42 = -7 ( z-3)

whats z?

Answer:

The numbers are --> x = -4 + √21 i and  x = -4 — √21 i

See the attachment for my step-by-step explanation

(solution is in red box)

The number that would have to be added in the given quadratic equation to complete the square is '-21' and this can be determined by using the factorization method.

Given :

Quadratic equation  --  [tex]x^2+8x+37 = 0[/tex]

The following steps can be used in order to determine the number that would have to be added to complete the square:

Step 1 - The factorization method can be used in order to determine the number that would have to be added to complete the square.

Step 2 - Write the given quadratic equation.

[tex]x^2+8x+37 = 0[/tex]

Step 3 - Now, if '-21' is added in the above quadratic equation then the above equation becomes the complete square.

[tex]x^2+8x+37+(-21) = 0[/tex]

[tex]x^2+8x+16 = 0[/tex]

[tex](x+4)^2 = 0[/tex]

For more information, refer to the link given below:

https://brainly.com/question/17177510

Answer:

-17/24

Step-by-step explanation:

[tex] - \frac{1}{3} + - \frac{3}{8} = - \frac{1}{3} - \frac{3}{8} = - ( \frac{1}{3} + \frac{3}{8} ) = - (\frac{8 + 9}{24} ) = - \frac{17}{24} [/tex]

Answer:

B is in 4th quadrant.

Step-by-step explanation:

If mid point of AB is on x-axis then and A is in 3rd quadrant then B must be on the opposite side of A.Therefore it is in 4th

B is in fourth quadrant when AB is the midpoint on y axis

If the center of AB is on the x-axis

A is in the third quadrant,

let two points ( -2, -2 ) in third quadrant .

then B must be on the side of A that is opposite from A.

B thus comes in fourth.

then points ( 2,-2 ) are in fourth quadrant  .

Learn more about Quadrants here:

brainly.com/question/7196312

#SPJ2

Answer:

6.3

Step-by-step explanation

Each side of a square is equal; therefore, to find the length of one side, we can find the square root of the area, which, rounded, is 6.3.

Answer:

a=A=40≈6.32456in

Answer:

gzhausiaoa

Step-by-step explanation:

hshshsshhehehehehhdhdhdhdhhdhdhdfhfh

[tex]\\ \sf\longmapsto \dfrac{2}{3}\:of\:180[/tex]

[tex]\\ \sf\longmapsto \dfrac{2}{3}\times 180[/tex]

[tex]\\ \sf\longmapsto 2(60)[/tex]

[tex]\\ \sf\longmapsto 120[/tex]

Convert to radians

[tex]\\ \sf\longmapsto 120\times \dfrac{\pi}{180}[/tex]

[tex]\\ \sf\longmapsto \dfrac{2\pi}{3}rad[/tex]

Answer:

a^2-ab+b^2

Step-by-step explanation:

factorize both of them.

Answer:

Step-by-step explanation:

Remember:

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\[/tex]

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\\\\\a^4+a^2b^2+b^4=a^4+2a^2b^2+b^4-a^2b^2\\\\=(a^2+b^2)^2-a^2b^2\\\\=(a^2+b^2-ab)(a^2+b^2+ab)\\\\HCF=a^2+b^2-ab\\[/tex]

Answer:

29.51%

Step-by-step explanation:

The change from 305 to 395 is the difference between the two numbers. So, it would be 395 - 305 or 90. Now, to find the percentage of change, we need to find what part of the original amount is the change. In other words, we would have to divide 90 by 305. By putting this in a calculator you get about 0.2951. To convert this decimal into a percent, we would multiply by 100 giving us 29.51%.

We know that:

There are n arithmetic means between the numbers 33 and -3

second last mean: second mean = 1:5

Using this, we can find that the value of n is 9.

Now let's see how we need to use the information.

"There are n arithmetic means between the numbers 33 and -3"

This means that we will have a sequence like:

33, a₁, a₂, ..., aₙ, -3

And by the given ratio, we know that:

aₙ₋₂:a₂  = 1:5

Also, because this is an arithmetic sequence we have:

a₁ = 33 + d

a₂ = 33 + d + d

aₙ ₋ ₂ = 33 + (n - 2)*d = -3 - 2*d

Because of the ratio, we will have that:

aₙ₋₂/a₂ = 1/5

We can replace what the left side by:

(-3 - 2*d)/(33 + 2*d) = 1/5

now we can solve this for d.

-3 - 2*d = (33 + 2*d)*(1/5)

5*(-3 - 2*d ) = (33 + 2*d)

-15 - 10d = 33 + 2d

-15 - 33 = 2d + 10d

-48 = 12d

-48/12 = -4 = d

So now we know that the value of d is -4.

Now we can use the equation

aₙ ₋ ₂ = 33 + (n - 2)*d = -3 - 2*d

to find the value of n:

33 + (n - 2)*d = -3 - 2*d

33 + (n - 2)*-4 = -3 - 2*-4

33 - 4n + 8 =  -3 + 8

41 - 4n = 5

-4n = 5 - 41 = -36

n = 36/4 = 9

The value of n is 9.

If you want to learn more, you can read:

https://brainly.com/question/11559160

Answer:

Step-by-step explanation:

HI. just posted a question can u help me out pleas please

is this the line diagram?

and if it is it's HI the second answer.

because  a line is named by either using two points on the line in capital letters with an arrow on the top or by using a lowercase letter.

[tex]\\ \sf\longmapsto \dfrac{sin40.sin120}{sin110-sin340}[/tex]

[tex]\\ \sf\longmapsto \dfrac{sin(90-50).sin(90+30)}{sin(90+20).sin(360-20)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{cos50.cos30}{cos20.(-sin20}[/tex]

[tex]\\ \sf\longmapsto \dfrac{cos50cos30}{-sin20cos20}[/tex]

[tex]\\ \sf\longmapsto -\dfrac{cos30cos50}{sin20cos20}[/tex]

It's 200

Step-by-step explanation:

200 = 2 × 2² × 5²

Answer:

Ann = 112.5 and Annie = 157.5

Step-by-step explanation:

7-5 = 2

One share = 45/2 = 22.50

Ann = 22.5 x 5 = 112.50

Annie = 22.5 x 7 = 157.50

You can check this is correct my subtracting them from each other and confirming that Annie has 45 more dollars than ann

Hope this helps!!

Answer:

5

Step-by-step explanation:

Solution is 8 in

Let´s call dimensions of the box

According to the problem statement

y = x + 3     and    h = 4 in

The volume of the box is:

V = x×y×h       V = 360 in³

Then  V = x × ( x + 3 ) × 4     ( by substitution of y as a function of x )

360 = x × ( x + 3 ) × 4

Simplifying by 4

90 =  x × ( x + 3 )

90 = x² + 3x

We got a second degree equation, solving for x

x² + 3×x - 90 = 0

x₁,₂ = ( -3 ± √ (3)² + 4×90 )/2   ⇒   x₁,₂ = ( - 3 ± 19,21 )/2

x₁   ⇒  is a negative value    x = - 11,1  so we dismiss such solution

x₂  = 16.21/2

x₂  =  8.1 in

rounding to the nearest integer number we get the value for the length f the box

x₂ = 8 in        ⇒ x = 8 in

Note: In Brainly.com in search bar ask for cube dimensions

Width = 2w , Length = w+5 , perimeter = 40

Perimeter of rectangle = 2 (Length + Width)

P= 2 (L + w)

40 = 2 [ (w+5) + (2w) ]

40 = 2 ( 3w+5)

40= 6w +10

6w= 40 – 10

6w= 30

w = 30/6

w = 5

Width = 2w = 2(5) = 10

Length = w + 5 = 5+5 = 10

I hope I helped you^_^

Answer:

10kg and 60 kg.

Step-by-step explanation:

Let the kid's mass be x kg, then the goat's mass is 6x.

x + 6x = 70

7x = 70

x = 10.

Answer:

245 boys

Step-by-step explanation:

54/100*750

=405 girls

so 750-405=245

Answer:

Equation: [tex]3x-5+2x=90[/tex]

Angle measures: 52 degrees and 38 degrees

Step-by-step explanation:

Hi there!

We're given that the two angles form a right angle, which means they add up to 90 degrees.

Knowing this, we can construct the following equation:

[tex]3x-5+2x=90[/tex]

Now, we must solve for x:

[tex]5x-5=90\\5x=95\\x=19[/tex]

Therefore, x=19. Plug this into the expression for each angle to find their measures:

[tex]3x-5\\= 3(19)-5\\= 57-5\\=52[/tex]

[tex]2x\\=2(19)\\=38[/tex]

Therefore, the two angles measure 52 degrees and 38 degrees.

I hope this helps!

Answer:

r/2 = w

Step-by-step explanation:

r = 2w

Divide each side by 2

r/2 = 2w/2

r/2 = w

Answer:

[tex] - 2z - xy = x + 7 \\ x + xy = - 2z - 7 \\ x(1 + y) = - 2z - 7 \\ \\ x = \frac{ - 2z - 7}{1 + y} [/tex]

I hope I helped you^_^

Answer:

8=3-5x

5x=3-8

5x=-5

x=-5/5

x=-1

is the required answer

Answer:

Step-by-step explanation:

Horizontal translations changes the x-axis

Vertical translations changes the y-axis

Answer:

14

Step-by-step explanation:

x+21=7(x+9)

x+21=7x+63

-6x=42

x=-7

(-7)^2+5(-7)

=49+(-35)

=49-35

=14

Answer:

3 × x³ - 10

Step-by-step explanation:

three times = 3×

difference = -

number cubed (unknown so we use x) = x³

10 = 10

Hope this helps!

I'm sorry if wrong :(

Answer:

The total interest of $320 will be the sum of the amount earned in each account.

Step-by-step explanation:

320 = x(0.04)(1) + (5000-x)(0.08)(1)

320 = 0.04x + 400 - 0.08x

-80 = -0.04x

2000 = x

5000 - x = 3000

$2,000 was invested at 4%

$3,000 was invested at 8%

Answer:

x= - 8/5

Step-by-step explanation:

-24x+2=18-14x

-24x+14=18-2

-10x=16

x= - 8/5