Answer:
[tex]\huge\boxed{f(x)=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x}[/tex]
Step-by-step explanation:
[tex]f(x)=a(x+3)(x-0)(x-7)=ax(x+3)(x-7)\\\\=ax\bigg((x)(x)+(x)(-7)+(3)(x)+(3)(-7)\bigg)\\\\=ax(x^2-7x+3x-21)=ax(x^2-4x-21)\\\\=(ax)(x^2)+(ax)(-4x)+(ax)(-21)\\\\=ax^3-4ax^2-21ax\qquad(*)\\\\f(-8)=-5[/tex]
[tex]\text{substitute}\ x=-8\\\\f(-8)=(a)(-8)^3-(4a)(-8)^2-(21)(-8)a=-512a-(4a)(64)+168a\\\\=-512a-256a+168a=-600a\\\\f(-8)=-5\\\\\text{therefore}\\\\-600a=-5\qquad|\text{divide both sides by (-600)}\\\\a=\dfrac{-5}{-600}\\\\a=\dfrac{1}{120}[/tex]
[tex]\text{Substitute to}\ (*):\\\\f(x)=\dfrac{1}{120}x^3-4\cdot\dfrac{1}{120}x^2-21\cdot\dfrac{1}{120}x=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x[/tex]
If the legs of each triangular base are 5 cm and 3 cm and the height of the prism is 4 cm, what
are the coordinates of the vertices of the prism?
The coordinates of the six vertices of the prism are listed below:
[tex](x_{1},y_{1}, z_{1}) = (0, 0, 0)\,[ft][/tex] [tex](x_{2}, y_{2}, z_{2}) = (0, 0, 5)\,[ft][/tex] [tex](x_{3}, y_{3}, z_{3}) = (3, 0, 0)\,[ft][/tex] [tex](x_{4}, y_{4}, z_{4}) = (0, 4, 5)\,[ft][/tex] [tex](x_{5}, y_{5}, z_{5}) = (0, 4, 0)\,[ft][/tex][tex](x_{6}, y_{6}, z_{6}) = (3, 4, 0)\,[ft][/tex]The number of vertices of a prism with a polygonal base ([tex]n[/tex]) is described by the following expression:
[tex]n = 2\cdot s[/tex] (1)
Where [tex]s[/tex] is the number of sides of the base.
If we know that [tex]s = 3[/tex], then the number of vertices of the prism are:
[tex]n = 2\cdot 3[/tex]
[tex]n = 6[/tex]
A prism with triangular base has six vertices, let suppose that the triangle of the base is right-angled. and coincides with a right-hand rectangular coordinate system. Then, we can conclude that the coordinates of the six vertices are the following:
[tex](x_{1},y_{1}, z_{1}) = (0, 0, 0)\,[ft][/tex] [tex](x_{2}, y_{2}, z_{2}) = (0, 0, 5)\,[ft][/tex] [tex](x_{3}, y_{3}, z_{3}) = (3, 0, 0)\,[ft][/tex] [tex](x_{4}, y_{4}, z_{4}) = (0, 4, 5)\,[ft][/tex] [tex](x_{5}, y_{5}, z_{5}) = (0, 4, 0)\,[ft][/tex][tex](x_{6}, y_{6}, z_{6}) = (3, 4, 0)\,[ft][/tex]We kindly invite to check this question on prisms: https://brainly.com/question/8828506
2yx= 4 is it a linear function?
Answer:
No, it is not a linear function, rather a rational function
Step-by-step explanation:
Because the term on the left-hand side contains both x and y, then neither variable varies directly with the other, hence, it's a rational function:
2yx=4
yx=2
y=2/x
Multiply.
3 1/2 times 2 2/3
Answer:
Step-by-step explanation:
What is the surface area of the rectangular prism below?
Answer:
8*8 *2=64
8*19 *2=304
8*19*2=304
672units is your answer
The surface area of the rectangular prism below is 736 square units
Surface area of rectangular prismThe formula for calculating the surface area of the rectangular prism is expressed as:
A = 2(lw + wh + lh)
Given the following parameters
l = 8
w = 19
h = 8
Substitute
SA = 2(8(19) + 8(19) + 8(8))
SA = 2(152 + 152 +64)
SA = 2(304+ 64)
SA = 2(368)
SA = 736 square units
Hence the surface area of the rectangular prism below is 736 square units
Learn more on surface area here:https://brainly.com/question/16519513
#SPJ6
Pls help brainlist pls help
Answer:
The slope of the function represents how much the function rises per amount that it moves horizontally.
Step-by-step explanation:
Evaluate. (w^2/x -3) ÷10 × z when w= -4, x = 0.8, and z = -4/5 Enter your answer as a simplified mixed number in the box.
Answer:
-1.36
Step-by-step explanation:
(-4^2/0.8-3)/10×-4/5=-1.36
Hanna and Dien are both getting a raise. Who will earn more
per hour after the raise?
Step-by-step explanation:
First, you need to calculate how much they will earn per hour by multiplying their raise per hour by there hours and adding it to their earnings divided by the hours worked. Then, whoever's is the highest will be the answer.
Hanna will earn more per hour after the raise, with an hourly rate of $10.75 compared to Dien's hourly rate of $10.60.
What is Division?A division is a process of splitting a specific amount into equal parts.
To find the new earnings per hour for Hanna and Dien
Divide their total earnings after the raise by the total number of hours they worked after the raise.
The raise per hour is already given, so we can simply add it to their old hourly rate.
For Hanna, her new hourly rate would be:
(New earnings) / (Hours worked) = (78 + 8) / 8
= 86 / 8
= $10.75
This means that Hanna will earn $10.75 per hour after the raise.
For Dien, his new hourly rate would be:
(New earnings) / (Hours worked) = (60.60 + 3) / 6
= 63.60 / 6
= $10.60
This means that Dien will earn $10.60 per hour after the raise.
Therefore, Hanna will earn more per hour after the raise, with an hourly rate of $10.75 compared to Dien's hourly rate of $10.60.
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ2
A pair of shoes is originally sold for $85. Currently, there is a 15% off sale. How much would the pair of shoes cost after the discount? Group of answer choices
Answer:
$72.75
Step-by-step explanation:
15% of $85 is $12.75
$85 - $12.75 = $72.25
Amelia and her children went into a grocery store and she bought $10 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. She bought a total of 12 apples and bananas altogether. By following the steps below, determine the number of apples, x,x, and the number of bananas, y,y, that Amelia bought.
Answer:
8 apples
4 bananas
Step-by-step explanation:
8 apples (8$)
4 bananas (4$)
12 total
10 $ total
hope it helps
Solve the inequalities from parts A and D for the variables b and n, respectively.
Part A:2b<56
Part D:n<56
Answer:
Part A: b < 28
Part D: n < 56
Step-by-step explanation:
part A: divide each term in and simplify.
Inequality Form: b < 28
part d: this is already solved but can be shown in multiple forms.
Inequality Form: n < 56
Interval Notation: ( -∞ , 56)
Find the value for x.
Answer:
x = 21Step-by-step explanation:
5x - 12 = 3x + 30
5x - 3x = 30 + 12
2x = 42
x = 21
---------------------
check
5 * 21 - 12 = 3 * 21 + 30
93 = 93
the answer is good
Please take a look at the picture
Answer:
B) -g/-h
Step-by-step explanation:
-g/-h=g/h
Rewrite the fraction.
-(-g/h) = g/h
Hope this helps :)
Which equation represents a line that is parallel to the line 4x-3y=15
1) y = -4/3x - 4
2) y = -3/4x - 2
3) y = 4/3x + 2
4) y = 3/4x - 6
Answer:
1
Step-by-step explanation:
because... it is
Find The slope of the line represented by the points in the table (use your notes to get the formula it needed).
4.
Number
of Hours
1
2.
3
4
Cost
($)
$17
$29
$41
$53
e/kaid_274404147475337871026587/assig!
Khan Academy
Percent word problems
Of the 50 U.S. states, 4 have names that start with the letter W.
What percentage of U.S. states have names that start with the letter W?
0
Stuck? Review related articles/videos or use a hint.
Answer:
Step-by-step explanation:
4/50 = 0.08
0.08(100) = 8%
a man walks for 45 minutes at a rate of 3 mi/h then jogs for 75 minutes at a rate of 5 mi/h then rests for 30 minutes and finally walks for 90 minutes at a rate of 3 mi/h. Write a piecewise-defined function expressing the distance he traveled as a function of time.
Answer:
Sorry need points
Step-by-step explanation:
An ice cream factory makes 300 quartz of ice cream in 10hr how many quartz can be made in 12 hours
Answer:
360
Step-by-step explanation:
Answer:
360 quarts
Step-by-step explanation:
300/10=30
30*12=360
What is the Bill of Rights?
The first amendment to the Constitution, which is actually a group of ten amendments
The list of laws that people of the United Stated needed to follow
The document that replaced the Constitution
The document that replaced the Articles of Confederation
Answer:
The first amendment to the Constitution, which is actually a group of ten commandments
Step-by-step explanation:
The first amendment to the Constitution is actually a group of ten amendments called the Bill of Rights. The Bill of Rights guarantees all Americans certain freedoms, such as freedom of religion, freedom of the press, freedom of speech, the right to bear arms, and the right to a fair trial.
pls help me find the missing angle
Answer:
b=114
c=43................
Issac wanted to make a homemade bubble solution to play with his friends. A bubble recipe he found requires 4 cups of warm water for every 1/2 cup of soap. If he had 2/3 cup of soap how many cups of warm water will he need
A- 1/12
B- 1 1/3
C- 5/13
D- 8
Answer: 8/3
You first do 4x2 than you would have to divide by 3. 4x2*3
The number of cups of warm water need for 2/3 cup of soap to make solution is [tex]5\frac{1}{3}[/tex]. Therefore, option C is the correct answer.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. 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.
Given that, a bubble recipe he found requires 4 cups of warm water for every 1/2 cup of soap.
Let the number of cups of warm water need for 2/3 cup of soap be x.
Now, the proportion is
4:1/2 :: x:2/3
1/2 x=4×2/3
x/2=8/3
x=16/3
x= [tex]5\frac{1}{3}[/tex]
Therefore, option C is the correct answer.
To learn more about the proportions visit:
https://brainly.com/question/7096655.
#SPJ6
The perimeter of a rectangle is represented by the expression 12x-2812x−28. The length of the rectangle is represented by the expression 2x+102x+10. Which expression represents the width of the rectangle?
Answer:
339,006 that's the answer
PLS HELP ME PLS HELP ME PLS HELP ME
Answer:
Step-by-step explanation:
3/8 + 1/8 + 2/3 - 1/2 =
Answer: 2/3 (answer in decimal form = 0.6)
Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly. Then do the rest of the operations.
(8 points) will mark brainliest!! pls help:)
Answer:
-0.366666666667
Step-by-step explanation:
that's what you get when you divide -22/5 (-4 2/5) by 4/3 (1 1/3)
Answer:
-24/5 is the correct answer.
Steps:
1) -4 x 2/5 = -8/5
2) 1 x 1/3 = 1/3
3) -8/5 : 1/3 = -24/5
You pay a real estate agent a 4% commission for selling your
house. After paying the commission, you receive $302,900. What
was the actual selling price of the house?
Yes
Answer:
Step-by-step explanation: 56
What is the equation for the line in slope-intercept form?
Enter your answer in the box.
Determine the ordinary simple interest on a 90-day loan of Php8000 at 8 ½ % interest rate.
Answer:
$170
Step-by-step explanation:
Help help help math please help help
Answer:
x=11
Step-by-step explanation:
We know that angles on a straight line equal 180 degrees, so we know that 8x+10+7x+5 = 180.
Simplify
15x+15=180
Solve
Take away 15 from both sides
15x = 165
Divide 165 by 15
x = 11
Is 27, 333 divisible by 3? Write the number 27,333 as the product of 3 and another factor.
Yes, 3 divides 27,333. We have
27,333 = 27,000 + 333
… = 27•1,000 + 333
… = 3•9•1,000 + 3•111
… = 3•(9•1,000 + 111)
… = 3•(9,000 + 111)
… = 3•9,111
What is the product?
(Y^2+3Y+7)(8y^2+y+1
Answer:
8y⁴+25y³+60y²+10y+7
Step-by-step explanation:
8y⁴+y³+y²+24y³+3y²+3y+56y²+7y+7
8y⁴+25y³+60y²+10y+7
Answer:
8y^4+25y^3+60y^2+10y+7
Step-by-step explanation:
(y^2+3y+7)(8y^2+y+1)
We are going to multiply the first term, y^2, by the whole second part (8y^2+y+1)
8y^4+y^3+y^2
now we multiply the 2nd term, 3y, by the whole second part (8y^2+y+1))
24y^3+3y^2+3y
now we do the same to the last term, 7.
56y^2+7y+7
now we need to add all three of our products together
(8y^4+y^3+y^2)+(24y^3+3y^2+3y)+(56y^2+7y+7)
adding like terms:
8y^4+y^3+24y^3+y^2+3y^2+56y^2+3y+7y+7
we get:
8y^4+25y^3+60y^2+10y+7