Answer:
log3 81 = 4
Step-by-step explanation:
Convert the exponential equation to a logarithmic equation using the logarithm base (3)(3) of the right side (81)(81) equals the exponent (4)(4).
log3(81)=4
or
you can remember this
loga Y= X
so, a^x =y
The logarithmic form of the equation 81=3^4 is log3 81 = 4. It uses the base number 3 (which is being raised to a power), the result of the multiplication (81), and the number of times 3 is multiplied by itself (4).
Explanation:The logarithmic form of the equation 81=3^4 can be found by applying the basic principles of logarithms. Remember, a logarithm is another way to express exponentiation, in a format that involves the base number, the exponent, and the result. Therefore, the logarithmic form of 81=3^4 is written as log3 81 = 4.
To understand this, consider the logarithmic expression log3 81 = 4. The base number (3 in this case) is the number being multiplied repeatedly (the number being raised to a power). The number 81 is the result of this multiplication, and 4 is the number of times base number, 3, is multiplied by itself to get 81. So, in this case, 3 to the power of 4 (3*3*3*3) equals 81.
So, in short, for the equation 81=3^4, the logarithmic form will be log3 81 = 4. This equation reads as "log base 3 of 81 equals 4".
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A graph uses the following intervals of 6-12, 13-19,20-26, 27-33, 34-40 to describe which set of data?
A: 40, 37, 33, 32, 29, 28.
28, 23, 22, 22, 22, 21,
21, 21, 20, 20, 19, 19,
18, 18, 18, 18, 16, 15,
14, 14, 14, 12, 12, 9,6
B: 25, 25, 22, 22, 19, 19,
18, 18, 18, 18, 16, 15,
14, 14, 14, 12, 12, 9,6
C: 30, 30, 30, 30, 29, 28,
28, 23, 22, 22, 22, 21,
21, 21, 20, 19, 19, 19,
18, 18, 18, 18, 16, 15,
14, 14, 14, 12, 12, 9,6
D: 55, 43, 33, 32, 29, 28,
28, 23, 22, 22, 22, 21,
21, 21, 21, 20, 19, 19,
18, 18, 18, 18, 16, 15,
14, 14, 14, 12, 12, 9,2
Answer:
A
Step-by-step explanation:
It Has The Most Matching Y Values with The Intervals (I could Be Wrong Tho)
Select the correct answer from each drop-down menu.
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same.
The volume of pyramid A is the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is the volume of pyramid A.
Answer:
lower section
Step-by-step explanation:
Given:
Pyramid A: Base is rectangle with length of 10 meters and width of 20 meters.
Pyramid B: Base is square with 10 meter sides.
Heights are the same.
Volume of rectangular pyramid = (L * W * H) / 3
Volume of square pyramid = a² * h/3
Let us assume that the height is 10 meters.
V of rectangular pyramid = (10m * 20m * 10m)/3 = 2000/3 = 666.67 m³
V of square pyramid = (10m)² * 10/3 = 100m² * 3.33 = 333.33 m³
The volume of pyramid A is TWICE the volume of pyramid B.
If the height of pyramid B increases to twice the of pyramid A, (from 10m to 20m),
V of square pyramid = (10m)² * (10*2)/3 = 100m² * 20m/3 = 100m² * 6.67m = 666.67 m³
The new volume of pyramid B is EQUAL to the volume of pyramid A.
The volume of the pyramid A is twice the volume of pyramid B. If the height of B is increased to twice, the volumes of A and B are equal.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given that,
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters.
The base of pyramid B is a square with 10-meter sides.
The heights of the pyramids are the same.
Volume of a rectangular pyramid = lwh / 3, where l, w and h are length, width and height respectively.
Volume of pyramid A = 10 × 20 × h /3 = 200/3 h
Volume of a square pyramid = a²h/3, where a is the side length of the base and h is the height.
Volume of pyramid B = 10²h/3 = 100/3 h
So volume of pyramid A = 2 × volume of B.
If height of B increased to twice that of pyramid A,
Volume of B = 100/3 (2h) = 200/3 h
So both are equal in this case.
Hence the volume of pyramid A is twice that of B in the first case and the volumes are equal in the second case.
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Three boys share 1.92 equally how much money does each boy get
Divide the total amount of money by the number of boys:
1.92/3 = 0.64 cents
Each boy gets 0.64 cents.
What is the area of this composite shape ?
Answer: 53 inches
Step-by-step explanation:
so to figure this out..
1. split the shape. there will be a 6 by 8 rectangle and a Height of 2 inches and the length of 5 inch triangle.
2.then find the area of 6 * 8 equals 48
3.Then find the area of the triangle. 5 * 2 equals 10. then Divide 10 / 2 your answer will be 5
4.Then add 48 and 5 together your answer will be 53
How many triangles satisfy the conditions a=14, b=2, and A=66?
Answer:
1
Step-by-step explanation:
0 Triangles satisfy the given condition.
What is the triangle inequality?
Triangle inequality theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c.
In this question:
a,b and A are three sides of triangle.
a=14
b=2 and
A=66
In this triangle
A+b=64>14A+a=80>2but, a+b=16<64 which violates the triangle inequality.Therefore, no such triangle with given dimension can exist.
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describe the graph of the functions y=|x+2|
To obtain the graph of the function y = |x+2| we have to make a table of values of x to find the values of y. The absolute value or modulus of a real number is its numerical value without care its sign. For example, the absolute value of |4| and |-4| is 4.
In order to make a graph we are going to use the values (-3, -2, -1, 0, 1, 2, 3) for x.
x = -3
y = |-3 + 2| = |-1| = 1
x = -2
y = |-2 + 2| = |0| = 0
x = -1
y = |-1 + 2| = |1| = 1
x = 0
y = |0 + 2| = |2| = 2
x = 1
y = |1 + 2| = |3| = 3
x = 2
y = |2 + 2| = |4| = 4
x = 3
y = |3 + 2| = |5| = 5
x ║ y
-3 1
-2 0
-1 1
0 2
1 3
2 4
3 5
Obtaining the graph shown in the image attached.
.
Does Maria have enough money for all three items? Explain.
Answer:
Yes, the art supplies cost $29.73, and I believe she has what looks on the picture to be $57
Step-by-step explanation:
Michael and 3 friends went to manny's pizza for lunch and their meal cost $32. If they left $4.80 for a tip what percent of their Bill did they leave as a tip? Show work please
Answer:
15%
Step-by-step explanation:
To calculate the percent of the bill that was left as a tip, you would divide the amount of the tip ($4.80) by the cost of the meal ($32) to get 0.15. This is then multiplied by 100 to give a tip percentage of 15%.
Explanation:To determine the percentage of the bill that was left as a tip, you would divide the amount of the tip by the cost of the meal and then multiply by 100 to convert the decimal to a percentage. This would calculate as follows:
Divide the tip amount ($4.80) by the meal cost ($32): $4.80/$32 = 0.15 Multiply by 100 to convert to a percentage: 0.15 x 100 = 15%.
So, Michael and his friends left a 15% tip on the bill.
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Which inequality is graphed below?
x > 7
x ≤ 7
x < 7
x ≥ 7
x < 7
It's not less than or equal to, because of the open circle on the seven
can i get brainliest if not thats fine
Answer:
x < 7
Step-by-step explanation:
did this for an assigment soooo
Place the following numbers in order from least to greatest.
3.9 , 113% ,
, 0.03 ,
A. 0.03 , , . , 3.9 , 113%
B.
, ,0.03 , 3.9 , 113%
C. 3.9 , 113%, , ,0.03
D. 0.03 , , 1, 113% , 3.9
Answer:
C.
Step-by-step explanation:
True or F alse : 5x + 2y = 0 is the equation of a line whose slope is undefined.
Answer:
False
Step-by-step explanation:
y = -(5/2)x
The slope is -(5/2)
Which list shows all the positive factors of 17?
Answer:
It's prime
Step-by-step explanation:
So there are no factors except 1 and 17
24) sin x = 1/3
Find cos x.
Answer:
[tex]\frac{2\sqrt{2} }{3}[/tex]
Step-by-step explanation:
The sine of an angle is defined as the ratio between the opposite side and the hypotenuse of a given right-angled triangle;
sin x = ( opposite / hypotenuse)
The opposite side to the angle x is thus 1 unit while the hypotenuse is 3 units. We need to determine the adjacent side to the angle x. We use the Pythagoras theorem since we are dealing with right-angled triangle;
The adjacent side would be;
[tex]\sqrt{9-1}=\sqrt{8}=2\sqrt{2}[/tex]
The cosine of an angle is given as;
cos x = (adjacent side / hypotenuse)
Therefore, the cos x would be;
[tex]\frac{2\sqrt{2} }{3}[/tex]
Answer:
[tex]cos(x) =\±2\frac{\sqrt{2}}{3}[/tex]
Step-by-step explanation:
We know that [tex]sen(x) =\frac{1}{3}[/tex]
Remember the following trigonometric identities
[tex]cos ^ 2(x) = 1-sin ^ 2(x)[/tex]
Use this identity to find the value of cosx.
If [tex]sen(x) =\frac{1}{3}[/tex] then:
[tex]cos ^ 2(x) = 1-(\frac{1}{3})^2[/tex]
[tex]cos ^ 2(x) =\frac{8}{9}[/tex]
[tex]cos(x) =\±\sqrt{\frac{8}{9}}[/tex]
[tex]cos(x) =\±2\frac{\sqrt{2}}{3}[/tex]
Show that (x-1)(x+2)(x+3) can be written in the form ax^3+bx^2+cx+d
Answer:
x³ + 4 x² + x - 6
Step-by-step explanation:
( x - 1 ) ( x + 2 ) ( x + 3 )
( x - 1 ) ( x + 2 ) = x² + 2 x - 1 x - 2 = x² + x - 2
( x² + x - 2 ) ( x + 3 ) = x³ + 3 x² + x² + 3 x - 2 x - 6 = x³ + 4 x² + x - 6
The expression (x-1)(x+2)(x+3) can be written as x³ + 4x² + x—6 after multiplication of the expression.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have:
= (x-1)(x+2)(x+3)
After multiplying first and second terms:
[tex]\rm =\left(x^2+x-2\right)\left(x+3\right)[/tex]
Again multiplying:
[tex]\rm =x^3+4x^2+x-6[/tex]
Thus, the expression (x-1)(x+2)(x+3) can be written as x³ + 4x² + x—6 after multiplication of the expression.
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Which system is equivalent to
Answer:
the forth one
Step-by-step explanation:
The answer above is right
not geometric
0. What is the 10th term of the sequence 64, 16, 4, ....
Answer:
[tex]\frac{1}{4096}[/tex]
Step-by-step explanation:
To solve this we are using the formula for the nth term of a geometric sequence:
[tex]a_n=a_1r^{n-1}[/tex]
where
[tex]a_1[/tex] is the first term
[tex]r[/tex] is the common ratio
[tex]n[/tex] is the position of the term in the sequence
The common ratio is just the current term divided by the previous term in the sequence, so [tex]r=\frac{16}{64} =\frac{4}{16} =\frac{1}{4}[/tex]. We can infer from our sequence that its first term is 64, so [tex]a_1=64[/tex].
Replacing values
[tex]a_n=a_1r^{n-1}[/tex]
[tex]a_n=64(\frac{1}{4} )^{n-1}[/tex]
We want to find the 10th term, so the position of the term in the sequence is [tex]n=10[/tex].
Replacing values
[tex]a_n=64(\frac{1}{4} )^{n-1}[/tex]
[tex]a_{10}=64(\frac{1}{4} )^{10-1}[/tex]
[tex]a_{10}=64(\frac{1}{4} )^{9}[/tex]
[tex]a_{10}=\frac{1}{4096}[/tex]
We can conclude that the 10th term of the sequence is [tex]\frac{1}{4096}[/tex]
Answer:
10th term of the sequence 64,16,4... = 1/4096
Step-by-step explanation:
Points to remember
nth term of GP is given by.
Tₙ = ar⁽ⁿ⁻¹⁾
Where r is the common ratio and a is the first term
To find the 10th term of given GP
It is given that,
64, 16, 4,......
a = 64 and 6 = 1/4 Here
T₁₀ = ar⁽ⁿ⁻¹⁾
= 64 * (1/4)⁽¹⁰⁻¹⁾ = 64 * (1/4⁹)
= 4³/4⁹ = 1/4⁶ = 1/4096
The quantities x and y are proportional.
x y
9 4.54
14 7
30 15
Find the constant of proportionality (r) in the equation y=rx
Answer:
its 1/2
Step-by-step explanation:
Final answer:
The constant of proportionality (r) in the equation y=rx can be found by dividing y by x for any given pair of values. Using the pair (14, 7), the constant of proportionality is calculated as r = 7 / 14 = 0.5.
Explanation:
The quantities x and y are said to be proportional if they relate via a constant of proportionality, which we refer to as r in the equation y=rx. To find the constant of proportionality, you can choose any given pair of values for x and y and divide them. For example, using the given pair (14, 7), we can find r by dividing 7 by 14.
r = y / x = 7 / 14 = 0.5
Therefore, the constant of proportionality r is 0.5. You can check this value with other given pairs to confirm it is consistent. For further confirmation, using the pair (30, 15), we have:
r = 15 / 30 = 0.5
which matches our previously calculated constant of proportionality.
las bases de un prisma recto son dos triangulos rectangulos cuyos catetos miden 1.5 cm y 1.8 cm, respectivamente, el prisma tiene una altura de 4.5cm. calcula su area total y volumen
Answer:
Part 1) The surface area is [tex]SA=35.1\ cm^{2}[/tex]
Part 2) The volume is equal to [tex]V=12.15\ cm^{3}[/tex]
Step-by-step explanation:
The question in English is
The bases of a right prism are two rectangle triangles whose legs measure 1.5 cm and 1.8 cm, respectively, the prism has a height of 4.5 cm. calculates its total surface area and volume
Part 1) Find the surface area
The surface area is equal to
[tex]SA=2B+Ph[/tex]
where
B is the area of the base
P is the perimeter of the base
h is the height of the prism
Find the area of the base B
[tex]B=(1.5)(1.8)=2.7\ cm^{2}[/tex]
Find the perimeter of the base P
[tex]P=2*(1.5+1.8)=6.6\ cm[/tex]
we have
[tex]h=4.5\ cm[/tex]
substitute the values
[tex]SA=2(2.7)+(6.6)(4.5)=35.1\ cm^{2}[/tex]
Part 2) Find the volume
The volume is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the prism
we have
[tex]B=2.7\ cm^{2}\\ h=4.5\ cm[/tex]
substitute
[tex]V=(2.7)(4.5)=12.15\ cm^{3}[/tex]
I need help with this..
Answer:
a0) 2
x<0
a1) x
0≤x<3
a2) 3
x≥3
Step-by-step explanation:
As shown in the given graph
function of y is a straight line at y=2 line till x=0
hence a0:
y= 2 for x<0
Then function becomes linear line from x=0 till x=3
hence a1:
y= x for 0≤x<3
Now after that graph of function y again shift to straight line from x=3 onward with y-axis value of 3
hence a2:
y= 3 for x≥3 !
Using the tax table, determine the amount of taxes for the following situations: (Do not round intermediate calculations. Round your answers to 2 decimal places.)
a. A head of household with taxable income of $58,500.
b. A single person with taxable income of $36,400.
c. Married taxpayers filing jointly with taxable income of $72,700.
To calculate taxes for each scenario, use the progressive tax rate schedules to find the correct tax bracket, apply the marginal tax rate, add any base tax amount, and complete the calculation for the head of household, single person, and married taxpayers filing jointly.
Explanation:To calculate the amount of taxes for the given situations, we use the tax rate schedules provided. For each scenario, the tax is calculated based on the income brackets and the corresponding tax rates in the tax table, which align with a progressive tax system. Detailed calculations are needed with step-by-step explanations for accuracy.
Head of Household with taxable income of $58,500: First, determine the tax bracket according to the tax table and then apply the relevant tax rate and base amount.Single person with taxable income of $36,400: Identify the appropriate bracket from the tax table, then calculate the taxes owed by applying the marginal tax rate.Married taxpayers filing jointly with taxable income of $72,700: Locate their bracket in the shared tax table and calculate the corresponding taxes using the stipulated rate and base amount.The mentioned tax brackets and rates are based on example tax tables; the actual calculations would depend on the specific tax brackets and rates set forth by the IRS for the given tax year.
Factorise:-
2x^2 -7x-15
Answer:
(x - 5)(2x + 3)
Step-by-step explanation:
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 15 = - 30 and sum = - 7
The factors are - 10 and + 3
Use these factors to split the x- term
2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )
= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term
= (x - 5)(2x + 3)
The factorization of the quadratic expression is presented as follows;
2·x² - 7·x - 15 is (2·x + 3)·(x - 5)
What is a quadratic expression?A quadratic expression is an expression that can be presented in the form a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.
In order to factorize the quadratic expression 2·x² - 7·x - 15, it is required to find two binomials with a product equivalent to the expression is to be found
The binomial can be found from the numbers p and q such that p + q = -7 and p·q = -30 (The product of the leading coefficient and the constant term)
A possible pair of such numbers is p = -10 and q = 3. Therefore, we get;
2·x² - 7·x -15 = 2·x² + (3·x - 10·x) - 15
The first two terms and the last two terms can be grouped and each group factorized separately as follows;
2·x² + (3·x - 10·x) - 15 = (2·x² + 3·x) + (-10·x - 15)
x·(2 + 3) - 5·(2·x + 3)
The above expression can be further factorized by taking out the common factor (2·x + 3) as follows;
x·(2 + 3) - 5·(2·x + 3) = (2·x + 3)·(x - 5)
Therefore, the factored expression is; 2·x² - 7·x - 15 = (2·x + 3)·(x - 5)
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What is the value of x?
Answer:
x = 3Step-by-step explanation:
Look at the picture.
Therefore we have:
[tex]\dfrac{4}{3}=\dfrac{x}{2.25}[/tex] cross multiply
[tex]3x=(4)(2.25)[/tex]
[tex]3x=9[/tex] divide both sides by 3
[tex]x=3[/tex]
Find the focus of the parabola that has a vertex at (0,0) and that passes through the points (-3,3) and (3,3)
Answer:
Focus = (0, [tex]\frac{3}{4}[/tex])
Step-by-step explanation:
(± 3, 3) are at an equal distance from y-axis.
axis of parabola = y-axis
vertex = (0, 0)
Parabola will be of the form: x² = 4ay, passing through(± 3, 3)
(± 3)² = 4 × a × 3 ⇒ 9 = 12a ⇒ a = [tex]\frac{9}{12}[/tex]
a = [tex]\frac{3}{4}[/tex]
Coordinates of focus are: (0, a) ⇒ (0, [tex]\frac{3}{4}[/tex])
Answer:
The focus of the parabola is (0 , 3/4)
Step-by-step explanation:
* Lets revise some facts about the parabola
- The standard form of the equation of a parabola of vertex (h , k)
is (x - h)² = 4p (y - k)
- The standard form of the equation of a parabola of vertex (0 , 0) is
x² = 4p y, from this equation we can find:
# The axis of symmetry is the y-axis, x = 0
# 4p equal to the coefficient of y in the given equation
# If p > 0, the parabola opens up.
# If p < 0, the parabola opens down.
# The coordinates of the focus, (0 , p)
# The directrix , y = − p
* Now lets solve the problem
∵ The vertex of the parabola is (0 , 0)
∴ The equation of the parabola is x² = 4p y
∵ the parabola passes through points (-3 , 3) and (3 , 3)
- Substitute the value of x and y coordinates of one point in the
equation to find the value of p
∴ (3)² = 4p (3) ⇒ we use point (3 , 3)
∴ 9 = 12 p ⇒ divide both sides by 12
∴ p = 9/12 = 3/4
- Now lets find the focus of the parabola
∵ The focus of the parabola is (0 , p)
∵ p = 3/4
∴ The focus of the parabola is (0 , 3/4)
Please help I need help I will mark brainliest
a:
Just divide both sides by 7. Since 7 is positive, you don't need to change the inequality sign:
[tex]7j>77\iff j>11\}[/tex]
In set notation, we write
[tex]\{j \in \mathbb{R}\ :\ j>11[/tex]
b:
Subtract 9 from both sides:
[tex]17\leq x+9 \iff 8\leq x[/tex]
In set notation, we write
[tex]\{x \in \mathbb{R}\ :\ x\geq 8\}[/tex]
identify the features of the graph
-is a positive parabola
-has two roots at x= 1 and x= 5
- has a y-intercept at y=5
- has a minimum at (3, -4)
- axis of symmetry is x=3
What they said ^^^^^^^^^^^^^^^
PLZZZ HELP ME SOLVE!!!!!!!
