This is freshman year math or algebra 1 please help me solve. <br><br><br> w=2hx-11x

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

3 more than w divided by 7 is 9

svlad2 [7]

3 + [_] ÷ 7 = 9

[_] ÷ 7 = 9 - 3

[_] = 6 x 7

[_] = 42

to check, just put 42 in the empty place and solve

5 0

3 years ago

I need help ASAP!!!!!!

topjm [15]

Answer:

1. YES 2. NO

Step-by-step explanation:

1. Since x=0.121212... and the question is asking for 100x, we need to multiply each side by 100. 0.121212... multiplied by 100 is 12.1212... So YES, 100x is still a repeating decimal.

2. 12.121212... minus 0.121212... would just be 12. This is because if we know that all the numbers behind the decimal point is 0.121212 and so on, 12.121212... minus 0.121212... the numbers behind the decimal would cancel out. So we are left with 12. So NO, the answer for 99x is NOT a repeating decimal.

6 0

3 years ago

A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front

Mariana [72]

Answer:

B. 32

Step-by-step explanation:

Let's start by defining the multiplication principle.

If a first experiment can happen in ''a1'' ways,a second experiment can happen in ''a2'' ways ... and finally a ''ni'' experiment can happen in ''ai'' ways ⇒ the total ways in which the whole experiment can take place are :

a1 x a2 x ... x ai

Let's also define the arrangement of ''n'' objects in a straight line.

This arrangement is the number n!

For example if we want all the arrangements for letters A,B and C (n = 3) this number is 3! = 3.2.1 = 6

For the problem we are going to calculate the arrangements in which the father is driving and then multiply that number by 2 to obtain the arrangements in which the father and the mother drive.

When the father drives there are 4 possible seats for 4 persons ⇒ 4! = 16 ways this 4 persons can sit.

Now we subtract the ways in which the two daughters are sitting next to each other.

This number is 2 x 2 x 2.

The ''first'' two is because the two daughters can seat one in the middle seat and one in the right window or one in the middle seat and one in the left window.

The ''second'' two is because the daughters are each different.

And the last two is the ways in which the mother and the son can sit ⇒

$4!-2^{3}=24-8=16$

If the father drive, there are 16 ways for this arrangement.

Now we multiply by 2 to obtain all the arrangements (we don't forget the case in which the mother drives).

$(16).2=32$

There are 32 possible seating arrangements.

6 0

3 years ago

{[9 x (7.3+10.7)} - 5} + [3 x (7.8 - 6.8)}

otez555 [7]

Answer:

160.

Step-by-step explanation:

Work out the innermost parentheses first:

{[9 x (7.3+10.7)} - 5} + [3 x (7.8 - 6.8)}

= {[9 x 18} - 5} + [3 x 1}

= {162 - 5} + 3

= 160.

6 0

3 years ago

This is freshman year math or algebra 1 please help me solve. w=2hx-11x