MATHEMATICS MIDDLE SCHOOL

the base length of a particular triangle is 4 inches mote than its height. it the area of the triangle is 10.5 square inches, find the base length and height brainly

Answers

Answer 1

Answer:

Answer:

Height = 3 inches and Base length = 7 inches

Step-by-step explanation:

1. Information provided to answer the question correctly:

Base of the triangle = x+ 4

Height of the triangle = x

Area of the triangle = 10.5 inches²

2. Find the base length and height

Let's recall the formula of the area of a triangle:

Area = (Base * Height)/2

Replacing with the values we know:

10.5 = x (x + 4)/2

21 = x²+ 4x

x²+ 4x - 21 = 0

(x + 7) (x - 3) = 0

(x₁ + 7) = 0 ⇒ x₁ = -7

(x₂ - 3) = 0 ⇒ x₂ = 3

We take x₂ as the answer because x₁ = -7 is not a valid height.

Height = 3 inches and Base length = 7 inches

Answer

$f(x)=3(2)^x$

Explanation

To solve this, we re using the standard exponential equation: $f(x)=ab^x$

Also, remember that $f(x)=y$

We know that our exponential function goes through the points (1, 6) and (2, 12), so we are going to replace the points in our stander exponential equation and solve for $a$ and $b$ :

For (1, 6)

$x=1$ and $y/f(x)=6$ , so:

$f(x)=ab^x$

$6=ab^1$

$6=ab$

$a=(6)/(b)$ equation (1)

For (2, 12)

$x=2$ and $y/f(x)=12$ , so:

$f(x)=ab^x$

$12=ab^2$ equation (2)

Replace equation (1) in equation (2) and solve for b

$12=ab^2$

$12=((6)/(b)) b^2$

$12=6b$

$b=(12)/(6)$

$b=2$ equation (3)

Replace equation (3) in equation (1) to find a

$a=(6)/(b)$

$a=(6)/(2)$

$a=3$

Now we can complete our exponential function:

$f(x)=ab^x$

$f(x)=3(2)^x$

We can conclude that the exponential function that goes through the points (1, 6) and (2, 12) is $f(x)=3(2)^x$

Proportional relationships!
Need help on!

Answers

Direct variation has this equation:

y = kx

where k is the constant of variation

y = -5 ; x = -15

y = kx
-5 = k(-15)
-5/-15 = k
1/3 = k

Choice D. y = 1/3 x

julian is mixing drops of food coloring to create green frosting for a cake he uses 18 drops of yellow dye and 12 drops of blue dye find the ratio of drops of blue dye to total drops of dye express as a SIMPLIFIED RATIO

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so the ratio is 18:12. you just divide each number down as much as you can so for this they are both divisible by 6 giving you a ratio of 3:2

Round 845,001 to the nearest

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-- Rounded to the nearest ten, hundred, or thousand,
845,001 becomes 845,000 .

-- Rounded to the nearest ten thousand, 845,001 becomes 850,000 .

-- Rounded to the nearest hundred thousand, 845,001 becomes 800,000 .

-- Rounded to the nearest million, 845,001 becomes 1,000,000 .

-- Rounded to the nearest ten million or any higher order of magnitude,
845,001 becomes zero.

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the base length of a particular triangle is 4 inches mote than its height. it the area of the triangle is 10.5 square inches, find the base length and height brainly

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