The net change between the given values of the variable is; - 3x² - 6xh - 3h² + 23
What is the Net Change of the Function?
We are given the function;
f(x) = 5 - 3x²
x = 3
x = 3 + h
The net change is just looking for the difference between f(3) and f(3 + h). Thus, we will evaluate the function at x = 3 and x = 3 + h and then calculate f(3 + h) - f(3).
f(3 + h) = 5 - 3(x + h)²
= 5 - 3x² - 6xh - 3h²
f(3) = 5 - 3(3)²
f(3) = 5 - 27
f(3) = -18
Net Change = f(3 + h) - f(3)
= 5 - 3x² - 6xh - 3h² + 18
= - 3x² - 6xh - 3h² + 23
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Find the simple interest.
Principal $300
The interest Rate 15%
Time 18 months
keeping in mind that a year has 12 months, thus 18 months is really 18/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$300\\ r=rate\to 15\%\to \frac{15}{100}\dotfill &0.15\\ t=years\to \frac{18}{12}\dotfill &\frac{3}{2} \end{cases} \\\\\\ I = (300)(0.15)(\frac{3}{2})\implies I=67.5[/tex]
One month Pablo rented 5 movies and 3 video games for a total of $39. The next month he rented 2 movies and 12 video games for a total of 75 . Find the rental cost for each movie and each video game.
we get that the rental cost for each movie is $ 4.5 and each video game is $ 5.5.
Let the cost of number of movies be x and the cost of number of video games be y.
So, the equations are:
5 x + 3 y = 39
2 x + 12 y = 75
2 x = 75 - 12 y
x = 75/2 - 6 y
Put it in the first one, we get that:
5 ( 75/2 - 6y) + 3y = 39
375/2 - 30 y + 3 y = 39
27 y = 187.5 - 39
27 y = 148.5
y = 148.5 / 27
y = $ 5.5
x = 75/2 - 6 y
x = 37.5 - 6 (5.5)
x = 37.5 - 33
x = $ 4.5
Therefore, we get that the rental cost for each movie is $ 4.5 and each video game is $ 5.5.
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1.) You need 13 flower arrangements for table decorations. Each arrangement sells for $12.25. How much will you spend on flowers?
Answer:
159.25
Step-by-step explanation:
you just have to multiply 13 by 12.25
One number is seven more than six times another number. If the sum of the numbers is 28, find the numbers
The value of the numbers x and y is a 3 and 25.
According to the statement
We have to find that the value of the numbers.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
One number is seven more than six times another number. If the sum of the numbers is 28.
Then
Let The first number = y
The second number = x
Hence, y = (7 + 6x)
Their sum is therefore;
x + 7 + 6x = 28
7x = 21
x = 3
Hence, the second number is a; 7 + 6x = 7 + 6(3);
y = 25.
So, The value of the numbers x and y is a 3 and 25.
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Which number below best represents a gain of $7.92?
A.
-7.92
B.
17.92
C.
-17.92
D.
7.92
Answer:
The Answer is D
Step-by-step explanation:
you just have to look for the letter that's giving you it not subtracting it. And look for the right amount.
13. Which products have 240 as a partial
product?
3 x 3,388
8 x 2,612
4 x 5,376
6 x 4,345
3 x 6,828
The products that have 240 as a partial product are 3 x 3,388 and 6 x 4,345
How to determine the product expression that has 240 as a partial product?The partial product is given as
240
Express 240 as a product of its factors
So, we have
240 = 1 * 240
240 = 2 * 120
240 = 3 * 80
240 = 4 * 60
240 = 5 * 48
240 = 6 * 40
240 = 9 * 30
Next, we test the options
3 x 3,388
Express all values other than the ten-place value as 0
3 x 0080
Evaluate the product
3 x 0080 = 240
8 x 2,612
Express all values other than the ten-place value as 0
8 x 0010
Evaluate the product
8 x 0010 = 80
4 x 5,376
Express all values other than the ten-place value as 0
4 x 0070
Evaluate the product
4 x 0070 = 280
6 x 4,345
Express all values other than the ten-place value as 0
6 x 0040
Evaluate the product
6 x 0040 = 240
3 x 6,828
Express all values other than the ten-place value as 0
3 x 0020
Evaluate the product
3 x 0020 = 60
Hence, the products that have 240 as a partial product are 3 x 3,388 and 6 x 4,345
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Two numbers have these properties.
Both numbers are greater than 6.
•
Their highest common factor (HCF) is 6.
•
Their lowest common multiple (LCM) is 60.
Find the two numbers, writing your answers on one line in the form,
The two numbers are ... and ..
With an HCF of 6 and an LCM of 60, the numbers 12 and 30 are greater than 6.
What are mathematical operations?An operation in mathematics is a function that takes zero or more input values and produces a well-defined output value. The operation's arity is determined by the number of operands. Similar to the principle of superposition denotes a mathematical operation (e.g., differentiation, multiplication by a constant) in which the action on the sum of two functions is the sum of the action on each function.Two numbers with HCF 6 can be:
6a, 6b where a, b are coprime numbers a, b > 1 as numbers greater than 6.
=> 6 × 60 = 6a × 6b=> 10 = abab = 1010 = 1 × 10 = 2 × 5a , b > 1As a result, a and b can be 2 or 5.
The numbers are 6 × 2 and 6 × 5.
Therefore, with an HCF of 6 and an LCM of 60, the numbers 12 and 30 are greater than 6.
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Harry needs wood pieces to complete a project in woodshop class. He needs six pieces of wood that have a length of two and five eighths feet and three pieces of wood that are one and one fifth feet. What is the total amount of wood that Harry will need for the project?
Answer:
19 7/20 feet
Step-by-step explanation:
1. [tex]2\frac{5}{8}[/tex] pieces of wood
[tex]2\frac{5}{8} * 6 = 15\frac{3}{4}[/tex]
2. [tex]1\frac{1}{5}[/tex] pieces of wood
[tex]1\frac{1}{5} * 3 = 3\frac{3}{5}[/tex]
3. Combined
[tex]15\frac{3}{5} +3\frac{3}{5} = 19\frac{7}{20}[/tex]
Rectangle p q r s had vertices p(1, 4) q(6, 4) r(6, 1) and s(1, 1).without graphins find the new coordinates of the vertices of the rectangle after the reflection over the x axis and then another reflection over the y axis
The coordinates of the new vertices of the rectangle are P''(x, y) = (- 1, - 4), Q''(x, y) = (- 6, - 4), R''(x, y) = (- 6, - 1) and S''(x, y) = (- 1, - 1).
What are the coordinates of the vertices of the image of a rectangle?
In this question we find the coordinates of the four vertices of the rectangle, whose locations are described in the statement. Each point must be transformed by the following sequence of rigid transformations:
Reflection over the x-axis: P'(x, y) = P(x, y) + (0, - 2 · p)Reflection over the y-axis: P''(x, y) = P'(x, y) + (- 2 · p', 0)If we know that P(x, y) = (1, 4), Q(x, y) = (6, 4), R(x, y) = (6, 1) and S(x, y) = (1, 1), then the locations of the images of the four vertices are:
P'(x, y) = (1, 4) + (0, - 8)
P'(x, y) = (1, - 4)
P''(x, y) = (1, - 4) + (- 2, 0)
P''(x, y) = (- 1, - 4)
Q'(x, y) = (6, 4) + (0, - 8)
Q'(x, y) = (6, - 4)
Q''(x, y) = (6, - 4) + (- 12, 0)
Q''(x, y) = (- 6, - 4)
R'(x, y) = (6, 1) + (0, - 2)
R'(x, y) = (6, - 1)
R''(x, y) = (6, - 1) + (- 12, 0)
R''(x, y) = (- 6, - 1)
S'(x, y) = (1, 1) + (0, - 2)
S'(x, y) = (1, - 1)
S''(x, y) = (1, - 1) + (- 2, 0)
S''(x, y) = (- 1, - 1)
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Ben can walk to the library 4 miles away, but it takes him 20 minutes longer than it would to walk to school 3 miles away. How long does it take Ben to walk to the library?
The time takes Ben to walk to the library is 80 minutes.
Given that, Ben can walk to the library 4 miles away, but it takes him 20 minutes longer than it would walk to school 3 miles away.
What is proportion?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the time taken Ben to walk to the school be x, so the time taken to walk to the library be x+20.
Now, 4 : x+20 :: 3 : x
⇒4x=3(x+20)
⇒4x=3x+60
⇒x=60
So, x+20=80
Therefore, the time taken by Ben to walk to the library is 80 minutes.
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Which of the terms best describes the following sequence?
162, 54, 18, 6, ...
