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ICE Princess25 [194]

3 years ago

9

Missy is getting married and addressing invitations. She has at least 140 envelopes and has addressed 26 of them. Write an inequ

ality that describes how many more invitations must be addressed.

1 answer:

d1i1m1o1n [39]3 years ago

8 0

To solve this, you must find out the total amount of envelopes she has, and the number of envelopes she has already mailed out. One equation that can work is:
140≥26+x or 140=26+x
X represents how many more envelopes she must mail out still
And you must use the ≥ or = symbol because 140 is the total amount of envelopes she has. She doesn’t have more than 140, 26+x must be equivalent to 140, or 140 must be greater or equal to 26+x.
Hopefully this made sense : )

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Which of the following numbers are solutions of the sentence x-3 < 2?

mrs_skeptik [129]

Answer:

O I, II, and III only

Step-by-step explanation:

x-3 < 2

Add 3 to each side

x-3+3< 2+5

x<5

-3 is less than 5

0 is less than 5

2 is less than 5

5 is not less than 5

I , II , II are true

5 0

3 years ago

Simplify the expression.<br> 3q+<br> 9<br> 25+6n+<br> 6<br> 25+7q−4n

Advocard [28]

Answer:

2n+10q+65

Step-by-step explanation:

3q+9+25+6n+6+25+7q-4n

Reorder so all like terms are by each other.

6n-4n+3q+7q+9+6+25+25

Now combine those like terms.

2n+10q+15+50

2n+10q+65

That's as far as it goes.

-hope it helps

4 0

2 years ago

How do I find the equation of the perpendicular bisector between (-2,5) and (2,-1)?

Arturiano [62]

Answer:

$y = \frac{2}{3} x + 2$

Step-by-step explanation:

Start by finding the slope of the given line.

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

Slope of given line

$= \frac{5 - ( - 1)}{ - 2 - 2}$

$= \frac{5 + 1}{ - 4}$

$= \frac{6}{ - 4}$

$= - \frac{3}{2}$

A perpendicular bisector cuts through the line at its midpoint perpendicularly.

The product of the slopes of two perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

$- \frac{3}{2} m = - 1$

$m = - 1 \div ( - \frac{3}{2} )$

$m = - 1 \times ( - \frac{2}{3} )$

$m = \frac{2}{3}$

$y = \frac{2}{3}x + c$ , where c is the y-intercept.

To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.

$\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}$

Midpoint of given line

$= ( \frac{ - 2+ 2}{2} , \frac{5 - 1}{2} )$

$=( \frac{0}{2} , \frac{4}{2} )$

= (0, 2)

$y = \frac{2}{3} x + c$

When x= 0, y= 2,

2= ⅔(0) +c

2= 0 +c

c= 2

Thus, the equation of the perpendicular bisector is $y = \frac{2}{3} x + 2$ .

7 0

3 years ago

Explain how the distance formula can prove Pythagoras' Theorem. In your

Paul [167]

Answer:

Given a triangle ABC, Pythagoras' Theorem shows that:

$c^2=a^2+b^2$

Thus,

$c = \sqrt{a^2+b^2}$

The distance formula, gives an equivalent expression based on two points at the end of the hypotenuse for a triangle.

$d^2 = (x_{2} -x_{1})^2 + (y_{2} -y_{1})^2$

$d = \sqrt{(x_{2}-x_{1})^2 + (y_{2} -y_{1})^2 }$

Therefore when given the hypotenuse with endpoints at

$(x_{1}, y_{1}) and {(x_{2}, y_{2})$

We know that the third point of the right triangle will be at

$(x_{2}, y_{1})$

and that the two side lengths will be defined by the absolute values of:

$(x_{2} - x_{1}) = a$

$(y_{2} - y_{1}) = b$

8 0

3 years ago

The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to

Harman [31]

*attachment contains the omitted graph

Answer:

$y = -\frac{4}{3}x + 9$

Step-by-step explanation:

The equation that represents the path of the swimmer to the shoreline can be represented in the slope-intercept form, given as $y = mx + b$ .

Where,

Slope (m) = the negative reciprocal of the slope of the shoreline, since it is perpendicular to it = ??

y-intercept (b) = ??

Find the slope of the shoreline using, (0, 1) and (4, 4):

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{4 - 0} = \frac{3}{4}$ .

Since the slope of the shoreline is ¾. The slope of the path of the swimmer would be the negative reciprocal of ¾.

The negative reciprocal of ¾ = -⁴/3.

The slope of the swimmer's path = -⁴/3.

Using the coordinate of the point of the swimmer (6, 1), and the slope of the path, we can find b, the y-intercept of the path.

Substitute x = 6, y = 1 and m = -⁴/3 into y = mx + b, to find b.

Thus:

1 = (-⁴/3)(6) + b

1 = -8 + b

Add 8 to both sides

1 + 8 = b

9 = b

b = 9

Substitute m = -⁴/3 and b = 9 into y = mx + b.

✅The equation that represents the path would be:

$y = -\frac{4}{3}x + 9$

8 0

3 years ago