Dina and Masha started out on a 10 km bike path at the same time. When Dina reached the end of the 10 km, Masha still had 2 km left to bike. If Dina’s biking speed was 5 km/h, find Masha’s biking speed.
Answer:
4 km/hr
Step-by-step explanation:
Dina and Masha started out on a 10 km bike path at the same time.
Distance = 10 km
Dina’s biking speed was 5 km/h
Time taken by Dina is Distance / speed
So [tex]time (Dina) = \frac{10}{5} =2[/tex]
Time taken by Dina is 2 hours
Same time is taken by Masha but 2 km left
So distance covered by Masha in 2 hours is 10-2 = 8 km
We know speed = distance / time
[tex]speed of Masha = \frac{8}{2}=4[/tex]
Masha’s biking speed= 4km/hr
Sarah's garden is 11.72 m long. Round to the nearest tenth of a meter
an ice cream factory makes 200 quarts of ice cream in 10 hours . How many quarts could be made in 12 hours? what was that rate per day ?
A dance school allows a maximum of 15 students per class. If 112 students sign up for dance class,how many classes does the school need to offer to accommodate all the students
the coffee is stirred with a spoon. The spoon gets hot due to convection conduction or radiation?? will give brainiseest
Which polynomial is prime? x3 + 3x2 – 2x – 6 x3 – 2x2 + 3x – 6 4x4 + 4x3 – 2x – 2 2x4 + x3 – x + 2
A prime polynomial is a polynomial that can't be factored.
In order to check which polynomial is prime, we need to check which polynomials could be factored.
x^3 + 3x^2 – 2x – 6 can be factored as (x+3)(x^2-2)
x^3 – 2x^2 + 3x – 6 can be factored as (x-2)(x^2+3)
4x^4 + 4x^3 – 2x – 2 can be factored as 2(x+1)(2x^3-1)
2x^4 + x^3 – x + 2 can't be factored.
Therefore, 2x^4 + x^3 – x + 2 is a prime polynomial.
In this exercise we have to use the knowledge of prime polynomials to find what cannot be factored, so we have;
A) Can be factored.
B) Can be factored.
C) Can be factored.
D) Can't be factored.
Is a base form of a polynomial in other words is a polynomial that can't be factored.
So we have to:
A) [tex]x^3 + 3x^2 - 2x - 6 =(x+3)(x^2-2)[/tex]
B)[tex]x^3 - 2x^2 + 3x - 6=(x-2)(x^2+3)[/tex]
C)[tex]4x^4 + 4x^3- 2x - 2= 2(x+1)(2x^3-1)[/tex]
D)[tex]2x^4 + x^3 - x + 2[/tex]
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-10+ (-15)=??? Plzzz help me show work plz <3
Am I correct? Please check my answer
3.695 to 4 name the place value to which each number was rounded
a company needs boxes to hold a stack of 8.5 inch by 11 inch papers. if they would like the volume of the to be 500 cubic inches, what should the night of the box be? round to the nearest tenth
In triangle QRS, QR = 2x + 5, RS = 3x - 1, and SQ = 5x. Solve for x.
To solve for x in triangle QRS, set up an equation using the given information. However, there is no unique solution for x.
Explanation:To solve for x in triangle QRS, we need to set up an equation using the given information. Firstly, observe that the sum of the lengths of the three sides of a triangle is equal to the perimeter of the triangle. So, we have (2x + 5) + (3x - 1) + (5x) = perimeter of QRS. Simplifying this, we get 10x + 4 = perimeter of QRS. Next, we need to consider the fact that the perimeter of a triangle is equal to the sum of the lengths of its sides. So, we can set up the equation 10x + 4 = QR + RS + SQ. Substituting the given lengths, we have 10x + 4 = (2x + 5) + (3x - 1) + (5x). Solving this equation will give us the value of x.
10x + 4 = 2x + 5 + 3x - 1 + 5x
10x + 4 = 10x + 4
When we simplify this, we see that both sides of the equation are equal. Therefore, x can take on any value and there is no unique solution for x in this case.
Given the inequality -8 < 2, explain what happens when you multiply or divide both sides by 2 and what happens when you multiply or divide both sides by -2.
When you multiply or divide each side by 2, the signs stay the same. −16 < 4 and −4 < 1. When you multiply or divide by −2, the inequality sign reverses. 16 > −4 and 4 > −1.
function rule for (1,3),(2,24),(3,81),4,192)
What is the product in simplest form?
−5/12 ⋅ 8/13
Theresa sells lemonade for $1, juice for $1.50, and coffee for $2. On one day, the number of coffees she sells is twice the number of lemonades she sells, and 4 more than the number of juices she sells. If she earns a total of $74, how many lemonades did she sell?
Which values of m and b will create a system of equations with no solution? Check all that apply.
y = mx + b
y = –2x +
m = –3 and b =
m = –2 and b =
m = 2 and b =
m = – and b =
m = –2 and b =
m = 3 and b =
THE ANSWER TO THIS PROBLEM IS B AND E
The sum of a number and six is seven times the number
Which is a given translation of the sentence into an equation?
A. n=7n+6
B. 7(n+6)=n
C. n-6=7n
D. n+6=7n
The sum of a number and six is seven times the number.
The word "sum" means addition
The translation of this sentence into an equation is written as:
n + 6 = 7 x n
n + 6 = 7n
The correct option is Option D.
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If d=rt and if r = 60 and t = 4 what does d equal
Factor. 3x(y−4)−2(y−4) Enter your answer in the box
The factor of the expression 3x(y−4)−2(y−4) are (3x - 2) (y - 4).
What is an expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The expression is,
3x(y - 4) - 2(y - 4)
Now, Solve the expression as;
The expression is,
3x(y - 4) - 2(y - 4)
Take (y - 4) as common;
(y - 4) (3x - 2)
Thus, The factor of the expression 3x(y−4)−2(y−4) are (3x - 2) (y - 4).
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Which is greater 9.1 or 9.099?
An architectural drawing of a building shows the elevation of the basement floor to be –12 feet. The elevation of the roof is 32 feet. What is the total distance from the roof to the basement floor?
The total distance from the roof to the basement floor in the architectural drawing is 44 feet, found by adding the basement's distance from ground level (12 feet) to the roof's elevation (32 feet).
Explanation:In the given scenario, we need to find the total distance from the basement to the roof. Given the elevation of the basement is -12 feet and the elevation of the roof is 32 feet, we simply need to add these two distances together. Since the basement is below ground level, its elevation is negative. Therefore, its distance from the ground level is 12 feet, not negative 12. We can treat this as an absolute value.
To calculate the total distance, we add the absolute value of -12 (which is 12) to 32, which gives us 44 feet. Thus, the total distance from the roof to the basement floor is 44 feet.
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Jason is standing on the ground and throws a ball vertically upward with an initial speed of 80 ft/sec. Its height after t seconds is given by h = 80t-16t^2
a) How high does the ball go?
b) How many seconds does it take to reach maximum height?
c) When does the ball hit the ground?
Tito walked three more miles than Danielle. If Danielle walked 2 miles, how many miles did Tito walk?
Answer:
What you need to do, is take Tito's amount of miles, and and add it to Danielle's amount of miles, to get how many miles Tito walked. Which is 3+2=5 miles, so Tito walked 5 miles.
Eleni works out 15 fewer minutes on Tuesday than on Monday. She worked out 70 minutes on Tuesday.
Use the five-step problem-solving plan.
How many minutes did she work out on Monday?
Enter you answer in the box.
______min
Answer: 85 Minutes on Monday
Step-by-step explanation:
Tyson always likes to have at least $150 in his savings account. currently he has $800 in the account. if he withdraws $35 each week, after how many weeks will the amount in his savings account be less than $150?
Hence, Tyson will take [tex]19[/tex] weeks will the amount in his savings account is less than $[tex]150[/tex].
What are savings?
Savings refers to the money that a person has left over after they subtract their consumer spending from their disposable income over a given time period.
Savings, therefore, represents a net surplus of funds for an individual or household after all expenses and obligations have been paid.
Here given that,
Tyson always likes to have at least $[tex]150[/tex] in his savings account. currently, he has $[tex]800[/tex] in the account. if he withdraws $[tex]35[/tex] each week.
So, if we multiply [tex]35[/tex] with [tex]19[/tex] then it would be [tex]665[/tex]
i.e., [tex]35[/tex] × [tex]19=665[/tex]
= $[tex]135[/tex]
Which is less than $ [tex]150[/tex]
Hence, Tyson will take [tex]19[/tex] weeks will the amount in his savings account is less than $[tex]150[/tex].
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To start the school year, a teacher spends $54.35 in school supplies for her classroom. During the course of the year, she will restock her supplies and will spend $22 each time she restocks the supplies. The expression below describes this situation.
22x+54.35
In this expression, what does the term 22x describe?
A. the amount she spends restocking her supplies
B. the total amount she spends money on restocking her supplies
C. the number of times she restocks her supplies
D. the amount she originally spends on supplies
Answer: B. the total amount she spends money on restocking her supplies
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
During the course of the year, she will restock her supplies and will spend $22 each time she restocks the supplies
22x+54.35
SO, the term 22x equals to $22 multiplied by the times she restocks the supplies. For example: if she restocks the supplies 5 times, the total amount will be:
22 (5)+ 54.35
So, the term 22x describes the total amount she spends money on restocking her supplies. option B
Mia is three years older than twice her sister Brooke's age. The sum of their ages is less than 30. What is the greatest age brook can be ?
a store sells coffee for $34 per bag. if a bag contains 6 lbs, find the cost of coffee per pound
Ron is five years older than twice his cousins Pat's age. The sum of their ages is less than 35. What is the minimum age Pat can be?
A.) 7
B.) 8
C.) 9
D.) 10
Select one of the factors of 3x^2 + 4x − 4.
A.) (x + 4)
B.) (3x + 2)
C.) (3x - 2)
D.) (x - 2)
I will disregard your answer if you do not explain the steps clear enough.
The requried factor of the given quadratic expression [tex]3x^2 + 4x - 4[/tex] is (3x-2). Option C is correct.
To find the factor of the quadratic expression [tex]3x^2 + 4x - 4[/tex], we need to identify two binomials that, when multiplied together, result in the given expression.
The expression is in the form of [tex]ax^2 + bx + c[/tex], where a = 3, b = 4, and c = -4.
To factor the quadratic expression, we look for two binomials of the form (mx + p) and (nx + q) such that:
(mn) = a (which is 3 in our case), and
(pq) = c (which is -4 in our case).
Now, we need to find the factors of 3 and -4:
Factors of 3: 1, 3
Factors of -4: 1, -1, 2, -2, 4, -4
Now, we need to find combinations of these factors such that their product is 3 (the coefficient of [tex]x^2[/tex]) and -4 (the constant term). The combination that works is:
3 * -1 = -3
So, the two binomials are (3x - 2) and (x + 2) because:
[tex](3x - 2) * (x + 2) = 3x^2 - 2x + 6x - 4\\ \ \ \ \ \ \ \ \ \ \ = 3x^2 + 4x - 4[/tex]
Therefore, the correct factor is C.) (3x - 2).
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