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1 year ago

6

The fourth-grade class donated 750 bottles of water for a 5K run. After the run, there were 89 bottles left. How many bottles of

water did the runners drink?

1 answer:

densk [106]1 year ago

4 0

Answer:

The runners drank 661 bottles of water.

Step-by-step explanation:

Subtract 661 from 750, and you are left with 89.

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⊙O and ⊙P are given with centers (−2, 7) and (12, −1) and radii of lengths 5 and 12, respectively. Using similarity transformati

goldenfox [79]

Answer:

Whereby circle $\bigodot$ P can be obtained from circle $\bigodot$ O by applying the transformations of a translation of T₍₁₄, ₋₈₎ followed by a dilation by a scale factor of 2.4, $\bigodot$ O is similar to $\bigodot$ P

Step-by-step explanation:

The given center of the circle $\bigodot$ O = (-2, 7)

The radius of $\bigodot$ O, r₁ = 5

The given center of the circle $\bigodot$ P = (12, -1)

The radius of $\bigodot$ P, r₂ = 12

The similarity transformation to prove that $\bigodot$ O and $\bigodot$ P are similar are;

a) Move circle $\bigodot$ O 14 units to the right and 8 units down to the point (12, -1)

b) Apply a scale of S.F. = r₂/r₁ = 12/5 = 2.4

Therefore, the radius of circle $\bigodot$ O is increased by 2.4

We then obtain $\bigodot$ O' with center at (12, -1) and radius r₃ = 2.4×5 = 12 which has the same center and radius as circle $\bigodot$ P

∴ Circle $\bigodot$ P can be obtained from circle $\bigodot$ O by applying similarity transformation of translation of T₍₁₄, ₋₈₎ followed by a dilation by a scale factor of 2.4, $\bigodot$ O is similar to $\bigodot$ P.

7 0

3 years ago

Step 1: –10 + 8x < 6x – 4 Step 2: –10 < –2x – 4 Step 3: –6 < –2x Step 4: ________ What is the final step in solving the

Tamiku [17]

Given:

The inequality is

$-10+8x$

To find:

The missing step in solving the given inequality.

Solution:

Step 1: The given equation.

$-10+8x$

Step 2: Subtract 8x from both sides.

$-10+8x-8x$

$-10$

Step 3: Add 4 on both sides.

$-10+4$

$-6$

Step 4: Divide both sides by -2 and change the sign of inequity as we divide the inequality by a negative number.

$\dfrac{-6}{-2}>\dfrac{-2x}{-2}$

$3>x$

Therefore, the missing step is $3>x$ .

8 0

3 years ago

Read 2 more answers

How is the graph of the parent quadratic function transformed to produce the graph of y = negative (2 x + 6) squared + 3?

bearhunter [10]

We start with the parent function

$f(x)=x^2$

The first child function would be

$g(x)=(2x)^2$

We have multiplied the input of the function by a constant: we have

$g(x)=f(2x)$

This kind of transformation result in a horizontal stretch/compression. If the multiplier is greater than 1, we have a compression. So, this first child causes a horizontal compression with compression rate 2.

The second child function would be

$h(x)=(2x+6)^2$

We added 6 to the input of the function: we have

$h(x)=g(x+6)$

This kind of transformation result in a horizontal translation. If the constant added is positive, we translate to the left. So, this second child causes a translation 6 units to the left.

The third child function would be

$l(x)=-(2x+6)^2$

We changed the sign of the previous function (i.e. we multiplied it by -1): we have

$l(x)=-h(x)$

This kind of transformation result in a vertical stretch/compression. If the multiplier is greater than 1 we have a stretch, if it's between 0 and 1 we have compression. If it's negative, we reflect across the x axis, and then apply the stretch/compression. In this case, the multiplier is -1, so we only reflect across the x axis.

The fourth child function would be

$m(x)=-(2x+6)^2+3$

We added 3 to previous function: we have

$m(x)=l(x)+3$

This kind of transformation result in a vertical translation. If the constant added is positive, we translate upwards. So, this last child causes a translation 3 units up.

Recap

Starting from the parent function $y=x^2$ , we have to:

Compress the graph horizontall, with scale factor 2;
Translate the graph 6 units to the left;
Reflect the graph across the x axis;
Translate the graph 3 units up

Note that the order is important!

5 0

3 years ago

Read 2 more answers

Which would be the correct answer?

Strike441 [17]

9514 1404 393

Answer:

(a) 5/6 < 1∴ product < 2 3/8

Step-by-step explanation:

Multiplying any number by a positive value less than 1 will reduce its magnitude. 5/6 × 2 3/8 will be less than 2 3/8 because 5/6 is less than 1.

5 0

3 years ago

Here are six cards arrange the card into three pairs with the same total -4 -2 -1 5 6 8

NeX [460]

8,-4

6,-2

and

5,-1

They all will equal 4. Hope this helps.

6 0

3 years ago

Read 2 more answers