Answer:
elliptical
Step-by-step explanation:
The earth rotates the sun in an oval shape, not circular. Hence the "elliptical" path being the correct terminology
Answer:
elliptical path
Step-by-step explanation:
The population of a city was 5/7 of a million in 2010 and 5 million in 2016. The population growth can be described as an arithmetic sequence. Find its common difference, which represents the annual growth of the population.
Answer:
HERE ARE FOLLOWS
Step-by-step explanation:
The population of a city was five-sevenths of a million in 2010 and five million in 2016. The population growth can be described as an arithmetic sequence. Find its common difference, which represents the annual growth of the population.
In this question, we’re told that we have an arithmetic sequence. This is a special type of sequence that has a common difference between each term. For example, the sequence two, seven, 12, 17, and so on has a common difference of five, as we add five each time to get the next term. The general term of any arithmetic sequence, written sub , is equal to sub one plus minus one multiplied by , where sub one is the first term in the sequence and is the common difference. It is this common difference that we are trying to calculate in this question.
In this question, we are told that the initial population in 2010 was five-sevenths of a million. So, we will let sub one, the first term, be five-sevenths. We are also told that the population in 2016 was five million. We can see that this would correspond to the seventh term in our sequence. This means that sub seven is equal to five. We can now substitute our values into the formula for the general term. The seventh term five is equal to five-sevenths plus seven minus one multiplied by . The right-hand side simplifies to five-sevenths plus six .
Noting that we can write five as 35 over seven, when we subtract five-sevenths from both sides of our equation, we get thirty sevenths is equal to six . We can then divide both sides of this equation by six, giving us is equal to 30 over 42. Both the numerator and denominator of our fraction are divisible by six. As 30 divided by six is five and 42 divided by six is seven, our fraction simplifies to five-sevenths.
We can therefore conclude that the common difference which represents the annual growth of the population is five-sevenths of a million.
find and sketch the domain of the function. f(x, y, z) = ln(81 − 9x2 − 9y2 − z2)
The function is defines for all (x,y,z) ∈ R³
Hence the domain of this equation is,
D = {(x, y, z) | 9x² + 9y² + z² ≤ 81
The function is bound by sphere.
The set of inputs that a function will accept is known as the domain of the function in mathematics. (f), " (f), where f is the function, are other ways to refer to it.
More specifically, the domain of f is X given a function Xto Yfcolon Xto Y. It should be noted that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.
The function f can be graphed in the Cartesian coordinate system in the particular situation where X and Y are both subsets of R In this instance, the graph's x-axis shows the domain as the projection.
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Perimeter of a rectangular sheet is 200m if the length is 35 cm find the breadth also find its area find the breadth of a rectangular plot of land if its area is 440 m² and the length is 22m² also find its perimeter
The square on the right is a scaled copy of the square on the left. Identify the scale
factor. Express your answer as a whole number or fraction in simplest form.
8
8
All the lengths in the original figure are multiplied by the same number to get a scaled replica.
How do you find the scale copy?Every length in the original figure is multiplied by the same number in a scaled copy, which is a copy of the original figure. For instance, triangle ABC is a scaled version of triangle DEF.
To find the matching side length on triangle DEF, each side length on triangle ABC was multiplied by 1.5. A figure that is geometrically identical to the original figure is called a scale copy. This indicates that the scale copy and the original figure are identical in shape but may vary in size.
The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).
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11. (6 points)
Reasoning Complete the following proof by providing
the reason for each statement.
One can say that two triangles are congruent if their measurements and appearance match. The other two triangles remain true even if we rotate, flip, or shift one of them.
What are congruent triangles?Two triangles with the same dimensions and appearance are said to be congruent. Even if we flip, rotate, or shift one of the triangles, the other two still hold true. If two triangles' sides are the same, they must have the same angles and, as a result, must be congruent.
Given that the bases of the triangle PWZ are the same (1 and 2) and that W and Z are the same distance from X and Y, where XY is the base of another triangle inside PWZ.
For PWZ
PWZ's two angles are the same, thus we know it is an isosceles triangle.
Because of this, another PXY is on the same base as a PWZ and is also located at the same distance from its point. These triangles are hence congruent triangles.
When viewed from that angle, we can claim that 1 and 2 are congruent pairs of alternate angles.
∠1 ≅ ∠2
In the same way, 3 and 4 are.
∠3 ≅ ∠4
As a result, the Triangles are congruent according to the ASA Theorem. The sides that the two angles encompass are similar.
Therefore, the correct answers are:
GivenIsosceles triangle theoremSASCPCT( Corresponding parts of a congruent triangles are congruent)The converse of Isosceles triangle theoremTo learn more about congruent triangle refer to:
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The correct answers are Isosceles triangle theorem, SAS, CPCT( Corresponding parts of a congruent triangles are congruent), The converse of Isosceles triangle theorem.
What are congruent triangles?Two triangles with the same dimensions and appearance are said to be congruent. Even if we flip, rotate, or shift one of the triangles, the other two still hold true. If two triangles' sides are the same, they must have the same angles and, as a result, must be congruent.
Given that the bases of the triangle PWZ are the same (1 and 2) and that W and Z are the same distance from X and Y, where XY is the base of another triangle inside PWZ.
For PWZ
PWZ's two angles are the same, thus we know it is an isosceles triangle.
Because of this, another PXY is on the same base as a PWZ and is also located at the same distance from its point. These triangles are hence congruent triangles.
When viewed from that angle, we can claim that 1 and 2 are congruent pairs of alternate angles.
∠1 ≅ ∠2
In the same way, 3 and 4 are.
∠3 ≅ ∠4
As a result, the Triangles are congruent according to the ASA Theorem. The sides that the two angles encompass are similar.
Therefore, the correct answers are:
Given
Isosceles triangle theorem
SAS
CPCT( Corresponding parts of a congruent triangles are congruent)
The converse of Isosceles triangle theorem
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You are given a small bar of an unknown metal. You find the density of the metal to be 10. 5 g/cm3. An x-ray diffraction experiment measures the edge of the unit cell as 409 pm. Assuming that the metal crystallizes in a face-centered lattice, what is the metal most likely to be?.
The metal is most likely to be Silver (Ag).
Density, d = 10.5 g/cm3.
z = 4 (as it is an FCC)
a = edge length = 409 pm = [tex]4.09 * 10^{-8} cm[/tex]
We have to find the Atomic Mass (M).
Perhaps the most common crystal structure is Face-Centered Cubic (FCC). The crystal structure is based on the Bravais lattice of the same name, with a single atom at each lattice point on the cube’s corners and faces. FCC is one of the most stable crystal structures and has the highest packing density. In some textbooks, FCC may also be abbreviated as CCP, which stands for Cubic Close-Packed.
The formula for density, d =
[tex]D = \frac{z * M}{N_{A} * V }[/tex]
where, V = volume.
Volume, V = a x a x a = a^3
V =[tex](4.09 * 10^{-8}) ^ 3 = 68.417 * 10^{-24} = 6.841 * 10^{-23}[/tex]
Using the density formula,
[tex]M = \frac{d * N_{A} * V }{z}[/tex]
[tex]M = \frac{10.5 * 6.023 * 10^{23} * 6.841 * 10^{-23} }{4}[/tex]
[tex]M = 108.15 amu[/tex]
The atomic weight is close to that of Silver (Ag).
Thus, the metal is most likely to be Silver (Ag).
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Eren constructed a rectangular paper box with a volume of 180in. His box has a length of x inches, a width of 5 inches less than its length, and a height 2 inches more than its length. What is the length of the box?
A. 7.52 in
B. 9.52 in
C. 5 in
D. 2.52 in
We know that the volume of a rectangular box is given by length times width times height. So, we have:
V = x * (x - 5) * (x + 2) = 180
Briefly defined, what is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
We can use this equation to find the length of the box.
Expanding the equation:
x^3 - 5x^2 + 2x = 180
Solving for x using a calculator or an algebraic equation solver we can find that x = 9.52
So the length of the box is 9.52 inches.
The answer is B. 9.52 in
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If a basketball player scores 25 out of 36 free throws, how many will he score out of 70 free throws?
Answer:
48 free throws
Step-by-step explanation:
25:36 is the ratio
Now divide 25 by 36 to find the probability of the basketball player scoring:
25/36=0.694
Now multiply this probability with the total number of free throws (70) in order to get the number of free throws that would be made:
70 * 0.694 = 48.6
You can't make 48.6 free throws, so you have to round down to the nearest integer since you can't make 0.6 free throws.
Hence, 48.6 ==> 48 free throws
PLEASE HELP I WILL GIVE BRAINLIEST TO THE BEST ANSWER
Answer:
Graph 1- No, Graph 2- No, Graph 3- Yes, Graph 4- Yes, Graph 5- No, Graph 6- No
4/x-4 -3/x*2-16 =6/x+4
-11/2
11/2
37/2
-42/2
The solution of the algebraic equation is 37/2
How to solve for the value of x in the algebraic equation?An algebraic equation is a statement that says that two algebraic expressions are equal. For example, the equation 3x + 2 = 6x
The algebraic expression 4/(x-4) -3/(x²-16) = 6/(x+4)
To solve this algebraic equation, you need to find the value of x.
4/(x-4) -3/(x²-16) = 6/(x+4)
4/(x-4) -3/(x-4)(x+4) = 6/(x+4)
The LCM of (x-4) and (x-4)(x+4) is (x-4)(x+4):
(4(x+4) -3)/(x-4)(x+4) = 6/(x+4)
(4x+16 -3)/(x-4)(x+4) = 6/(x+4)
4x+13/(x-4)(x+4) = 6/(x+4)
Multiply both sides by (x+4):
4x+13/(x-4) = 6
4x+13 = 6(x-4)
4x+13 = 6x-24
6x-4x = 13+24
2x = 37
x = 37/2
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find f ◦ g and g ◦ f , where f (x) = x2 + 1 and g(x) = x + 2, are functions from r to r.
The values of f ◦ g is equal to (x + 2)^2 + 1 and g ◦ f is equal to x^2 + 3.
f ◦ g is the composition of functions f and g, which means that for any x in the domain of g, we substitute g(x) into f(x) to get f(g(x)) = (x + 2)^2 + 1.
g ◦ f is the composition of functions g and f, which means that for any x in the domain of f, we substitute f(x) into g(x) to get g(f(x)) = x^2 + 1 + 2
So f ◦ g = (x + 2)^2 + 1 and g ◦ f = x^2 + 3
It's important to notice that the order of the functions matters when composing them, f ◦ g is not the same as g ◦ f. The composition of functions is a fundamental concept in mathematics and it's used to chain multiple functions together to create a new function.
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23. An exponential function of base e has horizontal asymptote at the line y = 1. Its graph contains the point (-1, 2) and the y-intercept is less than 2. What
is the equation of this function?
The equation of this function is f(x) = 2(x - 2) / x - 1
What are exponential functions?When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.
The parent function is given as:
y = 1.
we can see that the function is translated 3 units down and 2 units right.
This means that the transformation rule
(x, y) -> (x - 2, y - 3)
So, we have graph contains the point (-1, 2) and the y-intercept is less than 2.
Since the horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.
Hence, the equation of the graph is
f(x) = 2(x - 2) / x - 1
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2 + 3 + 4 x 8 - 2 + 4 + 6 x 8 divided 7 x 2
Answer:
640
Step-by-step explanation:
Answer:
=297/7
PEMDAS Hope this helps :)
What are the measures of the angles of an isosceles triangle in which each of the base angles is four times the vertical angles?
Thus the angles of the isosceles triangles are 80°, 80° and 20°
An isosceles triangle is a triangle that has two sides of the same length. It also has two equal angles on the right and left (base angles) and one vertical angle, in a total of 180°.
Let's assume the base angle of an isosceles triangle is a, and the vertical angle is b. Then we can apply the total angles of a triangle here.
180° = a + a + b
As we know that a = 4b, then we can rewrite the equation as follows:
180° = a + a + b
180° = 4b + 4b + b
180° = 9b
b = 20°
Then we calculate the value of a:
a = 4b
= 4x20°
= 80°
Thus the angles of the isosceles triangles are 80°, 80° and 20°
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Add or subtract the same amount from both sides is that the variable is by itself.
1) 10 = f - 9
2) I + 5 = 9
3) 23 = p + 13
Answer:
To solve these problems, you are going to use inverse operations. For example, if the problem is y+2=4, you would switch the positive (+) 2 to a negative (-) 2 and subtract on both side to get y=2.
1). 10=f-9
Change -9 to 9.
10+9=f-9+9
The 9s on the right cancel. Simplify 10+9.
19=f
2). l+5=9
Change 5 to -5.
l+5-5=9-5
The 5s on the left cancel. Simplify 9-5.
l=4
3). 23=p+13
Change 13 to -13.
23-13=p+13-13
The 13s on the right cancel. Simplify 23-13.
10=p
To check your answers, plug the answers into their corresponding variables.
1). 10=19-9
19-9=10
10=10
Correct
2). 4+5=9
4+5=9
9=9
Correct
3). 23=10+13
10+13=23
23=23
Correct
Please let me know if this helps (please mark brainliest if so!) and/or if you have any questions! Have a splendid day!!! :)
The question is in the ixl helppp
The value of the trigonometric relation tan D = 15/8 = 1.875
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as CDE
The triangle CDE is a right triangle with ∠CDE = 90°
Now , the measure of side CD = 8 units
The measure of side CE = 15 units
The measure of side DE = 17 units
From the trigonometric relations ,
tan θ = opposite / adjacent
Substituting the values in the equation , we get
tan D = 15 / 8
Hence , the value of tan D = 15/8
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Alicia is solving the equation. Which equations represent possible ways to begin solving for x? check all that apply.
Answer:
In solving any mathematical equation carrying x,we mainly begin by first understanding the question and breaking them down little by little and solving them separately to know which to add to get x,or which to subtract to get x,e.t.c,as the case may be
A cylinder as a length of 8cm and a height of 15cm what is the surface area?
Answer:
150.72 cm^2
If this help please set brainliest.
Step-by-step explanation:
The surface area of a cylinder can be calculated using the formula:
surface area = 2 * pi * r * h + 2 * pi * r^2
where r is the radius of the base of the cylinder, h is the height of the cylinder, and pi is approximately equal to 3.14.
To solve for the surface area of the cylinder you described, we first need to find the radius of the base. Since the cylinder has a height of 15cm and a length of 8cm, we can assume that the radius of the base is half of the length, or 8cm / 2 = 4cm.
Plugging this value into the formula, we get:
surface area = 2 * 3.14 * 4 * 15 + 2 * 3.14 * 4^2
= 100.48 + 50.24
= 150.72 cm^2
So the surface area of the cylinder is approximately 150.72 cm^2.
6.
Use $50 for d. What is the total cost of
the power tools? Write your answer in
the form of dollars and cents.
I
Type a response
*REQUIRED
1
Equation reads C=25n+2500, and the price to make 3000 toys is $77,500. Additionally, 1200 toys may be created for $32500.
What is a linear equation, exactly?A linear equation in algebra is one that only contains a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.
Let's use the equation y=mx+b, where n is the number of toys and C is the overall cost. The total cost of producing n toys would be equal to the initial development cost plus the production cost of each toy.
The cost to make a toy will equal m since m is multiplied by n, the quantity of toys. B will always equal the development cost since it is a constant and its value is unaffected by the number of toys.
Therefore, [tex]C=25n + 2500[/tex]
by above, equation put
[tex]n=1750\\C= 25(3000) + 2500\\C= $77,500[/tex]
Now, again by same equation, but C instead of n.
[tex]= > 32500= 25n +2500\\= > 30000=25n\\= > n = 1200[/tex]
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I need to know the answer
The compound interval for the given interval is (-∞, ∞).
What is compound inequality?A compound inequality is a combination of two inequalities that are combined by either using "and" or "or". The process of solving each of the inequalities in the compound inequalities is as same as that of a normal inequality but just while combining the solutions of both inequalities depends upon whether they are clubbed by using "and" or "or".
The given intervals are (-∞, -2] or [-3, ∞).
Now, the compound interval is (-∞, ∞)
Thus, the interval notation is -∞<x<∞
Therefore, the compound interval for the given interval is (-∞, ∞).
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Geometry (I only need the last 2 answers)
Applying the perpendicular bisector theorem, the values of the measures are:
y = 12
x = 7
PQ = 29
SR = 32
PT = 18
PR = 36
What is the Perpendicular Bisector Theorem?The perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the line segment.
In other words, if a point P is the perpendicular bisector of line segment AB, then the distances from P to points A and B are equal. This is true no matter where point P is located on the perpendicular bisector.
Since QT is the perpendicular bisector of PR, we would therefore have the following based on the above stated theorem:
PQ = QR
Substitute:
5y - 31 = 2y + 5
5y - 2y = 31 + 5
3y = 36
3y/3 = 36/3
y = 12
SP = SR
Substitute:
4x + 4 = 7x - 17 [congruent segments]
4x - 7x = -4 - 17
-3x = -21
x = 7
PQ = 5y - 31 = 5(12) - 31 = 29
SR = 7x - 17 = 7(7) - 17 = 32
PT = 6x - 2y = 6(7) - 2(12)
PT = 18
PR = 2(PT)
PR = 2(18)
PR = 36
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Apply the distributive property to create an equivalent expression.
5×(−2w−4
The equivalent expression when we apply distributive property is -10w -20
What is distributive property?You should understand that distributive property states that every term inside a grouping symbol multiplied by every term outside the grouping symbol yields the same result.
To this effect, the formula to do this is x(y+z) = xy+xz
The given expression is
5×(−2w−4)
= 5*-2w- 5*4
= -10w -20
In the expression every term outside the symbol is multiplied by every term inside the symbol to give the result of the expression
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together donal, yolanda, and iris made 27 birdhouses for a school fair. yolanda made n birdhouses. donal made one more birdhouse than yolanda, and iris made one more than donal. solve the equation n+(n+1)+(n+1+1)=27. find the number of birdhouses each one made step by step
Solving the equation
yolanda made 8 birdhouses, donai made 9 birdhouses, and iris made 10 birdhousesWhat is an equation?An equation is a mathematical expression that shows the relationship between two variables.
How to find the number of birdhouses each one made?Since together donal, yolanda, and iris made 27 birdhouses for a school fair. yolanda made n birdhouses. donal made one more birdhouse than yolanda, and iris made one more than donal. So, we solve the equation n +(n + 1) + (n + 1 + 1) = 27 to find the number of birdhouses each one made.
So, n + (n + 1) + (n + 1 + 1) = 27
Colecting like terms, we have that the equation is
n + (n + 1) + (n + 1 + 1) = 27
n + n + n + 1 + 1 + 1 = 27
3n + 3 = 27
Subtracting 3 from both sides of the equation, we have
3n = 27 - 3
3n = 24
Dividing oth sides by 3, we have
n = 24/3
n = 8
So, n + 1 = 8 + 1 = 9
and n + 1 + 1 = 8 + 1 + 1 = 10
So,
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A system of linear equations is graphed. Which ordered pair is the best estimate for the solution to the system.
The ordered pair that is the best estimate for the solution to the system is (0.5, 0)
What is a linear equation?You should know that any equation whose highest power of its variable is one is linear
Also, the graph of linear equation is always straight line. The solution set of the linear equation is the values of x and y where the two lines intersect.
From our graph, the coordinate of the points of intersection are 0.5 and 0
Reading from the graph to get the coordinates of points, We therefore conclude that the ordered pair is the best estimate for the solution to the system is (0.5, 0) respectively
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Can some please help me? Im in Pre-Calc
From a point (x, y) on a circle with radius r , we know that cos θ represents tha ratio of x/r .Therefore, cos θ = x/r. On the unit circle the radius of the circle is 1, which means x = cosθ.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
From the figure below,
We see that,
The point (x, y) = (x, 0)
Cos θ = x/r
Unit circle means r = 1.
So,
Cos θ = x/1
Cos θ = 1
Thus,
The given statement is filled as above.
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The sum of 50 and a number is equal to 6 times that number
The number for the expression is 5.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number = x
Now,
50 + x = 6x
Subtract x on both sides.
50 = 5x
Divide 5 into both sides.
x = 10
Thus,
The number is 5.
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A home improvement store is selling lawn chairs. There are 520 chairs in the inventory of those are green. Find the number of green chairs in the inventory O 104O 208O 312O 130
Number of green chairs in the inventory is 208.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Total number of chairs in the inventory = 520
Fraction of chairs that are green = 2/5 of 520
2 parts out of 5 parts are green.
Number of green chairs = 2/5 × 520
= 1040 / 5
= 208
Hence there are 208 green chairs in the inventory.
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thee more than four times a number is 15
Answer:
3
Step-by-step explanation:
Let's disect this sentence.
Three more (+3) than four times (x4) a number is 15 (=15)
So x · 4 + 3 = 15
Now we do algebra:
x · 4 + 3 (-3) = 15 (-3)
x · 4 = 12
x · 4 (÷4) = 12 (÷4)
x = 3
Answer:3
Step-by-step explanation:
Solve each system by graphing
4x + y = 4
x + y = -2
Graphing each of the equation gave the points
(2, -4)How to graph the pointsThe table of values for graphing the linear equation is done as follows
4x + y = 4 rearranging gives y = 4 - 4x
For x = -5, y = 4 - 4 * -5 = 24
For x = 0, y = 4 - 4 * 0 = 4
For x = 5, y = 4 - 4 * 5 = -16
table of values
x y
-5 24
0 4
5 -16
x + y = -2 rearranging gives y = -2 - x
For x = -5, y = -2 - (-5) = 3
For x = 0, y = -2 - (0 = -2
For x = 5, y = -2 - (5) = -7
table of values
x y
-5 3
0 -2
5 -7
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I am the product 30. Two of my factors are 3 and 2. What are my other factors?
Answer:
1, 5 6 10 15 30 because these numbers times certain numbers can also give 30 for instance 1 by 30 is30, 5 by6 is 30 6 by 5 is 30 10 by 3 is 30 15 by 2 is 30 30 by 1 is 30
