What is the slope of the linear equation that has the values shown in the table? Show your work
Answers
Slope can be found from two points using the equation [tex]\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex].
Take any two points to substitute in. In this example, I'll use the first two points, (-4, 15), and (-2, 9). Put these into the equation and you'll get
[tex]\frac{(9-15)}{(-2-(-4))}[/tex]. Simplify further to get [tex]\frac{-6}{2}[/tex]. Divide this and you'll get the slope, -3!
hope this helps!
Related Questions
b)______ is the number of times a particular value occurs in a given data
Answers
Answer:
the frequency is the number of times a particular value occurs in a given data.
The volume of the square-based pyramid shown is 72 m³. If the area of its
base is 36 m2, what is the height (h) of the pyramid?
base,
Answers
Answer:
Height = 6m
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] × 36 = 12
72 ÷ 12 = 6
Find the 45th term of the arithmetic sequence an = 2 + 4(n − 1).
145
182
178
264
Answers
The 45th term of the arithmetic sequence is 178. Option C
How to determine the term
Given the arithmetic sequence formula as;
an = 2 + 4(n − 1)
we have n = 45
Let's substitute the value of 'n' into the formula;
a = 2 + 4( 45 - 1)
expand the bracket
a = 2 + 4(44)
a = 2 + 176
a = 178
The 45th term is 178
Thus, the 45th term of the arithmetic sequence is 178. Option C
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Find two positive numbers satisfying the given requirements. the product is 242 and the sum is a minimum. (smaller value) (larger value)
Answers
The two positive numbers satisfying the given requirements are 15.56 and 15.56
For given question,
Let x and y be two positive numbers satisfying the given requirements.
⇒ xy = 242 .............(1)
The sum of given two positive numbers is a minimum.
Let the sum of given two positive numbers is S.
⇒ x + y = S ............(2)
From equation(1),
⇒ y = 242/x
Substitute above value of y in equation (2),
⇒ x + y = S
⇒ S = x + (242 / x)
Now, for above equation we find the derivative of x with respect to x.
⇒ 0 = 1 - [tex]\frac{242}{x^{2} }[/tex]
⇒ 242/x² = 1
⇒ x² = 242
⇒ x = ±15.56
Since the numbers are positive, x = 15.56
For x = 15.56
⇒ y = 15.56
Therefore, the two positive numbers satisfying the given requirements are 15.56 and 15.56
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3. Choose the two correct transformations for:
Ay
T
R'
RSTU to R'S'T'U'.
S'
A Rotation 180°clockwise
B Reflection across y = x
OC Reflection across y = -x
OD Rotation 180°counterclockwise
Answers
what is the volume of a triangular pyramid that is 5 feet tall and has a base area of 9 square feet
Answers
The volume of the triangular prism as described is; 15 cubic foot.
What is the volume of the triangular pyramid?A triangular pyramid simply refers to any geometric solid with a triangular base, and all three lateral faces are also triangles with a common vertex
It follows from the formula for calculating the volume of a triangular prism that;
Volume = (1/3) × base area × height.
Consequently,
volume of the prism is; = (1/3) ×9 × 5
Volume = 15 cubic foot
Therefore, volume of the triangular prism as described is; 15 cubic foot.
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The graph of y=√x is reflected in the x-axis and then translated
down 3 units. What is an equation that produces this transformation?
A. -√x-3
B. y= -3-(√x)
C. y= 3- (√x)
D. y= -(√x-3)
Answers
This is the same as y = - (√x) - 3
- 3 means the function is translated 3 units down since it is negative.
In order for the function to be reflected over the x-axis, the function (√x) has to be negative.
Note it cannot be D. because the function is being translated 3 units to the right, not down.
Find the slope of the line shown below
Answers
Answer:
[tex] \frac{3}{2} [/tex]
Step-by-step explanation:
From the attached photo, we can deduce:
(2,2) as (x1,y1)
(-2,-4) as (x2,y2)
Slope Formula =
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
Now we can substitute these values into the formula to find the slope.
Slope of line =
[tex] \frac{2 - ( - 4)}{2 - ( - 2)} \\ = \frac{2 + 4}{2 + 2} \\ = \frac{6}{4} \\ = \frac{3}{2} (reduced \: to \: simplest \: form)[/tex]
A set of n = 25 pairs of scores (x and y values) has a pearson correlation of r = 0. 80. how much of the variance for the y scores is predicted by its relationship with x?
Answers
The amount of variance for y that is predicted by its relationship with x is 64%.
How much variance is predicted?
Variance measures the rate of dispersion of a data point around the dataset. It can be calculated by finding the square of the standard deviation of a dataset. Variance measures the variation of a data set.
Correlation is a statistical measure used to measure the linear relationship that exists between two variables. The greater the correlation coefficient is closer to one, the greater the linear relationship that exists between the two variables. A positive correlation occurs when the two variables move in the same direction.
Variance = (correlation coefficient²) x 100
(0.80²) x 100
0.64 x 100 = 64%
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Given that………………………..
Answers
[tex]\sum^{\infty}_{n=1} (a/b)^n=5 \\ \\ =\frac{a/b}{1-\frac{a}{b}}=5 \\ \\ \frac{a}{b-a} =5 \\ \\ \frac{a}{b}=\frac{5}{6}[/tex]
So, we need to find
[tex]\sum^{\infty}_{n=1} n(5/6)^n
[/tex]
Let this sum be S.
Then,
[tex]S=(5/6)+2(5/6)^2 +3(5/6)^3+\cdots \\ \\ \frac{5}{6}S=(5/6)^2 + 2(5/6)^3+\cdots \\ \\ \implies \frac{1}{6}S=(5/6)+(5/6)^2+(5/6)^3+\cdots=5 \\ \\ \implies S=\boxed{30}[/tex]
Calculate the perimeter of 5y + 9 (3y+15) cm (7y+3)cm
Answers
Answer:
Step-by-step explanation:
assuming that the figure is a triangle with sides (5y + 9) and (3y + 15) and (7y + 3) we find the perimeter by adding everything
5y + 9 + 3y + 15 + 7y + 3 =
15y + 27
or
3(5y+9)
next time put all the data and figures, we are doing you a pleasure, at least put ALL the data.
You are playing a game with three cards. At the start, all three cards are face down. You know that a different real number is written on every card, but you do not know what the numbers are. The rules of the game are as follows: You can choose any card and turn it over (assuming that you have not already turned it over). You can either keep the card, or discard it. If you discard a card, then you cannot go back to it; you must choose a new card. If the card you have kept has the largest real number on it, then you win the game. If you use the optimal strategy, then what is the probability that you win the game
Answers
concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.
How to find the probability?
Now, we know that there are 52 cards in a normal deck, if we only keep the ones with real numbers, there are 40.
These numbers go from 1 to 10.
5.5 is the average real number in the cards, so, having a 6 or more in a card is what we expect.
This means that if the card that we turn up is smaller than 6, we discard it.
If the card has the value 6 or larger, we keep it.
In this case, the probability of losing is if one of the other cards has a value larger than 6.
The probability that a random card has a value larger than 6 is:
p = (number of cards with a value larger than 6)/(total number of cards)
p = (16/39)
(The quotient is 39 instead of 40, because we already know one of the cards)
This means that if keep the 6, the probability of winning is:
1 - 16/39 = 0.59
If instead, we got a 7, obviously we keep it, in that case the probability of winning is:
1 - 12/39 = 0.69
And so on, concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.
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For what value of x does 4^x=(1/8)^x+5
A) -15
B)-3
C)3
D) 15
Answers
the value of x is -3. Option B
How to determine the valueWE have the expression to be;
4^x=(1/8)^x+5
With the knowledge of indices, we have that;
2 = 2 ^1
4 = 2^2
8 = 2^3
16 = 2^4
32 = 2^5
So from this given information,
we can express the expression as;
4^x = 2^2x
1/8^x = 2^-3x
Substitute into the formula
2^2x = 2^-3x - 15
Cancel out the like terms
2x = -3x - 15
collect like terms
2x + 3x = - 15
x = -15/ 5
x = -3
Thus, the value of x is -3. Option B
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find PQ if possible
Answers
Answer:
11 units.
