Which expression can be used to find the surface area of the following triangular prism? *picture of triangular prism* Choose 1 answer: (Choice A) 24+24+ 120+160+20024+24+120+160+20024, plus, 24, plus, 120, plus, 160, plus, 200 (Choice B) 24+20024+20024, plus, 200 (Choice C) 24+24+200+120+12024+24+200+120+12024, plus, 24, plus, 200, plus, 120, plus, 120 (Choice D) 48+48+120+160+20048+48+120+160+200
Answers
Answer:
A) 24+24+120+160+200
Step-by-step explanation:
The two ends are 24 (1/2bh= 1/2(8*6)).
One side (the back) is 6x20=120
One side (the bottom) is 8x20=160
One side (the top) is 10x20=200
So the equation is 24+24+120+160+200
Related Questions
Kate wants to paddle
her canoe across the lake. To determine how far she must paddle, she paced out a triangle,counting the number of strides, as shown.
If Kate's strides average 3.5 ft, what is the
length of the longest side of the triangle?
What distance must Kate paddle across
the lake?
Answers
Answer:
1. Length of longest side of the triangle = 1,050 ft
2. Length = 437.5 ft
Step-by-step explanation:
Given:
Kate's strides average = 3.5 ft
Find:
1.longest side of the triangle
2.Distance must Kate paddle across the lake
Computation:
1.longest side of the triangle
longest side of the triangle = AE
So,
longest side of the triangle = 150 + 150
longest side of the triangle = 300
Length of longest side of the triangle = 300 × 3.5 ft
1. Length of longest side of the triangle = 1,050 ft
2.Distance must Kate paddle across the lake.
We know that,
ΔABD ~ ΔACE
So,
AB / AC = BD / CE
80 / 160 = BD / 250
BD = 125 Strides
Length = 125 × 3.5 ft
2. Length = 437.5 ft
Write as an inequality. "Four more than half a number is at most sixteen"
Answers
1/2 + 4 ≤ 16
four more = +4
half a number = 1/2
at most means less or greater which is ≤
Answer:
0.5n + 4 ≤ 16
Step-by-step explanation:
add 4 to half of the unknown number (n). It is at most 16 (less than or equal to).
0.5n + 4 ≤ 16
Find the measure of c.
Answers
Answer:
140°
Step-by-step explanation:
The circle has a central angle of 80. This means that the arc it intercepts is also 80°. Therefore, the rest of the circle not intercepted by the arc is 360-80=280°
Remember that inscribed angles have one-half of the arc-length it intercepts. We can see that Angle C intercepts the entire circle except for the arc intercepted by Angle O. Therefore, the arc intercepted by Angle C is 280°. This means that Angle C is the half of 280, or 140°.
Which of the following is a graph of f(x) =square root of x +5
Answers
Answer:
Step-by-step explanation:
You didn't include any graphs, so I can't tell you which one it is. However, the graph of [tex]f(x)=\sqrt{x+5}[/tex] looks like this:
Hope this helps!
The graph of the function [tex]\rm f(x) = \sqrt{x+5}[/tex] is attached below and this can be determined by using the rules of transformation.
Given :
[tex]\rm f(x) = \sqrt{x+5}[/tex]
The following steps can be used in order to sketch the graph [tex]\rm f(x) = \sqrt{x+5}[/tex]:
Step 1 - The rules of transformation can be used in order to sketch the graph [tex]\rm f(x) = \sqrt{x+5}[/tex].
Step 2 - First draw the graph of [tex]\sqrt{x}[/tex] which is in the shape of a parabola.
Step 3 - Now, translate the graph in the left direction, So the function of the graph obtained is [tex]\rm f(x) = \sqrt{x+5}[/tex].
The graph of the function [tex]\rm f(x) = \sqrt{x+5}[/tex] is attached below.
For more information, refer to the link given below:
https://brainly.com/question/14375099
Graph the solution of 7x+3<−4 or 2x−3≥9
Answers
Answer:
Step-by-step explanation:
To do this you would simplify both sides.
For the first one:
[tex]7x+3<-4[/tex]
[tex]7x<-7[/tex] (subtract 3 from both sides)
[tex]x<-1[/tex] (divide 7 from both sides)
and for the second one:
[tex]2x-3\geq 9[/tex]
[tex]2x\geq 12[/tex] (add 3 to both sides)
[tex]x\geq 6[/tex] (divide 2 from both sides)
When you graph these they will look like these pictures
Answer:
[tex]x<-1[/tex] and [tex]x\geq6[/tex]
Step-by-step explanation:
[tex]\bf 7x+3<-4[/tex]
You must subtract 3 from both sides.
[tex]7x+3-3<-4-3\\[/tex]
After subtracting, we got
[tex]7x<-7[/tex]
Let's make it into a fraction and divide
[tex]\frac{7x}{7}<\frac{-7}{7}[/tex]
Now we got the answer
[tex]x<-1[/tex]
[tex]\bf 2x-3\geq 9[/tex]
You must add 3 to both sides.
[tex]2x-3+3\geq 9+3[/tex]
After adding, we got
[tex]2x\geq 12[/tex]
Let's make it into a fraction and divide
[tex]\frac{2x}{2} \geq \frac{12}{2}[/tex]
Now we got the answer
[tex]x\geq 6[/tex]
Your answer is [tex]\bf x<-1[/tex] or [tex]\bf x\geq 6[/tex].
Please help me with this!!!
Answers
Answer:
(f•g)(2)=3 and (g•f)(6)=7
Step-by-step explanation:
look at the tables
where x is equal to both 2 and 7 is where you will find your answer
Hope this helps you!
write the percent as a fraction or mixed number in simpelst form 35% A) 3 1/2 B) 13/20 C) 6 1/2 D) 7/20
Answers
Answer:
7/20
Step-by-step explanation:It is the same thing as .35. So just turn it into fraction and simplify.
Answer:
D) 7/20
Step-by-step explanation:
Divide 35 by 100:
35 / 100 = .35
Convert into a fraction and simplify:
[tex].35=\frac{35}{100}=\frac{35/5}{100/5}=\boxed{\frac{7}{20}}[/tex]
Option D should be the correct answer.
Find the area of the shape shown below.
Answers
Answer:
31.5
Step-by-step explanation:
We can add the areas together
We have a rectangle and a triangle
The area of the rectangle is
A = lw
= 7*3
= 21
The area of the triangle is
A = 1/2 bh
= 1/2 (7)*3
= 21/2
= 10.5
Add them together
A = 21 + 10.5
=31.5
Answer:
31 1/2
Step-by-step explanation:
You find the area for the triangle on top and the rectangle on the bottom. In order to find the area of the triangle, multiply 7 and 3. Then divide the product which is 21 by 2. So the area of the triangle is 21/2 which could also be written as 10 1/2. Next, you find the area of the rectangle which is 7x3. You get 21. Finally, you add the two areas to get 31 1/2. It could also be written as 63/2 or 31.5
5.4(m-2)= -2(3m+3) please help asap
Answers
Answer:
m = 0.421
Step-by-step explanation:
5.4(m-2)= -2(3m+3) (expand parentheses by distributive property)
m(5.4) -2(5.4) = 3m(-2) + 3(-2)
5.4m - 10.8 = -6m - 6 (add 6m to both sides)
5.4m - 10.8 + 6m = - 6
11.4m - 10.8 = - 6 (add 10.8 to both sides)
11.4m = -6 + 10.8
11.4m = 4.8 (divide both sides by 11.4)
m = 4.8 / 11.4
m = 0.421
Answer:
m = 8/19
Step-by-step explanation :
5.4 (m-2) = -2 (3m +3)
54/10 (m-2) = (3m +3) as n = 1
2.3^3 / 2.5 (m-2) = (3m + 3)
4.868 (m-2) = (3m +3)
4.868 + 3 = (3m^2 * m-2)
8 / 9.5 * 2
m = 8 / 19
Circles
1. RS and ST are tangent lines. Find the value of x.
R
9x - 30
c.
S
3x
T
Answers
Answer:
x = 15
Step-by-step explanation:
9x-30 = 3x (tangent lines are congruent)
- move the variables to one side
9x-3x=30
6x=30
x=5
--------------
9(5)-30=3(15)
45-30=15
15=15
Done!
x = 15
the formula for a trapezoid is A= 1/2h(b1+b2) which equations are equivalent to the formula
Answers
Answer:
A=[tex]\frac{a+b}{2} (h)[/tex]
Step-by-step explanation:
Option first, option second, and option fourth are correct this expression is equivalent to the formula for a trapezoid.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
The options are:
h=2A/(b1+b2)b1=2A/h - b2b2= 2A/b1 - hb2= 2A/h - b1b1= 2A//b2 - hWe have a formula for finding the area of the trapezoid:
[tex]\rm A= \dfrac{1}{2}h(b_1+b_2)[/tex]
Make a subject h and solve for h:
[tex]\rm \dfrac{2A}{(b_1+b_2)}= h[/tex]
or
[tex]\rm h = \dfrac{2A}{(b_1+b_2)}[/tex]
[tex]\rm b_2 = \dfrac{2A}{h}- b_1[/tex]
[tex]\rm b_1 = \dfrac{2A}{h}- b_2[/tex]
Thus, option first, option second, and option fourth are correct this expression is equivalent to the formula for a trapezoid.
Learn more about the trapezoid here:
brainly.com/question/8643562
#SPJ1
Name five fractions between 6/7 and 9/10
Answers
Answer:
43/50, 22/25, 111/125, 1111/1250, and 179/200.
Step-by-step explanation:
6/7 = 0.8571428571
9/10 = 0.9
The fractions can be anywhere within that range.
The first fraction I would name would be a fraction that equals 0.86. 0.86 = 86/100 = 43 / 50.
The second fraction can be a fraction that equals 0.88. 0.88 = 88 / 100 = 44 / 50 = 22 / 25.
The third fraction will equal 0.888. 0.888 = 888 / 1000 = 444 / 500 = 222 / 250 = 111 / 125.
The fourth fraction will equal 0.8888. 0.8888 = 8888 / 10000 = 4444 / 5000 = 2222 / 2500 = 1111 / 1250.
The fifth fraction can equal 0.895. 0.895 = 895 / 1000 = 179 / 200.
Hope this helps!
Answer:
43/50, 22/25, 111/125, 1111/1250, and 179/200.
Step-by-step explanation:
6/7 = 0.8571428571
9/10 = 0.9
The fractions can be anywhere within that range.
The first fraction I would name would be a fraction that equals 0.86. 0.86 = 86/100 = 43 / 50.
The second fraction can be a fraction that equals 0.88. 0.88 = 88 / 100 = 44 / 50 = 22 / 25.
The third fraction will equal 0.888. 0.888 = 888 / 1000 = 444 / 500 = 222 / 250 = 111 / 125.
The fourth fraction will equal 0.8888. 0.8888 = 8888 / 10000 = 4444 / 5000 = 2222 / 2500 = 1111 / 1250.
The fifth fraction can equal 0.895. 0.895 = 895 / 1000 = 179 / 200.
Rearrange the tiles so that it shows the proper steps of solving this quadratic equation using square property
Answers
Answer:
see explanation
Step-by-step explanation:
Given
(x + 2)² = 25 ( take the square root of both sides )
x + 2 = ± [tex]\sqrt{25}[/tex] ← Step 1
x + 2 = ± 5 ← Step 2 ( subtract 2 from both sides )
x = - 2 ± 5 ← Step 3
Find all real zeros of the function.
g(x) = 2x (x - 5)2(x – 9)?
If there is more than one answer, separate them with commas.
zero(s):
Answers
Answer:
0, 5, 9
Step-by-step explanation:
g(x) = 2x (x - 5)^2(x – 9) = 0
x = 0 or x - 5 = 0 or x - 9 = 0
x = 0 or x = 5 or x = 9
It’s on khan academy
HELPP (ESPECIALLY PART B) Answer the questions in this part of the task based on your understanding of the definition and the standard equation for the conic you chose. part a Inspect the equation for the type of conic section you chose. What attributes are necessary to graph it? Be sure to include specific points or equations to complete your answer. part b Explain how, if you have the attributes given below for the conic you chose, you can derive its equation in standard form.
Answers
The conic section chosen is a parabola, and the attributes for graphing of
a parabola as well as the standard form of the equation are as follows;
Part A: The attribute necessary to graph the equation of the parabola are three points, including, the vertex, the y-intercept and the image of the reflection of the y-intercept across the axis of symmetry.Part B: The equation in standard form is x = -0.25·y² + y + 3Reasons:
Part A:
The equation of the conic section of a parabola is; (x - 3)² = 12·(y - 2)
The vertex form of the equation of a parabola is; y = a·(x - h)² + k
Where (h, k) = The vertex
Rearranging the given equation gives;
(x - 3)² = 12·y - 24
12·y - 24 = (x - 3)²
12·y = (x - 3)² + 24
[tex]\displaystyle y = \frac{1}{12} \cdot \left(x - 3\right)^2 + \frac{24}{12} = \frac{1}{12} \cdot \left(x - 3\right)^2 + 2[/tex]
[tex]\displaystyle y = \frac{1}{12} \cdot \left(x - 3\right)^2 + 2[/tex]
Therefore, the vertex of the parabola, (h, k) = (3, 2)
At the y-intercept, x = 0, which gives;
[tex]\displaystyle y = \frac{1}{12} \cdot \left(0 - 3\right)^2 + 2 = \frac{9}{12} + 2 = 2+\frac{3}{4}[/tex]
[tex]\displaystyle y = 2+\frac{3}{4} = 2.75[/tex]
The y-intercept = (0, 2.75)
The x-intercept is given at the point where y = 0, which gives;
(x - 3)² = 12·(0 - 2) = -24
x - 3 = √(-24) = An imaginary number
Therefore, the graph has no x-intercept
Given that a parabola is symmetrical about the vertex, we have a third
point on the parabola at the image of the y-intercept reflected across the
axis of symmetry as follows;
The y-intercept (0, 2.75) is 3 units to the left of the axis of symmetry, x = 3,
therefore, the third point will be 3 units to the right of the axis of symmetry
at the point (3 + 3, 2.75) = (6, 2.75)
Therefore, using the three points, (0, 2.75), (3, 2), and (6, 2.75), the curve
representing the parabola, (x - 3)² = 12·(y - 2), can be drawn.
Please find attached the graph of the parabola created with MS Excel
Part B; Given the attributes of the parabola; Vertex: (4, 2) and focus: (3, 2), we have;
The focus of a parabola is the point (h + p, k)
Where, (h, k) = The vertex
Therefore, by comparison, we have;
(h, k) = (4, 2)
h + p = 3
Therefore;
4 + p = 3
p = 3 - 4 = -1
The vertex form of the equation of the parabola is; (y - k)² = 4·p·(x - h)
Therefore, we get;
(y - 2)² = 4 × (-1) × (x - 4) = -4·(x - 4)
y² - 4·y + 4 = 16 - 4·x
4·x = 16 - (y² - 4·y + 4) = -y² + 4·y + 12
Which gives, the standard form as follows;
[tex]\displaystyle x = -\frac{y^2}{4} + y + 3 = -0.25 \cdot y^2 + y + 3[/tex]
Standard form of the the equation of the parabola; x = -0.25·y² + y + 3Learn more about the graph of a parabola here:
https://brainly.com/question/2489929
PLS HELP WILL GIVE BRAINLIEST
Answers
Explanation: none of them logically makes any sense in that form
Which relation is a function? {(–4, –6), (–3, –2), (1, –2), (1, 0)} {(–2, –12), (–2, 0), (–2, 4), (–2, 11)} {(0,1), (0, 2), (1, 2), (1, 3)} {(8, 1), (4, 1), (0,1), (–15, 1)}
Answers
Answer:
[tex]\{(8, 1), (4, 1), (0,1), (-15, 1)\}[/tex]
Step-by-step explanation:
Given
[tex]\{(-4, -6), (-3, -2), (1, -2), (1, 0)\}[/tex]
[tex]\{(-2, -12), (-2, 0), (-2, 4), (-2, 11)\}[/tex]
[tex]\{(0,1), (0, 2), (1, 2), (1, 3)\}[/tex]
[tex]\{(8, 1), (4, 1), (0,1), (-15, 1)\}[/tex]
Required
Determine which is a function
A relation is divided into 2; (x,y)
Where x represents the range and y stands for the domain
For a relation to be a function, the x column must be unique; in other words, there must be only one occurrence of x
Testing each of the given options
A. [tex]\{(-4, -6), (-3, -2), (1, -2), (1, 0)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](-4, -6)[/tex]
[tex](-3, -2)[/tex]
[tex](1, -2)[/tex]
[tex](1, 0)[/tex]
Notice that the third and fourth relation has the same x value of 1;
Hence, this is not a function
B. [tex]\{(-2, -12), (-2, 0), (-2, 4), (-2, 11)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](-2, -12)[/tex]
[tex](-2, 0)[/tex]
[tex](-2, 4)[/tex]
[tex](-2, 11)[/tex]
Notice that all relations has the same x value of -2;
Hence, this is also not a function
C. [tex]\{(0,1), (0, 2), (1, 2), (1, 3)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](0, 1)[/tex]
[tex](0, 2)[/tex]
[tex](1, 2)[/tex]
[tex](1, 3)[/tex]
Notice that the first and second relation has the same x value of 0 and the third and fourth relation has the same x value of 1;
Hence, this is also not a function
D. [tex]\{(8, 1), (4, 1), (0,1), (-15, 1)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](8, 1)[/tex]
[tex](4, 1)[/tex]
[tex](0, 1)[/tex]
[tex](-15, 1)[/tex]
Notice that relation has the unique x values of 8, 4, 0 and -15
Hence, this relation is a function
Which statement best compares the two functions?
The minimum of function A occurs 1 unit higher than the minimum of function B.
The minimum of function A occurs 3 units higher than the minimum of function B.
The minimum of function A occurs 5 units lower than the minimum of function B.
The minimum of function A occurs 7 units lower than the minimum of function B.
Answers
Answer:The minimum of function A occurs 1 unit higher than the minimum of function B.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Trust
if f(x) -3 and g(x) = 3x2+x-6, find (f+9)(x).
A. 4x2 - 9
B. 3x2 + x - 3
C. 3x2 + 2X-9
D. 3x2 - 4x = 3
Answers
Answer:
3x^2 +x -3
Step-by-step explanation:
f(x)= 3 and g(x) = 3x^2+x-6
f+g (x) = 3+ 3x^2+x-6
Combine like terms
= 3x^2 +x -3
I hope this helps
P. The inventory of a store 2 years ago was worth $45,000. This year it is
worth $49,500. What is the percent increase? Show your work
Answers
Answer:10% increase
Step-by-step explanation:
49500-45000=4500
4500/45000=0.1
0.1x100=10
10% increase
Answer:
10%
Step-by-step explanation:
follow the rules of calculating percentages.
fractions, decimals, etc.
pls mark brainliest
Simplify (−3c3w5)3. −9c6w8 −9c9w15 −27c6w8 −27c9w15
Answers
Answer:-9c3w5-36c6w8-36c9w15
Answer:
-27c⁹w¹⁵ the last choice
Step-by-step explanation:
Simplifying:
(−3c³w⁵)³= ⇒ each factor gets same power- 3³(c³)³(w⁵)³ = ⇒ power of power = product of powers- 27c⁹w¹⁵ ⇒ correct answer choice is the last oneA rope is cut into three pleces. The lengths are given as 2ab(a - b), 3^2(a + 2b), and b^2 (2a - b).
The expression representing the total length of the rope is_____?
If a = 2 inches and b = 3 inches, the total length of the rope is ____?
inches.
Answers
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]2ab(a-b)+3a^2(a+2b)+b^2(2a-b)\\\\=2a^2b-2ab^2+3a^3+6a^2b+2ab^2-b^3\\\\=\boxed{3a^3-b^3+8a^2b}[/tex]
For a = 2, b = 3 the total is
[tex]3\cdot 2^3-3^3+8\cdot 2^2 \cdot 3\\\\=3*8-27+96\\\\=24-27+96\\\\=\boxed{93}[/tex]
Thank you
Its very confusing so sry
help me plz i wnt help plz i want help
Answers
Answer:
C)28in
Step-by-step explanation:
To get the area of this face, we will divide it into 3 sections.
Area of the 1st section:
Given:
l=4in
w=2in
Formula:
a=l*w
Solution:
a=l*w
a=8in^2
Area of the 2nd section:
Given:
l=2in
w=2in
Formula:
a=l*w
Solution:
a=l*w
a=2in*2in
a=4in^2
Area of the 3rd section:
l=8in
w=2in
Formula:
a=l*w
Solution:
a=l*w
a=8in*2in
a=16in^2
a1+a2+a3=Area of the face
8in^2+4in^2+16in^2=28in^2
Hope this helps ;) ❤❤❤
Annie tried to solve a problem step by step: 7.5 + k = 10 7.5 + k - 7.5 = 10 - 7.5 step 1 k = 2.5 step 2 Find Annie's mistake: A. Step 1 B. Step 2 C. Annie did not make a mistake
Answers
Answer:
(C) Annie did not make a mistake
Step-by-step explanation:
To isolate the variable k in the equation [tex]7.5 + k = 10[/tex], we'd have to subtract 7.5 from both sides so we just had k on one side.
This is exactly what Annie did, and therefore, her answer is correct.
Hope this helped!
Answer:
C. Annie did not make a mistake
Step-by-step explanation:
Substitute 2.5 for k in the equation and see if it is correct
Each time you substitute you should see that Annie answered the equation correctly
pls help...1.The given right rectangular prism is composed of small cubes. Find the following is the volume of the prism and the volume of one of the small cubes.
Answers
Answer:
1. 1.3778 2. 0.0089
Step-by-step explanation:
to find the volume of the whole rectangle prism you would have to do the volume formula since it is a 3d shape. VOLUME FORMULA, LxWxH.
so 1x0.83x1.66= 1.3778
you can always convert the fraction into decimal to help you calculate the problem.
i don't know if this is correct but i give it a try, so if the whole volume of the triangle is 1.3378 than you can divide that by the the number of small cubes it has inside.
it is 5 by 10 so there are 150 cubes in total.
1.3378 divided by 150=0.0089
im confident about the 1st but not so much with the second
The volume of the rectangular prism is: 1.39 ft³
The volume of one of the small cubes is: 0.0046 ft³
What is the Volume of a Rectangular Prism?Volume of rectangular prism = length × width × height
Given the following:
Length = 1 ft
Width = 5/6 ft
Height = 1⅔ ft
Volume of the rectangular prism = 1 × 5/6 × 1⅔ = 1 × 5/6 × 5/3
Volume of the rectangular prism = 25/18 = 1 7/18 ft = 1.39 ft³
Length of the edge of 1 cube = 1/6 ft
Volume of the 1 cube = (1/6)³ = 1/216 = 0.0046 ft³
Learn more about volume of rectangular prism on:
https://brainly.com/question/12917973
simplified?
[tex]5 \sqrt{ - 8r} [/tex]
Im just confused on how the negative 8 will play out, and same with the non exponential variable.
Answers
Answer:
[tex]10i\sqrt{2r}[/tex].
Step-by-step explanation:
[tex]5\sqrt{-8r}[/tex]
= [tex]5\sqrt{-1 * 2 * 2 * 2 * r}[/tex]
= [tex]5i\sqrt{2^2 * 2 * r}[/tex] (i = the square root of -1)
= [tex]5i * 2\sqrt{2 r}[/tex]
= [tex]10i\sqrt{2r}[/tex]
Hope this helps!
5i*sqrt(8r) =
10i*sqrt(2r)
The i is an 'imaginary number' and it represents the square root of -1.
Town B is 250 km from town A on a bearing of 080°.
Town C is 250 km from town B on a bearing of 220°.
What is the bearing from town A to town C?
Answers
Answer:
Step-by-step explanation:
The answer would be 140
cqn someone answer this?
Answers
Answer:
-3Step-by-step explanation:
-11/2+27/4+(-17/4)(-22+27-17)/4(-12)/4-3help plz help me .me no good
Answers
Answer:
50,000,000
Step-by-step explanation:
5 * 10 ^7
The 7 in the exponent means move the decimal 7 places to the right
5. We need to add 7 zeros
50000000
50,000,000
On a map’s coordinate grid, Panthersville is located at (−3, 2), and Heel City is located at (4, 8). Falconton is the midpoint between Panthersville and Heel City. What is the approximate distance from Panthersville to Falconton? (Each unit on the grid represents 1 mile.) A. 3.25 miles B. 4.61 miles C. 5.00 miles D. 9.22 miles
Answers
Answer:
The approximate distance from Panthersville to Falconton is: B: 4.61 miles.
Step-by-step explanation:
Objective: Find the distance from Panthersville to Falconton. (Which is just half of the distance from Panthersville to Heel City because Falconton is the midpoint between both cities.)
First we need to find the distances from Panthersville to Heel City, which we are given the coordinates. ( Panthersville (-3,2) & Heel City (4, 8) )
-To find the distance between the two cities we use the distance formula:
d= √(x2 - x1) ^2 + (y2 - y1)^2 , so we set (-3,2) as x1 and y1 while (4,8) x2 and y2 and we just plug it in.
Once we plug it in we get:
d= √(4 - -3)^2 + (8 - 2) ^2
Then we solve the numbers in the parenthesis (4 - -3) = 7 and (8 - 2) = 6 so now we have:
d= √(7)^2 + (6) ^2
Next we solve for the exponents (7)^2 = (7 x 7 = 49) and (6)^2 = ( 6 x 6= 36) now it look like this:
d= √49 + 36
After that we just add both numbers together (49 + 36) = 85
d= √85
Now all we have to do is square root 85 which is just 9.219544457, just round it to the nearest hundredth and you will get 9.22.
So the distance from Panthersville to Heel City is about 9.22 miles.
Now we found the full distance we now need to find the distance from Panthersville to Falconton which is just half of that distance due to Falconton being the midpoint.
All we have to do is divide 9.22 by 2 and we get 4.61.
The distance from Panthersville to Falconton is 4.61 miles.
