The rational zero test is also known as the rational root test, and it is used to determine the potential root of a function.
(a) 1/2 is not a possible zero of the function
The function is given as:
[tex]f(x) =x^3 - 5x + \frac 25[/tex]
For a function,
[tex]f(x) = px^n +......q[/tex]
The list of possible roots is:
[tex]Roots = \pm\frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
Multiply both sides of [tex]f(x) =x^3 - 5x + \frac 25[/tex] by 5
[tex]5f(x) = 5x^3 - 25x + 2[/tex]
So, we have:
[tex]p= 5[/tex]
[tex]q = 2[/tex]
The factors are:
[tex]p =\pm 1, \pm 5[/tex]
[tex]q =\pm 1, \pm 2[/tex]
So, the possible roots are:
[tex]Roots = \pm\frac{1,2}{1,5}[/tex]
Split
[tex]Roots = \pm1, \pm \frac 15, \pm 2, \pm \frac 25}[/tex]
Hence, 1/2 is not a possible zero of the function
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how to solve the following system y=(1/2)x^2+2x-1 and 3x-y=1
Answer:
(0,-1),(2,5)
Step-by-step explanation:
3x-y=1
0.5[tex]x^{2}[/tex]+2x-1=y
Substitute the equation of y into the other equation
3x-(0.5[tex]x^{2}[/tex]+2x-1)=1
3x-0.5[tex]x^{2}[/tex]-2x+1=1
collect like terms
-0.5[tex]x^{2}[/tex]+x=0
Solve for x
x(-0.5x+1)=0
0=-0.5x+1
-1=-0.5x
x=2 x=0
Back substitute into the other original equation and solve for y
3(2)-y=1
6-y=1
y=5
(2,5)
3(0)-y=1
-1(-y)=-1(1)
y=-1
(0,-1)
please answer!!!!!!!!!
Answer:
C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 5.
Step-by-step explanation:
BRAINLIEST
Do one of the above and show your work
Answer:
10, C = circumference = 2 pi 11 = 69.11 since the radius = 6
PR = C / 2 = 34.6 since PR is 1/2 the circumference
PS = 34.6 - 16 = 18.6 since PS is 16 ft short of C/2
Answer:
Step-by-step explanation:
Which number is an integer? Negative three-fourths 0 2. 3 Pi.
The number that is an integer is 0.
An integer is a number that does not have fractions or decimals. Examples of integers are 50, - 1. A fraction is a number that is made up of numerators and denominators. An example is 3/4. A decimal is made up of tenths, hundredths and thousandths. An example is 2.3.
Negative three-fourths is not an integer because it is a fraction. 2.3 and pi is not an integer because it is a decimal.
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Given: triangle JKN J (3,1), K (5,2), N (1,5)
(all 3 need separate answers)
a) find the coordinates of the centroid.
b) find the coordinates of the orthocenter.
c) find the coordinates of the circumcenter and length of radius of circumscribed circle.
Answer:
Let the radius of the circumscribed circle be r.
The formula for calculating the radius r is
r
=
Δ
s
Where
Δ
is the area of the triangle
s
is the semi-perimeter.
s
for any triangle is calculated as
s
=
a
+
b
+
c
3
Where,
a
,
b
,
c
is the sides of the triangle
Δ
=
√
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
(Heron's Formula)
Plug in the values and get the answer.
Once you have the radius, you can easily find out the area of the circle.
Step-by-step explanation:
W
Enter the value of x-21.
(x - 21)
71
What addition statement does this show?
A. 5.2 + 6.4 = –11.6
B. –5.2 + 6.4 = –11.6
C. 5.2 + (–6.4) = –11.6
D. –5.2 + (–6.4) = –11.6
Answer:
D. –5.2 + (–6.4) = –11.6
Step-by-step explanation:
First, you can eliminate A and C because 5.2 is positive. Since the red arrow is pointing left, it indicates that the number (-5.2) is negative.
Then, you look at the second arrow, the green one. It is pointing left, so it would be -6.4.
I hope this helps :)
how to find r in a geometric sequence calculator
Step-by-step explanation:
We can find r by dividing the second term of the series by the first. Substitute values for a 1 , r , a n d n \displaystyle {a}_{1}, r, \text{and} n a1,r,andn into the formula and simplify. Find a1 by substituting k = 1 \displaystyle k=1 k=1 into the given explicit formula.
Juliet needs to rewrite 3 (x 2) = 6 y in slope-intercept form so she can easily graph it. Which step would be correct to start the process? She could combine the x and 2 to get 3 (2 x) = 6 y. She could divide both sides by 3 to get x 2 = 2 y. She could distribute the 3 to get 3 x 2 = 6 y. She could subtract the 6y to get Negative 6 y = 3 (x 2).
