Which type of triangle will always have exactly 1-fold reflectional symmetry?

Answer:

3rd graph is the correct graph

Step-by-step explanation:

Given is the equation of hyperbola as

[tex]y = ± \sqrt{x^2-5}[/tex]

Square both sides and rearrange to get

[tex]y^2=x^2-5 \\x^2-y^2 =5[/tex]

Vertices are [tex](\sqrt{5} ,0) \\(-\sqrt{5} ,0)[/tex]

Asymptotes would have the same equation as hyperbola except constant term as 0

[tex]x^2-y^2 =0[/tex]

are the asymptotes

Or [tex]y = ± x[/tex] option d is right.

Answer:

The distance CC' is [tex]\sqrt5units[/tex]

Step-by-step explanation:

Given the transformation T:  (x, y) (x + 2, y + 1)

we have to find the distance CC'

Let coordinate of C are (a,b).

Now, by using transformation T the coordinates of C' are (a+2,a+1)

By using distance formula,

[tex]CC'=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\= \sqrt{(a+2-a)^2+(b+1-b)^2}\\\\=\sqrt{4+1}=\sqrt5 units[/tex]

Hence, the distance CC' is [tex]\sqrt5units[/tex]

Final answer:

The sum of the infinite geometric series 2 + 2/5 + 2/25 + 2/125 + ... is 2.5, determined by using the formula for the sum of a convergent geometric series, which in this case is S = 2 / (1 - 1/5).

Explanation:

The question you've asked relates to the sum of an infinite geometric series. The series given is 2 + 2/5 + 2/25 + 2/125 + ..., which is a series where each term after the first is found by multiplying the previous term by 1/5. To find the sum of this infinite geometric series, we can use the formula for the sum of a convergent geometric series, which is S = a / (1 - r), where 'S' is the sum of the series, 'a' is the first term, and 'r' is the common ratio (the factor we multiply by to get each term in the series).

In this case, the first term 'a' is 2, and the common ratio 'r' is 1/5. So our formula becomes S = 2 / (1 - 1/5), which simplifies to S = 2 / (4/5) or S = 2 * (5/4), which gives us S = 2.5. Therefore, the sum of the infinite geometric series is 2.5.

The correct set of equations based on the information given about the pricing of apples, bananas, and coconuts by Old MacDonald is: a + 5b + c = 14, 3a + 3b + 3c = 18, and a + 2b + 3c = 14.

The student is asking which set of equations corresponds to the problem given, involving prices for apples, bananas, and coconuts. In the context of this problem, variables a, b, and c represent the price of an apple, a banana, and a coconut, respectively. By analyzing the problem's given information, we can deduce the following equations:

These equations reflect the costs of different combinations of fruit based on the prices provided by Old MacDonald. To solve for the variables a, b, and c, we could use a system of linear equations.

Answer:

[tex]144.9\leq x\leq 145.5[/tex]

Step-by-step explanation:

Let x represent actual weight of object.

We have been that the weight of an object on a particular scale is 145.2 lbs. The measured weight may vary from the actual weight by at most 0.3 lbs.

[tex]|\text{Actual}-\text{Ideal}|\leq \text{Tolerance}[/tex].

Upon substituting our given values, we will get:

[tex]|x-145.2|\leq 0.3[/tex]

Applying absolute value rule [tex]|u|\leq a=-a\leq u\leq a[/tex], we will get:

[tex]-0.3\leq x-145.2\leq 0.3[/tex]

Add 145.2 on each side:

[tex]-0.3+145.2\leq x-145.2+145.2\leq 0.3+145.2[/tex]

[tex]144.9\leq x\leq 145.5[/tex]

Therefore, our required range will be [tex]144.9\leq x\leq 145.5[/tex].

Answer: [tex]c=12x+3[/tex], where c is the total cost of x pizzas.

The cost of 5 pizzas = $63

Step-by-step explanation:

Given : Cost of each pizza = $9.00

Cost of each topping =  $1.50

⇒ Cost of 2 toppings =  2 x $1.50 = $3.00

Then, the cost of each pizza having 2 toppings =  $9.00+  $3.00=  $12.00

Let x be the number of pizzas .

Then , the cost of x pizzas = 12x

Since , Delivery charge =  $3.00

Then, the total cost of ordering x pizzas( in dollars) =  Cost of x pizzas+ Delivery charge = 12x+3

Function rule to show the total cost of the pizzas if the pizza ordered has 2 toppings : [tex]c=12x+3[/tex] , where c is the total cost.

Put x= 5

[tex]c=12(5)+3=60+3=63[/tex]

Hence, the cost of 5 pizzas = $63

Answer:

GH

Step-by-step explanation:

Answer: The correct option is,

A. <

Step-by-step explanation:

Given,

[tex]8=x+y-----(1)[/tex]

Also,

[tex]y > 0[/tex]

Adding x on both sides ( additive property of inequality )

[tex]x+y>x+0[/tex]

[tex]x+y>x[/tex]

From equation (1),

[tex]8>x[/tex]

Hence, x is less than 8,

We use < sign for less than,

⇒ x is '<' 8

Option A is correct.

Answer:

The answer is 30.

Step-by-step explanation:

f(-4) = 20 when evaluated in the given function f(n) = n^2 - n. This result was obtained through substitution in the function followed by simplification.

