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3 years ago

Write an expression to represent: Three more than the product of two and a number x.

2 answers:

7 0

Lets break this down:

“Three more” means +3. Imagine you have 2 apples, and I have 3 more than you. I have 5 apples then, right?

“Product” — the product of 2 and 1 is 2. The product of 3 and 5 is 15. So: the product is the result of multiplication. Thus, “the product of two and x” would mean we have to multiply 2 and x.

So lets combine these: “2*x+3” would be your answer, or if you want, shorten the “2*x” to just “2x”.

andriy [413]3 years ago

6 0

Answer:

2x + 3

Step-by-step explanation:

product means to multiply, hence

the product of 2 and a number x = 2 × x = 2x

3 more than means add on 3, thus

expression is 2x + 3

You might be interested in

1. The height of a triangle is 6 m more than its base. The area of the triangle is 56 m². What is the length of the base? Enter

Elodia [21]

Answers:
1. 8 m
2. 17 m
3. 7 cm
4. 2 s

Explanations:

1. Let x = length of the base
x + 6 = height of the base

Then, the area of the triangle is given by

(Area) = (1/2)(base)(height)
56 = (1/2)(x)(x + 6)
56 = (1/2)(x²  + 6x)

Using the symmetric property of equations, we can interchange both sides of equations so that

(1/2)(x²  + 6x) = 56

Multiplying both sides by 2, we have

x² + 6x = 112

The right side should be 0. So, by subtracting both sides by 112, we have

x² + 6x - 112 = 112 - 112
x² + 6x - 112 = 0

By factoring, x² + 6x - 112 = (x - 8)(x + 14). So, the previous equation becomes

(x - 8)(x +14) = 0

So, either

x - 8 = 0 or x + 14 = 0

Thus, x = 8 or x = -14. However, since x represents the length of the base and the length is always positive, it cannot be negative. Hence, x = 8. Therefore, the length of the base is 8 cm.

2. Let x = length of increase in both length and width of the rectangular garden

Then,

14 + x = length of the new rectangular garden
12 + x = width of the new rectangular garden

So,

(Area of the new garden) = (length of the new garden)(width of the new garden)

255 = (14 + x)(12 + x) (1)

Note that

(14 + x)(12 + x) = (x + 14)(x + 12)
= x(x + 14) + 12(x + 14)
= x² + 14x + 12x + 168
= x² + 26x + 168

So, the equation (1) becomes

255 = x² + 26x + 168

By symmetric property of equations, we can interchange the side of the previous equation so that

x² + 26x + 168 = 255

To make the right side becomes 0, we subtract both sides by 255:

x² + 26x + 168 - 255 = 255 - 255
x² + 26x - 87 = 0

To solve the preceding equation, we use the quadratic formula.

First, we let

a = numerical coefficient of x² = 1

Note: if the numerical coefficient is hidden, it is automatically = 1.

b = numerical coefficient of x = 26
c = constant term = - 87

Then, using the quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} = \frac{-26 \pm \sqrt{26^2 - 4(1)(-87)} }{2(1)} 
\newline x = \frac{-26 \pm \sqrt{1,024} }{2}
\newline
\newline x = \frac{-26 \pm 32 }{2}$

So,

$x = \frac{-26 + 32 }{2} \text{ or } x = \frac{-26 - 32 }{2}
\newline x = \frac{6 }{2} \text{ or } x = \frac{-58 }{2}
\newline \boxed{ x = 3 \text{ or } x = -29}$

Since x represents the amount of increase, x should be positive.

Hence x = 3.

Therefore, the length of the new garden is given by

14 + x = 14 + 3 = 17 m.

3. The area of the shaded region is given by

(Area of shaded region) = π(outer radius)² - π(inner radius)²
= π(2x)² - π6²
= π(4x² - 36)

Since the area of the shaded region is 160π square centimeters,

π(4x² - 36) = 160π

Dividing both sides by π, we have

4x² - 36 = 160

Note that this equation involves only x² and constants. In these types of equation we get rid of the constant term so that one side of the equation involves only x² so that we can solve the equation by getting the square root of both sides of the equation.

Adding both sides of the equation by 36, we have

4x² - 36 + 36 = 160 + 36
4x² = 196

Then, we divide both sides by 4 so that

x² = 49

Taking the square root of both sides, we have

$x = \pm 7$

Note: If we take the square root of both sides, we need to add the plus minus sign $(\pm)$ because equations involving x² always have 2 solutions.

So, x = 7 or x = -7.

But, x cannot be -7 because 2x represents the length of the outer radius and so x should be positive.

Hence x = 7 cm

4. At time t, h(t) represents the height of the object when it hits the ground. When the object hits the ground, its height is 0. So,

h(t) = 0 (1)

Moreover, since $v_0 = 27$ and $h_0 = 10$ ,

h(t) = -16t² + 27t + 10 (2)

Since the right side of the equations (1) and (2) are both equal to h(t), we can have

-16t² + 27t + 10 = 0

To solve this equation, we'll use the quadratic formula.

Note: If the right side of a quadratic equation is hard to factor into binomials, it is practical to solve the equation by quadratic formula.

First, we let

a = numerical coefficient of t² = -16
b = numerical coefficient of t = 27
c = constant term = 10

Then, using the quadratic formula

$t = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} = \frac{-27 \pm \sqrt{27^2 - 4(-16)(10)} }{2(-16)} \newline t = \frac{-27 \pm \sqrt{1,369} }{-32} \newline \newline t = \frac{-27 \pm 37 }{32}$

So,

$t = \frac{-27 + 37 }{-32} \text{ or } t = \frac{-27 - 37 }{-32} \newline t = \frac{-10}{32} \text{ or } t = \frac{-64 }{-32} \newline \boxed{ t = -0.3125 \text{ or } t = 2}$

Since t represents the amount of time, t should be positive.

Hence t = 2. Therefore, it takes 2 seconds for the object to hit the ground.

3 0

3 years ago

Read 2 more answers

What is the answer to 1/8(8x+15)=24

Korvikt [17]

Answer:

x = 177/8

Step-by-step explanation:

First, we must get rid of the fraction by multiplying 8 by both sides.

8 · 1/8(8x + 15) = 24 · 8

1(8x + 15) = 192

8x + 15 = 192

Then we simplify. First subtract 15 from both sides.

8x + 15 - 15 = 192 - 15

8x = 177

Then divide 8 from both sides.

8x/8 = 177/8

x = 177/8

4 0

3 years ago

I have a square piece of paper.

jarptica [38.1K]

Answer:

a) 30 cm

b) 20 cm

Step-by-step explanation:

Rectangle B's perimeter is 10+10+5+5 which is 30

Square C's perimeter is 5+5+5+5 which is 20

4 0

3 years ago

suppose you have 76 feet of fencing to enclose a rectangular dog pen. The function A=38x-x^2, where x= width, gives you the area

yan [13]

If A=38x-x^2 then

dA/dx=38-2x

d2A/dx2=-2

Since the acceleration, d2A/dx2 is a constant negative, when velocity, dA/dx=0, it will be an absolute maximum for A(x)

dA/dx=0 only when 38=2x, x=19

A(19)=38(19)-19^2

A(19)=722-361

A(19)=361 ft^2

So the maximum possible area is 361 ft^2

(This will always be true as the maximum possible area enclosed by a given amount of material will always be a perfect square...)

3 0

3 years ago

I don't understand how to go about solving this equation more specifically the "y". Any help is appreciated. (:

Archy [21]

Answer:

y^2/x^6

apply exponent rule:

x^-2/x^4=1/x^4-(-2)=y/y^-1 x^4 -(-2)

then you subtract 4-(-2)=6

y/x^6 y^-1

cancel out the common factor: y^-1 and you get

y^2

------

x^6

6 0

2 years ago