The characteristics of the given points are observed during the
geometric construction processes.
Responses:
Step 1: The point O is the center because it is equidistant from the three points
Step 2: PQ = PR = QR, therefore, ΔPQR is an equilateral triangle
b) The ratio of a leg to the hypotenuse side of ΔACF is 0.5, therefore, ΔACF is a 30°– 60°–90° triangle
c) The points of intersection of the diameter and a perpendicular bisector with the circumference of the circle are the vertices an inscribed square of the circle
Which process of geometric construction determines the characteristics of the given points?
Step 1: How to know that the point O is the center of the circle is as follows;
The perpendicular bisectors constructed are the locus of points
equidistant from the both points D and E and also the perpendicular
bisector gives the locus of points equidistant from points E and F
Therefore;
OE = OE, by reflexive property
OE is also equal to OF and OD by definition of the point O being on both
perpendicular bisectors.
Given that OE = OF = OD, we have that the point O is the center of a
circle with radius, OE = OF = OD passing through the points E, F, and D
Therefore;
The point O is the center because it is equidistant from the three pointsStep 2: Given that the center of the circles are the points P and Q, we have;
PQ = The radial length of the two circles
Similarly
PR and QR are radial lengths of circle P and Q respectively
Therefore;
PQ = PR = QR
Which gives;
The lengths of the sides of ΔPQR are equal and ΔPQR is an equilateral triangleb) FC is the diameter of circle M
Therefore;
∠ACF is 90° and ΔACF is a right triangle
The ratio of the a leg to the hypotenuse side of a 30°– 60°–90° triangle is 0.5
Length of FA = FM = MC
[tex]\dfrac{FA}{FC} = \dfrac{FA}{FM + FC} = \dfrac{FA}{FA + FA} = \dfrac{FA}{2 \times FA} = \dfrac{1}{2} = \mathbf{0.5}[/tex]
Given that the ratio of a leg to the hypotenuse side of ΔACF is 0.5, ΔACF is a 30°– 60°–90° trianglec) The steps that can be used to locate the vertices of a square inscribed
in a circle are;
Draw a diameter of the circle (passing through the center)Construct the perpendicular bisector of the diameter, and extend it to intersect with the circle at the possible two pointsThe points of intersection of the diameter and the perpendicular bisector with the circumference of the circle are the location of the vertices an inscribed square of the circle
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A farmer sells a 5 pound bag of potatoes for $7.28. Five years later the farmer sells a 5
pound bag of potatoes for $12.67. What is the percent increase? (Make sure you answer
is a percentage then round to the nearest hundredths place if needed)
I need help with this. can anyone help me please.
Answer:
21
Step-by-step explanation:
yeah 2+2 is 21 thanks for the very nonexistent question
Antonia is factoring the polynomial, which has four terms. 21x3−63x2 15x−45 3[7x3−21x2 5x−15] 3[7x2(x−3) 5(x−3)] Which is the completely factored form of her polynomial? 21x2(x − 3) 36x2(x − 3) 3(7x2 5) (x − 3) 3(12x2 5) (x − 3).
Answer:
21x2(x-3)
Step-by-step explanation:
Answer: Its C- 3(7x^2+5)(x-3)
Step-by-step explanation:
took it on edge2022
What is the value of the expression shown below?
3 over 5 to the power of 2 + 4 × 3 − 2 (4 points)
10 and 9 over 25
11 and 2 over 25
12 and 9 over 25
13 and 2 over 25
Answer:
10 and 9 over 25
hop you will like it
Please help ASAP!!!!
I think it's A if I'm wrong someone correct me have a great day!!
What is the volume of a cube with a length of 10 meters?
A. 10,000 m³
B. 1,000 m³
C. 100 m³
D. 30 m³
In this exercise we have to use the formula for volume of the cube and we find that:
Volume of cube is 1000m³
How is volume calculated?The formula is V = c * l * a, where:
V = volume, c = length, l = width, a = height.Given that the length of side of cube = 10m, and knowing the formula the volume of cube is:
[tex]Volume of cube = (side)^3\\Volume of cube= (10)^3\\Volume of cube = 1000 m^3[/tex]
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Caisha has a circular garden with a radius of 4 ft. She needs to put a layer of soil on top. Each bag of soil covers 9. 42 square feet. How many bags of soil will she need to buy? 5 bag 6 bags 7 bags 8 bags.
