Answer:
20 inches squared
This is because the area of a triangle is height times base divided by 2.
So it is 10*4/2, so the answer is 20 inches squared.
The area of the right angle triangle is 20 square inches.
What is the area of a right angle triangle ?The area of a right angle triangle is given by the formula,
Area = 1/2 * base * height .
where the base and height are the legs of the given triangle.
How to calculate the given area of the triangle ?It is given that the legs of a right triangle measure 10 inches and 4 inches.
Thus we have the base of the triangle as 4 inches and height of the triangle as 10 inches.
Area = 1/2 * 4 * 10 square inches .
∴ Area = 20 square inches.
Therefore, the area of the right angle triangle is 20 square inches.
To learn more about area of a triangle, refer -
https://brainly.com/question/18155830
#SPJ2
What is the name of the property given below?
If a: b = 0, then a = 0, b = 0, or both a = 0 and b = 0.
Answer:
This is the zero product rule.
Step-by-step explanation:
a: b = 0, then a = 0, b = 0, or both a = 0 and b = 0.
This is the zero product rule.
It shows that for the product to be zero, at least one factor must be zero
If a*b= 0: It shows that one of the factor is zero or may be both the factors are zero that is why their resultant product is 0....
Each week your science teacher gives a fifteen-point quiz. Your current scores are shown in the table. What is your mean quiz score?
The answer is 12 points
I have the table so I added the numbers to get 108, and there are 9 numbers, so yu do 108/9 equaling to 12
If opposite angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram. True or False?
Answer:
False
Step-by-step explanation:
This statement states that If opposite angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram.
This is a false statement.
Lets recall the properties of a parallelogram to understand the concept. The definition says that a quadrilateral is said to be a parallelogram if its opposite angles are congruent and two consecutive angles are supplementary.
Therefore the statement is false....
A rectangular prism has a volume of 300 ft. If the base measures 5 ft by 8 ft, what is the height of the prism?
40 ft
13 ft
23.1 ft
7.5 ft
Answer:
7.5 ft
Step-by-step explanation:
Volume of a prism is V = L*W*H.
In this case, the volume is V = 300 ft^3 (not 300 ft). Therefore,
300 ft^3 = L*W*H = (8 ft)(5 ft)(height)
Solving for the height, H, we get:
300 ft^3
H = --------------- = 7.5 ft
40 ft^2
Answer:
7.5 ft
Step-by-step explanation:
Vole is the length time the width times the height
V = l*w*h
Substituting what we know
300 = 5*8*h
300 = 40h
Divide each side by 40
300/40 =40h/40
7.5 =h
To bake one cake, Drew uses 18 ounces of flour. He has 850 ounces of flour. Let y represent the ounces of flour left and x represent the number of cakes he has baked. When the situation is modeled on a graph, what are the slope and the y-intercept of the line representing this situation?
A.
slope = 850 and y-intercept = 18
B.
slope = 18 and y-intercept = 850
C.
slope = -18 and y-intercept = 850
D.
slope = 850 and y-intercept = -18
Answer:
Choice C:
slope = -18x
y-intercept = 850
Step-by-step explanation:
Drew uses 18 ounces of flour
-18x represents the amount of flour used
850 ounces of flour
or (0,850) is the y-intercept and represents the total number of flour
Answer
slope = -18x
y-intercept = 850
Answer:
C
Step-by-step explanation:
C
Find the measure of a in the picture please
Answer:
a = 44 degrees
Step-by-step explanation:
Triangle AOB is an isosceles triangle.Angle A and B are same.All three angles of a triangle are equal to 180 degrees.angle 0 + angle a + angle b = 180 degrees
angle b = angle a
92 + a + b = 180 degrees
92 + 2a = 180 degrees
a = 44 degrees
!!
What is the exact distance from (−1, 4) to (6, −2)?
Answer:
The exact distance is √(29) or 29^(1/2)
Step-by-step explanation:
Find the answer using the distance formula (aka the Pythagorean theorem)
d=√(x1+x2)^2+(y1+y2)^2)
d=√(-1+6)^2+(4+-2)^2), Solve for d:
d= √((25)+(4))
d=√(29)
Answer:
[tex]\sqrt{35}[/tex]
Step-by-step explanation:
To calculate the distance (d) use the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)
d = [tex]\sqrt{(6+1)^2+(-2-4)^2}[/tex]
= [tex]\sqrt{7^2+(-6)^2}[/tex]
= [tex]\sqrt{49+36}[/tex] = [tex]\sqrt{85}[/tex] ← exact value
What is the position of F on the number line below? write your answer as a fraction or mixed number
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
There are 4 steps to complete to go from 0 to 1. Hence each step is:
1 out of 4, or simply [tex]\frac{1}{4}[/tex]
F is located at the 3rd mark, which will be [tex]\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}[/tex]
Hence, F is located at [tex]\frac{3}{4}[/tex]
Answer:
F is on [tex]\frac{3}{4}[/tex] on the number line
Step-by-step explanation:
Notice in the image that between 0 and 1 there are 4 subdivisions.
Then divide.
[tex]\frac{1}{4} = 0.25[/tex].
Each subdivision is equal to 0.25 units.
Point F is in the third subdivision.
This means that the distance between 0 and F is:
[tex]\frac{1}{4}*3 = \frac{3}{4} = 0.75[/tex].
Finally F is on [tex]\frac{3}{4}[/tex] on the number line
Factor this trinomial completely.
2x2 + 8x + 6
Answer:
[tex]2 {x}^{2} + 8x + 6 \\ 2( {x}^{2} + 4x + 3) \\ = 2( {x}^{2} + x + 3x + 3) \\ = 2(x + 1)(x + 3)[/tex]
Answer:
the answer is correct, just backwards. thanks for your help!
Step-by-step explanation:
Find the first five terms of the sequence in which a(1) = –10 and a(n) = 4a(n) – 1 + 7, if n ≥ 2.
options:
A –33, –125, –493, –1965, –7853
B 11, 15, 19, 23, 27
C 47, –10, –33, –125, –493
D –10, –33, –125, –493, –1965
Answer:
hello : answer: A
Step-by-step explanation:
a(1) = –10 and a(n) = 4a(n– 1) + 7, if n ≥ 2.
n=2 : a(2)=4a(1)+7 a(2) =4(-10)+7 = -33
n=3 : a(2)=4a(2)+7 a(3) =4(-33)+7 = -125
n=4 : a(2)=4a(3)+7 a(4) =4(-125)+7 = -493
n=5 : a(2)=4a(4)+7 a(5) =4(-493)+7 = -1965
n=6 : a(2)=4a(5)+7 a(6) =4(-1965)+7 = -7853
What is the rule for the reflection?
This image is being reflected over the y-axis. When reflecting over the y-axis the y-coordinate will stay the same, but the x-coordinate will have the opposite sign. Here is the rule for this reflection:
(-x, y)
Hope this helped!
~Just a girl in love with Shawn Mendes
HELP!!Use the figure to decide the type of angle pair that describe <6 and<4.
Angle 6, an acute angle, measures below 90 degrees, reflecting a sharp inclination. Angle 4, a right angle at precisely 90 degrees.
In the geometric configuration, Angle 6 is characterized as an acute angle, signifying that its measure falls between 0 and 90 degrees. Acute angles are typically associated with sharp inclinations, emphasizing a compact angular span. On the other hand, Angle 4 is identified as a right angle, precisely measuring 90 degrees.
Right angles are distinctive for their perpendicular alignment, forming the cornerstone of rectangular shapes and providing structural stability. The significance of Angle 4 lies in its pivotal role in defining perpendicularity within geometric constructs.
This geometric interplay showcases the diversity of angles, with acute angles like Angle 6 emphasizing sharpness and right angles like Angle 4 embodying orthogonality, contributing to the intricacies and precision inherent in geometric relationships.
Find the slope-intercept form of an equation for the line that passes through (–1, 2) and is parallel to y = 2x – 3.
For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the y axis.
By definition, if two straight lines are parallel then their slopes are equal. Thus, the slope of the line sought will be [tex]m = 2.[/tex]
[tex]y = 2x + b[/tex]
We substitute the given point to find b:
[tex]2 = 2 (-1) + b\\2 = -2 + b\\2 + 2 = b\\b = 4[/tex]
Finally the line is:
[tex]y = 2x + 4[/tex]
Answer:
[tex]y = 2x + 4[/tex]
Answer:
y = 2x + 4.
Step-by-step explanation:
The slope = the slope of y = 2x - 3 which is 2.
Using the point-slope form:
y - y1 = 2(x - x1)
Using the point (-1, 2):
y - 2 = 2(x - -1)
y = 2x + 2 + 2
y = 2x + 4 is the answer.
what is 1 1/4÷ by 3 4/5
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{3\frac{4}{5}}\implies \cfrac{3\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{19}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}\div\cfrac{19}{5}\implies \cfrac{5}{4}\cdot \cfrac{5}{19}\implies \cfrac{25}{76}[/tex]
Answer:
1/3
Step-by-step explanation:
covert the mixed number to an improper fraction
1x4+1 / 4
any expression multiplied by 1 remains the same
4+1 / 4
Add the numbers
5 / 4
Dividing is equivalent to multiplying with the reciprocal value
5 / 4 x 1 / 3 x 4 / 5
reduce the numbers with greatest common divisor 5
1 / 4 x 1 / 3 x 4
reduce the numbers with greatest common divisor 4
1 /3
The expression on the left side of an equation is shown below. 3x+9= []
If the equation has no solution, which expression can be written in the box on the other side of the equation?
A. –9
B. –3
C. 3x
D. 3x + 9
Answer:
C. 3x
Step-by-step explanation:
The first two choices give 1 solution each.
The last choice gives an infinite number of solutions.
Choice C. gives no solution.
3x + 9 = 3x
Subtract 3x from both sides.
9 = 0
Since 9 = 0 is false, equation 3x + 9 = 3x has no solution.
The expression can be written in the box on the other side of the equation as C. 3x.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given expression is
3x + 9 = _
Subtract 3x from both sides;
9 = 0
Since 9 = 0 is false,
The equation 3x + 9 = 3x has no solution.
Learn more about equations here;
https://brainly.com/question/10413253
#SPJ2
Ms. Jackson has 32 students. She needs to order a set of books for her class.
Each box has 12 books. How many boxes must she order to make sure each
student gets a book?
Answer:
3
Step-by-step explanation:
12 times table= 12,24,36..
if we have 24 books then not everyone can get a book.
it's best to get the 3 boxes of 36 as everyone can get one. As my teacher always said, the more the better.
If g of x equals x squares minus 1, find g of 2
Answer:
g(2) = 3
Step-by-step explanation:
g(x) = x² - 1.
Substituting 2 for x in this formula, we get:
g(2) = 2² - 1, or g(2) = 3
Answer:
g(2) =3
Step-by-step explanation:
g(x) = x^2 -1
Let x=2
g(2) = 2^2 -1
=4-1
=3
List three decimals between 4.2 and 4.3
Answer:
4.21 and 4.22 (answers will vary)
Step-by-step explanation:
There are a lot of different numbers you can pick. It just has to be between 4.2 and 4.3. This means that 4.200000000000000000000000000001 can be an answer and 4.29999999999999999999999999 can be an answer.
List all the perfect squares between 1 and 250
Answer: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.
Step-by-step explanation:
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 =49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
11 x 11 = 121
12 x 12 = 144
13 x 13 = 169
14 x 14 = 196
15 x 15 = 225
A couple finds that they are experiencing debt problems and decide to find a credit counseling agency. What are three (3) things that the couple should find out about an agency before they allow the agency to represent them?
Answer:
This is an odd question...
The couple should find out the following:
1.) is the agency legitimate?
2.) Will they be doing a hard inquiry on our credit history? if so, this could affect our current credit score
3.) Will they charge me to review my current credit reports?
Three things that should be considered about a credit agency are : Credibility and Reliability, Financial Efficiency, Accreditation and Acclamation
Given - The couple are facing debt issues. They need a credit counselling agency.
While choosing an agency, they should be careful about the following aspects of respective agency.
Credibility & Reliability - ie how trustworthy they are Financial Efficiency - denotes their competence in handling with funds Accreditation and Acclamation - represents the recognition and public image held by the agency.To learn more, refer https://brainly.com/question/1430582?referrer=searchResults
If two pyramids are similar and the ratio between the lengths of their edges is 3:4, what is the ratio of their volumes?
Answer:
The ratio of their volumes is 27/64
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
In this problem
The scale factor is 3/4
step 2
Find the ratio of their volumes
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
so
[tex](\frac{3}{4})^{3}=\frac{27}{64}[/tex]
A: what is the discriminators for the quadratic equation?
B:based on the discriminant which statement about the number and type of solutions in the equation is correct?
[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{\underline{one solution}}~~\textit{\Large \checkmark}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 6^2-4(1)(9)\implies 36-36\implies 0[/tex]
Answer:
0
Step-by-step explanation:
Descriminator is calculated by the following formula:
b*b - 4 * a * c, where a,b,c are the numbers in equitation.
Find the answer to each word problem.
29. Diane bought 48 bottles of water. Ewan
bought 60 bottles. The water came in
packs of the same number of bottles.
What is the greatest number of bottles
that could be in a pack?
Answer:
Step-by-step explanation:
This is a way of asking you what the highest common factor is. So factor into primes and find the highest that is between them.
48: 2 * 2 * 2 * 2 * 3
60: 2 * 2 * 3 * 5
The answer is Bolded and underlined.
HCF: 2 * 2 * 3
HCF: 12
The greatest number that could be in a pack is 12
The legs of a right triangle measure 5 centimeters and 12 centimeters. What
is the length of the hypotenuse?
Answer:
13
Step-by-step explanation:
Using pythag the. , we see the rule a2+b2=c2 (Square)
so, a2=25, b2= 144,
25+144=c2
c2=169
sqrt=13
What is the following product ^3sqrt16x^7*^3sqrt12x^9
Answer:
4x^5\sqrt[3]{3x}
Step-by-step explanation:
Given
[tex]\sqrt[3]{16x^7}\left(\sqrt[3]{12x^9}\right)\\\sqrt[3]{4^{2} x^7}\sqrt[3]{4(3)x^9}\\ 4^\frac{2}{3} . x^\frac{7}{3} . 4^\frac{1}{3} . 3^\frac{1}{3} . x^\frac{9}{3}\\ 4^\frac{2+1}{3} . 3^\frac{1}{3}. x^\frac{9+7}{3} \\4^\frac{3}{3} . 3^\frac{1}{3}. x^\frac{16}{3}\\ 4\sqrt[3]{3x^16}[/tex]
[tex]4\sqrt[3]{3} . x^\frac{16}{3} \\4\sqrt[3]{3} . x^\frac{15}{3} .x^\frac{1}{3} \\4\sqrt[3]{3} . x^5 .x^\frac{1}{3} \\4x^5\sqrt[3]{3x}[/tex] !
Answer:
The expression [tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex]
Required
Products of both
To do this, we have to apply the laws of indices,
Follow the highlighted steps
Step 1: Multiply both parameters directly
Since they both have the same roots, they can be multiplied directly according to the law of indices
[tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] becomes
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex]
Step 2: Apply the 1st law of indices
First law of indices states that
[tex]x^{a} * x^{b} = x^{a + b}[/tex]
So, [tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] becomes
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{7} * x^{9} }[/tex]
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{7+9} }[/tex]
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{16} }[/tex]
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{192 * x^{16} }[/tex]
Step 3: Rewrite the expression
[tex]\sqrt[3]{192 * x^{16} }[/tex] = [tex]({192 * x^{16} })^{\frac{1}{3} }[/tex]
Step 4: Expand the Expression in bracket
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]({64 * 3* x^{15} * x^{1} })^{\frac{1}{3} }[/tex]
Break down into bits
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]64^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex](4^{3}) ^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex](4^{3*\frac{1}{3}}) * 3^\frac{1}{3} * (x^{15}*^\frac{1}{3}) * (x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4 * 3^\frac{1}{3} * (x^{5}}) * (x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4 (x^{5}})* 3^\frac{1}{3} * (x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * (3^\frac{1}{3} * x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * (3x)^\frac{1}{3}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * \sqrt[3]{3x}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]
Hence, the expression [tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]
Factored form of x^12 y^16+1
Answer:
B
Step-by-step explanation:
let's recall that
1² = 1
1⁴ = 1
1¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 1
[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^{12}y^{18}+1\implies x^{4\cdot 3}y^{6\cdot 3}+1^3\implies (x^4)^3(y^6)^3+1^3\implies (x^4y^6)^3+1^3 \\[2em] [x^4y^6+1][(x^4y^6)^2-(x^4y^6)(1)+1^2]\implies (x^4y^6+1)(x^8y^{12}-x^4y^6+1)[/tex]
The figure shows the letter M and four of its transformed images—A, B, C, and D: Which of the four images was formed by a reflection of the letter M?
Answer:
Correct answer is figure D.
Step-by-step explanation:
According to the attached image Figure D is correct option.
In a reflection transformation, all the points of an object are reflected or flipped. It is a type of transformation where the new image is the mirror image of the original and x-coordinates and y-coordinates changes the place.
Figure A is rotation and translation and Figure B and C are translation
Thus the correct option is Figure D....
Solve by factoring or finding square roots
x^2-1=0
Answer:
{1,-1}
Step-by-step explanation:
Let's do both!
Factoring!
x^2-1 is a difference of squares.
The formula for factoring a difference of squares is: u^2-v^2=(u-v)(u+v).
So the factored form of x^2-1 is (x-1)(x+1).
So we want to solve the equation x^2-1=0 which is equivalent to solving
(x-1)(x+1)=0.
If you have A*B=0 then either A=0 or B=0.
So in our case we have x-1=0 or x+1=0.
Now we just solve the equations.
x-1=0 can be solved by adding 1 on both sides giving us x=1.
x+1=0 can be solved by subtracting 1 on both sides giving us x=-1.
Square root!
When you want to use square roots, you have to have a perfect square containing the variables and a constant. We have that here.
We have x^2-1=0 which is equivalent to x^2=1. You could get this last equation by adding one on both sides of x^2-1=0.
Anyway, once you have the square part equals the constant, all you have to do is square root both sides to get rid of the square on the variable part.
[tex]x^2-1=0[/tex]
[tex]x^2=1[/tex]
[tex]\sqrt{x^2}=\sqrt{1}[/tex]
[tex]x=\pm \sqrt{1}[/tex] It leads to two answers because [tex]\sqrt{x^2}=|x|[/tex].
[tex]x=\pm 1[/tex]
The solution to the equation x^2-1=0 is x = 1 or x = -1.
Explanation:To solve the equation x^2-1=0 by factoring or finding square roots, we can start by rearranging the equation to get x^2=1. This means that the square of x is equal to 1. To find the square root of both sides, we take the square root of 1, which gives us x=±1. So the solution to the equation is x = 1 or x = -1.
Learn more about Solving quadratic equations here:https://brainly.com/question/32403169
#SPJ2
Given the diagram below what is tan 60?
A. [tex]\sqrt{3}[/tex]
What is triangle and its properties?In the Geometry, the triangle is a 3-sided polygon that consists of 3 edges and 3 vertices. The most important property of the triangle is that the sum of the internal angles of the triangle is = to 180 degrees. its property is known as angle sum property of triangle.
We have been given the image of the right triangle and we are asked to find the value of the tan(60) for our given triangle
from we know that tangent represents the relation between opposite or adjacent of the right triangle.
[tex]tan = \frac{opposite}{adjacent}[/tex]
We can see that our adjacent side is not given, but corresponding angle to adjacent side is given that is 30 degrees. So we could conclude that our given triangle is 30-60-90 triangle.
from the sides corresponding to 30-60-90 triangle equals to[tex]x,x\sqrt{3}[/tex] and [tex]2x[/tex] , so the adjacent side for our given triangle will be,
[tex]x\sqrt{3} =8 \sqrt{3\\\\\\[/tex]
[tex]\frac{x \sqrt{3} }{\sqrt{3} } =\frac{8\sqrt{3} }{\sqrt{3} }[/tex]
[tex]x=8[/tex]
Upon substituting these values on above formula we will get,
[tex]tan( 60^{0} ) = \frac{8\sqrt{3} }{8} \\tan( 60^{0})=\sqrt{3}[/tex]
hence, the value of tan(60) is [tex]\sqrt{3}[/tex]and option B is the correct choice.
Learn more about triangle here https://brainly.com/question/2773823
#SPJ2
Which statements about the hyperbola are true? Check all that apply.
The center is located at (0, 0).
There is a vertex at (–6, 0).
The transverse axis of the graph is vertical.
The foci are located within the rectangular reference box.
The directrices are vertical lines.
Answer:
True options: 1, 2 and 5
Step-by-step explanation:
From the given diagram, you can see that the center of the hyperbola is placed at the origin, so first option is true (see attached diagram for definition of center, vertices, foci, i.e.)
There are two vertices of the hyperbola, they are placed at (-6,0) and (6,0), so second option is true.
The transverse axis is the segment connecting vertices, this segment is horizontal, so option 3 is false.
The foci are not placed within the rectangular reference box, so this option is false.
The directrices are vertical lines with equations [tex]x=\pm \dfrac{a}{e}[/tex], so this option is true.
Answer:1 2 5
Step-by-step explanation: