Makayla and Addison are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Makayla is 290 miles away from the stadium and Addison is 345 miles away from the stadium. Makayla is driving along the highway at a speed of 40 miles per hour and Addison is driving at speed of 51 miles per hour. Let MM represent Makayla's distance, in miles, away from the stadium tt hours after noon. Let AA represent Addison's distance, in miles, away from the stadium tt hours after noon. Write an equation for each situation, in terms of t,t, and determine the interval of hours, t,t, for which Makayla is closer to the stadium than Addison.
Answers
The linear functions for each situation are given as follows:
Makayla: 290 - 40x.Addision: 345 - 51x.Makayla is closer than Addision when:
x < 5.
How to define the linear functions?The linear functions in slope-intercept format for this problem are given as follows:
y = mx + b.
In which:
m is the slope, representing the velocity, as a negative as they are getting closer to the stadium with time.b is the intercept, representing the initial distance.Hence the functions are defined as follows:
Makayla: 290 - 40x.Addision: 345 - 51x.Makayla is closer when:
290 - 40x < 345 - 51x
11x < 55
x < 5.
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Related Questions
A lawn sprinkler located at the corner of a yard rotates through 80 degrees
and sprays water of 20 ft. What is the length of the arc of the sector watered?
(Express your answer to the nearest tenths.)
Answers
The length of the arc of the sectored watered is 27.9 feets
What is length of an arc?length of arc is the distance between two points along a section of a curve.In other words, it's the distance from one point on the edge of a circle to another, or just a portion of the circumference
The length of an arc is given by :
L = theta/360 × 2πr
where tetha is the angle substends
r is the radius
Here the radius is the length at which water is sprayed = 20 ft
tetha = 80°
therefore l = 80/360 × 2×3.14 × 20
L = 29feets
Therefore the length of the arc formed by the water is 27.9 feets
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What type of a polynomial is 4 2x3?
Answers
The polynomial 4 2x3 is a degree 3 polynomial, also known as a cubic polynomial.
What is polynomial?Polynomial is an expression consisting of variables, constants, and coefficients. It is an algebraic expression that can contain exponents, fractions, multiplication, addition, and subtraction. Polynomials are used to model many real-world situations, such as the volume of a cylinder or the area of a triangle. The degree of the polynomial is determined by the highest exponent of the variables in the expression. Polynomials can be divided, factored, and manipulated using the rules of algebra.
It consists of three terms and its general form is
ax³ m + bx² + cx + d, where a, b, c, and d are constants
and x is the variable. In this case,
a = 4, b = 2, c = 0 and d = 0,
so the polynomial is 4x³ + 2x².
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What is the name of longest side of triangle?
Answers
Answer: Hypotenuse
Step-by-step explanation:
The Hypotenuse is known as the longest side of a triangle.
PLEASEEE HELP ME!!!!
Answers
Answer:
girl I have the same question
What is the sum of all the positive two-digit integers where one of the digits is three times the other
Answers
The sum of all the positive two-digit integers where one of the digits is three times the other is 630.
To arrive at this result, the numbers can be broken down into two groups. The first group consists of numbers with 3 as the first digit, and the second group consists of numbers with 3 as the second digit.
For the first group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9. This gives a sum of 3+6+9+12+15+18+21+24+27 = 135.
For the second group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9 and then reversing the digits. This gives a sum of 30+60+90+12+51+81+21+42+72 = 495.
The total sum of all the positive two-digit integers where one of the digits is three times the other is 135+495 = 630.
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Mr. Brust can eat 3/4 of a bucket of wings in 3/4 hour. How many wings does Mr. Brust eat in one hour?
