Answer:
Both equal sides have a length of 29 cm.
The third inequal side is 9 cm.
Step-by-step explanation:
System of Equations
With the data provided in the problem, we can form a system of two equations with two unknowns.
Let's call x to each equal side of the isosceles triangle and y to the other side. One condition states that each equal side is 2 cm more than three times the other side. It can be written as:
\(x=3y+2\)
We also know the perimeter of the triangle is 67 cm. Since we have to equal sides to x:
\(x+x+y=67\)
\(2x+y=67\)
Let's put together both equations:
\(x=3y+2\)
\(2x+y=67\)
To solve the system, we can use the x from the first equation and replace it into the second equation:
\(2(3y+2)+y=67\)
Operating:
\(6y+4+y=67\)
Joining like terms:
\(7y=67-4=63\)
Solving for y:
\(y=63/7=9\)
The third inequal side is 9 cm. Now find the value of x.
\(x=3y+2=3(9)+2=27+2=29\)
Both equal sides have a length of 29 cm.
Is (4, 2) a solution to the system y-x=2 and -3x-2y=-8?
Answer:
It is only a solution to y = x - 2, not -3x - 2y = -8
Step-by-step explanation:
I) Check y = x - 2:
y = x - 2
2 = 4 - 2
As you can see, (4, 2) is a solution to this system.
II) Check -3x - 2y = -8:
-3x - 2y = -8
(-3)(4) - (2)(2) = -8
-12 - 4 =/= 8
-12 - 4 = -16, not 8. So (4, 2) is not a solution to this system.
Use the ALEKS graphing calculator to find all the real zeros of the quadratic function.
f(x)=-3x²-11x-5
Round to the nearest hundredth.
If there is more than one answer, separate them with commas.
If there are no real zeros, click on "None".
real zero(s):
0,0,...
X
None
Ś
The roots of the quadratic function f(x) = -3x² - 11x - 5 will be negative 3.14 and negative 0.53.
What are the roots of the equation?Let the equation be ax² + bx + c = 0.
Then the roots of the equation will be
\(\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}\)
The quadratic function is given below.
f(x) = -3x² - 11x - 5
Then the roots of the quadratic function will be given as,
x = [-(-11) ± √{(-11)² - 4 × (-3) × (-5)}] / [2 × (-3)]
Simplify the equation, then the roots of the equation are calculated as,
x = [-(-11) ± √{(-11)² - 4 × (-3) × (-5)}] / [2 × (-3)]
x = [ 11 ± √{121 - 60}] / [-6]
x = - (11 ± 7.81) / 6
x = - (11 + 7.81) / 6, - (11 - 7.81) / 6
x = - 3.14, -0.53
The solution of the quadratic function will be negative 3.14 and negative 0.53.
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whats 5x5? Maybe will mark brainiest
Answer:
25
Step-by-step explanation:
5x5 = 25
Answer:
25
Step-by-step explanation:
Let's go through our times tables really quick!
5x1 = 5 (5 + 0)
5x2 = 10 (5 + 5)
5x3 = 15 (5 + 5 + 5 [10 + 5])
5x4 = 20 (5 + 5 + 5 + 5 [15 (5x3) + 5)
As we can see, if we know 5x4, we can easily find 5x5! It's just 5x4 + 5
So, 5x5 is 25
Hope this helped!
A baker used 33 3/4 cups of flour to make
4
15 batches of cookies. How many more cups
of flour does the baker need if she wants to
make 21 batches of cookies?
The baker would need 47. 25 cups of floor
How to determine the valueWe need to know that proportion is a form of mathematical comparison with two equations made equal to each other.
From the information given, we have that;
baker used 33 3/4 cups of flour to make 15 batches of cookies
This is represented as;
Convert to improper fractions
135/4 cups = 15 batches of cookies
Then, x cups = 21 batches of cookies
cross multiply the values
15x = 708. 75
Divide both sides by the coefficient of x, we have ;
x = 708. 75/15
x = 47. 25 cups of floor
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Find x when () = 2. Please explain step by step
Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.
Step-by-step explanation:
linear regression model describing the relationship between the carat weight and price of very high quality diamonds is summarized below.
A diamond seller lists a very high quality diamond weighing 0.8 carats at a price of $10,999. Does this model over- or under-predict the price of this diamond? Select the option below that best summarizes the answer.
A. The model under-predicts the price of this diamond because the residual is positive.
B. The model over-predicts the price of this diamond because the residual is positive.
C. The model over-predicts the price of this diamond because the residual is negative.
D. We do not have enough information to answer this question.
E. The model under-predicts the price of this diamond because the residual is negative.
Answer:
A. The model under-predicts the price of this diamond because the residual is positive.
Step-by-step explanation:
The diamond seller has listed its 0.8 weighting diamonds at a price of $10,999. The price of the diamond is set as the market maker. The model is used to predict the price of the diamonds. This model has under predicted the value of diamonds and actual price of diamonds must be higher.
Use the given zero to find the remaining zeros of the polynomial function.
P(x) = 2x3 − 5x2 + 6x − 2; 1 + i
Using the given zero . The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.
What is the polynomial function?If 1 + i is a zero of the polynomial function P(x), then its conjugate, 1 - i, must also be a zero of the polynomial, since complex zeros of polynomial functions with real coefficients always come in conjugate pairs.
To find the remaining zero, we can use polynomial division or synthetic division to divide P(x) by (x - 1 - i)(x - 1 + i), which is the quadratic factor corresponding to the two known zeros:
2x^2 - 3x + 2
P(x) = --------------
(x - 1 - i)(x - 1 + i)
Now we need to solve for the roots of the quadratic factor 2x^2 - 3x + 2. We can use the quadratic formula:
x = [3 ± sqrt(9 - 4*2*2)] / (2*2)
= [3 ± sqrt(1)] / 4
= 1/2 or 2
Therefore, the remaining zeros of P(x) are 1/2 and 2. The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.
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Please help me with this.
Here are the correct matches to the expressions to their solutions.
The GCF of 28 and 60 is 4.
(-3/8)+(-5/8) = -4/4 = -1.
-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.
The solution of 0.5 x = -1 is x = -2.
The solution of 1/2 m = 0 is m = 0.
-4 + 5/3 = -11/3.
-2 1/3 - 4 2/3 = -10/3.
4 is not a solution of -4 < x.
1. The GCF of 28 and 60 is 4.
The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:
28 = 2 x 2 x 7
60 = 2 x 2 x 3 x 5
The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.
2. (-3/8)+(-5/8) = -1.
To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.
3. -1/6 DIVIDED BY 1/2 = -1/3.
To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.
4. The solution of 0.5 x = -1 is x = -2.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.
5. The solution of 1 m = 0 is m = 0.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.
6. -4 + 5/3 = -11/3.
To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.
7. -2 1/3 - 4 2/3 = -10/3.
To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.
8. 4 is not a solution of -4 < x.
The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.
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HELP me pls pls I beg you
Answer:B 25%
Step-by-step explanation:
6 people had 6-8 and there are 24 total people so the fraction is 6/24 which is equivalant to 1/4 which equals 25%
Answer:
25%
Step-by-step explanation:
add up all you get 24
add absences between 6 and 8 you get 6
6/24= 25
what is the value of the underlined digit in the number 27,416,385. 4 is the underlined number.
The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.
How can the digits be known?The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23. however amount is represented by a number.
It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.
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Emily split up the area of a rectangle to help her solve the division equation 5{,}360 \div 5=?5,360÷5=?5, comma, 360, divided by, 5, equals, question mark.
She splits the rectangle into parts that are easy to divide by 555:
Area model split into 4 parts, each with a width of 5 units. From top to bottom the parts have a height of A units and an area of 5,000 square units; a height of B units and an area of 300 square units; a height of C units and an area of 50 square units; a height of D and an area of 10 square units. A brace labeled H spans the top 4 parts.
Answer:
s
Step-by-step explanation:
Emily used an area model for 5,360 ÷ 5 split a rectangle into four parts: A=1,000, B=60, C=10, and D=2 units and total area = 5,360 after division the answer is 1,072.
To solve the division equation 5,360 ÷ 5, Emily used an area model split into 4 parts, each with a width of 5 units. Let's use the information provided to find the values of A, B, C, and D.
