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erastova [34]
3 years ago
13

For what value of do the expressions 2+3 and 3−6 have the same value?

a1" title="x" alt="x" align="absmiddle" class="latex-formula"> =
Mathematics
1 answer:
ladessa [460]3 years ago
4 0

Answer:

x = 9

Step-by-step explanation:

The expressions are 2+3 and 3−6.

We need to find the value of x such that the expressions 2+3 and 3−6  have same value.

2+3 = 3−6

Taking like terms together,

3+6 = 3x-2x

⇒ x = 9

So, the value of x is 9 such that 2+3 and 3−6  have same value.

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One positive integer is 6 less than twice another. The sum of their squares is 680 . Find the integers.
NemiM [27]

Let's call the two numbers x and y. The first sentence, one is 6 less than twice another, translates to

x = 2y-6

We also know the sum of their squares:

x^2+y^2 = 680

So, we have the following system:

\begin{cases} x = 2y-6 \\ x^2+y^2 = 680 \end{cases}

We can use the expression for x in terms of y from the first equation to turn the second equation into something involving y alone:

x^2+y^2 = 680 \to (2y-6)^2+y^2 = 680

Expand the square:

5y^2-24y+36 = 680

Subtract 680 from both sides:

5y^2-24y-644 = 0

Using the quadratic equation

y_{1,2} = \cfrac{-b\pm\sqrt{b^2-4ac}}{2a}

we find the two solutions

y_1 = -\cfrac{46}{5},\quad y_2 = 14

Since we know that both numbers are integer we can only accept the second solution. It yields the following x value:

x = 2x-6\ \land\ y = 14 \implies x = 2\cdot 14 - 6 = 28-6=22


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3 years ago
What is the equation for the logarithmic function shown in the graph?
svp [43]

Answer: f(x) = log(x+1)

Step-by-step explanation:

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A triangle has an angle that measures 10°. The other two angles are in a ratio of 7:10. What are the measures of those two angle
Sliva [168]

Answer:

100 degrees and 70 degrees

Step-by-step explanation:

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with a ratio of 7:10

7x + 10x = 170

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Answer:

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Step-by-step explanation:

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