Which sequence of transformations confirms congruence by mapping shape I onto shape II?

A. a reflection across the x-axis and then a translation 15 units left

B. a 90° clockwise rotation about the origin and then a translation 25 units up

C. a 90° counterclockwise rotation about the origin and then a translation 10 units left

D. a 180° rotation about the origin and then a translation 10 units right

a) So we know the formula of finding the circumference: 2*pi*R.

Assuming we make pi = 3.14:     2 * 3.14 * 7 = 43.96.

b) We also know the formula of finding the area: pi * r^2.

3.14 * 7^2. Using PEMDAS:

3.14 * 49 = 153.86

Answer:

c) 2/5

Step-by-step explanation:

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Final answer:

The choice that is NOT equal to the others is C) 2/5, because it is the only positive fraction, while the others represent the negative fraction − 2/5.

Explanation:

The student's question asks which of the given choices is NOT equal to the others. The choices provided include A) − 2/5, B) − 2/5, C) 2/5, and D) 2/ −5. To find the answer, we must compare the values.

Options A and B are the same, which is − 2/5 or negative two-fifths. Option D, which is 2/−5, simplifies to − 2/5 because division by a negative number yields a negative result, making it equivalent to options A and B. However, option C is the only one that is different because it is 2/5, which is positive two-fifths, not negative. Therefore, the answer is C) 2/5 as it is not equal to the other options, which are all negative two-fifths.

Answer:

12

Step-by-step explanation:

The given geometric series is

[tex] \sum_{n = 1}^{ \infty} 12( { - \frac{1}{9} })^{n - 1} [/tex]

We want to determine the first term of this geometric series.

Recall that the explicit formula is

[tex] a_{n} = 12( { - \frac{1}{9} })^{n - 1} [/tex]

To find the first term, we put n=1 to get:

[tex]a_{1} = 12( { - \frac{1}{9} })^{1 - 1} [/tex]

This gives us:

[tex]a_{1} = 12( { - \frac{1}{9} })^{0}[/tex]

[tex]a_{1} = 12(1) = 12[/tex]

Therefore the first term is 12

Answer:

12

Step-by-step explanation:

The last option, C is the answer. I just took the quiz :D

Answer:

See explanation

Step-by-step explanation:

PQRS is a parallelogram, then

[tex]PQ\parallel RS\\ \\QR\parallel SP[/tex]

and

[tex]PQ\cong RS\\ \\QR\cong SP[/tex]

Also

[tex]\angle P\cong \angle R\\ \\\angle Q\cong \angle S[/tex]

1. Consider triangles PQA and RQA, where A is the diagonals intersection point. In these triangles,

[tex]QA\cong QA\ [\text{Reflexive property}][/tex]

[tex]\angle PQA\cong \angle RQA\ [\text{Because QS is angle bisector}][/tex]

[tex]\angle QPA\cong \angle QRA\ [\text{Diagonal PR divides congruent angles in congruent halves}][/tex]

Hence, by AAS postulate triangles PQA and RQA are congruent. Congruent triangles have congruent corresponding parts, so

[tex]PQ\cong RQ[/tex]

2. Consider triangles PSA and RSA. In these triangles

[tex]SA\cong SA\ [\text{Reflexive property}][/tex]

[tex]\angle PSA\cong \angle RSA\ [\text{Because QS is angle bisector}][/tex]

[tex]\angle SPA\cong \angle SRA\ [\text{Diagonal PR divides congruent angles in congruent halves}][/tex]

Hence, by AAS postulate triangles PSA and RSA are congruent. Congruent triangles have congruent corresponding parts, so

[tex]PS\cong RS[/tex]

3. Since [tex]PQ\cong RS[/tex] and [tex]PQ\cong RQ[/tex], you have [tex]RS\cong RQ[/tex]

Therefore,

[tex]PQ\cong QR\cong RS\cong SP[/tex]

Parallelogram with all congruent sides ia a rhombus.

Answer:

132

Step-by-step explanation:

65+67=132 || 180-132=48 || 180-48=132

Answer:

132 Degrees.

Step-by-step explanation:

The interior of any triangle is 180 degrees.

Solve for angle DBC

65 + 67 = 132

180 - 132 = 48 degrees

Since the sum of DBA and DBC is 180, and we already know what 180 - 48 is, there you have it.

Answer:

see explanation

Step-by-step explanation:

Using the Addition/ Subtraction formulae for cosine

Consider the left side

cos(x - y) - cos(x + y)

= cosxcosy + sinxsiny - (cosxcosy - sinxsiny) ← distribute

= cosxcosy + sinxsiny - cosxcosy + sinxsiny ← collect like terms

= 2sinxsiny = right side ⇒ proven

Answer:

399

Step-by-step explanation:

Answer:

B.)

87.92 feet

Step-by-step explanation:

Given:

Area of the circular garden [tex]= 615.44 ft^2[/tex]

      [tex]\pi =3.14[/tex]

 Finding the radius of the circle.

Area of the circle= [tex]\pi r^2[/tex]

          [tex]615.44=\pi *r^2[/tex]

             [tex]r^2=\frac{615.44}{\pi } \\\\r^2=\frac{615.44}{3.14} \\r^2=196\\r=14 ft.[/tex]

Circumference of the garden:

                                           [tex]=2\pi r\\=2*3.14*14\\=87.92ft.[/tex]

None of the given points are solutions to the inequality.

To determine which of the given points is a solution to the inequality y > 1/2x + 2, you need to substitute the coordinates of each point into the inequality and check if the inequality holds true.

Let's start with point (1, 4):

4 > 1/2 * 1 + 2

4 > 1/2 + 2

4 > 2.5 + 2

4 > 4.5

The inequality does not hold, so point (1, 4) is not a solution to the inequality.

Now, let's try point (-1, 1):

1 > 1/2 * -1 + 2

1 > -1/2 + 2

1 > 1.5

The inequality does not hold, so point (-1, 1) is not a solution to the inequality.

Similarly, checking for points (2, 3) and (0, 2), we find that neither of them satisfy the inequality.

Therefore, none of the given points, (1, 4), (-1, 1), (2, 3), or (0, 2), are solutions to the inequality y > 1/2x + 2.

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Answer: C: 0 < x < 31

Step-by-step explanation: Because the < sign shows the line is going up towards the top. It starts from 0 and travels to the top-right to 31

A reasonable domain for this function to have would be 0 ≤ x ≤ 31.

We have f(x) as the number of fishes that are present in this water. The month is October and October has 31 days.

The x values is the maximum of the number of days in October. The minimum value is given as 0 because it is the population in the beginning of the month.

Hence we have 0 ≤ x ≤ 31

Which of the following is a reasonable domain for the function?

0 ≤ x ≤ 100

0 ≤ x ≤ 31

All positive integers greater than 100

All positive integers less than 100

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Length of base of isosceles triangle, x = 7

Step-by-step explanation:

Length of one leg = 3x - 4. Since two sides, other than the base of an isosceles triangle are equal, the length of the other leg = 3x - 4.

⇒ 41 = x + (3x - 4) + (3x - 4) = x + 2(3x - 4)

⇒ 41 = x + 6x - 8

⇒ 41 = 7x - 8

⇒ 49 = 7x

⇒ x = 7

Answer:

7

Step-by-step explanation:

To find the length of the rectangle, use the given information about the width and perimeter. Solve the equations to find the values of the variables and determine the length of the rectangle.

To find the length of the rectangle, we can use the information given in the problem. Let's let the width be represented by W and the length be represented by L. We are told that the length is 26 feet more than the width, so we can write the equation L = W + 26. We are also given that the perimeter of the rectangle is 60 feet, so we can write the equation 60 = 2(W + L). We can substitute the value of L from the first equation into the second equation to solve for W. After finding the value of W, we can substitute it back into the first equation to find the value of L.

Let's start with the first equation: L = W + 26. Since we have an equation with two variables, we'll need to use the second equation to solve for the variables. Let's substitute the value of L in the second equation: 60 = 2(W + (W + 26)). We can simplify this equation by combining like terms: 60 = 2(2W + 26). We can distribute the 2 to the terms inside the parentheses: 60 = 4W + 52. We can then subtract 52 from both sides of the equation: 8 = 4W. Finally, we can divide both sides of the equation by 4 to solve for W: W = 2.

Now that we have the value of W, we can substitute it back into the first equation L = W + 26. This gives us: L = 2 + 26. We can simplify this equation to find that L = 28.

Answer:

Step-by-step explanation:

20

Answer:

Scale factor = 5:8

Step-by-step explanation:

Step 1:  Write out as a scale

10cm : 16cm

Step 2:  Simplify

10 / 2 : 16 / 2

5:8

Answer:  Scale factor = 5:8

Solve by elimination.

 2x-3y=-19

+(4x+3y=7)

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

6x=-12

x=-2

2(-2)-3y=-19

-3y=-15

y=5

Intersection Point: (-2,5)

Answer:

Emma = 378 votes

Step-by-step explanation:

Carol = 189 votes

Emma = 2 * Carol

Substitute 189 in for Carol

Emma = 2 * 189

Emma = 378 votes

Hope this helps :)

Answer:

378

Step-by-step explanation:

you just had to multiply 189 by 2. Since twice means 2

The solutions to the quadratic equation 2x^2 - 8x + 7 = 0 are x = 2 + √2 / 2 and x = 2 - √2 / 2 using the quadratic formula.

