Answer:
C. The value of the comic book decreased by an average of $0.04 each month between m = 36 and m = 60.
Step-by-step explanation:
The average rate of change for the function f(x) from [tex]x_1=a[/tex] and [tex]x_2=b[/tex] is
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
It is a measure of how much the function changed per unit, on average, over that interval.
Actually, this is the slope of the line passing through two points on the graph of the function.
If the average rate of change of the function f(x) between m = 36 and m = 60 is -0,04, it means that the value of the comic book decreased (because of negative number -0.04) by an average of $0.04 each month (a unit in this case is a month) between m = 36 and m = 60.
Answer:
C. The value of the comic book decreased by an average of $0.04 each month between m = 36 and m = 60.
Step-by-step explanation:
What is the true solution to the equation below?
In elnx+ In enx=-2 In 8
To solve the given equation, w need to review some rules:
The given equation is :
⇒⇒⇒⇒ rule (2)
⇒⇒⇒⇒ rule (1) and rule (2)
⇒⇒⇒⇒ rule (3)
removing the nature logarithm from both sides
∴ x = 4
So, the correct answer is option (2) ⇒⇒⇒⇒ x = 4
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The solution of the logarithmic equation is x = 4
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
[tex]ln[e^{ln ( x )} ] + ln[e^{ln (x^{2} )} ] = 2ln(8)[/tex]
On simplifying , we get
The value of ln e = 1
From the laws of logarithm , we get log Aⁿ = n log A
ln ( x ) ln ( e ) + ln ( x )² ln ( e ) = 2 ln ( 8 )
On further simplification , we get
ln ( x ) + ln ( x )² = ln ( 8 )²
From the laws of logarithm , we get log A + log B = log AB
ln ( x )³ = ln ( 64 )
ln ( x )³ = ln ( 4 )³
So , the value of x = 4
Hence , the logarithmic equation is solved
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Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a total of $48. Which of the following are true? Select all that apply.
A. One pound of pistachios plus 1 pound of almonds cost $20.
B. The pistachios cost twice as much per pound as the almonds.
C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.
D. The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48.
E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
Answer:
A. One pound of pistachios plus 1 pound of almonds cost $20
C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.
E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
Step-by-step explanation:
Let
x ----> the cost of one pound pistachios
y ----> the cost of one pound of almonds
we know that
x=y+4 -----> equation A
2x+3y=48 -----> equation B
substitute equation A in equation B and solve for y
2(y+4)+3y=48
2y+8+3y=48
5y=48-8
y=8
Find the value of x
x=8+4 =12
therefore
The cost of one pound pistachios is $12 and the cost of one pound of almonds is $8
Verify all statements
case A) One pound of pistachios plus 1 pound of almonds cost $20.
Is True
x+y=$12+$8=$20
case B) The pistachios cost twice as much per pound as the almonds
Is false
Because
2y=2(8)=$16
$16≠$12
case C) Reducing the number of pounds of almonds by 1 results in a total cost of $40
Is True
Because
2x+2y=2(12)+2(8)=$40
case D) The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48.
Is false
The equation will be
2(a + 4) + 3a = 48.
case E) The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48
Is true
Because
p=a+4
Solve for a
a=p-4
Solve by factorisation 2x^2+3x-20
Answer:
(x + 4) × (2x - 5)
Step-by-step explanation:
Begin by writing 3x as a difference 2x^2 + 8x - 5x - 20Factor out 2x from the expression2x × (x + 4) - 5x - 20Factor out -5 from the expression2x × (x + 4) - 5 (x + 4)Factor out x + 4 from the expression (x + 4) × (2x - 5)Hope this helps!!
Answer:
Answer:
(2x−5)(x+4)
Step-by-step explanation:
Factor 2x2+3x−20
2x2+3x−20
=(2x−5)(x+4)
Answer:
(2x−5)(x+4)
In the diagram below angle AED=(4n-20)° and angle BEC=(2n-16)°. What is the measure of angle CED in degrees
(See picture)!!
Check the picture below.
so, bearing in mind that vertical angles are equal, thus ∡AED = ∡BEC, and we know that ∡BEC = 52 = ∡AED, so those two angles added up are 104°.
now, a circle has a total of 360°, if we take away those 104° from the red angles, what's leftover is just 256°, well, the green angles there are also vertical angles and thus twins, so each one will take half of 256°.
