Solve: log2(x-1)+log2(x+5)=4

Answer:

[tex]\sf{x = 2}[/tex]

Step-by-step explanation:

Question type: solving equations with variables on both sides.

[tex]\textsf{This is a question with variables on both sides, to solve this we need to get the variable x }[/tex]

[tex]\textsf{alone. (getting the x on one side)}[/tex]

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

[tex]\sf{-2x~+~4~=~2x~-~4[/tex]

Subtract 4 from both sides.

[tex]\sf{-2x~=~2x~-8[/tex]

Subtract 2x from both sides.

[tex]\sf{-4x~=~-8}[/tex]

Divide both sides by -4.

[tex]\bf{x~=~2[/tex]

Therefore, x would be 2.

[tex]-jurii[/tex]

Answer:

x=2

Step-by-step explanation:

Answer:

a. The linear model that represents the height of the plant after d days can be expressed as:

h(d) = 1.5d + 5

where h(d) is the height of the plant in centimeters after d days, and 1.5d represents the growth rate of 1.5 cm per day multiplied by the number of days (d). The constant term 5 represents the initial height of the plant, which is 5 cm.

b. To find the height of the plant after 20 days, we can substitute d = 20 into the linear model:

h(20) = 1.5(20) + 5

= 30 + 5

= 35

So, the height of the plant after 20 days will be 35 cm.

Answer:

a) 1/6

b) 1/2

c) 1/2

d) 1

e) 1/6

Step-by-step explanation:

a)Getting a six

=1/6

b)Gettingan even number =3/6=1/2

c)number greater than 3

=3/6=1/2

d)number greater than 0

=6/6=1

e)number greater than 4 and an odd number

=1/6

The six rational numbers between 3 and 4 are: 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6

To find 6 rational numbers between 3 and 4, we can start by finding the difference between 4 and 3, which is 1.

We can then divide this difference by any number and add it to 3

So that the number will be less than 4 but greater than 3

Now, we can add this gap size successively to 3, starting with the first rational number after 3, to find the six rational numbers between 3 and 4:

3.1, 3.2, 3.3, 3.4, 3.5, 3.6

So, the six rational numbers between 3 and 4 are: 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6

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The length of the hypotenuse is 28.3

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.

If a and b are the legs of the triangle and c is the other side(hypotenuse) then,

c² = a²+b²

c² = 19² +21²

c² = 361+441

c² = 802

c = √802

c = 28.3

therefore , if the two legs are 19 and 21, the length of the other side is 28.3

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The length of the hypotenuse is 28.3

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.

If a and b are the legs of the triangle and c is the other side(hypotenuse) then,

c² = a²+b²

c² = 19² +21²

c² = 361+441

c² = 802

c = √802

c = 28.3

therefore , if the two legs are 19 and 21, the length of the other side is 28.3

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The value of x, y, and z in the rhombus below x = 20, y = -7, z = -11

Recall that a  rhombus is an equilateral parallelogram with both pairs of opposite sides parallel and all sides the same length.

Sum of interior angles of a rhombus = 360°

The opposite angles of a rhombus are equal to each other.

The adjacent angles are supplementary (add up to 180°)

Therefore,

66 + (6x - 6) = 180

⇒ 66 + 6x - 6 = 180

⇒ 6x = 180 - 66 + 6

⇒ 6x = 120

⇒ x = 120 ÷ 6

⇒ x = 20

66 + (-10z + 4) = 180

⇒ 66 - 10z + 4 = 180

⇒ -10z= 180 - 66 - 4

⇒ -10z = 110

⇒ z = 110 ÷ -10

⇒ z = -11

(6x - 6) + (-10y - 4) = 180

⇒ 6x - 6 - 10y - 4 = 180

⇒ 120 - 6 - 10y - 4 = 180

⇒ -10y = 180 - 120 + 6 + 4

⇒ -10y = 70

⇒ y = 70 ÷ -10

⇒ y = -7

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Answer:

Step-by-step explanation:

To calculate the stock price, you can multiply the earnings per share (EPS) by the benchmark PE ratio.

The stock price would be:

$3.64 x 21 = $76.44

So you would pay $76.44 per share for the stock of The Dahlia Flower Company.

