All categories

3 years ago

What is the solution to the equation below? 4(3x + 5) = 5(x + 4) + 7x A infinite solutions OB no solution 0 со D 3

Mathematics

2 answers:

Anna35 [415]3 years ago

5 0

Answer:

Step-by-step explanation:

here you go mate

step 1

4(3x+5)=5(x+4)+7x equation

step 2

4(3x+5)=5(x+4)+7x simplify by distributing

12x+20=12x+20

step 3

12x+20=12x+20 subtract 12x

20=20

step 4

20=20 Divide

0=0

answer

all are real numbers

Alex787 [66]3 years ago

4 0

Answer: All Numbers Are Real Solutions (Note - Have An Amazing Day! :)

Comment If I'm Wrong!

Step-by-step explanation:

4(3x+5)=5(x+4)+7x

(4)(3x)+(4)(5)=(5)(x)+(5)(4)+7x

12x+20=5x+20+7x

12x+20=(5x+7x)+(20)

12x+20=12x+20

12x+20−12x=12x+20−12x

20=20

20−20=20−20

0=0

Answer: All real numbers are solutions

You might be interested in

Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Suppose that the future populat

yulyashka [42]

Answer:

The population will reach 34,200 in February of 2146.

Step-by-step explanation:

Population in t years after 2012 is given by:

$P(t) = 0.8t^{2} + 6t + 19000$

In what month and year will the population reach 34,200?

We have to find t for which P(t) = 34200. So

$P(t) = 0.8t^{2} + 6t + 19000$

$0.8t^{2} + 6t + 19000 = 34200$

$0.8t^{2} + 6t - 15200 = 0$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$0.8t^{2} + 6t - 15200 = 0$

So $a = 0.8, b = 6, c = -15200$

Then

$\bigtriangleup = 6^{2} - 4*0.8*(-15100) = 48356$

$t_{1} = \frac{-6 + \sqrt{48356}}{2*0.8} = 134.14$

$t_{2} = \frac{-6 - \sqrt{48356}}{2*0.8} = -141.64$

We only take the positive value.

134 years after 2012.

.14 of an year is 0.14*365 = 51.1. The 51st day of a year happens in February.

So the population will reach 34,200 in February of 2146.

6 0

2 years ago

Victoria wants to purchase a skateboard. She has $125 to spend. She finds one that regularly sells for $139.99 and is on sale fo

Pavel [41]

Well, to see if she can afford the skateboard, start by finding the discount and then finding the sales tax of that.

To find the discount, first find 15% of $139.99 and then subtract it since that's how much you're getting off.

Remember: to find percentage, convert the percentage into a decimal by dividing it by 100, and then multiplying it by what you're finding a percentage of.

15% ÷ 100 = 0.15

$139.99 x 0.15 = 20.9985, which can be rounded up to $21.

$139.99 - 21 = 118.99.

Now that we have the discount, we find the sales tax, which can be found the same way as the discount, but we add it to the total instead fo subtracting it.

7% ÷ 100 = 0.07

0.07 x 118.99 8.3293 or $8.33

118.99 + 8.33 = 127.32

This is the final total of how much the skateboard would cost.

So:

No, she would not have enough money to buy the skateboard. With the discount alone, she could afford it, since $118 falls in her budget range, but with the added tax, it's 13 dollars over and she cannot afford the skateboard.

