Answer:
The capacity of the remaining bottles = 4 pints.
Step-by-step explanation:
6*3 + 6*b = 42
6b = 42 - 18
6b = 24
b = 4.
The required quantity of the remaining 6 bottles is 4 pints.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Ben fills 42 pints of juice in 12 bottles. Six bottles have a capacity of 3 pints each.
Let b represent the capacity, in pints, of each of the remaining 6 bottles.,
Now,
42 = 3 × 6 + b × 6
42 = 18 + 6b
6b = 42 - 18
b = 24/6
b = 4
Thus, the required quantity of the remaining 6 bottles is 4 pints.
Learn more about models here:
https://brainly.com/question/22591166
#SPJ5
The pizza parlor is running a special on 3-toppings pizzas. The topping choices include pepperoni, sausage, bacon mushrooms, onions, green peppers, and black olives. The next customer who orders 3-topping pizza tells the chef to randomly choose 3 different toppings for their pizza. What is the probability that customer will get a pizza topped with pepperoni, mushrooms, green peppers? The teacher told us the solution is 1/35 but he wants an explanation of why is that solution correct.
Answer:
Well there are 6 toppings. For one person to select sausage, it is \frac{1}{6} . For two people, multiply them together and the probability is \frac{1}{36}
If f(x) = x^2 is vertically stretched by a factor of 6 to g(x) and reflected over the x-axis, what is the equation for g(x)?
A. g(x) = (-6x)^2
B. g(x) = -6x^2
C. g(x) = x^2-6
D. g(x) = -x^2+6
Answer:
Option B
[tex]g(x) = -6x^2[/tex]
Step-by-step explanation:
If the graph of the function [tex]g(x)=cf(x)[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
In this problem we have the function [tex]f(x)=x^2[/tex]
We now that this function is vertically stretched by a factor of 6 to g(x) and reflected over the x-axis
Then [tex]|c| =6 >0[/tex] and [tex]c=-6<0[/tex]
Therefore the graph of [tex]g(x)[/tex] is [tex]g(x) = -6f(x)[/tex]
[tex]g(x) = -6x^2[/tex]
In a certain region, the equation yˆ=19.485x+86.912 models the amount of a homeowner’s water bill, in dollars, where x is the number of residents in the home.
What does the slope of the equation represent in context of the situation?
The water bill increases by about $87 every month.
The water bill increases by about $19 every month.
The water bill increases by about $19 for every additional resident in the home.
The water bill increases by about $87 for every additional resident in the home
Answer:
The water bill increases by about $19 for every additional resident in the home
Step-by-step explanation:
This is because times x shows that it is to each and every person and it is increasing.
Answer:
The answer is C. The water bill increases by about $19 for every additional resident in the home.
Step-by-step explanation:
The equation above consists of y as the dependent variable, x as the independent variable, 19.485 as the slope, and 86.912 as the constant. The constant represent the fixed water bill. The x variable represents the additional water usage.
If she chooses a song to listen to at random, what is the probability that it will be a pop song? A) 1 5 B) 1 6 C) 2 15 D) 4 15
C because it would be the best amount
Answer:
d
Step-by-step explanation:
Which characteristic is correct for the function f(x)=−2x^3+3x ?
Answer:
Left ends is +ve infinity and Right end is -ve infinity. however both tends to be infinity.
Step-by-step explanation:
Let us under stand the basics of determining the end behavior of a graph , by just analyzing the degrees and coefficient of a polynomial.Please refer to the image we have shared with this for a better understanding also.
The rule is bifurcated in two broad category and and two sub category in them.
Category .
The nature of degree (Even / Odd )
Subcategory .
The coefficient of term containing degree ( Negative/Positive )
Rule 1 :
Degree : Even
If coefficient is
Rule 1(a) : Positive ⇒Both ends are towards +ve infinity
Rule 1(b) : Negative⇒Both ends are towards -ve infinity
Rule 2 :
Degree : Odd
If coefficient is
Rule 2(a) : Positive ⇒ Left ends is -ve infinity and Right end is +ve infinity
Rule 2(b) : Negative ⇒ Left ends is +ve infinity and Right end is -ve infinity
Let us see our function f(x) = [tex]-2x^3 + 3x[/tex] now
Here
Degree is 3 which is Odd
Its coefficient is (-2) which is negative
Hence we go to rule 2(b)
That is the Left ends is +ve infinity and Right end is -ve infinity. however both tends to be infinity.
For questions 2 and 4 calculate the perimeter and 4 questions 6/8 and 10 calculate the area
Answer:
Part 2) [tex]P=2[\sqrt{20}+\sqrt{45}]\ units[/tex] or [tex]P=22.36\ units[/tex]
Part 4) [tex]P=[19+\sqrt{17}]\ units[/tex] or [tex]P=23.12\ units[/tex]
Part 6) [tex]A=36\ units^{2}[/tex]
Part 8) [tex]A=16\ units^{2}[/tex]
Part 10) [tex]A=6.05\ units^{2}[/tex]
Step-by-step explanation:
we know that
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Part 2) we have the rectangle ABCD
[tex]A(-4,-4),B(-2,0),C(4,-3),D(2,-7)[/tex]
Remember that in a rectangle opposite sides are congruent
step 1
Find the distance AB
[tex]A(-4,-4),B(-2,0)[/tex]
substitute in the formula
[tex]AB=\sqrt{(0+4)^{2}+(-2+4)^{2}}[/tex]
[tex]AB=\sqrt{(4)^{2}+(2)^{2}}[/tex]
[tex]AB=\sqrt{20}\ units[/tex]
step 2
Find the distance BC
[tex]B(-2,0),C(4,-3)[/tex]
substitute in the formula
[tex]BC=\sqrt{(-3-0)^{2}+(4+2)^{2}}[/tex]
[tex]BC=\sqrt{(-3)^{2}+(6)^{2}}[/tex]
[tex]BC=\sqrt{45}\ units[/tex]
step 3
Find the perimeter
The perimeter is equal to
[tex]P=2[AB+BC][/tex]
substitute
[tex]P=2[\sqrt{20}+\sqrt{45}]\ units[/tex]
or
[tex]P=22.36\ units[/tex]
Part 4) we have the quadrilateral ABCD
[tex]A(-2,-3),B(1,1),C(7,1),D(6,-3)[/tex]
step 1
Find the distance AB
[tex]A(-2,-3),B(1,1)[/tex]
substitute in the formula
[tex]AB=\sqrt{(1+3)^{2}+(1+2)^{2}}[/tex]
[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]
[tex]AB=5\ units[/tex]
step 2
Find the distance BC
[tex]B(1,1),C(7,1)[/tex]
substitute in the formula
[tex]BC=\sqrt{(1-1)^{2}+(7-1)^{2}}[/tex]
[tex]BC=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]BC=6\ units[/tex]
step 3
Find the distance CD
[tex]C(7,1),D(6,-3)[/tex]
substitute in the formula
[tex]CD=\sqrt{(-3-1)^{2}+(6-7)^{2}}[/tex]
[tex]CD=\sqrt{(-4)^{2}+(-1)^{2}}[/tex]
[tex]CD=\sqrt{17}\ units[/tex]
step 4
Find the distance AD
[tex]A(-2,-3),D(6,-3)[/tex]
substitute in the formula
[tex]AD=\sqrt{(-3+3)^{2}+(6+2)^{2}}[/tex]
[tex]AD=\sqrt{(0)^{2}+(8)^{2}}[/tex]
[tex]AD=8\ units[/tex]
step 5
Find the perimeter
The perimeter is equal to
[tex]P=AB+BC+CD+AD[/tex]
substitute
[tex]P=[5+6+\sqrt{17}+8]\ units[/tex]
[tex]P=[19+\sqrt{17}]\ units[/tex]
or
[tex]P=23.12\ units[/tex]
Part 6) Calculate the area of rectangle ABCD
[tex]A(-1,5),B(3,5),C(3,-4),D(-1,-4)[/tex]
Remember that in a rectangle opposite sides are congruent
step 1
Find the distance AB
[tex]A(-1,5),B(3,5)[/tex]
substitute in the formula
[tex]AB=\sqrt{(5-5)^{2}+(3+1)^{2}}[/tex]
[tex]AB=\sqrt{(0)^{2}+(4)^{2}}[/tex]
[tex]AB=4\ units[/tex]
step 2
Find the distance BC
[tex]B(3,5),C(3,-4)[/tex]
substitute in the formula
[tex]BC=\sqrt{(-4-5)^{2}+(3-3)^{2}}[/tex]
[tex]BC=\sqrt{(-9)^{2}+(0)^{2}}[/tex]
[tex]BC=9\ units[/tex]
step 3
Find the area
The area is equal to
[tex]A=[AB*BC][/tex]
substitute
[tex]A=[4*9]=36\ units^{2}[/tex]
Part 8) Calculate the area of right triangle ABC
[tex]A(-3,3),B(-3,-1),C(5,-1)[/tex]
step 1
Find the distance AB
[tex]A(-3,3),B(-3,-1)[/tex]
substitute in the formula
[tex]AB=\sqrt{(-1-3)^{2}+(-3+3)^{2}}[/tex]
[tex]AB=\sqrt{(-4)^{2}+(0)^{2}}[/tex]
[tex]AB=4\ units[/tex]
step 2
Find the distance BC
[tex]B(-3,-1),C(5,-1)[/tex]
substitute in the formula
[tex]BC=\sqrt{(-1+1)^{2}+(5+3)^{2}}[/tex]
[tex]BC=\sqrt{(0)^{2}+(8)^{2}}[/tex]
[tex]BC=8\ units[/tex]
step 3
Find the distance AC
[tex]A(-3,3),C(5,-1)[/tex]
substitute in the formula
[tex]AC=\sqrt{(-1-3)^{2}+(5+3)^{2}}[/tex]
[tex]AC=\sqrt{(-4)^{2}+(8)^{2}}[/tex]
[tex]AC=\sqrt{80}\ units[/tex] -----> is the hypotenuse
step 4
Find the area
The area is equal to
[tex]A=(1/2)AB*BC[/tex]
substitute
[tex]A=(1/2)(4*8)=16\ units^{2}[/tex]
Part 10) Calculate the area of triangle ABC
[tex]A(3,0),B(1,8),C(2,10)[/tex]
step 1
Find the distance AB
[tex]A(3,0),B(1,8)[/tex]
substitute in the formula
[tex]AB=\sqrt{(8-0)^{2}+(1-3)^{2}}[/tex]
[tex]AB=\sqrt{(8)^{2}+(-2)^{2}}[/tex]
[tex]AB=\sqrt{68}\ units[/tex]
step 2
Find the distance BC
[tex]B(1,8),C(2,10)[/tex]
substitute in the formula
[tex]BC=\sqrt{(10-8)^{2}+(2-1)^{2}}[/tex]
[tex]BC=\sqrt{(2)^{2}+(1)^{2}}[/tex]
[tex]BC=\sqrt{5}\ units[/tex]
step 3
Find the distance AC
[tex]A(3,0),C(2,10)[/tex]
substitute in the formula
[tex]AC=\sqrt{(10-0)^{2}+(2-3)^{2}}[/tex]
[tex]AC=\sqrt{(10)^{2}+(-1)^{2}}[/tex]
[tex]AC=\sqrt{101}\ units[/tex]
step 4
we know that
Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.
Let
a,b,c be the lengths of the sides of a triangle.
The area is given by:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
where
p is half the perimeter
p=[tex]\frac{a+b+c}{2}[/tex]
we have
[tex]a=AB=\sqrt{68}=8.25\ units[/tex]
[tex]b=BC=\sqrt{5}=2.24\ units[/tex]
[tex]c=AC=\sqrt{101}=10.05\ units[/tex]
p=[tex]\frac{8.25+2.24+10.05}{2}=10.27\ units[/tex]
Find the area
[tex]A=\sqrt{10.27*(10.27-8.25)(10.27-2.24)(10.27-10.05)}[/tex]
[tex]A=\sqrt{10.27*(2.02)(8.03)(0.22)}[/tex]
[tex]A=6.05\ units^{2}[/tex]
At a deli, Aaron bought 2/3 of a pound of sliced turkey for $4.36. What is the unit price of sliced turkey at the deli? Round answers to the nearest cent.
$4.36 per pound
$6.54 per pound
$2.91 per pound
$5.03 per pound
$8.72 per pound
Answer:
$6.54 per pound
Step-by-step explanation:
we know that
To find the unit price divide the total cost by the total pounds
so
[tex]\frac{4.36}{(2/3)}=\frac{4.36*3}{2}=\$6.54\ per\ pound[/tex]
I have a flower vase with a 6 " diameter and is 12 " tall I want to fill it 2/3 of the way full how many cubic inches will I fill? Do not round your answer.
Answer:
[tex]72\pi\ in^{3}[/tex]
Step-by-step explanation:
step 1
Calculate the volume of the cylinder (flower vase)
The volume is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=6/2=3\ in[/tex] -----> the radius is half the diameter
[tex]h=12\ in[/tex]
substitute the values
[tex]V=\pi (3)^{2}(12)=108\pi\ in^{3}[/tex] ------> exact value
step 2
Calculate 2/3 of the volume
[tex]V=(2/3)108\pi=72\pi\ in^{3}[/tex]
If a cylinder has a height of 7 inches and a volume of 2908.33 in^3 find the radius
Answer:
The radius of the cylinder is [tex]11.5\ in[/tex]
Step-by-step explanation:
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]V=2,908.33\ in^{3}[/tex]
[tex]h=7\ in[/tex]
assume
[tex]\pi=3.14[/tex]
substitute the values and solve for r
[tex]2,908.33=(3.14)r^{2}(7)[/tex]
[tex]r^{2}=2,908.33/[(3.14)(7)][/tex]
[tex]r=11.5\ in[/tex]
Graph y=sin^-1 (1/4 x) on the interval -5≤x≤5.
Answer:
D
Step-by-step explanation:
The arcsine ([tex]\sin^{-1}[/tex]) function of x is defined as the inverse sine function of x when -1≤x≤1.
So, when
[tex]-4\le x\le 4,[/tex]
we have that
[tex]-1\le \dfrac{1}{4}x\le 1.[/tex]
This gives us the domain [tex]-4\le x\le 4[/tex] of the function [tex]y=\sin^{-1}\left(\dfrac{1}{4}x\right).[/tex]
The range of the function [tex]y=\sin^{-1}x[/tex] is [tex]-\dfrac{\pi }{2}\le x\le \dfrac{\pi }{2},[/tex] so the range of the function [tex]y=\sin^{-1}\left(\dfrac{1}{4}x\right)[/tex] is the same (options A and C are false).
When x=-4,
[tex]y=\sin^{-1}\left(\dfrac{1}{4}\cdot (-4)\right)=\sin^{-1}(-1)=-\dfrac{\pi}{2}.[/tex]
So, option B is false and option D is true.
15 points. Geometry question — HELP! See image.
Let point Q = (4,y)
√[ (4-0)^2 + (y-0)^2 ] = √[ (6-0)^2 + (0-0)^2 ]
Square both side
(4-0)^2 + (y-0)^2 = (6-0)^2 + (0-0)^2
4^2 + y^2 = 6^2
16 + y^2 = 36
y^2 = 36-16
y^2 = 20
y= √20
y= 2√5
Answer:
2√5
Step-by-step explanation:
On the graphic, you see point Q is roughly between 4 and 4.5 units on the Y-axis.
So, all we have to do is find a value similar to that in the answer choices. So, let's look at the values:
2√5: 2 * 2.23 = 4.46... that's pretty much what we're looking for.
4√2: 4 * 1.41 = 6.4. Way too big.
2√13: 2 * 3.6 = 7.2, way too big.
8√2: We know that will necessary be way bigger than 4.5, so let's not even evaluate it.
Given the parent function of f(x) = x3, what change will occur when the function is changed to f(x − 3)?
Shift to the right 3 units
Shift to the left 3 units
Shift up 3 units
Shift down 3 units
Answer:
Shift to the right 3 units.
Answer:
Shift to the right 3 units
Step-by-step explanation:
Translations are a type of rigid transformation of functions, in which the position of the graph of a function is modified. The general form of the graph of a function moves up, down, left, or right.
Vertical translations:
Let:
[tex]a >0[/tex]
[tex]y=f(x)+a[/tex] shifts the graph [tex]a[/tex] units up
[tex]y=f(x)-a[/tex] shifts the graph [tex]a[/tex] units down
Horizontal translations:
Let:
[tex]b>0[/tex]
[tex]y=f(x+a)[/tex] shifts the graph [tex]b[/tex] units to the left.
[tex]y=f(x-a)[/tex] shifts the graph [tex]b[/tex] units to the right.
Using the previous information we can conclude that the function:
[tex]f(x-3)[/tex]
Is a Horizontal translation in which the graph was shifted [tex]b=3[/tex] units to the right.
[tex]f(x-3)=(x-3)^3[/tex]
I leave you the graphs, so you can corroborate the answer easily.
Identify the volume of a cone with a base area 25π m^2 and a height equal to three times the radius.
Answer:
We apply the chain rule, along with the quotient rule, to find d ... 3. (4 pts) A particle moves on a line so that its coordinate at time t is y ... (10 pts) A cylindrical tank with radius 5 m is being filled with water at a rate of ... h/(t) = V /(t)/25π m2. ... cup has the shape of a cone with height 10 cm and radius 3 cm (at.
Step-by-step explanation:
Answer:
V = 392.7 m3
Step-by-step explanation:
To find the volume of the cone, first calculate the hieght and the radius.
To find the length of the radius, equate the given area to the formula for the area of a circle and solve for r.
πr2=25π
Divide both sides by π.
r2=25
Take the positive square root of both sides.
r=5 m
It is given that the height of the cone equal to three times the radius. So, use the radius to find the height.
h=3r
Substitute 5 for r.
h=3⋅5
Simplify.
h=15 m
To find the volume of the cone, use the formula for the volume of a cone.
V=13πr2h
Substitute 5 for r and 15 for h.
V=13⋅π⋅52⋅15
Simplify.
V=125π
Use a calculator to approximate.
V≈392.7 m3
Therefore, the volume of the cone is about 392.7 m3.
PLEASE HELP!!! Which equation is relevant to 4^x^+^3=64
I believe it’s the second option 2^2x+6=2^6
Answer:
[tex]\large\boxed{2^{2x+6}=2^6}[/tex]
Step-by-step explanation:
[tex]4^{x+3}=64\\\\4^{x+3}=4^3\\\\(2^2)^{x+3}=(2^2)^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(x+3)}=2^{(2)(3)}\\\\2^{2x+6}=2^6[/tex]
Which number in the standard equation for a circle centered at the origin should one increase to make the circle larger?
Answer:
increasing the radius makes the circle larger. (Answer B)
Step-by-step explanation:
The formula for the area of a circle is A = πr². Hence, Area of a Circle depends solely on the variable r and the constant of proportionality π.
Thus, increasing the radius makes the circle larger.
What are the leading coefficient and degree of the polynomial? 15w – w ⁸ - 5 + w ⁹
Leading coefficient:
Degree:
Answer:
leading coefficient is 1
degree is 9
Leading coefficient: 1
Degree: 9
The Venn diagram shows the results of two events resulting from rolling a number cube.
Events C and D are____.
P(C) = 1/3
P(D) = 1/3
P(C ∩ D) = 0
P(C | D) ≠ 0
This is geometry, dealing with conditional probability.
Answer:
Events C and D are mutually exclusive.
P(C ∩ D) = 0
Step-by-step explanation:
We notice that event C is even numbers and Event D is odd number. We cannot roll a die and have both events occur at the same time. That means they are mutually exclusive. Either one event occurs or the other occurs.
P(C ∩ D) = 0 This means the events do not intersect (overlap). Or are mutually exclusive.
PLEASE ANSWER
Which of the following statements are correct? Select all that apply.
-- Only two of three angle bisectors of the internal angles of a triangle are concurrent.
-- The circumcenter of a triangle is the point where the perpendicular bisectors of the sides meet.
-- Given any three non-collinear points, there exists exactly one circle that passes through the points.
-- A circumscribed circle is the circle that passes through all three vertices of a triangle and it is the smallest triangle contained within any triangle.
-- The incenter of a triangle is the point where the angle bisectors meet.
Answer:
Step-by-step explanation:
Given are some properties of triangles and we have to check whether they are correct
i) Only two of three angle bisectors of the internal angles of a triangle are concurrent.
This is incorrect since all three angle bisectors concur at incentre
ii) The circumcenter of a triangle is the point where the perpendicular bisectors of the sides meet.
-- correct because the meeting point is equidistant from all three vertices
iii) Given any three non-collinear points, there exists exactly one circle that passes through the points.
-- correct because any three points determine a circle
iv) Given any three non-collinear points, there exists exactly one circle that passes through the points.
-- Correct
v) The incenter of a triangle is the point where the angle bisectors meet.
-- Correct and the centre is equidistant from the sides of the triangle
Statements 2, 3, and 5 are correct.
Analyze each statement to determine which are correct:
Only two of three angle bisectors of the internal angles of a triangle are concurrent. This statement is incorrect. All three angle bisectors of the internal angles of a triangle are concurrent and meet at a single point called the incenter.The circumcenter of a triangle is the point where the perpendicular bisectors of the sides meet. This statement is correct. The perpendicular bisectors of the sides of a triangle meet at a point called the circumcenter, which is the center of the circle that passes through all three vertices of the triangle (circumscribed circle).Given any three non-collinear points, there exists exactly one circle that passes through the points. This statement is correct. For any three non-collinear points, there is exactly one unique circle that can pass through all three points. This is the circumscribed circle of the triangle formed by the points.A circumscribed circle is the circle that passes through all three vertices of a triangle and it is the smallest triangle contained within any triangle. This statement is incorrect. While a circumscribed circle does pass through all three vertices of a triangle, it does not describe any triangle, let alone the smallest one contained within another triangle.The incenter of a triangle is the point where the angle bisectors meet. This statement is correct. The incenter, where the angle bisectors meet, is the center of the inscribed circle that fits inside the triangle.You buy 50 shares of a stock on October 1 @ $72.30 per share. You sold those same shares on December 15 for $83.13 per share. What was your percentage gained on the transaction?
Answer:
around %114.98
Help me please !!!!!!!
Answer:
x = 13.7
Step-by-step explanation:
Sin = Opp./Hypo.
so
Sin (17) = x / 47
x = sin (17) * 47
x = 0.2924 * 47
x = 13.7
Mr green makes some compost he mixes soil, manure and leaf mould in the ratio 3:1:2 mr greenmakes 72 literes of the compost. How many litres of soil does he use?
Answer:
[tex]36\ liters\ of\ soil[/tex]
Step-by-step explanation:
we know that
The ratio of soil, manure and leaf mould is [tex]3:1:2[/tex]
That means
For every 6 liters of the compost, he use 3 liters of soil
so by proportion
Find how many liters of soil does he use for 72 liters of compost
[tex]\frac{3}{6}=\frac{x}{72}\\ \\x=3*72/6\\ \\x=36\ liters\ of\ soil[/tex]
A projectile is launched in the air with an initial velocity of 40m/s from a height of 1.2 meters. Which of the following equations represents the projectile's height, h, in meters over time, t, in seconds.
h=??
Hope y'all answer! :))
Would need a equation for it please
Answer:
H(t)= -16t^2+40t+1.2
Step-by-step explanation:
H(t) = -16t^2 + vt + s
I hope this is what you were looking for.
TONNN of points!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
How do you use special right triangles to solve for missing sides? (30-60-90 and 45-45-90 triangles)
Answer: see below
Step-by-step explanation:
30 - 60 - 90 triangles have angles in the triangle measuring 30, 60, and 90 degrees. A 30 - 60 - 90 triangle also has special side ratios according to a side's location in the triangle.
The side across from the 30 degree angle is represented by x.
The side across from the 60 degree angle is represented by x[tex]\sqrt{3}[/tex].
The side across from the 90 degree angle is represented by 2x.
45 - 45 - 90 triangles have angles in the triangle measuring 45, 45, and 90 degrees. A 45 - 45 - 90 triangle has special side ratios similar to the 30 - 60 - 90 triangle.
The side across from either of the 45 degree angles is represented by x.
The side across from the 90 degree angle is represented by x[tex]\sqrt{2}[/tex].
These ratios can be used to find missing sides. If you know that a triangle is one of these special triangles and you also know one of its side lengths, you can plug the known length in for x in the proper place.
EX: you have a 30 - 60 - 90 triangle with a side length of 2 across from the 30 degree angle. You then know that the side across from 60 is 2[tex]\sqrt{3}[/tex] and the side across from 90 is 4.
The blue triangle has been reflected to the red triangle. Choose the matrix which made this transformation.
Answer:
B) [tex]\left[\begin{array}{cc}1&0\\0&-1\end{array}\right][/tex]
Step-by-step explanation:
When the coordinates are represented by a column vector, the vertical reflection transformation (x, y) ⇒ (x, -y) looks like the matrix of answer choice B.
Nemo's aquarium is filled with 240024002400 cubic centimeters of water. The base of the aquarium is 20\text{ cm}20 cm20, space, c, m long and 12\text{ cm}12 cm12, space, c, m wide. What is the height of the water in Nemo's aquarium?
Answer:
10 cm
Step-by-step explanation:
Answer:
10 cm
Step-by-step explanation:
Since, the volume of a cuboid is,
V = l × w × h,
Where,
l = length,
w = width,
h = height,
∵ The shape of the aquarium must be cuboid,
We have, l = 20 cm, w = 12 cm, V = 2400 cm³,
By substituting the values,
2400 = 20 × 12 × h
2400 = 240h
[tex]\implies h = \frac{2400}{240}=10[/tex]
Hence, the height of the water in Nemo's aquarium would be 10 cm.
Please help!!!!!!!!!!
Answer:
[tex]\large\boxed{a=4\sqrt3}[/tex]
Step-by-step explanation:
We have the triangle 30° - 60° - 90°. In that triangle sides are in proportion
1 : √3 : 2 (look at the picture).
We have
[tex]a\sqrt3=12[/tex] multiply both sides by √3 (use √a · √a = a)
[tex]3a=12\sqrt3[/tex] divide both sides by 3
[tex]a=4\sqrt3[/tex]
[tex]b=2a\to b=2(4\sqrt3)=8\sqrt3[/tex]
There is a clown's face on the top of a spinner. The tip of his hat rotates to (−2, 5) during one spin. What is the cosine value of this function?
−2
5
5 square root of 29 over 29
negative 2 square root of 29 over 29
Answer:
The last choice is your answer
Step-by-step explanation:
Plot your point in an x/y coordinate plane. We are in QII where x is negative and y is positive. From that point, if you drop an altitude to the negative x axis, you have a right triangle with a base measure of -2, a height of 5 and a hypotenuse that is unknown as of right now. We will find it using Pythagorean's Theorem. [tex]5^2+(-2)^2=c^2[/tex]
The length of the hypotenuse is √29. That means that the cosine of that angle is the side adjacent over the hypotenuse. Rationalizing the denominator gives us [tex]-\frac{2\sqrt{29} }{29}[/tex]
State the domain and range for the function
Answer:
* Domain: all reals except multiples of 2π
* Range: (-∞ , -2] ∪ [2 , ∞)
Step-by-step explanation:
* Lets revise the period, the domain and the range of csc(x)
- The period of csc(x) is 2π
- To find the period of csc(x) use 2π / coefficient of x
- The domain of csc(x) is all x ≠ nπ
- The range is y ≤ -1 , y ≥ 1
* Lets revise the vertical and the horizontal stretch and compress
- A vertical stretching is the stretching of the graph away from
the x-axis
• if k > 1, the graph of y = k•f(x) is the graph of f(x) vertically
stretched by multiplying each of its y-coordinates by k.
- A vertical compression is the squeezing of the graph toward
the x-axis.
• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed
by multiplying each of its y-coordinates by k.
- A horizontal stretching is the stretching of the graph away from
the y-axis
• if 0 < k < 1 (a fraction), the graph is f (x) horizontally stretched by
dividing each of its x-coordinates by k.
- A horizontal compression is the squeezing of the graph toward
the y-axis.
• if k > 1, the graph of y = f (k•x) is the graph of f (x) horizontally
compressed by dividing each of its x-coordinates by k
∵ f(x) = 2csc(x/2)
- The coefficient of x is 1/2
∵ The period of x = 2π
∴ The period of x/2 = 2π/1/2 = 4π
∵ The domain of csc(x) is all x ≠ nπ
∴ The domain of csc(x/2) is all x ≠ n2π
∵ f(x) = 2csc(x/2)
∵ csc(x/2) multiplying by 2
- That means every y-coefficient multiplying by 2
∵ The range of csc(x/2) is y ≤ -1 and y ≥ 1
∴ The rang of f(x) = 2csc(x/2) is y ≤ -1(2) and y ≥ 1(2)
∴ The rang of f(x) = 2csc(x/2) is y ≤ -2 and y ≥ 2
* Domain: all reals except multiples of 2π
* Range: (-∞ , -2] ∪ [2 , ∞)
* Look to the graph attached
- The red is y = csc(x)
- The blue is f(x) = 2csc(x/2)
Please answer I’ll rate brainlyest
Answer:
The answer is AB.
Choice D.
Step-by-step explanation:
We are given four blood types and the number of females and males having each of the blood type. We are to determine the blood type that is independent of the gender.
It is evident that the disparity in the number of males and females in the blood types A, B and O is large.
Only in the blood type AB, the difference is very small. The number of males and females having AB blood type is more or less same. So, we can conclude that blood type AB is independent of gender.