MATHEMATICS HIGH SCHOOL

The perimeter of a rectangle of 150 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle

Answers

Answer 1
Answer:

Length (L): 2w

width (w): w

Perimeter (P) = 2L + 2w

               150 = 2(2w) + 2(w)

               150 = 4w + 2w

                150 = 6w

                 25 = w

Length (L): 2w   = 2(25)   = 50

Answer: width = 25 feet, length = 50 feet

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Find the x-intercept of the parabola with vertex (1,-13) and y-intercept (0,-11).

Answers

Standard form of equation for a parabola: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of vertex
using given coordinates of vertex:
y=A(x-1)^2-13
using given coordinates of y-intercept:
-11=A(0-1)^2-13
A=2
Equation of parabola: y=2(x-1)^2-13
x-intercepts

set y=0
0=2(x-1)^2-13
2(x-1)^2=13
(x-1)^2=13/2
x-1=±√(13/2)
x=1±√(13
1. find equation

general solutions are:
y = a x^(2) +bx +c \n \n (dy)/(dx) = 2ax +b

for P(0,-11)

-11 = 0a + 0b +c ⇒c = -11

for p(1,-13)
-13 = 1a + 1b -11 \n a+b = -2

and

0 = 2a + b \n b = -2a

solve for a and b:
a - 2a = -2 \n a = 2 \n b = -4

the total equation is now:

y = 2 x^(2) -4x -11

To find the x-intercept set y=0 and solve for x

0 = 2 x^(2) -4x-11

Which of the following points does not lie on the graph of y = log3x?(0, 1)
(27, 3)
(1, 0)

Answers

Answer:

(0,1) doesn't lie on the graph.

Step-by-step explanation:

We have been given the logarithmic equation y=\log_3(x)

We can check which point lie on the graph of the given function by substituting x coordinates in the equation and find the corresponding y coordinate.

For x = 0

y=\log_3(0)\n\ny=\log_30

The value of log 0, is undefined, Hence, we'll not get a real value for this x value.

Hence, (0,1) doesn't lie on the graph.

For x = 27

y=\log_3(27)\n\ny=\log_33^3\n\ny=3\log_33\n\ny=3

Hence, (27,3) lie on the graph.

For x = 1

y=\log_3(1)\n\ny=0

Hence, (1,0) lie on the graph.

Therefore, (0,1) doesn't lie on the graph.
(27, 3)
(1, 0)

Working;
Substituting the value of x;
x=27
y=log81
=1.9084
x=1
y=log 3
y=0.4771

the world's smallest country is Vatican City it covers 17/100 square mile what is Vatican City area written as a decimal

Answers

17/100 is the same as 17÷100. 17÷100 =0.17 sqr mile.
OR 17/100, the denominator means what place it is in. The denominator is100, so it's in the hundredth place. 0.17

Answer:

Step-by-step explanation:

17/100=17÷100=0.17 km2

I hope it'll help you much

Thank you for asking

Do you know these Answers plz??????

Answers

Answer:

d c a

Step-by-step explanation:

A rectangular lot that measures 125 feet by 185 feet is completely fenced. What is the length, in feet, of the fence?Can you please explain with some details?

Answers

620, because 125+125+185+185=620, and that would be the perimeter of the rectangle.

Write an equation of the line that passes through the points (3,6) and (4,10) using function notation. A.) f(x) = 4x - 6

B.) f(x) = x + 4

C.) y = x + 4

D.) y = 4x - 6

Answers

Given:
(3,6) and (4,10)

a) f(x) = 4x - 6
f(3) = 4(3) - 6         f(4) = 4(4) - 6
f(3) = 12 - 6            f(4) = 16 - 6
f(3) = 6                    f(4) = 10

b) f(x) = x + 4
f(3) = 3 + 4             f(4) = 4 + 4
f(3) = 7                    f(4) = 8

c) y = x + 4
y = 3 + 4                y = 4 + 4
y = 7                      y = 8

d) y = 4x - 6
y = 4(3) - 6            y = 4(4) - 6
y = 12 - 6               y = 16 - 6
y = 6                       y = 10

Among the choices, choice A and D have the same value. However, the problem says functions notation. Choice A. is the function notation. A.) f(x) = 4x - 6
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