Answer:
[tex]\displaystyle k = 20[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = 3x^3 - 2x + k[/tex]
Where (x + 2) is a factor of f. And we want to determine the vale of k.
Recall that from the Factor Theorem, if (x - a) is a factor of a polynomial P(x), then P(a) must equal 0.
We can rewrite our factor as (x - (-2)). Hence, a = -2. Our polynomial is f. Since (x + 2) is a factor, then from the Factor Theorem, f(-2) must be 0.
Using this information, we can now determine k:
[tex]\displaystyle\begin{aligned} f(x) & = 3x^3 -2x + k \\ \\ f(-2) = 0 & = 3(-2)^3 -2(-2) + k \\ \\ 0 & = (-24) + (4) + k \\ \\ k & = 20 \end{aligned}[/tex]
In conclusion, the value of k is 20.
you are hiking along a trail that in 13½ miles long.you plan to rest every 2¼miles.how many rest stops will you make?
Answer:
6 stops
Step-by-step explanation:
well if you stop every 2 1/4 miles for 13 1/2....13 1/2 divided by 2 1/4 is 6. So they'll stop 6 times.
The number of rest stops before finishing the trail is 5 rest stops.
Given,
You are hiking along a trail that is 13½ miles long.
you plan to rest every 2¼miles.
We need to find how many rest stops will you make.
How do distribute equally a given value?We divide the given value by the total number of items we want to distribute.
Example:
In 35 minutes how many 5 minutes?
= 35/5
= 7
We have,
Trail distance = 13 1/2 miles = 27/2 miles
Distance travelled before every each = 2 1/4 miles = 9/4 miles
The number of 4/9 miles in 27/2 miles.
= 27/2 / 9/4
= 27/2 x 4/9
= 27x4 / 2 x 9
= 3 x 2
= 6 times.
This means on the 6th time you have already finished the trail so,
You have rested 5 times before finishing the trail.
Thus the number of rest stops before finishing the trail is 5 rest stops.
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Plz hurry. Find the slope of each line
Answer:
there isn't enough info
Step-by-step explanation:
..................
Solve the equation for s.
s2 = 10,000
is it 5,000 or 100?
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]s = \pm 100[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
I am assuming that the equation given is:
[tex]s^2 = 10,000[/tex]
⸻⸻⸻⸻
[tex]s^2 = 10,000\\\rule{150}{0.5}\\\rightarrow \sqrt{s^2}= \sqrt{10,000}\\\\\rightarrow s = \boxed{\pm 100}\\\rule{150}{0.5}[/tex]
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
An iPhone costs £699 in London, €799 in Paris and $1,099 in New York. Using £1 = €1.13 and £1 = $1.37, state the lowest price of the iPhone in £. Give your answer to 2 dp.
Answer:
£699 in London
£902.87 in Paris
£1505.63 in New York
The lowest price of the iPhone is £699 in London.
The product of twice a number and four is the same as the difference of seven times the number and 7/3. Find the number.
Answer:
-4/9
Step-by-step explanation:
find the equation of a line that is parallel to y= 4-x and cuts the Y axis at (0,1)
Answer:
y=-x+1
Step-by-step explanation:
y=-x+4
Substitute (0,1)
1=0+1
-1 is the gradient, if parallel then the gradient stays the same
Answer:
y = - x + 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept
y = 4 - x , that is y = - x + 4 ← in slope- intercept form
with slope m = - 1
The slope crosses the y- axis at (0, 1 ) ⇒ c = 1
y = - x + 1 ← equation of parallel line
PLS HELP WILL MARK BRAINLIEST!
Answer:
25 - n
Step-by-step explanation:
n is a variable. It can represent any number. For example, 5 years ago, Mario would be 20 years old since 25-5 is 20.
So, if n is 8, you have to do 25 - 8 to find the answer to how old Mario was 8 years ago.
So his age n years ago, is 25 - n.
Hope this helps!
A website sells a dress at £50 and shoes at £35.
The website has an offer:
Buy a dress and shoes together and get
1
5
off the price.
There is also a shipping and handling charge of £6 added at the end, after any discount.
If Ruth buys both a dress and shoes, how much will she actually pay?
Answer:
$74
Step-by-step explanation:
1/5 of 85 is 17
85-17=68
68+6=74
please i need help with this
Answer:
=6^7-5
=6²
plz mark me as brainliest
Answer:
36
67
65
=
67
65
=
6*6*6*6*6*6*6
6*6*6*6*6
=6*6
=62
=36
You can solve the equation 2x – 3 = 1 by graphing y = 2x – 3 and y = 1 and finding their point of intersection. Use the drop-down menus to complete the statements below.
Answer:
2 and it is the solution to both
Step-by-step explanation:
i just did it lol
The point of intersection of y = 2x – 3 and y = 1 is (2,1).
Here, we have,
given that,
the equations are:
y = 2x – 3 ....1
and y = 1 .....2
now, we have to solve them.
so, putting the value of y from 2, in 1,
we get,
2x – 3 = 1
or, 2x = 4
or, x = 2
so, we have,
their point of intersection is (2,1).
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what is 5 divided by 8,350 (long division)
Answer:
0.625
the pictures I attached are the work. the pictures are in order from 1 to 5 in red.
What is an equation of the line that passes through the points (0, -1)(0,−1) and (6, 1)(6,1)?
[tex]slope = y2 - y1 \div x2 - x1[/tex]
[tex]1 - - 1 \div 6 - 0[/tex]
[tex]2 \div 6[/tex]
[tex]1 \div 3[/tex]
[tex]y = mx + c[/tex]
[tex]1 = 1 \div 3 \times 6 + c[/tex]
[tex]1 = 2 + c[/tex]
[tex]c = 3[/tex]
[tex]y = 1 \div 3x + 3[/tex]
0.5 : 3 (ratio) in its simplest form
Answer:
1:6
Step-by-step explanation:
5 divided by 5 and 30 divided by 6
5:30
1:6
The line passing through the points (2, 4) and (5, 4) has which of the following slopes?
A. Undefined
B. Zero
C. Positive
D. Negative
Answer:
B
Step-by-step explanation:
The line would be a horizontal line and therefore the slope is 0. If the line was going vertical, then the slope would have been undefined.
HELLPPPP WILL GIVE BRAINLIEST
Answer:
[tex]\frac{-1+-\sqrt{41} }{4}[/tex] (Third Option)
Step-by-step explanation:
Step 1: Use quadratic formula with a = 2, b = 1, c = -5.
[tex]x = \frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex] [tex]x = \frac{-(1)+-\sqrt{(1)^2-4(2)(-5)} }{2(2)}[/tex] [tex]x = \frac{-1+-\sqrt{1-8(5)}}{4}[/tex] [tex]x = \frac{-1+-\sqrt{1-40} }{4}[/tex] [tex]x = \frac{-1+-\sqrt{41} }{4}[/tex]Therefore, the answer is the third option, [tex]\frac{-1+-\sqrt{41} }{4}[/tex].
Akiba Ellis deposits the following in her checking account: 6 five-dollar bills, 5 two dollar bills, 12 one dollar bills, 9 half dollars, 6 quarters, 42 dimes, 10 nickels, 15 pennies, and a check for $97.23. what is her total deposit?
Answer:
$106.08
Step-by-step explanation:
Given:
6x $5.00
5x $2.00
12x $1.00
9x= 0.50
6x25 cent
42x10 cent
10x5 cent
15=15cent
$97.23
----------------------------------------------------------------------------------
6 five dollar bill is $30.00
so 5 two dollar bill is $10.00
12 one dollar bills is $12.00
9 half dollar bill mean 0.50 cent since it Half and that would make $4.50
6 quarter so 6x25 which equal $1.50
42 dimes and dimes =10 cent so 42x10 which equal $4.20
10 nickels and nickels = 5 cent so 10x5=0.50
15=15 pennies
-------------------------------------------------------------------------------------
30.00+10.00+12.00+4.50+1.50+4.20+0.50+0.15+97.23 =
$106.08 Total Deposit
Evaluate.
(w2x−3)÷10⋅z when w=−6, x = 1.2, and z=−6/7
Enter your answer as a simplified mixed number in the box.
Step-by-step explanation:
W=-6, x=1.2, and z=-6/7
(W²x-3)÷10-z
we substitute
((-6²)(1.2)-3)÷10-(-6/7)
((-36)(1.2)-3) ÷10-(-6/7)
(-43.2-3) ÷10(6/7)
(-46.2)÷60/7
-46.2÷60/7
-46.2*7/60
-46.2/1*7/60
-323.4/60
-5.39
Required value of (w²x−3)÷10⋅z when w=−6, x = 1.2, and z=−6/7 is (-4.69)
What is the value of of (w²x−3)÷10⋅z when w=−6, x = 1.2, and z=−6/7 ?
We know,
By BODMAS rule,
B - Bracket
O - Of
D - Division
M - Multiplication
A - Addition
S - Subtraction
We should maintain the following sequence,
Bracket - Of - Division - Multiplication - Addition - Subtraction
We are applying BODMAS rule.
Here,[tex]( {w}^{2} x - 3) \div 10 . z[/tex] and w=−6, x = 1.2, and z=−6/7
We are putting value of w,x,z in given expression and get
[tex]( {( - 6)}^{2} \times 1.2 - 3) \div 10 ( - \frac{6}{7} ) \\ = -(36 \times 1.2 - 3) \div \frac{60}{7} \\ = -(43.2 - 3) \div \frac{60}{7} \\ = -40.2 \div \frac{60}{7} \\= -40.2 \times \frac{7}{60} = -4.69[/tex]
Therefore, Required value of the given term is (-4.69)
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how much smaller is 25 that the product -12 and -3
Nathaniel is building a rectangular shed. The length of the shed is 5 feet less than 3 times the width. The perimeter of the shed is 158 feet. What is the width of the shed?
Answer:
w = 21 feet
Step-by-step explanation:
The width of the given rectangular shed is such that the length of the shed is 5 feet less than 3 times the width formed the perimeter of 158 feet is 21 feet.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Let's say the length of a rectangle is L while the width is W.
According to the given, L = 3W - 5
The perimeter of the rectangle is given as 2( length + width)..
Perimeter = 2(L + W)
2(3W - 5 + W) = 158
4W - 5 = 79
W = 21 feet.
Hence "The width of the given rectangular shed is such that the length of the shed is 5 feet less than 3 times the width formed the perimeter of 158 feet is 21 feet".
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The domain of a relation is
Answer : The domain of a function or relation is the set of all possible independent values the relation can take. It is the collection of all possible inputs. The range of a function or relation is the set of all possible dependent values the relation can produce from the domain values.
Person who gets this right gets brainliest
if manny the martian's shadow is 17.5 ft. in length and the shadow of a yard stick sitting perpendicular to the ground is 7.5 ft., what is manny's height
Answer:
Here the ratio of length of the shadow to the height of the object (in this case a yardstick) is 15:36. The ratio of shadow to the height of tree will also be the same. the shadow of tree is 25 feet long. So the height of tree will be (25*36)/15, that is 60 feet.
(I really hope this helps!)
What's a distributive property equation the =3
Answer:
4/16 ( 1 + 11) = 3
could be many answers as fractions see below
The last fraction seems more likely out the three or make it harder fraction.
Step-by-step explanation:
1/2 (2 + 4) = 3 as 1/2 of 4 is 2 1+2 = 3
or
1/4 (4 + 8) = 3 as 1/4 of 8 is 2 1+2 = 3
or
3/4 ( 2 + 2) = 3 as 3/4 of 2 is 1 1/2 1.5 + 1.5 = 3
or harder fraction
4/16 ( 1 + 11) = 3
What is the answer to [tex]-9(\sqrt{x} -9) -9[/tex]
The coordinates of a reflected point is (9, 4). What were the coordinates of the original point if the point was reflected over the y-axis? Explain.
Answer:
The coordinates of the original point would be (-9,4). This is because, by reflecting over the way y-axis, the point is moving across the x-axis and therefore, makes the x-coordinate negative.
(iv). Solve: 2x⁴ - 5x³ + 7x - 3 when x = 2.
Please help me..
Step-by-step explanation:
[tex]\longrightarrow\sf{ p(x) = 2{x}^{4} - 5{x}^{3} + 7x - 3}[/tex]
Now, substituting the value of x in equation, we get.[tex]\longrightarrow\sf{ p(2) = 2({2})^{4} - 5{2}^{3} + 7\times 2 - 3}[/tex]
[tex]\longrightarrow\sf{ 2\times 16 - 5\times 8 + 14 - 3}[/tex]
[tex]\longrightarrow\sf{ 32 - 40 + 14 - 3}[/tex]
[tex]\longrightarrow\sf{ - 8 + 14 - 3}[/tex]
[tex]\longrightarrow\sf{ + 6 - 3}[/tex]
[tex]\longrightarrow\sf{ 3 }[/tex]
Answer:
Step-by-step explanation:
f(x) = 2x⁴ - 5x³ + 7x - 3
f(2) = 2(2^4) - 5(2^3) + 7(2) - 3
f(2) = 32 - 40 + 14 - 3
f(2) = 3
The graph below shows what happens when x = 2 and y = 2x⁴ - 5x³ + 7x - 3
Notice that the graph shows the same intersect point (2,3) as what we got when putting x = 2 into the equation.
you have Spanish club every fourth day and math club every 10th day what days do you have both
Answer:
the 20th day
Step-by-step explanation:
Day Spanish) 4,8,12,16,20
Day Math) 10,20
Answer:
Every 20 days you will have both clubs.
Step-by-step explanation:
Find least common multiple and it will be reccuring
You need to find the least common multiple of 4 and 10.
4, 8, 12, 16, 20, 24, 28, 32, 36, 40
10, 20, 30, 40
As you can see every 20 days you will have both, 20, 40, 60, 80, 100, etc etc.
highest common factor of 275 and 350?
Answer:
25
Step-by-step explanation:
Factors of,
275 = 1, 5, 11, 25, 55, 275
350 = 1, 2, 5, 10, 7, 14, 25, 35, 50, 70, 175, 350
Highest common factor of 275 and 350 is 25.
The HCF of 275 and 350 is given by the equation A = 25
What is HCF and LCM?The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF
Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers
Product of HCF x LCM = product of two numbers
Given data ,
Let the HCF of the two numbers be represented as A
Now , the equation will be
Let the first number be p = 275
The factors of 275 = 1 , 5 , 11 , 25 , 55 and 275
Let the second number be q = 350
The factors of 350 = 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175 and 350
So , the highest common factor of 275 and 350 is 25
Therefore , the value of A is 25
Hence , the HCF is 25
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Bricks are stacked according to the pattern shown below.
Each row contains one more brick than the row above it.
Part A
Determine a quadratic function to model the total number of bricks in the stack,
f(x), given a number of rows, m.
Answer:
Part A
The Quadratic Function to model the total number of bricks the stack is f(x) = x²
Part B
The number of bricks we will have for 50 rows is 2500 bricks
Step-by-step explanation:
Part A
Let the Quadratic Function to model the total number of bricks the stack, f(x), where x is the number of rows be f(x) = a·x² + b·x + c
We have;
When x = 0, f(x) = 0, therefore, f(0) = a×0² + b×0 + c = 0 + 0 + c = 0
∴ c = 0
When x = 1, f(x) = 1, therefore, f(1) = a×1² + b×1 + 0 = 1
∴ a + b = 1...(1)
When x = 2, f(x) = 4, therefore, f(2) = a×2² + b×2 = 4
∴ 4·a + 2·b = 4...(2)
Multiply equation (1) by 2, and subtract it from equation (2) gives;
4·a + 2·b - 2×(a + b) = 4 - 2 × 1
2·a = 2
a = 1
From equation (1), we have;
b = 1 - a = 1 - 1 = 0
b = 0
∴ f(x) = a·x² + b·x + c = 1·x² + 0·x + 0 = x²
Therefore, the Quadratic Function to model the total number of bricks the stack, f(x), where x is the number of rows be f(x) = x²
Part B
If there are 50 rows in the stack, then we have, x = 50
Therefore;
f(50) = 50² = 2500
The number of bricks we will have for 50 rows is f(50) = 2500 bricks
(just found it on brainly)
Leo sold candy bars for a fundraiser. He spent $25 on a box of candy bars and
sold them for $2 each. If his profit (after earning back the $25) was $69, how
many candy bars did Leo sell?
Which equation can be used to solve the problem?
Answer:
He sold 47 candy bars
Step-by-step explanation:
Add 25 and 69 (94)
Divide by 2 and you get 47
Mark me as brainliest if this helps!
Answer: $2c - $25 = $69
I need help! And fast !!!!
Answer:
the answer is 12
Step-by-step explanation
i figured out that 12 times 20 is 240 so i multiplied all of the numbers by 12 and that's how i got my answer