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3 years ago

Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has vertices

Mathematics

2 answers:

zmey [24]3 years ago

5 0

The rule is (x - 3, y - 3).

gavmur [86]3 years ago

5 0

Answer:

Rotation about 90° counter clockwise (x , y) →→ ( -y, x ).

Step-by-step explanation:

Given : Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has vertices X'(–3, 1), Y'(0, 0), and Z'(–2, –1).

To find : Which rule describes the transformation.

Solution : We have given

vertices X(1, 3) →→ X'(–3, 1)

Y(0, 0) →→ Y'(0, 0),

Z(–1, 2) →→ Z'(–2, –1).

Here , we can see in each coordinates value of y become -x and x become y.

(x , y) →→ ( -y, x ) this the rule of rotation about 90° counter clockwise.

Therefore, rotation about 90° counter clockwise (x , y) →→ ( -y, x ).

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15 plus the difference of 10 and a number X is 15 (X=?)

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Is 7/8 equivalent to 3/4?

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3 years ago

12) Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

never [62]

Answer:

Part a) Domain of f : {-3, -2, -1, 0, 1, 2, 3}

Part b) Domain of g : {-1, 0, 1, 2, 3, 4}

Part c) Domain of f+g = {-1, 0, 1, 2, 3}

Part d) Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Step-by-step explanation:

Part a) Determining the domain of f

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

Part b) Determining the domain of g

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

As domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of g : {-1, 0, 1, 2, 3, 4}

Part c) Determining the domain of f+g

When there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains.

As,

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

and,

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

Domain of g : {-1, 0, 1, 2, 3, 4}

As when there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains

So, the domain of f+g = {-1, 0, 1, 2, 3}

Part d) List the ordered pairs of f-g

f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

and

g = {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

For f - g, we must focus on subtracting the second (y) coordinates of both function that correspond to the same element in the domain (x)

(f - g)(x) = f(x) - g(x)

(f - g)(x) = f(-1) - g(-1) = 14 - 4 = 10

(f - g)(x) = f(0) - g(0) = 7 - 5 = 2

(f - g)(x) = f(1) - g(1) = 4 - 6 = -2

(f - g)(x) = f(2) - g(2) = 5 - 1 = 4

(f - g)(x) = f(3) - g(3) = 7 - (-16) = 23

So,

Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Keywords: domain, function, f+g, f-g

Learn more about domain, and ordered pairs from brainly.com/question/11422136

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3 years ago

For the equation, find three ordered pair solutions by completing the table. Then use any two of the ordered pairs to graph the

Vikentia [17]

Answer:

Please see picture below.

Step-by-step explanation:

4 0

1 year ago

A safety officer wants to prove that μ = the average speed of cars driven by a school is less than 25 mph. Suppose that a random

Akimi4 [234]

Answer:

$t=\frac{24-25}{\frac{2.2}{\sqrt{14}}}=-1.70$

The degrees of freedom are given by:

$df=n-1=14-1=13$

The p value for this case would be given by:

$p_v =P(t_{(13)}$

Step-by-step explanation:

Information given

$\bar X=24$ represent the mean height for the sample

$s=2.2$ represent the sample standard deviation

$n=14$ sample size

$\mu_o =25$ represent the value that we want to test

t would represent the statistic

$p_v$ represent the p value for the test

Hypothesis to verify

We want to cehck if the true mean is lees than 25 mph, the system of hypothesis would be:

Null hypothesis: $\mu \geq 25$

Alternative hypothesis: $\mu < 25$

The statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$t=\frac{24-25}{\frac{2.2}{\sqrt{14}}}=-1.70$

The degrees of freedom are given by:

$df=n-1=14-1=13$

The p value for this case would be given by:

$p_v =P(t_{(13)}$

8 0

2 years ago