Find two numbers that add up to 158. The greater number is 40 more than the lesser number

For each 3 mm of coloured fabric Alex uses to make his curtains, he also uses 2 cm of white fabric. Express the amount of white

Leokris [45]

Answer: 2cm/.2cm

Step-by-step explanation:

5 0

2 years ago

A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two

Oliga [24]

Let

x-------> the length of the rectangle

y------> the width of the rectangle

we know that

The area of the rectangle is equal to

$A=x*y$

The area of the two congruent right triangles is equal to the area of the rectangle

$A=2*44=88\ in^{2}$

so

$88=x*y$ -------> equation A

$y=x-3$ -----> equation B

Substitute equation B in equation A

$x*[x-3]=88$

$x^{2} -3x-88=0$ --------> equation that can be used to solve for the length of the rectangle

Using a graph tool-------> solve the quadratic equation

see the attached figure

The solution is

$x=11\ in$ -----> the length of the rectangle

Find the value of y

$88=11*y$

$y=8\ in$ ----> the width of the rectangle

Statements

case A) The area of the rectangle is $88$ square inches

The statement is True

See the procedure

Case B) The equation $x*[x-3]=44$ can be used to solve for the dimensions of the triangle

The statement is False

Because, the equation $x*[x-3]=88$ can be used to solve for the dimensions of the triangle

case C) The equation $x^{2} -3x-88=0$ can be used to solve for the length of the rectangle

The statement is True

see the procedure

case D)The triangle has a base of $11$ inches and a height of $8$ inches

The statement is True

Because, the base of the triangle is equal to the length of the rectangle and the height of the triangle is equal to the width of the rectangle

case E) The rectangle has a width of $4$ inches

The statement is False

See the procedure

8 0

2 years ago

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Complete the equation describing how x and y are related. Help please!!!

Ivahew [28]

Answer:

-4

Step-by-step explanation:

Y = -4x+-2

Not quite sure how to explain it on here but substitute it and it works. :)

5 0

2 years ago

A caterer makes 3 extra sandwhiches for every 20 sandwhiches a customer orders. What is the ratio of ordered sandwiches to extra

VMariaS [17]

You can solve this by making a proportion.

$\frac{3}{20} = \frac{x}{184}$

you cross multiply and divide to solve this. your answer is 8.

4 0

2 years ago

LK is tangent to circle J at point K. Circle J is shown. Line segment J K is a radius. Line segment K L is a tangent that inters

Evgen [1.6K]

Answer:

$(B)r=\dfrac{85}{12}$

Step-by-step explanation:

Given a circle centre J

Let the radius of the circle =r

LK is tangent to circle J at point K

From the diagram attached

LX=6
Radius, XJ=JK=r
LK=11

Theorem: The angle between a tangent and a radius is 90 degrees.

By the theorem above, Triangle JLK forms a right triangle with LJ as the hypotenuse.

Using Pythagoras Theorem:

$(6+r)^2=r^2+11^2\\(6+r)(6+r)=r^2+121\\36+6r+6r+r^2=r^2+121\\12r=121-36\\12r=85\\r=\dfrac{85}{12}$

The length of the radius, $r=\dfrac{85}{12}$

8 0

2 years ago

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