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2 years ago

Find the area. The figure is not drawn to scale.

Mathematics

1 answer:

Rina8888 [55]2 years ago

6 0

Answer:
area = 13.8 cm²

Explanation:
The area of the triangle can be calculated using the following rule:
area of triangle = (1/2) * base * height

In the given:
base of triangle = 6.9 cm
height of triangle = 4 cm

Substitute with the givens in the above equation to get the area as follows:
Area = (1/2) * (6.9) * (4)
Area = 13.8 cm²

Hope this helps :)

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How to find (c,d,e) Please do a step by step working.Thank you.

Natasha2012 [34]

(a)
The inverse is when you swap the variables and solve for y.
g(t) = 2t - 1 (Note: g(t) represents y)
rewrite as: y = 2t - 1
swap the variables: t = 2y - 1
solve for y: t + 1 = 2y
   $\frac{t + 1}{2}$ = y
Answer for (a): $g^{-1}(t)$ = $\frac{t + 1}{2}$

(b)
Same steps as part (a) above:
h(t) = 4t + 3
rewrite as: y = 4t + 3
swap the variables: t = 4y + 3
solve for y: $y =\frac{t - 3}{4}$

Answer for (b): $h^{-1}(t)$ = $\frac{t - 3}{4}$

(c)
$g^{-1} ( h^{-1}(t)) = g^{-1} (\frac{t - 3}{4})$
replace all t's in the $g^{-1}(t)$ equation with $\frac{t - 3}{4}$
$g^{-1} (\frac{t - 3}{4})$ = $\frac{ \frac{t-3}{4} + 1}{2}$
= $\frac{ \frac{t-3}{4} + \frac{4}{4}}{2}$ = $\frac{ \frac{t - 3 + 4}{4}}{2}$ = $\frac{ \frac{t + 1}{4}}{2} = \frac{t + 1}{8}$
Answer for (c): $g^{-1} ( h^{-1}(t))$ = $\frac{t + 1}{8}$

(d)
h(g(t)) = h(2t - 1) = 4(2t - 1) + 3 = 8t - 4 + 3 = 8t - 1
Answer for (d): h(g(t)) = 8t - 1

(e)
h(g(t)) = 8t - 1
   y = 8 t - 1
   t = 8y - 1
t + 1 = 8y
$\frac{t + 1}{8}$ = y
Answer for (e): inverse of h(g(t)) = $\frac{t + 1}{8}$

8 0

2 years ago

Given that (5,-8) is on the graph of f(x), find

My name is Ann [436]

Answer:

The corresponding point for the function f(x + 2) is (3 , -8)

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) translated horizontally to the right by h units,

then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left by h units,

then the new function g(x) = f(x + h)

* Lets solve the problem

- There is a graph of f(x)

- Point (5 , -8) lies on the graph of f(x)

- The graph of f(x) change to f(x + 2)

∵ f(x) ⇒ f(x + 2)

∵ If the function f(x) translated horizontally to the left by h units,

then the new function g(x) = f(x + h)

∴ f(x) translated horizontally 2 units to the left

∴ Any point on the graph its x-coordinate translated 2 units

to the left

∴ The x-coordinate of any point on the graph is subtracted by 2

∵ Point (5 , -8) lies on the graph

∴ Its corresponding point is (5 - 2 , -8) = (3 , -8)

* The corresponding point for the function f(x + 2) is (3 , -8)

7 0

2 years ago

Ethan jogged 1 1/3 miles. Chloe jogged 1 1/4 times as far as Ethan. How many miles did Chloe jog?

Paul [167]

Ethan jogged 1 1/3 miles. Chloe jogged 1 1/4 times as far as Ethan. How many miles did Chloe jog?
2.7miles

3 0

2 years ago

According to the key of a particular park map, every 8 inches on the map represents 3 miles of trails in the park. How many inch

MA_775_DIABLO [31]

Answer:

24 inches represents 9 miles in the map

Step-by-step explanation:

To solve this problem you take into account that 8 inches represents 3 miles and that x represent the number of inches for 9 miles. That is:

8 ------- 3

x ------- 9

This is simply a rule of three, then you calculate:

$x=\frac{8\ x\ 9}{3}=\frac{72}{3}=24$

Hence, 24 inches represents 9 miles in the map

8 0

2 years ago

How many times does 50 go into 4000

iVinArrow [24]

Well, if you just divide 4000 by 50, you can see that the answer will come out as:
80
~TO check: 80 multiplied by 50 would come out to the answer of 4,000.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hope this helped! :D

8 0

2 years ago

Read 2 more answers