Answer: 5.26

Step-by-step explanation:

458,930/87,178 =
5.264 =
5.26

Answer:

Step-by-step explanation:

14% of the time the mean weight of 23 fruits will be greater than approximately 594.33 grams.

What is the Central Limit Theorem (CLT)?

According to the CLT, the distribution of sample means from a population with mean μ and standard deviation σ, will be approximately normal with mean μ and standard deviation σ/√n, where n is the sample size.

In this case, the population mean is 589 grams and the population standard deviation is 16 grams. We are picking a sample of 23 fruits at random, so the standard deviation of the sample means will be:

σ/√n = 16/√23 ≈ 3.33

To find the value of x such that 14% of the time the sample mean will be greater than x, we need to find the z-score that corresponds to the 86th percentile of the standard normal distribution. We can use a table or a calculator to find that z-score:

z = invNorm(0.86) ≈ 1.08

The sample mean is normally distributed with a mean of 589 grams and a standard deviation of 3.33 grams. Using the formula for z-score:

z = (x - μ) / (σ / √n)

We can solve for x:

x = z × (σ / √n) + μ

x = 1.08 × (16 / √23) + 589

x ≈ 594.33 grams

Therefore, 14% of the time the mean weight of 23 fruits will be greater than approximately 594.33 grams.

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The cost of capital for the second option, issuing new preferred stock, is 0.00356, or 0.356%. This means that for every dollar of capital raised through issuing preferred stock, the company will need to pay 0.356 cents in annual interest or dividend payments.

To calculate the cost of capital for the second option, we need to first calculate the cost of the preferred stock. The cost of preferred stock is the dividend yield, or the annual dividend divided by the market price of the stock. In this case, the annual dividend is $5.00 and the market price is $56,000.

Cost of preferred stock = Annual dividend / Market price of stock

Cost of preferred stock = $5.00 / $56,000

Cost of preferred stock = 0.000089

To calculate the cost of capital, we need to weight the cost of preferred stock with the proportion of capital that is financed by preferred stock. Let's assume that the preferred stock will finance 40% of the total capital.

Cost of capital = Cost of preferred stock * Proportion of capital financed by preferred stock

Cost of capital = 0.000089 * 0.40

Cost of capital = 0.0000356

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Para despejar "a" de la ecuación 2as = vf^2 - vo^2, podemos seguir los siguientes pasos:

2as + vo^2 = vf^2

a = (vf^2 - vo^2) / 2s

Por lo tanto, la fórmula para calcular "a" a partir de la distancia de desplazamiento "s", la velocidad final "vf" y la velocidad inicial "vo" es:

a = (vf^2 - vo^2) / 2s

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[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]

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this is the total cost for the round trip, the answer is (C) 583.20.

what is round trip ?

A round trip refers to a journey from a starting point to a destination and then back to the starting point. In other words, it involves traveling to a place and then returning to the original location.

In the given question,

To calculate the cost of gasoline for the round trip, we need to first find the total amount of gasoline they will use. We can calculate this by dividing the distance of the trip by the RV's average gas mileage:

Total gasoline used = distance ÷ gas mileage

Total gasoline used = 1,701 miles ÷ 10.5 miles per gallon

Total gasoline used = 162 gallons (rounded to the nearest whole number)

Now, we can find the total cost of gasoline by multiplying the total amount of gasoline used by the average cost of a gallon of gasoline:

Total cost of gasoline = total gasoline used × cost per gallon

Total cost of gasoline = 162 gallons × 3.60 per gallon

Total cost of gasoline = 583.20

Since this is the total cost for the round trip, the answer is (C) 583.20.

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Answer:

We can solve this equation by using substitution. We substitute each value of x in the given set and check which one makes the equation true.

Let’s start with A. 8(x - 20) = 304 becomes 8(49 - 20) = 304 which simplifies to 8(29) = 304 which is not true.

Let’s try B. 8(x - 20) = 304 becomes 8(none of these - 20) = 304 which simplifies to 8(-20) = 304 which is not true.

Let’s try C. 8(x - 20) = 304 becomes 8(29 - 20) = 304 which simplifies to 8(9) = 304 which is not true.

Finally, let’s try D. 8(x - 20) = 304 becomes 8(21 - 20) = 304 which simplifies to 8(1) = 304 which is not true.

