Which composition of transformations maps figure EFGH to figure E"F"G"H"?
a reflection across line k followed by a translation down
a translation down followed by a reflection across line k
a 180° rotation about point G followed by a translation to the right
a translation to the right followed by a 180° rotation about point G
Answers
The composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.
What is the transformations rule that was used here?A transformation is a rule that is used to manipulate the position of a point of geometric figure.
And from the figure, we can see that a translation is used, because of the movement of EFGH to figure E"F"G"H" which occurred in the same direction.
Hence, composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.
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Related Questions
(02.02 MC)
Given the function g(x) = 8x − 2, compare and contrast g(−2) and g(4). Choose the statement that is true concerning these two values.
Group of answer choices
The value of g(−2) is larger than the value of g(4).
The value of g(−2) is the same as the value of g(4).
The value of g(−2) is smaller than the value of g(4).
The values of g(−2) and g(4) cannot be compared.
Answers
Answer:
The value of g(-2) and g(4) cannot be compared because they are two different functions with two completely different values.
Step-by-step explanation:
So, you plug in -2 in the function of the x in g(x) = 8x - 2
Then, you multiply 8 by -2 in g(-2) = 8x - 2
8 × -2 would be -16
Afterwards you subtract -16 by 2 in g(-2) = -16 - 2
The function of g(-2) is -14 in g (x) = -14
You plug in 4 in the function of x in g(4) = 8x - 2
g(4) = 8 (4) - 2
Then, You multiply 8 by 4 which will give you 32 in
g(4) = 32 - 2
Lastly, you subtract the 32 by 2 and the function of the answer would be 30 in g(x) = 30
Find the angle [OA] makes with the positive x-axis if the x-coordinate of the point A on the unit circle is 0.222
Answers
By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.
How to find an angle in an unit circle
Unit circles are circles with radius of 1 and centered at the origin of a Cartesian plane, which are used to determine angles and trigonometric functions related to them. If we use rectangular coordinate system and the definition of the tangent function, we find that the angle OA is equal to:
[tex]\tan \theta = \frac{\sqrt{1 - x^{2}}}{x}[/tex]
[tex]\tan \theta = \frac{\sqrt{1-0.222^{2}}}{0.222}[/tex]
tan θ ≈ 77.173°
By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.
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A line with gradient of -3 passes through the points(3,k) and (k,8). Find the value of k and hence express the equation of the line in the form ax + by = c, where a,b and c are constants.
Answers
Answer:
3x + y = 9.5
Step-by-step explanation:
1) The equation of a line is in the form of y = mx + c, where m is the gradient and c is the y-intercept. Write the given values in that form.
y = -3x + c
2) Find the value of k by using the following formula: m = y2 - y1 / x2 - x1. We already know m.
-3 = 8 - k / k - 3
-3(k - 3) = 8 - k
-3k + 9 = 8 - k
-3k + k = 8 - 9
-2k = -1
k = -1/-2
k = 1/2
3) Therefore, a line with gradient of - 3 passes through the points (3, 1/2) and (1/2, 8). We can find the y-intercept (c). To do so, choose one of the coordinates and substitute.
y = -3x + c
1/2 = -3(3) + c
1/2 = -9 + c
1/2 + 9 = c
9.5 = c
Completed equation of the line: y = -3x + 9.5
4) Write it in the form of ax + by = c.
3x + y = 9.5
6x^2+18x=0 rounded the nearest 10th
Answers
By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.
How to solve a quadratic equation
In this question we must apply algebraic rules to find the roots of a quadratic equation, the roots are the values of the equation such that is equal to zero. Now we present the complete procedure:
6 · x² + 18 · x = 0
6 · x · (x + 3) = 0
x = 0 ∨ x = - 3
By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.
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Use the logarithm lays to simplify this expression
log2 8x^3/2 = log2 8x^3 - log2 2y
Answers
By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.
How to simplify a logarithmic expressions
Herein we must simplify an expression that uses logarithms by applying any of the following three laws:
[tex]\log_{a} (b \cdot c) = \log_{a} b + \log_{a} c[/tex] (1)
[tex]\log_{a} \left(\frac{b}{c} \right) = \log_{a} b - \log_{a} c[/tex] (2)
[tex]\log_{a}{b^{c}} = c \cdot \log_{a} b[/tex] (3)
Now we proceed to simplify the expression:
[tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex]
[tex]\log_{2} 2\cdot y = \log_{2} 8\cdot x^{3} - \log_{2} \frac{8\cdot x^{3}}{2}[/tex]
[tex]\log_{2} 2 \cdot y = \log_{2} \frac{\frac{8\cdot x^{3}}{1} }{\frac{8\cdot x^{3}}{2} }[/tex]
[tex]\log_{2} 2\cdot y = \log_{2} 2[/tex]
By the relationship between logarithms and powers of same base:
2 · y = 2
y = 1
By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.
