Suppose the math club is going on a field trip. Members will be riding in vans that will hold 7 people each including the
driver. More than 28 people will be going on the field trip. Do not put spaces in your answers.
Write an inequality to model this situation using V as the variable.
Solve the inequality.
What is the least number of vans needed to make the trip?
Answers
Since more than 4 vans will be required in total, at least 4 vans should be reserved.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal. The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It is an illustration of inequality. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3.
Here,
Since the total number of people is at least 28, then the total number of people must be 28 or more, so
7v≥28
v≥4
The total number of vans needed will be more than 4 that is at least 4 vans should be booked.
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Related Questions
What is the classification for this polynomial?
-6uv - 3u - 2v.
Click on the correct answer.
monomial
binomial
trinomial
Answers
1. -6uv
2. 3u
3. 2v
what is 3/4x(5/6-4/23)=43
Answers
Answer: 86 86/91 or 7912/91
Work: So you multiply 3/4x by what is in the parenthesis like this: 3/4x*5/6-3/4x*4/23. and you get 5/8x-3/23x=43. And then you simplify to get 91/184x=43 then u multiply both sides by 184 to get rid of the fraction. and you get 91x=7912. then you divide both sides by 91 and you get x=7912/91 or 86 86/91
Divide.
(x³ + x² + 3x + 5) ÷ (x + 4)
Answers
Using the long division method, we have divide ([tex]x^3+x^2[/tex] +3x+5) ÷ (x+4) then the remainder is −55 and quotient is x^2−3x+15.
We have to divide ([tex]x^3+x^2[/tex] +3x+5) ÷ (x+4)
In general, long division of two integers without any variables is performed in the same way as long division of a polynomial by a binomial:
Divide the polynomial's highest degree term by the binomial's highest degree term. Over the division line, type the outcome.
Subtract the resulting binomial from the polynomial after multiplying this result by the divisor.
x+4) [tex]x^3+x^2[/tex] +3x+5 (x^2−3x+15
−([tex]x^3+4x^2[/tex])
−−−−−−−−−−−−−−−−−−−
−3[tex]x^2[/tex] +3x
−(−3[tex]x^2[/tex] −12)
−−−−−−−−−−−−−−−−−−−
15x+5
−(15x+60)
−−−−−−−−−−−−−−−−−−−
−55
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PLEASE HELP ME
Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answers
Answer:
The correct answer is C. -29.
Step-by-step explanation:
insert -29 for x,
subtract -7 from -29,
then multiply by 2 to get your answer.
Without calculating, order the quotients smallest to largest.
Answers
The order of the quotient from smallest to largest is given as follows:
42.6/70, 426/70, 42.6/0.07, 42.6/0.07.
What is a quotient?A quotient is given by the division of two terms a and b, that is:
a / b.
From this, we have that the dividend a and divisor b are inverse proportional, that is:
A large quotient is achieved when a is large and b is small.A small quotient is achieved when a is small and b is large.There are three divisions with the same term a, hence they are ordered, from smallest to largest, as follows:
42.6/70, 42.6/0.07, 42.6/0.07.
(the smallest the value of b, the largest the quotient).
The final quotient is:
426/70.
Dividing by 10 to have an equivalent value of a, we have that:
426/70 = 42.6/7.
Which is the second largest value of b, hence the second smallest quotient.
Missing InformationThe problem is given by the image shown at the end of the answer.
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a local ice skating rink wishes to determine the age of its customers. the ages of customers are summarized in the relative frequency table below. what is the cumulative relative frequency of patrons, aged 47 or younger?
Answers
a local ice skating rink wishes to determine the age of its customers. then 10% of lottery winners are 70 years or older
Age____ Freq__R/freq____ Cumm Rel Freq
[20,29]___3____ 0.1________ 0.1
[30,39]__ 10__ 0.3333_____ 0.4333
[40,49]__ 2__ 0.0667______ 0.5
[50,59]__ 7 __0.2333 _____0.7333
[60,69]__ 4 ___0.1333 ____0.8666
[70,79]___ 3 ____0.1 ______0.9666
[80,89]___ 1 ___0.0333 ____0.9999
A.) What is the frequency of lottery winners of age between 19 and 40?
