We are given : g(x) = 5x + 2.
y = 1 x
h = x^2
r(x) = x
f/x = x^5 - 3
b(x) = 1/2 x^3
p/x = -7x
k(x) = - 3 x + 1
y = mx + b
fx = -x^3 + 4
Note: Function is written in the from of f(x) and read as function f of x.
There could be any letter used for function, like h(x), g(x), k(x).
Therefore, in the given options the following are in function notations only:
g(x) = 5x + 2.
r(x) = x
b(x) = 1/2 x^3
k(x) = - 3 x + 1.
Answer:
g(x) = 5x + 2.
r(x) = x
b(x) = 1/2 x^3
k(x) = - 3 x + 1.
Step-by-step explanation:
Christy went on a round-trip bicycle ride starting at her house. When she left, she traveled downhill at a rate of 24 kilometers per hour (kph). She rested for 30 minutes, and then returned to her house. Since the return trip was partly uphill, it took half an hour longer and Christy averaged only 20 kph. How long did the return trip take?
Answer:
The return trip took 3 hours.
Step-by-step explanation:
Suppose, the time required to travel downhill is [tex]t[/tex] hours.
Since the return trip was partly uphill, it took half an hour longer. So, the time required for the return trip will be: [tex](t+0.5)[/tex] hours.
Given that, the speed for travelling downhill was 24 kph and the speed for travelling uphill was 20 kph.
We know that, [tex]Distance= speed*time[/tex]
As, the distances traveled in both trips are equal, so the equation will be........
[tex]24t=20(t+0.5)\\ \\ 24t=20t+10\\ \\ 4t=10\\ \\ t=\frac{10}{4}= 2.5[/tex]
So, the time required for the return trip will be: [tex](2.5+0.5)= 3[/tex] hours.
Answer:
It took 3 hours to return home.
Step-by-step explanation:
1 hour for travelling downhill.30 minutes rest.1 hour and 30 minutes for travelling uphill.Total time taken = 1 hour + 30 minutes + 1 hour and 30 minutes = 3 hours total.
Write a function rule for the area of a rectangle whose length is 7
ft more than its width. What is the area of the rectangle when its width is
7ft?
Write a function for the area A of the rectangle using the independent variable width W.
A= ?
PLZ PROVIDE GOOD ANSWER WITH HOW YOU SOLVED IT
Final answer:
The function rule for the area of a rectangle is A = W² + 7W. When the width is 7 feet, the area of the rectangle is 98 square feet.
Explanation:
To write a function rule for the area of a rectangle, we need to express the area in terms of the independent variable, which in this case is the width (W). The length is given as 7 feet more than the width, so we can write the length as W + 7. The area (A) of a rectangle is given by the formula A = length × width. Substituting the values, we get A = (W + 7) × W = W² + 7W.
To find the area of the rectangle when the width is 7 feet, we can plug in W = 7 into the function rule. A = 7² + 7 * 7 = 49 + 49 = 98 square feet. Therefore, the area of the rectangle is 98 square feet when the width is 7 feet.
Can someone help me with this questions please?
Since supplementary angles equal 180. (2x+15) = 45, which can be found by subtracting 135 from 180. This means that x = 15. And since angle 1 corresponds to the previous angle, we can deduce that angle 1 = 45.
2. x = 15 deg; Δ=45 deg
Find three consecutive odd integers such that the sum of the smaller two is three times the largest increased by seven
three consecutive odd integers are : -17,-15,-13
Which expression is the completely factored form of x6−64y3 ?
We are given this
[tex]x^6 -64y^3[/tex]
write it as the difference of cubes
[tex](x^2)^3 -(4y)^3[/tex]
use the formula for the difference of cubes
[tex](x^2-4y) ((x^2)^2+x^2*4y+(4y)^2)[/tex]
Now use the formula for the difference of squares as [tex]4y = (2\sqrt{y} )^2[/tex]
[tex](x-2\sqrt{y}) (x+2\sqrt{y}) (x^4+4x^2y+16y^2)[/tex]
the diameter of a circle is 12yd. find the exact area and circumference of the circle. write your answers in terms of pie
The exact circumference of the Circle Measurements is 12π yards and the exact area is 36π square yards.
To find the exact area and circumference of the circle, we can use the formulas given:
Circumference of a circle = 2πr
Area of a circle = πr^2
Given that the diameter of the circle is 12 yards, we can find the radius by dividing the diameter by 2: r = 12 / 2 = 6 yards.
Now we can substitute the value of r into the formulas:
Circumference = 2πr = 2π(6) = 12π yards
Area = πr^2 = π(6^2) = 36π square yards
So, the exact circumference of the circle is 12π yards and the exact area is 36π square yards.
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Which equation is correct? Cos G= 8/15 ...
Answer:
(d) sin G = 15/17
Step-by-step explanation:
For angle G, opp = 15, adj = 8, hyp = 17.
cos G = adj/hyp = 8/17
sin G = opp/hyp = 15/17
Answer: (d) sin G = 15/17
a faucet drips 2\3 gallons of water in 10 hours. what is the unit rate of water dripped per day
To find out how much water drips per day from a faucet that drips 2/3 gallons in 10 hours, we first find the hourly rate which is 1/15 gallons per hour. Then, we multiply this by 24 (the number of hours in a day) to find that the faucet drips 1.6 gallons of water per day.
Explanation:The unit rate simply means how much of something you have per 1 unit of time or space. In this case, we want to know how much water drips per day from a faucet.
Firstly, we know that the faucet drips 2/3 gallons in 10 hours. We can convert it into how much it would drip in one hour by dividing 2/3 by 10 to get 2/30 or 1/15 gallons per hour. Secondly since one day contains 24 hours, you just multiply the hourly rate (1/15) by 24 to get the daily rate. So, 1/15 * 24 equals 1.6 gallons. Therefore, the faucet drips 1.6 gallons of water per day.
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The correct choice is (C) [tex]1\frac{3}{5}[/tex] gallons per day. To find the daily drip rate, first determine the hourly rate by dividing the given amount by 10 hours, then multiply this rate by 24 hours.
To find the unit rate of water dripped per day from a faucet that drips [tex]\frac{2}{3}[/tex] gallons of water in 10 hours, we first calculate how many gallons it drips in one hour. This is calculated by dividing the quantity of water by the time:
( [tex]\frac{2}{3}[/tex] ) gallons / 10 hours = ( [tex]\frac{2}{3}[/tex] ) * ( [tex]\frac{1}{10}[/tex] ) = [tex]\frac{2}{30}[/tex] = [tex]\frac{1}{15}[/tex] gallons per hour.Since there are 24 hours in a day, we multiply the hourly rate by 24 to find the daily drip rate:
( [tex]\frac{1}{15}[/tex] ) gallons/hour x 24 hours/day = [tex]\frac{24}{15}[/tex] = [tex]\frac{8}{5}[/tex] = [tex]1\frac{3}{5}[/tex] gallons/dayAs a result, the daily water drip rate is [tex]1\frac{3}{5}[/tex] gallons per day.
Complete question:
a faucet drips [tex]\frac{2}{3}[/tex] gallons of water in 10 hours. what is the unit rate of water dripped per day
(A) [tex]\frac{1}{15}[/tex] gallon per day
(B) [tex]\frac{5}{18}[/tex] gallon per day
(C) [tex]1\frac{3}{5}[/tex] gallons per day
(D) [tex]6\frac{2}{3}[/tex] gallons per day
x^2-4y^2=0
A.(x+4y)(x-y)
B. (x-4y)(x+y)
C. (x+2y)(x-2y)
D. (x-2y)(x-2y)
[tex]x^{2}[/tex]-4[tex]y^{2}[/tex] = 0
Solution
Here we have to find the factors.
[tex]x^{2} - 4y^{2} = 0[/tex]
Here we can write 4y^2 as (2y)^2
[tex]x^{2} - (2y)^{2} = 0[/tex]
Now we have to use the formula, a^2 - b^2 = (a + b)(a - b)
Here a = x and b = 2y
Therefore, we get
(x + 2y)(x -2y)
Hence, the answer isC. (x + 2y)(x -2y)
Which relation is a function?
{(5, 0), (0, –8), (5, –5)}
{(5, 0), (0, 5), (–5, –5)}
{5, 0, –8, –5}
{(5, 0), (–8, –5), (–8, 5), (–5, –8)}
Based on the analysis, the only relation that is a function is {(5, 0), (0, 5), (–5, –5)}.
How to determine Which relation is a function?A relation is considered a function if each input value (x-value) in the relation corresponds to exactly one output value (y-value).
1. {(5, 0), (0, –8), (5, –5)}
In this relation, the input value 5 corresponds to both 0 and -5. Therefore, this relation is not a function.
2. {(5, 0), (0, 5), (–5, –5)}
In this relation, each input value has a unique output value. For example, 5 corresponds to 0, 0 corresponds to 5, and -5 corresponds to -5. This relation satisfies the definition of a function since each input value has only one corresponding output value.
3. {5, 0, –8, –5}
This is not a relation since it consists only of individual numbers and does not show any pairings between input and output values. Therefore, it is not a function.
4. {(5, 0), (–8, –5), (–8, 5), (–5, –8)}
In this relation, the input value -8 corresponds to both -5 and 5. Therefore, this relation is not a function.
Based on the analysis, the only relation that is a function is {(5, 0), (0, 5), (–5, –5)}.
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Final answer:
The relation {(5, 0), (0, 5), (–5, –5)} is a function because each domain value maps to exactly one range value, which meets the definition of a function.
Explanation:
To determine which relation is a function, we must ensure that each input (or domain value) maps to exactly one output (or range value). A function cannot have one domain value paired with multiple range values.
Relation 1: {(5, 0), (0, –8), (5, –5)} is not a function because the domain value 5 is associated with two different range values (0 and –5).Relation 2: {(5, 0), (0, 5), (–5, –5)} is a function because each domain value is unique and maps to exactly one range value.Relation 3: {5, 0, –8, –5} is not a relation in the form of ordered pairs, so it cannot be considered a function.Relation 4: {(5, 0), (–8, –5), (–8, 5), (–5, –8)} is not a function because the domain value –8 has two different range values (–5 and 5).Therefore, the relation that is a function is the second one: {(5, 0), (0, 5), (–5, –5)}.
What is the fraction in simplest form?
14/16
To find a fraction's simplest form, you need to find the GCF. The greatest common factor is the largest number that can go into the numerator and the denominator.
We know that 1 is a factor, but let's keep going to make sure. 2 is also a factor.
14/2 = 7
16/2 = 8
Since 14 and 16 are not divisible by 3, 2 is the GCF (we know not to continue dividing).
Therefore, it's simplest form is 7/8.
The fraction 14/16 in simplest form is 7/8.
To simplify the fraction 14/16, find the greatest common divisor (GCD) of the numerator (14) and the denominator (16) and then divide both the numerator and denominator by the GCD.
Step 1: Find the Greatest Common Divisor (GCD) of 14 and 16.
The divisors of 14 are 1, 2, 7, and 14.
The divisors of 16 are 1, 2, 4, 8, and 16.
The largest number that appears in both lists is 2. Therefore, the GCD of 14 and 16 is 2.
Step 2: Divide both the numerator and denominator by the GCD (which is 2).
14 ÷ 2 = 7
16 ÷ 2 = 8
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Sally consumed 2.5 gallons of water in one day. How many milliliters are equal to 2.5 gallons, if 1 liter = 1,000 milliliters and 1 gallon = 3.785 liters?
there are 9463.53 milliliters in 2.5 gallons of water.
Answer:
9,462,5 milimiters.
Step-by-step explanation:
In order to be able to calculate how many milimeters there are in 2.5 gallons of water we just have to convert the units, so we first have to convert from gallons to liters, there are 3.785 liters in each gallon, so we just do the convertion:
[tex]\frac{1 gallon}{3.785 liters}=\frac{2.5 gallons}{x}[/tex]
If we clear the x we get:
[tex]x=\frac{(3.785 liters)(2.5gallons)}{1 gallon}[/tex]
[tex]x=\frac{(9.4625 liters*gallons)}{1 gallon}[/tex]
[tex]x=9.4625 liters[/tex]
Now we just ocnvert to mililiters, since there are 1000 mililiters in a liter we just multiply:
[tex]\frac{1 liter}{1000mililiter}=\frac{9.462liters}{x}[/tex]
[tex]x=\frac{(9.4625 liters)(1000mililiter)}{1 liter}[/tex]
[tex]x=9462.5 mililiters}[/tex]
Ben solved an equation as shown below, Equation 2 (-3×+1)=9×-8. what did he do wrong. step1. -6×+2=9×- 8. step2. -6×+9×=-8+2. step3. 3x=-6. step4. x=-2
failed to evaluate 9 × - 8
2( - 3x + 1) = 9 × - 8
- 6x + 2 = - 72 ( subtract 2 from both sides )
- 6x = - 74 ( divide both sides by - 6 )
x = [tex]\frac{-74}{-6}[/tex] = [tex]\frac{37}{3}[/tex]
2(3 – 4a) + 5(a – 7) what are the steps to solve this? please.
2(3 – 4a) + 5(a – 7)
Distribute 2 and 5 inside the parenthesis
Step 1: 2*3 - 2*4a + 5*a - 5*7
When we multiply it we will get
Step 2: 6 - 8a + 5a -35
Now we combine like terms. The terms that as same variables are like terms
-8a + 5a is -3a
6 - 35 is -29
6 - 8a + 5a -35
Step 3: -3a -29
Final answer is -3a-29
What is 8,01.47 in word form?
Eight thousand one and forty seven hundredths.
Hope this helps! :)
What is the value of x that makes the relation {(2,4),(3,6),(8,x)} a function?
16.
4 ÷ 2 = 2
6 ÷ 3 = 3
so,
8 x 2 = 16
if the sum of two numbers is 21 and their quotient is 2 what are they?
Set up the equations:
two numbers: a and b
sum: a+b=21
quotient: a/b=2
(the last one means b=a/2)
combine them:
a+a/2=3a/2=21
a=14
and so
b=7
the two numbers are 14 and 7
Final answer:
To find two numbers given their sum and quotient, set up and solve a system of equations. In this case, the numbers are 14 and 7.
Explanation:
The sum of two numbers is 21 and their quotient is 2. To find the two numbers, we can set up a system of equations:
Let the two numbers be x and y. We have the equations x + y = 21 and x/y = 2.
Solve the system by substituting y = 21 - x into the second equation to get x = 14 and y = 7.
Therefore, the two numbers are 14 and 7.
Name the property of equality that justifies this statement if RS=ST and ST=TU then RS=TU
Thanks
Answer:
This is called Transitive property of equality.
Step-by-step explanation:
If a quantity a=b and b=c, then we can say a=c, this property is called transitive property of equality.
marcela's dog gained 4.1 kilograms in two months. Two months ago, the dog's mass was 5.6 kilograms. What is the dog's current mass?
What error did Raj make?
Answer: the answer this b
Step-by-step explanation:
Bc I said so lol
which monomial has the highest degree
The degree of a monomial is the highest power of a variable.
For A, the highest power is 5 ( a^5)
For B, the highest is 6 (a^6)
For C, the highest is 4 ( both a^4 and b^4)
For D, the highest is 2 ( all 3 variables have ^2)
B has the highest degree.
Answer:
B
Step-by-step explanation:
a compass and a ruler cost $4. the compass is .90 cent more than the ruler. how much does the compass cost
A city library has 811 nonfition books they want to divided the books on a shelf by 79 each
Answer:
811÷77= 10.265....
Step-by-step explanation:
4 divided by 3,476........i need help pls!
the answer is 869. hope you pass!
Given that x and y vary directly, write the equation relating x and y if x = 3 when y=24. A.y=8x B.xy=8 C.y= 8/x D.y= x/8
The correct answer is A. Because if you substitute the x and y you will get the same outcome. y=8x substitute and you get 24= 8(3) and then multiply and you get 24 = 24
What is the blank for 3.441 <>= 3.409
) because its biggerrrrrr
the length of a rectangle is 5 cm more than its width and the area is 50cm2 find the legth, width, and the perimeter
Let the Width be x cm
Then the length which is 5cm more than width must be (x+5) cm
Using the formula for the area = length* width
x(x+5) =50
[tex]x^2+5x =50[/tex] (Distribute x on the parenthesis )
[tex]x^2+5x-50 =0[/tex] (subtract 50 )
[tex](x+10) (x-5) =0[/tex] (Factor)
[tex]x-5=0\\x+10=0[/tex]
we get
[tex]x=5[/tex] (Not x=-10 because negative side length not possible)
Width = 5 cm
Length = 5+5= 10 cm
Perimeter = 2(Length + width)
So
Perimeter = 2(10+5)
Perimeter = 2*15=30 cm
the length of a rectangle is 5 cm more than its width and the area is 50cm2 find the length, width, and the perimeter
L = W + 5 (5 cm more than its width)
Area = W * L
Substitute Area = 50 and L = W + 5
50 = W ( W+5)
Distributive property
50 = W^2 + 5W
Subtract 50 from both sides
0 = W^2 + 5W - 50
Re-write
W^2 + 5W - 50 = 0
Factor
(W + 10)(W - 5) = 0
W + 10 = 0; W = -10
W - 5 = 0; W = 5
Dimension cannot be negative so W = 5 cm
L = 5 + 5 = 10 cm
Double check: A = 5 x 10 = 50 cm^2
Perimeter = 2(L + W)
Perimeter = 2(5 + 10)
Perimeter = 2(15)
Perimeter = 30 cm
Answer
L = 10 cm
W = 5 cm
P = 30 cm
Hope that helps
the temperature t in fish haven Idaho starts at 20 degrees Fahrenheit at midnight when h=0. The temperature. drops 2 degrees every hour. what equation represents the temperature in T at hours H
hint: the rate of change or slope -2 degrees every o=hour. because the temperature is falling.
As the hint stated, the slope is -2 degrees.
So, the easiest way to make a equation is to use slope intercept.
Y=mx+b
M is the slope, and B is the Y-intercept.
so.
Y = (-2)x+20
Y = -2x+20
Answer:
[tex]T=-2h+20[/tex]
Step-by-step explanation:
the temperature t in fish starts at 20 degrees Fahrenheit at midnight when h=0.
So when h=0 the T=20 degree (0,20)
The equation of temperature is
[tex]T=m(H)+b[/tex]
Where m is the slope and b is the y intercept
y intercept is the initial degree , so b=20
m is the rate of change that is slope =-2
m=-2, b=20 , [tex]T=m(H)+b[/tex]
The equation becomes
[tex]T=-2h+20[/tex]
What is the interquartile range of this data set? 5,5,6,7,9,11,14,17,21,23
A. 7
B. 9
C. 11
D.13
Find the measure of ∠FEG.
1. 25°
2. 65°
3. 80°
4. 90°
The correct answer is 65 degrees.