RST is dilated about the origin,O, to creat R’S’T’. Point R is located at (3,9) and point R is located at (1.2, 3.6). Which scale factor was used to perform the dilation

Answer:

a) [tex]\frac{x^2}{16} +\frac{ y^2}{12} = 1[/tex]

b) [tex]\frac{x^2}{64} +\frac{ y^2}{16} = 1[/tex]

Step-by-step explanation:

a)

The vertices are located in the x-axis, so we have a horizontal ellipse.

The equation of an ellipse is given by:

[tex]\frac{(x - h)^2}{a^2} +\frac{ (y - k)^2}{b^2} = 1[/tex]

The coordinates of the foci and the vertices are given by:

Foci: [tex]F(h \pm c, k)[/tex]

Vertices: [tex]V(h\pm a, k)[/tex]

Comparing the coordinates with the values given, we have that:

h = 0, k = 0, c = 2, a = 4

To find the value of b we can use the following equation:

[tex]c^2 = a^2 - b^2[/tex]

[tex]4 = 16 - b^2[/tex]

[tex]b^2 =12[/tex]

So the equation of the ellipse is:

[tex]\frac{x^2}{16} +\frac{ y^2}{12} = 1[/tex]

b)

If the ellipse is centered at the origin, we have:

h = 0, k = 0

The major axis is 'a' and the other axis is 'b', so we have:

a = 8, b = 4.

So the equation is:

[tex]\frac{x^2}{64} +\frac{ y^2}{16} = 1[/tex]

Answer:

13w

Step-by-step explanation:

(19 - 6) * w

PEMDAS says parentheses first

19-6 = 13

13*w

13w

Answer:

13w

Step-by-step explanation:

(19-6)*W

PEMDAS

19-6= 13

13*W = 13w

Answer:

The value of c is 2

Step-by-step explanation:

p(x) = cx³ - 15x - 68

Since it's divisible by ( x - 4) that means when the value of ( x - 4) is substituted into the polynomial it leaves a remainder of zero that's no remainder.

x - 4 = 0

x = 4

Substitute it into the above expression

That's

c(4)³ - 15(4) - 68 = 0

64c - 60 - 68 = 0

64c = 60 + 68

64c = 128

Divide both sides by 64

c = 2

Hope this helps you

Answer:

h

Step-by-step explanation:

b

Answer:

D. 1/3

Step-by-step explanation:

Use the following equation to solve for the slope:

m (slope) = (y₂ - y₁)/(x₂ - x₁).

Let:

(x₁ , y₁) = (0 , 2)

(x₂ , y₂) = (3 , 3)

Plug in the corresponding numbers to the corresponding variables:

m = (3 - 2)/(3 - 0)

m = (1)/(3)

m = 1/3

D. 1/3 is your answer.

~

Answer:

The answer would be M = 6.5n because 6.50 per child would be 6.50 * n which can be simplified to 6.50n or 6.5n.

Answer:

correct answer is above :>

Step-by-step explanation:

Answer:

the answer is below

Step-by-step explanation:

Demand seems to be based on price.

Therefore we must consider two things:

that "x" is equal to the price and that "y" is equal to the average attendance.

Thus:

the two points would be:

(x1, y1) = (10,27000)

(x2, y2) = (6.39000)

The slope of a straight line is given by:

m = (y2-y1) / (x2-x1)

we replace:

m = (39000 - 27000) / (6 - 10) = 12000 / -4 = -3000

The equation of a straight line can be expressed like this

y = m * x + b.

where

m is the slope and b is the y-intercept.

we replace

y = -3000 * x + b.

To solve for b, replace x and y with the value of one of the points on the line.

We choose (6.39000). and we replace:

39000 = -3000 * 6 + b

39000 = -18000 + b

39000 + 18000 = b

b = 57000.

if we replace we have:

the equation becomes y = -3000 * x + 57000

since it is the demand and * x is the price.

t = d (x), therefore the equation becomes

d (x) = -3000 * x + 57000.

d (x) = 57000 - 3000 * x.

when x = 0, the price is 0 and the demand will be 57000, which will be more than the stadium can contain because the stadium can only contain 50,000.

So:

when x = 6, the price is 6 and the demand is 57000 - 18000 = 39000.

when x = 10, the price is 10 and the demand is 57000 - 30000 = 27000.

Answer:  [tex]\bold{G(t)=356e^{-0.59413t}}[/tex]

Step-by-step explanation:

Use the decay formula: [tex]P=P_oe^{kt}[/tex]   where

Given: P = 44.5, P₀ = 356, k = unknown, t = 210 minutes (3.5 hours)

[tex]44.5=356e^{k(3.5)}\\\\\\\dfrac{44.5}{356}=e^{3.5k}\\\\\\0.125=e^{3.5k}\\\\\\ln(0.125)=3.5k\\\\\\\dfrac{ln(0.125)}{3.5}=k\\\\\\-0.59413=k[/tex]

Input P₀ = 356 and k = -0.59413 into the decay formula

              [tex]\large\boxed{P=356e^{-0.59413t}}[/tex]

Answer:

the answer is 5 if it was helpful please give 5 star

Answer/Step-by-step explanation:

Below are the steps to take in solving the given equation, as well as justification forf each step:

[tex] \frac{2}{3}y + 15 = 9 [/tex]  => Given

[tex] \frac{2}{3}y + 15 - 15 = 9 - 15 [/tex] => subtraction property of equality

[tex] \frac{2}{3}y = - 6 [/tex] => simplification

[tex] \frac{2}{3}y * \frac{3}{2} = - 6 * \frac{3}{2} [/tex] => multiplication property of equality

[tex] y = - 9 [/tex] => simplification

Answer: Translation

Step-by-step explanation:

The shape its self has only shifted to the right. It hasn't been rotated or reflected.

Answer:

Translation

Step-by-step explanation:

defintion of translation: the process of moving something from one place to another.

The shpae is being moved to the right as shown by the arrow.

Answer:

[tex]c.\hspace{3}x=12[/tex]

Step-by-step explanation:

Isosceles triangles are a type of triangles in which two of their sides have an identical length. It should be noted that the angles opposite the sides that are the same length are also the same. This means that these triangles not only have two equal sides, but also two equal angles.

You can solve this problem using different methods, I will use pythagorean theorem. First take a look at the picture I attached.  As you can see:

[tex]x=2a[/tex]

And we can find a easily using pythagorean theorem:

[tex](\sqrt{45} )^{2} =3^{2} +a^{2}[/tex]

Solving for a:

[tex]a^{2} =(\sqrt{45} )^{2} -3^{2} \\\\a^{2} =45-9\\\\[/tex]

[tex]a^{2} =36\\\\a=\sqrt{36} \\\\a=6[/tex]

Therefore:

[tex]x=2a\\\\x=2(6)\\\\x=12[/tex]

Answer:

-6x^3 - x^2 + 2x

Step-by-step explanation:

We can first start with distributing the x using the distributive property

(3x^2 + 2x)(-2x+1) Remember that when x is multiplied with 3x, it increases the exponent to 3x^2)

Now we use FOIL to distribute (First, Outside, Inside, Last)

-6x^3 + 3x^2 - 4x^2 + 2x

We can combine the like terms (3x^2 and - 4x^2) into -x^2

-6x^3 - x^2 + 2x

Answer:

$1340.49

Step-by-step explanation:

From the attached image

Subtotal Cost of Purchased Items

[tex]= (20 \times 16.69)+(2 \times 20.78)+(2 \times 15.58)+(6 \times 21.38)\\+(118 \times 6.60)+(500 \times 0.22)+(10 \times 8.44)+(1 \times 150)\\\\=\$1658[/tex]

Since the builder receives a 20% contractor's discount, plus and additional 3% for paying in full within 30 days.

Discount = 23% of $1658 = 0.23 X 1658 =$381.34

Total (Less Discount) = 1658-381.34 = $1276.66

Tax on building materials is 5%.

Therefore:

Tax = 5% of $1276.66=0.05 X 1276.66

Tax=$63.83

Therefore, the total bill:

=$1276.66+63.83

Grand Total =$1340.49

Answer:

Step-by-step explanation:

2:3 is the correct answer

I hope this helps you

Answer:

See below.

Step-by-step explanation:

[tex](5x^2y^3)^0\div(-2x^{-3}y^5)^{-2}[/tex]

First, note that everything to the zeroth power is 1. Thus:

[tex]=1\div(-2x^{-3}y^5)^{-2}=\frac{1}{(-2x^{-3}y^5)^{-2}}[/tex]

Distribute using Power of a Power property:

[tex]=\frac{1}{(-2)^{-2}(x^{-3})^{-2}(y^5)^{-2})}[/tex]

Make the exponents positive by putting them to the numerator:

[tex]=\frac{(-2)^2(x^{-3})^2(y^5)^2}{1}[/tex]

[tex]=\frac{4x^{-6}y^{10}}{1}[/tex]

Make the exponent positive by this time putting it to the denominator:

[tex]=\frac{4y^{10}}{x^6}[/tex]

Answer:

4

Step-by-step explanation:

Converting 3kg to grams,

3 kg *  = 3000 g

If we divide 3000 g by 75, we will determine how many packets of butter there are.

3000 / 75 = 40.

40 packets of butter. If 10 go into a box, that means that

40 / 10 = 4 boxes.

Hence 4 such boxes can be made

Answer:

4 boxes can be made

Step-by-step explanation:

→ First work out the amount of small packets there are

3 kg = 3000g

3000 ÷ 75 = 40

→ Now we know that there are 40 small packets and one box can hold 10 packets so,

1 box  = 10 packets

?  boxes = 40 packets

40 ÷ 10 = 4

→ 4 boxes can be made

Answer:

D

Step-by-step explanation:

The correct option is option D as 2cos²(x)cos²(x) simplifies as follows:

2cos²(x)cos²(x) = {3 + 4cos(2x) + cos(4x)} / 4

The given expression is : 2cos²(x)cos²(x)

The square identity for cosine is given by:

2cos²(x) -1 = cos(2x)

Thus,

2cos²(x) = {cos(2x) +1}

simplifying again,

cos²(x) = {cos(2x) +1}/2

Simplifying the above using squared identities:

2cos²(x)cos²(x) = {cos(2x) +1}cos²x

                         = {cos(2x) +1} {{cos(2x) +1}/2}

                         [tex]= \frac{\{cos(2x) +1\}^2}{2}\\\\=\frac{cos^2(2x)+2cos(2x)+1}{2}\\\\=\frac{\frac{cos(4x)+1}{2}+2cos(2x)+1}{2}\\\\=\frac{3+4cos(2x)+cos(4x)}{4}[/tex]

so,

2cos²(x)cos²(x) = {3 + 4cos(2x) + cos(4x)} / 4

Hence option D is correct.

Learn more about squared identities:

https://brainly.com/question/14613683?referrer=searchResults

Answer:

25

Step-by-step explanation:

180-(21+73+51)=25

Hey there! :)

Answer:

C. m∠x = 35°.

Step-by-step explanation:

Begin by finding the value of the third angle of the triangle. Recall that all interior angles of a triangle sum up to 180°:

180 - 73 - 51 = 56°.

Since the top angle is split into x and 21°, simply subtract to solve for x:

56 - 21 = 35°. Therefore:

m∠x = 35°.

Answer:

Step-by-step explanation:

=-3.875/7. (divided by 16)

Answer:

22%

Step-by-step explanation:

Well if the ramp can hold 1000lbs and 6 people all weight 780 in total (they must be really fat lol, but anyway) we can make the following fraction.

780/1000

So now we simplify the fraction to 39/50.

And do 39 / 50 = .78

To make that a percent we move the decimal point 2 times to the right so 78% of the ramp‘s capacity is being used meaning there is stil 22% capacity left.

Answer: 2.12 seconds

Step-by-step explanation:

From the question, we are informed that Josie ran a lap in 45.23 seconds while Erica ran a lap in 43.11 seconds.

To calculate the extra amount of time it took Josie to complete the lap, we subtract Erica's time from Josie's time. This will be:

= 45.23 seconds - 43.11 seconds

= 2.12 seconds

Answer:

Your answer is E

Step-by-step explanation:

To make sure, plug the values in the place of N

[tex]-2 <-1, 0, 1, 2, 3, 4, 5, 6, \\ -1, 0, 1, 2, 3, 4, 5, 6, \leq 6[/tex]

Answer:

6^2 is the answer

Step-by-step explanation:

just trust me ik

Answer:

Hello!

____________________

Your answer would be (A) O point W.

Step-by-step explanation:  Intersection of the two lines is defined as the point where the two lines cross or meet each other.

It is given that the lines m and n intersect each other, which means that they must be intersecting each other at some point.

