Answer:
± i [tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the result that [tex]\sqrt{-1}[/tex] = i
[tex]\sqrt{-2}[/tex]
= ± [tex]\sqrt{2(-1)}[/tex]
= ± [tex]\sqrt{2}[/tex] × [tex]\sqrt{-1}[/tex]
= ± [tex]\sqrt{2}[/tex] × i
= ± i [tex]\sqrt{2}[/tex]
HELP ASAP I give total 100 points and big brain!! answer these pless
1.A system of equations consists of two lines. One line passes through (0, 4) and (1, 7) . The other line passes through (−1, −5) and (5, 13) .
Does the line through the first pair of points intersect the line through the second pair of points?
yes or no
2.
Select the correct choices to complete the sentence.
A system of equations consists of two lines. One line passes through (0, 2) and (9, −1) . The other line passes through (12, 7) and (−6, −5) .
Does the line through the first pair of points intersect the line through the second pair of points? yes or no
Step-by-step explanation:
Find the slopes of the lines and compare. The lines intersect if slopes are different.
Q1Slopes are
[tex]m_1= (7-4)/(1-0)=3\\[/tex][tex]m_2= (13+5)/(5+1)=3\\[/tex]Slopes are same, lines are parallel
Q2Slopes are
[tex]m_1= (-1-2)/(9-0)=-3/9=-1/3\\[/tex][tex]m_2= (-5-7)/(-6-12)=-12/-18=2/3\\[/tex]Lines intersect as slopes are different
Slopes must not be equal to get intersection
#1
For first line
m=7-4/1-0=3/1=3For second
m=13+5/5+1=18/6=3No,Parallel
#2
First
m=-1-2/9-0-3/-9=1/3Second
m=-5-7/-6-12=-12/-18=2/3Yes, Intersect
multi step equation 3x+3-x+12=x+5
Answer:
x= -10
if u need explanation pls let me know
which algebraic expression represents the number of cups of dog food per week needed to feed 3 dogs if each dog eats x CUPS per day
A 7+3x
B 7(3x)
C 7x
D 21÷x
I need help
a)104
b)128
c)120
d)74
e)87
Answer:
m∠JTS = 104° ⇒ (A)
Step-by-step explanation:
The measure of an exterior angle of a triangle at one of its vertices equals the sum of the measures of the opposite interior angles.
Let us use this fact to solve the question
In ΔTSR
∵ T ∈ ray RJ
∴ ∠JTS is an exterior angle of ΔTSR
→ By using the fact above
∴ ∠TSR and ∠TRS are the opposite interior angles to ∠JTS
∴ m∠JTS = m∠TSR + m∠TRS
∵ m∠JTS = 27x - 4
∵ m∠ TSR = 30°
∵ m∠TRS = 18x + 2
→ Substitute their values in the equation above
∴ 27x - 4 = 30 + 18x + 2
→ Add the like terms in the right side
∴ 27x - 4 = 18x + 32
→ Add 4 to both sides
∴ 27x = 18x + 36
→ Subtract 18x from both sides
∴ 9x = 36
→ Divide both sides by 9
∴ x = 4
→ To find m∠JTS substitute x by 4 in its measure
∴ m∠JTS = 27(4) - 4 = 108 - 4
∴ m∠JTS = 104°
What is the solution of the equation 6x - 4 = 2(3x - 2). Explain your steps.
Answer: x= 4/3 but in decimal form =1.333
Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4-(2*(3*x-2))=0
4 - 2 • (3x - 2) = 0
Pull out like factors :
8 - 6x = -2 • (3x - 4)
Solve : 3x-4 = 0
Add 4 to both sides of the equation :
3x = 4
Divide both sides of the equation by 3:
x = 4/3 = 1.333
Answer:
x= undefined
Step-by-step explanation:
In order to make u understand , if u multiply 2(3x-2) it becomes 6x-4 which is the exact same as the left hand side . Therefore u cant find x from here in this manner .
For this however we can try the method bellow .
Lets say f(x)=y=6x-4=2(3x-2)
we can get the followig points for inserting domains and finind the domains . we can make graph for each . (We will not do them however)
As we have seen that both of those parts of the equation are one and the same so they will produce the exact same Line or curve .
Therefore every signle points on them r the same exact points and there fore they are the same exact line .
So the value of x is undefined and can be anything between every points on that line (Which can be infinit amounts of points) .
9. Rusty can ride his bicycle 21 miles in 3 hours. Find the unit rate of the
situation. *
O A. 7 hours per mile
O B.6.7 miles per hour
O C.63 miles per hour
D. 7 miles per hour
Rate = distance / time
Rate = 21 miles / 3 hours
Rate = 7 miles / hour
The answer is choice A. Hope this helps.
The instructions for making iced tea say to mix
4 tablespoons of the drink mix with every 2 cups of water.
If Marie is making iced tea for a party, how much drink mix will she need if she is using 8 cups of water?
Can someone help me on this question? I’ll give brainliest if you answer soon!!!
The radius of a circle is 5 miles. What is the length of a 135° arc?
Answer:
75
Step-by-step explanation:
an arc is half a circle
5. The measure of the second angle of a triangle is 20 more than the measure of the first, and the measure of the third angle is 10 less than three times the first. What is the measure of each of the three angles of a triangle?
So first we have to find equation form angles.
Let :-first angle of triangle be xPart one :-Statement :- The measure of the second angle of a triangle is 20 more than the measure of the first.
Equation :-
second angle = 20 + x
{ Remember people get's confused when to multiply and when to add. when ever there "more than" then we will add and when there is ,"times" we will multiply}
Part 2 :-Statement :-
the third angle is 10 less than three times the first
Now just see first less means we have to subtract 10 from 3 times the first means 3 × first angle.
Equation :-
third angle = 3x - 10
Part 3 :-Now let's represent :-
First angle be ∠1Second angle be ∠2third angle be ∠3We know sum of angles of triangle is equal to 180°
So :-
∠ 1 + ∠ 2 + ∠ 3 = 180°x + 3x - 10 + 20 + x = 180°4x - 10 + 20 + x = 180°5x - 10 + 20 = 180°5x + 10 = 180°5x = 180° - 10°5x = 170x = 170/5x = 34°Measure of angles :-
∠1 = x∠ 1 = 34°∠2 = 20 + x∠2 = 20 + 34°∠2 = 54°∠3 = 3x - 10∠3 = 3 × 34 - 10∠3 = 102 - 10∠3 = 92°[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-We have given in the question that, The measure of second angle is 20 more than the measure of first angle The measure of third angle is 10 less than three times the first. To Find :- We have to find the measure of all the three angles of triangle. Let's Begin :-Let the first angle be x
According to the question,
Second angle = x + 20[ 2nd angle is 20 more than the first angle ]
Third angle = 3x - 10[ 3rd angle is 10 less than thrice times the first angle ]
By using Angle sum property
It states that the sum of the angles of triangles are equal to 180°That is,
[tex]\sf{ x + ( x + 20) + ( 3x - 10) = 180{\degree}}[/tex]
[tex]\sf{ x + x + 20 + 3x - 10 = 180{\degree}}[/tex]
[tex]\sf{ 5x + 10 = 180{\degree}}[/tex]
[tex]\sf{ 5x = 180 - 10}[/tex]
[tex]\sf{ 5x = 170}[/tex]
[tex]\sf{ x = }{\sf{\dfrac{ 170}{5}}}[/tex]
[tex]\sf{ x = }{\sf{\cancel{\dfrac{ 170}{5}}}}[/tex]
[tex]\bold{ x = 34{\degree}}[/tex]
Thus,
The first angle is 34°The second angle [tex]\sf{ = 34 + 20}[/tex][tex]\bold{ = 54{\degree}}[/tex]The third angle [tex]\sf{ = 3(34 ) - 10}[/tex][tex]\sf{ = 102 - 10}[/tex][tex]\bold{ = 92 {\degree}}[/tex]Hence, The three angles of the given triangle are 34° , 54° and 92°
[tex]\bold{\huge{\underline{ Verification }}}[/tex]
Here, we have
The first angle = 34°The second angle = 54°The third angle = 92°By using Angle sum property :-
[tex]\sf{ 34 + 54 + 92 = 180{\degree}}[/tex]
[tex]\sf{ 88 + 92 = 180{\degree}}[/tex]
[tex]\sf{ 180 = 180{\degree}}[/tex]
[tex]\bold{ LHS = RHS }[/tex]
Hence, Verified
You start driving north for 6 miles, turn right, and drive east for another 19 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.
Answer:
Okay, here's the method I'm going to use.
If you drive north 6 miles, and then drive east 19 miles, you are technically making a triangle.
19 miles
l_______________
6 milesl
l
You are just missing the last side of the triangle: the straight line stretching from across your starting point to the ending point. You can find this by using the Pythagorean theorem.
a^2 + b^2 = c^2
6^2 + 19^2 = c^2
36 + 361 = c
397 = c
[tex]\sqrt{397}[/tex] = 19.924859
Rounded to the nearest tenth, your answer is
19.9 miles
Is it A, B, C, or D?
Answer:
The answer is C.
Find the equation of a line that passes through the point (-3,-1) and has a gradient of -2. Leave your answer in the form y = m x + c
Answer:
Step-by-step explanation:
y-y1 = m (x-x1), where (x1,y1) is the point the line passes through and m is the slope
y-(-1) = 2 (x-3)
y+1 = 2x - 6
Select all of the expressions which correctly show how to convert 18 inches into yards
15. Find the value of x.
(68 - x)
3x
Answer:
17=x
Step-by-step explanation:
In this case, we need to use Vertical Angles Theorem to solve this problem. Basically, because of the position of the angles, they are congruent.
68-x = 3x
Add x to both sides
68=4x
Divide by 4
17=x
Hope this helps!
Answer:
The value of 'x' is: 17°
Step-by-step explanation:
From what is being shown, there are two angles that are given:
(68 - x)°
3x°
Since they are congruent angles, meaning they are equal to each other, they will be put into a(n) equation such like shown below:
(68 - x)° = 3x°
(Then remove the parenthesis)
68° - x° = 3x°
+ x°=+3x°
------------------
68° = 4x°
------------------
(Divide both sides by 4)
[tex]\frac{68}{4} = \frac{4x}{4}[/tex]
------------------
17° = x
------------------
Your value of 'x' is 17.
Is 1/4 equivalent to 1/8
Answer:
No.
Step-by-step explanation:
1/4 is equivalent to 2/8, but not with 1/8.
Answer:
No.
Step-by-step explanation:
To find equivalent fractions, multiply the numerator and denominator by the same number.
Start with 1/4.
Multiply the numerator and denominator by 2.
You get 2/8.
2/8 is an equivalent fraction to 1/4.
2/8 and 1/8 are not equivalent.
Answer: No.
A side of the triangle below has been extended to form an exterior angle of 161°. Find the value of x.
Answer:
111
Step-by-step explanation:
180-161=19
19+50=69
180-69=111
Answer:
x=111°..............
I'm being super dumb right now and request assistance
2+(-3/5)
Answer: 2+(-3/5) = 1.4
Step-by-step explanation: Remember work what is in the parentheses first!
Simplify the expression.
Exact Form: 7/4
Decimal Form: 1.4
Mixed Number Form: 1 2/5
Answer:
[tex]\frac{7}{5}[/tex]
Step-by-step explanation:
Equation: [tex]2-\frac{3}{5}[/tex]
1). Convert to fraction: [tex]\frac{2*5}{5}-\frac{3}{5}[/tex]
2). Same denominators = combine fractions
[tex]\frac{(2*5)-3}{5}=\frac{7}{5}[/tex]
hello people ~
A floor whose length and width is 50 m and 40 m respectively needs to be covered by rectangular tiles. The dimension of each tile is 1 m x 2 m. Find the total number of tiles that would be required to fully cover the floor.
Answer:
1000 tiles required.
explanation:
area of rectangle = Length * Width
Tiles dimension:
length: 1 meterwidth: 2 meterFloor dimension:
length: 50 meterwidth: 40 meterArea of floor:
Length * Width
50 * 40
2000 m²
Area of each tile:
Length * Width
1 * 2
2 m²
Number of tiles required = Area of floor ÷ Area of each tile
→ tiles = 2000/2
→ tiles = 1000
See below.
1000
area of rectangle = width x length
Given: width of floor = 40 m length of floor = 50 m ⇒ area of floor = 40 x 50 = 2000 m²
width of tile = 1 m length of tile = 2 m ⇒ area of tile = 1 x 2 = 2 m² Number of tiles needed = area of floor ÷ area of one tile = 2000 ÷ 2 = 1000
I tried.
Susan walked 1 2/3 miles in 1 1/4 hours how many miles Susan walked in 1 hour
Answer: 3/4 of a mile
Step-by-step explanation:
AM LACKING TIME
What operation would you use for your exponents when raising a power to a power
a
Division
b
Addition
c
Subtraction
d
Multiplication
Answer:
d multiplication
What is the median?
5, 10, 8, 9, 9, 9
TYPE ONLY THE NUMERIC ANSWER
Answer:
9
Step-by-step explanation:
5, 8, 9, 9, 9, 10
(9+9)/2=9
Answer:
3n
5,10,8,9,9,9
= 5 , 1 , 0
5-1=4 - 1 3
pls give me the correct answer and solution
due date : 1:30pm
Answer:
where's the question?
Step-by-step explanation:
carry on laern
Find the area of the shaded region of circle F below. Round your answer to the
nearest tenth if necessary.
Check the picture below, so the shaded area is really just the area of one quarter of a circle's area with a radius of 7, and a triangle whose base is 7 and height is 7, so let's simply sum both of them up.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{quarter of a circle}}{\cfrac{1}{4}(\pi)(7)^2}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(7)(7)}}\implies \cfrac{49\pi }{4}~~ + ~~\cfrac{49}{2}~~ \approx~~63.0[/tex]
Answer please ????
Answer:
[tex]\mathsf{\cos T=\dfrac{28}{53}}[/tex]
Step-by-step explanation:
[tex]\mathsf{\cos(\theta)=\dfrac{adjacent\ side}{hypotenuse}}[/tex]
[tex]\implies \mathsf{\cos T=\dfrac{28}{53}}[/tex]
What is the distance between (-2,1) and (-1,2) on a coordinate plane
Answer:
√2 or 1.414
Step-by-step explanation:
the distance between two points
Please help! 15 Points!
Answer:
Option C and D
Step-by-step explanation:
2π/3 refers 120°which falls in the second quadrant. In second quadrant sin value is positive and tan & cos value is negative.
tan 120 = - tan 60 = -√3
Solve each one
Thank you!
hope this helps! sorry if it didnt
Find the area of the figure. Use 3.14for.
18 m
22m
The area of the figure is about ____ m2
Area of triangle = 1/2 x base x height
Area of the triangle = 1/2 x 22 x 18 = 198 square m.
Area of semi circle = 1/2 x PI x r^2
Area of semi circle = 1/2 x 3.14 x 11^2 = 189.97 square m.
Total area = 198 + 189.97 = 387.97 square m.
Round up to 388 square m.
The length of a rectangle is 5 more than twice the width. If the perimeter of th
rectangle is 34, what is the length?
The length of a rectangle is 5 more than twice the width. If the perimeter of the rectangle is 34 cm find the length?
Explanation -:In this question we are provided with the perimeter of the rectangle = 34 cm and it is given that the length of the rectangle is 5 more than the twice it's breadth and asked to find out the length of the rectangle.
[tex] \small \orange{ \underline{\rm \blue{length \: of \: a \: rectangle \: is \: 5 \: more \: than \: twice \: the \: width.}}}[/tex]
Let us assume breadth as x then length = 2x +5
We know,
[tex] \star \: \large\boxed{ \rm{ Perimeter_{(rectangle)} = 2(length + breadth)}}[/tex]
Substituting the values we get
34 = 2(2x +5 + x)
→ 34 = 2(3x + 5)
→ 34 = 6x + 10
→ 34 - 10 = 6x
→ 24 = 6x
→ [tex]\dfrac{24}{6}[/tex] = x
x = 4
Length = 2x + 5 = 2 × 4 + 5 = 8 + 5 = 13 cm
Breadth = x = 4cm
Length = 13 cm.