The ratio of the side length of a square to the square's perimeter is always 1 to 4. Peter drew a square with a perimeter of 28 inches. What is the side length of the square Peter drew?

Answer:

false

Step-by-step explanation:

Dilations are transformations that generate an enlargement or a reduction. Translations are congruence transformations that move an object, without changing its size or shape.

this transformation here is a translation.

all points have been moved by +1 in x direction and +2 in y direction.

for a dilation the should have been a multiplication factor and not adding constants.

The general standard equation of circle is x²  - 3x + y²  - 0.5y - 0.25 = 0

(x−h) ² +(y-k)²=r²

This is the general standard equation for the circle centered at (h,k) with a radius of r

Circles can also be given in the expanded form, which is simply the result of expanding the binomial squares in the standard form and combining like terms.

The equation of the circle centered at (6/2, 1/2) with a radius of 6/2.

Putting these values in the equation : (x−h) ² +(y-k)²=r²

(x-3)² +(y-0.5)² = 3²

x²  + 9 - 3x + y² + 0.25 - 0.5y = 9

x²  - 3x + y²  - 0.5y - 0.25 = 0

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(1+i) ^18 ≈ 4.766×10^6 - 1.632×10^7i. a. To solve (e^-4-2i) ^2, we first need to simplify e^-4-2i. Using Euler's formula, we can rewrite e^-4-2i as e^-4 * e^-2i, which is equivalent to e^-4(cos (-2) +i*sin (-2)). Simplifying further, we get e^-4(cos(2)-i*sin(2)).

Now, we can square this expression to get (e^-4(cos (2)-i*sin (2))) ^2. Using the formula (a+bi)^2 = a^2 - b^2 + 2abi, we get:

(e^-4*cos(2))^2 - (e^-4*sin(2))^2 + 2*e^-4*cos(2)*i*sin(2)

Simplifying, we get:

e^-8 - e^-8*sin^2(2) + 2*e^-4*cos(2)*i*sin(2)

This is the form a+bi, so our final answer is:

a = e^-8 - e^-8*sin^2(2) ≈ 0.0153
b = 2*e^-4*cos(2)*sin(2) ≈ -0.0565

Therefore, (e^-4-2i)^2 ≈ 0.0153 - 0.0565i.

b. To solve (1+i)^18, we can use the binomial theorem, which states that (a+b)^n = Σ(n choose k)a^(n-k)*b^k, where Σ is the sum from k=0 to n. Applying this to (1+i)^18, we get:

(18 choose 0)1^18*i^0 + (18 choose 1)1^17*i^1 + (18 choose 2)1^16*i^2 + ... + (18 choose 18)1^0*i^18

Simplifying the coefficients using the formula (n choose k) = n!/((n-k)!k!), we get:

1 + 18i - 1530 - 3060i + 18564 + 145152i - 437580 - 947736i + 1352078 + 1081664i - 587863.5 - 575784i + 203887.5 + 405528i - 88749 + 35064i - 5400 + 304i

Adding up the real and imaginary parts separately, we get:

a = 4766436 ≈ 4.766×10^6
b = -16318512 ≈ -1.632×10^7

Therefore, (1+i)^18 ≈ 4.766×10^6 - 1.632×10^7i.

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The table has

x values 2,3,4,5 and

f(x) as 1, 14,20, 31

The statements A is true Intermediate value theorem, B is false mean value theorem, C is true extreme value theorem and D is true.

Given that,

The table has

x values 2,3,4,5 and

f(x) as 1, 14,20, 31

The function f is continuous.

A is true, From the figure.

Intermediate value theorem is let [a,b]be a closed and bounded intervals and a function f:[a,b]→R be continuous on [a,b]. If f(a)≠f(b) then f attains every value between f(a) and f(b) at least once in the open interval (a,b).

B is false because, mean value theorem, Let a function f:[a,b]→R be such that,

1. f is continuous on[a,b] and

2. f is differentiable at every point on (a,b).

Then there exist at least a point c in (a,b) such that f'(c)=(f(b)-f(a))/b-a

In the B part, the differentiability is not given do mean value theorem can be applied.

C is true because the extreme value theorem, if a real-valued function f is continuous on the closed interval [a,b] then f attains a maximum and a minimum each at least once such that ∈ number c and d in[a,b] such that f(d)≤f(x)≤f(c)∀ a∈[a,b].

D is true.

Therefore, The statements A is true, B is false, C is true and D is true.

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The probability that they are all girl's  is 10/17.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.

The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .

According to our question-

(10 + 8) students plus 2 equals 18 pupils.

Let S serve as the sample area.

There are then n(S) options to choose 3 students from a total of 18 students.

There are 10 C 3 possible selections from a group of 10 boys.

The number of favorable occurrences is n (E ) = 10 C 3.

The needed probability is therefore 10 C 3 18 C 3.

=\s10\s×\s9\s×\s8\s18\s×\s17\s×\s16\s=\s5\s34

(ii) Three of the eight girls can be chosen in one of eight C three ways.

Favorable number likelihood is equal to 8 C 3 and 18 C 3.

=\s8\s×\s7\s×\s6\s18\s×\s17\s×\s16\s=\s7\s102

(iii) In the range of 10 C 1 to 8 C 2, one male and two girls may be chosen.

Favorable amount of occasions=  10/17.

Hence, The probability that they are all girl's  is 10/17.

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it took her 10 minutes to fix

The area of the given figure is 62 mm².

Given is a figure we need to find the area of the figure,

The given figure is a composite figure, and to find the area of a composite figure we just split it into know geometric figures and then find their area and then add them.

So, here there are three rectangles with dimensions,

6 mm × 5 mm, 1 mm × 4 mm and 7 mm × 4 mm.

We know that the area of a rectangle is the product of their dimensions,

Hence the area of the figure =

= 6 mm × 5 mm + 1 mm × 4 mm + 7 mm × 4 mm

= 30 mm² + 4 mm² + 28 mm²

= 62 mm²

Hence the area of the given figure is 62 mm².

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Answer:

now first of all we should plug in 0.8 to y .

now we have this simple equation: 4x+8.(0.8)=40

4x+6.4=40

4x=33.6

x=8.4  (hope it helps :) )

Step-by-step explanation:

Answer:

\(4x + 8y = 40 \\ 4x + 6.4 = 40 \\ 4x = 40 - 6.4 \\ 4x = 33.6 \\ x = 8.4\)

Answer:

I think that the answer is either B or C

Step-by-step explanation:

I concluded to this answer simply by looking at where the lines were placed.

Remember that if a line is not touching, but next to another line, they are parallel to each other? Well, that doesn't change here. since, {m angle 1} and {m angle 2} added together equal 180, I would believe that the answer is C, but I may be wrong.

Well, I hope that helps :)

The net of a triangular pyramid consist of a total of 4 triangles. it has 4 faces with the base being one of them which is also in the shape of a triangle.

A net of the triangular pyramid is the pattern formed when the surface of it is laid out flat showing each triangular face of the figure, therefore we know that the net of a triangular pyramid consist of a total of 4 triangles.

Triangular pyramid  is a pyramid which has a triangular base. In geometry, vertices are essentially corners. All triangular-based pyramids, either regular or irregular, have four vertices.

It has 6 edges, 4 faces, 4 vertices.

A regular triangular pyramid has equilateral triangles all four faces

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Answer:

\((3 - 5i) + ( - 2 + 8i) \\ 3 - 5i -2 + 8i \\ 3 - 2 - 5i + 8i \\ 1 + 3i \\ \)

Answer:

Option C.

Step-by-step explanation:

\(\sf\:x^{2}-3x+7=0 \)

Use the biquadratic formula.

\(\sf\:\x=\frac{-\left(-3\right)(+/-)\sqrt{\left(-3\right)^{2}-4\times 7}}{2} \)

\(\sf\:x=\frac{-\left(-3\right)(+/-)\sqrt{9-4\times 7}}{2} \)

\(\sf\:x=\frac{-\left(-3\right)(+/-)\sqrt{9-28}}{2} \)

\(\sf\:x=\frac{-\left(-3\right)(+/-)\sqrt{-19}}{2} \)

\(\sf\:x=\frac{3(+/-)\sqrt{19}}{2} \)

Positive sign:

\(\boxed{\sf\:x=\frac{3+\sqrt{19}}{2}} \)

Negative sign:

\(\boxed{\sf\:x=\frac{3-\sqrt{19}}{2}} \)

Hope it helps ⚜

The road with alternating white and black stripes and each 50 cm wide is 7.5 m wide.

The road consists of alternating white and black stripes

No. of white stripes = 8

As the first and last stripe is white so in between the black stripes will be 7

No. of black stripes = 7

Total no. of stripes = 15

Width of black stripe = 50 cm

Width of white stripe = 50 cm

Width of whole road = total no. of stripes × width of each stripe

Width of whole road = 15 × 50

Width of whole road = 750 cm

To convert m into cm

Now, 1 m = 100 cm

1 cm = 1/100 m

750 cm = 750/100 m

750 cm = 7.5 m

Hence the width of the road is 7.5 m

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At age 9, Tammy was taller than Leslie because she was 3.68 inches taller.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

as per the details stated above

that Leslie measured 50 inches at age 9

and Tammy's height may be predicted by the equation

y = 2.2x + 35.5,

where y represents Tammy's height at x years of age,

one must carry out the following computation to establish who was taller at that age:

Tammy = 2.2 x 9 + 35.5

= 18.18 + 35.5

= 53.68.

Tammy was 3.68 inches taller than Leslie at age 9 as a result, Tammy was taller at that age.

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By 3.68 inches, Tammy was taller than Leslie when she was nine years old.

As per the data given in the above question are as bellow,

The provided details are,

Given that Tammy's height can be predicted by the equation

y = 2.2x + 35.5,

where y is her height at age x, and Leslie's height at age 9 was 50 inches,

The following computation must be done to establish who was higher at that age:

Leslie is 50.

Tammy = 2.22 x 9.5 + 35.5 = 18.18 + 35.5 = 53.68

Consequently, Tammy was taller at age 9 than Leslie since she was 3.68 inches taller.

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Answer:

5

Step-by-step explanation:

(13−(1+2))(2)

       4

=  (13−3)(2)

       4

=  (10)(2)

      4

= 20

  4

= 5 (the answer is 5)

Answer: 43.96 inches^2

Step-by-step explanation:

Answer:

where is the second one?

Step-by-step explanation:

The C program for RK 4th order .

C program,

#include<stdio.h>

//differential equation "dy/dx = (y-2*x*y)"

float f(float x, float y)

{

return(y-2*x*y);

}

int main()

{

// Finds value of y for a given x using step size h

int i,n;

float x0,y0,x,h,k1,k2,k3,k4;

printf("Enter the value of x:");

scanf("%f",&x);

//initial value y0 at x0.

printf("Enter the initial value of x & y:");

scanf("%f%f",&x0,&y0);

//step size

printf("Enter the value of h:");

scanf("%f",&h);

//prints the initial value of y at x and step size.

printf("x0=%f\t yo=%f\t h=%f\n",x0,y0,h);

//Count number of iterations using step size or

//step height h

n=(x-x0)/h;

// Iterate for number of iterations

for(i=1;i<=n;i++)

{

//Apply Runge Kutta Formulas to find

//next value of y

k1 = h*f(x0,y0);

k2 = h*f(x0+h/2,y0+k1/2);

k3 = h*f(x0+h/2,y0+k2/2);

k4 = h*f(x0+h,y0+k3);

//Update next value of y

y0 = y0+(k1+2*k2+2*k3+k4)/6;

//Update next value of x

x0=x0+h;

}

//print the value of y at entered value of x.

printf("at x=%f\t,y=%f\n",x,y0);

return 0;

}

Solution of DE,

y' = y - 2xy, y(0) = 1

The task is to find value of unknown function y at a given point x.

Below is the formula used to compute next value yn+1 from previous value yn. The value of n are 0, 1, 2, 3, ….(x – x0)/h.

Here h is step height and xn+1 = x0 + h

\(K_{1} = h f(x_{n} ,y_{n} )\)

\(K_{2} = hf( x_{n} + h/2 , y_{n} + K_{1}/2 )\)

Thus,

\(y_{n+1} = y_{n} + K_{1} / 6 + K_{2} / 3 + K_{3} / 3 + K_{4} / 6 +O(h^{5} )\)

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Answer:

Step-by-step explanation:

iven, the equation is (x - 1)² + 2(x + 1) = 0. We have to determine if the equation has a real root. By using algebraic identity, (a - b)² = a² - 2ab + b² (x - 1)² = x² - 2x + 1.

Use the equation formula to find the area of a circle

The radius is given on the question, replace this value on the equation and find the area.

The area of the circle is 201.06 mm^2

Condense the right side a single sine expression:

sin(6x) - cos(6x) = R sin(6x - t)

Expanding the right side gives

sin(6x) - cos(6x) = R sin(6x) cos(t) - R cos(6x) sin(t)

Then we have

R cos(t) = 1

R sin(t) = 1

Solve for R and t:

(R cos(t))² + (R sin(t))² = 1² + 1²

R² = 2

R = √2

and

(R sin(t))/(R cos(t)) = 1/1

tan(t) = 1

t = arctan(1) = π/4

So we rewrite the equation as

√2 sin(6x - π/4) = √2

Solve for x :

sin(6x - π/4) = 1

6x - π/4 = arcsin(1) + 2nπ

(where n is any integer)

6x - π/4 = π/2 + 2nπ

6x = 3π/4 + 2nπ

x = π/8 + nπ/3

Answer:

How much

Step-by-step explanation:

Answer:

1/3 x + 40 = 5/7 x

7x +(21)(40) = 15x

21*40 = 8x

x = 105cm3

Step-by-step explanation:

In a perfectly symmetrical distribution with a mean (µ) of 30, there is no specific mode because all values occur with equal frequency.

In a perfectly symmetrical distribution, such as a symmetric bell-shaped curve or a uniform distribution, each value occurs with the same frequency. This means that there is no value that occurs more frequently than others, resulting in multiple modes or no mode at all.

The mode is typically used to identify the most common value in a dataset, but in a perfectly symmetrical distribution, all values have equal frequency, and there is no single mode. Instead, the distribution is characterized by its symmetry around the mean (µ). The mean represents the central tendency of the distribution, indicating the balance point of the data. In this case, with a mean of 30, the distribution is centered around this value, with equal numbers of observations on either side.

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If there are twice as many less ten dimes as quarters and the total value of the jar is $30.95, the number of quarters is 71

The coins of the American dollar are the quarter, dime, nickel, and penny. The value of a quarter is 25 cents (25% of a dollar), that of a dime is 10 cents (10% of a dollar), that of a nickel is 5 cents (5% of a dollar), and that of a penny is 1 cent (1% of a dollar).

Pennies are made of zinc today, but they were once also made of copper and iron. Nickel and copper combine to form nickels. While silver was once used to make dime, they are now made of copper and nickel. Nickel and copper are also used to make quarters.

Let the no. quarters be Q

And no. dimes be D

There are twice as many less ten dimes as quarters, which gives us

D = 2Q - 10

We know 25Q + 10D = 3095 cents

Substituting the value of Q we get

⇒ 25Q + 10(2Q - 10) = 3095

⇒ 25Q + 20Q - 100  = 3095

⇒ 45Q = 3095 + 100

⇒ 45Q = 3195

⇒ Q = 3195/45

⇒ Q = 71

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The perimeter of the polygon with the vertices is: 22 units.

To find the perimeter of a polygon, we need to add all the side lengths together.

Given the polygon has the vertices (-3, 1), (5, 1), (-3, 4), and (5,4)​, we need to find the distance between each vertices in order to find the perimeter of the polygon.

Let:

A = (-3, 1)

B = (5, 1)

C = (-3, 4)

D = (5,4)​

The vertices have been plotted on the graph attached below. Therefore:

Perimeter of the polygon = CD + BD + AB + AC

Perimeter = 8 + 3 + 8 + 3 = 22 units.

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Answer:

(x + 13, y + 7)

Step-by-step explanation:

Hello there!

In order to find what the translation rule is, we need to find how much it move to the right/left and up/down

In this case, the line segment VW moved up 7 and to the right by 13

We can get this by checking how far apart the points are

I checked how far apart V and V prime

(V prime is the green V. When a point is primed, its just saying that the point has gone through translation, rotation, dilation, or reflection)

V is 13 units to the left of V prime and 7 units below V prime

This means that, to go from line VW to line V prime W prime, you need to shift the line up 7 units and to the right 13 units

So, the translation rule is (x + 13, y + 7)

*If you don't understand, tell me in the comments, I will try to explain further to your understanding. Thank you, and have a great rest of your day :)*

Step-by-step explanation:

x = cost of 1 kg mushrooms

y = cost of 1 kg turnips

2x + 2.5y = 8.55

3x + 4y = 13.10

so, we have a system of 2 equations with 2 variables.

this can be solved either by

or by

this here looks (for me) better for elimination.

we bring the first equation to something with 6x, and the second one to something with -6x, abd then we add them.

so, we multiply the first equation by 3, and the second equation by -2 :

6x + 7.5y = 25.65

-6x - 8y = -26.20

-------------------------------

0 -0.5y = -0.55

y = -0.55/-0.5 = £1.10

for x I suggest now to use the second original equation :

3x + 4y = 13.10

3x + 4×1.10 = 13.10

3x + 4.40 = 13.10

3x = 8.70

x = 8.70/3 = £2.90

a) 1 kg of turnips cost £2.90

b) 1 kg if mushrooms cost £1.10

a. D. magna is an effective grazer of the G. semen alga. b. a very strong negative correlation between the number of grazers and the net growth rate of G. semen.

a. The scatterplot of the data shows a clear negative correlation between the number of D. magna grazers and the net growth rate of G. semen. As the number of grazers increases, the net growth rate of G. semen decreases. This suggests that D. magna is an effective grazer of the G. semen alga.

b. The correlation coefficient between the number of grazers and the net growth rate is -0.996. This indicates a strong negative correlation between the two variables, which supports the interpretation that D. magna is an effective grazer of G. semen. The closer the correlation coefficient is to -1, the stronger the negative correlation between the two variables. In this case, the correlation coefficient is very close to -1, which indicates a very strong negative correlation between the number of grazers and the net growth rate of G. semen.

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