Describe two different ways to solve -10 =1/4(8y-12)

Solve the system by substitution. y = 4x + 22 y = -7x

Lesechka [4]

Answer:

x=-2

y=14

Step-by-step explanation:

-7x=4x+22

-11x=22

x=-2

y=-7(-2)

y=14

7 0

2 years ago

Read 2 more answers

One positive number is 14 less than another positive number. If the reciprocal of the smaller number is added to five times the

Kipish [7]

Let's call the two numbers $s$ and $l$ .

Given these variables, we can say: $s = l - 14$ , based on the first sentence in the problem.

Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:

$\dfrac{1}{s} + 5\Big( \dfrac{1}{l} \Big) = \dfrac{1}{4}$

To solve, we can simply substitute $l -14$ in for $s$ in the second equation and solve.

$\dfrac{1}{l - 14} + \dfrac{5}{l} = \dfrac{1}{4}$

Set up

$\dfrac{l}{l(l - 14)} + \dfrac{5(l - 14)}{l(l - 14)} = \dfrac{1}{4}$

Get terms on the left side to a common denominator for easier addition

$\dfrac{l + 5l - 70}{l(l - 14)} = \dfrac{1}{4}$

Simplify

$4(6l - 70) = l(l - 14)$

Cross multiplication ( $\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$ )

$24l - 280 = l^2 - 14l$

Simplify

$l^2 - 38l + 280 = 0$

Subtract $24l - 280$ from both sides of the equation

$(l - 10)(l - 28) = 0$

Factor left side of the equation

$l = 10, 28$

Zero Product Property

Now, notice that we have found two solutions, but the problem is only asking for one. This likely means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,

$s = 10 - 14 = -4$ ,

Since $s$ is not positive in this case, $l = 10$ is not a solution.

Thus, $l = 28$ is our only solution. In this case,

$s = 28 - 14 = 14$ ,

which means that the smaller number is 14 and the larger number is 28.

5 0

2 years ago

Use the dchnition of similarity to solve the following problem.

sveta [45]

Answer:

1063 ft

Step-by-step explanation:

For shadow problems, we assume the sun's rays are parallel, so the triangles formed are similar. That means the ratio of height to shadow length is the same for each object.

h/(580 ft) = (5.5 ft)/(3 ft)

h = (5.5 ft)(580/3) ≈ 1063 ft

The height of the monument is about 1063 feet.

8 0

2 years ago

Use synthetic substitution to find f (2) and f (-1) for the function. f (x) = x3 – x2 – 2x + 3

kotegsom [21]

Answer:

f(2)=7

f(-1)=+1

Step-by-step explanation:

f (2)= 2³-2²+3 =8-4+3=7

f (-1)= (-1)³-(-1)²+3= -1- (+1) +3= -1-1+3=+1

3 0

2 years ago

URGENT! if ABCD is dilated by a factor of 2, the coordinate of A' would be:

koban [17]

After dilating the quadrilateral ABCD by a factor of 2 and with respect to the origin, the point A(x, y) = (-3, -1) is transformed into the point A'(x, y) = (-9, -3).

<h3>How to determine the coordinates of an image after applying a rigid transformation</h3>

First of all, dilation is a type of rigid transformation. Rigid transformations are transformations applied on geometric loci such that the Euclidean distance at every point of the construction is conserved. Vectorially speaking, the dilation is expressed by the following formula:

A'(x, y) = A(x, y) + k · [A(x, y) - O(x, y)] (1)

Where:

A(x, y) - Original point
O(x, y) - Center of dilation
A'(x, y) - Resulting point
k - Dilation factor

If we know that A(x, y) = (-3, -1), k = 2 and O(x, y) = (0, 0), then the coordinates of A' are:

A'(x, y) = (-3, -1) + 2 · [(-3, -1) - (0, 0)]

A'(x, y) = (-3, -1) + (-6, -2)

A'(x, y) = (-9, -3)

After dilating the quadrilateral ABCD by a factor of 2 and with respect to the origin, the point A(x, y) = (-3, -1) is transformed into the point A'(x, y) = (-9, -3).

To learn more on dilations: brainly.com/question/13176891

#SPJ1

4 0

1 year ago