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4 years ago

Solve the literal equation for y. 4x-5=7+4y

Mathematics

1 answer:

Natalka [10]4 years ago

7 0

Answer:

y=x−3

Step-by-step explanation:

Flip the equation.

4y+7=4x−5

Add -7 to both sides.

4y+7+−7=4x−5+−7

4y=4x−12

Divide both sides by 4.

$\frac{4y}{4}= \frac{4x-12}{4}$

y=x−3

ik this doesnt make any sense but hope this helps :/

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Find the greatest common factor of 27, 9, and 45.

Anna [14]

Answer:

Step-by-step explanation:

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3 0

3 years ago

Read 2 more answers

The 4th and the last terms of an A.P. are 11 and 89 respectively. If there are 30 terms in the A.P., find the A.P. and its 23rd

Natali5045456 [20]

$\underline{\underline{\large\bf{Given:-}}}$

$\red{\leadsto}\:$ $\textsf{}$ $\sf Number \: of \:terms \: in \: A.P,n = 30$

$\red{\leadsto}\:$ $\textsf{}$ $\sf Fourth \: term ,a_4 = 11$

$\red{\leadsto}\:$ $\textsf{}$ $\sf last\:term, a_{30} = 89$

$\underline{\underline{\large\bf{To Find:-}}}$

$\orange{\leadsto}\:$ $\textsf{ }$ $\sf The \: A.P.$

$\orange{\leadsto}\:$ $\textsf{ }$ $\sf 23rd\: term, a_{23}$

$\\$

$\underline{\underline{\large\bf{Solution:-}}}\\$

The nth term of A.P is determined by the formula-

$\green{ \underline { \boxed{ \sf{a_n = a+(n-1)d}}}}$

where

$\sf a = first \:term$
$\sf a_n = nth \: term$
$\sf n = number \:of \:terms$
$\sf d = common \: difference$

Since ,

$\sf a_4 = 11$

$\longrightarrow$ $\sf a+(4-1) d= 11$

$\longrightarrow$ $\sf a+3d= 11\_\_\_(1)$

$\sf a_{30}= 89$

$\longrightarrow$ $\sf a+(30-1)d=89$

$\longrightarrow$ $\sf a+29d= 89\_\_\_(2)$

<u>Subtracting equation (1) from equation(2)</u>

$\begin{gathered}\\\implies\quad \sf a+29d-(a+3d) = 89-11 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a+29d-a-3d = 78 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a-a+29d-3d = 78 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf 26d = 78 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf d = \frac{78}{26} \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf d = 3 \\\end{gathered}$

Putting the value of d in equation (1) -

$\begin{gathered}\\\implies\quad \sf a+3(3) = 11 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a = 11-9 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a = 2 \\\end{gathered}$

First term of A.P, a = 2

Second term of A.P., $\sf a_2= 2+(2-1)\times 3$

$\quad\quad\quad\sf =2+3$

$\quad\quad\quad\sf =5$

Third term of A.P., $\sf a_3= 2+(3-1)\times 3$

$\quad\quad\quad\sf =2+6$

$\quad\quad\quad\sf =8$

$\longrightarrow$ Thus , The A.P is 2,5,8,. . . . . .

$\begin{gathered}\\\implies\quad \sf a_n = a+(n-1)d \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a_{23 }= 2+(23-1)\times 3 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a_{23} = 2+22 \times 3 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a_{23} = 2+66 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf a_{23} = 68 \\\end{gathered}$

$\longrightarrow$ Thus , 23rd term is 68.

3 0

3 years ago

Como parte de la propuesta de investigación de Iris, ella planifica desplazar un objeto a 5 m con la fuerza de 20N. Al probar su

ICE Princess25 [194]

Answer:

Joule.

Step-by-step explanation:

Dado que las unidades empleadas son del Sistema Internacional, la unidad a emplear es el Joule, cuya definición es Newton multiplicado por metro.

4 0

3 years ago

Write the trigonometric expression in terms of sine and cosine, and then simplify. cot()/sin()-csc()

OLEGan [10]

Answer:

First, we know that:

cot(x) = cos(x)/sin(x)

csc(x) = 1/sin(x)

I can't know for sure what is the exact equation, so I will assume two cases.

The first case is if the equation is:

$\frac{cot(x)}{sin(x)} - csc(x)$

if we replace cot(x) and csc(x) we get:

$\frac{cot(x)}{sin(x)} - csc(x) = \frac{cos(x)}{sin(x)} \frac{1}{sin(x)} - \frac{1}{sin(x)}$

Now let's we can rewrite this as:

$\frac{cos(x)}{sin(x)} \frac{1}{sin(x)} - \frac{1}{sin(x)} =\frac{cos(x)}{sin^2(x)} - \frac{1}{sin(x)}$

$\frac{cos(x)}{sin^2(x)} - \frac{sin(x)}{sin^2(x)} = \frac{cos(x) - sin(x)}{sin^2(x)}$

We can't simplify it more.

Second case:

If the initial equation was

$\frac{cot(x)}{sin(x) - csc(x)}$

Then if we replace cot(x) and csc(x)

$\frac{cos(x)}{sin(x)}*\frac{1}{sin(x) - 1/sin(x)} = \frac{cos(x)}{sin(x)}*\frac{1}{sin^2(x)/sin(x) - 1/sin(x)}$

This is equal to:

$\frac{cos(x)}{sin(x)}*\frac{sin(x)}{sin^2(x) - 1}$

And we know that:

sin^2(x) + cos^2(x) = 1

Then:

sin^2(x) - 1 = -cos^2(x)

So we can replace that in our equation:

$\frac{cos(x)}{sin(x)}*\frac{sin(x)}{sin^2(x) - 1} = \frac{cos(x)}{sin(x)}*\frac{sin(x)}{-cos^2(x)} = -\frac{cos(x)}{cos^2(x)}*\frac{sin(x)}{sin(x)} = - \frac{1}{cos(x)}$

5 0

3 years ago

Write an algebraic expression for each verbal expression: the difference of 10 and u 10-u 10+u 10u 10/u

Harlamova29_29 [7]

Answer:

=> expression of the difference of 10 and u

=> difference = result of subtraction

=> 10 is the number to be subtracted by u

=> u = is the unknown number to subtract to 10

=> 10 – u

Step-by-step explanation:

Algebraic expression is the expression that contains the combination of number, variables and operators like addition, division, subtraction and multiplication.

4 0

3 years ago