The estimated distance between the park and your school is 5 miles.
Here,
To estimate the distance between the park and your school, we can use the Pythagorean theorem, as the distance forms a right-angled triangle with the school, apartment, and park as its vertices.
Let's label the points as follows:
S = School
A = Apartment
P = Park
Given:
School (S) is 4 miles east and 1 mile south of the apartment (A).
Park (P) is 3 miles east and 4 miles south of the apartment (A).
Now, we have two right-angled triangles:
The triangle formed by S, A, and P. This is the triangle for which we want to estimate the distance between the school and the park.
The triangle formed by A, S, and P.
Since both triangles share the side AS (4 miles east), we can use the Pythagorean theorem for the triangle ASP to find the distance between the school and the park.
The Pythagorean theorem states that for a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, let's represent the distance between the school and the park as d (the hypotenuse), and the other two sides as 3 miles (east) and 4 miles (south).
Using the Pythagorean theorem:
[tex]d^2 = 3^2 + 4^2\\d^2 = 9 + 16\\d^2 = 25\\[/tex]
Now, take the square root of both sides to find d:
d = √25
d = 5
So, the estimated distance between the park and your school is 5 miles.
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Find the sum of -2 + i and its complex conjugate.
Write your answer in the form a + bi.
Answer:
- 4
Step-by-step explanation:
The conjugate of - 2 + i is - 2 - i, thus
- 2 + i + (- 2) - i
= - 2 + i - 2 - i ← collect like terms
= - 4 ← in the form a + bi with b = 0
The sum of -2 + i and its complex conjugate is:
w = -4 + 0i
How to find the sum?
The complex conjugate of a number z = a + bi is:
z' = a - bi.
Then the complex conjugate of -2 + i is -2 - i.
The sum will give:
w = -2 + i + (-2 - i) = -4 + 0
Writing it in the wanted form we get:
w = -4 + 0i
If you want to learn more about complex numbers, you can read:
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Apothem = (the answer is a sqaure root)
Answer:
[tex]\sqrt{20}[/tex]
Step-by-step explanation:
To find the Apothem of a shape, we need to find how long the distance is from a vertex to the center of the shape.
We can see that they've already showed us how to do it: We need to find the length of the hypotenuse of the red triangle.
To do this, we can use the Pythagorean Theorem, which states that [tex]a^2 + b^2 = c^2[/tex].
We know that a is going to be half of 4, which is 2. We also know that b is going to be 4, so we can substitute inside the equation.
[tex]2^2 + 4^2 = c^2\\\\4 + 16 = c^2\\\\20=c^2\\\\c=\sqrt{20}[/tex]
Hope this helped!
Draw a diagram. Write the Segment Addition Postulate for the points described. Then solve for missing length.
9. T is between M and N if NT=x+5, MN=3x, and MT=7, what is MN?
Please show all work and not just answers.
Answer:
MN= 18
Step-by-step explanation:
NT=x+5
MN=3x
MT=7
MT+NT=MN
=>7+x+5=3x
=>12+x=3x
=>x-3x=-12
=>-2x=-12
=>x=12/2
=>x=6
MN=3x=3 * 6 = 18
List the values in ascending order: -94%, -8/9, -.925, and -9/10
Answer:
-94%, -.925, -9/10, -8/9
Step-by-step explanation:
-.94, -.8, -.925, -.9
-.94, −0.925, −0.9, -0.8
C=2pi r. What is pi?
Answer: 3.14
Step-by-step explanation:
A ceramics teacher divided 20kg of clay as equally as possible among the 29 students in her class. About how much clay did each student get?
Answer:
.69 rounded to the nearest hundredth
Step-by-step explanation:
T is the midpoint of S and U. ST=7x+4 & TU=10x-2. What is the value of SU?
Answer:
SU = 36
Step-by-step explanation:
T is the mid point so the distance of ST and TU is the same. Since ST and TU are the same, 7x + 4 = 10x - 2.
Solve for x
7x + 4 = 10x - 2
7x - 10x = - 2 - 4
-3x = -6
x = 2.
