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LuckyWell [14K]

3 years ago

11

A triangle has an area of 221.16 in.² the height of the triangle is 29.1 inches what is the length of the base of the triangle

1 answer:

Zigmanuir [339]3 years ago

7 0

The formula you should use is Area = 1/2bh, in other words, area equals half times base times height. Now, substitute everything in, the equation should now be 221.16 = 1/2*b*29.1. This simplifies into 221.16 = 14.55b, now divide 14.55 on both sides, which leaves us to 15.2 = b. However, don't forget the units, which the answer (length of base) should be 15.2 in.^2.

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nikitadnepr [17]

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4 years ago

Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist

yuradex [85]

Answer:

0 < t < 5 is the required interval for the differential equation (t - 5)y' + (ln t)y = 6t to have a solution.

Step-by-step explanation:

Given the differential equation

(t - 5)y' + (ln t)y = 6t

and the condition y(1) = 6

We can rewrite the differential equation by dividing it by (t - 5) as

y' + [(ln t)/(t - 5)]y = 6t/(t - 5)

(ln t)/(t - 5) is continuous on the interval (0, 5) and (5, +infinity).

6t/(t - 5) is continuous on (-infinity, 5) and (5, +infinity)

We see that for these expressions, we have continuity at the intervals (0, 5) and (5, +infinity).

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The solution to differential equation is certain to exist at (0, 5)

Which implies that

0 < t < 5

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3 years ago

Calculate the speed of a car that traveled 100 meters in 10 seconds. SHOW YOUR WORK AND INCLUDE UNITS.

Varvara68 [4.7K]

Answer:

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Step-by-step explanation:

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3 years ago

Solve the following equation for x: 6(4x + 5) = 3(x + 8) + 3. Round to the nearest hundredth.

Vera_Pavlovna [14]

Answer:

$\boxed {x = -\frac{1}{7}}$

Step-by-step explanation:

Solve for the value of $x$ :

$6(4x + 5) = 3(x + 8) + 3$

-Use <u>Distributive Property</u>:

$6(4x + 5) = 3(x + 8) + 3$

$24x + 30 = 3x + 24 + 3$

-Combine like terms:

$24x + 30 = 3x + 24 + 3$

$24x + 30 = 3x + 27$

-Take $3x$ and subtract it from $24x$ :

$24x + 30 -3x = 3x - 3x + 27$

$21x + 30 = 27$

-Subtract both sides by $30$ :

$21x + 30 - 30 = 27 - 30$

$21x = -3$

-Divide both sides by $21$ :

$\frac{21x}{21} = \frac{-3}{21}$

$x = \frac{-3}{21}$

-Reduce the fraction to the lowest term by extracting and canceling out $3$ :

$x = \frac{-3\div3}{21 \div 3}$

$\boxed {x = -\frac{1}{7}}$

Therefore, the value of $x$ is $-\frac{1}{7}$ .

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