Given :
A motorboat travels 9 miles downstream (with the current) in 30 minutes.
The return trip upstream (against the current) takes 90 minutes.
To Find :
The speed of stream and motorboat.
Solution :
Let, speed of stream is u and speed of motorboat is v.
Now, we know distance is same in both case.
Distance( downstream ) = speed × time
[tex]9 = ( v +u ) \times 0.5\\\\v + u = 18[/tex]....1)
Distance( upstream ) = speed × time
[tex]9 = ( v- u ) \times 1.5\\\\v-u = 6[/tex]....2)
Solving equation 1 and 2 , we get :
v = 12 miles/hour and u = 6 miles/hour
Hence, this is the required solution.
Answer:
The speed of the stream is 6 mph, and the speed of the boat is 12 mph.
Step-by-step explanation:
Downstream:
9 miles in 30 minutes (0.5 hour).
9 mi / 0.5 h = 18 mph
Upstream:
9 miles in 90 minutes (1.5 h).
9 mi / 1.5 h = 6 mph
Let s = speed of stream.
The speed of the stream adds to the speed of the boat downstream and is subtracted fromt he speed of the boat upstream.
Let speed of boat be b.
b + s = 18
b - s = 6
Add the equations.
2b = 24
b = 12
b + s = 18
12 + s = 18
s = 6
The speed of the stream is 6 mph, and the speed of the boat is 12 mph.
product of 3 and e in algebra
Answer:
3e
Step-by-step explanation:
A builder uses the ratio of 3 parts of cement to 12 parts of sand to make a mixture that holds bricks together . How many parts of cement does the builder use for each part of sand ?
Answer:
1/4 parts of cement
Step-by-step explanation:
Given :
3 parts of cement = 12 parts of sand
For each part of sand, let the part of cement used = x
Writing the relation in the form of cross multiplication :
3 = 12
x = 1
Cross multiply :
12x = 3
x = 3 / 12
x = 1/4
Hence, for each part of sand, 1/4 parts of cement is used.
The figure below is a square. Find the length of side x in simplest
radical form with a rational denominator.
Please help!!! Will give brainliest!
Answer:hhhhhhhhhbbbbb
Step-by-step explanation:
44444444
(3/5x + 4) + (1/5x -1)
Answer:
4/5x+3
Step-by-step explanation:
remove the useless parenthesis, then calculate the x sum then the normal numbers sum
A table of values of a linear function is shown below.
Find the slope and y-intercept of the function's graph, and find the equation for the function.
WHich of the following has the steepest slope?
a. y = -4x + 1
b. y = 2x + 3
c. y = x+6
d. y = -3x - 4
Answer: Choice A)
y = -4x+1
=======================================
Explanation:
The general format of a linear equation can be written as y = mx+b
m = slope
b = y intercept
The steepest slope is the value of m that is furthest away from zero. If m > 0, then we're looking for the largest value of m or value to the right of 0. If m < 0, then we're trying to get as left as possible.
Of the choices we have, choice A has the m value furthest from 0. If you want, you can make each slope positive and then compare to see which slope is largest.
the coordiantes of three vertices of a square are (4,14), (10,14), and (4,8). what are the coordinates of the missing vertex
Answer:
(10, 8)
Step-by-step explanation:
The missing vertex can be found by plotting the given coordiantes on a graph.
An art teacher bought a pack of 96 drawing sheets.She kept aside 12 sheets for later use and distributed the remaining equally among 6 students. How many sheets did each student get?
Answer:
14
Step-by-step explanation:
First, find out how many she had to distribute
96 - 12 = 84
Now divide 84 by the number of students
84/6=14
How many triangles can a heptagon be divided into?
3
4
6
5
Answer:
5
Step-by-step explanation:
The lengths of the sides of a triangle are in the extended ratio 5: 8.9. The perimeter of the triangle is 44 cm. What are the lengths of the sides?
The lengths of the sides of the triangle in cm are
Answer:
10cm, 16 cm, 18 cm
Step-by-step explanation:
We have to find the sum of proportion: sum of ratios =
a : b : c = 5:8:9
Sum of proportion = 5 + 8 + 9
= 22
Length of side a
5/22 × 44 = 10 cm
Length of side b
8/22 × 44 = 16 cm
Length of side a
9/22 × 44 = 18 cm
Therefore: lengths of the sides of the triangle in cm are
10cm, 16 cm, 18 cm
Help me out please !!
Answer:
I'm thinking it's B
Step-by-step explanation:
Can you help me with these questions
Answer:
7) Unfilled dot at 5 with a line going right
8) A filled dot at 8 with a line going right
9) Unfilled dot at 22 with a line going left
10) A filled dot 13 with a line going left
11) x < 9
12) x > 14
13) x ≤ 11
14) x ≥ 7
Step-by-step explanation:
> means greater than
≥ means greater than or equal to
< means less than
≤ means less than or equal to
If something is greater than the given number then the variable increases in value and will be on the right side of the number line
If something is less than the given number then the variable decreases in value and will be on the left side of the number line
If a variable is < or > the dot is unfilled because it does not include that number
If a variable is ≤ or ≥ the dot is filled because it includes the given number
Solve for r.
0.5(r +2.75) = 3
Answer:
r = 3.25
Step-by-step explanation:
Start by eliminating the decimal fraction 0.5: 2(0.5)(r + 2.75) = 2(3) = 6
Then we have r + 2.75 = 6.
Isolate r by subtracting 2.75 from both sides. This leaves us with
r = 6 - 2.75 = 3.25.
r = 3.25
(trigonometry) solve for x
Answer:
x°=40.7°
Step-by-step explanation:
Sin(x°)=15/23
x°=Sin^-1(15/23)=40.7°
2hours to 1day as a ratio in its simplest form
Answer:
Step-by-step explanation:
convert 1 day into hours
1 day=24 hour
2/24
=1/12
1 day = 24 hours
So,
2 hours : 1 day2 hours : 24 hours1 : 12On friday a local burger shop sold a combined total of 336 ham burgers and cheese burgers. The number of cheese burgers sold was two times the number of hamburgers sold. How many burgers were sold on friday?
I need correct answers asap, if you have Inst4gr4m and you're good at math and can help me with 28 m0re questions, I'll be so much more than thankful
Answer:
6 hours
Step-by-step explanation:
Research is 5%, Games is 25%, so the diffrence is 20%
20% of 30 hours = 30 x2/10 = 6 hours
Tremaine played 6 hours more video games than research.
Answer:
F
Step-by-step explanation:
We can use a proportions to solve this problem:
time of researches (in percentages 100% is used to indicate the total)
5 : 100 = x : 30
x = (5 * 30)/ 100 = 1.5
time of games
25 : 100 = x : 30
x = (25 * 30)/100 = 7.5
7.5 - 1.5 = 6 hours
Anyone pls I need help plss
1 goes in the green space
70 goes in the gray space
==============================================
Explanation:
There are 5 gold and 350 total. That forms the fraction 5/350 which fully reduces to 1/70 after you divide both parts by the GCF = 5
A = 5, B = 350
A/GCF = 5/5 = 1 in the numerator of the final answerB/GCF = 350/5 = 70 in the denominator of the final answerThe fraction 1/70 can be thought of like saying "There's 1 gold coins in 70 coins total" or "there's 1 gold coin for every 70 coins".
Then we could scale up like so
1 gold : 70 total2 gold : 140 total3 gold : 210 total4 gold : 280 total5 gold : 350 totalfind f(3) if f(x) = -4x + 1?
Answer:
f (3) equals -11
Step-by-step explanation:
f (x) = -4x + 1
For f(3), just substitute 3 in the place of x:-
f (3) = -4 x 3 + 1
f (3) = -12 + 1
f (3) = -11Answer:
-11
Step-by-step explanation:
where x is out -3 so it would look like
-4(3)+1
which is -11
you do -4 * 3 first which = -12 than add one you will get -11
answer pls with a detailed explanation
Answer:
SA = 225 cm²
Step-by-step explanation:
The given pyramid dimensions are;
The length of the rectangular base of the pyramid, l = 12 cm
The width of the base, w = 6 cm
The area of the rectangular base, Aₐ = 12 cm × 6 cm = 72 cm²
The height of one of the triangles forming the side of the pyramid, h₁ = 8 cm
The base length of the above triangle, b₁ = 12 cm
The area of the above triangle, A₁ = (1/2)×12 cm × 8 cm = 48 cm²
The height of the other of the triangles forming the other side of the pyramid, h₂ = 9.5 cm
The base length of the above triangle, b₂ = 6 cm
The area of the above triangle, A = (1/2) × 9.5 cm × 6 cm = 28.5 cm²
The surface area of the pyramid, SA = Aₐ + 2 × A₁ + 2 × A₂
Therefore;
SA = 72 cm² + 2 × 48 cm² + 2 × 28.5 cm² = 225 cm²
SA = 225 cm²
¿Qué es un binomio al cuadrado perfecto?
Un binomio al cuadrado es una suma algebraica que se suma por sí misma, es decir, si tenemos el binomio a + b, el cuadrado de ese binomio es (a + b) (a + b) y se expresa como (a + b)2. ... Se le llama cuadrado perfecto, porque el resultado de su raíz cuadrada siempre es un binomio.
Which equations have no real solution but have two complex solutions? A 3x>2-5=-8 b 2x>2=6x-5 c 12x=9x>2 +4 d -x>2 - 10x =34
Answer:
[tex]3x^2-5x=-8[/tex]
[tex]2x^2=6x-5[/tex]
[tex]-x^2-10x=34[/tex]
Step-by-step explanation:
The equations are:
[tex]3x^2-5x=-8[/tex]
[tex]2x^2=6x-5[/tex]
[tex]12x=9x^2+4[/tex]
[tex]-x^2-10x=34[/tex]
(a) [tex]3x^2-5x=-8[/tex]
Add 8 to both sides
[tex]3x^2 - 5x + 8 =0[/tex]
To do this, we simply calculate the discriminant (d) using:
[tex]d =b^2 - 4ac[/tex]
If [tex]d < 0[/tex]
Then it has complex roots
Where: [tex]a = 3; b = -5; c = 8[/tex]
[tex]d = (-5)^2 - 4 * 3 * 8[/tex]
[tex]d = 25 - 96[/tex]
[tex]d = -71[/tex]
[tex]-71 < 0[/tex] --- complex root
(b) [tex]2x^2=6x-5[/tex]
Equate to 0
[tex]2x^2 - 6x + 5 = 0[/tex]
[tex]d =b^2 - 4ac[/tex]
[tex]d = (-6)^2 - 4 * 2 * 5[/tex]
[tex]d = 36 - 40[/tex]
[tex]d =-4[/tex]
[tex]-4 < 0[/tex] --- complex root
(c) [tex]12x=9x^2+4[/tex]
Equate to 0
[tex]9x^2 - 12x + 4 = 0[/tex]
[tex]d =b^2 - 4ac[/tex]
[tex]d = (-12)^2 - 4 * 9 * 4[/tex]
[tex]d = 144 - 144[/tex]
[tex]d = 0[/tex] ---- real roots
(d) [tex]-x^2-10x=34[/tex]
Equate to 0
[tex]-x^2 - 10x - 34 = 0[/tex]
[tex]d =b^2 - 4ac[/tex]
[tex]d = (-10)^2 - 4 * (-1) * (-34)[/tex]
[tex]d = 100 - 136[/tex]
[tex]d = - 36[/tex]
[tex]-36 < 0[/tex] ---- complex root
A researcher reports an F-ratio with df between = 3 and df within = 40 from an independent-measures ANOVA. How many treatment conditions were compared in the experiment?
There were 4 treatment conditions compared in the experiment.
When using independent-measures ANOVA (Analysis of Variance), the F-ratio is determined by contrasting the variability within and between treatment conditions.
The ratio of these two variances is known as the F-ratio.
Degrees of freedom (df) within a treatment condition are denoted as df within, and df between denotes the df between treatment conditions.
The formula for calculating the F-ratio is:
F = (Variance between groups) / (Variance within groups)
Given that the df between = 3 and df within = 40, we can use this information to find the number of treatment conditions (groups) compared in the experiment.
The number of treatment conditions (groups) can be calculated using the formula:
Number of groups = df between + 1
Therefore, in this case:
Number of groups = 3 + 1 = 4
So, there were 4 treatment conditions compared in the experiment.
Learn more about ANOVA click;
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PLEASE HELP ASAP FAST HURRY
The graph below shows the relationship between the number of tickets sold for a music concert and the amount of money collected from the sale of the tickets. (1 pt.)
Which equation represents the relationship between the tickets sold (t) and the money collected (c)?
Hlw Gøød Mørnîng.....Plz guys solve this immediately......
Answer:
The remainder is 7
Step-by-step explanation:
What we have to do here is to set g(x) to zero and solve for x
The value of x is then substituted into the polynomial p(x)
we have this as follows;
x-1 = 0
x = 1
P(1) = 1^3 -6(1)^2 + 9(1) + 3
P(1) = 1 - 6 + 9 + 3
P(1) = 7
This value is the remainder
it’s two different answers but i need help !!
Answer:
use this to help you determine your answer
Step-by-step explanation:
Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. ... and another pair of corresponding sides are equal in two right triangles.
Use long division to find the quotient below.
(2x3 + x2 + 25) /(2x+5)
Answer:
x^2 -2x +5
Step-by-step explanation:
x^2 -2x +5
----------------------------------------------------------
2x + 5 / 2x^3 + x^2 + 0x + 25
-(2x^3 + 5x^2)
----------------------------
-4x^2 + 0x
-( -4x^2 - 10x )
-----------------------------------------
10x + 25
-(10x + 25)
---------------------------
0
The desired quotient is x^2 -2x +5
Alex and payton each have a favorite pancake recipe. Alexs recipe uses 7 1/2 cups of flour for 5 batches, paytons recipe uses 3/4s cup of flour more per batch than alexs recipe ises for batch. What expression can be used to determine the number of cups of flour used to make z batches of paytons pancake recipe
Answer:
9/4z cups
Step-by-step explanation:
Alex recipe uses 7 1/2 cups of flour for 5 batches
Cups of flour per batch = 7 1/2 cups ÷ 5 batches
= 15/2 ÷ 5
= 15/2 × 1/5
= (15*1)/(2*5)
= 15/10
Alex recipe per batch= 3/2 cups of flour per batch
paytons recipe uses 3/4 cup of flour more per batch than alexs recipe
Payton's recipe per batch = Alex recipe per batch + 3/4 cups
= 3/2 + 3/4
= (6+3)/4
= 9/4 cups of flour
Payton's recipe per batch = 9/4 cups of flour
What expression can be used to determine the number of cups of flour used to make z batches of paytons pancake recipe
Payton's recipe for z batches = Payton's recipe per batch * number of batches
= 9/4 cups * z batches
= 9/4z cups
Payton's recipe for z batches = 9/4z cups
Please help!!
I'll give brainlist!
Step-by-step explanation:
Perpendicular : means two lines meet at 90°
1) angle B = 90° - 50°
= 40°
2) Angle D = 90° - 30°
= 70°