2 log x = log2 + log(3x − 4)

Please help
Solve the problem and explain round to the nearest 100th if you can
WILL GIVE 5 STARS

Answer:

(x-2)^2 + (y+3)^2 = 5.1^2

Step-by-step explanation:

The equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where h and k are the x and y values of the center of the circle respectively and r stands for the radius.

The center is given to us, at (2, -3) so we can plug that in:

(x-(2))^2 + (y- (-3))^2 = r^2

Simplify:

(x-2)^2 + (y+3)^2 = r^2

We can also solve for the radius by getting another point given to us: (3,2).

Using the pythagorean theorem, we can find how far the two points are away from each other:

a^2 + b^2 = c^2

1^2 + 5^2 = c^2
1 + 25 = c^2

26 = c^2

c ~ 5.1

Plug the radius we solved for in for r:
(x-2)^2 + (y+3)^2 = 5.1^2

To shift the graph left, we need to subtract 1 from x. This gives us F(x) = (x - 1)², which matches option D. Therefore, the correct answer is D.

The graph of F(x) is a parabolic graph, just like the graph of G(x)=x². F(x) is shifted to the left by 1 unit.

The equation for the graph of F(x) is F(x) = (x - 1)². This is because when a parabolic graph is shifted left or right, it affects the x-value of the vertex of the parabola.

The standard form of the equation for a parabolic graph is y = a(x - h)² + k, where (h, k) is the vertex of the graph and a determines whether the graph is facing up or down. In this case, the vertex of the graph of G(x)=x² is (0, 0).

When we shift this graph left by 1 unit, the vertex becomes (-1, 0). Therefore, the equation for F(x) is F(x) = a(x + 1)².

To determine the value of a, we can look at the y-intercept of the graph, which is (0, 1). Plugging these values into the equation, we get 1 = a(0 + 1)², which simplifies to 1 = a.

Therefore, the equation for F(x) is F(x) = (x + 1)². However, if we expand this equation, we get F(x) = x² + 2x + 1, which is not in the form given in the options.

To shift the graph left, we need to subtract 1 from x. This gives us F(x) = (x - 1)², which matches option D. Therefore, the correct answer is D.

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The values of w, x, y, z are 120°, 60°, 120° , 60° respectively.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

lines PQ and RS are parallel to each other and AB and CD are also parallel to each other. A pair of parallel line will serve as transversal.

Angles on parallel lines can be ;

Vertically opposite, alternate, corresponding and in each case the angles are equal.

w = 120°( vertically opposite angles)

x = 180-120 = 60( corresponding angles)

x = z = 60° ( corresponding angles)

y = 180-60 = 120°( angles on a straight line)

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The number the spinner is most likely to land on is 2

From the question, we have the following parameters that can be used in our computation:

The spinner

From the spinner, we have the number that covers the largest area to be 2

i.e.

Largest area = 2

This means that the number it is most likely to land on is 2 and it has the highest probability

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The equations that represent a line parallel to 3x - 4y = 7 and passes through the point (-4, -2) are:

0 = 3x - 4y - 4

3x - 4y = 4

To determine which equations represent a line that is parallel to the given line and passes through the point (-4, -2), we need to find the equations that have the same slope as the given line.

The equation 3x - 4y = 7 can be rewritten in slope-intercept form as y = (3/4)x - 7/4. From this form, we can see that the slope of the given line is 3/4.

Now let's analyze the options:

Oy = -3x + 1: This equation has a slope of -3, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.

0 = 3x - 4y - 4: This equation can be rewritten as 3x - 4y = 4. Comparing this to the given line, we can see that it has the same coefficients of x and y, which means it has the same slope of 3/4. Therefore, this option represents a line parallel to the given line.

4x - 3y = -3: This equation has a slope of 4/3, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.

Oy - 2 = -(x - 4): This equation can be rewritten as y = -x + 2. The slope of this line is -1, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.

Oy + 2 = 2(x + 4): This equation can be rewritten as y = 2x + 6. The slope of this line is 2, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.

In conclusion, the equations that represent a line parallel to 3x - 4y = 7 and passes through the point (-4, -2) are:

0 = 3x - 4y - 4

3x - 4y = 4

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Answer:

1) no special type; B

2) see below

Step-by-step explanation:

Additive inverse of the matrix is the negative of that number:

[ -7 6 -4]-> [7 -6 4]

[-3 4 -2] -> [ 3 -4 2]

The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.

To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.

The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:

-1/4 = -5/20

3/5 = 12/20

Now that the fractions have the same denominator, we can add them:

-5/20 + 12/20 = (-5 + 12)/20 = 7/20

Therefore, -1/4 + 3/5 is equal to 7/20.