Therefore, none of these values of x make the equation true

Step-by-step explanation:

The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.

In mathematics, an inequality is a statement that compares two values, often using the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Inequality graphs show the region of the coordinate plane that satisfies an inequality. The graph of inequality can be determined in a similar way to the graph of an equation, but with some additional steps.

Here we have

The inequality |2x + 2| > 6

To graph the solution to the inequality |2x + 2| > 6,

we can start by rewriting the inequality as two separate inequalities without the absolute value:

2x + 2 > 6 or 2x + 2 < -6

Simplifying these inequalities, we get:

2x > 4 or 2x < -8

x > 2 or x < -4

Therefore,

The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.

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Step-by-step explanation:

This is basically an inscribed angle in a circle which encompasses twice as many degrees of arc (246) as the angle measure : angle 3 = 123 degrees

Answer: you pay 18$

Step-by-step explanation:96 ounce×1pound/16ounce×3$/1pound=18$

The amount the cashier charged is incorrect. Based on the given information, the amount of fruit purchased is 96 ounces, which is equivalent to 6 pounds. Therefore, the total cost of the fruit should be 6 pounds x $3 per pound = $18.

The error the cashier made was converting ounces to pounds incorrectly. 96 ounces is equivalent to 6 pounds, not 1,536 pounds. The cashier multiplied 96 by 16 (the number of ounces in a pound) instead of dividing by 16 to get the number of pounds.

Answer:

To compare the texting rates of Student A and Student B, we need to calculate their respective rates of change.

For Student A, we can use the formula for the slope of a line:

slope = (change in y) / (change in x)

In this case, the "y" variable represents the number of texts sent, and the "x" variable represents the number of tests sent. Looking at the table, we can see that Student A sent 10.5 texts after sending 1 test, and 10 texts after sending 2 tests. So the change in y is -0.5 (10.5 - 10), and the change in x is 1. Therefore:

slope = (-0.5) / 1 = -0.5

So Student A's texting rate is -0.5 texts per test.

For Student B, we can look at the graph and find the slope of the line connecting any two points. Let's choose the points (2, 15) and (5, 23) because they are easy to read off the graph. The change in y is 8 (23 - 15), and the change in x is 3 (5 - 2). Therefore:

slope = 8 / 3 = 2.67

So Student B's texting rate is 2.67 texts per minute.

To find the difference in their texting rates, we simply subtract:

difference = Student B's rate - Student A's rate

difference = 2.67 - (-0.5) = 3.17

So the difference in their texting rates is 3.17 texts per test.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve the differential equation:

y′′′ + y = 3(y′ − 1)

we first find the characteristic equation:

r^3 + 1 = 0

The roots of this equation are:

r = -1, 0 ± i

So, the general solution of the homogeneous equation (y′′′ + y = 0) is:

y_h(t) = c1 e^(-t) + c2 cos(t) + c3 sin(t)

To find a particular solution of the non-homogeneous equation (3(y′ − 1)), we assume a solution of the form:

y_p(t) = a t + b

Taking the first, second and third derivatives of y_p(t), we get:

y′_p(t) = a

y′′_p(t) = 0

y′′′_p(t) = 0

Substituting these into the differential equation, we get:

0 + (a t + b) = 3(a - 1)

Solving for a and b, we get:

a = 1

b = 2

Therefore, the particular solution of the non-homogeneous equation is:

y_p(t) = t + 2

So, the general solution of the non-homogeneous equation is:

y(t) = y_h(t) + y_p(t) = c1 e^(-t) + c2 cos(t) + c3 sin(t) + t + 2

To find the values of c1, c2 and c3, we use the initial conditions:

y(0) = c1 + c2 + 2 = 1

y′(0) = -c1 + c2 + c3 = 0

y′′(0) = c1 - c2 = 0

Solving these equations simultaneously, we get:

c1 = c2 = 1/2

c3 = -1/2

So, the solution of the differential equation with initial conditions (0) = 1, ′(0) = 0, ′′(0) = 0 is:

y(t) = 1/2 e^(-t) + 1/2 cos(t) - 1/2 sin(t) + t + 2

Answer:

155000 milliliters of water

Step-by-step explanation:

We Know

The platoon drank 155 liters of water.

