Which equation can be used to find the two numbers whose ratio is 4 to 3 and that have a sum of 42?

Can someone help me with this math problem? I have no idea where to begin. Solve: |y + 8| ≥ 3

lorasvet [3.4K]

Since y+8 is positive, you don't have to find the absolute value since the absolute value is y+8. all you have to do is find a number that makes the statement true for y. the symbol between next to the 3 asks for a number that is greater or equal to 3. So your answer would be

≥-5

7 0

2 years ago

The length of a rectangle is 4 units less than the width. The area of the rectangle is 21 units. What is the length, in units, o

bazaltina [42]

The formula of an area of a rectangle:

A = wl

We have l = w - 4 and A = 21.

Substitute:

w(w - 4) = 21 use distributive property

(w)(w) + (w)(-4) = 21

w² - 4w = 21 subtract 21 from both sides

w² - 4w - 21 = 0

w² - 7w + 3w - 21 = 0

w(w - 7) + 3(w - 7) = 0

(w - 7)(w + 3) = 0 ↔ w - 7 = 0 ∨ w + 3 = 0

w = 7 ∨ w = -3 < 0

l = w - 4 → l = 7 - 4 = 3

<h3>Answer: the length = 3 u.</h3>

4 0

2 years ago

Help please . will give brainliest

marishachu [46]

Answer:

A

Step-by-step explanation:

the last number is the y intercept so the intercept in the line is -3.5 so I just matched them up.

3 0

3 years ago

How many grams of NH3 are required to produce 4.65 g of HF

nignag [31]

1.326 grams of NH3 are required to produce 4.65 g of HF.

Step-by-step explanation:

Balanced chemical reaction is written first to know the number of moles taking part in original reaction.

NH3 +3 F2 ⇒3 HF + NF3

Given:

mass of HF = 4.65

First the number of moles of HF in 4.65 grams is calculated by using the formula:

number of moles (n) = $\frac{mass}{atomic mass of 1 mole}$

atomic mass of HF = 20 grams/mole

putting the values in the above equation number of moles can be found.

n = $\frac{4.65}{20}$

= 0.235 moles of HF are given.

From the equation it can be said that:

1 mole of NH3 reacts to form 3 moles of HF

so, x moles of NH3 would react to form 0.235 moles of HF

$\frac{3}{1}$ = $\frac{0.235}{x}$

3x = 0.235

x = $\frac{0.235}{3}$

x = 0.078 moles of NH3 is required.

The moles are converted to mass by applying the formula:

mass = atomic mass X number of moles (atomic mass of NH3 = 17 grams/mole)

putting the values in the formula

mass = 17 X 0.078

mass = 1.326 grams

8 0

2 years ago

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

Tomtit [17]

Apparently my answer was unclear the first time?

The flux of F across S is given by the surface integral,

$\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S$

Parameterize S by the vector-valued function r(u, v) defined by

$\mathbf r(u,v)=7\cos u\sin v\,\mathbf i+7\sin u\sin v\,\mathbf j+7\cos v\,\mathbf k$

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2. Then the surface element is

dS = n • dS

where n is the normal vector to the surface. Take it to be

$\mathbf n=\dfrac{\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}}{\left\|\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}\right\|}$

The surface element reduces to

$\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\mathbf n\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\implies\mathbf n\,\mathrm dS=-49(\cos u\sin^2v\,\mathbf i+\sin u\sin^2v\,\mathbf j+\cos v\sin v\,\mathbf k)\,\mathrm du\,\mathrm dv$

so that it points toward the origin at any point on S.

Then the integral with respect to u and v is

$\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S=\int_0^{\pi/2}\int_0^{\pi/2}\mathbf F(x(u,v),y(u,v),z(u,v))\cdot\mathbf n\,\mathrm dS$

$=\displaystyle-49\int_0^{\pi/2}\int_0^{\pi/2}(7\cos u\sin v\,\mathbf i-7\cos v\,\mathbf j+7\sin u\sin v\,\mathbf )\cdot\mathbf n\,\mathrm dS$

$=-343\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}\cos^2u\sin^3v\,\mathrm du\,\mathrm dv=\boxed{-\frac{343\pi}6}$

4 0

3 years ago