Patrick is constructing the circumscribed circle for △RST.
Which construction could be his first step?
Construct the perpendicular bisector of ST¯¯¯¯¯ .
Construct the angle bisector of ∠T .
Construct a copy of ∠S that is adjacent to ∠R .
Construct the angle bisector of ∠R .
Answers
Construct the perpendicular bisector of ST¯¯¯¯¯ .
Hope this helps !
Photon
The first step Patrick will take in the construction of a circumscribed circle for △RST is: Construct the perpendicular bisector of line segment ST.
What is a Circumscribed Circle of a Triangle?A circumscribed circle for a triangle can be defined as a circle is placed inside a polygon or triangle such that it touches all the sides of the triangle.
An example of a circumscribed circle of a triangle is shown in the image attached below.
Therefore, the first step Patrick will take in the construction of a circumscribed circle for △RST is: Construct the perpendicular bisector of line segment ST.
Learn more about circumscribed circle on:
https://brainly.com/question/15605172
Related Questions
what is the product? 4k+2/k^2-4*k-2/2k+1
Answers
Is the square root of eight a rational or irrational number
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it just so happen that √2 is an irrational number, so any product with it as a factor, will yield an irrational number as well.
factoid: Ancient Greeks were scared of irrational numbers, and they steered clear from √2.
i really need help please :)
Answers
The basic idea is that you set your compass to have a distance somewhat greater than half the distance between the points you want to bisect. (Setting it to approximately their distance apart works pretty well.) Then you make arcs on either side of the line between the points.
Use the same compass setting to make arcs from both the points you want to bisect. The arcs should be drawn so they have points of intersection. The line between those intersection points is the bisector of the segment (and figure) between the given points.
That process of drawing the arcs and using a straightedge to connect their points of intersection constitutes the construction you are asked to do.
In (3), the point S is where your bisector crosses the given curve.
In (4), the two bisectors of AB and BC will be expected to cross each other at approximately the midpoint between A and C.
Rosalie wants to get the entire outside of a cabinet laminated. The cabinet is 3 feet long, 2 feet wide and 5 feet high. The cost of lamination is $2 per square foot. How much will it cost Rosalie to get the cabinet laminated?
Answers
We have then that the surface area is:
A = 2 * ((l) * (w)) + 2 * ((l) * (h)) + 2 * ((h) * (w))
Where,
l: long
w: width
h: high
Substituting the values:
A = 2 * ((3) * (2)) + 2 * ((3) * (5)) + 2 * ((5) * (2))
A = 62 feet ^ 2
The cost of lamination is $ 2 per square foot:
So:
(62) * (2) = $ 124
Answer:
it will cost $ 124 Rosalie to get the cabinet laminated
To laminate the cabinet, the total surface area is calculated and multiplied by the cost per square foot. The cabinet has a surface area of 62 square feet, and with a lamination cost of $2 per square foot, it will cost Rosalie $124.
To calculate the cost for laminating the outside of a cabinet, we first need to find the total surface area to be laminated. Since the cabinet is a rectangular prism, we can use the surface area formula for a rectangular prism: Surface Area = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. In this case, l = 3 ft, w = 2 ft, and h = 5 ft.
Surface Area = 2(3 ft)(2 ft) + 2(3 ft)(5 ft) + 2(2 ft)(5 ft)
Surface Area = 2(6) + 2(15) + 2(10)
Surface Area = 12 + 30 + 20
Surface Area = 62 square feet
Now to find the total cost, we multiply the surface area by the cost per square foot: Total cost = Surface Area times Cost per square foot.
Total cost = 62 sq ft times $2/sq ft
Total cost = $124
Therefore, it will cost Rosalie $124 to get the cabinet laminated.
A sandwich shop uses the box size shown to pack boxed lunches. They have determined that they need to use bigger boxes. If the side lengths of the square faces are changed to 7 inches, by how much will this increase the volume of the box?
Answers
We do the same for the new shape, which now has a 7 in place of the 5. So 7x7x10=490.
Lastly, we subtract the volume of the new shape from the volume of the old shape to see the difference. So, 490-250=240.
So the answer to this is 240.
Answer:
240 cubic cm
Step-by-step explanation:
Volume of the box before increament in sides = length*width*height
Length= 5 in.
Width=5 in.
Height = 10 in.
Putting these vales in formula
Volume of box = 5*5*10
=[tex]250cm^{3}[/tex]
Now If the side lengths of the square faces are changed to 7 inches,
So, Length will be 7 in.
Width will be 7 in.
So, new volume = 7*7*10
=[tex]490cm^{3}[/tex]
Thus increase in volume = 490-250 =240
Hence by 240 cubic cm will this increase the volume of the box
An angle measures 4.3 radians To the nearest degree, what is the measure of the angle? degrees
Answers
[tex]\bf \begin{array}{ccll} de grees&radians\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 180&\pi \\ d&4.3 \end{array}\implies \cfrac{180}{d}=\cfrac{\pi }{4.3}\implies \cfrac{180\cdot 4.3}{\pi }=d[/tex]
The measure of the given angle in degrees is:
246 degrees
Step-by-step explanation:We are given a angle measure in radians.
We have to convert the given angle measure to degrees.
We know the conversion that:
π radians= 180°
⇒ 1 radians= 180°/π
Hence, the value of 4.3 radians will be, we multiply both side of the equation by 4.3 :
4.3 radians=246.372°
Hence, to the nearest degree i.e. to the whole number of a degree we get the value of:
4.3 radians= 246°
Prism A is similar to Prism B. The volume of Prism A is 2080 cm³.
What is the volume of Prism B?
A.260 cm³
B.520 cm³
C.1040 cm³
D.16,640 cm³
Will give brainliest answer!
Answers
for two similar prisms, if the ratio of sides is a, the ratio of volume is a³
2080/260=8=2³
16640/2080=8=2³
2080/520=4, not a cubic number
2080/1040, not a cubic number
It is either A or D depending on which prism is bigger.
Final answer:
Prism B's volume is 8 times larger than Prism A's volume due to the dimensions being twice as large. Given the volume of Prism A as 2080 cm³, the volume of Prism B is 16640 cm³.
Explanation:
The student is asking about the volume of similar prisms. When two prisms are similar, their volumes are proportional to the cube of the ratio of their corresponding linear dimensions. In this case, Prism B is similar to Prism A, and the ratio of the volumes is given in the problem. Specifically, the volume of Prism B is 4 times the volume of Prism A because the dimensions of Prism B are twice that of Prism A, making the volume 23 or 8 times greater. However, you've also provided that the volume of Prism B is 4 times that of Prism A, this seems to be a conflict in the information, and there's an issue with typos in the provided content which makes it inconsistent (2L3 versus 213, 213). Based on the correct proportion which should be 8 times, if the volume of Prism A is 2080 cm3, then the volume of Prism B would be 2080 cm3 multiplied by 8 (8L3/L3), yielding 16640 cm3.
Which of the following would be a factor of the equation above.
Answers
The factorization would be (7x +3)(x -3).
Orlando bought a new couch for 2,736 , using the furniture store's finance plan. He will pay $114 a month for 24 months. Which equation can Orlando use to find out how much money he still owes after each month of the plan?
Answers
x = the number of months (from x = 0 to x = 24)
y = 2,736 - 114x
You can substitute any number between 1 and 24, and it will show how much Orlando continues to owe throughout the payment process.
Domingo works 40 hours per week as a tire store manager . If he made $29640 last year. how much he made per hour
A. $14.25
B. $16.50
C. $12.25
D.$11.00
Answers
Domingo made $14.25 per hour last year by dividing his annual income of $29640 by the total hours worked in the year, which is 2080 hours (40 hours/week imes 52 weeks).
Explanation:To calculate how much Domingo made per hour, divide his annual income by the total number of hours worked in a year. Domingo works 40 hours per week, and there are 52 weeks in a year, so the total hours worked in a year is 40 hours/week imes 52 weeks/year = 2080 hours/year.
The formula to find the hourly wage is:
Hourly Wage = Annual Income / Total Hours Worked
Thus, Domingo's hourly wage would be:
$29640 / 2080 hours = $14.25 per hour.
Therefore, the correct answer is A. $14.25.
find p(-3) and p(5) for the function p(x)=4x^4+8x^3-2x^2+13x+10
Answers
.. p(-3) = 61
.. p(5) = 3525
Which table represents a quadratic relationship?
A .x -2 -1 0 1 2 3
f(x) 4 2 1 0.5 0.25 0.125
B. x -7 -6 -5 -4 -3 -2
f(x) 135 128 105 72 35 0
C. x -2 -1 0 1 2 3
f(x) -23.4 -23.2 -23 -22.8 -22.6 -22.4
D. x -1 0 1 2 3 4
f(x) 90 56 26 0 -22 -40
Answers
In each case, the x-values are equally-spaced. Thus looking at second differences will tell you if the relation is quadratic. If the second differences are non-zero and constant, then the values have a quadratic relationship.
A. First differences are 2-4 = -2, 1-2 = -1, 0.5-1 = -0.5. Second differences are -1-(-2) = 1, -0.5-(-1) = 0.5. Since 1 ≠ 0.5, this relation is not quadratic. (It is exponential with a base of 1/2.)
B. First differences are 128-135 = -7, 105-128 = -23, 72-105 = -33. Second differences are -23-(-7) = -16, -33-(-23)=-10. Since -16 ≠ -10, this relation is not quadratic. (It is cubic, since 3rd differences are constant at +4.)
C. First differences are -23.2-(-23.4) = 0.2, -23.0-(-23.2) = 0.2, -22.8-(-23.0) = 0.2. Second differences are zero, so this is not a quadratic relation. (It is linear, with a slope of 0.2.)
D. First differences are 56-90 = -34, 26-56 = -30, 0-26 = -26. Second differences are -30-(-34) = 4, -26-(-30) = 4. These are constant (=4), so the relation is quadratic.
The appropriate choice is ...
... D. x -1 0 1 2 3 4
... f(x) 90 56 26 0 -22 -40
Answer: D. x -1 0 1 2 3 4
f(x) 90 56 26 0 -22 -40
Step-by-step explanation:
Find the area of A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is
Answers
where:
[tex]V[/tex] is the volume
[tex]r[/tex] is the radius
[tex]h[/tex] is the height
From the question we know that [tex]A=175[/tex] and [tex]h=7[/tex]. Lets replace those values in our volume formula:
[tex]175= \pi r^{2} 7[/tex]
Now we can solve for [tex]r[/tex] to find our radius:
[tex]r^{2} = \frac{175}{7 \pi } [/tex]
[tex]r^{2} = \frac{25}{ \pi } [/tex]
[tex]r= \sqrt{ \frac{25}{ \pi } } [/tex]
[tex]r= \frac{5}{ \sqrt{ \pi } } [/tex]
Now that we know the radius, we can use the formula for the area of a cylinder [tex]A=2 \pi rh+2 \pi r^{2} [/tex]
where:
[tex]A[/tex] is the area
[tex]r[/tex] is the radius
[tex]h[/tex] is the height
We know now that [tex]r= \frac{5}{ \sqrt{ \pi } } [/tex] and [tex]h=7[/tex], so lets replace those values in our area formula:
[tex]A=2 \pi ( \frac{5}{ \sqrt{ \pi } } )(7)+2 \pi ( \frac{5}{ \sqrt{ \pi } })^{2} [/tex]
[tex]A= \frac{70 \pi }{ \sqrt{ \pi } } +50[/tex]
[tex]A=174.07[/tex]
We can conclude that the area of a cylinder that has a volume of 175 cubic units and a height of 7 units is 174.07 square units.
If the polygon shown below is a regular nonagon what is the value of x?
Answers
The measure of angle x is 40 degrees and this can be determined by using the formula of the sum of interior angles of a polygon.
Given :
A regular nonagon.
The sum of interior angles of a polygon is given by the equation:
= (n - 2)180 --- (1)
where 'n' is the total number of sides of the polygon.
Given that the polygon is the regular nonagon that means the total number of sides is 9.
Now, substitute the value of 'n' in the equation (1).
= (9 - 2)180
= [tex]1260^\circ[/tex]
Now, divide the above expression by 9 in order to get the value of one interior angle.
[tex]= \dfrac{1260}{9}[/tex]
= [tex]140^\circ[/tex]
Now, the sum of one interior angle and the angle x is equal to 180 degrees that means:
140 + x = 180
x = [tex]40^\circ[/tex]
For more information, refer to the link given below:
https://brainly.com/question/19237987
An architect created plans for a house using a scale factor of 1:16 . In the plans, the floor of the house has an area of 7 square feet. What is area of the floor in the actual house? Enter your answer in the box.
A rectangle has a length of 6 inches and a width of 3 inches.
What is the effect on the perimeter when the dimensions are multiplied by 8?
The perimeter is increased by a factor of 8.
The perimeter is increased by a factor of 24.
The perimeter is increased by a factor of 64.
The perimeter is increased by a factor of 256.
This figure is made up of a triangle and a semicircle.
What is the area of this figure?
Use 3.14 for pi. Round only your final answer to the nearest tenth.
Enter your answer, as a decimal, in the box.
Answers
the area is 7 square feet
when calculating the area the scale factor is squared as well.
since the scale factor is 16, to find out area the scale should be squared that is,
16*16 = 256
then the new area is 7 square feet * 256
actual area = 256 * 7 = 1792 square feet
Q2. the rectangle with length 6 inches and width 3 inches.
the perimeter of the rectangle before changing dimensions are;
=(6*2) + (3*2)
= 12 + 6 = 18 inches
after multiplying the dimensions by 8,
new length = 6*8 = 48 inches
new width = 3*8 = 24 inches
new perimeter = (48*2) + (24*2)
= 96 + 48
= 144 inches
the perimeter ratio from new to old = 144:18
the perimeter has increased by (144/18) times
= 144/18 = 8
answer is perimeter increased by a factor of 8
q3)
area of the triangle
= 1/2 * height * base
= 1/2 * (5-2) *(4-(-3))
= 1/2 * 3 * 7
= 10.5 units²
area of semicircle
=pi*r2
r = 2-(-1.5)
= 3.5
area = 3.14 * (3.5)²
= 38.465 units²
total area = area of triangle + area of semicircle
= 10.5 + 38.465
= 48.965
round it off to the closest tenth
area = 49 units²
Answer for number 5?
Answers
192/16=(a)
(A)*5=length
(A)*3=width
P = 2L + 2W
Where,
L: side
W: width
On the other hand we have that the ratio is:
L / W = 5/3
Clearing L we have:
L = (5/3) * (W)
Substituting in the expression of the perimeter:
P = 2 ((5/3) * (W)) + 2W
Rewriting:
P = (16/3) W
The perimeter is 192:
192 = (16/3) W
We cleared W:
W = (3/16) * (192)
W = 36
Finally we substitute W in the expression for L:
L = (5/3) * (W)
L = (5/3) * (36)
L = 60
Answer:
The width and length are:
W = 36 yards
L = 60 yards
What form of a quadratic function would be graphed having the vertex at the same point as the y-intercept?
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A rectangular prism has a length of 212 centimeters, a width of 212 centimeters, and a height of 5 centimeters. Justin has a storage container for the prism that has a volume of 35 cubic centimeters. What is the difference between the volume of the prism and the volume of the storage container?
Answers
We have then:
V = (l) * (w) * (h)
Where,
l: long
w: width
h: height
Substituting the values we have:
V = (2 1/2) * (2 1/2) * (5)
V = 31.25 cm ^ 3
The difference between the container and the prism is:
35-31.25 = 3.75 cm ^ 3
Answer:
the difference between the volume of the prism and the volume of the storage container is:
3.75 cm ^ 3
The pair of points is on the graph of an inverse variation. Find the missing value. (1.6, 6) and (8, y) 0.03 30 1.2 0.83
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and that (8 , y) is another way to say x = 8 and y is who knows.
[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------[/tex]
[tex]\bf \textit{we know that } \begin{cases} x=1.6\\ y=6 \end{cases}\implies 6=\cfrac{k}{1.6}\implies 6(1.6)=k\implies 9.6=k \\\\\\ \qquad therefore\qquad \boxed{y=\cfrac{9.6}{x}} \\\\\\ \textit{when x = 8, what is \underline{y}?}\qquad y=\cfrac{9.6}{8}[/tex]
Answer: 1.2
Step-by-step explanation:
The formula for inverse variation is given by :-
[tex]x_1y_1=x_2y_2[/tex]
The given points : (1.6, 6) and (8, y)
It means at x = 1.6 , y=6 .
To find the value of y at x=8 , we substitute [tex]x_1=1.6,\ y_1=6\, \text{ and}\ x_2=8,\ y_2=y[/tex] in the above formula , we get
[tex]1.6\times6=8y\\\\\Rightarrow\ y=\dfrac{1.6\times6}{8}\\\\\Rightarrow\ y=1.2[/tex]
Thus, the missing value = 1.2
Use the rules of significant figures to answer the following question:
67.31 - 8.6 + 212.198
A. 270.9
B. 271
C. 270.908
D. 270
Answers
Answer:
A. 270.9
Step-by-step explanation:
We know that the rule of significant figures for addition and subtraction states that 'the number of places after the decimal point in the result is equal to the least number of decimal places in each term.'
So, 67.31 - 8.6 + 212.198 = 67.31 + 212.198 - 8.6 = 279.508 - 8.6 = 270.908
Now, the resultant number is 270.908
Using the rule of significant figures, we get that, the number of places after the decimal point in 270.908 will be equal to the least number of decimal places i.e. 1 ( in 8.6 )
Hence, 67.31 - 8.6 + 212.198 = 270.9
ASAP PLEASE:
Segment RS is congruent to segment DF. Which congruence statement is true?
- RS ≅ DF
- RS ≅ SFD
- RS ≅ SF
- RS ≅ RD
Answers
Answer:
A. [tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]
Step-by-step explanation:
We have been given a circle and we are told that segment RS is congruent to segment DF.
We can see that segment RS corresponds to arc RS and segment DF corresponds to arc DF.
As both segments are congruent, therefore, both arcs will be congruent as well.
We can represent this information as:
[tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]
Therefore, option A is the correct choice.
Write a complete sentence that states the type of transformation that was performed and explains the transformation in detail. Quadrilateral EFGH is the image.
ABCD A(-4,-1)B(-1,-4)C(-2,-8)D(-5,-4)
EFGH
E(0,-6)F(3,-9)G(2,-13)H(-1,-9)
Answers
the equation for the translation mentioned is;
T4, -5(x,y)
this means that every point in the image has moved down by 5 units and moved to the right by 4 units.
Point A to Point E
Point A - (-4,-1)
after translation (x+4, y-5) = (-4+4,-1-5)
= (0,-6) these are the coordinates of point E.
the other three points too have moved the same distance and direction as point A did.
If g(x) is the inverse of f(x) and f(x) = 4x+12 what is g(x)?
Answers
Answer:
Inverse function: A function g is the inverse of a function f if whenever y=f(x) then x=g(y).
In other words, we can write this in terms of the composition of f and g as g(f(x))=x.
For any input x, the function corresponding to f spits out the value y=f(x)=4x+12.
Now, we want to find the inverse function g(x)=[tex]f^{-1}[/tex] that takes the value y as an input and spits out x as the output.
In other words, y=f(x) gives y as a function of x and we want to find [tex]x=f^{-1}(y)[/tex] that will give us x as a function of y.
Given,the expression y=4x+12 for y as a function of x and solve for x.
Subtract 12 from both sides we get;
y-12 = 4x+12-12
Simplify:
y-12 = 4x
Divide by 4 to both sides we get;
[tex]\frac{y-12}{4} =\frac{4x}{4}[/tex]
Simplify:
[tex]x=\frac{1}{4}y - 3[/tex]
therefore, [tex]x = f^{-1}(y) = \frac{1}{4}y-3[/tex]
since, g(x) is the inverse of f(x)
⇒[tex] g(x)=\frac{1}{4}x-3[/tex]
Now, verify that g(x) is really the inverse of f(x), we should show that the composition of f and g doesn't do anything to the input.
[tex](g o f)(x) = g(f(x)) = g(4x+12) = \frac{1}{4}(4x+12) -3 = x+3 -3[/tex]
Simplify:
g(f(x)) = x for all x
⇒ g(x) is the inverse of f(x)
Therefore, [tex] g(x)=\frac{1}{4}x-3[/tex]
Using inverse functions, it is found that that:
[tex]g(x) = \frac{x - 12}{4}[/tex]
To find the inverse function, we exchange x and y in the original function, then isolate f.
The function f(x) is given by:
[tex]f(x) = 4x + 12[/tex]
Function g(x) is the inverse of f(x), then:
[tex]y = 4x + 12[/tex]
[tex]x = 4y + 12[/tex]
[tex]4y = x - 12[/tex]
[tex]y = \frac{x - 12}{4}[/tex]
[tex]g(x) = \frac{x - 12}{4}[/tex]
To learn more about inverse functions, you can take a look at https://brainly.com/question/16485117
need help thank thank you
Answers
$7.80/hour = ____ cents/minute?
Answers
Your Welocme
Explain why 0.04 divided by 3.6 has the same answer as 4 divided by 360
Answers
Hope that helped
Boyles law involves the pressure and volume of gas in a container. It can be repersented by the formula p sub 1 v sub 1= p sub 2 v sub 2. When the formula is solved for p sub 2, the results is
Answers
Boyle's Law can be rearranged to solve for p sub 2 (final pressure) using the formula p sub 2 = p sub 1 v sub 1 / v sub 2. This shows the inverse relationship between pressure and volume of gas at a constant temperature.
Explanation:The question is asking to solve the formula representing Boyle's Law (p sub 1 v sub 1 = p sub 2 v sub 2) for p sub 2. Boyle's Law states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. To solve for p sub 2, you rearrange the formula to be p sub 2 = p sub 1 v sub 1 / v sub 2. This formula means that the final pressure (p sub 2) equals the initial pressure (p sub 1) times the initial volume (v sub 1), all divided by the final volume (v sub 2). Therefore, if the volume increases, the pressure decreases, and if the volume decreases, the pressure increases, keeping the gas's temperature constant.
Learn more about Boyle's Law here:https://brainly.com/question/21184611
#SPJ12
Could use some help!
Answers
0<= x < ∞
Find the value of x.
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Use a^2 + b^2 = c^2
a = 6
c = 10
6^2 + b^2 = 10^2
36 + b^2 = 100
b^2 = 100 - 36
b^2 = 64
b = 8
Note: - 8 has not meaning.
Now by similar triangles using the small triangle and the middle sized triangle on your right
6/8 = 8/(x - 6) Reduce 6/8. You don't have to but it makes things easier.
3/4 = 8/(x - 6) Cross multiply
3(x - 6) = 4*8 Remove the brackets.
3x - 18 = 32 Add 18 to both sides
3x = 50 Divide by 3
x = 50/3 = 16.667 <<<=== answer
The function f(x)= 2 x 5^x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function ?
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because to get the y coordinate of (2,50) we multiply the y coordinate of (1,10) by 5, similarly to get the y coordinate of (3,250) we multiply that of (2,50) by 5