Given:
The pair of points.
5. P(1, 1), Q(–1, –1)
6. [tex]E\left(\dfrac{1}{2},4\dfrac{1}{4}\right), F\left(5,-\dfrac{1}{2}\right)[/tex]
To find:
The distance between the pair of points.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
5.
The distance between the pair of points P(1, 1) and Q(–1, –1) is:
[tex]PQ=\sqrt{(-1-1)^2+(-1-1)^2}[/tex]
[tex]PQ=\sqrt{(-2)^2+(-2)^2}[/tex]
[tex]PQ=\sqrt{4+4}[/tex]
[tex]PQ=\sqrt{8}[/tex]
[tex]PQ=2\sqrt{2}[/tex]
Therefore, the distance between P and Q is [tex]2\sqrt{2}[/tex].
6.
The distance between the pair of point [tex]E\left(\dfrac{1}{2},4\dfrac{1}{4}\right), F\left(5,-\dfrac{1}{2}\right)[/tex] is:
[tex]EF=\sqrt{\left(5-\dfrac{1}{2}\right)^2+\left(-\dfrac{1}{2}-4\dfrac{1}{4}\right)^2}[/tex]
[tex]EF=\sqrt{\left(\dfrac{10-1}{2}\right)^2+\left(-\dfrac{1}{2}-\dfrac{17}{4}\right)^2}[/tex]
[tex]EF=\sqrt{\left(\dfrac{9}{2}\right)^2+\left(\dfrac{-2-17}{4}\right)^2}[/tex]
[tex]EF=\sqrt{\dfrac{81}{4}+\left(\dfrac{-19}{4}\right)^2}[/tex]
On further simplification, we get
[tex]EF=\sqrt{\dfrac{81}{4}+\dfrac{361}{16}}[/tex]
[tex]EF=\sqrt{\dfrac{324+361}{16}}[/tex]
[tex]EF=\sqrt{\dfrac{685}{16}}[/tex]
[tex]EF=\sqrt{42.8125 }[/tex]
[tex]EF\approx 6.5[/tex]
Therefore, the distance between E and F is 6.5 units.
can someone help please
Peggy is laying 60 ft from the base of a tree. The angle of elevation for her to see
the top of the tree is 50º. Use a trigonometric ratio and calculator to find the
height of the tree to the nearest tenth of a foot.
Answer:
The height of the tree is approximately 71.5 feet
Step-by-step explanation:
The given parameters are;
The angle of elevation to see the top pf the tree = 50°
The distance Peggy is laying from the base of the tree = 50 ft.
In order to answer the question using trigonometric ratio, we assume that the angle the tree makes with the ground is 90° that is the tree is perpendicular to the ground
Therefore, the line of sight to the top of the tree, the height of the tree, and the distance from the base of the tree where Peggy is laying, forms a right triangle
Let, 's', represent the line of sight to the top of the tree, let 'h', represent the height of the tree, and let, 'd', represent the distance from the base of the tree where Peggy is laying
The third angle, θ, of the right triangle opposite 'd' is given by angle sum theorem of a triangle as follows;
θ = 180° - 90° - 50° = 40°
θ = 40°
By sine rule we have;
h/sin(50°) = d/(sin θ)
∴ h/sin(50°) = 60 ft./(sin 40°)
h = sin(50°) × 60 ft./(sin 40°) = 71.5052156 ft.
∴ The height of the tree, h ≈ 71.5 ft. by rounding to the nearest tenth
An Experienced ice skater spins on the ice, creating a perfect circle with a diameter of 4 feet. What is the circle's radius?
Answer:
2
Step-by-step explanation:
the radius is half the diameter from the middle!
The distance between points F and H is 3 units, and the distance between points H and G is 4 units. What is the distance between points F and G?
Answer:
[tex] {4}^{2} + {3}^{2} = 16 + 9 = \sqrt{25} = 5[/tex]
In this function, if the value of r were to increase, would the value represented by P also increase or stay the same? Why? Explain your answer using terms such as "rate of growth" and "initial value" in the context of the coin problem.
