The values for e, f, and g are -3, 4 and -2 respectively.
What are the values for e, f, and g?e × f = -12
e × g = 6
f × g = -8
From (1)
ef = -12
e = -12/f
From (3)
fg = -8
g = -8/f
Substitute e and g into (2)
e × g = 6
-12/f × -8/f = 6
96/f² = 6
cross product
96 = f² × 6
96 = 6f²
divide both sides by 6
f² = 96/6
f² = 16
find the square root of both sides
f = √16
f = 4
Hence,
e × f = -12
e × 4 = -12
4e = -12
e = -12/4
e = -3
e × g = 6
-3 × g = 6
-3g = 6
g = 6/-3
g = -2
f × g = -8
4 × -2 = -8
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Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex] units. What is a simplified expression for the difference in the areas of Circle A and Circle B
The simplified expression for the difference in the areas of Circle A and Circle B is = 12π/(x+2)²
Area of a Circle:The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is [tex]A = \pi r^2[/tex], where r is the radius of the circle. The unit of area is the square unit, for example, [tex]m^2, cm^2, in^2[/tex], etc.
We know that :
The formula of circle's circumference is = 2πr
We have :
Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units
and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex]
Now, First we calculate the area of circle A is:
8π/x+2 = 2πr
r = 8π/x+2 × 1/2π
r = 4/x+2
Area = πr² = (4/x+2)²π
Now, for circle B
4π/x+2 = 2πr
r = 4π/x+2 × 1/2π
r = 2/2x+2
Area =( 2/2x+2)²π
Simplified expression for the difference in the areas of Circle A and Circle B are:
(4/x+2)²π - ( 2/x+2)²π
= π/(x+2)²( 4²-2²)
= π/(x+2)²(16-4)
= 12π/(x+2)²
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The total surface area of a
rectangular prism is 1,060 cm². The
prism's base has measurements 8
centimeters and 10 centimeters.
What is the height of the prism?
Answer:
The surface area of a rectangular prism is given by the formula:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively. We are given that the surface area of the prism is 1,060 cm², and that the base has measurements 8 cm and 10 cm.
Substituting these values into the formula, we get:
1060 = 2(8)(10) + 2(8)h + 2(10)h
Simplifying and solving for h, we get:
1060 = 160 + 16h + 20h
1060 = 160 + 36h
900 = 36h
h = 25
Therefore, the height of the prism is 25 cm.
Step-by-step explanation:
Suppose x, y, z > 1 and integers, let :
p(x, y): x is a factor of y,
q(x, y, z): z = GCF(x, y), and
r(x): x is prime.
Check if the following argument is valid or not.
(∀x)(∃y)(p(x, y) ⇒ r(x)), (∀x)(∀y)(∀z)(¬q(x, y, z)), (∃x)(∀y)(p(x, y) ∨ r(x)).
Therefore, (∀y)(∃z)(∃x)q(x, y, z).
Yes, The argument is valid.
Now, We have;
(∀x) (∃y) (p(x, y) ⇒ r(x))
Means that for any integer x, there exists an integer y such that if x is a factor of y, then x is prime.
(∀x)(∀y)(∀z)(¬q(x, y, z)) means that for any integers x, y, and z, the greatest common factor of x and y is not z.
(∃x)(∀y)(p(x, y) ∨ r(x)) means that there exists an integer x such that for any integer y, either x is a factor of y or x is prime.
Therefore, (∀y)(∃z)(∃x)q(x, y, z) means that for any integer y, there exists integers z and x such that the greatest common factor of x and y is z.
To see why this conclusion follows, consider that if (∀y)(∃z)(∃x)q(x, y, z) were false, then there would be some integer y such that for all integers z and x, the greatest common factor of x and y is not z.
However, this would contradict (∀x)(∀y)(∀z)(¬q(x, y, z)), which states that for any integers x, y, and z, the greatest common factor of x and y is not z.
Therefore, the argument is valid.
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(a) If the point (8, 5) is on the graph of an even function, what other point must also be on the graph?
(b) If the point (8, 5) is on the graph of an odd function, what other point must also be on the graph?
(x, y) =
The answers are (-8, 5) and (-8, -5)
Given that, the point (8, 5) is on the graph of an even function, we need to find the other point must also be on the graph,
A function f(x) is said to be an even function if it satisfies the following equation: f(−x) = f(x)
A function satisfying this equation has a graph that is symmetric about the y-axis.
So, if the point (8, 5) is on the graph of an even function, the (-8, 5) must also be on the graph of the function.
Also, the point (8, 5) is on the graph of an odd function,
The graph of an odd function is symmetrical about the origin. Therefore, an odd function satisfies the following condition:
-f(x) = f(-x),
Therefore,
(8, 5) = (-8, -5)
Hence, the answers are (-8, 5) and (-8, -5)
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Mia and Lia are competing in a race. 50 people are in the race and medals are given 1st, 2nd, and 3rd place. What is the likelihood that Mia and Lia place in 1st or 2nd?
1/2450
99/2450
1/1225
1/2500
The probability that Mia and Lia place in 1st or 2nd is 99/2450. There are two possible scenarios in which Mia and Lia can place in 1st or 2nd: Mia places 1st and Lia places 2nd, or Mia places 2nd and Lia places 1st. The probability of the first scenario is (1/50) * (1/49) = 1/2450. The probability of the second scenario is also (1/50) * (1/49) = 1/2450. Since these two scenarios are mutually exclusive, we can add their probabilities to find the total probability: 1/2450 + 1/2450 = 2/2450. However, we must also account for the fact that there are 49 other people who could place in 3rd. So the final probability is (2/2450) * 49 = 98/2450. Adding the probability that neither Mia nor Lia place in 3rd (1/2450), we get 98/2450 + 1/2450 = 99/2450.
MARK ME BRAINLEISTReceived message. The probability that Mia and Lia place in 1st or 2nd is **99/2450**. There are two possible scenarios in which Mia and Lia can place in 1st or 2nd: Mia places 1st and Lia places 2nd, or Mia places 2nd and Lia places 1st. The probability of the first scenario is `(1/50) * (1/49) = 1/2450`. The probability of the second scenario is also `(1/50) * (1/49) = 1/2450`. Since these two scenarios are mutually exclusive, we can add their probabilities to find the total probability: `1/2450 + 1/2450 = 2/2450`. However, we must also account for the fact that there are `49` other people who could place in 3rd. So the final probability is `(2/2450) * 49 = 98/2450`. Adding the probability that neither Mia nor Lia place in 3rd (`1/2450`), we get `98/2450 + 1/2450 = 99/2450`.
Alan is going to eat a round lollipop that has a radius of 2 inches. What is the lollipop's circumference?
The circumference of the lollipop is 12.57 inches.
Circumference is the measurement of the distance around the outer edge of a closed curve, particularly a circle. It is the total length of the curve that makes up the boundary of the circle.
The circumference of the circle is given by the formula;
Circumference = 2 × π × radius
where π (pi) is the mathematical constant approximately equal to 3.14159265359...
Given that the radius of the round lollipop is 2 inches, we can substitute this value into the formula;
Circumference = 2 × π × 2
Using the approximate value of π as 3.14159265359..., we can calculate the circumference;
Circumference = 2 × 3.141592 × 2
Circumference ≈ 12.56
Therefore, the circumference of the lollipop is approximately 12.57 inches.
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An unknown number w is 30 more than an unknown number p. The number w is also p less than 5. The equations to find p and w are shown below: w = p + 30 w = −p + 5 Which is a correct step to find p and w? (1 point) Add the equations to eliminate p. Multiply the equations to eliminate w. Write the points where the graphs of the equations intersect the x-axis. Write the points where the graphs of the equations intersect the y-axis.
The correct step find p and w is - add the equations to eliminate p. The correct option is the first option
Solving for variables in a system of linear equations: Determining the correct step to find p and wFrom the question, we are to determine which of the given steps is a correct step to find p and w.
The given system of equations is:
w = p + 30
w = −p + 5
From the above equation, we can easily add the equations to eliminate p
That is,
w = p + 30
+ w = −p + 5
------------------------
2w = 35
We can then solve for by dividing both sides by 2
2w / 2 = 35 / 2
w = 17.5
To determine the value of p, we can substitute the value of w into any of the equations
w = p + 30
17.5 = p + 30
p = 30 - 17.5
p = 12.5
Hence,
The correct step is add the equations to eliminate p
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Here is part of a field.
11m
10m
Does he have enough fence?
You must show all your working.
18m
Diagram NOT
accurately drawn
This part of the field is in the shape of a trapezium.
A farmer wants to put a fence all the way around the edge of this part of the field.
The farmer has 50m of fence.
use the graph below to find the indicated function value
Answer:
Step-by-step explanation:
Use the Tree Diagram below to answer the following question.
Whats the probability that you will get a 15-inch monitor?
P(15-inch) = ?
a. 0
b. 1
c. 2/6
d. 3
50 points!
The probability that you will get a 15-inch monitor = 1/3
We know that probability of event is the ratio of number of possible outcomes of event A and the total number of outcomes.
Let us assume that event A = you will get a 15-inch monitor
The number of favourable outcomes for event A are 2
So, n(A) = 2
The sample space for this experiment would be,
n(S) = 6
Using the definition of probability, the required proabability would be,
P(A) = n(A) / n(S)
P(A) = 2/6
P(A) = 1/3
Therefore, the required probability = 1/3
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you want to buy a $32,000 car. The company is offering a 6% interest rate for 60 months. What will the monthly payments be?
The monthly payment will be $618.71
We know that the formula for the loans are:
[tex]P_0=\frac{d(1-(1+\frac{r}{k} )^{-Nk})}{\frac{r}{k}}[/tex]
where
P₀ is principal
d is monthly payment, annual payment
r is the annual interest rate in decimal form.
k is the number of compounding periods in one year.
and N is the length of the loan, in years.
Here, P₀ = $32,000
r = 0.06
N = 5
k = 12
Using above formula of loan we need to find value of d.
[tex]P_0=\frac{d(1-(1+\frac{r}{k} )^{-Nk})}{\frac{r}{k}} \\\\32000 =\frac{d(1-(1+\frac{0.06}{12} )^{-60})}{\frac{0.06}{12}}\\\\32,000 =\frac{d(1-(1+0.005)^{-60})}{0.005} \\\\32000\times 0.05=d(1-(1.005)^{-60})\\\\160=d\times (1-0.7414)\\\\d = 160/0.2586\\\\d=618.72[/tex]
Therefore, the monthly payment = $618.71
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NO LINKS!! URGENT HELP PLEASE!!!
Use a flowchart to prove the triangles below are congruent:
Answer:
- angle T is congruent to angle U (given)
- NS is congruent to SH (given)
- angle TSN is congruent to USH (vertical angles are congruent)
So triangle TNS is congruent to triangle UHS by AAS.
a. A train is traveling in a circular track of 53 km radius at 44 km per hour. Find in degrees the angle through which it turns in 1 minute.
Answer:
0.38 degrees.
Step-by-step explanation:
C = 2π(53) = 106π km
The train is traveling at a speed of 44 km/h, which is equivalent to (44/60) km/min since there are 60 minutes in an hour.
d = (44/60) km/min
θ = (d / C) x 360°
θ = [(44/60) / (106π)] x 360°
θ ≈ 0.38°
Therefore, the angle through which the train turns in 1 minute is approximately 0.38 degrees.
A
Find the approximate volume of a cylinder with a radius of 5 ft. and height of 40 ft.
Use the approximation 3.1416 or the calculator in your calculations. Round your answer to the nearest hundredth.
B
Find the approximate volume of a cylinder with a diameter of 2 ft. and height of 6 ft.
Use the approximation 3.1416 or the calculator in your calculations. Round your answer to the nearest hundredth.
Answer: Part A) 3,141.59 Part B) 75.40
Step-by-step explanation:
Sorry if this is wrong.
19. A restaurant wants to study how well its salads sell. The circle
graph shows the sales of salads during the past few days. If 5 of
the salads sold were Caesar salads, how many total salads did
the restaurant sell?
Salads Sold
56%
20%
24%
Caesar
Garden
Cobb
Answer:
56% Caesar
Step-by-step explanation:
The only salads sold were Caesar and it is majority
Right triangle XYZ, has vertex angles at the coordinates, X(0, 0), Y(-3, 0) and Z(-3, 4). Its Image, triangle X'Y'Z' has ve
angles at the coordinates, X(3, -5), Y(0, -5), and Z'(0, -1). Describe the horizontal and vertical translations that map
triangle XYZ onto its image, triangle X'Y'Z'.
Oright 5; down 3
Oright 3; up 5
Oright 3; down 5
O left 5; up 3
NEXT QUESTION
ASK FOR HELP
TURN
The horizontal and vertical translations that map triangle XYZ onto its image, triangle X'Y'Z' include the following: C. right 3; down 5.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.In order to map the two triangles, we would have to apply a vertical translation to f(x) by 5 units down and a horizontal translation by 3 units right.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Use Heron's formula to find the area of the triangle with side lengths 6, 9, and 12, as shown below.
Answer:
√(6 + 9 +12) = √27 = 3√3
√(-6 + 9 + 12) = √15 = √3√5
√(6 - 9 + 12) = √9 = 3
√(6 + 9 - 12) = √3
(1/4)(3√3)(√3√5)(3)(√3)
= (1/4)(27√3)(√5) = (27√15)/4 = 26.1
Answer:correct answer is 26.1
Step-by-step explanation:
Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is given by:
A = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter, which is half the perimeter of the triangle:
s = (a + b + c) / 2
In this case, the side lengths are a = 6, b = 9, and c = 12. Therefore, the semiperimeter is:
s = (6 + 9 + 12) / 2 = 27 / 2
Using Heron's formula, we can now calculate the area of the triangle:
what is the perimeter
Answer:
2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2
B is the correct answer.
Beatrice is standing on a cliff 70 feet above the ocean. She sees a boat in the ocean that is 600 feet from the base of the cliff. What is the angle of depression at which Beatrice sees the boat?
The angle of depression at which Beatrice sees the boat is 83.35°.
How to find the angle of depression at which Beatrice sees the boat?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Check the attached image for the sketch of triangle ABC.
From the sketch, the angle of depression is represented with x:
tan x = 600/70 (tan = opposite/adjacent)
x = tan⁻¹(600/70)
x = 83.35°
Therefore, the angle of depression at which Beatrice sees the boat is 83.35°.
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Solve for x assume that lines which appear to be diameters are actual diameters
The value of x in the circle that shows diameter is calculated as:
x = -7
What is the Diameter of a Circle?In a circle, the line segment that divides the circle into two halves is the diameter. Half of the circle is a semicircle which has a measure of 180 degrees.
Note: The measure of a central angle is also the same measure with that of the arc it intercepts.
Therefore, we have:
-8x + 9 + 50 + 65 = 180
-8x + 124 = 180
-8x = 180 - 124
-8x = 56
x = 56/-8
x = -7
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Lisa decides that she wants to know the 98% confidence interval for a population mean despite originally setting out to find the 95% confidence interval. How will this affect the width and the margin of error of her confidence interval for a population mean? Assume that the population standard deviation is unknown and the population distribution is approximately normal.
The breadth and error margin of the confidence interval will rise when the confidence level is raised from 95% to 98%.
We are more certain that the genuine population mean falls inside the interval if the confidence level is larger. The range of feasible values for the population means will be broader since we need to widen the interval in order to reach this higher degree of confidence.
Since the margin of error equals half of the interval's breadth, it is directly proportional to the interval's width. The margin of error will therefore expand as the confidence level does as well.
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need help please. i don't understand
Answer:
A) oblique hexagonal prism
Step-by-step explanation:
Answer:
right hexagonal prism
Step-by-step explanation:
as seen on the Image below the left one is a right hexagonal prism and the right one is a oblique hexagonal prism.
Please answer number 3
For 3 personal training session both gym cost same.
We have,
At Silver gym, membership is $25 per month and personal training sessions are $30 each.
At Fit Factor, membership is $65 per month, the and personal training sessions are $20 each.
let the number of personal session be x.
So, 25+ 30x = 65 + 20x
30x - 20x = 65 - 25
10x = 30
x= 3 sessions
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Jacob needs to know the volume of the cylinder shown. Which expression will give him the correct volume
Answer:
3.14 (24 square) (2.5)
Step-by-step explanation:
3.14 24 square 2.5
X radius squared X height???
gingerbread house is shaped like the image below. How many square centimeters of frosting will take to cover the outside?
The amount of frosting in square centimeters it will take to cover the outside of the gingerbread house, pyramidal in shape, is about 12.65 square centimeters.
What is a the surface area of a square pyramid?The surface area of a square pyramid is the sum of the area of the four triangular faces.
The surface area of the gingerbread house can be found as follows;
The height of the pyramid and the square base indicates;
The slant height of a face of the pyramid = √(3² + 1²) = √(10)
The surface area of the pyramid = 4 × (1/2) × 2 × √(10) = 4·√(10)
4·√(10) ≈ 12.65
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Need help with 1 question for trig
The exact values of s in the interval [-2π, π) that satisfy the given condition cot²s = 1 are s = -3π/2, -π/2, π/2, and 3π/2.
The given trigonometric equation is cot²s=1 and the interval is [-2π, π).
The given equation can be rearranged as cot²s = 1, which can be written as cot s = ±1.
Using the inverse cotangent identity cot⁻¹(±1) = ±π/2, we can find the exact values of s in the interval [-2π, π) that satisfy the given condition:
s = ±π/2 + 2kπ, where k is an integer.
Therefore, the exact values of s in the interval [-2π, π) that satisfy the given condition cot²s = 1 are s = -3π/2, -π/2, π/2, and 3π/2.
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Are there any other cost students need to consider when figuring out the total cost? If so, explain the additional cost 
The equation for contribution for each student is 185.5/14 = 13.25.
Price of new easel= $129
Set of blank canvases = $ 46
Sales tax = $ 10.50
So, the total amount is
= 129 + 46 + 10.5
= 185.5
Then, each student contribute
= 185.5 / 14
= 13.25
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Max made 2 gallons of lemonade. Which proportion can Max use to find how many quarts of lemonade he made? Responses 4 quarts1 quart =2 gallon? quarts 4 quarts1 quart =2 gallon? quarts 1 gallon4 quarts =2 gallons? quarts 1 gallon4 quarts =2 gallons? quarts 1 gallon2 quarts = 2 gallons? quarts 1 gallon2 quarts = 2 gallons? quarts 4 quarts1 gallon =2 gallon? quart
The proportion Max can use to find how many quarts of lemonade is 2 gallons divided by 4 quarts per gallon equals 8 quarts.
How to determine the proportion Max can use to find how many quarts of lemonadeMax can use the following proportion to calculate how many quarts of lemonade he made:
1 gallon equals 4 quarts
Max can calculate the number of quarts by multiplying 2 by 4 because he made 2 gallons of lemonade:
2 gallons divided by 4 quarts per gallon equals 8 quarts
As a result, Max created 8 pints of lemonade.
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How to solve for X and Y
The values of x and y are 4 and 2√2
What is trigonometric ratio?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.
Sin(tetha) = opp/hyp
tan(tetha) = opp/adj
cos(tetha) = adj/hyp
In the triangle;
y is the opposite to angle 45 and x is the hypotenuse
cos 45° = 2√2/x
1/√2 = 2√2/x
x = 2√2 ×√2
x = 2 × 2 = 4
since the triangle is isosceles,
y = 2√2
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Identify the rule for the function table
y =12 - x
y = x - 12
y = x ÷ 2
y = 2 ÷ x
The rule of the function table is,
⇒ y = 1/2x
Now, We have to given that;
Table is shown in image.
Let two points on the table is, (24, 12) and (12, 6)
Hence, We get;
The equation for table is,
y - 12 = (6 - 12) / (12 - 24) (x - 24)
y - 12 = - 6/-12 (x - 24)
y - 12 = 1/2 (x - 24)
y - 12 = 1/2x - 12
y = 1/2x
Thus, The rule of the function table is,
⇒ y = 1/2x
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