a transformation is applied to a figure to create a new figure on a coordinate grid. which transformation does not preserve congruence?

Answer:

First Question x = \(17\sqrt{2}\) Second Question x = 36

Step-by-step explanation:

First Question:

Since The triangle is isosceles, \(17^2 +17^2=x^2\) (Pythagoras)

\(x=17\sqrt{2}\)

Second Question

This is half an equilateral triangle, so \((\frac{1}{2}x)^2+(18\sqrt{3})^2=x^2\)

\(\frac{3}{4}x^2=972\)

\(x^2=1296\)

\(x=36\) (cannot be negative)

Hope you understand :)

Answer: C=59° b=5.5 c= ??

Step-by-step explanation:

Answer:

-16¹/₂ feet per second

Step-by-step explanation:

average change in altitude in feet per second = change in altitude in feet/change in time in seconds

= -41¹/₄ ft ÷ 2¹/₂ s

= -165/4 ft ÷ 5/2 s

= -165/4 × 2/5 ft/s

= -33/2 feet per second

= -16¹/₂ feet per second

Answer:

D

Step-by-step explanation:

Intersecting, but not perpendicular lines

Answer:d

D is the answer

Given the following inequality:

We will solve the inequality as follows:

First, add 2 to both sides

Second, divide both sides by 2

So, the answer will be, the solution using interval notation is as follows:

Answer:the slope is 2

Step-by-step explanation:

rise over run 2/1

Answer:

2

Step-by-step explanation:

The line rises by 2 and runs by 1.

Answer:

Te conozco y sé qué

Como Nuevo de fabrica el otro

Answer:

None are you sure you have the right expressions.

Step-by-step explanation:

(4x^4/2x^3)^3=(2x^4*x^3)^3=(2x^7)^3=8x^21

Step-by-step explanation:

the question is about distance.

what do we use to measure distance ? things like feet, yards, meters, ...

definitely not square feet (areas) or cubic feet (volume).

it is a right-angled triangle. so Pythagoras applies

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle). in our case the 48 ft side.

a and b are the legs. in our case x and x+6.

the saved walking distance is the difference between 48 ft and the sum of the legs (which would be the walking distance, when they cannot get though the lot).

48² = x² + (x + 6)² = x² + x² + 12x + 36

2304 = 2x² + 12x + 36

1152 = x² + 6x + 18

x² + 6x - 1134 = 0

the solution for such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a) =

= (-6 ± sqrt(6² - 4×1×-1134))/(2×1) =

= (-6 ± sqrt(36 + 4536))/2 =

= (-6 ± sqrt(4572))/2 =

= -3 ± sqrt(4572/4) = -3 ± sqrt(1143) =

= -3 ± sqrt(9×127) = -3 ± 3×sqrt(127)

x1 = -3 + 3×sqrt(127) = 30.80828301...

x2 = -3 - 3×sqrt(127) = -36.80828301...

negative numbers for a distance don't make any sense, so

x = 30.80828301... is our solution.

that means the 2 legs are

30.80828301... ft

36.80828301... ft

in total they are

67.61656602... ft

and so they save

67.61656602... - 48 = 19.61656602... ft ≈

≈ 19.617 ft

by walking across the lot.

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)

The number of ounces per golf ball is 1.6

The number of golf balls per ounce is 0.625

In mathematics, a model refers to a simplified representation of a real-world system or phenomenon that is used to better understand or analyze it.

Models can be created using various mathematical techniques and tools, such as equations, functions, graphs, and simulations.

Since the package contains 20 golf balls and the total weight of the golf balls is 32 ounces. We can say:

The number of ounces per golf ball = 32/20 = 1.6

The number of golf balls per ounce = 20/32 = 0.625

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Answer:

6²

Step-by-step explanation:

it's 12 and 3 on 4 sides sums up to 12

Answer:

6^2

Step-by-step explanation:

A perfect square number is an integer that is the square of another integer

Therefore, 6^2 is a perfect square number

Answer:

x= r/s+t

Step-by-step explanation:

The value of an excel formula that will square this number is,

⇒ N²

We have to given that;

A number is stored in cell a1.

Hence, We can formulate;

Type = N² into the empty cell, in which N is a cell reference that contains the numeric value you want to square.

And, We also get;

To display the square of the value in cell A1 into cell B1,

We can type = A1² into cell B1.

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To minimize costs, the optimal distribution schedule for Finnish Furniture would involve shipping 130 units from Reno to Phoenix, 20 units from Denver to Cleveland, and 160 units from Pittsburgh to Chicago. This allocation is determined by using the transportation algorithm, specifically the Vogel's Approximation Method (VAM), which considers the lowest shipping costs per unit for each source-destination combination. By following this approach, the total cost for the distribution is calculated to be $4,360.

To determine the optimal distribution schedule that minimizes costs, we need to allocate the available supplies from the manufacturing facilities to the retail stores based on the shipping costs per unit. We can achieve this by employing the transportation algorithm, such as the North-West Corner Rule or the Vogel's Approximation Method (VAM).

Using VAM, we begin by identifying the lowest shipping cost per unit for each row and column in the given table. We then select the highest difference between the two lowest costs, considering both rows and columns. This difference indicates the most cost-effective allocation.

In this case, the VAM suggests shipping 130 units from Reno to Phoenix since the shipping cost per unit is 10, which is the lowest for the Reno row. For Cleveland, Denver has the lowest cost at 14, so we allocate 20 units from Denver to Cleveland. Lastly, we allocate 160 units from Pittsburgh to Chicago, as the cost per unit is the lowest at 12 for the Pittsburgh column.

Now, let's calculate the total cost. The cost of shipping 130 units from Reno to Phoenix is 130 x 10 = $1,300. Shipping 20 units from Denver to Cleveland costs 20 x 14 = $280. Lastly, shipping 160 units from Pittsburgh to Chicago costs 160 x 12 = $1,920. Adding these costs together gives us a total cost of $1,300 + $280 + $1,920 = $4,360.

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The standard deviation of quiz scores is 0.

To find the standard deviation:

Therefore, the standard deviation of quiz scores is 0.

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Answer:

7 x 2 is 14.

Step-by-step explanation:

Its the same thing as 7 plus 7.

The Multiplication of 7 and 2 results to 14.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

We have to multiply 7 x 2.

So, we can either add 7 two times as

= 7 + 7

= 14

or we can multiply it

= 7 x 2

= 14

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Answer:

Rate of plane in still air = 1120 km/h

Rate of wind = 180 km/h

Step-by-step explanation:

Let the rate (speed) of the plane in still air = u km/h

Let the rate (speed) of the wind = v km/h

Formula for speed is:

\(Speed = \dfrac{Distance}{Time}\)

Given that against the wind, airplane travels 7520 km in 8 hours.

The speed against the wind will be slower so,

Against the wind, speed = (u -v ) km/h

Using above formula:

\((u-v) = \dfrac{7520}{8} km/h\\(u-v) = 940 km/h ..... (1)\)

Given that with the wind, airplane travels 6500 km in 5 hours.

The speed with the wind will be faster so,

With the wind, speed = (u +v ) km/h

Using above formula:

\((u+v) = \dfrac{6520}{5} km/h\\(u+v) = 1300 km/h ..... (2)\)

Adding (1) and (2) to solve for u and v:

\(2u = 2240\\\Rightarrow u = 1120\ km/h\)

Putting u in (1):

\(1120-u=940\\\Rightarrow u = 180\ km/h\)

So, the answers are:

Rate of plane in still air = 1120 km/h

Rate of wind = 180 km/h

The set of natural numbers divisible by 5 contains a countably infinite number of numbers.

A countable set is a set that can be put into one-to-one correspondence with the natural numbers. The set of natural numbers divisible by 5 can be put into one-to-one correspondence with the natural numbers by creating the following function:

f(n) = 5n

This function maps each natural number to the natural number that is 5 times larger. For example, f(1) = 5, f(2) = 10, and so on.

Since the natural numbers are countable, and the set of natural numbers divisible by 5 can be put into one-to-one correspondence with the natural numbers, the set of natural numbers divisible by 5 is also countable.

In other words, there are an infinite number of natural numbers divisible by 5, but we can still count them one by one.

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=====================================================

Explanation:

The value 12 is between the perfect squares 9 and 16

This means we can write the following inequality \(9 < 12 < 16\)

From here we apply the square root to all three sides and simplify like so

\(9 < 12 < 16\\\\\sqrt{9} < \sqrt{12} < \sqrt{16}\\\\3 < \sqrt{12} < 4\)

and we see that the square root of 12 is between 3 and 4.

Using a calculator would confirm this

\(\sqrt{12} \approx 3.464\)

Answer:

Step-by-step explanation:

Find the numbers closest to 12 on either side that are perfect squares:

1, 4, 9, 16, 25

12 is in between the numbers 9 and 16. The square root of 9 is 3 and the square root of 16 is 4. Therefore, the square root of 12 is in between 3 and 4.

Answer: C

Step-by-step explanation:

I think this one is it?

Answer:

c

Step-by-step explanation:

A) The end behavior of a polynomial graph is determined by the degree and leading coefficient of the polynomial. There are four possible cases:

1. Polynomial in standard form with an even degree:

If the leading coefficient (the coefficient of the highest degree term) is positive, the graph approaches positive infinity as x approaches both positive and negative infinity. If the leading coefficient is negative, the graph approaches negative infinity as x approaches both positive and negative infinity. This can be expressed as:

- Positive leading coefficient: f(x) → +∞ as x → ±∞

- Negative leading coefficient: f(x) → -∞ as x → ±∞

2. Polynomial in standard form with an odd degree:

Regardless of the leading coefficient, the graph approaches positive infinity as x approaches positive infinity and approaches negative infinity as x approaches negative infinity. This can be expressed as:

- f(x) → +∞ as x → +∞

- f(x) → -∞ as x → -∞

3. Polynomial in factored form with an even degree:

The end behavior of the graph depends on the signs of the leading coefficient and the factors with even powers. If the leading coefficient is positive and the factors with even powers are positive, the graph approaches positive infinity as x approaches both positive and negative infinity. If the leading coefficient is negative and the factors with even powers are positive, the graph approaches negative infinity as x approaches both positive and negative infinity. The behavior can be expressed as:

- Positive leading coefficient and positive even powers: f(x) → +∞ as x → ±∞

- Negative leading coefficient and positive even powers: f(x) → -∞ as x → ±∞

4. Polynomial in factored form with an odd degree:

The end behavior of the graph depends on the signs of the factors with odd powers. Regardless of the leading coefficient, if the factors with odd powers are positive, the graph approaches positive infinity as x approaches positive infinity and approaches negative infinity as x approaches negative infinity. The behavior can be expressed as:

- f(x) → +∞ as x → +∞

- f(x) → -∞ as x → -∞

B) The x-intercepts of a polynomial are the values of x where the graph intersects the x-axis. To find the x-intercepts:

1. Polynomial in standard form:

Set the polynomial equation equal to zero and solve for x. The solutions will give the x-intercepts. For example, consider the polynomial f(x) = ax^2 + bx + c. Set f(x) = 0 and solve the quadratic equation using factoring, completing the square, or the quadratic formula.

2. Polynomial in factored form:

The x-intercepts can be directly read from the factored form of the polynomial. If the polynomial is written as f(x) = a(x - r1)(x - r2)...(x - rn), where r1, r2, ..., rn are the roots of the polynomial, then the x-intercepts are the values r1, r2, ..., rn.

The graph can behave differently at the x-intercepts depending on the multiplicity of the roots. If a root has an odd multiplicity, the graph crosses the x-axis at that point. If a root has an even multiplicity, the graph touches or bounces off the x-axis at that point.

C) The y-intercept of a polynomial is the value of y when x is equal to zero. To find the y-intercept:

1. Polynomial in standard form:

Evaluate the polynomial by substituting x = 0 into the equation. The resulting value will be the y-coordinate of the y-intercept. For example, consider the polynomial f(x

) = ax^2 + bx + c. Substitute x = 0 to find f(0) = c, which gives the y-intercept as (0, c).

2. Polynomial in factored form:

To find the y-intercept from the factored form, set x = 0 in the equation and calculate the corresponding value of y. If the polynomial is written as f(x) = a(x - r1)(x - r2)...(x - rn), substituting x = 0 yields f(0) = a(-r1)(-r2)...(-rn), which gives the y-intercept as (0, a(-r1)(-r2)...(-rn)).

In both cases, the y-intercept is expressed as a coordinate point (0, y), where y is the calculated value.

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Answer:

\(75 {x}^{ \frac{3}{2} } {y}^{6} {z}^{ \frac{11}{2} } \)

Step-by-step explanation:

First thing is to multiply. We don't need to bother with the root for now.

\( \sqrt{15 {x}^{2} {y}^{11} {z}^{4} } \times \sqrt{5xy {z}^{7} } = \\ \sqrt{75 {x}^{3} {y}^{12} {z}^{11} } \)

All I did was multiply the numbers and added the exponents for the variables.

Now all we have to do is divide the exponents in half for the variables, nothing is needed additionally for the 75.

\(75 {x}^{ \frac{3}{2} } {y}^{6} {z}^{ \frac{11}{2} }\)

There you go, just a few steps and you have your answer.

You can simplify further by moving the answer for the root infront of the square root so it isn't as sloppy. This would make the simplest for to be

5xyz^5 (3xy)^(1/2)

Answer:

Well for the answers I believe

a. 5/32

b. 15

c. 16/21

d. 81/8

Step-by-step explanation:

For a. 5/8 divided by 4, I multiplied 5/8 times 1/4 to get 5/32

For b. 5 divided by 1/3, I multiplied 5 by 3 to get 15

For c. 1 7/9 divided by 2 1/3, I first made them into inproper fractions which is 16/9 divided by 7/3. Afterwards I wrote 16/9 multiply by 3/7... simplify that and I got 16/21

For d. 4 1/2 multiplied by 2 1/4, I turned them into improper fractions, multiplied and got 81/8

What do you need help with?

The distance between two points a and b on the real line is given by the absolute difference between the two points, which is calculated as the positive difference between the values of a and b regardless of their order.

The distance function, denoted as d(a, b), is a metric that satisfies the properties of non-negativity, symmetry, and the triangle inequality. It is used to quantify the distance between two points in one-dimensional space, and is an important concept in geometry, analysis, and other fields of mathematics. The distance formula can be extended to higher dimensions and is used in various applications such as optimization, clustering, and machine learning.

The distance between two points a and b on the real line is given by the absolute difference between the two points: d(a, b) = |a - b|

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Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Answer: We need 2.5 quarts of yellow paint.

Step-by-step explanation:

As per given, The ratio of blue paint to yellow paint is \(\frac34: \frac{5}{6}\).

\(=3\times6:5\times4\\\\=18:20\\\\ =9:10\)

Total green paint = \(4\frac34\) quarts

Quantity of yellow paint required = \(\frac{10}{9+10}\times4\frac34\)

\(=\frac{10}{19}\times\frac{19}{4}\\=\frac{5}{2}\\=2.5\ $$ quarts$$\)

Hence, We need 2.5 quarts of yellow paint.