Answer:
P will remain the same
Step-by-step explanation:
Given
[tex]V(t) = P(1 + r)^t[/tex] --- Coin value formula [Missing from the question]
Required
What happens to p when r increases
The coin value function is an exponential function which is of the general form:
[tex]y = a(1 + b)^x[/tex]
From the given function: [tex]V(t) = P(1 + r)^t[/tex]
P represents the initial value and r represents the rate
The rate of change (r) and the initial value (P) of a function are both independent, and they do not depend on one another for their values.
An increment or decrement in r will not affect the value of P.
Conclusively, when the rate (r) changes, the initial value (P) will remain the same.
2/3x - 7 < 9
help please
Answer:
x<24
*the answer will be incorrect if you meant 2/(3x) instead of (2/3)x
Step-by-step explanation:
First, add 7 to both sides of the inequality to get "2/3x<16." Then multiply both sides by 3 to get "2x<48." Finally, divide both sides by 2 to get "x<24"
for the table below, what is the range?
Answer:
second option
Step-by-step explanation:
mark me brainliest pls
Point p is the interior of angle abc. If angle abc=125deg and angle abp=62deg, what is the angle pbc?
Answer: The angle ∠ PBC is 63°.
Step-by-step explanation:
Given: Point P is in the interior of ∠ABC.
∠ ABC = 125°
∠ABP= 62°
To find : ∠ PBC
Since P is in the interior of ∠ABC.
Then
∠ ABC = ∠ABP + ∠ PBC
⇒ 125°= 62°+ ∠ PBC
⇒ ∠ PBC= 125° - 62°
⇒ ∠ PBC= 63°
Hence, the angle ∠ PBC is 63°.
How do I solve this equation? 2/3(x-4)=1/2
Answer:
19/4
Step-by-step explanation:
the answer is 19/4.From the photo
Please give me the correct answer.
Answer:
1:2
Step-by-step explanation:
The left side goes up one when the left goes up 2
Felipe grows tomatoes.
0
20
60
80
The box plot shows information about
the weights of Felipe's tomatoes.
40
Weight (grams)
Felipe says “at least half of my tomatoes weigh more than 50 grams each".
a) Which of the statements below describes Felipe's statement best?
A- He is correct because the Median weight is 48 grams.
B - He is wrong because the Median weight is above 50 grams.
C - He is correct because the Median weight is 56 grams.
(1)
b) Work out the range of weights of Felipe's tomatoes.
(1)
c) Work out the interquartile range of weights of Felipe's tomatoes.
(1)
Answer:
a) c
b) 62
Step-by-step explanation:
He is correct because the Median weight is 56 grams.
Option C is the correct answer.
The range of weights of Felipe's tomatoes is 62.
The interquartile range of weights of Felipe's tomatoes is 44 grams.
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
From the box plot,
Median = 56 grams
Now,
The statement that Felipe describe is correct because the median weight of 56 grams.
The range of the weights of the tomatoes.
= Highest value - Lowest value
= 78 - 16
= 62
The interquartile range of weights of Felipe's tomatoes.
= Upper quartile - Lower quartile
= 72 - 28
= 44 grams
Thus,
Median weight = 56 grams.
Range = 62
Interquartile range = 44 grams.
Learn more about median here:
https://brainly.com/question/28060453
#SPJ2
I NEED HELP OW RN rn please
Answer:
(4,10)
Step-by-step explanation:
Well, you just count each unit coming from the x-axis up and then do the same for the y axis going to the right. You can also see that the graph is counting by 2 if you look at the "O" coordinate
Each time Caroline goes shopping she decides whether or not to buy fruit.
The probability that she does buy fruit is 0.4.
Independently, she then decides whether or not to buy a CD, with a probability of 0.3 that she does buy a CD.
Work out the probability that she buys fruit or buys a CD or both.
Answer: 0.58
Step-by-step explanation:
Step 1 : Caroline buys fruit and buys cd ( buys both) = 0.12 ( 0.4 x 0.3)
Step 2 : Caroline buys fruit and not cd = 0.28 ( 0.4 x 0.7)
Step 3 : Caroline doesn't buy fruit but buys cd = 0.18 ( 0.6 x 0.3 )
STEP 4 (FINAL STEP) : Add all the probabilities ( 0.12 + 0.28 + 0.18)
Answer: 0.58
Step-by-step explanation:
Step 1 : Caroline buys fruit and buys cd ( buys both) = 0.12 ( 0.4 x 0.3)
Step 2 : Caroline buys fruit and not cd = 0.28 ( 0.4 x 0.7)
Step 3 : Caroline doesn't buy fruit but buys cd = 0.18 ( 0.6 x 0.3 )
STEP 4 (FINAL STEP) : Add all the probabilities ( 0.12 + 0.28 + 0.18)
ANSWER = 0.58
Evaluate:
(15 +12) - 3 to the second power
Answer:
Step-by-step explanation: (15+12)-3^2 power ------> 27-3^2 power ----> 27-9 ----> equals 18
ANSWER:
18
SOLUTION:
(15+12) -3^2
(15+12) = 27
=27-3^2
=27- 9
=18
anyone help pls!! will mark brainliest
Answer:
2.5 cm is the radius
Step-by-step explanation:
What is the value of' x'?
B.
D
3 ft
6 ft
A
С
4 ft
E
F
Х
help pls
Answer:
7..the way you worded the options was confusing
The path of an athlete's long jump is modeled by a function h(d)=−14d2+d, where d and h denote the distance and the height in meters respectively. The graph of h(d) is given by
Answer:9ft
Step-by-step explanation:
Which of the following is a one-to-one functions?
Answer:
A function f : X → Y is said to be one to one (or injective function), if the images of distinct elements of X under f are distinct, i.e., for every x1 , x2 ∈ X, f(x1 ) = f(x2 ) implies x1 = x2 . Otherwise, it is called many to one function.
Can someone help me with these word problems?
Answer:
First Answer: 12.5 weeks
Third Answer: 16 minutes(I think it was a really long decimal so I rounded it up)
In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=83°, and RS = 7 feet. Find the length of SQ to the nearest tenth of a foot.
Answer:
Step-by-step explanation
….
Answer: 0.9
Step-by-step explanation:
Elena raised $84 to support the animal shelter, which is 30% of her fundraising goal. What is Elena's fundraising goal
Find the value of h(45) for the function below.
Answer:
I agree with her her explain and her solving
the lengths of the sides of a triangle are 2n, n^2 and n+5 for what value of n do these lengths not make a triangle ?
Answer:
Step-by-step explanation:
Try n = 2
2n = 4
n^2 = 4
n+5 = 7 That works. It will make a triangle since the 2 smallest numbers are bigger than 7
Try n = 3
2n = 6
n^2 = 9
n + 5 = 8 That works. Same reason as above.
n = 4
2n = 8
n^2 = 16
n + 5 = 9 That works. Same reason.
n = 5
2n = 10
n^2 = 25
n+5 = 10 Aha! That doesn't work. the two smaller numbers only = 20.
There are likely many numbers that don't work. I'll try one more
n = 6
2n = 12
n + 5 = 11
n^2 = 36 This won't work either. Same reason as n = 5.
Could anybody help me with these few they're awfully confusing to me.
Answer:
how can I be of help
can't see anything actually
The tape diagram represents an equation.
I will give you a brainlist
A basketball court is a rectangle that is 28\,\text{m}28m28, start text, m, end text long and 15\,\text{m}15m15, start text, m, end text wide. A diagram on a coordinate plane shows a circle in the middle of the court centered at (0\,\text{m},0\,\text{m})(0m,0m)left parenthesis, 0, start text, m, end text, comma, 0, start text, m, end text, right parenthesis. The point (0.8\,\text{m}, 1.5\,\text{m})(0.8m,1.5m)left parenthesis, 0, point, 8, start text, m, end text, comma, 1, point, 5, start text, m, end text, right parenthesis is on the circumference of the circle.
Approximately what percentage of the court does the circle cover?
Answer:
48
Step-by-step explanation:
Answer:
B, 2%
Step-by-step explanation:
EASY 7TH GRADE MATH! FIRST PERSON MARKED BRAINLIEST, NEED HELP NOW!!!
Answer:
slope of 2 and y-intercept of 1
(3rd answer choice)
Step-by-step explanation:
Answer:
It's the last one doesn't matter which way you go they are both going to the negative way because they are going down and to the left so they are both negative. I hope this helps good luck.
Help please i don’t understand
Answer:
B or C
Step-by-step explanation:
Can someone help me?????
2. What is the area of the half circle ?
20 points
9 in
A) 31.7925 square feet
B) 63,585 square feet
C) 127.17 square feet
D) 254 34 square feet