The first ferry's speed is 18.5 mph and the second ferry, which is slower, travels at 13.5 mph.
How to find the calculation?Let x represent the first ferry's speed.
The second, slower ferry's speed is then x-5 (since 5 miles per hour slower)
First ferry time equals distance/speed equals
50/x
Time spent on the second ferry:
50 / x - 5
The difference in times is 1 hour because the second ferry departs an hour earlier.
50 / x - 5 - 50/x = 1
50x - 50(x - 5) = x (x - 5 )
250 = x² - 5x
x² - 5x - 250 = 0
(x - 10 )(x + 5) = 0
x = 18.5 - 13.5
Speed can never be detrimental.
Therefore, the first ferry's speed is 18.5 mph.
and the second ferry, which is slower, travels at 13.5 mph.
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HELP DUE IN 15 MINS!
x=??
Answer:
Step-by-step explanation:
Remark
The angle formed by the intersection of a tangent to a circle and an intersecting secant is 1/2 (Arc PS - arc PR)
PS = 208
PR = 74
Solution
x = 1/2 (208 - 74)
x = 1/2 (134)
x = 67
factorise fully -b -20
Answer:
−(b+20)
Step-by-step explanation:
The only thing we could possibly do is factor out the negative since there are no factors no squared numbers.
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The red Maserati traveled at a speed of 120km/h for 5 hours one day. The green Ford Pickup traveled at a speed of 74km/h for 6 hours the same day. Find the difference in the distance traveled by two vehicles.
Answer:
156km
Step-by-step explanation:
Given data
The red Maserati traveled at a speed of 120km/h for 5 hours one day.
Distance = speed*time
Distance= 120*5
Distance= 600km
The green Ford Pickup traveled at a speed of 74km/h for 6 hours
Distance = speed*time
Distance= 74*6
Distance= 444km
Hence the difference is
=600-444
=156km
Atiker wants to uile a rectangular wall which reasures Ambuy 2.5 m,
achtile measures 16 cm by 10 cm,
How many tiles will he need for the wall?
Tik
2.5 m
10 cm
16 cm
Answer:
Step-by-step explanation:
There are 100 cm in 1 meter. the dimensions are 400cm by 250cm. depending on which way you turn them, they will fit better. if you take 400 divided by 16, you will have a row of 25 wide and if you divide 250 by 10, you will have a length of 25. you now have 25 rows of 25. 25x25 is 625 tiles.
Hope this helps
Building blocks are in the shape of a cube. The dimensions of the building blocks are based on the length of the packaging box, which is defined as [tex]\frac{1}{12} x^{2}[/tex] centimeters, where x is the length of the packaging box. What is the volume of a building block in terms of x?
ily whoever answers right <3
The volume of the building block in terms of x is V = x⁶/1728
What is volume?Volume is the amount of space a substance occupies.
What is the volume of a building block in terms of x?Since building blocks are in the shape of a cube. The dimensions of the building blocks are based on the length of the packaging box, which is defined as x²/12 centimeters, where x is the length of the packaging box.
Since the building blocks are in the shape of a cube, its volume is the volume of a cube.
What is the volume of a cube?The volume of a cube is given by V = L³ where L = length of side of cube.
To find the volume of the building block, since the length of the building block is L = x²/12, then we find the volume of the building block by substituting L into V.
So, V = L³
V = (x²/12)³
= x⁶/12³
= x⁶/1728
So, the volume of the building block is V = x⁶/1728
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The equation of line R, shown below, can be
written in the form y = mx + c.
What are the values of m and c?
Give each of your answers as an integer or
as a fraction in its simplest form.
Straight line has the equation is, y = 5x - 4.
What is a straight line's mathematical equation?An endless number of points that are connected on both sides of the point make up a straight line.
The slope of a straight line, "m," is determined by:
m = y2 - y1 / x2 - x1
A linear equation has the expression y = mx + b in slope-intercept form. X and Y are the variables in the equation. The numbers m and b stand for the line's slope (m) and the value of y at x = 0.
The graph's acquired points are (0,-4) and (1,1)
The slope is ,
m = 1-(-4) / 1-0
= 5/1
= 5
The line's equation will be as follows since it crosses the y-axis at its intersection point, where C = -4.
⇒ y = mx + c
⇒ y = 5x + (-4)
⇒ y = 5x - 4
As a result, y = 5x - 4 is the equation for the straight line depicted below.
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if you can buy one bunch of cilantro for $1.60 how many can you buy with $38.40?
Answer: 24 bunches of cilantro
Step-by-step explanation:
1. Set a proportion with the given information, which should be 1/1.60 = x/38.40.
2. Cross multiply. Now the equation should 1.60x = 38.40.
3. Divide by 1.60 to get x alone to find out how many bunches of cilantro you can buy with $38.40. This should give you x = 24 bunches of cilantro.
Answer:
24 bunches
Step-by-step explanation:
The person below is correct
GIVEN: GH (congruent JH and FH (congruent) HI
PROVE: FG (congruent) IJ
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
What is Congruency of triangles?Triangle congruence: Two triangles are deemed to be congruent if all three of their corresponding sides and angles have the same magnitude. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "≅".
When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general. Finding all six dimensions is necessary, though.
Given that,
GH ≅ JH
FH ≅ HI
And,
∠GHF = ∠JHI
Therefore,
ΔGHF ≅ ΔJHI (SAS Congruency)
∴ FG = IJ (CPCT theorem)
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
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Which graph doesn't belong?
A
B
C
D
Answer:
i think it's C
Step-by-step explanation:
Lin is solving the inequality 15-x< 14. She knows the solution to the
equation 15 - x = 14 is x = 1
How can Lin determine whether x > 1 or x < 1 is the solution to the
inequality?
If Lin is solving the inequality [tex]15-x < 14[/tex] and she know the solution is x = 1 , then the solution of inequality is [tex]x > 1[/tex] .
The inequality that Line is solving is [tex]15-x < 14[/tex] ,
the solution of the equation [tex]15-x = 14[/tex] is given as x = 1 ;
we have to find the value of x for which the given inequality expression is true ,
Case(i) , let us take [tex]x > 1[/tex] ,
So , putting x = 2 , in the inequality ,
we get ; [tex]15-2 < 14[/tex]
= 13 < 14 , that is TRUE .
Case(ii) , let us take [tex]x < 1[/tex] ,
So , putting x = 0 in the inequality ,
we get ; [tex]15-0 < 14[/tex]
= 15 < 14 , that is FALSE .
Therefore , the solution of the inequality is x > 1 .
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Two ropes are used to stake a new tree. If they are each tied 3 feet up from the ground and 4 feet from the base of the tree. How many feet of rope do you need total?
Answer:
7
Step-by-step explanation:
find area of blue shaded region
Answer:
[tex] \approx \: 7.33 \: {cm}^{2} [/tex]
Step-by-step explanation:
Area of the blue shaded region
[tex] = \frac{ \theta}{360 \degree} \times \pi r_1^2 - \frac{ \theta}{360 \degree} \times \pi r_2^2 \\ \\ = \frac{ \pi\theta}{360 \degree} ( r_1^2 - r_2^2) \\ \\ ( r_1 = 4 \: cm, \: \: r_2 = 3\: cm, \: \: \theta = 120 \degree) \\ \\ = \frac{ 3.14 \times 120 \degree}{360 \degree} ( 4^2 - 3^2) \\ \\ = \frac{ 3.14 }{3} \times 7 \\ \\ = \frac{21.98}{3} \\ \\ = 7.32666667 \\ \\ \approx \: 7.33 \: {cm}^{2} [/tex]
help please I don't know this one
Answer:
21
Step-by-step explanation:
whats the value of q
Answer:
Incomplete Question. Send Full question pls.
Solve the following system of equations graphically on the set of axes below.
y= x-2
y=x−2
y= -3x-6
y=−3x−6
The solution of the equation is x = -1 and y = -3.
And the intersection point is (-1, -3).
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation.
And simultaneous equation is the system of equation.
Given system of equations:
y = x-2 ...... equation 1
y = −3x−6 ...... equation 2
To solve the system of equations:
Substitute the value of y from the equation 1 to equation 2,
we get,
x - 2 = -3x - 6
x + 3x = -6 + 2
4x = -4
x = -1
Then y = -1 -2 = -3.
By graphically:
1). Draw the linear equation on the graph.
2). And the intersection point of the lines is a solution of the equation.
3). The solution is x = -1 and y = -3.
The complete graph is given in the attached image.
Therefore, the solution is x = -1 and y = -3.
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Find the greatest number that divides 1626, 1950 and 2274 leaving a remainder of 6 in each case? Please help
Answer:
The common divisor that leaves a reminder of 6 is 324
Step-by-step explanation:
Given
1626, 1950 and 2274
Required
Common divisor that leaves a remainder of 6
First, we subtract 6 from each number
[tex]1626 - 6 = 1620[/tex]
[tex]1950 - 6 =1944[/tex]
[tex]2274 - 6 = 2268[/tex]
Next, we find the common divisor of 1620, 1944, 2268
[tex]1620 \to 2 * 2 *3 * 3*3*3*5[/tex]
[tex]1944 \to 2 * 2 * 2 * 3 * 3 * 3 * 3 * 3[/tex]
[tex]2268 \to 2 * 2 * 3 * 3 * 3 * 3 * 7[/tex]
The common factors are:
[tex]Common = 2 * 2 * 3 * 3 * 3 * 3[/tex]
[tex]Common = 324[/tex]
Together, Hermione and Luna bought 2016 Chocolate Frogs for Harry. If Hermione paid 98 coins and Luna paid 28 coins, for how many Chocolate Frogs did Hermione pay?
If Hermione paid 98 coins and Luna paid 28 coins, Hermione paid for 672 Chocolate Frogs.
We can start the problem by using algebra. Let x be the number of Chocolate Frogs that Hermione paid for. Then we know that:
x + (2016 - x) = 2016 (the total number of Chocolate Frogs)
Also, we know that the cost of the Chocolate Frogs Hermione paid is 98 coins, and the cost of the Chocolate Frogs Luna paid is 28 coins. Let's assume the cost of each Chocolate Frog is y. Then we can write:
x * y = 98 and (2016 - x) * y = 28
Now we have a system of two equations with two variables (x and y). To find the value of x, we can use any method to solve the system of equations, such as substitution or elimination.
Using substitution, we can solve for y in the second equation and substitute it into the first equation:
(2016 - x) * y = 28
y = 28 / (2016 - x)
x * (28 / (2016 - x)) = 98
x * (28 / (2016 - x)) = 98
x = 98 * (2016 - x) / 28
Solving for x, we get:
x = 2016/3
So Hermione paid for 2016/3 = 672 Chocolate Frogs.
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Answer:
Hermione paid for 1,568 frogs.
Step-by-step explanation:
First, do 98 + 28. That will give you 126. Then do 2,016 / 126. That gives you 16. 16 x 98 = 1568 frogs.
Let's do Luna's to check our work.
28 x 16 = 448 frogs. 448 + 1568 = 2,016. So, Hermione paid for 1,568 frogs.
Find the product of the factors 8.075*0.08
Answer: 8.075: gotta get somebody else to do this one...sorry. and 0.08 = 8
Step-by-step explanation:
Did this with a classmate couple months ago. Hope this helps. :)
What is an example of an x-intercept?
An example of x-intercept is (3,0).
Here x=3 is the x-intercept in this line.
By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.
We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.
The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.
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Which expression is equivalent?
Answer:
The first one 3^7 *1/3-4
Step-by-step explanation:
Colleen and Amy go shopping. The function below represents how much money each girl spent based on the number of hours they were shopping. If Colleen and Amy each go shopping for 3 hours, how much money did they spend together?
p(x)3x^4=x^4-3x^2+5
$32
$86
$248
$302
Answer:
$302
Step-by-step explanation:
p(x) 3x^4 = x^4-3x^2+5
We put 3 in for x and solve
3(3)^4 = 3^4 -3(3)^2 + 5
3(81) = 81 -3(9) + 5
243 = 81 - 27 + 5
243 = 59
Then we add 243 with 59 and get
$243 + $59 = $302
So, they spend together $302
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Find the area of the sector.
195°
9 m
Answer:B
Step-by-step explanation: Because it right
Factor this polynomial completely.
x2 + 3x - 18
A. (x - 2)(x+9)
B. (x+3)(x - 6)
C. (x - 3)(x + 6)
D. (x - 3)(x-6)
could someone help me out with this?
Step-by-step explanation:
ok so first use this formula. V= 4/3 * 3.14 * 9 to the power of 3. so multiply 4/3 and 3.14 and then multiply 9 and 9 and 9 and then multiply that all together
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Find the area of the figure. Round your answer to the nearest tenth.
Be sure to sketch the polygon and the associated triangle.
Given: A regular hexagon with radius = 8
Answer:
17.3 if I am right mark me brainless pls
Simplify the following using law of indices. a) 12x⁷ ÷ 4x³
b) (2x)² × (2x)³ × (2x)⁵
Answer:
a) 3[tex]x^{4}[/tex]
b) 1024[tex]x^{10}[/tex]
Step-by-step explanation:
[tex]\frac{12x^{7} }{4x^{3} }[/tex]
[tex]\frac{3(4)xxxxxxx}{4xxx}[/tex] We can cancel out a 4 and 3 x's. That leaves
3xxxx
or 3[tex]x^{4}[/tex]
[tex](2x)^{2}[/tex] x [tex](2x)^{3}[/tex] x [tex](2x)^{5}[/tex] can be written in expanded form
[(2)(2)xx] x [(2)(2)(2)xxx] x [(2)(2)(2)(2)(2)xxxxx]
(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)xxxxxxxxxx
1024[tex]x^{10}[/tex]
The screen on Lawrence’s new phone is 3.15 centimeters long. What mixed number represents the length of the phone screen?
Answer:
3 and 3/20
Step-by-step explanation:
Suppose $PABCD$ is a right square pyramid with apex $P$ and base $ABCD$. If $PBD$ is an equilateral triangle with side length 6, then what is the volume of $PABCD$
The volume of a right square pyramid PABCD is 50.91 cubic units
Let l be the side length of right squared pyramid and h be the height.
We know that the formula for the volume of the right squared pyramid.
V = a²h / 3
And the formula for the height of right squared pyramid.
h = (1/√2)a
Here, the side length (a) = 6 units
So, using above formula of height,
h = (1/√2) × 6
h = 6/√2
h = 3√2 units
Now using the formula for the volume of the right squared pyramid, the volume of pyramid PABCD would be,
V = (6² × 3√2) / 3
V = 6² × √2
V = 36√2
V = 50.91 cubic units
Therefore, the volume of PABCD is 50.91 cubic units
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Tom and his friend are driving to Louisville, Kentucky, next week. They figure that the trip will be about 432 miles round trip. If his car gets 31 mpg and the current cost of gasoline is $2.79, how much will they spend on gas? $51.61 $44.46 $38.88 $31.00
=====================================================
Explanation:
Let x be the number of gallons used up. It's some positive real number.
We'll use the formula
miles = (mpg)*(number of gallons)
to help figure out how much fuel is used. The trip is 432 miles, and the mpg rating is 31
So,
miles = (mpg)*(number of gallons)
432 = 31*x
31x = 432
x = 432/31
x = 13.9354838709678 which is approximate.
Multiply that with the 2.79 to get the final answer.
2.79*x = 2.79*13.9354838709678 = 38.8800000000001
The 1 at the very end is probably due to some rounding error, but then again it may be accurate. Either way, that value rounds to 38.88
Side note: The 31 mpg rating is very likely an average value and not the same throughout the trip. This is due to the car changing speeds at different points of the journey. In reality, the true answer will vary slightly from the 38.88 figure we just calculated (but it should be fairly close).
The total amount of money that Tom and his friend would spend on gas during the trip is $38.88.
How much would be spent on gas?
The first step is to determine the total amount of gas that would be needed during the trip.
Gas that would be needed = 432 / 31 = 13.94
The second step is to multiply the gas that would be needed by the cost of gasoline: $2.79 x 13.94= $38.88
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Mr.Rosado is making a stop at his favorite ice cream shop.
He can choose on flavor of ice cream: chocolate, strawberry, vanilla or rocky road.
He can put his ice cream in a sugar cone, waffle cone or a cup.
What is the p(chocolate ice cream AND a waffle cone)?
Answer:
1/12
Step-by-step explanation:
Assuming his choices are equally likely (important: he's choosing randomly)...
Probability of selecting chocolate: 1/4 (1 of 4 equally likely choices)
Probability of selecting waffle cone: 1/3
Probability of selecting both: 1/4 x 1/3 = 1/12
Now, if you'll excuse me, I'm off to get ice cream! :-)