Frequency = (3 + 10) = 13 winners
B.) What percentage of lottery winners are 70 years or older?
From the relative frequency table = 0.1 (3/30) = (0.1 * 100%) = 10%
complete question is
Given the frequency distribution for the data, Age Frequency Relative Frequency Cumulative Relative Frequency [20,29] 3 0.1 0.1 [30,39] 10 0.3333 0.4333 [40,49] 2 0.0667 0.5 [50,59] 7 0.2333 0.7333 [60,69] 4 0.1333 0.8666 [70,79] 3 0.1 0.9666 [80,89] 1 0.0333 0.9999 What is the frequency of lottery winners of age between 19 and 40? What percentage of lottery winners are 70 years or older?
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A pool's diving platform is 10 m above the water's surface. The
bottom of the pool is at -5 m, relative to the surface of the
water. What is the distance between the diving platform and
the bottom of the pool?
Answers
Zoe is driving on a long road trip. She currently has 13 gallons of gas in her car. Each
hour that she drives, her car uses up 0.75 gallons of gas. How much gas would be in
the tank after driving for 2 hours? How much gas would be left after t hours?
Gas left after 2 hours:
Gas left after t hours:
Answers
Gas left after 2 hours is 1.5 gallons and the function that represent the gas which is left in the tank after driving for t hours is 13 - 0.75t gallons.
Zoe is driving on a long road trip.
The amount of gas she has in her car = 13 gallons.
It is given that each hour that she drives, functions her car uses up 0.75 gallons of gas.
So, Gas used in the car for one hour = 0.75 gallons
Gas used in the car for two hours = 0.75*2 = 1.5 gallons
Hence, Gas left in the tank after driving for 2 hours = 13 - 1.5 = 11.5 gallons.
Now,functions
Gas used in the car for t hours = 0.75*t = 0.75t gallons
Gas left in the tank after driving for t hours = 13 - 0.75t gallons.
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Graph DFG with vertices D(2,8), F(1,2) and G(4,6) and image after the glide reflection with a translation along <3,3> and a reflection in the y=x
Answers
The vertices of the figure after geometric translations are (11, 5), (5, 4), and (9, 7).
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The vertices are D(2,8), F(1,2) and G(4,6).
Points become after reflection:
D'(8, 2), F'(2, 1), G'(6, 4)
After applying translation:
D''(8+3, 2+3) = (11, 5)
F''(2+3, 1+3) = (5, 4)
G''(6+3, 4+3) = (9, 7)
Thus, the vertices of the figure after geometric translations are (11, 5), (5, 4), and (9, 7).
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Select the correct answer.
Function h is the product of functions f and g.
f(x) = -5x − 9
g(x) = 8x − 4
Which equation defines function h?
A.
h(x) = -40x + 36
B.
h(x) = -40x2 − 52x + 36
C.
h(x) = -40x2 + 36
D.
h(x) = -40x2 − 13x + 36
Answers
The value of h(x) = -40x2 – 52x + 18. Option (b) is correct.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable is defined as a function.
Given functions
f(x) = -5x − 9
g(x) = 8x − 4
we have to determine which equation defines function h
f(x) = -5x − 9
g(x) = 8x – 4
(f x g) (x) = (-5x –9)(8x – 4)
(f x g) (x) = -40x2 + 20x – 72x + 36
(f x g) (x) = -40x2 – 52x + 18
Therefore the value of h(x) = -40x2 – 52x + 18. Option (b) is correct.
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- Pls help due tomorrow !
Answers
Its multiplication so in steps it would look like
(-3p + 6) x (-3p + 6)
= 9p^2 + -18p + -18p + 36
= (9p^2 -36p + 36)
Step 2:
(9p^2 -36p + 36) x (-3p + 6)
= (-27p^3 + 54p^2 + 108p^2 + 216p - 108p + 216)
By factoring completely you need to simplify it by just adding everything up that matches.
(-27p^3 + 162p^2 + 108p + 216)
is the simplified answer
hi i was wondering if somebody can help me with this question. Given the inequality 4x ≤ 28, determine the value of x.
S:{7}
S:{9}
S:{12}
S:{38}
Answers
Answer:
Step-by-step explanation:
OK:
1. Isolate the x on the left side of inequality. Always remember if a number or variable crosses inequality, it becomes opposite!
4x ≤28
x ≤28/4
x ≤7
2. Double Check!
4*7 ≤28
28 ≤28 TRUE
x=7(s) or Choice A
Part A
Rebecca's house cost $100000 in the year 2000.
In 2008 she sold it for $210000.
Was the change in price a positive or negative change?
Answer:
Part B
What was the percentage of change in the price of the house?
Answers
Answer:
Im guessing it would be a positive change
Step-by-step explanation:
part a had the cost of $100,000 while part b had the cost of $210,000
therefore, part b increased $110,000 from 2000 to 2008.
this is my guess.
5.
The area of a circle is 40 mm²,
determine the circumference.
Answers
Answer: the formula to find circumference is C=2times pie which is 3.14 times the radius. Radius is half of the diameter which in this case I believe would be 20 times that by 3.14 and get 62.8 then times that by two which gives you the answer of 125.6
Step-by-step explanation: correct me if I’m wrong
1. Is the game fair? We are flipping a coin twice. The first player wins if we get 2 tails, and the second player wins if we get 1 head and 1 tail. 2. Is the game fair? we are tossing two dice and the first player wins if the sum on the dice is 9 and the second player wins if the sum on the dice is 5.
Answers
Step-by-step explanation:
1) In the case of the coin, we will assume that it is a fair coin and there is an equal probability that the coin will land either heads or tails on each flip. In other words, we are assuming that flipping the coin is a completely random process.
When flipping a coin twice, there are 4 distinct possibilities, where H means the coin lands head side up and T means it lands tails side up. The first letter represents the first flip of the coin and the second represents the second flip. The possible outcomes are:
HH, HT, TH, TT
As you can see, there is only 1 possible outcome where the coin will land tails up twice, while there are 2 possible outcomes where the coin will land heads up once and tails up once. Since the game doesn't specify the order in which the coin needs to land on either side for player 2 to win, both of these possibilities are fair game.
Now, according to our earlier assumption that the process of flipping the coin is truly random, we can say that there is a 50/50, chance of the coin landing on either side before we flip it. There is also a 100% chance that, in 2 flips, the coin behaves according to one of the possibilities stated above. This means that each possibility has an equal 25% chance of happening. We determined there are 2 possible outcomes where the coin lands on both a head and a tail, opposed to the 1 possible outcome where the coin lands tails up on both flips. Adding the probabilities, this means that the second player has a 50% chance of winning the game while the first player only has a 25% chance of winning the game, and thus - it is not fair.
2) In the second game, we will also assume that the process of rolling the dice is completely random and there is an equal chance that it lands on each side. The possible outcomes for both dice combining to sum to 5 are:
1,4; 4,1; 2,3 and 3;2
and the possible outcomes for both dice combining to sum to 9 are:
4,5; 5,4; 2,6 and 6,2
Assuming the dice are normal, 6-sided dice, there is a 1/6 or a 16.67% chance of the dice landing on each side. The outcomes on these rolls are dependent on one another and represent compound probabilities. in other words, the probability of rolling a 2 on a single dice is 16.67%, and the probability of rolling a 6 on a single dice is also 16.67%, but the probability of rolling a 2 on one dice and (key word here being and) a 6 on the other dice is the product of the two individual probabilities;
1/6 * 1/6 = 1/36 (2.78%)
This means that it is less likely to roll the correct combination than it is to roll each of the numbers individually, which should intuitively make sense.
However, because there are an equal number of outcomes in which each player wins, this game is fair to both players. It is no more likely that the sum of the dice will be 9 than it is that it will be 9, even though both of these outcomes have relatively low probabilities. In most rolls, neither player will win - but the game is still fair to both players.
