = {2×3^0, 2×3^1, 2×3^3, ...}

So the next number in the sequence might be 2×3^3 = 54.

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Other Questions
6.) Write an addition expression to describe skateboardingsituation. Then determine the sum.Hank starts at the bottom of a half pipe 6 feet below streetlevel. He rises 14 feet at the top of his kickturn. Read this excerpt from the declaration of independence:He has obstructed the Administration of Justice, byrefusing his Assent to Laws for establishing Judiciarypowers. He has made Judges dependent on his Will alone,for the tenure of their offices, and the amount and paymentof their salaries. He has erected a multitude of NewOffices, and sent hither swarms of Officers to harass ourpeople, and eat out their substanceWhich of there rhetorical devices is used here?A. ParallelismB.) logos C.) Ethos D.) deductive reasoning PLEASE HELP !!Quadrilateral ABCD has vertices at A (0, 0), B (0, 3), C (5, 3), and D (5, 0). Find the vertices of thequadrilateral after a dilation with scale factor 2.5. A section of a high speed test track is circular with a radius of curvature R = 1860 m.At what angle of should the track be inclined so that a car traveling at 61.0 m/s (136 mph) would keep moving in a circle if there is oil on that section of the track, i.e., it would not slip sideways even with zero friction on that section. (Hint: The car's vertical acceleration is zero.) 2) What is more important to you: Menu design or content? Why? what is numrical in math and complex function?[tex] \sqrt{ - i} [/tex] tRNA Molecules(AspCodonsmRNALeuIntro(Arg)GluLysAnticodons5 of 6MetLeu)AC AAC a a d d d d 94445'3'Ribosome.For each codon, find the correct tRNA anticodon and drag it to the ribosome. Start with the AUG codonin the ribosome. Find and drag its match, the UAC anticodon, to it. Also, record this pair and theassociated amino acid, Met, to complete the first row of the data table.CytoplasmHO Counter 0 \A carpenter is making a wooden window frame that has a width of 1 inch.A window with a one-inch frame is shown. The frame is comprised of a rectangle and a semicircle. The rectangle has side lengths of 12 inches and 48 inches. The semicircle has a radius of 6 inches. The frame is 1-inch wider than the window.How much wood does the carpenter need to build the frame?5.5 + 106 square inches5.5 + 116 square inches5.5 + 153 square inches5.5 + 162 square inches Question 3 of 10For f(x) = 3x+1 and g(x)=x-6, find ( + g)(x).OA. x + 3x-5OB. 3x -17O. C. 3x-5OD. x + 3x +7 Multiply Conjugates Using the Product of Conjugates PatternIn the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern335. (7w + 10x)(7w 10x) The ________ stage in Russell Colley's hierarchical model of the communication process deals with getting the consumer to purchase the product. Group of answer choices How many H2O molecules are there in 4.5 g of water (see picture) Determine the launch speed of a horizontally launched projectile that lands 26.3m from the base of a 19.3m high cliff which of the following functions is graphed below ? An accenture technology team located in the us has added a new feature to an existing online ticketing platform. the team would like to have the new feature reviewed by other global teams using individual instances of the platform. which technology, when combined with agile and devops, will help the team receive real-time feedback? Select all that apply Benefits of small amounts of inflation include Multiple select question. more expansionary monetary policy. the elimination of the money illusion. the elimination of unemployment. the facilitation of relative prices changes. the placebo effect. The rate constant, k, for a reaction is 0.0354 sec1 at 40C. Calculate the rate constant for thesame reaction at 125C if the activation energy is 26.5 kJ/mol. A state law is:Laws that are the same across the entire country.Laws unique to that particular state.Laws that do not come from the Constitution.Laws that U.S. citizens must follow while visiting other countries. which one of these numbers could form a triangle? A bungee cord is essentially a very long rubber band that can stretch up to four times its unstretched length. However, its spring constant varies over its stretch. Take the length of the cord to be along the x-direction and define the stretch x as the length of the cord l minus its un-stretched length [tex]l_0[/tex]; that is, [tex]x=l-l_0[/tex] (see below). Suppose a particular bungee cord has a spring constant, for 0 x 4.88m , of [tex]k_1=204 N/m[/tex] and for x 4.88m , of [tex]k_2=111N/m[/tex]. (Recall that the spring constant is the slope of the force F(x) versus its stretch x.) (a) What is the tension in the cord when the stretch is 16.7 m (the maximum desired for a given jump)? (b) How much work must be done against the elastic force of the bungee cord to stretch it 16.7 m?please explain if possible!