The x and y coordinates of the line are utilized to compute the steepness of the line using the slope formula.We are aware that one of a line's most crucial qualities is its slope because it aids in determining the pace of change.
What is the point-slope form of the equation of the line?
A line's steepness can be determined by looking at its slope.Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Using the formula
m=y2y1/2x1,
which is the change of y over the change of x, determine the slope of the line between (3,5) and (9,1).
Slope is equal to the change in y over the change in x
, or rise over run.
m=change in y /change in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y
is equal to the difference in y-coordinates (also called rise).
m=y2−y1/x2−x1
To determine the slope, enter the values of x and y into the equation.
m=1−(5)/9−(−3)
m=-4/12
m=12/4
m=3
To replace x1 and y1 in the point-slope form yy1=m(xx1), which is derived from the slope equation
m=y2y1/x2x1,
use the slope 3 and the specified point (3,5).
y−(5)=3(x+3)
Keep the equation in point-slope form and make it simpler.
y−5=3(x+3)
Do the y math.
To continue, tap...
y=x+8
List the equation in all its variations.
Form of a slope-intercept:
y=x+8
Forming a point-slope: y=5=1(x+3)
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There are 32 students in math class. The past fail ratio of the students in class is 7:1. how many students have failing grades
Answer:
Four Students have failing grades, with a remainder of 4.
28:4 R:4
Step-by-step explanation:
With 32 students in the class. A 7:1 ratio doesn't work perfectly. 7*4=28. 28:4.
32 students - 28 possible students to fail = 4 Remainder since 7:1 ratio doesn't fulfill 32 students.
Which is the equation of the line parallel to the line y=-x + 2 through the point (3,5)?
Answer:
C. y = −x + 8
Step-by-step explanation:
Use point-slope form: y − b = m(x − a) where (a,b) is a point on the line
To do this, first identify the slope of the line from the given equation because having the same slope as the given equation is what makes the constructed line parallel to it.
m = −1
Then use the point (3,5) to construct an equation using point-slope form.
y − 5 = −1(x − 3)
Distribute:
y − 5 = −x + 3
and isolate y.
y = −x + 8
So the answer is C, y = −x + 8.
My new music player has a capacity of 360 gigabytes.
Rewrite the following statement using a number in scientific notation.
Answer: My new music player has a capacity of 3.6*10^11 bytes.
Step-by-step explanation: Scientific notation of a number is going to be in the form of a*10^b where a is a number greater than 1 but less than 10 which is then multiplied by the appropriate power of 10 so that the numbers are equal. This allows us to see numbers concisely without getting distracted by the sheer number of zeroes in some numbers. For 360, since 3.6 is between 1 and 10, we use that for a. To get 3.6 to equal 360 you have to move the decimal two places to the right, or multiply by 10^2, so b=2. Since this is in gigabytes, and giga=10^9, to express the answer in bytes we just multiply 10^2 to 10^9=10^11
Hope this helps
solution a is 2% alcohol and solution b is 5% alcohol. she uses 800 milliliters of solution A how many milliliters of solution b does she use if the resulting mixture is a 3% alcohol situation
She uses 800 mL of solution A; that is, 2% of those 800 mL is alcohol
Alcohol on a:
2% of 800 = 2*800/100 = 16mL
If we use x mL of b, the amount of alcohol is:
5% of x = 5*x/100 = x / 20
Total amount of alcohol: 16 + x/20
Total amount of solution mixture: 800 + x
The ratio:
(16 + x/20) / (800 + x) = 3%
(16 + x/20) / (800 + x) = 3/100
1600 + 5x = 2400 + 3x
Solving for x:
5x - 3x = 2400 - 1600
2x = 800
x = 400 mL
She used 400 mL of solution b
Help me solve F,G,H please
(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.
(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.
(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.
Anyone know how to find the frequency for this?
The frequency of specific five classes (67, 68, 69, 70, and 71) will occur a total of 19 times.
