The acceleration of the car will be 0.002 m / s².
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The velocity of the car = 35.9 m/hr
The time take by car = 8.2 seconds
Now,
Since, We know that;
⇒ Acceleration = (Final velocity - Initial velocity) / Time
Since, The driver accelerates her car from rest to a velocity of 35.9 mi/hr.
So, Initial velocity = 0
And, Final velocity = 35.9 m / hr
= (35.9 / 3600) m/s
= 0.01 m / s
So, We get;
⇒ Acceleration = (Final velocity - Initial velocity) / Time
⇒ Acceleration = (0.01 - 0) / 8.2
⇒ Acceleration = 0.01 / 8.2
⇒ Acceleration = 0.002 m / s²
Thus, The acceleration of the car will be 0.002 m / s².
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please help! where it says “select” the options are 1997-2006
We can find the average rate of change of change using the following expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]for the period betwen 1999 and 2002, we have the following:
[tex]\begin{gathered} m=\frac{1483-1336}{2002-1999}=\frac{147}{3}=49 \\ \Rightarrow m=49 \end{gathered}[/tex]therefore, the average rate of change of population between 1999 and 2000 is 49.
Next, we do the same for the period between 2001 to 2005:
[tex]\begin{gathered} m=\frac{801-1591}{2005-2001}=-\frac{790}{4}=-197.5 \\ \Rightarrow m=-197.5 \end{gathered}[/tex]thus, the average rate of change of population between 2001 and 2005 is 197.5
Finally, notice that the population increased from 1997 to 2001, while it decreased from 2002, to 2006
Over the last three evenings, Maria received a total of 154 phone calls at the call center. The second evening, she received 10 more calls than the first evening. The third evening, she received 4 times as many calls as the first evening. How many phone calls did she receive each evening?Number of phone calls the first evening:Number of phone calls the second evening:Number of phone calls the third evening:
Data
• Total phone calls: 154
,• Second evening ( ,s ,): 10 more calls than the first evening ( ,f ,)
,• Third evening ( ,t ,): 4 times as many calls as ,f
Procedure
We have to translate the given information into algebraic expressions.
• Maria received a total of 154 phone calls at the call center:
[tex]f+s+t=154[/tex]where f represents the first evening, s the second, and t the third.
• The second evening, she received 10 more calls than the first evening:
[tex]s=10+f[/tex]• The third evening, she received 4 times as many calls as the first evening:
[tex]t=4\times f[/tex]As t and s can be used in terms of f, we will replace the second and third equations that we build in the first one:
[tex]f+s+t=154[/tex][tex]f+(10+f)+(4\times f)=154[/tex]Eliminating the parenthesis we get:
[tex]f+10+f+4f=154[/tex]Solving for f:
[tex]6f=154-10[/tex][tex]f=\frac{144}{6}[/tex][tex]f=24[/tex]Thus, the number of phone calls the first evening was 24.
Then, we have to replace this calculated value in the other equations to get s and t.
• Solving for ,s
[tex]s=10+f[/tex][tex]s=10+24[/tex][tex]s=34[/tex]• Solving for ,t
[tex]t=4f[/tex][tex]t=4\cdot24[/tex][tex]t=96[/tex]To prove our answers are correct, we can do the following:
[tex]24+34+95=154[/tex][tex]154=154[/tex]Answer
• Number of phone calls the first evening: 24
• Number of phone calls the second evening: 34
• Number of phone calls the third evening: 96
The number of chirps per minutes made by a cricket is a function of the temperature (T). The function f(T) = 4(T-40). How many chirps would you except to hear when the temperature is 90?
Number of chirps would you expect to hear when the temperature is 90 is 200 .
A function from a fixed X to a hard and fast Y assigns to each detail of X exactly one element of Y. The set X is known as the area of the feature and the set Y is known as the codomain of the characteristic.
Calculation:
f(T) = 4(T-40)
= 4(90-40)
= 4 × 50
= 200
A feature is described as a relation between a fixed of inputs having one output each. In easy phrases, a feature is a courting among inputs in which each entry is related to precisely one output. each feature has a website and codomain or variety. A characteristic is commonly denoted by means of f(x) where x is the input.
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ZA and B are vertical angles. If m_A = (3x + 13) and mZB = (5x + 9), then find the measure of ZA.
EXPLANATION:
The first thing to do is graph the given points of the equation to find the position of the angles.
A=(3X+13)
B=(5X+9)
Both equations to find the angle z should give me a total of 180 degrees
By adding and joining both equations, we have the following:
[tex]\begin{gathered} (3x+13)+(5x+9)=180 \\ 3x+13+5x+9=180 \\ 3x+5x=180-13-9 \\ 8x=180-22 \\ 8x=158 \\ x=\frac{158}{8} \\ x=19.75 \end{gathered}[/tex]Now plugging the value of x into the first equation to find the angle A gives us:
[tex]\begin{gathered} A=3(19.75)+13 \\ A=59.25+13 \\ \textcolor{#FF7968}{A=72.25}\text{\textcolor{#FF7968}{ DEGREES}} \\ The\text{ measure }of\text{ the angle A is: 72.25} \\ \end{gathered}[/tex]To check if the measure of angle A is correct, we must also replace x in the second equation to find the value of angle B, which has to give us exactly what is missing to complete the 180 degrees.
[tex]\begin{gathered} B=5(19.75)+9 \\ B=98.75+9 \\ B=107.75 \\ \text{Now adding the angles A y B should give us 180 }degrees. \\ \textcolor{#FF7968}{A=72.25} \\ B=107.75 \\ AB=\textcolor{#FF7968}{72.25}+107.75=\textcolor{#FF7968}{180}\text{\textcolor{#FF7968}{ degrees.}} \end{gathered}[/tex]What is 3 to the 9th power times 3 to the 5th power
Answer:
3^14
Step-by-step explanation:
Multiplication of two values with same base and different exponent:
When we are multiplicating two values with the same base and different exponents, we keep the base and add the exponents. For example:
[tex]x^a\ast x^b=x^{a+b}[/tex]In this question:
[tex]3^9\ast3^5=3^{9+5}=3^{14}[/tex]Which of the following expressions are equivalent to…I will send a screenshot of the expression I need help with.
Explanation
We have an expression given as
[tex]-\frac{2}{-13}[/tex]To find the equivalent value, we will make use of the fact that when two negative signs divide or multiply each other, the resulting value is always positive
Thus
The simplified answer is
[tex]\frac{2}{13}[/tex]In our case, we will have a positive outcome
Therefore, the correct answers will be options A and B
The System of PolynomialsYou are aware of the different types of numbers: natural numbers, integers, rational numbers, and real numbers. Now you will work with a property of the number system called the closure property. A set of numbers is closed for a specific mathematical operation if you can perform the operation on any two elements in the set and always get a result that is an element of the set.Consider the set of natural numbers. When you add two natural numbers, you will always get a natural number. For example, 3 + 4 = 7. So, the set of natural numbers is said to be closed under the operation of addition.Similarly, adding two integers or two rational numbers or two real numbers always produces an integer, or rational number, or a real number, respectively. So, all the systems of numbers are closed under the operation of addition.Think of polynomials as a system. For each of the following operations, determine whether the system is closed under the operation. In each case, explain why it is closed or provide an example showing that it isn’t.1. AdditionType your response here:2. SubtractionType your response here:3. MultiplicationType your response here:4. DivisionType your response here:
Polynomials are closed under the operation of addition, subtraction, and multiplication only. Here's why:
1. Addition: (Closed)
Reason: Say we have two polynomials: (x⁴ + 2x³ - 4) and (3x³ - 2x² + 6x). If we add these two polynomials, (x⁴ + 2x³ - 4) + (3x³ - 2x² + 6x), it will result to x⁴ + 5x³ - 2x² + 6x - 4 which is also a polynomial.
When adding polynomials, the variables and the exponents don't change. This guarantees that the sum of these variables with exponents will always be a polynomial.
