Given:
A standard tire has 10/32 inches of tread.
The tire needs to be replaced when only 2/32 inches of tread remains left.
Here the tire is needed to be replaced after 40,000 miles.
To find:
The thickness of tire rubber lost every 1,000 miles.
Step-by-step solution:
According to the question,
The tire is replaced when only 2/32 inches of tread remain left.
The new tire has 10/32 inches of tread.
Thus tire needs to loose:
10/32 - 2/32 = 8/32 inches of tread.
This means upon traveling for 40,000 miles, 8/32 inches of tread is lost.
So their ratio equals:
40,000 = k (8/32)
k = 40,000 × 32 / 8
k = 40,000 × 4
k = 1,60,000
So to calculate for 1000 miles:
1000/x = 1,60,000
1/x = 1,60,000 / 1000
1/x = 160
x = 1 / 160 inches
Thus we can say for every 1000 miles, 1 / 160 inches of tread is lost.
Determine if the 2 lines are parallel, perpendicular, or neither based on their slope- intercept equations.
Equations of lines H & I;
Line H: y=z
Line I: y=-7z - 33
O Not Enough Information
O Perpendicular
O Neither
POSSIBLE PO
O Parallel
Equations of lines H & I; Line H: y=z Line I: y=-7z - 33 is Perpendicular. The lines are not parallel if the slopes differ. Perpendicular lines do meet, but parallel lines do not.
How can you demonstrate that two lines in an equation are parallel?Only if the slopes of two lines are equal can they be said to be parallel. The conventional version of the equation is 2x - 3y = 4. Since a line with the equation Ax + By = C typically has a slope of -A/B, line q must have a slope of -2/-3 = 2/3.
Their equations allow us to compare the slopes of two lines to determine if they are parallel. The lines are parallel if the slopes are the same and the y-intercepts are different.
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Find the ends of the major axisand foci.49x2 + 16y2 = 784Major axis (0,+[? ])
Answer:
Major axis (0, +-14)
Explanation:
The equation of an ellipse with the center in the origin is:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]So, to transform the equation into this form, we need to divide both sides by 784 as:
[tex]\begin{gathered} 49x^2+16y^2=784 \\ \frac{49x^2}{784}+\frac{16y^2}{784}=\frac{784}{784} \\ \frac{x^2}{16}+\frac{y^2}{49}=1 \end{gathered}[/tex]It means that a² = 16 and b² = 49. So, a = ±4 and b = ±7
Now, the major axis is 2 times the greater value between a and b. Since the greater value is b = 7, 2 times b is:
Major axis = (0, ±7*2) = (0, ±14)
An album received the following ratings on a 1-to-10 scale from10 music critics. What is the mean of the ratings?9.6, 9.8, 7.2, 6.4, 10.0, 8.9, 5.0, 9.8, 9.4, 6.8
Given:
The ratings are
[tex]9.6,9.8,7.2,6.4,10.0,8.9,5.0,9.8,9.4,6.8[/tex][tex]\begin{gathered} \text{Mean}=\frac{9.6+9.8+7.2+6.4+10.0+8.9+5.0+9.8+9.4+6.8}{10} \\ \text{Mean}=\frac{82.9}{10} \\ \text{Mean}=8.29 \end{gathered}[/tex]write an equation of the line that passes through the points in the table x=0,1,2,3 y=10,7,4,1
The line of equation (y + 3x = 10) passes through all the points in the given table.
What are equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.So, the equation will be:
Points:
x=0,1,2,3 y=10,7,4,1We know that when x = 0, then y = 10 and when we will increase x = 1, then y will decrease to y = 7.
The decrease in y is the difference of 3 (10 - 7 = 3)Then, y + 3x = 10 can be the equation.
Lets, 's check:
When x = 0:
y + 3x = 10y = 10 - 3(0)y = 10When x = 1:
y + 3x = 10y = 10 - 3(1)y = 7
When x = 2:
When x = 3:
y + 3x = 10y = 10 - 3(3)y = 1Since all the values of x and y are in proportion now, (y + 3x = 10) is the equation.
Therefore, the line of equation (y + 3x = 10) passes through all the points in the given table.