To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.

Thus, the final answer is 7/20.

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Answer:

Kirsten makes $12.50 per hour

Step-by-step explanation:

The total is $432.50

$5 is taken out of her paycheck, so that will be negative.

35 hours is the time she spent working.

The unknown variable we are looking for is the amount she makes in one hour.

Setting up the equation, we get:

$432.50 = $35x - $5

where x is the amount she makes every hour

Solve for x:

$437.50=$35x

$437.50 / $35 = x

Therefore, x = $12.50

The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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Answer:

If Delaware was proportional to Alabama in enrollment to the district, it would have approximately 37 districts.

The ratio of students to districts in Alabama is 630,683/137 = 4,603 students per district. If Delaware had the same ratio of students to districts, it would have 120,475/4,603 = 26.16 districts. Rounding to the nearest whole number, Delaware would have approximately 26 districts if it was proportional to Alabama in enrollment to the district.

The option that is not true about polynomial functions is:

Option D. The deg (f ^ 3) = 3m​

For polynomial functions f(x) and g(x), if deg(f) = m * deg(g) = n, then we have the following:

Option A: deg(f + g) = max(m, n)

This is true because we know that the degree of the sum of two polynomials is the maximum of their individual degrees.

Option B: deg(f * g) <= m + n

This is true because we know that the degree of the product of two polynomials is at most the sum of their individual degrees.

Option C: If g is a factor of f, then deg(f) <= m

This is true because If g is a factor of f, it means that f can be divided by g without leaving a remainder. In this case, the degree of f is less than or equal to the degree of g.

D. The deg(f ^ 3) = 3m

This is not true because the degree of the polynomial f raised to the power of 3 is not necessarily equal to 3 times the degree of f. The degree of f^3 will depend on the individual terms and their exponents.

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The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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Answer:

  (b)  x + 6

Step-by-step explanation:

You want the rule for the x-coordinate when the transformation is a right shift of 6 units.

A point that is the image of a pre-image point with x-coordinate x will be 6 units farther right of the y-axis than the pre-image point.

The x-coordinate measures how far right of the y-axis a point is. When that distance increases by 6 units, the x-coordinate increases by 6 units:

  x ⇒ x+6 . . . . . . the x-coordinate transformation rule

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Para calcular la población de bacterias al cabo de 4 horas, primero necesitamos determinar cuántos intervalos de 20 minutos hay en 4 horas.

4 horas son equivalentes a 240 minutos. Dividiendo 240 minutos entre 20 minutos por intervalo, obtenemos 12 intervalos.

Dado que la población de bacterias aumenta un 25% cada 20 minutos, podemos aplicar este crecimiento a cada intervalo de 20 minutos.

Para cada intervalo de 20 minutos, la población de bacterias aumentará en un 25%.

Por lo tanto, podemos calcular la población de bacterias al final de los 12 intervalos de la siguiente manera:

Población final = Población inicial * (1 + tasa de crecimiento)^número de intervalos

Población inicial = 32,200 bacterias

Tasa de crecimiento = 25% = 0.25

Número de intervalos = 12

Población final = 32,200 * (1 + 0.25)^12

Realizando los cálculos, obtenemos la población final de bacterias al cabo de 4 horas.

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Answer: Read the solution

Step-by-step explanation:

A. For diagram A, triangles ANC and BDE are similar. Thus, we can use similarity ratios to find the length of AC. (x+1)/12 = (x+5)/15. 15x+15=12x+60. Thus 3x=45, and x=15. Since we need to find AC, AC = 15+1 = 16.

B. For diagram B, triangles SRT and VUT are similar. Again, using similarity ratios, (4x-1)/14=(x+2)/6 or 14x+28=24x-6. 10x=34, x=3.4.

Navern Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 11.36%.

Value-added time is the time spent on activities that directly add value to the product.

Value-added time: Process time = 5 days (the process of manufacturing the elevators)

Total cycle time: Wait time + Inspection time + Process time + Move time + Queue time

= 12 days + 12 days + 5 days + 6 days + 9 days

= 44 days

MCE = (Value-added time / Total cycle time) * 100

= (5 days / 44 days) * 100

≈ 11.36%

Therefore, Navern Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 11.36%.

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a) The triangles in this problem are congruent.

b) The reason is the SAS congruence theorem.

The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.

The equal sides for this problem are given as follows:

Hypotenuses and PS.

As angle P is bisected, we have <1 = <2, which are the angles between the equal sides, hence the SAS theorem holds true for this problem.

