8. Sergei is buying tomatoes and finds that two different kinds are weighed in grams and

zhenek [66]

Hi there!

If you run into problems like this, remember to "Stay calm and find the common denom." That just means find the common denominator.

13/35 and 2/5 = 13/35 and 14/35

As you can tell, 2/5 is larger.

Hope this helps.

:)

5 0

3 years ago

Find the distance between the points (2, 7) and (-6, -2).

maw [93]

Answer:

Approximately 12.04 units.

Step-by-step explanation:

The find the distance between any two points, we can use the distance formula, which is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

We have the points (2,7) and (-6,-2). Let's let (2,7) be (x₁, y₁) and let's let (-6, -2) be (x₂, y₂). Substitute:

$d=\sqrt{(-6-2)^2+(-2-7)^2$

Subtract:

$d=\sqrt{(-8)^2+(-9)^2$

Square:

$d=\sqrt{64+81}$

Add:

$d=\sqrt{145}$

Approximate

$d=\sqrt{145}\approx12.04$

So, the distance between (2,7) and (-6,-2) is approximately 12.04 units.

And we're done!

7 0

4 years ago

The formula for the volume of this rectangular prism is:

juin [17]

Answer:

Step-by-step explanation: Explanation:

If

L

,

H

and

W

represent the length, height and width of the prism, then the volume of the rectangular prism is :

V

=

L

.

H

.

W

............. (1)

Given :

V

=

x

3

+

11

x

2

+

20

x

−

32

;

............... (2)

W

=

(

x

−

1

)

;

H

=

(

x

+

8

)

.

Let

L

=

(

x

+

l

0

)

be the expression for the length, then the RHS of equation (1) becomes

L

.

H

.

W

=

(

x

−

l

0

)

(

x

+

8

)

(

x

−

1

)

,

=

(

x

+

l

0

)

(

x

2

+

7

x

−

8

)

=

(

x

+

l

0

)

(

x

2

+

7

x

−

8

)

=

x

3

+

(

7

+

l

0

)

x

2

+

(

7

l

0

−

8

)

x

−

8

l

0

..... (3)

Comparing this to the LHS of equation (1), we get the following set of equations to solve for

l

0

,

7

+

l

0

=

11

;

7

l

0

−

8

=

20

;

8

l

0

=

32

;

l

0

=

4

Therefore

L

=

(

x

+

4

)

8 0

3 years ago

Find the measure Of K

Mariana [72]

Answer:

K = 10

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin K = 11 / 61

Taking the inverse sin of each side

sin ^-1 ( sin K) = sin ^-1 (11/61)

K =10.38885782

K = 10

7 0

3 years ago

The graphs below have the same shape. What is the equation of the red

anyanavicka [17]

Answer:

Option B is correct .

Step-by-step explanation:

According to Question , both the graph have same shape . If we look at the the first graph it cuts x - axis at (0 , 2) and ( 0 , -2) . Hence x = 2 and -2 are the zeroes of the equation .

And ,the given function is ,

$\implies f(x) = 4 - x^2 \\\\\implies f(x) = 4-x^2=0 \\\\\implies 2^2-x^2=0\\\\\implies (2-x)(2+x) = 0 \\\\\boxed{\red{\bf \implies x = 2 , (-2) }}$

Hence ,we can can see that x = 2 and (-2) are the zeroes of graph. 

This implies that if we know the zeroes , we can frame the Equation.

On looking at second parabola , it's clear that cuts x - axis at ( 1, 0 ) and (-1,0). So , 1 and -1 are the zeroes of the quadratic equation . Let the function be g(x) . Here , a and ß are the zeroes.

$\implies g(x) = (x-\alpha)(x-\beta) \\\\\implies g(x) = (1+x)(1-x) \\\\\boxed{\pink{\bf \implies g(x) = 1 - x^2}}$

Hence option B is correct .

8 0

3 years ago

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