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3 years ago

11

-7 - 7 ( 8x - 7 ) = - 19 + 5x

1 answer:

Yakvenalex [24]3 years ago

6 0

-7 - 7( 8x - 7 ) = -19 + 5x
⇔ -56x + 49 = -12 + 5x
⇔ -61x = -61
⇔ x = 1

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If a distance of 75 yds is measured back from the edge of the canyon and two angles are measured , find the distance across the

adelina 88 [10]

Answer:

Length of side $c$ :

$c = \rm AB \approx 115\; yds$ .

The distance across the canyon is approximately

$\rm 113\;yds$ .

Step-by-step explanation:

$c$ is the length of the side opposite to the angle $\rm A\hat{C} B$ .
$a$ is the length of the side opposite to the angle $\rm B\hat{A}C$ .

Apply the law of sine:

$\displaystyle \frac{c}{\sin{\rm A\hat{C}B} = \frac{a}{\sin{\rm B\hat{A}C}}$ .

In other words,

$\displaystyle c = \sin{\rm B\hat{A}C} \cdot \frac{a}{\sin{\rm A\hat{C} B}}$ .

However, the value of the angle $\rm B\hat{A}C$ isn't given. Don't panic. The three interior angles of a triangle shall add up to 180°. Two of the three angles are given. The value of the third angle is implied.

$\rm B\hat{A}C = 180\textdegree{} - A\hat{C}B - A\hat{B}C = 30\textdegree{}$ .

Apply the law of sine to find $c$ :

$\displaystyle \begin{aligned}c &= \sin{\rm A\hat{C}B} \cdot \frac{a}{\sin{\rm B\hat{A}C}}\\ &= \sin{50\textdegree{}}\cdot \frac{\rm 75\; yds}{\sin{30\textdegree{}}}\\ &\rm = 114.907\; yds\end{aligned}$ .

Refer to the diagram. The distance across the canyon will be

$\rm AB \cdot \sin{A\hat{B}C} = 114.907\times \sin{100\textdegree{}} \approx 113\;yds$ .

3 0

3 years ago

The width of a rectangle is 1 unit less than the length. The area of the rectangle is 72 units. What is the width, in units, of

denis-greek [22]

Answer:

$Length=9 units\\width=8 units$

Step-by-step explanation:

Width of the rectangle= W

Length= L

W=(L-1) units

Area= 72 square units

Area of a rectangle= Length*Width

$72=L*(L-1)\\\\72=L^2-L\\\\L^2-L-72=0$

Solving the quadratic equation using the factorization method:

$L^2+8L-9L-72=0$

Taking common from the equation:

$L(L+8)-9(L+8)=0\\(L+8)(L-9)=0$

$L+8=0\\L=-8$

OR

$L-9=0\\L=9$

The length cannot be negative, therefore: Length= 9 units

$Width=Length-1\\=9-1\\=8 units$

$Length=9 units\\width=8 units$

4 0

3 years ago

PLEASE ANSWER !!

ANEK [815]

Answer:

Check the explanation.

Step-by-step explanation:

As the graph of a linear function f passes through the point (-2,-10) and has a slope of 5/2.

As the slop-intercept form is given by:

$y = mx+b$

where m is the slope and b is the y-intercept.

substituting the values (-2, -10) and m = 5/2 in the slop-intercept form to determine y-intercept.

$y = mx+b$

$-10=\frac{5}{2}\left(-2\right)+b$

$-\frac{5}{2}\cdot \:2+b=-10$

$-5+b=-10$

$-5+b+5=-10+5$

$b=-5$

And the equation of the line in the slope-intercept form will be:

$y = mx+b$

putting b = -5 and slope = m = 5/2

$y = mx+b$

$y=\frac{5}{2}x+\left(-5\right)$

$y=\frac{5}{2}x-5$

Determining the zero of function.

As we know that the real zero of a function is the x‐intercept(s) of the graph of the function.

so let us determine the value of x (zero of function) by setting y = 0.

$0=\frac{5}{2}x-5$

$\frac{5}{2}x-5=0$

$\frac{5}{2}x=5$

$5x=10$

$x=2$

Therefore, the zeros of the function will be:

x = 2

3 0

3 years ago

12. The following list shows the number of new memberships that a gym

MrRissso [65]

The answer is B.

Arrange the data in ascending order:
0,2,2,3,4,8,9

The median is the 4th data
= 3

5 0

3 years ago

12 - 8 x 9 +16<br> Order of operation

olga nikolaevna [1]

Answer:

12-72+16
12-88
-76

7 0

4 years ago