Calvin thinks that only fractions with a denominator of 2, 4, 5, 10 and 20 will
change into terminating decimals. See if he is correct by converting every unit
fraction from ½ up to 1/25 into a decimal using your calculator. Try to explain your
findings
Answers
Answer: Calvin is incorrect because as you can see from my table, when we have the fraction ⅛ we get a terminating decimal proving that he is wrong.
Step 1: Create a table that shows the unit fraction and the decimal of each (the r stands for repeating, and ra stands for random numbers). To convert the unit fraction to a decimal, simply type it in your calculator, but use the division sign instead of the fraction bar. I stopped my table at ⅛ since that is where we find our answer, but you can keep going. My table is attached.
Step 2: Formulate a well thought out explanation of why he is wrong. Example: My answer above.
Point C is the midpoint of AB and point B is between points A and D . If AD=17 and BD=9 , what is CD ?
CD=
Answers
Answer: 13 units
Step-by-step explanation:Given that Point C is the midpoint of AB and point B is between points A and D. If AD = 17 and BD = 9
According to definition midpoint, AC = CB
According to definition of segment addition postulate, AD = AB + BD
AB = AD - BD
AB = 17 - 9
AB = 8
Again, AB = AC + CB
Therefore, CB = AB/2
CB = 8/2 = 4
Now, CD = CB + BD = 4 + 9
CD = 13 units
Hence, length of CD = 13 units
Find the value of x in the triangle below:
Answers
Answer:
x=12
Step-by-step explanation:
turn into and equation because angles in a triangle add up to 180°
so
6x-19+3x+7+84=180
collect like terms
9x+72=180
solve to find 'x'
9x=108
x=12
ASAP WILL GIVE 100 PTS
The line segment graphed on the coordinate plane represents a roof with several triangular supports. Each support is triangular, with a horizontal board that starts on the edge of the roof and connects with a vertical board that ends on the edge of the roof as shown.
(2,1)(6,3)
Does each support have the same starting coordinates? Explain.
Does each support have the same ending coordinates? Explain.
Does each support have the same change in x-values? Explain.
Does each support have the same change in y-values? Explain.
Does each support have the same ratio of change in y-values over change in x-values? Explain.
Answers
Answer:a) No, the first support starts at (0,0) and the 2nd one starts at (2,1)
b) No, first one ends at (2,1) 2nd one ends at (6,3)
c) No, 2 ( 0 to 2) does not equal 4 ( 2 to 6)
d) No, 1 ( 0 to 1) does not equal 2 (1 to 3)
e) Yes, this is the slope of the diagonal line: 1/2
MARK BRAINILEST I GOT SO CONFUSED BUT I UNDERSTAND NOW.... Peace Out?
Step-by-step explanation:
a tunnel is constructed with a semielliptical arch. the width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet. what is the height of the tunnel 5 feet from the edge? round your answer to the hundredths place.
Answers
As a result, the tunnel is 13.83 feet high, 5 feet from the edge.
An ellipse is an oval curve on a plane that contains two fixed points called foci. The sum of the distances between the two foci from each point on the ellipse is constant at all points.
Since the tunnel has an arch that is semi-elliptical, we can put the ellipse's center at the center of its 60-foot width.
What is an ellipse?
An ellipse is a two-dimensional shape that is defined by its axes in geometry. When a plane intersects a cone at an angle to its base, it creates an ellipse. It focuses on two things. For each point in the curve, the sum of the two distances to the focal point remains constant.
What are an ellipse and an example?
An ellipse is the locus of points whose sum of their distances from its two foci is constant and has an eccentricity of less than one. The two-dimensional egg shape and the running tracking in a sports stadium are simple examples of the ellipse in our everyday lives.
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a student earns Php 280.00 for a 5 hour shift on his summer job. The amount of money he earns varies directly to the number of hours worked. find the constant k, and the amount of money , he will earn for an 8-hour shift
Answers
Answer:
Below
Step-by-step explanation:
k = 280 / 5 = Php 56 /hr
money earned = k x where x = # of hours
For 8 hours : money earned = 56 * 8 = Php 448
What is the end behavior of the function f(x) = -5x³ + 2x² - 4x+6?
O down to the left, up to the right
O up to the left, down to the right
O up to the left, up to the right
Odown to the left, down to the right
Answers
Answer:
O up to the left, down to the right
Step-by-step explanation:
The function in your question will do the same thing that
f(x) = -x³ does.
Actually, even simpler, it will have the same end behavior as
f(x) = -x
which is just a line with negative slope, going down from left to right. The way end behavior is described: up to the left and down to the right.
In fact, all the functions with odd power as the biggest exponent will have the same end behavior.
(If the highest exponent is even, it acts like a parabola up+up or down+down.)
Eve play baketball. She make 4 free throw for every 3 free throw that he mie. If he mied 27 free throw at her lat practice, how many free throw did he make?
Answers
Using this probability, he would have to make 42.18% or 42 free throws, thus avoiding 27 free throws.
Averaged over 3 out of 4 free throws, the probability of a successful free throw is 0.75 and the probability of a missed free throw is 0.25.
There are several ways to score 3 of the 4 free throws.
Miss Hit Hit Hit
Hit Miss Hit Hit
Hit Hit Hit Hit Hit
So to calculate this probability we need to multiply the probability of each shot. Because when it comes to multiplication, the order of multiplication doesn't matter, it's just the numbers that matter, only her 4-day probability that the shot will be taken. be the same.
So 0.75 x 0.75 x 0.75 x 0.25 = 0.10546875
Since there are 4 ways to take a 3/4 shot, we have to multiply this by 4, so 4 x 0.10546875 = 0.4218 = 42.18% shot will be taken.
So 0.75 x 0.75 x 0.75 x 0.25 = 0.10546875
Since there are 4 ways to take a 3/4 shot, we have to multiply this by 4, so 4 x 0.10546875 = 0.4218 = 42.18%.
Hence, Eve had to make 42 free throws for getting 27 throws are mied.
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Which is greater -2/5 or -3/8 ?
Answers
Answer:-2/5
Step-by-step explanation: due to them being negative we are using the simple thing of which number is closer to zero. -2/5 is closer which means that is it greater. -2/5 would be ahead on number line if you need a visualization
Answer:
-3/8
Step-by-step explanation:
1) Work out the options you are given
-2/5 = -0.4-3/8 = -0.3752) Find which one is greater
As the numbers are decimal the 'seemingly greater number' might actually be the smaller one.
To find out which decimal is greater you can easily plot them into a number line.
The number that is further to the left is smaller and the number closer to the right is higher!
If we were to plot the numbers one a number line the -0.375 would be closer to the right meaning it is greater.
HINTS:
To make it easier to divide minus numbers, at first completely forget about the minus (you can plug it back in at the end).
For example, if you were given -2/5 get rid of the minus to get 2/5 and from this we can easily figure out 2 ÷ 5 which would give us 0.4.
At the point where you have your final number you can add the - back in making it -0.4
Hope this helps, have a great day!
Alice changes size several times. The ratio of her orginal height to her second height is 24 to 5. The ratio of her second height ot he rthird height is 1 to 12. The ratio of her orginal height to her fourth height is 16 to 1. The tallest of these four heights is 10 feet. What is her shortest height?
Answers
Answer:
3 inches
Step-by-step explanation:
Let's call the heights H1 thru H4.
So we have
H1/H2 = 24/5
H2/H3 = 1/12
Therefore if we multiply these, we have
H1/H3 = 2/5
Finally we are given
H1/H4 = 16/1.
By logic we can see that H3 is the tallest.
Thus if H3 = 10 feet, H1 = 4 feet
And from that,
H2 = 1/12 (10 feet) = 5/6 feet = 10 inches
and finally
H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot =
3 inches
Answer:
3 inches
Step-by-step explanation:
Let's call the heights H1 - H4
Here, we have
H1/H2 = 24/5
H2/H3 = 1/12
And so, we have
H1/H3 = 2/5
Finally
H1/H4 = 16/1.
Thus if H3 = 10 feet, H1 = 4 feet
And from that,
H2 = 1/12 (10 feet) = 5/6 feet = 10 inches
And last,
H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot = 3 inches
A 236-inch pipe is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
Answers
let length of one piece = x
length of other piece = 236-x
one piece is three times the length of the other
x=3(236-x)
x=708-3x
4x=708
x=177
so first piece is 177 inches long and second piece is (236-177)= 59 inches long
Answer:
first piece is 177 inches long and second piece is (236-177)= 59 inches long
Step-by-step explanation:
x=3(236-x)
x=708-3x
4x=708
x=177
The cost of endless chicken wings at Restaurant X is $4. The cost of chicken wings at Restaurant Z is 20 cent per wing plus a $1.60 charge for sauce. The total cost, c, of n chicken wings at either restaurant can be represented by an equation. Write and graph a system to find how many chicken wings you have to have for the cost to be the same at both restaurants.
Answers
Answer:
Step-by-step explanation:
Equation: $4 = 0.2x + $1.60
1. Subtract $1.60 from both sides to get $2.4 = 0.2x
2. Divide both sides by 0.2 to get the value of x. 12 = x.
ANSWER: You need to buy 12 chicken wings at restaurant Z for the cost to be the same. Hope this helped
1. (5x10^-4)x(3x10^-5) in standard form
2. (2.8x10^9) divided by (7x10^5) in standard form
3. (2x10^-14) divided by (4x10^-6) in standard form
Answers
the given numbers in standard form can be expressed as :
1. 1.5 × [tex]10^-10[/tex]
2. 4 × [tex]10^1 ^3[/tex]
3. 5 × [tex]10^-^2^1[/tex]
What do you mean by standard form ?Standard form refers to any number that can be expressed as a decimal number and falls within the range of 1.0 and 10.0 when multiplied by a power of 10. The standard form of 123,000,000 is 1.23 108 because, if you look closely, 1.23 is a decimal number between 1.0 and 10.0.
1. The given numbers are (5x10^-4)x(3x10^-5)
On multiplying the natural numbers first we get :
15 × [tex]10^{-9}[/tex]
1.5 × [tex]10^-10[/tex]
2. The given numbers are (2.8x10^9) and (7x10^5)
on dividing them we get
0.4 ×[tex]10^1 ^4[/tex]
4 × [tex]10^- ^1[/tex] ×[tex]10^1 ^4[/tex]
4 × [tex]10^1 ^3[/tex]
3. The given numbers are (2x10^-14) divided by (4x10^-6)
Thus after dividing the natural numbers we will get
0.5 ×[tex]10^- ^2 ^0[/tex]
On further simplifying we get
5 × [tex]10^ -^1[/tex] ×[tex]10^- ^2 ^0[/tex]
5 × [tex]10^-^2^1[/tex]
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What is the slope of the line?
Write the slope as a fraction.
Answers
Answer: the slope is 1/4
Step-by-step explanation:
(2,0.5) (4,1)
Use the formula for finding the slope:
[tex]\boxed {The\ slope=\frac{y_2-y_1}{x_2-x_1} }[/tex]
[tex]x_1=2\ \ \ \ x_2=4\ \ \ \ y_1=0.5\ \ \ \ y_2=1\\[/tex]
Hence,
[tex]\displaystyle\\The\ slope=\frac{1-0.5}{4-2}\\\\The\ slope=\frac{0.5}{2}\\\\The\ slope=0.25\\\\The\ slope=\frac{1}{4}[/tex]
need help, please and thank you
Answers
The length of the chord of the circle CD is 3.2.
What is a chord of the circle?A chord of a circle is a section of a straight line whose ends both fall on an arc of a circle. A secant line, often known as secant, is a chord's infinite line extension.
Given that the vertical length from the centre to the chord is 2.1 and the length up to the circle is 1.7.
Radius = 1.7 +2.4 = 4.1.
The chord length will be calculated as,
CD = √(4.1² - 2.4²)
CD = √(16.81 - 5.76)
CD = 3.2
Therefore, the length of the chord of the circle CD is 3.2.
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