quadrilateral \(abcd\) has vertices \(a(1,0)\), \(b(5,0)\), \(c(7,2)\), and \(d(3,2)\). use slope to prove that \(abcd\) is a parallelogram. show all of your work.

The pair of ratios that form a proportion is given by:

B) 5/15 and 4/12.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

A pair of ratios will form a proportion if the division of the denominator by the numerator is the same, hence:

The pair of ratios that form a proportion is given by:

B) 5/15 and 4/12.

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The slope of the line as shown in the diagram attached below = rise/run = 3/5.

The rise of a line over the run of a line would give us the slope of a line on a coordinate plane.

With the given line in the diagram, the image attached below shows the rise as represented by a red line while the run is represented by the blue line.

Therefore, we have:

Run = 10 units

Rise = 6 units

Slope (m) of the line = rise/run = 6/10

Simplify

Slope (m) of the line =  3/5

Therefore, the slope of the line as shown in the diagram attached below = rise/run = 3/5.

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Answer:

7: #3. 8: #2

Step-by-step explanation:

in the first question the format is simply (x, y) and because it is a translation, we are basically just moving the point by these numbers, with this information, it is simply moving x to the left(negative) 8 times, and y(up/positive) 4 times. The next question is simply moving the point across the x axis by the same amount that it is above the x axis, so it would be one down from the x-axis' bold line, or in this case moved 2 y-units down. Hope this helps mate :)

Answer:

x⅔

Step-by-step explanation:

1. we understand the concept that x÷x is a subtraction as an instance, x³/x² = x¹ so we can apply this knowledge in this question

2. x⅚ / x⅙ --> x⅚-⅙

--> x^4/6 [simplify this]

--> x^4/6 [ divide 2 at the numerator and also the denominator]

--> x⅔

Last but not least, you got your 2 points

Answer:

a. A = 647

   P = 120

b. A = 192

   P = 70

Step-by-step explanation:

a. A = (16 x 12) + (13 x 35) = 192 + 455 = 647

   P = 16 + 12 + 19 + 13 + 35 + 25 = 120

b. A = (12 x 8) + (8 x 12) = 96 + 96 = 192

   P = 12 + 8 + 7 + 8 + 12 + 8 + 7 + 8 = 70

The area and perimeter of a polygon with vertices (1,-2) , (1,5) , (7,-2)

A=23.27644 units^2

Let

A= (1,-2) ,

B=(1,5) ,

C=(7,-2)

Therefore, the equation for distance is  mathematically given as

d=\sqrt {(x^2-x^1)^2+(y^2-y^1)^2}

Therefore For AB

[tex]d=\sqrt {(-2-1)^2+(5-1)^2}[/tex]

d=5

For BC

[tex]d=\sqrt {(5-1)^2+(-2-7)^2}[/tex]

d=9.84

for CA

[tex]\sqrt {(5-1)^2+(-2-7)^2}[/tex]

9.486

Hence, Perimeter

P=9.486+9.84 +5

P=24.326

In conclusion, the Area of a triangle

A = √s(s−a)(s−b)

Where

s=24.326/2

Therefore

[tex]A=\sqrt{24.326/2((24.326/2)-5)((24.326/2)-9.486 )((24.326/2)-9.84 )}[/tex]

A=23.27644 units^2

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x=x

Step-by-step explanation:

finding by mathematical operation and distribution law over multiplication added with subtraction is the formula now it might be easy for you

x(x – 5) = 176 is the correct equation to find the greater integer.

As the question mentions, the greater integer is x. So, the smaller integer will be (x - 5). Also, we are informed that their product is 176.

Now, representing the given information as mathematical expression -

x(x – 5) = 176

On further multiplication on Left Hand Side, we get the equation -

x² - 5x = 176

Rewriting the equation -

x² - 5x - 176 = 0

Further solving the equation to validate it.

x² - 16x + 11x - 176 = 0

x (x - 16) + 11 (x - 16) = 0

(x - 16) (x + 11) = 0

x = 16, -11

As stated, the integers are positive. So, the value of x and hence greater integer is 16.

Value of small integer = 16 - 5

Value of small integer = 11

So, the two integers are 16 and 11. Their product is 176 hence, our formed equation is correct.

Therefore, the equation that can be used to find x is : x(x – 5) = 176.

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The complete question is -

Two positive integers have a product of 176. One integer is 5 less than the other integer. Which equation can be used to find the value of x, the greater integer?

x² + 5 = 176

x(x + 5) = 176

x(x – 5) = 176

x² – 5 = 176

The  proportion of initial sales were spent on marketing by small businesses  is between 5 and 10%.

The correct option is A.

The U.S. Small Business Administration estimates that small businesses typically want to spend between 7-8% of one‘s revenue on marketing, provided that their companies have profit margins of 10-12%.

In order for sales to know exactly where the buyers are and assist them in progressing toward a purchase, marketing can give sales representatives the opportunity to be as knowledgeable as the buyers themselves. In summary, marketing can actually improve sales representatives' performance, which can have an effect on revenue generation.

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I understand that the question you are looking for is:

In one study, small businesses starting out spent what percentage of sales on marketing?

A) 5 to 10%

B) 8 to 15%

C) 15 to 19%

D) 25 to 32%

Answer:

[tex]\frac{(5+a)}{(a-1)}[/tex]

Choice A

Step-by-step explanation:

[tex]f\left(x\right)\:=\:\frac{\left(3+x\right)}{\left(x-3\right)}[/tex]

[tex]x = a + 2[/tex]

Substitute x with a+2

Numerator becomes [tex]3 + (a+2) = 5+a[/tex]
Denominator becomes [tex](a+2) - 3 = a+2-3 = a - 1[/tex]

Therefore the fraction becomes [tex]\frac{(5+a)}{(a-1)}[/tex]

Answer:

1/4

Step-by-step explanation:

(0.2+0.3) / 2 = 0.25

0.25 = 25% = 25/100 = 1/4

Answer: 3/2

Step-by-step explanation:

[tex]\displaystyle\\0.3:0.2=\\\\\frac{3}{10} :\frac{2}{10}=\\\\ \frac{3}{10}*\frac{10}{2} =\\\\\frac{(3)(10)}{(10)(2)}=\\\\ \frac{3}{2}[/tex]

The solution of the equation 20x = x + 3 will be 3 / 19. Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

Ten times a number, x, is one-half the sum of the number and three. Then the equation will be

10x = 1/2(x + 3)

Simplify the equation, then we have

20x = x + 3

19x = 3

x = 3 / 19

Thus, the solution of the equation 20x = x + 3 will be 3 / 19. Then the correct option is A.

Your question was incomplete, probably the question was...

Ten times a number, x, is one-half the sum of the number and three. Which answer represents this situation?

A. 10x = 1/2(x + 3)

B. 10x = 1/2x

C. 10x = 1/2x + 3

D. 10x = (x + 3)

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It take 8.205 minutes to fill a queen sized mattress.

'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Given dimensions:

Twin sized air mattress (39 by 8.75 by 75 inches).

Queen sized mattress (60 by 8.75 by 80 inches)

Now, Volume of twin sized mattress

=39* 8.75* 75

= 25593.35 cubic inch

Volume of queen sized mattress,

=60* 8.75* 80

= 42000 cubic inch

as, To fill 25593.35 cubic inch it takes 5  minutes

so, to fill 1 cubic inch = 5/25593.35

and, So to fill 42000 cubic inch it will take = 42000* 5/25593.35

=8.205 minutes

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Answer: I think ok not sure but yet positive but i think it is  y= -7

Step-by-step explanation:

Answer: D $30

Step-by-step explanation:

$12.79 rounds to $13

$2.33 round to $2

$14.65 rounds to $15

Add the estimates: 13+2+15= $30

The answer is -28

We're asked to multiply 4 by -7

The multiplication is straight forward, the first number is a positive integer and the second number is a negative integer

4 × (-7)

= -28

Hence the multiplication of both numbers will give -28

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Answer:

Agnes would need to score a 85 to get an average of 80.

Step-by-step explanation:

[tex]\frac{82+69+84+x}{4}[/tex] = 80  multiply both sides by 4

82+69+84+X = 320

235+X = 320  subtract both sides by235

x = 85

Answer:

7/8

Step-by-step explanation:

add your decimal your fraction inside parentheses then divide it by the rest of the equation

The value of the expression [3.5⁷ / 3.5⁶]² will be 12.25. Then the correct option is D.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ [3.5⁷ / 3.5⁶]²

Simplify the expression, then the value of the expression will be

⇒ [3.5⁷ / 3.5⁶]²

⇒ [3.5]²

⇒ 12.25

The value of the expression [3.5⁷ / 3.5⁶]² will be 12.25. Then the correct option is D.

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The required function is P(t)=50000 + 5000t.

In this problem we need to form the function of the population in a town.

Here it is given that the initial population of the town is 50000.

the rate at which the population increases is 5000 per year.

So, the increase for the first year will be 5000. And the population will be 55000.

Then again for the next year the growth will be 5000 and the population will be 50000 + (5000×2)

        = 60000

So we can see clearly that the population is varying with time and we can write the function as P(t)=50000 + 5000t where t is the time in years.

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Probability that no zebras collide is 0.25

The zebras are represented as z1, z2 and z3.

Z1 to B, Z2 to C, and Z3 to A come first [tex]= (\frac{1}{2})^3[/tex]

Following that, z1 to C, z2 to A, and z3 to B = [tex](\frac{1}{2})^3[/tex]

Consequently, the likelihood of no collision is 2×1/8 = 0.25.

Discrete and continuous probability distributions are the two main categories in which probability distributions fall. There are numerous varieties of probability distributions within each category.

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Answer:

18

Step-by-step explanation:

-56+2(-3) - (-80)

Simplify.

-56+2(-3) - (-80)=

=-56 - 6 + 80=

=-62+80=18

Hope this helps!

Please mark as brainliest if correct!

Answer:

Step-by-step explanation:

If she made 60$ she only needs 140$ more to get to 200$

The dimensions of the rectangular play area should be: 41.5 x 8.3 feet.

Now,

Given:

To find: Length and Width.

Let the width of the rectangular play area be x.

Then, the length = 5x

According to the formula of perimeter of a rectangle,

100 = 2 (x + 5x)

=> 50 = 6x

=> x = 8.3 feet (Approx.)

That is the width of the play area = 8.3 feet

=> Length = 5(8.3) = 41.5 feet.

Hence, The dimensions of the rectangular play area should be: 41.5 x 8.3 feet.

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Answer:

4.     [tex]6.3 \times 10^4[/tex]

6.     [tex]3.75 \times 10^{-19}[/tex]

Step-by-step explanation:

9.45 * 10^10 / (1.5 * 10^6) = 9.45 / 1.5 * 10^10 / 10^6 = 6.3 * 10^4

9 * 10^(-11) / (2.4 * 10^8) = 9 / 2.4 * 10^(-11) / 10^8 = 3.75 * 10^(-19)

(b) We have 13 possibilities that a five-card hand will contain four of a kind.

(c) We have 12 possibilities that a five-card hand will contain a full house.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

The probability of an occurrence is a number between 0 and 1, with 1 representing certainty and 0 representing impossibility.

Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half (which could also be written as 0.5)

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The value of x as given in the diagram is 18

The sum of supplementary angles is 180 degrees. From the given figure;

The measure of the angle 2x and 8x are supplementary such that;

2x + 8x = 180

10x = 180

Divide both sides by 10 to have:

10x/10 = 180/10

x = 18

Hence the value of x as given in the diagram is 18

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Answer:

C

Step-by-step explanation:

y = mx +b  The b is where the graph crosses the y axis.  If you look a the graph it is crossing at 5.  The m is the slope.  It is the change in y over the change in x.  If you start at 5 and go up10 and over 1, you will be on the line.  So our slope is 10/1 which is just 10

Answer:

C

Step-by-step explanation:

it starts on 5 and goes up by 10