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2 years ago

Write an equation for the translation of x^2 + y^2 = 49 by 7 units right and 4 units up

Mathematics

1 answer:

Tatiana [17]2 years ago

8 0

Answer:

(x - 7)² + (y - 4)² = 49

Step-by-step explanation:

Given

Equation: x² + y² = 49

Required:

New Equation when translated 7 units right and 4 units up

Taking it one step at a time.

When the equation is translated 7 units right, this implies a negative unit along the x axis.

The equation becomes

(x - 7)² + y² = 49

When the equation is translated 4 units up, this implies a negative unit along the y axis.

(x - 7)² + (y - 4)² = 49

The expression can be further simplified but it's best left in the form of

(x - 7)² + (y - 4)² = 49

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3x – 2y = 17 <br> –2x – 5y = 14 <br> Solve using Elimination Please show work

OleMash [197]

Answer:

The solution is x=3 , y=-4 or (3,-4)

Step-by-step explanation:

Given equations (1 and 2) are:

$3x- 2y = 17\\-2x -5y = 14$

To solve a system of equation with elimination method, the co-efficients of one of the variables has to be equated and then the equations are added or subtracted to get an equation in one variable.

Multiplying equation 1 by 2:

$2(3x-2y) = 2*17\\6x-4y = 34\ \ \ \ \ Eqn\ 3$

Multiplying equation 2 by 3

$3(-2x-5y) = 3*14\\-6x-15y = 42\ \ \ \ Eqn\ 4$

Adding equation 3 and 4

$(6x-4y) + (-6x-15y) = 34+42\\6x-4y-6x-15y = 76\\-19y = 76\\\frac{-19y}{-19} = \frac{76}{-19}\\y = -4\\$

Putting y = -4 in equation 1

$3x-2(-4) = 17\\3x+8 = 17\\3x = 17-8\\3x = 9\\\frac{3x}{3} = \frac{9}{3}\\x = 3$

Hence,

The solution is x=3 , y=-4 or (3,-4)

3 0

2 years ago

Which is the inverse of this matrix? A. B. C. D. E. The matrix is noninvertible.

kvasek [131]

Answer:

-19 9 7

[15 -7 6 ]

-2 1 1

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

During a business trip, an individual stopped at two rest stops. In the parking lot of the first rest stop, they counted 20 cars

olganol [36]

Answer

given,

on first stop

number of car = 20 and number of trucks = 18

on second stop

number of car = 18 and number of trucks = 10

we need to calculate which rest stop has higher ratio of car to truck.

Rest Stop 1

ratio= r₁ = $\dfrac{cars}{trucks}$

r₁ = $\dfrac{20}{18}$

r₁ = $\dfrac{10}{9}$

Rest Stop 2

ratio= r₂ = $\dfrac{cars}{trucks}$

r₂ = $\dfrac{18}{10}$

r₂= $\dfrac{9}{5}$

hence, r₂ > r₁

rest stop 2 has more car to truck ratio than rest stop 1

3 0

2 years ago

Simplify (2z^5)(12z^3)/4z^4

Sphinxa [80]

Answer:

$6z^{4}$

Step-by-step explanation:

Given in the question an expression,

$\frac{ (2z^5)(12z^3)}{4z^4}$

Step 1

Apply exponential "product rule"

$x^{m}x^{n}=x^{m+n}$

$\frac{ 12(2)z^5)(z^3)}{4z^4}$

$\frac{ (24)z^5)(z^3)}{4z^4}$

$\frac{ 24(z^{(5+3)})}{4z^4}$

$\frac{ 24(z^{8})}{4z^4}$

Step 2

Apply exponential " divide rule"

$\frac{x^{m}}{x^{n}}=x^{m-n}$

$\frac{24/4(z^{8})}{z^4}$

$\frac{6(z^{8})}{z^4}$

$\frac{6(z^{8-4})}{1}$

$6z^{4}$

5 0

2 years ago

A line includes the points (10,-5) and (-10,-1). What is the equation in slope intercept form?

Elodia [21]

$\bf (\stackrel{x_1}{10}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{-10}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-(-5)}{-10-10}\implies \cfrac{-1+5}{-20}\implies \cfrac{4}{-20}\implies -\cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-5)=-\cfrac{1}{5}(x-10) \\\\\\ y+5=-\cfrac{1}{5}x+2\implies y=-\cfrac{1}{5}x-3$

8 0

2 years ago