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What is the value of the expression below when y=9 and z=6?
The numerical value of the expression 9y - 10z when y = 9 and z = 6 is 21.
This question is incomplete, the complete question is;
What is the value of the expression below when y = 9 and z = 6?
9y - 10z
What is the numerical value of the given expression?An algebraic expression is simply an expression that is made up of constants and variables, including algebraic operations such as subtraction, addition, division, multiplication, et cetera.
Given the data in the question;
9y - 10zy = 9z = 6Numerical value of the expression = ?To determine the numerical value of the expression, replace plug y = 9 and z = 6 into the expression and simplify.
9y - 10z
9( 9 ) - 10z
9( 9 ) - 10( 6 )
Multiply 9 and 9
81 - 10( 6 )
Multiply 10 and 6
81 - 60
Subtract 60 from 81
21
Therefore, the numerical value of the expression is 21.
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in a class the ratio of the boy to the girls is 7:8 what part of the whole class are girls
PLEASE ANSWER ASAP ! Thanks :)
The inverse function table of the function is given by the image at the end of the answer.
How to calculate the inverse function?A function y = f(x) is composed by the following set of cartesian points:
(x,y).
In the inverse function, the input of the function represented by x and the output of the function represented by y are exchanged, meaning that the coordinate set is given by the following rule:
Thus, the points that will belong to the inverse function table are given as follows:
x = -8, f^(-1)(x) = -2, as the standard function has x = -2 and f(x) = -8.x = -4.5, f^(-1)(x) = -1, as the standard function has x = -1 and f(x) = -4.5.x = -4, f^(-1)(x) = 0, as the standard function has x = 0 and f(x) = -4.x = 0, f^(-1)(x) = 2, as the standard function has x = 2 and f(x) = 0.More can be learned about inverse functions at https://brainly.com/question/3831584
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Answer:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} \vphantom{\dfrac12} x &-8 &-4.5 & -4&0 \\\cline{1-5} \vphantom{\dfrac12} f^{-1}(x) &-2 & -1& 0&2 \\ \cline{1-5}\end{array}[/tex]
Step-by-step explanation:
The inverse of the graph of a function is its reflection in the line y = x.
Therefore, the mapping rule to find the inverse of the given ordered pairs is:
(x, y) → (y, x)Therefore:
The inverse of (-2, -8) is (-8, -2)The inverse of (-1, -4.5) is (-4.5, -1)The inverse of (0, -4) is (-4, 0)The inverse of (2, 0) is (0, 2)Completed table:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} \vphantom{\dfrac12} x &-8 &-4.5 & -4&0 \\\cline{1-5} \vphantom{\dfrac12} f^{-1}(x) &-2 & -1& 0&2 \\ \cline{1-5}\end{array}[/tex]
For each value of y, determine whether it is a solution to y÷2 = 6.
y
6
16
10
14
Is it a solution?
Answer:
None are solutions.
Step-by-step explanation:
Divide each value of y by 2 and see if it equals 6. If it does, then it is a solution. If it doesn't then it isn't a solution.
6 ÷ 2 = 6
3 ≠ 6
not a solution
16 ÷ 2 = 6
8 ≠ 6
not a solution
10 ÷ 2 = 6
5 ≠ 6
not a solution
14 ÷ 2 = 6
7 ≠ 6
not a solution
Find 2 given that =−4/5 and < < 3/2
Find 2 given that =
−4/5 and < < 3/2
we know that
sin(2x) = 2 sin(x) cos(x)
so
step 1
Find the value of cos(x)
Remember that
[tex]\sin ^2(x)+\cos ^2(x)=1^{}[/tex]we have
sin(x)=-4/5
The angle x lies on III quadrant
that means
cos(x) is negative
substitute the value of sin(x)
[tex]\begin{gathered} (-\frac{4}{5})^2+\cos ^2(x)=1^{} \\ \\ \frac{16}{25}+\cos ^2(x)=1^{} \\ \\ \cos ^2(x)=1-\frac{16}{25} \\ \cos ^2(x)=\frac{9}{25} \\ \cos (x)=-\frac{3}{5} \end{gathered}[/tex]step 2
Find the value of sin(2x)
sin(2x) = 2 sin(x) cos(x)
we have
sin(x)=-4/5
cos(x)=-3/5
substitute
sin(2x)=2(-4/5)(-3/5)
sin(2x)=24/2515. [-/1 Points]DETAILSCURRENMEDMATH11 2.9.027.Divide the fraction. Express your answer to the nearest tenth. A calculator may be used.180,000120,000eBook16. [-/1 Points]DETAILSCURRENMEDMATH11 2.3.028.Divide the fraction. Express your answer to the nearest tenth. A calculator may be used.0.110.08eBook
You have the following fraction:
180000/120000
First of all you cancel zeros:
180000/120000 = 18/12
next, you can simplify
18/12 = 9/6 = 3/2
finally 3/2 is:
3/2 = 1.5
Hence: 180000/120000 = 1.5
Furthermore, for the following fraction:
0.11/0.08
Here, you can use a calculator. The result is:
0.11/0.08 = 1.375
that is approximately
1.375 ≈ 1.4
For other fractions:
350/10,000 = 35/1,000 = 0.035
which is approximately
0.035 ≈ 0.04
6.01/7.2 = 0.834 ≈ 0.83
PLEASE HURRY ASAP
Determine which integer in the solution set will make the equation true.
4s − 14 = −6
S: {−1, 0, 1, 2}
The solution of the equation is s=2.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+1. Where:
m= the slope. It can be calculated for Δy/Δx .
b= the constant term that represents the y-intercept.
For the given example: m=7and b=1.
For solving this question you should replace x for the given values ( −1, 0, 1, 2) in the equation 4s − 14 = −6. If you obtain -6, the value of s is a solution.
For s= -1 -> 4*(-1)-14= -4 -14= -20. Therefore, s=-1 is not the solution.
For s= 0 -> 4*(0)-14= 0 -14= -14. Therefore, s=0 is not the solution.
For s= 1 -> 4*(1)-14= 4 -14= -10. Therefore, s= 1 is not the solution.
For s= 2 -> 4*(2)-14= 8 -14= -6. Therefore, s=2 is the solution.
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Use percents to find price of each set of items.(1) You purchase one pair of jeans, 2 hoodies and 3 t-shirts. what is the Total cost with no Sale? You purchase the same items but now you receive a 40% off coupon, How much is your total including the discount?
We can multiply the number of items by the price of each item to find the total cost:
[tex]\begin{gathered} C=C_{jeans}+C_{hoodies}+C_{shirts}=1\cdot25+2\cdot30+3\cdot8 \\ C=25+60+24 \\ C=109 \end{gathered}[/tex]The total cost is $109.
If we have a 40% discount, we have to substract it from the total cost.
The discount is equal to 40% of the total cost, so we can calculate the discount as:
[tex]D=\frac{40}{100}\cdot C=0.4\cdot109=43.60[/tex]Then, we will pay a total cost with discount of:
[tex]C^{\prime}=C-D=109-43.60=65.40[/tex]The total including the discount is $65.40.
NOTE: we could also have calculated it as 109*(1-0.4)=109*0.6=65.40.
5) Find the volume of the cylinder whose radius is 10in and height is 20in.V-π r 2 h
Consider the graph below.(3,1) (4,2) (6,3) (4,4) (8,5) Which correlation coefficient and interpretation best represent the given points?1.) 0.625, no correlation 2.) 0.791. no correlation 3.) 0.625, positive correlation4.) 0.791. positive correlation
Given the information on the problem,we have that the correlation coefficient of the data given is:
[tex]r=\frac{\sum^{}_{}(x-\bar{y})(y-\bar{x})}{\sqrt[]{SS_x\cdot SSy}}=\frac{10}{\sqrt[]{16\cdot10}}=0.79[/tex]therefore, the value of the correlation coeficient is 0.79, which shows a strong positive correlation
Hello, is it possible to show me the steps to simplify this problem? I don't understand the solution provided in my textbook.
Explanation
We are asked to simplify the given question
[tex](\frac{75d^{\frac{18}{5}}}{3d^{\frac{3}{5}}})^{\frac{5}{2}}[/tex]To simplify the terms, we will follow the steps below
Step 1: simplify the terms in the bracket using the exponential rule
Thus for the terms in the parentheses
[tex](\frac{75d^{\frac{18}{5}}}{3d^{\frac{3}{5}}})=\frac{75}{3}\times d^{\frac{18}{5}-\frac{3}{5}}[/tex]Hence
[tex]25\times d^{\frac{18-3}{5}}=25d^{\frac{15}{5}}=25d^3[/tex]Simplifying further
[tex]25d^3=25d^3[/tex]Step 2: substitute the value obtained above in step 1 into the parentheses, so that
[tex](\frac{75d^{18\/5}}{3d^{3\/5}})^{\frac{5}{2}}=(25d^3)^{\frac{5}{2}}[/tex]Step 3: Simplify further, we will apply the rule
so that
[tex](25d^3)^{\frac{5}{2}}=25^{\frac{5}{2}}d^{3\times\frac{5}{2}}[/tex]Simplifying further
[tex]\begin{gathered} we\text{ will have} \\ \sqrt{25^5}\times d^{\frac{15}{2}}=3125d^{\frac{15}{2}} \end{gathered}[/tex]Hence, our final answer is
[tex]3125d^{\frac{15}{2}}[/tex]The diameter of the pool is 5 feet. What is the circumference of the pool?
5. Graph the function f (x) = 3sin (2x) + 1 Be sure to identify the midline, period, and amplitude.
Given that f(x) = 3 sin (2x) + 1
Given that : a sin (bx + c ) + d
let a = amplitude,
Midline is the that runs between the maximum and minimum value
[tex]\begin{gathered} \text{ Since, amplitude = 3} \\ \text{the graph is shifted 1 unit in positive y - coordinate} \\ \text{Maximum value = 3 - 1 = 2} \\ \text{ minimum value = -3 - 1 = -4} \\ \text{Midline is the center of (2, - 4)} \\ \text{Midline = }\frac{\text{2 - 4}}{2} \\ \text{midline = -1} \end{gathered}[/tex]Period is calculated as
[tex]\begin{gathered} \text{period = }\frac{2\pi}{|b|} \\ \\ \text{b = 2} \\ \text{Period = }\frac{2\pi}{2} \\ \text{Period = }\pi\text{second} \end{gathered}[/tex]Frequency = 1 / period
[tex]\text{frequency = }\frac{1}{\pi}\text{ Hz}[/tex]Find five soloutions of the equation select integer values for X starting with -2 and ending with 2. Complete the table of value below y=6x-8
The five solutions of the equation y = 6x - 8 for x starting with -2 and ending with 2 are: (-2, -20), (-1, -14), (0, -8), (1, -2) and (2, 4)
In this question, we have been given an equation y = 6x - 8
We need to find five solutions of the equation select integer values for x starting with -2 and ending with 2.
For x = -2,
y = 6(-2) - 8
y = -20
For x = -1,
y = 6(-1) - 8
y = -14
For x = 0,
y = 6(0) - 8
y = -8
For x = 1,
y = 6(1) - 8
y = -2
For x = 2,
y = 6(2) - 8
y = 4
Therefore, five solutions of the equation y = 6x - 8 for x starting with -2 and ending with 2 are: (-2, -20), (-1, -14), (0, -8), (1, -2) and (2, 4)
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The distance d (in inches) that a ladybug travels over time t(in seconds) is given by the function d (1) = t^3 - 2t + 2. Findthe average speed of the ladybug from t1 = 1 second tot2 = 3 seconds.inches/second
The Solution:
Given that the distance is defined by the function below:
[tex]d(t)=t^3-2t+2[/tex]We are required to find the average speed of the ladybug from t=1 second to t=3 seconds in inches/second.
Step 1:
For t=1 second, the distance in inches is
[tex]d(1)=1^3-2(1)+2=1-2+2=1\text{ inch}[/tex]For t=3 seconds, the distance in inches is
[tex]d(3)=3^3-2(3)+2=27-6+2=21+2=23\text{ inches}[/tex]By formula,
[tex]\text{ Average Speed=}\frac{\text{ distance covered}}{\text{ time taken}}[/tex]In this case,
Distance covered = change in distance, which is
[tex]\text{ change in distance=d(3)-d(1)=23-1=22 inches}[/tex]Time taken = change in time, which is:
[tex]\text{ Change in time=t}_2-t_1=3-1=2\text{ seconds}[/tex]Substituting these values in the formula, we get
[tex]\text{ Average Speed=}\frac{22}{2}=11\text{ inches/second}[/tex]Therefore, the correct answer is 11 inches/second.
factoring out: 25m + 10
Answer:
5(5m + 2)
Explanation:
To factor out the expression, we first need to find the greatest common factor between 25m and 10, so the factors if these terms are:
25m: 1, 5, m, 5m, 25m
10: 1, 2, 5, 10
Then, the common factors are 1 and 5. So, the greatest common factor is 5.
Now, we need to divide each term by the greatest common factor 5 as:
25m/5 = 5m
10/5 = 2
So, the factorization of the expression is:
25m + 10 = 5(5m + 2)
The polynomial is not written in order how many terms does the polynomial have
Answer:
[tex]\text{This polynomial has 4 terms.}[/tex]Step-by-step explanation:
a TERM is a variable, number, or product of a number and one or more variables with exponents.
Then, ordering the polynomial:
[tex]\begin{gathered} x^3+2x^2+4x-2 \\ \text{This polynomial has 4 terms.} \end{gathered}[/tex]What is eight plus four minus three equal?
Answer:
9
Step-by-step explanation:
8+4-3=9
im pretty sure 8+4-3=9
Find the slope of the line passing through points -8, 8 and 7,8
We can calculate the slope of a line using the formula
[tex]m=\frac{y_b-y_a_{}}{x_b-x_a}[/tex]Let's say that
[tex]\begin{gathered} A=(-8,8) \\ B=(7,8) \end{gathered}[/tex]Therefore
[tex]\begin{gathered} x_a=-8,y_a=8 \\ x_b=7,y_b=8 \end{gathered}[/tex]Using the formula
[tex]m=\frac{y_b-y_a}{x_b-x_a}=\frac{8-8}{7-(-8)}=\frac{0}{15}=0[/tex]The slope of the line passing through points (-8, 8) and (7,8) is 0. Which means it's a constant function (horizontal line).
Kacie is constructing the inscribed circle for △MNP. She constructed the angle bisectors of angle M and angle N and labeled the intersection of the bisectors as point A.Which construction is a correct next step for Kacie?Open the compass to the width of AM¯¯¯¯¯¯ and draw a circle centered at point A.Open the compass to the width of , A M ¯ , and draw a circle centered at point , A, .Construct the perpendicular bisector of AM¯¯¯¯¯¯ .Construct the perpendicular bisector of , A M ¯ , .Open the compass to the width of AP¯¯¯¯¯ and draw a circle centered at point A.Open the compass to the width of , A P ¯ , and draw a circle centered at point , A, .Construct the line that passes through point A and is perpendicular to NP¯¯¯¯¯¯ .
From the statement, we know that:
• Kacie is constructing the inscribed circle for △MNP,
,• she constructed the angle bisectors of angle M and angle N,
• and labelled the intersection of the bisectors as point A.
(1) Now, Kacy must construct a perpendicular from the centre point to one side of the triangle.
(2) After this, she must place the compass on the centre point while adjusting its length to the point where the perpendicular crosses the triangle.
(3) Finally, she must draw the inscribed circle.
So the answer is that Kacy must construct the perpendicular bisector of AM.
AnswerConstruct the perpendicular bisector of AM
Given a Cost of $9.00 and a Percent Markup on Cost of 30% find the Selling Price.
Markup (or price spread) is the difference between the selling price of a good or service and cost. It is often expressed as a percentage over the cost.
Given:
cost = $9.00
percent markup = 30%
Let the selling price be x
The formula form percent markup is:
[tex]\text{ \% markup = }\frac{\text{ Selling price - cost}}{\cos t}\text{ }\times\text{ 100 \%}[/tex]Substituting we have;
[tex]30\text{ = }\frac{x\text{ - 9}}{9}\text{ }\times100[/tex]Solving for x:
[tex]\begin{gathered} \text{x - 9 = 2.7} \\ x\text{ = 11.7} \end{gathered}[/tex]Hence, the selling price is $11.7
Answer: $11.7
State the domain using an appropriate notation and evaluate f(2)
The domain of a function or coordinates of a function are the input values of the function "x" for which the function exists.
For instance, given the coordinates of the function {(-7, 2), (0, -2), (2, 5), (8, 1)}, the corresponding value of the x-coordinates are the domain. Therefore the domain of the given coordinate points are given as;
[tex]\text{Domain}=\mleft\lbrace-7,0,2,8\mright\rbrace[/tex]Get the value of f(2).
To get the value of f(2), we will find the y-value of the coordinate with a domain of 2. From the given coordinates, we can see that the coordinate that has a domain of 2 is (2, 5) and the corresponding y-value of the coordinate is 5. Hence f(2) = 5
Question 3 10 pts When solving an absolute value equation, such as |2x + 51 = 13, it is important to create two equations: 2x + 5= [ Select] and 2.1 + 5 = [Select ] [ Select] Resulting in z = vor [Select] Question 4 5 pts
1) Solving that absolute value equation:
|2x+5|=13 Applying the absolute value eq. property
2x +5 = 13 subtracting 5 from both sides
2x = 13-5
2x= 8 Dividing by 2
x =4
2x +5=-13 subtracting 5 from both sides
2x = -13-5
2x = -18 Dividing by 2
x= -9
Then x=4 or x =-9
2) The equations 2x +5 =13 and 2x +15= -13
Resulting in x=4 or x =-9
If f(x)3(=- Vx-3, complete the following statement:x + 2f(19) ==Answer here
This exercise is about evaluating a function at a particular argument. To do that, we replace the variable with the argument in the formula of the function, and simplify.
Let's do that:
[tex]\begin{gathered} f(19)=\frac{3}{19+2}-\sqrt[]{19-3}, \\ \\ f(19)=\frac{3}{21}-\sqrt[]{16}, \\ \\ f(19)=\frac{1}{7}-4, \\ \\ f(19)=\frac{1-28}{7}, \\ \\ f(19)=-\frac{27}{7}\text{.} \end{gathered}[/tex]Answer[tex]f(19)=-\frac{27}{7}\text{.}[/tex]The shortest side of a right triangle measures 5, and the longest side measures 13. Determine the measurement of the unknown side.
The solution that we have that would have to do with the measurement of the unknown side would be 12.
How to solve for the unknown
The Pythagoras theorem says that the length of the suym of the square of a triangle is the same as the sum of the square of the other two sides.
From the definition that we have above.
We have the shortest side as 5.
The longest side as 13
Then we would have
13² - 5² = 25 - 169
= 144
Next we would have to take the square root of 144
= √144
= 12
Hence we would say that the length of the unknown is given as 12
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Which of the following shows a matrix and its inverse?
To find the inverse matrix, augment it with the identity matrix and perform row operations trying to make the identity matrix to the left. Then to the right will be the inverse matrix.
[tex]\mleft[\begin{array}{cc|cc}-2 & 1 & 1 & 0 \\ 0 & -3 & 0 & 1\end{array}\mright][/tex][tex]\begin{gathered} R_1=\frac{R_{1}}{2}\mleft[\begin{array}{cc|cc}1 & -\frac{1}{2} & \frac{1}{2} & 0 \\ 0 & -3 & 0 & 1\end{array}\mright] \\ R_2=\frac{R_{2}}{3}\mleft[\begin{array}{cc|cc}1 & -\frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 1 & 0 & -\frac{1}{3}\end{array}\mright] \\ R_1=R_1+\frac{R_{2}}{2}\mleft[\begin{array}{cc|cc}1 & 0 & \frac{1}{2} & \frac{1}{6} \\ 0 & 1 & 0 & \frac{1}{3}\end{array}\mright] \end{gathered}[/tex]These corresponds to:
[tex]\mleft[\begin{array}{cc}2 & -1 \\ 0 & 3\end{array}\mright]\mleft[\begin{array}{cc}\frac{1}{2} & \frac{1}{6} \\ 0 & \frac{1}{3}\end{array}\mright][/tex]