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Determine the equation of the linear function that generates the following table of values.
Answers
Answer:
y = -19x + 14
Step-by-step explanation:
For each increase of x by 1, y decreases by 19, giving us -19x. When x = 0, y = 14, therefore, y = -19x + 14
The following are the temperatures in
°C for the first 12 days of January:
-5.5, 6, -1.5, 3, 4, -2.5,
0, 6.5, -3, 2.5, -1, 5.5
What is the median temperature for
those 12 days?
Give your answer as a decimal.
ABC Check
↑
XI
Answers
Answer:
1.25 is the median for the first 12 days in January
Jason planted and staked a tree. The stakes are 21 ft from the base of the tree. They are connected to wires that attach to the trunk at a height of 20 ft. Find the length of a wire. O14 ft 15 ft 20 ft 29 ft Jason planted and staked a tree . The stakes are 21 ft from the base of the tree . They are connected to wires that attach to the trunk at a height of 20 ft . Find the length of a wire . O14 ft 15 ft 20 ft 29 ft
Answers
Answer:
29 ft
Step-by-step explanation:
The distance along the ground from one stake to the tree, 21 ft, and the distance up the trunk from the ground, 20 ft, are the legs of a right triangle. The length of the wire is the hypotenuse of the right triangle. We can use the Pythagorean theorem to solve this problem.
a² + b² = c²
(21 ft)² + (20 ft)² = c²
c² = 841 ft²
c = √(841 ft²)
c = 29 ft
Answer: 29 ft
A video game randomly chooses your car color and type. The
probability of getting a red car is 0.20, and the probability of
a getting a convertible is 0.30.
Event A = You get a red car.
Event B = You get a convertible.
A and B are independent events if
• A. The probability of getting a red car or a convertible is 0.06.
O
B. The probability of getting a red convertible is 0.06.
• C. The probability of getting a red car or a convertible is 0.50.
O D. The probability of getting a red convertible is 0.
Answers
The correct statement regarding when the events will be independent is given as follows:
B. The probability of getting a red convertible is 0.06.
What are independent events?Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this problem, the probabilities are given as follows:
P(A) = 0.2.P(B) = 0.3.The events will be independent if:
[tex]P(A \cap B) = 0.2 \times 0.3 = 0.06[/tex]
The intersection of events A and B is a red convertible car, hence the correct option is:
B. The probability of getting a red convertible is 0.06.
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The lines shown below are perpendicular.
Answers
[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]
The lines shown below are perpendicular. Is this statement true or false?
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
In order for a pair of lines to be perpendicular, they must intersect at a [tex]\bf{90^\circ}[/tex] angle. (a right angle)
[tex]\bf{Since\;the\;green\;line\;and\;the\;red\;one\;intersect\;at\;a\;right\;angle,}\\they\;are\;perpendicular.\\\\Hope\;you\;will\;have\;a\;fantabulous\;day!}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\boxed{\bf{aesthetic \not101}}[/tex]
PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
The Csc θ = [tex]\frac{8}{5}[/tex] is equivalent to which of the following expressions?
A. sin θ = [tex]\frac{5}{8}[/tex]
B. cos θ = [tex]\frac{5}{8}[/tex]
C. tan θ = [tex]\frac{5}{8}[/tex]
D. sin θ = [tex]\frac{8}{5}[/tex]
E. cos θ = [tex]\frac{8}{5}[/tex]
F. tan θ = [tex]\frac{8}{5}[/tex]
Answers
Answer:
A. sin θ = 5/8
Step-by-step explanation:
csc θ = 1/sin θ
csc θ = 8/5
1/sin θ = 8/5
sin θ = 5/8
-2+12-2^3 divided by 2^0 times 3
Answers
Answer:
The correct answer is -14
Step-by-step explanation:
What additional information would allow you to prove the quadrilateral is a parallelogram?
Answers
The additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ
How to prove a Parallelogram?The six basic properties of parallelograms are primarily;
Both pairs of opposite sides are parallelBoth pairs of opposite sides are congruentBoth pairs of opposite angles are congruentDiagonals bisect each otherOne angle is supplementary to both consecutive angles (same-side interior)One pair of opposite sides are congruent AND parallel.Now, looking at the parallelogram properties above and comparing with the given image of the quadrilateral attached, we can say that the additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ
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vase with a circular base exerts a force of 15 N on a table with a pressure of 700 N/m2.
Find the radius of the base of the vase in cm to 2 dp.
radius =
cm
Answers
The radius of the base is 8.245 cm
Given, a vase with a circular base exerts
Pressure = 700 N/m²
Force = 15 N
Area = ?
∴ area = πr²
By finding out the area of the vase we can calculate the radius.
We know that Pressure = Force/Area
According to the equation, pressure is inversely related to area but directly related to force. Pressure rises at a constant area as the force exerted increases in strength.
therefore apply the above the formula to find out the area and radius.
700 = 15/πr²
πr² = 15/700
πr² = 3/140
r² = 3/140 × 3.14
since π value is 3.14
r² = 0.0068
r = √0.0068
r = 0.0824 m
r = 0.0824 × 100
r = 8.245 cm
we get radius as 8.245 .
Hence we get the radius of the base of the vase as 8.245 cm.
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What is the value of the following radical expression?
Answers
Answer:
b.) 2
Explanation:
Given:
[tex]\sf - \sqrt[\sf 5]{\sf -32}[/tex]rewrite knowing 2⁵ = 32, (-2)⁵ = -32
[tex]\sf -\left(\sqrt[5]{(-2)^5}\right)[/tex]simplify, ⁿ√xⁿ = x
[tex]\sf -\left(-2}\right)[/tex]distribute inside parenthesis
[tex]\sf 2[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{-a}=-\sqrt[n]{a}, if \ n \ is \ odd \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{-32}=-\sqrt[5]{32} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{32}\right)} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Decompose \ the \ number \ into \ prime \ factors: 32=2^{5}. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{2^5}\right)} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^n}=a,\:\quad \:a\ge 0 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{2^5}=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Remove \ parentheses:\quad \:-\left(-2\right)=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=2 \ \ \to \ \ \ Answer} \end{gathered}$}[/tex]
{ Pisces04 }Prove: m∠TSE + m∠RSO = m∠TSK
Answers
Answer:
down there
Step-by-step explanation:
we can see that angel rso and esk are congruent because they are verticle angels.
we also know that angel tse plus esk is equal to tsk, so angel tse+rso=tsk by algebra
which number would be equivalent to the expression: 3 times 4 to the second power plus 6 divided by 2
Answers
The given expression is equivalent to the number 147.
We have given that,
[tex](3\times4)^2+\frac{6}{2}[/tex]
We have to determine the value of the given expression.
What is the expression?
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
[tex]=(12)^2+\frac{6}{2} \\=144+3\\=147[/tex]
Therefore the given expression is equivalent to the number 147.
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sin A - sin B - sin C=-4cos A 2 .sin B 2 .sin C 2
Answers
sinA+sinB+sinC
=2sin(A+B)/2cos(A-B)/2+sin C
=2sin(pi-C)/2cos(A-B)/2+2sin C/2cosC/2
=2cosC/2(cos(A-B)/2+cos(A+B)/2)
=4 cos A/2 cos B/2 cos C/2
= RHS
A patient admitted to the hospital was prescribed a pain medication to be given every 4 hr and an antibiotic to be given every 5 hr. Bandages applied to the patient's external injuries needed changing every 12 hr. The nurse changed the bandages and gave the patient both medications at 6:00 A.M. Monday morning. A patient admitted to the hospital was prescribed a pain medication to be given every 4 hr and an antibiotic to be given every 5 hr . Bandages applied to the patient's external injuries needed changing every 12 hr . The nurse changed the bandages and gave the patient both medications at 6:00 A.M. Monday morning.
Answers
Answer:
First Question: 1. 60 hours 2. Wednesday 6:00 PM
Step-by-step explanation:
Sorry but I couldn't figure out the answer to the second question :(
Hope this helped :D
2x + 15 = 3x + 10 help BRAINLIEST
Answers
Answer:
5
Step-by-step explanation:
2x + 15 = 3x + 10
3x + 10 = 2x + 15
3x - 2x = 15 - 10
x = 5
Answer:
[tex]x = 5[/tex]
Step-by-step explanation:
[tex]2x + 15 = 3x + 10[/tex]
• Group like terms together:
• Subtract 5 from both sides:
[tex]2x = 3x - 5[/tex]
• Subtract 3x from both sides:
[tex]-x = -5[/tex]
• Multiply both sides by -1:
[tex]x = 5[/tex]
Robert has 3/4 of a candy bar like he wants to share it with himself and two friends what fraction of the candy bar will each person get?
Answers
Answer:
significa que 1 barra de chocolate dividida entre 4 amigos es igual a 1 4. Por lo tanto, cada persona recibe 1 4 de la barra”. 6.
Step-by-step explanation:
Answer:
3/4 divided by 3 is 0.25
Step-by-step explanation:
We know that he has 3/4 of a candy bar and he wants to share it with himself plus 2 people.
The expression 3/4 divided by 3 represents this.
To change division to multiplication we use the reciprocal.
3/4 times 1/3 is 0.25.
Hope this helps. (:
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.
two to the seven eighths power, all over two to the one fourth power
Answers
The expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.
What are Exponents?Exponents are the base raised to a power, It is written in the superscript of a number.
The expression given in the statement can be written as
[tex]\rm \dfrac{ 2^{7/8}}{2^{1/4}}[/tex]
By the Exponent rule,
[tex]\rm \dfrac{a^m}{a^n} = a^{m-n}[/tex]
So the expression can be written as
=[tex]\rm { 2^{7/8-1/4}[/tex]=[tex]\rm 2^{5/8}[/tex]
=[tex]\rm \sqrt[8]{2^5}[/tex]
Therefore, in radical form, the expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.
The complete question is
Rewrite the rational exponent as a radical by extending the properties of integer exponents.
2 to the 7 over 8 power, all over 2 to the 1 over 4 power
the eighth root of 2 to the fifth power
the fifth root of 2 to the eighth power
the square root of 2 to the 5 over 8 power
the fourth root of 2 to the sixth power
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A shirt and a tie together cost $57. The shirt costs $33 more than the tie. What is the cost of the shirt?
Answers
Answer:
Shirt: $45 , Tie: $12
Step-by-step explanation:
Let s be the price of the shirt
Let t be the price of the tie
Given the information from the question,
s + t = 57 - Equation 1
s - t = 33 - Equation 2
We will use substitution method to find the prices.
We will rearranging equation 1.
s = 57 - t
We will substitute s into equation 2.
57 - t - t = 33
57 - 2t = 33
-2t = 33 - 57
-2t = -24
t = -24 / -2
= 12
We now substitute t into Equation 1.
s + 12 = 57
s = 57 - 12
= 45
From here we know, the shirt costs $45 and the tie costs $12
A runner can run 3miles in 15 minutes. At this rate, how many miles can he run in 45minutes?
Answers
Answer:
9 miles
Step-by-step explanation:
If 3 miles is equal to 15 mins
Then you do 3 miles and times by 3 cause if you times 15 by 3, you'll get 45 mins
So the answer= 9 miles
n August 31 of the current year, the assets and liabilities of Gladstone, Inc. are as follows: Cash $27,900; Supplies, $900; Equipment, $8,500; Accounts Payable, $7,300. What is the amount of stockholders’ equity as of August 31 of the current year?
Answers
The amount of stockholders’ equity as of August 31 of the current year is $26400.
How to calculate the equity?The owner's equity will be:
= Cash + Supplies + Equipment - Account payable
= 27900 + 900 + 8500 - 7300
= 26400
Therefore, the amount of stockholders’ equity as of August 31 of the current year is
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Find the range of the parent function below. y = |x| A. all real numbers B. all positive numbers C. all positive numbers and 0 D. all negative numbers
Answers
Answer:
c
Step-by-step explanation:
absolute values are positive and abs value of 0 = 0
Kristina invests a total of $28,500 in two accounts. The first account earned a rate of return of 10% (after a year). However, the second account suffered a 4% loss in the same time period. At the end of one year, the total amount of money gained was $1,310.00. How much was invested into each account?
Answers
$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of money invested at 10% and y represent the amount of money invested at a loss of 4%, hence:
x + y = 28500 (1)
Also:
(x * 1 year * 0.1) + (y * 1 year * -0.04) = 1310
0.1x - 0.04y = 1310 (2)
From equation 1 and 2:
x = 17500, y = 11000
$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.
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Which of the following is a true statement
5/6 > 10/12
8/16=1/4
3/4<4/6
11/15<4/5
Answers
Answer:
11/15 < 4/5
Step-by-step explanation:
1. 5/6 = 10/12, so the first answer is not correct
2. 1/4 = 4/16, so the second answer is not correct
3. 3/4 = 9/12 and 4/6 = 8/12, so the third answer is not correct
4. 4/5 = 12/15 > 11/15, so this answer is correct
How many terms of the G.P 3 , 3/2,3/4 are needed to give the Sum 3069 /512
Answers
Answer: 10
Step-by-step explanation:
The first term is 3 and the common ratio is 1/2.
Using the sum of a geometric series formula,
[tex]\frac{3069}{512}=\frac{3(1-(1/2)^{n}}{1-(1/2)}\\\\\frac{3069}{1024}=3(1-(1/2)^{n})\\\\\frac{1023}{1024}=1-(1/2)^{n}\\\\-(1/2)^{n}=-\frac{1}{1024}\\\\(1/2)^n=\frac{1}[1024}\\\\2^{-n}=2^{-10}\\\\n=10[/tex]
What is the domain of the following relation?
{(-3, -8), (-2, 9), (1, -1), (5,3)}
O {-8, -1, 3, 9}
O {-3, -2, 1, 5}
O (-3, -8)
O {-8, -3, -2, -1, 1, 3, 5, 9}
Answers
Answer: {-3, -2, 1, 5}
Step-by-step explanation:
The domain is the set of x-values.