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3 years ago

Triangles PQR and SQT are similar triangles.

Mathematics

1 answer:

aleksklad [387]3 years ago

8 0

Answer:

The side lengths of similar triangles are proportional

Step-by-step explanation:

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A recipe requires 5 cups of sugar. you can only measure with a 3/4 cup. How many 3/4 cups do you need for the recipe?

alekssr [168]

Answer:

1 1/2?

Step-by-step explanation:

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx....%7D%20%7D%20%7D%20%7D%20%20%3D%20%

andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

3 0

2 years ago

Answer for x.<br><br> 1. 3x - 10 = -21<br><br> 2. -22 - 4x = 12

ra1l [238]

Answer:

3x - 10 = -21

add 10 on both side

3x-10+10=-21+10

3x=-11

divide both side by 3

3x/3=-11/3

x=-11/3

Step-by-step explanation:

2. -22 - 4x = 12

add 22 on both side

-22+22-4x=12+22

-4x=36

divide both side by -4

-4x/-4=36/-4

c=-9 is your answer

4 0

3 years ago

I need help with number 5 please

JulsSmile [24]

C(t) = $2t + $8

This tells us that the basic cost of the pizza is $8, with no toppings, and that each topping costs an additional $2.

To graph this, plot a dot at (0,$8). Now move y our pencil point 1 unit to the right and then 2 units up. Plot a dot at this new location. Now draw a straight line connection (0, $8) and this new location (which is (1, $10) ).

5 0

3 years ago

I really don't get what I'm supposed to do...

rusak2 [61]

Answer:

check below

Step-by-step explanation:

1. c = 68-27 = 41

2. t = 7.9+1.5 =9.4

3. a = 21*3 = 63

4. (multiply whole equation by 8) 8r+6=7, r=1/8

5. x = 25.2/4.2 = 6

6. b = 75/15 = 5

7. A. 6C = 99

B. C = 99/6 = $16.50

The solution represents the cost of one ticket.

5 0

3 years ago

Read 2 more answers