Using what you know about angles and triangles, what is the measure of angle 6?
Answer:158
Step-by-step explanation:∠6 = 68 + 90 = 158°
What is the area of the region between the graphs of y=x^2 and y=-x from x=0 to x=2?
The area between [tex]\( y = x^2 \)[/tex] and [tex]\( y = -x \) from \( x = 0 \) to \( x = 2 \) is \( \frac{14}{3} \)[/tex] square units, found by integrating [tex]\( x^2 + x \)[/tex] from 0 to 2.
Intersection Points: To find the area between [tex]\( y = x^2 \)[/tex] and [tex]\( y = -x \)[/tex] from [tex]\( x = 0 \) to \( x = 2 \)[/tex], first find their intersection points by setting [tex]\( x^2 = -x \)[/tex]. This gives [tex]\( x^2 + x = 0 \)[/tex], which factors to [tex]\( x(x + 1) = 0 \)[/tex], yielding [tex]\( x = 0 \)[/tex] and [tex]\( x = -1 \)[/tex] as the intersection points.
Limits of Integration: We are interested in the area between these curves from [tex]\( x = 0 \) to \( x = 2 \)[/tex]. Since[tex]\( x = -1 \)[/tex] lies outside this interval, we only consider [tex]\( x = 0 \)[/tex].
Integration: The area can be calculated by integrating the difference between the upper curve [tex]\( y = x^2 \)[/tex] and the lower curve [tex]\( y = -x \) from \( x = 0 \) to \( x = 2 \):[/tex]
[tex]\[ \text{Area} = \int_{0}^{2} (x^2 - (-x)) \, dx \][/tex]
Sure, here is the rewritten line:
[tex]\[ \text{The area can be found by integrating} \, x^2 + x \, \text{from} \, x = 0 \, \text{to} \, x = 2: \, \int_{0}^{2} (x^2 + x) \, dx \][/tex]
Integrating term by term:
[tex]\[ = \left[ \frac{x^3}{3} + \frac{x^2}{2} \right]_{0}^{2} \][/tex]
[tex]\[ = \left( \frac{2^3}{3} + \frac{2^2}{2} \right) - \left( \frac{0^3}{3} + \frac{0^2}{2} \right) \][/tex]
[tex]\[ = \left( \frac{8}{3} + 2 \right) - 0 \][/tex]
[tex]\[ = \frac{8}{3} + 2 \][/tex]
[tex]\[ = \frac{14}{3} \][/tex]
Complete question:
What is the area of the region between the graphs of y=x² and y=-x from x=0 to x=2?
two dice are tossed what is the probability of obtaining a sum greater than 6
Paige rides her bike around town. She can ride one half of a mile in 1 30 ith of an hour. If she continues to ride at the same pace, how many miles could she travel in 1 hour?
We have been given that Paige can ride one half of a mile in 1/30 th of an hour. And we have to found the distance traveled in 1 hour if she continues to ride at the same pace.
Let d be the distance traveled in 1 hour.
In 1/30 th of an hour distance traveled is 0.5 mile
Hence, in 1 hour the distance traveled is given by
[tex]d=\frac{0.3}{1/30} \\ \\ d=0.5\times 30\\ \\ d=15[/tex]
Therefore, she will travel 15 miles.
AB is tangent to circle O at B. Find the length of the radius, r, for AB = 5 and AO = 13.
the radius is twelve
Which is the range for this set of data 38,17,55,40
Answer:
38
Step-by-step explanation:
Which of the following shows the correct evaluation for the exponential expression 6 over 7 to the power of 2?
6 over 7 plus 2 equals 2 and 6 over 7
6 over 7 times 2 equals 12 over 7 which equals 1 and 5 over 7
6 over 7 times 6 over 7 equals 36 over 49
6 over 7 divided by 2 equals 6 over 14
In 1983, a year-long newspaper subscription cost $12.75. Today, a year-long newspaper subscription costs $28.50. If the CPI is 193, what is the relation of the actual price of a year-long newspaper subscription to the expected price, to the nearest cent? a. The actual price is $14.79 higher than the expected price. b. The actual price is $3.89 higher than the expected price. c. The actual price is $9.20 lower than the expected price. d. The actual price is $11.86 lower than the expected price
Answer:
Option b - The actual price is $3.89 higher than the expected price.
Step-by-step explanation:
Given : In 1983, a year-long newspaper subscription cost $12.75. Today, a year-long newspaper subscription costs $28.50. If the CPI is 193
To find : What is the relation of the actual price of a year-long newspaper subscription to the expected price, to the nearest cent?
Solution :
CPI is the consumer price index.
The formula of CPI is
[tex]\text{CPI}=\frac{\text{Cost of newspaper subscription in Given Year}}{\text{Cost of newspaper subscription in Base Year}}\times 100[/tex]
We have given CPI = 193
Cost of newspaper subscription in Base Year = $12.75
We have to find cost of newspaper subscription in Given Year
[tex]193=\frac{\text{Cost of newspaper subscription in Given Year}}{12.75}\times 100[/tex]
[tex]\text{Cost of newspaper subscription in Given Year}=\frac{193\times12.75}{100}[/tex]
[tex]\text{Cost of newspaper subscription in Given Year}=\frac{2460.75}{100}[/tex]
[tex]\text{Cost of newspaper subscription in Given Year}=24.61[/tex]
The actual price of newspaper subscription = $28.50
The expected price of newspaper subscription = $24.61
Now, to find how much higher they expected is
$28.50 -$24.61 = $3.89
Therefore, Option b is correct.
The actual price is $3.89 higher than the expected price.
PLZ HELP ASAP GRAPH A CIRCLE FROM ITS STANDERED EQUATION
The graph of the circle with the equation (x - 3)² + (y + 3)² = 36, is a circle with center (3, -3) and radius of 6 units
Please find attached the graph of the circle (x - 3)² + (y + 3)² = 36, created with MS Excel
The details of the steps used to graph of the circle are as follows;
The standard form of the equation of a circle is; (x - h)² + (y - k)² = r², where the center of the circle is (h, k)
The equation of the circle in standard form is; (x - 3)² + (y + 3)² = 36
The comparison of the above equation with the form of the general equation of a circle in standard form indicates that the center of the circle is (3, -3)
The comparison of the radius of the circle with equation (x - 3)² + (y + 3)² = 36, with the general form of the equation of a circle in standard form indicates that the radius of the circle is; √(36) = 6
What is the highest decimal number that can be represented by two binary digits?
The answer is 3.
Bonus: Here is a fun challenge, try to decipher what Im saying here. (Use an online binary website.)
01001001 01100110 00100000 01111001 01101111 01110101 00100000 01100110 01101001 01101110 01100100 00100000 01101111 01110101 01110100 00100000 01110111 01101000 01100001 01110100 00100000 01110100 01101000 01101001 01110011 00100000 01110011 01100001 01111001 01110011 00101100 00100000 01001001 00100000 01110111 01101001 01101100 01101100 00100000 01100110 01101111 01101100 01101100 01101111 01110111 00100000 01111001 01101111 01110101 01110010 00100000 01100010 01110010 01100001 01101001 01101110 01101100 01111001 00100000 01100001 01100011 01100011 01101111 01110101 01101110 01110100 00100000 00111010 00101001
A triangle has side lengths 4, 7 and 9. What is the measure of the angle across from the longest side?
92 = 42 + 72 − 2g4g7cos(A)
81 = 16 + 49 − 56cos(A)
81 = 9cos(A)
9 = cos(A)
A cannot exist!
Gabe tried to use the law of cosines to find an unknown angle measure in a triangle. His work is shown. What is Gabe’s error?
Gabe reversed the order of the 9 and the 4.
Gabe squared the numbers incorrectly.
Gabe should not have subtracted 56 from
16 + 49.
Gabe incorrectly stated that cos–1(9) is not defined.
Answer:
Step-by-step explanation:
Given that a triangle has sides 4,7 and 9
A student Gabe tried to use law of cosines to find unknown angle measure
The angle is opposite side 9 because angle across the longest side is given
He used cosine formula for triangles
[tex]a^2=b^2+c^2-2bccosA\\9^2 = 4^2+7^2-2(4)(8) cosA\\81-65 =-56 cosA\\[/tex]
But instead he adjusted -56 with 16 +49 which is wrong
Because -56 has product as cosA it is not like term as other constants
So correct step should be
81 = 65-56 Cos A
Gabe should not have subtracted 56 from
16 + 49.
This is the correct answer
What is the volume of a right circular cylinder with a base diameter of 18yd. And a height of 3yd.
Answer:
[tex]Volume=254[/tex] to the nearest cubic yard.
Step-by-step explanation:
The volume of a right circular cylinder can be calculated using the formula;
[tex]Volume=\pi r^2h[/tex].
The diameter of the base is given to us. We divide it into two to obtain the radius.
[tex]r=\frac{18}{2}=9yd[/tex] and also the height of the cylinder is [tex]h=3yd[/tex].
We substitute these values into the formula to obtain;
[tex]Volume=9^2\times 3\pi yd^3[/tex]
[tex]Volume=243\pi yd^3[/tex]
[tex]Volume=763.4yd^3[/tex]
Answer:
answer= 254
Step-by-step explanation:
how can you write the expression with a rationalized denominator? √3/√4
Please do not answer unless you are pretty sure. Thanks!
Find the center, vertices, and foci of the ellipse with equationx^2/144+y^2/2525 = 1
Assume that the population of the world in 2010 was 6.9 billions and is growing at the rate of 1.1 percent a year. (a) set up a recurrence relation for the population of the world n years after 2010 (b) find an explicit formula for the population of the world n years after 2010. (c) what will the population of the world be in 2030
Answer:
a 1=6.9
a an =
(an-1)(1.1)
b an=
(6.9)
(1.1^n-1)
c
46.419
billion
Step-by-step explanation:
Using a rain gauge, Gerry determined that 1/2 inch of rain fell during 3/4 of an hour. What is the unit rate of rainfall in inches per hour?
Final answer:
To calculate the unit rate of rainfall in inches per hour, divide the amount of rainfall (1/2 inch) by the duration (3/4 hour), which gives 2/3 inches per hour.
Explanation:
The student is asking how to find the unit rate of rainfall in inches per hour when given that 1/2 inch of rain fell during 3/4 of an hour. To find the unit rate, divide the total amount of rainfall by the total time to get the amount of rain per one hour.
Step-by-step calculation:
Amount of rainfall: 1/2 inch
Duration of rainfall: 3/4 hour
To find inches per hour, divide the amount of rainfall by the duration:
(1/2 inch) / (3/4 hour) = (1/2) / (3/4) = (1/2) * (4/3) = 4/6 = 2/3 inches per hour.
Therefore, the unit rate of rainfall is 2/3 inches per hour.
The four vertices of a rectangle drawn on a complex plane are defined by 1 + 4i, -2 + 4i, -2 – 3i, and 1 – 3i. The area of the rectangle is square units.
Answer:
The area of rectangle =21 sq units .
Step-by-step explanation:
Given the four vertices of rectangle are 1+4i,-2+4i, -2-3i and 1-3i.
Consider ABCD is a rectangle and its vertices are 1+4i,-2+4i,-2-3i and 1-3i.
First we find sides of rectangle
AB=vertices of B- vertices of A
AB= -2+4i-(1+4i)=-3
If complex number=a+biThen modulus=[tex]\sqrt{a^2+b^2}[/tex]Length of AB= [tex]\sqrt{(-3)^2}[/tex]=3 ( Because magnitude = length always positive )BC= Vertices of C - vertices of B
BC=-2-3i-(-2+4i)=-7i
Length of BC=[tex]\sqrt{(-7)^2}[/tex]=7 ( Magnitude always positive)
CD= vertices of D- vertices of C
CD= 1-3i-(-2-3i)=3
Length of CD= [tex]\sqrt{3^2}[/tex]=3 ( Magnitude always positive)
DA= vertices of A - vertices of D
DA= 1+4i-(1-3i) =7i
Length of DA= [tex]\sqrt{7^2}[/tex]=7 ( Magnitude always positive)
AB=CD and DA= BC
Length BC=7 units
Breadth AB=3 units
Area of the rectangle = [tex]length\times breadth[/tex]
Area of rectangle =[tex]AB\times BC[/tex]
Area of rectangle= [tex]3\times 7[/tex]=21 sq units .Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of 6. The estimated value of is 3.14. The measure of the angle subtended by the arc is
The measure of the subtended angle by the arc is approximately 1.20 radians or 68.75 degrees. This is determined using the formula θ = s/r to find the subtended angle.
Explanation:To find the subtended angle, we need to use the formula θ = s/r, where s is the arc length and r is the circle's radius. The area of the circle with radius r, is πr², and given that it is 78.5 cm², we first need to find the radius. By solving the area equation, we get r = √(78.5/π), or approximately 5.00 cm. Using the radius in the angle formula (θ = 6/5.00), we get θ to be approximately 1.20 radians. However, if the question is asking for the result in degrees, we need to convert the result from radians to degrees by using the conversion factor 180/π. Thus, θ = 1.20 * (180/π) which gives approximately 68.75 degrees.
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Calculate the circle's radius first from the given area. Then, find the circumference of the circle and compare the arc length to the circumference to obtain the subtended angle. Therefore, the subtended angle is approximately 68.79 degrees.
Explanation:The subject of this question falls under the domain of geometry in Mathematics, where we identify the measure of angle subtended by a certain arc. In order to achieve this, we must understand that a complete circle with a 360-degree angle covers an arc length equivalent to its circumference. If we know the radius of the circle, calculated from the area, we can compare the known arc length to the circumference of the circle to find the angle subtended.
First, we find the radius using the given circle area using the formula [tex]A=\pi r^2[/tex], which gives r= √(A/π). So r= √(78.5 cm² / 3.14) =approx. 5cm. Now, the full circumference of a circle (C) is 2πr, which gives [tex]C = 2*3.14*5 cm = 31.4 cm.[/tex] The full angle covered by the circumference is 360 degrees. To find the angle subtended by an arc of length 6cm, we calculate as follows: (6 cm / 31.4 cm) * 360 degrees = approx. 68.79 degrees.
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Kevin rolled two number cubes each numbered 1 to 6.
what is the probability that both number cubes land on 3?
Simon has a scale model of the Concorde airplane. The actual length of the Concorde is approximately 200 feet. If the ratio of the actual length in feet to the length of the model in centimeters is 5 : 1, what is the approximate length of Simon's model?
Answer:
yur
Step-by-step explanation:
which of the following are geometric sequences?
A. 1,3,9,27,81
B. 10,5,2.5,1.25,0.625, 0.3125
C. 3,6,9,12,15,18
D. 5,10,20,40,80,160
Final answer:
Options A, B, and D are geometric sequences because they have a constant ratio between successive terms. Option A has a ratio of 3, option B has a ratio of 0.5, and option D has a ratio of 2. Option C is an arithmetic sequence and not geometric.
Explanation:
The question asks which of the listed sequences are geometric sequences. A geometric sequence is characterized by a constant ratio between successive terms. Let's analyze each option:
A. 1,3,9,27,81 - Each term is multiplied by 3 to get the next term, hence it is a geometric sequence with a common ratio of 3.
B. 10,5,2.5,1.25,0.625, 0.3125 - Each term is multiplied by 0.5 (or divided by 2) to get the next term, hence it is a geometric sequence with a common ratio of 0.5.
C. 3,6,9,12,15,18 - The difference between successive terms is constant (+3), making it an arithmetic sequence, not geometric.
D. 5,10,20,40,80,160 - Each term is multiplied by 2 to get the next term, hence it is a geometric sequence with a common ratio of 2.
Therefore, options A, B, and D are geometric sequences, while option C is not.
What are the zeros of the polynomial function f(x)=x^2+5x+6
A pizza that was ordered for a party was already cut into 6 slices. If each serving of pizza was 1 3 of a slice, how many servings of pizza were available? A) 18 Eliminate B) 2 C) 1 18 D) 1 2
Mary has three baking pans. Each pan is 8" × 8" × 3". Which expression will give her the total volume of the pans?
8^2 × 3
8 × 3^2
(8 × 2 × 3) × 3
(8^2 × 3) × 3
Answer:
D. (8^2 × 3) × 3
Step-by-step explanation:
its d on plato
Estimate the size of a crowd standing along 1 mile section of parade route that is 10 feet deep on both sides of the street assume that each person occupies 2.5 square feet
A) 21,120
B) 42,240
C) 84,480
D) 168,960
The correct answer is option B). The size of a crowd standing along 1 mile section of parade route that is 10 feet deep on both sides of the street is 42,240.
To estimate the size of the crowd, we need to calculate the total area occupied by the crowd and then divide by the area occupied by each person.
First, let's calculate the total area available for the crowd on both sides of the street:
The length of the parade route is 1 mile. Since there are 5280 feet in a mile, the length in feet is 5280.
The depth of the crowd on both sides of the street is 10 feet.
Therefore, the total area available for the crowd on both sides is:
Total area = 2 [tex]\times[/tex] (Depth of crowd) [tex]\times[/tex] (Length of parade route)
Total area = 2 [tex]\times[/tex] 10 feet [tex]\times[/tex] 5280 feet
Total area = 105,600 square feet
Next, we need to calculate how many people can fit in this area:
Each person occupies 2.5 square feet.
The number of people that can fit in the total area is:
Number of people = Total area / Area per person
Number of people = 105,600 square feet / 2.5 square feet per person
Number of people = 42,240.
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:
f(t) = −16t2 + 48t + 100
The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____ feet per second.
"7 less than a number t" written as an algebraic expression is:
Answer: The expression for the given statement is [tex]t-7[/tex]
Step-by-step explanation:
We are given a statement:
7 less than a number t
Let the number be considered as 't'
'Less' in the above statement means subtraction operation.
The numerical value written before the 'less' operation is written after in the expression.
Thus, the expression for the given statement is [tex]t-7[/tex]
The algebraic expression for '7 less than a number t' is t - 7. This represents taking the number t and subtracting 7 from it.
Explanation:The question requires an algebraic expression. '7 less than a number t' translates to t - 7 in algebraic terms. The phrase 'less than' is a clear indication to subtract in math context. So, take the number t and subtract 7 from it, hence, t - 7 is our answer. This is a common way to express relative quantities and operations in algebra.
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-4 × 7 with an absolute value is?
Pasha bought 3 pounds of onions for $2.67. which ratio is proportional to 3 pounds at $2.67?