Answer:
Find the Slope from a Graph
Identify rise and run from a graph
Distinguish between graphs of lines with negative and positive slopes
Find the Slope from Two Points
Use the formula for slope to define the slope of a line through two points
Find the Slope of Horizontal and Vertical Lines
Find the slope of the lines
x
=
a
and
y
=
b
Recognize that horizontal lines have slope = 0
Recognize that vertical lines have slopes that are undefined
Identify slopes of parallel and perpendicular lines
Given a line, identify the slope of another line that is parallel to it
Given a line, identify the slope of another line that is perpendicular to it
Interpret slope in equations and graphs
Verify the slope of a linear equation given a dataset
Interpret the slope of a linear equation as it applies to a real situation
Identify slope from a graph
The mathematical definition of slope is very similar to our everyday one. In math, slope is used to describe the steepness and direction of lines. By just looking at the graph of a line, you can learn some things about its slope, especially relative to other lines graphed on the same coordinate plane. Consider the graphs of the three lines shown below:
You can determine the slope of a line from its graph by looking at the rise and run. One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope. Let’s look at an example.
EXAMPLE
Use the graph to find the slope of the line.
A line that crosses the points (2,1) and (6,3). A blue line labeled Rise goes up two units from the point (2,1). A red line labeled Run goes left from the point (6,3) so that it forms a triangle with the main line and the Rise line. A formula says slope equals rise over run.
Show Solution
This line will have a slope of
1
2
no matter which two points you pick on the line. Try measuring the slope from the origin,
(
0
,
0
)
, to the point
(
6
,
3
)
. You will find that the
rise
=
3
and the
run
=
6
. The slope is
rise
run
=
3
6
=
1
2
. It is the same!
Let’s look at another example.
EXAMPLE
Use the graph to find the slope of the two lines.
A graph showing two lines with their rise and run. The first line is drawn through the points (-2,1) and (-1,5). The rise goes up from the point (-2,1) to join with the run line that goes right to the point (-1,5). The second line is drawn through the points (-1,-2) and (3,-1). The rise goes up from the point (-1,-2) to join with the run to go right to the point (3,-1).
Show Solution
When you look at the two lines, you can see that the blue line is steeper than the red line. It makes sense the value of the slope of the blue line, 4, is greater than the value of the slope of the red line,
1
4
. The greater the slope, the steeper the li
Step-by-step explanation:
an electrical appliance will not work unless component qk does. component qk's reliability is 0.95. every other part of the appliance is 100% reliable. assume that we add a second back up for qk with reliability of 0.80 (this back up is the same as component qk but purchased from another manufacturer, so the reliability is different but it is also cheaper). what is the probability that the appliance does not work? (in this case, you have qk with reliability 0.95, qk first back up with reliability 0.95 and a second backup with reliability 0.80)
Answer:
0.99 or 99%
Step-by-step explanation:
This is actually much more simple than it sounds
Take 95% and add 80% of 5 because 5% of the time the QK piece will not work. 80% of 5 is 4. 95+4=99
I'm thinking of a number and if I subtract 8 and
multiply by -3, I get 21, what is my number?
Answer:
15
Step-by-step explanation:
Answer:
The number is 1
Step-by-step explanation:
Let the number be x
Subtract 8 from x ==> x - 8
Multiply by -3 ==> -3(x - 8) = -3(x) -3(-8) = -3x - 24
This equals 21
So
-3x + 24 = 21
Subtract 24 from both sides:
-3x + 24 - 24 = 21 - 24
==> -3x + 0 = - 3
-3x = -3
Divide by -3
==> -3x/-3 = -3/-3
x = 1
Check
1 - 8 = -7
-3(1-8) = -3 x -7 = 21
What can be concluded from the graph shown here?
Correct answer is D. Nothing can be determined from the given graph.
What may a graph be used to analyze?A graph is a type of graphic used to display data and show relationships. Graph analysis is helpful for identifying the overall trend, connecting experiment findings to the hypothesis, and creating hypotheses for next studies.
You may compare various figures, comprehend how various components affect the overall, or examine patterns using a chart or graph. Charts and graphs can also be helpful for seeing data that deviates from what you're used to or for assisting in the understanding of group relationships.
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|5x|=3
this is absolute value of five x equals three
The value of the modulus function |5x| = 3 is x = 3/5 or x = -3/5.
What is a modulus function ?In mathematics modulus function is the absolute or numerical value of the function irrespective of the sign.It represents magnitude.We modulus functions when we want length, mass and for other variables when we want to represent their weight.
According to the given question |5x| = 3.
We know |x| = a implies x = a or x = -a.