She needs to buy 6 bags of soil. the correct option is B
Given
Caisha has a circular garden with a radius of 4 ft.
She needs to put a layer of soil on top. e
Each bag of soil covers 9.42 square feet.
What is the radius of a circular garden?The radius of the circular garden is equal to the pie times of the square of the radius.
The radius of the circular garden is;
[tex]\rm Area = \pi r^2\\\\Area = 3.14 \times (4)^2\\\\ Area = 3.14\times 16\\\\Area =50.24[/tex]
Therefore,
The number of bags of soil will she need to buy is;
[tex]\rm = \dfrac{Area }{Soil \ covers}\\\\= \dfrac{50.24}{9.42}\\\\= 5.33\\\\= 6 \ bags \ apporx[/tex]
Hence, she needs to buy 6 bags of soil.
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A city's baseball team coach recorded the ages of the players on the team. The players' ages are: {12, 16, 15, 12, 16, 14, 12, 16, 13} What is the interquartile range (IQR) of the players' ages? A.1 B.2 C.3 D. 4
Answer:
D. 4
Explanation:
I took the test and got this question correct!
Employment Frequency
The table shows the frequencies for the data from the
previous task about part-time employment for 15
randomly selected high school students. Use the
information to complete the relative frequency column of
the table. Express answers as percentages rounded to
the nearest whole number.
Relative
Frequency
7%
1
6
40%
babysitter
food service
lifeguard
retail
3
A
5
B
A=
=> 20%
B =
=> 33%
A= 20%
B= 33%
What is Relative Frequency?
Relative frequency is simply the number of outcomes in a particular subgroup (f) divided by the total number of outcomes in an experiment (n).
Thus, Relative frequency= f/n
In the above question, we need to find the relative frequencies of 2 subgroups- lifeguards and retail.
For lifeguards, f=3 and n=15
∴ Relative Frequency (A) = [tex]\frac{3}{15}[/tex]
Since we've to express it in percentage form,
A= [tex]\frac{3}{15}[/tex] * 100
= 20%
Similarly for retail-
B= [tex]\frac{5}{15}[/tex] * 100
= 33%
Thus, A= 20% and B= 33%
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The family size of sunscreen 12 fluid ounces(fl oz)of sunscreen.The regular bottle holds 75% less.
How many fewer fl oz does the regular bottle hold
Answer: 9
Step-by-step explanation: Given The family size sunscreen bottle contains 12 fluid ounces of sunscreen. The standard bottle holds only 75% as much. The normal sunscreen container contains how many fewer fluid ounces?
A 12-ounce family-size bottle is available. However, the regular bottle contains 75% less.
So, 75/100 x 12 = 9 ounces.
As a result, a standard bottle may store 9 ounces of liquid.
Hope this helps!
divide 5600 in the ratio 4 :5:7
Answer:
Step-by-step explanation:
So in our case, let assume 'x' as a common factor.
Thus,
4x + 5x + 7x = 5600;
16x = 5600;
x = 5600/16 = 350.
So,
4x= 350*4 =1400;
5x= 350*5 = 1750; &
7x= 350*7 = 2450.
Your answer is, 5600 = 1400+1750+2450 which is in ratio of 4:5:7.
A school is arranging a field trip to the zoo. The school spends 544.95 dollars on passes for 41 students and 4 teachers. The school also spends 348.91 dollars on lunch for just the students.how much money was spent per student
Answer: I believe it is $20.62
Step-by-step explanation: the student passes+ the food was $845.42 divede that by the 41 students.
How many solutions does -3(2x + 6) = -6x - 18 have
Answer: 0=0 The input is an identity or it is true for all values
-3(2x+6)=-6x-18
(-3*2x)+(-3*6)=-6x-18
-6x+-18=-6x-18
0=0
Please help I don’t understand this
E( _15_, _5_ )
F(_15_, _10_)
G(_15_, _10_)
H(_5_, _15_)
I'm not really sure if those are the right answers, but from what I was taught in school, I think so.
what is the length of vw?
[tex] \frac{vz}{zy} = \frac{vw}{wx} \ \: \\ \\ \frac{16.5 }{27.5} = \frac{vw}{36} [/tex]
so
vw= (16.5×36)÷27.5= 21.6
vw=21.6
I hope it helps
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(50pts) What is the equation for the line in slope-intercept form?
Answer:
y = 8x
Step-by-step explanation:
See attached image.
The parabola with equation y = a(x – 2)^2 + q passes through the points (-2,5) and (4, -1) Determine the coordinates of the vertex of the parabola.
please help!
Step-by-step explanation:
the standard form for a quadratic function is
y = ax² + bx + c
our parabola had the equation
y = a(x - 2)² + q
let's do the "math" :
y = a(x² - 4x + 4) + q = ax² - 4ax + 4a + q
so, we know (when comparing with the standard form)
b = -4a
c = 4a + q
for the vertex we need to find the axis of symmetry first by using the standard formula
x = -b/2a
which is in our case
x = -(-4a)/2a = 4a/2a = 2
to get y for this x we need to find a and q first.
we are using the given points for that :
5 = a(-2)² - 4a×(-2) + 4a + q
-1 = a(4)² - 4a×4 + 4a + q
the first equation then forms into
5 = 4a + 8a + 4a + q = 16a + q
the second equation forms into
-1 = 16a - 16a + 4a + q = 4a + q
let's subtract the second from the first equation
5 = 16a + q
- -1 = 4a + q
--------------------
6 = 12a + 0
12a = 6
a = 1/2
-1 = 4a + q = 4×1/2 + q = 2 + q
q = -3
so, the original equation for our parabola is
y = 1/2 × (x - 2)² - 3
so y for the vertex (remember, x = 2) is
y = 1/2 × (2 - 2)² - 3 = 1/2 × 0 - 3 = -3
so the vertex is (2, -3)
What is equivalent to (73)–2
Answer:
71
Step-by-step explanation:
(73)-2 is equivalent to 71
Answer:
71
Step-by-step explanation:
what is the equivalent to this fraction
6/8 & 3/4 = ?
Answer:
3/4 x 2/2= 6/8
Step-by-step explanation:
multiply 3/4 x 2/2 to equal = 6/8
I NEED HELP PLS I WILL GIVE CROWN: Mr. Crow, the head groundskeeper at High Tech Middle School, mows the lawn along the side of the gym. The lawn is rectangular, and the length is 5 feet more than twice the width. The perimeter of the lawn is 250 feet.
Answer:
Mr. Crow dimension of the lawn = 85 × 40
Area of the lawn = 3250 square feet
Step-by-step explanation:
Let x represents the width of the rectangle,
Then According to the question,
The length of the rectangle = 2 x + 5
Also it is given that the perimeter of the rectangle = 250 feet.
But we know that the perimeter of the rectangle = 2 × ( length + width)
Thus, the perimeter of the rectangle = 2( 2x+5+x) = 2(3x+5) = 6x+10
If x = 30, the perimeter of the rectangle = 6 × 30 + 10 = 190 < 250
Thus, x ≠ 10.
If x = 50, the perimeter of the rectangle = 6 × 50 + 10 = 310 > 250
Thus, x ≠ 50
If x = 40, the the perimeter of the rectangle = 6 × 40 + 10 = 250 = 250
Thus, x = 40
Therefore, the width of the rectangle, x = 40 feet.
And, the length of the rectangle, 2 x + 5 = 2 × 40 + 5 = 85 feet.
1) The dimension of the rectangle = 85 × 40
2)The area of the rectangle = length × width = 85 × 40 = 3250 square feet.Let x represents the width of the rectangle,
Then According to the question,
The length of the rectangle = 2 x + 5
Also it is given that the perimeter of the rectangle = 250 feet.
But we know that the perimeter of the rectangle = 2 × ( length + width)
Thus, the perimeter of the rectangle = 2( 2x+5+x) = 2(3x+5) = 6x+10
If x = 30, the perimeter of the rectangle = 6 × 30 + 10 = 190 < 250
Thus, x ≠ 10.
If x = 50, the perimeter of the rectangle = 6 × 50 + 10 = 310 > 250
Thus, x ≠ 50
If x = 40, the the perimeter of the rectangle = 6 × 40 + 10 = 250 = 250
Thus, x = 40
Therefore, the width of the rectangle, x = 40 feet.
And, the length of the rectangle, 2 x + 5 = 2 × 40 + 5 = 85 feet.
1) The dimension of the rectangle = 85 × 40
2)The area of the rectangle = length × width = 85 × 40 = 3250 square feet.
A stack of logs has 22 logs on the bottom layer. Each subsequent layer has 4 fewer logs than the previous layer. If the top layer has two logs, how many total logs are there in the pile?
Answer:
88
Step-by-step explanation:
If the top layer has two logs, there are a total of 88 logs in the pile
How to solveNumber of logs in the bottom layer = 22
Number of logs in the top layer = 2
Number of logs in each subsequent layer = 22 - 2 = 20
Number of layers in the pile = 22 - 2 + 1 = 21
Total number of logs in the pile = 22 + 20 + 18 + ... + 2
This is an arithmetic series with first term 22, last term 2, and common difference -4.
The sum of an arithmetic series is given by the following formula:
sum = (first term + last term)/2 * number of terms
sum = (22 + 2)/2 * 21 = 88
Therefore, there are a total of 88 logs in the pile.\
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Paul bought 4 DVDs for $9.95 each. What was his total cost?
Answer:
He bought 4 DVDs for $9.95 each, so $9.95*4= $39.8 is his total cost.
Step-by-step explanation:
Which equation can be used to find the measure of angle LKJ? cos−1(StartFraction 8. 9 Over 10. 9 EndFraction) = x cos−1(StartFraction 10. 9 Over 8. 9 EndFraction) = x sin−1(StartFraction 10. 9 Over 8. 9 EndFraction) = x sin−1(StartFraction 8. 9 Over 10. 9 EndFraction) = x.
The equation that can be used to find the measure of angle LKJ is
x = Sin⁻¹ (8.9/10.9).
what are trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
As we know that
sine of an angle = perpendicular/hypotenuse
Sine of ∠LKJ = 8.9/10.9
∠LKJ = Sin⁻¹ (8.9/10.9)
x = Sin⁻¹ (8.9/10.9)
Therefore, the equation that can be used to find the measure of angle LKJ is x = Sin⁻¹ (8.9/10.9).
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85 is 125% of what number?
Casey is selling adult tickets and student tickets for the school play. The adult tickets cost $6.00 and the student tickets cost $4.00. Casey sells 120 tickets and makes $560.00. Which system of equations could be used to find the cost of each ticket?
Samira babysits for 4. 5 hours and earns $22. 50. How much does she earn per hour?
P
Answer:
5$ per hour
Step-by-step explanation:
[tex] \frac{22.50}{4.5} = 5[/tex]
I need the answer along with the procedure.
Answer:
A (2.5, 4 )
Step-by-step explanation:
the coordinates of A are the intersection of the 2 lines AB and AC , that is
2x + 3y = 17 → (1)
4x - y = 6 → (2)
multiplying (2) by 3 and adding to (1) will eliminate y
12x - 3y = 18 → (3)
add (1) and (3) term by term to eliminate y
14x + 0 = 35
14x = 35 ( divide both sides by 14 )
x = [tex]\frac{35}{14}[/tex] = 2.5
substitute x = 2.5 into either of the 2 equations and solve for y
substituting into (1)
2(2.5) + 3y = 17
5 + 3y = 17 ( subtract 5 from both sides )
3y = 12 ( divide both sides by 3 )
y = 4
solution is (2.5, 4 )
A factory makes rectangular boxes. The area of the top surface can be modeled by the function: f(x) = 66x^2 + 17x + 1. The width of the top surface can be modeled by the function: g(x) = 6x + 1.
Write an expression, h(x), in standard form that describes the length of the top surface.
Answer in a complete sentence.
Thank you so much in advanced
The length of the top surface is given by h(x) = 11x + 1.
AreaArea is the amount of space occupied by a two dimensional object or figure. The area (A) of a rectangle is given by:
A = length * width
Let h(x) represent the width, hence:
66x² + 17x + 1 = (6x + 1)(11x + 1)
Since the width is g(x) = 6x + 1, hence the length = 11x + 1
The length of the top surface is given by h(x) = 11x + 1.
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I need the answer to this help?
Answer:
x = 20
You do 120 + 3x = 180
It's same-side interior.
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 59(0.59)
This equation represents exponential decay. Whenever the base is less than 1, the function represents decay. When the base is greater than 1, the function represents growth. In this case, the base is .59 which is less than 1, representing decay.