For each direct variation, find the constant of variation. Then find the value of y when x = -0.5.

21. y =4 when x = 0.5
22. y =2 when x = 3

Answer:

2187

Step-by-step explanation:

1. 3

2. 9

3. 27

4. 81

5. 243

6. 729

7. 2187

Answer:

Step-by-step explanation:

7th term of the first sequence is 14

first we need to find out the nth term so,

tn=Ti+(n-1)d

2(n-1)2

2+2n-2

2n+2-2

2n+0

Now we need to find out the 7th term

n=7

2(7)-0

14-0=0

Second sequences 7th term is 33

first we need to find the nth term

1(n-1)3

1+3n-3

3n+1-3

3n-2

so now we need to find 7th term

3(7)-2

35-3

33

the 4th sequence 7th term is 20

The value of the vertex for the x-coordinate is less in column 1 as compared to the value of the vertex of x -the coordinate for column 2.

What are the coordinates and vertex of an equation?

When a graph crosses its symmetry axes, the vertex formula in mathematics may be used to get the vertex coordinate of a parabola. The vertex point is often represented by (h, k). We are aware that a parabola's conventional equation is y=a[tex]x^{2}[/tex]+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient [tex]x^{2}[/tex] is positive. The apex of the U-shaped curve should be at the top of the coefficient  [tex]x^{2}[/tex] is negative.

In the given question, It is given:

The two equations are:

[tex]y=2x^{2}-4x+12[/tex]

and,

[tex]y=4x^{2}+8x+3[/tex]

We have to find the vertex of the x-coordinate.

So, for the equation: [tex]y=2x^{2}-4x+12[/tex]

In Column 1:

[tex]\begin{aligned}y &=-2 x^2-4 x+12 \\&=-2\left(x^2+2 x-6\right) \\&=-2\left((x+1)^2-7\right)\end{aligned}[/tex]

So, By comparing the equation, we can say that the x-coordinate of the vertex in the column is -1.

So, for the equation:[tex]y=4x^{2}+8x+3[/tex]

In Column 2:

[tex]\begin{aligned}y &=x^2-4 x+3 \\&=(x-2)^2+(-1)\end{aligned}[/tex]

So, By comparing the equation, we can say that the x-coordinate of the vertex in the column is 2.

So, Option b is correct.

Hence, The value of the vertex for the x-coordinate is less in column 1 as compared to the value of the vertex of x -coordinate for column 2.

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The difference between the sum of the numbers is 0.

To find the sum of even number between 305 and 609, and the sum of all the odd numbers between 304 and 608, we use the sum of an arithmetic progression.

Note that there are 103 even numbers between 305 and 609. The even numbers start from 306 and end at 608.

Also, there are 103 odd numbers between 304 and 608. The odd numbers start from 305 and end at 607.

Using the sum of an arithmetic progression S = n/2(a + T) where

Now, for the sum of even numbers between 305 and 609, we have

So, S = n/2(a + T)

= 103/2(304 + 608)

= 103(912)/2

= 103(456)

= 46968

Also, for the sum of odd numbers between 304 and 608, we have

So, S' = n/2(a + T)

= 103/2(305 + 607)

= 103(912)/2

= 103(456)

= 46968

So, the difference between S and S' is d = S - S'

= 46968 - 46968

= 0

So, the difference is 0.

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The two linear equations are parallel lines

parallel lines are straight line that never intersects or meet each other.

some features of parallel lines include

In the problem, x = 1 and x = -8 are both vertical lines. In a cartesian coordinate x = 1 is in the positive coordinate and x = -8 is in the negative coordinate

The slope of both lines are zero

The equal distance apart is calculated as

| -8 - 1 | = 9 units

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Answer: y=x-1

Step-by-step explanation:

to solve for the slope you do

4-1=3

5-2=3

3/3= 1x=x

to solve for the y-intercept you do

1=1(2)

1-2=-1

Answer:

The change will be that of run over run.

Step-by-step explanation:

In the equation, y= -3x - 2 it moves 3 spaces down directly on the y-axis and 1 space to the right from there in the direction of the x-axis. Although, if you were to change the slope from -3 to -1/3 it will move 1 space down directly on the y-axis and 3 spaces to the right from there in the direction of the x-axis.

Image in green is the equation of: y= -3x - 2

Image in red is the equation of: y= -1/3x - 2

Answer:

Okay let's start out with checking what p even equals.

Let's start with using 2 as a possible amount for p

5 x 2 to the 2nd power = 20.

2 is correct. So, p + 5 has a chance of equaling 7.

Step-by-step explanation:

Answer:

p=2

p+5=7

Step-by-step explanation:

5p^2=20

/5.      /5

p^2=4

Square root both sides

p=2

Now fill in p into p+5

2+5

7

Hopes this helps please mark brainliest

Answer:

2 4/9

Step-by-step explanation:

1.)  10/9-(-1 1/3)

2.) 10/9+ 1 1/3

3.) 3x1+1=4/3

4.)10/9+4/3

5.)(10×3)+(4×9)

6.)30+36

7.)66/27

8.) 2 4/9

To find the Area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.

A triangle's feature known as SAS, or "Side, Angle, Side," has two sides and an angle that are both known.

The space occupied between the sides of the SAS triangle in a plane can thus be calculated with the use of the SAS triangle area formula.

The formula to find area of SAS triangle is:

Area = ½ ab Sin C = ½ × 29 × 36 × sin 62

Thus, Area = 522 × sin 62 = 522 × 0.88 = 459.36

Hence, Area of SAS triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.

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Answer:

19.9

Step-by-step explanation:

As 21 is opposite the right angle this side must be the hypotenuse :

Pythagoras Theorem says :

a² + b² = c²

Where c is the hypotenuse.

Substituting values in gives us (a and b do not matter) :

x² + (√43)² = 21²

Now we simplify :

Using the surd law:

√a ×√a = a

(√43)² = √43×√43 = 43

21² = 441

x² + 43 = 441

Subtract 43 from both sides :

x² + 43 - 43 = 441 - 43

x² = 398

Square root both sides :

x = √398

√398 = 19.9 to 1 d.p.

Hope this helped and have a good day

The cost of running the ad for three weeks by Enrique will be $207.

To estimate the overall cost for three weeks, we need the amount for one week. Further, we need the cost for six lines advertisement. So, performing calculation for the cost of advertisement of six lines in one week.

Total cost in one week = charge for first two lines + number of additional lines × cost of each additional line

Keep the values in formula. Out of six lines, the additional will be 4 as (6-2=4).

Total cost in one week = 42 + 4×6.75

Performing multiplication

Total cost in one week = 42 + 27

Performing addition

Total cost in one week = $69

Cost for three weeks = 69×3

Performing multiplication

Cost for three weeks = $207

Thus, Enrique will pay $207 for three weeks.

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Two cars leave at the same time but travel at different speeds. Car a travels 20 miles per hour faster than car b. In the time it takes car a to travel 350 miles, car b travels 250 miles.

The number of hours needed for Car B to overtake Car A is greater then 5 hours, Car A = 60km/h; Car B= 75km/h.

After h hours, the number of kilometers covered by Car A is 60*h

After h hours, the number of kilometers covered by Car B is 75(h-1)… since Car B started one hour later.

For Car B to overtake Car A,

75(h-1) > 60h

75h- 75 > 60h

75h - 60h > 75

15h > 75

h > 75/15

h > 5 hours

Hence the answer is, the number of hours needed for Car B to overtake Car A is greater then 5 hours, Car A = 60km/h; Car B= 75km/h.

