. Find the slope and y-intercept of the line shown below.to10-8--10-8-6-4-2.co6-4-2---2--4--6--8--10-yX4 6 8 10
Answers
Solution:
Given the graph:
Using two points on the line to find the slope, m:
[tex]\begin{gathered} (0,-1),(5,-2) \\ \\ x_1=0,y_1=-1,x_2=5,y_2=-2 \\ \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} m=\frac{-2-(-1)}{5-0} \\ \\ m=-\frac{1}{5} \end{gathered}[/tex]Thus, the y-intercept and slope, m of the line respectively are:
[tex][/tex]
Related Questions
for each problem find the instantaneous rate of change of the function at the given value ...Thank you and God Bless
Answers
Answer:
The instantaneous rate of change of the function at the given value is -2.
[tex]f^{\prime}(0)=-2[/tex]Explanation:
The instantaneous rate of change of the function at point x=a can be written as;
[tex]f^{\prime}(a)=\frac{df(a)}{dx}[/tex]For the given function;
[tex]y=2x^2-2x+2[/tex]Then the derivative of the function is;
[tex]f^{\prime}(x)=y^{\prime}=4x-2[/tex]substituting x=0, we have;
[tex]\begin{gathered} f^{\prime}(0)=4(0)-2 \\ f^{\prime}(0)=-2 \end{gathered}[/tex]Therefore, the instantaneous rate of change of the function at the given value is -2.
[tex]f^{\prime}(0)=-2[/tex]Kelly bought a soda for three dollars and 7 candy barswent to the movies. She spent a total of $21. How much did eachcandy bar cost?Write equation and solve. Show work
Answers
She spent a total of $21 dollars.
The soda cost $3
Then, she bought 7 candy bars for x dollars
We set x because we don't know the price
3 + 7x = 21
Solve the equation for x
Subtract both sides by 3
3-3 + 7x = 21 -3
7x = 18
Divide both sides by 7
7x/7 = 18/7
x= 2.571
Each candy bar cost 2.57 aprox
Air pressure decreases exponentially with increases in elevation. The air pressure, y, (in atm units) at a given elevation, x, (in meters) can bemodeled using equation y = e where k is the decay constant.At an elevation of 5486 m where the air pressure is 0.5 atm, what is the value of k?O A k=In( 5486)0.5B. k =In(0.5)548654860.5D. k = - In ( 3956
Answers
Take natural log on both side of the equation to simplify it,
[tex]\begin{gathered} \ln y=\ln (e^{-kx}) \\ \ln y=(-kx)\ln e \\ \ln y=-kx \\ k=\frac{-\ln y}{x} \end{gathered}[/tex]S
What are two ways you can find 17-8? Explain.
Answers
The two ways to find solution of the expression (17-8) are by direct arithmetic method and indirect simplification method.
In arithmetic method, the first step is to determine whether the numbers are rational or irrational, so as to simplify the solution process. If numbers are rational, then they are checked for the sign determining their position on number line and then the calculations are performed. Here, 17 is positive rational number and -8 is negative rational number. Hence, 17-8 is equalized to 9. In indirect simplification method, the numbers to be subtracted are broken down to simpler terms which can be easily subtracted and reduced to get the answer. In the subtraction of 17-8, we break 8 in the form of (7+1). Then the expression becomes 17 - (7+1). Now, this expression can easily be solved to get the answer. Therefore, 17 - (7+1) = 10 - 1 = 9.
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Elon writes an algebraic expression to represent the product of 10 and the difference of 5y and 1. The factors of the expression are______and_____
Answers
The factors of the expression are 2.5 and 11/5.
What is an algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions. Similar to this, we are describing an algebraic expression when we explain an expression in words that has a variable (an expression with a variable). For instance, the algebraic expression for "3 more than x" can be written. x + 3.
Given Data
Elon writes an algebraic expression to represent the product of 10 and the difference of 5y and 1.
Algebraic expression:
The factors of the expression are:
10 = 5y -1
11 = 5y
y = 11/5
y = 2.5
The factors of the expression are 2.5 and 11/5.
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Simplify.3(x + 4)12 x3 x + 127x3(x+4)
Answers
We need to apply "Distributive Property" in order to get rid of the grouping symbols in the algebraic expression.
Such means to multiply 3 by each of the terms inside the parenthesis. That is:
3 times x and then 3 time 4:
3 times x remains as "3 x" since we don't know the value of "x", and 3 times 4 becomes 12:
3 (x+4) = 3 x + 12
Which seems to be the second option you listed.
A new social media site is increasing its user base by approximately 6% per month.Ir the site currently has 21,740 users, what will the approximate user base be 8 months from now?
Answers
Data
• Increase: 6% per month
,• Current users: 21,740
,• Users after 8 months: ?
Procedure
As we are increasing 6%, we have to multiply the original quantity, which represents the 100%, times 100% plus the increase (6%). However, this must be done in decimals:
[tex]\frac{100\%+6\%}{100\%}=\frac{106\%}{100\%}=1.06[/tex]Then, for the first month the user base will be:
[tex]21,740\times1.06=23,044.4[/tex]Then, for the second month the user base will be:
[tex]23,044.4\times1.06=24,427.06[/tex]The third month would be:
[tex]24,427.06\times1.06=25,892.70[/tex]We could do this for eight months or we can take a shortcut:
[tex]U=U_0\times i^n[/tex]where U represents the user, U0 is the initial users, i is the increase rate, and n is the number of months.
Replacing the data we have we get:
[tex]U=21,740\times1.06^8[/tex][tex]U=34,650.26[/tex]Answer: 34,650.26 users after 8 months with a 6% increase per month.
in the diagram the perpendicular bisectors of triangle MNP meet at point O the circumcenter find the measure of PO
Answers
The circumcenter must have equal distance between center and veriter
Data collected on types of fruit is given below.R = Red Fruit. B = Berries Given that:r1 =49r2 =10r3 =5r4 = 8A) how many types of fruit are not red?B) how many types of fruit are berries?C) how many types of fruit are red berries D) how many types of fruit are not red and not berries
Answers
You have the next diagram:
R=10+5=15
B=5+8=13
R∩B=5
U=49+5+8+10=72
A) how many types of fruit are not red?The number of fruits that are not reds is those that are outside of the set R: 57
[tex]\begin{gathered} R^{\prime}=U-R=72-15 \\ R^{\prime}=57 \end{gathered}[/tex]B) how many types of fruit are berries?The number of fruits that are berries is those that are in the set B: 13
[tex]B=13[/tex]C) how many types of fruit are red berriesThe number of fruits that are red berries is those that are in set R and in set B: 5
[tex]R\cap B=5[/tex]D) how many types of fruit are not red and not berriesThe number of fruits that are not red and not berries is those that are outside the sets R and outside the set B: 49
PLEASEE HELPP THIS IS DUE 2DAY!!!!!!
Create and solve a word problem using the equation 2x+12>2(x+6).include steps and strategies on how to solve the word problem.
Answers
A word problem of the scenario is "twelve more than twice a number is greater than double the sum of the number and six"
It has no solution
How to create a word problem?The inequality expression is given as
2x + 12 > 2(x + 6)
To create the word problem, we represent the variable with a real world concept
Take for instance, we can set the variable to "a number"
So, the representation of x is "a number"
This means that the word problem can be:
Twelve more than twice a number is greater than double the sum of the number and six
The solution of the word problemIn (a), we have
Twelve more than twice a number is greater than double the sum of the number and six
When represented as an inequality, we have
2x + 12 > 2(x + 6)
Open the bracket
2x + 12 > 2x + 12
Both sides of the inequality are the same and the inequality symbol is greater than
This means that the inequality has no solution
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We want to buy special tile for the shaded area. The tile costs $4.39 per square foot. How much does it cost to tile the shaded area?
Answers
If the area of the rectangle is 800 square feet. Then the cost to tile the shaded area will be $3,512.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The area of the rectangle is given below.
A = 20 x 40
A = 800 square ft
Then the cost to tile the shaded area will be given as,
C = 4.39 x 800
C = $3,512
If the area of the rectangle is 800 square feet. Then the cost to tile the shaded area will be $3,512.
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The missing diagram is attached below.
This composite figure is made up of three simpler shapes. What is the area of the figure? 3 cm 2 cm 8 cm 3 cm 12 cm A. 37 square cm B. 39 square cm C. 58 square cm D. 55 square cm
Answers
4/5(720-240)-180 step by step
Answers
To solve, we use the order of operations PEMDAS, where
P = Parenthesis
E = Exponets
M = Multiplication
D = Division
A = Addition
S = Subtraction
State the expression to be simplified:
Possibility 1
[tex]\frac{4}{5}(720-240)-180[/tex]Expanding the parenthesis:
[tex]\frac{4}{5}\times480-180[/tex]Multiplying then subtracting,
[tex]384-180[/tex]Therefore, the answer is 204.
Possibility 2
[tex]\frac{4}{5(720-240)}-180[/tex]Expanding parenthesis:
[tex]\frac{4}{5\times480}-180[/tex]Multiplying:
[tex]\frac{4}{2400}-180[/tex]Dividing then subtracting:
[tex]\begin{gathered} \frac{1}{600}-180 \\ =-179.998 \end{gathered}[/tex]Therefore, the answer is -179.998.