Step-by-step explanation:
What is the exact value of cos (67.5°)?
OA.
OB.
OC. -√2+√2
√2+√2
2
-
√2-√2
2
OD. √2+ √2
4
Answers
first off, make sure you have a Unit Circle, if you don't do get one, you'll need it, you can find many online.
let's double up 67.5°, that way we can use the half-angle identity for the cosine of it, so hmmm twice 67.5 is simply 135°, keeping in mind that 135° is really 90° + 45°, and that whilst 135° is on the 2nd Quadrant and its cosine is negative 67.5° is on the 1st Quadrant where cosine is positive, so
[tex]cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos(135^o)\implies cos(90^o+45^o)\implies cos(90^o)cos(45^o)~~ - ~~sin(90^o)sin(45^o) \\\\\\ \left( 0 \right)\left( \cfrac{\sqrt{2}}{2} \right)~~ - ~~\left( 1\right)\left( \cfrac{\sqrt{2}}{2} \right)\implies -\cfrac{\sqrt{2}}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]cos(67.5^o)\implies cos\left( \frac{135^o}{2} \right)\implies \pm \sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}\implies \stackrel{I~Quadrant}{+\sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}} \\\\\\ \sqrt{\cfrac{ ~~ \frac{2-\sqrt{2}}{2} ~~ }{2}}\implies \sqrt{\cfrac{2-\sqrt{2}}{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{\sqrt{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{2}[/tex]
Each day of the week mrs uses 3/4 of a gallon of gas what is the amount she uses in five days?
Answers
Answer:
3.75
Step-by-step explanation:
3/4 times 5 =3 3/4
Solve following equation:
[tex]4x+10=-2+4[/tex]
Answers
Step-by-step explanation:
4x + 10 = -2 + 4
4x = -2 + 4 - 10
4x = -8
x = -2
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{4x + 10 = -2+ 4}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{4x + 10 = 2}[/tex]
[tex]\huge\textbf{Subtract 10 to both sides:}[/tex]
[tex]\mathsf{4x + 10 - 10 = 2 - 10}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{4x = 2 - 10}[/tex]
[tex]\mathsf{4x = -8}[/tex]
[tex]\huge\textbf{Divide 4 to both sides:}[/tex]
[tex]\mathsf{\dfrac{4x}{4} = \dfrac{-8}{4}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = \dfrac{-8}{4}}[/tex]
[tex]\mathsf{x = -2}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
can someone help me with the graph I don't get it thanks
Answers
Answer: Refer to the histogram diagram below
The frequency table is in another attachment, and may be optional.
======================================================
Explanation:
The first task is to sort the values from smallest to largest. Luckily the data set is already sorted for us.
The smallest number is 22. This is the min. Since we're doing intervals of 10 percent, this means the first bin spans from 20% to 29%, assuming we're only involving whole number percentages. Then the next bin is from 30% to 39%, and so on, until reaching the last bin of 90% to 99%
The bin labels are shown along the bottom of the histogram.
-----------
The height of each bar represents how many students are in that specific bin. The first bar is 1 unit tall because there's only one student in the 20% to 29% range (that 22% mentioned earlier).
The next bar is 2 units tall because of the scores of 30% and 37%. They are in the range from 30% to 39%
The next bar is 4 units tall because of the scores 45,46,46,49.
This process is done with the other values to get the histogram you see below.
The frequency table is shown in a separate attachment, but your teacher may only want the histogram part. I would ask him/her for clarification.
The third column of the frequency table is optional to show where all the scores fit (and to help confirm the frequencies). This will help confirm the answer. Most histograms commonly only show the first two columns.
------------
While it's a good thing to know how to do this by hand, it's recommend to use software to generate the histograms when it comes to real world applications. Eg: making a presentation to the boss.
The program I used was LibreOffice which is free and effectively identical to excel. There are other options you could pick from.
Side note: There are no gaps between the bars when it comes to histograms. In contrast, a bar chart will have gaps.
Solve using the quadratic formula.
n2 + 2n + 1 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
n = ____
or n = ____
i wasnt ever smart lol please help quick
Answers
Answer:
-1
Step-by-step explanation:
n^2+2n = -1
n(n+2) = -1
The area of the regular octagon is approximately 54 cm2.
A regular octagon has an apothem with length 4 centimeters and an area of 54 centimeters squared. Line segment A B is a side of the octagon.
What is the length of line segment AB, rounded to the nearest tenth?
3.4 cm
4.8 cm
24 cm
27 cm
Answers
The length of the line segment of octagon which is AB equal to 3.4 cm.
Given that the area of the regular octagon is 54 [tex]cm^{2}[/tex], apothem of regular octagon is 4 cm. Line segment AB is side of the octagon.
We are required to find the length of the line segment AB.
A regular octagon has eight equal sides.
Area of regular octagon=Perimeter*apothem/2-----------1
We have to put the value of area and apothem in equation 1.
54=perimeter*4/2
Perimeter=(54*2)/4
=27 cm
Perimeter=27 cm.
Now we know that the perimeter is equal to the sum of the lengths of all sides of figure. So,
Perimeter=8*side
27=8*AB
AB=27/8
=3.375 cm
After rounding off it will be equal to 3.4 cm.
Hence the length of line segment is equal to 3.4 cm.
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Answer:
A
Step-by-step explanation:
The ratios of teachers:male students :female students is 2:17:18 the total number of students is 665 find the number of teachers
Answers
X 19
38 : 665
38 teachers!
Answer: 38 teachers.
Step-by-step explanation:
Let the share ratio be x.
So, quantity of teachers = 2x, quantity of male students = 17x,
quantity of female students = 18x.
17x+18x=665
35x=665
Divide the left and right sides of the equation by 35:
х=19.
2x=2*19
2x=38.
The function D(t)=18t2−130t gives the distance a car going a certain speed will skid in t seconds. Find the time it would take for the car to skid 150 feet.
Answers
The time it will take for the car to skid for 150 feet is 8.23 seconds.
How to find the time the car will skid?The function D(t) = 18t² − 130t gives the distance a car going a certain speed will skid in t seconds.
The time the it would take for the car to skid for 150 feet can be calculated as follows:
Therefore,
D(t) = 18t² - 130t
150 = 18t² - 130t
18t² - 130t - 150 = 0
divide by 3
9t² - 65t - 75 = 0
Hence,
t = 65 ± 5√277 / 18
t = 8.23425471586 or -1.01166666667
Hence,
t = 8.23 seconds.
Therefore, the time it will take for the car to skid for 150 feet is 8.23 seconds.
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Michael has $15 and wants to buy a combination of school lunches to feed at least three classmates. A sandwich costs $2, and hot lunch costs $3.
This system of inequalities models the scenario:
2x + 3y ≤ 15
x + y ≥ 3
Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a point in the solution set and interpret what it means in terms of the real-world context. (3 points)
Answers
The description of this graph tells us that the equation 2x + 3y ≤ 15 was shaded to the bottom while x + y ≥ 3 was shaded to the top as shown in the diagram.
How to create and explain the grapha. The first equation of the graph when it was drawn was shaded to the bottom, while the upper part of the shading has is that of the equation x + y ≥ 3.
b. (5,1) are the solutions for the equation 2x+3y<15. This is given that when x and y are substituted we would still have less than 15.
C The point in the graph would be 2,3. At this point, Michael would be able to buy 2 sandwiches and 3 hot lunches. This is still within his budget for 3 students.
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Answer:
Step-by-step explanation:
2,3 is the anwser
the square root of 7956
Answers
Answer:
89.19
Step-by-step explanation:
8 9 . 1 9
79,56 . 00, 00
8 | 64
| 1556
169 | 1521
| 3500
1781 | 1781
1719
17829| 6200
What are the solutions of the equation x4 6x2 5 = 0? use u substitution to solve.
Answers
The value of the x from the given equation is a +i and -i and +5i and -5i.
According to the statement
we have given that the equation [tex]x^4 + 6x^2 +5 =0[/tex]
and we have to find the value of x by the u substitution.
So,
The given equation is
[tex]x^4 + 6x^2 +5 =0[/tex]
Put [tex]x^2 = u[/tex]
By substitution method
Then the equation become
[tex]u^2 +6u +5 = 0[/tex]
And solve the equation then
[tex]u^2+ u +5u +5 = 0[/tex]
Then
u(u +1) + 5(u +1) = 0
(u+5) (u +1) = 0
Then
the value of u is -1 and -5 then
The value of x is
[tex]x = \sqrt{u}[/tex]
x = √-5 And √-1
Then the value of x is +i and -i and +5i and -5i.
So, The value of the x from the given equation is a +i and -i and +5i and -5i.
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Which function represents the following graph?
X
Answers
The last one because the other ones only go to the positive side and not the negative too since the cube root
pleaseeee hurrryyyyyyyy
Answers
Answer:I THINK IT IS 1,-3
Step-by-step explanation:
A ribbon is 5 m long. A piece of length 3 4/5 m is cut from it. What is the length of the remaining piece?
Answers
Answer:
1.2 meters long
Step-by-step explanation:
3(4/5)m=3.8m
5m-3.8m=1.2m
Find the median of the data set. round your answer to the nearest tenth if necessary. 13,13,15,15,15,15,17,17,19,20
Answers
Answer:
Hey Desmariesin7587, the median of the data set that you gave is 15.9
Step-by-step explanation:
Since the amount of values in the data set was not even, I could not find a middle number. Instead, I added up all of the values and divided the total sum by the amount of values that there were; in this case, 10.
----------------------
Have a great day,
Nish
The equation 2x2 − 12x 1 = 0 is being rewritten in vertex form. fill in the missing step. given 2x2 − 12x 1 = 0 step 1 2(x2 − 6x ___) 1 ___ = 0 step 2 2(x2 − 6x 9) 1 − 18 = 0 step 3 ✔ 2(x − 3)2 17 = 0 2(x − 3)2 − 17 = 0 2(x 3)2 − 17 = 0 2(x − 6)2 − 17 = 0
Answers
Given: [tex]2x^2 - 12x + 1 = 0[/tex]
Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]
Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]
Second answer: [tex]2(x - 3)^2 - 17 = 0[/tex]
Explanation in detail:
The quadratic equation a[tex]x^{2} + bx + c = 0[/tex]'s vertex form is
where a[tex](x - h)^{2} + k[/tex] equals zero
A is the [tex]x^{2}[/tex] coefficient, and h is the vertex's x-coordinate on the equation's graph.
The vertex of the equation's graph, k, has the y-coordinate.
The completing square can be used to determine the vertex form.
[tex]2x^{2} - 12x + 1 = 0[/tex] is the equation.
Put[tex]2x^{2} -12x[/tex] in a bracket and subtract 2 from them as a common component to utilize the completing square.
∵ [tex]2(x^{2} - 6x) + 1 = 0[/tex]
To determine the product of the first and second terms in the binomial, divide the second term by two.
∵ [tex]6x / 2 = 3x[/tex]
∵[tex]3x = 3 * x[/tex]
∴ The binomial's first and second terms are x and 3, respectively.
The phrase in the bracket's middle is (-)
∴ Middle of the binomial's sign is (-)
∴ The binary value is [tex](x - 3)^2[/tex]
Square 3 is nine.
To keep the equation from altering, you must deduct the same number from the bracket after adding 9 there.
∴ [tex]2(x^2 - 6x + 9 - 9) + 1 = 0[/tex]
- Remove the brace and multiply -9 by 2.
∵ [tex]2 *-9 = -18[/tex]
∴ [tex]2(x^2- 6x + 9) + 1 - 18 = 0[/tex]
- Construct a square binomial from [tex](x^{2} - 6x + 9)[/tex]
∵ [tex]x^2 - 6x + 9 = (x - 3)^2[/tex]
∴ [tex]2(x - 3)^2 + 1 - 18 = 0[/tex]
Include related terms.
∴[tex]2(x - 3)^2 - 17 = 0[/tex]
∴ The equation's vertex form is[tex]2(x - 3)^2 - 17 = 0.[/tex]
Given that: [tex]2x^2 - 12x + 1 = 0[/tex]
Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]
Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]
Step 3: [tex]2(x - 3)^2 - 17 = 0[/tex]
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