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3 years ago

A right triangle's height is 3 times the length of its base. if the area of the triangle is 486, what is the height?

1 answer:

4 0

The formula of the area of a triangle:
$A_\Delta=\dfrac{bh}{2}$
b - the bash - the height
We have:
b - the base3b - the height486 - the area

Substitute:
$\dfrac{3b\cdot b}{2}=486\ \ \ |\cdot2\\\\3b^2=972\ \ \ |:3\\\\b^2=324\to b=\sqrt{324}\\\\b=16\to h=3b=3\cdot18=54$
Answer: The length of the height is equal 54 units.

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the tens digit of a two digit number is twice the units digit. The sum of the digits is twelve. Find the original number.

KatRina [158]

X - tens digit
y - units digit

$x=2y\\
x+y=12\\\\
2y+y=12\\
3y=12\\
y=4\\\\
x=2\cdot4\\
x=8\\\\
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$

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3 years ago

3x - 1/5= x+1/3 Could you please solve this as soon as possible

VARVARA [1.3K]

x = 0.27

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3 years ago

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3 years ago

If you knew that the vertical intercept for a straight line was 150 and that the slope of the line was 4, then the dependent var

Maslowich

Answer:

Value of the independent variable = 25

Step-by-step explanation:

y-intercept form of a straight line is represented by the equation,

y = mx + b

here y = dependent variable

m = slope

b = y intercept or vertical intercept

x = independent variable

In our question,

y-intercept 'b' = 150

slope of the line 'm' = 4

dependent variable y = 250

We will plug in these values in the equation of the line to get the value of the independent variable.

250 = 4x + 150

250 - 150 = 4x

x = $\frac{100}{4}$

x = 25

Therefore, value of the independent variable is 25.

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3 years ago

The function y = x * ln(x + e) has two distinct x intercepts. One is at x = a and the other is at x = b. The value of a + b is

Snezhnost [94]

As points, x-intercepts take the form $(x,0)$ , so to find the intercepts we can set $y=0$ and solve for $x$ .

$x\ln(x+e)=0\implies\begin{cases}x=0\\\ln(x+e)=0\end{cases}$

From the first equation alone, we already know that $x=0$ is a solution, which means one intercept is $(0,0)$ .

The second equation gives

$\ln(x+e)=0\implies e^{\ln(x+e)}=e^0\implies x+e=1\implies x=1-e$

so that the second intercept occurs at $(1-e,0)$ .

So if $a=0$ and $b=1-e$ , we have $a+b=1-e$ , giving C as the answer.

3 0

2 years ago