Answer:
An outlier is the number that is much smaller or larger than the other numbers.
In this case it is 29 :)
Answer:
D: 29
Step-by-step explanation:
D: 29 is your outlier. It's quite different from the commonest values (which are in the range 8 - 17).
Find the missing lengths of the sides.
Answer:
b = 8√3 and c = 16
Step-by-step explanation:
Points to remember
If the angles of a right angled triangle with angles are 30°, 60, and 90 the their sides are in the ratio 1 : √3 : 2
To find the unknown side lengths
From the given figure we can see a right angled triangle
Angles are 30°, 60° and 90°
sides are in the ratio 1 : √3 : 2
1 : √3 : 2 = 8 : b : c
b = 8√3 and c = 8 * 2 = 16
Therefore b = 8√3 and c = 16
Nicole's cleaning company uses a linear model to determine the amount they charge their clients. They charged $144 for a cleaning job that took 4 hours. They charged $188 for a cleaning job that took 6 hours. Which equation could be used to determine the amount charged, C, for a cleaning job that takes t hours?A.C = 10t + 104B.C = 36t C.C = 44t + 56D.C = 22t + 56
Answer:
D
Step-by-step explanation:
Let the following point represent the first job: (4, $144). Let (6, $188) represent the second. Then we find the equation of the line through these two points. As we go from (4, $144) to (6, $188), x increases by 2 and y increases by $44. Thus, the slope of this line is m = rise/run = $44/(2 hrs), or $22/hr.
Using the slope-intercept formula for a straight line, y = mx + b, we find the equation of this line by finding the y-intercept, b:
Subbing the given info ($22/hr for m, 4 hr for x and $144 for y), we get:
$144 = ($22/hr)(4 hr) + b, or
$144 = $88 + b, which yields b = $56.
Thus, the desired equation is y = mx + b, or y = ($22/hr)x + $56. This matches the last answer (D)
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The graph of the function f(x) = x^3 – 7x – 6 intersects the x-axis at the points (–2, 0), (–1, 0), and (3, 0) as shown.
Which expression is equivalent to x^3 – 7x – 6?
The answer is D, (x + 1) (x + 2) (x - 3)
Answer: D) (x + 1))x + 2)(x - 3)
Step-by-step explanation:
The x-intercepts help us to form the equation of the curve:
(-2, 0) (-1, 0) and (3, 0)
--> x = -2, x = -1, x = 3
--> x + 2 = 0 x + 1 = 0 x - 3 = 0
--> (x + 2) × (x + 1) × (x - 3) = 0
This is the reverse order for the Zero Product Property
Subject Algebra 1
If [tex]y=3x^{2} + x^{2} -5[/tex] and [tex]z=x^{2} -12[/tex] which polynomial is equivalent to [tex]2(y+z)[/tex]?
Answer:
[tex]10x^{2}-34[/tex]
Step-by-step explanation:
Because we are told equivalent expressions for y and z we can plug those in to 2(y+z).
[tex]2((3x^{2}+x^{2}-5)+(x^{2}-12))[/tex]
Then simplify by combining like terms of the expressions. Values ending in x^2 can be combined with each other.
[tex]2(5x^{2}-17)[/tex]
Now we can distribute the 2 by multiplying each value in the parentheses by 2.
[tex]10x^{2}-34[/tex]
The explicit rule for a sequence is an=5(−2)^n−1
What is the recursive rule for the sequence?
1) an=−2(an+1)
a1=5
2) an=−5(an+1)
a1=2
3) an=−2(an−1)
a1=5
4) an=−5(an−1)
a1=2
Answer:
3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]
Step-by-step explanation:
Given that the explicit rule for a sequence is [tex]a_n=5(-2)^{n-1}[/tex].
Now we need to find about what is the recursive rule for the sequence and match with the given choices to find the correct choice.
1) [tex]a_n=-2a_{n+1}[/tex], [tex]a_1=5[/tex]
2) [tex]a_n=-5a_{n+1}[/tex], [tex]a_1=2[/tex]
3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]
4) [tex]a_n=-5a_{n-1}[/tex], [tex]a_1=2[/tex]
Plug n=1 into given formula to get first term
[tex]a_n=5(-2)^{n-1}[/tex]
[tex]a_1=5(-2)^{1-1}=5(-2)^{0}=5(1)=5[/tex]
base of the exponent part is (-2) so that means we need to multiply -2 to the previous term to get nth term
Hence correct choice is: 3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]
Answer:
3) an=−2(an−1)
a1=5
Step-by-step explanation:
A dice game pays a player $5 for rolling a3 ot a 5 with a single die. the player has to pay $2 for any other roll. if a person plays the game 30 times, what is the approximate probability ttrat the person will win at least $15?
The approximate probability that the person will win at least $15 is 0.255.
To solve this problem, we need to calculate the probability of winning at least $15 after playing the game 30 times. Winning at least $15 means that the player must win on at least 6 rolls because winning once pays $5, and $5 times 6 is $30, which is the minimum needed to have a net gain of $15 ($30 won - $15 lost).
First, let's calculate the probability of winning in a single roll. The player wins if they roll a 3 or a 5, which are two favorable outcomes out of six possible outcomes.
[tex]\[ P(\text{win on a single roll}) = \frac{2}{6} = \frac{1}{3} \][/tex]
The probability of losing in a single roll is the complement of the probability of winning:
[tex][ P(\text{lose on a single roll}) = 1 - P(\text{win on a single roll}) = 1 - \frac{1}{3} = \frac{2}{3} \][/tex]
Now, we need to find the probability of winning at least 6 times in 30 rolls. This can be modeled using the binomial probability formula:
[tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \][/tex]
where [tex]\( n \)[/tex] is the number of trials (30 in this case), [tex]\( k \)[/tex] is the number of successes (at least 6), [tex]\( p \)[/tex] is the probability of success on a single trial [tex](\( \frac{1}{3} \)), and \( \binom{n}{k} \)[/tex] is the binomial coefficient.
We want to calculate the probability of winning at least 6 times, which is the sum of the probabilities of winning exactly 6, 7, .. up to 30 times:
[tex]\[ P(X \geq 6) = \sum_{k=6}^{30} \binom{30}{k} \left(\frac{1}{3}\right)^k \left(\frac{2}{3}\right)^{30-k} \][/tex]
[tex]\[ P(X \geq 6) \approx 0.255 \][/tex]
please help me and plz explain thoroughly i need help asap!
Given the function f(x) = 2(x + 8), find x if f(x) = 12.
2
40
−2
14
f(x) = 2(x+8)
replace f(x) with 12 and then solve for x:
12 = 2(x +8)
Use the distributive Property on the right side:
12 = 2x +16
Subtract 16 from each side:
-4 - 2x
Divide both sides by 2:
x = -4 / 2
x = -2
Answer:
−2
Step-by-step explanation:
f(x) = 2(x+8)
f(x) = 12
12 = 2(x+8)
Divide each side by 2
12/2 = 2/2(x+8)
6 = x+8
Subtract 8 from each side
6-8 =x+8-8
-2 = x
Someone please help??
Answer:
x = 1
Step-by-step explanation:
The base is 3. The value of 3^x will be 3 only when x=1.
_____
The value of any exponential term will be equal to the base when the exponent is 1.
Find x to the nearest hundredth.
7.73 cm
8.12 cm
20.46 cm
23.78 cm
Answer:
23.78
Step-by-step explanation:
CAH
x/25
cos18=x/25
25cos18=x
x=23.78
Answer:
23.78 cm
Step-by-step explanation:
Since, We know that,
In a right angle triangle,
[tex]cos \theta=\frac{B}{H}[/tex]
Where, B represents base adjacent to [tex]\theta[/tex]
H represents the hypotenuse adjacent to [tex]\theta[/tex]
Thus, by the given diagram,
[tex]cos 18^{\circ}=\frac{x}{25}[/tex]
[tex]\implies x = 25\times cos 18^{\circ}=23.7764129074\approx 23.78\text{ cm}[/tex]
Hence, Last option is correct.
DO,h = (7,9) —> (14,18) the scale factor is ____.
Answer:
option B
2
Step-by-step explanation:
Given in the question
DO,h(7, 9) → (14, 18)
Formula to use
√(x1-x2)²+(y1-y2)²distance formula = √((7-0)²+(9-0)²) = √(7²+9²) = √130
distance formula = √((14-0)²+(18-0)²) = √(14²+18²) = 2√130
Scale factor
√130 = 2√130
d = 2d
Lucy and Katy are registering for a sports league for next year. There are 222 sports (volleyball and basketball) and 333 seasons (fall, winter, and spring) to choose from. They each created a display to represent the sample space of randomly picking a sport and a season. Whose display correctly represents the sample space?
Answer:
A. Lucy Only
Step-by-step explanation:
Got it right on Khan Academy
The possible sample space is: FV, WV, SV, FB, WB, and SB
What is probability?Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes
As, the sample space with all possibilities in which lucy and katy register a sports League.
Now, they have 2 sports and 3 seasons for the Sample space.
Mow let us consider, V is registered for Volleyball and B is registered for basketball .
and, F is registered Fall, W is registered for Winter and S is for Spring.
so, that the sample space is:
FV, WV, SV, FB, WB, and SB
where, FV is the registered possibility for fall and in volleyball.
WV is the registered possibility for Winter and in volleyball.
SV is the registered possibility for Spring and in volleyball.
and so on..
Therefore, the correctly representation for the sample space is the one that has all these possibilities.
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Combine the following expressions:
ANSWER
[tex](4n - 1)\sqrt{3 n} + 3\sqrt{n}[/tex]
EXPLANATION
The given expression is
[tex] \sqrt{48 {n}^{3} } + \sqrt{9n} - \sqrt{3n} [/tex]
We remove the perfect squares under the radical sign.
[tex]\sqrt{16 {n}^{2} \times3 n} + \sqrt{9n} - \sqrt{3n} [/tex]
We can now take square root of the perfect squares and simplify them further.
[tex] \sqrt{16 {n}^{2}} \times \sqrt{3 n} + \sqrt{9} \times \sqrt{n} - \sqrt{3n} [/tex]
This simplifies to:
[tex]4n\sqrt{3 n} + 3\sqrt{n} - \sqrt{3n} [/tex]
This further simplifies to:
[tex](4n - 1)\sqrt{3 n} + 3\sqrt{n} [/tex]
Answer:
Option B is Correct
Step-by-step explanation:
[tex]\sqrt{48n^3}+\sqrt{9n} - \sqrt{3n}[/tex]
We need to solve the above expression.
48 can be written as: 2x2x2x2x3
9 can be written as : 3x3
Putting values
[tex]\sqrt{2*2*2*2*3*n*n*n} +\sqrt{3*3*n}-\sqrt{3n}[/tex]
2*2 = 2^2 and n*n = n^2 and 3*3 = 3^2
we also know √ = 1/2
so, putting these values we get,
[tex]\sqrt{2^2*2^2*3*n^2*n} +\sqrt{3^2*n}-\sqrt{3n}\\(2^2)^{1/2} * (2^2)^{1/2} * (3)^{1/2} * (n^2)^{1/2} * n ^{1/2} + ((3^2)^{1/2} *n^{1/2}) -(\sqrt{3n})\\2*2*n * (3^{1/2} *n ^{1/2}) +(3 +n^{1/2}) -(\sqrt{3n})\\4n (\sqrt{3n})+(3 \sqrt{n}) -(\sqrt{3n})\\Rearraninging\\4n(\sqrt{3n}) - (\sqrt{3n})+(3 \sqrt{n})\\Taking \,\,\sqrt{3n} \,\,common\,\, from\,\, 1st\,\, and\,\, 2nd\,\, term\\\sqrt{3n}(4n-1)+(3 \sqrt{n})\\or \,\,it\,\,can\,\,be\,\,written\,\,as\,\,\\(4n-1)\sqrt{3n}+(3 \sqrt{n})[/tex]
So, Option B is Correct.
Which of the following are true statements? Check all that apply.
Answer:
Your answer is D.
Step-by-step explanation:
Although A and C are also correct, according to a graph using the free online program Desmos
Ms.Holmes decided to water her plants.She had 2 1/2 gallons of water.She gave each plant 1/4 gallon of water.Which expression could be used to determine how many plants Ms.Holmes had?
To determine how many plants Ms. Holmes had, divide the total amount of water she had by the amount of water she gave each plant. The expression that can be used is (2 1/2 gallons) divided by (1/4 gallon per plant). Simplifying the expression gives the answer of 10 plants.
Explanation:To determine how many plants Ms. Holmes had, we can divide the total amount of water she had (2 1/2 gallons) by the amount of water she gave each plant (1/4 gallon per plant).
So, the expression that can be used is (2 ½ gallons) ÷ (1/4 gallon per plant). To divide a fraction by a fraction, we multiply the first fraction by the reciprocal of the second fraction. Therefore, the expression simplifies to (2 ½ gallons) × (4 gallons per plant).
Simplifying further, we get 10 gallons. This means that Ms. Holmes had 10 plants.
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At a school supply store, binders cost $5 and pencil pouches cost $2. In one day, 42 of these items are sold for total sales of $144. Which system represents this (b represents binders and p represents pencil pouches), and how many binders were sold?
Answer:
Part 1) The system of equations that represent this situation is equal to
b+p=42 and 5b+2p=144
Part 2) 20 binders were sold
Step-by-step explanation:
Let
b -----> the number of binders sold
p -----> the number of pencil pouches sold
Part 1)
we know that
The system of equations that represent this situation is equal to
b+p=42
5b+2p=144
Part 2) How many binders were sold?
we have
b+p=42
p=42-b ------> equation A
5b+2p=144 -----> equation B
substitute equation A in equation B
5b+2(42-b)=144
5b+84-2b=144
3b=144-84
3b=60
b=20 binders
The length of a rectangle is 3 meters more than the width. The perimeter of the rectangle is 26 meters. If the width is b, which equation represents the situation? How many solutions will this equation have?
Answer:
Thehe answer is 75
Step-by-step explanation:
Answer with Step-by-step explanation:
The length of a rectangle is 3 meters more than the width.
If the width is b.
⇒ Length=b+3
The perimeter of the rectangle is 26 meters.
Since, Perimeter=2(Length+width)
⇒ 2(b+3+b)=26
dividing both sides by 2
⇒ b+3+b=13
⇒ 2b=13-3
⇒ 2b=10
dividing both sides by 2
⇒ b=5
⇒ Width=5 meter
and Length=5+3=8 meter
which equation represents the situation: 2(b+3+b)=26How many solutions will this equation have: UniqueFranco needs to pack 125 bottles of juice. Each box holds 8 bottles. How many boxes are needed to pack all of the juice?
Answer:
16 Boxes
Step-by-step explanation:
Total Bottles:125
Amount of Bottles A Box Is Able To Hold:8
125/8=15.625
Round Up To Nearest Whole Number
16 Boxes Are Needed To Hold 125 Bottles
Rewrite in a form that does not use exponents
Answer:
[tex]\boxed{18}[/tex]
Step-by-step explanation:
One of the rules of logarithms is ...
log(a^b) = b·log(a)
So ...
[tex]6\log_5{x^3}=6(3\log_5{x})=\bf{18}\log_5{x}[/tex]
A recipe includes 4 cups of flour and 2/3 cup of brown sugar. Write the ratio of the amount of flour to the amount of brown sugar as a fraction in simplest form.
Answer:
6/1
Step-by-step explanation:
So we are looking for a ratio of flour which is 4 and brown sugar which is 2/3.
So we divide 4 by 2/3.
4÷2/3 since we are diving by a fraction we keep 4÷2/3 change 4*2/3 flip 4*3/2. So now we are multiplying 4 and 3/2.
So that is 4/1*3/2= 12/2 that simplies to 6/1
Answer:
⁶/₁
Step-by-step explanation:
4 cups of flour, ⅔ cup of brown sugar. The ratio of flour to brown sugar is:
4 / ⅔
We need to simplify this. First, write 4 as a fraction:
⁴/₁ / ⅔
To divide by a fraction, multiply by the reciprocal:
⁴/₁ × ³/₂
¹²/₂
⁶/₁
Write the equation −2x−4y=−8 in slope-intercept form. Then graph the line described by the equation.
Answer:
y=-1/2x+2 start at y-intercept 2 and go down by 1 and right by 2
Step-by-step explanation:
The slope-intercept form of the equation −2x−4y=−8 is y = 0.5x + 2. Starting from the y-intercept (0,2), the graph of this line is drawn by moving a half unit up and one unit to the right from the intercept.
Explanation:The given mathematical equation is −2x−4y=−8. To convert this equation into slope-intercept form (y=mx+b), we want to isolate y. Start by dividing every term by -4, which simplifies the equation to 0.5x + y = 2. In this equation, the slope (m) is 0.5, and the y-intercept (b) is 2.
To graph this line, start by plotting the y-intercept (b) at the point (0, 2) on the y-axis. The slope (m) is 0.5, which we can interpret as a rise of 0.5 units for every run of 1 unit. So, from the y-intercept, move up half a unit and right one unit to plot your second point. Drawing a straight line through these points will give you the graph of your equation.
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Which of the following are possible rational roots of the polynomial function f(x)=5x^2-3x+3
You didn't post any option, but the ration roots theorem states that all possible rational roots of a polynomial come in the form
[tex]\pm\dfrac{p}{q}[/tex]
where p divides the constant term and q divides the leading term of the polynomial. So, in your case, p divides 3 (i.e. it is 1 or 3), and q divides 5 (i.e. it is 1 or 5).
So, the possible roots are
[tex]\pm 1,\quad \pm 3,\quad \pm\dfrac{1}{5},\quad \pm\dfrac{3}{5}[/tex]
For the record, this parabola has no real roots.
The possible rational roots of the polynomial function f(x) = 5x² - 3x + 3 are;
±1/5, ±3/5, ±1, ±3
We are given the polynomial function;
f(x) = 5x² - 3x + 3
The rational root theorem states that for a polynomial to have any rational roots, then the roots must be of the form;
±(Factors of coefficient of constant term/factors of the coefficient of the highest power)
Now, the coefficient of the highest power is 5 and the constant term is 3.
Factors of 5 = 1, 5
Factors of 3 = 1, 3
Thus, the possible rational roots are;
±1/5, ±3/5, ±1, ±3
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Maryanne began a job that gives her 3 days of vacation each year she is employed up to a maximum of 24 days of vacation time. How many years will she be at the company before she reaches the maximum amount of vacation time?
Answer:
8 years
Step-by-step explanation:
Answer:
she will be at the company for 8 years.
Step-by-step explanation:
The number of days of vacation for each year = 3
Maryanne is employed up to a maximum of 24 days of vacation time.
We need to find the number of years she will be in the company before she reaches the maximum amount of vacation of time.
The number of years she will be in the company = The number of maximum days of vacation time divided by the number of days of vacation for each year
= [tex]\frac{24}{3}[/tex]
= 8 years
Therefore, she will be at the company for 8 years.
A survey showed that hamburgers are preferred to hot dogs 5 to 3. What percent of those surveyed prefer hamburgers
Final answer:
62.5% of those surveyed prefer hamburgers.
Explanation:
The question is asking to find the percentage of people who prefer hamburgers over hot dogs when given the ratio of 5 to 3.
To calculate this, you would add the two parts of the ratio together to get the total number of parts, which is 5 + 3 = 8.
The number of parts that represent hamburgers is 5.
To find the percentage, you would divide the hamburger part by the total number of parts and then multiply by 100.
This gives you (5/8) × 100, which equals 62.5%.
Therefore, 62.5% of those surveyed prefer hamburgers.
Please help me out with this
Answer:
[tex]\frac{9}{64}[/tex] π in²
Step-by-step explanation:
The area (A) of the circle is calculated using the formula
A = πr² ← r is the radius
here the diameter = [tex]\frac{3}{4}[/tex]
and radius is half the diameter, hence
r = [tex]\frac{3}{8}[/tex], so
A = π × ([tex]\frac{3}{8}[/tex] )² = [tex]\frac{9}{64}[/tex] π in²
What us the length of the altitude of the equilateral triangle below
Answer:
Height ( h) = 12 units.
Step-by-step explanation:
Given : An equilateral triangle with side = 8 √3.
To find : What us the length of the altitude of the equilateral triangle .
Solution : We have given equilateral triangle with side = 8 √3.
By taking the half triangle,
By the Pythagorean theorem :
(Hypotenuse)² = ( adjacent)² + (opposite)².
Plug the values Hypotenuse = 8√3 , adjacent = 4√3 , opposite = h.
(8√3)² = ( 4√3)² + (h)².
192 = 48 + (h)².
On subtracting by 48 both sides.
192 -48 = (h)².
144 = (h)².
On taking square root .
h = 12 .
Therefore, Height ( h) = 12 units.
The guy is right trust me mate
for the dilation, Do, k = (10, 0 ) —> (5,0) , the scale factor is equal to ____.
•-5
•5
•0.5
•2
Answer:
•0.5
Step-by-step explanation:
We'll assume the dilation was done at the origin point, so it was done evenly.
Since the k point went from (10,0) to (5,0), we know it was reduced... so the scale factor has to be below 1. A scale factor means the size wasn't changed and a dilation/scale factor larger than 1 means it was enlarged.
So, we take the new X-value (5) and divide it by the original X-value (10).
Scale factor = 5/10 = 1/2... so 0.5
A circle has a diameter of 8 m. What is the approximate area of the circle? 200.96 m2 12.56 m2 25.12 m2 50.24 m2
Answer:
50.24
Step-by-step explanation:
area of a circle =pi r^2
diameter = 2 * radius
radius=8/2=4
area=pi 4^2
=pi 16
=50.26
Find the cosine of angle p
Answer: last option
Step-by-step explanation:
You need to remember the identity:
[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]
You need to find the cosine of angle P, then, you can identify in the figure that:
[tex]adjacent=PR=21\\hypotenuse=PQ=29\\\alpha=P[/tex]
Therefore, the next step is substitute these values into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex], then you get:
[tex]cos(P)=\frac{21}{29}[/tex]
You can observe that this matches with the last option.
Can someone help me with these questions please?
1. Which function pass through the points (1, 4), (2, 9), and (3, 16)?
y = (x + 1)2
y = (x + 3)2
y = 7x - 5
2. Suppose that after swimming 1 lap in a pool, you can swim 10 laps in an hour. What is an equation that represents the total number of laps you have swam y in terms of the number of hours x?
y(x) = 10 + x
y(x) = 10(x + 1)
y(x) = 10x + 1
3. Is the following an arithmetic sequence? If so, what is the common difference? {4, 2, 0, -2, -4, -6, …}
Yes, d = -2
No
Yes, d = 2
4. Which function has the following graph?
y = -2x + 4 b. y = 2x + 4 c. y =12x + 4
5. What is the slope of the line containing (3, 5) and (2, 7)?
m = 2 b. m = -2 c. m = 125
6. The graph of a line passes through the point (-3, 2) and has a slope of 4. What is an equation of the line?
y = 4x - 10
y = 4x - 11
y = 4x+ 14
7. Which line is parallel to y = 4x - 2?
y = -14x + 3
y = -4x + 5
y = 4x + 5
8. Which system of equations has (2, 3) as a solution?
y = 2x - 1 b. y = 2x + 1 c. y = 4x - 5
y = x + 1 y = x - 1 y = 2x
Answer:
the first function, y = (x + 1)^2, does pass through the points (1, 4), (2, 9), and (3, 16).
Step-by-step explanation:
Note that 4, 9 and 16 are squares of 2, 3 and 4. So it's likely that the parent function is of the form f(x) = x^2. Note that f(1) = 1, f(2) = 4, f(3) = 9 and f(4) = 16.
Let's now determine whether these three points satisfy the first given equation, y = (x + 1)^2: Does 4 = (1 + 1)^2? Does 4 = 2^2? YES.
Does 9 = (2 + 1)^2? Does 9 = 3^2? YES
Does 16 = (3 + 1)^2? YES
So the first function, y = (x + 1)^2, does pass through the points (1, 4), (2, 9), and (3, 16).
Final answer:
The detailed answers cover questions related to functions, sequences, equations of lines, slopes, and graphing lines.
Explanation:
Question 1:
The function that passes through the points (1, 4), (2, 9), and (3, 16) is y = (x + 1)^2.
Question 2:
The equation representing the total number of laps swum y in terms of hours x is y(x) = 10x + 1.
Question 3:
The sequence {4, 2, 0, -2, -4, -6, …} is an arithmetic sequence with a common difference of -2.
Question 5:
The slope of the line containing (3, 5) and (2, 7) is m = -2.
Question 6:
For a line passing through (-3, 2) with a slope of 4, the equation of the line is y = 4x + 14.
Please Help!
When Mario has to leave the house for a while, he tethers his mischievous puppy to the corner of a 12 ft-by-8 ft shed in the middle of his large backyard. The tether is 18 feet long. Which description fits the boundary of the locus of points in the yard that the puppy can reach?
A. semicircles of radii 18 ft, 10 ft, and 6 ft
B. a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
C. semicircles of radii 18 ft, 12 ft, and 8 ft
D. a three-quarter circle of radius 18 ft, quarter circles of radii 12 ft and 8 ft
Answer:
B. a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
Step-by-step explanation:
A diagram can be a useful aid to answering this question. At one corner of the shed, 8 ft of rope is no longer available, so the quarter circle has a radius of 18-8 = 10 ft. (That side of the shed is 12 ft, so the area is only a quarter circle.)
At the other corner of the shed, 12 ft of rope is no longer available, so the quarter circle has a radius of 18-12 = 6 ft. (That side of the shed is 8 ft, so the area is only a quarter circle.)
In the attached diagram, the 3/4 circle with radius 18 ft is shown red, and the quarter circles are shown in green.