The area of the first part is 5,000 square units, and its width is 5 units. Therefore, the height of this part (A) is:
A = Area / Width
A = 5,000 / 5
A = 1,000 units
The area of the second part is 300 square units, and its width is 5 units. Therefore, the height of this part (B) is:
B = Area / Width
B = 300 / 5
B = 60 units
The area of the third part is 50 square units, and its width is 5 units. Therefore, the height of this part (C) is:
C = Area / Width
C = 50 / 5
C = 10 units
The area of the fourth part is 10 square units, and its width is 5 units. Therefore, the height of this part (D) is:
D = Area / Width
D = 10 / 5
D = 2 units
Now, we have the following values:
A = 1,000 units
B = 60 units
C = 10 units
D = 2 units
To find the total area of the rectangle, we sum up the areas of all four parts:
Total Area = 5,000 + 300 + 50 + 10 = 5,360 square units
Now, we can calculate the division 5,360 ÷ 5:
5,360 ÷ 5 = 1,072
Therefore, using area model the answer to the division equation is 1,072.
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Mofor has homework assignments in five subjects. He only has time to do two of
them.
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.
If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:
1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.
2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.
3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.
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2 numbers are such that if 7 is added to the first number, a number twice the second number is obtained. If 20 is added to the second number, the number obtained is four times the first number. Find the two numbers
Answer:
1st= 47/7 or 6.71
2nd= 48/7 or 6.857
Step-by-step explanation:
1st number =X and 2nd number = Y
According to question, X+7=2Y
20+Y=4X
X=2Y-7 (from 1st condition)
putting in it second
20+Y=4(2Y-7)
20+Y=8Y-28
20+28=8Y-Y
48=7Y
Y=48/7
so X=2(48/7)-7
=96-49/7
47/7
4p = 5t + 2q\(x^{2}\) make q subject
Answer:
q = 4p - 5t / 2x^2
Step-by-step explanation:
2qx^2 + 5t = 4p
2qx^2 = 4p - 5t
q = 4p - 5t / 2x^2
Simplify -3 1/9 - (-8 1/3)
let's firstly convert the mixed fractions to improper fractions and then proceed.
\(\stackrel{mixed}{3\frac{1}{9}}\implies \cfrac{3\cdot 9+1}{9}\implies \stackrel{improper}{\cfrac{28}{9}} ~\hfill \stackrel{mixed}{8\frac{1}{3}}\implies \cfrac{8\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{25}{3}} \\\\[-0.35em] ~\dotfill\)
\(-\cfrac{28}{9}~~ - ~~\left( -\cfrac{25}{3} \right)\implies -\cfrac{28}{9}~~ + ~~\left( \cfrac{25}{3} \right)\implies -\cfrac{28}{9} + \cfrac{25}{3} \\\\\\ \stackrel{\textit{using the LCD of 9}}{\cfrac{1(-28)~~ + ~~3(25)}{9}}\implies \cfrac{-28+75}{9}\implies \cfrac{-47}{9}\implies {\LARGE \begin{array}{llll} -5\frac{2}{9} \end{array}}\)
dele took 25 minutes to walk to school and he arrived at exactly 8:00am, at what time did he leave his home
which expression is equivalent to n+n-0.18n
a. 1.18n
b. 1.82n
c. n- 0.18
d. 2n - 0.82
Answer:
Simplifying the expression `n + n - 0.18n`, we get:
n + n - 0.18n = 2n - 0.18n
Therefore, the expression `n + n - 0.18n` is equivalent to `2n - 0.18n`.
Looking at the answer choices:
a. 1.18n
b. 1.82n
c. n- 0.18
d. 2n - 0.82
We can see that choice d is equivalent to the simplified expression `2n - 0.18n`.
Therefore, the answer is d. 2n - 0.82.
Step-by-step explanation:
Can someone answer this for me. I NEED HELPPP
Find the value of y if m∠3 =65° and m∠1 =(15y+5)°
Answer: 4 i think
Step-by-step explanation:
65=15y+5
65 - 5 = 15y +5 -5
60 = 15y
60/15 = 15y/15
4 = y
find the perimeter of the given closed figure. guys help me
Create two data sets with 7
numbers in each set
Make a double dot plot
Find the mean, median, mode,
range, and IQR
Data Set 1:
Mean: 8.14
Median: 9
Mode: No mode
Range: 9
IQR: 5.5
Data Set 2:
Mean: 7.71
Median: 8
Mode: No mode
Range: 11
IQR: 7
Here are two data sets with 7 numbers each:
Data Set 1: 3, 5, 7, 9, 10, 11, 12
Data Set 2: 2, 4, 6, 8, 10, 11, 13
To create a double dot plot, we will represent each data set using a line with dots above the corresponding values. Here is a visual representation:
Data Set 1: Data Set 2:
3 2
5 4
7 6
9 8
10 10
11 11
12 13
Now let's calculate the mean, median, mode, range, and interquartile range (IQR) for each data set.
Data Set 1:
Mean: (3 + 5 + 7 + 9 + 10 + 11 + 12) / 7 = 57 / 7 ≈ 8.14
Median: 9
Mode: No mode (no repeated values)
Range: 12 - 3 = 9
IQR (Interquartile Range): The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) is the median of the upper half of the data. The IQR represents the variation between Q3 and Q1. In this case, the IQR is the difference between the medians of the two halves.
Q1: (5 + 7) / 2 = 6
Q3: (11 + 12) / 2 = 11.5
IQR: 11.5 - 6 = 5.5
Data Set 2:
Mean: (2 + 4 + 6 + 8 + 10 + 11 + 13) / 7 = 54 / 7 ≈ 7.71
Median: 8
Mode: No mode (no repeated values)
Range: 13 - 2 = 11
IQR: The median of the lower half of the data is represented by the first quartile (Q1), while the median of the higher half is represented by the third quartile (Q3). The IQR represents the variation between Q3 and Q1. In this case, the IQR is the difference between the medians of the two halves.
Q1: (4 + 6) / 2 = 5
Q3: (11 + 13) / 2 = 12
IQR: 12 - 5 = 7
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A recipe asks for 4/12pounds of chicken.
How many pounds of chicken are needed to make 1/2of a recipe?
Express the answer in simplest form.
Enter the answer in the box.
I need help ASAP no rush bc i just asked a question but pls hurry
Answer:
34 and 1/3
Step-by-step explanation:
Hey there!
The answer is \(\frac{1}{6}\)
To make \(\frac{1}{2}\) of a recipe is like dividing by 2, so \(\frac{4}{12}\) divided by 2 is \(\frac{2}{12}\), or \(\frac{1}{6}\).
Hope it helps and have a good day/night!
You saved $280 on your new laptop because you bought it online. If this was a 20% savings from the original price, find the original cost of the laptop.
Answer:
$350
Step-by-step explanation:
If $280 is the 20% savings from the original price, it is 80% of original price.
280 / 0.8 = 350
From this equation, we can know that 350 is 100% of original price, which makes it the original price.
Hope this helps!
The original price of laptop is $1400.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Saving on laptop = $280.
let the original price be x.
So, 20% of x = 280
20x /100= 280
x/5 = 280
x= 1400
Hence, the original price of laptop is $1400.
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What is the solution to the expression -2-3-(-4)?
---|---------|----------|-----------|-----------|-------|----
A. -9
B. -3
C. -1
D. 5
Answer:
the solution is -1 as the answer
Nikki bought a patio set on sale for $390. The original price was $850.
(a)
Find the amount of discount.
$ 460
(b)
Find the discount rate (in %). (Round to the nearest tenth of a percent.)
perdon ese fue mi error jaja señorita lee algunos números
The growth factor for one generation of a bacteria culture is given by the function g(t)=ln(2)t, in which t is the time it takes for the generation to mature to its full size based on the energy resources and environmental conditions available in the culture. What happens to t if g(t) is cut in half?
t=
Points possible: 1
Allowed attempts: 3
Question 2
What happens to t?
If g(t) is cut in half, then t is
If g(t) is cut in half, then t is doubled. Halving the growth factor halves the rate of growth, reducing the time required for a generation to develop to full size.
What do you mean by growth factor?Growth factor refers to a mathematical expression or a metric that measures the rate of increase or growth of a quantity over time. It is used in many fields such as biology, economics, finance, and others to quantify the increase in size, population, revenue, or any other variable of interest. The growth factor can be represented as a ratio, percentage, or an exponential function and is used to predict future growth based on past trends.
3 potential points
Three tries are permitted.
If g(t) is divided in half, t is also divided in half. This is because the growth factor is a measure of the rate of growth, and halving it equals halves the rate of growth. As a result, the time required for a generation to develop to full size is cut in half.
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❗❗100POINTS❗❗+BRAINLIEST FOR CORRECT ANSWER
Rationalise the denominator of
\( \frac{a + \sqrt{4b} }{a - \sqrt{4b} } \)
where a is an integer and b is a prime number.
thanks.
Answer:
\(\dfrac{(a+2\sqrt{b})^2 }{a^2-4b}\)
Step-by-step explanation:
To rationalise the denominator, multiply by the expression by \(\dfrac{a+\sqrt{4b} }{a+\sqrt{4b} }\):
\(=\dfrac{a+\sqrt{4b} }{a-\sqrt{4b} }\times\dfrac{a+\sqrt{4b} }{a+\sqrt{4b} }\)
\(=\dfrac{(a+\sqrt{4b}) (a+\sqrt{4b})}{(a-\sqrt{4b}) (a+\sqrt{4b})}\)
\(=\dfrac{(a+\sqrt{4b})^2 }{a^2-4b}\)
\(=\dfrac{(a+2\sqrt{b})^2 }{a^2-4b}\)
\(\\ \rm\hookrightarrow \dfrac{a+\sqrt{4b}}{a-\sqrt{4b}}\)
√4b be x\(\\ \rm\hookrightarrow \dfrac{a+x}{a-x}\)
\(\\ \rm\hookrightarrow \dfrac{(a+x)^2}{a^2-x^2}\)
\(\\ \rm\hookrightarrow \dfrac{a^2+2ax+x^2}{a^2-x^2}\)
x^2=√4b^2=4b\(\\ \rm\hookrightarrow \dfrac{a^2+2a\sqrt{4b}+4b}{a^2-4b}\)
Express each set using the roster method
A. The set of natural odd numbers greater than 2, but less than 11
B. {x|x€N and 4
The elements using rooster-method:
A){3,4,5,6,7,8,9,10}
B){5,6,7,8,9,10,11,12,13,14}
What is rooster-method?
By listing the items of a set inside brackets, the roster method may be used to display the elements of a set. One of three ways to describe a set is in rooster form. The items of a set are listed in the roster form between curly or following brackets, with commas separating each element. When items repeat in the set, the roster approach actually has an issue. Because the elements do not follow a pattern or have a specific order, it is impossible to describe the elements in roster notation if the set has a significant number of elements or any repeated elements.
A)Set of natural odd numbers greater than 2 but less than 11:
Let us represent the set using symbol O:
O = {3,4,5,6,7,8,9,10}
B){x| x∈ N and 4<x<15}
Given that x is a natural number greater than 4 but less than 15.
X={5,6,7,8,9,10,11,12,13,14}
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solve 3(x+4)-11=28 please
Answer:
\(\huge\boxed{\sf x = 9}\)
Step-by-step explanation:
Given equation:3(x + 4) - 11 = 28
Add 28 to both sides3(x + 4) = 28 + 11
3(x + 4) = 39
Distribute3x + 12 = 39
Subtract 12 from both sides3x = 39 - 12
3x = 27
Divide both sides by 3x = 27/3
x = 9\(\rule[225]{225}{2}\)
jul used one bag of flour. She baked two loaves of bread. Then she used the remaining flour to make 48 muffins. How much flour was in the bag when Makenzie began? Use the chart to help you solve the problem.
Recipe
Amount of flour needed
Bread
2 ¼ cups per loaf
Muffins
3 ¼ cups per 24 muffins
Pizza
1 ½ cups per pie
Answer:
momdhwdjwbdjwbdjwbdjwbdjwbd a amamamamamamama
Step-by-step explanation:
Find the distance between the points (0,-8) and (3,2). Round your answer to the nearest hundredth.
Answer:
10.44
Step-by-step explanation:
First plot each of the points on to a graph at their respective positions.
Following that create a 90° triangle out of the points. This will create a 3 by 10 triangle. (3 to 0 is 3) (-8 to 2 is a difference of 10)
You can then use the pythagorean theorem \(a^{2} +b^{2} = c^{2}\).
Insert the lengths of each of the sides that we got earlier which would be 3 and 10 into the equation. \(3^{2} + 10^{2} = c^{2}\)
Since we want to find the hypotenuse which is equal to c we work the equation to 9+100 = \(c^{2}\) which in turn is 109 = \(c^{2}\)
Then take the square root of 109 to remove the square from the c to get c = 10.44