The square of the sum of two consecutive positive even integers is greater than the sum of their squares by 48. Find the two integers.​

Answer:

[tex]\boxed{\sf m=-\frac{7}{5}}[/tex]

Step-by-step explanation:

[tex]\boxed{\sf{Slope}=\frac{y_2-y_1}{x_2-x_1}}[/tex]

→ [tex]\sf \left(x_1,\:y_1\right):\left(-3,\:4\right)[/tex]

→ [tex]\sf \left(x_2,\:y_2\right):\left(2,\:-3\right)[/tex]

[tex]\sf m=\cfrac{-3-4}{2-\left(-3\right)}[/tex]

[tex]\sf m=-\cfrac{7}{5}[/tex]

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Explanation:

Let's start off converting the mixed number 12 & 1/4 to an improper fraction.

[tex]a \frac{b}{c} = \frac{a*c+b}{c}\\\\12 \frac{1}{4} = \frac{12*4+1}{4}\\\\12 \frac{1}{4} = \frac{49}{4}\\\\[/tex]

Do the same for the other mixed number 2 & 1/3.

[tex]a \frac{b}{c} = \frac{a*c+b}{c}\\\\2 \frac{1}{3} = \frac{2*3+1}{3}\\\\2 \frac{1}{3} = \frac{7}{3}\\\\[/tex]

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From here, we divide the two fractions. I converted them to improper fractions to make the division process easier.

[tex]\frac{49}{4} \div \frac{7}{3} = \frac{49}{4} \times \frac{3}{7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{49\times 3}{4\times 7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{7\times 7\times 3}{4\times 7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{7\times 3}{4}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{21}{4}\\\\[/tex]

The last step is to convert that result to a mixed number.

[tex]\frac{21}{4} = \frac{4*5+1}{4}\\\\\frac{21}{4} = \frac{4*5}{4}+\frac{1}{4}\\\\\frac{21}{4} = 4+\frac{1}{4}\\\\\frac{21}{4} = 5 \frac{1}{4}\\\\[/tex]

Note that 21/4 = 5.25 and 1/4 = 0.25 to help check the answer.

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Therefore, she can make 5 cakes. The fractional portion 1/4 is ignored since we're only considering whole cakes rather than partial ones.

Answer:

-2

Step-by-step explanation:

2(x-3), x=2

Since we know what x equals, plug it into the equation

2(2-3)

2(-1)

-2

Answer:

2(2-3)

4-3

1

Step-by-step explanation:

[tex]2(2 - 3) \\ 4 - 3 \\ 1[/tex]

Step-by-step explanation:

3360832553 pass wZE2XQ

Answer:

Step-by-step explanation:

c. (18.5-17)/.9= 1.66666666667= 1.6667

d. .7107

e. .2185

f.  0.675=(x-17)/.9 x= 17.6075

Answer:

you cant factor it.

Step-by-step explanation:

Answer:

x = 131

Step-by-step explanation:

the angle adjacent to x on line l corresponds to 49° and are congruent, then

49 and x are adjacent and sum to 180° , that is

x + 49 = 180 ( subtract 49 from both sides )

x = 131

length is 84

c 35 is hypotenuse

equals 120 neareast tenth

Answer:

a) = 4.198

b) = 4.146

Step-by-step explanation:

a) 15.444/6+0.232*7

do pemdas

=15.444/6+(0.232*7)

=(15.444/6)+1.624

=2.574+1.624

a) = 4.198

b) (1.709+0.364)*6/3

pemdas again

=(2.073) *6 / 3

=12.438 / 3

b) =4.146

Hope this helps :)

Answer:

A 4.198 and b is 2.073

Step-by-step explanation:

i hope this is right

Answer:

6m

Step-by-step explanation:

Hope this helps!!!

Answer:

Step-by-step explanation:

l = 3 m

w = 2 m

Volume = 36 cubic meter

l * w * h = 36

3 * 2 * h = 36

6 * h = 36

      h = 36/6

h = 6 m

Answer:

"The quotient of 8 and y" is written as the following algebraic expression:

8÷y

Answer:

[tex](m^{4} + 5) - n^{3}[/tex] = 85

Step-by-step explanation:

[tex](m^{4} + 5) - n^{3}[/tex] given m = - 2, and n = -4

Substitute the given values into the polynomial expression:

[tex](m^{4} + 5) - n^{3}[/tex]

[tex][(-2)^{4} + 5] - (-4)^{3}[/tex]

= (16 + 5) - (-64)

= 21 + 64

= 85

Therefore, the correct answer is 85.

Answer: 85

Step-by-step explanation:

(m^4+5)-n^3

(-2^4+5)-(-4)^3

(16 + 5)-(-64)

21 + 64 = 85

Answer:

When x= 4, then f(x)= 13.

When x= g(x), then f(x)=g

When x= -3, then f(x)= -1

When x= -15(x), then f(x)= -15

Answer:

125

Step-by-step explanation:

5^3 = 5 x 5 x 5

5 x 5 x 5 = 25 x 5

25 x 5 = 125

answer:

125

step by step explaination:

5³

5×5×5 = 125

Answer:

B

Step-by-step explanation:

the roots are the x-values where the graph intersects the x-axis. to find the roots replace y with 0 and solve for x

Answer:

(-6,9)

Step-by-step explanation:

You first need to simplify the polynomial, which would equal to (x-9)(x+6). Then afterwords you would have to get the zeros of x by doing inverse operation, which would equal to (-6,9). Since these greater and lesser than the number within the graph they are parentheses instead of brackets.

Answer:

y = [5/2]x + [5]

Step-by-step explanation:

y= mx+b

m=rise/run

m=5/2

b=y intercept

b=5

y = 5/2x + 5

Answer:

discount = price times % off

discount = 22.50 x 0.20

discount = $4.50

Step-by-step explanation:

Answer:

y = 3[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Since sinθ = opp/hypoteneuse,

sin60 = y/6

y = sin60° * 6

= [tex]\frac{\sqrt{3} }{2}[/tex] * 6

≈ 3[tex]\sqrt{3}[/tex]

Hence, y = 3[tex]\sqrt{3}[/tex]

Hope this helps and be sure to have a wonderful time ahead at Brainly! :D

Answer:

Step-by-step explanation:

Answer:

1. Hight (in.)

2.Arm span (in.)

3.(30,27)

Answer:

1. Hight (in.)

2.Arm span (in.)

3.(30,27)

Step-by-step explanation:

I'm late but hope this helps

[tex]5x + 3 = - 9 \\ = > 5x = - 9 - 3 \\ = > 5x = - 12 \\ = > x = \frac{ - 12}{5} \\ = > x = - 2 \frac{2}{5} [/tex]

Option A .

[tex] - 2 \frac{2}{5} [/tex]

Answer:

Density (ρ) = 20000 kilogram/cubic meter

Step-by-step explanation:

Step-by-step explanation:

Let's pretend our point is actually a complex number. That would make the point -2–3i. Why would we do this? Well, rotation of complex numbers is simply a matter of multiplication, in this case by 1∠−90° , or -i.

So to start, you shift the point of rotation to 0+0i, rotate it by multiplying, then shift it back to the axis of rotation.

z=−i[(−2−x0)+(−3−y0)i]+(x0+iy0)

=−3−y0+x0+(2+x0+y0)i

x=Rz

y=Iz

Thus the new point is at (−3+x0−y0,2+x0+y0)

hence (-3,2)