How many milliliters did the platoon drink?

1 liter = 1000 milliliters

155 liters = 155 x 1000 = 155000 milliliters of water

So, the platoon drank 155000 milliliters of water.

The platoon drank 155,000 milliliters of water.

1 liter = 1000 milliliters

Therefore, 155 liters = 155,000 milliliters

So, the platoon drank 155,000 milliliters of water.

Answer:

3/8

Explanation:

I just know :) (;

The numeric value of the function at x = 4 is given as follows:

f(4) = 0.

The expression for the numeric value of the function in this problem is given as follows:

f(4).

This means that the input is given as follows:

x = 4.

Passing a vertical line through x = 4 the value of y in which the vertical line crosses the graph is given as follows:

y = 0.

Hence the numeric value is given as follows:

f(4) = 0.

The graph is given by the image presented at the end of the answer.

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If each person drove at a constant rate, the person who drove the fastest (in miles per hour) is: C. Nathan.

In Mathematics and Science, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;

In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

For Hank, we have:

Speed = 176/3.2 = 55 miles per hour.

For Laura, we have:

Speed = 150/2.5 = 60 miles per hour.

For Nathan, we have:

Speed = 112.5/2.25 = 50 miles per hour (Fastest).

For Raquel, we have:

Speed = 286/4.4 = 65 miles per hour.

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The height of the Zeta Tower as a percentage of the height of the Delta tower is the 94.72%

Here we know that:

The epsilon tower is 23% taller than the delta one, then the height is:

H = 55m*(1 + 0.23) = 67.65 m

And we know that the Zeta tower is 23 short than the epsilon one, then the height of this twoer is.

H' = 67.65m*(1 - 0.23) = 52.0905 m

The height of the delta tower is 55m, this is our 100%.

Then the height of the zeta tower written as a percentage will be:

(52.0905 m/55m)*100% = 94.72%

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The distance of P at north of Q is 34.98 km.

The distance of P at east of Q is 19.39 km.

The distance of P at the given directions is calculated by resolving the vector into vertical and horizontal components.

The distance of P at north of Q is calculated as follows;

Py = d sinθ

Py = 40 km x sin (61)

Py = 34.98 km

The distance of P at east of Q is calculated as follows;

Px = d cosθ

Px = 40 km x cos (61)

Px = 19.39 km

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All the values are,

Compound interest = $1280.2

Future value = $1280.2 + $x

Given that;

P = $865

r = 4%

T = 10 years

Formula is,

Compound Interest = P(1 + r)^t

Where, Principal = P, Interest rate = r, Number of compounds = n, Interest time = t

Plug, p = 865, r = 0.04, t = 10

Compound Interest = 865 (1 + 0.04)¹⁰

Compound Interest = 865 (1.04)¹⁰

Compound Interest = 865 x 1.48

Compound Interest = 1280.2

Hence, We get;

Future value = Compound Interest + Principal

Future value = $1280.2 + $x

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Answer: x=22

Step-by-step explanation:

see image for explanation

The standard form based on the information given will be:

a) 2.35 x 10^-3 = 0.00235 (in standard form)

b) 2.35 x 10^3 = 2350 (in standard form)

It should be noted that in mathematics and computer science, a normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.

Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way

he standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form.

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The polynomial function of lowest degree with rational coefficients P(x) = x⁴ + 20x² - 125

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

To find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. √5,5i​.

Since √5 and 5i​ are zeros, then their conjugates -√5, and -5i​ are also zeros.

So,

So, the factors of the polynomial are

So, multiplying the factors together, we get the polynomial.

So, P(x) = (x  - √5)(x - 5i)(x + √5)(x + 5i)

= (x  - √5)(x  + √5)(x - 5i)(x + 5i)

= [x² - (√5)²][x² - (5i)²]

= [x² - 5][x² - (5²i²)]

= [x² - 5][x² - 25(-1))]

= [x² - 5][x² + 25]

Expanding the brackets, we have

= [x² - 5][x² + 25]

= [x² × x² + 25x² - 5x² + 25 × (-5)]

= x⁴ + 20x² - 125

So, P(x) = x⁴ + 20x² - 125

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