Answer:
The parent function f(x) is equal to
The translations is 3 units to the left and 5 units down
Step-by-step explanation:
we have
The vertex of the function h(x) is the point (-3,-5)
we know that the parent function f(x) is equal to
The vertex of the function f(x) is the point (0,0)
so
The rule of the transformation of f(x) to h(x) is equal to
(x,y) -----> (x-3,y-5)
That means ----> The translations is 3 units to the left and 5 units down
Answer:
The result is significant.
Step-by-step explanation:
Here,
p = 30 ÷ 330 = 0.091
thus, q = 1 - p = 0.909
Also,
⇒
The z-score is:
Thus, at 95% confidence interval, p-value = 0.005
The result is significant at p < .05.
The price of 1 hat is $ 5 and price of 1 t-shirt is $ 8
<em><u>Solution:</u></em>
Let "s" be the price of 1 shirt
Let "h" be the price of 1 hat
<em><u>Given that Jones buys 7 t-shirts and 6 hats for $86</u></em>
Therefore, we can frame a equation as:
price of 1 shirt x 7 + price of 1 hat x 6 = 86
7s + 6h = 86 ------ eqn 1
<em><u>Also given that The price of each t shirt is $3 more than the price of each hat</u></em>
price of 1 shirt = 3 + price of 1 hat
s = 3 + h -------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
Substitute eqn 2 in eqn 1
7( 3 + h ) + 6h = 86
21 + 7h + 6h = 86
21 + 13h = 86
13h = 86 - 21
13h = 65
<h3>h = 5</h3>From eqn 2,
s = 3 + h = 3 + 5 = 8
<h3>s = 8</h3>Thus price of 1 hat is $ 5 and price of 1 t-shirt is $ 8
The image of the triangle is missing, so i have attached it.
Also, the options are;
A) The apothem can be found using the Pythagorean theorem.
B) The apothem can be found using the tangent ratio.
C) The perimeter of the equilateral triangle is 15 cm.
D) The length of the apothem is approximately 2.5 cm.
E) The area of the equilateral triangle is approximately 65 cm².
Answer:
Options A, B & D are true
Step-by-step explanation:
A) We are told that the triangle is an equilateral triangle.
Thus, the 3 sides equal 8.7 cm.
Now from the image, b is half of one of the sides.
Thus, b = 8.7/2 = 4.35 cm
Now, we want to find the apothem "a".
Using Pythagoras theorem, we have;
a² + 4.35² = 5²
a² = 25 - 18.9225
a² = 6.0775
a = √6.0775
a ≈ 2.5 cm.
Thus, option A is true as pythagoras theorem was able to calculate the apothem "a"
B) since the main triangle is equilateral, it means each angle is 60°.
Now,the radius line from one corner point to the centre will divide the 60° angle into 2 equal parts.
Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°
Now,from tangent ratios, we know that;
Opposite/Adjacent = tan θ
In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm
Thus;
a/4.35 = tan 30
a = 4.35 tan 30
a ≈ 2.5 cm.
Thus, option B is correct as Tangent ratio can be used to find the apothem
C) The perimeter of equilateral triangle = 3x
Where x is length of one side.
One side is 8.7 cm
Thus, perimeter = 3 × 8.7 = 26.1 cm
Thus option C is not correct.
D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.
Thus, option D is true.
E) Area of triangle is;
A = ½ × base × height
Base = 8.7 cm
To get height, we will use trigonometric ratio. Thus;
h/8.7 = sin 60°
h = 8.7 sin 60°
Thus;
A = ½ × 8.7 × 8.7 sin 60°
A = 32.77 cm²
Thus is not equal to 65 cm². Thus, option E is not correct.
