The solution is Option A.
Yes , The measure of angle 1 and angle 2 are same because they intercept the same arc of the circle
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle
Given data ,
From the circle , the four angles are 1 , 2 , 3 , and 4
And , from the circle theorem
In a circle, the measures of the angles subtended by the same arc on the circumference of the circle are equal
So , from the circle , we can see that
∠1 and ∠2 are subtended by the same arc AB at points C and D respectively
And , the points C and D lies on the circumference of the circle
So , the measures of the angle must be equal
Hence , The angles ∠1 and ∠2 have equal measures because they intercept the same arc of the circle
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If a || b and m∠2 = 71°, what is m∠1?
Match the inequalities on the left with the correct statement about that inequality on the right.
-4 r ≤ 22
Drop selections here
54 y+-8 ≥ -1
Drop selections here
-7d/4>3
Drop selections here
0>-8 n
Drop selections here
The statements which are correct about the inequalities in each case as required are as follows;
-4r ≤ 22; Flip the inequality sign.54y + -8 ≥ -1; Do not flip the inequality sign.-7d / 4 > 3; Flip the inequality sign.0 > -8n; Flip the inequality sign.Which statements are correct about the given inequalities?It follows from the task content that the statement which is correct about each of the inequalities is to be matched accordingly.
It is noteworthy to know that the underlying perspective is such that;
If the coefficient of a variable upon isolation on one side of the inequality is negative, it follows that the inequality sign must be flipped while multiplying or dividing both sides of the inequality by a negative number.
On the other hand, if the coefficient of the variable is positive, the inequality sign is not to be flipped.
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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground to the nearest tenth of a foot. y=-16x^2+261x+130
The time that the rocket will hit the ground to the nearest tenth of a foot is 17 secs.
How can the time be calculated?We were given the equation as y=-16x^2+261x+130 , thene we can equate this to zero. as
0=-16x^2+261x+130
from this we can see that this is a quadratic equation, where a= -16, b=261, c =130
Then input into the quadratic formular we have:
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
Then if we input the values we have [tex]x=\frac{-261+-\sqrt{261^{2}-4*-16*130} }{2*-16}[/tex]
Then the value of x are: -0.49 and 16.79
The positive value is the time that the rocket will hit the ground. Therefore, the rocket will hit the ground after 16.79 secs.
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lim x tends infinity, (2/3)^x = ?
The limit lim x → ∞ (2/3)ˣ = ∞
What are limits?A limit is the value of a function as the independent variable tends to a particular value.
How to find the given limit?Since we have lim x → ∞ (2/3)ˣ, to find this limit, using the fact that lim x → a ㏑f(x) = ㏑[lim x → a ㏑f(x) ]
So, since lim x → ∞ (2/3)ˣ, taking natural logarithm of both sides, we have that
lim x → ∞ (2/3)ˣ
㏑[lim x → ∞ (2/3)ˣ] = lim x → ∞ ㏑(2/3)ˣ
= lim x → ∞ x㏑(2/3)
So, substituting x = ∞ into the equation, we have that
lim x → ∞ x㏑(2/3) = ∞㏑(2/3)
= ∞
So, lim x → ∞ (2/3)ˣ = ∞
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Please answer quickly!!!!
Answer: y int is 8 the slope of the line is -1/2 and the equation of the line is y=-1/2x +8
Step-by-step explanation:
you can get slope by using the the points (6,5) and (8,4) to use y2-y1/x2-x1 and your y int is just where the line intersects the y axis which is 8. 8 then equals b in the equation y=mx+ b and you get m by using the first equation.
Find the length of the segment indicated.Round your answer to the nearest tenth if necessary
Answer:
7.9
Step-by-step explanation:
a blue parallelogram has a height of 6 inches and a base of 10 inches. a scale of 2:1 was applied to the blue parallelogram to create a green parallelogram. what is the area of the green parallelogram?
On using the scale value of 2 : 1, the area of green parallelogram is obtained as 120 in².
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
Height of blue parallelogram = 6 inches
Base of blue parallelogram = 10 inches
The scale value is given as = 2 : 1
Height of green parallelogram = 6 × 2 = 12 inches
Base of green parallelogram = 10 × 1 = 10 inches
It is known that area of parallelogram = base × height
So, area of green parallelogram is -
= 12 × 10
= 120 in²
Therefore, the area value is obtained as 120 in².
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1. Eleven decreased by k
2. p increased by 9
3. Sixteen multiplied by a number h
4. f less than twelve
5. Sixteen less than m
All the mathematical expressions are,
1) 11 - k
2) p + 9
3) 16h
4) f < 12
5) 16 < m
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
All the algebraic expression are,
1. Eleven decreased by k
2. p increased by 9
3. Sixteen multiplied by a number h
4. f less than twelve
5. Sixteen less than m
Now,
We can write all the expression as,
1. Eleven decreased by k
⇒ k - 11
2. p increased by 9
⇒ 9 + p
3. Sixteen multiplied by a number h
⇒ 16 × h
⇒ 16h
4. f less than twelve
⇒ f < 12
5. Sixteen less than m
⇒ 16 < m
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Angel has a deck that measures 20 feet by 25 feet. He wants to increase each dimension by equal lengths so that its area is increased by 50%. By how much should he increase each dimension?
Angel should increase the dimensions of the deck by 5 feet each
How to determine by how much the lengths should be increasedFrom the question, we have the following parameters that can be used in our computation:
Length = 20 feet
Width = 25 feet
So, the area is
Area = 20 * 25
Evaluate
Area = 500
When increased by 50%, we have
(20 + x) *(25 + x) = 500 * 1.50
Evaluate
(20 + x) * (25 + x) = 750
Express 750 as 25 * 30
So, we have
(20 + x) * (25 + x) = 25 * 30
This means that
20 + x = 25
25 + x = 30
Solve for x
x = 5 and x = 5
This means that
Increment = 5
Hence, the lengths should be increased by 5 feet
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The table below shows some values of a function g(x)
Which function represents the relationship shown in the table?
g(x) = 4x - 1/2
g(x) = -3x - 1/2
g(x) = -1/2x - 1/2
g(x) = 3x - 1/2
The linear function in the table is given as follows:
g(x) = 4x - 1/2.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change of the output variable y relative to the input variable .b is the intercept, representing the value of y when x = 0.When x increases by 0.5, y increases by 2, hence the slope m is obtained as follows:
m = 2/0.5
m = 4.
When x = 0, y = -0.5, hence the intercept b is given as follows:
b = -1/2.
The function is then defined as follows:
g(x) = 4x - 1/2.
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Question 5(Multiple Choice Worth 1 points)
(06.01 LC)
Choose the expression that represents a linear expression.
6 x+6
-6 x²+8 x-9
8 x³+9 x²-10 x+11
7 x⁴-8 x³+9 x²-10 x+11
Answer:
Option a) 6x+6 is correct.
Step-by-step explanation:
Option a) 6x+6 is correct.
The given expression 6x+6 represents a linear expression.
Step-by-step explanation:
Definition: Linear expression is a mathematical statement defining an equality. It is usually a polynomial equation having degree 1. It can be written as linear relationship with variables and a constant.
6x+6 expression represents a linear expression
Because it has degree 1.
Therefore Option a) 6x+6 is correct.
The given expression 6x+6 represents a linear expression.
a) 6x+6
The given expression 6x+6 represents a linear expression.
Definition:
Linear expression is a mathematical statement defining equality. It is usually a polynomial equation having a degree of 1. It can be written as a linear relationship with variables and a constant.
6x+6 expression represents a linear expression.
Because it has degree 1.
Therefore, a) 6x+6 is correct.
The given expression 6x+6 represents a linear expression.
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The following three shapes are based only on squares, semicircles, and quarter circles. find the perimeter and the area of each shaded part. give your answer as a completely simplified exact value in terms of π (no approximations).
The area and the perimeter of the figure are given as follows:
Area: 36(π + 2) cm².Perimeter: (24 + 4.2425π) cm.How to obtain the area of the figure?The figure is composed as follows:
Right triangle of sides 12 cm.Semi circle with diameter that is the hypotenuse of the right triangle.Applying the Pythagorean Theorem, the diameter of the circle is given as follows:
d² = 2 x 12²
[tex]d = \sqrt{2 \times 12^2}[/tex]
d = 16.97 cm.
Then the radius of the circle is given as follows:
r = 0.5d
r = 0.5 x 16.97
r = 8.485 cm.
The area of a circle of radius r is given by the multiplication of π and the square of the radius, as follows:
A = πr².
Hence, considering that the figure is a semi circle, we have that:
Ac = 0.5 x π x (8.485)²
Ac = 36π
The area of the right triangle is of:
At = 0.5 x 12 x 12
At = 72 cm².
Meaning that the area of the shape is given as follows:
A = Ac + At.
A = 36π + 72
A = 36(π + 2) cm².
How to obtain the perimeter of the shape?The perimeter of the shape is obtained by the sum of 2 times 12 cm and the circumference of the semi circle.
The circumference of a semicircle of diameter d is given as follows:
C = 0.5πd.
Hence:
C = 0.5π x 8.485
C = 4.2425π.
Meaning that the perimeter of the shape is given as follows:
P = (24 + 4.2425π) cm.
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(x+2)(x+8)=0 show work
The solutions of the quadratic equation:
(x+ 2)*(x + 8) = 0
are:
x = -2
x = -8
How to solve the quadratic equation?Here we have the following quadratic equation:
(x + 2)*(x + 8) = 0
And we want to solve it for x.
Remember the zero property, for any real number A, the product with zero gives:
A*0 = 0
Then:
(x + 2)*(x + 8) = 0
If either (x + 2) = 0 or (x + 8) = 0
Solving these two we get:
x + 2 = 0
x = -2
x + 8 = 0
x = -8
The two solutions of the quadratic equation are x = -2 and x = -8
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I want to buy a new sofa from the store. I open a savings account with $700
and save up another $50 weekly. I need to save
a minimum of $1,200 to buy the sofa. Write an
inequality to represent this situation.
Answer:
700 + 50x ≥ 1200
where x represents the number of weeks needed to save.
Step-by-step explanation:
Check the picture below.
whatever those savings are on week "x", they have to be at least $1200
700 + 50x ⩾ 1200
Jaylen's parents own a chocolate shop, and today he gets to help make the nut truffles. Each truffle starts with one of 2 kinds of nuts and is dipped in one of 6 kinds of chocolate. The truffle is then drizzled with one of 4 sauces. The finishing touch is one of 2 candied garnishes.
How many different nut truffles can they make?
Answer:
96
Step-by-step explanation:
2 x 6=12
12 x 4= 48
48 x 2=96
The graph of a function is shown. What is the function type?
The type of function that is shown in the given graph image is called a; Cubic Function
How to identify the graph function?The vertical line test is a tool in graph functions that is very important when we are trying to determine the function that a specific graph represents. Now, we can further say that the vertical line is typically one that includes all points alongside a specific x-value with the y-value of a point that a vertical line will intersect a graph to represent an output for that particular input x value.
Now, there are different types of graphs and they all depend on the particular type of function that is being graphed. The eight most popular graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each of the types of graphs are usually unique which means that is easy to visually differentiate from the rest.
In this given graph, we can see that the graph shows an image that corresponds to a cubic function because of the classical infinite branches, then the three real roots and then the two extrema values
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Amanda swims 40 meters per minute. She uses
the inequality below to calculate how many
minutes, m, it takes her to swim at least 1,500
meters.
40m ≥ 1, 500
Which set of numbers makes the inequality true? A. {24, 25, 37.5}
B
{25, 28.5, 37}
C {37, 39, 40.5}
D. (37.5, 42, 43.5}
(37.5, 42, 43.5} is the set of numbers that makes the inequality true
How to determine which set of numbers makes the inequality true?
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.
Given that:
Amanda uses the inequality below to calculate how many minutes, m, it takes her to swim at least 1,500 meters.
40m ≥ 1, 500
To determine which set of numbers makes the inequality true, solve for m and check the pick that contains the values greater than or equal to m:
40m ≥ 1, 500
m ≥ 1, 500/40
m ≥ 37.5
Thus, the set of numbers that makes the inequality true is (37.5, 42, 43.5}
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23 A commuter train moves from station A to D via B and C in that order, the distance to C via B is 70km and that of B to D via C is 88km. Between stations A and B the travels at an average speed of 48km/h and it takes 15minutes. The average speed of the train between C and D is 45km/h. Find; a) Distance between B and C b) Time taken between C and D c) If the train halts at B for 3 minutes and at C for 4 minutes and average speed for the whole journey is 50km/h. Find its average speed between B and C
The Distance between B to C = 58 km,
distance between C to D = 30 km
Average speed between B to C = 59.79 km/h
What is speed?The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined.
Given A commuter train moves from station A to D via B and C,
distance from A to C via B = 70 km
distance from B to D via C = 88 km
av. speed of the train from A to B = 48 km/h
av. speed of the train from C to D = 45 km/h
time taken by train to reach B = 15 min = 15/60 = 0.25 hour
distance between A to B = speed x time from A to B
distance between A to B = 48 x 0.25
distance between A to B = 12 km
A. Distance between B to C = distance from A to C - distance between A to B
Distance between B to C = 70 - 12 = 58 km
B. distance between C to D = distance from B to D - Distance between B to C
distance between C to D = 88 - 58 = 30 km
C. let av. speed from B to C is x
total distance covered by train = 12 + 58 + 30 = 100 km
av. speed for journey = 50 km/h
time taken to complete journey = 100/50 = 2 hours
time is taken from A to B = 0.25 hour
time is taken from B to C = 58/x
Time is taken from C to D = 30/45 = 0.66 hour
halt at b = 3 minute and halt at C = 4 minute
total halt = 3 + 4 = 7 minute = 7/60 = 0.12 hour
Total time = time taken from(A to B + B to C + C to D) + total hault
2 = 0.25 + 58/x + 0.66 + 0.12
58/x = 0.97
x = 59.79 km/h
Hence The Distance between B to C = 58 km,
distance between C to D = 30 km
Average speed between B to C = 59.79 km/h
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Determine the point estimate of the population mean and margin of error for the confidence interval. The lower bound is 17, upper bound is 25. What is the point estimate of the population mean?
The point estimate of the population mean is 21.
The point estimate of the population mean is the midpoint of the confidence interval.
To find the midpoint, add the lower and upper bounds of the interval and divide by 2. In this case, the lower bound is 17 and the upper bound is 25, so the point estimate of the population mean is (17 + 25) / 2 = 21.
On the other hand, the margin of error is a measure of the precision of the estimate. It is the amount by which the estimate could be off and still be considered accurate. The margin of error is typically expressed as a percentage of the point estimate. In this case, the margin of error would depend on the level of confidence you have in the estimate and the size of the sample you used to generate the interval. Without more information, it is not possible to determine the margin of error.
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Question 1 (Multiple Choice Worth 1 points)
A triangle has a perimeter of 9x+6. The first side of the triangle has a length of 5 x and the second side has a length of 3x-7. What a the length of third side of the triangle?
x+13
x-1
5 x-7
17 x-1
The length of third side of the triangle will be A. x + 13.
How to illustrate the perimeter?The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.
In this situation, triangle has a perimeter of 9x+6. The first side of the triangle has a length of 5 x and the second side has a length of 3x-7.
The length of third side of the triangle will be:
= 9x + 6 - (3x - 7 + 5x)
= x + 13
The correct option is A.
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6. Sue purchased a car for $18,000 three years ago. If the car depreciates at a rate of 20% per year, the value of the car now is
By writing and evaluating an exponential equation, we can see that the value of the car now is $9,216.
What is the value of the car now?
We know that the initial value of the car is $18.000, and the value depreciates at a rate of 20% per year.
If we define x as the number of years since the car was bought, we can write the value equation as:
V(x) = $18,000*(1 - 20%/100%)^x
V(x) = $18,000*(1 - 0.2)^x
V(x) = $18,000*(0.8)^x
The value of the car after 3 years is what we get if we evaluate the exponential equation in x = 3.
V(3) = $18,000*(0.8)^3
V(3) = $9,216
That is the value of the car now.
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Stephanie has 6 classes a day. Each class is 52 minutes. She goes to school 5 days a week. How much time does she spend in class? Show two different ways to solve this problem
Time spent in class per week is 6 × 52 × 5 = 1560 minutes.
Time spent in class per day is 6 × 52 = 312 minutes.
