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Answer: P=7+3√5+2√13 units      S=21 quadratic units

Step-by-step explanation:

[tex]A(1,-2)\ \ \ \ B(1.5)\ \ \ \ C(7,2)\\[/tex]

                  The perimeter of a triangle

[tex]|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2} \\|AB|=\sqrt{(1-1)^2+(5-(-2))^2} \\|AB|=\sqrt{0^2+(5+2)^2}\\|AB|=\sqrt{0+7^2}\\ |AB|= \sqrt{7^2} \\|AB|=7[/tex]

[tex]|BC|=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2} \\|BC|=\sqrt{(7-1)^2+(2-5)^2}\\ |BC|=\sqrt{6^2+(-3)^2}\\ |BC|=\sqrt{36+9}\\ |BC|= \sqrt{45} \\|BC|=\sqrt{9*5}\\ |BC|=3\sqrt{5}[/tex]

[tex]|AC|=\sqrt{(x_C-x_A)^2+(y_C-x_A)^2}\\ |AC|=\sqrt{(7-1)^2+(2-(-2)^2} \\|AC|=\sqrt{6^2+(2+2)^2}\\ |AC|=\sqrt{36+4^2}\\ |AC|=\sqrt{36+16} \\|AC|=\sqrt{52}\\ |AC|=\sqrt{4*13} \\|AC|=2\sqrt{13} \\[/tex]

[tex]Thus,\\\\P_{ABC}=|AB|+|BC|+|AC|\\\\P_{ABC}=7+3\sqrt{5}+2\sqrt{13}\ units[/tex]

                        The area of a triangle

Taking A as the first vertex, we find:

[tex]\displaystyle\\Find\ |\overline{AB}*\overline{AC}|\\\left|\begin{array}{cc}x_A-x_C&y_A-y_C\\x_B-x_C&y_B-y_C\\\end{array}\right|=\\\\\left|\begin{array}{ccc}1-7&-2-2\\1-7&5-2\\\end{array}\right| =\\\\\left|\begin{array}{ccc}-6&-4\\-6&3\\\end{array}\right| =\\\\|(-6)*3-(-6)*(-4)|=\\\\|-18-24|=\\\\|-42|=\\\\42\\\\S_{ABC}=\frac{1}{2} |\overline{AB}*\overline{AC}|\\\\S_{ABC}=\frac{1}{2}(42)\\\\S_{ABC}=21 \ quadratic\ units[/tex]

Using proportions, it is found that:

a. The equations are:

b. You would have saved $8 by switching the colors of the dining room and living room.

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.

For item a, considering that 5 cans were bought, there are two options:

Hence the equations are given by:

The solution for x is given by:

120 - 24x + 28x = 132

3x = 12

x = 4.

Considering the possible solution, of 4 cans of blue paint and 1 can of white paint.

Exchanging the colors, the price would be of:

4 x 24 + 1 x 28 = 124.

132 - 124 = $8.

You would have saved $8 by switching the colors of the dining room and living room.

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The length of side yz is 15.7 units.

The link between the angles and sides of all kinds of triangles, including acute, obtuse, and right-angle triangles, is known as the law of sines. It asserts that for all sides and angles in a certain triangle, the ratio of a triangle's side length to the sine of an angle opposite that side is the same.

You must know two sides of an angle in a triangle or two sides and an angle across from one of them in order to employ the law of sines. You will discover the law of sines in this article, along with its definition, formula, applications, difficulties, and proof. You will also learn when to employ the rule of sines.

Law of sines is expressed as follows: x/sin X = y/sin Y = c/sin Z.

We have the following:

X = 32°

z = 24

Z = 180 - 32 - 94 = 54°

Substituting the value in x / sin X = y / sin Y = z / sin Z

We get,

x/sin (32) = 24 / sin (54)

x = sin ( 32) × (24) / sin (54)

x ≈ 15.7 units

The length of the side yz is equal to x = 15.7 units.

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Answer:

c or d

Step-by-step explanation:

Answer:

Graph A

Step-by-step explanation:

Answer:

p = - 2x + 54

Step-by-step explanation:

The price-demand linear equation is

p = mx + b

which is the equation of a straight line in slope-intercept form

The parameters here are m = slope and b = y-intercept in line equation terms

x is the number of shirts sold and p is the price

Using values given, we can generate two equations which can solve for the parameters of the linear equation

To sell 10 shirts, the price has to be $34
==> 34 = m x 10 + b = 10m + b

Switch sides to get 10m + b = 34     (1)

To sell 20 shirts, the price has to be $14
==> 14 = 20m + b  
Switch sides to get 20m + b = 14   (2)

Subtract (2) from (1) to eliminate the term b

(1) - (2)
==> 10m+b - (20m+b) = 34 - 14    

==> 10m + b - 20m - b = 20
==> 10m - 20m = 20
==> - 10m = 20

==> m = 20/(- 10) = - 2.4  

==> m = - 2.0
This term is also referred to as the elasticity of demand ie how much demand changes with respect to price change. It is negative here because as you increase the price, the demand decreases

Now that we have value for m all we have to do is plug it into one of the equations (1) or (2) and solve for b

Using equation (2),
20(- 2) + b = 14

==> - 40 + b = 14
==> 0 + b = 14 + 54(Add 48 on both sides)

==> b = 54

So the price-demand equation is
[tex]\boxed{\sf{p=-2x + 54}}[/tex]

9514 1404 393

Answer:

  115 square units

Step-by-step explanation:

The area of a parallelogram is the product of base length and height. The height is the perpendicular distance between the bases.

  A = bh

  A = (23)(5) = 115 . . . . square units

Answer:

a) x and y are not inversely proportional.

b) x and y are inversely proportional.

The value of k is: k=30

Step-by-step explanation:

We need to find if x and y are inversely proportional

If x and y are inversely proportional we will have: [tex]k=yx[/tex]

a)

x      y       k=yx

3      8        24

4      6         24

5      4.8      24

5.5    4        22

As for all values of y and x, k is not constant so, x and y are not inversely proportional.

b)

x        y            k=yx

0.1    300        30

0.5     60         30

75       0.4       30

100      0.3      30

As for all values of y and x, k is constant so, x and y are inversely proportional.

The value of k is: k=30

Step-by-step explanation:

a(n) = a +(n-1)d

a=13

d=9-13=5-9=-4

°.° a(n) = 13 +(n–1)-4

hope this helps

Answer:

65.03   65 3/100

Step-by-step explanation:

Sixty-five and three hundredths can be written as a decimal number as

65.03.

The place value of a number is given as:

Example:

1234.567

1 = thousand place value

2 = hundred place value

3 = tens place value

4 = ones place value

5 = tenths place value

6 = hundredths place value

7 = thousandths place value

We have,

Sixty-five and three hundredths

Sixty-five = 65

Three hundredths = 0.03

Now,

We can write as a decimal number as,

65.03

Thus,

The decimal number is 65.03

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Answer: y = -2x +17

Step-by-step explanation:

y = mx + b

You are trying to make the equation look like that

So you subtract the 2x to the other side

Hope this helps! :)

Answer:

y=-2x+17

Step-by-step explanation:

subtract 2x on both sides

Answer:

3.5f − 19

Explanation:

2.7f + 0.8f − 14 − 5

= 2.7f + 0.8f + −14 + −5

[ Combine Like Terms ]

= 2.7f + 0.8f + −14 + −5

= (2.7f + 0.8f) + (−14 + −5)

= 3.5f + −19

-PNW

Answer:

5.7%

Step-by-step explanation:

The formla for calculating compound interest is expressed as;

A = P(1+r)^t

A is the amount = $430

P is the principal = $220

r is the rate

t is the time = 12 years

Substitute and get r;

430 = 220(1+r)^12

430/220 =  (1+r)^12

1.955 = (1+r)^12

1.057 = 1+r

r = 1-1.057

r = 0.057

r = 5.7%

The interest rate is 5.7%

Answer:

-3x+6

Step-by-step explanation:

Answer:

im going for b

Step-by-step explanation:

Answer:

B is correct

Step-by-step explanation:

You can tell by the equation and the direction of the "<" sign that b is correct.

I've done lots of these problems before.

Answer: a.70% b.38% c.100% d.31% e.67%

Step-by-step explanation:

The relation between x and y is the same.

Answer:

i think it's 56.1% but the decimal may be wrong

The value of the equation A = 23/41 is 56.1 %

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 23/41   be equation (1)

On simplifying the equation , we get

A = 0.56097

Now , the value of A in percentage is

A = 56.097 %

Now , on simplifying the equation , we get

A = 56.1 %

Therefore , the value of A is 56.1 %

Hence , the equation is 56.1 %

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Answer:

D. y = 5/4x - 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y-intercept (0, -4)

Random Point (4, 1)

Step 2: Find slope m

Step 3: Write Equation

Substitute

y = 5/4x - 4

Answer: indirect characterization

Step-by-step explanation:

Indirect characterization is a method of indicating what a character is like by revealing their personality through descriptions of their actions, speech, appearance, and interactions with other characters.

Answer:

[tex]\frac{35}{18}[/tex] π m

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{50}{360}[/tex] ( r is the radius )

     = 2π × 7 × [tex]\frac{5}{36}[/tex]

     = [tex]\frac{70}{36}[/tex] π

     = [tex]\frac{35}{18}[/tex] π

Answer:

(4.25-1.75)/0.25=10

she bought 10 erasers

Answer:

10 Erasers

Step-by-step explanation:

We can establish the following equation:

TP = NP*PP + NE*EP

Where:

TP = Total price; (4.25)

NP = Number of pencil packages; (1)

PP = Pencil Package's Price; (1.75)

NE = Number of erasers; (What we are looking for)

EP = Erasers Price; (0.25);

Then:

4.25 = 1*1.75 + NE*0.25;

4.25 - 1.75 = NE*0.25;

2.5/0.25 = NE;

10 = NE.

Answer:

16x=60

X=15/4

Step-by-step explanation:

Answer:

134.38 dollars

Step-by-step explanation:

9514 1404 393

Answer:

  y = (x -1)² -16

Step-by-step explanation:

Note the location of the vertex (point A) on the graph. Its x-coordinate is readily identifiable as 1. Its y-coordinate is some value between -15 and -20, closer to -15. (If you go to the trouble of finding the vertex coordinates, you discover they are (1, -16).)

Once you have determined what the vertex is, you can compare the offered answer choices to the vertex form ...

  y = (x -h)² +k

where (h, k) are the vertex coordinates. That is, you are looking for an answer choice that is something like ...

  y = (x -1)² -16

Answer:

$230

Step-by-step explanation:

To find out how much he received for the bike ONLY, you have to multiply a number by 5 because it is 5 TIMES the accessories.

45x5=230<-- How much he got from the bike.

45<--How much he got from the accessories.

230+45=276<--How much he got from the bike AND accessories.

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Answer:

Valerie will need to buy a new bag of dog food after 6 feedings because she would have 0.25 of feedings left.

Step-by-step explanation:

Total number of ounces of dog food = 75 ounces

Ounces that is fed to the dog is = 12 Ounces in the morning and 12 ounces at night.

Hence:

12 ounces = 1 feeding

75 ounces = x

Cross Multiply

12x = 75

x = 75/12

x = 6.25 feedings

Valerie will need to buy a new bag of dog food after 6 feedings because she would have 0.25 of feedings left.

Answer:

Step-by-step explanation:

The distributive property affects both terms.

1/2 * 10x + 1/2 * 20 y

5x + 10 y <===== Answer

Answer:

5x+10y

Step-by-step explanation:

1/2•10= 5

1/2•20= 10

5x+10y