What is equation of the following line ?

Answer:

This is an Obtuse triangle.

Step-by-step explanation:

A Equilateral Triangle is a triangle where all sides are equal. Here all sides are different so it is not an Equilateral Triangle.

Isosceles triangle is a triangle that has 2 sides that are equal. Here all sides are different therefore this is not an Isosceles triangle.

A right angled triangle is a triangle whose sides satisfy the following equality.

Lets say A triangle has sides a, b and c. Where c is the highest value.

Then, [tex]a^{2} +b^{2} =c^{2}[/tex]

Lets substitute the values to the above equation to see whether it the triangle we are given satisfies the above equality,

[tex]7^{2} +15^{2}[/tex] = [tex]49+225[/tex]=[tex]274[/tex]

[tex]17^{2} =289[/tex]

Therefore, [tex]7^{2} +15^{2}[/tex] ≠[tex]17^{2}

So it is not a Right Angled Triangle.

If the sum of squares of the shorter sides is greater than the square of the longer side then it is an Acute angle if not it is an obtuse angle.

[tex]7^{2} +15^{2}[/tex] = [tex]274[/tex]≤[tex]17^{2} =289[/tex]

Therefore, This is an Obtuse triangle.

The answer would be 9/5

Root 81 =9

Root 25 =5

{(–1, 1), (–2, 1), (–2, 2), (0, 2)}

In a function, each input has an output

Each domain has a range. In a function, range can be repeated but domain cannot be repeated. Same domain cannot have two range values.

Here domain is {-1, -2, -2, 0}

Range is { 1, 1, 2, 2}

Domain -2 is repeating so this relation is not a function

Answer : No; a domain value has two range values.

the best way to understand is putting a number in place of x and seeing if they are equal to eachother so just to make it simple i'll make x=6

so your first equation is 2(6)/3 =12/3=4 now the other equation would be (2/3)6 = 6

i actually solved it putting 2 in place of x and got the same answer for both so i think they're the same

The difference between 12 Celsius and -10 Celsius is 22 degrees.

There are 20 different, whole number, specific degrees between 12 and -10 Celsius.

Answer:

(c) 4.1 km

Explanation:

We are given that the height of the balloon is 4 km and that it is 1 km away from the station.

Setting up the diagram that describes the given scenario, we would end up with a right-angled triangle as the one shown in the attached image

where:

height of the balloon = 4 km represents one side of the triangle

distance between the base of the balloon and the station = 1 km represents the other side

distance between the balloon and the station is the length we want to find and it represents the hypotenuse of the triangle.

To get the length of the hypotenuse, we will use the Pythagorean theorem

[tex]hypotenuse = +\sqrt{(side1)^2 + (side2)^2}[/tex]

Substitute with the givens:

[tex]hypotenuse = +\sqrt{(4)^2 + (1)^2}[/tex] = √17 ≈ 4.1 km

Hope this helps :)

32.3 is a decimal number in which 3 is the digit at the tenth place.

Mixed number contains a whole number and a fraction part.

32.3 expressed as mixed fraction is [tex]32\frac{3}{10}[/tex] , here 32 is the whole number  and [tex]\frac{3}{10}[/tex] is the fraction part.

[tex]\frac{3}{10}[/tex] is the fraction in the simplest form.

For this reason, 32.3 expressed as a mixed number in the simplest form is [tex]32\frac{3}{10}[/tex].

Isolate the x. Treat the less than sign as equal sign. What you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 47 from both sides

4x + 47 (-47) < 7 (-47)

4x < -40

Next, divide 4 from both sides

(4x)/4 < (-40)/4

x < -40/4

x < -10

x < -10 is your answer

hope this helps

Let x = the smaller number.

Let 4+3x = the larger number.

So, 28 = 4+3x - x

24 = 2x

x = 12.

The smaller number is 12, now we need to find the larger number,

4+3(12)

40

So, the numbers are 12 and 40.

The equation can be solved by setting up two equations based on the information given, and then substitifying and simplifying the equations to solve for the two numbers. The two numbers are 12 and 40.

The subject of this question is dealing with equations in mathematics. To problem-solve this, we can first form an equation based on the information given: The larger number is equal to 'four more than three times the smaller number' and 'the difference between the two numbers is 28'.

So we can set up two equations:

By substituting the first equation into the second, it resolves as:

3S + 4 - S = 28

which simplifies to:

2S = 24

So, the smaller number S = 24/2 = 12. Substituting S = 12 into the first equation gives:

L = 3*12 + 4 = 36 + 4 = 40

So the two numbers are 12 and 40.

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To find the product of 0.54 and 8, multiply the two numbers together. The product is 4.32.

to calculate the product of 0.54 and 8:

Start by multiplying the whole numbers:

8 * 0 = 0

Next, multiply 8 by the decimal, 0.54:

8 * 0.54 = 4.32

So, you first calculate the product of the whole numbers (8 * 0 = 0), and then you calculate the product of the decimal and the whole number (8 * 0.54 = 4.32).

When you add these results together, you get the final product, which is 4.32.

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Option: D is the correct answer.

               D)       [tex]y=\dfrac{1}{2}x+2[/tex]

A line is said to be steepest if the modulus of the slope is greatest and it is least steep if the modulus of the slope i.e. |m| is least.

We know that the slope intercept form of a line is given by:

[tex]y=mx+c[/tex]

where m is the slope of the line and c is the y-intercept of the line.

A)

[tex]y=4x-3[/tex]

The slope of line is: 4

i.e. m=4

and |m|=4

B)

[tex]y=\dfrac{-3}{4}x+5[/tex]

the modulus of slope is:

[tex]|m|=\dfrac{3}{4}=0.75[/tex]

C)

[tex]y=-10x-8[/tex]

The modulus of slope of line is:

[tex]|m|=10[/tex]

D)

[tex]y=\dfrac{1}{2}x+2[/tex]

The slope of the line is:

[tex]|m|=\dfrac{1}{2}=0.5[/tex]

The modulus of slope of line in options D is smallest.

Hence, the line in option: D is least steep.

[tex]x=4.\overline{05}\\\\x=4.050505...\qquad|\cdot100\\\\100x=405.050505...\\\\100x-x=405.050505...-4.050505...\\\\99x=401\qquad|:99\\\\x=\dfrac{401}{99}[/tex]

So basically you just want to isolate the variable. So you want n on a side all by itself. so first you multiply by -2 to both sides, that will leave you with the equation n+4=18, then you subtract 4 from both sides, this will give you the equation n=14. To make sure this solution is correct, you can plug it back into the equation filling 14 in for n, this equation is 14+4/-2=-9, and this solution works. Hope this helped :)

X= be coffee

Y=be donuts

Set up equations

10x+5y=16.50

5x+10y=14.25

Now multiply first equation by -2 to get a negative

(-2)10x+5y(-2)=16.50(-2)

-20x-10y=-33

Now put both equations to solve for x

-20x-10y=-33

5x+10y=14.25

___________

-15x. = -18.75

Now divide -15 bith sides to get x alone

X= -18.75/-15

X= 1.25

The cost of each coffee cup$1.25

The cost of each coffee cup will be equal to $1.25.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that on Monday joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the office. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of 14.25.

The cost will be calculated by forming linear expressions below,

X= be coffee

Y=be doughnuts

The equations can be written as,

10x+5y=16.50

5x+10y=14.25

Now multiply the first equation by -2 to get a negative.

(-2)10x+5y(-2)=16.50(-2)

-20x-10y=-33

Now put both equations to solve for x

-20x-10y=-33

5x+10y=14.25

___________

-15x. = -18.75

Now divide -15 on both sides to get x alone,

X= -18.75/-15

X= $1.25

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To graph the equation, use the given slope and point to plot two points and draw a line through them.

To graph the equation y - 2 = -3/4 (x - 6) using the given point and slope, we can follow these steps:

Each piece of butter is 0.4 ounces

32.83 because using a calculator, you punch in numbers 4.9 and 6.7 together. Then, you press the equal sign to get 32.83

Standard Form is ...

ax + by = c

where a ≥ 0, b > 0 (if a=0), and {a, b, c} are mutually prime integers (unless irrational numbers are involved).

You can get there from where you're starting in a couple of steps. Multiply by the least common denominator of any fractions. (Here, you multiply by 4.) Then put the variable terms on the opposite side from the constant term. Make sure the leading coefficient is positive.

... 4y -4 = x -12

... x -4y = 8 . . . . add 12-4y

Your answer would be x=4.

6x-8=4x

sub 6x from both sides

-8=-2x

divide by -2 both sides

x=4

Hope This Helps!!!

Answer:

5.3

Step-by-step explanation:

One rational number can be 5.3

It is rational because it has terminating decimal expansion

The rate of change is the slope of a line.  The slope of the line can be calculated using the formula [tex]\frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }[/tex].  To find the slope of a line using this formula, it is necessary to know two of the points on the line.

Answer:

$375.00

Step-by-step explanation:

Answer: $15000

Step-by-step explanation:

The formula to calculate the simple interest is given by :-

[tex]S.I.=P\times r\times t[/tex], where P is the principal amount , r is the rate of interest and t is the time period.

Given: Interest amount = $3,375

Rate of interest = 4.5%=0.045

Time period = 5 years

Let P be the principal amount, then we have

[tex]3375=P\times 0.045\times 5\\\\\Rightarrow\ P=\dfrac{3375}{0.045\times 5}=15000[/tex]

Hence, the principal amount of the account was $15000.

The answer for a would be -2 and for b it would be -3. If you added both -2 and -3 together, you would get a sum of -5, and when for the other equation, the negative in front of b will cancel out the negative in front of -3, making it 3, and when you subtract -2 and 3, you'll end up with a difference of 1. a= -2  b= -3

f(x + 3) = 2x² + 9x + 13

substitute x = x + 3 into f(x)

f(x + 3) = 2(x + 3)² - 3(x + 3) + 4 = 2(x² + 6x + 9) - 3x - 9 + 4

f(x + 3 ) = 2x² + 12x + 18 - 3x - 9 + 4 = 2x² + 9x + 13

So here is how it would go

Answer: Hence, 25000 patients are fully satisfied with their treatment plan .

Step-by-step explanation:

In a sample of 600 patients , there are 500 patients who were fully satisfied with their treatment plan.

So fraction is given by

[tex]\frac{500}{600}=\frac{5}{6}[/tex]

Now, if we have 30,000 patients ,

then ,the number of patients who were fully satisfied is given by

[tex]\frac{5}{6}\times 30000\\\\=\frac{150000}{6}\\\\=25000[/tex]

Hence, 25000 patients are fully satisfied with their treatment plan .

Answer:

The correct answer is 9.

Step-by-step explanation:

Let's start by analyzing the information we have.

We know that Takala put 9 marbles in the box, jackie put in 7, and laird put in 11.

Before continuing, the most convenient is to add these three things:

9 + 7 + 11 = 27.

We now know that those 27 were divided equally to each other, that is 27: 3.

So we just have to divide:

27: 3 = 9

In this way we can verify that each person obtained 9.