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3 years ago

Identify a sequence of transformation that maps triangle ABC onto triangle A"B"C" in the image below.

Mathematics

2 answers:

Vladimir79 [104]3 years ago

5 0

I'd go with: D. clockwise 90 rotation; reduction

(Hope I helped :D

tia_tia [17]3 years ago

5 0

Answer:

C counterclockwise 90 rotation; enlargement

Step-by-step explanation:

From the photo, we can see that triangle A"B"C" is the product of triangle ABC after the transformation.

Please have a look at point C on line y-axis and after that it lies on x-axis. So we have possible reasons:

1. rotated either counterclockwise 90°

2. rotated clockwise 270°.

The rule is: $(x,y)\rightarrow (-y,x)$

The corresponding sides of image A"B"C" are bigger than the preimage ABC.

$k=\frac{A"B"}{AB}=\frac{6}{2}=3 > 0$

Because k >0, the transformation shows the enlargement

So we choose option C counterclockwise 90 rotation; enlargement

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Two less than two thirds times a number is ten

beks73 [17]

Let the number be x
2/3*x - 2 = 10
or, 2/3 * x =12
or x= 12*3/2
or, x = 18

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3 years ago

1.Anthony has decided to purchase a $19,000 car. He plans to put 20% down toward the purchase and to finance the rest at a 6.8%

Nikitich [7]

<h2>First step/Equation</h2>

Answer:

$362.57

Step-by-step explanation:

A suitable calculator or finance app can find the monthly payment for you. This result comes from a TI-84 calculator.

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The second attachment shows the parameters of the payment function. With 20% down, Anthony is only financing 80% of the price of his car. Of course, there are 12 months in a year, so 4 years worth of payments will be 48 payments. The calculator uses negative values for amounts you pay.

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No doubt your reference material shows you a formula for computing loan payments. One such is ...

A = Pr/(1 -(1+r)^-n)

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2 years ago

2 divided by one over 3 the awnser is a fraction

slamgirl [31]

Answer:

That would equal $\frac{2}{3}$ or approximately 0.67. If this helps, please rank Brainliest. Thanks!

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3 years ago

Read 2 more answers

Jamel watched his older brother Robert lift weights. The bar alone had a mass of 20 kg. On the bar he had tow 11.4 kg weights, t

slavikrds [6]

All you do is add them all together...
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3 years ago

What would y=x^2 +x+ 2 be in vertex form

balu736 [363]

Answer:

$y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

Step-by-step explanation:

$y = {x}^{2} + x + 2$

We can covert the standard form into the vertex form by either using the formula, completing the square or with calculus.

$y = a(x - h)^{2} + k$

The following equation above is the vertex form of Quadratic Function.

Vertex — Formula

$h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a}$

We substitute the value of these terms from the standard form.

$y = a {x}^{2} + bx + c$

$h = - \frac{1}{2(1)} \\ h = - \frac{ 1}{2}$

Our h is - 1/2

$k = \frac{4(1)(2) - ( {1})^{2} }{4(1)} \\ k = \frac{8 - 1}{4} \\ k = \frac{7}{4}$

Our k is 7/4.

Vertex — Calculus

We can use differential or derivative to find the vertex as well.

$f(x) = a {x}^{n}$

Therefore our derivative of f(x) —

$f'(x) = n \times a {x}^{n - 1}$

From the standard form of the given equation.

$y = {x}^{2} + x + 2$

Differentiate the following equation. We can use the dy/dx symbol instead of f'(x) or y'

$f'(x) = (2 \times 1 {x}^{2 - 1} ) + (1 \times {x}^{1 - 1} ) + 0$

Any constants that are differentiated will automatically become 0.

$f'(x) = 2 {x}+ 1$

Then we substitute f'(x) = 0

$0 =2x + 1 \\ 2x + 1 = 0 \\ 2x = - 1 \\x = - \frac{1}{2}$

Because x = h. Therefore, h = - 1/2

Then substitute x = -1/2 in the function (not differentiated function)

$y = {x}^{2} + x + 2$

$y = ( - \frac{1}{2} )^{2} + ( - \frac{1}{2} ) + 2 \\ y = \frac{1}{4} - \frac{1}{2} + 2 \\ y = \frac{1}{4} - \frac{2}{4} + \frac{8}{4} \\ y = \frac{7}{4}$

Because y = k. Our k is 7/4.

From the vertex form, our vertex is at (h,k)

Therefore, substitute h = -1/2 and k = 7/4 in the equation.

$y = a {(x - h)}^{2} + k \\ y = (x - ( - \frac{1}{2} ))^{2} + \frac{7}{4} \\ y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

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3 years ago