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Based on the compound interest, Erica owes a total of $10865 after 5 years

The given variables can be represented as:

The compound interest formula is given as

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

Also from the question, we have

n = 12

This is so because the loan is compounded 12 times in a year as a result of being compounded monthly

Solving further, we replace the variables with their values in the above equation

A = 5300 * (1 + (8%/12))^(6*12)

Evaluate the expression

A = 10865

Hence, the amount owed is $10865

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Total number of cases possible when 3 Dice roll= 6^3=216

Now we have to find the number of cases when values shown on two of the dice sum to the value shown on the remaining, probability is 0.28

Now we need to count the instances where the values on two dice add up to the value on the other die, which is one. If a die shows 6, the remaining two dice must either show (5,1) or (4,2), or (3,3)

Total number of scenarios that could occur in this situation: 3!+3!+3!/2!=15

2. If a die shows 5, the other two dice must either display (4,1) or (3,2)

The total cases that could occur in this scenario are 3!+3! =12.

3. If a die shows 4, the other two dice must either display (3,1) or (2,2)

Total number of scenarios that could occur in this situation: 3!+3!/2!=9

4. If a die shows 3, the other two dice must also show 3. (2,1)

The total number of cases possible in this scenario= is 3!/2! =3

Total cases possible= 15+12+9+6+3=45

Probability= 45/216=5/24= 0.208

probability is 0.208

correct option is (D).

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The question was incomplete. Check below the complete question.

Three fair six-sided dice are rolled. What is the probability that the values shown on two of the dice sum to the value shown on the remaining die?

(A) 1/6

(B) 13/72

(C) 7/36

(D) 5/24

(E) 2/9

Answer:

y = [tex]\frac{1}{2}[/tex] x + 5

Step-by-step explanation:

Perp means perpendicular?

Perpendicular slopes are the opposite reciprocals of each other.  So the slope would be [tex]\frac{1}{2}[/tex]

Use -4 for x and 3 for y and the slope of [tex]\frac{1}{2}[/tex] to find the y intercept

y=mx +b

3 = [tex]\frac{1}{2}[/tex](-4) + b  

3 = -2 + b  Add 2 to both sides

5 = b

y = mx +b  We know the slope (m) is [tex]\frac{1}{2}[/tex] and the y intercept (b)  is 5.

y=mx+ b

y = [tex]\frac{1}{2}[/tex] x + 5

The linear equation is written as:

y = (-1/2)*(x + 3) + 2

And its graph can be seen in the image at the end.

Here we don't have the options, so I will post the graph of the line.

A linear equation with a slope a and a known poing (h, k) is written as:

y = a*(x - h) + k

Here we know that the slope is -1/2 and the point is (-3, 2), then the linear equation is:

y = (-1/2)*(x + 3) + 2

To graph the linear equation we just need to find two points on the line and connect them with a line, we already know one, so let's find another.

If we use x = 1, then:

y = (-1/2)*(1 + 3) + 2

y = (-1/2)*4 + 2

y = -4/2 + 2 = -2 + 2 = 0

y = 0

The other point is (1, 0)

With these two we can draw the graph you can see below.

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Answer:

f(x) = 4x -9

Step-by-step explanation:

The slope-intercept form is f(x) = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope, m.

=  [tex]\frac{-5-(-17)}{1-(-2)}[/tex]

= [tex]\frac{12}{3}[/tex]

= [tex]4[/tex]

m = 4, and now we plug it into the equation, using any given point, (1,-5) in this case.

f(x) = 4x + b

(-5) = 4(1) + b

-5 = 4 + b

b = -9

Now we find the equation: f(x) = 4x -9, and if we plug (-2,-17) in, we should get the same number as if we plug in (1,-5).

Answer:

[tex]5x^4-24x^3-34x^2-12x[/tex]

The height and radius of the cone-shaped cup that will use the smallest amount of paper, that is the maximum volume is  3.72 and  2.632 respectively.

Formula used in the solution is

Volume of the cone= (1/3)π(r^2)h

Area of the cone= πr√(l^2 + r^2)

Given, the volume of the cone is 27 cm^3.

(1/3)π(r^2)h =27

Simplifying the equation to get the value of r.

π(r^2)=81/h

r^2=81/hπ

[tex]r=\sqrt{\frac{81}{\pi h} }[/tex]

Substituting the value of r in area, we get

[tex]A=\pi \sqrt{\frac{81}{\pi h} } \sqrt{h^{2} + \frac{81}{\pi h} }[/tex]

[tex]\frac{dA}{dh} =\pi \sqrt{\frac{81}{\pi h} } \sqrt{h^{2} + \frac{81}{\pi h} }[/tex]

dA/dh=√81 × (π - 162/[tex]h^{3}[/tex]) × 1/√(πh + 81/[tex]h^{2}[/tex])

At dA/dh=0, we will get,

√81 × (π - 162/[tex]h^{3}[/tex]) × 1/√(πh + 81/[tex]h^{2}[/tex])=0

√81 × (π - 162/[tex]h^{3}[/tex])=0

[tex]\pi - \frac{162}{h^{3} }=0[/tex]

Thus, [tex]\pi h^{3} -162=0[/tex]

[tex]\pi h^{3} =162[/tex]

[tex]h^{3} =\frac{162}{\pi}[/tex]

h^3= 51.5662015618

h= 3.7221

Now, substitute h in radius,

[tex]r=\sqrt{\frac{81}{\pi \times 3.7221} }[/tex]

r=2.632

Hence, the height of the cone shaped cup is 3.7221 and the radius is 2.632.

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Expression for the miles jonas ran this week is 6m + 3 where m is the miles ran in the last week.

Given that jonas ran 'm' miles in last week.

acc. to statement he run one mile more than twice the miles he ran last week, so the equation will now become:

2m + 1 = miles in this week.

Again if he tripled his goal then the equation would become :

3(2m + 1 ) = new goal

6m + 3 = new goal

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Torie will have 30 shells.

The relationship in quantity, amount, or size between two or more things.

Given that, Torie, Lara and Dalia collect shells on a beach. They decide to share the shells between them in the ratio 3:5:2. Lara and Dalia have 70 shells between them,

Let them have each 3x, 5x and 2x shells.

5x+2x = 70

7x = 70

x = 10

Then, Torie = 3*10 = 30

Hence, Torie will have 30 shells.

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Answer:

in the first one the water changed by 4 inch every hour and the second one has an increasing 1 to 3 to 5 inches  

Step-by-step explanation:

20 m longer it is to walk from A to B along the diagonal of the walk than to walk along the edges of the park.

Given:

Assume ABCD is a rectangular park of right triangles ABC of length = 40m, width = 30m, ∠C = 90

In the right-angled triangle ABC,

By Pythagoras' theorem,

AB² = AC² + BC²

AB² = 30² + 40²

AB² = 900 + 1600

AB² = 2500

AB² = [tex]\sqrt{2500}[/tex]

AB = 50m

The distance from A to B along the diagonal of the park = 50m

The distance from A through to C = 30m.

The distance from A through C to B = 30 + 40 = 70m.

Therefore, 20 m longer it is to walk from the diagonal of the park to walk along the edges of the park.

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The amount to be in the account after 11 years, assuming no deposits or withdrawals is $602.880

Given,

Ariana invested $400 in an account paying an interest rate of 3.8% compounded monthly.

What is the formula for the future value on compound interest?

A = P(1+r)ⁿ

P = $400

r = 3.8%

Amount after 11 years.

r = 3.8/100

= 0.38

= 400 (1+3.8/100)¹¹

= $602.880

Therefore the amount after 11 years the amount will be $602.880.

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The amount that is closest to Nathan's total costs after the 15% discount and including 6% sales tax, assuming tax is applied after the discount is applied would be $624. That is option A.

The discount on sales is the amount of money that is being deducted from the original price of an item by a seller to their customers.

The original price for labor= $299.88

The original price for parts = $ 307.54

The original price for others = $ 74.71

The total original price = $682.13

The discount of on the total price = 15%.

That is;

= 15/100 × 682.13

= 10,232.95/100

= $102.32

When discount is removed from the original price;

= 682.13 - 102.32

= $579.81

When the tax is acted on the discount total sales;

= 6/100 × 579.81

= $3,478.86/100

= $34.79.

The total cost after discount and tax would be;

= 579.81 + 34.79

= $614.59

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