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3 years ago

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Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represen

ts the decimal Letter C represents the decimal

1 answer:

jok3333 [9.3K]3 years ago

7 0

$10$ divisions between $15.59$ and $15.6$ so each division is $\frac{15.60-15.59}{10}=0.001$

A is 5 division from $15.59$, so, A is $15.59+5\times 0.001=15.595$

similarly, C is 4 division behind $15.59$ so it is $15.590-4\times0.001=15.586$

and B is $15.601$

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452 divided by 7 with remaining

ozzi

Answer: The answer is 64 remaining 5.

Step-by-step explanation:

6 0

3 years ago

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A forestal station receives the locations of two fires, one of them in a forest located 11 Km heading N69°W from the station. Th

loris [4]

Answer:

30.7 km

Step-by-step explanation:

The distance between the two fires can be found using the Law of Cosines. For ΔABC in which sides 'a' and 'b' are given, along with angle C, the third side is ...

c = √(a² +b² -2ab·cos(C))

The angle measured between the two fires is ...

180° -(69° -35°) = 146°

and the distance is ...

c = √(11² +21² -2(11)(21)cos(146°)) ≈ √945.015

c ≈ 30.74

The straight-line distance between the two fires is about 30.7 km.

8 0

3 years ago

Maths functions <br> please help!

Vlad [161]

Answer:

$\textsf{1)} \quad f(x)=-x+3$

2) A = (3, 0) and C = (-3, 0)

$\textsf{3)} \quad g(x)=x^2-9$

4) AC = 6 units and OB = 9 units

Step-by-step explanation:

Given functions:

$\begin{cases}f(x)=mx+c\\g(x)=ax^2+b \end{cases}$

<h3><u>Part (1)</u></h3>

Given points:

H = (-1, 4)
T = (4, -1)

As points H and T lie on f(x), substitute the two points into the function to create two equations:

$\textsf{Equation 1}: \quad f(-1)=m(-1)+c=4 \implies -m+c=4$

$\textsf{Equation 2}: \quad f(4)=m(4)+c=-1 \implies 4m+c=-1$

Subtract the first equation from the second to eliminate c:

$\begin{array}{r l} 4m+c & = -1\\- \quad -m+c & = \phantom{))}4\\\cline{1-2}5m \phantom{))))}}& = -5}\end{aligned}$

Therefore m = -1.

Substitute the found value of m and one of the points into the function and solve for c:

$\implies f(4)=-1(4)+c=-1$

$\implies c=-1-(-4)=3$

Therefore the equation for function f(x) is:

$f(x)=-x+3$

<h3><u>Part (2)</u></h3>

Function f(x) crosses the x-axis at point A. Therefore, f(x) = 0 at point A.

To find the x-value of point A, set f(x) to zero and solve for x:

$\implies f(x)=0$

$\implies -x+3=0$

$\implies x=3$

Therefore, A = (3, 0).

As g(x) = ax² + b, its axis of symmetry is x = 0.

A parabola's axis of symmetry is the midpoint of its x-intercepts.

Therefore, if A = (3, 0) then C = (-3, 0).

<h3><u>Part (3)</u></h3>

Points on function g(x):

A = (3, 0)
G = (1, -8)

Substitute the points into the given function g(x) to create two equations:

$\textsf{Equation 1}: \quad g(3)=a(3)^2+b=0 \implies 9a+b=0$

$\textsf{Equation 2}: \quad g(1)=a(1)^2+b=-8 \implies a+b=-8$

Subtract the second equation from the first to eliminate b:

$\begin{array}{r l} 9a+b & = \phantom{))}0\\- \quad a+b & =-8\\\cline{1-2}8a \phantom{))))}}& = \phantom{))}8}\end{aligned}$

Therefore a = 1.

Substitute the found value of a and one of the points into the function and solve for b:

$\implies g(3)=1(3^2)+b=0$

$\implies 9+b=0\implies b=-9$

Therefore the equation for function g(x) is:

$g(x)=x^2-9$

<h3><u>Part 4</u></h3>

The length AC is the difference between the x-values of points A and C.

$\implies x_A-x_C=3-(-3)=6$

Point B is the y-intercept of g(x), so when x = 0:

$\implies g(0)=(0)^2-9=-9$

Therefore, B = (0, -9).

The length OB is the difference between the y-values of the origin and point B.

$\implies y_O-y_B=0-(-9)=9$

Therefore, AC = 6 units and OB = 9 units

3 0

2 years ago

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Please help!!!! <br><br> If f(1) = 2 and f(n+1) = f(n)^2 – 3 then find the value of f(3).

Black_prince [1.1K]

Answer:

The value of f(3) is -2.

Step-by-step explanation:

This is a recursive function. So

$f(1) = 2$

Now, we find f(2) in function of f(1). So

$f(1+1) = f(1)^2 - 3$

$f(2) = f(1)^2 - 3 = 2^2 - 3 = 1$

Now, with f(2), we can find the value of f(3).

$f(2+1) = f(2)^2 - 3$

$f(3) = f(2)^2 - 3 = 1^2 - 3 = -2$

The value of f(3) is -2.

4 0

3 years ago

Help with a few questions pleaseeeeee

mel-nik [20]

29.99 * 3 =89.97 89.97 with 30% off = 62.98 and 5% of 62.98 =3.15 so 62.98 + 3.15 = 66.13$

180.00 + 14.95 + 8.95 = 203.09 - 15% = 173.44 + 4% = 180.38

5.65 + 5% of 5.65 = 5.93

i think this is all right you might want to check my work!

3 0

4 years ago