Prove that ABCD is a parallelogram. Show All Work Please!

Answer:

-5/18

Step-by-step explanation:

Graphing is the least accurate method for solving systems of equations, and it may only give an approximate answer. Hence, option A is the right choice.

A system of equations is made up of two or more equations that are solved at the same time.

There are three ways to solve a system of equations:

In the question, we are asked which method for solving systems of equations is the least accurate and may only give an approximate answer.

We have discussed all methods above.

Of these methods, when solving manually, as the degree of the equation gets bigger and bigger, the graphing of equations will become difficult, and thus the graphing method will be the least accurate.

Thus, graphing is the least accurate method for solving systems of equations, and it may only give an approximate answer. Hence, option A is the right choice.

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Answer:

The selling price of the cleaner is:

Step-by-step explanation:

First, we have the base of the value that is $120, now we know that the overhead is 5%, so we must calculate this value in dollars, the 5% of $120 is:

This value you must add to the base ($120), so the cost with the overhead is $126. How the store wants to make a profit of 10%, you must calculate this 10% of the total cost obtained ($126):

And you must add this value to obtain the final price in the store:

Answer:

0.894

Step-by-step explanation:

Data provided in the question

BC length = 17.89 unit

DC length = 16 unit.

Now, we have to compute the angle y with the help of the cosine function;

Cosine defines the ratio between the right angle adjacent side and the hypotenuse  

[tex]\cos = \frac{Adjacent side}{Hpotenuse}[/tex]

As per the triangle BDC;

Hypotenuse = BC =17.89 unit

And, the Adjacent side = 16 units

So;

[tex]\cos y =\frac{16}{17.89} =0.894354388[/tex]

[tex]y =\cos^{-1} (0.894354388) = 26.57^{\circ} (nearest\ to\ hundredths\ place)[/tex]

Now, determine the value of angle x

In right angle ΔABC;

As we know that

The three angles sum is 180 degrees

So,

[tex]\angle A + \angle B +\angle C =180^{\circ} ....(1)[/tex]

According to the given figure

[tex]\angle B=90^{\circ}, \angle A =x^{\circ}[/tex]

and

[tex]\angle C =y=26.57^{\circ}[/tex]

Now Substitute these in (1) for solving the angle x;

[tex]x^{\circ}+90^{\circ}+y^{\circ} =180^{\circ}[/tex]

or

[tex]x^{\circ}+90^{\circ}+26.57^{\circ} =180^{\circ}[/tex]

or

[tex]x^{\circ}+116.57^{\circ} =180^{\circ}[/tex]

[tex]x^{\circ}=180^{\circ} - 116.57^{\circ}=63.43^{\circ}[/tex]

Finally we have to determine the value of sin x;

Hence,

The value of [tex]\sin 63.43 =0.89438856[/tex]

or

= 0.894

Answer:

sin x = 0.894

Step-by-step explanation:

I hope you are refering to this figure:

Answer:

Option D is correct

Step-by-step explanation:

With x < 4 and y < 5:

P = 4x + 3y < 4(4) + 3(5) = 16 + 15 = 31

=> Option D is correct

Given the equation P = 4x + 3y  With constraints x > 0, x < 4 and y < 5:

Option D is correct that is 31.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given the equation P = 4x + 3y

With  constraints x > 0, x < 4 and y < 5:

The maximum value is

P = 4x + 3y < 4(4) + 3(5)

P = 16 + 15

P = 31

Hence, the Option D is correct.

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Answer:

Step-by-step explanation:

(7-4)/(-2-6)= 3/-8 = -3/8 is the slope

Answer:

Mean = 76

Median = 75.2

Step-by-step explanation:

Mean - put all the temperatures in order and pick the middle one.

Median - add all the temperatures together and divide by 20.

Answer:

y ≥ x - 2 and x + 2y < 4

Step-by-step explanation:

There are two lines graphed.

The dotted line passes through (0,2) and (4,0), then:

slope (m): (0 - 2)/(4 - 0) = -1/2

y-intercept (b): 2

equation:

y = mx + b

y = -1/2x + 2

multiplying by 2 at both sides, we get

2y = -x + 4

x + 2y = 4

The inequality is x + 2y < 4 because points below this line are shaded and points on the line are not included.

The solid line passes through (0,-2) and (2,0), then:

slope (m): (0 - (-2))/(2 - 0) = 1

y-intercept (b): -2

equation:

y = x - 2

The inequality is y ≥ x - 2 because points above this line are shaded and points on the line are included.

Answer:

The the equation of the line through the points (8, -2) and (5, 5) in slope-intercept form is

[tex]y=-\frac{7}{3} x+\frac{50}{3}[/tex]

Step-by-step explanation:

Let's start by calculation the slope of the line by finding the slope of the segment that joins the two given points (8, -2) and (5,  5):

[tex]slope=\frac{y_2-y_1}{x_2-x_1} \\slope=\frac{5-(-2)}{5-8}\\slope=\frac{7}{-3} \\slope=-\frac{7}{3}[/tex]

Now we use this slope in the general slope-intercept form of a line;

[tex]y=mx+b\\y=-\frac{7}{3} x+b[/tex]

and then we calculate the value of the intercept "b" by using one of the given points through which the line must pass (for example (5,5) ), and solving for b:

[tex]y=-\frac{7}{3} x+b\\5=-\frac{7}{3} (5)+b\\5=-\frac{35}{3} +b\\b=5+\frac{35}{3}\\b=\frac{50}{3}[/tex]

The the equation of the line is

[tex]y=-\frac{7}{3} x+\frac{50}{3}[/tex]

Answer:  y = 3x + 1

Step-by-step explanation:

In the equation y=mx+b (slope - intercept form), m represents the slope and b represents the y - intercept of the equation. We can use this to answer the problem.

Because the problem specifies here that the equation we are trying to solve for is parallel to y= 3x - 5, we can assume that its slope is 3 (the same as the line it is parallel to - this is so because of the definition of parallel lines).

m = 3

And finally, we know that the y-intercept will be in the form (0, b) - which is exactly what the given point is in. Substitute the value in, and we get:

b = 1

Now put these two values into one equation.

y = mx + b

y = (3)x + (1)

y = 3x + 1

The simplified form of an algebraic expression is x+9.

The given algebraic expression is x-5/5+10.

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.

Now, x-5/5+10=x-1+10

=x+9

Therefore, the simplified form of an algebraic expression is x+9.

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Answer:

10 nickels and 10 quarters

Step-by-step explanation:

Given

Number of coins: 20

Vaiue of coins = $3.00

Required

Number of Nickels and Quarters;

Let N =Nickels and Q =Quarters

The total coins is represented as:

[tex]N + Q = 20[/tex]

1 nickel is equivalent to $0.05 and 1 quarter is equivalent to $0.25; So

[tex]0.05N + 0.25Q = 3[/tex]

Make N the subject of formula in the first equation

[tex]N = 20 - Q[/tex]

Substitute this in the second equation

[tex]0.05(20 - Q) + 0.25Q = 3[/tex]

[tex]1 - 0.05Q + 0.25Q = 3[/tex]

Collect like terms

[tex]-0.05Q + 0.25Q = 3 - 1[/tex]

[tex]0.2Q = 2[/tex]

Multiply both sides by 5

[tex]5 * 0.2Q = 2 * 5[/tex]

[tex]Q = 10[/tex]

Recall that N = 20 - Q

[tex]N = 20 - 10[/tex]

[tex]N = 10[/tex]

Answer:

3 multiplied by 10^-10

Answer:

y = -[tex]\frac{4}{5}[/tex]  x  + [tex]\frac{27}{5}[/tex]      or

5y = -4x + 27

Step-by-step explanation:

To find the equation of a line with points (3,3) and is perpendicular to   5x+5-4y=0

we will follow the steps below:

First find write the equation:  5x+5-4y=0  in standard form  y= mx + c and find the slope

5x+5-4y=0

4y = 5x + 5

divide through by 4

4y /4= 5x/4 + 5/4

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

comparing the above with y = mx + c

m=  [tex]\frac{5}{4}[/tex]

since the equations are perpendicular.

To find the new slope

[tex]m_{1}[/tex][tex]m_{2}[/tex]  = -1

[tex]\frac{5}{4}[/tex] [tex]m_{2}[/tex]   = -1

multiply both-side of the equation by [tex]\frac{4}{5}[/tex]

[tex]\frac{4}{5}[/tex]× [tex]\frac{5}{4}[/tex] [tex]m_{2}[/tex]   = -1 × [tex]\frac{4}{5}[/tex]

[tex]m_{2}[/tex]   =  -[tex]\frac{4}{5}[/tex]

The slope of our new  equation is  -[tex]\frac{4}{5}[/tex]

The points are (3,3)

We can now go ahead and form our new equation

y - [tex]y_{1}[/tex]  =  m ( x - [tex]x_{1}[/tex])

y - 3 =  -[tex]\frac{4}{5}[/tex] ( x - 3)

y - 3 =  -[tex]\frac{4}{5}[/tex]  x  +  [tex]\frac{12}{5}[/tex]

y = -[tex]\frac{4}{5}[/tex]  x  + 3 +   [tex]\frac{12}{5}[/tex]

y = -[tex]\frac{4}{5}[/tex]  x  + [tex]\frac{27}{5}[/tex]

5y = -4x + 27

Answer:

A random movie is between 1.8 and 2.0 hours.

z=1.8-1.9/0.3= -0.33= 0.3707

z=2.0-1.9/0.3= 0.33= 0.6293

0.6293-0.3707= 0.2586

Therefore, the chance a random movie is between 1.8 and 2.0 hours long is 0.2586.

A movie is longer than 2.3 hours.

z=2.3-1.9/0.3 =1.33 =0.9082

1-0.9082= 0.0918

Therefore, the chance a movie is longer than 2.3 hours is 0.9082.

The length of movie that is shorter than 94% of the movies

z=x-1.9/0.3= 0.94

z=x-1.9/0.3= 1-0.94= 0.06

=x-1.9/0.3= 0.06= -1.56

x= 1.432

Therefore, the length of the movie that is shorter than 94% of the movies about 1.4 hours.  

Step-by-step explanation:

Answer:

9/16

Step-by-step explanation:

3/16 + 2/16 + 4/16 = 9/16

Answer:

9/16

Step-by-step explanation:

To solve this, you first need to give all the fractions a common denominator. In this case all the denominators can be mutiplied to 16, so that will be our common denominator. So now that all of the denomitors are the same,(3/16+2/16+4/16) we can start solving the problem. First, 3/16+2/16=5/16. Then do, 5/16+4/16=9/16.

Answer: r=-56

Step-by-step explanation:

multiply 7 on both sides

[tex]\frac{7r}{7}=7\left(-8\right)[/tex]

7*-8=-56

7 and 7 is eliminated

so x=-56

Answer:

r= -56

Step-by-step explanation:

The equation given is:

[tex]\frac{r}{7}= -8[/tex]

We want to solve for r. In order to do this, we must get r by itself.

Currently, r is being divided by 7. We want to perform the inverse, which is multiplication. Therefore, we should multiply both sides of the equation by 7.

[tex]7*\frac{r}{7}= -8 * 7[/tex]

[tex]r=-8*7[/tex]

[tex]r= -56[/tex]

Let's check our solution. Substitute -56 back in for r and solve.

[tex]\frac{r}{7}= -8[/tex]

[tex]\frac{-56}{7}= -8[/tex]

[tex]-8=-8[/tex]

Both sides of the equation are the same, so we know our answer is correct.

Answer:

cos(α2)= −1/5√2

Step-by-step explanation:

you are given  tan(α)=7/24 , so you can find the length of the hypotenuse using the Pythagorean theorem, which is  a2+b2=c2  with  a  and  b  being the legs of the triangle and  c  being the hypotenuse of the triangle.

c2=7^2+24^2  

⟹c2=49+576

⟹c2=625

⟹c=25

if  π<α<3π/2  , then  α  has to lie in quadrant III where cosine is negative. so cos(α)= −24/25

The half-angle identity for the cosine function is  cos(α2)=±√1+cos(α)/2  , so plugging the information in, we get

cos(α2)=±√  1+(−24/25)/2

⟹ cos(α2)=±√1/25 / 2

⟹cos(α2)=±√1/50

⟹cos(α2)=±1/5√2

Answer:

y = 8x - 26

Step-by-step explanation:  

Since we already have the ending equation in slope intercept form, all we need to do is fill in the blanks. We do that by putting it in point slope form which is [tex]y-y_{1}=m(x-x_{1})[/tex]

(You can plug either point in and get the same result but I'm going to use the first one)

[tex]y-(-2)=8(x-3)[/tex]

Distribute the [tex]m(x-x_{3})[/tex]

[tex]y-(-2)=8x-24[/tex]

Isolate the [tex]y[/tex]

[tex]y-(-2)=y+2[/tex]

[tex]y+2(-2)=8x-24(-2)[/tex]

[tex]y=8x-26[/tex]

And that's your answer!

Answer:

[tex](ab)(x)[/tex]

Step-by-step explanation:

Data provided in the question

a(x) = 2x - 4

b(x) = x + 2

Now we go through each options

First option

[tex](ab)(x)=(2x-4)(x+2)[/tex]

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

[tex]=2(x^2-4)[/tex]

[tex]=2x^2-8[/tex]

Second option

[tex]\dfrac{a}{b}(x)=\dfrac{2x-4}{x+2}[/tex]

Third option

[tex](a-b)(x)=(2x-4)-(x+2)[/tex]

[tex]=2x-4-x-2[/tex]

= x - 6

Fourth option

[tex](a+b)(x)=(2x-4)+(x+2)[/tex]

[tex]=2x-4+x+2[/tex]

= 3x - 2

As we can see from the above options only option A is correct i.e it only produced a quadric function

Answer:

11  1 /2

Step-by-step explanation:

Answer:

2000 ft x 2= 4000 ft

So the answer is 4000 ft

Step-by-step explanation:

Complementary angles mean that the sum of the angles equals 90 degrees.

This means that

A+B=90

(2x-13)+(4x-5)=90

expand and simplify

2x+4x-13-5=90

6x = 90+18 = 108

x = 108/6=18 degrees.

=>

B=4x-5=4*18-5=72-5=67 degrees

check:

A=2x-13=2*18-13=36-13=23 degrees

A+B=23+67=90 degrees => A and B are complementary

Answer:

19/64

Step-by-step explanation:

number of boys:

red haired boys:

The fraction:

Answer:

19/64

Step-by-step explanation:

number of boys: 11+21+13+19=64

red haired boys: 19

The fraction: 19/64

Answer:

Step-by-step explanation:

Volume = Length times width times height.

Here,

Volume = (4.5 in)(5 in)(3.75 in), which, when evaluated by calculator, comes out to 84.375 cubic inches.

This is equivalent to 84 3/8 cubic inches.

Answer:

[tex]84\frac{3}{8}in^3[/tex]

Step-by-step explanation:

V = L * W * H  

V = 4 1/2 * 5 * 3 3/4

V = 9/2 * 5/1 * 15/4

V = 675/8

V = 84 3/8

Answer:

f(2)= 2, f(3)= -9

Step-by-step explanation:

To find f(2) o f(3), you simply plug the respective number into the function, substituting it for x:

f(2)= -3(2)^2 + 4(2) + 6

f(2)= -12 + 8 + 6

f(2)= 2

f(3)= -3(3)^2 + 4(3) + 6

f(3)= -27 + 12 + 6

f(3)= -9

Answer:

1a.  {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

1b.   {5}

Step-by-step explanation:

For part 1:

A U B is the union of all values, so {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

Remember that union means to include all values.

A n B is the intersection of all values, so {5}

Remember that the intersection means "what do they have in common".