Will you please tell me what I did wrong here, and show me it should have been done correctly?

Answer:

Function, function

Step-by-step explanation:

Each input corresponds to one output. Thus, by the definition of a function, both graphs represent functions

Answer:

24

Step-by-step explanation:

To find the slope you need 2 points in this case I used (0,0) and (1,24)

So:

24-0/1-0 = 24/1 = 24

The prove to show that ΔABC is similar to ΔMNC is explained below.

Similar triangles are triangles that have the same shape but are not necessarily the same size. More precisely, two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

Considering the given diagram, we can say:

AM = MC    (Given)

BN = NC     (Given)

BC = BN + NC (addition property of a line segment)

AC = AM + MC (addition property of a line segment)

NC/ BC = MC/ AC = constant

∠ACB = ∠MCN  (Reflexive property)

Thus, ΔABC ~ ΔMNC (Side-Angle-Side theorem)

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All sides of a rhombus have equal measures, so TU = 8. Since a rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other, WU = 10. The diagonals of a rhombus are also perpendicular, meaning they form right angles. Using the Pythagorean theorem, you can find the length of TX. (TX)^2 + (WX)^2 = (WT)^2. Substituting in known values, (TX)^2 + 25 = 64. Solving gives you TX = the square root of 39. TV is double the length of TX, so TV = 2 times the square root of 39.

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

The number line model that represents the expression -2/5 + 4/5 is: Option B

To plot an inequality, such as x > 2, on a number line, first draw a circle over the number (e.g., 2). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in.

Now, in this case, the operation to solve is:

-2/5 + 4/5

Solving this gives 2/5

Now, since the operation shows a negative and positive fraction with the solution being positive, then we can easily say that Option B is the correct answer to the problem

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Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.

The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23.  however amount is represented by a number.

It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.

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What does that even say

Main Answer: The total surface area of cylinder B is approximately 476.7  square units.

Supporting Question and Answer:

How is the surface area of a cylinder calculated?

The surface area of a cylinder is the sum of the areas of its curved surface and two circular bases. It can be calculated using the formula:

A = 2πrh + 2π\(r^{2}\)

where "r" is the radius of the circular base, "h" is the height of the cylinder, and π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.

The first term, 2πrh, represents the area of the curved surface of the cylinder, while the second term, 2π\(r^{2}\), represents the combined area of the top and bottom circular bases.

Body of the Solution: Let the height and radius of cylinder A be "h" and "r" respectively. Then, the height and radius of cylinder B are "2h" and "R" respectively, since cylinder B has twice the height of cylinder A but the same radius.

The total surface area of a cylinder is given by the formula:

Area = 2πrh + 2π\(r^{2}\)

For cylinder A, we know that the surface area is 180, so we can substitute the values and solve for "r" as follows:

180 = 2πrh + 2π\(r^{2}\)

90 = πrh + π\(r^{2}\)

We can rearrange this equation to solve for r:

r² + rh - 90/π=0

Using the quAdratic formula,we get:

r = (-h ± √((h)² + 4(90/π)))/2

r = -h/2 ± √(h² + 4(90/π))/2

Now we have an expression for r in terms of h . We can use this expression to find the radius of cylinder B, since we know that cylinder B has twice the height of cylinder A.

R = 2r= -h ± √(h² + 4(90/π))

We can use this expression to find the surface area of cylinder B:

Surface area of cylinder B = 2πR² + 2πR(2h)

Surface area of cylinder B= 2π( -h ± √(h² + 4(90/π)))² + 4πh( -h± √(h² + 4(90/π)))

We can use the value we found for 2h using the quadratic formula in the expression to get:

Surface area of cylinder B = 476.7 square units (rounded to one decimal place)

Therefore, the total surface area of cylinder B is approximately 476.7  square units.

Final Answer: Therefore, the total surface area of cylinder B is approximately 476.7  square units.

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Answer:$2.81

Step-by-step explanation:

1.25 is 100% of the price

125% + 100% = 225%

x = price by august

x = 225% (1.25)

225% = 2.25

2.25(1.25) = 2.8125 ≈ $2.81

Another way to see it:

=

225(1.25) / 100 = 2.8125

Answer:

6

Step-by-step explanation:

using similar triangles

x/(x+8) =15/35

x/(x+8) =3/7

cross multiply the two sides which will give u

3(x+8) =x*7

3x +24 =7x

24=7x-3x

24=4x

using 4 to divide both sides

24/4=4x/4

6=x

x=6

Answer: AS 1

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

Formula:
P = (x/y) * 100

where x is 6 dollars and y is 8 dollars.

P = (6/8) * 100
P = 0.75 * 100
P = 75%

Answer:

This is the answer and I hope it helps. have a great time.

The area of the shaded region of the rectangle is approximately 573.92 square feet.

The figure in the image is that of a rectangle with a semi-circle inscribed in it.

The area of rectangle is expressed as:

Area = Length × Width

The area of semi-circle is expressed as:

Area = 1/2 × πr²

To determine the area of the shaded region, we simply subtract the area of the semi-circle from the area of the rectangle.

Area of shaded region = area of rectangle - area of semi-circle

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

From the image:

Length = 40 ft

Width = 20 ft

Radius r = 12 ft

Plug the values into the above formula:

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

Area of shaded region = ( 40 × 20 ) - ( 1/2 × 3.14 × 12² )

Area of shaded region = ( 800 ) - ( 226.08 )

Area of shaded region = 573.92 ft²

Therefore, the area is approximately 573.92 square feet.

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Answer:

Step-by-step explanation:

Most road bikes and touring bikes have thinner tires, while mountain bikes have big fat tires. ... A firm thin tire on the asphalt surface won't flatten much. The less the tire flattens out on the bottom, the less surface area is in contact with the road. Less contact in this case means less friction, and more speed.

please mark brainliest

Answer:

16ft by 16ft by 8ft.

Step-by-step explanation:

Let the total surface area of the rectangular tank be S = 2LW+2LH+2WH where;

L is the length of the box

W is the width of the box

H is the height of the box.

Since the box is openend at the top, S = lw + 2lh+ 2wh

If the base is a square base then, l = w

S = l(l) + 2wh+2wh

S = l²+4wh ............... 1

If volume = lwh

lwh = 2028 ft³

wh = 2048/l ................ 2

Substitute equation 2 into 1;

S = l²+4(2048/l)

S = l²+8192/l

dS/dl = 2l - 8192/l²

If dS/dl = 0 (since we are looking for dimensions of the tank with minimum weight.)

2l - 8192/l² = 0

2l = 8192/l²

2l³ = 8192

l³ = 8192/2

l³ = 4096

l =∛4096

l = 16 ft

Since the length is equal to the width, hence the width = 16ft (square based tank)

Given the volume V = lwh = 2048

lwh = 2048

16*16*h = 2048

256h = 2048

divide both sides by 256

256h/256 = 2048/256

h = 8ft

Hence, the dimensions of the tank with minimum weight is 16ft by 16ft by 8ft.

Answer:

65/100 that is the answer to this question

Answer:

f(x) = - 2x + 4

Step-by-step explanation:

Since we are only trying to move the graph up 3 units, the slope does not change. So, it would be -2.

We also know that the 1 in f(x)= -2x + 1 is the y-intercept (y=mx+b). But again, we are moving the graph 3 units up, so we have to add 3. That makes it 4 (3+1=4).

So, the new equation would be f(x) = -2x + 4

Step-by-step explanation:

it simply means that g(x) is f(x) just shifted 3 units upwards.

that means nothing else changes, only whatever y result f(x) produces is increased by 3.

so,

g(x) = f(x) + 3 = -2x + 1 + 3 = -2x + 4

therefore, as domain and range were the whole set of real numbers, the addition of 3 does not make any difference in relation to infinity. so, they remain unchanged.

the slope stays the same (g(x) is simply a parallel line to f(x)).

the y-intercept (the y-value when x = 0) also increases by 3, and is 4.

the x-intercept (the x-value when y = 0) changes :

0 = -2x + 4

2x = 4

x = 2

the x-intercept is 2.

Answer:

24 - 27 (answer would be -3)

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

78

1) To write any number from a Standard Notation into a Scientific Notation we're going to need to rewrite that number as a product of one number and a power whose base is ten.

2) In this case, we can see that there are 6 zeroes after the 78. So we can write down the following:

Note that, as we wrote it with one decimal place. We can count seven decimal places.

The correct answer is 21.5 days

Explanation:

We know Marissa has two paid days of vacation plus 1 day for every four months she works. In this context, the first step is to find how much paid days of vacation she will have for working 6.5 years and add this to the 2 paid days of vacation she was given when she began to work. The steps are shown below:

1. Find the number of months in 6.5 by considering each year has 12 months and half year (0.5) is equivalent to 6 months

6 (number of years)  x 12 months =  72 months

0.5 year = 6 months

72 months + 6 months = 78 months (Total of months in 6.5 years)

2. Divide the total of months into 4 considering every 4 months Marissa is given one paid day of vacation.

78 months ÷ 4 = 19.5 days (number of paid days of vacation for working 6.5 years)

Finally, add this result to the two paid days initially given 19.5 days + 2 days = 21.5 days

Answer:

6

Step-by-step explanation:

The main idea of how to solve it is to isolate the variable. Whatever you multiply, divide, add, or subtract on one side, you must do the same to the other side so that both sides are equal.

3(x-1) = 21

3(x-1) / 3 = 21 / 3

x - 1 = 7

  + 1 + 1

x = 6

Answer:

x = 8

Step-by-step explanation:

First distribute

then +3 to both sides

which becomes 3x = 21

then divide both sides by 3 to get X by itself  

Answer:

The polar form of a complex number is another way to represent a complex number. The form z=a+bi is called the rectangular coordinate form of a complex number. The horizontal axis is the real axis and the vertical axis is the imaginary axis.

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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