All categories

3 years ago

Solve for x in each of the equations or inequalities below, and name the property and/or properties used:

Mathematics

1 answer:

nordsb [41]3 years ago

4 0

Answer

a) 3/4 x = 9

x = $\dfrac{9\times 4}{3}$

x = 12

b) 10+ 3x = 5x

2 x = 10

x = 5

c) a + x = b

x = b - a

d) c x = d

x = $\dfrac{d}{c}$

e) $\dfrac{1}{2} x - g < m$

$\dfrac{1}{2} x< m + g$

x < 2( m + g)

f) q + 5 x = 7 x - r

q + r = 2 x

$x = \dfrac{q + r}{2}$

You might be interested in

Which of the following statements are true for sin (-430°)

stira [4]

Answer:

Step-by-step explanation:

sin(-430)=-sin(430)=-sin(360+70)=-sin 70

8 0

2 years ago

What's the explicit formula for 5,10,15,20,25,30

vivado [14]

Answer:

$a_{n}$ = 5n

Step-by-step explanation:

There is a common difference d between consecutive terms

d = 10 - 5 = 15 - 10 = 20 - 15 = 25 - 20 = 30 - 25 = 5

This indicates the sequence is arithmetic with explicit formula

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 5 and d = 5 , then

$a_{n}$ = 5 + 5(n - 1) = 5 + 5n - 5 = 5n

4 0

3 years ago

Indicate the equation of the line through (2, -4) and having slope of 3/5.

Nastasia [14]

Y = mx + b.....the m is for the slope , (2,-4)...x = 2 and y = -4
now we sub
-4 = 3/5(2) + b
-4 = 6/5 + b
-4 - 6/5 = b
-20/5 - 6/5 = b
- 26/5 = b

so ur equation is : y = 3/5x - 26/5 <== slope intercept form
or if u need it in standard form :
y = 3/5x - 26/5....(5)
5y = 3x - 26
-3x + 5y = -26...(-1)
3x - 5y = 26 <==standard form

5 0

3 years ago

Read 2 more answers

Y = x² + 6x + 3

olganol [36]

Vertex is at $\left(-3,-6\right)$

y-intercept is 3.

The parabola opens up.

Step-by-step explanation:

The graph of the equation is hereby attached in the answer area.

Vertex is the point on the parabola where the graph crosses its axis of symmetry. The axis of symmetry here( $x =-3$ ), is shown with the dotted line in the graph attached.

y-intercept is defined as the value of y where the graph crosses the y-axis. In other words, when $x=0$ . Putting

And, the graph opens up as shown the graph figure as well. It is also evident from the co-efficient of $x$ in the given equation $y =x^{2} + 6x + 3$ . Here, co-efficient of

So, vertex is at $\left(-3,-6\right)$

y-intercept is 3.

The parabola opens up.

7 0

3 years ago

Show the work please

Kay [80]

Answer:

1) (x + 3)(3x + 2)

2) x= +/-root6 - 1 by 5

Step-by-step explanation:

3x^2 + 11x + 6 = 0 (mid-term break)

using mid-term break

3x^2 + 9x + 2x + 6 = 0

factor out 3x from first pair and +2 from the second pair

3x(x + 3) + 2(x + 3)

factor out x+3

(x + 3)(3x + 2)

5x^2 + 2x = 1 (completing squares)

rearrange the equation

5x^2 + 2x - 1 = 0

divide both sides by 5 to cancel out the 5 of first term

5x^2/5 + 2x/5 - 1/5 = 0/5

x^2 + 2x/5 - 1/5 = 0

rearranging the equation to gain a+b=c form

x^2 + 2x/5 = 1/5

adding (1/5)^2 on both sides

x^2 + 2x/5 + (1/5)^2 = 1/5 + (1/5)^2

(x + 1/5)^2 = 1/5 + 1/25

(x + 1/5)^2 = 5 + 1 by 25

(x + 1/5)^2 = 6/25

taking square root on both sides

root(x + 1/5)^2 = +/- root(6/25)

x + 1/5 = +/- root6 /5

shifting 1/5 on the other side

x = +/- root6 /5 - 1/5

x = +/- root6 - 1 by 5

x = + root6 - 1 by 5 or x= - root6 - 1 by 5

4 0

3 years ago