The speed of Bicyclist A (heading north) is 16 km/h.
The speed of Bicyclist B (heading south) is 11 km/h.
Given:
- Let x be the speed of bicyclist A (heading north).
- Let y be the speed of bicyclist B (heading south).
- Bicyclist A is 5 km/h faster than Bicyclist B, so [tex]\(x = y + 5\)[/tex] (Equation 1).
- Time from 9:00 to 10:45 is 1.75 hours.
- The total distance covered by both bicyclists during this time is 47.25 km.
From the equation for time and distance, we have:
[tex]\[ x \times 1.75 + y \times 1.75 = 47.25 \][/tex]
Substituting Equation 1 into this equation:
[tex]\[ (y + 5) \times 1.75 + y \times 1.75 = 47.25 \]\[ 1.75y + 8.75 + 1.75y = 47.25 \]\[ 3.5y + 8.75 = 47.25 \]\[ 3.5y = 38.5 \]\[ y = \frac{38.5}{3.5} \]\[ y = 11 \text{ km/h} \][/tex]
Substituting the value of y back into Equation 1:
[tex]\[ x = 11 + 5 \]\[ x = 16 \text{ km/h} \][/tex]
Thus, the correct answer is:
- The speed of Bicyclist A (heading north) is 16 km/h.
- The speed of Bicyclist B (heading south) is 11 km/h.
Question :
At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 4 km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists’ rates.
The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 24.5 m/s is
h = 2 + 24.5t − 4.9t2
after t seconds. (Round your answers to two decimal places.)
The question requires solving various problems involving projectile motion, a physics topic, using kinematic equations and algebraic techniques to determine height, flight time, and impact speeds.
Explanation:The question involves calculating various aspects of projectile motion, which is a topic in physics. In these problems, equations of motion are used to determine the maximum height, time of flight, and speed at impact of objects thrown or released from certain heights.
Example Calculations
To calculate the maximum height, you can use the equation h = 2 + 24.5t − 4.9t2 and look for the time t when the velocity is zero.The time it takes for an object to reach the ground can be calculated by setting the height equation to zero and solving for t.To find the speed at impact, you use the conservation of energy or the kinematic equations to relate the initial velocity, acceleration due to gravity, and the distance fallen.Each of these problems requires an understanding of the kinematic equations for vertical projectile motion and the ability to apply algebraic and calculus techniques.
When this polynomial is simplified, what is the coefficient of x: 10x^2+8x-6x^3+4x^2+12x^3-x+20
...?
By applying the PEMDAS rule, the coefficient of x is equal to 7.
In Mathematics and Euclidean Geometry, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.
Based on the information provided, we have the following mathematical expression:
[tex]10x^2+8x-6x^3+4x^2+12x^3-x+20\\\\12x^3-6x^3+10x^2+4x^2+8x-x+20\\\\6x^3+14x^2+7x+20[/tex]
In this context, we can reasonably and logically deduce that the coefficient of x is 7.
Complete Question:
When this polynomial is simplified, what is the coefficient of x?
[tex]10x^2+8x-6x^3+4x^2+12x^3-x+20[/tex]
Which is the completely factored form of 12x^3 – 60x2 + 4x – 20?
4(3x^2 – 1)(x – 5)
4x(3x^2 + 1)(x – 5)
4x(3x^2 – 1)(x + 5)
4(3x^2 + 1)(x – 5)
The correct option is:
4(3x² + 1)(x – 5)
To find the completely factored form of the expression 12x³ – 60x² + 4x – 20, we can first factor out the greatest common factor, which is 4.
4(3x³ – 15x² + x – 5)
Next, we can factor the quadratic expression 3x³ – 15x² + x – 5 by grouping:
4[3x²(x – 5) + 1(x – 5)]
4(3x² + 1)(x – 5)
Therefore, the completely factored form of 12x³ – 60x² + 4x – 20 is:
4(3x² + 1)(x – 5
So, the correct option is:
4(3x² + 1)(x – 5)
What is x and y in 2x+4y=1 and 3x-5y=7
6 1/2 as an improper fraction
Keana’s piggy bank contains $4.30 in nickels and dimes only. If she has 59 coins in her bank, then what is the sum of the digits in the number of nickels in Keana’s bank? Write a system of equations for this situation and find its solution.
Final answer:
The question is about solving a system of equations to find the number of nickels and dimes in a piggy bank, given a total amount and quantity of coins. The solution involves using either the substitution or elimination method to find the values of the two variables representing nickels and dimes.
Explanation:
The question involves solving a system of equations to find the number of nickels and dimes in Keana’s piggy bank. Given the total amount is $4.30 and there are 59 coins in total, we can set up the following equations:
Let N represent the number of nickels and D the number of dimes.
The value equation is 0.05N + 0.10D = 4.30 or 5N + 10D = 430
The quantity equation is N + D = 59.
To solve these equations, we will use the substitution or elimination method. First, solve the quantity equation for one variable, for example, N = 59 - D. Then, substitute this expression for N in the value equation and solve for D. After finding D, substitute its value back into any of the original equations to find N. The sum of the digits in the number of nickels in Keana's bank is then found by adding together the digits of N.
we get, 5(59 - D) + 10D= 430
295 - 5D + 10D = 430
5D = 135 , Therefore D = 27
and N = 59 - D = 59 - 27 = 32.
To find the sum of the digits in the number of nickels (n=32), we add the digits 3+2=5
Therefore, the sum of the digits in the number of nickels in Keana’s bank is 5.
The slope of diagonal AB is , _ and its equation _ is .
In the diagram, transversal t cuts parallel lines a and b. Which angles form a pair of alternate exterior angles?
∠1 and ∠7
∠1 and ∠8
∠2 and ∠8
∠2 and ∠5
In the diagram, the pair of angles ∠1 and ∠7 form a pair of alternate exterior angles.
Here is the reason:
A transversal is a line where two parallel lines meet. In the diagram, line t is the transversal.Parallel lines: Parallel lines are two lines that never meet, no matter how distant they are amplified. Within the graph, lines a and b are parallel.Interchange exterior angles: When a transversal crosses two parallel lines, it makes eight points. The combination of points that are on the inverse sides of the transversal and exterior of the parallel lines are called substitute outside points.Within the graph, ∠1 and ∠7 are on the inverse sides of transversal t and exterior lines a and b. Subsequently, they are a combination of substitute outside points.
The other answer choices are not correct since:
∠1 and ∠8 are not on inverse sides of the transversal.∠2 and ∠8 are not both exterior parallel lines.∠2 and ∠5 are comparing points, not substituting outside points.What is the value of the expression 30n when n = 2?
WILL MARK BRAINLIEST Harry had $32. He spent all the money on buying 3 notebooks for $x each and 4 packs of index cards for $y each. If Harry had bought 5 notebooks and 5 packs of index cards, he would have run short of $18. A student concluded that the price of each notebook is $5 and the price of each pack of index cards is $1. Which statement best justifies whether the student's conclusion is correct or incorrect? The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2). The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (8, 2). The student's conclusion is correct because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (5, 1). The student's conclusion is correct because the solution to the system of equations 3x − 4y = 32 and 5x − 5y = 50 is (5, 1).
Answer:
The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2).
Step-by-step explanation:
To see if the answer to an equation is right, you just have to put the value of X and Y into the equation system, since we don´t have the equation system that the student used, we will make our own, so we will start by stating that Notebooks are represented by X and index cards are represented by Y.
Your equation would look like this:
3x+ 4y=34
The student said that the price of the notebook is $5 and the index card would be $1, now we put those values into the equation.
3(5)+4(1)=32
15+4=32
19=32
Since 19 is not equal to 32, the equation is wrong, therefore the student is wrong.
Now to solve it you get your other equation, since if he had bought 5 and 5 he would have needed 18 extra dollars that means that
5x+5y= 32 +18
5x+5y=50
With the two equations you just use elimination process to create a single equation:
(5x+5y=50)-3= -15x-15y=-150
(3x+4y=32)5 = 15x+20y= 160
You eliminate the x from the equation and are left with:
-15y+20y= -150+160
5y=10
y=[tex]\frac{10}{2}[/tex]
y=2
Now that you have the value of Y you just put it into the equation to know the value of x:
5x + 5(2) = 50
5x+10=50
You clear the x and the result would look like this:
x= [tex]\frac{50-10}{8}[/tex]
x=8
combine like terms 9x-5y-8y 10x 3=
Find the mode.19, 1, 17, 19, 3, 20, 5, 2
The mode of this set is 19.
1. **List the Numbers**: Start by listing out all the numbers in the set.
[tex]\[ 19, 1, 17, 19, 3, 20, 5, 2 \][/tex]
2. **Count Frequency**: Count how many times each number appears in the list.
- 19 appears twice.
- 1 appears once.
- 17 appears once.
- 3 appears once.
- 20 appears once.
- 5 appears once.
- 2 appears once.
3. **Identify the Most Frequent Number**: The mode is the number that appears most frequently. In this case, 19 appears twice, which is more than any other number in the set. Therefore, the mode of this set is 19.
How much money would need to be deposited into an account earning 5.25% interest compounded annually in order for the accumulated value at the end of 25 years to be $75,000?
P = the principal
t = 25 years the time in years
r = 0.0525 or 5.25% annual rate
m = 1 compounding periods per year
i = 0.0525 or 5.25% interest rate per period
n = t*m = 25 total number of compounding periods
A = $75,000 future value
A = P(1 + i)^n
P(1 + i)^n = A
P(1 + 0.0525)^25 = 75000
by solving we find:
P = $20,869.34
Let P be a point between points S and T on 2004-01-01-02-00_files/i0120000.jpg. If ST = 21, SP = 3b – 11, and PT = b + 4, solve for b.
A. –7
B. 7
C. 14
D. 32
If 80 is 80 percent of a value what is that value
Your cell phone company started a rewards club. For every three texts sent, you get 15 points. You need 1800 points for a prize. How many texts do you need to send to get that prize
Answer:
360 texts
Step-by-step explanation:
Given,
The points given for 3 texts = 15,
So, the points given for 1 text = [tex]\frac{15}{3}[/tex] = 5,
If x text are sent,
Then the number of points earned = x × points for 1 text
= 5x
According to the question,
5x = 1800
[tex]\impilies x = \frac{1800}{5} = 360[/tex]
Hence, 360 texts needs to send to get 1800 points.
As a salesperson at Roaring Waves Beach Supplies, Carissa receives a monthly base pay plus commission on all that she sells. If she sells $500 worth of merchandise in one month, she is paid $385. If she sells $1,000 of merchandise in one month, she is paid $470.
Find Carissa's salary when she sells $1,900 worth of merchandise. ...?
Answer:
$623
Step-by-step explanation:
Let us suppose that the
Earning = y
Fixed payment = c
Commission paid = m per unit
Case 1.
When 500 units are sold, Earning y = $385
Earning = Fixed Payment + Commission paid per unit * Number of units
385=c+m*500
385=c+500m ________(a)
Case 2.
When 1000 units are sold earning y = $470
Earning = c+m*1000
470=c+1000m _________(b)
Subtracting (a) from (b) we get
85=500m
[tex]m=\frac{85}{500}\\=0.17[/tex]
Putting this value of m in (a)
[tex]385=c+\frac{85}{500} * 500[/tex]
385=c+85
c=300
Hence the fixed payment is $300 and the commission given is $0.17 per unit
Case 3 :
Number of Units sold = 1900
Earning = 300+0.17*1900
Earning = 300+323
Earning = 623
Hence The earning will be $623
Part A
Ling and $44 each week for six weeks mowing lawns in his neighborhood. His weekly expenses for supplies are d. Write an expression to show the amount of money ling have after paying his expenses.
Part B
If Ling's expenses are $13 each week, how much money will ling have?
Describe the variation 3xy = 5.
A. y varies inversely as the square of x.
B. y varies inversely as x.
C. y varies directly as x.
D. y varies directly as the square of x.
Answer:
The answer is the option B
y varies inversely as x.
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]yx=k[/tex] or [tex]y=k/x[/tex]
In this problem we have
[tex]3xy=5[/tex] -----> rewrite
[tex]xy=5/3[/tex]
The value of k is equal to [tex]k=\frac{5}{3}[/tex]
therefore
y varies inversely as x.
Given 4x-8y=8, transform the equation into slope intercept form
write the equation in standard form. 8−5y=−2x8−5y=−2x the equation in standard form is .
Jeremy baked 9 cakes for the bake sale. He sifted 2 cups of powdered sugar evenly on the tops of the cakes. How much powdered sugar is on each cake?
imkim
What is 5 1/4 divided by 1 5/9 ?
Express the answer in simplest form.
Laplace Transform of t ^{2}sin(2t)? ...?
Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.
The Laplace transform of the given function is,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]
What is Laplace transformation?Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.
Given information-
The function given in the problem is,
[tex]t^{2}\sin(2t)[/tex]
By the Laplace transform we can write that,
[tex]L[t^{2}\sin(2t)]=(-1)^2\dfrac{d^2}{ds^2}L(\sin 2t)\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\;\dfrac{d}{ds}\dfrac{2}{s^2+4}\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\left [\dfrac{-4s}{(s^2+4)^2} \right ]\\[/tex]
Solve further to get the final result,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{(s^2+4)^2(-4)+4s(s^2+4)\times2s}{(s^2+4)^2} \right ]\\[/tex]
Simplify the above equation as,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]
Hence, the Laplace transform of the given function is,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]
Learn more about the Laplace transform here; https://brainly.com/question/17062586
2. A chemist wants to make 4 liters of a 7% acid solution by mixing a 10% acid solution and a 4% acid solution. How many liters of each solution should the chemist use? Write your answer as a complete sentence. Be sure to: • Define your variable and expressions for the quantities. • Write an equation that models the problem. • Solve the equation. • State the answer in a complete sentence.
Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 28°.
The flow chart with missing statements and reasons proves that the measure of angle ECB is 62°.
Which statement and reason can be used to fill in the numbered blank spaces?
Base angle theorem
Corresponding angle are congruent
Measure of angle AED is 28°.
Alternate interior angles are congruent
Base angle theorem
Measure of angle AED is 62°.
Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 28°.>> my answer?
Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 62°.
Answer:
(D)
Step-by-step explanation:
Given: Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 28°.
To prove: The measure of angle ECB is 62°.
Proof:
Step1. Segment DE joins the mid points of segments AB and AC (GIVEN).
Step 2. Segment DE is parallel to segment BC (MIDSEGMENT THEOREM)
Step3. Angle ECB is congruent to angle AED (CORRESPONDING ANGLES ARE CONGRUENT) that is ∠AED≅∠ACB.
Step 4. Measure of angle DAE is 90° (Definition of right angle)
Step 5. Measure of angle ADE is 28° (Given)
Step 6. Thus, by triangle sum theorem, we have
∠DAE+∠ADE+∠AED=180°
∠AED=180-118
∠AED=62°
Step 7. Thus, by substitution, we have
∠AED≅∠ACB that is ∠ECB=62°
Hence proved.
Which of the four triangles was formed by a translation of triangle XYZ?
A
B
C
D
Answer:
Options A & B
Step-by-step explanation:
Given is a triangle XYZ in the I quadrant. There are four more triangles A, B,C and D given.
We have to find that which one is the translation of XYZ
We know that by translation we must get a congruent triangle as XYZ.
By simply seeing we can say that C and D are not congruent with XYZ.
So these two are eliminated
Remaining are A and B.
Both A and B are right
This is because XYZ is transformed into B by shifting 7 units horizontal to the left.
A is the reflection of B about x=-5.5
Thus both A and B are right
archie earns 4$ each week for doing his chores.how much money will archie earn in 2 months if there are 4 weeks in each month?
Answer:
can we skip to the good part? oh oh oh ohhhhh mhhhmhmhmhhhhhhhmh
Step-by-step explanation:
drink some coco juice and add some keyboard and it will be HAPSOD
hapsod is the one who absorb the hapsod
PLEASE HELP
What is the equation in point slope form of the line that passes through the point (2, 6) and has a slope of 5?
How do you write 175% as a fraction, mixed number, or whole number in simplest form?
In fraction,
175% = 35/20
In mixed fraction,
175% = [tex]1\frac{15}{20}[/tex]
In simplest form,
175% = 1.75
The given percentage is,
175%
Now to write it into fraction,
Divide it by 100 we get
175% = 175/100
= 35/20
Thus,
175% = 35/20
Now divide 35 by 20 to write it into mixed fraction
20 ) 35 ( 1
- 20
___
15
Hence in simple fraction
175% = [tex]1\frac{15}{20}[/tex]
Now again proceed the division,
20 ) 35 ( 1.75
- 20
___
15 0
- 14 0
_____
10 0
- 10 0
____
x
Hence in simplest form,
175% = 1.75
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