Answer:
the respuesta is 54
Step-by-step explanation:
are not
Answer:
Geometric sequence with a common ratio of 1/3
Step-by-step explanation:
Each term is 1/3 of the previous term:
First term is : 162
Second term: 162 x 1/3 = 162/3 = 54
Third term : 54 x 1/3 = 54/3 = 18
and so on
The ratio of a term to its previous term is therefore 1/3 and this is called a common ration
This kind of sequence where each term is a multiple (1/3) of the previous term is called a geometric sequence
10. Given AXPS ADNF, find the values of x and y.
Answer:
x = 3
y = 15
Step-by-step explanation:
Suppose f(x) = - 2x² + 8x - 8. Compute the following:
A.) f(-1) + f(1) =
B.) f(1)-f(1) =
f(x) = -2x² + 8x - 8 by computing f(-1) + f(1) we get -20 and we don't need to calculate f(1) - f(1) it will be 0.
What is a function ?A function can be thought of as an output for the given inputs.
According to the given question f(x) = -2x² + 8x - 8 we have to compute
A. f(-1) + f(1) = { -2(-1)² + 8(-1) - 8 } + { -2(1) + 8(1) - 8 }.
f(-1) + f(1) = { (-2 - 8 - 8) + (- 2 + 8 - 8) }
f(-1) + f(1) = - 18 - 2.
f(-1) + f(1) = - 20.
B. f(1)-f(1) = 0 ( we don't need to calculate )
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What is the answer to 304✖️9
Answer:
2,736
Step-by-step explanation:
hope this helps! :)
Suppose we want to choose 7 letters, without replacement, from 9 distinct letters.
(a) How many ways can this be done, if the order of the choices is relevant?
(b) How many ways can this be done, if the order of the choices is not relevant?
The numbers of ways can this be done, if the order of the choices is relevant is 181,440 ways and the numbers of ways can this be done, if the order of the choices is not relevant is 36 ways.
Number of possible waysa. N permutations
N permutations = nPr = n!/ (n-r)!
N permutations = 9P7 = 9!/(9-7)!
N permutations = 9×8×7×6×5×4×3
N permutations= 181,440
b. N combinations :
N combinations = nCr = n!/((n-r)!r!)
N combinations = 9C7 = 9!/((9-7)!7!)
N combinations =9×8×7×6×5×4×3 ×2!/7!×2!
N combinations = 9×8×7×6×5×4×3 /7!
N combinations =181,440/7!
N combinations =36
Therefore the numbers of ways can this be done, if the order of the choices is relevant is 181,440 ways and the numbers of ways can this be done, if the order of the choices is not relevant is 36 ways.
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Erosion typically wears the Hawaiian volcano Mono Loa down about 20 cm in 5 years. Lava flows build the volcano up about 10 cm every time there is an eruption. Mono Loa erupts about once every 2 years. Is the volcano growing or wearing down?
The volcano is growing larger by 1 cm/year.
Is the volcano growing or wearing down?In order to determine if the volcano is growing or wearing down, determine the cm that the volcano wears down each year. To do this, we would be dividing the total cm the volcano wears down by the number of years.
Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
The cm the volcano wears down each year = 20 cm / 5 = 4cm
10 / 2 = 5cm
5cm - 4cm = 1 cm
This means that the volcano is growing at 1 cm per year.
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-2x 8y = 14
2x+8y= -14
Solve by elimination
Answer: x=-7, y=0
Step-by-step explanation:
You can see just by the set up that the x values cancel each other out without you having to do anything(-2x+2x=0). Because of this, you can add the two equations to eliminate the x values.
-2x+8y = 14
2x+8y= -14 --------> 16y=0
When you isolate the variable, you get y=0. Now you can choose one of the original equations and substitute 0 into the y value.
-2x+8y = 14 ---> -2x+8(0) = 14 ----> -2x+0 = 14 ---> -2x=14
When you divide both sides by -2, you get x=-7.
Q6. What percentage of 16 is 4?
O 30%
120%
25%
15%
Answer:
C. 25%
Step-by-step explanation:
if you add 4 4 times, you get 16, and .25 equals 1/4.
Hope this helps!
Answer:
25%
Step-by-step explanation:
4/16 = 0.25 = 25%
Write the equation of the line that passes through the points ( 7 , − 7 ) (7,−7) and ( 3 , 8 ) (3,8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:
horizontal line isywgwueve
Each side of a square floor tile is 182 mm long. Find the area of the square defined by one of these floor tiles.
Answer:
33124
Step-by-step explanation:
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There are 12 boys and 14 girls in the math club. They decide to run laps around the school track
to raise money for an upcoming competition. Each boy raised $8.00 per lap and ran at a rate of
What is the ratio of the total amount of money the boys raised in one hour to the total amount of
laps per hour. Each girl raised $10.00 per lap and ran at a rate of 4 laps every 30 minutes.
money the girls raised in one hour running around the track. HURRY
Answer:
The girls ran 8 laps in one hour, for the boys it is 48:6
Step-by-step explanation:
The girls ran 4 laps in 30 minutes so per hour is was be 8 laps because 4x2. So on the paper it would be 4x2=8
For the boys it would be 8x6 which is 48 dollars in one hour and 6 laps per hour so it would be 48:6 so just put 8x6=48 and it should work.
What are the correct answers?
Answer: The first 3 answers from the top
Step-by-step explanation:
Michael used a stopwatch to time the baseball pitches for three of his friends.Order from least to greatest.
Pete:0.537
Ivan:0.58
Kat:0.4996
Answer:
this is called as ascending order, it is when numbers are arranged from least to greatest
here is the answer:
ivan:0.58
pete:0.537
kat:0.4996
Step-by-step explanation:
so you have to look at the nmbers and how many digits they have for example,
ivan's number has 3 digits so its the least
kat has 5 digits so its the greatest
Over 5 months, Carlos wrote 5 checks for a total of $335.75 to pay for his cable TV service. His cable bill is the same amount each month. What was the amount of the cable bill for one month of service?
Carlos pays monthly for his cable bill $67.15
How to calculate the monthly payment ?For over 5 months Carlos wrote a total of 5 checks for $335.75 to make payment for his cable TV service.
The same amount is paid for the cable bill every month.
Therefore the amount paid every month can be calculated as follows
= 335.75/5
= 67.15
Hence the amount paid monthly for the cable bill is $67.15
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In 1980, the average price of a home in Lake County was $93,000. By 1985, the average price of a home was $118,000. Which of the following is a linear model for the price P of home in Lake County, in terms of the year t? Let t = 0 correspond to 1980.
[A] P=25,000t +93,000
[B] P=118,000-25,000t
[C] P = 5000t +93,000
[D] P=118,000-5000t
Answer: [C] P = 5000T + 93,000
Step-by-step explanation:
If Line t || Line v and m∠5 =5x + 45 and m∠7 = 12x - 11, find m∠5
The Line t || Line v the value of angle m∠5 is 69.28° .
What is line?
A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
Given:
Line t || Line v
m∠5 =5x + 45
m∠7 = 12x - 11,
According to given question we have
Line t || Line v
Using the property of interior angles on same sides we get
m∠5 =m∠7
5x + 45=12x - 11
compare like terms we get
45-11=12x-5x
34=7x
x=34/7°
By put the value of x
m∠5 =5x + 45
m∠5 =5*34/7+45
m∠5 =485/7=69.28°
m∠7 =12x - 11=12*34/7-11
m∠7 =331/7°
m∠7 =47.28°
Therefore, the Line t || Line v the value of angle m∠5 is 69.28° .
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10(v+3)-4v-2(3v+3)-9
Answer:
15
Step-by-step explanation:
Distribute where possible
10v + 30 - 4v -6v -6 -9
Combine like terms and do the math
15
9. Estimation
Doug is reading two
books. The first book is 122 pages.
The second book is 189 pages.
Rounded to the nearest ten, about
how many pages will Doug read?
Answer:
310
Step-by-step explanation:
189+122=311
(311 rounded to the nearest ten is 310.)
You buy 3.18 pounds of grapes, 1.45 pounds of peaches, and 2.76 pounds of oranges. Each pound of grapes cost 1.29, each pound of peaches cost 1.19, and each pound of oranges cost 0.99. What is my total bill?
a cat ’s heart beats approximately 45 times in 15 seconds. At this rate how many times does the cat ’ s heart beat per second ?
Answer:
3 heartbeats
Step-by-step explanation:
The cat's heartbeats are 45 per 15 seconds.
To find out how many heartbeats it does per second (instead of 15), we should divide this amount by 15.
[tex]\frac{45}{15} \to 3[/tex]
Answer:
Step-by-step explanation:
45beats/15sec = 3beats/sec