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3 years ago

Find the x and y intercepts of the graph of the equation 1. 3x-4y=24 2. -6x+3y=12

Mathematics

1 answer:

deff fn [24]3 years ago

7 0

Answer:

Step-by-step explanation:

Recall the intercept form of the line

x/a + y/b = 1

has intercepts at (1,0) and (0,b)

#1. Divide by 24 to get x/8 + y/-6 = 1

The intercepts are at (8,0) and (0,-6)

#2 Divide by 12

x/-2 + y/4 = 1

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Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and

Umnica [9.8K]

Answer:

The quadratic equation used to determine the thickness of frame is $\left(3+2x\right)\times \left(2+2x\right)=7$

Step-by-step explanation:

Refer to the attachment for the diagram.

Consider EFGH as the the frame and ABCD as the mirror which is to be hanged.

Let me the "x" be the thickness of the frame as shown in diagram.

Given that, BC = 3 ft and DC = 2 ft which is the dimensions of the mirror.

Now to calculate the length and width of the frame consider following calculation,

Width of frame HG = x + DC + x

Width of frame HG = x + 2 + x

Width of frame HG = 2 + 2x

2x is the addition of the thickness which is present on both side of mirror

Length of frame FG = x + BC + x

Length of frame FG = x + 3 + x

Length of frame FG = 3 + 2x

Since it is an rectangular frame, so using the formula for area of rectangle

$Area\:of\:rectangle = length \times width$

Given that area of frame is $7\:ft^{2}$

Substituting the value,

$7 = \left(3+2x\right)\times \left(2+2x\right)$

Therefore, the quadratic equation used to determine the thickness of frame is $\left(3+2x\right)\times \left(2+2x\right)=7$

8 0

3 years ago

Factor the expression completely over the complex numbers. X3+5x2+9x+45

shepuryov [24]

$x^3+5x^2+9x+45=x^2(x+5)+9(x+5)=(x+5)(x^2+9)=(*)\\\\x^2+9=x^2+3^2=x^2-(-1)(3^2)=x^2-(i^2)(3^2)=x^2-(3i)^2\\\\i=\sqrt{-1}\to i^2=-1\\\\(*)=(x+5)[x^2-(3i)^2]=(x+5)(x-3i)(x+3i)\\\\Used:\ a^2-b^2=(a-b)(a+b)\\\\Answer:\ x^3+5x^2+9x+45=(x+5)(x-3i)(x+3i)$

4 0

3 years ago

Read 2 more answers

. Which line is parallel to the line that passes through the points of (2,-5) and (-4,1)

Margaret [11]

Answer:

y= -x-5

Step-by-step explanation:

m=1-(-5)/-4-2

m=-1

-1= -x

y=-x-5

5 0

2 years ago

The time, t, required to travel a fixed distance varies inversely as the

Lemur [1.5K]

You must travel at 42 mph for 4 hours

Solution:

Time varies inversely as rate of motion

Let "t" be the time required

Let "r" be the rate of motion

Then, we get

$t \propto \frac{1}{r}\\\\t = k \times \frac{1}{r}\\\\t = \frac{k}{r} -------- eqn 1$

Where, "k" is the constant of proportionality

You travel 3 hours at a rate of 56 mph

Substitute t = 3 and r = 56 in eqn 1

$3 = \frac{k}{56}\\\\k = 3 \times 56\\\\k = 168$

Find the rate you must travel for 4 hours

r = ? and t = 4

Substitute t = 4 and k = 168 in eqn 1

$4 = \frac{168}{r}\\\\r = \frac{168}{4}\\\\r = 42$

Thus you must travel at 42 mph for 4 hours

4 0

3 years ago

Which one ,, giving 35 points to the right person

dybincka [34]

Answer:

31.5

Step-by-step explanation:

Triangular prism formula for volume is V = 1/2 a x c x h

V = 1/2 7 x 4.5 x 2

V = 1/2 63

V = 31.5 in 3

7 0

3 years ago