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Answer:

Step-by-step explanation:

                                                   error

Answer:

x ≈ 75.2

Step-by-step explanation:

using the tangent ratio in the right triangle

tan62° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{40}[/tex] ( multiply both sides by 40 )

40 × tan62° = x , then

x ≈ 75.2 ( to the nearest tenth )

The value of dy/dt  at x= 1 if y = [tex]3x^2[/tex] - 3 and dx/dt = 3 is 18.

To find dy/dt at x = 1, we need to differentiate the given equation y = [tex]3x^2[/tex] - 3 with respect to t and then substitute x = 1 and dx/dt = 3.

Let's begin by differentiating y = [tex]3x^2[/tex]- 3 with respect to t using the chain rule. Since y is a function of x and x is a function of t, we have:

dy/dt = (dy/dx) * (dx/dt)

Given dx/dt = 3, we can rewrite the equation as:

dy/dt = [tex](dy/dx) * 3[/tex]

Now, let's find the derivative of y = [tex]3x^2 - 3[/tex] with respect to x:

dy/dx = d/dx[tex](3x^2 - 3)[/tex]

= 6x

Substituting this back into the equation for dy/dt, we get:

dy/dt = [tex](6x) * 3[/tex]

= 18x

Finally, we can evaluate dy/dt at x = 1:

dy/dt at x = 1 = 18(1)

= 18

Therefore, the value of dy/dt at x = 1 is 18.

It's important to note that the value of dx/dt = 3 was given, and we used it to find dy/dt using the chain rule and the derivative of the equation with respect to x.


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Si un hombre camina a una velocidad promedio de 4 2/5 km por hora, podemos calcular la distancia que puede recorrer en 2 2/3 horas.

Primero, convertimos la velocidad promedio a una fracción impropia. 4 2/5 se puede expresar como 22/5. Por lo tanto, la velocidad es de 22/5 km por hora.

Luego, multiplicamos la velocidad por el tiempo para obtener la distancia. En este caso, la multiplicación sería (22/5) * (8/3) = 176/15 km.

Entoncs, el hombre puede llegar a una distancia de 176/15 km en 2 2/3 horas.

En resumen, el resultado es 176/15 km.

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The domain of the function y = 3 tan(2/3x) is all real numbers except for x = (3n + ³/₂)π., where n is an integer.

The function is given as: y = 3 tan(2/3x)

The function above is defined for all values of x except where the tangent function is undefined. The tangent function is undefined at angles where the cosine is zero. In this case, the cosine is zero when 2/3x is equal to an odd multiple of π/2.

So we set (2/3)x equal to (2n + 1)π/2, where n is an integer:

(2/3)x = (2n + 1)π/2.

To solve for x, we multiply both sides by 3/2:

x = (3/2)(2n + 1)π/2.

x = (3n + ³/₂)π.

Therefore, the function is undefined when x is equal to (3n + 3/2)π, where n is an integer.

The domain of the function y = 3 tan(2/3x) is all real numbers except for x = (3n + ³/₂)π., where n is an integer.

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Therefore, it would take approximately 36 minutes for 14 workers to complete the job.

To solve this inverse variation problem, we'll use the formula: t = k/w, where t represents the time needed, w represents the number of workers, and k is the constant of variation.

We can find the value of k by plugging in the given values of 9 workers and 56 minutes into the formula:

56 = k/9

To find the value of k, we multiply both sides of the equation by 9:

k = 504

Now that we know the constant of variation, we can determine the time it would take for 14 workers to complete the job. Plugging in the values into the formula:

t = 504/14

t ≈ 36

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The interval to the solution is (a) the interval from -7 to 6

From the question, we have the following parameters that can be used in our computation:

log(x + 9) + log(x - 9) = 0.47712

Apply the rule of logarithm

So, we have

log(x² - 9) = 0.47712

Take the exponent of both sides

x² - 9 = [tex]10^{0.47712[/tex]

So, we have

x² = 9 + [tex]10^{0.47712[/tex]

Evaluate

x² ≈ 12

Take the square root of both sides

x ≈ ±3.46

This value is between the interval -7 to 6

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Answer:

Yes, the triangle are similar.

Step-by-step explanation:

To prove that 2 triangle are similar you only need to prove that 2 corresponding angles are equal.

The sum of the interior angles add to 180.

< m on the left measures 30 degrees.

80 - 90 - 60 = 30

> t on the right measures 60 degrees.

180 - 90 - 30 = 60

If two corresponding angles of two triangles are equal that forces the third pair to be congruent, since the total of the angles must add up to 180.

Although we are not given the corresponding sides, there are proportional because the angles are equal.

