This means that the polynomial does not have any rational roots and must have irrational roots.
The Rational Root Theorem states that any rational roots of a polynomial equation must take the form p/q, where p is a constant term factor and q is a leading coefficient factor.
In this case, the constant term is 22 and the leading coefficient is 4. Therefore, the possible rational roots are
+1/-1, +2/-2, +11/-11, +22/-22.
None of these possible rational roots are actual roots of the equation, so the polynomial does not have any rational roots and must have irrational roots.
None of the possible rational roots are actual roots, so the polynomial must have irrational roots.
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What is range of function f/x )= x 1 which is defined everywhere on its domain?
The range of the given function is:
Function [tex]x^-^1[/tex] may take any real number hence it's range is all real numbers.
Now, According to the question:
What is Range?
In statistics, the range of data is the difference between the highest and lowest values.It can be used as a measure of variability.For example, for the given data {3, 5,7, 4, 8 ,9}, the highest value is 9 and the lowest value is 3 . So the range of the data is 9 - 3 = 6In relations and functions, domain and range are important terms. The range is the set of all possible dependent values a relation can produce from a domain value. In a function, there will be exactly one output value for an input value.The given function is :
f(x) = [tex]x^-^1[/tex]
The range of the given function is:
Function [tex]x^-^1[/tex] may take any real number hence it's range is all real numbers.
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if 12 labor takes 20 days to dig a land. in how many days 8 labor can dig the same land? calculate
Answer: 30 days
Explanation: 12 x 20 = k, where k is a constant. 8x = k, where x is the number of days. So 12 x 20 = 8x, 8x = 240, x = 30 (30 days).
which point of concurrency is equidistant from every vertex
Answer:
Circumcenter
Step-by-step explanation:
The locus of points equidistant from two points is the perpendicular bisector of the line segment connecting the points. The circumcenter is the point of concurrency of the three perpendicular bisectors of the sides of a triangle.
Which of the following angles has a reference angle of 30 degrees
120
150
240
315
Answer:
150 because when you get 180-30=150
in the binary value 1002, what is the place value of the 1?
Answer: 4s place
Also could you mark my answer as brainliest? It helps and doesnt hurt
Ricardo is creating a budget for himself to set goals on how much money he wants to save. At his current job, he makes $1,000 per week, and spends $300 each week on his expenses. If he wants to save a total of at least $30,800, how many weeks at minimum does he have to work for in order to reach his goal?
Ricardo has to save for a minimum of 44 weeks.
What is savings?For the salary earner, the way of savings is the way that he or she may be able to achieve the gals of life. In the case of the question that we have here, at his current job, he makes $1,000 per week, and spends $300 each week on his expenses.
The target amount that he wants to save is $30,800.
Total income per week = $1,000
Expenses per week = $300
Amount saved per week = $700
To save $30,800;
700n = $30,800
n = Number of weeks
n = $30,800/700
n = 44 weeks
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Lune bought a bag of grapefruit, 1 5/8 of apples, and 2 3/16 pounds of bananas. The total weight of her purchases was 7 1/2 pounds. How many did the bag of grapefruit weigh?
Answer: 3 11/16 pounds
Step-by-step explanation:
7 1/2 - 1 5/8 - 2 3/16 = 4 1/2 - 5/8 - 3/16 = 4 8/16 - 10/16 - 3/16 = 72/16 - 13/16 = 59/16 pounds = 3 11/16 pounds
I need help solving this
Answer:
the answer is in the picture
How do you know if F x is one to one?
If no two elements in the domain of f correspond to the same element in the range of f, then a function f is 1 to 1.
To put it another way, there is only one image in the range for each x in the domain. Additionally, there is no y in the domain that is the image of more than one x. It is simple to determine whether a function is one-to-one if the graph of the function f is known. The Horizontal Line Test is a good one. The function is 1 -to-1 if no horizontal line intersects the graph of the function f at more than one point.
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the ratio of a area of two circles is 4/9.(a) find the ratio of their radii (b) the smaller circle has a radius of 12cm,find the radius of the larger one.
(a) The ratio of their radii is 2 : 3.
(b) The radius of the larger one is 18cm.
What is the area of a circle?
A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = πr2, (Pi r-squared), where r is the circle's radius. The square unit, such as m2, cm2, etc., is the unit of area.
Here, we have
Given: the ratio of the area of two circles is 4/9.
We let the radius of the smaller circle be r and the radius of the larger circle be R.
Then compare the areas of the two circles with the ratio given.
(a) πr²/πR² = 4/9
r²/R² = 4/9
r/R = 2/3
Hence, the ratio of their radii is 2 : 3.
(b) r is the smaller circle
r = 12 cm
r/R = 2/3
12/R = 2/3
R = 18cm.
Hence, the radius of the larger one is 18cm.
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5. Find the product of:
a) -2x (4x²-5x - 3)
Answer:
-8[tex]x^{3}[/tex] + 10[tex]x^{2}[/tex] + 6x
Step-by-step explanation:
Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car?
The time required for the new guy to finish the car is given by the equation A = 10/3 hours = 3 1/3 hours
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 ,
Let the time required for the new guy to finish the car be A
Now , the equation will be
The total time worked by the two mechanics = 2 hours
The time for the 1st person to finish the car = 6 hours
So , the amount of work done in 2 hours by 1st person = 2/6 = 1/3 of total
The time for the 2nd person to finish the car = 8 hours
So , the amount of work done in 2 hours by 2nd person = 2/8 = 1/4 of total
And , the remaining work = 1 - ( 1/3 + 1/4 )
On simplifying the equation , we get
The remaining work = 1 - ( 7/12 ) = 5/12 of the work
Now , the time required for the 2nd person to complete 5/12 of the work =
A = 5/12 x 8
A = 5 x 2/3
A = 10/3
A = 3 1/3 hours = 3 hours and 20 minutes
Hence , the time required is 3 hours and 20 minutes
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How do you draw y =- 2 on a graph?
To draw the line y=-2 on a graph, you'll need to plot the points (x, y) where x is the value of x and y=-2 is the value of y.
For example, if x is -1, then the point will be (-1, -2). You can plot the points and then draw a line connecting them to see the graph of y=-2.
Graphs are an important tool for evaluating equations, as they allow you to visualize the relationship between two variables. By plotting points on a graph, you can see how the variables interact with each other and can also identify any points of intersection.
Graphs can also be used to identify the range of values for which the equation is valid and the range of values for which it is not. Graphs are a useful tool for understanding equations and can help you make more informed decisions when evaluating them.
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LOTS OF POINTS
The zero of a quadratic function is . What does this tell you about the graph of this quadratic function?
A The parabola touches the x-axis in one place,x=-1/2 .
B The parabola crosses the x-axis in two places, x=-1/2 and x=1/2
C The parabola touches the x-axis at the origin.
D The parabola crosses the x-axis at x=-1/2 . You can substitute this value into the quadratic function to find the location of the other zero.
Answer: I'm pretty sure the the answer is B I had a question like this and my answer was b
Step-by-step explanation: if not I am soo sorry
can one of y’all help me , i’ll give brainliest
Answer: least to greatest
-13, -9, -8.1, -8, -7.9, -7, -3, 0, 3, 7, 7.9
x-5(x-1)=x(-2x3) solve the equation
Answer:
x-5(x-1)=x(-2x3)
x-5x+5=-5x
-4x+5=-5x
-4x+5-5=-5x-5
-4x+5x=-5x+5x-5
x= -5Step-by-step explanation:
How do you find the distance between two points in 6th grade?
The distance between two given points x₁ and x₂ for the 6th grade can be calculated by :
a. If the points lie in the same quadrants then distance = | x₂ - x₁ |
b. If the points lie in the different quadrant then distance = |x₂| + |x₁|.
As given in the question,
The distance between the two given points can be calculated in the following way:
Let us consider two points in the coordinate plane whose one coordinate is constant be ( x₁, y) and ( x₂ , y ).
a. Distance between two points in the same quadrants is given by :
= | x₂ - x₁ |
b. Distance between two points in the different quadrants is given by :
= |x₂| + |x₁|
It is represented by absolute value as distance is always positive.
Therefore, the distance between two given points with one coordinate constant for the 6th grade is given by :
a. If the points lie in the same quadrants then distance = | x₂ - x₁ |
b. If the points lie in the different quadrant then distance = |x₂| + |x₁|.
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"55 miles per hour" translated
55 miles per hour is equivalent to 24.6992 meters per second.
Translate milles to meter / second?
To convert miles per hour (mph) to meters per second (m/s), you can use the conversion factor 1 mile = 1609.34 meters.
To convert miles per hour (mph) to meters per second (m/s), you can use the conversion factor 1 mph = 0.44704 m/s.
So to convert 55 mph to m/s, you can multiply 55 by 0.44704:
55 mph * 0.44704 m/s/mph = 24.6992 m/s
Therefore, 55 miles per hour is equivalent to 24.6992 meters per second.
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a parabola has a focus point of (4,-2) and a vertex of (4,8). what is the equation of the directrix?
The equation of the directrix is y = -2.
What is equation?An equation is a mathematical statement that two expressions are equal. It is usually written using an equals sign (=) and is used to represent a relationship between two values, such as the relationship between two variables or between an unknown expression and a known value. Equations are fundamental to mathematics, and they are used in all branches of mathematics and science, including physics, chemistry, biology, engineering, and economics.
The equation of the directrix for the given parabola can be determined by using the coordinates of the focus point and vertex. Since the y-coordinate of the focus point is lower than the y-coordinate of the vertex, the directrix will be a line in the form of y = k, where k is the y-coordinate of the focus point (in this case, k = -2). Therefore, the equation of the directrix is y = -2.
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A model dinosaur is 6 feet tall. The scale used to make the model is 1 ft. = 7.5 ft. How tall is the real dinosaur? can someone explain it step by step please
45 feet is the height of the real dinosaur.
What is Scale?The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary throughout a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of size significant in two different ways.
Given, A model dinosaur is 6 feet tall. The scale used to make the model is 1 ft. = 7.5 ft.
Since the scale is 1 ft. = 7.5 ft
That means in the model 1 foot is equal to the real size of 7.5 feet
thus,
Real dinosaur's height = 6 * 7.5
Real dinosaur's height = 45 feet
Therefore, the Height of the real dinosaur is 45 feet.
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Tyrell dilated a figure by a scale factor of 3/2 . Which of the following is a true statement?
Responses
The area of the new figure will be 3/2 times the area of the original figure. Option C is correct.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
Tyrell dilated a figure by a scale factor of 3/2.
It implies that the new figure will be larger than the original size.
And makes the area of the new figure will be 3/2 times the area of the original figure.
Thus, the area of the new figure will be 3/2 times the area of the original figure. Option C is correct.
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Question 5 of 23
What is the slope-intercept equation of the line below?
A. y = 5x-2
B. y = -4/5x-2
C. y = 4/5x-2
D. y = 5x+2
The slope-intercept equation of the line below is C. y = 4/5x-2.
What is slope-intercept equation?Slope-intercept equation is a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. It can be used to graph a line on a two-dimensional plane, and is used to calculate the rate of change (rise/run) between two points on the graph.
This slope-intercept equation can be determined by analyzing the given line. By looking at the graph, we can see that the slope of the line is 4/5, which means that the coefficient of x in the equation is 4/5. Additionally, the y-intercept is at -2, so the equation is y = 4/5x-2.
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Write an equation in slope-intercept form of the line.
Answer: y=4-1/2x
Step-by-step explanation:
Y int is 4, negative slope, and going down one right two.
How do you graph natural log equations?
To graph natural log equations, first find the y-intercept for the equation. Then, find any asymptotes or solutions by setting the equation equal to 0. Next, find the domain and range and plot any points that it intersects with. Finally, draw the graph of the equation.
1. Find the y-intercept: Set the equation equal to 0 and solve for y.
2. Find any asymptotes or solutions: Set the equation equal to 0 and solve for x.
3. Find the domain and range: The domain is all real numbers and the range is all real numbers greater than or equal to the y-intercept.
4. Plot any points of intersection: Use the values found in step 2 to plot points on the graph.
5. Draw the graph: Connect the points to form a continuous line.
To graph natural log equations, first find the y-intercept for the equation. Then, find any asymptotes or solutions by setting the equation equal to 0. Next, find the domain and range and plot any points that it intersects with. Finally, draw the graph of the equation.
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Which of the following value of K does not satisfy the condition that solution of pair of equations KX 3y K 3 12x Ky K is unique?
The value of K that does not satisfy the condition of a unique solution is K = 0. This is because if K = 0, then both equations are the same and there is no unique solution.
The condition for a unique solution of a pair of equations is that the equations must be different and the coefficient of one of the variables must be non-zero. In this case, KX 3y K 3 12x Ky K, the coefficient of one of the variables is K, which needs to be non-zero for a unique solution. If K is zero, then the two equations are the same and there is no unique solution. Therefore, the value of K that does not satisfy the condition of a unique solution is K = 0.
When K ≠ 0, the equations can be solved by subtracting the second equation from the first. This will result in the equation Kx 3y K 3 12, which can be rearranged to x 3y K 3 12/K. This equation can be further rearranged to y (Kx 3 K 3 12)/3, which will give the unique solution of the pair of equations. Therefore, any value of K other than zero will result in a unique solution.
