Answer:
Slope is 2/3
Step-by-step explanation:
Astronomers oftenmeasure largedistances usingastronomical units(AU) where 1 AU isthe average distancefrom Earth to theSun. In the image, drepresents thedistance from a starto the Sun. Using atechnique called"stellar parallax,astronomers determinedO is 0.00001389degrees.1. How faraway isthe starfrom theSun inastronomical units?Showyourreasoning.2. Write anexpression tocalculated for anystar.
In the given right triangle of the figure
we have that
sin(O)=1/d ----> by the opposite side divided by the hypotenuse in a right triangle
solve for d
d=1/sin(O)
[tex]d=\frac{1}{sin\left(0.00001389^o\right?}[/tex]d=4,124,966.13 AU -----> two decimal places
the expression to calculate d for any star is equal to
[tex]d=\frac{1}{sin\left(O\right)}[/tex]the equilateral triangle has a side length of 14. find the area of the triangle. round to the nearest tenth.
Answer: 85
To solve this, we need to calculate the height of the triangle. To do this, we divide the triangle verticaly, in two right triangles.
So, we have the hypotenuse of the two smaller triangles is 14. The short leg is half the side of the big triangle: 14/2=7 and the long leg is the height of the triangle and what we want to know.
By the pythagorean theorem:
[tex]14^2=7^2+x^2[/tex][tex]x=\sqrt[]{14^2-7^2}=7\sqrt[]{3}[/tex]And now we use the formula for the area of a triangle:
[tex]A=\frac{b\cdot h}{2}=\frac{7\cdot7\sqrt[]{3}}{2}=\frac{49\sqrt[]{3}}{2}[/tex]This is the area of each of the smaller triangles. To get the area of the big triangle, we add up the two smaller areas:
[tex]\frac{49\sqrt[]{3}}{2}+\frac{49\sqrt[]{3}}{2}=49\sqrt[]{3}[/tex]rounded to the nearest tenth is 85
7 Write the numbers in order from
GREATEST to LEAST.
-71.1 -71 1/2
Luther made $9,000 in interest by placing $60,000 in a savings account with simple interest for 3 years. What was the interest rate?
Answer:
[tex]5\%\text{ or }0.05[/tex]
Step-by-step explanation:
Simple interest rate means if I have "P" amount that I initially deposited, then every year this amount increases by "x% of P" or the original amount I deposited. So it's increasing by the same amount each year, unlike compound interest.
The formula for calculating the amount of interest is: [tex]I=P*r*t[/tex]
Where, r is the interest rate, t is the time unit, and P is the initial amount.
In most cases the t will be expressed in years, and one thing to note is the r is the interest rate in decimal form, so [tex]30\%=0.30[/tex], we want to convert it to decimal form by dividing by 100
We know the amount of interest, as it's given to us as 9,000, and the principle amount or initial amount, given to us as 60,000, and also the time which is given to us as 3 years.
So we know that:
[tex]I=9,000\\P=60,000\\t=3\\[/tex]
Plugging all these values into the equation we get:
[tex]9,000=60,000*3*r\\\\9,000=180,000*r\\\\\frac{9,000}{180,000}=r\\\\0.05=r[/tex]
as noted above, this interest rate, "r" is expressed in decimal form. Since we have to divide by 100 to convert from percentage to decimal, we have to multiply by 100 to convert from decimal to percentage.
this gives us: [tex]r=5\%[/tex]
The height of a tree increases as time passes. Your friend says that time is the dependent variable because size depends on time. Is your friend correct?
Given that the height of a tree increases as time passes.
Your friend says that is dependent because size deemds on time.
Leet's determine if your friend is correct.
Here, since the height of a tree increases as time passes, the height of the tree depends on the time.
Hence, size is the dependent variable while time is the independent variable.
Therefore, your friend is NOT correct.
ANSWER:
No, your friend is NOT correct.
Simplify the trigonometric expression. cos(theta+pi/2)
We have to simplify the expression:
[tex]\cos (\theta+\frac{\pi}{2})[/tex]We could see it graphically:
We see that for any angle theta, the cosine of theta + pi/2 is equal to negative sin of theta.
Then we can write:
[tex]\cos (\theta+\frac{\pi}{2})=-\sin (\theta)[/tex]The answer is -sin(theta).
