Write a function to model the data

x row consists of: -4, -2, 0, 2, 4

y row consists of: 0, -8, -8, 0, 16

The function is y =

The reflection and the horizontal compressions are illustrations of transformations.

The formula for function g(x) is [tex]\mathbf{g(x) = 9x}[/tex]

The function is given as:

[tex]\mathbf{f(x) = |x|}[/tex]

The rule of reflection over the y-axis is:

[tex]\mathbf{(x,y) \to (-x,y)}[/tex]

So, we have:

[tex]\mathbf{f'(x) = |-x|}[/tex]

[tex]\mathbf{f'(x) = x}[/tex]

The rule of horizontal compression is:

[tex]\mathbf{(x,y) \to (\frac xb,y)}[/tex]

So, we have:

[tex]\mathbf{g(x) = \frac{x}{1/9}}[/tex]

[tex]\mathbf{g(x) = 9x}[/tex]

Hence, the formula for function g(x) is [tex]\mathbf{g(x) = 9x}[/tex]

Read more about transformations at:

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A reflection over the y-axis changes x to -x and a horizontal compression by a factor of 1/9 replaces x by 9x. Hence, the function g(x) reflecting these transformations is |-9x|.

The original function is f(x) = |x|. When a function is reflected over the y-axis, it changes x to -x. Hence the function becomes f(-x) = |-x|. A compression by a factor of 1/9 in the horizontal direction is represented by replacing x by 9x, our function becomes f(9x) = |-9x|. So, the new function g(x) = f(-9x) = |-9x|.

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Answer:

  see below

Step-by-step explanation:

Use the distributive property to eliminate parentheses. Remember that the product (-1)(-1) is 1.

a-(1-b)+1 = a -1 +b +1 = a + b . . . . this one

__

-(1-a)-b+1 = -1 +a -b +1 = a - b

__

(a-1)-(b-1) = a - 1 - b + 1 = a - b

__

a-(-b-1)+1 = a +b +1 +1 = a + b + 2

Answer:

idiidhdmfnrbbbbbbrh

Step-by-step explanation:

yes

Answer:

x^2 + 4x * (3 - sqrt(x)) - 2(5 + sqrt(x))

Step-by-step explanation:

Firstly let us split this up, we need to first work out what g(h(x)) is:

h(x) = Sqrt(x) so g(h(x)) = g(sqrt(x)) = sqrt(x) - 2

Now to work out f(g(h(x))) = f(sqrt(x) - 2) = (sqrt(x) - 2)^4 + 6

= (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) - 6

= (x - 2 * sqrt(x) + 4) * (x - 2 * sqrt(x) + 4) - 6

= x^2 - 2x * sqrt(x) + 4x - 2x * sqrt(x) + 4x - 8 * sqrt(x) + 4x - 8 * sqrt(x) + 16 - 6

= x^2 - 4x * sqrt(x)  + 12x - 16 * sqrt(x) + 10

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

Answer:

Jamie will owe $ 41,95,725.83 ( approx ),

Accumulated interest is $ 36,95,725.83

Step-by-step explanation:

Since, the amount formula in compound interest is,

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where, P is the principal amount,

r is the annual rate of interest,

n is the compounding periods in a year,

t is the time in years,

Here, P =  $ 500,000,

r = 8.6 %=0.086,

n = 4,

t = 25 years,

By substituting the values,

[tex]A=500000(1+\frac{0.086}{4})^{100}[/tex]

[tex]=500000(1+0.0215)^{100}[/tex]

[tex]=500000(1.0215)^{100}[/tex]

[tex]=4195725.82746[/tex]

[tex]\approx 4195725.83[/tex]

Also, the accumulated interest = A-P = 4195725.83 - 500000 = $ 3695725.83

Answer:

Laptop: $2,270

Desktop: $1,820

Step-by-step explanation:

Let L identify the laptop price and D the desktop price.

We can first say:

L = D + 450 ( the laptop cost $450 more than the desktop)

Then we can say:

0.09 D + 0.06 L = 300 (The total finance charges for one year were $300)

Then we substitute L by its value from first equation into the second equation:

0.09 D + 0.06 (D + 450) = 300

0.09 D + 0.06 D + 27 = 300

0.15D = 273 (removed 27 on both sides, and simplified left side)

D = 1,820

The cost of the desktop was $1,820

The cost of the laptop was $2,270 (price of desktop + $450)

Final answer:

By setting up equations based on the given finance charges and interest rates, we find that before finance charges, the desktop computer cost $1820 and the laptop cost $2270.

Explanation:

The student's question asks to determine the cost of each computer before finance charges. Let's denote the cost of the desktop computer as D and the cost of the laptop as L. From the information provided, we know that L = D + $450. The total finance charges for the desktop at 9% per year and for the laptop at 6% per year amount to $300. Hence, the equation for the finance charge can be written as 0.09D + 0.06L = $300. Substituting the expression for L from the first equation into the second, we get 0.09D + 0.06(D + $450) = $300, which simplifies to 0.09D + 0.06D + $27 = $300. Adding the D terms together, we get 0.15D + $27 = $300. Subtracting $27 from both sides, we obtain 0.15D = $273. Dividing both sides by 0.15, the cost of the desktop computer is found to be D = $1820. To find the cost of the laptop, we use the first equation: L = $1820 + $450 = $2270.

In conclusion, before finance charges, the desktop computer cost $1820 and the laptop $2270.

Answer:

  The rectangle is 7 km by 14 km. The 14 km dimension is parallel to the river.

Step-by-step explanation:

Let x represent the length of fence parallel to the river. The remaining fence is divided into two equal pieces for the ends of the enclosure. Then (28 -x)/2 will be the length of the side of the rectangle perpendicular to the river.

The total area of the enclosure is the product of length and width:

  Area = (x)(28-x)/2

This expression describes a parabola opening downward with zeros at x=0 and x=28. The vertex (maximum) is halfway between those zeros, so is at ...

  x = (0 +28)/2 = 14

Area is maximized when the dimension parallel to the river is 14 km and the ends of the enclosure are 7 km.

To maximize the area of the sanctuary, set up an equation with the length of the riverbank side. Differentiate and solve for x to find the dimensions of the rectangle.

To maximize the area of the sanctuary, we need to find the dimensions of the rectangle.

Let the length of the riverbank side be x km.

The remaining two sides of the rectangle will each be (28 - x/2) km, as the total fence length should be equal to x km along the riverbank and (28 - x/2) km for the other two sides.

The area of the rectangle is given by A = x * (28 - x/2). To maximize the area, we can differentiate A with respect to x, set it equal to 0, and solve for x.

Taking the derivative of A, we get dA/dx = 28 - 3x/2. Setting this equal to 0, we find 28 - 3x/2 = 0. Solving for x, we get x = 18.67 km.

Therefore, the dimensions of the rectangle to maximize the area of the sanctuary are approximately 18.67 km along the riverbank and (28 - 18.67/2) km for the other two sides.

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Answer:  $ 290 thousand

Step-by-step explanation:

Given : According to a certain central bank from 2000 to 2016 the average price of a new home in a certain region increased by 62 % to $470 thousand.

Let X be the the average price of a new home in 2000 .

Then , the 62 % increase in price is given by :-

[tex]x+0.62(x)=x(1+0.62)=1.62x[/tex]

Since , the the average price of the home in 2016 = $470 thosand

[tex]1.62x=470\\\\\Rightarrow\ x=\dfrac{470}{1.62}=290.12345679\approx290[/tex]

Hence, the average price of a new home in 2000 =  $ 290 thousand .

The average price of a new house in 2000 is approximately 290,124 dollars.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

According to a certain central bank from 2000 to 2016 the average price of a new home in a certain region increased by 62 % to $470 thousand.

Let x be the average price of a new house in 2000. Then we have

[tex]\rm x = \dfrac{Present \ price}{1+Increased\ rate}\\\\\\x = \dfrac{470000}{1+0.62}\\\\\\x = \dfrac{470000}{1.62}\\\\\\x = 290123.4568 \approx 290124[/tex]

Thus, the average price of a new house in 2000 is 290,124 dollars.

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Answer: x=√7

x​=√2​i

We'll use factoring by grouping to solve the equation. This method involves grouping the terms of the polynomial into two binomials, such that the product of the leading coefficients of the binomials is equal to the constant term, and the sum of the products of the remaining terms is equal to the middle term.Steps to solve:

1. Factor the expression:

(x²−7)(x²+2)=0. Create separate equations and solve:

x²−7=0

x²+2=0. Solve the first equation:

x²−7=0

x=±√7​. Solve the second equation:

x²+2=0

x=±√2​i

Answer:

20

Step-by-step explanation:

Well it is quite simple.You can find the 20% of 100 by multiplying 20 with 100 (wich means 20 yellow frogs,in this case within 100 frogs) and then diviting it with 100 (so it can be expressed as a

presentage that is based to 100).If you have any questions don't hesitate to contact me.

Yours sincerely,

Manos

Answer:

Step-by-step explanation:

3

Answer:

Step-by-step explanation:

Using 2016 as a reference (t=0), the exponential equation for winnings can be written as ...

  w(t) = 1480000×(1480000/200)^(t/121)

where 1480000 is the winnings in the reference year, and the ratio 1480000/200 is the ratio of winnings increase over the 121 years from 1895 to 2016.

This can be approximated by ...

  w(t) ≈ 1,480,000×1.07640850764^t

In this form, we can see that the annual percentage increase is ...

  1.0764 -1 = 7.64%

__

Then the winner's check in 2043, 27 years after 2016, is predicted to be ...

  w(27) = $1,480,000×(1.0764...)^27 ≈ $10,805,478.41 ≈ $10,805,000

The percentage increase per year in the winner's prize money over the period is 6065.57%. The winner's prize money in 2043 would be approximately $15,190,712.55.

To calculate the percentage increase per year, we need to find the average annual growth rate over the time period. First, we calculate the total percentage increase by taking the difference between the final and initial values, divided by the initial value.

In this case, it is (($1,480,000 - $200) / $200) * 100 = 740,000%. Then, we divide this percentage by the number of years, which is 2016 - 1895 + 1 = 122. So the annual percentage increase is 740,000% / 122 = 6065.57%.

To calculate the winner's prize in 2043, we need to find the number of years from 2016 to 2043, which is 2043 - 2016 = 27.

Then, we use the compound interest formula to calculate the future value: $1,480,000 * (1 + (6065.57% / 100))^27 = $15,190,712.55. So the winner's prize in 2043 would be approximately $15,190,712.55.

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Answer:

Let's say that the mile that the cyclist going west  is a.

And so the one heading North is (a+5)

a+(a+5)=25

a+a+5=25

2a=20

a=10

So the one heading West has traveled 10 mi.

Answer:

  [tex]1000\pm 100\sqrt{55}[/tex]

Step-by-step explanation:

A TI-84 or "normal" calculator is designed to evaluate expressions numerically. It can tell you the numerical value of this expression is the set of values

  {1741.619849, 258.3801513}

but it cannot simplify the expression.

This expression can be simplified by evaluating the fraction and removing double factors from under the radical:

[tex]\dfrac{2000\pm\sqrt{2200000}}{2}=\dfrac{2000}{2}\pm\sqrt{\dfrac{2200000}{2^2}}=1000\pm\sqrt{550000}\\\\=1000\pm\sqrt{100^2\cdot 55}=1000\pm 100\sqrt{55}[/tex]

Try this option:

1] P(S)=0.84;

2] P(S or C, but not both)=0.4;

3] P(C)=0.76;

4] P(S∪C)=0.6;

5] P(C, but not S)=0.16;

6] P(S∩C)=1.00.

Answer:

We are given with a Venn diagram.

In Venn Diagram,

S represent Swam

C represent Built Sandcastles.

n( S - (S∩C) ) = 6

n( C - (S∩C) ) = 4

n( S ∩ C ) = 15

To find: P(S) , P(C) , P(S or C, but not Both) = P((S∪C) - (S∩C)) , P( S ∪ C ) ,

P(S ∩ C) , P(C , but not S ) =  P(C - (S∩C))

n(S) = n( S - (S∩C) ) + n(S∩C) = 6 + 15 = 21

n(C) = n( C - (S∩C) ) + n(S∩C) = 4 + 15 = 19

n(S∪C) = n( C - (S∩C) ) + n( S - (S∩C) ) + n(S∩C) = 6 + 4 + 15 = 25

Now, [tex]P(S)=\frac{21}{25}=0.84[/tex]

[tex]P(S\:or\:C,\:but\:not\:Both)=P((S\cup C)-(S\cap C))=\frac{10}{25}=0.40[/tex]

[tex]P(C)=\frac{19}{25}=0.76[/tex]

[tex]P(S\cup C)=\frac{25}{25}=1.00[/tex]

[tex]P(C\:,\:but\:not\:S)=P(C - (S\cap C))=\frac{4}{25}=0.16[/tex]

[tex]P(S\cap C)=\frac{15}{25}=0.60[/tex]

Therefore, Match the answers as above.

Answer:

  22 ft by 44 ft, with 22 ft parallel to the road

Step-by-step explanation:

Problems in optimizing rectangular area for a given perimeter or perimeter cost all have a similar solution: the length (or cost) of one pair of opposite sides is equal to that of the other pair of opposite sides.

Here, that means that the sides perpendicular to the road will have a total cost of $528/2 = $264, so will have a total length of $264/($3/ft) = 88 ft. Since it is a rectangle, the dimension perpendicular to the road is 44 ft.

Likewise, the sides parallel to the road will have a total cost of $264. If x is the length in that direction, this means ...

  9x +3x = 264

  12x = 264

  264/12 = x = 22

The length of the garden parallel to the road is 22 ft.

_____

If you solve this directly, you get the same result. Let x be the distance parallel to the road. Then the cost of fence for the two sides parallel to the road is (3x +9x) = 12x.

The length of fence perpendicular to the road will use the remaining cost, so that length will be (528 -12x)/(2·3). (Half of the remaining fence is used on each of the two parallel sides.) This expression for length simplifies to (88-2x).

Then the area of the garden will be the product of its length and width:

  area = x(88 -2x)

This is the equation for a downward-opening parabola with zeros at x=0 and x=44. The vertex is located halfway between those zeros, at x = 22.

The dimensions of the largest garden are 22 ft parallel to the road and 44 ft perpendicular to the road.

Answer:

1

Step-by-step explanation:

Blocks that have the same distance to the center cancel each other out.

The 4 rightmost and the 4 leftmost blocks cancel each other out.

In order to balance the remaining 4 1-blocks on the left side, the remaining right blocks must have the value 1.

Answer:

The correct option is B) 2.

Step-by-step explanation:

Consider the provided diagram.

There are 4 x blocks on the left side and 6 x blocks on the right side.

Also there are 4 small blocks have a value of 1.

Both the sides are balanced that means 4 x blocks + 4 small blocks equals to 6 x blocks.

4x + 4 = 6x

Subtract 4x from both the side.

4x + 4 - 4x = 6x - 4x

4 = 2x

Divide both the side by 2.

2 = x

Thus, the value of x is 2.

Hence, the correct option is B) 2.

Answer:14

Step-by-step explanation:

The plane [tex]z=9[/tex] lies above the paraboloid [tex]z=x^2+y^2[/tex], so the volume of the bounded region [tex]R[/tex] is given by

[tex]\displaystyle\iiint_R\mathrm dV=\int_{-3}^3\int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}}\int_{x^2+y^2}^9\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

Convert to cylindrical coordinates, setting

[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=z\end{cases}\implies\mathrm dx\,\mathm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz[/tex]

and the integral is equivalent to

[tex]\displaystyle\int_0^{2\pi}\int_0^3\int_{r^2}^9r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=2\pi\int_0^3(9r-r^3)\,\mathrm dr=\boxed{\frac{81\pi}2}[/tex]

The volume of the solid enclosed by the paraboloid z = x² + y² and the plane z = 9 is found by using double integrals in polar coordinates. The volume is calculated as 81π cubic units.

To find the volume of a solid enclosed by the paraboloid z = x² + y² and the plane z = 9, you have to use the method of double integrals in polar coordinates. The cone extends from z = 0 at its apex to z = 9 at the top, which is given by the plane. Hence, we can imagine this region as a bunch of thin disks or pancakes that lie above circles in the xy-plane and pile up to form the parcel of the parabolic solid under the plane z = 9.

In this case, we have to integrate over the region R, which is a disk of radius 3 (it's the projection on the xy-plane under the plane z = 9), with the height of a 'thin disk' as z = x² + y² = r² (in polar coordinates). Therefore, the volume V can be given as:

V = ∫∫R(z*r*dr*dθ) = ∫02π∫03(r²*r*dr*dθ) = 2π* [03 0.25r⁴] = 2π*(40.5-0) = 81π cubic units.

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Answer:

The equation is:

[tex]3(2) ^ t=1,536[/tex]

After [tex]t=9\ months[/tex]

Step-by-step explanation:

This situation can be represented by an exponential growth equation of the form

[tex]y = a (b) ^ {t}[/tex]

Where a is the initial amount

b is the growth rate

t is the time in months

In this case the initial amount is $ 3. Then [tex]a=3[/tex]

if she initially saves $3 and plans to double the amount she saves each month then

[tex]b=2[/tex]

The bike Jane wants is $1,536 at the local bike shop.

Then [tex]y=1,536[/tex]

The equation is:

[tex]3(2) ^ t=1,536[/tex]

Now we solve the equation for t

[tex]3(2) ^ t=1,536[/tex]

[tex](2) ^ t=\frac{1,536}{3}[/tex]

[tex](2) ^ t=512[/tex]

[tex]log_2(2) ^ t=log_2(512)[/tex]

[tex]t=log_2(512)[/tex]

[tex]t=9\ months[/tex]

Answer:

t=9 months. hope this helps

Answer: Option 'e' is correct.

Step-by-step explanation:

Since we have given that

The number of accidents in Small  town during the last six years as follows:

0,1,1,2,3,5.

First we calculate :

1) Mean :

[tex]\bar{X}=\dfrac{0+1+1+2+3+5}{6}=\dfrac{12}{6}=2[/tex]

2) Median:

0,1,1,2,3,5

As we know that "Median" is the middle value of data:

Median = [tex]\dfrac{1+2}{2}=\dfrac{3}{2}=1.5[/tex]

3) Mode:

0,1,1,2,3,5

As we know that Mode is the most occurring element among the data.

So, Mode = 1

Now, we can say that Mode< Median < Mean

Hence, Option 'e' is correct.

Answer:

Correct answer is (E)

Step-by-step explanation:

Took the test on Plato Math and got it right

Hope I helped :D

ANSWER

[tex]y = \cot(x - \frac{\pi}{3} ) + 2[/tex]

EXPLANATION

The cotangent function that is fully transformed is of the form

[tex]y =a \cot(bx + c) + d[/tex]

where 'a' is the amplitude.

[tex] \frac{\pi}{b} = \pi[/tex]

is the period.

This implies that b=1

The phase shift is

[tex] \frac{c}{b} = - \frac{\pi}{3} [/tex]

Substitute b=1 to get;

[tex]c = - \frac{\pi}{3} [/tex]

and d=2 is the vertical shift.

We choose a=1 to get the required function as

[tex]y = \cot(x - \frac{\pi}{3} ) + 2[/tex]

The test statistic, z, is approximately 1.154. This value indicates a slight but potentially non-significant increase in the proportion of cell phone-related accidents compared to the previous value of 13%.

Null and Alternative Hypotheses:

Null Hypothesis (H0): The proportion of accidents caused by cell phones has not changed, p = 0.13.

Alternative Hypothesis (Ha): The proportion has changed, p ≠ 0.13.

Test Statistic:

We can use the z-test for proportions to calculate the test statistic.

z = (Observed proportion - Expected proportion) / Standard Error

Observed proportion = 0.14 (14% from the sample)

Expected proportion = 0.13 (previous value)

Standard Error = sqrt(p * (1-p) / n) ≈ sqrt(0.13 * 0.87 / 10,000) ≈ 0.003

Calculation:

z = (0.14 - 0.13) / 0.003 ≈ 1.154

Therefore, the z-statistic is approximately 1.154.

Interpretation:

A z-score closer to 0 indicates no evidence against the null hypothesis (no change). Higher positive or negative values suggest increasing evidence for the alternative hypothesis (change). In this case, z = 1.154 is slightly positive, suggesting a potential but not conclusive increase in the proportion of cell phone-related accidents. Further analysis, such as p-value calculation, is needed to determine the statistical significance of this difference.

Final answer:

You can assign up to (n-1) values freely in a list of n values that must have a specific known mean. The last value is then determined by ensuring the sum of all n values achieves the required total that reflects the known mean.

Explanation:

To construct a list of n values with a predetermined mean, you can think of the sum total that these n values should add up to, as the mean (let's call it μ) multiplied by the number of items in the list, n. If you want to freely assign a certain number of values, let's call it k, then these k values can be anything that respects the constraints of the data (like being positive if you're measuring something that can't be negative). Once you have assigned these k values, the sum of the remaining (n-k) values is determined because it must make up the difference needed to reach the predetermined total sum that corresponds to the known mean. Therefore, you can freely assign up to (n-1) values and the last value will be determined by the mean constraint.

Answer:

0.5122 or 51.22%

Step-by-step explanation:

In a certain city, in June Probability of cloudy days = P(cloudy) = 0.41

Probability of cloudy and rainy = P(cloudy and rainy) = 0.21

Probability of rainy if we already know it is cloudy = [tex]\frac{\text{[P(cloud and rainy)]}}{[P(cloud)]}[/tex]

= [tex]\frac{0.21}{0.41}[/tex] = 0.512195122 ≈ 0.5122

Therefore, the probability that a randomly selected day in June will be rainy if it is cloudy is 0.5122 or 51.22%

The probability that a randomly selected day in June will be rainy if it is cloudy is approximately 51.22%.

To determine the probability that a randomly selected day in June will be rainy if it is cloudy, we can use conditional probability. The conditional probability formula is:

P(A|B) = P(A and B) / P(B)

Where,

Here, event A is 'rainy', and event B is 'cloudy'. Given data:

To find the conditional probability P(Rainy | Cloudy), we apply the formula:

P(Rainy | Cloudy) = P(Cloudy and Rainy) / P(Cloudy) = 0.21 ÷0.41 ≈ 0.5122

So, the probability that a randomly selected day in June will be rainy if it is cloudy is approximately 0.5122, or 51.22%.

Answer:

The equation is:

[tex]y = 103- 23d[/tex]

Step-by-step explanation:

The initial amount was 103 grams.

After one day of use the remaining amount of soap was 80 grams.

So the amount of time he spent in one day was:

[tex]103-80 = 23[/tex]

Each day margaret spends 23 grams of soap.

if d represents the number of days elapsed then, the amount of soap "y" that Margaret spends after days is:

[tex]y = 103- 23d[/tex]

Margaret uses 5.75 grams of soap each day. The equation that shows the amount of soap remaining after d days of use is: S = 103 - 5.75d.

Based on the information provided, we can find the rate of soap loss, measured in grams per day. Initially, Margaret's soap weighed 103 grams and 4 days later, it weighed 80 grams so we know that a total of 23 grams of soap was used over this 4-day period.

Therefore, Margaret is using (103-80) / 4 = 23 / 4 = 5.75 grams of soap each day. Given this daily usage rate, we can say that after d days, the amount of soap remaining can be calculated by subtracting the total soap used from the initial weight. So, our equation will be: S = 103 - 5.75d, where S represents the soap remaining and d represents the number of days.

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Answer: a) k >4.08

b) k = 4.08

c) k<4.08

Step-by-step explanation:

Since we have given that

[tex]f(x)=-3x^2+7x-k[/tex]

a) For what values of k will the function have no zeros?

It mean it has no real zeroes i.e. Discriminant < 0

As we know that

[tex]D=b^2-4ac[/tex]

Here, a =-3

b = 7

c = -k

So, it becomes,

[tex]D<0\\\\b^2-4ac<0\\\\7^2-4\times -3\times -k<0\\\\49-12k<0\\\\-12k<-49\\\\k>\dfrac{49}{12}\\\\k>4.08[/tex]

b) For what values of k will the function have one zero?