How to determine how time does she spend in class?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Since Stephanie has 6 classes a day. Each class is 52 minutes. She goes to school 5 days a week. The time she spend in class can written as:
time in class = 6 × 52 × 5 = 1560 minutes per week
The time can also be written in form of the time spent per day:
time in class = 6 × 52 = 312 minutes per day
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A car traveled 200 kilometers in 3 hours. If the car travels at the same average rate, how far will the car travel in 9 hours?
Answer: 600km
Step-by-step explanation:
Using the concept of proportion, with the same average rate,
3 hours -> 200 km
9 hours -> A km
Hence,
9/3 = A/200
A = 200 x 9/3 = 200 x 3
= 600
Answer: 600 km
Step-by-step explanation:
We need to apply the concept of Time speed distance here.
When speed is constant, T ∝ D
D = S*T
200 km = 3hrs
X km = 9hrs
X = 200*9/3
= 200*3
= 600km
What is the distance between the points (-3, 8) and (16, 8)?
Distance: 19
Steps:
Distance (d) = √(16 - -3)2 + (8 - 8)2
= √(19)2 + (0)2
= √361
= 19
Name a point that is not coplanar with R, S, and T.
The required point is W.
What is the co-plaer and non co-planer?
Co-planar refers to a set of objects that lie in the same plane or lie on the same flat surface. They have the same elevation and do not intersect each other.
Non-coplanar refers to a set of objects that are not in the same plane or do not lie on the same flat surface. They have different elevations and may intersect each other.
W is a point that is not co-planar with R, S, and T.
Consider the provided plane.
We need to find the point that is not co-planar with R, S, and T.
Co-planar: Two object or points are said to be co-planer if they lie in the same plane.
Non co-planar: Two object or points are said to be non co-planer if they don't lie in same plane.
Now consider the provided plane, the point W is not lie in the plane V.
While point R, S and T lie in the plane V.
Hence, the required point is W.
W is a point that is not co-planar with R, S, and T.
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Gina charges an initial fee and an hourly fee to babysit. Using the table below find the hourly fee and the initial fee that
Gina charges to babysit. Show work.
Cost in Dollars
Answer:
13 dollars
Step-by-step explanation:
The population (in millions) of a certain country can be modeled by the exponential equation P=3.5(1.4)x where x represents the amount of decades since 1800. Find P(8)
A. 6.86 million
B. 1,715.18 million
C. 51.65 million
D. 74.83 million
E. 26.52 million
F. 65.92 million
G. 331 million
The value of the function P(8) given that P(x) = 3.5(1.4)ˣ is (c) 51.65 million
How to determine the value of the function P(8)From the question, we have the following parameters that can be used in our computation:
An exponential function
The equation of the exponential function is then given as
P=3.5(1.4)x
Express properly
So, we have
P(x) = 3.5(1.4)ˣ
where x represents the amount of decades since 1800
From the question, we have
x = 8
Substitute the known values in the above equation, so, we have the following representation
P(8) = 3.5(1.4)⁸
Evaluate the expression
P(8) = 51.65261696
Approximate
P(8) = 51.65
Hence, the value of P(8) is (c) 51.65 million
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4. Chrissy had 4 gallons of gas in her tank when she arrived at the gas
station. She pumped gas into her car at a rate of 3/10 gallon per
second. How many gallons of gas were in the tank after s seconds?
I need Helpp asap please
Area of triangle 8,10,16
Answer:
Area: T = 24
Perimeter: p = 24
Semiperimeter: s = 12
Step-by-step explanation:
We know the lengths of all three sides of the triangle, so the triangle is uniquely specified.
a=6
b=8
c=10
The triangle perimeter is the sum of the lengths of its three sides
p=a+b+c=6+8+10=24
The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.
Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.
which expression is equivalent to -5(8x+9)-7x ?
The expression -5 (8x + 9) - 7x is equivalent to the expression - 47x - 45
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ -5 (8x + 9) - 7x
Simplify the expression, then we have
⇒ -5 (8x + 9) - 7x
⇒ - 40x - 45 - 7x
⇒ - 47x - 45
The expression -5 (8x + 9) - 7x is equivalent to the expression - 47x - 45
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