Answer:
Below
Step-by-step explanation:
If -5 is one of the roots then that means (x+5) is one of the factors
divide (x+5) into x^3 + 3x^2 -12x -10
to get x^2-2x-2 which you can easily (using Quadratic Formula) find the roots 1 + sqrt 3 and 1 -sqrt 3
('roots' and 'zeroes' are the same thing)
Josie calculated 1/5+1/2 and said the answer was 2/7 is it wrong and why
Answer:
It's wrong because you don't add fractions the way you would add normal numbers.
Step-by-step explanation:
To add 1/5 to 1/2 you would need to write all numerators above the least common denominator which is 10. Then add the numerators, 5 + 2, which gives you 7/10.
Can anyone solve this
Answer:
Step-by-step explanation:
y= 53/3 prob wrong but idek
The cost in dollars of making x items is given by the function C(x)=10x+900 .
a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item.
Fixed cost =$
b. What is the cost of making 25 items?
C(25)=$
c. Suppose the maximum cost allowed is $1900 . What are the domain and range of the cost function, C(x) ?
Domain:
Range:
Step-by-step explanation:
when we give a function an actual value as argument, we are using the variable(s) in the functional definition as intended : as placeholders for actual values.
so, we only need to replace any occurrence of the variable by the actual value and calculate.
a.
zero items are produced means x = 0.
C(0) = 10×0 + 900 = $900
fixed cost = $900
b.
making 25 items means x = 25.
C(25) = 10×25 + 900 = 250 + 900 = $1,150
c.
the domain is the interval or set of all valid values for x.
the range is the interval or set of all valid values for y (the functional result).
now, the maximum cost allowed is $1900.
how many items are that ?
1900 = 10x + 900
1000 = 10x
x = 100
so, the domain is
0 <= x <= 100
the range is
$900 <= y <= $1900
Given f(x)= x^2 +2x-8 and g(x)= x+2, find (fog)(x). Help is greatly appreciated. Thanks!
For given functions f(x)= x^2 +2x-8 and g(x)= x+2,
(fog)(x) = x^2 + 6x
For given functions f(x)= x^2 +2x-8 and g(x)= x+2,
we need to find (fog)(x).
We know that the composition of function f(x) and g(x) would be,
(fog)(x)
= f(g(x))
= f(x + 2)
= (x + 2)^2 + 2(x + 2) - 8
= x^2 + 4x + 4 + 2x + 4 - 8
= x^2 + 6x + 8 - 8
= x^2 + 6x
Therefore, for given functions f(x)= x^2 +2x-8 and g(x)= x+2,
(fog)(x) = x^2 + 6x
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NO LINKS!! Please help me with the Angle Proofs Part 4
Answer:
1. Given.
2. Definition of a linear pair.
3. Given.
4. Congruent Supplements Theorem.
Step-by-step explanation:
Statement 1
∠JKM and ∠MKL form a linear pair.
Reason: Given
Statement 2
∠JKM and ∠MKL are supplementary
Reason: Definition of supplementary angles.
A linear pair is a pair of adjacent, supplementary angles.
If ∠JKM and ∠MKL form a linear pair then they are supplementary by definition.
Statement 3
∠JKM and ∠LKN are supplementary.
Reason: Given.
Statement 4
∠MKL ≅ ∠LKN
Reason: Congruent Supplements Theorem.
If two angles are supplements of the same angle, then the two angles are congruent.
As ∠MKL and ∠LKN are both supplementary to ∠JKM then ∠MKL and ∠LKN are congruent.
Find the y-coordinate of the y-intercept of the polynomial function defined below.
f(x) = -2(x-3)
Someone please help…
Answer:
(x-5),(y+2)
Step-by-step explanation:
Given the equation k over 12.6 equals 7.4, determine the value of k.
93.24
20.0
5.2
1.70
The value of k from the given equation as in the task content is; 93.24.
What is the value of k?It follows from the task content that the value of k for which the given equation is true is to be determined.
On this note, since the given equation is;
k / 12.6 = 7.4
Therefore, to isolate k, both sides of the equation must be multiplied by; 12.6 as follows;
k = 7.4 × 12.6
Ultimately, the value of k for which the given equation is true is; 93.24.
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a\b − c+d if a=7\8 , b=−7\16 , c=0.8 , and d=1\4
By solving the equation a\b − c +d, we get the answer -2.55
Given,
In the question:
The equation is given as:
a\b − c + d
The values are given as:
a=7\8 , b=−7\16 , c=0.8 , and d=1\4
Now, According to the question:
Substitute the values a=7\8 , b=−7\16 , c=0.8 , and d=1\4 into a\b − c + d.
Now,
[tex]\frac{7}{8}[/tex] × [tex]\frac{16}{-7}[/tex] - 0.8 + 1/4
Cross out the common factor:
= -2 - 0.8 + 1/4
Taking L.C.M
= [tex]\frac{-8-3.2+1}{4}[/tex]
Calculate the sum or difference:
= -10.2/4
= - 2.55
Hence, By solving the equation a\b − c +d, we get the answer -2.55
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Use the ray tool to graph f(x) = |-x – 5|.
First plot the endpoint of the ray, then any point on the ray.
The graph of the given absolute function is attached below and the end points (-5,0) (0, 5) of the rays are marked in it.
Absolute value function:
The function that contains an algebraic expression within absolute value symbols is called as absolute value function.
Given,
Here we have the absolute value function f(x) = |-x - 5|
Now, we have to plot the graph for this function and we have to mark the end point of the rays.
Here the given function is written as,
=> f(x) = | -x - 5|
In order to plot the graph for the function we need the table of values to point it on the graph,
For that we have to take following sample values,
When x = -5, then f(-5) = |-5 -5| = 0
When x = 0, then f(0) = |0 - 5| = 5
Therefore, the end points of the rays are (-5,0) and (0,5)
Now, we have to plot these values on the graph.
Then we get the graph like the following.
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The vaule of 5-a is 20 greather than the vaule of 6a-1
The value of a when the value of 5-a is 20 greater than the vaule of 6a-1 is -2.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Since the value of 5-a is 20 greater than the vaule of 6a-1. This will be:
5 - a > 6a - 1 + 20
Collect like terms
-a - 6a > - 1 + 20 - 5
-7a > 14
Divide
a > 14 / -7
a > -2
Therefore, a is greater than -2.
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Is 11/16 greater than less than or equal to 3/8
Answer:
Greater than
Step-by-step explanation:
3/8 = 6/16
6<11
therefore, 11/16 is greater than 3/8
During a building project, a brick is
dropped from a height of 1,936 ft. If the
equation for height as a function of time is
h(t) = -16t2 initial height where t is time
in seconds and h(t) is height in feet, how
many seconds will it take for the brick to
hit the ground?
Answer:
11 seconds
Step-by-step explanation:
[tex] - 16 {t}^{2} + 1936 = 0[/tex]
[tex] - 16 {t}^{2} = - 1936[/tex]
[tex] {t}^{2} = 121[/tex]
[tex]t = 11[/tex]
the sum of a number with the square of its following algebraic language
Answer:
a + (a+1)²
Step-by-step explanation:
The following of the number "a" is:
a+1
Then:
The sum of a number with the square of its following algebraic language is:
a + (a+1)²
The algebraic expression for the sum of a number with the square of its following number can be written as:
x + ( x + 1)²Where x is the given number and (x + 1 )² represents the square of the following number.
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15. Todd purchased two CDs and three cassette tapes for $75. Paulena went to the same
music store and purchased one CD and five cassette tapes for $76. If all CDs are the
same price and all the cassette tapes are the same price, find the cost of each CD and
each cassette tape.
The cost of each CD is $21 and the cost of each cassette tape is $11.
According to the question,
We have the following information:
Todd purchased two CDs and three cassette tapes for $75. Paulena went to the same music store and purchased one CD and five cassette tapes for $76.
Now, let's take the cost of each CD to be $x and the cost of each cassette tape to be $y.
So, we have the following expressions:
2x+3y = 75 ..(1)
x+5y = 76
x = 76-5y ..(2)
Putting the value of x in equation 1:
2(76-5y)+3y = 75
152-10y+3y = 75
152-7y = 75
Subtracting 152 from both sides:
-7y = 75-152
-7y = -77
y = 77/7
y = $11
Putting this value in equation 2:
x = 76-5y
x = 76-5*11
x = 76-55
x = $21
Hence, the cost of each CD is $21 and the cost of each cassette tape is $11.
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The graph represents function 1, and the equation represents function 2: A coordinate plane graph is shown. A horizontal line is graphed passing through the y-axis at y = 6. Function 2 y = 2x + 7 How much more is the rate of change of function 2 than the rate of change of function 1? (4 points) a 1 b 2 c 3 d 4
The rate of change of function 2 is greater than the rate of change (slope) of function 1 by: B. 2.
How to determine the difference in the rate of change?Since the line on this graph is perpendicular to the y-axis (horizontal line), we can reasonably and logically deduce that its rate of change (slope) is equal to zero (0) because there is no change in the y-value on the y-axis.
This ultimately implies that, the rate of change (slope) of function 1 (y = 6) with an horizontal line is equal to zero (0).
Next, we would calculate the rate of change (slope) of function 2 i.e y = 2x + 7. Mathematically, the standard form of the equation of a straight line function is given by;
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the y-intercept.By comparing the two (2) equations, we have the following:
y = mx + c ≡ y = 2x + 7
Therefore, the rate of change (slope) of function 2 is equal to 2.
Now, we can calculate the difference between the rate of change (slope) of function 2 and the rate of change (slope) of function 1 as follows:
Difference = 2 - 0
Difference = 2.
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Solve for b.
b - 14 = -10
Answer:
b=4
Step-by-step explanation:
b-14 =-10
b-14+14=-10+14
b=4
2) The Peponi tuckshop sells + different kinds of muffin. Apple, blueberry, cherry and damson. A cherry muffin costs the same as two apple muffins. A blueberry muffin costs the same as two damson muffins. A Cherry muffin and two damson muffins costs the same as an apple and two blueberry muffins. All four types cost an integer multiple of 100 shillings. If Aanya buys one of each kind, which of these could be the amount she spends? 1,600, 1,800, 2000, 2200 or 2400 shillings.
Answer:
1800
Step-by-step explanation:
c = 2a;
b = 2d;
c + 2d = a + 2b
2a + b = a + 2b
a = b
a = b
c = 2a
d = b/2
Assume a = 100.
b = 100
c = 200
d = 50
This cannot be, but we can continue.
Add them: 100 + 100 + 200 + 50 = 450
The total must be an even multiple of 450.
The total can be 900, 1800, 2700, etc.
Answer: 1800
The annual fundraising goal of a is $100,000. So far $46,088 has been raised. How much more money is needed to reach the goal? What???
If annual fundraising goal of a is $100,000 and so far $46,088 has been raised, then they have to raise $53912 to reach the goal
The goal of the annual fund raising = $100000
The raised amount = $46088
The amount of money needed to reach the goal = The goal of the annual fund raising - The raised amount
Here we have to use the subtraction
Substitute the values in the equation
The amount of money needed to reach the goal = 100000 - 46088
= $53912
Hence, if annual fundraising goal of a is $100,000 and so far $46,088 has been raised, then they have to raise $53912 to reach the goal
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Please help I was sick and missed out on class.Thank you
==========================================
Explanation:
Both points have the same x coordinate, which immediately tells us both points are on the same vertical line.
All vertical lines have an undefined slope. This is because when it comes to rise/run, the "run" is zero. Dividing by zero is not allowed.
Check out the steps below.
[tex](x_1,y_1) = (-10,9) \text{ and } (x_2,y_2) = (-10,18)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{18 - 9}{-10 - (-10)}\\\\m = \frac{18 - 9}{-10 + 10}\\\\m = \frac{9}{0}\\\\m = \text{UND}\\\\[/tex]
The "UND" is shorthand for "undefined". Some textbooks may use the notation "NaN" to refer to "not a number".
How many words with or without meaning each of 2 vowels and 3 consonants can be formed from the letters of the word "Honesty" ?
Answer:
The number of words with two vowels and 3 consonants from the letters of the word ‘HONESTY’ is 1200.
Step by step explanation:
The median monthly rent in 2005 was $694 and $810 in 2010. What was the percent increase in the median monthly rent prices from 2005 to 2010? Round to the nearest tenth of a percent.
The percent increase in the median monthly rent prices from 2005 to 2010, using proportions, was of:
16.7%.
What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of a problem.
One application of proportions is to obtain the percent increase in the context of a problem, as it is calculated as the division of the increase by the total amount and multiplied by 100%.
The parameters to obtain the percent increase in the context of this problem are given as follows:
Initial amount: $694.Increase: 810 - 694 = $116.Hence the percent increase in the median monthly rent prices from 2005 to 2010 is calculated as follows:
P = 116/694 x 100% = 16.7%.
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Solve.
1) Jake bought a bicycle that cost $65.00 when it was new...
If he eventually sold it for 20% of the original cost, how
much was it sold for?
Answer:
Jake sold the bicycle for $13.00
Step-by-step explanation:
All you have to do is know the equation would be 20% of $65.00.
That equals 65x0.20.
If you solve it, the answer is $13.00
Jake sold the bicycle for $13.00
Hope this helps!
Answer:
its 13 dollars
Step-by-step explanation:
when you have to find a precent of something you multiply the number by the percentage and divide the answer by 100
Write an expression having only two terms that is equivalent to 2x – 3. Explain how you wrote the expression and how you can check that it is equivalent.
i will provide any pics, etc if neccesary
The equivalent two-term expression of 2x - 3 is 2(x - 1) - 1
What are Equivalent Algebraic expression?Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other. In addition, you can also determine if two expressions are equivalent when values are substituted in for the variable and both arrive at the same answer.
2x - 3 can be written by expressing -3 as a sum of two numbers in which one of the numbers is -2, those two numbers are -1 and -2
so that,
2x -2 -1
now we can factorize 2x -2, which is 2(x - 1)
Finally the expression becomes 2( x - 1) -1
To check that it is equivalent we substitute any number in to 2( x -1 ) -1 and 2x - 3, if it gives same answer, then they are equivalent.
using x = 1
2( 1 - 1) -1 = -1
2(1) -3 = -1
In conclusion, 2(x-1) -1 is the equivalent expression
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Solve negative 5 times y plus seven thirds times y equals negative 5 minus eight thirds times y minus 4 for y.
The solution to the equation as written is y = -96/161.
What is a linear equation?The term linear equation has to do with an equation in which the highest power of the variable is 1. In this case, we have been given a word problem and we would have to convert it to equation.
The equation is now to be written as;
5y + 7/3y = 5/8y - 4
Collect like terms and apply BODMAS;
5y + 7/3y - 5/8y = -4
22y/3 - 5/8y = -4
161y/24 = -4
24(-4) = 161y
y = 24(-4)/161
y = -96/161
Having solved the equation, the solution that is obtained for the linear system is y = -96/161
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Please help me giving 100 pts to whoever can help me the fastest!!!!!
Answer:
0.4294
Step-by-step explanation:
need help ASAP plspldplsplsplspls
1) The linear system has only one solution.
2) The linear system has infinite number of solutions.
3) The linear system has only one solution
4) The linear system has only one solution.
5) The linear system has only no solution.
What is meant by a linear equation?In the algebraic form y= mx+ b, where m denotes the slope and b the y-intercept, a linear equation is defined as a first-order (linear) term and a constant. The aforementioned is occasionally described as a linear equation with two variables, where x and y are the variables.
An equation is linear if the graph of the equation is a straight line. This will happen once x has the highest power of 1, which is. The equation is linear if it can be represented as a straight line.
1) x+y+7=0
x-y+1=0
By solving these two equations we get,
x=-4
y=-3
(x, y)=(-4,-3)
Consequently, there is only one solution to the linear system.
2) 3x+y-2=0
6x+2y-4=0
a₁/a₂=3/6
a₁/a₂=1/2
b₁/b₂=1/2
c₁/c₂=1/2
Therefore,
a₁/a₂=b₁/b₂=c₁/c₂
So, the linear system has infinite number of solutions.
3) x-y-5=0
x+5y+7=0
By solving these two equations we get,
y=-2 and x=3
(x, y)=(3, -2)
Consequently, there is only one solution to the linear system.
4) x+y-4=0
2x-3y-3=0
By solving these two equations we get,
x=3 and y=1
(x, y)=(3,1)
Consequently, there is only one solution to the linear system.
5) 5x-y-5=0
5x-y-15=0
a₁/a₂=1
b₁/b₂=1
c₁/c₂=1/3
∴ a₁/a₂=b₁/b₂≠c₁/c₂
Therefore, the linear system has no solution.
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Evaluate. [(1 1/5−2/5)⋅(−3/4)3]÷(−9) What is the value of the expression? Enter your answer as a simplified fraction in the box. NEED ANSWER NOW PLEASE!!!!!!!!!!!!!!!
Answer:9/20
Step-by-step explanation:
11/5-2/5=9/5
-3/4*3= 9/4
9*-9=-81
5*4=20
-81/20 /-9
9/20
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 25 pounds each, and the small boxes weigh 50 pounds each. There are 105 boxes in all. If the truck is carrying a total of 3, 875 pounds in boxes, how many of each type of box is it carrying?
Choose one:
Number of large boxes: 5
Number of small boxes: 10
Number of large boxes: 50
Number of small boxes: 55
Number of large boxes: 38
Number of small boxes: 75
Number of large boxes: 55
Number of small boxes: 50
Answer:
There are 105 boxes in all. If the truck is carrying a total of 3, 875 pounds in boxes, how many of each type of box is it carrying?
50 large boxes
55 small boxes
4a² + 4ab-3b² = (2a+3b)(_)
Complete the factoring
Answer:
(2a + 3b)(2a - b)
Step-by-step explanation:
4a² + 4ab - 3b²
consider the factors of the product of the coefficient of a² and b² which sum to give the coefficient of the ab- term.
product = 4 × - 3 = - 12 and sum = 4
the factors are + 6 and - 2
use these factors to split the ab- term
= 4a² + 6ab - 2ab - 3b² ( factor the first/second and third/fourth terms )
= 2a(2a + 3b) - b(2a + 3b) ← factor out (2a + 3b) from each term
= (2a + 3b)(2a - b)