Answers
Answer:
1 bucket
Step-by-step explanation:
3/4 buckets = 3/4 hours
multiply both sides by 4/3 to get one hour
(4/3) * (3/4) buckets = (4/3) * (3/4) hours
1 bucket = 1 hour
“Theresa’s Transportation” rental car company charges $30 to rent a car and $0.60 per mile for each rental. “Pete’s propulsions” rental car company charges $20 to rent a car and $0.85 per mile. After how many miles will it be more expensive to rent from Pete’s Propulsions than Theresa’s Transportation
Answers
On solving the provided question, we got to know that he fraction can bake 200/57 loaves or 3 29/57 loafs.
what is fraction?Mathematically speaking, fractions are represented by integers that indicate a portion of a whole. In the same way that a whole can be any quantity, value, or object, a fraction can be a portion or subset of any quantity of a whole. As an example, let's try to comprehend this idea. The pizza in the picture below is cut into 8 equally sized pieces. The chosen slice of pizza might now be expressed as 1/8 if we wanted to. This indicates that we are talking about one of eight equally sized sections. It denotes a ratio of 1/8. Reading options include: One-eighth, or
1 by 8
13 1/3 divided by 3 4/5
Let's first convert these mixed numbers to incorrect fractions.
13 1/3 = 13(3) + 1 = 39 + 1 = 40/3
3 4/5 = 3(5) + 4= 19/5
Now that we have divided 40/3 by 19/5, we can just switch the operation to multiplication and flip the second fraction because we know how to divide fractions.
40/3 x 5/19 = 200/57
he can bake 200/57 loaves or 3 29/57 loafs.
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26. Pregnancy length The length of human pregnancies from conception to birth
follows a Normal distribution with mean 266 days and standard deviation 16 days.
Choose a pregnant woman at random. Let X = the length of her pregnancy.
(a) Find P(X2 240) and interpret the result.
(b) What is P(X> 240)? Explain.
(c) Find the value of c such that P(X ≥ c) = 0.20. Show your work.
Answers
There is a chance (probability) of about 94.84% that the pregnancy last at least 240 days and P (X ≥ 240) = 0.9484 and the the value of c such that P(X ≥ c) = 0.20 is 279.44
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur,
Given that Mean (μ) = 266
and Standard deviation(σ) = 16
The z-score is the value decreased by the mean divided by the standard deviation:
z = (x−μ)/σ = (240−266)/16
≈−1.63
Determine the corresponding probability using the normal probability table in the appendix:
P (X ≥ 240)
= 1 - P (X < 240)
= 1 - P(Z < -1.63)
= 1 - 0.0516
=0.9484
(a) There is a chance of about 94.84% that the pregnancy last at least 240 days
(b) P (X ≥ 240) = 0.9484
(C) Given that 20% is greater than z, then we know that 80% or 0.80 is smaller than z.
The area of 0.7995 is closest to 0.8, and it is located in the row 0.8 and column .04
thus, the z-value is z=0.84.
x = μ+zσ = 266+0.84*(16 )
=279.44
The the value of c such that P(X ≥ c) = 0.20 is 279.44
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There is a chance (probability) of about 94.84% that the pregnancy last at least 240 days and P (X ≥ 240) = 0.9484 and the the value of c such that P(X ≥ c) = 0.20 is 279.44
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur,
Given that Mean (μ) = 266
and Standard deviation(σ) = 16
The z-score is the value decreased by the mean divided by the standard deviation:
z = (x−μ)/σ = (240−266)/16
≈−1.63
Determine the corresponding probability using the normal probability table in the appendix:
P (X ≥ 240)
= 1 - P (X < 240)
= 1 - P(Z < -1.63)
= 1 - 0.0516
=0.9484
(a) There is a chance of about 94.84% that the pregnancy last at least 240 days
(b) P (X ≥ 240) = 0.9484
(C) Given that 20% is greater than z, then we know that 80% or 0.80 is smaller than z.
The area of 0.7995 is closest to 0.8, and it is located in the row 0.8 and column .04
thus, the z-value is z=0.84.
x = μ+zσ = 266+0.84*(16 )
=279.44
The the value of c such that P(X ≥ c) = 0.20 is 279.44
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The table shows the number of students going on a field trip one chaperone is needed for every 12 students
Answers
Answer:
I'm not sure what equation is needed here. Could you share the table?
Either way, you can take the number of students there are and multiply that to the number of chaperones needed per group of 12- basically see how many groups of 12 you can fit in the overall group of students
Use the distributive property to simplify the expression
6(8x+5)
Answers
Step-by-step explanation:
6(8x+5)
Use the distributive property to multiply 6 by 8x+5.
48x+30
Hope it Helps!
