This shows that the two circles intersect at a point P, and that the distance between their centers, OP1OP2, is less than the sum of their radii, r1 + r2. Thus, the two circles touch each other internally at point P.
How can you demonstrate how two circles internally contact one another?You must calculate each circle's radius and centre in order to accomplish this. The circles will externally touch if the total of the radii and the space between the centres are identical. The circles will internally touch if the variations in radii and the separation between their centres are equal.
Let C1 and C2 stand for the two circles, with O1 and O2 serving as their respective centres. Let r1 and r2 represent the radius of C1 and C2, respectively.
Let's say that point P is where the two circles converge. The Pythagorean Theorem thus gives us:
OP1² = r1²
OP2² = r2²
OP1² + OP2² = (r1 + r2)²
Simplifying the third equation, we get:
OP1² + OP2² = r1² + 2r1r2 + r2²
The left half of this equation can be rewritten as (OP1 + OP2)2 - 2OP1OP2. When we simplify the equation above and substitute this, we get:
(OP1 + OP2)² = (r1 + r2)² + 2OP1OP2
Since OP1 and OP2 are both positive, we have:
(OP1 + OP2)²> (r1 + r2)²
Therefore, we must have:
OP1OP2 < r1 + r2
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Find the maximize z = 4x + y. Subject to the constraints x + y ≤ 50, 3x + y ≤ 90, x,y ≥ 0
The maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.
How to deal with inequality?To find the maximum value of z = 4x + y subject to the given constraints, we can use linear programming.
Graph the constraints:
First, we will graph the constraints to visualize the feasible region.
The constraint x + y ≤ 50 represents the region below the line x + y = 50:
The constraint 3x + y ≤ 90 represents the region below the line 3x + y = 90:
The feasible region is the shaded region that satisfies both constraints:
Identify the corner points of the feasible region:
The feasible region has four corner points: (0, 0), (0, 50), (30, 20), and (45, 0).
Evaluate z at each corner point:
z(0, 0) = 4(0) + 0 = 0
z(0, 50) = 4(0) + 50 = 50
z(30, 20) = 4(30) + 20 = 140
z(45, 0) = 4(45) + 0 = 180
Compare the values of z at the corner points:
The largest value of z is 180, which occurs at the corner point (45, 0).
Therefore, the maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.
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I need help solving this question
Answer:
C. y = 3/2x + 4
Step-by-step explanation:
C. y = 3/2x + 4
Suppose that a and b are positive numbers for which log, (a) = log15(b) = log25 (a + 2b). What is the value of a
Answer: The value of "a" is given by a = 25 - 2b, where "b" is a positive number.
Step-by-step explanation:
Given that log(a) = log15(b) = log25(a + 2b), we can use the properties of logarithms to solve for the value of a.
Since log(a) = log15(b), we can equate the bases and eliminate the logarithms:
a = 15^log15(b) .....(1)
Similarly, since log(a) = log25(a + 2b), we can equate the bases and eliminate the logarithms:
a = (a + 2b)^log25(a + 2b) .....(2)
Now, we can equate the right-hand sides of equations (1) and (2) since they are both equal to a:
15^log15(b) = (a + 2b)^log25(a + 2b)
Taking the logarithm of both sides with base 15, we get:
log15[15^log15(b)] = log15[(a + 2b)^log25(a + 2b)]
Using the property that loga(a^x) = x, we can simplify the left-hand side:
log15(b) = log15[(a + 2b)^log25(a + 2b)]
Now, we can equate the bases and eliminate the logarithms:
b = (a + 2b)^log25(a + 2b)
Taking the logarithm of both sides with base (a + 2b), we get:
log(a + 2b)(b) = log(a + 2b)[(a + 2b)^log25(a + 2b)]
Using the property that loga(a^x) = x, we can simplify the right-hand side:
log(a + 2b)(b) = log25(a + 2b)
Since log(a + 2b)(b) = log(a + 2b)/logb(a + 2b) by the change of base formula, we can rewrite the equation as:
log(a + 2b)/logb(a + 2b) = log25(a + 2b)
Now, we can equate the numerators and denominators separately:
log(a + 2b) = log25(a + 2b)
1 = log25(a + 2b)/(log(a + 2b))
Since loga(a) = 1, we can rewrite the equation as:
log25(a + 2b) = log(a + 2b)/(log(a + 2b))
Using the property that loga(a^x) = x, we get:
log25(a + 2b) = 1
This implies that 25^1 = a + 2b, since we are using the definition of logarithm which states that loga(b) = c is equivalent to a^c = b.
Therefore, a + 2b = 25.
Given that a and b are positive numbers, we can deduce that a + 2b > 0.
Solving for a, we get:
a = 25 - 2b
Since a and b are both positive, a = 25 - 2b > 0.
So, the value of a is greater than zero and is given by a = 25 - 2b, where b is a positive number.
Find the interquartile range of the given data set.
8.4, 7.1, 6.3, 6.8, 9.2, 7.3, 8.8, 7.9, 5.3, 8.2
Thus, the interquartile range of the given data set. are -
1st quartile (Q1) = 6.8 ; 2nd quartile (Q2) = 7.6 and 3rd quartile (Q3) = 8.4 .interquartile range = 1.60.
Explain about the interquartile range:The interquartile range in descriptive statistics reveals the spread of your distribution's middle half.
Each distribution that is sorted from low to high is divided into four equal portions using quartiles. The third and second quartiles, or the centre half of your data set, are contained in the interquartile range (IQR).
The interquartile range provides the range of a middle half of a data set, whereas the range provides the spread of the entire data set.
Given data set:
8.4, 7.1, 6.3, 6.8, 9.2, 7.3, 8.8, 7.9, 5.3, 8.2
arrange the data set in ascending order:
5.3, 6.3, 6.8, 7.1, 7.3, 7.9, 8.2, 8.4, 8.8, 9.2
Total term = 10 (even)
2nd quartile (Q2) 50% quartile - (5th + 6th) /2 = (7.3 + 7.9) /2 = 7.6
Now:
1st quartile (Q1) 25% quartile - 3rd term = 6.8
3rd quartile (Q3) 75% - 8th term = 8.4
Thus, the interquartile range of the given data set. are -
1st quartile (Q1) = 6.8 ; 2nd quartile (Q2) = 7.6 and 3rd quartile (Q3) = 8.4 .
interquartile range = maximum - minimum
interquartile range = 8.4 - 6.8 = 1.60.
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y= 3 ( x − 1 ) ^2 − 8 in standared form
y = 3(x-1)^2 - 8
y = 3(x^2 - 2x + 1) - 8 [Using the identity (a-b)^2 = a^2 - 2ab + b^2]
y = 3x^2 - 6x + 3 - 8 [Distributing the 3]
y = 3x^2 - 6x - 5 [Simplifying]
*IG:whis.sama_ent
Answer:
y=3x^(2)-6x-5
[tex]y=3x^2 -6x-5[/tex]
hope this helps ;)
Question 5 of 10
A circle is the collection of points in a plane that are within a certain distance
from a given point in the plane.
True
False
The collection of all points in a plane that are equally spaced from a given point, referred to as the circle's center, is referred to as a circle. The radius of the circle is the distance measured from any point on the circle to its center.
A circle is described as the collection of all points on a plane that is at the same distance, or radius, from a fixed point known as the circle's center.
Every location inside the circle is, therefore, closer to the center point than the radius, and any point outside the circle is farther away from the center point than the radius.
Therefore, a circle is made up of points that are spaced out by a particular amount, known as the radius, from the circle's center.
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Determine the equation of the circle graphed below.
The equation for the circle graphed in the coordinate axis is:
(x - 5)^2 + (y - 6)^2 = 16
How to determine the equation for the circle?Remember that the equation for a circle whose center is at (a, b) and has a radius R is.
(x - a)^2 + (y - b)^2 = R^2
On the graph, we can see that the center of the circle is at (5, 6), and the radius of the circle is R = 4 units. Then the equation for the circle in the graph is:
(x - 5)^2 + (y - 6)^2 = 4^2
(x - 5)^2 + (y - 6)^2 = 16
That is the equation we wanted to find.
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Which choice is equivalent to the product below when x≥ 0?
√10x² √5x
A. 5x√2x
B. x√15
C. √15x²
D. 5x√2
SUBMIT
Answer:
Step-by-step explanation:
We can simplify the given product using the properties of radicals:
√10x² √5x = √(10*5)x^(2+1) = √50x^3
We can further simplify the radical by factoring out the largest perfect square from 50, which is 25:
√50x^3 = √(25*2)x^3 = 5x√2
Therefore, the product √10x² √5x is equivalent to 5x√2, when x≥0.
To simplify the product √10x² √5x, we can combine the square roots and simplify:
√10x² √5x = √(10x² * 5x) = √(50x³) = √(25x² * 2x) = 5x√2x
Therefore, the choice that is equivalent to the original product when x≥0 is A. 5x√2x.
5. Patty starts at the bottom of a Ferris wheel with a radius of 8 m. The Ferris wheel rotates so Patty is now at the top. Arlene is on a merry-go-round with a radius of 6 m. The merry-go-round moves two- thirds of the way around its axle. Who travels farther? How much farther to the nearest tenth of a metre ?
Answer is down below!
Step-by-step explanation:
This is of the form h = a + b cos ct, where: a = 40 m. This is the height of the axle of the Ferris wheel. b = -30 m. The magnitude of this number is the radius of the wheel.
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If the given angle is in standard position, find two positive coterminal angles and two negatives coterminal angles.
a. 110° positive angles:
negative angles:
b. 165° positive angles:
negative angles:
c. -10° positive angles:
negative angles:
Answer:
a. 110°
Positive coterminal angles: 110° + 360° = 470°, 110° + 2(360°) = 830°
Negative coterminal angles: 110° - 360° = -250°, 110° - 2(360°) = -610°
b. 165°
Positive coterminal angles: 165° + 360° = 525°, 165° + 2(360°) = 885°
Negative coterminal angles: 165° - 360° = -195°, 165° - 2(360°) = -555°
c. -10°
Positive coterminal angles: -10° + 360° = 350°, -10° + 2(360°) = 710°
Negative coterminal angles: -10° - 360° = -370°, -10° - 2(360°) = -730°
Step-by-step explanation:
When an angle is in the standard position, it means that the initial side of the angle is the positive x-axis, and the terminal side of the angle is located in one of the four quadrants of the coordinate plane.
To find coterminal angles, we need to add or subtract multiples of 360 degrees to the given angle while keeping the terminal side in the same position. This is because a full rotation around the origin in the coordinate plane is 360 degrees.
For positive coterminal angles, we add multiples of 360 degrees to the given angle. In the case of 110 degrees, we can add 360 degrees once or twice to get 470 degrees or 830 degrees, respectively.
For negative coterminal angles, we subtract multiples of 360 degrees from the given angle. In the case of -10 degrees, we can subtract 360 degrees once or twice to get -370 degrees or -730 degrees, respectively.
It's important to note that there are infinitely many coterminal angles for any given angle, but we usually restrict our answers to the smallest positive and negative angles that differ from the given angle by a multiple of 360 degrees.
1. A cart moving at 20 m/s is brought to a stop by the force plotted in the force-time graph shown here. Find the impulse and the approximate mass of the cart. Show all your work.
The required value of impulse is 88 N-s and the mass of the cart is 8.8 kg.
How to find the impulse?Newton's Second Law relates an object's acceleration as a function of both the object's mass and the applied net force on the object.
Given data:
The speed of cart is, v = 10 m/s.
We are given the Force-time graph for which the area of the force-time graph will provide the value of impulse. So from the graph, the maximum force is,
F = 22 N
And time interval is,
t = 4.5 s - 0.5 s
t = 4 s
So, the impulse is,
I = Area of graph
I = F × t
I = 22 × 4
I = 88 N-s
Now the standard expression for the impulse as per the impulse-momentum theorem is,
I = ΔP (Change in momentum)
I = m ×( v - u )
Here, u is the final velocity, and since the cart stops finally, then u = 0 m/s. And m is the mass of the cart.
Solving as,
88 = m ×( v - u )
88 = m ×( 10 - 0 )
m = 8.8 kg
Thus, we can conclude that the required value of impulse is 88 N-s and the mass of car is of 8.8 kg.
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Mrs. Matthews gave a test to her 120 science
students. If she gives 5 bonus points to each
test grade, how will this affect the mean,
median, and mode scores?
Adding 5 bonus points to each test grade in Mrs. Matthew's class will increase the mean, median, and mode of the scores by 5 points each.
Explanation:The addition of 5 bonus points to each test grade will affect the mean, median, and mode in the following ways:
Mean: The mean is calculated by adding all the scores together and dividing by the total number of scores. If every student gets an additional 5 points, it would effectively increase the mean by 5 points.Median: The median is the middle score when all scores are listed in numerical order. If you add 5 points to each test grade, the median will also increase by 5 points because each score has increased by the same amount.Mode: The mode is the score that appears most frequently. If every score increases by 5, the mode will also increase by 5 points.So, in conclusion, adding 5 bonus points to each student's test score will raise the mean, median, and mode of the scores by 5 points each.
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You rented a sedan for 37.45 per day and unlimited miles. she paid a CDW fee of 19.40 per day. Her total rental cost was 646.50. She spend 78 for gasoline and her final cost per mile was 0.77. How many days did You rented the car?
You rented the car for 10 days.
Mathematical word problemLet's begin by setting up the equation to solve for the number of days:
Total rental cost = (daily rental cost + CDW fee) x number of days + gasoline cost
We know that the daily rental cost is 37.45, and the CDW fee is 19.40, so we can substitute those values into the equation:
646.50 = (37.45 + 19.40) x number of days + 78
Simplifying the equation:
646.50 = 56.85 x number of days + 78
Subtracting 78 from both sides:
568.50 = 56.85 x number of days
Dividing both sides by 56.85:
number of days = 10
Therefore, You rented the car for 10 days.
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The tables show the numbers of lawns mowed by you and your friend each
month for a year.
a. Make a back-to-back stem-and-leaf plot for the data.
b. Use the stem-and-leaf plot to compare the mean and median of the data
for you and your friend. Explain your reasoning.
c. Compare the range of the data for you and your friend.
Lawns Mowed by You
5 12 7 10 25 30
12 8 21 17 20 4
Lawns Mowed by Your Friend
19 32 27 35 40 38
35 29 31 30 32 28
Stem Leaf
0 1 3 4 6
1 0 4
2 5 7
3 1 1 9
4 1 5
Key: 1 | 0 10 plays
Pages Printed
24 32 47 12 31 9
7 10 26 28 20 40
1. A back-to-back stem-and-leaf plot for the data would be
Mowed by you stem mowed by your friend
8 7 5 4 0
7 2 2 0 1 9
5 1 0 2 7 8 9
0 3 0 1 2 2 5 5 8
4 4
KEY: 3 | 1 ⇒ 31
2. The mean for you = 14.25 and your friend 31.3. This means that your friend has a higher mean than you. The median for you is 11 and your friend is 30.5. Given that both the mean and median of your friend is higher than yours, it means that your friend mowed more lawns than you
3. The range of data for you is 26 and for your friend is 21.
How do you find the mean, median and range?To find the mean for each data set, add all the number together and divide it by the set number. For example;
4 + 5 + 7 + 8 + 10 + 12 + 12 + 17 + 20 + 21 + 25 + 30
= 171 / 12
= 14.25
To find the range for the data set, simply take the highest number of a set and minus it by the lowest number. For Example;
For your data set, it is 30 - 4 = 26
To find the median for the data sets, simply look for the number in the middle. However, in your data set, there are two middle numbers. take the sum of the two numbers and divide it by 2.
(10 + 12) / 2 = 11
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Amelia bought a t-shirt for 15$ and 3 pairs of pants. She spent a total of 117$ wich equation matches this problem
The equation that matches this problem is 15 + 3p = 117
Which equation matches this problemLet the cost of one pair of pants be represented by the variable p.
Then, the cost of three pairs of pants is 3p.
We are also given that the cost of a t-shirt is $15.
The total cost of Amelia's purchase is $117.
Therefore, the equation that matches this problem is:
15 + 3p = 117
This equation represents the total cost of Amelia's purchase, which includes the cost of one t-shirt and three pairs of pants.
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Need help quick please!
Answer: cos∅= [tex]\frac{\sqrt{7} }{4}[/tex]
Step-by-step explanation:
All numbers are positive because it is first quadrant. Draw a line out.
sin = opp/hypotenuse. the opposite line of the angle (y) =3
and hypotenuse=4
use pythagorean theorem to find x
4²=3²+x²
[tex]x=\sqrt{7}[/tex]
now use cos=adjacent/hypotenuse
cos∅= [tex]\frac{\sqrt{7} }{4}[/tex]
Chanasia buys a plastic bucket. The bucket weighs 460 g. The label on the bucket says made with 20% recycled plastic. How many grams of recycled plastic are used to make Chanasia’s bucket?
show work please
Using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.
What is the percentage?A% is a mathematical figure or ratio that denotes a percentage of 100.
Ratios, fractions, and decimals are some of the numerous ways to represent a dimensionless connection between two numbers.
The symbol "%" is generally written after the integer to denote percentages.
A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics.
So, in the given situation we will use percentages to get what % of recyclable plastic is used as follows:
= 460/100 * 20
= 4.60 * 20
= 92 grams
Therefore, using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.
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what is 12 plus 12 and take away 67 and then add 24
Answer:
-19
Step-by-step explanation:
First you need to add all of the positive and negative numbers together, which would look like (12+12+24) + (-67) OR 48 + -67. Now add -67 to 48.
-67 + 48 is -19. Therefore the answer is -19.
IM SO SORRY IF THIS DID NOT MAKE SENSE!
Answer:12+12=24
24-67=-43
-43+24=-19
Step-by-step explanation:
An individual depositing in a non-IRA account has to pay income taxes on the funds deposited and on interest earned in each year but does not have to pay taxes on withdrawals from the account.
Sarah, who is five years from retirement, receives a $10,000 bonus at work. She is trying to decide whether to save this extra income in an IRA account or in a regular savings account. Both accounts earn 8 percent nominal interest, and Sarah is in the 30 percent tax bracket in every year (including her retirement year)
If Sarah invests in the normal savings account, her net value (after taxes) five years from now will be?:
After five years, her IRA account's net worth (after taxes) will indeed be $14,322.88 ($10,000 + $4,322.88).
What do you mean by interest earned?Sarah will be required to file taxes just on interest received each year if she places the $10,000 inside a standard savings account, which will lower her net worth.
She will have earned $800 in pre-tax interest every year, assuming she receives nominal interest of 8% annually.
She will, however, be liable for $240 in taxes just on interest generated each year (30% of $800) since she falls into the 30% tax bracket.
Her pre-tax interest earnings after five years will total $4,000 ($800 x five years). She will still have paid $1,200 in total in taxes just on interest generated ($240 x 5)
She will therefore have a net worth of $12,800 ($10,000 + $4,000 - $1,200) in the normal savings account after five years (after taxes).
Sarah won't have to pay taxable income on the $10,000 invested in such an IRA account or the interest accrued until she starts taking distributions in retirement.
She will have earned $800 in pre-tax interest every year, assuming she receives nominal interest of 8% annually.
She will have the whole $800 to reinvest & compound each year, though, as she is not subject to income taxation on the interest gained each year.
She will have earned $4,322.88 in pre-tax interest after five years, and she won't have to pay any taxes until she starts taking withdrawals in retirement.
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solve this........ w/3 - 1 ≥ 4
The equivalent value of the inequality is w ≥ 15
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
w/3 - 1 ≥ 4
On simplifying , we get
Adding 1 on both sides , we get
w/3 ≥ 5
Multiply by 3 on both sides , we get
w ≥ 15
Therefore , the value of w is greater than or equal to 15
Hence , the inequality is w ≥ 15
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Math calculator help me please
The third player hit 4 more home runs than the first player. The algebraic expression that shows the relationship between a and b is: a = 3b. So option A is correct
What is a linear equation and examples?A linear equation in one variable is an equation that has only one variable. It is of the form Ax B = 0, where A and B are two real numbers and x is an unknown variable with only one solution. For example, 9x + 78 = 18 is a linear equation in one variable.
2) Each player's home runs are labeled A, B, C, and D, where A is the first baseman, B is the second baseman, C is the third baseman, and D is the shortstop. We know this:
C = 2B (the third player hit twice as many home runs as the second player)
C/B = D/B = A/C (numbers for first baseman and shortstop are proportional to numbers for third baseman and second baseman)
B = D 4 (second baseman hit 4 more home runs than shortstop)
To solve for the values of A, B, C, and D, we can use the second equation to write:
C/B = D/B
C = D (multiply both sides by B)
C = B - 4 (using the fourth equation to substitute D)
2B = B - 4 (using the first equation to substitute C)
B = 4 (interface to both sides 4)
C = 8 (using the first equation to find C)
D = 4 (using the fourth equation to find D)
A = C/2 = 4 (use another equation to find A)
Therefore the third player (C) hit 8 home runs and the first player (A) hit 4 home runs, so the third player hit 4 more home runs than the first player.
3) The relative relationship between a and b can be expressed as follows:
a/b = 6/2 = 3/1
To write this relationship as an algebraic equation, we can cross multiply to get:
a = 3b
Therefore, the algebraic expression that shows the relationship between a and b is:
a = 3b. So option A is correct
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12,110 members is what percent of 21,625 members? Please show work
Answer:
56
Step-by-step explanation:
12110 × 100
21625
=1211000
21625
=56
If October 15 falls on a Wednesday, then November 11 of that same year falls on which day of the week? (October has 31 days)
Answer:
There are 31 days in October, so there are 31 - 15 = 16 days left in October after October 15.
16 days is equivalent to 2 weeks and 2 days (since there are 7 days in a week), so November 11 is 2 weeks and 2 days after October 15.
Therefore, November 11 falls on a Wednesday + 2 weeks + 2 days = Friday.
So November 11 of that same year falls on a Friday.
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Select all that apply
c. Symmetric with respect to the origin
Answer:
To determine if the given equations are symmetric with respect to the origin, we need to check if replacing x with -x and y with -y results in the same equation.
For the equations given:
y=7x-4 is not symmetric with respect to the origin since replacing x with -x and y with -y gives y=-7x+4, which is not the same equation.
y= -x+7 is not symmetric with respect to the origin since replacing x with -x and y with -y gives y=x-7, which is not the same equation.
y = -7x^2 is symmetric with respect to the origin since replacing x with -x and y with -y gives -y = -7(-x)^2, which simplifies to -y = -7x^2. Thus, the equation remains the same.
y = 6x^2 - 9 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y = 6(-x)^2 - 9, which simplifies to -y = 6x^2 - 9. Thus, the equation is not the same.
x=1/4 y^2 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -x = 1/4 (-y)^2, which simplifies to -x = 1/4 y^2. Thus, the equation is not the same.
x = -y^2 + 9 is symmetric with respect to the origin since replacing x with -x and y with -y gives -x = -(-y)^2 + 9, which simplifies to -x = -y^2 + 9. Thus, the equation remains the same.
y=-1/6 x^3 is symmetric with respect to the origin since replacing x with -x and y with -y gives -y=-1/6(-x)^3, which simplifies to -y=-1/6 x^3. Thus, the equation remains the same.
y=x^3-1 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=(-x)^3-1, which simplifies to -y=-x^3-1. Thus, the equation is not the same.
y=sqrt(x) is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=sqrt(-x), which is not the same equation.
y=sqrt(x)-6 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=sqrt(-x)-6, which is not the same equation.
Therefore, the only equation that is symmetric with respect to the origin is y = -7x^2.
Answer:
i can only see b not c
Step-by-step explanation:
Find the surface area of the figure ( on photo)
The surface area of the figure is 344 m².
What is area?Area is the region bounded by a plane shape.
To calculate the surface area of the figure, we use the formula below.
Formula:
A = bh+L(a+b+c)..................... Equation 1Where:
A = Surface areab = Base of the triangleh = Height of the triangleL = Length of the prisma, c = Other two sides of the triangular baseFrom the diagram,
Given:
b = 6 mh = 4 ma = 5 mc = 5 mL = 20 mSubstitute these values into equation 2
A = (6×4)+20(5+5+6)A = 24+320A = 344 m²Hence, the area is 344 m².
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jasmine said that commutative property always works for addition but never for subtraction
No, Jasmine is not completely correct. The commutative property states that the order of the numbers can be changed without affecting the result of the operation.
In addition, the commutative property is true: a + b = b + a for any two numbers a and b.
For subtraction, the commutative property is not true in general: a - b is not equal to b - a.
However, there are some special cases where the commutative property does hold true for subtraction. For example, if a and b are equal, then a - b = b - a.
So, in general, Jasmine's statement that the commutative property never works for subtraction is not correct. While it is true that the commutative property does not hold true for subtraction in the same way that it does for addition, there are some special cases where it does apply.
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Which of the points below correctly plots the point (4,4π/3)?
Answer: the correct answer is B
Step-by-step explanation:
Remember that the coordinates (4,4π3) tell us the radius r=4 and the angle θ=4π3. So the point should be on the circle labeled 4 and form an angle of 4π3 with the positive x-axis. Point B is the correct point.
Question 7 (3 points)
The graph and table below represent the constant rate for the amount of time it takes for a given
number of gallons of water to flow from a hose.
a. Find the rate of both the graph and table. Be sure to show all work.
b. Which one has the greater rate? Explain how you know.pl
The slope from the table is greater than the slope from the graph hence the table shows a greater rate.
What is the slope of a graph?The slope of a graph is the measure of how steep a line is. It is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Mathematically, slope is represented as:
Slope (m) = (change in y)/(change in x)
The slope from the table is;
y2 - y1/x2 - x1
m = 42 - 30/7 - 5
= 6
The slope from the graph is;
8 - 0/1.5 - 0
m = 5.33
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Find the surface area of the figure
The surface area of the square pyramid given above would be = 400ft²
How to calculate the surface area of the given shape?To calculate the surface area of the given figure, the formula that should be used would be = b² +2bs
where B = base length= 10ft
s = slant height= 15ft
Surface area = 100+2(10×15)
= 100+300
= 400ft²
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. The formula 9x - 5y = -160 relates the
temperature in degrees Fahrenheit y to
the temperature in degrees Celsius x.
Tell whether the relationship is a direct
variation. Explain your answer.
Answer: formula 9x - 5y = -160 is not a direct variation.
Step-by-step explanation: The provided expression, 9x - 5y = -160, does not exemplify direct variation.
Direct variation is a correlation existing between two variables, wherein one is a constant scalar multiple of the other. Stated differently, should one variable increase by a defined magnitude, the corresponding variable will also experience a commensurate increase of identical magnitude.
The formula provided indicates the absence of a constant proportionality between the temperature in degrees Celsius (x) and the temperature in degrees Fahrenheit (y). It is noteworthy that the correlation amidst the variables x and y is non-linear in nature, thereby precluding its representation in the form of a direct proportionality.
Answer: It is not a direct variation.
Step-by-step explanation:
While a linear equation is a direct variation, the y-intercept of a direct variation relationship must be 0. Here, that is not the case. Let us manipulate this equation into a slope-intercept equation.
Given:
9x - 5y = -160
Add 5y and 160 to both sides of the equation:
5y = 9x + 160
Divide both sides of the equation by 5:
y = [tex]\frac{9}{5}[/tex]x + 32
32 ≠ 0