From the figure, it can be seen that in plane A, the lines m and n intersect each other at point W, thus point W is the point of intersection of the two line m and n.

Hence, option A is correct.

Hope this helped you!

Answer: point w hope this helped

Step-by-step explanation:

Answer:

(2, -3)

Step-by-step explanation:

These are the steps I used:

(6x+2y=6) x3 -> 18x+6y=18

(7x+3y=5) x2 -> 14x+6y=10

When you subtract the equations you get:

4x=8

x=2

The solution to the system of equations is -3 and -2

The correct option is A

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one.

6x+2y=6 is equation (1)

7x+3y=5 is equation (2)

Multiplying equation (1) by (3)

18x+6y=18 is equation(3)

By multiplying (2) by 2

14x+6y=10 is equation (4)

Substrate equation (4) from (3)

4x=8 Now, divide both sides by 4

X=2

Substitute x=2 in (1)

6(2)+2y=6

12+2y=6

Substrate 12 from LHS and RHS

2y=-6

Divide both sides by 2

y=-3

Hence x=2 and y=-3

learn more about system of equations here;

https://brainly.com/question/25180086

#SPJ6

Answer:

25/64

Step-by-step explanation:

ratio of perimeters = 15/24 = 5/8

ratio of areas = square of ratio of perimeters

ratio of areas = (5/8)^2 = 25/64

Answer:

Step-by-step explanation:

In this scenario, the probability of success, p is 28% = 28/100 = 0.28

Number of samples, n = 160

Probability of failure, q = 1 - p = 1 - 0.28 = 0.72

Mean,µ = np = 0.28 × 160 = 44.8

Standard deviation, σ = √npq = √160 × 0.28 × 0.72 = 5.68

Let x be the random variable representing the number of wood samples from long-leaf pine trees with a fungal disease. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

the probability that you’ll have at least 50 diseased samples to return to your boss is expressed as

P(x ≥ 50) = 1 - P(x < 50)

For P(x < 50)

z = (50 - 44.8)/5.68 = 0.91

Looking at the normal distribution table, the probability corresponding to the z score is 0.819

Therefore,

P(x ≥ 50) = 1 - 0.819 = 0.181

Answer:

thats tough

Step-by-step explanation:

Answer:

[tex]\dfrac{6}{7}[/tex].

Step-by-step explanation:

It is given that the sum of first two terms of an infinite GP is 6.

nth term of a GP is

[tex]a_n=ar^{n-1}[/tex]

[tex]a+ar=6[/tex]     ...(1)

Each term is 5 times the sum of the succeeding terms.

[tex]a_n=5(a_{n+1}+a_{n+2}+...+\infty)[/tex]

[tex]ar^{n-1}=5(ar^n+ar^{n+1}+...+\infty)[/tex]

[tex]ar^{n-1}=5ar^n(1+r+r^2+...+\infty)[/tex]

Divide both sides by a.

[tex]r^{n-1}=5r^n(\dfrac{1}{1-r})[/tex]    [tex][\text{Sum of infinite GP}=\dfrac{a}{1-r}][/tex]

[tex]\dfrac{r^n}{r}=\dfrac{5r^n}{1-r}[/tex]

[tex]\dfrac{1}{r}=\dfrac{5}{1-r}[/tex]

[tex]1-r=5r[/tex]

[tex]1=6r[/tex]

[tex]\dfrac{1}{6}=r[/tex]

The common ratio is 1/6.

Put r=1/6 in (1).

[tex]a+a(\dfrac{1}{6})=6[/tex]

[tex]6a+a=36[/tex]

[tex]7a=36[/tex]

[tex]a=\dfrac{36}{7}[/tex]

Second term [tex]ar=\dfrac{36}{7}\times \dfrac{1}{6}=\dfrac{6}{7}[/tex]

Therefore, the second term is [tex]\dfrac{6}{7}[/tex].

*The box plots are shown in the attachment

Answer/Step-by-step explanation:

Range is the difference between the largest value of a data set and the lowest value in that data set.

In a box plot, the highest value is located at the end of the whisker to our right, while the lowest value is located at the beginning of the whisker of the box plot at our left.

For Crackers, the range = 100-70 = 30

For Cookies, the range = 115-70 = 45

Therefore, we can conclude that the range value of the number of calories in crackers (30) is less/lower than that of cookies (45).

Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.