Which decimal is equivalent to ?<br> 29/11<br> Choose 1 answer:<br> 2.63<br> 2.6363<br> 2.63<br> 2.6

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

1 year ago

Read 2 more answers

A shop sells chocolate, vanilla and strawberry ice cream cones. In one day, 45% of the ice cream cones sold are vanilla and 17%

True [87]

Answer:

950

Step-by-step explanation:

As, 45% will be vanilla, and 17% will be strawberry

So chocolate will be = 38%

As, 45%+17%+38% = 100%

So 38% of 2,500 = chocolate cones

= 38/100 x 2,500 = 950

So the number chocolate ice cream cone sold is 950.

8 0

3 years ago

Need some help on this question please:(

xxTIMURxx [149]

Answer:

B

Step-by-step explanation:

sorry if its wrong

5 0

3 years ago

45-45-90 method <br> Please help and show your work!!!

Dvinal [7]

Answer:

hope this helps and u understood it

check the steps in the picture attached

3 0

3 years ago

A player moves a knight from location (3, 2) to (5, 1) on a chessboard. If the bottom-left square is labeled (1, 1), which descr

Kitty [74]

Translation , <span>in geometry ,is described as the movement of a function or graph to a certain distance.Or simply the transformation of the image to a certain level without rotating or reflecting.
Hence,
Using the idea of translation I have concluded the movement of </span><span>location (3, 2) to (5, 1) on a chessboard will result:
</span>
2 units to the right and 1 unit down.
1 unit to the right and 2 units up

5 0

4 years ago

Which decimal is equivalent to ? 29/11 Choose 1 answer: 2.63 2.6363 2.63 2.6