Graph the line with slope -2 passing through the point (3, -5).

The shortest distance between Caroline's and Mattie's houses is 10 block.

Let Caroline started from point A and goes towards north 6 blocks to O. and goes to B 8 blocks in east.

AO = 6

BO = 8

Formula for the Shortest distance can be solve by pythagoras theorem:

[tex]AB^{2} = AO^{2} +OB^{2}[/tex]

[tex]AB^{2} = 6^{2} +8^{2}[/tex]

[tex]AB^{2} = 36+64[/tex]

[tex]AB^{2} = 100[/tex]

[tex]AB = \sqrt{100}[/tex] can

[tex]AB = 10[/tex].

The shortest distance AB = 10 block.

#1234

10 blocks are the shortest distance between Caroline and Mattie's homes.

Given data,

Caroline steps outside and makes a 6 block trek to the north. To go to Mattie's house, she does a turn and travels 8 blocks to the east.

To get the shortest distance between Caroline and Mattie's houses we need to it as a triangle and apply the Pythagorean theorem.

Pythagorean theorem:

The well-known geometric axiom is that the hypotenuse (the side across from the right angle) of a right triangle is equal to the sum of the squares on its legs. Or, in popular algebraic form, a² + b² = c².

The shortest distance (c);

Let, a = 6

      b = 8

⇒ a² + b² = c²

   6² + 8² = c²

   36 + 64 = c²

   c = [tex]\sqrt{100}[/tex]

   c = 10

Therefore, the shortest distance between Caroline’s and Mattie’s houses is 10 blocks.

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The trigonometric expression [tex]\left(\dfrac{tan( x)}{1+sec( x)} +\dfrac{1+sec( x)}{tan( x)}\right)[/tex] can be simplified to prove that it equals 2·csc(x), by plugging in [tex]\left(tan(x) = \dfrac{sin(x)}{cos(x)}\right)[/tex],

[tex]\left(sec(x) = \dfrac{1}{cos(x)}\right)[/tex]  and [tex]\left(csc(x) = \dfrac{1}{sin(x)}\right)[/tex] to give the following

trigonometric identity;

Trigonometric identities are equations of trig functions which are valid for all values of the input variable at which the expressions on both sides of the equality are defined.

The trigonometric expression in the question is simplified as follows;

[tex]\dfrac{tan( x)}{1+sec( x)} +\dfrac{1+sec( x)}{tan( x)} = \dfrac{tan( x)}{1+\dfrac{1}{cos(x)} } +\dfrac{1+\dfrac{1}{cos(x)}}{tan( x)}[/tex]

[tex]\dfrac{tan( x)}{1+\dfrac{1}{cos(x)} } +\dfrac{1+\dfrac{1}{cos(x)}}{tan( x)} = \dfrac{cos(x)\times tan( x)}{cos(x)+1} } +\dfrac{cos(x)+1}{cos(x)\times tan( x)}}[/tex]

[tex]\dfrac{cos(x)\times tan( x)}{cos(x)+1} } +\dfrac{cos(x)+1}{cos(x)\times tan( x)}} = \dfrac{sin(x)}{cos(x)+1} } +\dfrac{cos(x)+1}{sin( x)}}[/tex]

[tex]\dfrac{sin(x)}{cos(x)+1} } +\dfrac{cos(x)+1}{sin( x)}} = \dfrac{sin^2(x)+(cos(x)+1)^2}{sin( x)\cdot (cos(x)+1)} }[/tex]

[tex]\dfrac{sin^2(x)+(cos(x)+1)^2}{sin( x)\cdot (cos(x)+1)} }=\dfrac{sin^2(x)+cos^2(x)+2\cdot cos(x)+1}{sin( x)\cdot (cos(x)+1)}[/tex]

[tex]\dfrac{2\cdot cos(x)+2}{sin( x)\cdot (cos(x)+1)} =\dfrac{2\cdot (cos(x)+1)}{sin( x)\cdot (cos(x)+1)} = \dfrac{2}{sin( x)}[/tex]

[tex]\dfrac{2}{sin( x)} = 2\cdot csc(x)[/tex]

[tex]\therefore \dfrac{tan( x)}{1+sec( x)} +\dfrac{1+sec( x)}{tan( x)} =2\cdot csc(x)[/tex]

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Answer:

You need 8 picnic tables.

Step-by-step explanation:

You need 8 picnic tables because there are 30 friends and 4 sits at each table, and 4 x 8 is 32. There is 2 more extra seats. But it does fit all 30 friends.

Answer:y

=5/4x+-3

Step-by-step explanation:

first you find the slope which is 5/4 then you do y=mx+b but replace the y and the x with points on the line giving you 2=5/4•4+b then you solve for b and get -3 giving you your answer.

Answer: -5/4x+7

Step-by-step explanation:

1)First find the slope passing through (8,-3) (4,2) using this formula

y2-y1/x2-x1 (this: 2--3/4-2) to get -1.25 or -5/4. this is your slope.

2) Then to get the y-intercept choose one of your points (doesn't matter which I chose (8,3) but you can choose any of the two) and create this formula y=mx+b.

3) Input your x and y from the point you chose and your slope (m) to create this -3=(8)+b.

4) Now solve for b. This should get you Postitve 7 (REMEMBER it is VERY IMPORTANT if you result is negative or positive. One mess up could make the whole thing wrong.)

5) Finally take your slope and y-intercept and put it together to get:

y=-5/4x+7

Follow those steps every time you get a problem like this and it should help :)

A. The bacteria sample that had a smaller initial population is;

Sample A; 100 bacteria.

B. The sample that was larger in the 5th week was;

Sample A; by 8,300.

An exponential function is defined by the general expression;

y = abˣ

where;

a is initial value.

b is rate of change.

For Sample A, the values of the above parameters are given as;

a = 100

b = 3

Thus, the exponential function is:

f(x) = 100(3)ˣ

In the 5th week, the population will be calculated as;

f(5) = 100 * 3⁵

f(5) = 24300.

For Sample B, the exponential function is expressed as:

g(x) = 500(2)ˣ

In the 5th week, the population will be;

g(5) = 500 * 2⁵

g(5) = 16000.

The difference of the larger population in Sample A and the smaller population in Sample B is;

24300 - 16000 = 8300.

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If 1200 square centimeters of material is available to make a box with a square base and an open top,

The largest possible volume of the box is V = 4000cm^3.

We have 1200 cm^2 worth of material. This represents the surface area of a box with a square base and an open top.

the dimensions of the box.

Square base implies the length and width are the same.

Let x = length/width.

The box has a height as well.

Let h = height

the surface area ; S.

S = (area of base) + (area of 4 walls)

The area of the base is x^2

The area of one of the walls is length times height, or xh. Since there are 4 of them, it would be 4 times xh, or 4xh.

S = x^2 + 4xh

And we know that S = 1200cm^2, so

x^2 + 4xh = 1200

Let's solve for h.

4xh = 1200 - x^2

h = (1200 - x^2) / (4x)

we require the volume formula.

V = (length) x (width) x (height)

And we know all of these.

V = (x)(x)(h)

V = (x^2) h

putting h = (1200 - x^2) / (4x) in the formula

V = (x^2) ( 1200 - x^2)/(4x)

We get a cancellation,

V = x(1200 - x^2)/4

V = (1/4)x (1200 - x^2)

This will be our volume function, V(x).

V(x) = (1/4)(x)(1200 - x^2)

To maximize V(x), we must first take the derivative and then make it 0. Using the product rule (and ignoring the constant 1/4), we have

V'(x) = (1/4) [ (1200 - x^2) + (x)(-2x) ]

Simplify,

V'(x) = (1/4) [ 1200 - x^2 - 2x^2 ]

V'(x) = (1/4) [ 1200 - 3x^2 ]

V'(x) = (1/4) [ 3(400 - x^2) ]

V'(x) = (3/4) [ 400 - x^2 ]

To maximize, make V'(x) = 0, and solve for x.

0 = (3/4) [ 400 - x^2 ]

0 = 400 - x^2

x^2 = 400

x = +/- 20

Therefore,

x = { 20, -20 }

However, since x represents a dimension, it can never be negative, and we must discard the negative solution. That means

x = 20.

This tells us that the maximum volume occurs when x = 20. However, the question is asking WHAT the largest volume of the box is. Solving this is as simple as plugging x = 20 into our volume function, V(x).

V(x) = (1/4)(x)(1200 - x^2)

Therefore,

V(20) = (1/4) (20) (1200 - 20^2)

V(20) = (1/4) (20) (1200 - 400)

V(20) = (1/4) (20) (800)

V(20) = (20/4)(800)

V(20) = 5(800)

V = 4000cm^3

Hence the answer is, the largest possible volume of the box is V = 4000cm^3.

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The cost ruler is £ 1.5 and the cost of rubber is £ 1.0.

Cost of 01 ruler be x pound.

Cost of 01 rubber be y pound.

according to question,

[tex]5x + 3y = 5.5[/tex]         ------------------------------------ (1)

[tex]3x + 2y = 3.5[/tex]         ------------------------------------(2)

multiplying equation (2) by 2 and equation (1)

[tex]10x + 6y = 11[/tex]       -------------------------------------(3)

[tex]9x + 6y = 10.5[/tex]      -------------------------------------(4)

subtracting equation (4) by (3), we get

[tex]x = 0.5[/tex]

putting the value of [tex]x = 0.5[/tex] in equation (2),

3×0.5 + 2y = 3.5

⇒1.5 +2y = 3.5

⇒2y= 2.0

⇒y = 1

∴ the cost of ruler is £ 0.5 and the cost of £1.0

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Answer:

The original equation

Distributive property

subtract 5x from both sides

add 12 to both sides

divide both sides by -14

Answer: 4

Step-by-step explanation: x is multiplied by 4

Answer:

31542

Answer:

8

Step-by-step explanation:

you divide so you can get the average

Answer:

in average she makes 8 friend in a week.

Step-by-step explanation:

You divide 80 by 9 that is 8 remaining 1, so yeah.

By using the properties of parallel lines, the result obtained is-

The correct options are first, second and fourth

What are parallel lines?

Two lines are said to be parallel if on extending them indefinitely, they will never intersect

Here,

From the figure,

For the first option,
m∠1=m∠5 [Corrosponding angles are equal]

First option is correct

For the second option,
m∠7=m∠11 [Corrosponding angles are equal]

Second option is correct

For the third option,
m∠5 ≠ m∠12 [ c is not parallel to b]

Third option is wrong

For the fourth option,
m∠4 = m∠5 [Alternate interior angle are equal]

Fourth option is correct

So the correct option are first, second and fourth

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Complete Question

The diagram has been attached

Answer: The answer is below

Step-by-step explanation:

a₁₁=1 of the given matrix.

Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array.

Given Matrix is [tex]\left[\begin{array}{cccc}1&3&8&5\\5&4&6&2\\6&7&1&8\\2&9&3&7\end{array}\right][/tex]

The matrix will be in the form[tex]\left[\begin{array}{cccc}a_{11} &a_{12} &a_{13} &a_{14} \\a_{21} &a_{22} &a_{23} &a_{24} \\a_{31} &a_{32} &a_{33} &a_{34} \\a_{41} &a_{42} &a_{43} &a_{44} \end{array}\right][/tex]

The given matrix is a 4 cross 4 matrix, which has 4 rows and 4 columns.

a₁₁ means it is the first element of first row and first element of first column.

By comparing the given matrix with standard form a₁₁=1

Hence, a₁₁=1 of the given matrix.

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The height of a can of fruit juice used as a prop, if it's actual height is 7 inches, should be of:

3.85 inches.

A proportional relationship is a linear function that has intercept of zero and hence it has the output variable y as the multiplication of the input variable x and the constant of proportionality k, as follows:

y = kx.

The input and the output variables in this problem are given as follows:

From the table given at the end of the answer, the constant is given as follows:

k = 44/80

k = 0.55.

Hence the equation is:

y = 0.55x.

Then the height on the set when the actual height is of 7 inches is given by:

y = 0.55(7) = 3.85 inches.

The table is given by the image at the end of the answer.

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After simplifying the percentage, if 120% of a is equal to 80% of b, then a+b is 5.

In the given equation,

If 120% of a is equal to 80% of b, then we have to find the value of a+b.

We firstly express the statement in the algebraic equation.

It is given in the statement that 120% of a.

We write it as 120%×a.

From the statement, 80% of b.

We write its as 80%×b.

Both are equal to each other.

So the expression should be

120%×a=80%×b

Divide by 12% on both side

120%/120% ×a=80%/120% ×b

Simplifying

a=80%/120% ×b

As we know that % means 100 but both number 80 and 120 have % sign. So the % sign emitted.

So a=80/120 ×b

Divide by b on both side

a/b=80/120 ×b/b

a/b=80/120

Simplifying the ration

a/b=2/3

Hence, the value of a=2 and b=3.

Now finding the value of a+b.

a+b = 2+3

a+b = 5

Hence, if 120% of a is equal to 80% of b, then a+b is 5.

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Answer: 90

Step-by-step explanation:

VolBigCube = 1.5x1.25x0.75 = 1.40625 in^3

VolSmallCube = 0.25x0.25x0.25 = 0.015625 in^3

VolBigCube/VolSmallCube = 1.40625/0.015625 = 90

There are 2520 ways to seat 8 people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors.

There are a total of seven different ways for eight individuals to sit around a circular table: (8-1)!=7!. We are using the concept of circular permutation.

By using circular permutation we have,

7!=5040

All of the seating is included in these 5040 ways. Given that everyone has the same two neighbors, regardless of whether they are left or right neighbors, two seating are said to be equal. To achieve the desired outcomes, we must divide the total number of methods by 2.

5040/2

=2520 ways

Therefore, there are 2520 ways to seat 8 people around circular table where two seating are considered the same.

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Answer:

Step-by-step explanation:

6,000 = 6 × 1000 = 6 × 10³

Answer: B)

Could you please merk me as "Brainliest"

The inference rule is ({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q}).

In the given question, we have to define the semantics (inference rule) of the if statement: {P} if (E) S1 else S2 {Q}.

A way of inferring the veracity of one assertion based on the significance of other assertions is known as an inference rule.

(S1, S2, ........, Sn)/S

According to the rule, if S1, S2,..., and Sn are real, then S's validity can be derived.

Given,

{P} if (E) S1 else S2 {Q}

The inference rule is

We know that if if E and P are true then it is S1 with postcondition {Q} or if E and P is false then it is else part that is S2 with postcondition {Q}

i.e. {E and P} S1 {Q},{not E and P} S2 {Q}

So the inference rule is:

({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q})

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Answer:

a =-13/24 b = 5/3

Step-by-step explanation:

From given

8a + 5b = 4 (1)

3b = 5 (2)

Using (2)

b = 5/3

Putting the value of b into (1) gives

8a + 5(5/3) =4

8a + 25/3 = 4

8a = 4 - 25/3

8a = -13/3

a = -13/(3*8)

a = -13/24

The function f(x)  = [tex]-x^2 + 3x +11[/tex] of the value is 7.

Given,

In the question:

The function is given as:

f(x) = [tex]-x^2 + 3x +11[/tex]

To find the f(-1)

Now, According to the question:

The function is :

f(x) = [tex]-x^2 + 3x +11[/tex]

To put the value of x = -1 in above function's equation:

f(x) = [tex]-x^2 + 3x +11[/tex]

f(-1) = [tex]- (-1)^2 + 3(-1) +11[/tex]

Solve the equation:

Determine the sign:

f(-1) = -1 -3 +11

Calculate the sum or difference:

f(-1) =7

Hence, The function f(x)  = [tex]-x^2 + 3x +11[/tex] of the value is 7.

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The value of x that makes m ║n is 60 degree.

What is consecutive interior angles?

Pairs of angles that are between two lines and on the same side of the line that cuts through the lines are referred to as consecutive internal angles.

The "consecutive interior angle theorem" asserts that each pair of consecutive interior angles is supplementary, meaning that the sum of the consecutive interior angles equals 180°, if a transversal intersects two parallel lines.

Here to make m ║n  the angles x and 2x are consecutive interior angles.

Since consecutive interior angles are supplementary.

So,

x + 2x = 180

3x = 180

x = 180/3

x = 60 degree.

Therefore, the value of x is 60 degree that makes m ║n.

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Answer:

Artur has 2 dogs

Step-by-step explanation:

we know he feeds the one fifth per dog so two fifth will be 2 dogs

Answer Two dogs,

Step-by-step explanation:

1/5 + 1/5 = 2/5 I mean cmon now that's easy

The  probability of getting face card in all 4 attempts is 0.0018 approximately.

What are face cards?

Any of the twelve cards in a deck with an image of a face on it is referred to as a face card. King, Queen, and Jack are the face cards in this deck.

Main Body:

Jack, Queen, and King are face cards, each of the four suits has one of each, so 12 face cards.

12/52 is the chance that the first one will be a face card.

Then it’s 11/51, 10/50, and 9/49.

And the chance for all four is thus all four multiplied together.

(12 / 52) * (11 / 51) * (10 / 50) * (9 / 49) = 0.001828

Hence the probability of getting face card on all attempt is 0.0018

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Answer:

19 1/4

Step-by-step explanation:

1 3/4 × 11 = 7/4 × 11/1 = 77/4 = 19 1/4

The flour that Karina's mother has won't be enough for the recipe and she requires extra 3/20 together with the quality owed by the mother.

Flour is defined as a food product that is the main ingredient for baking of different recipes such as cakes, breads, plate pies just to mention a few.

The amount of flour needed by Karina for the recipe= 3/5 = 0.6.

The amount of flour owed by the mother = 3/7 = 0.45

The difference between the available flour = 0.6 - 0.45 = 0.15

This shows that extra flour of 0.15 or 3/20 is needed in addition to the quantity of flour owed by the mother to be able to make the recipe.

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Answer:

65 cents

[tex]85 \div 17[/tex]

85/17 =5

so for 1 inch of wire is 5 cents but we want to know for 13 inches

so times 5 by 13

5cents*13=65cents

The probability of getting 3 on both of the dice is 1/36.

What is probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. An event's possibility is a number between 0 and 1, where, practically speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Main Body:

The probability of getting 3 on a dice = 1/6

As Jemmy throws the dice twice

P( 3 on both dice) =(1/6)*1/6

P ( 3 on both dice) = 1/36.

Hence the probability of getting 3 on both dice = 1/36.

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