Answer:
The height of the lighthouse is approximately 166.6 feet.
Step-by-step explanation:
Let the height of the lighthouse be represented by s, then;
Tan 48° = (opposite) ÷ (adjacent)
Tan 48° = s ÷ 150
⇒ s = 150 × Tan 48°
= 150 × 1.1106
= 166.59
s ≅ 166.6 feet
Therefore, the height of the lighthouse is approximately 166.6 feet.
Answer:
The height of the lighthouse is approximately 42.
Step-by-step explanation:
This situation forms a right triangle so the angles would be 90 and 48
90+48+x=180
138+x=180
x=180-138
x=42
If $x \geq 0$ and $y \geq 0$, how many lattice points does the line $y = -2x + 18$ pass through?
A set of circular cups are placed so that they are touching rim to rim, as close together as possible. It is not possible to fit more cups inside the group if the longest straight line is five cups long, how many cups are there altogether?
Answer:
The total number of cups in arranged in an hexagonal area = 19 cups
Step-by-step explanation:
The pack the most circles within an area, the arrangement with the densest packing is the hexagonal lattice structure similar to the bee's honeycomb as has been proved Gauss and Fejes Toth.
Therefore, we pack the circles in an hexagonal lattice structure in an assumed hexagonal area where we have;
The longest straight line is five cups the next on either side are four cups and the final line on either side has three cups
The total number of cups = 3 + 4 + 5 + 4 + 3 = 19 cups
The total number of cups = 19 cups.
After years of maintaining a steady population of 32,000, the population of a town begins to grow exponentially. After 1 year and an increase of 8% per year, the population is 34,560. Which equation can be used to predict, y, the number of people living in the town after x years? (Round population values to the nearest whole number.) y = 32,000(1.08)x y = 32,000(0.08)x y = 34,560(1.08)x y = 34,560(0.08)x
Answer:
y = 32,000(1.08)^x
Step-by-step explanation:
The exponential growth equation is y = a(1 + r)^x, where a is the initial amount, r is rate as a decimal, and x is the time.
In this situation, 32,000 is the initial amount (a) and 0.08 is the rate (r)
If we plug these into the equation, we get the equation y = 32,000(1.08)^x
So, y = 32,000(1.08)^x is the correct answer.
Answer:
A
Step-by-step explanation:
on edge 2020
[tex] \frac{ {9x}^{2} - {(x}^{2} - 4) {}^{2} }{4 + 3x - {x}^{2} } [/tex]
pls help me need help asap
Answer:
[tex] { x^2+3x-4} [/tex]
Step-by-step explanation:
Factor top and bottom.
The numerator is a difference of two squares, and the denominator is a quadratic.
[tex] \frac{ {9x}^{2} - {(x}^{2} - 4)^{2} }{4 + 3x - {x}^{2} } [/tex]
= [tex]\frac{ (3x+x^2-4)(3x-x^2+4) }{(1+x)(4-x)}[/tex]
= [tex] \frac{ (x-1)(x+4) (1+x)(4-x) }{(1+x)(4-x)} [/tex]
If x does not equal -1 and does not equal 4, we can cancel the common factors in italics to give
= [tex] { (x-1)(x+4)} [/tex]
= [tex] { x^2+3x-4} [/tex]
Answer:
The answer is
x² + 3x - 4Step-by-step explanation:
[tex] \frac{9 {x}^{2} - ( { {x}^{2} - 4})^{2} }{4 + 3x - {x}^{2} } [/tex]
To solve the expression first factorize both the numerator and the denominator
For the numerator
9x² - ( x² - 4)²
Expand the terms in the bracket using the formula
( a - b)² = a² - 2ab + b²
(x² - 4) = x⁴ - 8x² + 16
So we have
9x² - (x⁴ - 8x² + 16)
9x² - x⁴ + 8x² - 16
- x⁴ + 17x² - 16
Factorize
that's
(x² - 16)(-x² + 1)
Using the formula
a² - b² = ( a + b)(a - b)
We have
(x² - 16)(-x² + 1) = (x + 4)(x - 4)( 1 - x)(1 + x)
For the denominator
- x² + 3x + 4
Write 3x as a difference
- x² + 4x - x + 4
Factorize
That's
- ( x - 4)(x + 1)
So we now have
[tex] \frac{(x + 4)(x - 4)( 1 - x)(1 + x)}{ - (x - 4)(x + 1)} [/tex]
Simplify
[tex] \frac{ - (x + 4)(1 - x)(1 + x)}{x + 1} [/tex]
Reduce the expression by x + 1
That's
-( x + 4)( 1 - x)
Multiply the terms
We have the final answer as
x² + 3x - 4Hope this helps you
after allowing 5 percent discount on the marked price of a radio 10 percent vat is charged on it , then its price became rs 1672 .how much amount was given in the discount
Answer:
Marked price= RS 1600
Discount= RS 80
Step-by-step explanation:
Let
x= the marked price
Discount= 5%
Discount = 5% of x
=0.05x
Cost after discount = x-0.05x
= 0.95x
Vat=10%
=0.1
Cost of the radio including vat=0.95x + 0.1(0.95x)
=0.95x + 0.095x
=1.045x
Price became rs 1672
Therefore,
1.045x=1672
Divide both sides by 1.045
x= RS 1600
Discount=5% of 1600
=0.05 * 1600
=rs 80
The term to term rule of a sequence is "multiply by 3 and add 1". The third term is 13. Work out the first term of the sequence.
Answer:
The first term is 1
Step-by-step explanation:
The forward term to term rule is "multiply by 3 and add 1"
The backward rule is therefore
"subtract 1, then divide by three"
Apply the backward rule twice to go from 3rd to first term:
(13-1)/3 = 4
(4-1)/3 = 1
The first term is 1
Answer:
a_1 = 1
Step-by-step explanation:
your sequence is a_n = a_(n-1) * 3 + 1
if your 3rd one is 13 then:
a_3 = a_2 * 3 + 1 = (a_1 * 3 + 1) *3 + 1
13 = 9_a1 + 3 + 1
9 = 9*a_1
a_1 = 1 :)
8 more than a number
Answer:
[tex]\boxed{ 8 + x}[/tex]
Step-by-step explanation:
Hey there!
In most cases "the number" would be x.
So if the statement says 8 "more than a number",
It is saying 8 plus x or 8 + x.
Hope this helps :)
Answer:
x + 8 is the meaning.
Step-by-step explanation:
“more” means addition. Take the number as “x”, so it will be x + 8.
That's the answer.
Enter the coordinates of the point
on the unit circle at the given angle.
60°
Answer:
(1/2, [tex]\frac{\sqrt{3} }{2}[/tex])
Step-by-step explanation:
Don't totally trust me on this...
*This Question Has 3 Questions in it
Question 1 Use a calculator to find [tex]\sqrt{61.6}[/tex] to the nearest hundredth.
Question 2 Which of the following statements is true?
Refer to Question 2 . PNG
Question 3 simplify [tex]\sqrt{0.81}[/tex]
Answer:
Ques 1: 7.85
Ques 2: both [tex]\sqrt{0.25}[/tex] and [tex]-\sqrt{16}[/tex] are rational.
Ques 3: 0.9
Step-by-step explanation:
Ques 1:
Solving the [tex]\sqrt{61.6}[/tex], we get 7.8485.
Rounding off to nearest hundredth, we see that next digit is 8, so we increase the previous digit by 1.
So, the answer to nearest hundredth is 7.85.
Ques 2:
[tex]\sqrt{0.25}[/tex] and [tex]-\sqrt{16}[/tex]to be checked whether they are rational or irrational.
We know that [tex]\sqrt{16}[/tex] is equal to 4.
[tex]-\sqrt{16}[/tex] = -4 which is a rational value.
Let us solve [tex]\sqrt{0.25}[/tex] now.
[tex]\sqrt{0.25} = \sqrt{\dfrac{25}{100}}\\\Rightarrow \dfrac{5}{10}[/tex]
Which is a rational value.
So, both are rational.
Ques 3:
Simplify [tex]\sqrt{0.81}[/tex]
0.81 can be written as [tex]\frac{81}{100}[/tex] in rational form.
Now, taking the square root, we need to take the square root for both Numerator and Denominator and then we can divide to get the desired square root.
[tex]\sqrt{0.81} = \sqrt{\dfrac{81}{100}}\\\Rightarrow \dfrac{9}{10} = \bold{0.9}[/tex]
So, the answers are:
Ques 1: 7.85
Ques 2: both [tex]\sqrt{0.25}[/tex] and [tex]-\sqrt{16}[/tex] are rational.
Ques 3: 0.9
Which of the following terms correctly describe the object below?
Check all that apply.
a. polyhedron
b. pyramid
c. prism
d. solid
e. cube
f. polygon
*will mark brainliest :))
Answer:
The given figure is:
a. Polyhedron
c. prism
d. solid
Step-by-step explanation:
First of all, let us consider the given image.
It is a 3 dimensional figure.
It has 2 equal bases which are pentagonal.
Its faces are made along the sides of the bases and are rectangular in shape.
Now, let us classify the given image in following:
a. Polyhedron:
A polyhedron is a 3-D (three dimensional) shape in which there are flat faces.
The faces can be of 'n' number of edges (Polygonal faces).
Its edges are straight, has sharp corners which are also known as vertices.
The given image is a polyhedron as per above definition.
b. Pyramid:
It is also a 3D shape which can have a polygonal base and its faces are triangular which converge on the top to one point.
The given image does not converge to a point on the top, so not a pyramid.
c. Prism:
It is a 3D shape which has it two bases as polygonal structure.
The two bases are equal in shape and size.
There are faces on the body of prism which are formed by joining the edges of the bases.
The given image is a prism with pentagonal bases.
d. Solid:
Any 3D image is called a solid and has a length, width and height.
So, the given image is a Solid.
e. Cube:
Cube is a 3D figure, which has all its faces in square shape.
All the sides are equal for a cube.
The given image is not a cube.
f. Polygon:
A polygon is a closed figure in 2 dimensions which has n number of sides.
The given image is not a polygon.
Answer: The given figure is:
a. Polyhedron
c. prism
d. solid
The given figure is a Polyhedron, prism and solid.
What is a polyhedron?A polyhedron is a three-dimensional geometry having plane surfaces connected together with sharp edges and pointed vertices.
First of all, let us consider the given image. It is a 3-dimensional figure. It has 2 equal bases which are pentagonal. Its faces are made along the sides of the bases and are rectangular in shape.
Now, let us classify the given image in the following:
a. Polyhedron:
A polyhedron is a 3-D (three dimensional) shape in which there are flat faces. The faces can be of 'n' number of edges (Polygonal faces). Its edges are straight, has sharp corners which are also known as vertices. The given image is a polyhedron as per the above definition.
c. Prism:
It is a 3D shape which has it two bases as a polygonal structure.The two bases are equal in shape and size. There are faces on the body of prism which are formed by joining the edges of the bases. The given image is a prism with pentagonal bases.
d. Solid:
Any 3D image is called a solid and has a length, width and height. So, the given image is a Solid.
To know more about Polyhedrons follow
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What is the value of x ?
Answer:
x = 3
Step-by-step explanation:
Given two secants drawn from an external point to the circle, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is
x(x + 21) = (x + 1)(x + 1 + 14)
x² + 21x = (x + 1)(x + 15) ← expand using FOIL
x² + 21x = x² + 16x + 15 ( subtract x² + 16x from both sides )
5x = 15 ( divide both sides by 5 )
x = 3
why is gravitational force between two object usually unnoticeable
Answer:
gravitational attraction is based upon mass.More the mass more the force.When the object is as big as a moon it has a very less gravity.When we are talking about small objects like 2 pencils the force exists but is so weak that no noticabke movement takes place
Answer:
To notice that force, the objects have to have a big mass and be close to each others.
Generally in eveydays life, you don't notice this force since it is weak but that doesn't mean it does't exist.
If you go the space, you can notice this force since planets have big mass. If you get close to the gravitational field of a planet, you will feel a force that is pulling you toward the planet.
If A = C + 3A=C+3, B = 2CB=2C, and C = 4C=4, which is the correct order from least to greatest?
Answer:
B, C, A.
Step-by-step explanation:
A = C + 3A = C + 3
A = C + 3
A = C + 3A
C + 3A = C + 3
3A = 3
A = 1
A = C + 3
1 = C + 3
C + 3 = 1
C = -2
B = 2C
B = 2(-2)
B = -4.
So, from least to greatest, B = -4, C = -2, and A = 1.
Hope this helps!
Mrs. Winthrop went to a store, spent half of her
money and then $ 10 more. She went to a
second store, spent half of her remaining money
and $ 10 more. But she then had no money left.
How much money did she have to begin with
when she went to the first store?
Answer:
Step-by-step explanation:
Ok so I go to the store
I spend X/2 - 10 and I'm left with x/2
Then I got to store 2 and spend x/2 - 10 again and now have no money left.
So
x/2-10=0
x/2=10
x=20
Before that, she had:
x/2-10=20
x/2=30
x=60
So she started out with $60
She has $60, to begin with when she went to the first store.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
The operator that performs arithmetic operations is called an arithmetic operator.
Operators let do basic mathematical calculations.
+ Addition operation: Adds values on either side of the operator.
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
For example 4 + 2 = 6
Let she had x money before the second store.,
So x-x/2–10=0 => x = 20.
Let she had y money before the first store,
where x = y-y/2–10.
So y/2 = 20+10=30
⇒ y = 60
Hence, she has $60, to begin with when she went to the first store.
Learn more about Arithmetic operations here:
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A piece of blue yarn is 5/ 3/7 yards long. A piece of pink yarn is 5 times as long as the blue yarn. How much longer is the pink yarn than the blue yarn?
Answer:
27 1/7
Step-by-step explanation:
Multiply 5×5=25 and afterwards multiply 3/7×5=2 1/7
Murphy purchases two bags of rice of weights 56 kg and 72 kg. Find the maximum value of weight which can measure the weight of the rice exact number of times.
Answer:
8
Step-by-step explanation:
In order to answer this question we need to find the greatest common divisor of the two quantities which will give us the maximum number by which both can be divided.
The greatest common divisor of a group of integers is the largest common divisor that divides each of the integers. The first step to find it is write down the integers as a product of primes, so we have:
[tex]56=(28)(2)=(14)(2)(2)=(7)(2)(2)(2)= 2^3[/tex]·[tex]7[/tex]
[tex]72=(24)(3)=8(3)(3)=2^3[/tex]·[tex]3^2[/tex]
Now, in order to find the gcd we are going to take the factors that they have in common. In this case they both share the [tex]2^3[/tex].
Thus, [tex]2^3=8[/tex] is the greatest common divisor and therefore the maximum value of weight which can measure the weight of the rice exact number of times.
Find the value of x. A. 74 B. 244 C. 52 D. 64
Answer:
Step-by-step explanation:
The formula you need to solve for angle x is:
∠x = 1/2(large arc - small arc)
We have enough info to find what we need to solve for the arcs. 58° is an inscribed angle. The rays of the angle cut off an arc on the circle and that arc measure is twice the measure of the angle. So the smaller arc is 58 * 2 = 116. Since around the outside of the circle measures 360°, then the larger arc measures 360 - 116 = 244. So the larger arc is 244. Filling in the formula to solve for the angle x:
∠x = 1/2(244 - 116) and
∠x = 1/2(128) so
∠x = 64
D is your answer.
Answer:
D.) 64
Step-by-step explanation:
I got it correct on founders edtell
Anne can make 6 headbands from 3/5 meters of cloth. Which expression shows the amount of cloth needed to make 1 headband? What is the solution to the expression? The expression that shows the amount of cloth needed to make 1 headband is . The solution to the expression is meters.
Answer:
Needed to make one band = 3/5 / 6 meters.
The solution is 1/10 meters.
Step-by-step explanation:
The expression is 3/5 / 6
= 3/5 * 1/6
= 3/30
= 1/10
Answer:
6 x (3/5)
1/10
Step-by-step explanation:
The Cartesian coordinate system can be applied to three-dimensional solids. Instead of two axes, the coordinate system has three. What are the labels? Check all that apply.
A. z
B. y
C. a
D. x
E. w
Answer:
its z y and x
Step-by-step explanation:
can i pls get brainliest
Water flows from a bathroom tap at a rate of 2 gallons every 6 seconds. At this rate, how many minutes will it take to fill an 80-gallon tub?
Answer:
240 minutes
Step-by-step explanation:
i divide 80 divided by 2 then multiply the answer which is 40 by 6 and get 240
answer these questions with Always,never it sometimes
An exterior angle of a triangle is equal to the sum of its adjacent angle and one remote interior angle
An isosceles triangle is an equilateral triangle
An equilateral triangle is an isosceles triangle
Answer:
sometimes. exterior angle of a triangle is equal to the sum two remote interior angles. But in a special case when the adjacent angle is equal to the remote interior angle, it is true
sometimes. Only when the isosceles triangle is equilateral
always. This is always true by definition.
Double a number decreased by 25.6 is equal to 90 Find the number
Answer:
Step-by-step explanation:
2x-25,6=90
2x=90+25,6
2x=115,6
x=57,8
Answer:
The number is 57.8
Step-by-step explanation:
Let x = number
2x -25.6 = 90
Add 25.6 to each side
2x-25.6 +25.6 = 90+25.6
2x=115.6
Divide by 2
2x/2 =115.6/2
x =57.8
Make the biggest possible number using the digits below only once 3 , 1 , 3 answer
Answer:
331 the biggest possible number
Which of the following systems of linear equations has a solution of (-4,3)? 1. −4x+2y=22 −y=−3x−9 2. −4x+2y=22 y=−3x−9 3. −4x−2y=22 y=−3x−9 4. −4x−2y=22 −y=−3x−9
Hey there! I'm happy to help!
SYSTEM #1
-4x+2y=22
-y=-3x-9
We can multiply both sides of the second equation by -1 to see what y equals.
y=3x+9
We can substitute this value for y into the first equation and solve for x.
-4x+2(3x+9)=22
We use distributive property to undo the parentheses.
-4x+6x+18=22
We combine like terms.
2x+18=22
Subtract 18 from both sides.
2x=4
Divide both sides by 2.
x=2
Our x has to be -4 to be the correct answer, so this option is incorrect.
SYSTEM #2
-4x+2y=22
y=-3x-9
We plug this y value into the first equation to solve for x.
-4x+2(-3x-9)=22
We use distributive property to undo the parentheses.
-4x-6x-18=22
We combine like terms.
-10x-18=22
Add 18 to both sides.
-10x=40
x=-4
We have the correct x-value to be the answer, so let's find the y-value by plugging our x-value into one of the equations.
y=-3(-4)-9
y=12-9
y=3
So, the solution of this system of equations is (-4,3), so the correct answer is 2. -4x+2y=22, y=-3x-9
Have a wonderful day! :D
Helppp meeeew pleaseeeee
Answer:
Hey there!
1 1/10=1.1
2/25=0.08
Each serving requires 0.08 kg, and he has 1.1 kg.
Thus, he can make 1.1/0.08, or 13.75 servings.
Let me know if this helps :)
Answer:
13 servings of tofu dish.
Step-by-step explanation:
First, convert the fractions to decimal numbers:
1 1/10 kg = 0.1 kg
2/25 kg = 0.08 kg
Now find how many servings of tofu dish will cover 0.1 kg of tofu:
2/25 kg = 1 serving
1 1/10 kg = ?
= 1 1/10 ÷ 2/25 kg
= 11/10 × 25/2
= 55/4
= 13.75 servings
Approximate it to a whole number:
13 servings.
Is this right? Can someone please check?
Answer: Yes, Substitution property is the correct option.
Step-by-step explanation:
Substitution property of equality says that if 'a= b', then 'a' can be substituted in for 'b' in any equation, and 'b' can be substituted for 'a' in any equation.Given: m∠A+m∠B =70° ...(i), m∠X=m∠A
Then, substitute m∠X for m∠A in (i) , we get
m∠X+m∠B =70°
So, the correct option is "Substitution property"
Cindy and victor are playing a math game. The winner must get three in a row of the same type of real numbers and justify how do numbers are alike. Cindy said that Cindy and Victor are playing a math game. The winner must get three in a row of the same type of real numbers and justify how the numbers are alike. Cindy said she won because she was able to get three rational numbers on a diagonal. Victor said he won with three positive numbers in a column. Can both players say they won, for different reasons? Explain
Please see attachment for question
Answer:
Yes both players can say they won. Cindy and Victor won
Step-by-step explanation:
Both players can say they won because they both kept to the rules of the game. Cindy got rational real numbers on a diagonal while Victor got positive numbers on a column which are real numbers too. Pi on the last row on his column for the diagram on the right(see attachment) is 22/7 or 3.14159... is an irrational real number but is still a positive real number.
Find the slope and y-intercept of the line. y = x – 8
Answer:
y- intercept= -8
slope= 1
Step-by-step explanation:
Looking at the question, the y- intercept is always the number were the line on the graph passes over on the y- axis. The slope is always the number with x in front of it.
Answer:
Y-intercept = -8
Slope = 1
Step-by-step explanation:
The Y-intercept is the constant or the integer in the equation.
So, the y-intercept is "-8".
The slope is the number with which "x" is multiplied with.
So, the slope is 1, because 'x' and '1x' are similar; therefore the slope is 1.
This system of linear inequalities can be used to find the possible heights, in inches, of Darius, d, and his brother William, w. d ≥ 36;w < 68;d ≤ 4 + 2w
Which statements must be true about their heights?
Answer:A,C,F
Step-by-step explanation:edge2020
Answer:
A,C,F
Step-by-step explanation:
PLEASEEEEEEEE HELPPPPPPPPP MEEEEEEEEEE
Answer:
b
Step-by-step explanation:
In general
Given
y = f(x) then y = f(Cx) is a horizontal stretch/ compression in the x- direction
• If C > 1 then compression
• If 0 < C < 1 then stretch
Consider corresponding points on the 2 graphs
(2, 2 ) → (4, 2 )
(4, - 2 ) → (8, - 2 )
Indicating a stretch in the x- direction.
y = f([tex]\frac{x}{2}[/tex] ) with C = [tex]\frac{1}{2}[/tex] , that is 0 < C < 1
stretches the graph in the x- direction by a factor of 2
Thus
y = f([tex]\frac{x}{2}[/tex] ) → b
