ABCD is a parallelogram. Determine the value of a.

Answer:

y= -x -3

Step-by-step explanation:

A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).

Let's find the slope of the line segment.

\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }slope=x1−x2y1−y2

Slope of line segment

= \frac{4 - ( - 8)}{5 - ( - 7)}=5−(−7)4−(−8)

= \frac{4 + 8}{5 + 7}=5+74+8

= \frac{12}{12}=1212

= 1

The product of the slopes of 2 perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

m(1)= -1

m= -1

y= -x +c

To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.

Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.

\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}midpoint=(2x1+x2,2y1+y2)

Midpoint of line segment

= ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )=(25−7,24−8)

= ( \frac{ - 2}{2} , \frac{ - 4}{2} )=(2−2,2−4)

= (-1, -2)

y= -x +c

When x= -1, y= -2,

-2= -(-1) +c

-2= 1 +c

c= -2 -1

c= -3

Thus, the equation of the perpendicular bisector is y= -x -3.

Answer:

$51.36

$77.04 i think

Step-by-step explanation:

Multiply the cost of the number of pairs of jeans by the sales tax amount, 7%.

cost of 2 pairs:   48 + 7/100 x 48 = $51.36

cost of 3 pairs:   72 + 7/100 x 72 = $77.04

Answer:

(2,2)

Step-by-step explanation:

The solution to a system is the point on the graph where both lines intersect.

Answer:

1a. 2 is the solution

1b. -3 is because square root of 1 doesn't equal -1.

1c.-3

Step-by-step explanation:

1.

[tex](x + 2 = \sqrt{3x + 10} [/tex]

Square both sides

[tex](x + 2) {}^{2} = 3x + 10[/tex]

Remeber perfect square Rule

[tex](x + y) {}^{2} = {x}^{2} + 2xy + {y}^{2} [/tex]

So now we got

[tex]x {}^{2} + 4x + 4 = 3x + 10[/tex]

[tex] {x}^{2} + x + 4 = 10[/tex]

[tex] {x}^{2} + x - 6 = 0[/tex]

Factor into binomial.

[tex](x + 3)(x - 2) = 0[/tex]

So our solution is 3 or 2. However, let's check our work.

[tex] - 3 + 2 = \sqrt{3( - 3) + 10} [/tex]

[tex] - 1 = \sqrt{1} [/tex]

However square root of 1 is 1. It could be 1 but in Math, We only take the principal square root which is positive always. So -3 isn't a solution.

So let try 2.

[tex]2 + 2 = \sqrt{3(2) + 10} = 4 = \sqrt{16} = 4 = 4[/tex]

So this is indeed the solution.

Make up equation for 2 and 3. Ask me if you need help.

Answer:

half-class

Step-by-step explanation:

Answer:

42.86%

Step-by-step explanation:

Event = Girl

Therare 6 girls and 8 boys, which are thus 6+8 =14 students in total and thus there are 14 possible out comes.

# of possible outcomes = 14

There are 6 girls in the class and thus there are 6 favorable outcomes.

# of favorable outcomes = 6

The probability is the number of favorable outcomes divided by the number of possible outcomes.

P(Girl) = # of favorable outcomes

            # of possible outcomes

= [tex]\frac{6}{14}[/tex]

= [tex]\frac{3}{7}[/tex]

≈ 0.4286

= 42.86%

Result

[tex]\frac{3}{7}[/tex] ≈ 0.4286 = 42.86%

Answer:

Dean ran 8.0467 kilometers

Step-by-step explanation:

First, you need to know how much kilometers are in a mile. 1 mile is 1.60934 kilometers, so once you found that out, then you would do 1.60934x5 which gets you 8.0467. Hope it helps!

No. Tripling the dimensions (the side of the square base and the height) would increase the surface area of the pyramid by a factor of [tex]3^2[/tex] or [tex]9[/tex]

Let

[tex]h=\text{the height of the pyramid}\\s=\text{length of one side of the square base}\\t=\text{total surface area of the pyramid}[/tex]

The total surface area of the square-based pyramid is given by

[tex]t=b(b+\sqrt{4h^2+b^2})[/tex]

Let the tripled dimensions be given by [tex]B=3b[/tex] and [tex]H=3h[/tex], then the new surface area will be

[tex]T=B(B+\sqrt{4H^2+B^2})\\=3b(3b+\sqrt{4(3h)^2+(3b)^2})\\=3b(3b+\sqrt{9(4h^2+b^2)})\\=3b(3b+3 \sqrt{4h^2+b^2})\\=9b(b+\sqrt{4h^2+b^2})\\=9t[/tex]

The new surface area will be greater than the original by a factor of [tex]9[/tex]

Learn more about scale factors here: https://brainly.com/question/1440011

Answer:  It will be more than triple the area because you square the side to find the area of the base.

Step-by-step explanation:

It will be more than triple the area because you triple the side to find the area of the base. To calculate the surface area of a square pyramid, you need to first calculate the area of the base. To do this, you will need to multiply the length of one side of the square by itself (or square it). Since you are tripling the dimensions of the square pyramid, you will need to triple the side of the base, which will result in an area that is more than three times larger.

[tex]x^{\tfrac 16} \left(x^{\tfrac 16} + x^{\tfrac 34} \right)\\\\\\=x^{\tfrac 16} \cdot x^{\tfrac 16} + x^{\tfrac 16} \cdot x^{\tfrac 34}\\\\\\=x^{\left(\tfrac 16 + \tfrac 16\right)} + x^{\left(\tfrac 16 +\tfrac 34\right)}\\\\\\=x^{\tfrac 26} + x^{\tfrac {11}{12}}\\\\\\=x^{\tfrac 13} +x^{\tfrac{11}{12}}[/tex]

Answer: 2135

step by step explanation:

I don't really think this is necessary

Answer:

D

Step-by-step explanation:

(point D)

Answer:

Point D

Step-by-step explanation:

5 units right on the x axis, 3 units down on the y-axis.

Answer:

Step-by-step explanation:

He has sold (16+1/4) bushels/day x 5 days = (16 x 5) + (1/4 x 5) = 80 + 5/4 = 81 + 1/4 = 81.25

The change in the number of bushels is 140 - 81.25 = 58.75 or 58 and 3/4 bushels

In other words, he has 58.75 (or 18 and 3/4) bushels remaining and has sold 81.25 (or 81 and 1/4) bushels

Answer:W= B-3 or 3=B-W

Step-by-step explanation:

Answer:

F(x)=-x+2

Step-by-step explanation:

equation

mx+b

m= slope

x

b = y-intercept

Answer:

true i think

Step-by-step explanation:

Answer:

n = 34/13

Step-by-step explanation:

13 x 4 = n x 26

=> 68 = 26n

=> n = 68/26

=> n = 34/13

Therefore, n = 34/13

Hoped this helped.

[tex]GeniusUser[/tex]

we can change cos to sin by saying cosx=sin(90-x)

now we drop sin and make the angles equal (nothing needs to be added or subtracted since its in the first quadrant)

90-x=20+x+k.360.......kEZ (k is an element of set of integers) (we say k.360 if it's cos and sin and k.180 if it's tan)

-x-x=20-90+k.360........kEZ

-2x=-70+k.360.........kEZ

divide all terms by -2

x=35-k.180.......kEZ

Answer:

x=35°

Step-by-step explanation:

If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is 35°.

Answer:

Step-by-step explanation:

25 km / 100 km/hr = 0.25 hr or 15 minutes

It will take 0.25 hours to travel 25 km.

Given

A train travels from point A to B at a speed of 100km/h.

Distance;

Distance is defined as the product of speed and time.

The following formula is used to calculate the time;

[tex]\rm Time =\dfrac{Distance}{Speed}\\\\[/tex]

Substitute all the values in the formula;

[tex]\rm Time =\dfrac{Distance}{Speed}\\\\\rm Time =\dfrac{25}{100}\\\\Time = 0.25 \ hours[/tex]

Hence, it will take 0.25 hours to travel 25 km.

To know more about distance click the link given below.

https://brainly.com/question/3615948

If my calculations are correct, the percentage decrease faced here is roughly 38.2%. Based on the calculations, the bicycle costs 199$ and when the cost is subtracted from 520, you would create the percentage of 38.2%.

Answer:

The y-intercept is 1.

Step-by-step explanation:

The y-intercept is where a line crosses the y-axis, so from looking at the graph, we can see that it crosses at (0,1), giving you a y-intercept of 1.

Answer:

y = [tex]\frac{5}{4}[/tex] x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{5}{4}[/tex] and c = 2 , then

y = [tex]\frac{5}{4}[/tex] x + 2 ← equation of line

Answer:

the answer is the 4 option

Answer:

AOB forms must be collected every time a beneficiary fills a Medicare part b prescription

okkkkkkkkkkkkkkkkkkkkkkkkkkk

Answer:

Step-by-step explanation:

The decrease in value is ...

  15% of $233,000 = $34,950

The current house value is ...

  $233,000 -34,950 = $198,050

The most no. of tickets sold is 60.

The pictorial representation of data in the form of vertical or horizontal rectangular bars, whose length is proportional to the data's measurement, is known as a bar graph. Data are typically grouped in this way. Bar charts are another name for them. In statistics, bar graphs are one way to handle data.

Given  the graph between total student and number of ticket sold,

where students shown in Y axis and tickets sold in X axis,

as Shown in graph maximum number of tickets sold are 51 to 60

Hence the maximum number of ticket sold is 60.

Learn more about bar graph;

https://brainly.com/question/13298277

#SPJ2

Hey there!

“Product” is multiplication so let’s say it means “multiply” & “difference” is subtraction so let’s say it means “subtract”

p & q is/are the variables, whereas -12 is a coefficient

“The [PRODUCT of -12] and the [DIFFERENCE of p & q]”

Product = multiply/multiplication

“-12 ×”

DIFFERENCE

“p - q”

So, based on that information we have your answer: “-12 × p - q”

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

12x

Step-by-step explanation:

I am not really sure how to explain it I just looked it up

Answer:

so you just use the equation to get the formula and extract the common denominator

Step-by-step explanation:

because i said so

Answer:

I don't know

Step-by-step explanation:

Answer:

11/18

Explanation:

Find the LCM

6 × 3 = 18

9 × 2 = 18

Since you found the LCM, multiply the numerators by the number you multiplied the denominators by.

[tex]\frac{5 *3}{6*3}= \frac{15}{18}[/tex]

[tex]\frac{2*2}{9*2}=\frac{4}{18}[/tex]

Now subtract.

[tex]\frac{15}{18} -\frac{4}{18} =\frac{11}{18}[/tex]