To solve the equation 2x2 - 8x + 7 = 0, we will use the quadratic formula, where 'x' equals minus 'b', plus-or-minus the square root of 'b' squared minus four 'a' 'c', all over two 'a'. The coefficients in this case are a = 2, b = -8, and c = 7.

First, we calculate the discriminant, which is b2 - 4ac. Substituting our values we get:

(-8)2 - 4(2)(7) = 64 - 56 = 8.

The square root of 8 can be simplified to 2√2, because 8 = 4 × 2 and √4 = 2.

Finally, we substitute the values into the quadratic formula:

x = (-(-8) ± √8) / (2 × 2)

x = (8 ± 2√2) / 4

Dividing each term by 4 gives us:

x = 2 ± √2 / 2

Therefore, the solutions to the equation are:

x = 2 + √2 / 2 and x = 2 - √2 / 2

Answer:

d

Step-by-step explanation:

[tex]-\frac{6}{5}[/tex] is rational

3.5 is rational

0.5 repeating is rational

[tex]\sqrt{4}[/tex] is rational

[tex]\sqrt{5}[/tex] is NOT rational

The answer correct answer is D.

Answer:

Step-by-step explanation:

let P represent the perimeter of the rectangle

P = 2×(12 + 18) = 2×(30) = 60 m

then

the number of shrubs = 3×(60) = 180

Answer:

(x + 4)² + (y + 5)² = 73

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 4, - 5), thus

(x - (- 4))² + (y - (- 5))² = r², that is

(x + 4)² + (y + 5)² = r²

The radius is the distance from the centre to a point on the circle.

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (4, - 2)

r = [tex]\sqrt{(4+4)^2+(-2+5)^2}[/tex]

  = [tex]\sqrt{8^2+3^2}[/tex]

 = [tex]\sqrt{64+9}[/tex] = [tex]\sqrt{73}[/tex] ⇒ r² = 73, thus

(x + 4)² + (y + 5)² = 73 ← equation of circle

Answer: [tex](x+4)^{2} +(y+5)^{2} = 73[/tex]

Step-by-step explanation:

the formula for finding equation of circle is given as :

[tex](x-a)^{2}+(y-b)^{2} = r^{2}[/tex]

where ( a,b) is the coordinate of the center and r is the radius

The radius is the distance between the point and the center , the formula for calculating the distance between two points is given by :

d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

d = [tex]\sqrt{(4-(-4))^{2}+(-2-(-5))^{2}}[/tex]

[tex]d = \sqrt{(4+4)^{2}+(-2+5)^{2}}[/tex]

[tex]d = \sqrt{8^{2}+3^{2}}[/tex]

[tex]d = \sqrt{73}[/tex]

since "r" is the distance , then

[tex]r = \sqrt{73}[/tex]

The the equation of the circle , using the formula [tex](x-a)^{2}+(y-b)^{2} = r^{2}[/tex] , will be

[tex](x+4)^{2} +(y+5)^{2} = 73[/tex]

Answer:

Step-by-step explanation:

Answer:

28)  B

33)  D

Step-by-step explanation:

28)   Numbers on the dice

1, 2, 3, 4, 5, 6

Numbers greater than 4

5, 6

There are 2 possibilities of rolling a number greater than 4 on the cube

2 numbers greater than 4 / Total amount of numbers

2/6 = 1/3

There is a 1/3 chance of rolling a number greater than 4

If the cube is tossed 120 times, about 1/3 of the time the number will be greater than 4

120 (1/3) = 120/1 * 1/3  = 120/3 = 40

The best estimate is 40 times, B

33)

These are all of the possibilities:

W - shaded

W - unshaded

X - shaded

X - unshaded

Y - shaded

Y - unshaded

Z - shaded

Z - unshaded

The answer that corresponds with all of these possibilities is D

Hope this helps :)

Answer:

X=7

Y=10

Step-by-step explanation:

Replace expression Y=2x-4 in 17x + 36y = 479

Now, replace X=7 in expression Y=2x-4

Step-by-step explanation:

[tex]area \: of \: sector = \frac{ \theta}{360 \degree} \times \pi {r}^{2} \\ \\ = \frac{110\degree}{360\degree} \times 3.14 \times {(16)}^{2} \\ \\ = \frac{110\degree}{360\degree} \times 3.14 \times 256 \\ \\ = \frac{88,422.4}{360} \\ \\ = 245.617778 \\ \\ \approx245.62 \: {in}^{2} [/tex]

No if you simplify 27/8 it equals 3 3/8.

