Solve the inequality. Then graph the solution and give interval notation. -29 < - 9x - 2 < 7 + -5 -4 -3 -2 -1 0 1 2 3 4 5 Clear All Draw: Interval notation for the above graph and inequality is

Answer:

im pretty sure the answer is a

Step-by-step explanation:

and follow me plz

Since the two lines are parallel, then m<EDB = 40^o.

Two angles are said to be vertical opposite angles when they are produced by two lines which intersect at a point. Thus the measure of vertically opposite angles are equal.

Two parallel lines which are crossed by a transversal produces a series of vertical opposite angles.

Given that CE and FH are parallel lines and intersected by a transversal, then it can be deduced that;

m<CDG = m<EDB  (vertical opposite angles are congruent)

Thus,

m<EDB = 40^o.

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When the former image is rotated, the dots will be located at section 2 and 7.

When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.

From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.

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A line segment that measures 92 millimeters in length can be drawn using scale.

Given that,

A line segment has to be drawn which has a measure of length 92 millimeters.

We know that,

10 millimeters = 1 centimeter

1 millimeter = 1/10 centimeters

92 millimeters = 92/10 = 9.2 centimeters

So it is enough to draw a line segment of length 9.2 centimeters.

In the scale, between a centimeter, there are 9 small lines which indicates the millimeters.

In between 9 and 10, there are 9 lines which indicates, 9.1, 9.2, 9.3, ....., 9.9 and after that is 10 cm.

So draw a line segment starting from 0 to 9.2.

Hence the line segment is drawn with scale.

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The polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

\(\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n\)

It is given that the zeroes of the polynomial are, x= -2, x=7

The polynomial expression is obtained as,

=(x+2)(x-7)

=x²-7x+2x+14

=x²-5x+14

Thus, the polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14.

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Answer:

Correct option is c, -15

Answer:

47 inches

Step-by-step explanation:

45 + 48 + 49 + 40 + 53 = 235

235/5 = 47

According to the information provided, it can be inferred that the conclusion reached by Alex is that there are no advantages to honor roll students.

To calculate the percentages of students who received the requested classes, we must take into account the data in the table. Additionally, we must perform the following operations:

144 ÷ 100 = 1.44

64 ÷ 1.44 = 44.44%

According to the above, the percentage of students who are on the honor roll and receive their classes is 44.44%.

To calculate the percentage of students who are not on the honor roll and receive their classes, we do the following operation.

356 ÷ 100 = 3.56

315 ÷ 3.56 = 88.48%

According to the above, it can be inferred that the students who are on the honor roll do not have advantages over the others because the percentage of students who are not on the honor roll and receive their science classes is greater than the percentage of students who are on the honor roll and receive their classes.

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The interval where function f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)

We have,

The function f(x) crosses the x-axis at (-3, 0), (-1.1, 0), and (0.9, 0), it means that f(x) is negative for x values less than -3, between -1.1 and 0.9, and greater than 0.

Therefore, we can say that:

f(x) < 0 for x < -3 and -1.1 < x < 0.9

And,

The function f(x) has a minimum value of (0, -3) and a maximum value of (-2.4, 17).

This means that f(x) is positive for x values greater than -2.4. Therefore, we can say that:

f(x) > 0 for x > -2.4

Now,

Combining these inequalities, we can say that f(x) is negative over the intervals (-∞, -3) and (-1.1, 0.9), and positive over the interval (-2.4, ∞).

So,

The interval where f(x) is negative and greater than 0 is:

(-∞, -3) U (-1.1, 0)

Thus,

The interval where f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)

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The 19  tykes  given away by the Shelter, that have room for only 4  tykes  per family.        

The number of different canine families that could be created from the 19  tykes  given away by the  sanctum, we need to calculate the number of combinations. room for only 4  tykes , we need to choose 4  tykes  from the aggregate of 19  tykes . The order of the  tykes  in the family doesn't count, as long as we choose different  tykes  for each family.  The number of combinations can be calculated using the formula for combinations  C( n, r) =  n!/( r!( n- r)!)  Where C( n, r) represents the number of combinations of choosing r  particulars from a set of n  particulars.  In this case, we've n =  19( total number of  tykes ) and r =  4( number of  tykes  per family).  Plugging these values into the formula, we get  C( 19, 4) =  19!/( 4!( 19- 4)!)  Calculating the factorial values  19! =  19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =  ! =  4 × 3 × 2 × 1 =  24  15! =  15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =   Substituting these values into the formula  C( 19, 4) = /( 24 ×)  ≈ 91,390  The 19  tykes  given away by the  sanctum, considering that you have room for only 4  tykes  per family.

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3(3)-4 = 5

Hope this helped

With a 12% housekeeping gratuity, the hotel bill for 4 nights comes to $891.52.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

Total cost = Bill before tip + Tip

Total cost = $796 + $95.52

Total cost = $891.52

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Answer:

Solution given:

radius [r]= 9cm

volume of hemisphere =2/3 ×(πr³)=2/3×π×9³

=486πcm³ is your answer

Answer:

x = 100

Step-by-step explanation:

180-57 would equal 123 which means 123 = x +23 and you can simplify this equation by moving 23 over to 123 and subtracting them leaving x = 100

123 = x+ 23

-23 + 123 = x

100 = x

x = 100

sorry, i'm really bad at explaining

180 degree angles when added

180-57 (for known angle)= 123

x+23=123<- we need to take off the all known angles to get x

123-123=100

x=100 is the answer

$450 if you need the process ask me will give it to you

a. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (0,-6) is y = -1/m * x - 6

b. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (2,-2) is y = -1/m * x - 2

what is intercepts?

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

a. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (0, -6) can be written as:

                                    y = mx + b

  where m is the slope and b is the y-intercept.

Since the line is perpendicular to the graph, the slope of the line is the negative reciprocal of the slope of the graph. The y-intercept is (-6).

Therefore, the equation of the line is y = -1/m * x - 6

b. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (2, -2) can be written as:

                                  y = mx + b

  where m is the slope and b is the y-intercept.

Since the line is perpendicular to the graph, the slope of the line is the negative reciprocal of the slope of the graph. The y-intercept is (-2).

Therefore, the equation of the line is y = -1/m * x - 2

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Answer:

The midpoint (x,y)=(6,9)

Step-by-step explanation:

We need to find midpoints(x,y) of the line segment having endpoints S(8, 8) and T(4, 10)

The formula to find midpoint is:

\(Midpoint(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\\)

We are given: \(x_1=8, y_1=8, x_2=4 , y_2=10\)

Putting values and finding midpoint

\(Midpoint(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\Midpoint(x,y)=(\frac{8+4}{2},\frac{8+10}{2})\\Midpoint(x,y)=(\frac{12}{2},\frac{18}{2})\\Midpoint(x,y)=(6,9)\)

So, the midpoint (x,y)=(6,9)

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

a) 0.2098

b) 0.036

c) 0.1866

d) 0.9849

Step-by-step explanation:

Image is color coordinated for each part below,

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Answer: The amount of the mark up is 20$

Step-by-step explanation:

find 50 percent of the 40

50 percent is the same as 0.5

0.5*40=20

The estimate for when the population will exceed 6371 is t > 20.33. This means that at a time greater than 20.33 units

To estimate when the population will exceed 6371, we can set up the inequality:

p(t) > 6371

where p(t) is the population at time t, as given by the equation \(p(t) = 1950e^{0.16t}\)

Substituting the expression for p(t) into the inequality, we get:

\(1950e^{0.16t} > 6371\)

Next, we can divide both sides of the inequality by 1950 to isolate the exponential term:

\(e^{0.16t} > 6371 / 1950\)

To solve for t, we can take the natural logarithm (ln) of both sides, which will eliminate the exponential term:

\(ln(e^{0.16t} > ln(6371 / 1950)\)

Using the property of logarithms that ln(e^x) = x, we get:

\(0.16t > ln(6371 / 1950)\)

Now, we can divide both sides of the inequality by 0.16 to solve for t:

\(0.16t / 0.16 > ln(6371 / 1950) / 0.16\)

Simplifying, we get:

\(t > ln(6371 / 1950) / 0.16\)

Using a calculator, we can find the approximate value of \(ln(6371 / 1950) / 0.16\), which is approximately 20.33 (rounded to two decimal places).

So, the estimate for when the population will exceed 6371 is t > 20.33. This means that at a time greater than 20.33 units

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The equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.

From the given options, the equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.

To determine the equation of a hyperbola, we examine the standard form:

For a hyperbola centered at (h, k), with vertical transverse axis, the standard form is:

(y - k)²/a² - (x - h)²/b² = 1

From the given graph, we can observe that the center of the hyperbola is (-2, 3). This corresponds to the values of (h, k) in the standard form.

Next, we need to determine the values of a and b, which are the lengths of the transverse and conjugate axes, respectively. Looking at the graph, we see that the transverse axis has a length of 2a = 4, so a = 2. The conjugate axis has a length of 2b = 10, so b = 5.

Plugging these values into the standard form, we obtain:

(y - 3)²/4 - (x + 2)²/25 = 1

The equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.

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The correct equation representing the hyperbola shown in the graph is:

(x + 2)²/25 - (y - 3)²/4 = 1.

The equation that represents the hyperbola shown in the graph is:

(x + 2)²/25 - (y - 3)²/4 = 1

Let's analyze the options provided:

(x - 2)²(v + 3)² = 1:

This equation is not a valid representation of a hyperbola because it contains a term (v + 3)², which is not consistent with the variable used in the graph.

(x + 2)²/25:

This equation represents a horizontal parabola, not a hyperbola.

(x - 2)²/25:

This equation represents a horizontal parabola, not a hyperbola.

(y - 3)²/1:

This equation represents a vertical line, not a hyperbola.

(y - 3)²/4:

This equation represents a hyperbola with a vertical transverse axis and a conjugate axis length of 2b = 4 (b = 2).

The equation is in the standard form for a hyperbola with a vertical transverse axis.

The equation is provided as a standard form assuming the given coordinates and graph match the standard form representation of a hyperbola.

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9514 1404 393

Answer:

  5120

Step-by-step explanation:

The recursive formula ...

  a[1] = 5

  a[n] = 4·a[n-1]

defines a sequence with first term 5 and common ratio 4. The explicit formula for a term in this sequence can be written ...

  a[n] = 5·4^(n-1)

We can use this formula to find a[6]:

  a[6] = 5·4^(6-1) = 5·1024

  a[6] = 5120

_____

If you like, you can write out the first 6 terms of the sequence using the recursive formula. Each is 4 times the previous.

  5, 20, 80, 320, 1280,  5120, ...

The absolute value equation that has the solution set  is |x + 6| = 2

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

Solution set = -4 and -8

The midpoint of the above solution is

c = (-4 - 8)/2

So, we have

c = -6

So, we have

|x + 6| = d

Using any of the points, we have

|-4 + 6| = d

Evaluate

d = 2

So, we have

|x + 6| = 2

Hence, the absolute value equation that has the solution set  is |x + 6| = 2

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Therefore, the area of the triangle ABC is approximately 18096.3 square units.

What is the area of the triangle?

To calculate the area of a triangle, use the formula area = 1/2 * base * height.

We can use Heron's formula to find the area of the triangle ABC when the lengths of its three sides are known:

\(Area = {\sqrt{(s(s-a)(s-b)(s-c))}\)

where "s" is the semiperimeter of the triangle, which is half the sum of the lengths of its three sides:

s = (a + b + c)/2

In this case, we have:

a = AB = 154

b = BC = 346

c = AC = 349

So the semiperimeter is:

s = (a + b + c)/2 = (154 + 346 + 349)/2 = 424.5

Now we can use Heron's formula to find the area of the triangle

\(Area = \sqrt{(s(s-a)(s-b)(s-c))}\\\\Area = \sqrt{(424.5(424.5-154)(424.5-346)(424.5-349))}\\\\Area= 18096.3\)

Therefore, the area of the triangle ABC is approximately 18096.3 square units.

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Answer:

23x+250 and that would equal your total cost

Answer:

45

Step-by-step explanation:it gives you the answer chiices if you plug each number into x and then do the equation you will get 180

Answer:  45

Step-by-step explanation:

Did the test.

The density of the ball is the percentage of the density of water

equivalent to the percentage of the volume immersed in water

Correct response:

Given:

A ball floating on water

Percentage of the ball immersed in water = 25% = 0.25

Required:

The density of the ball

Solution:

According to Archimedes' principle, we have;

The weight of the ball = Weight of the water displaced

Therefore;

Mass of the ball = Mass of the water displaced

Volume of water displaced = 25% of the volume of the ball

Let r represent the radius of the ball, we have;

\(Volume \ of \ water \ displaced = 0.25 \times \dfrac{4}{3} \cdot \pi \cdot r^3 = \mathbf{\dfrac{1}{3} \cdot \pi \cdot r^3}\)

Mass of the ball = Mass of water displaced

Density of water = 997 kg/m³

Which gives;

\(Mass \ of \ ball\ W = \mathbf{ 997 \times \dfrac{1}{3} \cdot \pi \cdot r^3}\)

\(Density = \mathbf{\dfrac{Mass}{Volume}}\)

Therefore;

\(Density = \dfrac{997 \times \dfrac{1}{3} \cdot \pi\cdot r^3 }{\dfrac{4}{3} \cdot \pi \cdot r^3} = \dfrac{997}{4} = \mathbf{249.25}\)

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10 times 8 times 6 = 48 times 10 = 480cm³