Identify all of the root(s) of g(x) = (x2 + 3x - 4)(x2 - 4x + 29).


-1


1


-4


4


2 + 5i


2 - 5i


-2 + 10i


-2 - 10i

If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.

A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :

g(x) = {-(1/2)x + 1,    for x<-2

       = {-(x+1)²,        for -2≤x≤1

      =  {4                 for x>1

We have to find the value of g(-5) ,g (-2), and g(-1),

For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,

⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,

For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function

"-(x+1)²" will be used,

⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,

For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,

⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,

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Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:

3.5km

Step-by-step explanation:

Kendrick walked 500 m per day

1 day = 500m

How many kilometres did he walk for the week?

1 week = 7 days = 500 * 7 = 3500m

Convert to kilometres

3500m / 1000 = 3.5km

We need to find two relations, and use them to find the value of y when z = 15.

We will see that the value of y in that case is 4,860.

We know that y  varies inversely with the square of  x, also y  is also proportional to the cube of  z

Then we can write:

y = k/x^2

y = c*z^3

We also know that:

When x = 3, y = 80.

Replacing that in the first equation to find the value of k:

80 = k/3^2

80 = k/9

80*9 = k = 720

We also know that when x = 2, z = 5

From the first relation we have:

y = 720/2^2 = 720/4 = 180

Now we replace this in the equation of y and z:

y = c*z^3

180 = c*5^3

180 = c*125

180/125 = c = 1.44

Now we need to calculate y when z = 15, then we just need to replace z by 15 in the equation for y and z:

y = 1.44*(15)^3 = 4,860.

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Answer:

it's a right triangle:)

Step-by-step explanation:

Answer:

the answer is obtuse

Step-by-step explanation:

Answer:

Fountain= 147.65 square yards

path= 28.28 square yards

Step-by-step explanation:

pi*47 <---square root cancels out the square

=147.65

pi*56=175.93

175.93-147.65=28.28

The best way to assign values for a simulation using random digits table will be option A.

The best way to assign values for a simulation using a random digits table would be to use a table with at least 10 digits (0-9) in each row.

For Country X, we would assign Blood type O with the digits 0-5, Blood type A with digits 6-7, Blood type B with digit 8, and Blood type AB with digit 9. If a digit outside of these ranges is generated, it would be ignored.

For Country Y, we would assign Blood type O with the digits 0-5, Blood type A with digits 6-7, Blood type B with digit 8, and Blood type AB with digit 9. Again, if a digit outside of these ranges is generated, it would be ignored.

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Answer:

Correct Answer 4 Secs

Step-by-step explanation:

#Platolivesmatter

Hope this helped :)

The time it takes for the friend in the left seat to move upward, downward, and then back to the initial position is 4 seconds.

A relation is a function if it has only One y-value for each x-value.

Two friends are sitting on a seesaw at the park.

The height, h(t), of the left seat, in inches above the ground, is modeled by a sine function.

Let t represent the time, in seconds, since the friends started seesawing.

t       0    1    2  3  4   5   6

h(t)  24 48 24 0 24 48 24

The friends start see sawing with the plank in a level position.

The initial position at 0 of them is at 24.

The group has to come back to this position after moving upward and downward.

The time it takes to reach upward is,

f(48)=1

The time it takes to reach downward after going upward is,

f(0)=3

Coming back to initial potion,

f(24)=4

Hence, the time it takes for the friend in the left seat to move upward, downward, and then back to the initial position is 4 seconds.

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Answer:

$3109.97.

Step-by-step explanation:

Number of hours in a year = 365*24 = 8760 hours

Balance = 3000(1 + 0.018/8760)^(2*8760)

= 3109.967.

The balance for each value of n is calculated by using the formula A = P(1 + r/n) ^nt. The rounded balance values are shown in the last column of the table above.

To complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and compounded n times a year.

The formula for calculating compound interest is as follows:

A = P(1 + r/n) ^nt,

where P represents the principal investment amount, r is the interest rate, n is the number of times the interest is compounded, t represents the time in years, and A represents the total amount, which includes the principal amount and the interest earned.

The table is given below:
\(\begin{array}{|c|c|c|} \hline \text{n} &

\text{A = P(1 + r/n) }^{nt} &

\text{Balance (rounded to nearest cent)} \\ \hline \text{1} &

\text{3100(1 + 0.04/1)}^{1*10} &

\text{\$4788.03} \\ \hline \text{2} &

\text{3100(1 + 0.04/2)}^{2*10} &

\text{\$4798.76} \\ \hline \text{4} &

\text{3100(1 + 0.04/4)}^{4*10} &

\text{\$4817.46} \\ \hline \text{12} &

\text{3100(1 + 0.04/12)}^{12*10} &

\text{\$4861.94} \\ \hline \end{array}\)

The balance is obtained by substituting the values of P, r, n, and t into the compound interest formula.

In this case, the investment is $3100, the annual interest rate is 4%, the investment is for 10 years, and n is the number of times the interest is compounded.

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Answer:

it'd be d: 13/50 !!

Answer:

D. 13/50

Step-by-step explanation:

0.26 ⇔ 26/100 ⇔ 13/50

Answer: 4

This problem requires basic division. If the restaurant divided 4/5 kg of butter with 1/5 kg on each dish, you would need to compute 4/5 divided by 1/5.

4/5 ÷ 1/5

Using the "KFC" method, or Keep, Change, Flip, you would keep the first number (in this case, 4/5), change the division sign, and flip the fraction to 5/1, or 5. We now have this:

4/5 x 5

To compute this equation, you must multiply the numerators of both of the numbers together. In this case, you would compute (4x5)/5, resulting with 20/5, or 4.

You can check this answer by re-multiplying the numbers together. 1/5 kg of butter per dish, multiplied by the total amount of dishes, 4, you would result in the original 4/5 kg of butter.

Hope this helps!

Answer:

it will take them 1.71 hours to finish cutting the lawn if they work together.

Step-by-step explanation:

If Marsha cuts the lawn by herself it will take her 3 hours, this mean that in one hour she cuts 1/3 of the lawn.

On the other hand Bob needs one more hour to finish the lawn, this means it takes him 4 hours to cut it and therefore he cuts 1/4 of the lawn per hour.

Now, to know how much they cut by working together we need to sum up the amount of lawn they cut per hour:

Working together in one hour: Marsha's one hour + Bob's one hour

Working together in one hour: \(\frac{1}{3}+ \frac{1}{4}=\frac{4+3}{12}=\frac{7}{12}\)

Therefore, working together they will cut 7/12 in one hour.

Now, to know how long will it take it to cut the entire lawn (which is equivalent to 12/12), we can write this in terms of proportions

Time        Total amount of lawn

1 hour               7/12

x hours             12/12

Solving for x (to know the amount of hours it will take them) we have:

\(x=\frac{12}{12}\)÷\(\frac{7}{12}\)=\(1\)×\(\frac{12}{7}=\frac{12}{7}=1.714\)

Rounded to the nearest hundredth, we have that working together it will take them 1.71 hours to finish cutting the lawn.

Answer: Henrik grew 147 more potatoes than Derek

Step-by-step explanation:

⇛L = W + 5

⇛L × W = 150 sq. units

⇛W (W + 5) = 150

⇛W² + 5W = 150

⇛W² + 5W - 150 = 0

⇛[(W - 10) (W + 15)] = 0

⇛W = -10 , 15 (reject negative width)

☞ Width of rectangle is 10 units

☞ Length of rectangle is 15 units

Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given two triangles, Where the base of these triangles are same

And also given that the two angles are the same.

Since,

Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).

Thus, the third angle is also equal

From AAS:

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,

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Answer:

sorry not having idea about ans

Answer:

A construction company can remove

1/3 metric tons of dirt from a construction site in 1/6

hours.

What is the unit rate in metric tons per hour?

Me too

Answer:

Im pretty sure every hat and mask is 1 dollar

Answer:

Step-by-step explanation:

(4x - 9) + 12 = 2x - 5           Remove the brackets

4x - 9 + 12 = 2x - 5             Combine the left

4x + 3 = 2x - 5                    Subtract 2x from both sides

4x - 2x + 3 = - 5                 Combine

2x + 3 = - 5                         Subtract 3 from both sides

2x + 3 -3 = - 5 -3                Combine

2x = - 8                               Divide by 2

x = -8/2

x = -4

Answer:

Step-by-step explanation:

According to the central limit theorem, if independent random samples of size n are repeatedly taken from any population and n is large, the distribution of the sample means will approach a normal distribution. The size of n should be greater than or equal to 30. Given n = 100 for both scenarios, we would apply the formula,

z = (x - µ)/(σ/√n)

a) x is a random variable representing the salaries of accounting graduates. We want to determine P( x > 52000)

From the information given

µ = 50402

σ = 6000

z = (52000 - 50402)/(6000/√100) = 2.66

Looking at the normal distribution table, the probability corresponding to the z score is 0.9961

b) x is a random variable representing the salaries of finance graduates. We want to determine P(x > 52000)

From the information given

µ = 49703

σ = 10000

z = (52000 - 49703)/(10000/√100) = 2.3

Looking at the normal distribution table, the probability corresponding to the z score is 0.9893

c) The probabilities of either jobs paying that amount is high and very close.

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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Answer: w=6

Step-by-step explanation: 1. Simplify. Distribute the -4 to the w and the -3. -4*w is -4w and -4*-3 is +12, so your left with 3w-4w+12=6.

2. simplify again. 3w-4w is -w.

3. -w+12=6. Subtract w to both sides, so its -w=-6. The negatives cancel out, so w just equals 6.

Answer:

11

Step-by-step explanation:

2x+3=x+7

x=4

Plug 4 into Ad which is 2x+3 and you get 11

Answer:

Step-by-step explanation: evagline has 3/5 of box of nuts.she uses it to fill 6 bowls

Answer: 3rd answer is the correct answer.

Applying the Pythagorean theorem, we find that the length of the hypotenuse is equal to the square root of 2. In other words, the hypotenuse is root 2 times the length of either leg.

The value of line RS is 23

From the diagram shown, we have that line PS, line PQ, line QR and line RS form a square.

Note that the sides of a square are equal to each other.

The relationship is represented as;

Line PS = Line PQ = Line QR = Line RS

We have that;

Substitute the expressions

6x - 5 = 9x - 4

Now, collect like terms

6x - 9x = - 4 - 5

Subtract the like terms

-3x = -9

Make 'x' the subject of formula

-3x/-3 = -9/-3

x = 3

Then, RS = 9x - 4 = 9(3) - 4 = 27 - 2 = 23

Hence, the value is 23

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The final velocity of the parameters is 13.5m/s

In this question, the given parameters are represented as

Formula: v = u + at

Initial velocity = 3m/s

Acceleration = 1.5m/s²

Time = 7 seconds

When these parameters are represented using their required notation, we have the following representations

u = 3m/s

a = 1.5m/s²

t = 7 s

Next, we substitute the above parameters in the above equation

So, we have the following representation

v = 3 + 1.5 * 7

Evaluate the products

This gives

v = 3 + 10.5

Evaluate the sum

So, we have the following representation

v = 13.5

The notation v represents the final velocity

Hence, the final velocity is 13.5m/s

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Answer:

it should be the second one

The value of the probability P(x < 3) is 0.8

From the question, the table of values is given as

x = -1,0,1,2,3.

P(X = x) 0.2, 0.2, 0.2, 0.2, 0.2

To calculate the probability P(x < 3). we make use of the probability values where x is less than 3

This means that

P(x < 3) = P(-1) + P(0) + P(1) + P(2)

Substitute the known values in the above equation

So, we have

P(x < 3) = 0.2 + 0.2 + 0.2 + 0.2

Evaluate the sum

P(x < 3) = 0.8

Hence, the probability value is 0.8

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