The step that would be correct to start the process is she could distribute the 3 to get 3x+2=6y
Note that the standard equation of a line in slope-intercept form is expressed as y = mx + b
m is the slopeb is the y-interceptGiven the function 3(x+2)=6y, for Juliet to write in slope-intercept form, the best approach is to first divide both equations by 6 as shown:
[tex]3(x+2)=6y \\\frac{3(x+2)}{6} =\frac{6y}{6} \\\frac{x+2}{6}=y[/tex]
Swap sides
[tex]y=\frac{x+2}{6}\\y=\frac{1}{6}x +\frac{1}{3}[/tex]
She could as well distribute the 3 over x + 2 to have:
3(x + 2) = 6y
3x + 3(2) = 6y
3x + 6 = 6y
Hence based on the option, the step that would be correct to start the process is she could distribute the 3 to get 3x+2=6y
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Answer:
Its C
Nevermind Its Not its A or B
Step-by-step explanation:
:)
You must write your answer in fully simplified form.
8a= 5
Answer:
x = 5/8
Step-by-step explanation:
[tex]\frac{8x}{8} = \frac{5}{8}[/tex]
x=[tex]\frac{5}{8}[/tex]
The teacher collected some snowfall data during one of the snow days last year. Estimate the total snowfall throughout the day.
The total snowfall throughout the day is the expected value of the distribution.
The estimated total snowfall during the day is 30 inches
Start by calculating the average rate of snow collected on that day.
[tex]Rate = \frac{0 + 1.5 + 2.5 + 2.0 +1.0 +0.5}{6}[/tex]
This gives
[tex]Rate = \frac{7.5}{6}[/tex]
Divide 7.5 by 6
[tex]Rate = 1.25[/tex]
There are 24 hours in a day.
So, the total snowfall is:
[tex]Total = Rate \times Hours[/tex]
This gives
[tex]Total = 1.25 \times 24[/tex]
Multiply
[tex]Total = 30[/tex]
Hence, the estimated total snowfall during the day is 30 inches
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Convert this improper fraction to a Mixed Number 40/10 plz i need help
Answer:
4
Step-by-step explanation:
How many times does the denominator go into the numerator, in this case 10 goes into 40 4 times.
a quter of 30 is=
pleas help
Answer:
7.5
Step-by-step explanation:
If 'quter' is quarter, then 30(1/4) is 7.5
A quarter of 30 is 7.5
All you gotta do is divided 30 by 4 cause a quarter is half of the half. It's the 1/4th part of the whole.
nolan is taking a multiple choice test his grade is given by the equation y=70-2x where y represents his final score and x represents the number of questions he got wrong . waht could the number 70 represents in the equation?
Answer:
70 could represent the total number of points nolan can earn on the test
Step-by-step explanation:
A store manager predicts that 100 hats will be sold if each hat costs $12. The manager predicts that 4 less hats will be sond for every $1 increase in price. For what prices can the manager predict that 60 hats will be sold?
Answer:
100-60=40
40/4=10
10*$1=$10
$12+$10=$22
The table shows the distance between Greenville and nearby towns. The distance between Astaville and
Greenville is 14 miles less than the distance between Greenville and Jonesborough,
Distance between Greenville and
Nearby Towns(miles)
Jonesborough
24
Willfower 21
Maybem 30
Part 1 out of 2
Enter two equations that state the relationship of the distances between the three towns. Use x as the
variable
Monty Ricker obtained a used car loan of $6,000.00 at 8% for 36 months. The monthly payment is $ 187.80. The balance of the loan after 12 payments is $ 4,159.90. The balance after the 34th payment is $ 380.60.
Answer:
What is the intrest for the 13th payment?
Answer: What is the interset
Step-by-step explanation:
46. A sphere shaped bowl has a radius of 5.5 inches How much water can the bowl hold? Round to the nearest tenth.
Answer:
try 17.89 cm..then 18 for answer
The blueprint for Moreno's living room has a scale of 2 inches equals 3 feet. The family wants to use a scale of 1 inch equals 2 feet. What is the width of the living room on the new blueprint? (The width is 8)
Answer:
Part a) The scale of the new blueprint is
Part b) The width of the living room in the new blueprint is
Step-by-step explanation:
we know that
The scale of the original blueprint is
and
the width of the living room on the original blueprint is 6 inches
so
Find the actual width of the living room, using proportion
Find the actual length of the living room, using proportion
Find the scale of the new blueprint, divide the length of the living room on the new blueprint by the actual length of the living room
simplify
Find the width of the living room in the new blueprint, using proportion
for each fraction below find an equivalent fraction with a denominator 200.
fraction 14/25
Answer:
112/200
Step-by-step explanation:
To find an equivalent fraction with a new denominator you can simply multiply by 1. However, you must multiply by different forms of 1. Remember that any number divided by itself is equal to 1. Additionally, because of the identity property of multiplication, any number multiplied by 1 is still equivalent.
In this case, you should multiply by a fraction that will make 25=200. To get 200 from 25 you must multiply by 8. So, multiply the whole fraction by 8/8. This gives you (14/25)*(8/8)=112/200.
