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2 years ago

Graph the line with slope -2 passing through the point (4, 1)

Mathematics

1 answer:

Scrat [10]2 years ago

4 0

Answer:

Use points (4,1) and (3,-1)

Step-by-step explanation:

Let's say the other coordinates are (x,y).

Then, we know (1-y)/(4-x)=2. So if y is -1, and x is 3, then we get:

[1-(-1)]/(4-3)=2/1=2

So draw the two points, (4,1) and (3,-1) on a coordinate plane, and use a ruler to make a line that goes through both the points.

You might be interested in

The volume of a cylinder is 628 cm3. Find the radius of the base if the cylinder

kirza4 [7]

Radius is 5 cm. is the answer

8 0

2 years ago

Maths functions question!!

Marina86 [1]

Answer:

5) DE = 7 units and DF = 4 units

6) ST = 8 units

$\textsf{7)} \quad \sf OM=\dfrac{3}{2}\:units$

8) x ≤ -3 and x ≥ 3

Step-by-step explanation:

<u>Information from Parts 1-4:</u>

brainly.com/question/28193969

$f(x)=-x+3$

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

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

Points A and D are the <u>points of intersection</u> of the two functions.

To find the x-values of the points of intersection, equate the two functions and solve for x:

$\implies g(x)=f(x)$

$\implies x^2-9=-x+3$

$\implies x^2+x-12=0$

$\implies x^2+4x-3x-12=0$

$\implies x(x+4)-3(x+4)=0$

$\implies (x-3)(x+4)=0$

Apply the zero-product property:

$\implies (x-3)= \implies x=3$

$\implies (x+4)=0 \implies x=-4$

From inspection of the graph, we can see that the x-value of point D is <u>negative</u>, therefore the x-value of point D is x = -4.

To find the y-value of point D, substitute the found value of x into one of the functions:

$\implies f(-4)=-(-4)=7$

Therefore, D = (-4, 7).

The length of DE is the difference between the y-value of D and the x-axis:

⇒ DE = 7 units

The length of DF is the difference between the x-value of D and the x-axis:

⇒ DF = 4 units

To find point S, substitute the x-value of point T into function g(x):

$\implies g(4)=(4)^2-9=7$

Therefore, S = (4, 7).

The length ST is the difference between the y-values of points S and T:

$\implies ST=y_S-y_T=7-(-1)=8$

Therefore, ST = 8 units.

The given length of QR (⁴⁵/₄) is the difference between the functions at the same value of x. To find the x-value of points Q and R (and therefore the x-value of point M), subtract g(x) from f(x) and equate to QR, then solve for x:

$\implies f(x)-g(x)=QR$

$\implies -x+3-(x^2-9)=\dfrac{45}{4}$

$\implies -x+3-x^2+9=\dfrac{45}{4}$

$\implies -x^2-x+\dfrac{3}{4}=0$

$\implies -4\left(-x^2-x+\dfrac{3}{4}\right)=-4(0)$

$\implies 4x^2+4x-3=0$

$\implies 4x^2+6x-2x-3=0$

$\implies 2x(2x+3)-1(2x+3)=0$

$\implies (2x-1)(2x+3)=0$

Apply the zero-product property:

$\implies (2x-1)=0 \implies x=\dfrac{1}{2}$

$\implies (2x+3)=0 \implies x=-\dfrac{3}{2}$

As the x-value of points M, Q and P is negative, x = -³/₂.

Length OM is the difference between the x-values of points M and the origin O:

$\implies x_O-x_m=o-(-\frac{3}{2})=\dfrac{3}{2}$

Therefore, OM = ³/₂ units.

The values of x for which g(x) ≥ 0 are the values of x when the parabola is above the x-axis.

Therefore, g(x) ≥ 0 when x ≤ -3 and x ≥ 3.

8 0

8 months ago

Read 2 more answers

write the slope-intercept form for the equation of the line described through (4,-5) and parallel to y=--5/4x-4

Tems11 [23]

Answer:

y = -5x/4 + 0

Step-by-step explanation:

Find the slope

y = -5/4x - 4

Slope is the coefficient of x

Slope m = -5/4

Substitute m into point slope form equation

y - y1 = m(x - x1)

y - y1 = -5/4( x - x1)

Substitute the point into the equation

( 4 , -5)

x1 = 4

y1 = -5

y - y1 = -5/4( x - x1)

y - (-5) = -5/4( x - 4)

y + 5 = -5/4(x - 4)

Using a slope intercept form equation

y = mx + c

y - intercept point y

m - slope

x - intercept point x

c - intercept

open the bracket with -5/4

y + 5 = -5(x - 4)/4

y + 5 = (-5x + 20)/4

y = (-5x + 20)/4 - 5

LCM = 4

y =( -5x + 20 - 20)/4

y = ( -5x + 0)/4

Rearrange in

y = mx + c

y = -5x/ 4 + 0/4

y = -5x/4 + 0

The equation of the line is

y = -5x/4 + 0

3 0

2 years ago

Is this statement about equivalent expressions true?<br> (2 + 5) + 8 = 2 + (5 + 8)

alexdok [17]

Yes

(2+5)+8=2+(5+8)
7+8=2+13
15=15

6 0

2 years ago

A circle with radius 16 centimeters is inscribed in a square.Which is the area of the shaded region? A. 804.25 square feet B. 10

Dmitrij [34]

<u><em>Answer:</em></u>

Area of shaded region = 220.16 ft²

<u><em>Explanation:</em></u>

The diagram associated with this question is shown in the attached image

Unit in diagram is ft, so I'll use this unit in the answer

We are given that a circle with radius 16 ft is inscribed in a square

We know that the radius of an inscribed circle in a square is equivalent to half the length of the side of the square

<u>This means that:</u>

side length of the square = 2 × radius = 2 × 16 = 32 ft

<u>From the diagram, we can note that:</u>

area of shaded region = area of square - area of circle .............> equation I

<u>1- getting area of square:</u>

Area of a square is the square of its side length

<u>This means that:</u>

Area of square = (32)² = 1024 ft²

<u>2- getting the area of the circle:</u>

Area of circle = πr² = 3.14 × (16)² = 803.84 ft²

<u>3- getting area of shaded region:</u>

<u>Use equation I</u>

area of shaded region = area of square - area of circle

area of shaded region = 1024 - 803.84 = 220.16 ft²

Hope this helps :)

5 0

2 years ago