All categories

3 years ago

Find the value of x in the equation 3(x + 2) = x.

1 answer:

4 0

First number = x
Consecutive number = x+1
"squares differ by 31" means to square both numbers and subtract them:
(x+1)^2 - (x)^2 = 31
x^2+2x+1 - x^2 = 31
2x+1 = 31
2x = 30
x = 15 (first number)
x+1 = 15+1 = 16 (consecutive number)

You might be interested in

PLEASE HELPPP -

Lena [83]

Answer:

Step-by-step explanation:

it is not strait

Hope this works!

7 0

2 years ago

Can you prove that DEF = HGF.!? Justify your answer.

frosja888 [35]

Step-by-step explanation:

$In \: \triangle DEF \: \& \: \triangle HGF \\ EF \: \cong \: GF...(given) \\ \angle EFD \cong \angle GFH \\ (vertically \: opposite \: angles) \\ \ DF \: \cong \: HF...(given) \\ \therefore \: \triangle DEF \cong \triangle HGF \\ (By\: SAS \:criterion\: of \:congruence)$

7 0

3 years ago

Graph a triangle (LMN) and rotate it 180° around the origin to create triangle L′M′N′.

andreev551 [17]

When a triangle is rotated, it must be rotated through a center of rotation.

Assume the coordinate of LMN is

$\mathbf{L = (1,1)}$

$\mathbf{M = (1,7)}$

$\mathbf{N = (3,6)}$

The rule of 180-degree rotation is:

$\mathbf{(x,y) \to (-x,-y)}$

So, we have:

$\mathbf{L' = (-1,-1)}$

$\mathbf{M' = (-1,-7)}$

$\mathbf{N' = (-3,-6)}$

See attachment for the graphs of LMN and L'M'N

(a) Describe the transformation

When triangle LMN is rotated 180 degrees across the origin, the x and y coordinates of LMN are negated to form triangle L'M'N'

(b) Lines LL' and MM'

The distance between point L and the center of origin is the same as the distance between point M' and the center of origin

Similarly, the distance between point L and the center of origin is the same as the distance between point M' and the center of origin

(c) Line NN'

Line NN' will assume the same characteristics as lines LL' and MM'

Read more about transformations at:

brainly.com/question/11707700

7 0

3 years ago

If h(x) = 2x4 - 4x2 - 2x, then h(3)=

Kruka [31]

Answer:

h(3)=-6

Step-by-step explanation:

sub 3 into all the positions which variable X is present

$h(3) =( 2 \times 4) - (4 \times 2) - 2(3)$

$h(3) = 8 - 8 - 6$

$h(3) = - 6$

6 0

2 years ago

Read 2 more answers

Which graph shows the solution to the system of linear inequalities? y< 2x-5 y>-3x + 1

trapecia [35]

Answer:

See explanation

Step-by-step explanation:

Plot the solution sets to both inequalities.

1. For the inequality $y$ First, plot the dotted line $y=2x+5$ (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

$2\cdot 0-5=-5$

so the origin does not belong to the needed part. Shade the part, which does not include origin.

2. For the inequality $y>-3x+1.$ First, plot the dotted line $y=-3x+1$ (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

$-3\cdot 0+1=1>0$

so the origin does not belong to the needed part. Shade the part, which does not include origin.

3. Find the common region of these two shaded parts - this is the solution to the system of two inequalities.

5 0

3 years ago