We are working on integers, and I just don’t get the concept, if you could do an EXAMPLE problem for me that would be great I understandan this I just need further instruction
The history of integers begins with the natural numbers (1,2,3,...), which are also called the counting numbers. They arise naturally by the need of counting things. But there is a problem. "There is a missing number". If you have a number n of things and you subtract all of them, what remains? Intuitively, it must be a number, a number representing nothing (to have nothing). This is the origin of zero.
Now, as time passes, the man began to do trades and arose the money. This leads to a problem. Other numbers are missing now. How do you express how much money you owe someone? counting numbers are not useful here, for they mean "the money you have". Th
0.04 divided by 0.628
Answer:
0.1 also 0.0636942675
Describe a series of transformations Matt can perform to device if the two windows are congruent
The three transformations—rotations, reflections, and translations—can be combined to produce congruent shapes. The truth is that any pair of congruent shapes can be matched to one another by combining one or more of these three transformations.
Explain transformations.A point, line, or geometric figure has four different transformations that can be applied to alter its appearance. While the term "Image" refers to the position and final shape of the object, "Pre-Image" refers to the object's shape before transformation.
Given Information
The size and shape of the figures are preserved during stiff transformations, as we already know (reflections, translations, and rotations). Always in harmony with one another is the pre-image.
These transformational skills are all possessed by Matt:
Reflection
The reason a reflection maintains its original form Similar spots from the pre-image to the image remain apart from the line of reflection.
The transformation of rotations into congruence
Any rotating figure will twist. Although it is the same size and shape as before, the figure appears to have toppled over. A clock is a perfect example of how rotation works in real life. A clock's connecting arms turn around its axis every hour or every day. A rotation's degree determines what kind of rotation it is; typical rotations include 90, 180, and 270 degrees. Before turning around and going back to where it started, the figure does a full 360-degree turn. the direction of a rotation, whether it be clockwise or counterclockwise. The degree, amount, and other factors can be determined using this information .a revolution's speed, direction, etc.
Transformative translational congruence
When an object or shape is moved without altering its size, shape, or orientation, the movement is referred to as a translation. When doing a translation, also known as a slide, every point on an object or shape is moved uniformly and in one direction.
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The side of a square is represented by (s - 4);1. Write an expression that could represent the perimeter of the square.2. If the perimeter of the square is no more than 80 ft, what is the maximum value of s?
We have a square with sides (s-4).
The perimeter of a square is 4 times the length of the side, so we can write:
[tex]P=4\cdot(s-4)=4s-16[/tex]If P is no more than 80 ft, we can find the maximum value for s as:
[tex]\begin{gathered} P<80 \\ 4s-16<80 \\ 4s<80+16 \\ 4s<96 \\ s<\frac{96}{4} \\ s<24 \end{gathered}[/tex]Answer:
1) The perimeter is P = 4s-16
2) The maximum value for s, if the perimeter is no more than 80 ft, is 24 ft.
Find the midpoint of AB given A (-3,-5) and B (-1,8)
A: (-3,-5)
B: (-1,8)
To find the midpoint we have to add each coordinate and divide by 2:
Midpoint: (-3-1)/2 , (-5+8)/2 = -4/2, 3/2 = -2,1.5
Midpoint: (-2, 1.5)
How long is the control line? I couldn’t figure this out
Solution:
Given the circle with center A as shown below:
The plane travels 120 feet counterclockwise from B to C, thus forming an arc AC.
The length of the arc AC is expressed as
[tex]\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ \text{where} \\ \theta\Rightarrow angle\text{ (in degre}e)\text{subtended at the center of the circle} \\ r\Rightarrow radius\text{ of the circle, which is the }length\text{ of the control line} \\ L\Rightarrow length\text{ of the arc AC} \end{gathered}[/tex]Given that
[tex]\begin{gathered} L=120\text{ f}eet \\ \theta=80\degree \\ \end{gathered}[/tex]we have
[tex]\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ 120=\frac{80}{360}\times2\times\pi\times r \\ cross\text{ multiply} \\ 120\times360=80\times2\times\pi\times r \\ \text{make r the subject of the equation} \\ \Rightarrow r=\frac{120\times360}{2\times\pi\times80} \\ r=85.94366927\text{ fe}et \end{gathered}[/tex]Hence, the length of the control line is 85.94366927 feet.
What is the equation of a circle with radius 2 and center (3, 1)? (x - 3)2 – (y - 1)2 = 4 O (c - 3)2 + (y - 1)2 = 4 (x ) O (x + 3)2 + (y + 1)2 = 4 (x - 3)² + (y - 1)2 = 2
Given the radius of a circle as r = 2 and centre = (3,1)
We want to find the equation
Solution
First, the equation of a circle centre (a,b) and radius r is given by
[tex](x-a)^2+(y-b)^2=r^2[/tex]From the question
[tex]\begin{gathered} a=3 \\ b=1 \\ r=2 \end{gathered}[/tex]We put the parameters into the equation ans simplify
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (x-3)^2+(y-1)^2=2^2 \\ (x-3)^2+(y-1)^2=4 \end{gathered}[/tex]Therefore the correct option is Option B
Select True or False for each statement.
A right triangle always has obtuse exterior angles at two vertices.
Answer:
true
Step-by-step explanation:
it is true ........
Explanation:
A right triangle has exactly one angle that is 90 degrees. This is called a right angle.
The other two angles are acute, which means they are less than 90 degrees. An example would be 30 degrees and 60 degrees.
If 30 degrees is an interior acute angle, then 180-30 = 150 degrees is the exterior obtuse angle. Similarly, the adjacent angle to the 60 is 180-60 = 120 degrees.
This example shows we have two obtuse exterior angles. This applies to any right triangle, and not just this particular one.
A ship leaves port on a bearing of 34.0 degrees and travels 10.4 mi. The ship then turns due east and travels 3.9 mi. How far is the ship from port, and what is its bearing from port?
→
r
=
13.5
mi
, at a bearing angle of
50.4
o
Explanation:
We're asked to find the total displacement, both the magnitude and direction, of the ship after it leaves the port with the given conditions.
First, I'll explain what a bearing is.
A bearing is NOT a regular angle measure; normally, angles are measured anticlockwise from the positive
x
-axis, but bearing angles are measured clockwise from the positive
y
-axis.
Therefore, a bearing of
34.0
o
indicates that this is an angle
90.0
o
−
34.0
o
=
56.0
o
measured normally. We'll use this angle in our calculations.
We're given that the first displacement is
10.4
mi
at an angle of
56.0
o
(as calculated earlier). Let's split this up into its components:
x
1
=
10.4
cos
56.0
o
=
5.82
m
y
1
=
10.4
sin
56.0
o
=
8.62
m
Our second displacement is a simple
4.6
mi
due east, that is, the positive
x
-direction. The components are thus
x
2
=
4.6
mi
y
2
=
0
mi
To find the total displacement from the port, we'll add these two vectors' components and use the distance formula:
Δ
x
=
x
1
+
x
2
=
5.82
mi
+
4.6
mi
=
10.42
mi
Δ
y
=
y
1
+
y
2
=
8.62
mi
+
0
mi
=
8.62
mi
r
=
√
(
x
total
)
2
+
(
y
total
)
2
=
√
(
10.42
mi
)
2
+
(
8.62
mi
)
2
=
13.5
mi
The direction of the displacement vector is given by
tan
θ
=
Δ
y
Δ
x
so the angle is then
θ
=
arctan
(
Δ
y
Δ
x
)
=
arctan
(
8.62
mi
10.42
mi
)
=
39.6
o
The question asked for the bearing angle, which is just this angle subtracted from
90
o
:
Bearing angle
=
90
o
−
39.6
o
=
50.4
o
someone please help…
Q.12 The polynomials are 2 and 3
What is polynomial ?
A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7.
Given, p(x) = -x² + x + 2
p has a degree 2
Let, a = 1 + i√2
b = 1 - i√2
a + b = 1 + i√2 + 1 - i√2
= 2
a * b = (1 + i√2) * (1 - i√2 )
= 1 - (i√2)²
= 1 - i²*2 (where, i² = -1)
= 1 + 2
= 3
Therefore, the polynomial are 2 and 3
Q.13 The polynomial is x³ + x
Given, Q(x) = x³ - 2x² - 1
Q has a degree of 3
=>(x - 0) (x - i) (x + i)
=>(x² - ix) (x + i)
=>x³ + x²i - ix² - i²x (where i² = -1)
=>x³ + x
Therefore, the polynomial is x³ + x
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the bearing of L from Q is 90° what is the bearing of Q for L
Given:
the bearing of L from Q is 90°
Required:
what is the bearing of Q for L
Explanation:
There is a 180 degree difference in bearing between two location(L from Q, Q from L)
If L from Q is 90 degree then
Q from L is
180-90=90degree
Required answer:
90 degree
A teacher records the cost in dollars, y, of purchasing and maintaining a classroom aquarium for x months. Theequation shown models the data.y = 48x + 250What does 250 represent in this situation?A the monthly cost of the aquariumB the purchase cost of the aquariumC the total cost of the aquarium after x monthsD the cost of maintaining the aquarium for x months
B the purchase cost of the aquarium
Explanation
we have the equation
[tex]y=48x+250[/tex]this is a linear equation in the form
[tex]\begin{gathered} y=\text{ mx+b} \\ \text{where m is the slope and b is the y-intercept} \end{gathered}[/tex]hence
[tex]\begin{gathered} y=48x+250\rightarrow y=mx+b \\ \text{slope}=48 \\ y-\text{intercept}=250 \end{gathered}[/tex]so, if we have the sentence
the cost in dollars, y, of purchasing and maintaining a classroom aquarium for x months
let
cost in dollars = y
as x is the variable, let x for the variable in the text, in this case, what changes is the number of months,so
number of months= x
the factor of x ( 48), is the value for the mainting the classroom ( as we can see it depends on the number of months , x)
so
the monthly cost of the aquarium=48
finally , we have 250, this values is a constant, it does not depend on the number of months, so it is
the purchase cost of the aquarium=250
so,the answer is
B the purchase cost of the aquarium
I hope this helps you
What is x2 + 6x complete the square
You have the following expression:
x² + 6x
In order to complete the square, take into account that 6 is two times the product of the first coeffcient by the second one in the binomial (a+ b)², then, you have:
6 = 2ab
a=1 because is the coeffcient of the term with x², then for b you obtain:
b = 6/2(1) = 3
the third term of the trynomial is the squared of b.
Evaluate. 12⋅(1/4+1/3)to the power of2+2/3 Enter your answer as a mixed number in simplest form by filling in the boxes.
12×(1/4+1/3)to the power of2+2/3 using PEDMASand INDICIES rule gives 7^8/3
What is Indices? lndicies is expressed as Ax^n. Where A is the coefficient, x is the base and n is the power or index.
12×(1/4+1/3)to the power of2+2/3
Evaluating the expression
= (12×( 1/4+1/3))^2+2/3
using PEDMAS
= (12× 7/12)^8/3
opening the bracket, we therefore have
= 7^8/3
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How do you find the square root of 18? Needs to be in decimal form and we cannot use calculators
Given:
[tex]\sqrt{18}[/tex]To find:
The root of 18 without using a calculator
There is a formula that gives an approximation of a square root without a calculator. This is given as:
[tex]\begin{gathered} \sqrt{N}\text{ = }\frac{N\text{ + M}}{2\sqrt{M}} \\ where\text{ N = is the number we want to find its root} \\ M\text{ = is a perfect square close the number we are to find} \\ That\text{ is a number we can find its root } \end{gathered}[/tex][tex]\begin{gathered} \text{N = 18} \\ M\text{ = 16 is the closest number to 18 we can find its root} \\ \\ substitute\text{ the values into the formula:} \\ \sqrt{18}\text{ = }\frac{18\text{ + 16}}{2\times\sqrt{16}} \\ \\ \sqrt{18}\text{ = }\frac{34}{2(4)} \end{gathered}[/tex][tex]\begin{gathered} \sqrt{18}\text{ = }\frac{34}{8} \\ \\ \sqrt{18}\text{ = 4.25} \end{gathered}[/tex]Function A gives the audience in millions
Using function concepts, it is found that:
a) The meaning of each expression is given as follows:
A(4) = audience after four hours.A(0.5) = 1.5 = the audience after 0.5 hours is of 1.5 million peopleb) The expression is: A(4) = 1.3.
c) The expression is: A(2) = A(2.5).
FunctionIn the context of this problem, the format of the function is:
A(t).