2([tex]\frac{2}{5}[/tex]x + 4) =  [tex]\frac{4}{5}[/tex]x + 4 which is the second option is the equivalent expression.

Explanation:

First,  we need to calculate the value of two-fifths of x. It means 2 portions out of the five portions of x which equates to [tex]\frac{2}{5}[/tex]x.

Now we calculate the values of the two expresssions on the LHS.

1) 2 (two-fifths x + 2) = 2 ([tex]\frac{2}{5}[/tex]x + 2) = [tex]\frac{4}{5}[/tex]x + 4.

2)  (two-fifths x + 4) = 2([tex]\frac{2}{5}[/tex]x + 4) =  [tex]\frac{4}{5}[/tex]x + 8.

Now we determine values of the four expressions on the RHS.

1) Two and two-fifths x + 1 = 2[tex]\frac{2}{5}[/tex]x + 1

2) Four-fifths x + 4 = [tex]\frac{4}{5}[/tex]x + 4

3) Four-fifths x + 2 = [tex]\frac{4}{5}[/tex]x + 2

4) Two and two-fifths x + 8 = 2[tex]\frac{2}{5}[/tex]x + 8.

Out of the various LHS and RHS values, the [tex]1^{st}[/tex] LHS value and [tex]2^{nd}[/tex] RHS value is the same. So option 2 is the answer.

Answer:

second option

Step-by-step explanation:

Step-by-step explanation:

We have,

f(x) = (x + 9)(x − 4)(6x + 1)

To find, all zeroes of the given equation = ?

∴ f(x) = (x + 9)(x − 4)(6x + 1)

⇒ (x + 9)(x − 4)(6x + 1) = 0

⇒ x + 9 = 0 or, x − 4 = 0 or, 6x + 1 = 0

⇒ x + 9 = 0 ⇒  x = - 9

⇒ x − 4 = 0 ⇒ x = 4

⇒ 6x + 1 = 0

⇒ 6x = - 1

⇒ x = [tex]\dfrac{-1}{6}[/tex]

∴ x = - 9 , [tex]\dfrac{-1}{6}[/tex], 4

Thus, the required 'option a)  - 9 , [tex]\dfrac{-1}{6}[/tex], 4' is correct.

Final answer:

To find the zeros of the function f(x) = (x + 9)(x − 4)(6x + 1), we solve for x in each factor: x = -9, x = 4, and x = -1/6, which means the zeros are -9, 4, and -1/6.

Explanation:

To identify the zeros of a function, you need to find the values of x for which the whole expression equals zero. The function given is f(x) = (x + 9)(x − 4)(6x + 1). To find the zeros, we set each factor equal to zero and solve for x.

(x + 9) = 0 → x = -9

(x − 4) = 0 → x = 4

(6x + 1) = 0 → 6x = -1 → x = -1/6

Therefore, the zeros of the function are -9, 4, and -1/6.

Answer: the answe is b

Step-by-step explanation:

The left side of the data looks similar to the right side in the seventh-grade data, but not in the fifth-grade data.

A dot plot is a method of visually representing expectations for some data series. A dot plot visually groups the number of data points in a data set based on the value of each point.

2 dot plots with number lines going from 0 to 10.

A dot plot titled fifth grade has 0 dots above 0, 2 above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, and 0 and 9 and 10.

A dot plot titled seventh grade has 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.

statement correctly compares the shape of the data in the plots

The left side of the data looks similar to the right side in the seventh-grade data, but not in the fifth-grade data.

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Answer:

For x = 0, the value of y will be 10 miles.

Step-by-step explanation:

Mark is in training for a marathon race. Each day he runs 10 miles for this training purpose. He will  be increasing his running by this weekly formula: [tex]y = 10(1.1)^{x}[/tex], where y is the number of miles he  will run each day, x represents the number of weeks from now.

Now, for x = 0, the value of y will be [tex]y = 10(1.1)^{0} = 10[/tex] miles. (Answer)

Answer:

The Value of y is 10

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

give me brainly

Final answer:

To express 0.230769231 as a fraction, the numerator is 230769231 and the denominator is 10^9.

Explanation:

To express the decimal 0.230769231 as a fraction, we need to determine the numerator and denominator. The numerator is the decimal without the decimal point, which is 230769231. The denominator is based on the number of decimal places, which is 9 because there are 9 digits in the decimal part. Therefore, the fraction is 230769231/10^9.