Helping in the name of Jesus.

Answer:

Similar triangles are triangles that have the same shape but different sizes. In other words, if two triangles are similar, then their corresponding angles are congruent and their corresponding sides are in equal proportion.

For Question:

In Δ MSK and ΔQRT

∡S=∡R right angle

∡K=∡T=180°-90°-30°=60° Given

∡M=∡Q=180°-90°-60°=30° Given

Therefore,

Δ MSK  [tex]\bold{\sim}[/tex]  ΔQRT

By AA similarity.

Hence Proved:

Using the Venn diagram, each set and the number of elements in each set are:

a. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12}

b. A = {1, 3, 4, 5, 6, 8}

c. B = {4, 5, 6, 7, 9, 11}

d. C = {6, 8, 9, 12}

e. A ∪ B = {1, 3, 4, 5, 6, 7, 8, 9, 11}

f. A ∩ B = {4, 5, 6}

A Venn diagram is a pictorial representation used to visualize the relationships between different sets of objects or concepts.

a.) U is the universal set. This implies it contains all the elements in the set. Thus:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12}

b.) A is all element (number) is set A (circle A). Thus:

A = {1, 3, 4, 5, 6, 8}

c.) B is all element is set B (circle B). Thus:

B = {4, 5, 6, 7, 9, 11}

d.) C is all element is set C (circle C). Thus:

C = {6, 8, 9, 12}

e.) A ∪ B is all element is sets A and B (circles A and B). Thus:

A ∪ B = {1, 3, 4, 5, 6, 7, 8, 9, 11}

f.) A ∩ B is all element is sets A and B (circles A and B) have in common. Thus:

A ∩ B = {4, 5, 6}

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Answer:

3.36643191324

-1.36643191324

Step-by-step explanation:

subtract 23 from both sides so that everything is on one side

5x²-10x-23=0

you can't factor this, so you need to use the quadratic formula:

(-b±√(b²-4*a*c))/2a

in our case, a= 5 b= -10 and c = -23

(-(-10)±√(10²-4*5*(-23)))/(2*5)

(10±√(100+460))/10

(10±√560)/10

we solve this twice. once where ± is + and again where ± is -

(10+√560)/10 = 3.36643191324

(10-√560)/10= -1.36643191324

The time taken for 1414 people to paint 14 walls is 6,430.44 minutes.

To find out how many minutes it would take 1414 people to paint 14 walls, we can use the information given to find the ratio.

We know that it takes 9 people 41 minutes to paint 9 walls.

Let's find the ratio:

(9 people) : (1414 people) = (41 minutes) : (x minutes)

Use the mutual multiplication property of the resulting ratio:

9 * x = 1414 * 41

Right simplification:

9x = 57974

To solve this problem, create a ratio using the information provided:

(9 people) : (1414 people) = (41 minutes) : (x minutes)

We can multiply the ratios:

9 * x = 1414 * 41

On the right side of the equation, calculate the product of 1414 and 41, which equals 57974.

4 444 So:

444 9x = 57974 To separate

4 share both sides of the equation with 9:

4 x = 57974/9

share both sides with 9:

4 x = 6430.44

It will take 6,430.44 minutes for 1,414 people to paint 14 walls.

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To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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Therefore, an appropriate confidence interval for μ30−μ60μ30​−μ60​ (the difference in mean body temperature) would be −0.796−0.796 to −0.404−0.404 (rounded to the appropriate decimal places).

To estimate the difference in the mean body temperature after exercising for 30 minutes versus 60 minutes, we can construct a confidence interval. Since the conditions for inference have been assumed to be met, we can proceed with the following steps:

   Calculate the difference in sample means: xˉ30−xˉ60=38.3−38.9=−0.6xˉ30​−xˉ60​=38.3−38.9=−0.6.

   Determine the standard error of the difference, which is given by the formula:

   SE=(s302n30)+(s602n60)SE=(n30​s302​​)+(n60​s602​​)

Substituting the values, we have:

SE=(0.27218)+(0.29224)≈0.100SE=(180.272​)+(240.292​)  ​≈0.100.

   Choose an appropriate confidence level. Let's say we want a 95% confidence interval.

   Using the standard error, calculate the margin of error, which is given by multiplying the critical value (corresponding to the chosen confidence level) by the standard error. For a 95% confidence level, the critical value is approximately 1.96.

   Margin of Error = 1.96 * 0.100 ≈ 0.196.

   Construct the confidence interval by subtracting and adding the margin of error to the difference in sample means:

   −0.6−0.196−0.6−0.196 to −0.6+0.196−0.6+0.196.

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