Find the Slope of the line through the points (4, -5) and (2, 2) then graph it.Slope =
Answers
The Slope of the line through the points (4, -5) and (2, 2) then graph it. Slope [tex]m=-\frac{7}{2}$$[/tex]
Slope between two points: [tex]$\quad$[/tex]Slope [tex]$=\frac{y_2-y_1}{x_2-x_1}$[/tex]
[tex]$$\begin{aligned}&\left(x_1, y_1\right)=(4,-5),\left(x_2, y_2\right)=(2,2) \\&m=\frac{2-(-5)}{2-4}\end{aligned}$$[/tex]
Refine
[tex]m=-\frac{7}{2}$$[/tex]
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
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Related Questions
Use a calculator to find the natural logarithm, base e. In 0.0746 In 0.0746
Answers
By using a calculator,
ln 0.0746 = - 2.596
anyone know this one i was having troble
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The zero of the linear function will be at (1, 0).
A linear function is the one which can be represented in the form y = ax + b where a, b are coefficients and x, and y are independent and dependent variables respectively. The zero of a line is the point where the line crossed the x-axis which is also known as the x intercept. The equation of the line in slope intercept form is given as y = mx + c where m is the slope and c is the y intercept. The slope of line from points (0, 5) and (2, -5) can be found by m = -5 - 5/2 -0
m = -10/2
m = -5
Now, putting this and the point (0, 5) in y = mx + c we get
5 = -5×0 + c
=> c = 5
Now, equation of line is y = -5x + 5 and for x intercept we put y = 0
0 = -5x + 5
5x = 5
=> x = 1
=> (1, 0) which is the required point
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Suppose line g is the line with equation y=x. Given A(8,−5), B(7,3), and C(−1,−7), what are the coordinates of the vertices of △A′B′C′ for the reflection?
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The point (x,y) on the reflection about y = x axis changes to,
[tex]A(x,y)\rightarrow A^{\prime}(y,x)[/tex]Determine the coordinates of the vertices of triangle after reflection.
[tex](6,3)\rightarrow(3,6)[/tex][tex](8,-3)\rightarrow(-3,8)[/tex][tex](-2,-6)\rightarrow(-6,-2)[/tex]So vertices of triangle after reflection is,
(3,6), (-3,8) and (-6,-2)
3. Compare the numbers 5/9 and 0.5^- Use the symbols <, >, or =.
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So 5/9 is equal to 0.5- so the right answer is
[tex]\frac{5}{9}=0.\bar{5}[/tex]the little line on the top of the number means that this number will be repeated Infinitely is like 0.555555555...
The table below shows the population of the state of Washington for several decades starting in1900.Year1900191019201930194019501960Populationin millions0.521.151.371.571.742.392.86If the population is modeled by an exponential function of the form P(t) = a(b)^t, where t is yearssince 1900, which of the following would be a reasonable value for a?0.522.860.0351900
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a represents the initial value of the function. Since the function starts at 1900, the associated population value for this year should be the answer. The answer is 0.52.
Specifically, I need the surface are which can be found by using this formula: S= Ph+2B
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The surface area of a prism of heigh H and base of sides a, b, and c is:
A = PH + 2B
Where P = a + b + c is the perimeter of the base and B is its area.
We can see in the figure a prism of height H = 14 in, base sides of 10 in, 10 in, and 12 in. The height of the base is also given as h = 8 in.
Calculate the perimeter of the base:
P = 10 in + 10 in + 12 in = 32 in
The area of the base is:
[tex]B=\frac{12\text{ in }\cdot8\text{ in}}{2}=48\text{ }in^2[/tex]Calculate the surface area:
[tex]\begin{gathered} A=PH+2B \\ A=32\text{ in }\cdot\text{14 in}+2\cdot48\text{ }in^2 \\ A=448\text{ }in^2+96\text{ i}n^2 \\ A=544\text{ }in^2 \end{gathered}[/tex]The area is 544 square inches
Here are two expressions whose product is a new expression, A: 1. What could we put in the boxes to make A be a polynomial?
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We are given the following product:
[tex](-2x{}^3+B)(x^n+15)=A[/tex]For "A" to be a polynomial the value of the first box "B" must be a constant or a term of the form:
[tex]ax^n[/tex]We will use a constant. We will substitute the first box for "1":
[tex](-2x^3+1)(x^n+15)=A[/tex]For the second box, we need to use an exponent that is a positive whole number.
We will use 2:
[tex](-2x^3+1)(x^2+15)=A[/tex]With these values, the result of the product is a polynomial.
Coupon A: $25 rebate on $96 shoes coupon B; 40% off of $96 shoes
Answers
Answer: Coupon B is more profitable
49. Calculate the limit. Some of these limits are made easier by considering the logarithm of the limit first, and some are not.
lim x^lnx
x→0+
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The limit of xlnx when x is tending towards zero is zero.
What is limit in mathematics?
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches a particular value. Without limits, it is impossible to perform calculus or mathematical analysis; limits are also necessary to compute continuity, derivatives, and integrals.
Given limit is:
[tex]\lim_{x \to 0} x lnX[/tex]
Considering f = x, and g = ln x
The limit of f and g are both zero or both ±∞, and the limit f′/g′ exists, then the limit f/g equals it.
The wrong in the expression x lnx is we are individually defining f and g doesn't meet the hypothesis. so, we write it as
[tex]\frac{lnx}{1/x}[/tex]
We now use L' Hospital rule with f(x) = lnx, g(x) = 1/x as
The limits
[tex]\lim_{x \to 0^+} lnx= - \infty[/tex], and
[tex]\lim_{x \to 0^+} \frac{1}{x}[/tex]
The limits [tex]\lim_{x \to 0^+} \frac{f'(x)}{g'(x)}[/tex] exists as:
[tex]\lim_{x \to 0^+} \frac{1/x}{-1/x^2} = \lim_{x \to 0^+} -x = 0[/tex]
Hence the answer is 0.
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What is the slope of the line that passes through the points (9, -10) and (14, 5)?
Write your answer in simplest form.
Answers
What is the slope of the line that passes through the points (9 , -10 ) and (14 , 5)? Write your answer in simplest form.
From inspection on the given problem:
[tex] \sf{(x_1, y_1) = (9, -10)}[/tex][tex] \sf{(x_2, y_2) = (14, 5)}[/tex]To calculate the slope of the line passing through the given points, we must use the formula below:
[tex] \sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}[/tex]Substitute the given values into the slope formula and solve for m:
[tex] \sf{m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{5 - (-10)}{14 - 9} = \dfrac{15}{5} = \pmb{3}}[/tex]
Therefore, the slope of the line that passes through the given points is 3.
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x=0,0.5,1,3,3.5,4,5y= 63,72,75,81,84,90,93calculate the correlation coefficient, r.round answer to the 3 decimal places
Answers
In order to find the correlation coefficient r, we can use the formula:
[tex]r=\frac{7\sum ^{}_{}(xy)-\sum ^{}_{}x\sum ^{}_{}y}{\sqrt[]{\lbrack7\sum ^{}_{}x^2-(\sum ^{}_{}x)^2\rbrack\cdot\lbrack7\sum ^{}_{}y^2-(\sum ^{}_{}y)^2\rbrack}}[/tex]where the sum must be taken upon all 7 values of x and y.
So, let's find each term and then use them in the formula:
[tex]\begin{gathered} 7\sum ^{}_{}(xy)=7(0\cdot63+0.5\cdot72+1\cdot75+3\cdot81+3.5\cdot84+4\cdot90+5\cdot93) \\ =7\cdot1473=10311 \end{gathered}[/tex][tex]\begin{gathered} \sum ^{}_{}x\sum ^{}_{}y=(0+0.5+1+3+3.5+4+5)\cdot(63+72+75+81+84+90+93) \\ =17\cdot558=9486 \end{gathered}[/tex][tex]\begin{gathered} 7\sum ^{}_{}x^2-(\sum ^{}_{}x)^2 \\ 7\cdot(0^{2^{}}+0.5^2+1^2+3^2+3.5^2+4^2+5^2)-(0+0.5+1+3+3.5+4+5)^2 \\ 7\cdot63.5-17^2 \\ 444.5-289 \\ 155.5 \end{gathered}[/tex][tex]\begin{gathered} 7\sum ^{}_{}y^2-(\sum ^{}_{}y)^2 \\ 7\cdot(63^2+72^2+75^2+81^2+84^2+90^2+93^2)-(63+72+75+81+84+90+93)^2 \\ 7\cdot45144-558^2 \\ 316008-311364 \\ 4644 \end{gathered}[/tex]Now, we need to use them in the formula to find r:
[tex]r=\frac{10311-9486}{\sqrt[]{155.5\cdot4644}}=\frac{825}{\sqrt[]{722142}}\cong0.9708[/tex]Finally, round the answer to the 3 decimal places, we find
r = 0.971
find the equation of a parabola with a focus of (0, -1) and directrix y = 1
Answers
Solution
For this case we see that the focus is (0,-1)
And the directrix is y=1
So then we have a parabola that open downwards:
The vertex is given by V= (h,k)
The focus is given by: F = (h, k+p)
And the directrix is given by: y= k-p
So then replacing we got:
1 = k-p (1)
h = 0
k+p = -1 (2)
Using equation (1) we got k:
k = p+1
Replacing into second equation we got:
p+1+p = -1
2p = -2
p= -1
k = -1 +1= 0
Then the vertex is given by: V= (0, 0)
And the formula is given by:
[tex](x-0)^2=4(-1)(y-0)[/tex]And thats equivalent to :
[tex]x^2=-4y[/tex]Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. simplify using order of operations. Show all of your work and one operation at a time to receive all possible points. 90 divided by [10 plus (3^2-4)]
Please help!
