on the map , a line of length 5cm represents 40km, how many kilometers would a line of length 7 1/2 cm represents​

The expansion and simplification of the expression (x - 2)² is x² - 4x + 4.

An algebraic expression is a combination of variables with constants, numbers, and values using the mathematical operands addition, subtraction, multiplication, or division.

(x - 2)²

Expanding the square:

(x - 2)² = (x - 2)(x -2)

Distributing the square:

x(x - 2) - 2(x - 2)

x² - 2x - 2(x -2)

x² - 2x - 2x + 4

x² - 4x + 4

Thus, after expanding and simplifying the algebraic expression (x - 2)², the solution is x² - 4x + 4.

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Answer:

Step-by-step explanation:

You want the perimeter and area of a figure consisting of a 4 × 11 rectangle with semicircles attached to each straight edge.

If you trace the perimeter of the figure, you see you are tracing the circumference of a circle 4 units in diameter and the circumference of a circle that is 11 units in diameter. The circumference of a circle is given by ...

  C = πd

so the total circumference is ...

  C1 +C2 = π(4) +π(11) = π(4+11) ≈ 47.12 . . . . units

The perimeter of the figure is about 47.12 units.

The area of two half-circles is the area of one whole circle of the same diameter. The area of a circle of diameter d is given by ...

  A = (π/4)d²

The total area of the circles of diameters 4 and 11 is ...

  A1 +A2 = (π/4)·4² +(π/4)·11² = (π/4)(4² +11²)

The area of the central rectangle is added to the areas of the semicircles. Its area is ...

  A = LW

  A = (11)(4)

The area of the entire figure is the sum of the circle areas and the rectangle area:

  total area = (π/4)(4² +11²) +(4)(11) ≈ 151.60 . . . . square units

The area of the figure is about 151.60 square units.

__

Additional comment

You usually see the formula for the area of a circle as ...

  A = πr²

Since r = d/2, we can express this using d as ...

  A = π(d/2)² = π(d²)/(2²) = (π/4)d²

You may notice that a square that circumscribes the circle will have a side length of d, and an area of d². The fraction π/4 tells you the fraction of that enclosing square that is covered by the circle. This fact can help you estimate areas and volumes of circles and cylinders.

The equation for g(x) in vertex form is g(x) = (x - 2)^ + 3

From the question, we have the following parameters that can be used in our computation:

The graph of g(x)

Also, we have

The graph of g(x) is a translation of f(x)=x^2

From the graph, we can see that

Using the above as a guide, we have the following:

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

Substitute the known values in the above equation, so, we have the following representation

g(x) = (x - 2)^ + 3

Hence, the equation for g(x) in vertex form is g(x) = (x - 2)^ + 3

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Answer:

90

Step-by-step explanation:

Answer:

It seems like the chat transitioned to a different topic. However, based on the search results, it appears that the query was related to solving distance problems using linear equations. One common application of linear equations is in distance problems, where you can create and solve linear equations to find the distance between two points or the rate of travel. Here's an example problem:

Joe drove from city A to city B, which are 120 miles apart. He drove part of the distance at 60 miles per hour (mph) and the rest at 40 mph. If the entire trip took three hours, how many miles did he drive at each speed?

To solve this problem, you can use a system of two linear equations. Let x be the number of miles driven at 60 mph, and y be the number of miles driven at 40 mph. Then you have:

x + y = 120 (total distance is 120 miles) x/60 + y/40 = 3 (total time is 3 hours)

To solve for x and y, you can multiply the second equation by 120 to eliminate fractions and then use the first equation to solve for one of the variables. For example:

x/60 + 3y/120 = 3 x/60 + y/40 = 3 2x/120 + 3y/120 = 3 x/60 + y/40 = 3 x/60 = 3 - y/40 x = 180 - 3y/2 (from the first equation)

Substitute the expression for x into the second equation and solve for y:

x/60 + y/40 = 3 (180 - 3y/2)/60 + y/40 = 3 3 - 3y/160 + y/40 = 3 3 - 3y/160 = 2.75 -3y/160 = -0.25 y = 20

Substitute y = 20 into the expression for x to get:

x = 180 - 3y/2 x = 120

Therefore, Joe drove 120 - 20 = 100 miles at 60 mph and 20 miles at 40 mph.

Step-by-step explanation:

The surface area of the triangular prism is 70.2 yd²

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of a prism is expressed as ;

SA = 2B +ph

where h is the height,

B is the base area and

p is the perimeter of the base

Base area = 1/2 bh( since the base Is a triangle)

Base area = 1/2 × 3 ×3 = 4.5yd²

The other side of the triangle is calculated as;

x= √ 3²+3²

x = √9+9

x = √18

x = 4.2

Therefore perimeter = 4.2 + 3+3 = 10.2yds

SA = 2× 4.5 + 10.2 × 6

SA = 9 + 61.2

SA = 70.2 yd²

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Answer: x is greater than or equal to 5 (I can't put the symbol in)

Step-by-step explanation:

Add 5 to both sides then simplify, which will get you 2x is greater than or equal to 10, then divide by 2.

Answer:

Step-by-step explanation:

3x+10<3

3x<3-10

3x<-7

x<-7/3

2x-5≥5

2x≥5+5

2x≥10

x≥10/2

x≥5

so x<-7/3 or x≥5

Step-by-step explanation:

Area of a traingle = 1/2 * base * height

   area = 1/2 * 6 * 4 = 12 cm^2

We can see here that the statement means that H is a subgroup of a group, and aЄ H is an element of that subgroup.

We can define a mathematical statement to be a claim that, depending on the circumstances, may be true or false. It frequently incorporates mathematical objects and their relationships or characteristics, such as integers, sets, functions, or geometric shapes.

We can see here that it shows that a is an element of the subgroup of H.

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Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Answer:

8.) is D

9.) is B

10.) is A

Step-by-step explanation:

mark brainliest

Answer: D, B, A

Step-by-step explanation:

When multiplying or dividing - and + numbers, rules are as follows:

If the signs are the same, your answer will be +

[tex]\frac{-a}{-b} =+\frac{a}{b}[/tex]

[tex]\frac{+a}{+b} =+\frac{a}{b}[/tex]

If the signs are different, your answer will be -

[tex]\frac{-a}{+b} =-\frac{a}{b}[/tex]

[tex]\frac{+a}{-b} =-\frac{a}{b}[/tex]

If there is no sign in front of number, it is positive

8.

a. 18 / -9 = -2   negative because signs are diff

b. -35 / -7  +5   signs same so +

c.  -12 / -6 = +2          same signs so +

d. 70 / -10 = -7        diff signs so -

Order from least to greatest:

-7    -2   2   5

Answer: D

9.  Follow rules from above:

Be careful with fractions  1/5  is not the same as 5/1.

With the fraction problems they do not divide into the number because 1 cannot be divided by 5 evenly, leave as a fraction and we are only taking care of the signs.

a.  +1/5

b.  -1/5

c.  +1/10

d.  +1/10

Order from least to greatest:

-1/5    1/5   1/10    1/10

Answer: B

10.

a. -2/3

b.  +1/25

c.  +3/25

d.  +1/50

The smallest number is the negative number

Answer A

By the principle of mathematical induction, the statement holds for all positive integers n.

Using mathematical induction:

Base case:

For n=1, results into:

2 = 2^2 + 1 - 2

which is true.

Inductive step:

For some positive integer k, we have:

2+4+8+...+2^k = 2^(k+1) + 1 - 2

This implies the statement for n=k+1, i.e.,

2+4+8+...+2^k+2^(k+1) = 2^(k+2) + 1 - 2

From the left-hand side of the equation, we can rewrite it as:

2+4+8+...+2^k+2^(k+1) = (2+4+8+...+2^k) + 2^(k+1)

Applying the induction hypothesis, substitute the expression for 2+4+8+...+2^k:

2+4+8+...+2^k+2^(k+1) = (2^(k+1) + 1 - 2) + 2^(k+1)

Simplify:

2+4+8+...+2^k+2^(k+1) = 2^(k+2) - 1

Using the formula for the sum of a geometric series to simplify the right-hand side of the original statement:

2^(k+2) + 1 - 2 = 2^(k+2) - 1

Thus, the statement holds for n=k+1, supposing it holds for n=k. By the principle of mathematical induction, the statement holds for all positive integers n.

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Answer:

Parallels lines:
y = 8x - 43

Perpendicular line:

y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]

Step-by-step explanation:

y = 8x -7

Parallel lines have the same slope.

The slope will be 8.  We will use the x from the point (5,-3) and the y from the point (5,-3) to find the y-intercept  (b)

y = mx + b  Substitute in -3 for y, 8 for m, and 5 for x.

-3 = 8(5) + b

-3 = 40 + b  Subtract 40 from both sides

-3 - 40 = 40 - 40 + b

-43 = b

Substitute in 8 for m and -43 for b to write the equation

y = mx + b

y = 8x - 43

Perpendicular slope are opposite reciprocals of each other, so the perpendicular slope is [tex]\frac{-1}{8}[/tex]

Substitute  [tex]\frac{-1}{8}[/tex] doe m, -3 for y and 5 for x.

y = mx + b

-3 = [tex]\frac{-1}{8}[/tex](5) + b

-3 = [tex]\frac{-5}{8}[/tex] + b   add [tex]\frac{5}{8}[/tex] from both sides

-3 +  [tex]\frac{5}{8}[/tex] = [tex]\frac{-5}{8}[/tex] +  [tex]\frac{5}{8}[/tex] + b

[tex]\frac{-24}{8}[/tex] + [tex]\frac{5}{8}[/tex] = b

[tex]\frac{-19}{8}[/tex] = b

Substitute [tex]\frac{-1}{8}[/tex] for m and [tex]\frac{-19}{8}[/tex] for b

y = mx + b

y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]

Helping in the name of Jesus.

Answer:

Step-by-step explanation:
150/2 = 75
500/75 = 6.6666666667 hours

it will take 6.2/3 hours to reach 500 bacteria cells

NOT SURE ABOUT EXPERSION BUT YOU COULD TRY THIS

p = 75t

Given that a culture of bacteria grows at a rate proportional to its size. Where the culture starts with 50 cells, then grows 150 after time, "t" equals 2 hours.

We are asked to:

> (a) Find an expression, P(t), to model the number of cells present after "t" hours.

> (b) Determine the time at which the population is at 500 cells.

For part (a):

Since the culture of bacteria grows at a rate proportional to its size, we can model it as the following differential equation.

[tex]\Rightarrow \frac{dP}{dt}=kP; \ Where \ P =P_0 \ at \ t=0 \ and \ P=3P_0 \ at \ t=2[/tex]

Solve the first-order separable differential equation with the given initial condition.

[tex]\Longrightarrow \frac{dP}{dt}=kP \Longrightarrow \frac{1}{P}dP=kdt \Longrightarrow \int\limits {\frac{1}{P} } \, dP=\int\ {k} \, dt \Longrightarrow ln(P)=kt+c[/tex]

[tex]\Longrightarrow e^{ln(P)}=e^{kt}+e^{c} \Longrightarrow P=ce^{kt}[/tex]

Plug in the initial condition.

[tex]\Longrightarrow P_0=ce^{k(0)} \Longrightarrow P_0=c(1) \Longrightarrow \boxed{c=P_0}[/tex]

[tex]\Longrightarrow P=ce^{kt} \Longrightarrow \boxed{P=P_0e^{kt}}[/tex]

Use the second initial condition to find "k."

[tex]\Longrightarrow 3P_0=P_0e^{k(2)} \Longrightarrow 3=e^{k(2)} \Longrightarrow 3=e^{2k} \Longrightarrow ln(3)=ln(e^{2k})[/tex]

[tex]\Longrightarrow k=\frac{ln(3)}{2} \Longrightarrow \boxed{k \approx 0.5493}[/tex]

Thus, the equation to model the situation is,

[tex]\boxed{\boxed{P(t)=50e^{0.5493t}}} \therefore Sol.[/tex]

For part (b):

[tex]P=10P_0[/tex]

[tex]\Rightarrow 10P_0=P_0e^{0.5493t} \Longrightarrow 10=e^{0.5493t} \Longrightarrow ln(10)=ln(e^{0.5493t})[/tex]

[tex]\Longrightarrow ln(10)=0.5493t \Longrightarrow t=\frac{ln(10)}{0.5493} \Longrightarrow \boxed{t=4.192 \ hrs}[/tex]

Thus, the time it takes the population to reach 500 is approx. 4.192 hours.

The graph of the cubic equation is in the equation of the end.

To do it, we need to find some points that are solutions of the equation. Then we can graph these points on a coordinate axis and then connect these points with a curve proper of a cubic relation.

when x = 0

g(0) =  -2*0³-8*0² +18*0+72 = 72

So we have the point (0, 72)

when x = 1

g(1) =  -2*1³-8*1² +18*1+72

      = -2 - 8 + 18 + 72 = 80

So we have the point (1, 80)

when x = -1

g(-1) =  -2*-1³-8*-1² +18*-1+72

      =    2 - 8 - 18 + 72 = 48

(-1, 48)

And so on, when you have enough points, you can connect them. The graph that should you get is one like the graph in the image at the end.

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Answer:

-13

Step-by-step explanation:

The sides show that we have an equilateral triangle

An equilateral triangle is a triangle in which all three sides are of equal length. Since all three sides are equal, all three angles are also equal and measure 60 degrees each.

We know that;

12x - 22 = 10x - 6

Collect like terms;

12x - 10x = -6 + 22

2x = 16

x = 8

Thus the sides of the triangle are;

12(8) - 22 = 74

10(8) - 6 = 74

7(8) + 18 = 74

In the second triangle;

4x - 25 = x + 14

4x - x= 14 + 25

3x = 39

x = 13

Thus the sides are;

4(13) - 25 = 27

13 + 14 = 27

6(13) - 51 = 27

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If the sample size was increased, the 95% confidence interval would decrease. A larger sample size would provide more precise and accurate data, resulting in a narrower confidence interval.

A confidence interval is a range of values within which a population parameter is estimated to lie with a certain level of confidence. It is commonly used in statistical inference to estimate the true value of a population parameter based on a sample from that population.

If the sample size was increased, the 95% confidence interval would likely decrease. This is because a larger sample size typically leads to more precise estimates and less variability in the data, resulting in a narrower confidence interval. However, the exact size of the decrease would depend on various factors such as the amount of variability in the data and the level of statistical significance chosen for the study.

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The coordinates of the point that corresponds to -5π/4 on the unit circle is (-1/√2, 1/√2).

Given that,

We have to find the coordinates of the point that corresponds to -5π/4 on the unit circle.

We know that any point on the unit circle can be defined as,

(cos θ, sin θ)

where θ is the angle formed with the X axis.

-5π/4 will be the point the corresponds to -225°.

Cos(-5π/4) = cos (5π/4)

                  = cos (π + π/4)

                  = -cos (π/4)

                  = -1/√2

sin (-5π/4) = -sin (5π/4)

                  = -sin (π + π/4)

                  = sin (π/4)

                  = 1/√2

Hence the coordinate of the unit circle is (-1/√2, 1/√2).

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The velocity of the rock as a function of time is given by:

[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]

where 4.9 is the value of mg in SI units.

The forces acting on the rock are the force due to gravity and the force due to air resistance. The force due to air resistance is given by 0.5v, where v is the velocity of the rock.

The force due to gravity is given by the mass of the rock (0.2 kg) times the acceleration due to gravity [tex](9.8 m/s^2)[/tex]. Using Newton's second law, we can set up the following differential equation:

[tex]m(dv/dt) = -mg - 0.5v[/tex]

where m is the mass of the rock, g is the acceleration due to gravity, and v is the velocity of the rock as a function of time t.

We can simplify this differential equation by dividing both sides by m:

[tex]dv/dt = (-g - 0.5v/m)v[/tex]

This is a separable differential equation, which we can solve using the separation of variables:

[tex](1/(-g - 0.5v/m)) dv = dt[/tex]

Integrating both sides gives:

[tex]-2ln(-g - 0.5v/m) = t + C[/tex]

where C is a constant of integration.

Solving for v gives:

[tex]v(t) = -0.5mg + C'exp(-2t/m)[/tex]

where C' = exp(C).

We can find the value of C' using the initial condition that the initial velocity of the rock is 3 m/s:

[tex]v(0) = -0.5mg + C' = 3[/tex]

[tex]C' = 0.5mg + 3[/tex]

Substituting this into the equation for v(t) gives:

[tex]v(t) = -0.5mg + (0.5mg + 3)exp(-2t/m)[/tex]

Therefore, the velocity of the rock as a function of time is given by:

[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]

where 4.9 is the value of mg in SI units.

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Answer:

The answer should be 1,260

Answer:

75

Step-by-step explanation:

.

The total surface area of the composite figure is: 288.62 mm²

From the attached image, we can see that the composite figure is made up of 2 triangles and one rectangle. Thus:

Formula for area of rectangle is:

A = Length * Width

Formula for area of triangle is:

A = ¹/₂ * base * height

Using Pythagoras theorem, length of rectangle is:

L = √(10.4² + 15.3²)

L = 18.5 mm

Thus:

TSA = (18.5 * 7) + 2(¹/₂ * 15.3 * 10.4)

TSA = 129.5 + 159.12

TSA = 288.62 mm²

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Answer:

1.5

Step-by-step explanation:

its a decimal number

Answer: the number 15/10 is a fraction.

Step-by-step explanation:

any two numbers that have a slash in the middle are fractons. :)

The multiplying integers -2x24= -48

Here is some rules of multiplication of integers:

1. Positive integer × negative integer = negative.

2. Positive integers × Positive integers =  positive.

3.  Negative integers × Negative integers = positive.

Here, To find the  the multiplying integers

-2x24 = -48

When you multiply integers :

Negative x Positive = Negative

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The mathematical induction has been used to prove that the statement is true for all positive integers: 30 + 138 + 318.

In mathematics, mathematical induction is a way of proving propositions. The method entails demonstrating that a statement is true for a base case, usually the smallest feasible value, and then demonstrating that if the statement is true for some value, it is likewise true for the next value.

The key to the proof is the inductive step. It is typically accomplished by assuming that the statement is true for some value and then utilizing that assumption to establish that the statement is true for the following value.

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Answer:

$1092

Step-by-step explanation:

The answers to the given questions about annual interest are given below:

a.

A = 4,000 (1 + 0.05/2)^(2 x 2)

  = $4,415.25

b.

A = 4,000 x e^(0.045 x 2)

  = $4,376.70

c. $100 more than option 2 = 4,376.70 + 100

                                             = $4,476.70

t (in years) = ln(4,476.70/4,000) /  ln(1 + 0.05/2)

                = 2.27986 years

Annual interest denotes the rate of interest levied or gained on a loan or investment for a duration of one year. This indicates the portion, expressed as a percentage, of the original amount that is utilized for interest payments or gained as a profit within a twelve-month period.

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Answer:

Put your calculator in degree mode.

[tex] \cos(x) = \frac{12}{13} [/tex]

[tex]x = {cos}^{ - 1} \frac{12}{13} = 22.6[/tex]

Angle x measures 22.6°.