The equation that represents the set of points that are 8 units from (-8,-7) is [tex]x_{1} ^{2}[/tex] + 16[tex]x_{1}[/tex] + [tex]y_{1} ^{2}[/tex] + 14[tex]y_{1}[/tex] + 49 = 0.
What is the distance between two points ?
Distance between two points is the length of the line segment that connects the two locations in a plane.
We know that the distance between two points is calculated by using the distance formula which is given as :
D = [tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }[/tex]
Here ; let's assume the first point is (x1, y1). It is given that other point is (x2, y2) = (-8 , -7) and distance D = 8 units. Now use these data to find out the equation :
8 = [tex]\sqrt{(-8 - x_{1})^{2} + (-7- y_{1})^{2} }[/tex]
Squaring on both sides , we get :
64 = [tex](-8 - x_{1} ) ^{2}[/tex] + [tex](-7 - y_{1})^{2} }[/tex]
64 = 64 + [tex]x_{1} ^{2}[/tex] + 16[tex]x_{1}[/tex] + 49 + [tex]y_{1} ^{2}[/tex] + 14[tex]y_{1}[/tex]
[tex]x_{1} ^{2}[/tex] + 16[tex]x_{1}[/tex] + [tex]y_{1} ^{2}[/tex] + 14[tex]y_{1}[/tex] = 64 - 64 - 49
[tex]x_{1} ^{2}[/tex] + 16[tex]x_{1}[/tex] + [tex]y_{1} ^{2}[/tex] + 14[tex]y_{1}[/tex] = -49
or
[tex]x_{1} ^{2}[/tex] + 16[tex]x_{1}[/tex] + [tex]y_{1} ^{2}[/tex] + 14[tex]y_{1}[/tex] + 49 = 0
Therefore , the equation that represents the set of points that are 8 units from (-8,-7) is [tex]x_{1} ^{2}[/tex] + 16[tex]x_{1}[/tex] + [tex]y_{1} ^{2}[/tex] + 14[tex]y_{1}[/tex] + 49 = 0.
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Answer:
No, i cant
Step-by-step explanation:
8c = 56
two step equation
Answer: c=7
Step-by-step explanation:
8c = 56 Divide both sides by 8
[tex]\frac{8}{8}c = \frac{56}{8}[/tex]
c = 7
solve x-5/y = z for y
Answer:
y=5x−z
Step-by-step explanation:
Step 1: Multiply both sides by y.
xy−5=yz
Step 2: Add -yz to both sides.
xy−5+−yz=yz+−yz
xy−yz−5=0
Step 3: Add 5 to both sides.
xy−yz−5+5=0+5
xy−yz=5
Step 4: Factor out variable y.
y(x−z)=5
Step 5: Divide both sides by x-z.
y(x−z)x−z=5x−z
y=5x−z
Solve 7ax + 8ax = 9 ax + 6 for x. Assume a ≠0.
A. = x=1/6a
B. x=1/a
C. x= a
D. x = 6a
The answer is B (1/a)
Which value is equivalent to 7 x 5 x 2 divided by 7 x 3 to the 2nd power x 5 to the 0 power divided by 2 to the negative 3rd power x 2 to the negative 9 power
Answer:
This is hard to read, but i guess that the equation is:
[tex]7*5*2/7*3^2*5^0/2^{-3}*2^{-9}[/tex]
So we have some things to solve:
First, for any number:
x^0 = 1
then 5^0 = 1.
And for negative powers,
x^-n = (1/x)^n.
And we
Then we can rewrite our equation as:
[tex]\frac{7*5*2*3^2*1*2^3}{7*2^9}[/tex]
now we can cancel the seven in the numerator and the denominator
[tex]\frac{5*2*3*2^3}{2^9}[/tex]
now, remember the relation:
a^x*a^y = a^(x+y)
then:
2*2^3 = 2^4
and 2^4/2^9 = 2^-5 = (1^2)^5
Then our equation is:
[tex]\frac{5*3}{2^5}[/tex]
15/2^5 = 0.46875
HELP PLS I NED THIS LUV U GUUS
Answer:
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
Step-by-step explanation:
What is the distance between M(9, −5) and N(−11, 10)?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{25 \: units}}}}}[/tex]
Step-by-step explanation:
Let M ( 9 , -5 ) be ( x₁ , y₁ ) and N ( - 11 , 10 ) be ( x₂ , y₂ )
Finding the distance between these points
[tex] \boxed{ \sf{distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}[/tex]
[tex] \longrightarrow{ \sf{ \sqrt{ {( - 11 - 9)}^{2} + {(10 - ( - 5))}^{2} } }}[/tex]
[tex] \longrightarrow{ \sf{ \sqrt{ {( - 20)}^{2} + {(10 + 5)}^{2} } }}[/tex]
[tex] \longrightarrow{ \sf{ \sqrt{ {( - 20)}^{2} + {(15)}^{2} } }}[/tex]
[tex] \longrightarrow{ \sf{ \sqrt{400 + 225}}} [/tex]
[tex] \longrightarrow{ \sf{ \sqrt{625}}} [/tex]
[tex] \longrightarrow{ \sf{ \sqrt{ {(25)}^{2} } }}[/tex]
[tex] \longrightarrow{ \sf{25 \: units}}[/tex]
Hope I helped!
Best regards! :D
Help ASAP!!! Which one?
1. 16 square units
2. 64 square units
3. 48 square units
4. 32 square units
Answer:
64
Step-by-step explanation:
16+16 on the 2 big sides
then 8x4=32
32+32
64 is ur answer
is 0.65 repeating greater than or less than 13/20?
Answer:
its equal
Step-by-step explanation:
Answer:
Since 13/20 is exactly 0.65, then 0.6565656565......(repeating) is greater than 13/20.
Covert this repeating decimal into a fraction:
3.00121212121212...
If 42-8, then 400x2=
Answer:
800
Step-by-step explanation:
write 3/19 in lowest terms
Answer: do you mean simplified because if so that is the lowest it will go but in percentage form it is 15.79%
Step-by-step explanation:
the perimeter of a rectangle is 48. The length is 2x and the width is twice the length. Find the length and the width.
Please answer!!!
Hope it helped
Thank YouOn an actual basketball court, the bench area is 9 meters long. How long should the bench be on the scale drawing?
Step-by-step explanation:
Note: It is not given that, 1 cm represents 2m
The bench area on an actual basketball court is 9 meters long.
We need to find how long should the bench be on the scale drawing. Since 1 cm represents 2m. It means 1 m represents 0.5 cm
9 meters will represent,
[tex]\dfrac{9}{0.5}\ cm\\\\=18\ cm[/tex]
Hence, the bench is 18 cm long.
Patric made a simple sugar solution using 3 parts sugar and 4 parts water. Thomas made a sugar solution using 6 parts sugar and 7 parts water. Whose solution was more sugary. Explain. Pls h
Answer: thomas
Step-by-step explanation:
because patrick’s is 75% sugar and thomas’s is more
Answer:
Step-by-step explanation:
3:4= patrick 6:7= Thomas
=3/4 =6/7
=0.75 =about 0.86
= 75% = 86%
Thomas’ is more sugary.
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator
24 min to 64 min
Answer: 3/8
Step-by-step explanation:
24 min to 64 min as a fraction is [tex]\frac{24}{64}[/tex]
Now write the fraction is simplest form by dividing it by their greatest factor.
The GCF of 24 and 64 is 8
24/8 = 3
64 /8 = 8
So the ratio will be 3/8
A room is 12 m long and 8 m wide and 10 m high, find the area of the room.
Answer:
96 square meters
On Gabriela’s first birthday, her parents gave her a $50 savings account. On every birthday after that her parents added to the account, increasing the amount they deposited by $25 each year. Complete the recursive definition for the sequence that represents this situation by finding the values for a1 and d. Calculate the total amount Gabriela’s parents will have deposited into the account on her birthdays by her 18th birthday.
Answer: [tex]a_1=50,d=25[/tex] and $475 deposited into the account on her birthdays by her 18th birthday.
Step-by-step explanation:
It is given that, on Gabriela’s first birthday, her parents gave her a $50 savings account.
Initial term : [tex]a_1=50[/tex]
On every birthday after that her parents added to the account, increasing the amount they deposited by $25 each year.
Common difference : [tex]d=25[/tex]
It forms an AP: 50,75,100,...
nth term of an AP is
[tex]a_n=a_1+(n-1)d[/tex]
Substitute [tex]a_1=50[/tex] and [tex]d=25[/tex] in the above formula.
[tex]a_n=50+(n-1)25[/tex]
It represents the amount deposited into the account after n birthdays.
We need to find the amount by her 18th birthday.
Put n=18 in the above equation.
[tex]a_{18}=50+(18-1)25[/tex]
[tex]a_{18}=50+(17)25[/tex]
[tex]a_{18}=50+425[/tex]
[tex]a_{18}=475[/tex]
Therefore, $475 deposited into the account on her birthdays by her 18th birthday.
We are to calculate total amount given to Gabriela on her 18th birthday
Total amount Gabriela’s parents will have deposited into the account on her birthdays by her 18th birthday is $475
Amount given to her on her first birthday = $50
Additional amount given to her each year = $25
number of years, n = 18
a1 = $50
d = $25
n = 18
Sum = a1 + (n - 1)d
= 50 + (18 - 1)25
= 50 + (17)25
= 50 + 425
= 475
sum = $475
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pleas help I need both answers please and thank you
Answer:
17-4=13
13+3=16
16+6=22
Step-by-step explanation:
so it in the 22nd floor
Answer:
17 - 4 +3 +6= 17 +5= 22It is on 22nd floor.
you want to know the number of minutes that you can use on a $35 phone card. The card company charges $0.25 for the card and $0.10 for each minute used. The equation $0.25 + $0.10m= $35.00, where m is the number of minutes on the card, represents this situation. Solve the equation.. If necessary, round your answer to the nearest hundredth
Help me
The digit 1 in witch number represents a value of 1 tenth?
A.2.916
B.718
C.5108
66.7 - 6 x 14 + 99 x -6 = ?
Answer:
? = -611.3
I used a calculator.
hope this helps
I need help with how to solve this
Answer:
[tex]-\dfrac{5\sqrt{11}}{11}[/tex]
Step-by-step explanation:
Use the relationship between the various trig functions.
[tex]\tan{\theta}=\dfrac{\sin{\theta}}{\cos{\theta}}=\dfrac{\left(-\dfrac{5}{6}\right)}{\left(\dfrac{\sqrt{11}}{6}\right)}=-\dfrac{5}{\sqrt{11}}\\\\=-\dfrac{5}{\sqrt{11}}\cdot\dfrac{\sqrt{11}}{\sqrt{11}}=\boxed{-\dfrac{5\sqrt{11}}{11}}[/tex]
Draw Conclusions Suppose that A and C are real numbers and A is not 0. What are the x- and y-intercepts of the equation Ay = C? Explain.
Answer:
Horizontal line which goes through the y -axis at the coordinate ( 0, C/A ).
Step-by-step explanation:
Since A is not 0 then C can not be 0 This is a logical deduction from the given formula Ay = C
The equation of any line is y = ax + b, where a is the incline and b is the intercept between the line and the y- axis.
Ay = C
Divide left and right of the = sign by A and you get:
y = C/A
This is the formula for a horizontal line which goes through the y -axis at the coordinate ( 0, C/A ).
Because it is a horizontal line it has an incline of 0.
So a = 0
y = ax + b
a = 0 and b = C/A
y = 0*x + C/A
y = 0 + C/A
y = C/A
You pack sandwiches for a mountain hike with your friends. each sandwich takes 2 slices of bread, and you pack 3 sandwiches for each hiker. how many slices of bread are used for n hikers? write your answer as an expression.
2*3n would be the equation.
The green turtle, Monique, traveled 250 centimeters in 8.7 minutes.
-26 - 4m = -2(2m + 13)
Answer:
Your answer would equal the same on the other side.
-26-4m=-4m-26
if you minus 26 from both sides youll have -4m on both sides also. So it would equal. So you have an Equaled equation if that makes sense.
3. Which numbers are rational?
a. Square root of 81
b. Square root of 50
c.-12
d. 0
e. 12/5
f. 6.54
Answer:
i wanna say its C,D,E,F but i get rational and irrational mixed u0
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through -3, -6) and parallel to the line whose equation is y=-4x+1
Step-by-step explanation:
Hey there!
The equation of a st.line passing through point is;
(y + 6) = m1(x+3).........(i). [ Use one point formula]
y = -4x + 1............(ii)
Comparing 2nd equation with y = mx+c, we get;
Slope (m2) = -4.
For parallel lines;
[tex]m1 = m2[/tex]
(i.e m1=m2 = -4)
Putting value of slope in 1st equation,
[tex](y + 6) = - 4(x + 3)[/tex]
Smplify them to get equation.
[tex](y + 6) = - 4x - 12[/tex]
[tex]y = - 4x - 12 - 6[/tex]
[tex]y = - 4x - 18[/tex]
Therefore the required equation is y = -4x-18.
Hope it helps..
during a promotion bags of sweets contain 30% extra free. There are 65 sweets in a bag during the promotion. How many sweets are there normally
Answer:
if y is the normal number of sweets then the normal number plus 40 percentage equals 42
y+4y=42
1.4y=42
y=42/1.4=30
hope this helps!
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