The perimeter of an equilateral triangle is 17 inches more than the perimeter of a square, and the side of the triangle is 8 inches longer than the side of the square. Find the side of the triangle ( Hint: An equilateral triangle has three sides the same length.)​

The inverse function of f(x) = 4x is:

f⁻¹(x) =  (1/4)*x

So the correct option is the fourth one.

For any function f(x) we define the inverse f⁻¹(x) such that:

f(f⁻¹(x))  =x

f⁻¹(f(x)) = x

In this case we have f(x) = 4*x

Then the inverse is also a linear function:

f⁻¹(x) = a*x + b

Using the rules for inverses we get:

f⁻¹(f(x)) = a*f(x) + b = a*(4x) + b = x

a*(4x) + b = x

Then we have b = 0

a*4x  = x

a*4 = x/x

a*4 = 1

a = 1/4

The inverse is:

f⁻¹(x) =  (1/4)*x

The correct option is the last one.

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Answer:

Step-by-step explanation:

Let x represent the number.

The expression is built in two parts as:

Subtract the second part from the first part:

The value of y when x is 2 1/2 is 350

Direct variation can be defined as mathematical or arithmetic relationship having two variables that can be expressed with an equation with one variable equivalent to the a specific constant times the size of the other variable.

From the information, we have that;

y varies directly with x.

This can be expressed as;

y α x

Add a constant;

k = y/x

Now, let's determine the constant of their variation, k' by substituting the values, we have;

k = 35/1/4

Take the inverse of the divisor and multiply

k = 35(4)/1

k = 140

To determine the value of 'y' for x = 21/2 = 5/2. we have

k = y/x

140 = y ÷ 5/2

cross multiply

y = 140 × 5/2

cross multiply

y = 350

Hence, the value is 350

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The equation that is represented by the graph is

y = x2 + 4x + 1

This is further explained below.

Generally, The collection of ordered pairings where f(x)=y exists constitutes the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the typical situation when x and f(x) are real integers.

In conclusion, Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (-2,-3)

Focus:[tex]\left(-2,-\frac{11}{4}\right)[/tex]

Axis of Symmetry: x=-2

Directrix: [tex]y=-\frac{13}{4}[/tex]

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The list that shows the numbers |-0.12|, 1/8, 1/9 in order from smallest to largest is:

1/9, |-0.12|, 1/8.

The absolute value of a number is the distance of the number to the origin, hence it is represented by the number without the signal.

In the context of this problem, the absolute value of -0.12 is:

|-0.12| = 0.12.

To convert a fraction to decimal, we divide the top term of the fraction, called numerator, by the bottom term of the fraction, called the denominator.

Hence, in the context of this problem, the decimal representation of the fractions is given as follows:

To order the three numbers, both have integer part 0, hence we look at which one has the greater decimal part, hence they are ordered as 1/9, |-0.12|, 1/8, from least to greatest.

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The value of 'd' in the proportion 3:d:27:45 is 5

A proportion can simply be defined as a mathematical comparison of two different numbers.

The numbers mostly describes a comparison between people, elements, quantities, or things.

It is also seen as an equation having two ratios which are proportionally  set equal to each other.

The mathematical operations involved in proportion includes;

Given the expression:

3:d:27:45

This is represented as;

3 = d

27 = 45

To determine the value of 'd', we have;

cross multiply

27d = 135

Make 'd' the subject of formula by dividing both sides by 27

d = 135/27

d = 5

Hence, the value is 5

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The complete question:

3:d:27:45 . Find the value of d in the proportion

Using the mathematical operation of division, Dan has so far collected 2,000 signatures.

The division operation is one of the basic mathematical operations for deriving numerical results.

The division operation involves sharing the dividend by the divisor to obtain the result of the mathematical operation known as the quotient.

The total number of signatures needed for the petition = 10,000

The number of times that n needs to be to reach 10,000 = 5x

The number of signatures gathered so far, n, = 2,000 (10,000/5).

Thus, based on division operation, the number of signatures that Dan has collected is 2,000.

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Using the mathematical operation of division, It is found that Dan has collected 2000 signatures.

The division is defined as one of the basic mathematical operations for deriving numerical results; Which involves sharing the dividend by the divisor to obtain the result of the mathematical operation known as the quotient.

The total number of signatures, needed for the petition is; 10,000

The number of times, that n needs to be to reach 10,000 would be;

5x

The number of signatures gathered so far, n, will be;

2,000 (10,000/5).

Hence, based on division operation, the signatures that Dan has collected is; 2,000.

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The most appropriate choice for square root will be given by-

Number of integers lying between [tex]\sqrt{60}[/tex] and [tex]\sqrt{145}[/tex] = 5

What is square root of a number?

If the number is raised to the power of [tex]\frac{1}{2}[/tex], then the result obtained is called square root of the number.

[tex]\sqrt{60} = 7.75\\\sqrt{145} = 12.04\\[/tex]

Integers lying between 7.75 and 12.04 = 8, 9, 10, 11, 12

Number of integers lying between 7.75 and 12.04 = 5

Number of integers lying between [tex]\sqrt{60}[/tex] and [tex]\sqrt{145}[/tex] = 5

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The correct answers are point of intersection and point plotted on an object.

Answer:

y = - x - 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x ← is in slope- intercept form

with slope m = - 1

• Parallel lines have equal slopes , then

y = - x + c ← is the partial equation of the parallel line

to find c substitute (- 8, 2 ) into the partial equation

2 = 8 + c ⇒ c = 2 - 8 = - 6

y = - x - 6 ← equation of parallel line

1 . For the two-variable linear equation, produce three points » ordered pair solutions (x, y).

2 . Put each point on a coordinate plane and plot it.

3 . Draw an arrow at each end of a line that passes through the indicated spots.

When two equations are given and we are supposed to draw a graph.

We first have to take any random value of x preferably a small number like 1, 2 etc. and put this value in the equation and get the value of y .

Similarly, do the same for the second equation and get atleast three to four values of both x and y and plot them in a graph .

To cross check whether the graph plotted is correct ; HINT : they should form a straight line .

The graph is given below :

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Answer:

file has been attached

Step-by-step explanation:

Answer:

x = 42°

Step-by-step explanation:

 m∠AOB = 180°     {AB is a straight line}

m∠AOE + m∠EOF + m∠FOB = ∠AOB

x + 2x + 34 + 20 = 180°

Combine like terms,

       3x + 54 = 180

subtract 54 from both sides,

            3x  = 180 - 54

            3x  = 126

Divide both sides by 3

              x = 126 ÷ 3

              x = 42°

The integers that are closest to the number √54 are 7 and 8.

The inequality is 7 <√54 < 8.

Inequality is a mathematical comparison of two integers or algebraic expressions that uses the terms greater than, larger than or equal to, less than, or less than or equal to.

The given number is √54.

Now, we need to find the square root of two numbers that are closest to the given number.

√49 and √64 are two square roots nearest to √54.

√49 = 7 and √64 = 8

Put these values in the inequality to complete it,

7 <√54 < 8

Therefore, 7 and 8 are the required integers closest to √54.

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 y = 1/5x - 5 is the equation of slope-intercept form .

What is slope-intercept form explain?

equation y = 1/5 x - 4

compare y = mx + c , m = 1/5

put points (5,-4) in equation

                        y = mx + c

                        - 4 = 1/5 * 5 + c

                         - 4 = 1 + c

                             c = -5

put value of c in equation

                     y = 1/5x - 5

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Answer: We will be needing 78.54 square meters of sheet metal to make the grain storage silo shown.

Step-by-step explanation: to calculate he total square meters of sheet metal needed to make this grain storage silo we need to calculate the total surface area of the entire structure

for the given structure,

Total surface area = Curved surface area of the cone + curved surface area of the cylinder

curved surface area of cone = [tex]\pi rl[/tex] where r= radius of the base of cone

Given, [tex]2r= 4m[/tex]

⇒[tex]r = \frac{4}{2}=2 metres[/tex]    

slant height of cone [tex]l=\sqrt{(r^{2}+h^{2} ) }[/tex]   where h=1.5 m is the vertical height of the cone

∴ [tex]l = \sqrt{(2^{2}+1.5^{2} ) }=\frac{5}{2}=2.5 m[/tex]              

∴curved surface area of cone [tex]= \pi rl= \pi *2*2.5=5\pi =15.71m^{2}[/tex]             (1)

curved surface area of cylinder(without the floor) =[tex]2\pi rh[/tex]

where r= radius of cylinder and h= height of the cylinder

Given r= 2 m and h=5 m

∴curved surface area of cone =[tex]2\pi rh[/tex]=[tex]2*\pi *2*5=20\pi =62.83m^{2}[/tex]           (2)

From results (1) and (2)

the total surface area of silo = (15.71 + 62.83)[tex]m^{2}[/tex] = 78.54[tex]m^{2}[/tex]

Thus we need 78.54 [tex]m^{2}[/tex] of sheet metal to make the grain storage silo

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Answer:2.04x10 to the 4th

Step-by-step explanation:

multiply 20.4 x 1000

Then write the answer like this: 20,400

now make a decimal under ten countaining all #s that arent 0: 2.04

count the decimal places between the end of the 2 and the last 0 in the number 20,400

There are 4 places so thats 10 the power of 4

Now just put it all together

====================================================

Explanation:

Sean can make 1 paper crane in 6 minutes. His unit rate is 1/6 of a paper crane per minute.

Emily's unit rate is 1/8 of a paper crane per minute.

Their combined unit rate is 1/6 + 1/8 = 4/24 + 3/24 = 7/24 of a paper crane per minute.

Each minute, they can make 7/24 of a paper crane. Put another way, every 24 minutes, they can make 24*(7/24) = 7 cranes.

Let x be the number of minutes needed to make 112 paper cranes.

Multiply the combined unit rate with x and set it equal to 112

(combined unit rate)*(amount of time) = amount made

(7/24)x = 112

x = 112*(24/7)

x = 384

They need 384 minutes if they work together to make 112 paper cranes.

Sean can make 384/6 = 64 paper cranes while Emily can make 384/8 = 48 paper cranes. As a check, 64+48 = 112 to help confirm the answer.

Answer:

(64799/1296) = 49.999

Step-by-step explanation:

If I understand this correctly...

10 × 5 - 6² ⁺ ⁻⁸

(10 × 5) - 6² ⁻ ⁸

(50) - (6⁻⁶)

50 - (1/46656)

(2332799/46656) = 49.999

or

10 × 5 - 6² ⁺ ⁻⁸

(10 × 5 - 6)² ⁻⁸

(50 - 6)⁻⁶

(44)⁻⁶

(1/7256313856)

I hope this helps!

Answer:

7inches

Step-by-step explanation:

using Pythagoras a²+b²=c²

so it's rearranged to c²-b²=a² or c²-a²=b²

first we get 13²-11²

next we do  169-121

this makes 48

square root 48 is 6.90 inches

this rounds up to 7 Inches

your answer would be : 7 inches

Answer:the answer is 6

Step-by-step explanation:

The angles with sides HA and HE are ∠AHE and ∠EHA.

There are some angles given from which we need to find those with sides HE and HA.

The angles given are :

A. ∠AHE B. ∠AGE C. ∠EHA D. ∠EGA E. ∠AHB

For this first we need to understand the naming of angles.

An angle is either named by a single alphabet, mostly when the angle is not divided, or it is named using three letters from which we can clearly understand the sides of the angles.

For example, ∠XYZ has sides XY and YZ with the angle at the point Y.

So we will try to find the sides of each angles given in options.

A. ∠AHE has sides HA and HE with angle at the point H.

B.  ∠AGE has sides AG and GE with angle at the point G.

C. ∠EHA has sides HE and HA with angle at the point H.

D. ∠EGA has sides EG and GA with angle at the point G.

E. ∠AHB has sides HA and HB with angle at the point H.

Hence the angles for which HA and HE are sides are ∠AHE and ∠EHA.

The question is incomplete. Find the complete question below:

Select all the angles for which HA and HE are the sides.

A. ∠AHE B. ∠AGE C. ∠EHA D. ∠EGA E. ∠AHB

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The age of Raj is 4 years.

Amaan's age is 8, more than 4 times the age of Raj.

Amaan is 24 years old.

The age of Raj can be found as follows;

Therefore, the situations will form an algebraic equation.

let

the age of Raj = x

The age of Amaan is 8 more than 4 times the age of Raj.

Hence, the age of Amaan can be represented as follows:

Amaan age = 8 + 4x

Hence,

24  = 8 + 4x

subtract 8 from both sides of the equation

24 - 8 = 8 - 8 + 4x

16 = 4x

divide both side by 4

x = 16 / 4

x = 4

Therefore,

age of Raj = 4 years

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Answer:

32

Step-by-step explanation:

(4[tex]\sqrt{2}[/tex] )²

= 4[tex]\sqrt{2}[/tex] × 4[tex]\sqrt{2}[/tex]

= 4 × 4 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex]

= 16 × 2

= 32

The day that they will shop at same time based on the information is in 40 days.

It should be noted that from the information given, Mrs Jannah goes to the store every 8 days and Mrs Byrne goes to the store every 10 days.

It should be noted that if they both went to shopping today, the date that they will shop at same time will be the least common multiple of 8 and 10. This will be:

Multiple of 8 = 8, 16, 24, 32, 40

Multiple of 10 = 10, 20, 30, 40

Therefore, the days is 40 days.

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Answer:

  V = 11 +3j volts

Step-by-step explanation:

You want the voltage in a circuit with current (3 -j) and impedance (3 +2j).

The voltage is the product of current and impedance.

  V = (3 -j)(3 +2j) = 3(3 +2j) -j(3 +2j)

  = 9 +6j -3j -2j² = 9 -2(-1) +(6 -3)j

  = 11 +3j

The voltage is V = 11 +3j.

__

Additional comment

In electronics, the letter j is used in place of the letter i to mean √(-1). This is because i means something else. (Here, i is used for "impedance." It is conventionally used for "current.")

The multiplication is carried out as though the values were polynomials. In the end, j² is replaced by -1.

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!! how to solve for the x

6) to solve for x just simplify both equations and set it to 180; they are co-interior angles which is why they both add to 180.

12x-29 + 4x + 1

16x -28 = 180

16x = 208;

x = 13

8) 4x - 18 = 90;

4x = 108

x = 27