Possibility 3
[tex]\frac{4}{5(720-240)-180}[/tex]
Expanding parenthesis:
[tex]\frac{4}{5\times480-180}[/tex]Multiplying:
[tex]\frac{4}{(2400-180)}[/tex]Further expanding the parenthesis then dividing:
[tex]\begin{gathered} \frac{4}{2220} \\ =0.0018 \end{gathered}[/tex]Therefore, the answer is 0.0018.
Which is closest to X, the distance between the base of the lighthouse and the boat
Answers
we have
then, we use the trigonometric tangent identity:
[tex]\begin{gathered} \tan 25=\frac{22}{x} \\ x=\frac{22}{\tan 25} \\ x=47.2 \end{gathered}[/tex]answer: x = 47.2
The number of boots that 25 students had in their homes in Florida were recorded below:
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 9
a) What value would you predict to be an outlier?
b) How does the outlier affect the median?
c) How does the outlier affect the mean?
d) Which measure of center would best describe the data?
e) How does the outlier affect the standard deviation?
f) How does the outlier affect the interquartile range?
g) Which measure of spread would best describe the data?
PLEASE ANSWER, WILL MARK BRAINLIEST
Answers
1.The outlier affect the Min = 0 for the minimum
2. the outlier affect the median is 2
Q₁ = 0 Q₃ = 3 Maximum Max = 8
The middle value in a sorted data set is known as the median.
what is more about?
Think of your sorted data as being
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 8
1.Min = 0 for the minimum
The median
The middle value in a sorted data set is known as the median.
2.Since there are 25 items,
the 13th item is the median.
median is 2
3. The median of the data set's lower half is the first quartile, or Q1.
Between 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, the median is 0.
Q₁ = 0
Pretend that your s
4.Third quartile
The top half of the data set's median is Q3.
2, 2, 2, 2, 2, 3, 3, 3, 4, 5, and 8 have a median value of 3 each.
Q₃ = 3
5. Maximum Max = 8
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What can you observe about the
segments that connect
corresponding
vertices?
Answers
It is observed about the segments that the two triangles are congruent, the corresponding angle pair is congruent. also the two corresponding side pairs are also congruent.
What is segment?
In mathematics, the line segment is one of the part of the straight line. It has two endpoints which can be used to calculate the length of the respective segment. It is measured in different units called as meter, centimeter, etc.
According to the question, the given data for the line segment is as follows:
DD' = 58.4 cm; EE' = 58.4 cm; FF' = 58.4 cm
All three segments are equal in length.
In this, the ΔDEF and ΔD'E'F' are equal from angle as well as length sides. And the relationship between two triangles and their vertex state that they are forming two congruent Polygon shapes as well as generating a segment between them. Thus, if there is congruence among the pentagons, it will exist between the formed triangles.
Therefore, it is observed about the segments that connect corresponding vertices that the two triangles are congruent and its corresponding angle pair is congruent. also the two corresponding side pairs are also congruent.
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Consider the figure. If <7 and <11 are supplementary then lines
Answers
Solution
- The two angles, <7 and <11 are supplementary. This implies that the line q is a transversal line upon which angles <7 and <11 are drawn.
- In order for line q to be the transversal and <7 and <7 to be supplementary, it implies that the lines r and s are parallel.
Final Answer
The answer is "r and s"
Sum of two rational numbers are 2/15 , if one rational number is 2/3 . Find the other rational number
Answers
Step-by-step explanation:
the answers is attached
hope it helps
Which sequences are geometric? Select three options.
–2.7, –9, –30, –100, ...
–1, 2.5, –6.25, 15.625, ...
9.1, 9.2, 9.3, 9.4, ...
8, 0.8, 0.08, 0.008, ...
4, –4, –12, –20, ..
Answers
(i) –2.7, –9, –30, –100, ... case of a geometric sequence
(ii) –1, 2.5, –6.25, 15.625, ... case of a geometric sequence
(iii) 9.1, 9.2, 9.3, 9.4, ... not a case of a geometric sequence
(iv) 8, 0.8, 0.08, 0.008, ... case of a geometric sequence
(v) 4, –4, –12, –20, .. not a case of a geometric sequence
What is a geometric sequence?
A geometric sequence is one in which the ratio of two succeeding terms is fixed. The common ratio is what's known as this ratio.
Checking each sequence one by one right now.
(i) –2.7, –9, –30, –100, ...
r=(-9/2.7)=3.33
=(-30/9)=3.33
=(-100/9)=3.33
⇒This is a case of a geometric sequence
(ii) –1, 2.5, –6.25, 15.625, ...
r=(2.5/-1)=2.5
=(-6.25/2.5)=2.5
=(15.625/-6.25)= 2.5
⇒This is a case of a geometric sequence
(iii) 9.1, 9.2, 9.3, 9.4, ...
since the ratio between terms is not the same.
⇒This is not a case of a geometric sequence
(iv) 8, 0.8, 0.08, 0.008, ...
since the ratio between terms is the same.
⇒This is a case of a geometric sequence
(v) 4, –4, –12, –20, ..
since the ratio between terms is not the same.
⇒This is not a case of a geometric sequence
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Answer:
option 1,2,4,5 are correct answers
Step-by-step explanation:
helpppp me out please will give brainiest to first right answer
Answers
Answer:
-490
Step-by-step explanation:
:]
Solve the equation algebraically
-3(h+6)-7=5
Write your answer as an internet or reduced fraction.
H=
Answers
Answer:
h = -10
Step-by-step explanation:
-3(h+6) - 7 = 5
-3h - 18 - 7 = 5
-3h - 25 = 5
+25 +25
-----------------------
-3h = 30
÷-3 ÷-3
-----------------------
h = -10
I hope this helps!
The teacher is handing out note cards to her students. She gave 84 note cards to the first
student, 76 note cards to the second student, 68 note cards to the third student, and 60 note
cards to the fourth student. What kind of sequence is this?
arithmetic
geometric
both
neither
Answers
Answer: Arithmetic
Step-by-step explanation: Because its decreasing at a constant rate of the same number 8
Solve for X.
X =?]
5X - 16 x + 10
Answers
5x-16x+10
calculate the difference
= -11x+10
-11x + 10
Help 40 points
Two questions!
Answers
The resultant of the product of 7 and 6 added to the quotient of 121 and 11 is 53.
The point (3,9) satisfies the equation y = 8x - 15 thus it will be the solution of the equation.
What is a number system?Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
01)
The quotient of 121 and 11 is 11.
As per the given,
Product of 7 and 6 ⇒
7 × 6 + 11 = 53
Hence "The resultant of the product of 7 and 6 added to the quotient of 121 and 11 is 53".
02)
As per the given equation,
y = 8x - 15
Substitute,(3,9)
9 = 8(3) - 15
9 = 9
Since it is satisfying thus it will be the solution.
Hence "The point (3,9) satisfies the equation y = 8x - 15 thus it will be the solution of the equation".
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10. The value of the 8th term is 78.The sequence is increasing by 10 at each step.Explicit equation: y = 10x - 2Recursive: now = previous term + 10Find the 9th term.Explanation:
Answers
We have the explicit equatiion:
[tex]\text{ y = 10x - 2}[/tex]The 8th term is 78
y = 10 * 8 - 2
y = 80 - 2
We replaced x by 8
Therefore, for finding the 9th term, we calculate the value this way:
y = 10 * 9 - 2
y = 90 - 2
y = 88
The 9th term of the series is 88
The question: Rounded to the nearest integer, what is the approximate surface area of this right triangular prism with an equilateral triangle for a base? I just need help solve it because I’m confused
Answers
Okay, here we have this:
Considering the provided figure, we are going to calculate the requested surface area, so we obtain the following:
Then we will substitute in the following formula:
Surface Area of Triangular Prism=(√3a^2)/2+3(a+h)
Replacing:
Surface Area of Triangular Prism=(√3*8^2)/2+3(8+6)
Surface Area of Triangular Prism=(√3*64)/2+3(14)
Surface Area of Triangular Prism=(√3*64)/2+42
Surface Area of Triangular Prism=(√3*32)+42
Surface Area of Triangular Prism=32√3+42
Surface Area of Triangular Prism=97 ft^2
Finally we obtain that the aproximately surface area is 97 ft^2.
Answer:
199FT
Step-by-step explanation:
I took the quiz
Which is bigger 978cm or 12m?
Answers
It is given that there are two quantities 978cm and 12 m.
The units are different so convert in same units.
It is known that 1m=100cm
So 12m=1200cm.
Since 1200>978 so it follows
1200cm>978cm.
so 12m>978cm.
Hence 12 meters is greater than 978cm.
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. cos 75° = ___
Answers
Answer:
0.26
Explanation
Given the expression
Cos 75°
According to the calculator
Cos 75° = 0.2588
Converting to the nearest hundredth
Cos 75 = 0.26
Hence the required answer is 0.26
Angles A and B are supplementary angles. If m
Answers
Answer:
138 degrees
Explanation:
Two angles are said to be Supplementary if they add up to 180 degrees.
Given that Angles A and B are supplementary and:
[tex]\begin{gathered} m\angle A=(2x-24)^0 \\ m\angle B=(5x-27)^0 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} m\angle A+m\angle B=180^0 \\ 2x-24+5x-27=180 \\ 7x=180+27+24 \\ 7x=231 \\ x=\frac{231}{7} \\ x=33^0 \end{gathered}[/tex]Therefore, the measure of angle B will be:
[tex]\begin{gathered} m\angle B=(5x-27)^0 \\ =5(33)-27 \\ =165^0-27^0 \\ =138^0 \end{gathered}[/tex]The measure of angle B is 138 degrees.
Simplify 7-0.65r+3 to the lowest