In which the meaning of each variable is given as follows:
t is the time in hours after the beginning of the show.A(t) is the audience, in millions of hours.Which gives the meaning of each expression in item a.
For item b, the expression is given as follows:
A(4) = 1.3.
As 4 hours after the episode premiered, the audience was of 1.3 million people.
For item c, the expression is given as follows:
A(2) = A(2.5).
As the audience after 2 hours = 120 minutes is the same as the audience half an hour = 30 minutes later.
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A rectangle has a length that is 7 less than 4 times the width. The perimeter is 100 in. Find the length and the width.
Answer:
136 m
Step-by-step explanation:
Let w = the width of the rectangular field.
Let l = the length of the rectangular field.
The formula for the perimeter P of the rectangular field is:
P = 2w + 2l
Since the length l is 7 m less than 4 times the width w, then we can write the following equation that relates l and w:
l = 4w - 7 m
Since l = 4w - 7 and it's given that perimeter P = 136 m, then we can substitute this information into the perimeter formula as follows:
P = 2w + 2l
136 m = 2w + 2(4w - 7 m)
136 m = 2w + 2(4w) - 2(7 m)
136 m = 2w + 8w - 14 m
136 m + 14m = 10w - 14 m + 14 m
150 m = 10w + 0
10w = 150 m
(10w)/10 = 150 m/10
(10/10)w = 150 m/10
(1)w = 15 m
w = 15 m
Therefore, l = 4w - 7 m
l = 4(15 m) - 7 m
l = 60 m - 7m
l = 53 m
CHECK:
P = 2w + 2l
136 m = 2(15 m) + 2(53 m)
136 m = 30 m + 106 m
136 m = 136 m
Solve the systems of equations Y= 6x+35Y= 9x+14X=Y=
y = 6x + 35
y = 9x + 14
Combining these equations, we get:
6x + 35 = 9x + 14
35 - 14 = 9x - 6x
21 = 3x
21/3 = x
x = 7
Substituting this result in the first equation:
y = 6*7 + 35
y = 42 + 35
y = 77
Hello me with part B pleaseeee
Answer:
0, 0, 0
Step-by-step explanation:
You want the sum of a number and its opposite for the numbers ...
3, 7.5, and -2 2/3
Additive inverseThe definition of the additive inverse (opposite) of a number is that it is the number that produces 0 when summed with the original number.
Any number summed with its opposite will give zero.
The sums are ...
3 + (-3) = 07.5 + (-7.5) = 0-2 2/3 + (2 2/3) = 0A shipping container will be used to transport several 150-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 26500 kilograms. Other shipments weighing 12100 kilograms have already been loaded into the container. Which inequality can be used to determine x, the greatest number of 150-kilogram crates that can be loaded onto the shipping container?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given values
[tex]\begin{gathered} \text{constant + Variable = Output} \\ \text{constant}=12100 \\ \text{Variable}=x \\ \text{Output}=\text{greatest value} \end{gathered}[/tex]STEP 2: Get the inequality
[tex]\begin{gathered} \text{ If }26500kg\text{ is the greatest value, this means that;} \\ \text{the addition of constant and variable must be less than or equal to 26500} \\ So\text{ we have;} \\ \\ 150x+12100\le26500 \end{gathered}[/tex]Hence, the answer is:
[tex]150x+12100\le26500[/tex]helppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
55.17
Step-by-step explanation:
[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]
I'll give brainliest!
Answer:
24
Step-by-step explanation:
8y^0 + 2y^2 * x^-1
8(4)^0 + 2(4)^2 * 2^-1
8 + 2 * 16 * 2^-1
8 + 2 * 2^-1 * 16
8 + 2^1 - 1 * 16
8 + 16
24
Hope this helps! :)
Consider the following equation of the circle. Graph the circle
Explanation
Given the equation;
[tex](x+6)^2+(y+7)^2=4[/tex]Using a graphing calculator, the graph of the circle becomes;
Answer:
I'm behind in geometry if you could teach me this I would highly appreciate it
We know that AC and BD bisect each other, but AC is not equal to BD.
Basically, the problem is saying that these segments are bisectors of each other, that can be represented as the image below shows
As you can see in the image, AC and BD bisect each other, but their lengths are not equal.