The inequality that reflects the given region, according to the Factor Theorem, is:
y< -(x+40)(x+50)
What is the Factor Theorem?When completely factoring polynomials, the factor theorem is employed in mathematics. It is a theorem that relates the factors and zeros of a polynomial. If f(x) is a polynomial of degree n 1 and 'a' is any real number, then (x-a) is a factor of f(x) if f(a)=0.
According to the Factor Theorem, a polynomial function with roots x₁, x₂, ....xₙ is given by
f(x)=a(x-x₁)(x-x₂)...(x-xₙ)
In which a is the leading coefficient.
The roots are given as follows:
x₁=-40, x₂=-50
Hence:
y = a(x + 40)(x +50)
It includes the point (-55,-75), hence:
-75 = a(-55 + 40)(-55 +50)
a = 75/(15 x 5)
a = 1
The equation that is less than the region is:
y< -(x+40)(x+50)
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Answer:
d
Step-by-step explanation:
if X-2₁ X-3 and X+4 are factors of f(x)=x³ +ax² + bx+c then what are the possible Values of ab and c?
The values of a, b, c are a = -1, b = -14, c = 24
Given expression is f(x)=x³ +ax² + bx+c,
To find out the values of a, b, c:
There are two methods
Method - 1:
(x-2)(x-3)(x+4)= x³ +ax² + bx+c
Now we have to compare coefficients as
a = -1, b = -14, c = -24
Method - 2:
If (x-2) is a factor, then x = 2 is a solution. If x = 2 is a solution, then if we substitute x = 2, the polynomial will equal 0.
The same with x-3 and x+4. We can form 3 equations which we can solve simultaneously.
So, Equation 1 = 8+4a+2b+c = 0
Equation 2 = 27+9a+3b+c = 0
Equation 3 = -64+16a-4b+c = 0
As you can see, we get the same answer, just with a different methods.
Hence the answer is, the values are a = -1, b = -14, c = 24.
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La orden es: Despejar las siguientes ecuaciones y encontrar 4 valores y graficar en un solo plano cartesiano cada par de ecuaciones
Las ecuaciones son:
4x+8y=16 x-4y=12
-3y+9y=27 8x-4y=24
-4x+4y=16 -x+6y=12
4x-8y=33 X=4y=48
AYUAAA
Answer: huh?
Step-by-step explanation:
huh?
What would the monthly payment be on a $9,000 car loan at 8.85% interest for a five-year term?
Answer:
186.17
Step-by-step explanation:
Which answer choice uses exponents to show the expression below?
10(5 · 5 + 10) − 2 · 2 · 2
Answer:
5² · 10 + 10² - 2³
Step-by-step explanation:
10(5 · 5 + 10) − 2 · 2 · 2 =
= 5² · 10 + 10² - 2³
If the second term of an arithmetic sequence is 7 and the fourth term is 1, what is the 15th term? (non complicated answer would be extremely appreciated <3)
⇒[tex]T_{n} =a+(n-1)d[/tex] is the formula to find the general term of the arithmetic sequence.
⇒Note to find the second term we will plug in 2 in the place of n in the formular and simplify.
⇒[tex]T_{2} =a+(2-1)d\\T_{2} =a+(1)d\\T_{2} =a+d[/tex]
⇒It is given that the second term is 7 meaning in the place of [tex]T_{2}[/tex] in the equation above since we do not know the value of a and d we will plug in 7 and have the equation [tex]7=a+d[/tex] as our first equation.
⇒ For the fourth term [tex]T_{4}[/tex] we follow the same step of using the general formula to find the nth term by plugging in 4 in the place of n and and simplify
[tex]T_{4} =a+(4-1)d\\T_{4}=a+(3)d\\T_{4}=a+3d[/tex]
In the place of [tex]T_{4}[/tex] plug in 1 for the fourth term is equal to 1 to have the second equation
[tex]1=a+3d[/tex]
Note we can now use the two equations we have now to find the value of a which is the first term and d which is the difference.
7=a+d......1st equation
1=a+3d...2nd equation
∴from the first equation by making a the subject of the equation we get
a=7-d
from the second equation making a the subject of the equation we get a=1-3d
Now let us equate first equation and the second equation since they are both equal to a and solve for d.
[tex]7-d=1-3d\\-d+3d=1-7\\2d=-6\\\frac{2d}{2} =\frac{-6}{2} \\d=-3[/tex]
⇒Now you can see that we have the difference of the arithmetic sequence equal to -3
⇒To find the value of a you can use any of the equations from the ones we created . I will use the equation a=7-d
[tex]d=-3\\a=7-d\\a=7-(-3)\\a=7+3\\a=10[/tex]
⇒ to get the 15th term we will go back to the general formula of finding the nth term in the place if n we will plug in 15 and simplify the formula
[tex]T_{15} =a+(15-1)d\\T_{15}=a+(14)d\\T_{15}=a+14d\\[/tex]
⇒Now we find that the 15th term is equal to a plus 14(d)
⇒Note we already have the value of a and we can just plug them in to find the value of the 15th term and simplify.
[tex]a=10,d=-3\\T_{15}=a+14d\\\\T_{15}=10+14(-3)\\T_{15}=10-42\\T_{15}=-32[/tex]
⇒The 15th term is -32
Explain negative exponents. Why do you find the reciprocal of the base and then, make the exponent positive?
Answer:
Step-by-step explanation: A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.
the lengths of the upper end lower bases of a trapezoid are 6 centimeters and 10 centimeters respectively, and the distance between them is 15 centimeters. what is the area of the trapezoid
Given data:
The upper end length of the trapezoid is: a=6 cm
The lower end length of the trapezoid is: b=10 cm
The height of the trapezoid is: h=15 cm
The expression to calculate the area of the trapezoid is,
[tex]A=\frac{1}{2}\times h\times(a+b)[/tex]Substitute vall known values in the above expression.
[tex]\begin{gathered} A=\frac{1}{2}\times15\times(6+10) \\ =\frac{1}{2}\times15\times16 \\ =\frac{240}{2} \\ =120cm^2 \end{gathered}[/tex]Thus, the area of the trapizoid is 120 square centi meter.
A ferry travelled from Jetty A to Jetty B in 3 h. It then travelled from Jetty B back to
Jetty A in 2 h. The distance between the two jetties was 80 km.
Find the total time taken for the whole journey.
Find the average speed for the whole journey.
Average Speed = 160÷5= 32km/hr
Given,
A ferry traveled from Jetty A to Jetty B in 3 h. It then traveled from Jetty B back to Jetty A in 2 h. The distance between the two jetties was 80 km.
To find,
Total time for the whole journey,
Solution: Time is taken from Jetty A to Jetty B = 3 hours
and Jetty B to Jetty A = 2 hours
Total time = 3 h + 2 h = 5 h
Average Speed = Total Distance ÷ Total Time
Since, Total distance = 80×2= 160
Average Speed = 160÷5= 32km/hr
a) 5 hours
b) 32km/hr
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The following is a pie chart that presents the percentages spent by a certain household on its five largestannual expenditures. What percentage of the money was spent on housing, insurance, and utilities?Choose one. 5 pointsHOUSING 24.8% , FOOD 27.7%, insurance 26.7%, recreation 7.9% UTILITIES 12.9
1) Since in this pie chart, we have a budget. Let's locate the sectors for Housing, Insurance, and utilities
2) Enlisting them:
Housing: 24.8%
Insurance: 26.7%
Utilities: 12.9%
\%
So we can add them up:
[tex]undefined[/tex]On a floor plan, Bella's rectangular basement measures 3 centimeters by 5 centimeters If the floor plan has a scale of 1 centimeter = 2 meters what is the actual area of Bella's basement?
Answer:
60 meters^2
Step-by-step explanation:
1/2= 3/x
2(3)=x
6=x
1/2=5/x
x=2(5)
x=10
And then we multiply the 2 sides together
10x6
60
Hopes this helps please mark brainliest
what 6y=3x-9, in the simplest form
Answer: x=2y+3
Step-by-step explanation:
Switch around the 6y
3x-9=6y
Add 9 to both sides
3x-9+9=6y+9
3x=6y+9
Divide everything by 3
x=2y+3
Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y= 6x-8
Step-by-step explanation:
you pick two y values and subtract them. then take two x values and subtract them. divide those two awnsers with y on top. the -8 is the y intercept because when x is 0, the y is -8.
Answer:
Step-by-step explanation:
recall slope m is:
slope = m
m = (y2-y1) / (x2-x1)
point P1 (0,-8) in the form (x1,y1)
point P2(1,-2) in the form (x2,y2)
m = { -2-(-8) } / { 1-0 }
m = { -2+8 } / 1
m = 6 /1
m = 6
then plug in any point, I'll use P1
y - y1 = m(x -x1) (point-slope formula)
y - (-8) = 6*(x-0)
y+8 = 6x
y= 6x -8 (slope-intercept formula) :)
A Saint Bernard puppy weighs 21 1/2pounds at nine weeks old. After that, it gains 2/5 pounds perweek on average. How many weeks old must the puppy be if it weighs 25 1/10 pounds
From the information available, the puppy weighs 21 1/2 pounds (or 21.5 pounds) at nine weeks old. We shall take this to be the initial value. Hence, we can deduce the following function that relates the weight to the age (in weeks).
[tex]f(x)=21\frac{1}{2}[/tex]However,the puppy gains weight at the rate of 2/5 pounds per week.
Using the weight at nine weeks as the initial value as shown above, we would now have the function re-written as;
[tex]f(x)=21\frac{1}{2}+\frac{2}{5}x[/tex]However, the weight currently is given as 25 1/10 pounds, and we can insert this into the output of the function and then derive the input, as follows;
[tex]undefined[/tex]I'm having some problems with this logarithmic question I will upload a photo
The Solution.
[tex]Let\log _{\frac{1}{9}}(\frac{1}{9})=x[/tex]Writing the above equation in index form, we have
[tex]\begin{gathered} (\frac{1}{9})^1=(\frac{1}{9})^x \\ Then\text{ it follows that} \\ 1=x \\ x=1 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _749=x \\ So\text{ we have} \\ 49=7^x \\ \text{Making the base of both sides equal, we have} \\ 7^2=7^x \\ x=2 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _{\frac{1}{4}}16=x \\ \\ 16=(\frac{1}{4})^x \\ 16=4^{-1\times x} \\ 4^2=4^{-x} \\ -x=2 \\ x=-2 \end{gathered}[/tex][tex]\begin{gathered} \text{Let }\log _{125}5=x \\ \text{cross multiplying, we have} \\ 5=125^x \\ 5^1=5^{3x} \\ 3x=1 \\ \text{Dividing both sides by 3, we get} \\ x=\frac{1}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _8(\frac{1}{8})=x \\ \\ \frac{1}{8}=8^x \\ \\ 8^{-1}=8^x \\ -1=x \\ x=-1 \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _9(1)=x \\ 1=9^x \\ 9^0=9^x \\ x=0 \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }\log _{\frac{1}{9}}(-1)=x \\ \\ -1=(\frac{1}{9})^x \\ \\ No\text{ solution because it has no real value.} \end{gathered}[/tex]10. What is the equation of the directrix for the parabola-8(y - 3)=(x +4)2?A) y=5B) y=1C) y=-2D) y=-6
SOLUTION:
Step 1:
In this question, we are given the following:
The equation of the directrix for the parabola:
[tex]-8\text{ \lparen y-3\rparen= \lparen x+ 4\rparen}^2[/tex]Step 2:
The details of the solution are as follows:
Next, we can see that the equation of the directrix for the parabola is at:
[tex]\text{y = 5 }[/tex]This is because:
[tex]\begin{gathered} y\text{ -3 = \lparen}\frac{-1}{8})\text{ \lparen x + 4 \rparen}^2 \\ y\text{ = \lparen-}\frac{1}{8})\text{ \lparen x + 4\rparen}^2+\text{ 3} \end{gathered}[/tex]Then, y = k - p
y = 3 - p
p = 1/ 4a
p = 1 / 4(-1/8)
p = -2
y = 5
1. A contractor is building a new room onto the back of
Darnell's house. The contractor adds a diagonal brace to
the frame of one of the walls. The frame is 15 feet long
and 8 feet tall. How long is the diagonal brace?
Answer:
the answer is 23
Step-by-step explanation: use the formala of a triangle
which means you either add or subtract the sides and since it is the big side you are missing you have to add and when you do you get 23
find area and perimeter
Answer:
Area: 20cm^2
perimeter: 20cm
(4*2) + (4*3) =
8 + 12 = 20cm^2
Determine if the expression -b^{3}c−b 3 c is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The expression -b³c is the polynomial. The type of the polynomial is cubic polynomial and the degree is 3.
Polynomial:
Polynomial is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
Given,
Here we have the expression -b³c.
And we need to find the following:
1) check it if is polynomial or not
2) type of the polynomial
3) degree.
As per the given definition, the expression -b³c is the polynomial.
Here we have the expression -b³c the highest power value for this polynomial is 3.
Therefore, the degree of this polynomial is 3 and the type of the is cubic polynomial.
Because we have identify the type based on the degree value here the value of degree is 3 so the type of the polynomial is cubic one.
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A toy rocket was fired into the air. The height, h,of the rocket at time t seconds is recorded in the tablebelow. Using an equation to model the data, find theheight of the rocket after 5 seconds.
we have the ordered pairs
(0,0)
(1,76)
(2,120)
(3,132)
(4,112)
Plot the given points
see the attached figure
In this problem we have a vertical parabola open downward
The vertex represents a maximum
The equation is of the form
y=ax^2+bx+c -----> quadratic equation
using a quadratic regression calculator
we have that
a=-16
b=92
c=0
therefore
y=-16x^2+92x
For x=5 sec
substitute
y=-16(5)^2+92(5)
y=60
the answer is
the height is 60 unitsAlternative method (approximate solution)
The quadratic equation in vertex form is equal to
y=a(x-h)^2+k
where
(h,k) is the vertex
I will assume that the vertex in this problem is the point (3,132)
so
(h,k)=(3,132)
substitute
y=a(x-3)^2+132
Find out the value of a
we have the point (0,0)
substitute in the equation
0=a(0-3)^2+132
0=9a+132
a=-132/9
a=-14.67
therefore
y=-14.67(x-3)^2+132
For x=5
y=-14.67(5-3)^2+132
y=73.33 units
Third Method
using the equation
y=ax^2+bx+c
points (0,0), (1,76) and (2,120)
(0,0) --------> 0=a(0)^2+b(0)+c ----------> c=0
y=ax^2+bx
(1.76) ------> 76=a(1)^2+b(1) ----------> a+b=76 ------> equation 1
(2,120) ----> 120=a(2)^2+b(2) ----> 4a+2b=120 ----> equation 2
solve the system of equations
the solution of this system is
a=-16
b=92
therefore
the equation is
y=-16x^2+92x (same first method)what is this help me i need fast help
The solution for the equations are :
She subtracts 12 from w , divides by 3 , then multiplies by 6 = 2w - 24
She subtracts 12 from w , multiplies by 3 , then divides by 6 = w/2 - 6
She multiplies w by 3 , subtracts 12 , then divides by 6 = w/2 - 2
She divides w by 3 , subtracts 12 , then multiplies by 6 = 2w - 72
She multiplies w by 6 , subtracts 12 , then divides by 3 = 2w - 4
She divides w by 6 , subtracts 12 , then multiplies by 3 = w/2 - 36
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Winnie is thinking of a number = w
Now ,
a)
She subtracts 12 from w , divides by 3 , then multiplies by 6
So , the equation will be
A = ( (w - 12 ) / 3 ) x 6
A = ( w - 12 ) x 2
A = 2w - 24
Therefore , the equation is 2w - 24
b)
She subtracts 12 from w , multiplies by 3 , then divides by 6
So , the equation will be
A = ( ( w - 12 ) x 3 ) / 6
A = ( w - 12 ) / 2
A = w/2 - 6
Therefore , the equation is w/2 - 6
c)
She multiplies w by 3 , subtracts 12 , then divides by 6
So , the equation will be
A = ( 3w - 12 ) / 6
A = w/2 - 2
Therefore , the equation is w/2 - 2
d)
She divides w by 3 , subtracts 12 , then multiplies by 6
So , the equation will be
A = ( ( w/3 - 12 ) ) x 6
A = ( w/3 ) x 6 - 12 x 6
A = 2w - 72
Therefore , the equation is 2w - 72
e)
She multiplies w by 6 , subtracts 12 , then divides by 3
So , the equation will be
A = ( 6w - 12 ) / 3
A = ( 6w ) / 3 - 12/3
A = 2w - 4
Therefore , the equation is 2w - 4
f)
She divides w by 6 , subtracts 12 , then multiplies by 3
So , the equation will be
A = ( w/6 - 12 ) x 3
A = ( w/6 ) x 3 - 12 x 3
A = w/2 - 36
Therefore , the equation is w/2 - 36
Hence , the equations are evaluated and solved
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what is minus sixteen minus minus twenty
Answer: (-16)-(-20)= 4
Step-by-step explanation:
A football is kicked into the air from an initial height of 4 feet. The height, in feet, of the football above the ground, is given by s(t) = -16t^2 + 50t + 4, where the t is time, in seconds, and t>= 0. At what time will the football be 25 feet above the ground?
The time at which the football is 25 feet above the ground is 1/2 seconds and 21/8 seconds.
Given that:-
[tex]s(t) = -16t^2 + 50t + 4[/tex]
Where s(t) represents the distance traveled by the football after t seconds.
We have to find the time at which the football is 25 feet above the ground.
Putting s (t) = 25 feet, we get,
[tex]25 = -16t^2 + 50t + 4\\\\ -16t^2 + 50t -21=0\\\\ 16t^2 - 50t - 21=0[/tex]
Using middle term split theorem to solve the equation, we get,
[tex]16t^2 -42t -8t+ 21=0[/tex]
2t(8t - 21) -(8t-21) = 0
(8t - 21)(2t - 1) = 0
t = 21/8 and 1/2 seconds.
Hence, the time at which the football is 25 feet above the ground is 1/2 seconds and 21/8 seconds.
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PLEASE 95 POINTS TO WHOEVER ANSWER'S THIS QUESTION
The coordinate plane below shows the map of a school and some of the locations:
What is the distance between Math and English, rounded to the nearest tenth of a unit?
The distance between points Math(-3, -5), and English(2, 2) is 8.60 units after using the distance formula.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
It is given that:
Math(-3, -5)
English(2, 2)
Using distance formula:
D = √[(x₂ - x₁)² + (y₂ - y₁)²]
D = √[(2 - (-3))² + (2 - (-5)₁)²]
D = √74
D = 8.60 units
Thus, the distance between points Math(-3, -5), and English(2, 2) is 8.60 units after using the distance formula.
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two angles are supplementary. One angle measures 12 degrees less than 3 times the other. find the measure of each angle
Angle 1 = A
Angle 2 = B
They are supplementary, that means that they add 180 degrees, then: A + B = 180
One angle measures 12 degrees less than 3 times the other, tahn means: A - 12 = 3B
Equation 1: A + B = 180
Equation 2: A - 12 = 3B
Solving for A in equation 1:
A + B = 180
A = 180 - B
Using this value into equation 2, and solving for B:
A - 12 = 3B
(180 - B) - 12 = 3B
180 - B - 12 = 3B
168 = 3B + B = 4B
4B = 168
B = 168/4 = 42
B = 42
Using the expression we found for A:
A = 180 - B = 180 - 42 = 138
A = 138
Answer
42 degrees and 138 degrees
i need help i suck at dividing decimal
Answer: 1. 0.185185185 keeps going
2. 56
3. 63.02
Step-by-step explanation:
6. A sandwich store charges a $10 delivery fee, and $4.50 for each sandwich.
a. What is the total cost (sandwiches and delivery charge) if an office orders 6
sandwich?
Answer:
Step-by-step explanation:
4.50 per sandwich
6 sandwiches
4.50 x 6 = 27
+ Delivery fee $10
$27 + $10 =
$37 total
Clarissa had 72 candy bars to sell. She sold 4 per day for 8 days. She ordered 15 more candy bars to share with her 3 friends. The following expression can be used to find the number of candy bars Clarissa had left.
(I need the answer ASAP please!
72 – 4 • 8 – 15 ÷ 3
Based on this expression, how many candy bars did Clarissa have left?
The number of candy bars Clarissa had left are 55
Given,
In the question:
Clarissa had 72 candy bars to sell. She sold 4 per day for 8 days. She ordered 15 more candy bars to share with her 3 friends.
To find the number of candy bars Clarissa had left.
Now, According to the question:
Total candy sells is 72
Sold candy = 4 per day for 8 days
Sharing candy is 15
Based on the given conditions,
Formulate:
15 + 72 - 8 x 4
Calculate the product or quotient:
15 + 72 - 32
calculate the sum or difference
87 - 32
= 55
Hence, the number of candy bars Clarissa had left are 55.
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Answer: 35
Step-by-step explanation:
graph the linear function identify the x-intercept.
y=-x
The x-intercept of the given linear function is 0 and the graph of the linear ufnction is shown.
What is the x-intercept?A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = MX + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.So, plot the linear function:
Plot y = -x as follows:(Refer to the graph attached below)
We can clearly see that the x-intercept is 0.Therefore, the x-intercept of the given linear function is 0 and the graph of the linear ufnction is shown.
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(04.02 MC) The table below shows the number of cookies in different numbers of packs: Number of Packs Number of Cookies 2 6 3 9 4 12 5 25 Is this true or false? The numbers in the table represent a proportional relationship. O True O False
According to the given table, the y-values are triple than x-values except by the last pair (5,25), this means the table does not represents a proportional relationship because the last pair doesn't follow.
Hence, the answer is False.
Im doing a practice assignment and im not the best at word problems Im not understanding the question
A sample statistic is is any quantity from the sample of a population.
We can see in the last option, that from the population (total of subjects of study) Kaisa, selected 84 of the total students. This fits in to the definition of sample statistic.
Thus, the correct option is the last one.