2. Subtraction: (Closed)
Reason: Say we have two polynomials: (x⁴ + 2x³ - 4) and (3x³ - 2x² + 6x). If we subtract these two polynomials, (x⁴ + 2x³ - 4) - (3x³ - 2x² + 6x), it will result to x⁴ - x³ + 2x² - 6x - 4 which is also a polynomial.
When subtracting polynomials, the variables, and the exponents don't change. This guarantees that the difference of these variables with exponents will always be a polynomial.
3. Multiplication: (Closed)
Reason: Say we have two polynomials (x + 2) and (x - 4). If we multiply these two polynomials, (x + 2)(x - 4), it will result in x² - 2x - 8, which is also a polynomial.
When multiplying polynomials, the variables do not change but the exponents will be added to each other. In this case, we can guarantee that the new exponents will be positive whole numbers still and this guarantees that the answer will be a polynomial.
4. Division: (Not closed)
Reason: When dividing polynomials, exponents are being subtracted from each other, therefore, we might have a result of a negative exponent. Negative exponents are not allowed in a polynomial. Example, say we have two polynomials (x²) and (x⁴), if we divide (x²) by (x⁴), the resulting value would be:
[tex]\frac{x^2}{x^4}=x^{-2}[/tex]The resulting value is x to the power of negative 2, and is not a polynomial.
I need help solving this I thought it was 7 but I’m not too sure now
We are given a triangle such that two line segments are drawn as medians:
[tex]MX\text{ and YL are median lines}[/tex]A meadian line has three points that are off importance as follows:
[tex]\begin{gathered} \text{Strats from one of the vertex of a triangle} \\ \text{Passes through the centroid of the triangle} \\ Bi\sec ts\text{ the opposite side of the triangle} \end{gathered}[/tex]Hence, using the above information we can extract that:
[tex]\begin{gathered} Y\text{ is the mid-point of MK} \\ X\text{ is the mid-point of KL} \\ \text{\textcolor{#FF7968}{AND}} \\ A\text{ is the centroid of the entire triangle} \end{gathered}[/tex]We can also use the properties of median length that states:
[tex]\begin{gathered} \text{Length from vertex to centroid : Centroid to bisection point of opposite side} \\ \end{gathered}[/tex]The ratio of the above two lengths for any median line of a triangle remains true for:
[tex]2\text{ : 1}[/tex]This means that the line segment from centroid to bisection ( mid ) point of the opposite side is shorter than the preceeding length; hence, the ratio is ( 2 : 1 ).
We are given the length of the line segment MA the larger part of the median line:
[tex]MA\text{ = 14 units}[/tex]We can use the property of ratio of lengths for the median lines and determine the length of the smaller part of the median line as follows:
[tex]\begin{gathered} \text{ 2 : 1} \\ MA\text{ : AX} \\ ======== \\ AX\text{ = }\frac{MA}{2} \\ \\ AX\text{ = }\frac{14}{2}\text{ = 7 units} \end{gathered}[/tex]From the above property we determined the length of the shorter line segment. Now we have lengths for the both constituent line segments of median line ( MX ). We can simply sum the individual lengths as follows:
[tex]\begin{gathered} MX\text{ = AX + MA} \\ MX\text{ = 7 + 14} \\ \textcolor{#FF7968}{MX}\text{\textcolor{#FF7968}{ = 21 units}} \end{gathered}[/tex]Hence, the answer is:
[tex]\textcolor{#FF7968}{MX}\text{\textcolor{#FF7968}{ = 21 }}\textcolor{#FF7968}{\ldots}\text{\textcolor{#FF7968}{ Option C}}[/tex]What is the equation of the line parallel to 3x + 5y = 11 that passes through the point (15, 4)?3x-29= 3x - 295y-y-x-21y--x+533y=-5* +13Mart this and returnSavond uit
Recall that two equations in standard form represent parallel lines if they are as follows:
[tex]\begin{gathered} Ax+By=C_1, \\ Ax+By=C_2, \end{gathered}[/tex]Where A>0, and all the coefficients are integers.
Therefore the equation of a parallel line to the given line is as follows:
[tex]3x+5y=k[/tex]Since the parallel line passes through (15,4) then:
[tex]3*15+5*4=k.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} 45+20=k, \\ k=65. \end{gathered}[/tex]Therefore:
[tex]3x+5y=65.[/tex]Solving the above equation for y we get:
[tex]\begin{gathered} 3x+5y-3x=65-3x, \\ 5y=-3x+65, \\ \frac{5y}{5}=-\frac{3x}{5}+\frac{65}{5}, \\ y=-\frac{3}{5}x+13. \end{gathered}[/tex]Answer: Last option.
Answer:
D
Step-by-step explanation:
The slope of the the straight line equation 3x+5y=11 is (−35)Hence the slope of the line parallel is same to the given line i.e,(−35) We can write the equation in the following form slope intercept form i.e, y=mx+cHere c=−6 and m=−35The answer is y=−35x−6⇒5y=−3x−30⇒3x+5y=−30Hope it helps...Thanks you...
A mandatory competency test for high school sophomores has a normal distribution with a mean of 553 and a standard deviation of 90. The top 3% of students receive a $500 prize. What is the minimum (cutoff) score you would need to receive this award?
Answer:
The minimum (cut off) score you need to receive this award is;
[tex]722.2[/tex]Explanation:
Given that the top 3% of the students receive a $500 prize.
[tex]P=1-0.03=0.97[/tex]We will then find the z-score that corresponds to the given probability.
[tex]z=1.88[/tex]Recall that;
[tex]z=\frac{X-\mu}{\sigma}[/tex]Given;
[tex]\begin{gathered} \mu=553 \\ \sigma=90 \end{gathered}[/tex]substituting the values;
[tex]\begin{gathered} 1.88=\frac{X-553}{90} \\ X-553=1.88\times90 \\ X=553+1.88\times90 \\ X=722.2 \end{gathered}[/tex]Therefore, the minimum (cut off) score you need to receive this award is;
[tex]722.2[/tex]
What is y=6/5 x+9 written in standard form
Answer:
6/5x -y = -9
Step-by-step explanation:
The standard form is ax + by =c so you would have to use the properties of equality to solve.
Given : y = 6/5x+9
Subtract -9 from both sides: 6/5x = y-9
Subtract y from both sides: 6/5x -y = -9
Julia ran 1,000 meters in 9 minutes. How many meters/minute did she run?
Answer:
111.11111111111111111
Step-by-step explanation:
can someone please help me solve this
For the carpenter to be sure that both length of the beam to be same length the base angles of the triangle must be the same.
What are isosceles triangle?An isosceles triangle is a triangle having two sides of equal length. The angles opposite the equal sides are also equal.
In other words, an isosceles triangle is a triangle with two sides equal and the base angles equal to each other.
The carpenter builds a set of triangular roof support . The carpenter wants the both sides of the slanted beam to be the same in lengths,
Therefore, for the carpenter to be sure the both length of the beam is the same, the base angles must be the same. This follows the rules of an isosceles triangle where two sides are the same and the base angles must be the same.
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The graph of a linear relationship passes through (0, 2), (1,5), and (3, 11) but not through (2,7). Which of the following is the equation for this linear relationship?A.O y = 2x + 3 B.O y = 3x + 2C. O y = 5xD. O y= 4x-1
There is a point that doesnt go in the curve.
So the procedure is to replace x by 2 ,and y by 7 in every option to see which doesnt belongs
So we see
(4x + 2)(6x^2 - z + 2)
Answer:
24x^3 - 4xz + 12x^2 -2z + 8x + 4
Step-by-step explanation:
We just need to simplify the equation
PLS HELP ASAP THIS IS DUE TODAY!!!!
line AD is parallel to line HE. Identify one pair of alternate interior angles.
The alternate interior angles : ∠4 and ∠5
∠3 and ∠6
In this question, we have been given line AD is parallel to line HE.
We need to identify one pair of alternate interior angles.
We know that the alternate interior angles are formed when a transversal intersects two lines which are coplanar. These angles, lie on the inner side of the parallel lines but on the opposite sides of the transversal.
For given figure alternate interior angles are:
∠4 and ∠5
∠3 and ∠6
Therefore, the alternate interior angles : ∠4 and ∠5
∠3 and ∠6
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Whats the product 0.4(-1.08)
Use the information to answer the question.Point P is located at 16 on the number line, Point Q is located at -9 on the number line.What is the distance between Point P and Point on the number line? Enter the answer in the box.units
Answer:
25units
Explanation:
Given the following points on the number line
Point P at 16
Point Q at -9
Distance between the points = Point P - Point Q
Distance between the points = 16 - (-9)
Distance between the points = 16 + 9
Distance between the points = 25
Hence the distance between Point P and Point Q on the number line is 25units
3x^4+2x^3-12x-6solve for ;x=-2
The function f(x) = 3x⁴ + 2x³ - 12x - 6 is equal to 60 for x = -2.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following equation -
[tex]3x^4+2x^3-12x-6[/tex]
We have -
f(x) = 3x⁴ + 2x³ - 12x - 6
for x = - 2
f(- 2) = 3(-2)⁴ + 2(-2)³ - 12(-2) - 6
f(-2) = 48 - 16 + 24 - 6
f(- 2) = 48 + 8 - 6
f(- 2) = 60
Therefore, the function f(x) = 3x⁴ + 2x³ - 12x - 6 is equal to 60 for x = -2.
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10 less than 7 times a number is the same as 3 times the number plus 18
Answer:
yes, it is the same
Step-by-step explanation:
7x - 10 = 3x + 18
7x-10+10 = 3x + 18 + 10
7x = 3x + 28
7x - 3x = 3x - 3x + 28
4x = 28
4x ÷ 4 = 28 ÷ 4
x=7
Plug x back in and check the answer.
7x-10 = 3x+18
7(7)-10 = 3(7)+18
49-10 = 21+18
39 = 39
So, YES they are the same.
Write the equation of the line in fully simplified slope-intercept form.
plss help
Answer: y=2x-5
Step-by-step explanation:
Nhan is getting dressed. He considers two different shirts, three pairs of pants, and three pairs of shoes. He chooses one of each of the articles at random. What is the probability that he will wear his khakis but not his sandals? Enter your answer as a fraction in simplest form. Shirt Pants Shoes collared khakis sneakers T-shirt jeans flip-flops shorts sandals The probability that Nhan will wear his khakis but not his sandals = .
The probability that Nhan will wear his shirt is 0.375.
How to calculate the probability?From the information, Nhan considers two different shirts, three pairs of pants, and three pairs of shoes.
The total number will be:
= 2 + 3 + 3
= 8
Therefore, since we want to calculate the probability of the shirt which is the khaki, this will be:
= P(shirt) / Total number
= 3/8
= 0.375
There, the probability is 0.375.
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(b) Antonio compares his plan to another friend, Brielle's. Given that both Antonio and Brielle will only be charged for full minutes, is there an amount of time when their two plans cost the same? Explain. ven that bo Brielle's plan: Monthly cost = 2(1.50m+12)+m-4 where m is the number of minutes used
Antonio's plan is
[tex]3(0.75m+10)+2.50m-15[/tex]Brielle's plan is
[tex]2(1.50m+12)+m-4[/tex]Then, we express both expressions as equivalent to finding the number of minutes needed to cost the same.
[tex]3(0.75m+10)+2.50m-15=2(1.50m+12)+m-4[/tex]First, we use the distributive property.
[tex]2.25m+30+2.50m-15=3m+24+m-4[/tex]Then, we reduce like terms.
[tex]4.75m+15=4m+20[/tex]Then, we subtract 4m on each side.
[tex]\begin{gathered} 4.75m-4m+15=4m-4m+20 \\ 0.75m+15=20 \end{gathered}[/tex]Now, we subtract 15 on each side.
[tex]\begin{gathered} 0.75m+15-15=20-15 \\ 0.75m=5 \end{gathered}[/tex]At last, we divide the equation by 0.75.
[tex]\begin{gathered} \frac{0.75m}{0.75}=\frac{5}{0.75} \\ m\approx6.67 \end{gathered}[/tex]This means after 6.67 minutes both plans will cost the same.
This decimal result means that both plans won't be equivalent because only full minutes are charged. In other words, at 6 minutes the plans are not equal.You want to take a bus to go visit your friend in a different city. The distance between two cities is 200 kilometers and the bus drives 80 kilometers per hour. If the bus is 20 kilometers away from your friend’s city, which of the following equations represents the hours, h, the bus has travelled?
The required equation will be 200-80h=20 as the statement says, "You want to take a bus to go visit your friend in a different city. The distance between two cities is 200 kilometers and the bus drives 80 kilometers per hour. If the bus is 20 kilometers away from your friend’s city".
What is equation?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. In mathematics, an equation is a relationship of equality between two expressions written on both sides of the equal to sign. 3y = 16 is an example of an equation. Equations can be classified into three types based on their degree:
The linear equationQuadratic formulaThe cubic equationHere,
The distance between two cities=200 KM
The speed of bus=80 KM/hour
Time travelled=h hours
The distance travelled by bus=80h
The difference between distance=20
200-80h=20
As stated in the statement, the required equation is 200-80h=20 "You want to take the bus to see a friend in another city. The distance between the two cities is 200 kilometers, and the bus travels at an average speed of 80 kilometers per hour. If the bus is 20 kilometers away from your friend’s city".
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find finish homework soon as possible
Sale tax rate = 6.85%
To calculate the sale tax on a $14,000 Car, multiply 14,000 by the sale tax rate in decimal form ( divided by 100)
14,000 x (6.85/100) = 14,000 x 0.0685= $959
To find the final cost, add the sale tax amount to the price:
14,000 + 959 = $14,959
Questions-PartA what is the perimeter of this hexagon if the side is 15 cm?Part BWhat is the apothem of this hexagon each side is 15 cm round to the nearest whole number?Part CWhat is the area of the hexagon?(I just need a brief explanation with the answer)
Step 1:
The formula for the area of a hexagon can also be given in terms of the apothem as,
Area of hexagon
[tex]=\text{ }\frac{1}{2}\text{ }a\text{ }\times\text{ P}[/tex]where 'a' is the length of the apothem and 'P' is the perimeter of the hexagon.
Step 2:
Length of the sides = 15 cm
[tex]\begin{gathered} \text{perimeter = 6 }\times\text{ 15} \\ P\text{ = 90} \end{gathered}[/tex]Step 3:
Find the Apothem ' a '
Find each angle
[tex]\text{Each interior angle = }\frac{360}{6}\text{ = 60}[/tex]Next
[tex]undefined[/tex]Assume that each circle shown below represents one unit. Express the shaded
amount as a single fraction and as a mixed number.
Answer: what shown below?
Step-by-step explanation:
What is the slope of the line passing through the points (1, -5) and (4, 1)?
Answer: 2
Step-by-step explanation: i used my brain
i have to solve for ABC n round to nearest whole number
Answer:
90degrees
Explanation:
The sum of interior angle of a triangle si 180degrees
Hence, 7x-1 + 4x+1 + 3x - 2 = 180
Collect the like terms;
7x+4x+3x-1+1-2 = 180
14x - 2 = 180
14x = 180+2
14x = 182
x = 182/14
x = 13
Get m
From the triangle;
mSubstitute x = 13 into the expression
mmm
Hence the measure of m
Identify the correlation you would expect to see between the weight and the age of a child. Explain.
The correlation between the weight and the age of the child is negative.
Correlation
There are 4 types of correlation they are positive correlation, negative correlation, perfect correlation, and no correlation.
Given,
Here we need to find the correlation you would expect to see between the weight and the age of a child.
According to the type of correlation,
We know that, when the two variables are not related to each other then there is no relationship between the variables.
It is always based on the direction of the variable we decide the types of correlation.
Here the type of the correlation is negative correlation because the weight of a child decreases with age.
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