Using the Factor Theorem, the function factored into linear factors is given as follows:
[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
-9 is a zero of f(x), hence [tex]x_1 = -9[/tex] and:
3x³ + 23x² - 35x + 9 = (x + 9)(ax² + bx + c)
ax³ + (b + 9a)x² + (9b + c)x + 9c = 3x³ + 23x² - 35x + 9
The coefficients are given as follows:
a = 3.9c = 9 -> c = 1.b + 9a = 23 -> b = -4.Hence:
3x³ + 23x² - 35x + 9 = (x + 9)(3x² - 4x + 1)
[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]
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Evaluate the following expression when y=2.
9y−8y+2
Answer:4
Step-by-step explanation: 9y-8y+2, when y=2
9(2)-8(2)+2=
18-16+2
=4
for csc 330:
a) state value of the ratio exactly
b) find one equivalent expression
c) draw a diagram to illustarte.
The value of the ratio based on the angle illustrated is 1:12.
How to illustrate the information?From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:
= 360° - 330°
= 30°
The equivalent expression based on the angle will be:
= 30/360
= 1/12
= 1:12
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this table shows values that represent an exponential function.
x y
1 7
2 9
3 13
4 21
5 37
what is the average rate of change for this function for the interval from x = 1 to x = 3?
a. 4 b. 2 c. 3 d. 8
The average rate of change for this function for the interval from x = 1 to x = 3 is 3
How to determine the average rate of change?The average rate of change is calculated as:
m = (f(b)- f(a))/(b - a)
The interval is given as:
x = 1 to x = 3
From the table of values, we have:
f(1) = 7
f(3) = 13
So, we have:
m = (13-7)/(3-1)
Evaluate
m = 3
Hence, the average rate of change for this function for the interval from x = 1 to x = 3 is 3
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A conduit of circular cross section has 7 cables all same diameter. Inside diameter of conduit is 30cm. What is the cross sectional area of the conduit not part of the 7 cables
The cross sectional area of the conduit not part of the 7 cables is; 706.5cm²
What is the cross sectional area of the conduit not part of the 7 cables?It follows from the task content that the conduit in discuss has 7 cables all same diameter and has a circular cross section.
Since, the cross sectional area of the conduit not part of the 7 cables is required; it follows that the cross sectional area of the inside cavity can be evaluated as follows;
where radius, r = D/2 = 30/2.
Area = πr² = 3.14 × (30/2)² = 706.5cm²
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Find the coordinates of the vertices of the triangle if it’s rotated 270° counterclockwise.
If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;
X' = (3, -1)
Y' = (2, -2)
Z' = (-1, -3)
Rotation of coordinatesIf the coordinates (x, y) is rotated 270° counterclockwise, the resulting coordinate point will be;
(x, y) - > (y, -x)
From the given triangles, the coordinate points are expressed as
X = (1, 3)
Y = (2, 2)
Z = (3, -1)
If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;
X' = (3, -1)
Y' = (2, -2)
Z' = (-1, -3)
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16
3. A Ferris wheel with a radius of 25 m makes 2 rotations every minute.
a. State the period of the Ferris wheel.
b. Complete a tables of values showing the height above the ground for 2 rotations of the
Ferris wheel by assigning the correct variables
c. Graph 2 rotations of the Ferris wheel. (Hint: Time Vs Height above the platform)
d. State the amplitude of the Ferris wheel.
A) The Period is 30 seconds
D) The amplitude is 25 m
How to find the period and amplitude?
A) Since the Ferris wheel makes 2 rotations every minute, then we can say that the period is;
T = 1/2 = 0.5 minutes = 30 seconds
B) Let t be time in seconds and let h be height and as such, we have the formula; h = 25 - 25 cos ((2π/30)t)
Thus, the table is attached showing input values of t and their corresponding h values.
C) The graph of the table above is as attached below.
D) The amplitude is;
Amplitude = (Maximum Point - Minimum Point)/2
Amplitude = (50 - 0)/2
Amplitude = 25
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Which graph best represents the solution to the system of equations shown below? y = -2x + 14 y = 2x + 2 A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 8, 3. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 8, negative 3. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, 8.
The graph whuch best represents the solution to the system of equations is; A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.
What is the graphical solution of the system big equations?As an alternative, solving the system of equations algebraically, we have;
-2x +14 = 2x +2
x = 3 and by substitution;
y = 8.
On this note, the point (3,8) is a solution of the graph and hence, the answer choice with two lines intersecting at (3,8) is correct.
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FRACTIONS
Equivalent fractions
Fill in the blank to make the two fractions equivalent.
blank over 30=4/5
The complete fraction is 24/30=4/5
How to create an equivalent fraction?The expression is given as:
blank over 30=4/5
Represent the blank with x.
So, we have:
x/30=4/5
Multiply both sides by 30
x = 30 * 4/5
Evaluate
x = 24
Substitute x = 24 in x/30=4/5
24/30=4/5
Hence, the complete fraction is 24/30=4/5
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(-2) * n * (8) * n * (-n)
Answer:
16[tex]n^{3}[/tex]
Step-by-step explanation:
we evaluate from left side to right side
so -2*n =-2n
-2n *8 = -16n
-16n * n =-16n^2
-16 n * -n =16 n^3
hope this helps
Mr. Bellman orders a cube of clay for each of his art classes. The height of the
cube is 20 inches. How much clay, in cubic inches, would Mr. Bellman order
for three classes?
Write and evaluate an expression to find your answer.
20 cubed is 20 times 20 and then that answer times 20.
length X width x height = cube
20 to the 3rd power or 203
A
B
C
60 cubic inches
400 cubic inches
8,000 cubic inches
Answer:
20 x 20 x 20 = 8000
a) Out of all items sent for refurbishing, %40 had mechanical defects, %50 had electrical
defects, and %25 had both. Denoting defectmechanicalahasitemanA and
defectmechanicalahasitemanB . Fill the probabilities into the Venn diagram and
determine the quantities listed below.
(i) AP [2 Marks]
(ii) BAP [1 Mark]
(iii) BAP c
i. P(A) = 0. 4
ii. P(AB) = 0. 9
iii. P(A∩B) =0. 25
How to determine the probability
From the information given,
Universal set = 40% + 50% + 25% = 0.40 + 0. 50 + 0. 25
A = Mechanical defects = 40%
B = Electrical defects = 50%
A∩B =25%
i. Probability of A , P(A)
= [tex]\frac{40}{100}[/tex]
= [tex]0. 4[/tex]
ii. Probability of B, P(AB)
= [tex]\frac{40}{100} + \frac{50}{100}[/tex]
= [tex]0. 4 + 0. 5[/tex]
= [tex]0. 9[/tex]
iii. Probability of A∩B entails the common factor between A and B
P(A∩B) = [tex]\frac{25}{100}[/tex] = [tex]0. 25[/tex]
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ayuda, no le entiendo :)
Trabajando 10 horas por día, en 6 días se producen 3000 ruedas.
¿Cuántos dias tardarán en fabricar 3000 ruedas si trabajan 10 horas diarias?Sabemos que trabajando 8 horas, en 5 dias producen 2000 ruedas.
El número total de horas que trabajan en esos 5 dias es:
(8 horas)*5 = 40 horas
Entonces se producen 2000 ruedas en 40 horas, es decir, la razon de trabajo es:
(2000 ruedas)/(40 horas) = 50 ruedas por hora.
Ahora, sí en la fabrica trabajan 10 horas al día, entonces van a producir:
10h*(50 ruedas por hora) = 500 ruedas por día.
El número x de días que deben trabajar para producir 3000 ruedas es:
x*(500 ruedas por dia) = 3000 ruedas
x = (3000 ruedas)/(500 ruedas por dia) = 6 dias.
Trabajando 10 horas por día, en 6 días se producen 3000 ruedas.
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Write an equation for a line perpendicular to y=5x+1 and passing through the points (5,-2)
__________________________________________________________
[tex]\text{\textbf{Hello!} In this question, we are trying to find the equation of a line}\\\text{that is \underline{perpendicular} to our given equation}[/tex]
__________________________________________________________
[tex]\textbf{Explanation:}\\\\\text{To help us answer our question, we need to note some of our given info:}\\\\\text{Equation: y = 5x + 1}\\\\\text{Point passed through: (5, -2)}\\\\\text{We can use the above information to help us find our perpendicular equation.}\\\\\text{We will be using the slope-intercept form equation to help get us our answer:}\\\\\text{y = mx + b}[/tex]
[tex]\text{When a line is perpendicular to an equation, it means that its slope is }\\\text{\textbf{opposite} which results in the lines to meet at a \underline{90-degree} angle.}[/tex]
__________________________________________________________
[tex]\textbf{Solve:}\\\\\text{To get our perpendicular slope, we will use the formula:}\\\\\text{m1 = }-\frac{1}{m2}\\\\\text{m1 will be our given slope (5) and m2 will be our already provided slope. }\\\\\text{This is also known as a \underline{negative reciprocal}. }\\\\\text{Therefore: m1 = }-\frac{1}{5}\\\\\text{Since we now know our slope, we can plug it into our "m" variable in the}\\\text{slope intercept equation:}\\\\\text{y = }-\frac{1}{5}x+b\\[/tex]
[tex]\text{To find where the point is on the y-intercept, we will plug in our point}\\\text{(5, -2) to it's corresponding spots in our new equation above.}\\\\\text{Plug "5" to x and "-2" to y and solve:}\\\\\text{-2 = }-\frac{1}{5}(5)+b\\\\\text{-2 = }-1+b\\\\\text{Add 1 to both sides.}\\\\\text{-1 = }b\\\\\text{Therefore, our y-intercept is -1.}[/tex]
[tex]\text{When we plug -1 into our new equation, we get:}\\\\\text{y = }-\frac{1}{5}x-1\\\\\text{Therefore, our perpendicular equation is: }\boxed{y = -\frac{1}{5}x-1}[/tex]
__________________________________________________________
[tex]\textbf{Answer:}\\\\\boxed{y = -\frac{1}{5}x-1}[/tex]
__________________________________________________________
[tex]\textbf{Additional Info:}\\\\\text{You can learn more about \textbf{slope-intercept form} below:}[/tex]
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__________________________________________________________
who knows ow to solve this triangle?
The measure of x in the right angled triangle shown is 4.09
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
From the diagram shown:
sin(17) = x / 14
x = 4.09
The measure of x in the right angled triangle shown is 4.09
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A zoo has a black rhinoceros that weighs 18 times as much as an average-size chimpanzee. The rhinoceros weighs 2,250 pounds.
How much does an average-size chimpanzee weigh?
Enter the answer in the box. [_]
Answer: 125 pounds
Step-by-step explanation:
Let's first represent the weight of the black rhinoceros and chimpanzee with variables. We will assign r for the rhinoceros and c for the chimpanzee.
In the question, we were given that the weight for a black rhinoceros is 18 times as much as an average-size chimpanzee. This makes 18 times the chimpanzee's weight equal to the rhinoceros' weight.
Let's put this into an equation.
[tex]r=18*c[/tex]
Now, let's put in the values we know to find the weight of the chimpanzee (i.e., c). We know the weight of a rhinoceros (represented by r) is 2250 pounds, so we can replace it for r in the equation.
[tex]2250=18*c[/tex]
To solve this equation, we can divide both sides by 18 to get c by itself and know what it's value is.
[tex]\frac{2250}{18}=\frac{18*c}{18}[/tex]
We can remove the [tex]\frac{18}{18}[/tex] from the right side to be left with c. We can also divide 2250 by 8 to get the weight of an average-size chimpanzee.
[tex]c=\frac{2250}{18}\\ c=125[/tex]
Hence, an average-size chimpanzee weighs 125 pounds.
Which of the following best describes the pattern in the diagram shown
below?
1
2
3
O A. As you move from left to right, the number of points in the star
decreases by 1.
O B. As you move from left to right, the number of points in the star
increases by 1.
C. As you move from left to right, the number of points in the star
remains the same.
OD. As you move from right to left, the number of points in the star
increases by 1.
As you move from left to right, the number of points in the star increases by 1 and is the best option which describes the diagram which is therefore denoted as option B.
What is a Point?This can be referred to an important object in geometry and is usually represented by a dot. It also helps to tell the exact location of substances or objects and doesn't have certain parameters such as the length or width.
We can deduce that Star 1 has four points, star 2 has five points and star 3 has six points. We can therefore infer that the stars in the diagram given below has some amount of points which increases by one as we move from left to right thereby making it the most appropriate choice in this type of scenario.
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Compute the monthly payments for the add on interest loan. The amount of the loan is $8,276.17. The annual interest rate is 5.7%. The term of the loan is 5.5 years.
The monthly payments for this add on interest loan are of $164.71.
Given Information and Formula Used
It is given that for an add on interest loan,
Principal Amount, p = $8,276.17
Annual Interest Rate, r = 5.7%
Term of the loan, T = 5.5 years
The formula for simple interest is given as follows,
I = (p)(r)(t)/100 ............... (1)
The formula for total amount of add on interest is given by,
A = p + I ....................... (2)
Computing the Interest
Substitute the given values of p, r, and t in the formula (1) of interest to get,
I = (8276.17)(5.7)(5.5)/100
I = 259457.9295/100
I = $2,594.58
Computing the Monthly Payment for Add-on Interest Loan
Substituting the values of p and I in the formula (2), we obtain the total amount as,
A = $ (8276.17 + 2594.58)
A = $ 10,870.75
Monthly payment for the add on interest loan = A/t(in months)
= $ (10,870.75/66)
= $164.71
Therefore, monthly payments of $164.71 are to be made for the add on interest loan.
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The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Considering the vertex of the parabola, the correct statement is given by:
The range of the function is all real numbers less than or equal to 9.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point, which means that the range is all real numbers less than or equal to [tex]y_v[/tex].If a > 0, the vertex is a minimum point, which means that the range is all real numbers greater than or equal to [tex]y_v[/tex].In this problem, we have that:
a = -1 < 0, hence the vertex is a maximum point.The vertex is (-2,9).Hence the range is described by:
The range of the function is all real numbers less than or equal to 9.
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scientist released 8 rabbits into a new habitat in year 0. Each year, there were twice as many rabbits as the year before. How many rabbits were there after X years? Write a function to represent this scenario.
Answer:
Step-by-step explanation:
his function will be an exponential function, because the number of rabbits double each year
the basic form for exponential functions is
where s is the starting number, c i s the constant (rate of change like double, triple, etc.) and x is the number repeats (in this case, years)
so in this case, the starting number (year 0) is 8, and the rate of change is 2
therefore, the equation is:
f(X) =8 times 2
hope this helps!
p.s. can i have brainliest?
_+_+_= 30
Use only
1,3,5,7,9,11,13,15
You can repeat it
Answer
1 possible solution:
(5x7) in the first blank
(-3!) in the second blank
(-1) in the third blank
Step-by-step explanation:
(5x7) + -(3!) + -(1) 3! equals 3x2x1 or 6
35 + (-6) + (-1)
F(x) = | sin 3x | -3 find the maximum and minimum value
Answer:
-2 and -3
Step-by-step explanation:
The minimum of |sin 3x| is 0 and the max is 1 (since the sine function ranges from -1 to 1)
Therefore, the maximum is 1 - 3 = -2 and the minimum is 0 - 3 = -3.
The earth travels around the sun at about 1,110 miles per minute.
About how many miles does the earth travel around the sun per second?
Drag and drop the answer into the box.
The earth travels around the sun about ___ Response area miles per second.
Answer:
18.5 miles
Step-by-step explanation:
the Sun at an average speed of 67,000 mph, or 18.5 miles a second.
which quantity is scalary
Step-by-step explanation:
find the greatest number which divides 225 and 1029 leaving remainder of 5 in each case
During a recent poll with a travel agency, 24 customers were surveyed to determine the most popular cities in the US to visit.
The Venn diagram shows this information for the three most popular cities: New York, Los Angeles, and Orlando.
a. Which customers chose Orlando but not New York or Los Angeles?
b. How many customers chose New York and Los Angeles, but not Orlando ?
c. Which customers liked Orlando and New York only?
Based on the Venn diagram with results from the travel agency and the popular cities to visit, the following are true:
5 people.1 person.2 people.What cities were the most popular in the U.S.?The Venn diagram shows that the number of people who chose Orlando alone are 5 people namely: John, Michael, Angel, Andrew, and Sally.
Only one customer in the person of Jordan preferred New York and Los Angeles.
2 people liked Orlando and New York only and they were Luke and Robert.
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A coin has two sides head and tails a die has six sides if you roll the die what is the probability that you flip heads and roll a number greater than 5
Using it's concept, the probability that you flip heads and roll a number greater than 5 is: [tex]\frac{1}{12}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
The probability of a head is 1/2.The probability of a number greater than 5 is 1/6.Hence the probability of both events is:
[tex]p = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex].
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How to find the missing side?
Answer:
refer to the attachment
if sinA=4/5 solve sin2A, cos2A and tan2A
Step-by-step explanation:
1) if m(∠A)∈[0;90°), then
[tex]cos(A)=\sqrt{1-sin^2A} =\frac{3}{5};[/tex]
[tex]sin2A=2sinAcosA=2*\frac{3}{5} *\frac{4}{5}=\frac{24}{25};[/tex]
[tex]cos2A=cos^2A-sin^2A=\frac{9}{25}-\frac{16}{25}=-\frac{7}{25};[/tex]
[tex]tan2A=\frac{sin2A}{cos2A}=-\frac{\frac{24}{25}}{\frac{7}{25}}=-\frac{24}{7}.[/tex]
2) if m∠A∈[90°;180°), then
cos(A)=-0.6;
sin2A=-0.96;
cos2A=-0.28;
tan2A=-24/7.
How many kilometers are equal to 750 meters?
Answer:
[tex]0.75[/tex]
Step-by-step explanation:
750metres÷1000
PLSSSSSSSSSSSSSSS HELP pls
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: 10x + 30 = 90[/tex]
[ according to given figure ]
[tex]\qquad \sf \dashrightarrow \: 10x = 90 - 30[/tex]
[tex]\qquad \sf \dashrightarrow \: 10x = 60[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 60 \div 10[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 6 \degree[/tex]
Correct choice is D
m(t)=120e−0.018t
How much mass remains after 50 years? Round to 2 decimal places.
The mass that would remain after 50 years is 48. 79 kilograms
How to determine the amountIt is important to note that half - life is the time it takes for amount of a substance to reduce to half of its initial value.
Given the equation
m(t)=120e−0.018t
Where
m(t) is the amount = unknown
t = time = 50 years
[tex]m(t) = 120e^0^.^0^1^8^t[/tex]
Substitute the value into the equation
[tex]m(t) = 120e^0^.^0^1^8^(^5^0^)[/tex]
[tex]m(t) = 120e^-^0^.^9[/tex]
Find the exponential value
[tex]m(t) = 48.788399[/tex]
m(t) = 48. 79 kilograms in 2 decimal places
Thus, the mass that would remain after 50 years is 48. 79 kilograms
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