Lily has 7 fewer ribbons than Dora. Lily has 13 ribbons. How many ribbons does Dora have?
Answer: 6
Step-by-step explanation:
13-7=6
(03.02 MC)
The vertices of AGHI are G (2, 4), H (4,8), and I (8,4). The vertices of AJKL are ) (1.), K (2, 3), and L (4,1). Which conclusion is true about the triangles?
whats the answer
Answer:
The coordinates of J are missing. Plus, I don't see options for the conclusions. I made an imaginary point J, which you could correct to form the proper triangle.
Step-by-step explanation:
See the attachment. Plot all the vertices, including a corrected point J and draw the resulting triangle. It might be that AJKL is a slightly smaller, shifted version of AGHI. Enter the correct coordinates and then compare.
PLS HELP ME I DON'T GET IT
Answer:
(a) $14,912 saved
(b) $58,000 aid needed
Step-by-step explanation:
(a)Nola is saving $200 each month. That means she will have saved 60 times that amount after 60 months:
60 × $200 = $12,000
When she adds that to her current savings she will have saved a total of ...
$12,000 +2,912 = $14,912 . . . by the time she starts college
__
(b)The figure is telling you Nola will need $72,912 for 4 years of college. If she funds $14,912 from her own savings, then she will need an additional amount of ...
$72,912 -14,912 = $58,000 . . . . amount of financial aid needed
Which equation represents the function f(x) = (1. 6)x after it has been translated 5 units up and 9 units to the right? g(x) = (1. 6)x 5 â’ 9 g(x) = (1. 6)x 5 9 g(x) = (1. 6)x â’ 9 5 g(x) = (1. 6)x 9 5.
The equation that represents they function f(x) = (1.6)^x after it has been translated 5 units up and 9 units to the right is;
g(x) = [(1.6)^(x - 9)] + 5
We are given the function;
f(x) = (1.6)^x
Now,when we translate a function 9 units to the right, it means that we will subtract 9 from the x unit to give;
g(x) = (1.6)^(x - 9)
Now, when we translate it 5 units upwards, it means we are adding 5 to f(x). Therefore, we now have;
g(x) = [(1.6)^(x - 9)] + 5
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To reach the roof , how far away from the building should he place the base of the ladder ?
Answer: many be 5-10 feet
So far, Charlie has pures 456.6 Glories. He wants to burn a total of 500 calorierHow many more calories must Charlie burn?
| 0
2
A motorcycle can run 108km in 2h20mn Find the average speed
Answer:
do it got a picture
on the edge2020
Step-by-step explanation:
Why does demand for a product or service play a significant role in starting a new business?
Answer:
Basic economics like demand should important to you whether you run a seasonal business, buy a vacation property for passive income, or run a more traditional firm.
Write an EQUATION with an undefined slope:
Answer:
Example of an equation with an undefined slope: x = 2
Step-by-step explanation:
DefinitionsThe standard form of linear equations with an undefined slope is x = a, whose graph represents a vertical line. The value of a in the standard form is the x-intercept, (a, 0).
The slope is the ratio of the vertical change in y-values to the horizontal change in x-values.
[tex]\displaystyle\mathsf{Slope(m) =\:\frac{\triangle y}{\triangle x}\:=\frac{y_2 - y_1}{x_2 - x_1}}[/tex]
The slope of a vertical line is undefined because if we were to solve its slope, the denominator will be zero. As we know, division by zero is an undefined operation.
Example:For example, suppose that we have the following points (2, 5) (2, 10).
Let (x₁, y₁) = (2, 5)
(x₂, y₂) = (2, 10)
Substitute these values into the slope formula:
[tex]\displaystyle\mathsf{Slope(m) =\:\frac{\triangle y}{\triangle x}\:=\frac{y_2 - y_1}{x_2 - x_1}\:=\:\frac{10\:-\:5}{2\:-\:2}\:=\frac{5}{0}}[/tex]
Dividing the numerator, 5, by the denominator, 0, will have an undefined quotient.
Thus, the equation of the vertical line will be: x = 2, where a = 2.
1. Calculate the equation of the line through the points (1, 1), (4, 3), (10, 7) and (40, 27).
Answer:
y = (2/3)x + 1/3
Step-by-step explanation:
Check that a single straight line will actually go through all four of these points. Going from (1, 1) to (4, 3), the 'rise' is 2 and the 'run' is 3, which would make the slope, m, equal rise/run = 2/3. Going from (4,3) to (10, 7), m = rise/run = 4/6 = 2/3 (again).
Let's find the slope-intercept form of the equation of this line: y = mx + b
Arbitrarily choose the point (1, 1). Here x = 1, y = 1 and m = 2/3. Then
we have
1 = (2/3)(1) + b, or 1 = 2/3 + b, so that b must be 1/3.
The equation in question is y = (2/3)x + 1/3