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The complete question is
Which of the following value of K does not satisfy the condition that solution of pair of equations KX 3y K 3 12x Ky K is unique K = 0
What is the parent graph of a parabola?
The parent graph of the parabola is illustrated below.
The term parabola is defined as the quadratic function is a U-shaped curve is called a parabola.
Here we need to define the parent graph of the parabola.
As we all know that the parent graph is the graph of a relatively simple function and it is known as the process before the transforming the function in various ways such as the graph can be translated, reflected, or otherwise changed.
For example here we have take the simplest parabola is y = x² whose graph is shown below and while we looking into the graph we have identified that it passes through the origin (0,0) and is contained in Quadrants I and II.
As this graph is known as the "Parent Function" for parabolas also known as quadratic functions.
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NEED HELP USING SUPPLEMENTARY AND VERTICAL ANGLES
The following are the measures of the vertical angles:
m∠DBE = 140°m∠EBD = 30°m∠ABC = 40°m∠ABC = 54°How to evaluate for the vertical anglesm∠ABD = m∠CBE {vertical angles}
(5x - 60)° = (x + 20)°
(5x - x)° = 20° + 60°
4x = 80°
x = 80°/4 {divide through by 4}
x = 20°
so;
m∠ABD = 5(20) - 60 = 40°
m∠DBE + m∠ABD = 180° {supplementary angles}
m∠DBE + 40° = 180°
m∠DBE = 180° - 40° {subtract 40° from both sides}
m∠DBE = 140°
m∠ABC + m∠CBD = 180° {supplementary angles}
(4x - 2)° + (20x - 10)° = 180° {collect like terms}
24x - 12 = 180°
x = (180° - 12)/24 {make x the subject}
x = 8
so;
m∠ABC = 4(8) - 2 = 30°
m∠EBD = m∠ABC {vertical angles}
so;
m∠EBD = 30°
m∠ABC + m∠CBD + m∠EBD = 180° {supplementary angles}
(50 - x)° + 80° + (2x + 40)° = 180° {collect like terms}
x + 170° = 180°
x = 180° - 170° {subtract 170° from both sides}
x = 10°
so;
m∠ABC = 50° - 10° = 40°
m∠ABE + m∠EBD = 180° {supplementary angles}
(9x - 9)° + (3x + 9)° = 180° {collect like terms}
12x = 180° {divide through by 12}
x = 180°/12
x = 15
so;
m∠EBD = 3(15) + 9 = 54°
m∠ABC = m∠EBD {vertical angles}
m∠ABC = 54°
Therefore, the vertical angles m∠DBE, m∠EBD, m∠ABC, and m∠ABC have the measures 140°, 30°, 40°, and 54° respectively.
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AB || CD and CD || EF. How long is the space dedicated to growing beans?
CARROTS
3 ft
C
CELERY
2 ft
6 ft
D
BEETS
F
BEANS
1. 5 ft
PEAS
ROSES
TOMATOES
A.
2 ft
B.
3 ft
C.
2. 5 ft
D. 4 ft
The space dedicated to growing beans is 4 ft.
"AB || CD" and "CD || EF" mean that lines AB and CD are parallel and lines CD and EF are parallel as well. Since lines AB and EF are parallel and the length of line CD is 6 ft, the length of line AB and line EF is also 6 ft.
From the information given, we can see that the space dedicated to growing beans is the distance between lines CD and EF.
We also know that the space dedicated to growing beets is 3ft, and the space dedicated to growing celery is 2ft.
Therefore, we can subtract 3ft + 2ft from 6ft to find the space dedicated to growing beans: 6ft - 3ft - 2ft = 4ft.
So the answer is 4ft.
Therefore, The space dedicated to growing beans is 4 ft.
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what is -x +5=2x+9
thank you for your help
Answer:x=-4/3
Step-by-step explanation:
[tex] - x + 5 = 2x + 9[/tex]
[tex] - x - 2x = 9 - 5[/tex]
[tex] - 3x = 4[/tex]
[tex]x = - \frac{4}{3} \\ [/tex]
How is log x calculated?
Log x is calculated by taking the logarithm of x, usually with base 10, which is written as log10(x). This is done by using a calculator or a computer program.
1. Choose a base for your logarithm, usually base 10.
2. Type in the equation log10(x) into the calculator or computer program.
3. Enter the number x into the equation in place of the variable.
4. Hit the “enter” or “calculate” button to find the logarithm of x.
Log x is calculated by taking the logarithm of x, usually with base 10, which is written as log10(x). This is done by using a calculator or a computer program.
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