Answers
the equation you summited is
90÷10+3²-4
Answer:
the answer to the question is 14
Step-by-step explanation:
90÷10+3²-4
Follow the PEMDAS order of operations
3²=9
90÷10+9-4
Multiply and divide from left to right
90÷10=9
9+9-4
Add and subtract from left to right
9+9=18
18-4=14
So the answer to your question is 14
ASAP FREE PONTS! HELP! The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Use the constraints of the real-world situation to predict the height of the water balloon at 15 seconds. Use complete sentences to support your answer.
Answers
The height of the water balloon at 15 seconds based on the potential rupturing effect of the balloon's initial gravitational potential energy on the membrane of the balloon upon impact with the ground and that addition forces are not added, is at the ground level or zero feet.
What is gravitational potential energy?Gravitational potential energy is the energy possessed by a body by virtue of its elevation above ground level.
The points on the path of the water balloon thrown from the building's roof are;
(0, 4), (2, 7), (7, 5), (6, 4), (9, 1), (9.5, 0)
The location of the water balloon, 9.5 seconds after it is thrown off the roof is therefore at the point, h(9.5) = 0 feet, which can be taken as the ground level or base of the building.
According to Newton's third law of motion, which is a physics or natural law, and which states that all bodies remain at rest or continue perpetually in a straight line unless acted upon by a force.
Given that no additional force is specified after the water balloon is thrown from the building, and that a water balloon can be treated as a large drop of water, where the elastic balloon membrane, represents the surface tension holding the large droplet together, we have that the energy of impact of collision of the balloon when it lands, which is obtained from the initial gravitational potential energy of the water balloon, can potentially rupture the membrane, such that the water is spilled and remains on the floor, well after 9.5 seconds, such that at 15 seconds, the height of the balloon remains at ground level.
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Consider the matrix.[k q h][w p r]Which statement is true?A. The matrix has 2 rows and 2 columns.B. The matrix has 2 rows and 3 columns.C. The matrix has 3 rows and 2 columns.D. The matrix has 3 rows and 3 columns.
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10. A 300-room hotel collects $125 per occupied room and does not collect any money for vacantrooms. Which of the following functions best represents how many dollars, d, the hotel generates ifthere are v vacant rooms in the hotel?O d = 125(300 + V)O d = 300(75 - v)O d = 300(75+)O d = 125(300 - V)
Answers
If there are v vacant rooms, the number of occupied rooms is 300-v (in total there are 300 rooms).
As every occupied makes the hotel collect 125, the dollars the hotel generates are:
[tex]d=125(300-v)[/tex]It means that the correct answer is the last option.
What is the slope-intercept equation of the line below?y-intercept = (0, 3)5slope =4
Answers
Step-by-step explanation:
the slope-intercept form is
y = ax + b
a is the slope, b is the y- intercept (the y-value when x = 0).
so, the equation is
y = -5/4 x + 3
The midpoint of AB is (2,7) and point A is located at (5,-3).
What are the coordinates of point B?
Answers
The coordinates of point B =(5,10)
what is coordinates?
Coordinates are a set of values which helps to show the exact position of a point in the coordinates plane.
step - by - step explanation
5-2 = 3
2-3= -1 = the x coordinate of B
-7-3= -10
-7-10 = -13 = the y coordinate of B
(-1, -13) is the point B
A is 3 to the right of the midpoint ,so B is 5 to the left to the midpoint
A is 10 up from the midpoint so B is 10 down from the midpoint.
so the coordinates of point B is (5,10)
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Can you help me ?
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Fill in the blank question.
The cost of a school lunch is $2.50.
Complete the table to show the total cost of 1, 2, 3, and 4 lunches.
Lunches Bought 1 2 3 4
Total Cost ($)
Part B
Select the correct choices to complete the sentence.
The total cost is , 1 of 2.
Select Choice
to the number of lunches bought because the ratios between the quantities , 2 of 2.
Select Choice
the same unit rate.
Answers
The cost for the lunches will be:
1 lunch = $2.50
2 lunches = $5
3 lunches = $7.50
4 lunches = $10
How to calculate cost?From the information, the cost of a school lunch is $2.50. Therefore, the cost of 1 lunch will be:
= 1 × $2.50
= $2.50
The cost of 2 lunches will be:
= 2 × $2.50
= $5.00
The cost of 3 lunches will be:
= 3 × $2.50
= $7.50
The cost of 4 lunches will be:
= 4 × $2.50
= $10
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When your grandmother got out of the hospital, she was so excited that she gave you some money. You decided to go to Canada where the exchange rate is 1.06 Canadian dollars to $1 US dollar as of November 2015. You have $10,000 to take with you. How many Canadian dollars do you have to spend? (Show all work using dimension analysis, round to nearest cent if necessary)
Answers
Answer:
10,600 Canadian dollars
Step-by-step explanation:
[tex] \frac{1.06}{1} = \frac{x}{10000} [/tex]
[tex]x = 10000(1.06) = 10600[/tex]
hello this is all 1 math problem together may I get help with the solve and check .
Answers
The given expression is,
[tex]7n+14=-21[/tex]So bringing "14" to the other side of the euals,
[tex]\begin{gathered} 7n=-21-14 \\ =-35 \end{gathered}[/tex]On division,
[tex]\begin{gathered} 7n=-35 \\ n=-\frac{35}{7}=-5 \end{gathered}[/tex]Now, let us substitute -5 for n,
[tex]7\times(-5)=-35[/tex]Hence checked.
HELP PLS
Do anybody know answer to these problomes?
Answers
you can do this easily by BODMAS Frist open small bracket and slove it then open curly bracket and solve it at last open third bracket and open it then solve
Remember you should always open divide first then multiply then add and then subtract
Practice it is easy.
Step-by-step explanation:
[tex]28 \div (1 + 2 \times (19 - 16))[/tex]
[tex]28 \div (1 + 2 \times 3) [/tex]
[tex]28 \div (1 + 6)[/tex]
[tex]28 \div 7[/tex]
[tex]4[/tex]
what is the slope of a line that passes through (1,3) and (-7,-5)
Answers
LetW = the set of whole numbersF = the set of (non-negative) fractionsI = the set of integersN = the set of negative integersQ = the set of rational numbersSelect each set that is closed under addition.
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Verify each set
W ---------> are closed under addition
F ------> are closed under addition
I ------> are closed under addition
N ----> are closed under addition
Q ----> are closed under addition
Are there more buildings that have 10-19 bricks or buildings that have 50-59 bricks ?
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We can see from the graph that there are 10 buildings that have 10-19 bricks and 2 buildings that have 50-59 bricks. So there are more buildings with 10-19 bricks in the neighborhood.
Answer: 10-19 bricks
Answer and explanation pls
Answers
Ray is a part of a line that has a fixed starting point but no endpoints.
There is no end point of any of those rays.
The point V labeled in the diagram is not on any of those rays.
What is a ray?Ray is a part of a line that has a fixed starting point but no endpoints.
We have,
Four rays:
SP, SQ, SU, and SW
A ray has a starting point but does not have an endpoint.
There is no end point of any of those rays.
There are seven points in the diagram.
P, Q, S, V, T, U, and W.
We see that point V does not lie on any of the four rays.
Thus,
There is no end point of any of those rays.
The point V labeled in the diagram is not on any of those rays.
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In the diagram below, if < 2 = 123 °, what would be the measure of < 7?
Answers
Given:
[tex]\angle2=123^{\circ}[/tex]To find:
The angle 7.
Explanation:
We know that,
The sum of the exterior angles is supplementary.
So, we can write
[tex]\begin{gathered} \angle2+\angle7=180 \\ 123^{\circ}+\angle7=180 \\ \angle7=180-123 \\ \angle7=57^{\circ} \end{gathered}[/tex]Therefore, angle 7 is 57 degrees.
Final answer:
Angle 7 is 57 degrees.
3/4x = 24/3 × fraction ? x = ___ × 4/3× = fraction × 4/3x = ___ or 2 2/3
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Given that 3/4x = 2
[tex]\begin{gathered} \frac{3}{4}x\text{ = 2} \\ \text{This can be written as} \\ \frac{3\cdot\text{ x}}{4}\text{ = 2} \\ \frac{3x}{4}\text{ = 2} \\ \text{Cross multiply} \\ 3x\text{ = 2 x }4 \\ 3x\text{ = }8 \\ x\text{ = }\frac{8}{3}\cdot\text{ }\frac{1}{1} \\ \text{x = }\frac{8}{3} \\ x\text{ = 2}\frac{2}{3} \end{gathered}[/tex][tex]undefined[/tex]No correlation means that as the x-values increase, the y-values O a have no effect Ob increase Ос decrease
Answers
we know that
If there is no correlation between x and y, that just means that there's no relationship, connection, or interdependence between the two variables
No correlation means that as the x-values increase, the y-values have no effect
the answer is the option A
The graph of a function g is shown below.
Find g (0)