Write the equation of the line that passes through the points
(3,-2) and (6, 1).
y=x-5
y = 5x + 1
y = -x + 5
Answer:
It is y = x - 5
Step-by-step explanation:
General equation of a line:
[tex]{ \bf{y = mx + c}}[/tex]
m is the gradient, and c is y-intercept.
For gradient:
[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1}} [/tex]
substitute:
[tex]slope = \frac{1 - ( - 2)}{6 - 3} \\ \\ = \frac{3}{3} \\ slope \: = 1[/tex]
m = 1
for y-intercept:
consider point (6, 1):
[tex]y = mx + c \\ 1 = (6 \times 1) + c \\ 1 = 6 + c \\ c = 1 - 6 = - 5[/tex]
therefore:
[tex]{ \sf{equation \: is \: \{y = x - 5 \}}}[/tex]
A man is37years old and his child is eight.how many years ago was the product of their ages 96 as in quadratic equation step by step
Answer:
5 years
Step-by-step explanation:
Let x be the unknown numer of years ago when the product of the man and his child's age was 96.
》 x years ago, the man's age = 37 - x
the child's age = 8 - x
(37 - x)(8 - x) = 96
296 - 37x - 8x + x² = 96
x² - 45x - 296 - 96 = 0
x² - 45x - 200 = 0
x² - 5x - 40x - 200 = 0
x(x - 5) -40(x - 5) = 0
(x - 5)(x - 40) = 0
x = 5 years ago or x = 40 years ago
but x = 40 > son's present age.
Thus, x = 5.
Therefore, 5 years ago the product of the ages of the man and his child was 96.
Two-thirds a numberx plus 4 is 8.
Answer:
n = 6
Step-by-step explanation:
To solve this you can use an equation such as:
[tex]\frac{2}{3} n+4=8\\\\[/tex]
We need to so for n. Subtract 4 from both sides to get the variable (n) alone. 4 - 4 and 8 - 4 equals:
[tex]\frac{2}{3}n=4[/tex]
So now we divide both sides by 2/3.
This now equals:
[tex]n=6[/tex]
Find the minimum value of the function:
f(x) = x2 + 9x – 16.
1. Write each of these products as a quadratic
expression of the form x2+bx+c. That is, write
each product in standard form.
a. (x+3)(x + 5)
b. (x – 4)(x + 7)
C. (x-6)(x - 2)
Step-by-step explanation:
maybe I am wrong sorry for that but try to understand it
have a great day
someone help me asap
Answer:
19/20 cups
Step-by-step explanation:
Add the amounts together
1/4 + 7/10
Get a common denominator of 20
1/4 *5/5 + 7/10 *2/2
5/20 + 14/20
19/20
Answer:
19/20
Step-by-step explanation:
find a common denominator then do the same with the numerator then add.
-2(-6n-3)-8=82 solve for n
Answer:
n = 7
Step-by-step explanation:
-2(-6n-3)-8=82,
12n + 6 - 8 = 82,
12n -2 = 82,
12n = 84,
n = 7
Answer:
n=7
Step-by-step explanation:
-2(-6n-3)-8=82
Add 8 to both sides
-2(-6n-3)-8+8=82+8
Simplify
-2(-6n-3)=90
Divided both sides by -2
-2(-6 -3) = 90
2 -2
Simply
-6n-3=-45
Add 3 to both sides
-6n-3+3=-45+3
Divided both side by -6
-6n = -42
-6. -6
Simply
n=7
Find the output, y, when the input, s, is – 7.
y =
y
1
8+
6+
4+
2+
个
CC
-8
-6
-4
-2
2
4
6
8
-2-
M
-4-
-6+
-8
Answer:
school:
cleaned class rooms and background
cooking equipment are laboratory tested of being germs free and also bacteria free
community: clean environment
Step-by-step explanation:
what is the opposite of 7 plus the opposite of 9
Answer:
-7.11111111111
Step-by-step explanation:
HELPPP!!!!!!
How far is weather station A from the storm?
44.6 miles
19.7 miles
42.2 miles
31.2 miles
This value is approximate.
============================================================
Explanation:
Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.
Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.
Based on those two interior angles, angle C must be...
A+B+C = 180
107+42+C = 180
149+C = 180
C = 180-149
C = 31
----------------
To sum things up so far, we have these known properties of triangle ABC
angle A = 107 degreesside c = side AB = 24 milesangle B = 42 degreesangle C = 31 degreesLet's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).
b/sin(B) = c/sin(C)
b/sin(42) = 24/sin(31)
b = sin(42)*24/sin(31)
b = 31.1804803080182 which is approximate
b = 31.2 miles is the distance from the storm to station A
Make sure your calculator is in degree mode.
The weather station A is 31.2 miles from the storm
From the triangle shown:
m<B = 90° - 48°
m<B = 42°
m<A = 17° + 90°
m<A = 107°
m<A + m<B + m<C = 180° (Sum of angles in a triangle)
107° + 42° + m<C = 180°
m<C = 180° - 149°
m<C = 31°
The distance between the weather stations A and B = 24 miles
That is, AB = 24 miles
The storm is at point C
The length AC is found by using the rule of sines:
[tex]\frac{sinC}{AB}=\frac{sinB}{AC} \\\\\frac{sin31}{24}=\frac{sin42}{AC} \\\\\frac{0.515}{24} = \frac{0.669}{AC} \\\\0.02146=\frac{0.669}{AC}\\\\AC=\frac{0.669}{0.02146} \\\\AC=31.2 miles[/tex]
The weather station A is 31.2 miles from the storm
Learn more on sine rule here: https://brainly.com/question/4372174
if m<8= 23° find each measure.
straight angles ( 1 , 2 , 3 , 4 ) parallel to straight angles Angles ( 5 , 6 , 7 , 8 )
m<8 = m< 6 = 23° [ Opposite angles]
m< 4 = m< 2 = 23°
m<8 + m< 5 = 180°
23° + m< 5 = 180°
m<5 = 180 - 23 = 157
m< 5 = m< 7 = 157° [ Opposite angles]
m< 1 = m< 3 = 157° [ Opposite angles]
straight angles ( 1 , 2 , 3 , 4 ) parallel to straight angles Angles ( 5 , 6 , 7 , 8 )
So;m< 1 = 157m< 2 = 23m< 3 = 157m<4 = 23m< 5 = 157m< 6 = 23m< 7 = 157m< 8 = 23I hope I helped you^_^
please help me will mark braniliest
Answer:
The correct answer is option A. Line DB
Step-by-step explanation:
When you write that M is a line, the sign for this would be a line with arrows on both of its end like this : <------------>
Now, due to the fact that lines look like this <------------>, we can cross out option C and D as they both aren't lines but points. Points go like this: ---->
Option B says, "line EB", this can't be true because E corresponds with the letter F, it can't become a line with B hence why the only option true here is choice A.
Can someone pls help me with problems 4 and 5 pls this is due in a bit and I’m in a rush I’ll give 100 points it’s all I have
Answer:
Step-by-step explanation:
Answer:
#4Let M is the midpoint of DE.
Since D is at 8 and DE = 5.
DM = ME = 5/2 = 2.5
Point M is at:
8 + 2.5 = 10.5 if E is to the right of D8 - 2.5 = 5.5 if E is to the left of D#5Given
XY = 7, YZ = 2x - 1, XZ = 30Since XZ = XY + YZ, set up an equation and solve for x:
7 + (2x - 1) = 302x + 6 = 302x = 24x = 12#6The distance from your house to friend's is LN.
We have:
M is midpoint of LN, so LM = MNLM = 3xMN = 2x + 2Set up an equation, solve for x:
3x = 2x + 23x - 2x = 2x = 2Find the distance LM:
LM = 3*2 = 6Find the distance LN:
LN = 2*LM = 2*6 = 12polygons are similar find the scale factor of the smaller figure to the larger figure
Answer:
Step-by-step explanation:
Help me bro like this is difficult
Is 15.7 an integer ,whole number,natural number
Using the graph, find the equation of the line in slope-intercept form.
What is the slope-intercept form of the equation of the line?
y =
Answer:
y = 2x + 2
BRAINLIEST, PLEASE!
Step-by-step explanation:
(-2, -2) (-1, 0)
y = mx + b (m = slope, b = y-intercept)
m = rise/run = change in y / change in x
change in y: +2
change in x: + 1
change in y/change in x = 2/1 = 2
m = 2, y = 2x + b
We can plug -1 in for x, and 0 in for y.
0 = 2(-1) + b
0 = -2 + b
b = 2
y = 2x + 2
Answer:
y = 2x + 2
Step-by-step explanation:
(−2x + 8) + (−8x^2− 8x)
Answer:
-8x^2 -10x + 8
Step-by-step explanation:
there is no multiplying just adding
Which numbers in set A = ( -7,-4, 2, 14, 21,34, 42) are elements of b and c, shown below? Set b= ( even numbers) set c: ( multiples of 7) enter answers from largest to smallest.
Answer:
(14, 42)
Step-by-step explanation:
(-4, 2, 14, 34, 42) are all elements of b, and (-7. 14, 21, 42) are all elements of c. (14, 42) are the only elements that are in both sets
2(k + 1) = -4(k - 2)
Answer:
1
Step-by-step explanation:
2(k + 1) = -4(k - 2)
2k + 2 = --4k+8
2k+4k=8-2
6k=6
k=6/6
k=1
Alicia has 8 more dollars than Fred. Altogether, Alicia and Fred have 26. dollars. Let "f" represent the amount of money, in dollars, that Fred has. Use "f" to write an expression that represents the amount of money that Fred has.
Use “f” to write an expression that represents the amount of money that Alicia has.
Write de equation to represent the problem situation
Solve your equitation showing each step of the solution
Based on your solution to your equation, state how much money Fred has
Based on your solution to your equation, state how much money Alicia has
Answer:
Fred has = 9 $
Alicia has = 9 + 8 =17 $
Step-by-step explanation:
Let, Fred has = f $
Then, Alicia has = f + 8 $ ;[as Alicia has 8 more dollars than fred]
Now, the required expression is
∴[tex]f+(f+8)=26\\=>2f+8=26\\=>2f=18\\f=9[/tex]
So, Fred has = 9 $
Alicia has = 9 + 8 =17 $
Hope you have understood this.....
ask me if you have any confusion.....
if you liked it pls mark it as the brainliest
What is the reference angle for 283°?
3 Factorise 5y - 6py
Step-by-step explanation:
5y-6py
y(5-6p)
Answer
hope it helps
Answer:
5y - 6py
y(5-6p)
is the answer
What is the equation of the line graphed below?
5
(2, 1)
O A. y=-2x
B. y -
C. y = 2x
o D. y = 1/2 x
Answer:
C. Y=2x
Step-by-step explanation:
I hope this help you
X
6.
The table shows all the possible sums when rolling two number cubes numbered 1
What is the probability that rolling two cubes results in a sum of 8P
6
1
2
3
4
5
6
7
1
2
3
4
5
6
2 3 4 5
3 4 5 6
4 5 6 7
5 6 7 8
6 7 8 9
7 8 9 10
8 9. 10 11
7
8
9
10
11
12
Done
Answer:
Step-by-step explanation:
You can roll an 8 in the following ways
3 - 5
5 - 3
4 - 4
6 - 2
2 - 6
That's 5 ways that it can be done. There are a total of 36 ways to throw 2 dice.
The probability of getting an 8 is 5/36
How would I prove the congruency of these triangles?
Step-by-step explanation:
the radius cuts the segment into two equal parts because it is perpendicular to the chord
Answer:
Step-by-step explanation:
As O is the mid point of the circle
Similarly, B also becomes the mid point of the line AC.
So, line OB divides AB and BC equally.
Hence, lines AB = AC, but they are asking to prove congruency of triangles.
So, u have to join OA and OC.
Same way, line OB divides ∠OBA and ∠OBC.
So it is proved that AB = AC
Find the distance between the points (-16, 10) and (4, 10).
Help plz I pay 5 bucks if you solve this
Answer:
20
Step-by-step explanation:
The distance formula is just
[tex]d = \sqrt{(x2-x1)^2+(y2-y1)^2} \\d = \sqrt{(-16-4)^2+(0)^2}\\d = \sqrt{(-20)^2} \\d = \sqrt{400} \\d = 20[/tex]
7. Is 5.787787778... a rational or irrational number?
Explain.
Answer:
Irrational
Step-by-step explanation:
Its irrational as it has no pattern of numbers after decimal point and the number are infinite
Answer:
irrational because it has a coma after one number
Pls answer this It will help me understand this question
r:-
[tex]\\ \rm\hookrightarrow r+60+50=180[/tex](Supplementary)
[tex]\\ \rm\hookrightarrow r+110=180[/tex]
[tex]\\ \rm\hookrightarrow r=180-110[/tex]
[tex]\\ \rm\hookrightarrow r=70[/tex]
p:-[tex]\\ \rm\hookrightarrow p=50(Opposite\: angles)[/tex]
q:-
[tex]\\ \rm\hookrightarrow q=70+60(Opposite \:angles)[/tex]
[tex]\\ \rm\hookrightarrow q=130[/tex]
Answer:
[tex]{ \sf{60 \degree + r + 50\degree = 180\degree}} \\ { \sf{ \{angles \: on \: straight \: line \}}} \\ { \sf{r + 110\degree = 180\degree}} \\ { \underline{ \sf{r = 70\degree}}}[/tex]
[tex]{ \sf{q + 50\degree = 180\degree}} \\ { \sf{ \{angles \: on \: straight \: line \}}} \\ { \sf{q = 180\degree - 50\degree}} \\ { \underline{ \sf{q = 130\degree}}}[/tex]
[tex]{ \sf{p + q = 180\degree}} \\ { \sf{ \{angles \: on \: straight \: line \}}} \\ { \sf{p + 130\degree = 180\degree}} \\ { \sf{ \underline{p = 50\degree}}}[/tex]
or:
[tex]{ \underline{ \sf{p = 50\degree \: \{alternate \: angles \}}}}[/tex]
María va de compras a una tienda departamental y adquiere los siguientes productos: 2 pantalones, 4 blusas, 3 pares de calcetas y 2 pares de tenis. El precio de los artículos por unidad es: pantalones $ 600.00, blusas: $350.00, calcetas: $120.00 y tenis: $ 950.00. Si María contaba con $5000.00, calcula cuánto dinero le sobró después de las compras realizadas.
Answer:
Pantalones = $600.00 × 2
$ 1,200.00
Blusas = $350.00 × 4
$ 1,400.00
Calcetas = $120.00 × 3
$ 360.00
Par de tenis = $950.00 × 2
$ 1,900.00
Total a pagar = $4,850.00
$5,000.00
- $4,860.00
Sobrante = $140.00