Find SU
SU = ST + TU
= (7x + 4) + (10x - 2)
substitute the value for x into the equation (x=2)
[7(2) + 4] + [10(2) - 2] = 36
I hope this helps :)
Describe a ratio in words about the coins that compares the whole coin collection to one part of it. Then write the ratio in at least two different ways.
Answer:
Kindly check explanation
Step-by-step explanation: A ratio which compares a whole coin collection to a part of it would be expressed in such a way that, the numerator will be the part of the coin which is being compared and the denominator being the value of the entire coin. Mathematically, It could be expressed in proportion form as ;
(Part or amount of the coin which is being compared / total value of entire coin)
A / B such that;
A = value or amount of coin which is being compared.
B = value of the entire coin.
Or in the form
A : B
part of coin being compared : blue of entire coins
b) Sajid makes a scale model of a lorry.
He uses a scale of 1:32
The length of Sajid's model lorry is 45 cm.
Chitra makes a scale model of the same lorry.
She uses a scale of 1:72
Work out the length of Chitra's model lorry.
Can y’all help please
Answer:
-4, 4
Step-by-step explanation:
it seems the most reasonable answer since the dot is not super close to the 6, 6 and it isnt close enough to be 1, 5 or 5, 1 so the answer must be -4, 4
if 5 a solution of 3x + 30 = 9x?
Answer:
x = 5
Step-by-step explanation:
This equation can be rearranged in order to easily solve.
First, rearrange the equation by simply flipping it.
3x + 30 = 9x → 9x = 3x + 30
Then, you may solve for x.
9x = 3x + 30 subtract 3x from both sides of the equation
6x = 30 divide by 6 on both sides of the equation
x = 5
IF DE = 10x + 12, EF = 4x - 15, and DF = 2x + 21, find DF. [In your solution, put
DF =YOUR ANSWER]
Answer:
Hey there!
10x+12+4x-15=2x+21
14x-3=2x+21
12x=24
x=2
DF= 2x+21
DF=4+21
DF=25
Let me know if this helps :)
Lines b and c are parallel. Which pairs of angles are supplementary?
Select all that apply.
1 and 8
2 and 4
3 and 5
6 and 7
Answer:
3 and 5
The angles that are vertically adjacent to the transversal.. when it cuts two parellel lines are always supplementary.. that is they make 180 degree.. hence, in the given pair 3 and 5 are supplementary..
as they lie on the transversal
sorry for the trouble
Step-by-step explanation:
Hey, there!
As it is a Right angled triangle, taking reference angle as angle B.
hypotenuse (h)= AB
perpendicular (p)= 12
base (b)= 24.
Now, let's look which ratio can be used here as p and b are given. Let's use tan ratio here.( as tan = p/b)
[tex] \tan(theta) = \frac{p}{b} [/tex]
[tex]tan(theta) = \frac{12}{24} [/tex]
[tex] \tan(theta) = \frac{1}{2} [/tex]
or, tan theta = (0.5)
Shifting tan to right side making it inverse.
or, theta = tan inverse (0.5)
Therefore, theta = 26.56° or 27° { by rounding off 26.56° we get 27°}.
Hope it helps......
Please help on this question
Answer:
Hey mate!
Using Unitary Method, we get :
2 people -> 5 hours
1 person -> 5/2 = 2.5 hours
3 people -> 2.5 hours * 3 peoples
-> 7.5 hours
-> 7.5 * 60 = 450 mins.
I am always glad to help :)
Answer:
3 people can plow a field in 450 minutes.
Step-by-step explanation:
This is a rate/ratio problem, so we have to make sure it's fully simplified.
First, you already know the ratio is 2 people can plow a field in 5 hours, so 2:5.
But that's not the unit rate.
To find the unit rate, you find how much an individual by itself can do their work, and divide numerator by denominator.
In this case, you do 5/2: which is 2.5.
It take's 2.5 hours for one person. Now you multiply by 3 people to get the ratio; since you already found the rate.
