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3 years ago

What is the solution set for −4 x + 10 ≥ 5 x + 55?

Mathematics

1 answer:

valentina_108 [34]3 years ago

8 0

Answer:

(-5,0)

Step-by-step explanation:

Put -4x+10 ≥ 5x+55 in Desmos Scientific Calculator and you have your answer

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Find the area of the triangle defined by the given system?

just olya [345]

Look at my pfp it tells you the answer

6 0

3 years ago

Please help me.......... only 32,and 33

kupik [55]

Answer:

Step-by-step explanation:

Step 1 : Draw PQ = 6cm

Step 2 : Construct 60 degree at Q. [Given PQR = 60=> Q = 60 ]

Step 3 : Take 5 cm on compass and mark 5cm on the 60 degree

line constructed at Q.

Step 4 : The arc of 5cm and 60 degree line meets is the point R.

[Given QR = 5cm ]

Step 5 : Given PQ || SR so construct a 120° at R ,

because ∠PQR and ∠QRS are supplementary angle.

[ ∠PQR + ∠QRS = 60 + 120 = 180° ]

Step 6 : At P , take 6.5 cm on compass and mark on the line drawn in

Step 5, to get S. [ Given PS = 6.5 ]

Given adjacent sides : 4.8 and 4.2

And it is a rectangle.

Step 1 : construct AB = 4.8 cm

Step 2 :At A and B construct 90 degree

Step 3: On the compass take 4.2cm and mark on the 90degree lines

from A and B.

Step 4 : Mark that as C and D respectively.

Step 5 : Join CD

8 0

3 years ago

Determine the equation of g(x) that results from translating the function f(x)=x^2+9 upward 10 units.

Rus_ich [418]

The simple/ common sense method:
The typical lay out of a quadratic equation is ax^2+bx+c
'c' represents where the line crosses the 'y' axis.
The equation is only translated in the 'y' (upwards/downwards) direction, therefore only the 'c' component of the equation is going to change.
A translation upwards of 10 units means that the line will cross the 'y' axis 10 places higher.
9+10=19,
therefore c=19.
The new equation is: y=x^2+19 

The most complicated/thorough method:
This is useful for when the graph is translated both along the 'y' axis and 'x' axis.
ax^2+bx+c
a=1, b=0, c=9
Find the vertex (the highest of lowest point) of f(x).
Use the -b/2a formula to find the 'x' coordinate of your vertex..
x= -0/2*1, your x coordinate is therefore 0.
substitute your x coordinate into your equation to find your y coordinate..
y= 0^2+0+9
y=9.
Your coordinates of your vertex f(x) are therefore (0,9) 
The translation of upward 10 units means that the y coordinate of the vertex will increase by 10. The coordinates of the vertex g(x) are therefore:
(0, 19) 
substitute your vertex's y coordinate into f(x)
19=x^2+c
19=0+c
c=19
therefore g(x)=x^2+19

7 0

3 years ago

Read 2 more answers

A group of three undergraduate and five graduate students are available to fill certain student government posts. If four studen

creativ13 [48]

Answer:

$Pr = 0.4286$

Step-by-step explanation:

Given

Let

$U \to\\$ Undergraduates

$G \to$ Graduates

So, we have:

$U = 3; G =5$ -- Total students

$r = 4$ --- students to select

Required

$P(U =2)$

From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.

First, we calculate the total possible selection (using combination)

$^nC_r = \frac{n!}{(n-r)!r!}$

So, we have:

$Total = ^{U + G}C_r$

$Total = ^{3 + 5}C_4$

$Total = ^8C_4$

$Total = \frac{8!}{(8-4)!4!}$

$Total = \frac{8!}{4!4!}$

Using a calculator, we have:

$Total = 70$

The number of ways of selecting 2 from 3 undergraduates is:

$U = ^3C_2$

$U = \frac{3!}{(3-2)!2!}$

$U = \frac{3!}{1!2!}$

$U = 3$

The number of ways of selecting 2 from 5 graduates is:

$G = ^5C_2$

$G = \frac{5!}{(5-2)!2!}$

$G = \frac{5!}{3!2!}$

$G =10$

So, the probability is:

$Pr = \frac{G * U}{Total}$

$Pr = \frac{10*3}{70}$

$Pr = \frac{30}{70}$

$Pr = 0.4286$

5 0

3 years ago

How do i solve the question in the image provided ?

Mars2501 [29]

Answer:

0.19+0.46i and 0.19-0.46i

Step-by-step explanation:

$\neq (-b+\sqrt{b^2-4ac} )/2a\\and\\(-b-\sqrt{b^2-4ac} )/2a\\\\a=8\\b=3\\c=2\\(-3+\sqrt{3^2-4*8*2} )/(2*8)\\= - 0.1875+0.463512i\\(-3-\sqrt{3^2-4*8*2} )/(2*8) = -0.1875-0.463512i$

hope its right

6 0

3 years ago