1819221 pointZA and ZB are supplementary angles. If ZA = 6x + 3 and ZB = 8x - 5, write an algebraic equation to find x, mZA and mZB.20

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

The number of ways that 4 books can be arranged on a shelf are= 24. That is option 2.

To calculate the number of ways 4 books can be arranged is the find the permutation.

That is ,

4! = 4×3×2×1

4! = 24

Therefore, the number of ways that 4 books can be arranged on a shelf are= 24

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Answer:

3 1/3 or 3 and 1 third

Step-by-step explanation:

it's an answer

The area of triangle ADE is,

⇒ A = 48 square units

We have to given that,

In the diagram , DE is a midsegment of triangle ABC.

And, The area of triangle ABC is 96 square units

Now, We know that,

Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.

Hence, the area of triangle ADE is half the area of triangle ABC,

That is,

A = 96 / 2

A = 48 square units

Thus, The area of triangle ADE is,

⇒ A = 48 square units

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Answer:

its 7/10

Step-by-step explanation:

The probability of randomly selecting an item with white or red on it is 3/10.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

A store display shows two red shirts, one blue shirt, and three shirts with red and white stripes.

The display also shows two pairs of blue jeans, one pair of white pants, and one pair of white shorts.

The probability of randomly selecting an item with white or red on it is given by;

\(\rm Probability=\dfrac{Total \ number \ of \ items}{Total \ red \ or \ white \ items}\\\)

Total items =  2 + 1 + 3 + 2 + 1 + 1 = 10 itens.

Substitute all the values in the formula

\(\rm Probability=\dfrac{Total \ number \ of \ items}{Total \ red \ or \ white \ items}\\\\\rm Probability=\dfrac{3}{10}\\\\\)

Hence, the probability of randomly selecting an item with white or red on it is 3/10.

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the answer is 3 3/20

3.15 = 63/20 = 3/20

Answer:

C. 3 3/20

Step-by-step explanation:

Answer:0.375

Step-by-step explanation:

1/8 + 1/4 = 3/ 8=0.375

Here we have a polynomial of even degree with positive leading coefficient, so the end behavior is:

as x → ∞, f(x) → ∞

as x → -∞, f(x) → ∞

How is the end behavior of F(x)?

Here we have the function:

F(x) = 2x^4 - x^3 + 5x - 9

For any polynomial of even degree, we will have the same end behavior in both ends of the domain.

If the leading coefficient is positive, in both ends the function will tend to infinity.

If the leading coefficient is negative, in both ends the function will tend to negative infinity.

In the case of our function:

F(x) = 2*x^4 - x^3 + 5x - 9

We can see that the leading coefficient is 2, so it is positive, which means that the end behavior is:

as x → ∞, f(x) → ∞

as x → -∞, f(x) → ∞

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Answer:

h = 1,268 cm

Step-by-step explanation:

                   V = (π·r²·h)/3, general formula

                 83 = (π·4²·h)/3, substitute what is given V= 83 cm³ and r = 4 cm

             83 ·3 = (π· 16·h)·3/3, multiply both sides by 3 and solve 4² = 16

               249 = π·16·h, multiply 83·3 = 249 and 3/3 = 1

      249/ π·16 = h , divide both sides by π·16

1,268.146587 = h, solve

             1,268 ≈ h , is rounded to the nearest cm

Answer:

Lob is the answer the the 2

The measure of central angle AOB is 2.

The measure of the central angle stands twice the measure of the inscribed angle subtended by the identical arc. (An inscribed angle exists an angle whose vertex fibs on the circumference of the circle.) The sum of the measurements of the central angles of a circle with no common points stands 360°.

Central angles exist subtended by an arc between those two points, and the arc length stands the central angle of a circle of radius one.

The measure of central angle AOB is 2.

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Answer:

  (b)  4.2

Step-by-step explanation:

The distance from a point to a line can be found using the formula. To use it, we need the equation of the line in general form.

We notice that the coordinates of the given points have the same y/x = 2/3 ratio. This means they lie on the line y = 2/3x. The equation for that line, written in general form is ...

  y = 2/3x

  3y = 2x

  2x -3y = 0 . . . . . . general form equation for the line through the points.

The formula for the distance from (x, y) to the line ax+by+c=0 is ...

  d = |ax +by +c|/√(a²+b²)

The distance from (x, y) to our line is given by the formula ...

  d = |2x -3y|/√(2² +(-3)²)

  d = |2x -3y|/√13

For point P(9, 11), the distance to the line is ...

  d = |2·9 -3·11|/√13 = |18 -33|/√13 = 15/√13 ≈ 4.2

1)

The axis of symmetry is x = -6.

2)

Vertex is (-6, 26).

3)

f(x) has a maximum value.

4)

f(x) is concave down.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

f(x) = -x² - 12x - 10

This is in the form of ax² + bx + c.

a = -1, b = -12, c = -10

The axis of symmetry is x = -b/2a

x = 12/(-2)

x = -6

Now,

f(x) = -x² - 12x - 10

f(x) = -(x² + 12x + 10)

f(x) = - { (x² + 12x + 36) - 36 + 10}

f(x) = -(x + 6)² + 26

This is in the form of f(x) = a (x - h)² + k

a = -1, h = -6, k = 26

Vertex = (h, k) = (-6, 26)

Now,

f(x) = -x² - 12x - 10

f'(x) = -2x - 12

f''(x) = -2

It is a negative value.

This means f(x) has a maximum value.

Now,

From the graph, we see that f(x) is concave down.

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Answer:

x₁ = 179 , x₂ = 17 , x₃ = - 3

Step-by-step explanation:

x₁ - 9x₂ + 7x₃ = 5 → (1)

      x₂ + 7x₃ = - 4 → (2)

              x₃ = - 3

substitute x₃ = - 3 into (2) and solve for x₂

x₂ + 7(- 3) = - 4

x₂ - 21 = - 4 ( add 21 to both sides )

x₂ = 17

substitute x₂ = 17 and x₃ = - 3 into (1) and solve for x₁

x₁ - 9(17) + 7(- 3) = 5

x₁ - 153 - 21 = 5

x₁ - 174 = 5 ( add 174 to both sides )

x₁ = 179

solution is x₁ = 179 , x₂ = 17 , x₃ = - 3

he net income for the year is $16,550.

Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)

Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500

Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800

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a) The distance of the stone above ground level at time t :

d(t)= -4.9t² + 950

b) It takes 13.92 seconds the stone to reach the ground

c)  With 136.42 m/s velocity the stone strikes the ground.

d) If the stone is thrown downward with a speed of 8 m/s, it will take 13.13 seconds to reach the ground

Here, a  stone is dropped from the upper observation deck of a tower, 950 m above the ground.

(a)  the distance of the stone above ground level at time t would be,

d(t)  = 0.5 (-9.8) t² + v(0) t + d(0)

      = (-4.9)t² + 0t + 950

      = -4.9t² + 950

(b) Now we find the time the stone takes to reach the ground.

i.e., the value of 't' when d = 0

Substituting d(t) = 0 in the above equation.

-4.9t² + 950 = 0

t² = (-950) / (-4.9)

t² = 193.88

t = 13.92 seconds

(c) We need to find the velocity the stone takes to strike the ground

i.e., the velocity when t  = 13.92 seconds

v(t) = v(0) + gt      

v(13.92) = 0 + (9.8)(13.92)

v = 136.42 m/s

(d) here, v(0) = -8 m/s  

Velocity is negative because stone is being thrown downward.

d(t) = 0

(-4.9)t² + v(0) t + d(0) = 0

(-4.9)t² -8t + 950 = 0

Using the quadratic formula we solve above equation for,

t = -14.76, 13.13

We can disregard the negative solution

So, we get t = 13.13 seconds.

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Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

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Answer: A,E or F.

Step-by-step explanation: That's the only ones that have X's and then x is 0

Answer: 10%

Step-by-step explanation:

The difference between his estimated and actual distance is 15 - 13.5 = 1.5

The percentage of error is the difference divided by the actual value.

1.5÷15 = 0.10

Converted to a percentage, it is 10%

Answer:

10%

Step-by-step explanation:

The system of inequalities that can be used to find the possible original prices of a laptop, x, and of a printer, y is: x + y ≥ 1050 and 0.8x + 0.9y > 860

Let x be the original price of the laptop and y be the original price of the printer.

So, the discounted price of the laptop is 0.8x and the discounted price of the printer is 0.9y

If the two are purchased together, the total discounted price is:

0.8x + 0.9y

This exceeds $860

0.8x + 0.9y > 860

The original prices of the two together is at least $1,050.

This can be written as:

x + y ≥ 1050

So, we have

x + y ≥ 1050 and 0.8x + 0.9y > 860

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Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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The value of x in the triangle is 17 .

The perimeter of the triangle ABC is 86 units.

Triangle Proportionality Theorem states that If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.

Therefore, let's use the theorem to find the value of x in the triangle.

Hence,

20 / 4 = 2x - 4 / 6

cross multiply

120 = 4(2x - 4)

120 = 8x - 16

120 + 16 = 8x

136  = 8x

divide both sides by 8

x = 136 / 8

x = 17

Hence, let's find the perimeter of the triangle ABC.

perimeter of the triangle ABC = 24 + 26 + 2(17) - 4 + 6

perimeter of the triangle ABC = 50 + 30 + 6

perimeter of the triangle ABC = 86 units

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The rectangles approximate ln(2) as 0.693. The approximation is an under-estimate, as the rectangles only cover a portion of the graph. The closest estimate is the fourth one, as it is closest to the value given by the calculator.

1. Slice the graph into 4 equal parts by drawing vertical lines at x=0.5, x=1, and x=1.5.

2. Find the midpoints of each slice by calculating the average of the x-values of each slice. The midpoints are x=0.25, x=0.75, x=1.25, and x=1.75.

3. Determine the height of each rectangle at the midpoints. The heights are y=0.253, y=0.572, y=0.854, and y=1.092.

4. Sketch in the rectangles using the midpoints and heights calculated.

5. Approximate ln(2) as the sum of the areas of the four rectangles, which is 0.693. This is an under-estimate.

6. The closest estimate is the fourth one, as it is closest to the value given by the calculator (0.693).

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Answer:

328÷17=19 nights and approximately 3 hours

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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The surface area of a cylinder is 284m² and it's volume is 366.9m³

To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:

From the given question, the data are;

a. The surface area of the cylinder is;

SA = 2π(4)² + 2π(4)(7.3)

SA = 283.999≈284m²

b. The volume of the cylinder is

v = πr²h

v = π(4)²(7.3)

v = 366.9m³

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Answer:

11.25 :D

Step-by-step explanation: