MATHEMATICS HIGH SCHOOL

What are the solutions of the equation (x + 2)2 + 12(x + 2) – 14 = 0? Use u substitution and the quadratic formula to solve.a) x= -8+5 square root 2
b) x=-6+5 square root 2
c) x= -4+5 square root 2
d) x= -2+5 square root 2

Answers

Answer 1

Answer:

The solution to the equation is x = -8 ± 5√2, the correct option is A.

What is a Quadratic Equation?

A quadratic equation is what can be written in the form of ax²+bx+c=0

The quadratic equation is

(x + 2)² + 12(x + 2) – 14 = 0?

Let y = x+2

then the equation will be of the form

y² +12y -14 = 0

This in the form of ax² +bx+c =0

The formula for solving is,

$\rm y =(-b \pm√(b^2 -4ac))/(2a)$

$\rm y= \frac{ -12 \pm \sqrt {(-12)^2 -4 *1*(-14)}}{ 2* 1}$

y = -6 ± 5√2

x +2 = -6 ± 5√2

x = -8 ± 5√2

To know more about Quadratic Equation

brainly.com/question/2263981

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Answer 2

Answer: (x + 2)² + 12(x + 2) – 14 = 0

(x +2) ² we use the formula (a+b)² = a² + 2ab + b²

(x² + 2*2*x + 4 ) + (12*x + 12 * 2 ) - 14 = 0
(x² + 4x + 4) + (12x + 24) - 14 = 0
x² + 4x + 4 + 12x + 24 - 14 = 0

we sort expressions
x² + 4x + 12x + 4 + 24 - 14 = 0

reduce
x² + 16x + 14 = 0

a = 1 b = 16 c=14

Δ = b² - 4ac = 16² - 4*1*14 = 256 - 56 = 200
√Δ = √(2*10*10) = 10√2

$x_(1) = (-b - √(delty) )/(2a) = (-16 - 10 √(2) )/(2*1) = (-8 -5 √(2) )/(1) = -8 -5 √(2)$

$x_(2) = (-b + √(delty) )/(2a) = (-16+ 10 √(5) )/(2*1) = (-8 + 5 √(2) )/(1) = -8 + 5 √(2)$

Answer A

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Show me how to divide 28.8 divided by 4

Answers

28.8 ÷ 4
put the decimal point in the quotient
4 can't go in 2 so 28
28 can by 7 and 7 in the ones digit
0.8 forget it's just 8 divided by 4 = 2
7.2 is the answer!

At a picnic there were 3 times as many adults as children and twice as many women as men. If there was a total of x men, women, and children at the picnic, how many men were there, in terms of x?A. x/2
B. x/3
C. x/4
D. x/5
E. x/6

Answers

Answer:

I believe the answer is c.) x=4

Step-by-step explanation:

I saw this on a webpage:

The moment we see “x,” we can consider picking numbers. The key here is contemplating how complicated the number should be. Swim with the current – let the question tell you. A quick look at the answer choices reveals that x could be something simple. Ultimately, we’re just dividing this value by 2, 3, 4, 5, or 6.

Keeping this in mind, let’s think about the first line of the question. If there are 3 times as many adults as children, and we’re keeping things simple, we can say that there are 3 adults and 1 child, for a total of 4 people. So, x = 4.

Now, we know that among our 3 adults, there are twice as many women as men. So let’s say there are 2 women and 1 man. Easy enough. In sum, we have 2 women, 1 man, and 1 child at this picnic, and a total of 4 people. The question is how many men are there? There’s just 1! So now we plug x = 4 into the answers and keep going until we find x = 1. Clearly x/4 will work, so C is our answer. The key was to let the question dictate our approach rather than trying to impose an approach on the question.

Answer: C

x/4

Step-by-step explanation:

See attached for explanation.

G.o has 3 orange picks for every 2 green.if there are 25 picks in all how many picks are orange

Answers

there would be 8 picks out of it all

How many solutions exist for the given equation?

1/2(x + 12) = 4x – 1

Answers

$(1)/(2) (x+12)=4x-1$

Multiply both sides by 2 :

$(1)/(2)(x+12)*2 = 4x*2-1*2$

$x+12=8x-2$

$x+12-12=8x-2-12$

$x=8x-14$

Subtract 8 x from both sides:

$x-8x=8x-14-8x$

$-7x=-14$

Divide both sides by -7 :

$(-7x)/(-7) = (-14)/(7)$

$x = (14)/(7)$

$x = 2$

1 solution

hope this helps!

Answer:

B.one

Step-by-step explanation:

there is only one solution to the problem.

!50 POINTS! (1 SIMPLE GEOMETRY QUESTION)

QUESTION BELOW
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Answers

Answer:

x= 40.33

Step-by-step explanation:

In geometry, alternate exterior angles are a pair of angles that are on the outer side of two parallel lines but on opposite sides of the transversal. In other words, they are the angles that are not on the same line as the parallel lines.

The alternate exterior angles are always equal in measure. This is because when a transversal intersects two parallel lines, it creates two pairs of alternate exterior angles, and each pair of angles is supplementary to each other (meaning that their measures add up to 180 degrees).

In this case:

a° = b°

Since,, the alternate exterior angles are always equal in measure.

3x+17 = 138

subtracting 17 on both sides

3x + 17-17 = 138-17

3x = 121

dividing both sides by 3.

$(3x)/(3) = (121)/(3)$

$\sf x \approx 40.33$

The value of x is 40.33 which proves that r is parallel to s.

Answer:

c) 40.3

$\hrulefill$

Step-by-step explanation:

According to the Alternate Exterior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are exterior to the parallel lines and on the alternate sides of the transversal are congruent.

Therefore, if lines r and s are parallel, then a° = b°.

To find the value of x that proves line r is parallel to line s, solve a° = b° for x.

$\begin{aligned}a^(\circ)&=b^(\circ)\n\n3x+17&=138\n\n3x+17-17&=138-17\n\n3x&=121\n\n(3x)/(3)&=(121)/(3)\n\nx&=40.33333....\n\nx&=40.3\; \sf (nearest\;tenth)\end{aligned}$

Therefore, the value x that proves line r is parallel to line s is:

$\Large\boxed{x=40.3}$

PLEASE HELP!!!!!!!! A cardboard box is 32 centimeters long, 15 centimeters wide, and 6 centimeters tall. The box does not have a top. How much cardboard was used to make the box?