The function g is defined by g(x) = ( 2x – 3 )( x + k )
Given that g(0) = – 15 find (i) k (ii) x such that g(x) = 0

Answer:

\(Speed = \frac{3}{2}\)mph

Step-by-step explanation:

Given

Distance = \(\frac{1}{2}\) mile

Time = \(\frac{1}{3}\) hour

Required

Determine the speed

To do this, we simply divide distance by time

\(Speed= \frac{Distance}{Time}\)

\(Speed = \frac{1}{2} / \frac{1}{3}\)

\(Speed = \frac{1}{2} * \frac{3}{1}\)

\(Speed = \frac{3}{2}\)

Hence, the speed is \(\frac{3}{2}\) mile per hour

Tyler's speed is 1.5 miles per hour.

The formula for speed is:

= Distance / Time

Distance = 1/2 miles

Time = 1/3 hours

Tyler's speed is therefore:

= 1/2 ÷ 1/3

= 1 / 2 x 3/1

= 3/2 miles per hour or.

= 1.5 miles per hour

Tyler's speed is therefore 1.5 miles per hour.

Find out more at https://brainly.com/question/10722020.

Answer: A is the answer

Answer:

24

Step-by-step explanation:

11 12 33 21

Answer:

Step-by-step explanation:

If the arrows in the segments [AB] and [DE] means that the lines (AB) and (DE) are parallele than

we use the dilation  of center C which image of

D is A

E is B

has for ratio 5/2=2.5.

A) The image of the triangle CDE is the triangle CAB which are similar.

B)

\(\dfrac{CE}{CB} =\dfrac{DE}{AB} \\\\==>\ \dfrac{3}{3+y} =\dfrac{2}{5}\\\\==>\ 6+2y=15\\\\==>\ 2y=9\\\\\\==>\ y=\dfrac{9}{2} \\\\\\The\ image\ of\ \widehat{CDE}=\widehat{CAB}\ ==>\ x=48^o\\\\\)

Answer:

Step-by-step explanation: Nk all day ∴

Over a period of 1.5 hours, a continuous IV infusion at a rate of 15 gtt/min (with a drop factor of 10 gtt/ml) will result in 135 milliliters being infused.

To calculate the number of milliliters that will infuse over 1.5 hours, we need to convert the infusion rate from drops per minute to milliliters per hour.

Infusion rate: 15 gtt/min

Drop factor: 10 gtt/ml

First, we can calculate the infusion rate in milliliters per minute:

Infusion rate (ml/min) = Infusion rate (gtt/min) / Drop factor (gtt/ml)

Infusion rate (ml/min) = 15 gtt/min / 10 gtt/ml = 1.5 ml/min

Next, we can convert the infusion rate to milliliters per hour:

Infusion rate (ml/hour) = Infusion rate (ml/min) × 60 min/hour

Infusion rate (ml/hour) = 1.5 ml/min × 60 min/hour = 90 ml/hour

Finally, we can calculate the total volume that will infuse over 1.5 hours:

Volume (ml) = Infusion rate (ml/hour) × Time (hours)

Volume (ml) = 90 ml/hour × 1.5 hours = 135 ml

Therefore, 135 milliliters will infuse over 1.5 hours.

To learn more about infusion rate visit : https://brainly.com/question/28790508

#SPJ11

The correct choice below the elements AU(BNC) = b.{d, f, g, b}

To find the set AU(BNC), to determine the individual sets BNC and then take the union with set A.

Set BNC consists of elements that are in both B and C but not in A.

BNC = (B ∩ C) - A

= ({b, f, g} ∩ {a, b, c, e}) - {d, f, g}

= {b} - {d}

= {b}

find the union of set A and set BNC.

AU(BNC) = A ∪ BNC

= {d, f, g} ∪ {b}

= {d, f, g, b}

To know more about elements  here

https://brainly.com/question/31950312

#SPJ4

Complete question:

Let U= (a, b, c, d, e, f, g), A=(d, f, g), B = {d, f, g, b), and C= {a, b, c, e}. Find the following set. AU (BNC) Select the correct choice below and fill in any answer boxes within your choice. A. AU (BOC) = {} B. AU (BNC) =Ø

There are 5 different sums possible when spinning the two spinners.

We have,

To find the number of different sums possible when spinning the two spinners, we need to determine all the possible combinations of numbers that can be obtained by selecting one number from each spinner and adding them together.

Spinner 1 has the numbers: 5, 2, 4, 3

Spinner 2 has the numbers: 5, 3, 4

Let's calculate all the possible sums:

From Spinner 1:

Selecting 5: 5 + 5, 5 + 3, 5 + 4

Selecting 2: 2 + 5, 2 + 3, 2 + 4

Selecting 4: 4 + 5, 4 + 3, 4 + 4

Selecting 3: 3 + 5, 3 + 3, 3 + 4

These combinations give us the following sums:

10, 8, 9

7, 5, 6

9, 7, 8

8, 6, 7

Now, let's count the unique sums:

5 unique sums: 10, 8, 9, 7, 6

Therefore,

There are 5 different sums possible when spinning the two spinners.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ12

Answer:

C is the answer!

Step-by-step explanation:

Answer:

:)

Step-by-step explanation:

quiz scores:

a. arrange them all from least to greatest to figure out the median first

your quiz: 15, 16, 17, 18, 19     middle # = 17        median = 17

friend's quiz: 12, 13, 17, 20, 20     middle # = 17       median = 17

now for mean add all of your quiz scores up and divide by how many #s

15 + 16 + 17 + 18 + 19 = 85 / 5 = 17          mean = 17

now your friend's:

12 + 13 + 17 + 20 + 20 = 82 / 5 = 16.4       mean = 16.4

mode is which number is used the most

your mode = you don't have a mode       your friend's mode = 20

b. you have a higher mean than your friend

world populations:

a. range is to subtract the smallest number from the largest

803 - 31 = 772

b. mean is adding it all up and dividing by how many numbers there are:

803 + 487 + 348 + 368 + 730 + 31 = 2767 / 6 = 461.17

median is arranging them in order and finding the middle #

31, 348, 368, 487, 730, 803

368 + 487 = 855 / 2 = 427.5

mean = 461.17

median = 427.5

mode = no mode

tomato plants:

a. range is subtracting the smallest from the largest

52 - 36 = 16

b. mean is adding all the #s and dividing by how many #s there are:

36 + 45 + 52 + 40 + 38 +41 + 50 + 48 = 350 / 8 = 43.75

median is the middle from least to greatest

36, 38, 40, 41, 45, 48, 50, 52

41 + 45 = 86 / 2 = 43

mean = 43.75

median = 43

mode = no mode

hope this helps! :)

The graph of the inequality is a downward-opening parabola that passes through (0, 7) and (8, -9). The shaded region is below the curve.

y≤-1/2x² + 4x + 7

The inequality is a quadratic function in standard form.

To graph it, we can find the vertex and the x-intercepts.

The vertex is at the point (h, k) where h = -b/2a and k = f(h), and f(x) = -1/2x² + 4x + 7.

a = -1/2, b = 4, and c = 7,

so h = -b/2a = -4/(-1) = 4, and

k = f(h) = -1/2(4)² + 4(4) + 7 = 15.

So the vertex is at (4, 15).

Now let us find the x-intercepts by setting y value as 0 and solve for x:

0 ≤ -1/2x² + 4x + 7

1/2x² - 4x - 7 ≤ 0

x² - 8x - 14 ≤ 0

We find roots by using the quadratic formula

x = (8 ± √8² - 4(1)(-14))) / 2

x = 4 ± √18

So the x-intercepts are  0.34 and 7.66.

Hence, the graph of the inequality is a downward-opening parabola that passes through (0, 7) and (8, -9). The shaded region is below the curve.

To learn more on Inequality click:

https://brainly.com/question/28823603

#SPJ1

Explain the graph of the inequality y≤-1/2x² + 4x + 7?

Answer:

Mango = 0.5, Peach = 1.75

Step-by-step explanation:

Let x represent the price of mango

Let y represent the price of peach

Melanie: 8x + 6y = 14.50

Jaya: 4x + 7y = 14.25

Isolate for a variable in one of the equations (just pick a random one, you don't have to pick mine)

4x + 7y = 14.25 => x = (14.25 - 7y)/4 = 3.5625 - 7/4y

Plug into other equation

8x + 6y = 14.50

8(3.5625 - 7/4y) + 6y = 14.5

28.5 - 14y + 6y = 14.5

28.5 - 14.5 = 14y - 6y

14 = 8y

y = 1.75

4x + 7y = 14.25

4x + 7(1.75) = 14.25

4x + 12.25 = 14.25

4x = 2

x = 0.5

Answer:

Her Monthly allowance is 60 dollars

12= 20% of 60

Answer: I and III

Step-by-step explanation:

The origin is at (0,0).

When we look at the graph, we can see that the only visible x and y intercepts are at the origin, (0,0) (an x or y intercept is where the graph intersects the x or y axis). We also know that because the graph is going outwards, it will not have another x or y intercept. So, I is correct.

II would be incorrect because the maximum point would be WAY further up. The maximum point is the highest point the graph will reach.

III is correct because the origin is the lowest point, which means that the origin is the minimum point.

Answer: 1 decameter

Step-by-step explanation:

Answer:

1 decameter

Step-by-step explanation:

1 decameter is 10 meters or 1000 centimeters

The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

Learn more about Linear programming:

https://brainly.com/question/14309521

#SPJ11

(a) The probability that all 4 of your answers are incorrect is 0.4823.

The probability of getting one question wrong is 5/6, so the probability of getting all four questions incorrect is (5/6)^4 = 0.4823 (rounded to four decimals).

(b) The probability that all 4 of your answers are correct is 0.0008.

The probability of getting one question correct is 1/6, so the probability of getting all four questions correct is (1/6)^4 = 0.0008 (rounded to four decimals).

Look here to know more about probability

https://brainly.com/question/31158335

#SPJ11

Answer:

x = 5

Step-by-step explanation:

x² - 5x = 0

(x² - 5x) /x = 0/x

x²/x - 5x/x = 0

x - 5 = 0

x = 5

Check:

x² - 5x = 0

5² - 5*5 = 0

25 - 25 = 0

The solution to the equation is:

x = 0 or x = 5

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

We have:

x²-5x = 0

We can solve the equation as follow:

x²-5x = 0

Factorize:

x(x - 5) = 0

x = 0 or (x -5) = 0

x = 0 or x = 5

Learn more about quadratic equation on:

brainly.com/question/29228193

#SPJ6

The 9th term of this geometric sequence 10, 40, 250, 1250, ....​ include the following: 655,360.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical equation (formula):

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = 40/10

Common ratio, r = 4

For the 9th term, we have:

a₉ = 10(4)⁹⁻¹

a₉ = 655,360.

Read more on geometric sequence here: brainly.com/question/16423479

#SPJ1

The distance from the point (0, 0, 12) to the line x = 4t, y = -2t, z = 2t is (8√15) / 3.

The distance from the point (0, 0, 12) to the line defined by x = 4t, y = -2t, z = 2t can be found using the formula for the distance between a point and a line in three-dimensional space.

The formula is given by:

Distance = |(P - Q) × V| / |V|,

where P is a point on the line, Q is the given point, V is the direction vector of the line, and × denotes the cross product.

In this case, we can choose any point on the line to represent P. Let's choose P as (4, -2, 2). The direction vector of the line is V = (4, -2, 2).

Using the formula, we can calculate the distance as follows:

Distance = |((0, 0, 12) - (4, -2, 2)) × (4, -2, 2)| / |(4, -2, 2)|.

Simplifying the expression, we get:

Distance = |(-4, 2, 10) × (4, -2, 2)| / |(4, -2, 2)|.

To find the cross product, we can use the determinant method:

((-4, 2, 10) × (4, -2, 2)) = [(2 * 2 - 10 * -2), (10 * 4 - (-4) * 2), ((-4) * (-2) - 2 * 4)]

= (4 - 20, 40 - (-8), 8 - 8)

= (-16, 48, 0).

Now we can substitute the values back into the distance formula:

Distance = |(-16, 48, 0)| / |(4, -2, 2)|.

Taking the magnitude of the vectors, we get:

Distance =\(\sqrt((-16)^2 + 48^2 + 0^2) / √(4^2 + (-2)^2 + 2^2)\)

= √(256 + 2304 + 0) / √(16 + 4 + 4)

= √2560 / √24

= 16√10 / 2√6

= 8√10 / √6

= (8√10 / √6) * (√6 / √6)

= (8√60) / 6

= (8√15) / 3.

Learn more about vector here:

https://brainly.com/question/24256726

#SPJ11

The electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.

To determine the electron domain charge cloud geometry of \(BrF_5\), we need to examine the number of electron domains around the central atom (Br).

\(BrF_5\) consists of one central bromine atom (Br) surrounded by five fluorine atoms (F). Each bond and lone pair of electrons represents an electron domain.

In \(BrF_5\), there are five bonding pairs (Br-F) and no lone pairs around the central bromine atom. Therefore, the total number of electron domains is five.

Based on this information, the electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.

To know more about electron, refer here:

https://brainly.com/question/12001116

#SPJ4

Answer:

t¹⁰

Step-by-step explanation:

The 10th power of t:

t¹⁰

Answer:

10.375

Step-by-step explanation:

3/8ths equal 0.375 and then you have ten as the whole number therefore you add the lower number onto the whole number and then you get your answer.

The most appropriate choice for parallelogram will be given by

\(\Delta ABD \cong \Delta CDB\) has been proved

What is a parallelogram?

Parallelogram is a quadrilateral in which each pair of opposite sides are parallel and equal.

There are different properties of parallelogram-

Opposite sides of a parallelogram are equal

Opposite angles of a parallelogram are equal

Diagonals of a parallelogram bisect each other

Here,

AD || BC [Definition of Parallelogram]

\(\angle ADB \cong \angle CBD\) [Alternate interior angle theorem]

AB || CD [Definition of Parallelogram]

\(\angle ABD \cong \angle CDB\) [Alternate interior angle theorem]

\(DB \cong DB\) [DB is the common side]

\(\Delta ABD \cong \Delta CDB\) [ASA axiom]

To learn more about Parallelogram, refer to the link:

brainly.com/question/20526916

#SPJ13

PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction. The solution to the Expression (3^0 * 8^2)^-2 is 1/4096.

The expression (3^0 * 8^2)^-2, the order of operations, which is typically referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Step 1: Simplify the exponent expressions within the parentheses:

(3^0 * 8^2) = (1 * 64) = 64

Step 2: Rewrite the expression with the simplified value:

(64)^-2

Step 3: Apply the exponent rule for a negative exponent:

(64)^-2 = 1 / (64)^2

Step 4: Evaluate the expression within the parentheses:

(64)^2 = 64 * 64 = 4096

Step 5: Rewrite the expression with the simplified value:

1 / 4096

Therefore, the solution to the expression (3^0 * 8^2)^-2 is 1/4096.

To know more about Exponents.

https://brainly.com/question/13669161

#SPJ11

Answer:

c = 2

Step-by-step explanation:

6c + 3y = 18

6c + 3(2) = 18

6c + 6 = 18

6c = 12

c = 2

Step-by-step explanation:

When y =2, then

Hence, c=2

The given equation: r(t) = (8 sin t) i + (6 cos t) j + (12t) k gives the position of a particle in space at time t. The velocity of the particle at time t can be calculated using the derivative of the given equation: r'(t) = 8 cos t i - 6 sin t j + 12 k We know that acceleration is the derivative of velocity, which is the second derivative of the position equation.

The magnitude of the velocity at time t is given by:|r'(t)| = √(8²cos² t + 6²sin² t + 12²) = √(64 cos² t + 36 sin² t + 144)And the direction of the velocity is given by the unit vector in the direction of r'(t):r'(t)/|r'(t)| = (8 cos t i - 6 sin t j + 12 k) / √(64 cos² t + 36 sin² t + 144)Similarly, the magnitude of the acceleration at time t is given by:|r''(t)| = √(8²sin² t + 6²cos² t) = √(64 sin² t + 36 cos² t)And the direction of the acceleration is given by the unit vector in the direction of r''(t):r''(t)/|r''(t)| = (-8 sin t i - 6 cos t j) / √(64 sin² t + 36 cos² t)Therefore, the velocity vector is: r'(t) = (8 cos t i - 6 sin t j + 12 k) / √(64 cos² t + 36 sin² t + 144)The acceleration vector is: r''(t) = (-8 sin t i - 6 cos t j) / √(64 sin² t + 36 cos² t)

To know more about position visit:

brainly.com/question/12650352

#SPJ11

if you know the answer .... tell me ..... cz I don't know

Answer:

y = - x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (5, - 12 ) and (x₂, y₂ ) = (- 3, - 4 )

m = \(\frac{-4-(-12)}{-3-5}\) = \(\frac{-4+12}{-8}\) = \(\frac{8}{-8}\) = - 1 , then

y = - x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (5, - 12 ) , then

- 12 = - 5 + c ⇒ c = - 12 + 5 = - 7

y = - x - 7 ← equation of line

Answer:

3(x - 2) = 4x + 2

→ 3x - 6 = 4x + 2

→ 3x - 4x = 2 + 6

→ - x = 8

→ x = - 8