The side of an equilateral triangle is given as 8 cm, correct to the nearest centimetre. What is the least possible length of its perimeter?​

Answer:

3x² +6

Step-by-step explanation:

(f-g)(x) = f(x) -g(x) = (4x²+1) -(x²-5) . . . . . substitute the function definitions

... = 4x² +1 -x² +5 . . . . . . . . . . . eliminate parentheses

... = (4-1)x² +(1+5) . . . . . . . . . . . collect like terms

... = 3x² +6

Answer:

X=20; the labeled angles are 80 and 100

Step-by-step explanation:

These angles are "consecutive interior angles" so they will add up to be 180.

180 = 5x + 4x

180 = 9x

180/9 = 9/x

20=x

Answer:

Inverse variation here gives out a function [tex]xy=(-32)[/tex].

Step-by-step explanation:

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases. While direct variation describes a linear relationship between two variables, inverse variation describes another kind of relationship.

An inverse variation can be represented by the equation

[tex]xy=k \\or \\y=kx[/tex]. That is, y varies inversely as x if there is some nonzero constant k.

Here, the product is given by

[tex]xy=(-4)[/tex]×[tex]8[/tex]

[tex]xy=(-32)[/tex]

We will be plotting the graph of the function [tex]xy=(-32)[/tex]

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The probability that exactly 6 of 8 adult use their smartphones in meetings or classes is 0.147 or 14.7% .

The complete question is

Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes.

Probability is the measure of likeliness of an event to happen.

The probability given is

p = 54% = 0.54

n =8

r = 6

The binomial Probability is given by

[tex]\rm P(x) = ^n C_r p^r q^{n-r}[/tex]

The probability that exactly 6 people use smartphones in a class of 8 student is given by

[tex]P(x) = \dfrac{n!}{r! (n-r)!} p^r q^{n-r}[/tex]

Here q represents the complement

q = 1 -p

q = 1-0.54 = 0.46

[tex]P(6) = \dfrac{8!}{6! (2)!} 0.54^6 0.46^{2}\\\\\P(6) = \dfrac{8 * 7}{ 2} 0.54^6 0.46^{2}\\\P(6) = 0.147[/tex]

Therefore The probability that exactly 6 of 8 adult use their smartphones  in meetings or classes is 0.147 or 14.7% .

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If the angles of a triangle are all equal, then the sides of a triangle are all equal. The correct answer is option A.

A triangle having all the three sides equal and all the angles equal is called the equilateral triangle.

As we can see that if the triangle is having all the angles equal then all three sides of the triangle must be equal. The triangle is termed the equilateral triangle.

Therefore the angles of a triangle are all equal, then the sides of a triangle are all equal. The correct answer is option A.

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Answer:

y = ± [ √(x+4) ] / 3

Step-by-step explanation:

1) To find the inverse of the function y = 9x2 – 4, exchange the variables x and y, and then solve for the new y.

2) Exchange of the variables: y = 9x^2 – 4 → x = 9y^2 – 4

3) Solve for y:

=> 9y^2 = x + 4

=> y^2=> y = ± [ √(x + 4) ] / 9

= > y = ± [ √(x + 4) ] / 3

Answer:

see below

Step-by-step explanation:

To find the coordinates of the midpoints, add the x's and divide by 2 and add the y's and divide by 2.

The coordinates of D, the midpoint of AB, (1+3)/2 will be the x-coordinate and (4+0)/2 will be the y-coordinate.

D (2,2)

You could also see this on a graph, see image.

E, the midpoint of AC has the x-coordinate (1+-3)/2, which is -1 and y-coordinate (4+-2)/2 which is 1.

E is (-1,1)

Then we are able to calculate the slope of DE and BC.

To calculate slope, subtract the y's and put that on top of a fraction and subtract x's and put that on the bottom of a fraction. If the slopes are the same the segment are parallel.

Slope of DE:

(2-1)/(2--1)

= 1/3

Slope of BC:

(0--2)/(3--3)

=2/6

=1/3

The slopes of BC and DE are equal, so the segments are parallel.

(Alternatively, you could show that Triangle ABC and Triangle ADE are similar. Then find the segments parallel because corresponding angles are congruent.)

Answer:

(-1, -1)

Step-by-step explanation:

Assuming the dilation is centered at the origin, we can multiply each of the coordinates by the scale factor.

This gives A'(-1, -1)

Answer:

Zero Slope

Step-by-step explanation:

Horizontal lines like line L have ZERO SLOPE

Answer:

width=14 &Length = 70( can add unit behind the answer e.g.cm or mm etc..)

