Square GHIJ shares a common center with regular hexagon ABCDEF on a coordinate plane. AB¯¯¯¯¯ is parallel to GH¯¯¯¯¯. If the combined figure rotates clockwise about its center, at which angle of rotation will the image coincide with the preimage?
60°
180°
90°
240°
a square needs to rotate 90 to coincide with itself
but the hexagon would need to rotate 180
the answer is 180 degrees
Answer:
Option B 180° is the right answer.
Step-by-step explanation:
Given is : GHIJ is a square and ABCDEF is a regular hexagon having common centre O.
We know that a square is symmetric at a rotational angle of 90°.
A regular hexagon is symmetric at a rotational angle of 60°.
We will find the LCM of 90 and 60, to know how much to rotate, to get a preimage.
Moreover, a hexagon needs to rotate 180 degrees to coincide with itself.
LCM(60°,90°)=180°.
So, the correct option is B. 180°.
Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 3 inches, and the larger gear has a radius of 7 inches.
Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation?
Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?
Show all work.
A tree that is 50 feet tall casts a shadow that is 60 feet long. Find the angle of elevation to the nearest degree of the sun
To find the angle of elevation of the sun, set up a right triangle with the height of the tree and the length of the shadow.
To find the angle of elevation of the sun, we need to set up a right triangle with the height of the tree (50 feet), the length of the shadow (60 feet), and the line from the top of the tree to the end of the shadow.
Using the information given, we can apply the tan(angle) = opposite/adjacent formula to find the angle of elevation.
By calculating the inverse tangent of the ratio of the height of the tree to the length of the shadow, we can determine the angle of elevation to be approximately 45 degrees.
The angle of elevation to the nearest degree of the sun is approximately 40 degrees.
To find the angle of elevation to the sun, we can use the tangent function in trigonometry.
Let's denote:
- Height of the tree = h = 50 feet
- Length of the shadow = b = 60 feet
The tangent of the angle of elevation (θ) is given by:
tan(θ) = opposite / adjacent
tan(θ) = h / b
Substitute the given values:
tan(θ) = 50 / 60
tan(θ) = 5 / 6
Now, to find the angle θ, we need to take the arctangent (inverse tangent) of the ratio:
θ = arctan(5/6)
θ ≈ 39.8 degrees
Therefore, the angle of elevation to the nearest degree of the sun is approximately 40 degrees.
Find two numbers a a and b b whose sum a + b a+b is 0 and whose difference a − b a-b is 2. your answer is
To find two numbers a and b whose sum a + b is 0 and whose difference a - b is 2, we can set up a system of equations and solve for the values of a and b.
Explanation:To find two numbers a and b whose sum a + b is 0 and whose difference a - b is 2, we can set up a system of equations:
a + b = 0
a - b = 2
We can solve this system by adding the two equations:
(a + b) + (a - b) = 0 + 2
2a = 2
a = 1
Substituting the value of a back into one of the equations, we find that b = -1.
Therefore, the two numbers are 1 and -1.
What is the difference between a sample mean and the population mean called?
Julio has a house worth $220,000. He has a $175,000 mortgage. Julio says that in this situation, his asset is really only $45,000. Which statement explains whether Julio is correct?
A. Julio is correct because the $45,000 equity in the house is the real asset.
B. Julio is correct because he can pay $45,000 and have no more liabilities.
C. Julio is not correct because the same item cannot represent both an asset and a liability.
D. Julio is not correct because the house cannot be worth more than the mortgage.
The statement that explains whether Julio is correct is: A .Julio is correct because the $45,000 equity in the house is the real asset.
What is asset?Asset is anything that add value to you or things that are valuable. Example of assets are:
BuildingEquipmentLand etcReal asset=House worth-- Mortgage
Real asset=$220,000-$175,000
Real asset=$45,000
Based on the information given we are told the asset was only $45,000 which means that the $45,000 equity in the house is the real asset.
Inconclusion the statement that explains whether Julio is correct is: A .Julio is correct because the $45,000 equity in the house is the real asset.
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How could you confirm that a transformation is not a rigid motion by using a protractor
Final answer:
To confirm that a transformation is not a rigid motion, use a protractor to check for any changes in angles within a shape post-transformation. If the angles have changed, the transformation is not rigid. Corresponding side length changes further confirm this.
Explanation:
To confirm that a transformation is not a rigid motion using a protractor, you must look for changes in the shape's size or the angles between any two adjacent sides. A rigid motion, also known as an isometry, will preserve distances and angles between all points on a shape. Therefore, if after a transformation, using a protractor shows that the angles within the shape have changed, or that the corresponding sides are not congruent, then the transformation is not a rigid motion.
For example, if you have a triangle and apply a transformation, such as dilation or shearing, the new angles can be measured with a protractor. If they are different from the original triangle's angles, this confirms the transformation was not a rigid motion. Additionally, if the distances between corresponding points on the figure have changed, which you can measure with a ruler, this also confirms that the transformation is not rigid.
Monica went to the fair and paid for her lunch as well as tickets to ride several rides. The expression 1.5x + 9 represents her total costs.
What do the different parts of the expression model?
Drag the parts of the expression into the boxes to match each description.
Cost of lunch Number of ride tickets Total cost of ride tickets
Answer choices: 9, 1.5, x, 1.5x
There are (32)4 ⋅ 30 bacteria in a petri dish. what is the total number of bacteria in the dish? (1 point)
Answer:
[tex]3^{8}[/tex]
Step-by-step explanation:
[tex]3^{8}[/tex]x1 any expression multiplied by 1 remains the same
alternative form - 6561
Car insurance that pays for your injuries when you're in an accident in your car is _______ insurance.
A. collision B. liability C. comprehensive D. medical
What is the maximum value for the function on the interval [-2,3]?
a. -1
b. 2
c. 3
d. 4
Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula? Quadratic formula: x =
Answer:
[tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex] shows correct substitution of the values a, b, and c from the given quadratic equation [tex]-3x^2-2x+6=0[/tex] into quadratic formula.
Step-by-step explanation:
Given: The quadratic equation [tex]-3x^2-2x+6=0[/tex]
We have to show the correct substitution of the values a, b, and c from the given quadratic equation [tex]-3x^2-2x+6=0[/tex] into quadratic formula.
The standard form of quadratic equation is [tex]ax^2+bx+c=0[/tex] then the solution of quadratic equation using quadratic formula is given as [tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Consider the given quadratic equation [tex]-3x^2-2x+6=0[/tex]
Comparing with general quadratic equation, we have
a = -3 , b = -2 , c = 6
Substitute in quadratic formula, we get,
[tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex]
Simplify, we have,
[tex]x_{1,2}=\frac{2\pm\sqrt{76} }{-6}[/tex]
Thus, [tex]x_{1}=\frac{2+\sqrt{76} }{-6}[/tex] and x_{2}=\frac{2-\sqrt{76} }{-6}
Simplify, we get,
[tex]x_1=-\frac{1+\sqrt{19}}{3},\:x_2=\frac{\sqrt{19}-1}{3}[/tex]
Thus, [tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex] shows correct substitution of the values a, b, and c from the given quadratic equation [tex]-3x^2-2x+6=0[/tex] into quadratic formula.
You can use the standard form of quadratic equation to find the correct substitution of the values a, b and c.
The correct substitution of the value a,b and c from the given quadratic equations into the solution form is [tex]x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4 \times -3 \times 6}}{2 \times (-3)}[/tex]
What is the standard form of quadratic equations?The standard form of quadratic equations is [tex]ax^2 + bx + c = 0[/tex]
What are the solutions of standard quadratic equation?[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
From given equation [tex]0 = -3x^2 -2x + 6[/tex], we deduce that a = -3, b = -2 and c = 6.
Thus, substituting these values in the solutions' equation:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\ \\ x = \dfrac{2 \pm \sqrt{4 + 72}}{-6} = \dfrac{2\pm 2\sqrt{19}}{-6} = \dfrac{-1 \mp 2\sqrt{19}}{3}[/tex]
Thus, the correct substitution of the value a,b and c from the given quadratic equations into the solution form is [tex]x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4 \times -3 \times 6}}{2 \times (-3)}[/tex]
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A container is holding 2 1/3 liters of water.only 2/5 of the container is filled.how much will the whole container hold?
The whole container can hold [tex]5\frac{5}{6}[/tex] liters, calculated by setting up a proportion based on the part of the container currently filled with water ([tex]2\frac{1}{3}[/tex] liters representing 2/5 of the container).
To determine the full capacity of the container, we set up a proportion. Since [tex]2\frac{1}{3}[/tex] liters represent 2/5 of the container's capacity, we want to find out how much 5/5 (the whole) of the container can hold. To set up the proportion, we have:
(2/5) of the container = [tex]2\frac{1}{3}[/tex] liters
(5/5) of the container = x liters
Then, we multiply [tex]2\frac{1}{3}[/tex] liters by 5/2 to solve for x:
x = ([tex]2\frac{1}{3}[/tex] liters) * (5/2)
x = (7/3 liters) * (5/2)
x = 35/6 liters
x = [tex]5\frac{5}{6}[/tex] liters
So the whole container would hold [tex]5\frac{5}{6}[/tex] liters.
while driving with his father, Amit his guys breath whenever they pass through a particular tunnel. Amit counts the number of seconds he holds his breath, from the beginning of the tunnel to the end of the tunnel, and finds he good his breath, on average, for about 8 seconds. if his father drives the car at 60 miles per hour through the tunnel, according to the average time Amit his his breath, about how long is the tunnel? (there are 5280 feet in a mile)
Answer: 704 feet
Step-by-step explanation: speed of car is V= 60 miles per hour
First convert the speed from miles per hour to feet per second .
[tex]V=\frac{60\times 5280}{60\times 60} \frac{ft}{s} = 88 \frac{ft}{s}[/tex]
Now Length of tunnel , L= speed of car x time taken
Therefore [tex]L=88\times 8 feet=704 feet[/tex]
To earn a fitness award, your average heart rate while walking must be between 80 and 89 beats per minute, inclusive. Suppose you recorded 85, 81, and 87 beats per minute on your first three recordings. What are the possible heart rates you can have on the fourth and final recording in order to earn a fitness award?
Answer:
between 67 and 103 beats per minute inclusive
A pattern for 1 uniform uses 12 yards of material. Boleslaw wants to know how many yards are needed for 8 uniforms. Chantal wants to know how many yards she will need to make 15 uniforms.
The number of yards that she will need to make 8 uniforms and 15 uniforms will be 96 yards and 180 yards, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A pattern for 1 uniform uses 12 yards of material. Boleslaw wants to know how many yards are needed for 8 uniforms will be given as,
⇒ 8 x 12
⇒ 96 yards
Chantal wants to know how many yards she will need to make 15 uniforms will be given as,
⇒ 15 x 12
⇒ 180 yards
The number of yards that she will need to make 8 uniforms and 15 uniforms will be 96 yards and 180 yards, respectively.
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Identify the horizontal translation of the parent function f(x) = x^2
Y= (x+5)^2
2a7 – 16a6 + 18a5
Consider the degree of each polynomial in the problem.
The first factor has a degree of????? .
The second factor has a degree of ?????/ .
The third factor has a degree of ????? .
The product has a degree of ??????.
The first factor has a degree of 7, the second has a degree of 6, and the third has a degree of 5. The product has a degree of 7, the highest among them.
To determine the degree of each polynomial in the expression[tex]2a^7 - 16a^6 + 18a^5[/tex], we need to understand that the degree of a polynomial is the highest exponent of the variable in that polynomial.
The first factor is[tex]2a^7[/tex]. Here, the highest exponent of the variable 'a' is 7. So, the degree of the first factor is 7.
The second factor is[tex]-16a^6[/tex]. In this case, the highest exponent of 'a' is 6. So, the degree of the second factor is 6.
The third factor is [tex]18a^5[/tex]. Here, the highest exponent of 'a' is 5. So, the degree of the third factor is 5.
Now, to find the degree of the product of these three factors when added together, we need to find the highest degree among them. In this case, the highest degree is 7 (from the first factor). Therefore, the product has a degree of 7.
In summary:
The first factor has a degree of 7.
The second factor has a degree of 6.
The third factor has a degree of 5.
The product has a degree of 7.
These degrees reflect the highest power of 'a' in each term of the polynomial expression.
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On an average day, 38 customers buy a bag of grapes at Jerry's Market. There are an average of 47 grapes in each bag. Round to the nearest ten and then multiply to estimate the number of grapes Jerry's customers buy every day.
Answer:
40 x 50 = 2,000
Step-by-step explanation:
When we round a number, first identify the digit to round. Then proceed with the following two rules:
(a) If the number to the right of the digit to round is 0, 1, 2, 3, or 4 (that is, less than 5), then keep the digit to round and change the rest of the digits to the right of the digit to round to zero.
(b) If the number to the right of the digit to be rounded is 5, 6, 7, 8, or 9 (that is, greater than or equal to 5), then add one to the digit to round and change the rest of the digits to the right of the digit to round to zero.
In our case, we apply the two rules, rounding to the nearest ten, as follows:
For 38 = 40
Apply rule (b) since 8 is greater than or equal to 5, then add 1 to 3 to get 4, then change 8 to zero. The result is 40.
For 47 = 50
Apply rule (b) since 7 is greater than or equal to 5, then add 1 to 4 to get 5, then change 7 to zero. The result is 50.
Now, multiply to estimate the amount of grapes that Jerry customers buy every day.
40 x 50 = 2,000
Hope this helps!
A graph of a quadratic function y = f(x) is shown below.
We are given a graph of a quadratic function y = f(x) .
We need to find the solution set of the given graph of a quadratic function .
Note: Solution of a function the values of x-coordinates, where graph cut the x-axis.
For the shown graph, we can see that parabola in the graph doesn't cut the x-axis at any point.
It cuts only y-axis.
Because solution of a graph is only the values of x-coordinates, where graph cut the x-axis. Therefore, there would not by any solution of the quadratic function y = f(x).
So, the correct option is 2nd option :∅.Answer:
Option B. ∅
Step-by-step explanation:
If a quadratic function f(x) is in the form of f(x) = ax²+bx+c then the solution of the function is the value of x.
If we analyze the graph for f(x) ≤ 0 solution of the function is null because parabola doesn't intercept at x axis.
Therefore there is no solution for the graphed function f(x).
Option B is the answer.
Which of the following are always classified as a trapezoid? Select all that apply.
A. quadrilaterals
B. parallelograms
C. rectangles
D. rhombuses
E. squares
Answer:
everything except for a quadrilateral
Step-by-step explanation:
Brainliest for the correct answer
What is the effective rate of a $30,000 non-interest-bearing simple discount 5%, 60-day note? A. 6.0% B. 5.14% C. 5.04% D. 5%
The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 degree angles.
What is? (attached)
The dashed line segments form 30-degree angles in the given diagram of a regular hexagon and triangle.
In the given diagram, hexagon GIKMPR and triangle FJN are regular. The dashed line segments form 30-degree angles.
Since hexagon GIKMPR is regular, all its interior angles are equal. Each angle of a regular hexagon is 120 degrees, so angle GIK is 120 degrees.
The angle at GIK can be split into two equal angles by the dashed line segment, so each of these angles measures 60 degrees.
Similarly, since triangle FJN is regular, each of its angles measures 60 degrees.
Therefore, the dashed line segments form two 30-degree angles each side of the regular hexagon and triangle.
The correct answer is option d. The image of [tex]\overline{OQ}[/tex] after a rotation of 300 degrees about point O is [tex]\overline{OF}[/tex].
To find the image of line segment [tex]\( \overline{OQ} \)[/tex] after a rotation of [tex]\( 300^\circ \)[/tex] about point O, we need to understand that a rotation of [tex]\( 300^\circ \)[/tex] is equivalent to rotating [tex]\( 60^\circ \)[/tex] clockwise. This is because rotating [tex]\( 360^\circ \)[/tex] would bring us back to the original position, so a rotation of [tex]\( 300^\circ \)[/tex] is the same as rotating [tex]\( 360^\circ - 60^\circ = 300^\circ \)[/tex].
Given that line segment [tex]\( \overline{OQ} \)[/tex] forms a [tex]\( 30^\circ \)[/tex] angle with the dashed lines, after a rotation of [tex]\( 300^\circ \)[/tex], it will form a [tex]\( 30^\circ \)[/tex] angle with the new position of the dashed lines.
Therefore, the image of line segment [tex]\( \overline{OQ} \)[/tex] after the rotation is [tex]\( \overline{OF} \)[/tex].
The complete question
The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 degree angles.
Find the image of [tex]\overline{OQ}[/tex] after a rotation of 300 degree about point O.
a. [tex]\overline{OJ}[/tex]
b. [tex]\overline{OH}[/tex]
c. [tex]\overline{OQ}[/tex]
d. [tex]\overline{OF}[/tex]
Which expression is equal to (5−2i)−(1+3i)?
4+3i
4+i
6−5i
4−5i
Which expression is equal to −2i(−9+6i) ?
−12+18i
18−12i
18+12i
12+18i
first one is 4-5i
second one is 12+18i
The expression (5−2i)−(1+3i) is equal to 4−5i option (d) is correct and the expression −2i(−9+6i) is equal to 12+18i option (c) is correct.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
It is given that:
(5−2i)−(1+3i)
After using distributive property:
= 5 - 2i - 1 - 3i
= 4 -5i
−2i(−9+6i)
After using distributive property:
= 18i - 12(i)²
= 18i - 12(-1)
= 18i + 12 = 12 + 18i
Thus, the expression (5−2i)−(1+3i) is equal to 4−5i option (d) is correct and the expression −2i(−9+6i) is equal to 12+18i option (d) is correct.
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What is the inverse of f(x) =1/3 x + 2?
Answer:
h(x)= 3x - 6
Step-by-step explanation:
Edge 2020
The inverse of function f(x) = [tex]\frac{1}{3}x + 2[/tex] is -
y = 3(x - 2)
We have a function - f(x) = [tex]\frac{1}{3}x + 2[/tex]
We have to find the inverse of a function.
What is the necessary condition for a function to be invertible?We say that a function f : A → B is invertible if for every b ∈ B there is exactly one a ∈ A such that f(a) = b.
According to question, we have -
y = f(x) = [tex]\frac{1}{3}x + 2[/tex]
Replace x with y, to find inverse function f, and compute the resulting equation for x. Exchanging the variables, we get -
x = [tex]\frac{1}{3}y + 2[/tex]
x - 2 = [tex]\frac{1}{3} y[/tex]
y = 3(x - 2)
Hence, the inverse of function f(x) = [tex]\frac{1}{3}x + 2[/tex] is -
y = 3(x - 2)
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Which is a property of an angle?
has two sides that each extend forever in both directions
has two endpoints
has two center points
has two rays that share a common endpoint
Answer:
has two rays that share a common endpoint
Step-by-step explanation:
An angle is formed by a two rays that share a common endpoint. The distance between the two rays is what makes the measure of the angle wider or smaller. Each ray extends in one direction forever; however since they share an endpoint, the rays do not extend in both directions forever. There is only one endpoint, not two, and there is only one center point (vertex), not two.
As a student you are able to earn extra money by assisting your neighbors with odd jobs if you charged $10.25 an hour for your assistance about how many hours would you need to work earn $8,425
Which graph represents the solution set of the system of inequalities?
x+y<1
2y≥x−4
I think its the one in the top right corner (the highlighted one)
Give the name of a quadrilateral that is formed when you have two bisected diagonals.
Which of the following is the linear parent function
Answer: The answer is C.
A Linear parent function is a function of the form f(x) = x
or y = x. This is the simplest of the linear functions, where the slope is 1 and the function pases for the point (0,0) (which is the same of saying that the intercept is 0).
a) isnt a linear function.
b) is a quadratic function.
d) is also a linear function, but it has a slope = 2, so it isn't the linear parent function.