Let 'x' be the distance from THE far bank where 700 is the distance to the NEAR bank
boat one has travelled 700 (rate = 700/unit time) boat two has travelled x rate = x / unit time
boat one then travels x + 400 more and boat two travels 700 + (700+x -400) more when they meet
The time is the same rate x time = distance distance/rate = time equate the distances divided by the respective rates
(700 + x + 400)/700 = ( x + 700 + (700+x-400) )/x
1100x + x^2 = 1400x + 700000
x^2-300x -700000 = 0 quadratic formula yields x = 1000
One boat travels 700 the other 1000 whe they first meet.....width of river = 700+ 1000 = 1700 m
What are the roots of the equation x²+2x+17=0 in simplest a+bi form?
Answer:
-1 ±4i
Step-by-step explanation:
The quadratic can be written in vertex form as ...
x² +2x +17 = 0
(x² +2x +1) +16 = 0 . . . . . . . . identify the part that can be a perfect square
(x +1)² = -16 . . . . . . . . . . . . subtract 16
x +1 = ±√(-16) = ±4i . . . . take the square root
x = -1 ±4i . . . . . . . . . . . subtract 1
The roots of the equation are x = -1-4i and x = -1+4i.
_____
Additional comment
It can be worthwhile to remember the form of a perfect square trinomial:
(x +a)² = x² +2ax +a²
If you know the coefficient of x, you can use half of it as the constant in each binomial factor.
In the above, we had 2a=2, so a=1 and a²=1. The constant 17 then is resolved into two parts: one part (1) is used to "complete the square" and the other part (16) is the y-coordinate of the vertex. It is used to find the "radical" portion of the roots.
The roots of the equation [tex]x^2 + 2x + 17 = 0[/tex] are [tex]x = -1 +4i[/tex] and [tex]x = -1 - 4i[/tex].
To find the roots of the equation [tex]x^2 + 2x + 17 = 0[/tex] in simplest a + bi form, we can use the quadratic formula.
The quadratic formula states that for an equation in the form[tex]ax^2 + bx + c = 0[/tex], the roots can be found using the formula:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
We have a = 1, b = 2, and c = 17.
Substituting these values into the quadratic formula, we get:
[tex]x = \frac{-2 \pm \sqrt{4 - 68}}{2}[/tex]
[tex]x = \frac{-2 \pm \sqrt{-64}}{2}[/tex]
[tex]x = \frac{-2 \pm \sqrt{64i^2}}{2}[/tex]
[tex]x = \frac{-2 \pm 8i}{2}[/tex]
[tex]x = -1 \pm 4i[/tex]
So, [tex]x = -1 +4i[/tex] and [tex]x=-1-4i[/tex] are roots.
To learn more on Quadratic equation click:
https://brainly.com/question/17177510
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How to use a protractor.
Answer:
You can see below!
Step-by-step explanation:
Basically, a protractor is used to measure angles. You probably have a semi-circle shaped one. Looking at the bottom middle of the protractor should show you lines intersecting each other at a point. If you have an angle on a piece of paper, place that point on the ends of the line segments making up the angle. Then, check where each line of the angle crosses the numbers on the outer rim. That shows you the measure of the angle you are examining. It can be a bit tricky, but with practice you'll get it in no time!
what is 5 x 1284
plz answer thanks
Answer:
6420
Step-by-step explanation:
hope this helps
How to solve quadratic using completing the square.
Answer:
You can solve quadratic equations by completing the square. Completing the square involves creating a perfect square trinomial from the quadratic equation, and then solving that trinomial by taking its square root.
Step-by-step explanation:
_______ x 0.7 = 0.287
Answer:
0.41
Step-by-step explanation:
Simply reverse it:
0.287 / 0.7 = 0.41
Answer:
0.41 is the answer for _______×0.7=0.287
HELP ME PLEASE!!!!!!!!!!!!
i frist 1 1 2
Step-by-step explanation:
Y
Answer:
Step-by-step explanation:
i think for number 1 is growth and number 2 decay and for 3 growth...hope this helps!
The width of a rectangle measures (7f-4)(7f−4) centimeters, and its length measures (2f+5)(2f+5) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
Perimeter is 18f+2
Step-by-step explanation:
Given : rectangle having width (7f-4) and length (2f+5)
To Find : Expression For Perimeter = ?
Solution : We know that, perimeter of rectangle is 2(L+B)
-> 2(7f-4+2f+5)
-> 2(9f+1)
-> 18f + 2
I hope this helps.
Identify the slope and y-intercept for 3x + 4y = 9.
10x is greater than or equal to 120 cm^2
Answer:
x greater than or equal to 12cm^2
Step-by-step explanation:
MP Construct Arguments Raul finds a way to divide
48 building blocks into 6 equal groups. Jerry finds a
way to divide 48 building blocks into 8 equal groups.
Whose way has the greater number of building blocks
in each group? Explain.
Answer:
Raul
Step-by-step explanation:
Since 8 groups of building blocks has a smaller amount than 6 equal groups of building blocks, so Raul has more blocks in each group
0.0346 written in standard form
Answer:
3.46x10-2
×
10
−
2
3.46
×
10
−
2
Explanation:
a number expressed in
standard form
is.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
a
×
10
n
2
2
∣
∣
∣
−−−−−−−−−−−−
where
1
≤
a
<
10
and n is an integer
express
0.0346
as a number between 1 and 10
3
∙
46
we now have to move the decimal point 2 places to
the left to retain equality
move to the right
→
then n is positive
move to the left ←
then n is negative
⇒
0.0346
=
3.46
×
10
−
2
100 POINTS WHEN ANSWERED AND BRAINLIEST GIVEN TO FIRST CORRECT ANSWER WHENEVER IT LETS ME
Hello there, below here is an attached file of the particular question I have. Thank you so much for coming here to answer! I appreciate you, and I hope have a good day or night!
Answer:
a: 0
b: 1,3
c: 2
Step-by-step explanation:
a: 4 is the y intercept meaning 0 is the number of seconds when the ball is 4 feet in the air
b: to easily find this, we can graph.
1st screenshot is for B.
We see that y=52 intersects twice with the graph, meaning the ball was at 52 feet twice. the times are 1 second and 3 seconds
a: we graph again, but with y=68 we see that it only intersects once. at x=2.
Is this a function?
Answer:
No, because if you do the vertical line test, the line will hit that two times, Therefore it is not a function.
Step-by-step explanation:
4 + 4 + 4 + 4 + 4 if it is converted into multiplication form it becomes
What value of n make the equation true ?
-15 n + 7 = 2
A sweatshirt at Macy’s costs $68. If you have a 30% coupon, how much will the sweatshirt be after the discount is applied?
Answer:
$47.60
Step-by-step explanation:
Answer:
$47
Step-by-step explanation:
PLS HELP ASAP !!
i'll mark as brainliest if u answer:))
Answer:
A = 60
B:25
Step-by-step explanation:
A looks about 1/3 of a 180
B looks about 1/3 of A
The regular hexagon has a radius of 4 in. A regular hexagon has a radius of 4 inches. What is the approximate area of the hexagon? 24 in. 2 42 in. 2 48 in. 2 84 in. 2.
The approximate area of the hexagon is 48 square inches.
Given that the regular hexagon has a radius of 4 inches, to determine what is the approximate area of the hexagon the following calculation must be performed:
Area of a regular hexagon = (perimeter x apothem) / 2 (4 x 6 x 4) / 2 = X (24 x 4) / 2 = X 48 = X
Therefore, the approximate area of the hexagon is 48 square inches.
Learn more about maths in https://brainly.com/question/18500585
table value equation for y=2x + 4
Answer:
below
Step-by-step explanation:
All we need to do is substitute the x values given in the table to find each value of y thats blank.
When x = -1,
y = 2(-1) + 4
y = -2 + 4
y = 2
When x = 1,
y = 2(1) + 4
y = 2 + 4
y = 6
Whe x = 2,
y = 2(2) + 4
y = 4 + 4
y = 8
Best of Luck!
pls give all numbers
Can someone pls help me
Please show your work
Answer:
-5=x
Step-by-step explanation:
Angle 105º = (110+x)º
Solve for x.
105=110+x
Subtract 110 from both sides of the equation.
-5=x
Hope this helps :)
what is the decimal of 967.567
Answer:
I believe its 0.567 because its the decimal part of the whole number (i hope thats what you asked)
Answer:
567
967---------
1000
Step-by-step explanation:
multiply to remove 3 decimals
Please help i will give brainliest :)
Solve for j.
j − –95 = 822
j =
Answer:
j = 727
Step-by-step explanation:
j - (-95) = 822j + 95 = 822j = 822 - 95j = 727The system of equations y = -2x + 3 and y = x is graphed. What is the solution to the system of equations? ( graph above)
(0,0)
(1,1)
no solution
infinitely many solutions
the answer is y=1x because you have to use rise over run and the y intercept is 0.
Which expression is undefined? (-4+0) O A. OB. 0 : 11 O c. OD. –
Answer:
C
Step-by-step explanation:
Third expression asks you to basically divide by zero. That is, find a number that multiplied by 0 gives you 3, which is impossible.
Hello!
-----------------------------------------------------------------------------------------------------------------
Option C
Division by 0 is undefined.
6-6=0, and any expression that has 0 it its denominator is undefined.
I hope it helps you! (:
~SparklingFlower
-----------------------------------------------------------------------------------------------------------------
In a fraction, the value that represents the number of parts as compared to the whole is the ______
Answer:
Its the Denominator. Hope I helped please mark brainliest if you can and thanks! <3
Step-by-step explanation:
Answer:
21
Step-by-step explanation
OUI BONSEIUR
what is the formula for surface area of a pyramid?
what is the forumla for surface area of a square
for pysamid is ph+B2
hope it helps
simplify 12b+4b^2-10b
Answer:
4 b 2 + 2 b
Step-by-step explanation: hope it helps
1.
Which of the following equations describes the graph?
A. y= -x^2 + 1
B. y= x^2 - 1
C. y= x^2 + 1
D. y= -x^2 - 1
Answer:
A. y= -x^2 + 1
Step-by-step explanation:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(
0
,
1
)
Focus:
(
0
,
3
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
5
4
x
y
−
2
−
3
−
1
0
0
1
1
0
2
−
3
________________________________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
−
1
)
Focus:
(
0
,
−
3
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
−
5
4
x
y
−
2
3
−
1
0
0
−
1
1
0
2
3
__________________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
1
)
Focus:
(
0
,
5
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
3
4
x
y
−
2
5
−
1
2
0
1
1
2
2
5
_________________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(
0
,
−
1
)
Focus:
(
0
,
−
5
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
−
3
4
x
y
−
2
−
5
−
1
−
2
0
−
1
1
−
2
2
−
5