Step-by-step explanation:
Using FOIL, we have
(x + 2)(x² - 3x + 4)
= (x³ - 3x² + 4x) + (2x² - 6x + 8)
= x³ - x² - 2x + 8.
Dave found the blueprint of his house. It shows the hallway is 4 inches long. If the scale factor is 1 inch: 1.25 feet, then what is the length of the hallway in real life?
Answer:
5 feet
Step-by-step explanation:
The scale factor = 1 inch: 1.25 feet
The length of the Hally = 4 inches
The length of the hallway in real life is calculated as:
1 inch = 1.25 feet
4 inches = x feet
Cross Multiply
x feet = 4 × 1.25 feet
x feet = 5 feet
Therefore, the length of the Hallway in real life is 5 feet
Two cruise ships leave the same port with a 35° angle between their path. Cruise A is traveling at 18 miles per hour and Cruise B is traveling at 15 miles per hour. If they travel in a straight path, find the distance between the cruise ships after 2 hours
Answer:
[tex]20\:\mathrm{miles}[/tex]
Step-by-step explanation:
After travelling two hours, the two cruise ships form a triangle. One of the legs of this triangle will be the distance Cruise A travelled, and another will be the distance Cruise B travelled. We can find the distance they travel using:
[tex]s=\frac{d}{t}, d=s\cdot t[/tex]
Cruise A is travelling at 18 miles per hour for 2 hours. Therefore, Cruise A has travelled:
[tex]d=s\cdot t=18\cdot 2=36\:\mathrm{miles}[/tex]
Cruise B is travelling at 15 miles per hour for 2 hours. Therefore, Cruise B has travelled:
[tex]d=s\cdot t=15\cdot 2=30\:\mathrm{miles}[/tex]
Because we are given the angle between these legs, we can use the Law of Cosines to find the third leg. The Law of Cosines is given by:
[tex]c^2=a^2+b^2-2ab\cos C[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are interchangeable. Let [tex]c[/tex] represent the distance between the two cruises. We have:
[tex]c^2=36^2+30^2-2\cdot36\cdot30\cdot \cos 35^{\circ},\\c^2=426.63,\\c\approx \fbox{$20\:\mathrm{miles}$}[/tex](one significant figure).
9514 1404 393
Answer:
20.7 miles
Step-by-step explanation:
The distance that A travels in the same direction as B is ...
(18 mi/h)(2 h)cos(35°) = 29.489 mi
So, the difference in distances in that direction is ...
(15 mi/h)(2 h) -29.489 mi = 0.511 mi
__
The distance A travels in the direction perpendicular to B is ...
(18 mi/h)(2 h)sin(35°) = 20.649 mi
So, the straight-line distance between the ships is the hypotenuse of the right triangle with these distances as legs:
AB = √(0.511² +20.649²) = √426.632 . . . miles
AB = 20.655 miles ≈ 20.7 miles . . . separation after 2 hours
Halfway through the bowling season, Will had 32 strikes. He averages 2.5
strikes per game. Which inequality would be used to find the number of
games that it will take for Will to have at least 68 strikes?
Answer:
67
Step-by-step explanation:
IM NOT SUPER SURE
SOMEONE PLEASE HELP ME ANSWER THIS QUESTION
Answer:
We have height as a function of time:
x = tme, y = height
Our two points are: (2, 400), (6, 700)
Rate of change = slope
m = (700-400)/(6-2) = 300/4 = 75 ft per hour
Step-by-step explanation:
hope this helps please give brainiest
Can someone please answer quick there’s a math test and I only have one minute to answer this question please it’s my last question.
Answer:
The equation of the line in slope-intercept form is:
y = 3/5x + 5
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the slopeb is the y-interceptTaking two points
(-5, 2)(5, 8)Taking two points (-5, 2) and (5, 8) to determine the slope
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-5,\:2\right),\:\left(x_2,\:y_2\right)=\left(5,\:8\right)[/tex]
[tex]m=\frac{8-2}{5-\left(-5\right)}[/tex]
Refine
[tex]m=\frac{3}{5}[/tex]
We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
From the graph, it is clear
at x = 0, y = 5
Thus, the y-intercept b = 5
now, substituting b = 5 and m = 3/5 in the slope-intercept form of the line equation
y = mx+b
y = 3/5x + 5
Therefore, the equation of the line in slope-intercept form is:
y = 3/5x + 5
write an equation in slope-intercept form of the line perpendicular to y= -1/5x + 1/4 that passes through the point (3,4)
Answer: y=5x-11
Step-by-step explanation:
y=5x-11 is the equation of the line perpendicular to y= -1/5x + 1/4 that passes through the point (3,4).
