What is the distance between (5, 9), (−7, −7)?
Answers
Answer:
20
Step-by-step explanation:
Use the distance formula to determine the distance between the two points.
\(\text{Distance}=\sqrt{(x_2=x_1)^2+(y_2-y1)^2}\)
Substitute the actual values of the points into the distance formula.
\(\sqrt{((-7)-5)^2+((-7)-9)^2}\)
Simplify.
⇒ Subtract 5 from 7.
\(\sqrt{(-12)^2+((-7)-9)^2}\)
⇒ Raise -12 to the power of 2.
\(\sqrt{144+((-7)-9)^2}\)
⇒ Subtract 9 from -7.
\(\sqrt{144+(-16)^2}\)
⇒ Raise -16 to the power of 2.
\(\sqrt{144+256}\)
⇒ Add 144 and 256.
\(\sqrt{400}\)
⇒ Rewrite 400 as 20².
\(\sqrt{20^2}\)
⇒ Pull terms out from under the radical, assuming positive real numbers.
20
Related Questions
in triangle ABC with the right triangle at vertex C, sin a=35/7
Answers
factorize ma+na+nb+mb
Answers
Answer:
(a + b)(m + n).
Step-by-step explanation:
ma+na+nb+mb
= ma + na + mb + nb
We factor this by grouping:
= a(m + n) + b(m + n) m + n is common to both parts so we have:
(a + b)(m + n)
determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 1, s2/5, s4/5, s6/5, . . .
Answers
Answer: The common ratio r is s2/5 = sqrt(s2), the fifth term is ar^4 = s8/5 = 25s4/5, and the nth term is ar^(n-1) = s2/5 * sqrt(s2)^(n-1).
Step-by-step explanation:
The general form of a geometric sequence is given by:
a, ar, ar², ar², ...
where a is the first term and r is the common ratio.
In this case, we have:
a = 1
ar = s2/5
ar² = s4/5
ar³ = s6/5
We can use the second and third equations to solve for r:
ar / a = (s2/5) / 1
r = s2/5
ar² / ar = (s4/5) / (s2/5)
r = sqrt(s4/5 / s2/5) = sqrt(s4/s2) = sqrt(s2)
Since we have two expressions for r, we can equate them and solve for s:
s2/5 = sqrt(s2)
s2 = (s2/5)²
s2 = s4/25
25s2 = s4
s4/5 = 25s2/5
Therefore, the common ratio r is s2/5 = sqrt(s2), the fifth term is ar^4 = s8/5 = 25s4/5, and the nth term is ar^(n-1) = s2/5 * sqrt(s2)^(n-1).
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$13 per hourIf you WORKED 39:45 EveryWEEK, WHAT WOULD YOUR,Gross Monthly Income?
Answers
A sports medicine major wanted to conduct anexperiment to determine if there is a correlationbetween the members of the soccer teams legstrength and the time it takes to sprint 40 yards.He sets up the following test and records thedata.Every day for a week he counts how many timeseach player can leg press 350 pounds. Thefollowing week, he has each player sprint 40yards every day. The table shows the averagenumber of leg-press repetitions and the average40-yard dash time (in seconds) for sevenrandomly selected players. What is the equationof the line of best fit? How many seconds shouldbe expect a player to take to run 40 yards if thatplayer can do 22 leg-press repetitions? Roundany values to the nearest tenth, if necessary.
Answers
Given
The data,
To find:
1) The equation of the line of best fit.
2) The time when the player can do 22 leg press repetitions.
Explanation:
It is given that,
That implies,
The equation of the line of best fit is given by,
\(T=kL+b\)Then,
\(k=\frac{\bar{LT}-\bar{L}\bar{T}}{\bar{L^2}-(\bar{L})^2},\text{ }b=\bar{T}-k\bar{L}\)Therefore,
\(\begin{gathered} \bar{L}=\frac{12+32+11+7+23+28+15}{7} \\ =\frac{128}{7} \\ =18.3 \end{gathered}\)Also,
\(\begin{gathered} \bar{T}=\frac{8.6+14.6+7.1+8.3+11.9+13.4+9.5}{7} \\ =\frac{73.4}{7} \\ =10.5 \end{gathered}\)Also,
\(\begin{gathered} \bar{L^2}=\frac{12^2+32^2+7^2+11^2+23^2+28^2+15^2}{7} \\ =\frac{2876}{7} \\ =410.9 \end{gathered}\)Also,
\(\begin{gathered} \bar{LT}=\frac{12\times8.6+32\times14.6+7\times7.1+11\times8.3+23\times11.9+28\times13.4+15\times9.5}{7} \\ =\frac{1502.8}{7} \\ =214.7 \end{gathered}\)That implies,
\(\begin{gathered} k=\frac{214.7-(18.3\times10.5)}{410.9-(18.3)^2} \\ =\frac{214.7-192.15}{410.9-334.89} \\ =\frac{22.55}{76.01} \\ =0.3 \end{gathered}\)And,
\(\begin{gathered} b=\bar{T}-k\bar{L} \\ =10.5-(0.3\times18.3) \\ =10.5-5.49 \\ =5 \end{gathered}\)Hence, the equation of the best line of fit is,
\(T=0.3L+5\)And, the time taken when L=22 is,
\(\begin{gathered} T=0.3(22)+5 \\ =6.6+5 \\ =11.6 \end{gathered}\)Hence, the time taken to complete 22 Leg press repetition is 11.6.
Diego is making a large mural.He draws a hexagon with a perimeter of 10.5 meters. Each side of the hexagon is the same length
Answers
To find the length of each side of the hexagon, we divide the perimeter by the number of sides, which in this case is 6. Therefore, each side of the hexagon has a length of 10.5 meters / 6 = 1.75 meters.
Diego can use this information to plan his mural. With a hexagon as the base shape, he can create a variety of designs within the boundaries of the hexagon. The length of each side being 1.75 meters gives him a reference for the scale and proportions of his artwork.
Diego may choose to divide the hexagon further into smaller sections or use the entire shape as a canvas. He could explore geometric patterns, abstract designs, or even depict recognizable images within the hexagon's boundaries.
The possibilities are endless, and Diego's creativity will shape the final outcome of his mural.
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A number is selected randomly from the integer from 10to30 what is the probability of picking a multiple of 4or5
Answers
Answer:
\(\frac{3}{7}\)
Step-by-step explanation:
Start by finding how many integers there are from 10-30...
30-10+1=20+1=21
Note we have to add 1 since it is inclusive.
Now, let's find how many multiples of 4 or 5 there are from 10-30...
4*3=12
4*4=16
4*5=20
4*6=24
4*7=28
5*2=10
5*3=15
5*4=20
5*5=25
5*6=30
5+5-1=9
Note we have to subtract 1 since 20 is counted twice.
The probability would be...
\(\frac{Multiples\ of\ four\ and\ five\ from\ 10-30}{Amount\ of\ integers\ between\ 10-30}=\frac{9}{21}=\frac{3}{7}\)
Train A leaves New York for California at the same time Train B leaves California for New York. They are 2900 miles apart. They both travel at an average speed of 120 mph. A. What is the velocity of train A? B. What is the velocity of train B? C. How long will it take before they meet? Show your work.
Answers
Answer:
(A) 120 mph
(B) -120 mph
(C) 12 hours 5 minutes.
Step-by-step explanation:
Given that,
New York and California are 2900 miles apart,
Both the trains A as well as B travel at an average speed of 120 mph.
Assuming that the path between the starting point in New York and the ending point in California is straight, so the given distance of 2900 miles is actually the shortest distance which is the displacement between the source and destination.
So, the given speed on the straight path is actually the velocity.
Assuming that the velocity is positive in the direction from New York towards California.
(A) So, the velocity of train A (towards California) = 120 mph.
(B) The velocity of train B (towards New York) = -120 mph.
(C) Bothy are moving towards each other, so the relative velocity between them is 120+120=240 mph, and the initial distance between them is 2900 miles.
When they meet, the displacement between them becomes zero, displacement covered= 2900-0=2900 miles.
So, the time, t, taken to cover the displacement 2900 miles with a relative velocity of 240 mph is
\(t=\frac{2900}{240}\) [as time= displacement / relative velocity]
\(\Rightarrow t=12\frac{1}{12}\) hours
=12 hours 5 minutes.
A number is chosen at random from 1 to 10. Find the probability of selecting a 6 or greater.
Answers
Answer:
1/2
Step-by-step explanation:
p(event) = (number of desired outcomes)/(total number of outcomes)
How many different outcomes are there? You can choose 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10, so the total number of possible outcomes is 10.
How many outcomes are desired. The desired outcomes are any outcomes with a number 6 or higher. Which numbers are 6 or higher? 6, 7, 8, 9, 10. There are 5 outcomes that are 6 or higher, so there are 5 desired outcomes.
p(event) = (number of desired outcomes)/(total number of outcomes)
p(event) = 5/10 = 1/2
Answer: 1/2
Find the quadratic function whose graph is shown to the right. Write the function in the form
f(x)= a(x-h)² + k.
f(x) =
(Do not simplify.)
16
Answers
= 3(x^2 + 4x/3) + 2
= 3(x^2 + 4x/3 + 4/9) + 2 - 3(4/9)
= 3(x+2/3)^2 + 2/3
f(x) = a(x-h)^2 + k where a=3, h=-2/3 and k = 2/3
vertex = (h,k) = (-2/3, 2/3) = minimum point on the parabola
y intercept =2 or (0,2)
x intercepts when 3x^2 +4x + 2 = 0
x = -4/6 + or - (1/6)sqr(16-4(12)(2))
there are no real x intercepts, just imaginary as the discriminate <0
axis of symmetry is x = -2/3
It's an upward opening parabola
Please help fast!
Evaluate-
Answers
Step-by-step explanation:
Given
\( = 27^{ \frac{1}{3} } \times 16^{ \frac{ - 1}{4} } \\ = {3}^{3 \times \frac{1}{3} } \times 2 {}^\frac{ - 1 \times 4}{4} \\ = 3 \times - 2 \\ = - 6\)
Hope it will help :)❤
Molly now blends 6 ml of blue paint with 5 ml of white paint. She decides that she likes this color and wants to make more. If she wants to keep this same ratio, how much blue paint will she need to add if she adds 40 ml of white paint? Guys this is do tonight at 11:59 i really need help
Answers
9514 1404 393
Answer:
48 mL
Step-by-step explanation:
The amount of white paint she added is 40/5 = 8 times the amount she already had. So, Molly needs to add 6·8 = 48 ml of blue paint to her mix.
Which search method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line
Answers
The wide-area search method employs the use of markers such as knots at regular intervals along the search line.
Given the method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line.
In order to locate, relieve distress, and preserve the life of a person who has been reported missing or is believed to be lost, stranded, or is considered a high-risk missing person, wide area search and rescue refers to activities occurring within large geographic areas. It also refers to the removal of any survivors to a safe location.
Hence, the wide-area search method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line
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A 40-foot wire is attached to a pole and runs to the ground as shown below.
The pole is 35 feet tall.
About how far away from the pole is the wire attached to the ground?
Answers
Answer:
5 feet away
Step-by-step explanation:
i am not sure but did mental math
Harriet and Maya share £300 in the ratio of 7:5. Wirk out how much money harriet gets
Answers
Answer:
$175
Step-by-step explanation:
you need to specify if harriet got the 7 portion or the 5 portion. I'll answer as if she got the 7 portion.
They split it into 12 portions because the ratio is 7:5 and 7+5=12. So do $300/12=25
Assuming Maya got the 5 portion, do $25 x 5 = $125, so Maya got $125.
Assuming Harriet got the 7 portion, do $25 x 7 = $175, so Harriet got $175.
pls help asap if you can!!!!!
Answers
Answer:
x = 24
Step-by-step explanation:
if a and b are parallel then
62 and 5x - 2 are same- side interior angles and sum to 180° , that is
5x - 2 + 62 = 180
5x + 60 = 180 ( subtract 60 from both sides )
5x = 120 ( divide both sides by 5 )
x = 24
thus for a to be parallel to b , then x = 24
5) A warehouse outside of a factory currently has an inventory of 1245 boxes. After an 8-
hour work day, the warehouse has 2000 boxes. Assume the warehouse was being filled at a
constant (linear) rate.
a) How many boxes per hour is the factory able to provide to the warehouse?
b) What would be the inventory at the end of a 40-hour work week?
c) How long will it take to fill the warehouse to its 50,000 box capacity?
6) In the year 2007, a FOREVER stamp cost cost $0.41. In 2023, the cost of a FOREVER
stamp was $0.63. Assume that the cost of stamps increased at a constant (linear) rate.
a) If price increases continue at the current rate, how much will a FOREVER stamp
cost in 2035?
b) In what year would you expect a FOREVER stamp to cost one dollar?
7) In January of 2021, there were 980,000 games available on the Apple App Store. By July
of 2021, there were 984,200 games available. If we assume that the number of available
games is steadily increasing at a constant (linear) rate,
a) How many games does this pattern predict will be available in January 2022?
b) At this rate, when will there be 1,000,000 games available for purchase in the Apple
App Store?
Answers
Thee factory is able to provide 94.38 boxes per hour to the warehouse.
How to calculate the valueRate = (2000 - 1245) / 8 = 94.38 boxes per hour
Therefore, the factory is able to provide 94.38 boxes per hour to the warehouse.
Boxes added in 40 hours = rate * time = 94.38 * 40 = 3,775.2
Therefore, the inventory at the end of a 40-hour work week would be:
1245 + 3775.2 = 5020.2 boxes
rate = (50000 - 1245) / time
Simplifying this equation, we get:
time = (50000 - 1245) / rate = 511.64 hours (rounded to two decimal places).
Therefore, it will take approximately 511.64 hours to fill the warehouse to its 50,000 box capacity,
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Levi has a collection of 120 coins. How many coins represent 20% of his collection?
Answers
due very soon but I can buy myself some time.
please at least explain how to do it and/or how to set it up.
also, ignore the empty set sign on 5 I realized it was probably wrong but didn't want to take another picture
Answers
Answer:
4) 16√3 in²
5) 63 cm²
Step-by-step explanation:
The formula to use in these cases is ...
A = (1/2)ab·sin(θ)
where a, b are the side lengths and θ is the angle between them.
It helps to know the trig functions of the "special" angles used here.
sin(120°) = sin(60°) = (√3)/2
cos(60°) = 1/2
sin(135°) = cos(45°) = (√2)/2
__
4) The external angle at the base is the supplement of 120°, so is 60°. Then the length of the missing segment between the end of the base and the right angle at h is ...
x = (8 in)cos(60°) = (8 in)(1/2) = 4 in
So, the bottom edge of the triangle is 12 in - 4 in = 8 in.
The area is ...
A = (1/2)(8 in)(8 in)sin(120°) = (1/2)64(√3)/2 in² = 16√3 in²
__
5) As in the previous problem, the difference between the given horizontal dimension and the base of the triangle is ...
x = (18 cm)cos(180°-135°) = 18(√2)/2 cm = 9√2 cm
Then the base of the triangle is ...
16√2 cm -9√2 cm = 7√2 cm
The area is then ...
A = (1/2)(18 cm)(7√2 cm)(√2)/2 = 63 cm²
What is 51/2-7 equal
Answers
Answer:
give me brainliest
Step-by-step explanation:
37/2 = 18.50000
What is the measure of /x?
Angles are not necessarily drawn to scale.
PLS HELP I REALLY NEED TO GET THIS RIGHT!!
Answers
Answer:
x = 66°
Step-by-step explanation:
First, you can use exterior angle theorem to say that
\(m<JIH = m<JDI + m<DJI\)
and you can substitute to get:
105° = 39° + m<DJI
m<DJI = 66°
m<DJI and m<AJF are vertical angles, so they equal each other:
m<DJI = m<AJF
m<AJF = x = 66°
4.97 ft
1.06 ft
Without using a calculator, determine
which of the following could
reasonably be the area of the largest
rectangle. All four-sided figures are
rectangles.
2.05 ft
+
a. 10.1885 square feet
b. 12.3615 square feet
c. 16.16 square feet
d. 22.1396 square feet
e. 107.79981 square feet
Answers
Answer:
a is the area of the largest rectangle
Classify the following triangle. Check all that apply.
Answers
Answer:
Equilateral and acute
Step-by-step explanation:
Notice that the angles of the triangle are all 60 degrees which is less than 90 degrees. Also notice the lines in the middle of the triangle lines, those signify that the lines are the same length. Thus making it acute and equilateral
Answer:
Its both equilateral and acute
Step-by-step explanation:
It's equilateral because it has same equal angles and acute because its less than 90 degrees for each angle.
Can someone help me please
Answers
Answer:
B) -4, - 1, 2, 5, 8
Step-by-step explanation:
Hope it helps you in your learning process
find (a) the slope of the curve at the given point p, and (b) an equation of the tangent line at p. y= 1/x; p(5,1/5)
Answers
Answer:
(a) -1/25
(b) y = -1/25x +2/5
Step-by-step explanation:
You want the slope and tangent line equation for the curve y = 1/x at point P(5, 1/5).
(a) SlopeThe slope is the derivative of the function at the given point:
y = 1/x = x^(-1)
y' = (-1)x^(-1-1) = -1/x²
At x=5, the slope is ...
m = -1/5² = -1/25
(b) EquationThe equation of the tangent line is conveniently written using slope-intercept form:
y -k = m(x -h) . . . . . . . . equation for line with slope m at point (h, k)
y -1/5 = -1/25(x -5) . . . . equation for line with slope -1/25 at point (5, 1/5)
Rearranging, we have the slope-intercept form ...
y = -1/25x +2/5
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What is the answer to this- 76.2 divided by 18.4 ?
Answers
Answer:
-4.14130434783
Step-by-step explanation:
what is the sum of the first fifteen terms of the sequence $2, 8, 14, \dots$, in which each term is six more than the preceding term?
Answers
The sum of the first fifteen terms of the given sequence is 220.
The given sequence can be expressed as: \($2, 8, 14, \dots$\), in which each term is six more than the preceding term. This is an arithmetic sequence, where the common difference between terms is 6. The formula to calculate the sum of the first n terms of an arithmetic sequence is given by \($S_n = \frac{n}{2}(a_1 + a_n)$\), where \($a_1$\) is the first term and \($a_n$\) is the nth term.
In the given sequence, the first term \($a_1$\) is 2 and the 15th term \($a_n$\) is 42. So, plugging these values to the formula gives us, \($S_{15} = \frac{15}{2}(2+42) = \frac{15\times 44}{2} = 220$\).
Therefore, the sum of the first fifteen terms of the given sequence is 220.
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find the slope and y intercept for the graph of : 2x+4y=20
Answers
you can either graph it or solve it algebraically
move the parts of the equation to fit the sctructure of y = mx + b
2x + 4y = 20
4y = -2x + 20
divide by 4 on both sides to get 'y' by itself
y = -2/4x + 20/4
y = -1/2x + 5
this equation tells you the 'y intercept' and the slope
slope; -1/2
y intercept; 5
Simplify 3.7-4.6n -2n+5
Answers
Answer: =-6.6n+8.7
3.7-4.6n-2n+5.
add the similare elimants : -4.6n - 2n= -6.6n,
=3.7 - 6.6n +5.
Then add the numbers: 3.7+5=8.7.
= -6.6n+8.7
HOPE THIS HELPED YOU, IF NOT SO SORRY MATE!!! :) IF WRONG PLEASE DO NOT REPORT THIS.
please help me with this. thanks a lot
Answers
Answer:
Part A)
Approximately 318.1318 meters.
Part B)
Approximately 137.7551 meters.
Step-by-step explanation:
The path of a projectile is given by the equation:
\(\displaystyle y = \sqrt{3} x -\frac{49x^2}{9000}\)
Part A)
The range of the projectile will be given by the difference between its starting point and landing point. In other words, its two zeros.
Let y = 0 and solve for x:
\(\displaystyle 0 = \sqrt{3}x - \frac{49x^2}{9000}\)
Factor:
\(\displaystyle 0 = x\left(\sqrt{3} - \frac{49x}{9000}\right)\)
Zero Product Property:
\(\displaystyle x = 0 \text{ or } \sqrt{3} - \frac{49x}{9000} = 0\)
Solve for each case:
\(\displaystyle x = 0 \text{ or } x = \frac{9000\sqrt{3}}{49}\approx 318.1318\)
Hence, the range of the projectile is approximately (318.1318 - 0) or 318.1318 meters.
Part B)
Since the equation is a quadratic, the maximum height is given by its vertex. Recall that the vertex of a quadratic is given by:
\(\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)\)
In this case, a = -49/9000 and b = √3.
Find the x-coordinate of the vertex:
\(\displaystyle x = - \frac{(\sqrt{3})}{2\left(\dfrac{-49}{9000}\right)} = \frac{4500\sqrt{3}}{49}\)
Then the maximum height will be:
\(\displaystyle \displaystyle \begin{aligned} y\left(\frac{4500\sqrt{3}}{49}\right) &=\sqrt{3} \left(\frac{4500\sqrt{3}}{49}\right) -\frac{49\left(\dfrac{4500\sqrt{3}}{49}\right)^2}{9000} \\ \\ &= \frac{13500}{49} -\frac{6750}{49}\\ \\ &=\frac{6750}{49}\\ \\ &\approx 137.7551\text{ meters}\end{aligned}\)
The maximum height reached by the projectile will be 137.7551 meters.