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3 years ago

Please help meeeeeeeeeeeeeeeeeeeeeeeeeeee

Mathematics

2 answers:

Ira Lisetskai [31]3 years ago

7 0

7)a=1.5
8)m=2/5
9)z=5/6
10)a=4/5
11)b=1.3
12)z=7/100

Gala2k [10]3 years ago

4 0

Answer:

With all or just 1

Step-by-step explanation:

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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:

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

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:

$f(x)=-x+3$

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).

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:

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

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

Read 2 more answers

I’m stuck on this question. any help would be greatly appreciated

Mademuasel [1]

Using the Pythagorean theorem we get:

$y^2+8^2=12^2.$

Simplifying the above result we get:

$y^2+64=144.$

Subtracting 64 from the above equation we get:

$\begin{gathered} y^2+64-64=144-64, \\ y^2=80. \end{gathered}$

Therefore:

$y=\sqrt{80}\approx8.9.$

Answer:

$y=8.9.$

4 0

2 years ago

Leo has already taken 1 page of notes on his own, and he will take 1 page during each hour

sattari [20]

Answer:

49 Hours

Step-by-step explanation:

If it takes him 1 hour to finish 1 page of notes and he already finished 1, he would need to do a total of 49 hours to get 49 more pages done.

Hope this helps!

8 0

3 years ago

What's the Answer ~ <br><br><img src="https://tex.z-dn.net/?f=%20%5Csf%20%5Ctiny%7B14%20%20%2B%20%2014%20%5Cdiv%207%7D" id="TexF

butalik [34]

Step-by-step explanation:

remember the priorities of the different mathematical operations

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

so,

14 + 14/7 = 14 + 2 = 16

8 0

2 years ago

Read 2 more answers

The radius of the base to the right circular cone shown below is 5 inches, and the height of the cone is 7 inches. Solving which

Yuri [45]

Step-by-step explanation:

In right angled triangle

Tan = opposite side / adjacent side

Opposite side = 7 inches

Adjacent side = 5 inches

Tan = 7/5

5 0

3 years ago