A line goes through the points (8,9) and (-2,4) .
(a) What is the slope of the line? Show your work
(b) Write the equation of the line in point-slope form. Show your work
(c) Write the equation of the line in slope-intercept form.
show steps
The equation of the line in slope-intercept form would be; y=1/2x+5.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
(a) The slope of line passing through two points is given by;
[tex]m = \dfrac{y-q}{x-p}[/tex]
Here m = 4 - 9/ -2 - 8
m = 5/10
m = 1/2
(b) The equation of line passing through a point and having slope is given by ;
y-y₁ = m(x-x₁)
Here, y-4 = 1/2(x+2)
(c) The slope intercept form;
y-4=1/2(x+2)
y-4=1/2x+1
y=1/2x+5
Hence, the equation of the line in slope-intercept form would be; y=1/2x+5.
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Lonnie ordered 12$ copies of the same book.h3 books cost 19$ each and the order has a 15$ charge.what is the total cost of Lonnie's order?
Factor the trinomial below. x2 – 2x – 35 A. (x – 5)(x + 7) B. (x – 5)(x – 7) C. (x + 5)(x – 7) D. (x + 5)(x + 7)
Evaluate the expression for a = 2 and b = 5. 100 20 50 625
25 POINTS PLEASE HELP SOMEONE WHO CAN
Solve the system by substitution
-x-y-z=-8
-4x+4y+5z=7
2x+2z=4
A chess board has 64 squares. if you put one grain of rice on the first square, two grains on the second square, four grains on the third, eight grains on the fourth, and so on. how many grains are on the last square. no calculators.
Please help! Use the quadratic function to predict y if x equals 6. Y=2x^2-2x-2
A) y= -58
B) y= 58
C) y=-60
D) y= 60
Answer:
The correct option is B.
Step-by-step explanation:
The given quadratic function is
[tex]y=2x^2-2x-2[/tex]
We have to find the value of the function y at x=6.
Substitute x=6 in the given function.
[tex]y=2(6)^2-2(6)-2[/tex]
[tex]y=2(36)-12-2[/tex]
[tex]y=72-14[/tex]
[tex]y=58[/tex]
The value of the function is 58 at x=6 is 58.
Therefore the correct option is B.
"if calvin buys 4 pounds of starfruit and 3 pounds of oranges, how much is his total utility"
The Calvin has a total of 252 utility coming from Oranges and Starfruit.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that oranges cost $2 per pound and starfruit costs $5 per pound.
The utility coming from Oranges and Starfruit, therefore he needs to spend his $26 on buying the oranges and starfruit
Since all in all he also spend $23 on it, and still has remaining $3 in his pocket,
Thus his total utility is 252.
Hence, The Calvin has a total of 252 utility coming from Oranges and Starfruit.
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The complete question is
The oranges cost $2 per pound and starfruit costs $5 per pound. calvin has $26 to spend. if calvin buys 4 pounds of starfruit and 3 pounds of oranges, how much is his total utility?
the ordered pair (2 16) is a solution to which equation(s)
A. y=(2x)^2
B. y=2x^2
C. y=2x+2
D. y=(x+2)^2
How to find the angle measure of an isosceles triangle if you only know the side lengths?
Which is the directrix of a parabola with equation x^2=y
Which compound inequality has no solution? x ≤ –2 and 2x ≥ 6 x ≤ –1 and 5x ≤ 5 x ≤ –1 and 3x ≥ –3 x ≤ –2 and 4x ≤ –8
Answer:x <= -2 and 2x >= 6 is the smae as
x <= -2 and x >= 3
Step-by-step explanation:
HELP PLEASE SOS :))
PLease PLease help with the questions below
Given: AB = 12
AC = 6
Prove: C is the midpoint of AB.
Proof:
We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments.
Answer:
Pretty sure its the Transitive Property
Step-by-step explanation:
It's a dropdown on Edge so there's no A B C or D
To prove that point C is the midpoint of segment AB, we apply the segment addition property and the definition of congruent segments.
Explanation:To prove that point C is the midpoint of segment AB, we can use the segment addition property. We are given that AB = 12 and AC = 6. By applying the segment addition property, we get AC + CB = AB. Substituting the given values, we have 6 + CB = 12. Solving for CB using the subtraction property, we find that CB = 6.
Now, by using the symmetric property, we can see that 6 = AC. Since CB = 6 and 6 = AC, we can conclude that AC is congruent to CB by the definition of congruent segments. This implies that C is the midpoint of AB, as it divides AB into two congruent segments.
Which undefined geometric term is described as a location on a coordinate plane that is designated by an ordered pair, (x, y)?
What is two times a number n is three times the sum of n and nine
Is it possible to draw a graph of this system? If yes, draw it.
[tex] \left \{ {{3x-1=0} \atop {4x+2y=0}} \right. [/tex]
Thanks in adavance!
Determine if the statement is always, sometimes or never true. A natural number is a whole number.
A professional basketball player makes 80 % of the free throws he tries. assuming this percentage will hold true for future attempts, find the probability that in the next 8 tries, the number of free throws he will make is exactly 8.
Se the change of variables s=xy, t=xy^2 to compute \iint_r xy^2\,da, where r is the region bounded by xy=3,\ xy=7,\ xy^2=3,\ xy^2=7.
The value of [tex]\int\limits^._R {xy^2} \, dA[/tex] is 16.
What is integration?The calculation of an integral is called integration. In math, many useful quantities like areas, volumes, displacement, and so on can be found using integrals. When we discuss integrals, we typically refer to definite integrals. Antiderivatives make use of the indefinite integrals. Apart from differentiation, one of the two major calculus topics in mathematics is integration.
Given xy =3, xy = 7,
xy² = 3, xy² = 7
s = xy and t = xy²
dividing t by s we get
t/s = xy²/xy
y = t/s
and x = s/y = s²/t
now differentiate x and y partially with respect to s and t
∂x/∂s = 2s/t
∂x/∂t = -s²/t²
∂y/∂s = -t/s²
∂y/∂t = 1/s
The Jacobian is
∂(x, y)/∂(s, t) = [tex]\left|\begin{array}{ccc}dx/ds&dx/dt\\dy/ds&dy/dt\end{array}\right|[/tex]
∂(x, y)/∂(s, t) =[tex]\left|\begin{array}{ccc}2s/t&-s^{2}/t^{2} \\-t/s^{2} &1/s\end{array}\right|[/tex]
∂(x, y)/∂(s, t) =2/t - 1/t
∂(x, y)/∂(s, t) = 1/t
so for [tex]\int\limits^._R {xy^2} \, dA[/tex] = [tex]\int\limits^a_b \int\limits^a_b {t}\frac{d(x, y)}{d(s, t) } \, dsdt[/tex]
for (s, t) (3 ≤ s ≤7, 3 ≤ t ≤ 7)
= [tex]\int\limits^7_3 \int\limits^7_3 {t}*1/t } \, dsdt[/tex]
= [tex]\int\limits^7_3ds \int\limits^7_3 dt[/tex]
=[s]₃⁷ [t]₃⁷
= (7 - 3)(7 - 3)
= 16
Hence the value is 16.
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Multiply. (7x+3)(4x−5) Enter your answer, in standard form, in the box.
(7x+3) x (4x-5)
7x*4x = 28x^2
7x*-5 = -35x
3+4x = 12x
3*-5 = -15
so you get 28x^2 -23x -15
Answer: The required multiplied expression is [tex]28x^2-23x-15.[/tex]
Step-by-step explanation: We are given to multiply the following linear factors and write the answer is standard form :
[tex]M=(7x+3)(4x-5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following distributive property :
[tex](a+b)(c+d)=a(c+d)+b(c+d).[/tex]
From (i), we get
[tex]M\\\\=(7x+3)(4x-5)\\\\=7x(4x-5)+3(4x-5)\\\\=28x^2-35x+12x-15\\\\=28x^2-23x-15.[/tex]
Thus, the required multiplied expression is [tex]28x^2-23x-15.[/tex]
2 sides of an isoceles triangle are 2 and 12. find the length of the third side
The third side of the isosceles triangle with the given sides of 2 and 12 is 12 units.
To find the length of the third side of an isosceles triangle where two sides are given as 2 and 12, we must consider two cases.
In an isosceles triangle, two sides are equal in length and the two angles opposite these sides are also equal. This means either the two given sides are the equal sides, which is not possible since they are different lengths, or one of the given lengths will be the base and the equal sides are yet to be determined.
Case 1: If the side of length 2 is the base, the length of the equal longer sides will both be 12.
Case 2: If the side of length 12 is the base, then the length of the two equal sides must both be 2.