∡BEA = 128° = ∡CED.
write three numbers that have GCF of 7
Answer:
21, 35 , 49
Step-by-step explanation:
21 = 3 * 7
35 = 5 * 7
49 = 7 * 7
GCF = 7
Is 21/32 greater than 3/4
Answer:
Step-by-step explanation:
It's highly advisable to find and use the LCD in problems like this.
21/32 has the denominator 32; if we multiply numerator and denominator each of 3/4, we get the equivalent fraction 24/32.
Now, compare 21/32 and 24/32. It's pretty obvious that "21/32 greater than 3/4" is false; 24/32 is greater than 21/32, so 3/4 is greater than 21/32.
A bottlenose dolphin can swim 2.68 meters per second. Find the dolphin speed in miles per hour
Answer:
The dolphin speed in miles per hour is 6
Step-by-step explanation:
we know that
1 mi=1,609.34 m ------> 1 m=1/ 1,609.34 mi
1 h= 3,600 sec ----> 1 sec=1/3,600 h
we have
[tex]2.68\frac{m}{sec}[/tex]
Convert to mi/h
[tex]2.68\frac{m}{sec}=2.68\frac{(1/1,609.34)}{(1/3,600)}=6\frac{mi}{h}[/tex]
Answer:
6
Step-by-step explanation:
4. At 840,000 square miles, Greenland is the largest island
in the world. The second-largest island is
New Guinea, at 306,000 square miles. How much large
is Greenland than New Guinea?
Answer:
840,000 / 306,000 = 2.7450980392
So, Greenland is about 2 and 3/4 times larger than New Guinea.
Step-by-step explanation:
Greenland, the largest island in the world, is 534,000 square miles larger than New Guinea.
Explanation:Greenland is 840,000 square miles and New Guinea is 306,000 square miles. To find out how much larger Greenland is than New Guinea, we subtract the area of New Guinea from the area of Greenland:
840,000 - 306,000 = 534,000 square miles
Therefore, Greenland is 534,000 square miles larger than New Guinea.
To determine how much larger Greenland is than New Guinea, one must subtract the size of New Guinea from the size of Greenland. Given that Greenland, the largest island in the world, is 840,000 square miles and New Guinea is 306,000 square miles, you would perform the following calculation:
840,000 - 306,000 = 534,000 square miles
Therefore, Greenland is 534,000 square miles larger than New Guinea.
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in an isosceles triangle if a base angle has a measure of 55 degrees then the vertex angle must have a measure of 70 degrees as well
Answer:
True
Step-by-step explanation:
The base angles of an isosceles triangle are equal.
The sum of the 3 angles in a triangle = 180°, thus
vertex angle = 180° - (55 + 55)° = 180° - 110° = 70°
In the number 76,129, which digit
has the least value?
Answer:
1
Step-by-step explanation:
It would be 1 because it is the least number there
rearrange the formula to make a) f the subject and b) v the subject. 1/v+1/u=1/f
Answer:
see explanation
Step-by-step explanation:
Multiply through by the lowest common multiple of u, v and f, that is uvf
uvf × [tex]\frac{1}{v}[/tex] + uvf × [tex]\frac{1}{u}[/tex] = uvf × [tex]\frac{1}{f}[/tex], that is
uf + vf = uv ← factor out f on the left side → (1)
f(u + v) = uv ← divide both sides by (u + v)
f = [tex]\frac{uv}{u+v}[/tex]
(b)
Using line (1)
uf + vf = uv ( subtract uv from both sides )
uf + vf - uv = 0 ( subtract uf from both sides )
vf - uv = - uf ← factor out v on the left side
v(f - u) = - uf ← divide both sides by (f - u)
v = - [tex]\frac{uf}{f-u}[/tex]
Faye has 5 pieces of ribbon, each 1 yard long. She cuts each ribbon into sixths.
a. How many sixths will she have after cutting all the ribbons?
b. How long will each of the sixths be in inches?
Answer:
a ) total number of sixth in 5 ribbon will be 6\times 5 = 30
b) length of each sixth will be = 5.97 inches
Step-by-step explanation:
given data:
Number of pieces of ribbon is 5
each piece length 1 yard
total number of cut in one piece of ribbon = 6
a) one piece of ribbon consist of 6 sxiths
therefore total number of sixth in 5 ribbon will be 6\times 5 = 30
b) each ribbon length is 1 yard
so, whole ribbon is divided into 1\6 yard length which is length of individual division
we know that one yard is 36 inches
therefore, in 1/6 yard = 5.97 inches
Answer:
a. She will have 30 sixths after cutting all the ribbons.
b. 6 inches.
Step-by-step explanation:
a. You know that the lenght of each piece of ribbon is 1 yard.
She cuts each ribbon into sixths, then the lenght of each one of them is:
[tex]\frac{1}{6}\ yd[/tex]
So:
[tex]\frac{6}{6}=1\ yard[/tex]
Since Faye has 5 pieces of ribbon, after cutting all the ribbons she will have:
[tex](5)(\frac{6}{6})=\frac{30}{6}[/tex]
She will have 30 sixths after cutting all the ribbons.
b. You need make the conversion from yards to inches.
Knowing that [tex]1\ yd=36\ in[/tex], you get:
[tex](\frac{1}{6}\ yd)(\frac{36\ in}{1\ yd})=6\ in[/tex]
What is the value of the expression?
6.4−2.4÷0.1
Enter your answer in the box as a decimal.
HELP ILL GIVE 5 STAR IF ITS RIGHT
Hey!
-------------------------------------------------
Steps To Solve:
~Follow PEMDAS
6.4 − 2.4 ÷ 0.1
~Divide
6.4 − (2.4 ÷ 0.1)
~Simplify
6.4 - 24
~Subtract
(6.4 - 24)
~Simplify
-17.6
-------------------------------------------------
Answer:
[tex]\large\boxed{-17.6}[/tex]
-------------------------------------------------
Hope This Helped! Good Luck!
Answer:
-17.6
Step-by-step explanation:
6.4 - 2.4 ÷ 0.1
6.4 - 24 *Order of operations tells you
to divide first
-17.6 *Subtract
Subtract 582,295 from670,63
Answer: 100,335
Step-by-step explanation: Whenever you see the terms "subtract _____ from blank," the numbers in the equation will be reverse. For example, subtract 76 from 100 would be translated as 100-76. This applies here. The equation is 670,630-582,295, which is 100,335
What quadrilateral has exactly one pair of parallel opposite sides?
A trapezoid has exactly one pair of parallel sides.
I hope I was helpful! :)
If G={(-1,7),(8,2),(0,0),(6,6)}, then the range of G is
Answer: [tex]Range:\{0,2,6,7\}[/tex]
Step-by-step explanation:
By definition:
1) The Domain is the the set of all the input values, which are the x-coordinate of each ordered pair (the first number in each pair).
2)the Range is the set of all output values, which are the y-coordinate of each ordered pair (the second number in each pair).
In this case you have the following relation "G":
[tex]G=\{(-1,7),(8,2),(0,0),(6,6)\}[/tex]
Based on the definition shown before, you can conclude that the Domain of G is:
[tex]Domain: \{-1,0,6,8\}[/tex]
And the Range of G is the following:
[tex]Range:\{0,2,6,7\}[/tex]
which of the following values are in the range of the function graphed below? check all that apply
Answer:
Option D. 1
Option E. 1/2
Step-by-step explanation:
we know that
Looking at the graph
The domain is the interval ----> [-1,1]
[tex]-1\leq x\leq 1[/tex]
The domain is all real numbers greater than or equal to -1 and less than or equal to 1
The range is the interval ----> [0,1]
[tex]0\leq y\leq 1[/tex]
The range is all real numbers greater than or equal to 0 and less than or equal to 1
therefore
The values that are in the range are
1 and 1/2
Answer:
D.1
E.[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
We have to find the values lie in the range of function in given graph.
Let f(x) be given function
Domain takes along x- axis and range takes along y- axis.
From given graph , we can see that
Domain of function =[-1,1]
It means
[tex]-1\leq x\leq 1[/tex]
Range of function:[0,1]
It means
[tex]0\leq y \leq 1[/tex]
The value of range of given function from 0 to 1.
Hence, option D and E are correct.
D.1
E.[tex]\frac{1}{2}[/tex]
Use the graph shown to fill in the blank.
When x = -3, then y = a0.
Answer: -6
Step-by-step explanation:
When X = - 3, then Y = -6
Slope is 2.
Answer:
When x = -3, then y = -6
Step-by-step explanation:
We need to find out the value of y when x=-3
From the graph we look at the value of y
x is the input of the graph and y is the output .
In x axis the positive numbers on the right side and negative numbers on the left side . In y axis the positive numbers at the top and negative numbers at the bottom.
Given x=-3, Lets find the value of
At x=-3 the graph is at the bottom of x axis
Draw a line down at x=-3 , the line meets the graph at -6
So at x=-3 the value of y is -6
When x = -3, then y = -6
5b + 2= 17 two step equation
Answer: 5b = 15
Step-by-step explanation:
5b + 2 = 17
- 2 -2
5b = 15
The two steps are:
step 1 : 5b = 17 - 2
step 2 : b = 15/5
Given,
5b + 2= 17
Now,
The equation given two us is in linear form with one variable .
So,
Simplifying the equation,
5b + 2= 17
Take 2 from LHS to RHS
5b = 17 - 2
5b = 15
b = 15/5
b = 3
Thus the value of b is 3 .
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Michael saves $423 dollars a month for college.
a. About how much money will he have saved after 4 years?
b. Will your estimate be lower or higher than the actual amount Michael will save? How do you know?
Answer:
(a). $20,000
(b). The estimate will be lower than the actual amount.
Step-by-step explanation:
We have been given that Michael saves $423 dollars a month for college.
(a). We know that 1 year equals 12 months.
4 years = 4*12 months = 48 months.
[tex]\text{Actual amount saved}=\$423\times 48[/tex]
Since we are asked to find the estimated amount of money Michael will save in 4 years, so we will estimate both quantities as:
[tex]423\approx 400\\\\48\approx 50[/tex]
[tex]\text{Actual amount saved}=\$400\times 50[/tex]
[tex]\text{Actual amount saved}=\$20,000[/tex]
Therefore, Michael will save approximately $20,000 in 4 years.
(b).
The estimate will be lower than the actual amount as we rounded $423 down $23 to nearest hundred that is $400 and rounded 48 up 2 to nearest ten that is 40.
Therefore, the estimate will be lower than the actual amount.
If y represents a number, then write an expression for negative two times the sum of y and 7
The required expression would be -2(y+7) represents which is negative two times the sum of y and 7.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
What are Arithmetic operations?
Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
We have been given that y represents a number.
To determine the expression for negative two times the sum of y and 7.
As per the given statement,
So the expression would be -2(y+7).
Hence, the required expression would be -2(y+7) represents which is negative two times the sum of y and 7.
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−2(−5x−4)+2x−2=114
Answer:
x=9
Step-by-step explanation:
-2(-5x - 4) + 2x - 2 = 114
-2(-5x - 4) + 2x = 116
10x + 8 + 2x = 116
12x + 8 = 116
12x = 108
x = 9
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Answer:
the answer is A
Step-by-step explanation:
Answer:
(-1,5)
Step-by-step explanation:
(?,0)
(-1,0)
(5,0)
What is the solution to the linear equation? StartFraction 2 Over 5 EndFraction plus p equals StartFraction 4 Over 5 EndFraction plus StartFraction 3 Over 5 EndFraction p. + p = + p p = 1 p = 2 p = 8 p = 10
For this case we must solve the following equation:
[tex]\frac {2} {5} + p = \frac {4} {5} + \frac {3} {5}[/tex]
Since the denominators on the right side of the equation are equal, then we add the fractions:
[tex]\frac {2} {5} + p = \frac {4 + 3} {5}\\\frac {2} {5} + p = \frac {7} {5}[/tex]
We subtract [tex]\frac {2} {5}[/tex]on both sides of the equation:
[tex]p = \frac {7} {5} - \frac {2} {5}\\p = \frac {7-2} {5}\\p = \frac {5} {5}\\p = 1[/tex]
Thus, the value of p is 1.
Answer:
[tex]p = 1[/tex]
The solution to the linear equation is; p= 1.
Solution to linear equationsThe equation given in the task content is;
2/5 + p = 4/5 + 3/5On this note, By isolating the unknown variable, p, we have;
p = 4/5 + 3/5 -2/5By taking the LCM, we have; p = (4+3-2)/5
P = 5/5p = 1Read more on solving linear equations;
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At just under 30,000 feet, mount Everest is the world's tallest mountain. Olympus Mon, which is on Mars, is the tallest mountain in the solar system. What is the height of Olympus Mons?
Answer:The volcano has a height of nearly 22 km (13.6 mi or 72,000 ft) as measured by the Mars Orbiter Laser Altimeter (MOLA). Olympus Mons is about two and a half times Mount Everest's height above sea level.
Olympus Mons - Wikipedia
Step-by-step explanation:
Olympus Mons on Mars is the tallest mountain in the solar system, standing over 20 kilometers above its surroundings and nearly 30 kilometers above the lowest points on Mars.
Explanation:The height of Olympus Mons, which is the tallest mountain in the solar system, located on Mars, is incredibly impressive in comparison to mountains on Earth. Olympus Mons towers more than 20 kilometers above its surroundings, reaching nearly 30 kilometers above the lowest elevation areas on Mars. When converted to more familiar units, this equals approximately 22 miles in height, a figure that dwarfs the height of Mount Everest, which stands at 29,029 feet or about 8.848 kilometers.
Which equation has solutions of 6 and -6?
Answer:
x^2-36=0
Step-by-step explanation:
x^2-36=0
(x-6)(x+6)
Answer:
[tex]x^2-36=0[/tex]
Step-by-step explanation:
Solution is 6 and -6. Lets check with each option
[tex]x^2-12x+36=0[/tex]
[tex](x-6)(x-6)=0[/tex]
x-6=0 so x=6
Solutions are 6 and 6. First option does not gives us solution 6 and -6
[tex]x^2+12x-36=0[/tex]. It is not factorable
[tex]x^2+36=0[/tex]. It is not factorable
[tex]x^2-36=0[/tex]
[tex](x+6)(x-6)=0[/tex]
x-6=0 , so x=6
x+6=0, so x=-6
[tex]x^2-36=0[/tex] is the final answer
Colin works for his dad during summer vacation.his dad pays him $5.20 per hour and works 20 hours per week. How much will Colin earn during his 8 week summer vacation
Answer:
$5.20 x 20 = $104.00
$104.00 ×8= $832.00
find the decimal that is equivalent to 7/12
Answer: 0.58333333333333
Step-by-step explanation: To find the decimal that is equivalent to 7/12, remember that fractions are division problems so we can divide the numerator by the denominator.
Numerator = 7
Denominator = 12
7 ÷ 12 = 0.58333333333333.
Answer:
_
.583
Step-by-step explanation:
In order to convert 7/12 to a decimal you must divide 7/12. The answer won't be a rational number, but will be a repeating decimal. You end up with .583 with 3 repeating. To show that this is repeating, you must put a little bar over the 3 (Because the 3 is the only repeating number) like so:
_
.583
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Mary has 12 hair ribbons. 3 of the ribbons are red. What percent of her ribbons are red?
Answer:36%
Step-by-step explanation:
Answer:
25%
Step-by-step explanation:
3 ribbons/ 12ribbons= 1/12
If You simplify dividing by 3 it becomes =1/4 = 0.25
so.. this is the 25 %
The length of a rectangle is 15 and its width is w.
The perimeter of the rectangle is, at most, 50,
Which inequality can be used to find the longes
possible width?
A
30+ 2x < 50
B. 30 + 2w < 50
D. 30+ 2w > 50
C.30 + 2w > 50
A rectangle with sides 15 and w has perimeter
[tex]2p = 2(15+w) = 2w+30[/tex]
We want this quantity to be at most 50, so it must be less than or equal to 50:
[tex]2w+30\leq 50[/tex]
For the record, this implies that
[tex]2w\leq 20 \iff w \leq 10[/tex]
So, the width can be at most 10.
Answer:
2x+30< 50 ...answer : A
Step-by-step explanation:
the perimeter is : P = 2(L+W)
let : L= x given : L=15
P= 2(x+15)
The perimeter of the rectangle is, at most, 50: P<50
2(x+15) < 50
2x+30< 50 ...answer : A