Percent decrease from 275 to 242

Answer:

10x+15

Step-by-step explanation:

area of the two rectangles combined is one big rectangle

area of rectange= base*height

base length: 2x+3

height: 5

(2x+3)*5

=(2x*5)+(3*5)

=10x+15

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:

Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).

Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).

Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).

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Answer:

16-g=x

Step-by-step explanation:

You know you need to subtract because it says ate out of. Next you don't know how many gumdrops Logan ate so they gave a the variable g. Since you don't know how many gumdrops he ate you don't know how many are left. You need another variable to represent how many gumdrops are left.

Answer:

25.35

Step-by-step explanation:

25.2+25.3+25.8+25.1. /. 4

= 25.35

The greatest number of teams Mrs. Flossi can form from 40 students and 24 staff members, so the number of students and staff members on each team is 8.

The greatest number of teams Mrs. Flossi can make using 40 students and 24 staff members is equivalent to the Highest Common Factor (HCF or GCF) of 40 and 24.

The common factors of 40 and 24 are 8, 1, 2, and 4.

From the above common factors, 8 is the greatest common factor of both numbers.

When 40 is divided by 8, it gives a quotient of 5.  Five students will be on each team.  When 24 is divided by 8, the resulting quotient is 3.  Three staff members will appear on each team.  Each team consists of 8 members, 5 students, and 3 staff members.

Thus, the greatest number of teams Mrs. Flossi can make is 8.

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Mrs. Flossie is hosting a trivia contest for 40 students and 24 staff members. To be fair Mrs. Flossi wants there to be the same number of students and the same number of staff members on each team. What is the greatest number of teams Mrs. Flossi can make?

Answer:

412

Step-by-step explanation:

You have to follow PEMDAS and solve the problem carefully.

\(\frac{3+(2+8)^{2} }{4*(\frac{1}{2} )^{2} } =\frac{3+(10)^{2} }{4*(\frac{1}{2} )^{2} } = \frac{3+100}{4*(\frac{1}{2} )^{2} } = \frac{103 }{4*(\frac{1}{2} )^{2} }\)

\(\frac{103 }{4*(\frac{1}{2} )^{2} } = \frac{103 }{4*(\frac{1}{16})} } = \frac{103 }{\frac{1}{4} } =\\103*4\\=412\)

It took approximately 151 seconds to decrease 9 ft water in conical tank.

The volume of a conical tank with vertex down and radius 8 ft and height 20 ft is V = (1/3)πr²h

When the water is 9 ft deep

= (1/3) ×3.14×(8)²×(9)

= 602.88 ft³

We know that the rate of change of volume is 4 ft³/sec. So, the rate of change of depth can be calculated as follows:

Rate of change of depth (dh/dt) = Volume of tank/4 ft³ per sec

= 602.88/4

= 150.72 sec

Therefore, it took approximately 151 seconds to decrease 9 ft water in conical tank.

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Answer:

(-6,-12)

Step-by-step explanation:

A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.

\( - 2 \times 3 = - 6\)

\( - 4 \times 3 = - 12\)

So our new coordinates is

(-6,-12)

Answer:

(-6,-12)

Step-by-step explanation:

A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.

So our new coordinates is

(-6,-12)

Step-by-step explanation:

Answer:

5n-30

Step-by-step explanation:

5 times n= 5n. 5 times -6 is -30. 5n-30.

The value of x in the right angle placed is equal to 16

A right angle is an angle that measures 90 degrees. It is the most commonly seen angle in our day-to-day life. It can be seen in the corners of a room, the edges of boxes, the screen of a mobile phone, and so on. The sides of a square and a rectangle always form a right angle with each other. In radians, it is represented as π/2. Let us discuss more about a right angle in this article.

A right angle is an angle of 90°. When two rays intersect and form a 90˚ angle or are perpendicular to each other at the intersection, they are said to form a right angle.

In the given question, we can set an equation and find the value of x

90 = 26 + 4x

Lets solve for x

4x = 90 -26

4x = 64

x = 16

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Answer:

slope (m) = 2/3

Step-by-step explanation:

slope = change in x /change in y

Also, slope is y2 - y1 / x2 -x1. That is what I apply for this activity, hence:

slope = 3 - (-1) / 0 - (-6)

         = 3 + 1 / 0 + 6

         = 4 / 6

         = 2/3

∴ slope(m) = 2/3

Answer:

2/6 chance bc you have two dice that both need to roll a 6

Step-by-step explanation:

The required, general solution for x that satisfies the equation cos(x + 30) = -1 is x = (2n + 1)π - 30.

To find the general solution for the equation cos(x + 30) = -1, we can start by considering the general form of the cosine function. The cosine function has a period of 2π, meaning it repeats every 2π radians.

