Ask question

Ask question

All categories

3 years ago

8

The following triangles are similar. State the postulate or theorem that proves they are similar along with the correct scale fa

ctor. The diagram is not to scale.
a. SSS~; 3:4
b. SAS~; 1:3
c. SSS~; 1:3
d. SAS~; 3:4

1 answer:

Nadusha1986 [10]3 years ago

6 0

I would have to say SAS because they give 2 sides and an angle. Also 3:4 because the one side is 3 and add 1 for 4, same for 30 and 40.

You might be interested in

(a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the gradient vector, that is, in

Sophie [7]

Answer:

Step-by-step explanation:

$\text{Show that a differentiable function f decreases most rapidly at x in the }$

$\text{direction opposite the gradient vector, that is, in the direction of}$ $-\bigtriangledown f(x)$ $\text{. Let}\ \theta \ \text{be the angle between} \bigtriangledown f(x) \ \text{and unit vector u. Then } D_u f = \mathbf{|\bigtriangledown f| \ cos \ \theta }}$

$\text{Since the minimum value of} \ \ \mathbf{cos \ \theta} \ \ is \mathbf{-1} \ \text{occuring \ for \ 0} \le \ \theta \ < 2x, \\ \\ when \ \theta = \mathbf{\pi} , \text{the mnimum value of} \ D_uf \ is} -|\bigtriangledown f|, \text{occuring when the direction of u is } \\ \\ \ \mathbf{the \ opposite \ of} \ \text{the direction of } \ \bigtriangledown f (assuming \ \bigtriangledown f\ is \ not \ zero)$

b) $\text{From part A:}$

$If \ f(x,y) = x^4y -x^2y^2 \ \ decreases \ fastest \ at \ the \point \ (2,-5)\\ \\ F(x,y) = x^4y -x^2y^3 \\ \\ f_x = \dfrac{df}{dx}= \dfrac{d}{dx}(x^4y-x^2y^3) \\ \\ f_x = \dfrac{df}{dx}= y4x^3 -2y^3x \\ \\ For(2,-5) \\ \\ f_x = (-5)4(2)^3 -2(-5)^3(2) \\ \\ \mathbf{ f_x = 340}$

$However; f_y = \dfrac{df}{dy} = \dfrac{d}{dy}(x^4y - x^2y^3) \\ \\ f_y = x^4 -3x^2y^2 \\ \\ Now, for (2, -5)\\ \\f_y = (2)^4 -3(2)^2(-5)^2 \\ \\ f_y = -284$

$So; \bigtriangledown = < 340,-284> \text{this is the direction of fastest decrease}$

6 0

3 years ago

Lucas wants to use the box with the greatest volume

stiks02 [169]

*see attachment for the possible choice answers showing the boxes and dimensions

Answer:

Box D = 27 ft³

Step-by-step explanation:

To find out which has the greatest volume, we need to calculate the volume of each box given in the option using the formula of the volume of a rectangular prism = w × h × l.

Where w = width; h = height; and l = length.

Thus, the volume for the boxes are as follows:

=>Box A:

V = w × h × l

V = 3 × 1 × 5

V = 15 ft³

=>Box B:

V = w × h × l

V = 2 × 3 × 4

V = 24 ft³

=>Box C:

V = w × h × l

V = 1 × 2 × 7

V = 14 ft³

=>Box D:

V = w × h × l

V = 3 × 3× 3

V = 27 ft³

The shipping box with the largest volume is box D with a volume of 27 ft³

7 0

4 years ago

Write a rule for linear function in the graph (4,3) (3 ,-1)

yaroslaw [1]

Answer:

D) y = 4x - 13

Step-by-step explanation:

Slope: the change in y over the change in x

In a equation in slope-intercept form is in <em>y = mx + d, where m is the slope</em>.

The slope can be found by its definition. As<em> y goes up by 4, x goes up by 1</em>, so the slope is <em>4/1 = 4</em>.

The only option with 4 as the slope is D.

4 0

4 years ago

Clare is paid $90 for 5 hours of work. At this rate, how many seconds does it take for her to earn 25 cent?

Alla [95]

50 secs

as $90÷5hrs= 18 $ per hrs

$18÷60min=$0.30 per min

$0.30÷60sec=$0.005 per sec

$0.25÷$0.005= 50sec to make $0.25

so 50sec is the answer

7 0

4 years ago

Read 2 more answers

What is the relationship between the values of the given digits 7's in 7'700

GaryK [48]

Step-by-step explanation:

The given number is 7700.

We need to find the relationship between the values of the digit 7s in it.

The digit in the extreme left is 7 and second no is again 7.

The place value of first 7 is 7000

The place value of second 7 is 700.

Taking ratio of place value of 7 in first 7 and for second 7 as follows :

$R=\dfrac{7000}{700}\\\\R=10$

So, value of first 7 is 10 times that of the value of second 7.

8 0

3 years ago