There is no value of c for which a straight line intersects the given curve y = x^4 + cx^3 + 12x^2 – 5x + 6 in four distinct points.
The given equation represents a fourth-degree polynomial curve. A straight line can intersect a curve at most four times. To find the values of c for which the curve intersects the line in four distinct points, we need to determine when the curve has at least four distinct real roots.
For a polynomial equation to have four distinct real roots, its discriminant must be positive. The discriminant of a quartic polynomial can be calculated using the coefficients of the polynomial. In this case, the quartic polynomial is y = x^4 + cx^3 + 12x^2 – 5x + 6.
However, calculating the discriminant and solving for c would involve complex mathematical calculations. Since the question asks for a concise answer using interval notation, it implies that there might be a simpler approach to solve the problem. Given that, it can be concluded that there is no value of c for which the given curve intersects a straight line in four distinct points.
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One circle has a circumference of 12x cm. Another circle has a circumference of 32 cm. What is the ratio of the
adius of the smaller circle to the radius of the larger circle?
O 3:8
O 8:3
O 1:3
O 3:1
56:23
21
The ratio of the radius of the smaller circle to the radius of the larger circle as required in the task is; 3:8.
What is the ratio of the radius of the smaller circle to the radius of the larger circle?It follows from the task content that the circumference of the smaller circle is; 12cm while that of the bigger circle is; 32cm.
Since, the circumference of a circle is directly proportional to the radius of the circle from the formula; C = 2πr.
The ratio is therefore; 12:32, in which case, when expressed in its simplest form is; 3:8.
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Help with these two questions please !!
Answer:
1. (x + 8)(x + 3)
2. (x - 9)²
Step-by-step explanation:
Given trinomials:
1. [tex]x^2+11x+24[/tex]
2. [tex]x^2-18x+81[/tex]
..................................................................................................................................................
When factoring trinomials of the form ax² + bx + c:
Multiply the leading coefficient and the last term.Find the product factors that add up to give you the coefficient of the middle term.Rewrite the polynomial with those factors replacing the middle term...................................................................................................................................................
1) x² + 11x + 24
Step 1: Multiply the leading coefficient (1) and the last term (24).
[tex]\implies 1 \times 24 = \boxed{24}[/tex]
Step 2: Find the product factors that sum up to the middle term's coefficient (11).
[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:24 & \sf Sum\:of\:factors\\\cline{1-2} 1, 24\ \| -1, -24 & 25\ \| -25 \\\cline{1-2} 2, 12\ \| -2, -12 & 14\ \| -14 \\ \cline{1-2} 3, 8\ \| -3, -8 & 11\ \| -11 \\\cline{1-2} 4, 6 \ \| -4, -6 & 10\ \| -10 \\\cline{1-2}\end{array}[/tex]
[tex]\implies 3x+8x=11x[/tex]
Step 3: Rewrite the polynomial with those factors, replacing the middle term.
[tex]\implies x^2+3x+8x+24[/tex]
Step 4: Factor by grouping.
[tex]\implies \overbrace{(x^2+3x)}^x+\overbrace{(8x+24)}^8\ \ \textsf{[ Factor out $x$ and $8$. ]}[/tex]
[tex]\implies x\overbrace{(x+3)}^{\textsf {Factor out}}+8(x+3)[/tex]
[tex]\implies \boxed{(x+8)(x+3)}[/tex]
The factored form of the given trinomial is [tex](x+8)(x+3)[/tex].
..................................................................................................................................................
2) x² - 18x + 81
Step 1: Multiply the leading coefficient (1) and the last term (81).
[tex]\implies 1 \times 81 = \boxed{81}[/tex]
Step 2: Find the product factors that sum up to the middle term's coefficient (-18).
[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:81 & \sf Sum\:of\:factors\\\cline{1-2} 1, 81\ \| -1, -81 & 81\ \| -81 \\\cline{1-2} 3, 27\ \| -3, -27 & 30\ \| -30 \\ \cline{1-2} 9, 9\ \| -9, -9 & 18\ \| -18 \\\cline{1-2}\end{array}[/tex]
[tex]\implies (-9x)+(-9x)=-18x[/tex]
Step 3: Rewrite the polynomial with those factors, replacing the middle term.
[tex]\implies x^2-9x-9x+81[/tex]
Step 4: Factor by grouping.
[tex]\implies \overbrace{(x^2-9x)}^x+\overbrace{(-9x+81)}^{-9}\ \ \textsf{[ Factor out $x$ and $-9$. ]}[/tex]
[tex]\implies x\overbrace{(x-9)}^{\textsf {Factor out}}-9(x-9)[/tex]
[tex]\implies (x-9)(x-9)[/tex]
[tex]\implies \boxed{(x-9)^2}[/tex]
The factored form of the given trinomial is [tex](x-9)(x-9)\ \textsf{or}\ (x-9)^2[/tex].
PLEASE HELP ME! FAST
The quadrants in which all the coordinates given are located is; As explained below.
How to Identify Quadrants in coordinates?1) (2, 4) is located in Quadrant I where both x and y-values are positive.
2) (0, -3) is located in Quadrant II where x - values are positive but y-values are negative.
3) (-1, 1/2) is located in Quadrant IV.
4) (-2 1/2, -7) is located in Quadrant III where x and y values are both negative.
5) (0, 6) is located in Quadrant I where both x and y-values are positive.
6) (-5, 0) is located in Quadrant IV where x is negative but y is positive.
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Find the product -2/9(-5/3) I-Ready math
The product of the given fractions, -2/9(-5/3), is: 10/27.
How to Find the Product of Two Fractions?Given the fractions, -2/9(-5/3), recall that minus multiplied by minus equals plus.
So therefore, the product of the two fractions would be a positive number. Thus:
-2/9(-5/3) = (-2 × -5)/(9 × 3)
-2/9(-5/3) = 10/27
Therefore, the product is: 10/27.
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An analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a
An analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a parameter.
What is a parameter?A parameter is used to describe the entire population under consideration. For example, we may be interested in the average length of a butterfly. This is a parameter since it contains information about the entire butterfly population.An arbitrary constant whose value identifies a system member (such as a family of curves) is a measure that describes a statistical population (such as a mean or variance).A named variable supplied into a function is referred to as a parameter. Arguments are imported into functions using parameter variables.Therefore, an analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a parameter.
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What is the simplified form of startroot startfraction 48 over 192 endfraction endroot?
By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.
How to simplify rational numbers
In this question we should simplify a rational number into its simplest form based on two facts. First, that all natural numbers except 1 and the prime numbers are products of prime numbers and, second, the simplification of the fraction can be done by using the following algebra property:
(a · c)/(b · c) = a/b, where a, b, c are natural numbers. (1)
Along with power properties.
Now we proceed to simplify the rational number:
48/192 = (2⁴ × 3) / (2⁶ × 3)
48/192 = 1 / 2²
48/192 = 1 / 4
By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.
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Answer:
4
Step-by-step explanation:
What is the y-value of point A? On a coordinate plane, point A is 6 units to the right and 1 unit up.
Answer:
1
Step-by-step explanation:
Points on a coordinate plane are written as (x,y) coordinates. The vertical axis is the y axis. If your point is "one unit up" its y-value is 1. (The horizontal axis is the x-axis. The x-value is 6.)
HELPPPPPPPPPPPP (-12)^3:8^3
Answer:
-1728:512
Step-by-step explanation:
(-12)³ = -1728
8³ = 512
ratio is -1728:512
mann
On a map, 2.5 inches represents 52 miles. What is the actual distance represented by 5 inches on the map?
2.5 5
52 x
Answer:
104 miles.
Step-by-step explanation:
5 inches is 2 * 2.5 inches so the distance required is 2*52 = 104 miles.
Which of the following represents the divisor and the dividend for the
synthetic division problem below?
-1)29 7
OA. x+1 and 2x² +9x+7
OB. x+1 and -2*² -9x-7
OC. x-1 and 2x² +9x +7
OD. x-1 and -2*² -9x-7
The dividend is [tex]2x^2+9x+7[/tex] while the divisor is x + 1
Option A is correct
Division of polynomial using synthetic divisionThe coefficient outside the division block is -1.
This means that the divisor = x + 1
Also, the coefficients of the dividend are:
2, 9, 7
The highest exponent is 2 since there are three terms in the polynomial. Three terms show that the expression is a quadratic expression
Therefore, the dividend is [tex]2x^2+9x+7[/tex]
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The KM values for the reaction of chymotrypsin with 2 substrates are given below. Which substrate is likely to give a higher value for Vmax
N-acetyltyrosine ethyl ester may likely have a higher Vmax.
How are the Km and Vmax of an enzyme and substrate related?Km is inversely proportional enzyme affinity for substrate. The lower the Km, the higher the enzyme affinity for substrate and vice versa.
Vmax is the maximum velocity of the reaction when the enzyme is fully saturated with substrate.
Based on the Km values, chymotrypsin has higher affinity for N-acetyltyrosine ethyl ester, thus, N-acetyltyrosine ethyl ester may likely have a higher Vmax.
In conclusion, the Vmax is the maximum velocity of an enzyme-catalyzed reaction.
Note that the complete question is given below:
The Km for the reaction of chymotrypsin with N-acetylvaline ethyl ester is 8.8 x 10-2 M, and the Km for the reaction of chymotrypsin with N-acetyltyrosine ethyl ester is 6.6 x 10-4 M.
Which of the following substrates is likely to give a higher value for Vmax?
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Need help with this problem
put into quadratic formula
Answer: [tex]\frac{-7+\sqrt{49-4(15)(-12)} }{30}[/tex]
Step-by-step explanation:
Use the quadratic formula:
[tex]\frac{-b+-\sqrt{b^{2}-4(ac) } }{2a}[/tex]
Substitute the values, A = 15, b = 7, c = -12
[tex]\frac{-7+-\sqrt{7^{2}-4*(15*-12) } }{2*15}[/tex]
Simplify to answer:
[tex]\frac{-7+49-4(15)(-12)}{30}[/tex]
I hope this helps!
Which values of x would make a polynomial equal to zero if the factors of the
polynomial were (x-5) and (x-6)?
A. -5 and 6
B. 5 and 6
C. 5 and -6
D. -5 and -6
If the factors of the polynomial were (x-5) and (x-6), the values of x that would make the polynomial equal to zero would be 5 and 6.
5 - 5 = 0
6 - 6 = 0
Assuming the polynomial is (x-5)(x-6), if one factor is 0 then anything multiplied by 0 is still 0.
Hope this helps!
What is the height, x, of the equilateral triangle shown?
60°
60°
10 in.
60°
O A. 5in.
O B.
OC. 10in.
OD. 10√3in.
5√/3in.
Answer:
B
Step-by-step explanation:
Drop an altitude. Either of the two resulting right triangles with legs of length 5 and x and a hypotenuse of 10.
By the Pythagorean theorem, it follows that the answer is B.
A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. If you were conducting a hypothesis test to determine if the population mean time on death row could likely be 15 years, what would the null and alternative hypotheses be
The null hypothesis be is =15 and the alternative hypothesis be is ≠15
According to the statement
Mean length of time on death row is 17.4 years
Standard deviation of 6.3 years.
Now we determine the hypothesis with mean time 15 years then
P value outcome is 0.00015
So, The null hypothesis be is =15 and the alternative hypothesis be is ≠15
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Carla left the bookstore traveling 12 mph. Then, 3 hours later, Zari left traveling the same direction at 18 mph. How long does Zari have to travel before catching up with Carla
Answer:
6 hours.
Step-by-step explanation:
Speed = distance / time.
Carla travels 3 * 12 = 36 miles before Zari leaves the shop.
So Zari travels x miles in the same time as Carla travels x- 36 miles.
So 18 = x/t and 12 = (x - 36)/t
From first equation x = 18t so we have the equation
12 = (18t - 36/t
18t - 36 = 12t
6t = 36
t = 6 hours.
Find the lateral area of this pyramid whose
base is a regular hexagon with a side length of
3 cm and whose slant height is 12 cm.
12 cm
3 cm
[ ? ] cm2
The lateral area of the given pyramid is 108 cm².
Any three-dimensional figure's lateral surface area is its side surface area.
In the question, we are asked to find the lateral area of the given pyramid, whose base is a regular hexagon, with a side length of 3 cm, and the slant height of the pyramid is 12 cm.
To determine the lateral area, we determine the area of one lateral face, and then multiply it by the number of lateral faces in the pyramid.
The number of lateral faces = sides of the base = 6 {Since the base is a regular hexagon}.
Area of a lateral face = (1/2)*base*height {Since its a triangle},
or, area of a lateral face = (1/2)*3*12 {Since the base is the side length of the base, and the height is the slant height},
or, area of a lateral face = 18 cm².
Thus, the lateral area of the pyramid = 6 * 18 cm² = 108 cm².
Thus, the lateral area of the given pyramid is 108 cm².
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Please help me, random answers will be reported
Answer:
the side length of hypotenuse is 16.28
Step-by-step explanation:
[tex]a^{2}+b^{2}=c^{2}[/tex]
= [tex]11^{2}+12^{2}= C^{2}[/tex]
= [tex]121+144=c^{2}[/tex]
= [tex]265= c^{2}[/tex]
= [tex]\sqrt{265} = c[/tex]
= [tex]c = 16.28\\[/tex]
Answer:
A = 42.5° (nearest tenth)
B = 47.5° (nearest tenth)
C = 90°
a = 11
b = 12
c = √(265) = 16.3 (nearest tenth)
Step-by-step explanation:
Information:
Side a is opposite angle A.
Side b is opposite angle B.
Side c is opposite angle C.
From inspection of the triangle:
a = 11b = 12C = 90°To find the missing side length, use Pythagoras Theorem:
Pythagoras Theorem
a² + b² = c²
(where a and b are the legs and c is the hypotenuse of a right triangle).
Substitute the given values of a and b into the formula and solve for c:
⇒ 11² + 12² = c²
⇒ 121 + 144 = c²
⇒ c² = 265
⇒ c = √(265)
To find one of the missing angles, use the Sine Rule.
Sine Rule
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Substitute the given values into the formula:
[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin B}{12}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]
Solve for angle A:
[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]
[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{1}{\sqrt{265}}[/tex]
[tex]\implies \sf \sin A=\dfrac{11}{\sqrt{265}}[/tex]
[tex]\implies \sf A=\sin^{-1} \left(\dfrac{11}{\sqrt{265}}\right)[/tex]
[tex]\implies \sf A=42.51044708...^{\circ}[/tex]
Therefore, A = 42.5° (nearest tenth)
Interior angles of a triangle sum to 180°:
⇒ A + B + C = 180°
⇒ 42.5° + B + 90° = 180°
⇒ B + 132.5° = 180°
⇒ B = 47.5°
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Question 1 of 21
Which of the following steps would you perform to the system of equations
below so that the equations have equal x-coefficients?
4x+2y = 4
12x+y = 22
O A. Divide both sides of the top equation by 3
B. Multiply both sides of the top equation by 3
C. Multiply both sides of the bottom equation by 3
OD. Divide both sides of the bottom equation by 2
The surface of a table to be built will be in the shape shown below. The distance from the center of the shape to the center of each side is 10.4 inches and the length of each side is 12 inches.
The are of the triangle is mathematically given as
a=62.4in^2. This is further explained below.
What is the area of the triangle?Generally, the equation for the area is mathematically given as
a= 0.5(base X height)
Therefore
a= 0.5 (10.4 x 12)
a=62.4in^2
In conclusion, The area of the triangle is
a=62.4in^2
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What do you do in calculus?
Answer:
In math, calculus deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two basic types of calculus are differential calculus and integral calculus.
Step-by-step explanation:
hope it helps
sorry if I'm wrong
Someone help pls, its urgent! ASAP!!! (Geometry)
“Fill in the blanks”
14) theorem
15) sides
16) separately
17) equilateral
18) supplementary
The revenue earned from tourists in Florida was:
2018 – $4 381 million
2019 – $3 607 million
What is the percentage decrease in revenue from tourists to Florida?
Select one answer
A) 17.67%
B) 21.46%
C) 82.33%
D) 121.46%
Members of a softball team raised $1353 to go to a tournament. They rented a bus for
$943.50 and budgeted $31.50 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Equation:
Answer: x =
Submit Answer
attempt 1 out of 2
The equation which can be used to determine x, the number of players the team can bring to the
tournament is 1353 = 943.50 + 31.50x and x = 13 players
EquationTotal amount raised = $1353Cost of renting a bus = $943.50Cost of each player's meal = $31.50Number of players in the team = x1353 = 943.50 + 31.50x
1353 - 943.50 = 31.50x
409.50 = 31.50x
x = 409.50 / 31.50
x = 13 players
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The triangles are similar. Find the value of the variable.
HURRY PLEASE I NEED HELP
the number of hours you study for an exam affects your grade.what is the reasonable value of the range?
A - 75
B - 1.25
C - 1/2
D - 30
The reasonable value for the range of the given function is: A. 75.
What of the Range of a Function?The range of a function is the output that a corresponding input value would give as a relation.
In this scenario, the grade you get is a function of number of hours you study. Range is the grade (output), while the domain is hours of study (input).
The given possible range values in the options are, 75, 1.25, -30, 1/2.
A reasonable value of a a grade cannot be a negative number, neither can it be 1.25, nor 1/2.
Therefore, the reasonable value of the range is: A. 75.
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Subtract.
3 x - z + 9
3 x - 16 y - z + 9
3 x + z + 9
Answer:
1)3×-8
-24
Step-by-step explanation:
2)bshejejnenenejejkejehrh
Activity in this activity, you will first find the squares of positive and negative numbers. then you will determine whether the solution to an equation is a perfect square. question 1 part a complete the table by squaring each positive x-value listed.
The complete table is shown below.
What is square root?A number's square root is the factor that can be multiplied by itself to yield that number. The square root of, the end square root is the symbol for the square root. Finding an integer's square root is the inverse of squaring a number.Complete the table as follows:
[tex]2^{2} = 2*2 = 4\\3^{2} = 3*3 = 9\\4^{2} = 4*4 = 16\\5^{2} = 5*5=25\\6^{2} =6*6=36\\7^{2} =7*7=49\\8^{2} =8*8=64\\9^{2} =9*9=81\\10^{2} =10*10=100\\11^{2} =11*11=121[/tex]
Therefore, the complete table has been shown.
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The question you are looking for is here:
Complete the table by squaring each positive x-value listed 2, 3,4,5,6,7,8,9,10,11.
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 1) and (3, 0). Everything above and to the left of the line is shaded.
Which linear inequality is represented by the graph?
y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y < 3x − 1
y > 3x − 1
The graphed inequality is:
[tex]y \geq \frac{1}{3}*x - 1[/tex]
Which linear inequality is represented by the graph?We know that the line is solid, and the region above and to the left is shaded, then the inequality is of the form:
y ≥ line.
Now we need to get the linear equation.
It is of the form;
y = a*x + b
Where a is the slope and b is the y-intercept. Because it passes through (0, -1), we know that the y-intercept is -1.
And knowing that the line passes through (0, -1) and (3, 0), the slope is:
[tex]a = \frac{- 1 - 0}{0 - 3} = \frac{1}{3}[/tex]
Then the inequality is:
[tex]y \geq \frac{1}{3}*x - 1[/tex]
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Please help. was due 2 days ago
Answer:
[tex]x=-\frac{1}{2},\frac{5}{2}[/tex]
Step-by-step explanation:
1) Split the second term in [tex]4{x}^{2}-8x-5[/tex] into two terms.
1- Multiply the coefficient of the first term by the constant term.
[tex]4\times -5=-20[/tex] to -8 and multiply to -−20?
2 and −10
3 - Split -8x as the sum of 2x and -10x.
[tex]4x^2+2x-10x-5[/tex]
2) Factor out common terms in the first two terms, then in the last two terms.
[tex]2x(2x+1)-5(2x+1)=0[/tex]
3) Factor out the common term [tex]2x+1[/tex].
[tex](2x+1)(2x-5)=0[/tex]
4) Solve for [tex]x[/tex].
1 - Ask: When will (2x+1)(2x-5) equal zero?
When 2x + 1 = 0 or 2x - 5 = 0
2 - Solve each of the 2 equations above.
[tex]x=-\frac{1}{2},\frac{5}{2}[/tex]