It means it has one real root i.e equal roots.

So, in this case, D = 0

So, it becomes,

[tex]D=b^2-4ac=0\\\\D=7^2-4\times -3\times -k=0\\\\49-12k=0\\\\49=12k\\\\k=\dfrac{49}{12}\\\\k=4.08[/tex]

c) For what values of k will the function have two zeros?

It means it has two real roots.

In this case, D>0

So, it becomes,

[tex]D=7^2-4\times -3\times -k>0\\\\49-12k>0\\\\-12k>-49\\\\12k<49\\\\k<4.08[/tex]

Hence, a) k >4.08

b) k = 4.08

c) k<4.08

For 11 days, you'd do 3 assignments. That'll knock off 33 assignments. Then, for 5 days, you'll 2 assignments, which will leave you with 2 assignments. Then for one day, you'll only have to do 1 assignment. The last day you are free!!! :)

Answer:

The total cost of resurface the path is [tex]\$600[/tex]

Step-by-step explanation:

step 1

Find the area of the path

The area of the path is equal to the area of the path plus the swimming pool minus the area of the swimming pool

[tex]A=(14+3+3)(30+3+3)-(14)(30)[/tex]

[tex]A=(20)(36)-(14)(30)[/tex]

[tex]A=300\ ft^{2}[/tex]

step 2

Find the cost of resurface the path

Multiply the area of the path by $2 per square foot

[tex]300*2=\$600[/tex]

the total cost of resurfacing the path is $600.

To calculate the total cost of resurfacing the path around the swimming pool, you first need to determine the area of the path. The swimming pool measures 14 feet by 30 feet, and the path is 3 feet wide. To find the area of the outer rectangle, which includes the pool and the path, you calculate the width and length including the path. This gives you a width of (14 + 2*3) feet and a length of (30 + 2*3) feet, as the path goes all the way around, adding twice the width of the path to each dimension.

The outer rectangle's dimensions are therefore 20 feet by 36 feet. The area of the outer rectangle is 20 feet * 36 feet = 720 square feet. The area of the pool itself is 14 feet * 30 feet = 420 square feet. To find the area of just the path, you subtract the area of the pool from the area of the outer rectangle: 720 square feet - 420 square feet = 300 square feet. The cost to resurface the path is $2 per square foot, so the total cost is 300 square feet * $2/square foot = $600.

Answer:

x=5t-4 , y=5t+4 , z=-6t-2

Step-by-step explanation:

So we are going to use (-4,4,-2) as an initial point, p.  

The direction vector is v=5i+5j-6k or <5,5,-6>.

The vector equation is r=vt+p.

That means we have r=<5,5,-6>t       +      <-4,4,-2>.

So the parametric equations are

x=5t-4

y=5t+4

z=-6t-2

The parametric equations are:

x  =  -4  +  5t

y  =  4  +  5t

z  =  -2  - 6t

The given direction vector is:

[tex]\bar{V} = 5i + 5j - 6k[/tex]

The direction vector can also be written as:

[tex]\bar{V} = <a, b, c> = <5, 5, -6>[/tex]

The point X₀ = (x₀, y₀, z₀) =  (-4, 4, -2)

The parametric equation is of the form:

[tex]X = X_{0} + \bar{V}t[/tex]

This is:

[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}x_0\\y_0\\z_0\end{array}\right] + \left[\begin{array}{ccc}a\\b\\c\end{array}\right]t[/tex]

[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-4\\4\\-2\end{array}\right] + \left[\begin{array}{ccc}5\\5\\-6\end{array}\right]t[/tex]

The parametric equations are therefore:

x  =  -4  +  5t

y  =  4  +  5t

z  =  -2  - 6t

Learn more here: https://brainly.com/question/13072659

Answer:

2

Step-by-step explanation:

We can observe from the box plot the medians of both days.

The line in the middle of the box plot represents the median.

The median for Day 1 is: 6

The median for Day 2 is: 8

We have to find the difference between medians of both box plots so the difference is:

8 - 6 = 2

The difference between the medians is 2 ..

Answer:

its B

Step-by-step explanation: