Determine the length of the missing side in the triangle shown.
right triangle with one leg labeled 13 and hypotenuse labeled 16

square root of 425
square root of 3
square root of 29
square root of 87

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{10}}} \implies \cfrac{ 5 }{ -2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{5}{2}}(x-\stackrel{x_1}{10}) \\\\\\ y-3=-\cfrac{5}{2}x+25\implies {\Large \begin{array}{llll} y=-\cfrac{5}{2}x+28 \end{array}}[/tex]

Answer:

[tex]{ \rm{ - \frac{2}{3}( - \frac{1}{5} ) }} \\ \\ = { \rm{( - 1 \times - 1)( \frac{2}{3} \times \frac{1}{5} )}} \\ \\ = { \rm{( \frac{2 \times 1}{3 \times 5} )}} \\ \\ = { \rm{ \frac{2}{15} }}[/tex]

Answer: [tex]\frac{2}{15}[/tex]

Step-by-step explanation:

1. Simplify the expression

[tex]-2/3(-1/5)[/tex]

2. Multiply the fractions

[tex]\frac{\left(-2\cdot -1\right)}{\left(3\cdot 5\right)}\\[/tex]

3. Simplify the arithmetic

[tex]\frac{2}{\left(3\cdot 5\right)}[/tex]

4. Simplify the arithmetic

[tex]\frac{2}{15}[/tex]

Answer:

firstly we need multiply out the bracket.

7×9=63

7×f= 7f.

then you subtract 63-7f= 56

your answer is 56

The lowest score that Keiko is trying to score to get in the "ryo" range is , the inequality to represent this story is (x+85+57+78)/4 > 70  .

In the question ,

it is given that

Keiko need to score average above 70 to get in the ryo range

let x be the marks that Keiko scores in the next test ,

so, the average = (x+85+57+78)/4

According to the question

Average > 70

Substituting the value of average , the inequality becomes

(x+85+57+78)/4 > 70

x+85+57+78 > 280

x+220 > 280

x > 280-220

x > 60

the lowest score that Keiko should get is greater than 60 .

When the inequality x > 60 , will be graphed then the limit will be an open circle as equal to sign is not included in the inequality .

as when the numbers increases , it move towards right side

So, When the inequality is graphed, the line will have an arrow pointing towards the right .

Therefore , the lowest score that Keiko is trying to score to get in the "ryo" range is , the inequality to represent this story is  greater than 60 ,

the inequality to represent this story is (x+85+57+78)/4 > 70 ,

the limit of graph will be open circle and arrow will be pointing towards right .

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Answer:

most have 455 T-shirts

Step-by-step explanation:

if u do $7,280÷$16= 455

Answer:most have 455 T-shirts

Step-by-step explanation:if u do $7,280÷$16=

Answer: 2

Step-by-step explanation:

The greatest divisor of 8 that is less than 18 is 16, and 16 divided by 8 is 2.

The next digit of quotient is 16.

Here given that,

4184 is divisible by 8

since we know that,

Division is a process of repeated subtraction. It is the inverse action of multiplication. It is characterised as the formation of equal groupings. When we divide numbers, we split them down into smaller amounts so that the multiplication of those smaller numbers equals the larger number taken.

4184 is divisible by 8 we get,

⇒ 4148/8

⇒ 516

So, the quotient is 516

Hence,

The next digit is 16.

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Answer:

$3.25

Step-by-step explanation:

This question tests on the concept of conversion.

Given from the question,

8.5 pounds = $27.63

(8.5 ÷ 8.5) pounds = $27.63 ÷ 8.5

1 pound = $3.25 (Rounded off to 2 decimal places)

The cost of a rugby ball is $6.57

The cost of a golf ball is $1.75

Let x represent the cost of a rugby ball and y represent the cost of a golf ball

2x + 3y= 18.39.........equation 1

5x + 7y= 45.10.........equation 2

multiply equation 1 by 5 and equation 2 by 2

10x + 15y= 91.95

-

10x + 14y= 90.2

y= 1.75

Substitute 1.75 for y in equation 2

5x + 7(1.75)= 45.10

5x + 12.25= 45.10

5x= 45.10-12.25

5x= 32.85

x= 32.85/5

x= 6.57

Hence the cost of a rugby ball is $6.57 and the cost of a golf ball is $1.75

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You can see the following steps to know the solvation

x² = 36

x = √36

x = 6.

The numerical value of side RS of the rectangle with a perimeter of 144 units is 30 units.

A rectangle is simply a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

The perimeter of a rectangle is expressed as;

P = 2( l + w )

Given the data in the question;

First we determine the value of the variable z, plug the given values into the perimeter formula and solve for z.

P = 2( l + w )

144 = 2( (4z + 2 ) + (3z) )

144 = 2( 4z + 2+ 3z )

144 = 2( 7z + 2 )

144 = 14z + 4

14z = 144 - 4

14z = 140

z = 140/14

z = 10

Now, find the numerical value of side RS.

Width RS = 3z

RS = 3( 10 )

RS = 30

Therefore, the length of side RS of the rectangle is 30 units.

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Answer:

80

Step-by-step explanation:

Use trial and error until you find a common multiple.

In the given parallelogram,

∠W = 85°

∠WXV = 59°

Since, VW is parallel to XY,

So,

∠YVX = ∠WXV ............... (Alternate interior angles)

⇒ ∠YVX = 59°

Now,

∠W = ∠Y .................. (Opposite angles of a parallelogram are equal)

⇒ ∠Y = 85°

As we know that opposite sides of a parallelogram are equal,

Therefore,

VW = YX

⇒ 2x = 6

⇒ x = 6/2 = 3 units

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If you plot the point,  - 8.85 on the number line you would put it left of -8.8

- 8.85 is left of -8.8

This is further explained below.

Generally, A image of a graded straight line is what is known as a number line, and its purpose is to provide a visual representation of the actual numbers. It is generally accepted that a real number may be assigned to each point on a number line, and that each point can be assigned to a real number.

In conclusion, The number line follows natural arithmetic rules, Hence

Since

-3,-2,-1,0,1,2,3 is the sequence of the  natural arithmetic rules hence,

- 8.85 is left of -8.8

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566567889988766433678

Answer: x=17

Step-by-step explanation:

1.Identify relationship

Since both the angles are on the inside of both parallel lines and on the same side of the transversal you know that you have a same side interior relationship that makes them supplementary

2. set up equation

because they are supplementary you know that they are equal to 180 which gives the equation: 3x+6+123=180

3. solve the equation

3x+6+123=180

3x+129=180 | combine like terms

3x=51 | subtract 123 from both sides

x=17 | divide by 3 on both sides

Answer:

x = 7 units

Step-by-step explanation:

Left area = (3x-1)(4)

Right area = 8*12  - (4 (  x -3))     and the areas are =

(3x-1)4 = 8*12 - ( 4(x-3))    expand both sides

12x - 4  = 96 - 4x + 12       solve for x = 7 units

Answer:

Area of big rectangle: 8 x 12 =96

Area of white part : 4(x-3)

96-(4(x-3))

96-(4x-12)

96-4x+12

Area of rectangular grey part: 108-4x

Area of other grey figure:

4(3x-1)

= 12x- 4

Finding x:

12x-4 = 108 -4x

-4-108 = -4x - 12x

112 = 16x

x= 7

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In linear equation, Number of members in liberal party = 32 * 77 = 2464

What does the term "linear equation" mean?

A mathematical function where the variables only occur in the first degree, where the constants are multiplied, and where the only possible combinations are addition and subtraction.

45% Of liberals switch to the conservative party

total number of eligible votes in the country =7700

Number of members change to liberal to conservative  = 45% of 7700

                                                         = 45/100 * 7700

                                                          = 45 * 77 = 3465

32% of conservative  switch to the liberals party  = 32 % of 7700

                                                      = 32/100 * 7700

Number of members in liberal party = 32 * 77 = 2464

An equilibrium in campain contributions one for the each party among the set of contribution to the party.

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The complete question is -

in a certain county there are two political parties, liberal and conservative. it has been observed that between elections a fixed percentage, 45% of liberals switch to the conservative party and a fixed percentage, 32% of conservatives switch to the liberal party. the other voters remain in the same party. assume that there are altogether 7700 eligible voters in the county. Find the equilibrium Values for the system if any?

The current temperature based on the information given about Sussane is 74°.

It should be noted that temperature is used to illustrate the hotness and the coldness that's in a a particular body.

Let the current temperature be represented as x.

Since Susanne checks the temp. at 11:00am and she notices that if the temp. rises by 8 more degrees it will break the record high temp. for the day witch is 82 degrees, the current temperature will be:

x + 8 = 82

x = 82 - 8

x = 74°

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The probability that the three tax returns submitted were self-prepared is 0.0325.

So, the formula for the binomial probability distribution of x successes in n tries:

Where the probability of success is p, and n is the number of trials.

If three electronically filed tax returns are randomly chosen, the likelihood that all three were prepared by the taxpayer is given by:

Therefore, the probability that the three tax returns submitted were self-prepared is 0.0325.

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The correct question is given below:

Suppose that a poll finds that 31.9​% of taxpayers who filed their tax returns electronically​ self-prepared their taxes. If three tax returns submitted electronically are randomly​ selected, what is the probability that all three were​ self-prepared?

Answer:

Step 3, she forgot to square half of the middle term before adding it to both

sides.

Step-by-step explanation:

yw

The domain of the given function is (-∞,5) and the range is (5,∞).

All the independent variable, x, for which y is defined, is the domain and range of a function. Every possible value of the dependent variable y comes within a function's range.

From the graph, we can see that x varies from -∞ to -5

So, the domain is the interval of (-∞,-5)

The function of f(x) varies from (5,∞)

So, the range is (5,∞).

Therefore, the domain of the given function is (-∞,-5) and the range is (5,∞).

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Answer:

2533 km/hr

Step-by-step explanation:

time = 8 hours 30 minutes

        [tex]\sf = 8\dfrac{1}{2} \ hours\\\\ =\dfrac{17}{2} \ hours[/tex]

Distance = 298 km

[tex]\sf \boxed{\bf Average \ speed = Distance * time}[/tex]

                             [tex]\sf = 298 * \dfrac{17}{2}\\\\ = 149 * 17\\\\= 2533 \ km / hr[/tex]

Total 20 students should go to the trip to not to lose money.

Cost of bus = 100 dollars

For students the charge is 7 dollars per student.

Amount professor donated to defray the cost is 40 dollars.

School is charging 10 dollars per student for the trip.

Therefore, reduced cost = 100 - 40 = 60 dollars

Profit earned from each student is 10 - 7 = 3  dollars.

Hence, minimum students should go to the trip will be 60 ÷ 3 = 20.

Since, 20 × 3 = 60, the cost is covered and no money is lost.

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The number of tapes cut is 3 pieces.

He has a roll of tape that is 4 1/2 yard long.

He cuts the tape into pieces that are each 3/2 yard long.

Therefore, the number of roll of tape cut can be calculated as follows:

Initial length of the tape in yard = 4 1 / 2 = 9 / 2 yards

Length of the tape cut in yard = 3  /2 yards

Hence,

number of tape cut = 9 / 2 ÷ 3 / 2

number of tape cut =  9 / 2 × 2 / 3

number of tape cut = 9 / 3

number of tape cut =  3 pieces

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The answer to the following verbal expressions of inequality are:

A: x ≤ 69;

B: The option that shows the graph of the inequality d<2 is Option C.

C: The option that shows the graph of the inequality of x ≤ 5 is option B.

D: represents the graph of the inequality given in option C that is x > -8

E: The inequality that describes the situation is ≥ 49 (Option B)

In mathematics, inequality is defined as a declaration of an order connection between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).

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Yes the acceptable move that proves the two equation are equivalent.

What is equivalent equation?

equivalent equation are algebraic equations that have identical solutions or roots. Adding or substracting the same number or expression to both side of an equation produce an equivalent equation. Systems of equations that have the same solutions are said to be equivalent equations. Finding and resolving equivalent equations is an important skill for everyday life as well as for algebra classes. Consider some illustrations of equivalent equations, how to solve them for one or more variables, and practical applications of this knowledge.

Sol-

By observing both equations

In equation A : -3(x+9)=18

Divide the equation A by -3

=> (x+9)=-6

And this result equals to equation B

Hence both equations are equivalent

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By using the method of subtraction, the profit earned by charles is £4.8

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given that,

There are 15 pens in each pack.

Each pack costs £4.20.

Charles sells each pen for 60p but he only manages to sell of the pens.

60p x 15 = 9

So, the profit earned by charles is 9- 4.20 = 4.8

Therefore, the profit earned by charles is £4.8

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Answer:

the answer is A

Step-by-step explanation: the reason i said A is because the answer is litteraly in the question if you think about it

Answer: C.

Step-by-step explanation:

X would represent the number of golf balls he brought back and .10 is the amount of money he makes for each of them.

Answer:

0.10x

Step-by-step explanation:

x stands for the amount of golf balls he brings back to the shop and 0.10 stands for the 10 cents he gets paid for each ball.