In this equation, we have cos(x + 30) = -1. Since the cosine function has a maximum value of 1 and a minimum value of -1, the only way for cos(x + 30) to equal -1 is if x + 30 is an odd multiple of π. We can write this as:

x + 30 = (2n + 1)π

Here, n is an integer representing the number of periods of the cosine function. To find the general solution, we can solve for x by subtracting 30 from both sides:

x = (2n + 1)π - 30

This equation gives us the general solution for x that satisfies the equation cos(x + 30) = -1. We can see that for each integer value of n, we have a different solution.

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Answer:

5/18 ÷ 4/9

Step-by-step explanation:

because 3/8 ÷ 3/5 equals to  5/8 and 5/18 ÷ 4/9 also equals to 5/8

Answer:

give me brainliest for a free cookie!

Step-by-step explanation:

Step-by-step explanation:

Answer: there are 11 calories in one glass of milk and 14 calories in one snack bar.

Step-by-step explanation:

Take milk to to be M and snack bars to be S.

Use algebra, so

2m + 3s = 64 and also

4m + 2s = 72

Multiply the top equation by 2 so both have 4m, so

4m + 6s = 128 and also

4m + 2s = 72

Then minus the numbers form the top equation by the bottom equation, so

4m + 6s = 128

- - -

4m + 2s = 72

This gives you 4s=56 so divide by 4 so s=14

No put 14 into the equation for s and rearrange to solve for m, so

2m+3s=64 So

2m+3x14=64

2m+42=64

Then minus 42

2m=22

m=11

Answer::))

Step-by-step explanation::))

Answer:

Your welcome

Step-by-step explanation:

indeed it is humourous

Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

Answer:4124966.126

Step-by-step explanation:

Distance between star from the sun is d = 4124966.128 AU

What is Trigonometry?

Trigonometry is the branch of mathematics that deals with particular angles functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle.

The astronomical unit distance between the star and the Sun can be calculated using the trigonometric function.

As per the given data:

distance from Earth to the Sun (P) = 1 AU

θ = 0.00001389 degrees

From tanθ:

tanθ = P/B

{P = perpendicular and B = base}

From the diagram:

tanθ = 1/d

tan(0.00001389) = 1/d

d = 1/tan(0.00001389)

d = 4124966.128 AU

The separation between the sun and the star is d = 4124966.128 AU.

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Answer:

9

Step-by-step explanation:

1/3 times9=3

Answer:

4/11

Step-by-step explanation:

convert to improper fraction from there the reciprocal becomes 4/11

Subtracting decimals, just like adding decimals, is similar to subtracting whole numbers. Just like adding decimals, the only difference is that we line up according to the decimal point instead of the last digit

One type of number that has a whole number and a fractional component separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.

Comparable to subtracting whole numbers is the operation of adding and subtracting decimals. The only difference between adding decimals and doing so is that we line up according to the decimal point rather than the last digit.

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Answer:

50 cent

Step-by-step explanation:

Answer:

.50¢

Step-by-step explanation:

50 cents = 1 pound

$1.00 = 2 pound

$1.50 = 3 pounds

$2.00 = 4 pounds

basically adding 50 cents equals to $2

Answer:

60

Step-by-step explanation:

56-7+22÷2

56-7+11

67-7=60

hope it helps thanks

please type properly your spelling was wrong

The prove of the given trigonometric function is given below.

The given trigonometric function is,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x))

Now proceed left hand side of the given expression:

We can write the expression  as,

⇒[(sin²(x))² - (cos²(x))²]/(sin²(x) - cos²(x))

Since we know that ,

Algebraic identity:

a² - b²  = (a-b)(a+b)

Therefore the above expression be

⇒(sin²(x) - cos²(x))(sin²(x) + cos²(x))/(sin²(x) - cos²(x))

⇒(sin²(x) + cos²(x))

Since we know that,

Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities include one or more trigonometric functions (such as sine, cosine, and tangent).

Then,

sin²(x) + cos²(x)² = 1 is an trigonometric identity

Hence,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x)) = 1

Hence proved.

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Answer:

∠B = 156°

Step-by-step explanation:

A line intersects two parallel lines this means that their opposite angles are transversals specifically the angles, A and B. And transversal angles are congruent so I can make this claim below:

\(∠A = ∠B \\ 8x +78 = 2x +144\)

Solving for x:

\(8x +78 = 2x +144 \\ 8x -2x +78 = 2x -2x +144 \\ 6x +78 -78 = 144 -78 \\ 6x = 66 \\ \frac{6x}{6} = \frac{66}{6} \\ x = 11\)

Solving Angle B if x = 11.

\(∠B = 2x +144 \\ ∠B = 2(11) +144 \\ ∠B = 22 +144 \\ ∠B = 166\)