Using the digits 5, 6, 7, 8, 9 and repetition is allowed how many options are there to

Can someone please help me: Slove 17+3(z-2)-11z=-7(z+2)+14

gayaneshka [121]

Answer:

z = 11

Step-by-step explanation:

Simplifying

17 + 3(z + -2) + -11z = -7(z + 2) + 14

Reorder the terms:

17 + 3(-2 + z) + -11z = -7(z + 2) + 14

17 + (-2 * 3 + z * 3) + -11z = -7(z + 2) + 14

17 + (-6 + 3z) + -11z = -7(z + 2) + 14

Combine like terms: 17 + -6 = 11

11 + 3z + -11z = -7(z + 2) + 14

Combine like terms: 3z + -11z = -8z

11 + -8z = -7(z + 2) + 14

Reorder the terms:

11 + -8z = -7(2 + z) + 14

11 + -8z = (2 * -7 + z * -7) + 14

11 + -8z = (-14 + -7z) + 14

Reorder the terms:

11 + -8z = -14 + 14 + -7z

Combine like terms: -14 + 14 = 0

11 + -8z = 0 + -7z

11 + -8z = -7z

Solving

11 + -8z = -7z

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '7z' to each side of the equation.

11 + -8z + 7z = -7z + 7z

Combine like terms: -8z + 7z = -1z

11 + -1z = -7z + 7z

Combine like terms: -7z + 7z = 0

11 + -1z = 0

Add '-11' to each side of the equation.

11 + -11 + -1z = 0 + -11

Combine like terms: 11 + -11 = 0

0 + -1z = 0 + -11

-1z = 0 + -11

Combine like terms: 0 + -11 = -11

-1z = -11

Divide each side by '-1'.

z = 11

Simplifying

z = 11

4 0

3 years ago

Read 2 more answers

Estimate the difference using front-end estimation.<br> 987.12 - 342.5

lukranit [14]

987-343= 644

Not rounded is 644.62

7 0

3 years ago

Help fast?

Alexxandr [17]

The last equation is the correct one since if we multiply the slope of the given line by the slope of the line of this equation, you'll get -1, and if you substitute the coordinates of the given point in this equation, you'll get -2=3/2(-2)+1=-2 which means that this point belongs to the line of this equation

6 0

3 years ago

Read 2 more answers

During the afternoon, and 18 foot tall tree casts a shadow 25 feet long. What is the approximate andle of elevation from the end

Karo-lina-s [1.5K]

a tree casts a 25-foot shadow on sunny day. If the angle of elevation from the tip of the shadow to the top of the tree is 32 degree, what is the height of the tree to the nearest tenth of a foot?

Tan(32)=H/25

0.624869=H/25

H=.624869 X 25

H=15.6 feet-Height of the tree.

6 0

3 years ago

given abc with a(-4 -2), b(4,4), and c(18,-8). write the equation of the line that contains the altitude that passes through b i

Tresset [83]

check the picture below.

so red line of BD is perpendicular to AC, hmmmm let's firstly find the slope of AC, bearing in mind that perpendicular lines have <u>negative reciprocal</u> slopes.

$\bf A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{18}~,~\stackrel{y_2}{-8}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-8-(-2)}{18-(-4)}\implies \cfrac{-8+2}{18+4} \\\\\\ \cfrac{-6}{22}\implies -\cfrac{3}{11} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{11}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{11}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{11}{3}}}\impliedby \textit{BD's slope}$

so we're really looking for the equation of a line whose slope is 11/3 and runs through B(4,4). Keeping in mind that

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf B(\stackrel{x_1}{4}~,~\stackrel{y_1}{4})~\hspace{10em} slope = m\implies \cfrac{11}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{11}{3}(x-4)$

$\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}\textit{ to do away with the denominators}}{3(y-4)=3\left( \cfrac{11}{3}(x-4) \right)\implies 3y-12=11(x-4)} \\\\\\ 3y-12=11x-44\implies 3y=11x-32 \\\\\\ -11x+3y=-32\implies \blacktriangleright 11x - 3y= 32\blacktriangleleft$

4 0

3 years ago