Answer:
D. 6^30
explanation:
(6^36)/(6^6)= 6^30
You are riding your bicycle to prepare for a race. it takes you 12 minutes to go 2.5 miles. what was your speed in miles per hour?
Answer:
12.5 miles per hour.
Step-by-step explanation:
There are 60 minutes in 1 hour so:
12 minutes = 12/60 = 1/5 of an hour.
So his speed in mph
= distance in miles / time in hours
= 2.5 / 1/5
= 2.5 * 5
= 12.5 miles per hour.
The speed in miles per hour is 12.5 miles/hour
How to calculate speed?
We define speed as :
Speed= Distance/Time
In other words, it is the distance travelled in a unit time
Here,
Distance=2.5 miles
Time=12 minutes that is 12/60 =1/5 hours
[tex]Speed=\dfrac{2.5}{1/5}[/tex]
Speed= 2.5*5=12.5 miles/hour
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A shooting star forms a right triangle with the Earth and the Sun, as shown below:
A right triangle is shown with the vertices labeled Earth, Sun, and Shooting Star. The angle formed by the Sun is labeled x deg
A scientist measures the angle x and the distance y between the Sun and the shooting star. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the Sun. (10 points)
Answer:
- The scientist can use these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Cosine of an angle.
- The scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] and solve for the distance between the Earth and the Sun.
Step-by-step explanation:
Let's assume that the right triangle formed is like the one shown in the figure attached, where "d" represents the distance between the Earth and the Sun.
Then:
The scientist can use only these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Cosine of an angle.
The scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex], and solve for the distance "d".
Knowing that:
[tex]\alpha=x\°\\adjacent=d\\hypotenuse=y[/tex]
Then:
[tex]cos(x\°)=\frac{d}{y}[/tex]
And solving for "d":
[tex]ycos(x\°)=d[/tex]
The scientist can use the tangent function in trigonometry with the measured angle x and distance y to calculate the distance between the Earth and the Sun by rearranging the formula to solve for the opposite side of the right triangle formed.
Explanation:The scientist can calculate the distance between the Earth and the Sun using the measurements of angle x and distance y through a process known as triangulation or the parallax method. The right triangle formed with vertices at the Earth, Sun, and Shooting Star allows for the application of trigonometric functions. Specifically, the scientist can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side over the adjacent side.
To find the distance between the Earth and the Sun, the scientist applies the formula:
tan(x) = opposite/adjacent
Where opposite is the distance between the Earth and the Shooting Star, and adjacent is the distance between the Sun and the Shooting Star (y). By rearranging the formula to solve for the opposite side, we get:
Distance between Earth and Sun = y * tan(x)
This calculation allows the scientist to determine the distance from the Earth to the Sun, given that they have the measurements of angle x and distance y.
These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.
Answer:
[tex]36.5\ cm^{2}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let
z ----> the scale factor
x----> the perimeter of the larger figure
y ----> the perimeter of the smaller figure
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=28\ cm[/tex]
[tex]y=20\ cm[/tex]
substitute
[tex]z=\frac{28}{20}=1.4[/tex]
step 2
Find the area of the larger figure
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x----> the area of the larger figure
y ----> the area of the smaller figure
[tex]z^{2} =\frac{x}{y}[/tex]
we have
[tex]z=1.4[/tex]
[tex]y=18.6\ cm^{2}[/tex]
substitute
[tex]1.4^{2} =\frac{x}{18.6}[/tex]
[tex]x=1.96*(18.6)=36.5\ cm^{2}[/tex]
Image point B'(4, -8) was transformed using the translation (x - 2, y + 3). What were the coordinates of B?
(2, -5)
(6, -5)
(2, -11)
(6, -11)
Answer:
(6,-11)
Step-by-step explanation:
Given
Point B' = (4,-8)
And the translation formula (x-2, y+3)
In order to get the coordinates of the point before translation, both given points have to be put equivalent.
So, for x-coordinate
x-2 = 4
x= 4+2
x= 6
And for y-coordinate
y+3 = -8
y = -8-3
y=-11
So the old coordinates of old point were (6,-11) ..
your answer is (6, -11)