A straight line has a gradient of 4 and passes through the point (2,9).
Work out the equation of the line.
Give your answer in the form y = mx + c, where m and c are integers or
fractions in their simplest forms.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) ~\hfill AB=\sqrt{(~~ 7- (-9)~~)^2 + (~~ 4- 4~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 16)^2 + ( 0)^2}\implies \boxed{AB=16} \\\\\\ B(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{7}~,~\stackrel{y_2}{-8}) ~\hfill BC=\sqrt{(~~ 7- 7~~)^2 + (~~ -8- 4~~)^2}[/tex]

[tex]~\hfill BC=\sqrt{( 0)^2 + ( -12)^2}\implies \boxed{BC=12} \\\\\\ C(\stackrel{x_1}{7}~,~\stackrel{y_1}{-8})\qquad A(\stackrel{x_2}{-9}~,~\stackrel{y_2}{4}) ~\hfill CA=\sqrt{(~~ -9- 7~~)^2 + (~~ 4- (-8)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -16)^2 + (12)^2}\implies CA=\sqrt{400}\implies \boxed{CA=20} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Perimeter}{16~~ + ~~12~~ + ~~20\implies \text{\LARGE 48}}[/tex]

The triangle formed by the feet of angle bisectors of a triangle with a single angle measure of 120° is the Right Triangle.

So,

In triangle ABC, ∠A = 120°.

As a result, DE is the exterior angle bisector of ABCD.

Similarly, for the ABC, F is ex-center because AB is the exterior angle bisector and CF is the interior angle bisector.

As a result, DF is the exterior angle bisector.

BC is a straight line.

So, DEF is the right triangle.

As a result, the triangle formed by the feet of angle bisectors of a triangle with a single angle measure of 120° is the Right Triangle.

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The correct form of the question is given below:
Prove in any ΔABC, if one angle is 120°, the Δ formed by the feet of the angle bisectors is right-angled.

The expression for m from the given equation is m = E/o^2

The subject of formula is a way of representing a variable with another variable

Given the equation

E = mo^2

We are to make m the subject of the formula. To do that, we will divide both sides of the equation by o^2 to have:

E/o^2 = mo^2/o^2

E/o^2 = m

Swap

m = E/o^2

Hence the expression for m from the given equation is m = E/o^2

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By unitary method we can say that number of stacks of papers Lashona will pass back  from 140 if each stack conatins 28 papers is 5.

According to the given question.

Total number of papers Lashonna passed back = 140

And one stack is made up of 28 papers.

As we know that, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Therefore,

By unitary method number of stacks of papers would be made from 140 if each stack conatins 28 papers

= 140/28

= 5

Hence, by unitary method we can say that number of stacks of papers Lashona will pass back  from 140 if each stack conatins 28 papers is 5.

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Answer:

F(x) = -6x - 3

F(x) = -6(-8) - 3

F(x) = 48 - 3

F(x) = 45

7.86 liters  of purple paint in each container.

volume of red paint is 8.54 liters.

volume of blue paint is 8.31 liters.

Number of container taken is 2 container.

Paint left after equally poured in 2 container.

and we have to find how many liters of paint are in each container.

Volume of RED Paint + Volume of BLUE Paint =  Volume of PURPLE Paint

8.54 liters + 8.31 liters = 16.85 liters.

(16.85/2) - (1.13/2) = 15.72/2

                            =7.86 liters

7.86 liters of purple paint in each container.

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Answer:

1.6

Step-by-step explanation:

| -1.6 | = 1.6

Answer:

ssdf

Step-by-step explanation:

dbd beddbees sveveusbs wie eje edidjebebe djebejdjebe ejd s

Answer:

x can be -3, or +3

Step-by-step explanation:

The equation would be

5[tex]x^{2}[/tex] = 45

Divide both sides by 5

[tex]x^{2}[/tex] = 9

Take the square root of both sides

x = ± 3

The value of the constant of variation is 130

Constant of variation can be defined as the ratio between two variables in  an inverse variation on a direct variation.

From the information given, we have that;

The number of hours is x

The temperature is y

x α 1/ y

x = k/y

k = xy

Substitute the values

k = 2 × 65

k= 130

Thus, the value of the constant of variation is 130

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The complete question:

the number of hours it takes for a block of ice to melt varies inversely as the temperature. If it takes 2 hours for a square inch of ice to melt at 65 degrees find the constant of variation

Answer:

-1 yard per play

play 6 - play 3=0

play 2 - play 4=0

play 1 - play 5 = -6

hope it helped

Answer: x= 33

Step-by-step explanation: hope this helps!!!

Answer:

AP = 29,37,45,...

d= t2-t1

=37-29

=8

n=59

t59=?

tn=a+(n-1)d

t59=29+(59-1)8

t59=28+58×8

t59=28 + 464

t59=492

Step-by-step explanation:

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The two numbers by setting up a linear equation are 56 and 32

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

Let the two numbers be x and y

Where

y = 4 + 1/2x

So, we have

x + y = 88

Substitute y = 4 + 1/2x in x + y = 88

x + 4 + 1/2x = 88

Evaluate

1.5x = 84

Divide by 1.5

x = 56

Substitute x = 56 in y = 4 + 1/2x

y = 4 + 1/2 * 56

Evaluate

y = 32

Hence, the two numbers by setting up a linear equation are 56 and 32

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Answer:

It's rational, because it can be converted into a reasonable fraction.

➯ Hope this helps!

The probability that:

Probability refers to the possibility of the occurrence of an event.

P(E) = probability of occurrence of an event E = [tex]\frac{Number Of Favourable Outcomes}{Total Number Of Outcomes}[/tex]

Now,

(a) Total number of books = 5 + 3 + 1 = 9

Probability of getting a dictionary = [tex]\frac{1}{9}[/tex]

(b) Number of ways to select 3 books out of 9 books = [tex]\binom{9}{3}[/tex] =  [tex]\frac{9!}{3!(6!)} = \frac{9\times\ 8 \times 7}{6}[/tex] = 84

Number of ways to select 1 out of 3 books of poems = [tex]\binom{3}{1} = \frac{3!}{2!}[/tex] = 3

Number of ways to select 2 out of 5 novels = [tex]\binom{5}{2} = \frac{5!}{2! 3!} = \frac{5\times 4}{2} = 10[/tex]

Thus, the probability of getting 2 novels and 1 book of poem = [tex]\frac{3\times10}{84} = \frac{10}{28} = \frac{5}{14}[/tex]

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(COMPLETE QUESTION:

If three books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that (a) a dictionary is selected? (b) 2 novels and 1 book of poems are selected?)

a)

Solution,

Given,

Cost for 1 pen = $ 1.50

= 1.50×100 cents

= 150 cents

Cost for 1 ruler = 80 cents

No. of Pens needed to be bought = x

No. of rulers needed to be bought = x+10

Now,

Cost for x pens = x×150 cents

= 150x cents

Cost for (x+10) rulers = (x+10)×80 cents

= 80x cents+800 cents

Then,

Total cost = 150x cents+(80x cents+800 cents)

= 150x cents+80x cents+800 cents

= 230x cents+800 cents

= $(230x ÷ 100)+$(800 ÷ 100)

= $2.3x + $8

Therefore,Louise spent $2.3x and $8 as total amount

b)

Sorry,I dont know inequality

The expression that gives the distance, d, between the ships after t hours is d = 25t

From the question, we are to write an expression that gives the distance, d, between the ships after t hours

First, we will determine the distance the ships have traveled after t hours

Using the formula,

Distance = Speed × Time

Thus,

The first ship would have traveled

20 × t miles

= 20t miles

The second ship would have traveled

15 × t miles

= 15t miles

Using the Pythagorean theorem,

The distance, d, between the ships after t hours is

d² = (20t)² + (15t)²

d² = 400t² + 225t²

d² = 625t²

d = √(625t²)

d = 25t miles

Hence, the expression that gives the distance, d, between the ships after t hours is d = 25t

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Answer: BABABAB

Step-by-step explanation:

BHBAHBABAHBABHABHBAHBABHABHBAbhaBHBA

The value of the numbers given will be:

1. 108

2. 1618

1. The expression given will be calculated as:

= 97.83 - 4.378 + 5.92

= 98 + 4 + 6

= 108

2. 1,342.8+ 85.32 + 173.54 + 16

= 1343 + 85 + 174 + 16

= 1618

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[tex]Answer:\ -55.102^0F\leq t^0\leq 595.958^0F[/tex]

Step-by-step explanation:

[tex]\displaystyle\\C^0=\frac{5}{9} (F^0-32^0)\\[/tex]

Let's multiply both parts of the equation by 9/5:

[tex]\displaystyle\\\frac{9}{5} C^0=F^0-32^0\\\\\frac{9}{5} C^0+32^0=F^0-32^0+32^0\\\\\frac{9}{5} C^0+32^0=F^0\\\\Thus,\\\\F^0=1.8C^0+32^0[/tex]

[tex]t=-48.39^0C\\Hence,\\t^0(F)=1.8(-48.39^0)+32^0\\t^0(F)=-87.102^0+32^0\\t^0(F)=-55.102^0[/tex]

[tex]t=313,31^0C\\Hence,\\t^0(F)=1.8(313,31^0)+32^0\\t^0(F)=563.958^0+32^0\\t^0(F)=595.958^0[/tex]

[tex]Thus,\\-55.102^0F\leq t^0\leq 595.958^0F[/tex]

1/3 is the probability of rolling either a 5 or a 6 using a normal six-sided die.

Probability can be defined as the ratio between the number of favorable outcomes and the total number of outcomes of an event.

Given:

Six-sided dice rolled once

Let n be the number of outcomes

let x be the number of favorable outcomes

We know that,

[tex]Probability=\frac{x}{n}[/tex]

When the six-sided dice roll, The possible outcomes are,

[tex]\{1,\;2,\;3,\;4,\;5,\;6\}[/tex]

Therefore,

[tex]Number\;of\;outcomes,\;n=6[/tex]

[tex]Probability\;rolling\;5\;is\;\frac{1}{6}[/tex]

[tex]Probability\;rolling\;6\;is\;\frac{1}{6}[/tex]

Therefore, Probability of rolling either 5 or 6 is,

[tex]P(5\;or\;6)=\frac{1}{6} +\frac{1}{6}[/tex]

[tex]P(5\;or\;6)=\frac{2}{6}[/tex]

[tex]P(5\;or\;6)=\frac{1}{3}[/tex]

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The Associative property is not  displayed by any of the given equations.

The associative property of several binary operations in mathematics states that the outcome will not change if the parenthesis in an expression are rearranged.

The order in which the operations are carried out within an expression that has two or more instances of the same associative operator in a row doesn't matter as long as the order of the operands is left untouched.

Examples of associative property :

[tex]{\displaystyle {\begin{aligned}(7+8)+1&=7+(8+1)=9\,\\5\times (3\times 7)&=(5\times 3)\times 7=24.\end{aligned}}}[/tex]

The parentheses were rearranged on each line, but the expression values were left alone. It can be argued that "addition and multiplication of real numbers are associative operations" because this is true for addition and multiplication of all real numbers.

Here 8=8+0 displays additive identity property.

10×1=10 displays multiplicative identity

5+0=5 displays displays additive identity property.

[tex]5\times \frac{1}{5}=1[/tex]  displays multiplicative inverse property.

[tex]3+\frac{3}{4} =3+\frac{3}{4}[/tex]  displays reflexive property.

Hence no equation displays associative property.

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Answer:

Step-by-step explanation:

20 divided by 5x20+10=90

Answer:

90

Step-by-step explanation:

this is easiest if you know your order of operations PEMDAS so there are no parenthesis or exponents so next is multiplication and division. so 20/5= 4 then 4*20 is 80 and 80+10=90.

here's an easy way to remember PEMDAS

Please Excuse My Dear Aunt Sally

Answer:

122 degrees

Step-by-step explanation:

43 + 15 = 58 - 180 = 122

Answer:

64,100

Step-by-step explanation:

64,100are the values that are perfect square

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Answer:

Step-by-step explanation:

jeans           $42.95

sweater    + $36.99

total          = $69.94

tax             + 5% ($3.497 round to nearest hundredth ($3.50))

total with tax = 73.44

hope this helped!!!! let me know if you need anymore help with this :) have a good day!

Harry's speed on the freeway is 67 miles per hour

Time Harry drove on freeway = 3 hours

Time Harry drove on country road = 6 hours

Total distance covered by him = 483 miles

Let his speed be x miles per hour

Formula to be used:

Speed*Time = Distance

Therefore, the distance covered by him on the freeway  = 3x -----(1)

Distance covered by him on country road = 6(x - 20)------(2)

Formulating the equations using (1) and (2)

3x + 6(x-20) = 483

3x + 6x - 120 = 483

9x = 603

x = 67 miles per hour

So, his speed on the freeway is 67 miles per hour and on the country road it is 47 miles per hour

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The tax on the product will be $1.964.

It should be noted that from the information, the sales tax is 6% and the price of the product is $32.74.

Therefore, the value of the tax will be:.

Tax percentage × Price

= 6% × $32.74

= 0.06 × $32.74

= $1.9643

Therefore, the tax on the product will be $1.964.

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