Answer:
y = - x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (4, - 1)
m = [tex]\frac{-1-5}{4+2}[/tex] = [tex]\frac{-6}{6}[/tex] = - 1, thus
y = - x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (4, - 1 ), then
- 1 = - 4 + c ⇒ c = - 1 + 4 = 3
y = - x + 3 ← equation of line
Irum is sitting on the beach, watching the tide go in and out. Irum's distance from the shoreline (in meters) as a function of time (in hours) is graphed. What is the approximate average rate at which Irum's distance from the shoreline increases, between the 9th and the 13th hour marks?
Answer:
Hi, the Answer is 0.75.
Step-by-step explanation:
it is 0.75 because if you look on the graph, and you calculate the 3/4 slope between the two, 3/4= 0.75
Answer:
A) 0.75 meters per hour
Step-by-step explanation:
Complete the equation: x2 + 10x + ___ = 2
Hope anybody can help me to solve it...
Answer:
7.8 cm
Step-by-step explanation:
Let's find the volume of the water bottle first. The radius is 5.5/2 = 2.75 cm
V = πr²h = 3.14 * 2.75² * 20 = 474.925 cm³
If we call the minimum side length of the cube as x we can write:
x³ = 474.925 because the volume of the cube is x * x * x = x³
x ≈ 8 cm
Considere a equação 5x + 5 = 4x - 2. a) substituindo x por -7 e efetuando os cálculos, mostre que -7 é a solução da equação. b) agora mostre que 5 não e a solução da equação.
Responda:
Explicação passo a passo:
Dê = n a equação 5x + 5 = 4x - 2, para mostrar que x = -7 é a solução, as seguintes etapas devem ser seguidas.
Etapa 1: Subtraia 5 de ambos os lados da equação
5x + 5 - 5 = 4x - 2 - 5
5x = 4x - 7
Etapa 2: Subtraia 4x de ambos os lados da equação resultante
5x = 4x - 7
5x - 4x = 4x - 7 - 4x
x = -7
Isso prova que a solução é x = -7
b) Para mostrar que 5 não é a solução, substituiremos x = 5 em ambos os lados da equação e verificaremos se são iguais ou não. Se eles não são iguais, significa que 5 não é uma solução.
Para o lado direito da equação, ou seja, 5x + 5
f (5) = 5 (5) + 5
f (5) = 25 + 5
f (5) = 30
Para o lado esquerdo da equação, ou seja, 4x-2
f (5) = 4 (5) - 2
f (5) = 20-2
f (5) = 18
Como os dois valores não são os mesmos, [tex]30\neq 18[/tex] ou seja, isso mostra que 5 não é uma solução
look at the image and answer it
Answer:
The circumference of circle is 14π cm.
Step-by-step explanation:
Given that the formula of circumference is C = 2×π×r where r represents radius of circle. In this case, diameter of circle is 14cm so the radius will be 7cm. Then, you have to substitute the value into the formula :
[tex]c = 2 \times \pi \times r[/tex]
[tex]let \: r = 7[/tex]
[tex]c = 2 \times \pi \times 7[/tex]
[tex]c = 14\pi \: \: cm[/tex]
Answer:
14[tex]\pi[/tex]
units = cm
Step-by-step explanation:
circumference = 2 x [tex]\pi[/tex] x r
c = 2 x [tex]\pi[/tex] x 7 - it's 7 because the diameter is 14 and radius is half the diameter
c = 14 x [tex]\pi[/tex]
c = 43.98229715
in terms of pi c = 14 [tex]\pi[/tex]
units = cm
Find the coefficient of fourth term of (-x -3)^5
Answer:
-270
Step-by-step explanation:
Here, we want to know the coefficient of the fourth term.
The coefficients according to pascal triangle for the expansion is 1 5 10 10 5 1
So the expansion looks as follows;
1[(-x)^5(-3)^0] + 5[(-x)^4(-3)^1)] + 10[(-x)^3(-3)^2) + 10[(-x)^2(-3)^3] + ...........
So the fourth term we are dealing with is
10[(-x)^2(-3)^3)]
So the value here is
10 * x^2 * -27
= -270 x^2
So the coefficient is -270
Two numbers are in the ratio 3: 7. If 1 is added to the smaller number and 7 is added to the larger, they will be in the ratio 1: 3. Find the numbers.
Answer:
6 and 14
Step-by-step explanation:
The numbers are in the ratio 3 : 7 = 3x : 7x (x is a multiplier )
adding 1 to smaller number is 3x + 1 and 7 to the larger is 7x + 7, then
3x + 1 : 7x + 7 = 1 : 3
Expressing the ratio in fractional form
[tex]\frac{3x+1}{7x+7}[/tex] = [tex]\frac{1}{3}[/tex] ( cross- multiply )
3(3x + 1) = 7x + 7
9x + 3 = 7x + 7 ( subtract 7x from both sides )
2x + 3 = 7 ( subtract 3 from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
Thus the numbers are
3x = 3(2) = 6
7x = 7(2) = 14
A ball, thrown vertically upwards, from the ground, has its height h (in meters) expressed as a function of time t (in seconds), elapsed after the launch, by the law h(t) = 20t - 5t2. According to this information, determine the height at which the ball is 3 seconds after the throw and the maximum height reached by the ball.
Answer:
a. 15 meters.
b. 20 meters.
Step-by-step explanation:
a. The height of the ball at 3 seconds. 20 * 3 - 5 * (3)^2 = 60 - 5 * 9 = 60 - 45 = 15.
The ball will be 15 meters high.
b. The maximum height reached by the ball.
To get that, we need to find the vertex of the parabola. We do so by doing -b/2a to find the x-coordinate of the vertex.
In this case, a = -5 and b = 20.
-20 / 2(-5) = -20 / -10 = 20 / 10 = 2.
Then, we find the y-coordinate by putting 2 where it says "t".
h(2) = 20(2) - 5(2)^2 = (40) - 5(4) = 40 - 20 = 20 meters.
Hope this helps!
Answer:
pen
Step-by-step explanation:
The scale on a map indicates that 1 cm represents 50 km. If two cities are 400 km apart, then how far apart would the cities be on this map?
Answer:
8 cm apart
Step-by-step explanation:
First, let's consider our unit rate.
1 cm = 50 km
Next, divide 400 km (the distance between two cities) by 50 (the unit rate).
400/50 = 8 km
There you go! The two cities are 8 km apart!
Hope this helps you and maybe earns a brainliest!!
Bye!
If two cities are 400 km apart. Then the length of distance between the cities on this map will be 8cm.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
The scale on a map indicates that 1 cm represents 50 km.
Then the scale factor will be 1/50.
If two cities are 400 km apart.
Then the length of distance between the cities on this map will be
⇒ 400 x (1/50)
⇒ 8 cm
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ2
Geometry help? prove triangle PQR~ triangle TSR
Answer:
Step-by-step explanation:
The third step's reason is given. Then you must make <QRP and <SRT congruent because all right angles are congruent. Then you have two angles in each triangle congruent and can thus prove the triangles congruent by AA.
Which ordered pair is a solution if the equation? 2x + 3y = 10
Answer:
See below.
Step-by-step explanation:
Try each ordered pair in the equation. Each ordered pair is of the form (x, y). Replace x and y in the equation by values of x and y, respectively, in each ordered pair. Whichever ordered pair makes the equation a true statement is the answer.
For example:
Try (2, 3):
2x + 3y = 10
2(2) + 3(3) = 10
4 + 9 = 10
13 = 10
Since 13 = 10 is a false statement, (2, 3) is not a solution.
Try (2, 2):
2x + 3y = 10
2(2) + 3(2) = 10
4 + 6 = 10
10 = 10
Since 10 = 10 is a true statement, (2, 2) is a solution.
Find the equation of the line passing through the point (–1, –2) and perpendicular to the line y = –1∕2x + 5. Choices are in the attachment...
Help is appreciated. Easy I just am always confused
Answer:
BA=BC
Step-by-step explanation:
how to find out the value of the lettered sides
Step-by-step explanation:
asin 46°= a/12.8
a = sin46° * 12.8 = 9.20
bcos59°=b/16.8
b = cos59°*16.8 = 8.65
Answer:
a = 9.2b = 8.65Step-by-step explanation:
First Question
To find a we use sine
sin ∅ = opposite / hypotenuse
a is the opposite
12.8 is the hypotenuse
sin 46 = a / 12.8
a = 12.8 sin 46
a = 9.2Second question
To find b we use cosine
cos∅ = adjacent / hypotenuse
b is the adjacent
16.8 is the hypotenuse
cos 59 = b / 16.8
b = 16.8 cos 59
b = 8.65Hope this helps you
Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
Simplify [Q - R] + [S - T].
10m - 7n - 14
10m + 5n - 24
10m - 5n + 24
10m + 7n - 14
Answer:
The answer is 10m + 7n - 14
Step-by-step explanation:
Q = 7m + 3n
R = 11 - 2m
S = n + 5
T = -m - 3n + 8
[Q - R] + [S - T] is
[ 7m + 3n - (11 - 2m) ] + [ n + 5 - ( - m - 3n+8)]
Solve the terms in the bracket first
That's
( 7m + 3n - 11 + 2m ) + ( n + 5 + m + 3n - 8)
( 9m + 3n - 11 ) + ( m + 4n - 3)
Remove the brackets
That's
9m + 3n - 11 + m + 4n - 3
Group like terms
9m + m + 3n + 4n - 11 - 3
The final answer is
10m + 7n - 14Hope this helps you
Can someone help me with this question please.
Answer:
98
Step-by-step explanation:
3 bed house= 33 rooms
4 bed house 40 rooms
4 bed house 25 rooms
each house is worth 2 houses. so u double everything
hope I got it right
Identify the relationship (complementary, linear pair/supplementary, or vertical) and find the measure of angle b in the image below.
Answer:
complementary
b = 45 deg
Step-by-step explanation:
Angles b and 45-deg are complementary since their measures ad to 90 deg.
45 + b = 90
b = 45
Answer:
Complementary
45°
Step-by-step explanation:
b + 45° = 90°
b = 90° - 45°
b = 45°
What are the solutions to the system of equations graphed below?
Answer:
B) (2,0) and (0,-4)
Step-by-step explanation:
The answer to the system of equations is where the two intersect on the graph, in this case on the points (2,0) and (0,-4)
help me asap please i dont understand
Answer:
We have 2 rational solutions
0 irrational solutions
0 complex solutions
Step-by-step explanation:
a^2 + 8a + 12 = 0
Using the discriminant
b^2 -4ac where ax^2 + bx+ c
so a =1 b = 8 and c = 12
8^2 -4(1)*12
64 - 48
16
Since the discriminant is greater than 0, we have 2 real solutions
since we can take the square root of 16, we have rational solutions
We have 2 rational solutions
Since this is a quadratic equations, there are only 2 solutions so there are
0 irrational solutions
0 complex solutions
Answer:
2 Rational Solutions
0 Irrational Solutions
0 Complex Solutions
Step-by-step explanation:
The discriminant of the quadratic formula is the name given to the portion underneath the radical (or the square root)"
[tex]x = \frac{1}{2} (-b\frac{ + }{ - } \sqrt{ {b}^{2} - 4ac })[/tex]
Discriminant = D = b²-4ac
If D is less than 0 you have two complex solutions.
If D is equal to 0 you'll have one real solution.
If D is bigger than 0 you'll get two real solutions.
So here we have:
a=1
b=8
c=12
Which means D=64-4(1)(12)=64-48=16>0
D is bigger than 0, so you'll have two real solutions. And since 16 is a perfect square, they'll both be rational numbers.
rapezoid FGHI is shown below. Trapezoid F G H I. Sides F G and I H are parallel. Which sides of the trapezoid are parallel? Side F G and Side I H Side G H and Side F I Side G H and Side I H Side F G and Side G H
Answer:
Side F G and Side I H
Step-by-step explanation:
No picture attached but from the description, we got:
Trapezoid F G H I
F G ║I H
Which sides of the trapezoid are parallel?
Side F G and Side I H - yes, already given as parallelSide G H and Side F I - no, non-parallel opposite sidesSide G H and Side I H - no, intersect on point HSide F G and Side G H- no, intersect on point GAnswer:
the top answer is correct
Step-by-step explanation:
Help, please!!! What is the mN?
Answer:
61°
Step-by-step explanation:
Given:
∆MNO,
Side MO (n) = 18
MN (o) = 6
m<O = 17°
Required:
m<N
Solution:
Using the sine rule, [tex] \frac{sin N}{n} = \frac{sin O}{o} [/tex] , solve for N.
Plug in the values of M, n, and m
[tex] \frac{sin N}{18} = \frac{sin 17}{6} [/tex]
Cross multiply
[tex] 6*sin(N) = sin(17)*18 [/tex]
[tex] 6*sin(N) = 0.292*18 [/tex]
Divide both sides by 6
[tex] \frac{6*sin N}{6} = \frac{0.292*18}{6} [/tex]
[tex] sin N = \frac{0.292*18}{6} [/tex]
[tex] sin N = \frac{5.256}{6} [/tex]
[tex] sin N = 0.876 [/tex]
[tex] N = sin^-1(0.876) [/tex]
[tex] N = 61.16 [/tex]
m<N ≈ 61°
Can somebody please help me!!
Step-by-step explanation:
Simply you replace X and Y by their values
Given: x=-1 y=-4
10 - (-X)^3 + y^2
=10 + X^3 + Y^2
Now replace X and Y
=10 + (-1)^3 + (-4)^2
=10 - 1 + 16
= 25
Find the center and radius of the circle x2 + y2 –6y – 16 = 0
Answer:
centre=(0,3) radius =5
Step-by-step explanation:
What is the slope of the line given by the equation y=-3X?
A. 1/3
B. -1/3
C. -3
D. 3
Answer:
[tex]\boxed{-3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation is determined by the constant equation [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept of the line.
Therefore, we can use the equation given and implement it to find your slope.
[tex]y=-3x[/tex]
Our equation does not have a y-intercept, [tex]b[/tex]. Therefore, it can just be inferred as [tex]+0[/tex].
Because we do have a [tex]m[/tex], we can then find out what our slope is: [tex]\boxed{-3}[/tex].
– StartFraction 5 Over 3 EndFraction v plus 4 equals 8 minus StartFraction 1 Over 3 EndFraction v.(6x – 3) = –
Answer:
v=11/5 or v=2.2
Step-by-step explanation:
The wording of this question is a little confusing but if it says what I think it does (5/3v+4=8-1/3) then this is the answer.
Which equation represents a circle with a center at (2,-3) and a radius of 11
Answer:
x^2-4x+y^2+6y-108=0
Step-by-step explanation:
[tex]The- equation- of- circle- with -center- at- (h,k) -and -a -radius- of- r -is: \\(x-h)^2 +(y-k)^2 = r^2\\h = 2 , \\ k = -3\\r = 11\\(x-2)^2+(y-(-3))^2 = 11^2\\(x-2)^2+(y+3)^2 = 121\\x^2-4x+4 +y^2+6y+9 = 121\\x^2 -4x+y^2+6y+4+9=121\\x^2 -4x+y^2+6y+13=121\\x^2 -4x+y^2+6y=121-13\\x^2 -4x+y^2+6y= 108\\x^2 -4x+y^2+6y-108 = 0[/tex]
A soda factory has a special manufacturing line to fill large bottles with 2 liters of their beverage. Every process is computerized. However, it doesn't always fill exactly 2 liters. It follows a normal distribution, with a mean of 1.98 liters and a variance of 0.0064 liters. If the amount of soda in a bottle is more than 1.5 standard deviations away from the mean, then it will be rejected.
Find the probability that a randomly selected bottle is rejected.
a. 0
b. 0.07
c. 0.04
d. 0.13
e. 0.19
PLEASE HELP ASAP don’t have much time.
Answer: 4
Step-by-step explanation:
numerator - denominator
Numerator: w¹³ Denominator: w⁸ · w¹
13 - (8 + 1)
13 - 9 = 4
What else would need to be congruent to show that ABC was DEF by ASA
Answer:
ABC≅DEF ASA POSTULATE
There must be two angles and one side of ABC congruent to DEF
Step-by-step explanation:
Answer:
BC=EF
Step-by-step explanation:
Process of elimination and I just took the test so trust me.
Raymond works for an architecture firm. His company has a contract to design a building on a rectangular plot of land that has an area of 421,808 square meters. The plot of land is 328 meters wide. What is the length of the plot?
Answer:
1286 meters long
Step-by-step explanation:
421,808 divided by the width of the plot gives you 1,286 meters for the width.