If 2 pints = 1 quart and 1 quart = 1 pint then how many pints are 2 quarts?
Step-by-step explanation:
1 qt = 2 pts multiply both sides by two
2 qt = 4 pints
Beth and Kelly spent the same total amount of money for dog sitting while on vacation. Beth took her dog, Pockets, to Rover Sleepover and was charged $24.50 per day and a fee of $90.50 for food and cleaning. Kelly took her dog, Monty, to Pet Palace and was charged $32 per day and a $45.50 cleaning fee. How many days were Beth and Kelly on vacation?
Beth and Kelly were on vacation for 6 days.
Let's assume that Beth and Kelly were on vacation for "x" days.
For Beth:
The cost per day for dog sitting at Rover Sleepover is $24.50.
Beth also paid a fee of $90.50 for food and cleaning.
So the total cost for Beth's dog sitting can be expressed as:
Total cost for Beth = (Cost per day × Number of days) + Cleaning fee
Total cost for Beth = ($24.50 × x) + $90.50
For Kelly:
The cost per day for dog sitting at Pet Palace is $32.
Kelly also paid a fee of $45.50 for cleaning.
So the total cost for Kelly's dog sitting can be expressed as:
Total cost for Kelly = (Cost per day × Number of days) + Cleaning fee
Total cost for Kelly = ($32 × x) + $45.50
Since both Beth and Kelly spent the same total amount of money, we can set up an equation:
($24.50 × x) + $90.50 = ($32 × x) + $45.50
Simplifying the equation, we get:
$24.50x + $90.50 = $32x + $45.50
Moving the variables to one side and constants to the other side:
$32x - $24.50x = $45.50 - $90.50
Combining like terms, we have:
$7.50x = $45
Dividing both sides of the equation by $7.50:
x = $45 / $7.50
x = 6
Therefore, Beth and Kelly were on vacation for 6 days.
Learn more about equation, click;
https://brainly.com/question/29657983
#SPJ1
(09.01 LC)
What is the relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc
length s of the arc?
A)C=360°(s)(A)
B)C=360 degrees s over A
C)C=360 degrees(s+A)
D)C = 360°A over s
The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is
B) C=360 degrees s over A
How to find the relationshipThe relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:
s = A / 360 * C
Make C the subject of the formula
s = AC / 360
360s = AC
rearranging
AC = 360s
C = 360 degrees s / A
C = (s / A) * 360°
Learn more about arc length at
https://brainly.com/question/2005046
#SPJ1
Answer:
[tex]\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}[/tex]
Step-by-step explanation:
In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.
This is because:
The circumference (C) represents the distance around the entire circle, and so an arc (s) is a fraction of the whole circumference. In a circle, there are 360° in total, and so a central angle (A) is a fraction of 360°.Therefore, this can be expressed as:
[tex]\dfrac{s}{C}=\dfrac{A}{360^{\circ}}[/tex]
Cross multiply:
[tex]360^{\circ} \cdot s=C \cdot A[/tex]
Now, divide both sides by A to isolate C:
[tex]\dfrac{360^{\circ} \cdot s}{A}=C[/tex]
Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:
[tex]\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}[/tex]
which quadratic equation has the roots 3 + i and 3 - i
The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.
The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.
The roots of the quadratic equation are the values of x that make the equation equal to zero.
Therefore, if a quadratic equation has the roots 3 + i and 3 - i, it can be written in the factored form as (x - (3 + i))(x - (3 - i)) = 0. Expanding this product yields x² - (3 + i + 3 - i)x + (3 + i)(3 - i) = 0.
Simplifying this expression further results in the quadratic equation x² - 6x + 10 = 0.
The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.
To learn more about : quadratic
https://brainly.com/question/1214333
#SPJ8
Find the surface area
of the figure below:
19 cm
30 cm.
The surface area of the figure is approximately 997.5π cm².
We have,
The figure has two shapes:
Cone and a semicircle
Now,
The surface area of a cone:
= πr (r + l)
where r is the radius of the base and l is the slant height.
Given that
r = 15 cm and l = 19 cm, we can substitute these values into the formula:
= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)
The surface area of a semicircle:
= (πr²) / 2
Given that r = 15 cm, we can substitute this value into the formula:
= (π(15)²) / 2
= 112.5π cm² (rounded to one decimal place)
The surface area of the figure:
To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:
Now,
Total surface area
= 885π + 112.5π
= 997.5π cm² (rounded to one decimal place)
Therefore,
The surface area of the figure is approximately 997.5π cm².
Learn more about cones here:
https://brainly.com/question/13798146
#SPJ1
Which of the following is the result of expanding ____
A.8.5
b.15.5
C.32
D.60
The sum between n = 1 and n = 5 is 15.5, so the correct option is the second one.
Which is the value of the summatory?Here we have the summatory:
[tex]\sum^{5}_{n = 1} 2^{n - 2}[/tex]
So we just need to add the 5 terms (between n = 1 and n = 5)
So we will get the sum:
S = [ 2¹⁻² + 2²⁻² + 2³⁻² + 2⁴⁻² + 2⁵⁻²]
S = [2⁻¹ + 2⁰ + 2¹ + 2² + 2³]
S = [0.5 + 1 + 2 + 4 +8]
S = 15.5
So the correct option is the second one.
Learn more about summatories at:
https://brainly.com/question/30518693
#SPJ1
xA radioactive isotope is decaying at a rate of 20% every hour. Currently there are 15 grams of the substance.
Questions:
A. Write an equation that will represent the number of grams present after n hours
B. How much will be left after 24 hours (one day)? (Round to the nearest hundredth)
C. After how many hours will there be approximately one gram left?
B. After 24 hours, approximately 2.49 grams will be left.
C. After approximately 18.13 hours, there will be approximately one gram left.
A. To represent the number of grams present after n hours, we can use the equation:
N(n) = 15 × (1 - 0.2)^n
Where:
N(n) is the number of grams present after n hours,
15 is the initial amount of the substance in grams,
0.2 represents the decay rate of 20% per hour, and
^n represents the exponentiation operation.
B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:
N(24) = 15 × (1 - 0.2)^24
Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.
C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:
1 = 15 × (1 - 0.2)^n
To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:
log(0.8)(1/15) = n
Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.
Therefore, the answers are:
B. After 24 hours, approximately 2.49 grams will be left.
C. After approximately 18.13 hours, there will be approximately one gram left.
for such more question on grams
https://brainly.com/question/13439286
#SPJ8
Picture included!!! Please help! Suppose a = 10 and b = 24. Give the value of each of the following. Give answers as integers or rounded to 2 decimal places as appropriate.
Answer:
A = 22.62°
B = 67.38°
c = 26
Step-by-step explanation:
[tex]a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c[/tex]
[tex]\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ[/tex]<-- You can also use other trig ratios
[tex]B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ[/tex]
There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The angle ABC in the circle is 70 degrees.
How to find the angle in a circle?The intercepted arc is the arc that is inside the inscribed angle and whose
endpoints are on the angle. The arc angle is half the the inscribed angle.
The intercepted arc that is formed is equal to the inscribed angle,
multiplied by two (intercepted arc measure = inscribed angle × 2).
Therefore, let's find the arc angle ABC as follows:
∠ ABC = 1 /2 (360 - 120 - 100)
∠ ABC = 1 /2 (360 - 220)
∠ ABC = 1 /2 (140)
Therefore,
∠ ABC = 70 degrees
learn more on circle here: https://brainly.com/question/31408211
#SPJ1
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The area of the kite is 38 mm squared.
How to find the area of a kite?A kite is a quadrilateral with two pairs of adjacent sides equal. The diagonals of a kite are perpendicular. The vertex angle are bisected by the diagonals.
It has two pairs of consecutive equal sides and perpendicular diagonals.
Therefore,
area of a kite = ab / 2
where
a and b are the diagonalsTherefore,
a = 9.5 mm
b = 4 mm
Therefore,
area of a kite = 9.5 × 4 / 2
area of a kite = 38 / 2
area of a kite = 19 mm²
learn more on area here: brainly.com/question/22965641
#SPJ1
Answer:
The area of the kite would be 19 mm².
Step-by-step explanation:
A kite is a quadrilateral with two pairs of equal-length adjacent sides. The diagonals of a kite are perpendicular to each other and intersect at a right angle, dividing the kite into four right triangles. The area of a kite can be calculated by finding the product of the lengths of its diagonals and dividing it by 2.
If we assume that the height and width you provided are the lengths of the diagonals, we can calculate the area using the following formula:
Area = (height * width) / 2
Substituting the given values:
Area = (9.5 mm * 4 mm) / 2
= 38 mm² / 2
= 19 mm²
Therefore, if the height and width represent the lengths of the diagonals, the area of the kite would be 19 square millimeters.
#SPJ8
for more such Questions visit this:
https://brainly.com/question/25292087
long division method of 616265
2.63 is the value or quotient of 616/265 using long division.
We have to find the value of 616/265
In the given division the numerator is a dividend and the number in the denominator is a divisor.
616 is the dividend and 265 is the divisor.
When we perform long division the quotient will be 2.63 which is the require value.
2.63
____________
265 | 616
-530
______
860
-795
______
650
-530
______
120
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ1
30 POINTS!! PLEASE
A surveyor wants to determine the width of a river. She surveys the area and finds the following measures below.
She uses a pair of similar triangles, to help her find the answer.
Answer:
D = 90 FT
Step-by-step explanation:
40 / d = 20 / 45
cross multiply
45 × 40 = 20d
1800 = 20d
divide both sides by 20
1800 / 20 = 20d / 20
d = 90 ft
Adjusted Trial Balance from Buildex Company
The preparation of the income statement of Buildex Company's adjusted trial balance is as follows:
Buildex Company
Income StatementServices revenue $70,500
Interest revenue 5,700
Total revenue $76,200
Expenses:
Depreciation expense $4,700
Wages expense 52,000
Insurance expense 4,400
Supplies expense 2,700
Utilities expense 1,700
Total expenses $65,500
Net income $10,700
What is the income statement?The income statement is a financial statement that shows the financial performance of a business over a period.
In the income statement, the total expenses are deducted from the total revenue to compute the profit or loss.
Learn more about the income statement at https://brainly.com/question/28936505.
#SPJ1
Question Completion:Use the following selected accounts and amounts with normal balances from Buildex Company's adjusted trial balance to prepare its income statement for the year ending December 31. Hint: Not all accounts need to be used.
Cash $10,400 Depreciation expense $4,700
Building 185,000 Wages expense 52,000
Accounts payable 9,400 Insurance expense 4,400
Services revenue 70,500 Supplies expense 2,700
Interest revenue 5,700 Utilities expense 1,700
In the given circle the m∠J
is 88°, mArc DF is 62° and mArc BD is 136° what is the m∠
C ?
The measure of angle C is 13°.
To find the measure of angle C in the given circle, we need to use the properties of angles subtended by arcs in a circle.
Given information:
m∠J = 88° (angle J)
mArc DF = 62° (arc DF)
mArc BD = 136° (arc BD)
We can start by using the fact that the measure of an angle formed by a chord and an arc is equal to half the measure of the intercepted arc.
Since mArc DF = 62°, the measure of angle DJF (angle formed by chord DF and arc DF) is 62°/2 = 31°.
Next, we can use the fact that angles subtended by the same arc are equal.
Since mArc BD = 136°, angle BJD (angle formed by chord BD and arc BD) is also 136°.
Now, let's find angle BCD (angle formed by chord BD and chord CD). The sum of angles in a triangle is 180°, so angle BCD = 180° - angle DJF - angle BJD.
Angle BCD = 180° - 31° - 136°
Angle BCD = 180° - 167°
Angle BCD = 13°
For similar question on angle.
https://brainly.com/question/31615777
#SPJ8
Help me please!!! what is the volume of this figure? I will mark you brainliest!
The volume of the trapezoidal prism is 420 cm³
What is volume?Volume is the amount of space that is occupied by a three dimensional shape or object.
The volume of a trapezoidal prism is the product of the base area and its height.
For the trapezoidal prism:
Area of base = (1/2)(15 + 5) * 7 = 70 cm²
Volume of Prism = Area of base * height = 70 cm² * 6 cm = 420 cm³
The volume of the figure is 420 cm³
Find out more on volume at: https://brainly.com/question/27710307
#SPJ1
∆ACB is bisected by segment CP. m
What is the approximate area of ∆ACB?
NO SPAM OR I WILL REPORT YOU AND BAN YOU IMMEDIATELY
Where the above is given, Area of Δ ACB ≈ 282.62
Why is this so?
The area of a triangle is given as
Area = 1/2 Base x Height
In this case,
Base = AB
Height = CP
Thus, it is correct to state that Area of Δ ACB = 1/2AB * CP.
How is this so?
First we need to find the height and hypotenuse of the triangle.
that is CP and CB.
CB = a/Cos (63)
CB = 26.43227
CP = √(CB²-PB²)
CP = √(26.4322711750232² - 12²)
CP = 23.55133
Area of ΔPCB = (CP x PB)/2
(12 × 23.551326066062)/ 2
= 141.30796
Since ΔPCB = ΔPCA
and ΔACB = ΔPCB + ΔPCA
Thus,
Area of ΔACB = 141.30796 + 141.30796 = 282.61592
≈ 282.62
Learn more about triangle at:
https://brainly.com/question/29869536
#SPJ1
Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
The circumference of the cylinder below is 4 cm and the height is 6 cm. What is the curved surface area of the cylinder? If your answer is a decimal, give it to 1 d.p. circumference 4 cm Height 6 cm
The curved surface area of the cylinder is 24 cm².
We have,
To find the curved surface area of a cylinder, we need to know its height (h) and the circumference of its base (C).
Given:
Circumference (C) = 4 cm
Height (h) = 6 cm
The formula to calculate the curved surface area of a cylinder is A = Ch, where A is the curved surface area, C is the circumference, and h is the height.
Substituting the given values:
A = 4 cm x 6 cm
A = 24 cm²
Therefore,
The curved surface area of the cylinder is 24 cm².
Learn more about cylinder here:
https://brainly.com/question/15891031
#SPJ1
If (2x-7), (x-1), 3x, x, (x+2), 30 and 10
1. Find the value of x
2. Find the value of the largest angle
PLEASE HELP ME ASAP
The value of x in arithmetic progression is 5/3 and the largest angle is 30.
The given sequence is: (2x-7), (x-1), 3x, x, (x+2), 30, 10.
In an arithmetic progression, the common difference (d) between consecutive terms remains constant.
The common difference between the terms = (x - 1) - (2x - 7) = x - 1 - 2x + 7 = 6 - x
6 - x = 3x - (x - 1)
6 - x = 3x - x + 1
6 - x = 2x + 1
-x - 2x = 1 - 6
-3x = -5
x = -5 / -3
x = 5/3
Therefore, the value of x is 5/3.
2x-7 = 2 ×5/3 -7 = -3.66
x-1 = 5/3-7 = -5.33
3x = 3 × 5/3 = 5
x + 2 = 5/3+2 =3.66
Thus, the largest angle is 30.
Learn more about arithmetic progression, here:
https://brainly.com/question/30364336
#SPJ1
Your question is incomplete, most probably the full answer is:
If (2x-7), (x-1), 3x, x, (x+2), 30 and 10 are in AP, then
1. Find the value of x
2. Find the value of the largest angle
Complete the proof that HJ LGI.
4
I
5
Statement
K
1
ZHKI ZGKH
2
m2GKH + mZHKI = 180°
3 m2GKH+mZGKH= 180°
mZGKH = 90°
HJ L GI
G
H
Reason
Given
Angles forming a linear pair sum to 180°
Definition of congruence
(
The complete sentence is shown below:
Reason: Given
Reason: Angles forming a linear pair sum to 180° (Given)
Reason: Substitution from Statement 1.
To complete the proof that HJ GI, we can use the given statements and reasons:
Statement 1: <HKI = <GKH
Reason: Given
Statement 2: m<GKH + m<HKI = 180°
Reason: Angles forming a linear pair sum to 180° (Given)
Statement 3: m,GKH + m<GKH = 180°
Reason: Substitution from Statement 1
Statement 4: m<GKH = 90°
Reason: From Statement 2 and Statement 3, we can subtract m<GKH from both sides, which results in m<GKH = 180° - m<GKH.
Since the angles forming a linear pair sum to 180°, m<GKH + m<GKH = 180° implies that m<GKH = 90°.
Therefore, based on the given statements and reasons, we can conclude that HJ and GI are congruent (m<GKH = 90°)
Learn more about Linear Pair here:
https://brainly.com/question/1757859
#SPJ1
Does 10, 15, 18 equal a right triangle
Answer:
Not a right triangle
Step-by-step explanation:
[tex]10^2+15^2\stackrel{?}{=}18^2\\100+225\stackrel{?}{=}324\\325\neq324[/tex]
As the sides of the triangle do not follow the Pythagorean Theorem, then the triangle is not a right triangle.
El valor de la asintota vertical
The vertical asymptote of the function are x = ±1/2
Given that we need to determine what is value of the vertical asymptote of the function =
(2x + 1) / (4x²-1)
To find the vertical asymptote of the function f(x) = (2x + 1) / (4x² - 1), we need to determine the values of x for which the denominator becomes zero.
This is because division by zero is undefined, and the function may have vertical asymptotes at those points.
The denominator of the function is 4x² - 1.
To find the values of x that make the denominator zero, we can set it equal to zero and solve for x:
4x² - 1 = 0
Adding 1 to both sides:
4x² = 1
Dividing both sides by 4:
x² = 1/4
Taking the square root of both sides:
x = ±√(1/4)
Simplifying further, we get:
x = ±1/2
Therefore, the values of x that make the denominator zero are x = -1/2 and x = 1/2. These are the vertical asymptotes of the function.
Learn more about vertical asymptotes click;
https://brainly.com/question/29260395
#SPJ1
Translation =
What is value of the vertical asymptote of the function =
(2x + 1) / (4x²-1)
For what value of x is the rational expression below undefined?
x-3
3+x
A. 3
OB. -1
O C. 0
OD. -3
The value of x that makes the rational expression undefined is x = -3.
The rational expression is undefined when the denominator is equal to zero, because division by zero is undefined.
In the given rational expression (x - 3) / (3 + x), we need to find the value of x that makes the denominator (3 + x) equal to zero.
To find this value, we set the denominator equal to zero and solve for x:
3 + x = 0
Subtracting 3 from both sides:
x = -3
Therefore, the value of x that makes the rational expression undefined is x = -3.
for such more question on rational expression
https://brainly.com/question/29061047
#SPJ8
1. Find the volume of the rectangular prism. Use the
volume formula V = L*W*H to justify your answer.
10 cm
L= 10cm
W= 8cm
H=12cm
Volume = 80cm
12 cm
8 cm
V=
Step-by-step explanation:
prism
v=1/2 X 12cm X 8cm
V= 48
rectangular prism
v=80cm+48cm
v=128cm
determine the volume of the following spheres with the given dimensions. to break the code find the mean of all your answers. round your answers to the hundreth place. use 3.14 for an approximation for pi.
The calculated volume of the sphere is 44602.24 ft³
How to determine the volume of the sphereFrom the question, we have the following parameters that can be used in our computation:
Radius = 22 ft
The volume of a sphere can be expressed as;
V = 4/3πr³
Where
r = 22
substitute the known values in the above equation, so, we have the following representation
V = 4/3π * 22³
Evaluate
V = 44602.24
Therefore the volume of the sphere is 44602.24 ft³
learn more about volume from
brainly.com/question/10171109
#SPJ1
Question
Determine the volume of the following spheres with the given dimensions. to break the code find the mean of all your answers. round your answers to the hundreth place. use 3.14 for an approximation for pi.
Radius = 22 ft
Problem whenejewwssss
[tex] \begin{aligned}3 ^{3k} &= \frac{1}{81} \\3^{3k} &= \frac{1}{3^{4} } \\ 3^{ \blue{3k}} &= 3^{ - \blue{4}} \\ 3k&= - 4 \\ k&= \frac{ - 4}{3} \\ k&= \bold{ - \frac{4}{3} } \end{aligned}[/tex]
[tex]\rm{The\:value\:of\:\mathit{k}\:is\:\bold{ - \frac{4}{3}}} \\ \\ \small{ \blue{ \mathfrak{That's\:it\: :)}}}[/tex]
What is the surface area of this composite solid? show your work
The surface area of this composite solid is 265.36 units².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
Surface area of a rectangular prism = 2(LH + LW + WH)
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;
Surface area of rectangular prism = 2[3 × 5 + (3× 10) + (5 × 10)]
Surface area of rectangular prism = 2[15 + 30 + 50]
Surface area of rectangular prism = 190 units².
Surface area (SA) of a cylinder = 2πrh + 2πr²
Surface area (SA) of a cylinder = 2 × 3.14 × 2 × 4 + 2 × 3.14 × 2²
Surface area (SA) of a cylinder = 50.24 + 25.12
Surface area (SA) of a cylinder = 75.36 units².
Therefore, we have:
Surface area of composite solid = 190 units² + 75.36 units².
Surface area of composite solid = 265.36 units²
Read more on surface area of a rectangular prism here: brainly.com/question/28185251
#SPJ1
What does the x-intercept of the graph represent in terms of the football?
a. The x-intercept represents the maximum vertical height that the football reaches.
b . The x-intercept represents the time it took for the football to reach its maximum height.
c. The x-intercept represents the height where the football was when the ball was kicked.
d. The x-intercept represents how far away the football landed from where it started horizontally.
The x-intercept in the graph represent the height where the football was when the ball was kicked.
How to find the x-intercept?The x-intercept is the point where the graph of the line crosses the x-axis.
Therefore, the x-intercept the value of x when y equals to zero.
Therefore, let's find what the x-intercept of the graph represent in terms of the football.
The graph shows the height of the ball in metres after t second.
The y axis represent the height while the x-axis represent the time.
Hence, he x-intercept represents the height where the football was when the ball was kicked.
learn more on x-intercept here: https://brainly.com/question/30097124
#SPJ1
find the center of the circle that you can circumscribe about triangle ABC. A(2,8) B(0,8) C(2,2)
The center of the circumscribed circle is (1, 5).
How do we calculate?We calculate the midpoint and slope of the line segment AB:
Midpoint of AB = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Midpoint of AB = ((2 + 0) / 2, (8 + 8) / 2)
Midpoint of AB = (1, 8)
Slope of AB = (y₂ - y₁) / (x₂ - x₁)
= (8 - 8) / (0 - 2)
Slope= 0
We can notice that the equation of the perpendicular bisector of AB is x = 1.
We also find midpoint and slope of the line segment BC
Midpoint of BC = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
= ((0 + 2) / 2, (8 + 2) / 2)
= (1, 5)
Slope of BC = (y₂ - y₁) / (x₂ - x₁)
= (2 - 8) / (2 - 0)
= -3
y - 5 = -3(x - 1)
y - 5 = -3x + 3
3x + y = 8
we have the equations of two perpendicular bisectors which are
x = 1 and 3x + y = 8.
We Substitute x = 1 into 3x + y = 8:
3(1) + y = 8
3 + y = 8
y = 5
In conclusion, center of the circumscribed circle is (1, 5).
Learn more about slope at:
https://brainly.com/question/3493733
#SPJ1
What is the 10th term of the geometric sequence where a1 = 384 and a7 = 6?
0.75
3
6
1.5
Answer:
(a) 0.75
Step-by-step explanation:
You want the 10th term of the geometric sequence with a1 = 384 and a7 = 6.
N-th termThe equation for the n-th term can be written ...
an = a1·b^(n-1)
Using a1 = 384, we can find b from ...
a7 = 6 = 384·b^(7-1)
(6/384)^(1/6) = b
10th termThen the 10th term is ...
a10 = 384·(6/384)^((10-1)/6) = 0.75
The 10th term of the sequence is 0.75.
<95141404393>
Tariq has $640 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $291.24.
He buys 4 bicycle reflectors for $19.56 each and a pair of bike gloves for $16.52.
He plans to spend some or all of the money he has left to buy new biking outfits for $50.80 each.
Write and solve an inequality which can be used to determine
x, the number of outfits Tariq can purchase while staying within his budget.
Let's solve the inequality to determine the number of outfits Tariq can purchase while staying within his budget.
Given:
Amount Tariq has to spend: $640
Cost of a new bicycle: $291.24
Cost of 4 bicycle reflectors: $19.56 each
Cost of bike gloves: $16.52
Cost of each biking outfit: $50.80
Let's assume the number of outfits Tariq can purchase is represented by x.
The total cost of the items he has already purchased is:
Cost of bicycle = $291.24
Cost of 4 bicycle reflectors = $19.56 * 4 = $78.24
Cost of bike gloves = $16.52
The remaining amount Tariq has to spend can be calculated as:
Remaining amount = Total amount - (Cost of bicycle + Cost of reflectors + Cost of gloves)
Remaining amount = $640 - ($291.24 + $78.24 + $16.52)
Now, we need to determine the maximum number of outfits Tariq can purchase with the remaining amount. Each outfit costs $50.80.
Inequality: x * $50.80 ≤ Remaining amount
Substituting the values:
x * $50.80 ≤ $640 - ($291.24 + $78.24 + $16.52)
Simplifying further:
x * $50.80 ≤ $640 - $385
x * $50.80 ≤ $255
To solve for x, we divide both sides of the inequality by $50.80:
x ≤ $255 / $50.80
x ≤ 5
Therefore, the maximum number of outfits Tariq can purchase while staying within his budget is 5.