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4 years ago

The difference of six times a number and 7 is -49

1 answer:

5 0

Greetings!

"The difference of six times a number and 7 is -49"...

In number and variables, this would be:
 $6x-7=-49
$

Add 7 to both sides.
 $(6x-7)+7=(-49)+7$
Simplify.
 $6x=-42$
Divide both sides by 6.
$(6x)/6=(-42)/6$
Simplify.
$x=-7$

Hope this helps.
-Benjamin

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Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question.

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Let

x------> the number of multiple choice question

y------> the number of free response question

we know that

$3x+8y=55$ -----> equation A

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$x=15-y$ -----> equation B

Substitute equation B in equation A

$3[15-y]+8y=55$

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3 years ago

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A pendant is formed using a cylinder and cone. Once assembled, as shown below, the pendant is painted. How many square millimete

solmaris [256]

Surface area of cylinder is given by area of circle + area of the rectangle that curved around the cylinder

Area of the base of the cylinder = $\pi r^{2} = 8^{2} \pi =64 \pi$
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Note that the wall of the cylinder is in the shape of a rectangle. The width of the rectangle is the height of the cylinder. The length of the rectangle is the circumference of the circle base.

Surface area of cone is given by $\pirl$ where $l$ is the slanted height of the cone

SA of cone = $\pi (8)(10)=80 \pi$

Hence total painted surface area is $80 \pi +192 \pi +64 \pi =336 \pi$

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3 years ago

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4vir4ik [10]

The sum of the interior triangles in a triangle is 180, so if we add all the angle measures together, we should get 180. Therefore, we can make an equation like this,

$110-2x+x+50+5x-40=180$

Simplify this.

$4x+120=180$

$4x=60$

$x=15$

Now we can find each angle measure.

$110-2x$

$110-2(15)$

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$15+50$

$65$

$5x-40$

$5(15)-40$

$75-40$

$35$

So the angle labeled $110-2x$ is the largest angle in the triangle.

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3 years ago

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If f (x)= x-3 and g (x)= 2x-4, find (f+g)(x)

const2013 [10]

(f∘g)(x) is equivalent to f(g(x)). We solve this problem just as we solve f(x). But since it asks us to find out f(g(x)), in f(x), each time we encounter x, we replace it with g(x).

In the above problem, f(x)=x+3.

Therefore, f(g(x))=g(x)+3.

⇒(f∘g)(x)=2x−7+3

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Basically, write the g(x) equation where you see the x in the f(x) equation.

f∘g(x)=(g(x))+3 Replace g(x) with the equation

f∘g(x)=(2x−7)+3

f∘g(x)=2x−7+3 we just took away the parentheses

f∘g(x)=2x−4 Because the −7+3=4

This is it

g∘f(x) would be the other way around

g∘f(x)=2(x+3)−7

now you have to multiply what is inside parentheses by 2 because thats whats directly in front of them.

g∘f(x)=2x+6−7

Next, +6−7=−1

g∘f(x)=2x−1

Its a lts easier than you think!

Hope this helped

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3 years ago