Describe a sequence of transformation that maps triangle DOG onto triangle CAT
Answers
The transformation of the function is given by reflection along y axis and a translation of 5 units up
What is Reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Given data ,
Let the transformation be represented as A
Now , the equation will be
Let the triangle be represented as ΔODG
Now , the coordinates of ΔODG is
O = O ( -1 , -2 )
D = D ( -5 , -3 )
G = G ( -2 , -4 )
Now , the transformed triangle is ΔACT
The coordinates of ΔACT is
A = A ( 1 , 3 )
C = C ( 5 , 2 )
T = T ( 2 , 1 )
Now , on reflecting the triangle ΔODG along y axis , we get
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse
So , the coordinates of triangle O'D'G' , we get
O' = O' ( 1 , -2 )
D' = D' ( 5 , -3 )
G = G' ( 2 , -4 )
Now , translating the triangle ΔO'D'G' up by 5 units , we get
The y coordinate of the triangle gets incremented by 5
So ,
A = O' ( 1 , -2 + 5 )
C = C ( 5 , -3 + 5 )
T = T ( 2 , -4 + 5 )
And , the coordinates of the triangle ΔACT is
A = A ( 1 , 3 )
C = C ( 5 , 2 )
T = T ( 2 , 1 )
Hence , the transformation is reflection along y axis and followed by translation of 5 units up
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Explain the concept of extraneous solutions. Give examples with the different types of functions explored.
Answers
Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.
What is a function ?
Function can be defined as a relation , which relates an input to output is called as function.
In Mathematics, an extraneous solution (or spurious solution) is an solution, consisting of that to an equation, that emerges from the procedure of solving the hassle but isn't always a legitimate strategy to the problem.[1] A missing solution is an answer that is a valid strategy to the hassle,
however disappeared all through the process of solving the problem. each are frequently the consequence of acting operations that are not invertible for a few or all values of the variables, which prevents the chain of logical implications inside the proof from being bidirectional.
Hence , The Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.
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What is one way you could use the positive feelings from a situation toward a future motivation?
Develop a positive personal process and focus
Remember the “How could I do better?” mentality
Tell the adults in your life to hold you accountable
Be content with not being successful at everything
Answers
Answer:
One way to use positive feelings from a situation towards future motivation is to focus on the positive aspects of the experience and try to replicate them in the future. For example, if you had a particularly enjoyable and successful project at work, you might try to identify the specific factors that contributed to your success and seek out similar opportunities in the future. This approach can help you to build on your strengths and experiences and maintain a positive and motivated outlook. Additionally, setting specific goals for yourself and tracking your progress can help to keep you motivated and on track towards future success.
6. Given:
Prove: AB = DC
I need helpppp PLEASEEEEEEE
Answers
I don’t know I just need the answer
Answers
Graph each equation.
12. y + 3 = 2(x - 1)
Answers
Given line in point-slope form:
y + 3 = 2(x - 1)Point-slope form is:
y - y₁ = m(x - x₁), where m - slope, (x₁, y₁) is the point on the lineWe know that to graph a line it is enough two have two points.
One of the points is (x₁, y₁) = (1, - 3).
Find one more point, when x = 3:
y + 3 = 2(3 - 1)y + 3 = 4y = 1The point is (3, 1).
Plot and connect these two points to get the line.
Solve by using substitution. x+2y=−1 x=y+5
Answers
Answer:
Step-by-step explanation:
the first equation we konw x=-2y-1,
then -2y-1=y+5
so, y = -2, x=3
Answer:
y = -2
x = 3
Step-by-step explanation:
y + 5 + 2y = -1 (substitute)
3y + 5 = -1 (Simplify)
3y = -6 (Get rid of 5)
y = -2 (Divide)
x = -2 + 5 (plug in y)
x = 3 (simplify)
hope this helps :)
please help quickly +25pts
X, Y, and Z are collinear. Y is between X and Z.
XY = 12 and XZ = 14
YZ = ___ units
Answers
The value of YZ = 2 units.
What are collinear points?The Latin words "col" and "linear" are combined to form the word "colinear." "Col" stands for "together," and "Linear" is a line. Collinear points are hence points that are situated along a single line. Numerous instances of collinearity can be observed in daily life, such as a line of pupils standing together.
Given X, Y, and Z are collinear. Y is between X and Z.
so XY + YZ = XZ
given XY = 12 units and XZ = 14 units
XY + YZ = XZ
12 + YZ = 14
YZ = 14 - 12
YZ = 2 units
Hence measure of YZ is 2 units.
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quickkkkk plss help me
Answers
√2x – 1- x = −8
How do I solve this equation?
Answers
The solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].
What is an equation?
An equation is a statement that two expressions are equal to each other. It is a mathematical sentence that asserts the equality of two expressions. An equation can be written in the form of:
expression_1 = expression_2
The given equation is √2x – 1- x = −8.
[tex]2x=x^2-14x+49[/tex]
[tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex]
Hence, the solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].
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1/4 gallon of paint costs $8. 99. What is the unit price of one gallon of paint?
Answers
The unit price of one gallon of paint is going to be $35.96.
We can use the unitary method to solve this problem. The unitary method is a technique used for solving a problem by first finding the value of a single unit, and finding the necessary value by multiplying the single unit value.
In this question, it is given that 1/4 gallon of paint costs $8.99 so for 1 gallon we will have to multiply both the paint amount and the money which buys it to 4 which will conclude that 1 gallon costs $8.99 × 4 is equal to $35.96. So, 1 gallon of paint will cost $35.96.
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Write and solve the inequality that represents negative one third is greater than or equal to the product of negative two fifths and a number.
negative one third is greater than or equal to negative two fifths y where y is greater than or equal to negative five sixths
negative one third is greater than or equal to negative two fifths y where y is greater than or equal to five sixths
negative two fifths is greater than or equal to negative one third y where y is less than or equal to negative two fifteenths
negative two fifths is less than or equal to negative one third y where y is greater than or equal to two fifteenths
Answers
The inequality that represents negative one third is greater than or equal to the product of negative two fifths and a number is: B. negative one third is greater than or equal to negative two fifths y where y is greater than or equal to five sixths.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Note: Let the variable y represent the unknown number.
Next, we would translate the word problem "negative one third is greater than or equal to the product of negative two fifths and a number" into an algebraic inequality as follows;
-1/3 ≥ -2/5 × y
-1/3 ≥ -2y/5
Multiplying both sides of the algebraic inequality by -5/2, we have:
-1/3 × -5/2 ≥ -2y/5 × -5/2
5/6 ≤ y
y ≥ 5/6.
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What is the difference of the two polynomials 9x2 8x 2x2 3x?
Answers
The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.
What is polynomials?A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.
Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).
To find the difference between
(9x² + 8x) - (2x² + 3x)
We do calculation
= 9x² + 8x - 2x² - 3x
= 9x² - 2x² + 8x - 3x
= 7x² + 5x
Thus, the difference between the polynomials is 7x² + 5x.
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Gianna has $760 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $356.46.
She buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72.
She plans to spend some or all of the money she has left to buy new biking outfits for $45.35 each.
Write and solve an inequality which can be used to determine
o
o, the number of outfits Gianna can purchase while staying within her budget.
Answers
Answer:
Gianna has $760 to spend and she has already spent $356.46 on a new bicycle, $10.01 on 2 bicycle reflectors, and $20.72 on a pair of bike gloves.
The total amount spent on these items is $356.46 + $10.01 + $20.72 = $387.19.
Gianna has $760 - $387.19 = $<<760-387.19=372.81>>372.81 left to spend on biking outfits.
She wants to buy biking outfits that cost $45.35 each.
We can write an inequality to represent the number of outfits Gianna can purchase while staying within her budget as follows:
45.35o <= 372.81
This inequality can be solved by dividing both sides by 45.35:
o <= 8.24
Therefore, Gianna can purchase 8 biking outfits while staying within her budget.
Step-by-step explanation:
At a banquet hall there are 25 tables that seat 4 people and 30 tables that seat 6 people. There are no other tables in the banquet hall. What is the ratio of the number of tables that seat 4 people to the total number of tables in the banquet hall?
Answers
Answer:
1:11
Step-by-step explanation:
We know
There are 25 tables that seat 4 people
First, we find the total number of tables by taking
25 + 30 = 55 tables
Then we find the ratio of tables that seat 4 people to the total number of tables by
5 / 55 = 1/11 = 1:11
So, the ratio is 1:11
Valentina is baking jumbo cinnamon rolls for a family breakfast. She uses all the dough she made to form 12 cinnamon rolls of equal weight. The recipe usually makes 36 ounces of dough, but Valentina made more dough than that so she can have larger cinnamon rolls.
Answers
The required inequality to represent the above data regarding Valentina is x > 3.
How to illustrate the inequality?Valentina uses more than 36 ounces of dough 12 cinnamon rolls made by Valentina of weight ounces of dough represented by x ,then required inequality is given by 12x > 36.
Number of cinnamon rolls made by Valentina = 12
Weight of all 12 cinnamon rolls are equal
x represents the ounces of dough used by Valentina to make cinnamon roll.
Ounces of dough used by Valentina is more than 36.
Required inequality to represent the above data is given by:
12x > 36
Divide by 12 form both the sides we get,
12x /12 > 36/12
x > 3
The inequality is x > 3.
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Complete question
Valentina is baking jumbo cinnamon rolls for a family breakfast. She uses all the dough she made to form 12 cinnamon rolls of equal weight. The recipe usually makes 36 ounces of dough, but Valentina made more dough than that so she can have larger cinnamon rolls. Let x represent how many ounces of dough Valentina uses for each cinnamon roll. Which inequality describes the problem?
Find the perimeter of the rectangle
A. 46
B. 136
C. 23
D. 25
Answers
Answer:
A.46
Step-by-step explanation:
rectangle divided in two by the diagonal, we find the missing side (x) with Pythagoras
x² = 17² - 8²
x² = 289 - 64
x² = 225
x = √225
x = 15in
now we have all the sides and we add them to find the perimeter8 + 15 + 8 + 15 =
46in
What does it mean to solve an equation by substitution?
Answers
The value of a variable from one equation is substituted in the other equation when using the substitution method.
The graphic approach and the algebraic method are the two main categories into which simultaneous linear equations can be solved. One of the categories of the algebraic approach is the substitution method. The algebraic approach to solving simultaneous linear equations is known as the substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.
Steps for Substitution method:
Simplify the given equation by expanding the parenthesisSolve one of the equations for either x or ySubstitute the step 2 solution in the other equationNow solve the new equation obtained using elementary arithmetic operationsFinally, solve the equation to find the value of the second variableTherefore in the Substitution method, The value of a variable from one equation is substituted in the other equation.
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A bag contain 27 ball. The ratio of red to blue to yellow ball i 6:1:2 find how many red, blue and yellow ball there are
Answers
On solving the provided question we can say that by linear equation number of, Red Balls = 6x 18; Blue Balls = 3; Yellow Balls = 6
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
A bag contains 27 balls
• The ratio of red to blue to yellow balls is 6:1:2
To Find : The number of red,blue and yellow balls present in the bag
Let us take the variable as 'x' to represent the number of balls in the bag
When we Put the values in a equation,
6X+X+2x = 27
9x = 27
x = 3
Hence the number of,
Red Balls = 6x 18
Blue Balls = 3
Yellow Balls = 6
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9. Samuel is comparing the average EPA ratings on 4 types of vehicles. He wants to drive a pickup truck, but he can see from the table below that he would use less gasoline if he drove a compact car. If Samuel
drives an average of 13,000 miles per year, how many more gallons of gas would he need to buy for a pickup truck compared to a compact car?
4-door Sedan
Compact Car
Pickup Truck
Small SUV
EPA rating: 26 mpg (combined city and EPA rating: 32 mpg (combined city EPA rating: 20 mpg (combined city and EPA rating: 22 mpg (combined city and
highway)
and highway)
highway)
highway)
O221.25 gallons
243.75 gallons
250.25 gallons
O261.75 gallons
Answers
Answer:
If Samuel drives a compact car, he would need to buy 243.75 gallons of gas per year. If he drives a pickup truck, he would need to buy 250.25 gallons of gas per year. So he would need to buy 6.5 more gallons of gas per year if he drives a pickup truck compared to a compact car.
Step-by-step explanation: