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3 years ago

A first number plus twice a second number is 4. Twice the first number plus the second totals 20. Find the numbers

Mathematics

1 answer:

pychu [463]3 years ago

4 0

Answer:

The first number is 6

The second number is -1

6+(-2)=4

6*2=12 12+(-1)=11

Step-by-step explanation:

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Solve for x & y. 30x−42y=−6 and 5x−7y=−1

vladimir1956 [14]

Um.. Both of those equations are the exact same. Divide both sides of the first equation by 6. You get:

$\frac{30x - 42y}{6} = \frac{-6}{6} \\ 5x - 7y = -1$

That is the exact same as the second equation. This system has an infinite number of solutions. 5x - 7y = -1 is a line, so basically every point on that line is a solution to the system.

For example, $x = 0$ and $y = \frac{1}{7}$ would work, but so would $x = 1$ and $y = \frac{6}{7}$

4 0

2 years ago

Please help thank you

Shkiper50 [21]

Answer:

x = 0.25

Step-by-step explanation:

When logs are added together, they are actually multiplied and then the logs taken of the product.

That sentence is actually correct, but you are going to have to read it a couple of times. You might understand it if I actually just solve the problem.

ln(2x) + ln(2) = 0 Combine the two subjects to make 1 ln.

ln (2)(2x) = 0 Now take the antilog

ln(4x) = 0

antilog ln(4x) = e^0 e^0 = 1

4x = 1 See your last problem.

x = 1/4

Now the question is "What's the answer?" It might be 1/4 but I doubt it. A better choice would be x = 1/4 or x = 0.25

I'd try the last one first.

6 0

3 years ago

Guys i actually need help

maria [59]

Answer:

Rotation

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Find the derivative of the function at P 0 in the direction of A. f(x,y,z) = 3 e^x cos(yz), P0 (0, 0, 0), A = - i + 2 j + 3k

Alik [6]

The derivative of $f(x,y,z)$ at a point $p_0=(x_0,y_0,z_0)$ in the direction of a vector $\vec a=a_x\,\vec\imath+a_y\,\vec\jmath+a_z\,\vec k$ is

$\nabla f(x_0,y_0,z_0)\cdot\dfrac{\vec a}{\|\vec a\|}$

We have

$f(x,y,z)=3e^x\cos(yz)\implies\nabla f(x,y,z)=3e^x\cos(yz)\,\vec\imath-3ze^x\sin(yz)\,\vec\jmath-3ye^x\sin(yz)\,\vec k$

and

$\vec a=-\vec\imath+2\,\vec\jmath+3\,\vec k\implies\|\vec a\|=\sqrt{(-1)^2+2^2+3^2}=\sqrt{14}$

Then the derivative at $p_0$ in the direction of $\vec a$ is

$3\,\vec\imath\cdot\dfrac{-\vec\imath+2\,\vec\jmath+3\,\vec k}{\sqrt{14}}=-\dfrac3{\sqrt{14}}$

3 0

3 years ago

Can someone please help me with this? I keep getting half of the answer and I'm doing everything right. ------------------------

serg [7]

9514 1404 393

Answer:

a. x, x+2, x+4

b. 10 ≤ 3x+6 ≤ 24

c. 6 ft, 8 ft, or 10 ft

Step-by-step explanation:

Given:

The lengths of the sides of a certain triangle, in feet, are consecutive even integers.
The perimeter of this triangle is between 10 feet and 24 feet inclusive.

Find:

a. Using one variable, write three expressions that represent the lengths of the three sides of the triangle.

b. Write a compound inequality to model this problem.

c. Solve the inequality. List all possible lengths for the longest side of the triangle.

Solution:

You have let x represent the shortest side. (Note that the question asks for the length of the longest side.)

a. The expressions for side lengths can be x, x+2, x+4 when x is the shortest side.

b. Here is the compound inequality

10 ≤ x+(x+2)+(x+4) ≤ 24

c. Here is the solution

10 ≤ 3x+6 ≤ 24 . . . . collect terms

4 ≤ 3x ≤ 18 . . . . . . . subtract 6

4/3 ≤ x ≤ 6 . . . . . . . . divide by 3

Your working is correct, but incomplete. The values of interest are the even integers x+4.

5 1/3 ≤ x+4 ≤ 10

The longest side may be 6 ft, 8 ft, or 10 ft.

6 0

2 years ago