The distance by which Mika will be ahead is equal to 36 m from present location.
According to the question Gretchen and Mika are at the same point when Gretchen runs backward at the speed of 4 m/s in opposite direction to pick her baton and Mika runs in the direction of the race at the speed of 3 m/s. We need to find the distance covered by Mika form the current location in the time when Gretchen picks her baton up. Let us assume that the time taken by Gretchen to pick up her baton be equal to t. It is given that 48 meters from her current location she dropped her baton. Since she is running at the speed of 4 m/s then the time will be equal to t = 48/4 = 12 seconds. Now, Gretchen will be able to pick up the baton in 12 seconds. Thus, the distance covered by Mika in 12 seconds will be equal to 3×12 = 36m.
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Complete Question:
Gretchen and Mika are involved in a relay race. Both runners are at the same point on the course when Gretchen realizes that she dropped her baton and has to turn around to retrieve it. Gretchen runs backwards at a speed of −4 m/s, relative to the direction of the race. Mika continues running at a speed of 3 m/s. If Gretchen dropped her baton −48 meters from her current location, relative to the direction of the race, how far ahead will Mika be when Gretchen picks her baton up?
Find the product and write your answer in proper scientific notation (4.5 x 10³)/(3 x 10⁶)
Answer:
[tex]1.5\times10^{-3}[/tex]Explanation:
Given the rational expression
[tex]\frac{4.5\times10^3}{3\times10^6}[/tex]We can rewrite the fraction as:
[tex]=\frac{4.5}{3}\times\frac{10^3}{10^6}[/tex]We then simplify and apply the division law of indices to obtain:
[tex]\begin{gathered} =1.5\times10^{3-6} \\ =1.5\times10^{-3} \end{gathered}[/tex]Note: When you have the same base of an exponent and the terms are being divided, we simply subtract the power of the numerator from that of the denominator.
Which graph best represents the solution set for all possible combinations of x, the number of hours she worked at her 1st job, and y, the number of hours she worked at her second job, in one week?
The equation must be x + y < 48
Graph
Evaluate.
1045+(834−612)
Enter your answer as a mixed number in simplest form by filling in the boxes.
The value of the expression given as 1045 + (834 − 612) is 1267
How to evaluate the expression?The expression is given as
1045+(834−612)
Evaluate the brackets in the above expression
So, we have the following equation
1045 + (834 − 612) = 1045 + 222
Evaluate the sum in the above expression
So, we have the following equation
1045 + (834 − 612) = 1267
The above equation/expression cannot be solved further
So, we make our conclusion
Hence, the solution to the expression is 1045 + (834 − 612) = 1267
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A recipe requires 2 and 1 third cups of flower the chef needs to increase the recipe bya factor of 4 how many cups of flower does the chef need
The number of cups needed by the chef is 9 1/3 cups.
How to calculate the fraction?A fraction simply means a part of a whole number.
In this case, the recipe requires 2 and 1 third cups of flower the chef needs to increase the recipe by a factor of 4.
The cups needed will be:
= 2 1/3 × 4
= 7/3 × 4
= 28/3
= 9 1/3 cups.
This illustrates the concept of fractions.
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Four points W, X, Y, Z are chosen at random on the circumference of a circle. What is the probability that WX > YZ?
The probability to choose WX > YZ is 1/2.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
Four points W, X, Y, Z are chosen at random on the circumference of a circle.
Now,
By the four points W, X, Y, Z we make two line WX and YZ.
So, There are two relation between the line WX and YZ.
Thus, The probability to choose WX > YZ is;
Probability = Possible event / Total possibility
= 1/2
Therefore, The probability to choose WX > YZ is 1/2.
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Find the area and perimeter of a rhombus with a diagonals 15 in and 20 in
Given data:
The diagonals of rhombus d1 = 15 in and d2 = 20 in
The area of the rhombus,
[tex]\begin{gathered} A=\frac{1}{2}\times d1\times d2 \\ A=\frac{1}{2}\times15\times20 \\ A=150\text{ inches sq.} \end{gathered}[/tex]Now, to find the perimeter of rhombus we first find the side of rhombus.
The diagonal of the rhombus is considered as diameter, so the radius will be
d1 = r1 = 7.5
d2 = r2 = 10
So, by using the pythagorean theorem we find the side of the rhombus
[tex]\begin{gathered} h^2=(7.5)^2+(10)^2 \\ h^2=56.25+100 \\ h^2=156.25 \\ h=12.5 \end{gathered}[/tex]The perimeter of the rhombus is,
[tex]\begin{gathered} P=4\times side \\ P=4\times12.5 \\ P=50\text{ inches} \end{gathered}[/tex]Thus, the area is 150 in. sq. and perimeter is 50 in.
A boat heading out to sea starts out at Point AA, at a horizontal distance of 1035 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 8^{\circ} ∘ . At some later time, the crew measures the angle of elevation from point BB to be 5^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
The angle of elevation reduces. The distance between points A and B is roughly 1,269.9 ft.
The distance between point A and the lighthouse is 968 feet.
The angle of elevation from point A to the lighthouse is 7 degrees.
Elevation angle from point B to the lighthouse = 3°
The distance between points A and B.
tan 7° = Height of the sea / 968 feet
tan(7°) 968 feet 118.86 feet = height to the lighthouse
We have from point B;
tan 3° = 118.86 / Horizontal distance from B to HL
Therefore;
Horizontal distance from LH to boat = 118.6 / tan 30° = 2237.9 = feet
Therefore;
D is the distance between A and B.
D = Horizontal distance between B and LH - Horizontal distance between A and LH
A to B distance = 2237.9 feet − 968 feet 1269.9 feet
The distance between points A and B is 1,269.9 ft.
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Answer:
The Boat traveled 628 ft, from point A to point B.
Step-by-step explanation:
Its 628 bc I just got it correct on my hw.
Find the turning point of y=h(x) if h(x)=f(-x)f(x)=x^2-4x+12
Given:
[tex]y=h(x)\text{ where }h(x)=f(-x)\text{ and }f(x)=x^2-4x+12.[/tex]Required:
We need to find the turning point of y=h(x).
Explanation:
Replace x =-x in the function f(x) to find h(x).
[tex]f(-x)=(-x)^2-4(-x)+12.[/tex][tex]f(-x)=x^2+4x+12.[/tex]Replace f(-x)=y in the equation.
[tex]y=x^2+4x+12.[/tex][tex]y=x^2+2\times2x+4+8.[/tex][tex]y=x^2+2\times2x+2^2+8.[/tex][tex]Use\text{ }(a^2+2ab+b^2)=(a+b)^2.[/tex][tex]y=(x+2)^2+8.[/tex]Which is of the form
[tex]y=a(x-h)^2+k.[/tex]where a=1, h=-2, and k=8.
The point (h,k)=(-2,8) is the turning point.
Final answer:
The turning point of y=h(x) is (-2,8).
Ganymede is one of Jupiter’s moons. It takes Ganymede 7 days, 3 hours, and 15 minutes to make one rotation around Jupiter. How many hours does it take Ganymede to complete a full rotation? Show your work using the correct conversion factors and make sure all conversion factors are labeled with appropriate units. You should have more than one conversion factor shown.
The number of hours it will take Ganymede to complete a full rotation is; 171.25 hours.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
The first step must be to convert days to hours. A day is equivalent to the 24 hours.
1 day = 24 hours
24 x 7 = 168 hours
The second step must be to convert minutes to hours,
60 minutes = 1 hour
15 / 60 = 0.25 hours
Now, add up all the converted hours together;
Total hours = 168 hours + 3 hours + 0.25 hours
Total hours = 171.25 hours
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I need help with this problem
Answer:
y = x-13
Step-by-step explanation:
So this question asks for two numbers. Let's call them x and y.
Since we know that x is larger than y, and the difference between them is 13, x must be greater than y by 13. So, x = y + 13
x = y + 13 isn't what the question is asking for though, so we have to isolate y to make one side contain only x and numbers. To do that, subtract both sides by 13 to get:
x - 13 = y
rearrange:
y = x - 13
A six -sided fair number cube is rolled once . What is the probability that the result is a 2 or a 5? Select one :1/61/32/55/6
total number of sides = 6
sides that are 2 or 5 = 2
Divide the sides thata re 2 or 5 (2) by the total sides:
2 /6 = 1/3
Evaluate the expression a-5 -b, when a= 10 and b=4
Given the expression:
a - 5 - b
we want to evaluate it when a = 10 and b = 4. To do it, we have to replace these values into the equation as follows:
10 - 5 - 4 = 1
Factor the expression 54x2-6y^2?
Solve. Richard Saltwood's car averages 270 miles on its 18-gallon tank of gas. If Richard runs out of gas and a mechanic comes to his rescue with 2 3/10 gallons of gas, determine how far his car can go. Round to the nearest mile.
ANSWER:
35 miles
STEP-BY-STEP EXPLANATION:
We can make a proportion, since we know the number of miles per 18 gallons, so for 2 3/10 gallons we can calculate the number of miles proportionally
[tex]\begin{gathered} 2\frac{3}{10}=\frac{23}{10} \\ \text{The proportion is} \\ \frac{270}{18}=\frac{x}{\frac{23}{10}}\rightarrow\frac{270}{18}=\frac{10x}{23} \end{gathered}[/tex]solving for x:
[tex]\begin{gathered} 18\cdot10x=270\cdot23 \\ 180x=6210 \\ x=\frac{6210}{180} \\ x=34.5\cong35 \end{gathered}[/tex]Therefore you can travel a total of 35 miles.
7/9 ÷ 3/9 = ????????
7/9 ÷ 3/9 =
= (7•9)/( 3•9)
= 63/27 = 7/3
Answer is 7/3
can anyone solve? 14 x 3 - 2 + 3
Answer:
43
Step-by-step explanation:
So, the key to solving this is PEMDAS, or parenthesis, exponents, multiplication/division from left to right, and addition/subtraction from left to right. So, you start off with 14x3, which is 42. So, you have 42-2+3. Next, you have to do 42-2, which is 40. Finally, you do 40+3, which is 43.
Answer:
43
Step-by-step explanation:
14 x 3 - 2 + 3
PEMDAS says multiply before adding or subtracting
42 - 2 + 3
Then subtract
40 +3
Then add
43
A. F(x) = -x^7+4x^3-2x^2B. F(x)= x^9+12x^8+x^7C. F(x) =x^8+4x^4+20x^2D. F(x) = -x^6+x^3-x^2
answer:
A. F(x) = -x^7+4x^3-2x^2
A car rental company offers two plans for renting a car.
Plan A: 35 dollars per day and 10 cents per mile
Plan B: 55 dollars per day with free unlimited mileage
How many miles would you need to drive in one day for plan B to save you money?
Answer:
Less than 200 miles, A is cheaper
At 200 miles, they are the same
Over 200 miles, B is less expensive
Step-by-step explanation:
There area 17,60 gaffs in a mile . What is the number of yards in a mile rounded to the nearest hundred? 1- How many places are in this number?2- What are the places? 3- What place are you rounding to?4- What digit is in that place?5- What place is to the right of the place you are rounding to?6- What digit is in that place?Is this digit 5 or greater?7- What is the rule for digits 5 or greater? 8- Will you need to change the hundreds digit? If so, to what? 9- Which places will you change to 0s?10- What is the number of yards in a mile rounded to the nearest hundred?
itWe were given the following:
[tex]1760yard=1mi[/tex]1.
There are 4 places in this number
2.
1 thousand + 7 hundred + 6 tens + 0 units
3.
We are rounding to the hundreds place
4.
Seven (7)
5.
To the right, we have the ''tens''
6.
Six(6). Yes, the digit is 5 or greater
7.
Digits that are 5 or greater than are approximated to the next digit
8.
Yes. From 7 to 8
9.
The tens place will be changed to 0
10.
The number of yards in a mile rounded to the nearest hundred is:
[tex]\begin{gathered} 1,760yards=1mi \\ 1,760\approx1800 \\ =1,800yards(to\text{ the nearest hundred)} \end{gathered}[/tex]What is the value of the function at x=−3? Responses y = 3 y, = 3 y = 0 y, = 0 y = 4 y, = 4 y=−3
The function has a value of y = 4 when x =-3
How to determine the value of the function?The graph that completes the question is added as an attachment
From the graph, we can see that:
The graph of the function is a linear function
This is so because the function is a straight line
Note that:
Linear equations are equations that have constant average rates of change.
On the straight line, we can see that
The value of the function when x = -3 is 4
This means that
y = 4
Hence, the value of the function at x = -3 is y = 4
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What is the volume of this container? 4 in.
4 in.
1 in.
4 in.
2 in.
64 in²
56 in³
56 in²
64 in³
An object's capacity is expressed in terms of volume.
The container's volume is 56 in3.
How to find the container's volume?The capacity of an object is expressed in terms of volume.
A cup's capacity is said to be 100 ml, for instance, if it can hold 100 ml of water in its brim.
The quantity of space a three-dimensional item takes up can also be referred to as volume.
The figure's volume is equal to Bh.
V = Bh
where
B is the base's region.
h is the figure's height.
h = 4 in
The area of the base B is
B = (4*4) - (1*2) = 14 in
V = 14*4 = 56 inch cube.
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How can you solve, write and graph inequalities on a number line?
Let's use the following inequation as an example:
[tex]2y>6[/tex]First let's simplify it dividing the inequation by 2:
[tex]y>3[/tex]Now, let's draw a number line, and include the point 3 in it:
We want the values of y that are greater than 3, that is, the numbers to the right of the number 3 in the number line. So we mark the area that corresponds to the values of y that satisfies the inequation:
The number 3 is not part of the answer, because 3 is not greater than 3, so we draw a small empty circle on the number 3. If the number 3 was part of the answer, the circle would be filled.
Suppose you are driving to your vacation destination. You are driving at an average rate of 60 miles per hour. You must drive a total of 235 miles. If you had already driven 55 miles, how long will it take you to reach your destination?
What is the measure of angle 1 in the picture below?2135°O 90 degreesO 225 degreesO 45 degreesO 135 degrees
1 and 135 are corresponding angles.
Corresponding angles on parallel lines are equal
m<1= 135 degrees
What is the solution set to -3x - 39 > 12
Answer:
x < -17
Step-by-step explanation:
-3x - 39 > 12 Add 39 to both sides
-3x > 51 Divide by -3 and flip the inequality sign
x<-17
Answer: x < -17
Step-by-step explanation: add 39 to both sides then divide 3 on 3x and 51 That is how you answer it. flip the sign to a positive
Jordan is constructing a aregular hexagon inscribed in a circle. He labels the points on the circle as shown
Given,
The diagram of the circle with the vertex of the hexgon.
Required
The measure of arc VX, angle ZXV.
As known that,
The measure of the circle is 360 degree.
The measure of arc VX is,
[tex]Arc\text{ VX = 60 degree.}[/tex]The measure of angle ZXV is,
[tex]\angle ZXV=60^{\circ}[/tex]The measure of arc WZ is 180 degree.
Answer:
VX=120
ZXV=60
WZ
Step-by-step explanation: YOUR WELCOME PUTAS
how would i rewrite the polynomial in the form ax^2+bx+c and then identify the values of a,b, and c1/3x^2+7-6x
Answer:
a=1/3, b=-6, c=7
Explanation:
Given the polynomial:
[tex]\frac{1}{3}x^2+7-6x[/tex]We reorder it to rewrite the polynomial in the form ax²+bx+c:
[tex]\frac{1}{3}x^2-6x+7[/tex]Next, by comparing:
• a is the coefficient of x²: a=1/3
,• b is the coefficient of x: b=-6
,• c is the constant: c=7
[tex]a=\frac{1}{3},b=-6,c=7[/tex]Please help !
Place the following real numbers in order from least to greatest.
227
-3
-4.5
165
Answer: -4.5,-3,165,227
Step-by-step explanation:
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
I only need the answer
THANK YOU!!
The expression is √3/2 (sin x) - (cos x)/2
Here we have
sin( x + 11π/6)
We have to express it in terms of sin(x) and cos(x)
sin ( 2π - π/6 + x)
sin ( 2π + ( x - π/6))
sin(2π + Ф ) = sin Ф
So
sin( x - π/ 6)
Formula :
sin(A -B) = sin A cos B - cos A sin B
sin( x - π/ 6)
sin x cos π/6 - cos x sin π/6
con π/6 = √3/2 and sin π/6 = 1/2
√3/2 sin x - 1/2 cos x
Therefore the expression is √3/2 sin x - 1/2 cos x.
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