5 0

2 years ago

Consider the equation and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”. For example, “(0, 3) R (0, 2)”

Leviafan [203]

Answer:

The equation determine a relation between x and y

x = ± $\sqrt{1-(y-2)^{2}}$

y = ± $\sqrt{1-x^{2}}+2$

The domain is 1 ≤ y ≤ 3

The domain is -1 ≤ x ≤ 1

The graphs of these two function are half circle with center (0 , 2)

All of the points on the circle that have distance 1 from point (0 , 2)

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation x² + (y - 2)² and the relation "(x , y) R (0, 2)", where

R is read as "has distance 1 of"

- This relation can also be read as “the point (x, y) is on the circle

of radius 1 with center (0, 2)”

- “(x, y) satisfies this equation , if and only if, (x, y) R (0, 2)”

* Lets solve the problem

- The equation of a circle of center (h , k) and radius r is

(x - h)² + (y - k)² = r²

∵ The center of the circle is (0 , 2)

∴ h = 0 and k = 2

∵ The radius is 1

∴ r = 1

∴ The equation is ⇒ (x - 0)² + (y - 2)² = 1²

∴ The equation is ⇒ x² + (y - 2)² = 1

∵ A circle represents the graph of a relation

∴ The equation determine a relation between x and y

* Lets prove that x=g(y)

- To do that find x in terms of y by separate x in side and all other

in the other side

∵ x² + (y - 2)² = 1

- Subtract (y - 2)² from both sides

∴ x² = 1 - (y - 2)²

- Take square root for both sides

∴ x = ± $\sqrt{1-(y-2)^{2}}$

∴ x = g(y)

* Lets prove that y=h(x)

- To do that find y in terms of x by separate y in side and all other

in the other side

∵ x² + (y - 2)² = 1

- Subtract x² from both sides

∴ (y - 2)² = 1 - x²

- Take square root for both sides

∴ y - 2 = ± $\sqrt{1-x^{2}}$

- Add 2 for both sides

∴ y = ± $\sqrt{1-x^{2}}+2$

∴ y = h(x)

- In the function x = ± $\sqrt{1-(y-2)^{2}}$

∵ $\sqrt{1-(y-2)^{2}}$ ≥ 0

∴ 1 - (y - 2)² ≥ 0

- Add (y - 2)² to both sides

∴ 1 ≥ (y - 2)²

- Take √ for both sides

∴ 1 ≥ y - 2 ≥ -1

- Add 2 for both sides

∴ 3 ≥ y ≥ 1

∴ The domain is 1 ≤ y ≤ 3

- In the function y = ± $\sqrt{1-x^{2}}+2$

∵ $\sqrt{1-x^{2}}$ ≥ 0

∴ 1 - x² ≥ 0

- Add x² for both sides

∴ 1 ≥ x²

- Take √ for both sides

∴ 1 ≥ x ≥ -1

∴ The domain is -1 ≤ x ≤ 1

* The graphs of these two function are half circle with center (0 , 2)

* All of the points on the circle that have distance 1 from point (0 , 2)

8 0

3 years ago

A 100 gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. the function f(

Alexxx [7]

Answer:

Shifted 5 unit right side then stretched vertically by the factor 100

Step-by-step explanation:

Here, parent function,

$f(x)=\frac{1}{x}$

Transformed function,

$f(x) = \frac{100}{x-5}$

Since, if a function f(x) gives cf(x), where c is any number,

Then the function was vertically stretched by factor c,

While, the function gives f(x-c),

Then the function was shifted c unit right.

Hence, the graph of $f(x)=\frac{1}{x}$ was shifted 5 unit right side then stretched vertically by the factor 100 to create the graph of $f(x)=\frac{100}{x-5}$

4 0

3 years ago

Nemo's aquarium is filled with 2,4002{,}400 2,400 2, comma, 400 cubic centimeters of water. The base of the aquarium is 20 cm 20

kolezko [41]

The water in the aquarium is a rectangular prism with dimensions 20, 12 and h (where the height is unknown).

We know that the volume is the product of the dimensions, and that it is 2400, so we have

$V=2400=20\cdot 12 \cdot h \iff 240h=2400 \iff h=10$

6 0

2 years ago

What is the solution to the equation below? 4(3x + 5) = 5(x + 4) + 7x A infinite solutions OB no solution 0 со D 3​

What is the solution to the equation below? 4(3x + 5) = 5(x + 4) + 7x A infinite solutions OB no solution 0 со D 3