<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B2x%7D%20%2B%2012%20%3D%20x%20%2B%208%20" id="TexFormula1" title=" \sqrt{2x} + 12

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Nookie1986 [14]

3 years ago

= x + 8 " alt=" \sqrt{2x} + 12 = x + 8 " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Helga [31]3 years ago

4 0

First note that $x\ge0$ ; otherwise $\sqrt{2x}$ is undefined as long as we're only looking for real solutions.

We can write

$\sqrt{2x}+12=x+8$
$\sqrt{2x}=x-4$
$2x=(x-4)^2$
$2x=x^2-8x+16$
$x^2-10x+16=0$
$(x-8)(x-2)=0$

$\implies x=8,x=2$

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ladessa [460]

12x + 7y=60
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5 0

3 years ago

The scale on a map reads 1/2 inch = 75 miles. If the distance between two cities on the map is 3 and 1/4 inches, find the actual

muminat

Answer:

487.5 miles

Step-by-step explanation:

since 1/2 inch represents 75 miles and the distance is 3 1/4 inches you need to mulitply 75 X 6 = 450 and then divide 75/2=37.5 then add the two totals

450 + 37.5 = 487.5 miles

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4 years ago

Write the algebraic expression that matches each graph

Sophie [7]

Answer:

1. y= |x| -15

2. y = -|x| +3

Step-by-step explanation

.The V shape means absolute value (the | | ), since its upside down, the equation has to be negative. The tip of the V doesn't start at 0 like normal, it's up 3, so the equation has a +3 at the end. The x intercept at (3, 0) is just so you can check your work. If we plug in 3 for x, we do in fact get 0 for y.

Not sure, if correct but here.

4 0

3 years ago

Read 2 more answers

Please can any one please help me with both of these

alexandr402 [8]

Answer:

Question 3: $4x^3+x^2-12x-3$

Question 4: $\frac{1}{2x}, x\neq 0$

Step-by-step explanation:

Question 3

g(x) * h(x) means to multiply both the functions given.

Also note the distributive property:

$(a+b)(n+p)=an+ap+bn+bp$

Now, lets multiply:

$g(x)*h(x)=(4x+1)(x^2-3)\\=(4x)(x^2)-3(4x)+1(x^2)-1(3)\\=4x^3-12x+x^2-3\\=4x^3+x^2-12x-3$

The 2nd answer choice is right

Question 4

$(\frac{f}{g})(x)$ means to divide both the functions and simplify, if possible. Lets do this:

$(\frac{f}{g})(x)=\frac{6x-3}{12x^2-6x}=\frac{3(2x-1)}{6x(2x-1)}=\frac{3}{6x}=\frac{1}{2x}$

This is the correct answer.

The restriction on the domain is any x value that we CANNOT PUT IN THE FUNCTION.

We know we cannot divide by 0, so what makes this fraction division by 0??

If we put x = 0, the function is undefined. So x CANNOT be 0.

Third answer choice is right.

7 0

3 years ago

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s344n2d4d5 [400]

Step-by-step explanation:

the area of a rectangle is length×width.

area of the original rectangle (before its sides are. multiplied) :

Ao = length original × width original

length new = length original × 4

width new = width original × 4

the area of the new rectangle is then :

An = length new × width new =

= length original × 4 × width original × 4 =

= length original × width original × 4 × 4 =

= length original × width original × 16 =

= Ao × 16

so, the fourth answer option is correct. the area increases by a factor 16.

two objects of shapes are similar, if their angles are the same, and exchanged side length of one object correlates with the corresponding side length of the other b object with the same ratio.

we see the ratio of one corresponding pair of side lengths is 2/4 = 1/2. so, every side length of the small prism is half as long as the corresponding side length in the large prism.

the volume of such a prism is the multiplication of 3 side lengths : length, width, height.

each one has now a scaling factor of 1/2.

so, the volume decreases by the cube of the scaling factor: 1/2×1/2×1/2 = 1/2³ = 1/8

so,

Vsmall = Vlarge × 1/8 = 2720/8 = 340 cm³

therefore, again, the fourth answer option is correct.

7 0

2 years ago