Answers
Answer: I hope it helps :)
x=6 , y=6√3x =23√3 , y=23u =12 , v= 6a =18√2 , b =18x = 13 , y= 13Step-by-step explanation:
1.
[tex]Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = \frac{adj}{hyp} \\Cos 60 = \frac{6}{x} \\\frac{1}{2} =\frac{6}{x} \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\\sqrt{108} =\sqrt{y^2} \\y=6\sqrt{3}[/tex]
2.
[tex]Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =\frac{opp}{adj} \\Sin 60=\frac{x}{46}\\\\\frac{\sqrt{3} }{2} =\frac{x}{46} \\2x=46\sqrt{3} \\x = \frac{46\sqrt{3} }{2} \\x =23\sqrt{3} \\\\Hyp^2=opp^2+adj^2\\46^2=(23\sqrt{3} )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\\sqrt{529} =\sqrt{y^2} \\y = 23[/tex]
3.
[tex]Hypotenuse = u\\Opposite =6\sqrt{3} \\Adjacent = v\\\alpha =60\\Sin\: 60 = \frac{6\sqrt{3} }{u} \\\frac{\sqrt{3} }{2} =\frac{6\sqrt{3} }{u} \\12\sqrt{3} =u\sqrt{3} \\\\\frac{12\sqrt{3} }{\sqrt{3} } =\frac{u\sqrt{3} }{\sqrt{3} } \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6\sqrt{3} )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\\sqrt{36} =\sqrt{v^2} \\\\v =6[/tex]
4.
[tex]Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=\frac{18}{b}\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\\sqrt{hyp^2} =\sqrt{648}\\ \\a =18\sqrt{2}[/tex]
5.
[tex]Hypotenuse = 13\sqrt{2}\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13\sqrt{2}\\ \\\frac{\sqrt{2} }{2} =\frac{x}{13\sqrt{2} } \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13\sqrt{2})^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\\sqrt{169} =\sqrt{y^2} \\13 = y[/tex]
Related Questions
Simplify.
a3 x a9 over a4
PLEASE HELP!!! ASAP!!!
Answers
Answer:
[tex]\frac{\left(a^3\right)\left(a^9\right)}{a^4}=a^8[/tex]
Step-by-step explanation:
[tex]\frac{\left(a^3\right)\left(a^9\right)}{a^4}\\\\= \frac{a^3a^9}{a^4}\\\\=a^3a^9\\\\=a^{3+9}\\\\=a^{12}\\\\=a^{12-4}\\=a^8[/tex]
Answer:
a⁸
Step-by-step explanation:
a³*a⁹/a⁴
Product law:Says that if the base of the number being multiplied is the same, then we can add the exponents
Therefore
a to the power of 3+9/a⁴
a¹²/a⁴
Quotient law:Says that when we divide two numbers with the same base,we can subtract the exponents
Therefore
a to the power of 12-4
a⁸
Which is the best estimate of A.2 B.6 C.12 D.24
Answers
Answer:
24
Step-by-step explanation:
90/7 ÷ 1 3/4
Change to an improper fraction
90/7 ÷ ( 4*1 +3 ) /4
90/7 ÷ 7/4
Copy dot flip
90/7 * 7/4
90/4
22.5
Best estimate is 24
Answer:
A:2
Step-by-step explanation:
A is the answer because 90 divided by 7 is 12.8 which would be 13, and the 1 and 3/4 would be 7. 13 divided by 7 would equal 1.85. When rounded your answer would be 2.
If y varies directly with x and y is -6 when x is 2, what is x when y is -22?
Answers
Answer:
x = [tex]\frac{22}{3}[/tex]
Step-by-step explanation:
Given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = - 6 when x = 2, then
- 6 = 2k ( divide both sides by 2 )
- 3 = k
y = - 3x ← equation of variation
When y = - 22, then
- 22 = - 3x ( divide both sides by - 3 )
x = [tex]\frac{-22}{-3}[/tex] = [tex]\frac{22}{3}[/tex]
How do you solve a system of equations approximately using tables, without using graphs or equations ? Please I need to figure out how to do it with out graphing or equations
Answers
Answer:
Ok, a system of equations means that we have a given number of equations with the same solutions.
If we only have tables, this means that we need to have one table for each equation:
For example, if we are working only with two variables, x and y, in those tables we can see the pints (x, y) that belong to each equation.
Now, a point (x, y) will be a solution of the system of equations only if it belongs to the data table for each equation
This would mean that if we graph those data sets, the graphs will intersect at the point (x, y) that belongs to all the tables of data.
Other way may be using the data in the tables to construct the equations, but you said that you only want to use the tables, so this method can be discarded.
Yo tenía $2.00
Mi mamá medio$100
Mi papá medio$100
Mi tío y mi tía me dieron $100
Y yo tenía otros $5.00
Cuanto tenía??
Answers
Answer:
$307
Step-by-step explanation:
$2.00 + $100 + $100 + $100 + $5.00 = $307
A ladder leans against a 15-foot building to form a right triangle. The ladder is placed so that it is 8 feet from the building. What is the length of the ladder?
Answers
Answer:
17 feet
Step-by-step explanation:
[tex]15^{2}+8x^{2} = x^{2} \\225 + 64 = x^{2} \\289 = x^{2} \\17 = x[/tex]
PLEASE HELP MEE I need help finding x a b and c
Answers
Answer:
Step-by-step explanation:
Because of the Isosceles Triangle Theorem, both the base angles of that triangle measure a. We also know that a + b = 180 because of the definition of supplementary angles. So we have 2 equations from that info. First is the fact that
a + 7x = 180 and the second is
2x + a + a = 180 because of the Triangle Angle-Sum Theorem. If the left side of the first equation = 180 and the left side of the second equation also = 180, then by the transitive property of equality,
a + 7x = 2x + a + a and
a + 7x = 2x + 2a and
5x = a. Now that we know that a = 5x, we go back to our triangle and fill in 5x as a:
5x + 5x + 2x = 180 (the Triangle Angle-sum Theorem again) and
12x = 180 so
x = 15. If x = 15, then
a = 5(15) = 75,
b = 7(15) = 105, and
c = 2(15) = 30
whats the equation for this
Answers
Answer:
[tex]x^2 + y^2 + 4x + 4y = -119/16[/tex]
Step-by-step explanation:
The axes x and y are calibrated in 0.25
If the circle is carefully considered, the radius r of the circle is:
r = -1.25 - (-2)
r = 0.75 units
The equation of a circle is given by:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
The center of the circle (a, b) = (-2, -2)
Substituting (a, b) = (-2, -2) and r = 0.75 into the given equation:
[tex](x - (-2))^2 + (y - (-2))^2 = (3/4)^2\\\\(x + 2)^2 + (y + 2)^2 = (3/4)^2\\\\x^2 + 4x + 4 + y^2 + 4y + 4 = 9/16\\\\x^2 + y^2 + 4x + 4y + 8 = 9/16\\\\16x^2 + 16y^2 + 64x + 64y + 128 = 9\\\\16x^2 + 16y^2 + 64x + 64y = -119\\\\x^2 + y^2 + 4x + 4y = -119/16\\[/tex]
In a state lottery 25 balls numbered from 1 to 25 and placed in machine. 6 numbers randomly drawn. And here is the chart what can win a player by buying single lottery ticket: 6 number match $10,000 5 number match $ 5,000 4 number match $ 1000 3 number match $ 5,00 2 number match $ 50 1 number match $ 10. what is the probablity that a player will will 10000 dollars
Answers
Answer: 0.00000565
Step-by-step explanation:
Required to win:
6 number match $10,000
5 number match $ 5,000
4 number match $ 1000
3 number match $ 5,00
2 number match $ 50
1 number match $ 10
Therefore, to win $10,000 ;
All 6 numbers must match
Number of right numbers = 6
Total numbers = 25
Since it is without replacement :
Probability = required outcomes / Total possible outcomes
P(First number match) = 6/25
P(second number match) = 5/24
P(third number match) = 4/23
P(fourth number match) = 3/22
P(fifth number match) = 2/21
P(sixth number match) = 1 / 20
Therefore, Probability of winning $10000 :
(6/25) * (5/24) * (4/23) * (3/22) * (2/21) * (1/20) = 720 / 127512000 = 0.0000056465
= 0.00000565
Arrange the systems of equations in order from least to greatest based on the number of solutions for each system.
Answers
Answer:
work is shown and pictured
Answer:
case 1
3x-7y=9
-4x+5y=1
using a graph tool
the solution is the point (-4,-3)------------------> one solution
case 2
y=6x-2
y=6x-4
two parallel lines
the system has no solution---------------> zero solution
case 3
-5x+y=10
-25x+5y=50
is the same line----------------> infinite solutions
which line segment could be a midsegment of ∆abc
Answers
Answer:
[tex]\overline{DF}[/tex] could be a midsegment of ∠ABC.
Step-by-step explanation:
A midsegment of a triangle must be two things:
1. Parallel to the 3rd side, in this case, [tex]\overline{AD}[/tex].
2. Half the length of the 3rd side, in this case, [tex]\overline{AD}[/tex].
Since we don't know the lengths, we can only go off of 1. There is only one line that is parallel to [tex]\overline{AD}[/tex] and it is [tex]\overline{DF}[/tex].
Hope this helped!
A regular polygon has 10 sides. What is the measure of each interior angle of the polygon? 36° 1440° 144° 72°
Answers
Answer:
144°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 10, thus
sum = 180° × 8 = 1440°
Each interior angle = 1440° ÷ 10 = 144°
Answer:
144 deg
Step-by-step explanation:
Sum of the measures of the angles of a polygon with n sides:
(n -2)180
For a 10-sided polygon, n = 10.
The sum of the measures is
(10 - 2)180 = (8)180 = 1440
Since the polygon is regular, all angles have the same measure, so the measure of 1 angle is
1440/10 = 144
Answer: 144 deg
3/x-2, i'm confused as to what the horizontal asymptote is. The resources I found online conclude that it has a horizontal asymptote of y=0. I know that in order for a horizontal asymptote to be y=0, the denominator has to have a greater degree than the numerator. Im confused because doesn't the numerator have the same degree as the denominator (degree of 1)?
Answers
Answer:
The Horizontal Asymptote is at x=3
Step-by-step explanation:
Here is a way to remember this
One way to remember this is the following pnemonic device: BOBO BOTN EATS DC
EABOBO -Exponents are bigger on bottom, y=0
EABOTN -Exponents are bigger on top, none
EATS DC - Exponents are the same, divide coefficients
3/x-2 the exponents are the same, divide leading coefficients
3/1 = 3 the horizontal asymtote is at x=3
What is the volume of the following rectangular prism? the height is 5 and 1/4 and the base is 8
Answers
Answer:
V = 42 units ^3
Step-by-step explanation:
The volume of a rectangular prism is
V =Bh
V = 8*5 1/4
Changing to a mixed number
V = 8* ( 5*4+1) /4
=8*21/4
= 42 units^3
Answer:
[tex]\huge\boxed{V=42\ u^3}[/tex]
Step-by-step explanation:
Th formula of a volume of a prism:
[tex]V=BH[/tex]
B - base
H - height
We have
[tex]B=8;\ H=5\dfrac{1}{4}=\dfrac{5\cdot4+1}{4}=\dfrac{20+1}{4}=\dfrac{21}{4}[/tex]
Substitute:
[tex]V=(8)\left(\dfrac{21}{4}\right)[/tex] simplify 8 and 4
[tex]V=(8\!\!\!\!\diagup)\left(\dfrac{21}{4\!\!\!\!\diagup}\right)=(2)(21)=42[/tex]
A box contains 6 red, 3 white, 2 green, and 1 black (total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting: at least three the same color?
Answers
Answer:
We shall need to pick at least 4 balls to be sure that we are getting balls with the same color
Step-by-step explanation:
Here, we want to know the least number of balls to be taken out of the box to be sure that we have all the three colors represented.
We know there are 12 identical balls, with the least numbers of balls being 1 and 2. Hence, to be able to know we have all the colors of balls represented, we will need to have taken all the less represented ones i.e the 1 and 2 , and this means that the next number of ball which would be taken will confidently confirm that we have taken all the colors since we would have exhausted picking other balls at this point.
So we shall be needing at least 4 balls picked to ensure that we have all the colors represented
Find three solution of equation 4x+3y=12
Answers
Answer:
1.(X,Y)=(1,8/3) 2.(X,Y)=(2,4/3) 3.(X,Y)=(3/2,2)plz.. mark me as brainiestn Fill in the blank. The _______ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further. The (1) for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.
Answers
Answer: sample space
Step-by-step explanation: In determining the probability of a certain event occurring or obtaining a particular outcome from a set of different possible outcomes, such as in the toss of coin(s), rolling of fair die(s), the sample space comes in very handy as it provides a simple breakdown and segmentation of all possible events or outcomes such that in Calculating the probability of occurrence of a certain event, the event(s) is/are located in the sample space and the ratio taken over the total number of events.
Which expression can be used to find the surface area of the following triangular prism? A 16+16+55+55+8816+16+55+55+8816, plus, 16, plus, 55, plus, 55, plus, 88 (Choice B) B 10+10+55+55+8810+10+55+55+8810, plus, 10, plus, 55, plus, 55, plus, 88 (Choice C) C 8 +8+55+55+888+8+55+55+888, plus, 8, plus, 55, plus, 55, plus, 88 (Choice D) D 16+8816+8816, plus, 88
Answers
Answer:
8+8+55+55+88
Step-by-step explanation:
The surface area is the sum of all the sides
We have 5 sides
Top and bottom are the same
The area of the top is
1/2 bh = 1/2 (8)(2) = 8
The left and right sides are the same
The area of the left side is
5*11 = 55
The area of the front is
8*11 = 88
The sum of all the 5 sides are
top + bottom + left + right + front
8+8+55+55+88
Answer:
8 + 8 + 55 + 55 + 88
Step-by-step explanation:
Calculate area of base.
8 × 2 × 1/2 = 8
There are two triangles:
8 + 8
Calculate area of rectangle.
8 × 11 = 88
Calculate the areas of two rectangles.
5 × 11 = 55
55 + 55
how do you know if the solutions to a quadratic equation are inside, outside, on, inside and on, or outside and on the parabola??
Answers
Answer:
Plug in the x and y values into the equation
Step-by-step explanation:
Movie tickets for 2 adults and 3 children cost $44.50. Tickets for the same movie cost $25.50 for 1 adult and 2 children. (a) Let a represent the cost of a ticket for an adult and c represent the cost of a ticket for a child. Write a system of equations that can be used to find a and c. (b) What is the total cost of tickets for 1 adult ticket and 1 child ticket?
Answers
Answer:
a) 2a + 3c = $44.50
a + 2c + $25.50
b) $19
Step-by-step explanation:
Simultaneous equations. A = adult. C = children
2a + 3c = $44.50 (EQUATION 1)
a + 2c = $25.50 (EQUATION 2)
Now solve this using the method of elimination:
2a + 3c = $44.50 (EQUATION 1)
a + 2c = $25.50 (EQUATION 2)
Multiply equation 2 by 2 so that both equations have the same a coefficient.
2a + 4c = $51 (NEW EQUATION 2)
Now subtract equation 1 from equation 2:
2a - 2a + 4c - 3c = $51 - $44.50 (2a cancels out)
c = $6.50
Now substitute c into one of the equation, in this case, I'm using original equation 2.
a + 2($6.50) = $25.50
a + $13 = $25.50
a = $12.50
Total cost of one adult and child = $6.50 + $12.50
= $19
Answer:
option d
Step-by-step explanation:
hope this helps
Cassie reduced the size of a poster to a
height of 2 inches. What is the new width if the poster
was originally 18 inches wide and 2 feet tall?
Answers
Answer: 3 feet²
Step-by-step explanation:
Simply do 2*18 (In a rectangle A = l*w) to get 36 inches, or 36/12 feet, or 3 feet.
Hope it helps <3
Answer:
Width = 1.5 Inches
Step-by-step explanation:
Original Height: 24 Inches
Original Width: 18 Inches
Given Height: 2 inches
24 divided by 2 = 12. This means the poster was dilated by 12.
18 divided by 12 = 1.5
When you conduct a t test, the calculated value of t can be negative. True/False
Answers
Answer:
True.
Step-by-step explanation:
In t-test test the value of t can be either negative or positive.
If value of t is negative, then it lies to the left of the mean.
If value of t is Positive, then it lies to the right of the mean.
The given statement is "When you conduct a t test, the calculated value of t can be negative.".
Therefore, the given statement is true.
Area of a triangle is 1400 cm² the base of the triangle is 5 times the height what is the height of the triangle
Answers
Answer:
≈23.66
Step-by-step explanation:
Height ---> x
base ---> 5x
Formula for area of triangle: (base*height)/2
((5x)(x))/2 = 1400
[tex]5x^{2}[/tex]/2 = 1400
[tex]5x^{2}[/tex] = 1400 · 2 = 2800
[tex]x^2[/tex] = 2800/5 = 560
x= √560 ≈ 23.66
The side length of an equilateral triangle is 6 cm. What is the height of the triangle? 2
Answers
Answer:
h=3√3 cm
Step-by-step explanation:
An equilateral triangle has 3 Equal sides
The height of an equilateral triangle with side a =a√3/2
That is,
h=a√3/2
Where,
h=height of the equilateral triangle
a=side length
From the triangle given,
a=6cm
Therefore,
h=6√3/2
=3√3
h=3√3 cm
Aubrey has a new art box in the shape of a rectangular prism. The box is 12 cm by 20 cm by 5 cm. The
only thing in the art box is a new pink eraser with the dimensions shown below.
0.5 cm
2 cm
4 cm
What is the volume of the art box not taken up by the eraser?
Answers
Answer:
1196cm³
Step-by-step explanation:
Step 1
Find the volume of the Rectangular Prism = Length × Width × Height
Length = 12 cm
Width = 20 cm
Height = 5 cm
Volume of a Rectangular prism = 12 × 20 × 5
= 1200cm³
Step 2
Volume of the Eraser
The Eraser has the shape of a box.
Volume = Length × Width × Height
Length = 0.5 cm
Width = 2 cm
Height = 4 cm
Volume = 4cm³
Step 3
Find the volume of the art box not taken up by the eraser
Volume of the art box not taken up by the eraser = Volume of the Art box - Volume of the Eraser
= 1200cm³ - 4cm³
= 1196cm³
Therefore, volume of the art box not taken up by the eraser is 1196cm³
What is the volume in cubic inches of the solid figure, rounded to the nearest cubic inch? Do not use units or commas in your answer.
Answers
Answer:
The volume of the figure is approximately 1244 in³
Step-by-step explanation:
The figure is formed by a rectangular prism and a hemisphere, therefore its total volume is formed by the the sum of the volume of each of these forms. The volume of a rectangular prism can be found by using the expression:
[tex]V_{rect} = length*width*height[/tex]
While the volume of a hemisphere is given by:
[tex]V_{hemis} = \frac{2}{3}*\pi*r^3[/tex]
The radius of the hemisphere is the difference between the total length of the figure and the length of the prism, therefore:
[tex]r = 17 - 11 = 6 \text{ in}[/tex]
We can now find the volume of the figure:
[tex]V = V_{rect} + V_{hemis}\\V = 11*6*12 + \frac{2}{3}*\pi*(6)^3\\V = 792 + 144*\pi\\V = 792 + 452.39\\V = 1244 \text{ in}^3[/tex]
f(x) = x^2. What is g(x)?
Answers
Answer:
A. g(x)=1/2x²
Step-by-step explanation:
Given:
f(x)=x²
We have to find g(x)
Since, we are given that g(2)=2
1. g(x)=1/2x²
x=2
g(x)=1/2(2)²
=1/2(4)
=4/2
=2
2. g(x)=1/4x²
x=2,
g(x)=1/4(2)²
=1/4(4)
=4/4
=1
3. g(x)= 2x²
at x=2,
g(x)=2(2)²
=2(4)
=8
4. g(x)=(1/2x)²
x=2
g(x)={1/2(2)}²
=(1/4)²
=1/16
A. g(x)=1/2x² is the answer
Can anyone help me with this please? And QUICK!
Answers
Answer:
30.6
Step-by-step explanation:
The following data were obtained from the question:
Angle θ = 23°
Opposite = 13
Adjacent = y
The value of y can be obtained by using the following trig ratio:
Tan θ = Opposite /Adjacent
Tan 23° = 13/y
Cross multiply
y × Tan 23° = 13
Divide both side by Tan 23°
y = 13/Tan 23°
y = 30.6
Therefore, the value of y in the diagram above is 30.6
Um empresário possui um espaço retangular de 100 m por 750 m para corrida. Determine quantos metros percorreu um atleta que deu apenas 6 voltas pelas extremidades do espaço: * (A) 300 (B) 1700 (C) 10200 (D) 75000 (E) 7500
Answers
Answer:
(C) 10200m
Step-by-step explanation:
Dizem-nos na pergunta que um homem de negócios tem um espaço retangular de 100 m por 750 m para correr.
O primeiro passo é calcular o perímetro do retângulo.
Perímetro de um rectângulo = 2 (Comprimento × Largura)
Da pergunta,
Comprimento = 100m
Largura = 750m
Perímetro do rectângulo = 2 ( 100 + 750)
= 2(850)
= 1700m
Perímetro do rectângulo = 1700m
Somos questionados na pergunta para determinar quantos metros (Distância) um atleta viajou que tem apenas 6 voltas ao redor das extremidades do espaço.
A distância total percorrida pelo atleta ao correr é calculada como:
6 × perímetro do rectângulo.
= 6 × 1700
= 10200m
Quantos metros percorreu um atleta que deu apenas 6 voltas pelas extremidades do espaço = 10200
Please answer it now in two minutes
Answers
Answer:
Area = 19.9 mm²
Step-by-step explanation:
Step 1: Find Angle V.
m < V = 180 - (131 + 27) (sum of angles in a triangle)
V = 22°
Step 2: Find UW using the law of sines.
[tex] \frac{UW}{sin(V)} = \frac{UV}{sin(W)} [/tex]
Plug in your values
[tex] \frac{UW}{sin(22)} = \frac{8}{sin(27)} [/tex]
Multiply both sides by sin(22) to solve for UW
[tex] \frac{UW*sin(22)}{sin(22)} = \frac{8*sin(22)}{sin(27)} [/tex]
[tex] UW = \frac{8*sin(22)}{sin(27)} [/tex]
[tex] UW = 6.6 mm [/tex]
Step 3: Find the area of ∆UVW
Area = ½*UW*UV*Sin(U)
Area = ½*6.6*8*sin(131)
Area = 3.3*8*sin(131)
Area = 19.9 mm² (to the nearest tenth)