However, we must recognize that the first case is incorrect because it does not form a triangle (a triangle cannot have two sides of length 12 and one side of length 2, as the two longer sides would be parallel and never meet to form a triangle).
Therefore, the correct answer is given by Case 2: the third side of the triangle, which is the base, is 12 units long, and the two equal sides are 2 units long each.
ray OJ bisects angle IOK, if angle IOJ= 2x-5 and measure of angle JOK=x+11, then find measure of angle IOJ
Given ray OJ bisects angle IOK, we can set an equation for angles IOJ and JOK, solve for x and substitute x into the given measure of angle IOJ: 2*(16)-5 equals 27 degrees.
Explanation:Since ray OJ bisects angle IOK, it means that angle IOJ and angle JOK are equal in measurement. Given in the problem, angle IOJ= 2x-5 and angle JOK= x+11. Because they are equal, we can set up the equation 2x-5 = x+11.
To solve for x, we subtract x from both sides of the equation, resulting in x-5 =11. And then, if we add 5 to both sides of the equation, the end result is x = 16.
Substituting x into the given measurement for angle IOJ, which is 2x-5, we would get the measure of angle IOJ as 2*(16)-5 = 27 degrees.
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A donkey weighs 570 pounds and an elephant weighs 5 tons. How much more does the elephant weigh?
The correct answer is:
5 tons = 10,000 lb
10,000 lb − 570 lb = 9,430 lb = 4 tons and 1,430 lb
This answer is if you want it in tons and pounds.
can you please explain to me which functions are odd?
f(x)=-1/2x^4+5
f(x)=-8x^3+5x
f(x)=-4/x^3-x+1
f(x)=x^5/x^4-1
f(x)=-sqrt2x
f(x)=3sqrtx -x^3
thank you!
How many license plates can be made using 3 digits and 4 letters if repeated digits and letters are not allowed?
Two cards are drawn at random without replacement from a standard 52-card deck. what is the probability we see at least one club and at least one ace?
The probability we see at least one club and at least one ace would be 0.019225
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
The Total number of cards in a deck = 52
Number of aces in a standard deck = 4
Number of clubs in a standard deck = 13
The Probability = required outcome / Total possible outcomes
P(ace) = 4 / 52 = 0.0769
P(club) = 13 / 52 = 1/4 = 0.25
Therefore, the probability we see at least one club and at least one ace
0.0769 x 0.25
= 0.019225
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The sum of two numbers is 68 . the smaller number is 12 less than the larger number. what are the numbers?
Final answer:
To solve the problem, we defined two variables for the larger (x) and smaller (y) numbers. Using the provided information, we set up two equations and solved them to find the numbers: x (the larger number) is 40, and y (the smaller number) is 28.
Explanation:
Step-by-Step Solution to Find the Two Numbers
Let's denote the larger number as x and the smaller number as y. We are given two pieces of information:
The sum of the two numbers is 68.
The smaller number is 12 less than the larger number.
These two statements can be turned into two equations:
x + y = 68 (Equation 1)
y = x - 12 (Equation 2)
Now, we can substitute Equation 2 into Equation 1 to find x:
x + (x - 12) = 68
2x - 12 = 68
Add 12 to both sides:
2x = 80
Divide both sides by 2:
x = 40
Now that we know the larger number, x, we can find y using Equation 2:
y = 40 - 12
y = 28
So, the two numbers are 40 and 28
HELP ME PLEASE ! I NEED TO DO THIS QUICKLY !!!!! Translate each sentence into an equation!!!!!!!!!!!! 7 berries are 5 less than twice them number of berries Mickey had for lunch! AND also another one Negative 4 times the difference of a number and 7 is 12
Using exponents what is the simplified form of the expression 12x^5/6x^2
The required simplified form of the expression 12x⁵/6x² is 2x³.
What are exponential expressions?Exponential expressions, as the name indicates, involve exponents. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. To answer the exponential expressions, we may need to apply the relationship between exponents and logarithms.
The exponential expression is given in the question as:
12x⁵/6x²
To simplify the expression 12x⁵/6x², we can start by dividing 12 by 6 to get:
12x⁵/6x² = (12/6)x⁵/x² = 2x⁵/x²
Then, we can use the quotient of powers rule, which states that when we divide two powers with the same base, we can subtract the exponents to get:
2x⁵/x² = 2x⁵⁻² = 2x³
Therefore, the expression is 2x³ equivalent to the given expression 12x⁵/6x².
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