Answers
Answer:
[tex]\mathrm{Distance\:between\:}\left(-3,\:10\right)\mathrm{\:and\:}\left(7,\:15\right)=\:5\sqrt{5}[/tex][tex]\mathrm{Midpoint\:of}\left(-3,\:10\right)\mathrm{\:and\:}\left(7,\:15\right)=\:\left(2,\:\frac{25}{2}\right)[/tex]Step-by-step explanation:
Given the two points
(-3, 10)(7, 15)Determining the distance between the points
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]\mathrm{The\:distance\:between\:}\left(-3,\:10\right)\mathrm{\:and\:}\left(7,\:15\right)\mathrm{\:is\:}[/tex]
[tex]=\sqrt{\left(7-\left(-3\right)\right)^2+\left(15-10\right)^2}[/tex]
[tex]=\sqrt{\left(7+3\right)^2+\left(15-10\right)^2}[/tex]
[tex]=\sqrt{10^2+5^2}[/tex]
[tex]=\sqrt{100+25}[/tex]
[tex]=\sqrt{125}[/tex]
[tex]=\sqrt{5^3}[/tex]
[tex]=\sqrt{5^2\cdot \:5}[/tex]
[tex]=5\sqrt{5}[/tex]
Therefore,
[tex]\mathrm{Distance\:between\:}\left(-3,\:10\right)\mathrm{\:and\:}\left(7,\:15\right)=\:5\sqrt{5}[/tex]
Determining the midpoints between the points
Given the two points
(-3, 10)(7, 15)[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-3,\:10\right),\:\left(x_2,\:y_2\right)=\left(7,\:15\right)[/tex]
[tex]=\left(\frac{7-3}{2},\:\frac{15+10}{2}\right)[/tex]
[tex]=\left(2,\:\frac{25}{2}\right)[/tex]
Therefore,
[tex]\mathrm{Midpoint\:of}\left(-3,\:10\right)\mathrm{\:and\:}\left(7,\:15\right)=\:\left(2,\:\frac{25}{2}\right)[/tex]
Related Questions
What is the value of x?
Enter your answer in the box
672
X=
D
60°
х
Basic
45°
А.
B
Answers
9514 1404 393
Answer:
x = 3
Step-by-step explanation:
It is convenient to remember the ratios of side lengths of these "special triangles."
The side ratios of ΔABC are 1 : 1 : √2, so BC = AC/√2 = 6.
The side ratios of ΔBCD are 1 : √3 : 2, so BD = BC/2 = 6/2 = 3.
The value of x is 3.
If y= 1-x+x²/1+x-x² than how about y'=?
This question is about derived function.
Answers
Answer:
as
[tex]\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)=0[/tex]
so
[tex]y'=0[/tex]
Step-by-step explanation:
Given the function
[tex]y=\:1-x+\frac{x^2}{1}+x-x^2[/tex]
Taking derivative
[tex]\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)[/tex]
[tex]\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'[/tex]
[tex]=\frac{d}{dx}\left(1\right)-\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{1}\right)+\frac{d}{dx}\left(x\right)-\frac{d}{dx}\left(x^2\right)[/tex]
as
[tex]\frac{d}{dx}\left(1\right)=0[/tex] ∵ [tex]\mathrm{Derivative\:of\:a\:constant}:\quad \frac{d}{dx}\left(a\right)=0[/tex]
[tex]\frac{d}{dx}\left(x\right)=1[/tex] ∵ [tex]\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1[/tex]
[tex]\frac{d}{dx}\left(\frac{x^2}{1}\right)=2x[/tex] ∵ [tex]\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}[/tex]
[tex]\frac{d}{dx}\left(x\right)=1[/tex] ∵ [tex]\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1[/tex]
[tex]\frac{d}{dx}\left(\frac{x^2}{1}\right)=2x[/tex] ∵ [tex]\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}[/tex]
substituting all the values in the expression
[tex]=\frac{d}{dx}\left(1\right)-\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{1}\right)+\frac{d}{dx}\left(x\right)-\frac{d}{dx}\left(x^2\right)[/tex]
[tex]=0-1+2x+1-2x[/tex]
[tex]=0[/tex]
Hence,
[tex]\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)=0[/tex]
Therefore,
[tex]y'=0[/tex]
Max has 8 pennies.
Jen has 3 more pennies than max.
how many pennies do max and jen have in all
Answers
Answer:
19
Step-by-step explanation:
8+(8+3)
...........
Find the value of X.
Answers
63+x=90
Answer
X=27
Item 2
Multiply. Write the answer in simplest form.
3/7×1/4=
Answers
Answer:
in multiplication we just multiply
Step-by-step explanation:
3/7×1/4
3/28
What is the answers help me please part A B C
Giving extra points
Correct answer
Answers
Answer:
A, 38, 40
Step-by-step explanation:
a. A has to be the first graph because it starts at $ 25 and it rises as more work needs to get done
b.if you go from 50 up until you get to the line, then look left at the axis is about $38
c. C=25+s*0.25, substitute c=35 and find s
35=25+s*0.25 subtreact 25 from both sides
35-25= s*0.25
10=s*0.25 divide both sides by 0.25
10/0.25=s
40=s
Will give brainliest!!!!
Explain how solving -7y > 161 is different from solving 7y > -161.
Answers
To solve -7y > 161, we divide both sides by -7 and we get y < -23. The inequality sign flipped because we divided both sides by a negative number.
To solve 7y > -161, we divide both sides by 7 and it leads to y > -23. The inequality sign does not flip in this case, because we are not dividing both sides by a negative number.
The similarities is that we end up with -23 on the right side, but the inequality signs are different.
The equation 9 y minus 12 x = 36 is written in standard form. What is the first step when writing an equivalent equation which solves for y?
Answers
Answer:
9y-12x=36
9y=36+12x
y=(36+12x)÷9
Answer: y=8 and x=3
Example: Because 9*8=72 and 12*3=36
72-36=36
Find the unit rate. 12 laps in 30minutes.
Asking for fraction
Answers
Answer:
4/10 maybe cuz 12 divided by 30 is 0.4 and 0.4 would be 4/10
What is the approximate value of x? Round to the nearest tenth
Answers
Answer:
10
Step-by-step explanation:
Michael spent $210 on school supplies and books. This amount was 30% of his savings.
How much was his savings?
Answers
What is the area, height, and base of this triangle?
Answers
can someone help me answer this question please!!
Answers
Answer:
i think its A
Step-by-step explanation:
Brandon enters bike races.
He bikes 8 /2 miles every 1/2 hour.
How fast did he go
Answers
Answer:
He goes 8 miles an hour
Step-by-step explanation:
8/2 is equal to 4. If Brandon bikes 4 miles in half an hour and keeps a constant speed he ends up biking 8 miles in an hour since two halves of an hour make one.
Chris has a collection of dimes and quarters worth $4.25. If she has 22 coins total, how many quarters does she have?
Answers
Given:
Chris has a collection of dimes and quarters worth $4.25.
To number of coins = 22
To find:
The number of quarters.
Solution:
Let x be the number of dimes and y be the number of quarters.
Total coins : [tex]x+y=22[/tex] ...(i)
we know that, 1 dime = $0.10 and 1 quarter = $0.25.
Total value : [tex]0.10x+0.25y=4.25[/tex] ...(ii)
Multiply equation (i) by 0.10 and subtract the result form (ii).
[tex]0.10x+0.25y-0.10(x+y)=4.25-0.10(22)[/tex]
[tex]0.10x+0.25y-0.10x-0.10y=4.25-2.20[/tex]
[tex]0.15y=2.05[/tex]
Divide both sides by 0.15.
[tex]y=\dfrac{2.05}{0.15}[/tex]
[tex]y=13.6667[/tex]
Number of quarter cannot be a decimal value.
[tex]y\approx 17[/tex]
Therefore, the number of quarter is about 17.
which represents the area of the figure
ASAP PLS
Answers
The Answer is B so pick it.
Answer:
What does a goat say?BBBBBBB
Step-by-step explanation:
6. The Awesome Bowl Factory makes two kinds of bowls. They produce a
basic bowl every 9 minutes and a gigantic bowl every 12 minutes. They
start at 8:00 A.M. At what time are the basic bowl and the gigantic bowl
first produced together?
Answers
Answer: 8.36 a.m
Step-by-step explanation:
To solve this, first we need to calculate the lowest common multiple of 9 and 12.
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108.
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120.
Here, the lowest common multiple = 36
Therefore, we will add 8.00am plus 36 minutes. This will be:
= 8:00 a.m + 36 minutes
= 8.36 am
The time that the basic bowl and the gigantic bowl are first produced together is 8.36 am.
Geraldo has 3 fewer marbles than Yan. Together, they have 21 marbles. Which equation
represents this situation?
x + (3 - x) = 21, where x is the number of marbles Geraldo has
x + (3 - x) = 21, where x is the number of marbles Yan has
x + (x - 3) = 21, where x is the number of marbles Yan has
x + (x - 3) = 21, where x is the number of marbles Geraldo has
Done
My Progress >
Answers
Answer:
x + (x-3) = 21
x + x - 3 = 21
2 x - 3 = 21
Explanation:
In this problem, let us first analyze the situation. It says here that Geraldo and Yan both had marbles of their own. The problem states that together, they have a total of 21 marbles. However, we know here from the problem that they have different number of marbles each. Geraldo seems to have lesser number of marbles than Yan. Yan have three marbles more than Geraldo.
We can write the equation starting from assigning the unknown.
We'll use x.
x is the number of marbles that Yan have.
if x is Yan's, then, we can say that x-3 is Geraldo's.
Put them together into the equation.
Yan's plus Geraldo's is equal to 21.
Substitute using the represented unknowns.
x + (x-3) = 21.
In solving, we can also rule out that:
x + x - 3 = 21
2 x - 3 = 21
2 x = 21 + 3
2 x = 24
x = 12
x - 3 = 9
Yan has 12 marbles
and Geraldo has 9 marbles.
Answer: X+(X-3)=21 or C
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 15 gallons of fuel, the airplane weighs 1984 pounds. When carrying 40 gallons of fuel, it weighs 2124 pounds. How much does the airplane weigh if it is carrying 50 gallons of fuel?
Answers
I need help
1/2 + 1/3
Answers
Answer:
5/6
Step-by-step explanation:
1/2x3= 3/6
1/3x2=2/6
3/6+2/6=5/6
Graph a line with a slope of
−
2
5
−
5
2
minus, start fraction, 2, divided by, 5, end fraction that contains the point
(
−
3
,
5
)
(−3,5)
Answers
help me out really fast pleaseee
Answers
Distributive because he changed the fractions to the way it would go.
A= 20 square root of 2
B= 5
C=20
D=10
Answers
Find the slope of the line through the
given points: (5,-4) & (-1,-4).
Answers
Answer:
m=0
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
Since -4-(-4)=0, we know that the slope has to be zero since the numerator is zero.
HTH :)
8x^(2)+16x=42 completeing the square
Answers
x
2
+
16
x
=
42
Step 2: Subtract 42 from both sides.
16
x
2
+
16
x
−
42
=
42
−
42
16
x
2
+
16
x
−
42
=
0
For this equation: a=16, b=16, c=-42
16
x
2
+
16
x
+
−
42
=
0
Step 3: Use quadratic formula with a=16, b=16, c=-42.
x
=
−
b
±
b
2
−
4
a
c
2
a
x
=
−
(
16
)
±
(
16
)
2
−
4
(
16
)
(
−
42
)
2
(
16
)
x
=
−
16
±
2944
32
x
=
−
1
2
+
1
4
46
or
x
=
−
1
2
+
−
1
4
46
Answer:
x
=
−
1
2
+
1
4
46
or
x
=
−
1
2
+
−
1
4
46
50 points, need help ASAP
Solve this system of equations, then determine what y equals.
x + 5y= 7
2x + 4y = -4
y=-18
y=3
y=8
y=-8
Answers
2x+10y=14
2x + 4y = -4
Subtract
6y = 18
Divide by 6
Y = 3
Answer: [tex]y = 3[/tex]
1. First, solve for unknown x.
[tex](x+5y=7)2[/tex]
2. Balance the equation.
[tex]2x+10y=14[/tex]
[tex]\mathrm {2x + 4y = -4}[/tex]
3. Now, we subtract.
[tex]6y = 18[/tex]
[tex]6[/tex] × [tex]3 = 18[/tex]
4. Finally, divide.
[tex]18/6=3[/tex]
Grade:
Subject: Ma
Stream: Advanced
Number of P
End of Term 1 Exam
Academic Year 2018/2019
Part 1
Circle the letter corresponding to the correct answer.
1) Write an algebraic expression for "3 times X squared minus 4 times X"
a) 3x - 4x?
c) 3x² - 4
b) 3x - 4x
d) 3x2 - 4x
Answers
The regular price of a laptop computer is $914.00. This week, it is on sale for $886.00 of
What is the sale price of the computer?
Answers
Answer:
3.1%
Step-by-step explanation:
Subtract.
914 - 886 = 28
Divide by the original price.
28/914 = 0.0306345...
Multiply by 100%.
0.0306345... * 100% = 3.06345%
Round if needed.
3.06345% -> 3.1%
Best of Luck!
Uhh I tried
Lmk,
Two scuba divers are swimming below sea level. The locations of the divers can be represented by -30 feet and -42 feet. Which measure represents the location that is closest to sea level.
Answers
Answer:
-30 feet
Step-by-step explanation:
it is -30 feet because that one is closest to sea level because -42 feet is -12 feet more than -30 feet. plsss give me brainliest plssss
Find the lcm for 96 and 24
Answers
Answer: 96
Step-by-step explanation: