Answer:
1)
[tex]\text{ Slope = -3}[/tex]
2)
[tex]y+4=-\frac{7}{8}(x-7)[/tex]
3)
[tex]y=-\frac{7}{8}x+\frac{17}{8}[/tex]
Step-by-step explanation:
We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.
1)
First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:
[tex]m=\frac{3-(-4)}{-1-7}[/tex]
Subtract. So, our slope is:
[tex]m=\frac{7}{-8}=-7/8[/tex]
2)
Now, let's use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:
[tex]y-(-4)=-\frac{7}{8}(x-7)[/tex]
Simplify. So, our point-slope equation is:
[tex]y+4=-\frac{7}{8}(x-7)[/tex]
3)
Finally, we want to convert this into slope-intercept form. So, let's solve for our y.
On the right, distribute:
[tex]y+4=-\frac{7}{8}x+\frac{49}{8}[/tex]
Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:
[tex]y=-\frac{7}{8}x+\frac{49}{8}-\frac{32}{8}[/tex]
Subtract. So, our slope-intercept equation is:
[tex]y=-\frac{7}{8}x+\frac{17}{8}[/tex]
And we're done!
Answer: Shown Below
Step-by-step explanation:
1. -7/8
2. y+4= (-7/8)(x-7)
3. y=(-7/8)x+ (17/8)
Just did it
UGH ONLY EXPERT GIVE ME ANSWER PPL DO WRONG ANSWERS Find the number of rectangles in 6×6 chessboard. ITS NOT 36
Answer:
I think it is 441
Step by step explanation:
To make a rectangle you need to pick any two of the vertical lines, and any two of the horizontal lines. So there would be 91 squares and 441 rectangles.
Write the equations after translating the graph of y = | 1 /2 x−2|+3 one unit down,
Answer:
[tex]y=|\frac{1}{2} x-2|+2[/tex]
Step-by-step explanation:
If your original function is:
[tex]y=|\frac{1}{2} x-2|+3[/tex]
the translation of its graph vertically down one unit, can be obtained by simply subtracting 1 from the whole functional expression:
[tex]y=|\frac{1}{2} x-2|+3-1=|\frac{1}{2} x-2|+2[/tex]
determine which function has the greatest rate of change as x approaches infinity
f(x)= 2^x- 10
g(x)=16x-4
h(x) = 3x^2-7x+8
there is not enough information to determine the answer
Answer:
f(x)= 2^x-10
Step-by-step explanation:
Exponential functions are ALWAYS greater in the long run!
Answer:
A) f(x) = 2^x − 10
Step-by-step explanation:
I graph all of these functions and f(x) = 2^x − 10 surpasses the other two functions. Exponential growth functions always exceed linear growth functions over time.
A person stands 12 meters east of an intersection and watches a car driving away from the intersection to the north at 4 meters per second. At a certain instant, the car is 9 meters from the intersection. What is the rate of change of the distance between the car and the person at that instant (in meters per second)?
Answer: the rate of change of the distance between the car and the person at that instant is 4 meters per second
Step-by-step explanation:
According to the Pythagorean theorem, we have:
d^2 = (12^2 + 9^2)
Differentiating both sides with respect to time:
2d * (dd/dt) = 0 + 2(9) * (9''), Simplifying the equation, we get:
2d * (dd/dt) = 2(9) * (9'')
Substituting the given values:
2d * (dd/dt) = 2(9) * (4) [the car is moving at a constant velocity of 4 m/s]
Simplifying further:
2d * (dd/dt) = 72
we divide both sides by 2d:
dd/dt = 72 / (2d)
substitute this value into the equation to find the rate of change of the distance:
dd/dt = 72 / (2 * 9) = 4 m/s
The rate of change of the distance between the car and the person at that instant is -12/5 meters per second.
Given information:
The person is standing 12 meters east of the intersection.
The car is driving away from the intersection to the north at a constant speed of 4 meters per second.
At a certain instant, the car is 9 meters from the intersection.