2.5x3 is 7.5, and that's in hours. 1 hour is 60 minutes, to find 7 hours, you do 60x7 and get 420 minutes. You add 30 minutes from the remaining half hour.
that results in 450 minutes.
3 people can plow a field in 450 minutes.
Laurie was completing the treasurer's report for her son's Boy Scout troop at the end of the school year. She didn't remember how many boys had paid the $24 full-year registration fee and how many had paid a $16 partial-year fee. She knew that the number of boys who paid for a full-year was ten more than the number who paid for a partial-year. If $400 was collected for all the registrations, how many boys had paid the full-year fee and how many had paid the partial-year
Answer:
14 boys paid for the full year fee and 4 boys paid for the partial year fee
Step-by-step explanation:
Create a system of equations, where x is the number that paid for the $24 fee and y is the number that paid for the $16 fee:
24x + 16y = 400
x = y + 10
Solve by substitution by plugging in y + 10 as x:
24x + 16y = 400
24(y + 10) + 16y = 400
Solve for y:
24y + 240 + 16y = 400
40y + 240 = 400
40y = 160
y = 4
Then, plug in 4 as y to find x:
x = y + 10
x = 4 + 10
x = 14
So, 14 boys paid for the full year fee and 4 boys paid for the partial year fee.
There are four triangles and 16 squares what is the simplest was ratio of triangles to squares
Use the number line to find the coordinate of the point with a fraction
distance of 1/6 from A to B. *
10 points
A
B
-8-7-6-5-4-3-2-1
0
1
1
2
3
4
5
6
-5
-1
2
O 1
Answer:
-5
Step-by-step explanation:
Coordinate of A = -7
Coordinate if B = 5
Distance of AB = |-7 - 5| = |-12| = 12
We are asked to find the coordinate of the point that would be ⅙ from the A to B, which is ⅙ of AB.
Let's find what ⅙ of AB is.
AB = 12
Therefore, ⅙ of AB = ⅙*12 = 2.
From point A (-7), we move 2 points towards B which will give us ⅙ from A to B.
The coordinate = -7 + 2 = -5
-5 is the coordinate of the point with a fraction distance of ⅙ from A to B.
How do you solve non-perfect squares to the nearest tenth
Answer:using math
Step-by-step explanation:
When x=3 ,y=16 and when x=6 y=8. Which inverse variation equation can be used to model this function?
Answer:
[tex]y=\frac{48}{x}[/tex]
Step-by-step explanation:
When x = 3, y = 16
When x = 6, y = 8
We need to model the inverse variation.
Inverse Variation : When one value increase another value decrease. But product of both always constant.
[tex]xy=k[/tex]
when x=3, y=16
k=48
When x=6, y=8
k=48
Model of the inverse variation:
[tex]y=\frac{48}{x}[/tex]
Hence, The model of inverse variation is
[tex]y=\frac{48}{x}[/tex]
Answer:
The inverse variation equation can be used to model this function is:
[tex]y=\frac{48}{x}[/tex]
Step-by-step explanation:
An inverse relationship between two variables implies that if the value of one variable increases the value of the other variable will decreases and vice-versa.
The inverse function describing the relationship between x and y is as follows:
[tex]y=\frac{a}{x}[/tex]
Here, a is a constant.
It is provided that when the value of x is 3 the value of y is 16.
Compute the value of a as follows:
[tex]y=\frac{a}{x}[/tex]
[tex]16=\frac{a}{3}\\\\[/tex]
[tex]a=48[/tex]
It is also provided that when the value of x is 6 the value of y is 8.
Compute the value of a as follows:
[tex]y=\frac{a}{x}[/tex]
[tex]8=\frac{a}{6}\\\\[/tex]
[tex]a=48[/tex]
The value of a is 48.
Then the inverse variation equation can be used to model this function is:
[tex]y=\frac{48}{x}[/tex]
(-18)+(-7)+25 my answer was 36 but i just want to confirm
Answer:
0
Step-by-step explanation:
Note that + (- 7) = - 7 , thus
- 18 + (- 7) + 25 = - 18 - 7 + 25 = - 25 + 25 = 0
Which of the following lists has numbers arranged in INCREASING order?
Answer:
C
Step by step explanation:1/7 is greater than 1/8 so 1/7 must go after it. but negative is always less then positive so the correct order is
-1/8, -1/7, 1/8, 1/7
The numbers arranged in increasing order is
-1/8, -1/7, 1/8, 1/7
There are 4 values given:
1/7, 1/8, - 1/7, - 1/8
Negative figures are generally lesser than positive figures
1/7 is greater than 1/8
In negative values, the greater number becomes the smaller number
Therefore,
-1/8 is the the smaller number
Arrangements in increasing order =
-1/8, -1/7, 1/8, 1/7
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Sam found $1.8 After finding the money in his pocket, Sekou finds an additional $0.75 in his backpack. Then he decides to buy a slice of pizza for $1.50. How many packs of gum will he be able to buy after this, if each pack costs $0.13? PLEASE HELP I WILL MARK YOU BRAINLIEST AND PLEASE EXPLAIN
Answer:
Hey there!
Sam's Money=1.80 dollars + 0.75 dollars.
1.80+0.75-1.50=1.05
1.05/0.13= 8.08.
He will be able to buy 8 pieces of gum.
Let me know if this helps :)
Simplify three to the negative ninth divided by three to the negative twelfth
Answer:
27
Step-by-step explanation:
sorry if i'm wrong
If you have a 4 pound bag of soil and you divide it into pots how muh did you put in one pot.
Answer:
1/2 pound
Step-by-step explanation:
8 pots / 8 equal to 1 pot.
4 lbs / 8 1/2 lbs
Answer:
1/2 pound per pot!
Step-by-step explanation:
4 pound to 8 pots
so we create a fraction 4/8
then reduce = 1/2
so 1/2 pound per pot!
Hope this helps! :)
f(x)=x^2+4x-6 a) f(x) can be written in the form (x+m)^2+n find the value of m and the value of n b) use your answer to part (a) to find the positive solution to x^2+4x-6=0
Answer:
see explanation
Step-by-step explanation:
Using the method of completing the square.
Given
f(x) = x² + 4x - 6
add/subtract ( half the coefficient of the x- term )² to x² + 4x
f(x) = x² + 2(2)x 6 + 4 - 4 - 6
= (x + 2)² - 10
with m = 2 and n = - 10
To solve the equation let f(x) = 0 , that is
(x + 2)² - 10 = 0 ( add 10 to both sides )
(x + 2)² = 10 ( take the square root of both sides )
x + 2 = ± [tex]\sqrt{10}[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\sqrt{10}[/tex]
The positive solution is
x = - 2+ [tex]\sqrt{10}[/tex] ≈ 1.16 ( to 2 dec. places )
Combine these radicals.
Answer:
2 root 3 (b)
Step-by-step explanation:
root 27 -root 3
root 27 is 3root 3
3 root 3-root 3
so, 2root3.
I think this is the ans.
Answer:
2 root 3
Step-by-step explanation:
Maiden earned 84$ last week. Peter earned only 12$. Maidens earnings are how many times greater than Peter's. Write an equation for the problem, and solve.
Answer:
7 times greater
Step-by-step explanation:
This is because 84 divided by 12 is 7, so i guess that is your answer.
hope this helps
Represent 3kg 9gm using decimals
Answer:
I did not understand the questions well but If I try it out.
1. the difference b/w Kg and g is 1000,000.
2. as the 3 is kg I only convert the 9 grmas into Kg and it will look like this.
3.000009kgs.
the volume of the box is modeled by the function V (x) = 5x²+ 5x. whats the volume when x=4
Answer:
100
Step-by-step explanation:
V (x) = 5x²+ 5x
x=4
We plug in the x value:
V (x) = 5(4)²+ 5(4)
Now we sovle the equation:
5(4)² + 5(4)
5(16) + 5(4)
80 + 20
= 100
Hope that helps, and sorry if its incorrect
Answer:
100 cubic units
Step-by-step explanation:
just took the test on PLATO