Answer:
The correct options are 1 and 2.
Step-by-step explanation:
The vertices of triangle are S(-4,4), T(-1,4), R(-1,1).
If triangle translated 2 units left,
[tex](x,y)\rightarrow (x-2,y)[/tex]
and then reflected over the y-axis,
[tex](x-2,y)\rightarrow (-x+2,y)[/tex]
The relation between image and preimage is
[tex](x,y)\rightarrow (-x+2,y)[/tex] ..... (1)
The vertices of image are
[tex]S(-4,4)\rightarrow S'(6,4)[/tex]
[tex]T(-1,4)\rightarrow T'(3,4)[/tex]
[tex]R(-1,1)\rightarrow R'(3,1)[/tex]
Therefore the vertices of image are S'(6,4),T'(3,4), R'(3,1).
1. A reflection over the y-axis and then a translation 2 units right is defined as
[tex](x,y)\rightarrow (-x+2,y)[/tex]
It is equivalent to relation 1, therefore option 1 is correct.
2. A 180 rotation about the origin, then a translation 2 units right, and then a reflection over the x-axis is defined as
[tex](x,y)\rightarrow (-x+2,y)[/tex]
It is equivalent to relation 1, therefore option 2 is correct.
3. A reflection over the y-axis and then a translation 2 units left is defined as
[tex](x,y)\rightarrow (-x-2,y)[/tex]
It is not equivalent to relation 1, therefore option 3 is incorrect.
4. A 180 rotation about the origin, then a translation 2 units left, and then a reflection over the x-axis is defined as
[tex](x,y)\rightarrow (-x-2,y)[/tex]
It is not equivalent to relation 1, therefore option 4 is incorrect.
5. A reflection over the x-axis and then a translation 2 units right is defined as
[tex](x,y)\rightarrow (x+2,-y)[/tex]
It is not equivalent to relation 1, therefore option 5 is incorrect.
6. A reflection over the x-axis and then a translation 2 units left is defined as
[tex](x,y)\rightarrow (x+2,-y)[/tex]
It is not equivalent to relation 1, therefore option 6 is incorrect.
Therefore the correct options are 1 and 2.
Answer:
1 and 2 are the correct answers.
Step-by-step explanation:
a school has 18 classes with 35 students in each class in order to reduce the class size 30 how much new classes much must be formed
Answer: 3 classes
If we removed 5 students from each of the classrooms, we would be able to keep the 18 classes and give them exactly 30 students. However, we would also have the leftover students to put into classrooms.
If there are 18 classrooms with 5 extra students from each, we can use 18*5 to find how many total students we have.
18 * 5 = 90.
If each class size is 30, we need to divide 90 by 30 to find how many classes we need.
90 / 30 = 3 classes
Therefore, to reduce the class size to 30 students per class, 3 new classes must be formed.
To reduce the class size from 35 students to 30 students in a school with 18 classes, we need to calculate the total number of students and then determine how many new classes are needed.
1. **Total number of students:**
[tex]\[ \text{Total students} = 18 \text{ classes} \times 35 \text{ students/class} = 630 \text{ students} \][/tex]
2. **Number of classes required with 30 students per class:**
[tex]\[ \text{Required classes} = \frac{630 \text{ students}}{30 \text{ students/class}} = 21 \text{ classes} \][/tex]
3. **New classes to be formed:**
[tex]\[ \text{New classes} = \text{Required classes} - \text{Current classes} = 21 - 18 = 3 \text{ classes} \][/tex]
what is the mean of 17, 19, 21, 23
Answer:
20
Step-by-step explanation:
Answer:
i got 15.5
Step-by-step explanation:
The blades of a windmill turn on an axis that is 40 feet from the ground. The blades are 15 feet long and complete 3 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.
a is the ___
The vertical shift, k, is the _____________
a =
k =
Answer:
a is the _amplitude_(Length of the blades)_
The vertical shift, k, is the _Mill shaft height_
[tex]a = 15\ ft\\\\k = 40\ ft[/tex]
[tex]y = 15sin(\frac{\pi}{10}t) + 40[/tex]
Step-by-step explanation:
In this problem the amplitude of the sinusoidal function is given by the length of the blades.
[tex]a = 15\ ft[/tex]
The mill is 40 feet above the ground, therefore the function must be displaced 40 units up on the y axis. So:
[tex]k = 40\ ft[/tex]
We know that the blades have an angular velocity w = 3 rotations per minute.
One rotation = [tex]2\pi[/tex]
1 minute = 60 sec.
So:
[tex]w = \frac{3(2\pi)}{60}\ rad/s[/tex]
[tex]w = \frac{\pi}{10}\ rad/s[/tex]
Finally:
a is the _amplitude_(Length of the blades)_
The vertical shift, k, is the _Mill shaft height_
[tex]a = 15\ ft\\\\k = 40\ ft[/tex]
[tex]y = 15sin(\frac{\pi}{10}t) + 40[/tex]
Answer:
a is the length of the blade
the vertical shift , k, is the height of the windmill
a= 15 k= 40
the period is 20 seconds
b = pi/10
y=15sin(π/10t)+40
Step-by-step explanation:
What 1/4 plus 1/2 is
Answer:
the answer is 3/4
Step-by-step explanation:
Answer:
The correct answer is 3/4
Step-by-step explanation:
1/2+1/4=3/4
The equation of a line is x = -4 what is the slope
The slope is undefined because it is a vertical line
Answer:
The slope is undefined.Step-by-step explanation:
The vertical line equation has the form x = a (a - any real number).
The vertical line has an undefined slope.
We have x = -4. It's a vertical line. Therefore, the slope is undefined.
What does the line y= 5x-13y=7 look like horizontal vertical slanted right upwards slanted right downward
Answer:
The line y = 5x - 13, looks slanted right upwards
Step-by-step explanation:
To easily solve this question, we use a graphing tool, or a calculator to plot the graph.
Please see image below.
From looking at the graph, we know that the function is slanted right upwards.
Which function is represented by the graph?
a). f(x)=-2x+6
b). f(x)2x+6
c). f(x)1/2x +6
d). f(x)=-1/2x +6
Answer:
d). f(x)=-1/2x +6 (see attachment)
Step-by-step explanation:
Rewrite the number in scientific notation. 0.000000000045 = 4.5 × 10
Answer:
4.5 * 10^-11
Step-by-step explanation:
the reason why is there is 11 zeros in front of the 45
hope this helps :)
the volume V of a gas at a constant temperature varies inversely with the pressure P. when the volume is 100 cubic inches the pressure is 25 pounds per square inch. what is the pressure when the volume is 125 cubic inches
Answer:
The pressure is [tex]20\ psi[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
In this problem we have
[tex]V*P=k[/tex]
where
V is the volume of a gas at a constant temperature
P is the pressure
we have
For [tex]V=100\ in^{3}[/tex],[tex]P=25\ psi[/tex]
step 1
Find the value of k
substitute the values of V and P
[tex]100*25=k[/tex]
[tex]k=2,500[/tex]
The equation is equal to [tex]V*P=2,500[/tex]
step 2
Find the pressure when the volume is 125 cubic inches
For [tex]V=125\ in^{3}[/tex]
substitute in the equation and solve for P
[tex]125*P=2,500[/tex]
[tex]P=2,500/125=20\ psi[/tex]
Simplify this expression. 35 ÷ 33 A. 27 B. 9 C. 6 D. 3
Hello, this is a bet tough so follow the steps!
First we need to set up long division.
__
33|35
If we calculate 33 divided by 35 we get 1 with a remainder of 2.
Our work:
1
__
33|35
-33
_____
2
So therefore we get 1 with a remainder of 2.
Enjoy your day!
Answer: The correct option is (B) 9.
Step-by-step explanation: We are given to simplify the following expression :
[tex]E=3^5\div 3^3.[/tex]
We will be using the following property of exponents :
[tex]\dfrac{x^a}{x^b}=x^{a-b}.[/tex]
Therefore, the simplification of the given expression is as follows :
[tex]E\\\\=3^5\div 3^3\\\\\\=\dfrac{3^5}{3^3}\\\\\\=3^{5-3}\\\\=3^2\\\\\=9.[/tex]
Thus, the required simplified answer is 9.
Option (B) is CORRECT.
Which of the following statements best describes the location of −(−4) on a number line?
It is 4 units to the left of 0.
It is 4 units to the right of 4.
It is 4 units to the left of 4.
It is 4 units to the right of 0.
Answer:
Step-by-step explanation:
Two negatives make a positive, so -(-4) = +4. On a number line, -(-4) would be located 4 units to the right of 0.
The statement "It is 4 units to the right of 0" best describes the location of −(−4) on a number line.
When you have a double negative like −(−4), it becomes positive, so −(−4) is equal to 4, and it is 4 units to the right of 0 on the number line.
The statement "It is 4 units to the right of 0" accurately describes the location of −(−4) on a number line. When dealing with a double negative like −(−4),
it effectively becomes a positive value. In this case, −(−4) simplifies to 4. Therefore, the point −(−4) is located at the position corresponding to the number 4 units to the right of the origin, which is represented by 0 on the number line.
Moving to the right on the number line means increasing the numerical value, so, as a result, −(−4) is found 4 units to the right of 0.
This concept highlights the fundamental principle that negating a negative value results in a positive value, and the position of that positive value is to the right of the origin on the number line.
For similar question on number line.
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what is minus root 6, minus root six
➷ It would be [tex]-2\sqrt{6}[/tex]
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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Rebecca must complete 15 hours of volunteer work .she does 3 hours each day . Write a linear equation in slope intercept form to represent the house Rebecca still has to work for after x days
Answer:
Step-by-step explanation:
House?
Number of hours left to work(x) = 15 hours - (3 hours/day)x
Note how this Number of hours decreases steadily from its initial value (15 hours) at the rate of 3 hours/day. The domain of x is [0,5].
By slope intercept form, the number of days that the Rebecca should volunteer exists 5 days.
What is meant by slope intercept form?The "equation of the straight line exists y = mx + c this form exists named slope intercept form".
Rebecca must complete 15 hours of volunteer work. She does 3 hours each day.
The linear equation exists in slope intercept form exists y = mx + c, where 'm' exists the slope straight line and 'c' exists y-intercept.
y = 15 hours - 3 hours/day x days
y = 15 - 3x ............(1)
To find y-intercept put x=0 in (1) we get,
y = 15 - 3(0)
= 15
y = 15
which exists the amount of volunteer hours.
Rebecca must complete at day 0.
0 = 15 - 3x
3x = 15
x = 5 [Number of days Rebecca would have to volunteer]
Therefore, utilizing slope intercept form, the number of days that the Rebecca should volunteer exists 5 days.
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Simplify: 3^2 * 3^4
3^2 = 9
3^4= 81
9 x 81 = 729
Your answer is 729 . Good luck (:
Find slope of line perpendicular to given line x=3
perpendicular means negative reciprocal so it would be -1/3
Answer:
slope = 0
Step-by-step explanation:
x = 3 is a vertical line parallel to the y- axis with undefined slope.
A line perpendicular to x = 3 is a horizontal line parallel to the x- axis with a slope of zero.
Can anybody help me please
Answer:
Not entirely positive of about the answers, but all of the values would equal 15
First Y = 5
First X = 15
Second X = -3
Answer:
x / y
0/5
15/0
-3/6
Step-by-step explanation:
78.2 times 10 to the fourth power in standard form
you would move the decimal to the right four times giving you 782000
Plz help!!!!!!!!!!!!
Answer: [tex]\bold{x^{\frac{1}{3}}}[/tex]
Step-by-step explanation:
[tex]\sqrt[6]{x^2} =x^{\frac{2}{6}}=x^{\frac{1}{3}}[/tex]
Find the volume of 5.4 inches 2 inches 7.1 inches round to the nearest 10th is necessary
Answer:
If it is a cube, the answer would be 76.7 .
Step-by-step explanation:
What's the volume of a pipe at a port that is 4 feet in diameter 24 ft long
A. 603.1872
B. 150.7968
C. 314.1632
D. 301.5936
answer: D
explanation:
volume is equal to length * surface area.
surface of a tube base is a circle, so it' surface are can be calculated as:
[tex]\pi \: {r}^{2} [/tex]
where r is a radius
[tex] r \: = \frac{1}{2} diameter[/tex]
so you calculate volume V as:
[tex]v \: = \pi( {r}^{2} ) \times length \: = \pi \times \frac{1}{4} \times {diameter}^{2} \times length[/tex]
[tex]v = 3.14 \times \frac{1}{4} \times 4 \times 4 \times 24 = 301.44[/tex]
so the answer is D
How to solve this equation
[tex]\bold{Hey\ there!}[/tex]
[tex]\bold{x^2=81}[/tex][tex]\bold{Take\ your\ particular\ root\ (square\ root\ preferably)}[/tex][tex]\rightarrow{\bold{x=\pm\sqrt{81}}}[/tex][tex]\bold{\frac{\sqrt{81}}{9}=9}[/tex][tex]\boxed{\boxed{\bold{Answer:x\rightarrow9\ or\ x\rightarrow-9}}}\checkmark[/tex][tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Help me with this question
Answer:
A
Step-by-step explanation:
This is an even polynomial because both ends end up. This means the degree of the polynomial is even. This means b and c are not solutions since their degrees are odd.
To determine between A and D look at the x-intercepts. The x-intercepts of a polynomial graph have a special relationship with its equation. The x-intercepts are the solutions or roots of the factors. This means that when each factor is set equal to 0 and solved, its solution is an x-intercept. Here the x-intercepts are x = -1, 0,3. This means the factors are x(x+1)(x-3).
Notice at x = -1, the function touches but does not cross? This means the factor has an even exponent on it.
So the expression is likely x(x+1)^2 (x-3).
Since only one factor has an exponent, the answer is A.
Use the quadratic formula to solve Round irrational solutions to the nearest tenth
Answer:
C. x = -5.6 and x = -1.4
Step-by-step explanation:
The quadratic formula is [tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]. Here a=1, b=7, and c=8.
Substitute and you'll have:
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-7+/-\sqrt{7^2-4(1)(8)} }{2(1)}=\frac{-7+/-\sqrt{49-32} }{2)}[/tex]
[tex]\frac{-7+/-\sqrt{17} }{2}=\frac{-7+/-4.1 }{2}= -1.4, -5.6[/tex]
In the diagram below P is circumscribed about quadrilateral ABCD. What is the value of x?
Answer:
(A) [tex]x=60^{\circ}[/tex]
Step-by-step explanation:
Given: It is given that the circle P is circumscribed about quadrilateral ABCD and ∠BCD=120°.
To find: The value of x
Solution: It is given that the circle P is circumscribed about quadrilateral ABCD and ∠BCD=120°.
Now, we know that the sum of opposite angles in a cyclic quadrilateral is 180°, therefore
[tex]{\angle}BAD+{\angle}BCD=180^{\circ}[/tex]
substituting the given values, we get
[tex]x+120^{\circ}=180^{\circ}[/tex]
[tex]x=60^{\circ}[/tex]
Thus, the value of x is 60°.
Hence, option A is correct.
Answer: 60
Step-by-step explanation:
PLEASE HURRY!!!
The graph of g(x) is a reflection and translation of f(x) = 3 √x. Which equation represents g(x)?
Answer:
it’s d
Step-by-step explanation:
just took the test
The graph represents the equation g(x) = -∛(x - 1).
Option D is the correct answer.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
f(x) = ∛x
Reflection over the x-axis.
f(x) = -∛x
And,
Translated one unit to the left.
g(x) = -∛(x - 1)
The graph of g(x) = -∛(x - 1) is shown on the given graph.
Thus,
The graph represents the equation g(x) = -∛(x - 1).
Learn more about translation here:
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For what values of t can 3(x^2) + tx + 8 be written as the product of two binomials and what are the pairs of binomials?
Final answer:
Explanation of values of t for which the given expression can be factored into binomials.t = 0; pairs of binomials: (x) and (3x + 8)
t = 1; pairs of binomials: (x + 1) and (3x + 8)
t = 2; pairs of binomials: (x + 2) and (3x + 4)
Explanation:
Values of t for which 3(x²) + tx + 8 can be factored into binomials: To factor this expression, we need to identify values of t that allow the expression to be split into two binomials that, when multiplied, give the original expression.
t = 0; pairs of binomials: (x) and (3x + 8)
t = 1; pairs of binomials: (x + 1) and (3x + 8)
t = 2; pairs of binomials: (x + 2) and (3x + 4)
Solve please!!!!!!!!!!
I'm pretty sure the answer is D
Answer:
The answer is D
Step-by-step explanation:
To find the slope you do y2-y1/x2-x1. This will leave you with 3/1 which is equivalent to 3.
Evaluate the expression 5 to the second power (72-45) divided by 5
Answer:
Step-by-step explanation:
5^2(72-45)/5
25(27)/5
675/5
135
Final answer:
The evaluated expression of 5 to the second power (72 - 45) divided by 5 is 135. This is found by subtracting inside the parentheses, squaring the number 5, multiplying these results, and finally dividing by 5.
Explanation:
Evaluating the Expression
To evaluate the expression 5 to the second power (72 - 45) divided by 5, we follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, we calculate the value within the parentheses:
72 - 45 = 27
Next, we raise 5 to the second power (also known as squaring a number):
52 = 5 × 5 = 25
Now, we multiply this result by the value we found within the parentheses:
25 × 27 = 675
Last, we divide by 5:
675 ÷ 5 = 135
Therefore, the evaluated expression is 135.
find the surface area of a prism
The surface area of a rectangular prism is SA = 2wl + 2lh + 2hw
Answer:
There is no prism
Step-by-step explanation:
A photograph is 6 in x4 in. If you make a copy of the photograph with double the length and width, what is the area of the copy?
The area of the copy would be 36 in x16in
The area of the copy of the photograph, with doubled dimensions of 12 inches by 8 inches, is 96 square inches, which is four times the area of the original photograph.
To find the area of a copy of a photograph with dimensions that are double the original, you first find the new dimensions. Since the original photograph is 6 inches by 4 inches, doubling both the length and the width gives us dimensions of 12 inches by 8 inches for the copy.
The area of a rectangle is found by multiplying the length by the width. Therefore, the area of the copied photograph is 12 inches x 8 inches, which equals 96 square inches. This is four times the area of the original photograph since the scale factor for both the length and the width is 2, and the area scales with the square of the scale factor (22).
In conclusion, the area of the copied photograph is 96 square inches. This calculation demonstrates that when you change the linear dimensions of a figure by a scale factor, the area changes by the square of that scale factor.