Using the Pythagorean theorem, determine D(t) in terms of the car's distance from the intersection, which we'll call x(t).
Since the person is 12 meters east of the intersection, the distance D(t) can be expressed as:
[tex]D(t) = \sqrt{(x(t)^2 + 12^2)[/tex]
Differentiating both sides of the equation with respect to time, we get:
[tex]dD/dt = (1/2) * (x(t)^2 + 12^2)^{(-1/2)} * 2x(t) * dx(t)/dt[/tex]
So, dx(t)/dt = -4
Substituting this value into the equation for dD/dt, we have:
[tex]dD/dt = (1/2) * (x(t)^2 + 12^2)^{(-1/2)} * 2x(t) * (-4)[/tex]
[tex]dD/dt = -4x(t) / \sqrt{(x(t)^2 + 144)[/tex]
At the instant when the car is 9 meters from the intersection, substitute x(t) = 9 into the equation:
[tex]dD/dt = -4(9) / \sqrt{(9^2 + 144)[/tex]
= -36 / √(81 + 144)
= -36 / √225
= -36 / 15
= -12/5
Therefore, the rate of change is -12/5 meters per second.
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why is it important to break down the radical into its prime factor?
Answer:
The prime factors of a number are all the prime numbers that, when multiplied together, equal the original number. You can find the prime factorization of a number by using a factor tree and dividing the number into smaller parts.
Step-by-step explanation:
A particular movie theater charges $7.00 per adult and $4.50 per child. Suppose 450 people attended a movie and the total revenue from ticket sales was $2650. Write linear equations for the two constraints, where z represents the number of adults attending the
movie and y represents the number of children attending the movie. 1= ,2=?
Answer:
7z + 4.5y = 2650
z + y = 450
Step-by-step explanation:
The first equation represents the amount of money made from ticket sales for both adult and child tickets.
The second equation represents the amount of customers, both adult and child, that attended the theatre.
Using both equations you cans find the number of adults and children that attended the theatre.
Cheers.
-----------------------------------------------------
Edit: Solving for the variables
There are two easy ways to solve for these values. The first is using an augmented matrix and solving with that method.
7 4.5 | 2650
1 1 | 450
After are augmented matrix is set up, we simply use row operations on the matrix to solve for 1s on the diagonal.
The second method for solving is equation addition or variable substitution to solve for each variable.
7z + 4.5y = 2650
z + y = 450
7(450-y) + 4.5y = 2650
3150 - 7y + 4.5y = 2650
-2.5y = -500
y = 200
Plug back in y into one of the equations to solve for z.
z + 200 = 450
z = 250
So there were 250 adults and 200 children.
Find the measure of y.
When solving this system of linear equations with the elimination method,
you can multiply the bottom equation by 3.
3x +6y - 38
3( 5x - 2y) = 3(-30)
This step works because of the
O A. commutative property
O B. multiplication property of equality
O C. distributive property
O D. addition property of equality
Answer:
B.
Step-by-step explanation:
Multiplication property of equality.
A simple example is
x = x Multiply by 3:
3x = 3x
This step works because of the distributive property - option C.
System of Linear EquationsSystem of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
Properties of MultiplicationThe properties of multiplication are:
Distributive: a(b±c)= ab±acComutative: a . b = b. aAssociative: a(b+c)= c(a+b)Identity: b.1=bFor the given system linear system was used the distributive property. Because it was used as a common factor to multiply an expression with a sum.
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In a particular year, a total of 44,064 students studied in two of the most popular host countries when traveling abroad. If 8382 more students studied in the most popular host country than in the second most popular host country, find how many students studied abroad in each country. There were _______ students who studied abroad in the most popular host country.
Answer:
The answer would be 35066 :)
Step-by-step explanation:
(y+5554) + y = 64578
Combine like terms
2y = 64578-5554
2y = 59024
y = 29512
x = 29512 + 5554 = 35066
The graph of F(x), shown below, has the same shape as the graph of
G(x) = x2. Which of the following is the equation of Fx)?
ASAP
Answer:
B. f(x) = x^2 -2
Step-by-step explanation:
The graph of f(x) is the graph of g(x) moved down 2 units, so is ...
f(x) = g(x) -2
f(x) = x^2 -2
_____
Adding a constant to the value of a function moves the graph vertically by the value of the added constant.
Use the Venn diagram to list the elements of the set in the roster form
Answer:
Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!
Step-by-step explanation:
Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!
Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!
What is the Domain and Range *DON'T FORGET PARENTHESES AND BRACKETS*
Answer:
D= {-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6}
R={-6,-5,-4,-3,-2,-1,1,2,5)
Step-by-step explanation:
A cylinder has a volume of 675.1 cubic centimeters. The diameter of the cylinder is 10 cm. What is the height of the cylinder? (Assume = 3.14)
Answer:
8.6 cm
Step-by-step explanation:
V=pi r-squared h
diameter of 10 means radius of 5
675.1=3.14x5x5xh
675.1=78.5h
8.6
The factorization of x2 + 3x – 4 is modeled with algebra tiles. An algebra tile configuration. 2 tiles are in the Factor 1 spot: 1 is labeled + x, 1 is labeled negative. 5 tiles are in the Factor 2 spot: 1 is labeled + x and 4 are labeled +. 10 tiles are in the Product spot: 1 is labeled + x squared, 1 is labeled negative x, the 4 tiles below + x squared are labeled + x, and the 4 tiles below the negative x tiles are labeled negative. What are the factors of x2 + 3x – 4? (x + 4) and (x – 4) (x + 3) and (x – 4) (x + 4) and (x – 1) (x + 3) and (x – 1)
Answer:
[tex]\Large \boxed{(x+4)(x-1)}[/tex]
Step-by-step explanation:
Hello,
[tex]x^2+3x-4\\\\\text{*** The product of the zeroes is -4=-1*4 and their sum is -3=-4+1. ***}\\\\\text{*** So we can factorise. ***}\\\\x^2+3x-4=x^2-x+4x-4=x(x-1)+4(x-1)=\large \boxed{(x+4)(x-1)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The factors of given function are (x + 4) and (x - 1)
To undestand more, check below explanation.
Factors of function:The modeled for algebra tiles is given as,
[tex]f(x)=x^{2} +3x-4[/tex]
We have to find the factors of given function.
Factoring means finding expressions that can be multiplied together to give the given equation.
If a quadratic equation can be factored, it is written as a product of linear terms.
[tex]f(x)=x^{2} +3x-4\\\\f(x)=x^{2} +4x-x-4\\\\f(x)=x(x+4)-1(x+4)\\\\f(x)=(x+4)(x-1)[/tex]
Hence, the factors of given function are (x + 4) and (x - 1)
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PLEASE HELPPPPPPPPP!!! Graph the line that represents a proportional relationship between d and t with the property that an increase of 3 units in t corresponds to an increase of 4 units in d. What's the unit rate of change of d with respect to t? (That is, a change of 1 unit in t will correspond to a change of how many unites in d?) The unit rate is _____? Graph the relationship.
Answer:
Draw a straight line through these two points (0, 0) and (1, 3).
Step-by-step explanation:
"Proportional relationship" implies line or curve that goes through the origin; there is no "y-intercept" in this case.
Plot a dot at (0, 0). Next, move your pencil point 1 unit to the right (you'll end up at (1, 0), and then move it from there up to (1, 3). Draw a straight line through these two points (0, 0) and (1, 3).
Answer:
The unit rate of change of d with respect to t is 4/3.
The graph should be: (0,0) and (3/4).
Step-by-step explanation:
I got it wrong on khan academy :/
so i went over here and answer it
Multiply 4/5 × 3/20. in simplest form
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▹ Answer
3/25
▹ Step-by-Step Explanation
[tex]\frac{4}{5} * \frac{3}{20} \\\\= \frac{12}{100} \\\\\frac{12}{100} divide each side by 4\\\\\frac{12}{100} \\\\= \frac{3}{25}[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
*PLEASE ANSWER ASAP TY* Which of the following statements best describes a segment of a circle? a.) A segment is a portion of a sector that is bound by a chord and the major arc formed by that chord. b.) A segment is a portion of a sector that is bound by a radius and the minor arc formed by that radius. c.) A segment is a portion of a sector that is bound by a radius and the major arc formed by that radius. d.) A segment is a portion of a sector that is bound by a chord and the minor arc formed by that chord.
Answer: D
Step-by-step explanation:circle by a secant or a chord
A segment of a circle can best be described as: D. A segment is a portion of a sector that is bound by a chord and the minor arc formed by that chord.
What is a Segment of a Circle?The segment of a circle can be described as the region that is covered or surrounded by a chord and the corresponding arc that lies at both endpoints of the chord.
An example of a segment of a circle is shown in the picture attached below.
Therefore, the statement that best describes a segment of a circle is: D. A segment is a portion of a sector that is bound by a chord and the minor arc formed by that chord.
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Rectangle GHJK is rotated 180º using the origin as the center of rotation. What are the coordinates of the image’s point K after the rotation? On a coordinate plane, rectangle G H J K has points (2, negative 3), (8, negative 3), (8, negative 7), (2, negative 7). (–2, 7) (–7, –2) (–7, 2) (2, 7)
Answer:
(-2,-7)
Step-by-step explanation:
Answer:
-2,-7
Step-by-step explanation:
In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answer: 16384
Step-by-step explanation:
Given: Total marbles = 7 (All are distinct)
Total jars = 4
Assume that, the jar is empty.
When we put marbles in the jar, we need to choose jar each time.
For each marble, total choices = Total jars = 4
Then, by using the fundamental counting principle,
The number of ways to put seven marbles in different colors into four jars =
[tex]4^7[/tex]
= 16384
Hence, the required number of ways =16384
Answer:
your answer is 16384
Step-by-step explanation:
have a nice day.
Which value is equivalent to 7 multiplied by 3 multiplied by 2 whole over 7 multiplied by 5, the whole raised to the power of 2 multiplied by 7 to the power of 0 over 5 to the power of negative 3, whole to the power of 3 multiplied by 5 to the power of negative 9?
Answer:
36/25
Step-by-step explanation:
((7*3*2)/7*5)^2 * ((7^0)/(5^-3))^3 * 5^-9
(42/35)^2 * (1/5^-9) * 5^-9
36/25 * 5^9 * 5^-9
36/25 * 5^(9-9)
36/25 * 1
Answer:
35/25
Step-by-step explanation:
i hope this helps
Help please I will name the Brainily answer
Answer:
B
Step-by-step explanation:
So, for five cups of water, you need one cup of sugar. 1s=5w.
Now, you divide both sides by five.
1/5s=1/w
Find the magnitude of the vector.
(-2,-7)
Answer:
[tex]\sqrt{53}[/tex]
Step-by-step explanation:
[tex]\begin{pmatrix}-2&-7\end{pmatrix}\\=\sqrt{\left(-2\right)^2+\left(-7\right)^2}\\\\[/tex]
Then you need to simplify:
[tex]=\sqrt{2^2+\left(-7\right)^2}\\=\sqrt{2^2+7^2}\\=\sqrt{4+7^2}\\=\sqrt{4+49}\\=\sqrt{53}[/tex]
Answer:
53
Step-by-step explanation:
Pls help with this question thank u all
Answer:
4 cm (A)
Step-by-step explanation:
triangle BAC is just a larger version of triangle EAD. given that ED is 5cm, and BC is 10cm, triangle BAC must be twice the size of EAD. since the ratio of AD to ED is 4:5, and BC is twice the size, all we need to do is multiply both sides by 2 to find length AC. 4*2 = 8. now we can subtract length AD from AC to get CD. 8 - 4 = 4.
sorry if what i wrote is a little confusing
plz help me i have a fever and i don't want to do math
Answer:
Four books because there are the most dots over that spot on the bottom number line thingy
Find the value of x in the isosceles triangle shown below.
Answer:
x=10
Step-by-step explanation:
We can use the Pythagorean theorem to find x
The height meets the base at a right angle
The base is bisected ( cut in half) so the base is 6 the height is 8
a^2 + b^2 = c^2
6^2 + 8^2 = x^2
36+64 = x^2
100 = x^2
Taking the square root of each side
sqrt(100) = sqrt(x^2)
10 = x
Answer:
10
Step-by-step explanation:
This triangle is divided into 2 identical rigth triangles.
We will use the pythagorian theorem:
●8^2+ (12/2)^2 =x^2
● 64 + 36 = x^2
● x= 10
So x is 10
At Paul Bunyan’s tree farm they sell Fraser firs and blue spruce trees. They plant saplings of these two kinds of trees that are 8 inches in 5 inches tall, respectively. The Fraser firs grow at a constant rate of 12 inches per year, and a blue spruce trees grow at a constant rate of 14 inches per year. After how many years will these trees be at the same height? Express your answer as a common fraction.
Answer: 3/2
Step-by-step explanation:
Hi, to answer this question we have to write the next expressions::
Height 1= 8 +12 y
Height 2 =5 +14y
Where y = number of years
Since both heights must be the same
Height 1 = height 2
8+12y = 5+14y
solving for y:
8-5 =14y-12y
3 = 2y
3/2 =y
y = 3/2 years
Feel free to ask for more if needed or if you did not understand something.
8 + 12y = 5 + 14y
12y + 8 = 14y + 5
12y + 8 - 8 = 14y + 5 - 8
12y = 14y - 3
12y - 14y = 14y - 3 - 14y
-2y = -3
(-2y)/-2 = -3/-2
y = 3/2
Which of the following equations have exactly one solution? Choose all answers that apply:
A -13x+12=13x+13
B -13x+12=13x-13
C 12x+12=13x+12
D 12x+12=13x-12
I need correct answer and description, so I can put Brainliest
Answer:
a
b
c
d
Step-by-step explanation:
Well lets look,
a)
If both slopes are different and have different y intercepts they have 1 solution.
So a has 1 solution
b)
Both slopes are different with different y intercepts.
1 solution
c)
Both slopes are different with different y intercepts
1 solution
d)
Different slopes different y intercepts
1 solution.
For proof look at the images below.
Thus,
the answer is a,b,c, and d.
Hope this helps :)
HELPPPP FIRST GET BRAINLLEST Measure the difference between the lower quartile of Data Set A and the lower quartile of Data Set B. Round to the nearest tenth when performing all operations.
Answer:
26
Step-by-step explanation:
Let's find first the lower quartile in both A and B
steps:
look for the smallest sum of two consecutive numbers divide by 2 to get the lower quartile A73 and 75 are the smallest consecutive numbers
73+75 = 148 148/2 =74The lower quartile in A is 74
B47 and 49 are the smallest consecutive numbers
47+49 = 9696/2 = 48The lower quartile in B is 48
74-48 = 26Answer:
29
Step-by-step explanation:
To find the lower quartile of each you need to find the median to split them into 2 groups (upper and lower quartile).
Lower quartile of Set A: 73, 75, 79, 81, 84, 85
Lower quartile of Set B: 47, 49, 51, 51, 55, 56
Now you find the median of the 2
Set A: 80
Set B: 51
Lastly you subtract A & B and get 29
Match each solution to the equation it solves.
Hi there! Hopefully this helps!
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Answer to the first equation: 3.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer to the second equation: 7
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer to the third equation: -2.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer to the fourth equation: -3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer:
3
7
-2
-3
Step-by-step explanation:
in that exact order
If a function f has an inverse function, then fis one-to-one.
A) True
B) False
Answer:
true
Step-by-step explanation: