Answer:
f(x) = 2+5
g(x) = 2(-(x−3))+5
Step-by-step explanation:
If you remember, an absolute value can have two different answer, a positive and negative answer because the absolute value symbol makes all values in it positive. Example: |-2|=2 and |2|=2
So if y = 2|x−3|+5
then the two possibilities are
y = 2(x−3)+5 and
y = 2(-)+5
Set one of them equal to f(x) and the other one to g(x)
f(x) = 2(x−3)+5
g(x) = 2(-(x−3))+5
You can also write it as a piecewise function.
[tex]y(x)=$\begin{array}{cc} \{ & \begin{array}{cc} -(x-3) & x<3 \\ 0 & x=3 \\ (x-3) &x>3 \end{array}\end{array}$[/tex]
Match each circular flower bed on the left to its circumference and its area on the right. Some answer options on the right will not be used.
To find the circumference of a circle, use the formula C = 2πr. To find the area, use the formula A = πr^2.
Explanation:The question asks to match each circular flower bed on the left to its circumference and its area on the right. In order to find the circumference of a circle, we use the formula C = 2πr, where r is the radius of the circle.
To find the area of a circle, we use the formula A = πr^2. We can use these formulas to calculate the circumference and area of each circular flower bed and match them to the options on the right.
For example, if a circular flower bed has a radius of 3 meters, we can find its circumference by plugging the radius into the formula: C = 2π(3) = 6π meters. Similarly, we can find its area by plugging the radius into the formula: A = π(3^2) = 9π square meters.
The human appendix has no known function
Which term applied to structures like this?
O adaxial
O homologous
O obligatory
O vestigial
Answer:
Vestigial.
Step-by-step explanation:
It might have had a use in the past and man's evolution has rendered it of no known use.
A certain number was multiplied by 7.4 was then taken away from the product. Finally that difference was then divided by 9, resulting in 5. Find the initial number.
The initial number is 7.
Step-by-step explanation:
Let the initial number be 'x'.
The number was multiplied by 7 ⇒ 7x4 was then taken away from the product ⇒ 7x-4That difference was then divided by 9 resulting in 5 ⇒ (7x-4)/9 = 5⇒ 7x-4 = 45
⇒ 7x = 49
⇒ x = 7
The initial number is 300. Multiply by 7.4 to get 2220, subtract 2220, then divide by 9 to get 247. Confirming: 7.4(300) - 2220 = 247(9) = 5.
Let's denote the initial number as ( x ). According to the given information:
1. Multiply by 7.4: ( 7.4x )
2. Take away from the product: ( 7.4x - (7.4x) )
3. Finally, divide by 9:[tex]\( \frac{{7.4x - 7.4x}}{9} \)[/tex]
We know that this resulting expression equals 5:
[tex]\[ \frac{{7.4x - 7.4x}}{9} = 5 \][/tex]
Now, let's solve for ( x ):
[tex]\[ \frac{{0}}{9} = 5 \][/tex]
As ( 7.4x ) cancels out, we are left with ( 0 = 5 ), which is not a valid equation.
Polynomial functions with an even degree have y-axis symmetry
Polynomial functions with an even degree have y-axis symmetry is a true statement.
Explanation:
A function symmetrical with respect to the y-axis is called an even function. A function that is symmetrical with respect to the origin is called an odd function. f(x). Since f(−x) = f(x), this function is symmetrical with respect to the y-axis.
So a function that has an even degree in it, be it a polynomial function, has a y-axis symmetry always. The equations with odd degrees may or may not have a y axis symmetry.
A train has 3 passenger cars and each car has 4 columns of seats and each column holds 40 passengers. If one of the cars has 15 people standing in addition to all of the sitting passengers, and the rest of the cars are full without anyone standing, how many passengers are on the train?
Answer:
There are a total of 495 people on the train
Step-by-step explanation:
Let's identify what we know:
1) The train has 3 passenger cars
2) Each passenger car has 4 columns, and each can accommodate 40 people.
3) All three passenger cars are full, but one of them has 15 additional people standing.
We can create a formula to model the problem:
x = ((3 x 4) x 40) + 15
x = the total number of passengers!
There are a total of 180 people sitting, and 15 additional people standing in one of the passengers cars, equaling a total of 495 passengers on the train.
The train has a total of 495 passengers.
Explanation:To calculate the number of passengers on the train, we first need to determine the seating capacity of each car. Since each car has 4 columns of seats and each column holds 40 passengers, each car can seat a total of 4 x 40 = 160 passengers.
Next, we need to account for the 15 people standing in one of the cars. This means that one car has 160 + 15 = 175 passengers.
Finally, since the rest of the cars are full without anyone standing, we can assume that the other two cars also have 160 passengers each. Therefore, the total number of passengers on the train is 175 + 160 + 160 = 495.
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If r=4 units and x=8 units then what is the volume of the cylinder?
Answer:
To answer this you will use the formula V = pi x radius ^2 x height. The substitution for this would be 3.14 x 4^2 x 8. The approximate answer is 401.92 cubic units. 3.14 is an approximation of pi.
Note: It does not say that x is the height, but this is the only piece of information missing without an obvious label, so I am using it as the height.
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Step-by-step explanation:
how can you describe pi?
Step-by-step explanation:
The number π is a mathematical constant. Originally defined as the ratio of a circle's circumference to its diameter.
It is an irrational number
[tex]\pi = 3.14159265359...[/tex]
The area of a rectangular sandbox is (5x + 40) feet. Factor 5x + 40 to find possible
dimensions of the sandbox.
The possible dimensions of the sandbox are 5 and [tex](x+8)[/tex].
Important information:
The area of the rectangular sandbox is [tex]5x+40[/tex].We need to find the possible dimensions of the sandbox.
Area of a rectangle:Formula for the area of a rectangle is:
[tex]\text{Area}=\text{Length}\times \text{Width}[/tex]
Factorize the given expression to find the possible dimensions of the sandbox.
[tex]5x+40=5x+5\times 8)[/tex]
[tex]5x+40=5(x+8)[/tex]
Thus, the possible dimensions of the sandbox are 5 and [tex](x+8)[/tex].
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-8x+2y=-2
4x+4y=-4
What is the solution to the system
The solution to system is x = 0 and y = -1
Solution:
Given system of equations are:
-8x + 2y = -2 ----------- eqn 1
4x + 4y = -4 ---------- eqn 2
We have to solve the system of equations
We can solve the equations by elimination method
Multiply eqn 2 by 2
8x + 8y = -8 ------ eqn 3
Add eqn 1 and eqn 3
-8x + 2y = -2
8x + 8y = -8
( + ) ---------------
0x + 2y + 8y = -2 - 8
10y = -10
Divide both sides by 10
y = -1
Substitute y = -1 in eqn 1
-8x + 2(-1) = -2
-8x - 2 = -2
-8x = -2 + 2
x = 0
Thus the solution to system is x = 0 and y = -1
Which length is longer 64 inches or 5 feet
If Talia’s old bedroom measured 1 feet by 10 feet how much larger or smaller will her new bedroom be ?
Expression: [tex]\((x - 3)(x + 5)\)[/tex]. If original is 10 × 10, new is 105 sq ft. New is 5 sq ft larger.
1. **Expression representing the two binomials for the area of Talia's new bedroom:**
Let [tex]\( x \)[/tex] represent the original length of the square bedroom.
The original bedroom's dimensions: [tex]\( x \times x \)[/tex]
The new bedroom's dimensions: [tex]\( (x - 3) \times (x + 5) \)[/tex]
So, the expression representing the two binomials would be: [tex]\((x - 3)(x + 5)\)[/tex]
2. **Finding the difference in size between old and new bedrooms:**
If the original bedroom measured 10 feet by 10 feet, then [tex]\( x = 10 \)[/tex] (since it's a square).
Substituting into the expression: [tex]\( (10 - 3)(10 + 5) = (7)(15) = 105 \)[/tex] square feet.
So, the new bedroom's area is 105 square feet.
The original bedroom's area is [tex]\( 10 \times 10 = 100 \)[/tex] square feet.
The difference is: [tex]\( 105 - 100 = 5 \)[/tex] square feet.
Therefore, her new bedroom will be 5 square feet larger than her old bedroom.
The complete question is here:
Talia has a square bedroom. Her family is moving and her bedroom in her new apartment will be 3 feet shorter in one direction and 5 feet longer in the other direction. Write an expression that represents the two binomials you would multiply together to find the area of Talia's new bedroom.
2nd Part
If Talia's old bedroom measured 10 feet by 10 feet, how much larger or smaller will her new bedroom be?
What is the nth term of the geometric sequence -2,10,-50
Answer:
[tex]T_n=-1(-5)^n^-^1[/tex]
Step-by-step explanation:
We are given;
A geometric sequence;
-2,10,-50
Required to determine the nth term
The nth term in a geometric sequence is given by the formula;
[tex]T_n=a_1r^n^-^1[/tex]
where [tex]a_1[/tex] is the first term and r is the common ratio;
In this case;
[tex]a_1=-2[/tex]
r = 10 ÷ -2
= -5
Therefore;
To get the nth term in the given geometric sequence we use;
[tex]T_n=-1(-5)^n^-^1[/tex]
Thus, the nth term is [tex]T_n=-1(-5)^n^-^1[/tex]
Are all squares proportional?
Answer:
Yes each side will always be of the same size unless you are purposely trying to make an uneven shape
Step-by-step explanation:
Arrange the following measurement in order from smallest to largest. 2000 milititers 4.1 liters 0.7 liters
answer is
o.7 liters 2000 milliliters and 4.1 liters
Step-by-step explanation:
1 / 5
1 \text{ liter} ={1{,}000}\text{ milliliters}1 liter=1,000 milliliters1, start text, space, l, i, t, e, r, end text, equals, 1, comma, 000, start text, space, m, i, l, l, i, l, i, t, e, r, s, end text
So, 1 \text{ milliliter} = \dfrac1{1{,}000}\text{ liter}1 milliliter=
1,000
1
liter1, start text, space, m, i, l, l, i, l, i, t, e, r, end text, equals, start fraction, 1, divided by, 1, comma, 000, end fraction, start text, space, l, i, t, e, r, end text
Hint #22 / 5
We know \maroonD{0.7}0.7start color #ca337c, 0, point, 7, end color #ca337c liters is less than \greenD{4.1}4.1start color #1fab54, 4, point, 1, end color #1fab54 liters. But where does \blueD{2{,}000}2,000start color #11accd, 2, comma, 000, end color #11accd milliliters fit?
We need to convert \blueD{2{,}000}2,000start color #11accd, 2, comma, 000, end color #11accd milliliters to liters before we can compare.
Hint #33 / 5
\begin {aligned}{\blueD{2{,}000} \text{ mL}}&= {\blueD{2{,}000} \text{ mL}}\times \dfrac{1 \text{ L}}{{1{,}000 \text{ mL}}} \\\\ &= {\dfrac{\blueD{2{,}000} \cancel{\text{ mL}}}{1}}\times \dfrac{1 \text{ L}}{{1{,}000 \cancel{\text{ mL}}}} \\\\ &=\dfrac{\blueD{2{,}000}\text{ L} }{1{,}000}\\\\ &=\blueD{2{,}000}\text{ L}\div1{,}000\\\\ &=\blueD{2}\text{ L} \end{aligned}
2,000 mL
=2,000 mL×
1,000 mL
1 L
=
1
2,000
mL
×
1,000
mL
1 L
=
1,000
2,000 L
=2,000 L÷1,000
=2 L
Is 9 bigger than negative 10??
Answer:
Yes 9 is larger than -10
Step-by-step explanation:
Any positive number is larger than a negative number
Answer: yes
Step-by-step explanation: this is so because on the number line 9 comes first while -10 is far behind from -1
What is the problem answer for 25% of 450
Answer:
112.5
Step-by-step explanation:
25/100 x450/1 =
11250/100=112.5
with a head wind, it takes 7 hours to fly 2800 miles from miami to seattle. with a tailwind, and the same airspeed, it takes 5 hours to fly in the opposite direction, from seattle to miami. find the airspeed and the windspeed
Answer:
Plane speed: 480mph
Wind speed: 80mph
Step-by-step explanation:
Miami to Seattle: time = 7hrs
Speed (s) = 2800mph
D = speed/time = 2800/7
= 400mph
Seattle to Miami:
Same speed = 2800mp
Time = 5hrs
Distance (D) = speed/time
= 2800/5 = 560mph
Let p be speed of plane and w wind speed.
Therefore, P+w = 560. . .1
P-w = 400. . .2
2p = 960
P = 960/2 = 480
Therefore, P + w = 560
480 + w = 560
W = 80mph
While P = 480mph
Substitution and to solve
Answer:
x=1 y=2, there are your answers. Have a good dayStep-by-step explanation:
y=−3x+5;5x−4y=−3
Step: Solve: y=−3x+5for y:
Step: Substitute: −3x+5foryin5x−4y=−3:
5x−4y=−3
5x−4(−3x+5)=−3
17x−20=−3 (you have to simplify both sides of the equation)
17x−20+20=−3+20(then add 20 to both sides)
17x=17
17x
17
=
17
17
(Divide both sides by 17)
x=1
Step: Substitute1forxiny=−3x+5:
y=−3x+5
y=(−3)(1)+5
y=2( again Simplify both sides of the equation)
The Answer Is:
x=1 and y=2
Am I incorrect?
On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 118 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual.
b. Find the probability that a randomly selected person's IQ is over 115.
Answer:
0.5675
Step-by-step explanation:
We have that, the IQ of the ruling species is normally distributed with a mean of 118 and a standard deviation of 18.
We want to find the probability that a randomly selected person's IQ is over 115.
We need to find the z-score of 115
using
[tex]z = \frac{x - \mu}{ \sigma} [/tex]
We substitute x=115 to get:
[tex]z = \frac{115 - 118}{18} [/tex]
This implies that:
[tex]z = \frac{ - 3}{18} = - \frac{1}{6} = - 0.17[/tex]
We read from the normal distribution table to get;
P(X>115)=0.5675
By converting the IQ score of 115 into a Z score and finding the area to the right of this Z score in a standard normal distribution, we find that the probability of a randomly selected individual's IQ being over 115 is approximately 0.57 or 57%.
Explanation:To answer this question, we need to understand how a normal distribution works. A random variable X, such as an individual's IQ, that is normally distributed can be converted into a standard normal variable Z, using the formula Z = (X - mean) / standard deviation.
In our case, the mean IQ is 118 and the standard deviation is 18. Therefore, to find the probability that a randomly selected individual's IQ is over 115, we convert 115 into a Z score using the aforementioned formula: Z = (115 - 118) / 18 = -0.167. This is the Z score for an IQ of 115.
To find the probability that a randomly selected individual's IQ is more than 115, we find the area to the right of Z = -0.167. From standard normal tables, we know that the area to the left of Z = -0.167 is approximately 0.4332. Therefore, the area to the right (which is the probability we want) is 1 - 0.4332 = 0.5668.
So, the probability that a randomly selected individual's IQ is over 115 is approximately 0.57 (or 57% when expressed as a percentage).
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Ignore the stuff around it ,could someone explain me this?
Answer:
The lines blue and green are perpendicular
Step-by-step explanation:
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
step 1
Find the slope of the blue line
we have the points
(-1,-3) and (0,3)
substitute
[tex]m=\frac{3+3}{0+1}[/tex]
[tex]m=\frac{6}{1}=6[/tex]
step 2
Find the slope of the red line
we have the points
(3,-3) and (4,2)
substitute
[tex]m=\frac{2+3}{4-3}[/tex]
[tex]m=\frac{5}{1}=5[/tex]
step 3
Find the slope of the green line
we have the points
(-4,-1) and (2,-2)
substitute
[tex]m=\frac{-2+1}{2+4}[/tex]
[tex]m=-\frac{1}{6}[/tex]
step 4
Compare the slopes
Blue line ----> [tex]m=6[/tex]
Red line ----. [tex]m=5[/tex]
Green line ---> [tex]m=-\frac{1}{6}[/tex]
so
The slope of the blue line and the green line are opposite reciprocal ( their product is equal to -1)
therefore
The lines blue and green are perpendicular
Leroy is going to take a flight from Buffalo, New York, to Dallas, Texas. The
flight leaves Buffalo at 10:15 a.m. Buffalo time and arrives in Dallas at 1:33
p.m. Dallas time. If Buffalo is in the eastern time zone and Dallas is in the
central time zone, how long is the flight?
Use the following to help you answer the question,
12:00 p.m. eastern time = 11:00 a.m. central time = 10:00 a.m. mountain
time = 9:00 a.m. Pacific time.
O
A. 4 h 18 min
O
O
O
B. 5 h 18 min
C. 2 h 18 min
D. 3 h 18 min
Answer:
A- 4h 18min
Step-by-step explanation:
First you look at the data provided that shows that this is this latest time, so when it is 10:15 in buffalo, it is 9:15 in Dallas. He arrives in Dallas at 1:33, so you can either think in central time which is 9:15-1:33, or in eastern time which is 10:15-2:33. From there you can subtract 15 from 33 getting 18, and from 10 o’clock to 2 o’clock (or 9 o’clock to 1 o’clock) is 4 hours.
If the area of a square is 121cm2 what is it’s side length
Answer:
Step-by-step explanation:
Area of a square
Area = l*l
121=l^2
l=√121
L=11cm
what type of triangle is this?
ifyou choose one without looking, the probability you choose a green marble is StartFraction 20 Over 40 EndFraction
. How can you write this probability as a decimal? Write this probability as a decimal. Use a word or phrase to describe this probability.
How do you change the fraction to a decimal?
A.
Multiply the numerator and denominator by 3.
B.
Divide the numerator by the denominator.
C.
Divide the denominator by the numerator.
D.
Multiply the numerator by the denominator.
a) To write the probability as a decimal, we divide the numerator (20) by the denominator (40). This gives us the decimal representation of the probability.
b) To change the fraction to a decimal, we divide the numerator by the denominator.
So, the correct answer is option B: Divide the numerator by the denominator.
Explanation:
To change the fraction [tex]\( \frac{20}{40} \)[/tex] to a decimal, we perform the division [tex]\( \frac{20}{40} \)[/tex].
[tex]\[ \frac{20}{40} = 0.5 \][/tex]
Therefore, the probability of choosing a green marble as a decimal is 0.5.
Which of the following is not a perfect square (a) 2025 (b) 3210 (c) 4900 (d) 7744
Answer:
the right answer is b
Step-by-step explanation:
since its square root does not result in an integer
Evaluate the function for x=-2
Y=2(4)x
Answer:
= -16
Step-by-step explanation:
If x= -2, then replace it on Y=2(4)X
Y=2x(4)x(-2)
Y=-16
Note:
2 multiplied by 4 = 8
8 multiplied by -2 = -16
Answer:
Step-by-step explanation:
y= 2(4)(-2)
y = 8(-2)
y =-16
Which of the following are examples of rational numbers? Select all that apply
Answer:
1.5,
Step-by-step explanation:
The examples of rational numbers are: a, d, and e.
A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
Let's evaluate each option:
a. [tex]\( \sqrt{4} + \sqrt{16} = 2 + 4 = 6 \)[/tex]
This is a rational number because it can be expressed as the integer 6.
b. [tex]\( \sqrt{5} + \sqrt{36} = \sqrt{5} + 6 \)[/tex]
This is not a rational number because it involves the irrational square root of 5.
c. [tex]\( \sqrt{9} + \sqrt{24} = 3 + 2\sqrt{6} \)[/tex]
This is not a rational number because it involves the irrational square root of 6.
d. [tex]\( 2 + \sqrt{4} = 2 + 2 = 4 \)[/tex]
This is a rational number because it can be expressed as the integer 4.
e. [tex]\( \sqrt{49} + \sqrt{81} = 7 + 9 = 16 \)[/tex]
This is a rational number because it can be expressed as the integer 16.
f. [tex]\( 3\sqrt{12} = 3 \times \sqrt{4 \times 3} = 3 \times 2\sqrt{3} = 6\sqrt{3} \)[/tex]
This is not a rational number because it involves the irrational square root of 3.
So, the examples of rational numbers are: a, d, and e.
The complete Question is given below:
Which of the following are examples of rational numbers? Select all that apply
a. √4+√16
b. √5+√36
c. √9+√24
d. 2+√4
e. √49+√81
f. 3√12
What is 3 4/15 divided by ( 8 times 6 3/10
Susie wants to deposit $6000 into a savings account and plans to leave her money in the account for 10 years. The bank offers two types of savings accounts
• Account 1: offers 4.5% simple interest.
• Account 2: offers 4% interest compounded annually.
Which statement about the savings accounts is true?
A. Susie should invest her money in Account 1 because the account will earn $300.00 more in interest than Account 2 after 10 years.
B. Susie should invest her money in Account 1 because the account will earn $436.35 more in interest than Account 2 after 10 years.
C. Susie should invest her money in Account 2 because the account will earn $617.82 more in interest than Account 1 after 10 years.
D. Susie should invest her money in Account 2 because the account will earn $181.47 more interest than Account 1 after 10 years.
Answer:
Option D
Step-by-step explanation:
step 1
Account 1
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=10\ years\\ P=\$6,000\\r=4.5\%=4.5/100=0.045[/tex]
substitute in the formula above
[tex]A=6,000(1+0.045*10)[/tex]
[tex]A=6,000(1.45)[/tex]
[tex]A=\$8,700[/tex]
step 2
Account 2
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$6,000\\ r=4\%=4/100=0.04\\n=1[/tex]
substitute in the formula above
[tex]A=6,000(1+\frac{0.04}{1})^{1*10}[/tex]
[tex]A=6,000(1.04)^{10}[/tex]
[tex]A=\$8,881.47[/tex]
step 3
Find the difference
[tex]\$8,881.47-\$8,700=\$181.47[/tex]
therefore
Susie should invest her money in Account 2 because the account will earn $181.47 more interest than Account 1 after 10 years
There are 19 animals , total of legs are 54 and the animals are pigs and ducks. How many pigs and ducks are there?
Final answer:
Using a system of equations, we established that there are 8 pigs and 11 ducks among the 19 animals with a total of 54 legs.
Explanation:
To solve the problem of determining how many pigs and ducks there are when there are 19 animals in total and 54 legs, we set up two equations. Let's assume the number of pigs is x and the number of ducks is y. Pigs have 4 legs, and ducks have 2 legs. We can summarize this information in the following system of equations:
Equation 1: x + y = 19 (because there are 19 animals total)
Equation 2: 4x + 2y = 54 (because the total number of legs is 54)
We can solve this system using the substitution or elimination method. Simplifying Equation 2 by dividing every term by 2 gives us 2x + y = 27, which we'll call Equation 3.
Equation 3: 2x + y = 27
We can now subtract Equation 1 from Equation 3 to find the value of x:
(2x + y) - (x + y) = 27 - 19
(2x - x) + (y - y) = 8
x = 8 (number of pigs)
Substitute x back into Equation 1:
x + y = 19
8 + y = 19
y = 19 - 8
y = 11 (number of ducks)
Therefore, there are 8 pigs and 11 ducks among the 19 animals.