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given equation of line is y= -1/5x + 1/4
The slope of the perpendicular line is 5.
We need to find line perpendicular to y= -1/5x + 1/4 that passes through the point (3,4)
4=5(3)+b
-11=b
Hence, y=5x-11 is the equation of the line perpendicular to y= -1/5x + 1/4 that passes through the point (3,4).
To learn more on slope of line click:
https://brainly.com/question/14511992
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6у = 8 - 9 + 6y
solve for y
Answer:
No solution exists
Step-by-step explanation:
PLEASE HELP! NEED HELP NOWWWW!!!! PLS! HELPPPP
Write the linear equation for the following word problem:
Tickets for the school play are $4 in advance and 5$ at the door. Total ticket sales were $440
Which expressions are equivalent?
A.
B.
C.
D.
An equilateral triangle has a perimeter of 12x + 33. What is the length of each side of the triangle?
Answer:
4x + 11
Step-by-step explanation:
Here all sides of the triangle have the same length. Thus, if the Perimeter is 12x + 33, and there are three sides, then the length of one side is
12x + 33
------------- = 4x + 11
3
ummmmmmmmmmmmmmmmmmm
Answer:
x=120
Step-by-step explanation:
This shape has 6 sides. It is a 720 degree shape.
to find an angle just get 720 divided by 6
720/6=
120
A test of a new car results in 490 miles on 10 gallons of gasoline. Calculate the unit rate of miles per gallons. Sentence Frame: The new car test indicates ____ per ____.
Answer:
the answer is 49 miles per gallon
When our family went out to dinner, the bill came to $55.75. There was 7%
tax and we left a 20% tip. Find the total price.
A.$15.05
B.$40.70
C.$82.75
D.$70.80
Simplify the expression to a polynomial in standard form:
(3x – 10)(x2+ 2x - 1 )
Answer:
[tex]3x ^{3} - {4}^{2} - 23x + 10[/tex]
Find the value of X
help asap plz
Answer:
12!! Glad I could help!!
Answer:
D) 12
Step-by-step explanation:
I would say that this is 12 because the angle x looks the same as the other shown angle.
Hope it helps!
Caleb rides his horse with a constant speed of 10 miles per hour. How long will he take to travel a distance of 15 miles?
Answer:
1 hour and 30 minutes
Step-by-step explanation:
Answer:
1 hour and 30 minutes
Step-by-step explanation:
15 is 10+1/210 1/2 is also known as 1515 miles at a constant of 10 miles per hour then equals 1 hour and a half 1 hour and 30 minutesWhat is the approximate area of the circle shown below?
Answer:
c
Step-by-step explanation:
Solve: 6^2х-3 = 6^-2x+1 x = -1 х = 0 x= 1 х = 4
Answer:
[tex] \huge \boxed {x = 1}[/tex]
Step-by-step explanation:
Both bases are the same so you will be able to solve the equation from exponent and exponent.
[tex]2x - 3 = - 2x + 1 \\ 2x + 2x = 1 + 3 \\ 4x = 4 \\ x = 1[/tex]
Answer Check
Substitute x = 1 in the equation.
[tex] {6}^{2(1) - 3} = {6}^{ - 2(1) + 1} \\ {6}^{2 - 3} = {6}^{ - 2 + 1} \\ {6}^{ - 1} = {6}^{ - 1} [/tex]
Both are same each sides. Therefore the equation is true.
Right answer gets brainlist.
Answer:
2309
Step-by-step explanation:
V=[tex]\pi r^{2} h[/tex]
plug in
V=2309.07
My guys do you thing giving brainliest!!!!
Answer:
Length = 49 feet
Step-by-step explanation:
Since 35/5 is equal to 7, that means for every inch on the drawing it represents 7 feet. So you could multiply 7(7) to get the actual length.
Which is an incorrect rounding for 53.864?
54
53.87
50
53.9
Answer: 50
Step-by-step explanation:
X
An airplane climbs at an angle of
16° with the ground. Find the
ground distance the plane travels
as it moves 2500 m through the
air.
Help me
Answer:
[tex]2403\:\mathrm{m}[/tex]
Step-by-step explanation:
We can form a right triangle and use trigonometry for a right triangle to solve this. The ground distance the plane travels is its displacement in the x-direction. The 2500 meters the plane moves through represents the hypotenuse of right triangle, and the ground distance is the adjacent leg of the [tex]16^{\circ}[/tex] angle. Therefore, we set up the following equation:
[tex]\cos 16^{\circ}=\frac{x}{2500}[/tex], where [tex]x[/tex] is the ground distance.
Solving, we get [tex]x=2500\cdot \cos 16^{\circ} \approx \fbox{$2403\:\mathrm{m}$}[/tex].
Round this “0.7660444431”into 4 decimals places!!!!!
Answer:
.7660
Step-by-step explanation:
when you get to 0 at 7660 you round with the number next to it if its 5 or bigger you add a one to the number since 4 isn't greater than or equal to 5 than your numbers stay the same
An 8 ft tall tent standing next to a man casts a 16 ft shadow. If the man is 6 ft tall, then how long is his shadow?
Answer:
The man's shadow is 12 feet long.
Step-by-step explanation:
In this question, we are given that an 8 foot tall tent casts a 16 foot shadow, and we are asked the calculate the length of the shadow a 6 foot tall man casts.
To solve this problem, find the relationship between 8 and 16- 16 is twice as much as 8, as 8 x 2 = 16.
From this we have: "The shadow of an object is twice as long as the object."
We can use this to calculate the length of the shadow for a 6 foot tall man. Since the height of the man is 6 feet, the length of his shadow would be 12 feet.
Let me know if this helps!
Find the difference (5x3-3x+6) - (2x2-4x+8)
Answer:
wait 3x+6?????
Step-by-step explanation:
Answer:
5x^3 -2x^2+x-2
Step-by-step explanation:
Either Table L or Table M shows a proportional relationship.
Table
X
-1
0
1
2
у
-2
0
2.
4
Table M
х
-1
0
1
2.
y
0
6
9
Answer:
M
Step-by-step explanation:
The table of x, y values for a proportional relationship show that y is 0 when x is 0. This applies to the second table (M).
How would the equilibrium change if the temperature were increased in
SO2(g) + NO2(9) = NO(g) + S03(g) + heat?
A. Only the reaction rate would change.
B. The equilibrium constant would decrease.
C. The amount of NO and SO3 would increase.
D. The amount of NO2 and SO2 would increase.
Answer:
D. The amount of NO2 and SO2 would increase.
Step-by-step explanation:
This is an exothermic reaction as Heat is among the products. Increasing the temperature would lead to more products in the reaction system. In order for the system to annul this change, more reactants would be formed.
The correct option is;
D. The amount of NO2 and SO2 would increase.
helpp me i need to get a 67 as my grade because i dont understand
Answer:
6.5 minutes
Step-by-step explanation:
Divide T (total number of minutes) by M (total number of miles)
Answer:
6.5Step-by-step explanation:
10 miles/65 minutes
65 minutes/10 miles
you need to find minutes per mile
Divide (Total number of Minutes) by (Total number of miles)
65/10=6.5
Tres maquinas (A,B,C) producen el 40 % , 35% y 25 % respectivamente , del total de las piezas manufacturadas en una fabrica .Los porcentajes de produccion defectuosa de estas maquinas son del 3% 4 % y 5 % respectivamente
Answer:
La probabilidad de que la pieza elegida sea defectuosa, P(D), 0.0385
La máquina con mayor probabilidad de haber producido la pieza defectuosa es A
Step-by-step explanation:
Sea D= "la pieza es defectuosa" y N= "la pieza no es defectuosa". La información del problema puede expresarse en el diagrama de árbol adjunto.
Para calcular la probabilidad de que la pieza elegida sea defectuosa, P(D), por la propiedad de la probabilidad total,
P(D) = P(A) · P(D/A) + P(B) · P(D/B) + P(C) · P(D/C) =
= 0.40 · 0.03 + 0.35 · 0.04 + 0.25 · 0.05 = 0.0385
Debemos calcular P(B/D). Por el teorema de Bayes,
P(B/D)= P(B) x P(D/B) / P(A) x P(D/A) + P(B) x P(D/B) +P(C) x P(D/C)
= 0.35 · 0.04 / 0.40 · 0.03 + 0.35 · 0.04 + 0.25 · 0.05
Calculamos P(A/D) y P(C/D), comparándolas con el valor de P(B/D) ya calculado. Aplicando el teorema de Bayes, obtenemos:
0.012
0.0385
P(A/D)= 0.311
0.014
0.0385
P(B(D)=0.363
0.0125
0.0385
P(C/D)=0.324
La máquina con mayor probabilidad de haber producido la pieza defectuosa es A
hi can u guys help me pla
Answer:
yes
Step-by-step explanation: