Express x^2 + 4x - 7 in the form (x + a)^2 - b where a and b are intergers

Answer:

x = 2.2, y = -1.8, z = -1.6

Step-by-step explanation:

Put the coefficients of each variable and their constants into a matrix, as shown below.

1 1 -1 2

2 1 1 1

2 -1 2 3

Now use the rref( function to essentially "solve" the equation for all of its variables. You end up with the following matrix:

1 0 0 2.2

0 1 0 -1.8

0 0 1 -1.6

Remember that the first three columns are the coefficients on our variables, and the last column is the constant on the other side. That means that this matrix is essentially telling us the value of each variable.

x + 0y + 0z = 2.2

0x + y + 0z = -1.8

0x + 0y + z = -1.6

Are these converses true? The answer is yes. Each of these converses can be a way to show that a quadrilateral is a parallelogram. However, the Consecutive Angles Converse can be a bit tricky, considering you would have to show that each angle is supplementary to its neighbor

(∠A

and

∠B, ∠B

and

∠C, ∠C

and

∠D

, and

∠A

and

∠D)

. We will not use this converse.

Step-by-step explanation:

The given equations are:

(i)

3x+2y−4=0...(1)

2x−3y−7=0...(2)

put x=0 in (1),

3(0)+2y−4=0

y=2

put y=0 in (2),

2x−3(0)−7=0

x=

2

7

put x=0 in (2),

2(0)−3y−7=0

y=−

3

7

put y=0 in (1),

3x+2(0)−4=0

x=

3

4

(x=0,y=−

3

7

)

(x=

3

4

,y=0)

(x=0,y=2)

(x=

2

7

,y=0)

(ii)

3x+2y−11=0...(1)

2x−3y+10=0...(2)

put x=0 in (1),

3(0)+2y−11=0

y=

2

11

put y=0 in (2),

2x−3(0)+10=0

x=−5

put x=0 in (2),

2(0)−3y+10=0

y=

3

10

put y=0 in (1),

3x+2(0)−11=0

x=

3

11

(x=

3

11

,y=0)

(x=0,y=

3

10

)

(x=0,y=

2

11

)

(x=−5,y=0)

Answer:

(5,-2)

Step-by-step explanation:

4x – 6y = 32

2x + 3y = 4      (multiply everything by 2. This will allow for the elimination of                        one of the variables. In this case, the y. )

4x – 6y = 32

4x + 6y = 8       (Now add them together)

__________

8x        = 40      (Divide by 8, both sides)

x   = 5

4(5) - 6y = 32  ( Substitute the x value into one of the original equations)

20 - 6y = 32    (Subtract the 20 from both sides)

-6y = 12            Divide by the -6, both sides)

y = -2

Answer: (-2,1) deduced from graph

the point where the two lines intersect is the solution

Step-by-step explanation:

Answer:

(- 2, 1 )

Step-by-step explanation:

Given a system of equations graphically then the solution is at the point of intersection of the 2 lines.

The point of intersection = (- 2, 1 ) ← solution

I wrote it down, sorry if it’s a little bit messy.

The correct option regarding the discriminant and the number of real roots for this equation is given by:

D. -23; no real roots

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The discriminant is:

[tex]\Delta = b^2 - 4ac[/tex]

The solutions are as follows:

In this problem, the function is:

x² + 3x + 8.

Hence the coefficients are a = 1, b = 3, c = 8, and the discriminant is given by:

[tex]\Delta = b^2 - 4ac = 3^2 - 4(1)(8) = -23[/tex]

Negative discriminant, hence no real roots, and option D is correct.

More can be learned about the discriminant of a quadratic equation at https://brainly.com/question/19776811

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Answer:

Step-by-step explanation:

Vì tam giác ABC vuông tại C nên ta áp dụng định lí pitago=> AB²=AC²+BC²=0.9²+1.5²=3.06=>AB= (3 căn bậc hai của 34)/10

sin B=AC/AB=(3 căn bậc hai của 34)/34

cos B=BC/AB

tan B= AC/BC

cot B= BC/AC

Tương tự suy ra tỉ số lượng giác góc A

Answer:

Step-by-step explanation:

If ABC i.e angle of centra = 124°Then, we know that angle at any where of Circle is 1/2 if central angle So, ADC = 124/2 => ⛰ ADC = 62

Answer:

3/2

Step-by-step explanation:

Rate of change is given by

f(x2) -f(x1)

-----------------

x2 -x1

We know x2 is 0 and x1 is -2

f(x2) is -1 and f(x1) is -4

-1 - ( -4)

----------

0 - -2

-1 +4

--------

0+2

3/2

Answer:

Here,

C.P.=RS 640

S.P.=RS 672

Now,

we know that,

profit= S.P. - C.P.

= rs 672- rs 640

= rs 32.

and,

p % = profit/c.p *100

= rs 32/rs 640*100

=rs 5

wish its help you

Answer:

9.41 km/h

Step-by-step explanation:

The total distance of the race, d = 8 km

The time Sarah took to run the race, t = 55 mins

The time Jo started the race = 3 mins later than Sara

The point Jo caught up with Sarah = 6 km into the race

The rate at which Jo and Sarah ran = Constant speed

The required information = Jo's speed

From the information given, Sarah's speed, v = 8 km/(55 mins) = (8/55) km/min × 60min/h = 96/11 km/h

The time it would take Sarah to run 6 km = 6 km/(8 km/(55 mins)) = 41.25 mins

Given that Jo started 3 minutes late, and they both arrive at 6 km into the race at the same point in time, the time it took Jo to arrive at 6 km into the race = The time it took Sarah - 3 minutes

∴ The time it took Jo to run the 6 km = 41.25 minutes - 3 minutes = 38.25 minutes

Given that Jo ran at a constant speed, and speed = distance/time, we have;

Jo's speed = 6 km/(38.25 min) = 8/51 km/min × 60 min/h = (160/17) km/h ≈ 9.41 km/h.

Answer:

400×16

Step-by-step explanation:

let the number be n.

[tex] \frac{n}{16 } = 400 \\ 16 \times \frac{n}{16} = 400 \times 16\\ n = 400 \times 16[/tex]

Answer:

i only know 4 number only

Answer: (0,3) and (2,2)

There are infinitely many possible answers.

======================================================

Explanation:

If we plug in x = 0 and solve for y, then we get,

x+2y = 6

0+2y = 6

2y = 6

y = 6/2

y = 3

So x = 0 and y = 3 pair up together. We get the ordered pair (x,y) = (0,3)

This is one point on the line.

------------------------

Pick any other value you want for x. Let's say we go for x = 2

x+2y = 6

2+2y = 6

2y = 6-2

2y = 4

y = 4/2

y = 2

The point (x,y) = (2,2) is also on the line, and also another solution.

------------------------

One last example. Let's plug in x = 4

x+2y = 6

4+2y = 6

2y = 6-4

2y = 2

y = 2/2

y = 1

The point (x,y) = (4,1) is another solution.

--------------------------

Refer to the graph below.

for X=0

0+2y=6

2y = 6

6

y= ---- =3

2

so, (0,3) is also a solution

for y=0

X + 2(0) = 6

X+0 =6

X = 6

so, (6,0) is a solution

Step-by-step explanation:

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Answer:

10.34

Step-by-step explanation:

Four sf=four numbers only

Answer:

10•34

1 is less than 5

n/b that u will begin from the no before the decimal place

Answer:

a) 20 minutes

b) 36 km/h

c) 33.67 km

d) continuous driving without any stationary phases.

Step-by-step explanation:

by the way, speed is specified in distance per time unit. in your example as km/h. and that is how your write this.

not km/h¯¹. that would be wrong, as that would actually be km×h. but you can write e.g. km×h¯¹. that is the same as km/h.

between minutes 5 and 25 there is no progress in distance. so, for these 20 minutes the bus was stationary.

in the first 5 minutes the bus drove 7-4=3 km.

so, in 5 minutes 3 km. to determine the speed we need to calculate up to see, how many km would be have driven in a full hour (60 minutes). the same factor for the time has then to be applied also to the distance to keep the ratio unchanged.

5 × x = 60

x = 12

3 × 12 = 36

so, the speed in these first 5 minutes was 3 km/5 min.

or then in km/h : 36 km/h

between the minutes 25 and 45 the bus drove with a speed of 80km/h.

and the starting point there was at 7 km.

so, the bus drove s-7 km in 20 minutes.

as before, let's first find the scaling factor to deal with a full hour instead of only 20 minutes.

20 × x = 60

x = 3

as before : distance × scaling factor = distance for km/h

(s-7) × 3 = 80

3s - 21 = 80

3s = 101

s = 33.666666666... km

Answer:

honestly for division of fractions the only sentence you need to know is...

"mine is not to question why, but to invert and multiply"...

fractional division can be done with "an inverse multiplication:

5/6 ÷ 1/6 can be changed to 5/6 * 6/1 = 30/6 = 5

3/5 ÷1/10 can be changed to 3/5 * 10/1 = 30/5 = 6

Step-by-step explanation:

Answer:

486

Step-by-step explanation:

Surface Area =

[tex]6(9) {}^{2} \\ = 486[/tex]

Answer:

37deg

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the shapes or their coordinates are not given.

The general explanation, however, is as follows:

To dilate a shape around the origin (i.e. (0,0)), we simply multiply the side length of the shape or the coordinates of the shapes by  the scale factor.

Take for instance:

A triangle of side lengths 3,4,5 dilated around the origin by a scale factor of 2.

The new triangle will have 6, 8 and 10 as its side lengths (i.e. we multiply 3, 4 and 5 by 2).

Another instance is:

A rectangle with the following coordinates: (1,1) (4,1), (4,5) and (1,5)

When dilated around the origin by a scale factor of 2, the new rectangle will have the following coordinates: (2,2) (8,2), (8,10) and (2,10)

Answer:

11/2

Step-by-step explanation:

when you do 11/4 divided by 1/2, think of it as 11/4 TIMES 2 because you can flip equations with division, so your answer would be 22/4 or 11/2

Answer:

-3

Step-by-step explanation:

1-7           -6

------ =   -------- =    -3

0--2          2

Answer:

[tex]y=1[/tex]

Step-by-step explanation:

Given:

[tex]6=2(y+2)[/tex]

Distribute the parenthesis

[tex]6=2y+4[/tex]

Subtract both sides by 4

[tex]2=2y[/tex]

Divide both sides by 2 to get [tex]y[/tex] alone

[tex]1=y[/tex]

Hope this is helpful

Answer:

Step-by-step explanation:

[tex]\frac{2x}{x-1} -\frac{2x-5}{x^2-3x+2} =\frac{-3}{x-2} \\\frac{2x}{x-1} +\frac{3}{x-2} =\frac{2x-5}{x^2-3x+2} \\\frac{2x(x-2)+3(x-1)}{(x-1)(x-2)} =\frac{2x-5}{x^2-3x+2} \\\frac{2x^2-4x+3x-3}{x^2-2x-x+2} =\frac{2x-5}{x^2-3x+2} \\\frac{2x^2-x-3}{x^2-3x+2} =\frac{2x-5}{x^2-3x+2} \\x\neq 1,x\neq 2,x^2-3x+2\neq 0\\multiply~by~x^2-3x+2\\2x^2-x-3=2x-5\\2x^2-3x+2=0\\x=\frac{3\pm\sqrt{9-4*2*2} }{2*2} \\x=\frac{3 \pm\sqrt{-7} }{4} \\x=\frac{3 \pm \sqrt{7} i}{4}[/tex]

The solutions of the given rational equation are 13/4 and 11/4.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is 2x/(x-1) - (2x-5)/(x² -3x+2) = -3/(x-2)

Here, 2x/(x-1) - (2x-5)/(x² -2x-1x+2) = -3/(x-2)

2x/(x-1) - (2x-5)/(x(x-2)-1(x-2)) = -3/(x-2)

2x/(x-1) - (2x-5)/((x-2)(x-1)) = -3/(x-2)

(2x(x-2)-(2x-5))/((x-2)(x-1)) = -3/(x-2)

(2x²-4x-2x+5)/(x-1)=-3

2x²-4x-2x+5= -3(x-1)

2x²-6x+5=-3x+3

2x²-6x+5+3x-3=0

2x²-3x+2=0

By using quadratic formula, we get

x=3±√(9-8)/4

x=3± 1/4

x= 3+1/4 and x=3-1/4

x=13/4 and x=11/4

Therefore, the solutions of the given rational equation are 13/4 and 11/4.

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Answer:

Angle of elevation = 56.31°

Step-by-step explanation:

Answer:

the first option

Step-by-step explanation:

because x^3 is exponential while ab^2 is linear

Step-by-step explanation:

the answer is in the image above

Answer:

12

Step-by-step explanation:

[tex]\sqrt{0^{2} + 12^{2} }[/tex]

12