∴ |5x| = 3 is
5x = 3
x = 3/5
Or
5x = -3.
x = -3/5.
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For two events X and Y, P(X) = , P(Y) = , and P(X|Y) = . Find the probabilities. 1. P(Y · X) = 2. P(Y/X) =
1. The probability given as P(Y∩X) is; 2/25
2. The probability given as P(Y) * P(X) is; 4/15
What is the probability?
We are given the following probabilities;
P(X) = 2/3 , P(Y) = 2/5 , and P(X|Y) = 1/5
1. We want to find P(Y ∩ X).
This means probability of the set intersection of Y and X
Since P(X) = 2/3 , P(Y) =2/5 , and P(X|Y) =1/5, it means that we have a conditional probability.
Thus; P(Y∩X) = P(Y) * P(X|Y)
P(Y∩X) = 2/5 × 1/5
P(Y∩X) = 2/25
2. We want to find P(Y) * P(X)
Plugging in the relevant values gives;
P(Y) * P(X) = 2/3 × 2/5
P(Y) * P(X) = 4/15
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Complete question is;
For two events X and Y, P(X) =2/3 , P(Y) =2/5 , and P(X|Y) =1/5 . Find the probabilities.
1. P(Y∩X) = ____
2. P(Y)· P(X) =____
Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total $1215 x $445
was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor was needed to complete the job?
Joy was charged the labor of 11 hours .
Joy was charged a total of $1215 from the landscaper for listed parts and labor.
He was charged $445 for listed parts
He was charged the rest for labor
The hourly rate for labor is $ 70
Let the number of hours worked by labor be x
so, we can form a linear equation here as 445 + 70x = 1215
Now we have to solve this linear equation
445 + 70x = 1215
70x= 1215 - 445
70x = 770
x = 770/ 70
x = 11
Therefore, 11 hours of labor were needed to complete the job.
The correct question is Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total $1215. $445 was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor were needed to complete the job?
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5+5/3-3/2 giải hộ mình với cảm ơn bạn nhiều
Answer:
5.16666666,...
Step-by-step explanation:
5 + (5/3) - (3/2)
5 + 1.66666666667 - 1.5
5 + 0.16666666666
5.16666666666,...
Nhân chia trc cộng trừ sau
Answer:
31/6 ( or 5 1/6)
Step-by-step explanation:
5 + 5/3 - 3/2 =
5 + 1/6 =
31/6
Amy bought 8 packs of cherry fruilt snacks. Each pack has 7 fruilt snacks Mary bought tropical fruit snacks. Each tropical fruit snack packs has 9 trult
snacks
Amy bought 11 more fruit snacks than Mary. How many packs of tropical fruit snacks pid Mary buy?
A 12
B 5
C 8
D 10
Answer:
B - 5
Step-by-step explanation:
Amy = 8 packs × 7 snacks
Amy = 56 snacks altogether
Mary = Amy - 11
Mary = 56 - 11
Mary = 45 snacks altogether
Mary = 45 snacks / 9 tropical fruit snacks
Mary = 5 packs of tropical fruit snacks
Hope this Helps! :)
- Riona
Look at this graph.
y
x
-100
-80
-60
-40
-20
20
40
60
80
100
-100
-80
-60
-40
-20
20
40
60
80
100
0
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
The equation of the line in the graph in slope-intercept form is: y = -5x - 30.
How to Write an Equation of a Line in Slope-intercept Form?To be able to write the equation of a line in slope-intercept form, y = mx + b, find the value of the slope (m) = rise/run, and the value of the y-intercept (b), which is the value of y where the line intercepts the y-axis.
From the given graph, we have:
Slope (m) = rise/run = -50/10
Slope (m) = rise/run = -5
The y-intercept (b) = -30
Substitute m = -5 and b = -30 into y = mx + b:
y = -5x + (-30)
y = -5x - 30
Thus, the equation of the line in the graph in slope-intercept form is: y = -5x - 30.
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Multiply and simplify. 3∛2x² . 7 ∛32x⁴
On multiplying and then simplifying 3∛2x² . 7 ∛32x⁴, we get, 84x⁶
How can square roots be multiplied?1. Split the radicands in half. A number known as a radicand appears underneath the radical symbol.
2. To multiple radicands, multiply the integers as if they were whole numbers. Always keep the item beneath a single radical sign.
3. Use factoring to exclude any perfect squares from the radicand. To achieve this, check whether any perfect squares have the radicand as a factor.
4. Position the square root of the ideal square before the radical sign. Don't change the second component of the radical symbol.
5. Square the square's root. Sometimes it is necessary to multiply a square root by itself.
Given,
3∛2x² . 7 ∛32x⁴
⇒ [tex]21 (2^{1/3} ) x^{2+4} . 32^{1/3}[/tex]
⇒ [tex]21 (2^{1/3} ) x^{6} . 2^{5/3}[/tex]
⇒ [tex]21 (2^{1/3 + 5/3} ) x^{6}[/tex]
⇒ [tex]21 (2^{2} ) x^{6}\\84x^{6}[/tex]
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11. Reflected over the x-axis, 2 units left and down 5 units. what is the equation?
Answer: its (2,5) or (2,-5)
Step-by-step explanation:
basically it depends on the location like for example: if a dot is in the Q4 area which is (-x,-y) or Q3 is (-x,y) and Q2 is (x,-y) and Q1 is (x,y) so yeah hope it helps
The function
models the height of a gymnast on a trampoline over time, where
is feet above the ground level and is the number of seconds since the start of their jump.
Using the function, approximately how high is the gymnast above the ground level after 1.2 seconds?
The approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to approximate the height of the gymnast above the ground level after 1.2 seconds?The complete question is added at the end of the solution
The equation of the height function is given as
h(t) = -5t² + 10t+4
After 1,2 seconds, we have:
t = 1.2
Substitute t = 1.2 in the equation h(t) = -5t² + 10t+4
So, we have
h(t) = -5 x 1.2² + 10 x 1.2 + 4
Evaluate the exponent
So, we have
h(t) = -5 x 1.44 + 10 x 1.2 + 4
Evaluate the products
So, we have
h(t) = -7.2 + 12 + 4
Evaluate the sum
So, we have
h(t) = -7.2 + 16
Evaluate the difference
So, we have
h(t) = 8.2
Hence, the approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet
This means that the required approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet
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Complete question
The function h(t) = -5t² + 10t+4 models the height of a gymnast on a trampoline over time, where is feet above the ground level and is the number of seconds since the start of their jump.
Using the function, approximately how high is the gymnast above the ground level after 1.2 seconds?
Find the acceleration of a car that takes 4 seconds to stop at a red light from a velocity of 80 km/h
Given the initial speed and time elapsed by the car, the negative acceleration that brings the car to a stop at the red light is -5.56m/s².
What is the acceleration of the car?
Newton's first equation of motions states that;
v = u + at
Where v is final velocity, u is initial velocity, a is acceleration and t is time.
Given the data in the question;
Since the car is stopping, final velocity v = 0Initial velocity u = 80 km/hTime elapsed t = 4sAcceleration = ?First, convert the unit of the initial velocity from kilometer per hour to meter per seconds
Initial velocity = 80 km/h = ( 80 × 5/18 )m/s = 2.2222 m/s
Now, plug these values into the equation above and solve for a.
v = u + at
0 = 22.2222m/s + ( a × 4s )
a × 4s = -22.2222m/s
a = 22.2222m/s ÷ 4
a = -5.56m/s²
Negative sign shows that the car is slowing down.
Given the initial speed and time elapsed by the car, the negative acceleration that brings the car to a stop at the red light is -5.56m/s².
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Please help me with this.
Consider the function f(x)= -3x^3-4x^2+x+2
A partial graph is shown below, find all the zeros of the function using division and factoring. Please show all work.
Using division and the graph, the zeroes of the function are given as follows:
x = -1 with multiplicity 2.x = 2/3 with multiplicity 1.How do we find all the zeros of the function?The function in this problem is defined as follows:
f(x) = -3x³ -4x² + x + 2.
From the graph, we have that x = -1 is a zero of the function, meaning that it can be written as follows:
-3x³ -4x² + x + 2 = (x + 1)(ax² + bx + c).
The other zeros will be the zeros of ax² + bx + c. To find the coefficients, we use a system of equations, hence:
(x + 1)(ax² + bx + c) = -3x³ -4x² + x + 2
ax³ + (a + b)x² + (c + b)x + c = 2.
Hence the coefficients are given by:
a = -3.c = 2.a + b = -4 -> b = -1.Thus the quadratic equation that we have to solve is:
-3x² - x + 2 = 0
3x² + x - 2 = 0.
Hence:
[tex]\Delta = 1^2-4(3)(-2) = 25[/tex][tex]x_1 = \frac{-1 + \sqrt{25}}{6} = \frac{2}{3}[/tex][tex]x_2 = \frac{-1 - \sqrt{25}}{6} = -1[/tex]The zeroes of the function are given as follows:
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What is the logarithmic form of each equation?
b. 8/27 = (2/3)³
The expression becomes 3log₁₀2-3log₁₀3
Logarithm is a mathematical tool used to make high value calculations simple.
It is the exponent to the power of which a number must be raised to give a certain result.
Some of the important formulas in logarithm are:
logₐb where a is considered as base of the logarithm and b is the argument
is given as nlogab
when base and the argument is same , log is given as 1
logₐbc where a is the base is given as logₐb + logₐc
logₐbc where a is the base is given as logₐb-logₐc
Now it is given to us to find the logarithmic form of 8/27=(2/3)^3
Let us consider the base of the logarithm to be 10
thus log₁₀8/27=log₁₀(2/3)^3
log₁₀8/27=log₁₀(2/3)^3
We know that logₐb can be written as log₂b/log₂a
Hence
log₁₀8/27= 3(log2/3)
log₁₀8/27=3(log2-log3)
log₁₀8/27= 3log2-3log3
Hence the expression becomes 3log2-3log3
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B is between A and C, AB=13.7 and BC=8.3. Find AC.
AC = 20
AC = 22
AC = 17
AC = 19
Answer:
22
Step-by-step explanation:
add ab and bc to get ac
The measure of ∠BQS is 78°. What is m∠NQS? *picture of the question is at the bottom*
Step-by-step explanation:
BQS=78
BQN=48
BQS+BQN=78+48=126
180-126=54°
NQS=54°
comfirm=BQN+BQS+NQS=180
48+78+54=180
Answer:
30°
Step-by-step explanation:
∠NQS + ∠BQN = ∠BQS
Knowing this information, we use the known measures to find ∠NQS
∠NQS + 48° = 78°
∠NQS = 78° - 48°
∠NQS = 30°
Thus, angle NQS is 30 degrees.
Hope this helps!
the y-intercept is (0,12)
the axis of summer is x=4
the vertex is ( , )
f(x)=x^2-8x+12
Answer:
The vertex is (4,-4)
Step-by-step explanation:
Plug in x=4 in the equation
What is this " the temperature is 1f at dusk. it is 8 degrees colder at dawn what is the temperature at dawn?'
The temperature at dawn is -7 F.
What is the temperature at dawn?If it is 8 degrees colder at dawn than it is at dawn, it means that the temperature is lower in the dawn than it is in the dusk. Thus, to determine the temperature at dawn, subtract 8 from the temperature at dusk.
Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign used to represent subtraction is -.
Temperature at dawn = termpature at dusk - difference in termpature
1 - 8 = -7
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12z=108 what’s the value of z
Answer:
z = 9Step-by-step explanation:
12z=108 what’s the value of z
12z = 108
z = 108 : 12
z = 9
check
12 * 9 = 108
108 = 108
the answer is good
Last year at a certain high school, there were 150 boys on the honor roll and 84 girls
on the honor roll. This year, the number of boys on the honor roll decreased by 12%
and the number of girls on the honor roll decreased by 25%. By what percentage did
the total number of students on the honor roll decrease? Round your answer to the
nearest tenth (if necessary).
The total percentage decrease in the number of students on the honor roll is 16.67%.
What is the percentage decrease?
Percentage is a measure of frequency that is used to express a number as a fraction of an amount out of 100. The sign used to denote percentage is %. In order to convert a number to percentage, multiply the number by 100.
The first step is to determine the number of boys on the honor roll this year.
Number of boys on the honor roll this year : (1 - percentage decrease) x number of boys last year
(1 - 0.12) x 150
0.88 x 150 = 132
The second step is to determine the number of girls on the honor roll this year.
Number of girls on the honor roll this year : (1 - percentage decrease) x number of girls last year
(1 -0.25) x 84
0.75 x 84 = 63
Total number of students on the honor roll last year = 150 + 84 = 234
Total number of students on the honor roll this year = 63 + 132 = 195
Percentage decrease :[ (195 /234) - 1] x 100 = 16.67%
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How to solve system of equations?
8q-15r=-40
4q+2r=56
Answer:
q=10, r=8
Step-by-step explanation:
You have to first cancel one of the variables.
8q-15r=-40
4q+2r=56
To do this, multiply the second equation by -2.
8q-15r=-40
-2(4q+2r)=(56)(-2)
Multiply it out.
8q-15r=-40
-8q-4r=-112
Combine like terms.
-19r = -152
Divide by -19 to get the value of r.
r=8
Substitute r back into one of the equations, it does not matter which one. I'll do both.
8q-15(8)=-40
8q-120=-40
8q=80
q=10
4q+2(8)=56
4q+16=56
4q=40
q=10
You should get the same value for q for both.
In the instance where the variables are x and y, which they usually are, you would write your answer as an ordered pair, (x, y).
(10, 8)
Answer:
q=10 and r=8
Step-by-step explanation:
8q-15r=-40 ...........equation(i)
4q+2r=56................eqn(ii)
Now,
Multiplying eqn (ii) by 2 then we get,
8q+4r=112..........eqn(iii)
Here, Subtracting eqn (i) and (iii)
8q-15r=-40
8q+4r=112
(-) (-) (-)
---------------------
-19r=-152
r= -152/-19
r= 8
Again, Putting the value of r in eqn (ii)
4q+2r=56
4q+2×8=56
4q=56-16
q=40/4
q=10
I need help please……
Answer:
Its 3D 6U
or -2/-2
Step-by-step explanation:
What is the value of the expression below when y=5?
3y^2 +7y+2
Answer:
112
Step-by-step explanation:
3y^2 + 7y + 2
if y = 5, then 3(5^2) + 7(5) + 2
= 3(25) + 35 + 2
= 75 + 37
= 112
-3xy = ? when x = 8 and y = -9
Answer:
[tex] {6}^{12} \times 36 =[/tex]
Answer:
216
Step-by-step explanation:
If x = 8 & y = -9
Put in place -3 (8)(-9)
-24 * -9 = 216
Given f(x) = x² + 5x +6 and g(x) = x +2, find (g ◦ f)(x)
Answer:
x² + 5x + 8
Step-by-step explanation:
This issue is about "function composition",
(g ° f) means
g(f(x)) = g(x² + 5x +6)
= x² + 5x +6 + 2
= x² + 5x +8
Someone please help me! Ik its Sunday but i got sick so i couldnt do it over the weekend
Step-by-step explanation:
6 = 5/2x + k
6 = ( 5/2 . 2/1) + k
6 = 10/2 +k
6-5 = k
k = 1
Solve each equation.
log x-log 2=3
value of x in given logarithmic equation is = 2000
What is logarithmic function ?In, mathematics a logarithmic function is inverse of exponential function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .
where, a is the base of function
x is the expression
Mathematically, if [tex]a^x = N[/tex] is and exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex].
Some important formulas of logarithms :
[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]According to given statement,
log x - log 2 =3
using formula, log a - log b = log a/b
=> log x/2 = 3
=> x / 2 = 10³
=> x = 2 . 10³ = 2000
Thus solution for this equation is x =2000.
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26.
A gallon of milk costs $2.30 per gallon.
What is the cost per cup of milk?
What is the cost per fluid ounce of milk?
What is the cost per quart of milk?
The cost per cup of milk as required in the task content is; $0.14375.
The cost per fluid ounce of milk as required in the task content is; $0.018.
The cost per quart of milk as required in the task content is; $0.575.
What is the cost per unit measure of milk as given in each case scenario in the task content?It follows from the task content that the cost of each unit measure of milk is to be determined. Therefore, since the cost per gallon of milk is; $2.30.
1). Since there are 16 cups of milk per gallon, it follows that the cost per cup of milk is; 2.30/16 = $0.14375
2). Also, Since there are 128 fluid ounces of milk per gallon, it follows that the cost per fluid ounce of milk is; 2.30/128 = $0.018
3). Also, Since there are 4 quarts of milk per gallon, it follows that the cost per quart of milk is; 2.30/4 = $0.575
Ultimately, the cost per unit measure of milk in each case scenario has been determined and is as represented above.
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Life expectancy for all the different countries in the world ranges from a low of only 52.2 years (in sierra leone) to a high of 84.7 years (in hong kong). life expectancies are clustered at the high end, with about half of all the countries having a life expectancy between about 74 and the maximum of 84.7. a few countries, such as sierra leone, have a very low life expectancy.
a. what is the shape of the distribution of life expectancies for all countries?
a) symmetric.b) skewed to the right.c) skewed to the left.d) none of these.b. from the information given, estimate the median of the life expectancies.c. will the mean be larger or smaller than the median?
From the given distribution, we have that:
a) The distribution is skewed to the left.
b) The median is of 74.
c) The mean will be smaller than the median.
Figuring the skewness with the mean and the median:Mean greater than median: Positively(right) skewedMean less than the median: Negatively(left) skewedSince life expectancies are clustered at the high end, the outliers are small life expectancies, meaning that the mean will be smaller than the median and the distribution is skewed to the left.
The median of a data-set is the 50th percentile, the value that separates the bottom 50% of the data-set from the upper 50%.
In this problem, we have that about half of all the countries having a life expectancy between about 74 and the maximum of 84.7, meaning that 74 is the median.
More can be learned about the skewness of a distribution at https://brainly.com/question/28315480
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