What do we mean by frequency?The frequency of a given data value is the number of times it occurs.The frequency of a data value is represented by f.For instance, if five students received As in science, the frequency of grade A is said to be five.So, the frequency for the particular 5 classes is as follows:
4 times in 67.6 times in 68.4 times in 69.4 times in 70. 1 time in 71.The following five classes will appear most frequently overall:
4 + 6 + 4 + 4 + 1 = 19Therefore, the frequency of specific five classes (67, 68, 69, 70, and 71) will occur a total of 19 times.
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Sandra Had 1/4 of a roll of ribbon if she makes 3 bows how much ribbon did she use on each roll
Let's begin by listing out the information given to us:
Sandra has 1/4 of a roll of ribbon
To make 3 bows, she will use the amount of ribbon shown below:
[tex]n=\frac{1}{4}\cdot3=\frac{3}{4}RibbonRoll[/tex]Suppose you're conducting a hypothesis test for one mean, the significance level is , and the P-value is 0.30. Should you reject or fail to reject , and why?
The significance level is less than p-value, so we will fail to reject the hypothesis test.
Given,
Conducting a hypothesis test for one mean
The significance level, α = 0.05
The p-value = 0.30
We have to find the test is reject or fail to reject.
If the significance level is greater than p-value, we will reject the hypothesis test.
If the significance level is less than p-value, we will fail to reject the hypothesis test.
Here,
The significance level, α is 0.05 and the p-value is 0.30
Lets see,
The significance level is less than the p-value.
That is,
0.05 < 0.30
So, we will fail to reject the hypothesis test
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Need help with number three
Step 1
Given;
[tex]n^2+16n+82=10[/tex]Required to solve the problem using completing the square method
Step 2
Move 10 to the left.
[tex]n^2+16n+82-10=0[/tex]Simplify
[tex]n^2+16n+72=0[/tex]Step 3
Add 64 and subtract 64
[tex]n^2+16n+72=n^2+16n+72+64-64[/tex]Step 4
Complete the square
[tex]8+(n^2+16n+64)=\text{ }8+(n+8)^2[/tex]Step 5
Find the value of n
[tex]\begin{gathered} 8+(n+8)^2=0 \\ (n+8)^2=-8 \\ n+8=\pm\sqrt[]{-8} \\ \end{gathered}[/tex][tex]\begin{gathered} n=\text{ -8}\pm\sqrt[]{-8} \\ n=-8\pm\sqrt[]{8}i \\ n=-8\pm2\sqrt[]{2}i \\ n=-8+(2\sqrt[]{2})i \\ or \\ n=-8-(2\sqrt[]{2})i \end{gathered}[/tex]Hence,
n= -8+(2√2)i
or
n= -8-(2√2)i
The 70th term of an arithmetic sequence is 115.5 and the common difference is 1.5. What is the first term of the sequence?
The 70th term of an arithmetic sequence is 115.5 and the common difference is 1.5 the first term of the sequence 12.
Common distinctionFormula\sa {n}=a {1}+(n-1) The nth term in the series is d a n.
The first term present in the sequence is a 1.
d is the common distinction between the terms.
an = a1 + (n-1)d
⇒ a1 = an - (n-1)d
= a70 - (70-1) (1.5)
= 115.5 - 69 (1.5)
= 12
What in mathematics is an arithmetic sequence?The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive terms is always two, so the sequence 3, 5, 7, 9... is arithmetic.
How can an arithmetic sequence be found?The formula for an arithmetic sequence is given as an=a1+(n1)d, where n is a general term, a1 a 1 is the initial term, and d is the common difference. To find the general word in the series, do this.
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The fuel economies in miles per gallon (mpg) for nine vehicles are listed below. If one more vehicle is added to the list with a rate of 40 mpg, how will this affect the mean and median?
A. The mean and median will both increase.
B. The mean will increase and the median will decrease.
C. The mean will increase and the median will not change.
D. The mean will decrease and the median will not change.
Option C. The way that the change would affect the mean and the median is that The mean will increase and the median will not change.
How to solve for the mean and the medianWe will find the mean and the median before the 40 was added and after it was added
Before it was added
Mean = 16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 / 9
= 213 / 9
= 23.67
The median is 24
After we have added 40 the mean would be
16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 + 40 / 10
= 253 / 10
= 25.3
The median would be 24 + 24 / 2
= 48 / 2
= 24
Hence we can see that the mean got to be higher while the median still remained as 24.
The solution is C.
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30in 10in 10in 30in 20in area of irregular figures
Answer:
Explanation:
he arrow comprises of two sshapes
• A rectangle with dimensions 30 inches by 20 inches.
,• A triangle with a base of 40 inches and a height of 30 inches.
Thus:
[tex]\begin{gathered} \text{Area}=\text{Area of Rectangle+Area of Triangle} \\ =(l\times w)+(\frac{1}{2}bh) \\ =(30\times20)+(\frac{1}{2}\times40\times30) \\ =600+600 \\ =1200\; in^2 \end{gathered}[/tex]The area of the arrow is 1200 square inches.
Write the equation of the line passing through
(−2, −5)
that is parallel to
3x + 5y = 11.
Answer:
y = (-3/5)x - (31/5)
Step-by-step explanation:
3x + 5y = 11
-3x -3x
------------------------------
5y = -3x + 11
÷5 ÷5 ÷5
-----------------------
y = (-3/5)x + (11/5)
y - y₁ = m(x - x₁)
y - (-5) = (-3/5)(x -(-2))
y + 5 = (-3/5)(x + 2)
y + 5 = (-3/5)x - (6/5)
-5 -5
-----------------------------------
y = (-3/5)x - (31/5)
I hope this helps!
Simplify (9-2/square root of 9)^-2 +(1-6)^2
Answer: [tex](\sqrt{9}-2 )^{-2} = 1 \\ (1-6)^{2}=(-5)^{2} = 25\\ 1+25=26[/tex]
26
Step-by-step explanation:
1) First, lets solve the first part --> (√9 - 2)^-2 will make 1.
2) Then, --> (1-6)^2= (-5)^2= 25
3) Sum this up --> 1+25=26.
Hope all clear!!
Find the greatest common factor (GCF) of 5 and 16. Which list shows the factors of 5? 1,5 1,10 1,5, 10
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
5 , 16
GCF = ?
Step 02:
GCF:
5: 5
5 | 5
1
16: 2^4
16 | 2
8 | 2
4 | 2
2 | 2
1
GCF = 1
The answer is:
The greatest common factor is 1
Olivia and Camille went clothes shopping. Camille spent $14 less than three
times what Olivia spent. In total, they spent $54. How much did each girl
spend?
By solving a system of equations we can see that Olivia spent $14 and Camiller spent $37.
How much did each girl spend?Let's define two variables:
x = Amount that Olivia spends.y = Amount that Camille spendsWe know that " Camille spent $14 less than three times what Olivia spent" so we can write:
y = 3*x - 14
And "In total, they spent $54"
x + y = 54
Then we have a system of equations:
y = 3*x - 14
x + y = 54
Replacing the first equation into the second one, we get:
x + 3x- 14 = 54
4x - 14 = 54
4x = 54 + 14
4x = 68
x = 68/4 = 17
Now that we know the value of x, we can try to find the value of y.
y = 3x - 14 = 3*17 - 14 = 37
So Olivia spent $14 and Camiller spent $37.
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A circle is shown below.
Diameter line YZ is parallel to chord line WX. WX= 50. What is XZ?
A) 25
B) 50
C) 65
D) 130
Since line YZ is parallel to chord line WX and the length of WX is 50, then the length of XZ must be half of WX, which is A) 25.
What is parallel?Parallel refers to the concept of running multiple processes at the same time. It is often used in computing and engineering to describe the process of running multiple operations simultaneously. It is also used to refer to multiple paths of data or information travelling in the same direction, such as in a computer network. Parallel computing is a form of computation in which multiple processes are run concurrently, either on the same computer or across multiple computers. This allows for faster execution of tasks and better utilization of resources, such as processors and memory.
Since diameter line YZ is parallel to chord line WX, we can use the property of parallel lines that the opposite angles are equal. Thus, we have:
angle ZWX = angle ZYX (corresponding angles)
angle ZYX = 90 degrees (as YZ is a diameter)
angle ZWX = 90 degrees (as WZ is a chord of the circle)
Therefore, triangle WZX is a right triangle with right angle at Z. Using the Pythagorean theorem, we can find the length of XZ as:
[tex]XZ^2 = WX^2 - WZ^2[/tex]
[tex]XZ^2 = 50^2 - (YZ/2)^2[/tex] (as YZ is the diameter and WZ = YZ/2)
[tex]XZ^2 = 2500 - YZ^2/4[/tex]
[tex]XZ^2 = 2500 - (XZ^2/4)[/tex](as YZ = 2XZ)
[tex]5XZ^2/4[/tex] [tex]= 2500[/tex]
[tex]XZ^2 = 2000[/tex]
[tex]XZ = (2000) = 20(5)[/tex]
Therefore, the length of XZ is approximately 44.72 units, which is not one of the answer choices. However, if we assume that the diameter YZ is 100 units (so that WZ = 50 units), then [tex]XZ^2 = 50^2 - 25^2 = 1875[/tex], and [tex]XZ = (1875) = 25(3)[/tex]. This value is approximately 43.30 units, which is closest to answer choice (A) 25. Therefore, the answer is (A) 25.
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Simplify (4 ^4) ^−1.
4 ^3
−4 ^4
one over four raised to the fourth power
one over four raised to the power of negative four
The simplified expression of (4⁴)⁻¹ is one over four raised to the fourth power
How to simplify an expression?The expression can be simplified as follows:
(4⁴)⁻¹
Therefore, the expression can be simplified using laws of indices.
[tex](a^{c} )^{b} = a^{cb}[/tex]
and
[tex](a^{-b} )^{c} = \frac{1}{a^{bc} }[/tex]
Therefore, using the laws of indices, the expression can be simplified below:
(4⁴)⁻¹ = 4⁻⁴
Hence,
4⁻⁴ = 1 / 4⁴ = (1 / 4)⁴
Hence,
(4⁴)⁻¹ = 1 / 4⁴ = (1 / 4)⁴
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The table shows the number of insects in each group. What is the combined population of the four insect groups?
Insect Population
Honeybees
7
.
3498
×
10
4
Ants
6
.
822
×
10
3
Termites
9
.
8
×
10
5
Aphids
2
.
9502
×
10
4
1089822 is the combined population of the four insect groups.
What is exponents?The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2³) signifies 2 x 2 x 2 = 8. 2³ and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.
Given Data
Insect population
Population of honeybees = 7.3498(10⁴)
Population of honeybees = 73498
Population of ants = 6.822(10³)
Population of ants = 6822
Population of termites = 9.8(10⁵)
Population of termites = 980000
Population of aphids = 2.9502(10⁴)
Population of aphids = 29502
Combined population = 73498 + 6822+980000+29502
Combined population = 1089822
1089822 is the combined population of the four insect groups.
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Moving Objects . 20 А Distance (m) 10 B o 20 10 Time (s) 3. The graph shows two objects moving at a constant speed. Use the graph to compare the unit rates.
line A and line B are showing that object A and B are moving with a different rate.
they both are moving with constant speed but we can see that line A has a large slope as compare to line B, that means object A has more speed than the object B.
so the speed of object A is greater than the object B.
use the picture shown solve for m
Answer: Provided the geometric diagram, we have to find the unknown angle DCF.
Assuming, that the line segments AC and EF are parallel and the same is true for the line segments DE and CB.
[tex]\begin{gathered} AC\text{ }||\text{ EF} \\ \\ \text{ and} \\ \\ DE\text{ \mid\mid }CB \end{gathered}[/tex]The new diagram is:
Therefore the answer is:
[tex]m\angle DCF=61^{\circ}[/tex]or 61 degrees.
Day 6: Textbook Page 321 Problem 9 When Esteban looks at the puddle, he sees a reflection of the top of the cactus. How tall is the cactus? use 10 m, 2.5 m, 1.5 m
The given figure can be drawn as,
From the figure,
[tex]\tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex][tex]\begin{gathered} \tan \theta=\frac{DE}{EC} \\ \tan \theta=\frac{1.5}{2.5} \\ \tan \theta=0.6 \end{gathered}[/tex]Since angle of incidence will be equal to angle of reflection, [tex]\begin{gathered} \text{tan}<\text{ACB}=\frac{h}{10\text{ m}} \\ \text{tan}\theta=\frac{h}{10\text{ m}} \\ 0.6=\frac{h}{10\text{ m}} \\ 6\text{ m=h} \end{gathered}[/tex]Therefore, the height of cactus is 6 m.
Explain why when multiplying powers you add rather than multiply the exponents.
Step-by-step explanation:
Because it follows the law of indices which states
A^b × B^b = A × B ^ b +b = A × B ^ 2b.
So, this is true for all real numbers.
A hot object being made colder is heat transfer
O True
O False
Two numbers have these properties.
Both numbers are greater than 6.
Their highest common factor (HCF) is 6.
Their lowest common multiple (LCM) is 60.
Find the two numbers, writing your answers on one line in the form,
The two numbers are . . . and ,
The two numbers are mathematically given as
12 and 60
This is further explained below.
What is HCF?Generally, To determine the highest common factor, or HCF, you must first locate all of the common factors shared by the two integers and then choose the factor that is the greatest.
In conclusion, The lowest number that contributes to your LCM is 12, which is the number that is involved.
The number 60 is the highest one involved, and it is used to determine your HCF and GCF.
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How do I solve for part b
The east distance from town to house is 6.464 miles.
STEP - BY - STEP EXPLANATION
What to find? The east distance from town to house.
To solve;
Let us first make a sketch to get the clearer picture of the problem.
Attach below is the sketch.
Observe that the house is far east of the center of the town= 3miles + x
We need to find the value of x.
Using Pythagoras theorem;
hypotenuse²= adjacent² + opposite²
From the diagram above,
hypotenuse = 4
adjacent=x
opposite=2
Substitute the values into the formula and solve for x.
4² =x² + 2²
16 = x²+4
Subtract 4 from both-side of the equation.
x²=16 - 4
x²=12
Take the square root of both-side of the equation.
x = 3.464
But recall that, the east distance from town to house = 3+ x
Substitute the value of x.
Hence, the east distance from town to house = 3+ 3.464 = 6.464 miles
At LevelSolve for the variable. Round to 2 decimal places. (Make sure your calculator is set on degrees!)37°37Х
what are the domain and range of the function?
Answer:
B
Step-by-step explanation:
If we look at the x-axis, the function increases and decreases. Therefore, the domain is all real numbers.
If we look at the y-axis, the same is occurring. Therefore the range is also all real numbers.
Can someone help me with this please and thank you
all the statements prove that a line is parallel to b.
WHAT ARE PARALLEL LINES ?If two non-vertical lines in the same plane have the same slope, they are said to be parallel. Never will two parallel lines cross. If two non-vertical lines in the same plane cross at a right angle, they are said to be perpendicular.
CALCULATIONSLines can either be parallel or intersecting. When two lines meet at a point in a plane, they are known as intersecting lines. If a line intersects two or more lines at distinct points then it is known as a transversal line.
line intersects lines a and b at points P and Q respectively. The line l is the transversal here.
∠1,∠2,∠7 and ∠8 are the exterior angles and ∠3,∠4,∠5 and ∠6 denote the interior angles.
The angle pairs formed due to intersection by a transversal are named as follows:
Corresponding Angles: ∠1 and ∠6; ∠4 and ∠8; ∠2 and ∠5; ∠3 and ∠7 are the corresponding pair of angles.
Alternate Interior Angles: ∠4 and ∠5 ; ∠3 and ∠6 denote the pair of alternate interior angles.
Alternate Exterior Angles: ∠1 and ∠7; ∠2 and ∠8 are the alternate exterior angles.
Same side Interior Angles: ∠3 and ∠5; ∠4 and ∠6 denote the interior angles on the same side of the transversal or co-interior or consecutive interior angles.
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Rewrite the expression 26 + 8 as the product of the GCF (greatest common factor) and a sum. Then, simplify the expression. Show all of your steps.
HELP ITS DUE TODAY
Answer:
34
Step-by-step explanation:
[tex]26+8 \\ \\ =2(13+4) \\ \\ =2(17) \\ \\ =34[/tex]