Step-by-step explanation:

we know that in a rectangle not all side are same compare to a square..

therefore:

1) write the formula for perimeter down

perimeter = the sum of all side

perimeter = 2x(width) + 2x(length)

P=2(w)+2(L)

2) substitute into the equation

P =2(w)+2(L)

84=2(w)+2(5*w)

3) perform opposite operation to make w become the subject of the formula inorder to find width

48=2(w)+2(5*w)

48=2w+10w

48=12w

48/12=12w/12( the twelves cancels out)

7=w or the width is 7

4) rewrite the formula and solve

P=2(w)+2(L)

P =2(7) + 2(5*7)

P = 14 + 70

P = 48

The equation of linear system in the form of inequality will be x + y ≥ 2 or y ≥ 2 – x.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The graph is given below.

The graph is a linear equation.

Then the equation of linear system in the form of inequality will be

The two point are given as (0, 2) and (1, 1). Then the equation of linear system will be

y – 2 ≥ [(2 – 1) / (0 – 1)] (x – 0)

y – 2 ≥ – x

x + y ≥ 2

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Answer:10X^2 +7

Step-by-step explanation:

A graph which represents the given system of inequalities is Graph C.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

Based on the graph for the given system of inequalities (see attachment), we can infer and logically conclude that Graph C best represents them.

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Answer:

x = -6

Step-by-step explanation:

5x² + 60x + 180 = 0

5 x 180 = 900

you need 2 numbers that multiplies into 900 and adds into 60. these numbers are 30 and 30. now we can rewrite it

5x² + 30x + 30x + 180 = 0.

split it in half and factorise

5x(x + 6) + 30(x + 6) = 0

this means the brackets are:

(5x + 30)(x + 6) = 0

5x + 30 = 0

5x = -30

x = -6

x + 6 = 0

x = -6

therefore, x = -6.

The table that could be used to model his climb will consist of 125 ft/h for the first two hours and 87.5 ft/h for the next 4 hours.

The equation that can be used to model the motion of the climber is calculated as follows;

(1, 150)

(2, 275)

(4, 525)

(6, 700)

m = (275 - 150)/(2 - 1) = 125 ft per hour

m = (700 - 525)/(4 - 2) = 87.5 ft/hr

Thus, the table that could be used to model his climb will consist of 125 ft/h for the first two hours and 87.5 ft/h for the next 4 hours.

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Answer:

The constant of proportionality is 6. This makes the relation y = 6x.

Step-by-step explanation:

Concept: As the number of apples are increasing, the number of slices are also increasing. Given that x is the number of apples and y is the number of slices. This means that y is directly proportional to x.

y ∝ x

Let the constant of proportionality be k.

y = kx

For x = 1, y = 6. So, k = 6.

For x = 2, y = 12. So, k = 6.

This follows for all the values.

Clearly, the constant of proportionality is 6.

The relationship will become y = 6x.

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The inverse of the function f(x) = 2x - 10 is f-1(x) would be x/2 + 5.

Lets try to solve it,

We will be using the inverse function to solve this.

f(x) =[tex]2x - 10[/tex]

Replace f(x) with y.

[tex]y = 2x - 10[/tex]

Interchange x and y

[tex]x = 2y - 10[/tex]

Solve for y

[tex]y = (x + 10) / 2[/tex]

Replace y with f-1(x).

[tex]f-1(x) = x/2 + 5[/tex]

Thus, the inverse of the function f(x) = 2x - 10 is f-1(x) = x/2 + 5

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Answer:

telmhtkhknrkh

Step-by-step explanation:

eg

Answer:

4.08x^2

Step-by-step explanation:

Answer:

C. The note on the package only told customers to call in the event that they had a concern, which could bias the results negatively.

Explanation:

Since customers were only told to call if they had concerns, all of the calls were about concerns or problems that they were having - meaning all of the calls were negative. However, they were never informed to call if they were happy or content with the product, meaning they were never informed of the people who had positive comments, only negative.

Answer: 79

Step-by-step explanation:

[tex]\sqrt{k+2}-9=0\\\\\sqrt{k+2}=9\\\\k+2=81\\\\k=\boxed{79}[/tex]

Answer:

D) k = 79

Step-by-step explanation:

Given equation: [tex]\sf\sqrt{k+2}-x=0[/tex]

Steps:

1. Substitute 9 as the value of x in the equation:

[tex]\sf\sqrt{k+2}-9=0[/tex]

2. Add 9 to both sides:

[tex]\sf\sqrt{k+2}-9+9=0+9\\\\\Rightarrow \sqrt{k+2}=9[/tex]

3. Square both sides of the equation:

[tex]\sf\left(\sqrt{k+2}\right)^2=9^2\\\\\Rightarrow k+2=81[/tex]

4. Subtract 2 from both sides:

[tex]\sf k+2-2=81-2\\\\\Rightarrow k = 79[/tex]

5. Check your work:

[tex]\sf\sqrt{k+2}-x=0\ \textsf{[ substitute 79 for k, and 9 for x ]}\\\\\sqrt{79+2}-9=0\ \textsf{[ add ]}\\\\\sqrt{81}-9=0\ \textsf{[ take the square root ]}\\\\9-9=0\ \textsf{[ subtract ]}\\\\0=0\ \checkmark[/tex]

[tex]\mathbf{\frac{23}{90}}[/tex] fraction of all shapes are circles.

Given that the ratio of the number of white shapes to black shapes is 7:3

Let the number of white shapes be [tex]7n[/tex]

Then the number of black shapes be [tex]3n[/tex]

So total number of shapes [tex]=7n+3n=10n[/tex]

Now ratio of white circles to white squares is 2:7

So the fraction of circles to all white shapes [tex]=\frac{2}{2+7}=\frac{2}{9}[/tex]

Hence the number of white circles [tex]=\frac{2}{9}\times7n=\frac{14n}{9}[/tex]

Again given that the ratio of black circles to the number of black sqaures is 1:2

So the fraction of circles in all black shapes [tex]=\frac{1}{1+2}=\frac{1}{3}[/tex]

The number of black circles [tex]=\frac{1}{3}\times3n=n[/tex]

Total number of circles [tex]=\frac{14n}{9}+n=\frac{14n+9n}{9}=\frac{23n}{9}[/tex]

The fraction of all shapes are circle is [tex]=\frac{\frac{23n}{9}}{10n}=\frac{23n}{90n}=\frac{23}{90}[/tex]

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To graph this situation we must take into account the data and the organization of each of them on the X axis and Y axis.

To graph this situation we must take into account the data we have:

Based on these data, we assign the horizontal axis to count years and the vertical axis to count tickets per year. We must continue the pattern of increased attendance over the years.

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Answer:

x=4

Step-by-step explanation:

2x-8-x+4-6=0

or,2x-x-8+4=0

or,x-4=0

or,x=0+4

•°•x=4

ans

Answer:

x = 2 or 7

Step-by-step explanation:

(x-4)² - (x-4) - 6 = 0

x²-8x+16-x+4 -6 = 0

           x²-9x+14 = 0

           (x-2)(x-7) = 0

∴x = 2 or 7

Answer:

True

Step-by-step explanation:

• Parallel lines have equal slopes

the equation of a line in slope- intercept form is

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

6x + 3y = 7 ( subtract 6x from both sides )

3y = - 6x + 7 ( divide terms by 3 )

y = - 2x + [tex]\frac{7}{2}[/tex] → in slope- intercept form

with slope m = - 2

y = - 2x + 3 ← is in slope- intercept form

with slope m = - 2

since both lines have equal slopes then they are parallel lines

Answer:

C

Step-by-step explanation:

The horizontal line, y=2, is solid and shaded above, so it represents

[tex]y \geqslant 2[/tex]

The slanted line, y=x is dashed and shaded below, so it represents y<x.

The correct answer is option D which is the probability is 1.

The complete question is given below:-

Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer. Which value represents the probability that he will win the election?

0

1/4

3/4

1

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The probability of Event E is given by,

P = favourable outcomes / Total outcomes

Jamaal is the only candidate running in the class treasurer election.

There for Total No. of outcomes = 1

Here Event E is Jamaal winning the Election.

So, No. of favorable outcome = 1

P(E) = 1 / 1

P(E) = 1

This type of event is called a SURE EVENT Because the probability of a sure event is always 1.

The Probability of Jamaal winning the election is 1. So, Option D is correct.

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The probability that he will win the election will be 1. Then the correct option is D.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

The value of the probability of an event will be varying from zero to one.

Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer.

Then the probability that he will win the election will be

If the event will certainly happen, then the probability will be one.

P = 1

Then the correct option is D.

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Answer:

A and D

Step-by-step explanation:

Since tangent is opposite/adjacent,

Tan 40 in this case would be x/3.8 (i used x because we don't know what the value is)

So, you set it up as an algebra problem

Tan40 = x/3.8

Multiply both sides by 3.8

3.8tan40 = x, Option A

And then, angle E is 50 degrees

So tan 50 = 3.8/x

Multiply both sides by x

tan50x = 3.8

Divide both sides by tan50

x= 3.8/tan50

So, A and D are both correct

The equation of this circle in standard form is (x-2)² + (y+3)² = 18

The center of the circle is at the point  (2,-3), and its radius is 4.2426 units

Circle is the 2D geometry which is round in shape with radius R.

Given is the general form of the equation of a circle is

7x² + 7y² − 28x + 42y − 35 = 0.

Dividing by 7, we get

x² -4x + y² + 6x = 5

Completing the squares, we have

x² -4x + 4 + y² +6x + 9 = 5 +4 + 9

(x-2)² + (y+3)² = 18 = (3 √2)²

Circle's center is (2,-3) and  radius = 3 √2 = 4.2426 units

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Answer:

(x-2)^2 + (y+3)^2 = 18,

2,-3

3(2^(1/2)) units

Step-by-step explanation:

Below