In this problem, you are given a function f(n) = n^2 - n. To find the value of f(-4), you simply need to substitute -4 in place of n in the function and compute.

So,

f(-4) = (-4)^2 - (-4)

= 16 - (-4)

= 16 + 4 = 20

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Final answer:

The standard form equation of the line through the points (-1, 1) and (1, 4) is 3x - 2y = -5.

Explanation:

The standard form equation of a line can be represented as Ax + By = C, where A, B, and C are constants. To find the equation of the line through the points (-1, 1) and (1, 4), we can use the point-slope form.

First, find the slope using the formula m = (y2 - y1)/(x2 - x1). In this case, m = (4 - 1)/(1 - (-1)) = 3/2.

Next, choose one of the given points, let's say (-1, 1), and substitute the values into the point-slope formula. y - y1 = m(x - x1). We have y - 1 = (3/2)(x - (-1)).

Simplify the equation by distributing the slope and rearranging the terms. y - 1 = (3/2)x + 3/2.

Finally, convert the equation to standard form by moving all terms to one side and multiplying by a common denominator. 3x - 2y = -5.

Answer:

Its False c:

Step-by-step explanation:

Answer:

width of the rectangular prism is 4.5 inches.

Step-by-step explanation:

Carltren solves for w and writes the equivalent equation as [tex]w=\frac{V}{lh}[/tex]

Now, we have to find the width of a rectangular prism that has a volume of 138.24 cubic inches a height of 9.6 inches and a length of 3.2 inches.

Thus, we have

V = 138.24 cubic inches

l = 3.2 inches

h = 9.6 inches.

Substituting these values in the above formula to find w

[tex]w=\frac{138.24}{3.2\cdot9.6}[/tex]

On simplifying, we get

[tex]w=4.5[/tex]

Thus, width of the rectangular prism is 4.5 inches.

The equivalent of log base 27 of 9 is 2/3, as 27^(2/3) equals 9.

Thus, the correct answer is b. 2/3 among the provided choices.

To find an equivalent expression for log base 27 of 9, we need to determine the exponent to which 27 must be raised to obtain 9. In other words, we want to find x in the equation 27^x = 9.

Recognizing that 27 is 3^3 (as 3 times 3 times 3 equals 27), we can rewrite the equation as (3^3)^x = 9. Applying the exponent rule (a^b)^c = a^(bc), this simplifies to 3^(3x) = 9.

Now, equating the exponents, 3x = 2 since 3^2 equals 9. Solving for x, we find x = 2/3. Therefore, log base 27 of 9 is 2/3.

Among the provided choices:

a. 1/3

b. 2/3

c. 3/2

d. 0.798

The correct equivalent is b. 2/3, as it matches the determined value of log base 27 of 9.

The question probable may be:

Which of the following is equivalent to log27 9?

answer choices:

a 1/3

b 2/3

c 3/2

d 0.798

The equivalent of log base 27 of 9 is 2/3, as 27^(2/3) equals 9.

Thus, the correct answer is b. 2/3 among the provided choices.

We must ascertain the exponent to which 27 must be raised in order to

achieve 9 in order to discover an analogous formula for log base 27 of 9.

Put otherwise, we wish to determine x in the formula 27^x = 9.

Since 3 times 3 times 3 is 27, we may express the equation as (3^3)^x = 9 since we know that 27 is 3^3.

Applying the exponent rule (a^b)^c = a^(bc), this simplifies to 3^(3x) = 9.

Now, equating the exponents, 3x = 2 since 3^2 equals 9.

Solving for x, we find x = 2/3. Therefore, log base 27 of 9 is 2/3.

Among the provided choices:

a. 1/3

b. 2/3

c. 3/2

d. 0.798

The correct equivalent is b. 2/3, as it matches the determined value of log base 27 of 9.

Question

Which of the following is equivalent to log27 9?

answer choices:

a 1/3

b 2/3

c 3/2

d 0.798

Answer:

SV=   41 units

QT: 21 units

Step-by-step explanation:

hope it helps:)

Given TR = 17 units, TRS = 9x - 4, VRS = 3x + 2, and QRV = 4x + 1, with x ≈ 1.583. SV ≈ 6.749 units and QT ≈ 7.332 units.

To find the lengths of SV and QT, we'll first set up equations based on the given relationships between the lengths of the segments.

Given:

- Length of TR = 17 units

- Length of TRS = 9x - 4

- Length of VRS = 3x + 2

- Length of QRV = 4x + 1

We need to find the lengths of SV and QT.

1. Length of TRS + Length of VRS = Length of TR (by the segment addition postulate)

  9x - 4 + 3x + 2 = 17

  12x - 2 = 17

  12x = 17 + 2

  12x = 19

  x = 19 / 12

  x ≈ 1.583

Now that we have found the value of x, we can find the lengths of SV and QT.

2. Length of SV = Length of VRS = 3x + 2

  Length of SV = 3(1.583) + 2

                 ≈ 4.749 + 2

                 ≈ 6.749 units

3. Length of QT = Length of QRV = 4x + 1

  Length of QT = 4(1.583) + 1

                 ≈ 6.332 + 1

                 ≈ 7.332 units

So, the lengths are:

- SV ≈ 6.749 units

- QT ≈ 7.332 units

Answer:

D

Step-by-step explanation: