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Phrase Clause

The general slope intercept form equation of a line is as stated below;

where m is the slope and b is the intercept.

If we compare the given equation y = 5x-1 with the equation of a line, we can deduce that the slope, m, is 5.

The slope of a line perpendicular to another is always given as -1/m, therefore the line perpendicular to the line y=5x-1 will have a slope of -1/5;

So let's go ahead and substitute m= -1/5, into the point slope equation to determine the line that passes through (-5,7);

Remember, the point slope form equation of a line is given as;

Substituting the above values, we'll have

Let's open up the parenthesis first, we'll have;

Let's isolate y by adding 7 to both sides of the equation;

The above equation is the required equation of the line in slope intercept form which can be compared to the one earlier written above(y = mx + b).

4π/ 5 radians = ?

Then if

π radians= 180°

(4/5)•π radians = 180• 4/5

. = 144

Answer is

4pi/5 radians = 144 degrees

First we need to find the 17% of 11,000

Answer:

-8 < x < 5

Step-by-step explanation:

-3 < x + 5 < 10

=> Minus 5 in all sides

=> -8 < x < 5

Answer:

hi how are you . i cant find the answer youre looking for

Answer:

1) 6 ( a - b )

2) x² - 2xy + y²

Step-by-step explanation:

1) 4 ( a - c ) + 2 ( a - b )

First, solve the brackets.

4a - 4c + 2a - 2b

Combine like terms.

6a - 6b

Take the common factor out.

6 ( a - b )

2) x ( x - y ) + y ( y - x )

First, solve the brackets

x² - xy + y² - xy

Combine like terms.

x² - 2xy + y²

The figure below has an area equivalent to 88 square units.

In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides.

The opposing or confronting sides and the opposing angles in a parallelogram are of equal length.

Area = length * breadth is the formula for computing the area of a parallelogram.

Substituting the given values

Area = x * h

Area of the parallelogram = 8 * 11

Area of the parallelogram = 88 square units.

Consequently, the parallelogram above has an area of 88 square units.

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The measure of <5 is 47

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

m<4=5x-42

and m<5=-x+82

as, <4 and <5 are in co- interior angle

<4 + <5 = 180

5x - 42 + (-x + 82) = 180

5x -42 - x + 82= 180

4x +40 = 180

4x = 140

x= 140/4

x= 35

Hence, the measure of <5 = -x+ 82 = -35 + 82 = 47

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f is the given profit function whose input is number of cones and output is profit, f(50)=80 tells that $80 profit is made by selling 50 cones of ice cream.

A function is a relation that assigns each element of a set a unique element of another set.

f(x) denotes that function f works on the input values x and give output f(x).

If f is a function and f(x) = x+2, then if we have to check x= 1 , then

f(1) = 1+2 = 3 is the value of the function f at x=1

A La Mode Ice Cream Parlor uses a function f as profit function

The input x is the number of cones it sells and output is profit

f(50) = 85

⇒x = 50 and f(50) = 85

It means that when the parlor sells x = 50 cones , it makes  profit $ f(50) = 85

or On selling 50 cones the profit made is $80

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Answer:3

Step-by-step explanation: 105 divided by 3 is 35 there are 3 groups so 1 ten would go in each group.

The meaning of each statement is shown below.

Step-by-step explanation:

Assume that the given statements are

(a) c(0)=0

(b) c(3)=c(8)

(c) c(n)=29

(d) c(13)<c(12)

Let c(t) be the number of customers in a restaurant t hours after 8 A.M.

We need to find the meaning of each given statement.

(a) c(0)=0 means the number of customers 0 hours after 8 A.M (i.e., 8 A.M.) is 0.

(b) c(3)=c(8) means the number of customers 3 hours after 8 A.M (i.e., 11 A.M.) is equal to the number of customers 8 hours after 8 A.M (i.e., 4 P.M.).

(c) c(n)=29 means the number of customers n hours after 8 A.M is 29.

(d) c(13)<c(12) means the number of customers 13 hours after 8 A.M (i.e., 9 P.M.) is less than the number of customers 12 hours after 8 A.M (i.e., 8 P.M.)

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Answer:

<3 and <4 are complementary

Answer:

v=-0.5

Step-by-step explanation:

v=2+(-5×0.5)

v=2-2.5

v=-0.5

The number of ways that the company can choose four workers is 40920 ways.

From the information, the building company employs 3 laborers 12 joiners 8 electrician 4 plumbers. The total number of workers will be:

= 3 + 12 + 8 + 4

= 27 workers

It should be noted that combination will be used to choose the 4 workers. This is illustrated as

Combination formula

ⁿCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time.

where n = 33

r = 4

ⁿCr = n! / ((n – r)! r!)

³³C₄ = 33! / (33 - 4)! 4!

= 33! / 29! 4!

= 33 × 32 × 31 × 30 / 4 × 3 × 2

= 40920 ways

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I f Bill wants to maximize his utility while spending $31 on apple. Bill van buy 10 whole pounds of Apples

given data

Apples cost $3 per pound

Bananas cost $5 per pound

amount Bill has to spend $31

The number of whole apple Bill can buy

Using $31 the number of whole apples this can buy is gotten  dividing the  the total amount by the price of apple per pound.

= amount Bill has to spend $31 / Apples cost $3 per pound

= 31 / 3

= 10.33

Since we are solving for whole pounds of apple Bill can buy 10 whole pounds of apples

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Answer:

Step-by-step explanation:

Here in all these questions we need to follow the rules of BODMAS which tells us the steps to solve and mathematical operation.

B-Bracket

O-Of

D- Division

M-Multiplication

A-Addition

S-Subtraction

now,

A. 19+(8-25)

we need to solve what's inside the bracket first

so, 8-25= -17

=19+(-17)

=2

B. (-15+6)-(23-18)

=(-9)-5

= -14

C. (154-6)+3-(-9+7)

= 148+3-(-2)

=148+3+2

= 153

D. -13+(5+8)- (-4+8)

= -13+13-4

= -4

E. (-5)-(17+(-13))-((-8) -(+2))

= -5 -(4)-(-10)

= -5-4+10

= 1

F. (12-(-3))-(12-(-3))

= 15-15

=0

G. 15 -(-3-((+12)-16))

= 15-(-3-(-4))

= 15- 1

= 14

That's how we do it try the last one by your self!

The quotient of the triangle side lengths are same as below for different triangle ( please refer attached image for better understanding)-

For ABC - 9/4 or 2.25, 9/6 or 1.5, 6/4 or 1.5

For DEF - 18/8 or 2.25, 18/12 or 1.5, 12/8 or 1.5

For GHI - 27/12 or 2.25, 27/18 or 1.5, 18/12 or 1.5

For JKL - 4.5/2 or 2.25, 4.5/3 or 1.5, 3/2 or 1.5

Quotient in mathematics, can be defined as the result of the division of a number by any divisor.

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Answer:

74 inches

Step-by-step explanation:

6 feet= 72 inches plus 2 inches equals this amazing height

A graph of the linear function (y = 2x - 3) which matches the answer is shown in the image attached below.

A graph refers a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

Generally speaking, the graph of any proportional relationship such as a linear function is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis decreases or increases, the values on the y-axis decreases or increases simultaneously as shown in the image attached below.

In conclusion, a graph representing the given linear function shows a proportional relationship between the value of x and y.

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The difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours (f − g)x = 5x - 25.

A function can be defined as the set of inputs that results in output.

Given, Cynthia earns 20 dollars per hour working as a camp counselor plus an additional 25 dollars as a bonus which is f(x) = 20x + 25, and as a lifeguard 15dollars per hour and an additional 50 dollars bonus which is g(x) = 15x = 50.

We know (f - g)x = f(x) - g(x).

∴  The difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours is f(x) - g(x).

=  (20x + 25) - (15x + 50).

= 20x - 15x + 25 - 50.

= 5x - 25.

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Sulfhuric acid, boric acid and vinegar have 7 atoms present in them

To find the compounds with equal number of atoms, we must take each individual atoms and find how many atoms are present in them.

In the first compound, we have sulfuric acid.

[tex]H_2SO_4 = 7 atoms\\[/tex]

Second compound, we have phosphoric acid

[tex]H_3PO_4 = 8 atoms[/tex]

Third compound, we have vinegar

[tex]C_2H_3O_2 = 7 atoms[/tex]

Fourth compound, we have boric acid

[tex]H_3BO_3 = 7 atoms[/tex]

From the above, only sulfuric acid, vinegar and boric acid have equal number of atoms present in them.

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Answer:

Step-by-step explanation:

Convert the first one above:

Apply this to each term of the given expression to get:

The value of n is 89.

Answer:

n = 89

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Tan double angle identity}\\\\$\tan (A - B)=\dfrac{\tan A - \tan B}{1 + \tan A \tan B}$\\\end{minipage}}[/tex]

Rewrite the tan double angle identity to isolate tanAtanB:

[tex]\implies 1 +\tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}[/tex]

[tex]\implies \tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}-1[/tex]

Therefore:

[tex]\implies \tan 1^{\circ} \tan 2^{\circ}+\tan2^{\circ}\tan3^{\circ}+...+\tan88^{\circ}\tan89^{\circ}[/tex]

[tex]\implies \left(\dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (1 - 2)^{\circ}}-1\right)+\left(\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (2 - 3)^{\circ}}-1\right)+...+\left(\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (88 - 89)^{\circ}}-1\right)[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}-1+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}-1+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-1[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}+\tan 2^{\circ}- \tan 3^{\circ}+...+\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}}{\tan (-1)^{\circ}}-\dfrac{ \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]

[tex]\textsf{Apply the identity}\quad \boxed{ \tan(-x)=-\tan(x)}:[/tex]

[tex]\implies \dfrac{\tan 1^{\circ}}{-\tan 1^{\circ}}+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]

[tex]\implies -1+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]

[tex]\implies \dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-89[/tex]

[tex]\textsf{Apply the identity}\quad \boxed{\tan(90-x)=\cot(x)}:[/tex]

[tex]\implies \dfrac{\cot1^{\circ}}{\tan1^{\circ}}-89[/tex]

[tex]\implies \cot 1^{\circ} \cdot \dfrac{1}{\tan1^{\circ}}-89[/tex]

[tex]\textsf{Apply the identity}\quad \boxed{\dfrac{1}{\tan(x)}=\cot(x)}:[/tex]

[tex]\implies \cot 1^{\circ} \cdot \cot 1^{\circ}-89[/tex]

[tex]\implies \cot^21^{\circ}-89[/tex]

Therefore, n = 89.

The slope between the two pair of points is 3/2. Yes, Dan's productivity is constant.

Number of model are represented on y axis and the hours are represent on x axis.

As we can observe,

One pair of points on the graph is (4,6) and (2,3) and the other pair of points is (6,9) and (0,0)

The slope m between any two points (a,b) and (c,d) can be calculated as,

m = (d-b)/(c-a)

The two points we have are (4,6) and (2,3), so the slope M between them is,

M = (3-6)/(2-4)

M = -3/-2

M = 3/2.

And the slope M' between other two point (6,9) and (0,0) is,

M' = (9-0)/(6-0)

M' = 9/6

M' = 3/2.

As we can see, the slope is same. The slope represents the ratio of number of models and hours. We can conclude that Dan's productivity is constant.

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The size of the angle x in the pentagon is 36 degrees.

A regular pentagon is a polygon with five sides. The angles of a regular polygon is equal to each other.

Therefore,

the sum of angles in a regular pentagon = 540 degrees.

Each angle in a regular pentagon is 540 / 5 = 108 degrees.

The rhombus is inside the pentagon. Opposite angles in a rhombus are equal.

Therefore, the sum of interior angles of a rhombus adds up to 360 degrees

Hence,

108 + 108 + 2y  = 360

where

y is the angle of the rhombus on the x variable.

Therefore,

2y = 360 - 216

2y = 144

y = 144 / 2

y = 72°

Therefore,

x = 108 - 72

x = 36 degrees

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The vertex and the range of the absolute value function are given as follows:

(−2, −3); −3 ≤ y < ∞.

The absolute value function in the context of this problem is defined according to the following rule:

y = |x + 2| − 3.

For the general equation, with vertex (h,k), the definition is given as follows:

y = |x - h| + k.

Hence, in the context of this problem, the coefficients of the vertex are given as follows:

h = -2, k = -3.

Hence the vertex is:

(-2,-3).

The range of a function is the set containing all the output values assumed by the function. For the absolute value function, it is given by the following interval:

k ≤ y < ∞

Hence, for the function defined in this problem, the interval is given by:

-3. ≤ y < ∞

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Answer:

No answer

Step-by-step explanation:

An absolute cannot equal a negative number

Answer:

X = 12

Explanation:

3x/6 + 1= 7

/2 + 1 = 7

x/2 + 1 = 7

x/2 + 2/2 = 7

X+2/2 = 7

X = 12

hope this helps you :)

Answer:

Hope the picture will help you.......