Translate triangle A by vector (-3,1) to give triangle B. Then rotate your triangle B 180 degrees around the origin to give triangle C. Describe fully the single transformation that maps triangle A onto triangle C.

Answer:

-7

Step-by-step explanation:

7m+28=3m

7m-3m=-28

4m=-28

m=28/4

m=-7

Answer:

166 legos are required

Step-by-step explanation:

In this case, let's analyze the data. We need 3 trophies, using at most 324 legos in total. The big trophy requires 220 legos, the smallest requires 135, so we need to know how much will be used in the medium trophy. This number should be 135 < X < 220

Now, if we know that the total legos to be used are 324, then, we can make a difference and sum for all the legos, and then, calculate the number of legos used.

Total legos = A + B + C

324 = 220 + 135 + C

324 = 355 + C

C = -31

This means that there is difference of 31 legos between the smallest and biggest trophy, therefore, this difference should be used and added to the smallest trophy and see how much Tristen use in the final trophy:

135 + 31

= 166 legos

So we need to use 166 legos to build the final trophy.

Answer:

he already used 355 so 166

Step-by-step explanation:

Answer:

2102

Step-by-step explanation:

The polynomial function P(x)=x^5-8x^3-x^2+2, if it is divided by x-5, first we need to get x from the divisor as shown

since d(x) = x-5

x-5 = 0

x = 5

Substitute x = 5 into the expression to get the remainder

P(x)=x^5-8x^3-x^2+2

P(5)=(5)^5-8(5)^3-(5)^2+2

P(5) = 3125-1000-25+2

p(5) = 2100+2

P(5) = 2102

Hence the remainder is 2102

Answer:

The exact value of the other leg is 10.

Step-by-step explanation:

Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.

Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.

Substituting known values, we get:

(10√2)^2 = 10^2 + b^2

200 = 100 + b^2

b^2 = 100

b = 10

Therefore, the exact value of the other leg is 10.

Regression equation correctly models the data is: y = -43.98x + 1,279.93

To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.

Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.

The slope (m) can be calculated using the formula:

\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)

Plugging in the values from the table:

m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)

m = (776,600 - 3,708,800 / 6(18,109) - 89,401)

m = (-2,932,200 / 66,654)

m ≈ -43.98

The y-intercept (b) can be calculated using the formula:

b = (Σy - m(Σx)) / n

Plugging in the values from the table:

b = (12,400 - (-43.98)(299)) / 6

b ≈ 1,279.93

The correct regression equation that models the data is:

y = -43.98x + 1,279.93

Out of the given options, the correct regression equation is:

y = -43.98x + 1,279.93

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Answer:

add me as a friend and give me thanks

Step-by-step explanation:

the answer is A for sure

Answer:

4 unit, 3 units

Step-by-step explanation:

It can be observed that there are 4 units on each side of the square and the triangle has a height of 3 units using the picture

Answer:

the last one is the correct, cause it is showing 90degree and right angled triangle ️ have 90 degrees.

Cone - A cone is a three-dimensional geometric object used in mathematics that smoothly taper from a flat, typically circular base to a point known as the apex or vertex.

The following is the formula for a cone's volume:

\(V = (1/3)πr^2h\)

where the volume is \(V\), the radius is \(r\), and the height is \(h\).

In putting the values provided yields:

\(48 = (1/3)πr^2(9)\)

By dividing both sides by \(3\), we arrive at:

\(144/π = r^2(9)\)

When we multiply both sides by \(9\), we get:

\(16/π = r^2\)

When we square the two sides, we obtain:

\(r = √(16/π)\)

(Rounded to two decimal places) \(r = 2.52 feet\)

As a result, the radius is roughly \(2.52 feet.\)

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There are 1140 different possible ways to select 3 restaurants out of 20 for the promotional program.

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.The combination formula, which is: can be used to resolve this issue.

n C r = r! * (n-r)!

where r is the number of restaurants to be chosen, and n is the total number of restaurants (20 in this case). (3 in this case).

By replacing these values, we obtain:

20 C 3 = 20! / (3! * (20-3)!) = 20! / (3! * 17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140

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The length of the side JH in the triangle ΔHIJ is 97.9.

We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.

Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".

IJ ∝ FG

IJ = k*FG

k = IJ/FG

k = 47/12

The side JH is proportional to the side GE.

JH = k*GE

x = (47/12)*25

x = 97.9

Hence, the length of the side JH is 97.9 units.

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Answer:

6825

Step-by-step explanation:

area=largo X ancho

area= 105 x  65=  6825

Answer:

9 Prizes

Step-by-step explanation:

She begins with 420 tickets.

She goes on 2 rides for 75 tickets each so 420-75-75= 270

She then attends the concert for 180 tickets so 270-180= 90

Now she is left with 90 tickets. 10 tickets = 1 prize therefore you can do 90/10 = 9

9 PRIZES

Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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Answer:

56

Step-by-step explanation:

First, convert the 70% so that we can use it with the 80 cups. To do this, convert the percent to a decimal by moving the decimal 2 spaces to the left:

70% → 70.00 → 0.70 → 0.7

70% percent can be seen as 0.7. Multiply this by 80:

\(80*0.7=56\)

So, 70% of 80 is 56. Desmond sold 56 cups on the second Saturday.

:Done

Answer: C. -12 - 3 + 9

Step-by-step explanation:

-12 because the fish are 12 m below the ocean.

-3 because the fish swim down.

+9 because the fish swim up.

Answer:

21/3 i think

Step-by-step explanation:

uh-

well 2+2 is 4 and 7/3x=2/3 is 2/7

To find the polar equation of a conic with focus at the pole, directrix y=3, and eccentricity of 2, we can use the definition of a conic in polar coordinates.

The general form of the polar equation for a conic with focus at the pole is given by:

r = \(\frac{ed}{1+e\cos(\theta-\theta_0)}\)

Where:

- r is the distance from the origin (pole) to a point on the conic.

- e is the eccentricity.

- d is the distance from the pole to the directrix.

- θ is the angle between the polar axis and the line connecting the pole to a point on the conic.

- θ_0 is the angle between the polar axis and the line connecting the pole to the focus.

In this case, the focus is at the pole, so θ_0 = 0. The directrix is y = 3, which means its distance from the pole is d = 3. The eccentricity is given as 2, so e = 2.

Substituting these values into the general equation, we get:

r =\(\frac{2\cdot3}{1+2\cos(\theta-0)}\)

Simplifying further:

r =\(\frac{6}{1+2\cos(\theta)}\)

Therefore, the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2 is:

r =\(\frac{6}{1+2\cos(\theta)}.\)

This equation describes the shape of the conic in polar coordinates, where r represents the distance from the origin to a point on the conic, and θ represents the angle between the polar axis and the line connecting the origin to the point.

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Answer:

2x2=4

4x4=16

6x6=36

8x8=64

Answer:

x+x+64=180

2x+64=180

2x=116

x=58

The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression

Given data ,

Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.

So , on simplifying the equation , we get

= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²

= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²

= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²

Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.

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Website B gains more new subscribers per amount of content than Website A as subscribers/amount are 100 and 81.8 respectively based on average number of posts.

Gain may be characterized as the quantity of gains in any object.

The websites' information is included in a table.

the website with the highest rate of new subscribers relative to content.

The following are the two websites:

The ratio of new subscribers to the total quantity of material posted can be used to symbolize new subscribers per amount of content on average.

New subscribers per volume of material for Website A is 9000/110, or 81.8

New members per quantity of material for Website B = 20000/200 = 100

According to the information above, Website B has a greater ratio of new subscribers to total content.

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The canister holds 80 cups and they need 84 cups of flour to make a dozen pizzas. So, the cooks cannot make a dozen pizzas without refilling the canister. The solution has been obtained by using unitary method.

What is the unitary method?

The unitary technique is used to first calculate the value of each individual unit, and only then is the value of the necessary quantity of units calculated.

We are given that a pizzeria stores flour in a 5-gallon container. We assumed that 16 cups make 1 gallon.

So, number of cups that will make 5 gallon is 16 * 5 = 80 cups

Since, each pizza they make uses 7 cups of flour. So, for making 12 pizzas, they require 12 * 7 = 84 cups of flour.

Hence, the cooks cannot make a dozen pizzas without refilling the canister.

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Answer:

100

Step-by-step explanation:

Forming algebraic equations and solving:

Let the number of boys originally  at the stop = 'x'

Let the number of girls originally at the stop = 'y'

25  girls get on the first bus.

⇒ The number of girls now at the stop = y -25

Ratio of boys to girls:

        \(\sf \dfrac{x}{y -25}= \dfrac{3}{2}\\\\Cross \ multiply,\\\\2x = 3*(y- 25)\\\\2x = 3y - 3*25\\\\2x = 3y - 75 ------\)(I)

15 boys get on the second bus.

Now, the number of boys at the stop = x - 15

Number of girls at the stop = y - 25

Ratio of boys to girls,

     \(\sf \dfrac{x - 15}{y -25} = \dfrac{1}{1}\\\\Cross \ multiply, \\\\x - 15 = y -25\\\\\)

             x = y -25 + 15

             x = y - 10

Plugin x = y - 10 in equation (I)

          2*(y-10) = 3y -75

          2y - 20  = 3y -75

                -20 = 3y - 75 - 2y

                -20 = y -75

         -20 +75 = y

                 \(\sf \boxed{\bf y = 55}\)

Plugin y = 55 in equation (I)

       x = 55 -10

        \(\sf \boxed{\bf x = 45}\)

Number of students originally at the stop = x + y

                                                                     = 55 + 45

                                                                     = 100

The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

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The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%

The percentage of a data set is when part of the data is represented per 100 with a symbol of %.

It was stated in the question that 80% of Americans report being afflicted by stress.

Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.

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Answer:

$1

Step-by-step explanation:

1.50/3=0.5

unit price is $0.5

$0.5 * 2 kg = 1

Answer:

$1

Step-by-step explanation:All you do is divide 1.5 by 3 and you get .5 and because you need the cost for 2 kg you would add .5+.5=1