The polynomial function with the given properties is; y = 2(x - 3)³(x + 4)²
How to construct polynomial functions?Polynomials are defined as algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.
We need to form a polynomial expression with the following properties;
fifth-degree, 3 is a zero of multiplicity 3, −4 is the only other zero and ,the leading coefficient is 3. Thus, the polynomial will be;
y = 2(x - 3)³(x + 4)²
Read more about Polynomial functions at; https://brainly.com/question/7693326
#SPJ1
What is the volume of a cone with a height of 22 and a radius of 6
Answer:
3041.06
Step-by-step explanation:
The formula of a cone is [tex]\pi r^{2} \frac{h}{3}[/tex] , so plugging both the height and radius will result in the answer!
Can y’all help me with ! I need correct anwsers ! Please
Answer:
Im pretty sure its B, 1.75. Not exactly sure though
Step-by-step explanation:
What is the value of y?
Answer:
Step-by-step explanation:
I can give you the meaning of Y
Y is the vertical value in a pair of coordinates. In other words how far up or down the point is. The Y coordinate is always written second in an ordered pair of coordinates (x,y) when used. A example from the internet is:
Select the correct interpretation of the following expression.
2(3x+1)(9x-5)
A.
double the sum of 3x + 1 and 9x - 5
B.
the sum of 2, 3x, 1, 9x, and -5
C.
the product of 2, 3x + 1, and 9x - 5
D.
the product of 2, 3x, 1, 9x, and -5
Answer:
C
Step-by-step explanation:
you are multiplying so it is the product of the three
2 ( ... ) ( ... )
and you must solve the brackets first so C and not D
Gold has a density of 19.32 grams per cubic centimeter. How much does one-half of a cubic centimeter weigh? Gold has a density of 19.32 grams per cubic centimeter . How much does one - half of a cubic centimeter weigh ?
Substituting into the formula [tex]d=\frac{m}{v}[/tex],
[tex]19.32=\frac{m}{0.5}\\\\m=\boxed{9.66 \text{ grams}}[/tex]
the table shows the length of time in hours ,some children spent watching tv last week
The histogram of the distribution plotted on the y - axis and the interval for the length of time on the x - axis is attached below.
How to denote the histogram?The first bar denotes the length of time between 0 and 10 having a frequency of 8. The second bar denoted the interval between 10 and 15 with a frequency of 15
The third bar denoted the interval between 15 and 20 with a frequency of 10. The fourth bar denoted the interval between 20 and 30 with a frequency of 11
Therefore, the histogram of the distribution is attached below.
Learn more about histograms on:
brainly.com/question/14421716
#SPJ1
The measures of the angles of a triangle are shown in the figure below. Solve for x.
83 ⁰
to
59°
The value of x is 38 degree.
What is a Triangle ?A triangle is a polygon with three sides , three angles and three sides .
The sum of all angles in a triangle is equal to 180 degree
The angles of the triangle given are
83 degree and 59 degree and x degree
83 + 59 + x = 180
x = 38 degree
Therefore the value of x is 38 degree.
To know more about Triangle
https://brainly.com/question/2773823
#SPJ1
Samantha invests $11,000 at 6% simple interest for 25 years.
Round your answers to the nearest cent.
Answer:
$27,500.00
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 6%/100 = 0.06 per year.
Solving our equation:
A = 11000(1 + (0.06 × 25)) = 27500
A = $27,500.00
The total amount accrued, principal plus interest, from simple interest on a principal of $11,000.00 at a rate of 6% per year for 25 years is $27,500.00.
Prove Triangle ABC is congruent to Triangle CDA.
The triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.
What is the similarity?If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.
In the given triangles we can see that:-
Angle BAC is congruent to Angle DCA Angle B and Angle D are congruent.The two triangles are sharing common side which is AC.Therefore we can see that the triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.
To know more about congruency follow
https://brainly.com/question/2938476
#SPJ1
4
Which are correct representations of the inequality 6x ≥ 3 + 4(2x - 1)? Select three options.
01 ≥ 2x
O
O
6x ≥ 3 + 8x - 4
-1.5
-1.5
0- -1.5
-1
-1
-1
-0.5
-0.5
-0.5
0
0
0
0.5
0.5
0.5
1
1
1.5
1.5
1.5
Answer:
6x > 3+4(2x -1)
6x > 3+ 8x - 4
6x > (-1) + 8x
6x - 6x > (-1) + 8x - 6x
subtracting 6x from both sides
0 > 2x - 1
adding +1 on both sides
1 > 2x
1/2 > x
x < 1/2
The correct representations of the inequality 6x ≥ 3 + 4(2x - 1) is,
⇒ x ≤ 1/2
What is mean by Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ 6x ≥ 3 + 4(2x - 1)
Now, We can simplify as;
⇒ 6x ≥ 3 + 4(2x - 1)
⇒ 6x ≥ 3 + 8x - 4
⇒ 6x ≥ 8x - 1
⇒ 1 ≥ 8x - 6x
⇒ 1 ≥ 2x
⇒ x ≤ 1/2
Thus, The correct representations of the inequality 6x ≥ 3 + 4(2x - 1) is,
⇒ x ≤ 1/2
Learn more about the inequality visit:
https://brainly.com/question/25944814
#SPJ5
St^2 e^-10t dt
Evaluate the intergral
It looks like you're talking about the indefinite integral
[tex]\displaystyle \int t^2 e^{-10t} \, dt[/tex]
Integrate by parts:
[tex]\displaystyle u\,dv = uv - \int v\,du[/tex]
Let
[tex]u = t^2 \implies du = 2t \, dt[/tex]
[tex]dv = e^{-10t} \, dt \implies v = -\dfrac1{10} e^{-10t}[/tex]
Then
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \int t e^{-10t} \, dt[/tex]
Integrate by parts again, this time with
[tex]u = t \implies du = dt[/tex]
[tex]dv = e^{-10t} \, dt \implies v = -\dfrac1{10} e^{-10t}[/tex]
Then
[tex]\displaystyle \int t e^{-10t} \, dt = -\frac1{10} t e^{-10t} + \frac1{10} \int e^{-10t} \, dt[/tex]
Putting everything together, we get
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \int t e^{-10t} \, dt[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \left(-\frac1{10} t e^{-10t} + \frac1{10} \int e^{-10t} \, dt\right)[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} + \frac1{50} \int e^{-10t} \, dt[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} + \frac1{50} \left(-\frac1{10} e^{-10t}\right) + C[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} - \frac1{500} e^{-10t} + C[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = \boxed{-\frac{e^{-10t}}{500} \left(50t^2 + 10t + 1\right) + C}[/tex]
what is (4-¹)(2³-4-2) 4 - ¹ ) ( 2³ - 4-2 )
Answer:
[tex](4-¹)(2³-4-2) 4 - ¹ ) ( 2³ - 4-2 )[/tex]
[tex]4 {}^{ - 2} (2 {}^{3 } - 4 - 2)(2 {}^{3} - 4 - 2)[/tex]
[tex]4 {}^{ - 2} (2 {}^{3} - 4 - 2) {}^{2} [/tex]
[tex] \frac{1}{16} (8 - 4 - 2) {}^{2} [/tex]
[tex] \frac{1}{16} (4 - 2) {}^{2} [/tex]
[tex] \frac{1}{16} \times 4[/tex]
[tex] \frac{1}{4} [/tex]
Given mCT=26 and m/CAT =124° find the length of CA, the radius in Circle A. Use
π = 3.14 in your calculation and round to the nearest tenth.
Answer:
[tex]\text{length of \textit{CA}} \ = \ 12.0 \ \ \ (\text{nearest tenth})[/tex]
Step-by-step explanation:
Radian measure is the ratio of the length of a circular arc to its radius.
A radian is the measurement of the central angle which subtends an arc whose length is equal to the length of the radius of the circle.
In the case of the unit circle, as shown in the figure below, one radian is the angle of the sector with a radius of 1 and circular arclength of 1.
Following this definition, the magnitude, in radians, of one complete revolution of a unit circle is the circumference of the unit circle divided by its radius, [tex]\displaystyle\frac{2\pi}{1}[/tex] or [tex]2\pi[/tex]. Thus, [tex]2\pi[/tex] radians is equal to [tex]360^{\circ}[/tex] degrees. Alternatively, one radian is equal to [tex]\displaystyle\frac{180^{\circ}}{\pi} \ \approx \ 57.296^{\circ} \ \ \ (3 \ d.p.)[/tex].
Since radian measure is defined as the ratio of the arc length of a sector to its radius, hence
[tex]\displaystyle\frac{s}{r} \ = \ \theta \\\\ s \ = \ r\theta[/tex]
where [tex]s[/tex] is the arclength, [tex]r[/tex] is the radius, and [tex]\theta[/tex] is the central angle, in radians.
Therefore, the length of CA is
[tex]\displaystyle\frac{s}{\theta} \ = \ r \\ \\ r \ = \ \displaystyle\frac{26}{124^{\circ} \ \times \ \displaystyle\frac{\pi}{180^{\circ}} \ \text{rad}} \\ \\ r = \displaystyle\frac{26 \ \times \ 45}{31 \ \times \ 3.14} \\ \\ r\ = \ 12.0 \ \ \ \ \left(\text{nearest tenth}\right)[/tex]
Which trig expression can be used to find the height on the tree where the top guy wire attaches if the base of the wire is four feet from the base?
The trigonometric expression that can be used to find the height of the tree where the top guy wire attaches is tan(45 + 30)
How to use trigonometric rations to find height?The height of the tree can be found using trigonometric ratios.
Therefore,
tan ∅ = opposite / adjacent
Hence,
for the higher wire
tan 75 = h / 4
4 tan 75 = h
This can be express as follows:
tan 75 = tan(45 + 30)
Hence,
4 × 3.73205080757 = 14.9282032303 ft = 14.9ft
Hence, the trigonometric expression that can be used to find the height of the tree where the top guy wire attaches is tan(45 + 30)
learn more trigonometry here: https://brainly.com/question/17064152
#SPJ1
Fill in the blank. In the triangle below, x=?. Round your answer to two decimal places.
Answer:
Hello
DiinoMahFill in the blank. In the triangle below, x=?. Round your answer to two decimal places.
The Pythagorean Identity states that: (sin x)^2 + (cos x)2 = 1
Given sin 0 = 2/5, find cos 0.
cos 0 = ?/?
Answer:
[tex]\cos \theta =\dfrac{\sqrt{21}}{5}[/tex]
Step-by-step explanation:
Given:
[tex]\sin \theta=\dfrac{2}{5}[/tex][tex](\sin x)^2+(\cos x)^2=1[/tex]Substitute the given value of sin θ into the given identity and solve for cos θ:
[tex]\begin{aligned}(\sin x)^2+(\cos x)^2 & =1\\\implies (\sin \theta)^2+(\cos \theta)^2 & =1\\\left(\dfrac{2}{5}\right)^2+(\cos \theta)^2 & =1\\\left(\dfrac{2^2}{5^2}\right)+(\cos \theta)^2 & =1\\\dfrac{4}{25}+(\cos \theta)^2 & =1\\(\cos \theta)^2 & =1-\dfrac{4}{25}\\(\cos \theta)^2 & =\dfrac{21}{25}\\\cos \theta & =\sqrt{\dfrac{21}{25}}\\\cos \theta & =\dfrac{\sqrt{21}}{\sqrt{25}}\\\cos \theta & =\dfrac{\sqrt{21}}{5}\end{aligned}[/tex]
Sarah conducted an experiment regarding the effectiveness of two mathematics tutoring programs: Math Master and Excel. She randomly selected 20 students from her high school and assigned 10 students to the Math Master program. Sarah then assigned the remaining 10 students to the Excel program.
Finding the percent increase, it is found that the correct option is given by:
C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.
What is the percent increase?The percent increase is given by the difference between the final and the initial score, divided by the initial score and multiplied by 100%.
Researching the problem on the internet, we have that:
In the Master program, the average score increased from 75 to 87.In the Excel program, the average score increased from 73 to 81.The percent increases are given as follows:
M = 12/75 x 100% = 16%,E = 8/73 x 100% = 10.96%.Hence the correct option is given by:
C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.
More can be learned about percent increase at https://brainly.com/question/24906920
#SPJ1
Use point-slope form − 1 = ( − 1) to find the equation of the line that passes through the point (−3,5) and has slope = −2 . Write the answer in slope-intercept form = + .
Answer:
y - 5 = -2(x + 3)
Step-by-step explanation:
When you write an equation in point-slope form, you only need two things: a point and a slope.
Given:
point: (-3, 5)
slope (m): -2
The standard point-slope equation is
y - y₁ = m(x - x₁)
Plug in what you know.
y - (5) = -2(x - (-3))
Simplify.
y - 5 = -2(x + 3)
This is your equation.
Learn with another example:
brainly.com/question/24436844
find the least common denominator 3/2x+4 and -11/3x+6
Answer: 6x+12
Step-by-step explanation: Both denominators can be multiplied to create 6x + 12.
2x + 4
2x(3) + 4(3)
6x+12
3x + 6
3x(2) + 6(2)
6x+12
I hope this helps!
MATH: Composition of two functions...help needed with this problem
The equation of Q(n) is [tex]Q(n) = \frac89 * (88n + 23)[/tex]
How to determine the formula of Q(n)?The functions are given as:
[tex]R(d) = \frac89 d[/tex]
[tex]P(n) = 88n + 23[/tex]
From the question, we understand that:
d = P(n)
This means that:
d = 88n + 23
Substitute d = 88n + 23 in R(d)
[tex]R(n) = \frac89 * (88n + 23)[/tex]
Also, from the question
Q(n) = R(n)
So, we have:
[tex]Q(n) = \frac89 * (88n + 23)[/tex]
Hence, the equation of Q(n) is [tex]Q(n) = \frac89 * (88n + 23)[/tex]
Read more about composite functions at:
https://brainly.com/question/10687170
#SPJ1
Pam ask you to help her with the catering for the funeral. you decide to use juice concentrate to serve as a refreshing drink. to create this delicious you must dilute the concentrate in the ratio 1:4 you must make 25litres of juice. what volume of concentrate is needed to make the juice
Answer:
6.25 litres
Step-by-step explanation:
ratio 1:4
25/4 = 6.25
4 * 6.25 = 25
1 * 6.25 = 6.25
= 6.25 litres of concentrate
Answer:
6.25 litres of juice concentrate
A 450-pound circus tiger eats 15 pounds of meat per day. How many pounds of meat would you expect a 360-pound tiger to eat per day? A 450 - pound circus tiger eats 15 pounds of meat per day . How many pounds of meat would you expect a 360 - pound tiger to eat per day ?
Solve for x in the equation 4/x-3=x
Answer:
jenejebdjdndnr
r
r
r
r
r
r
Answer:
Step-by-step explanation:
Comment
Multiply through by x - 3
Then factor the result
4*(x - 3) / (x - 3) = x*(x - 3)
4 = x * (x - 3 ) Remove the brackets
4 = x^2 - 3x Subtract 4 from both sides
4-4 = x^2 - 3x - 4 Simplify
0 = x^2 - 3x- 4
This factors
0=(x - 4)(x + 1)
Answer
x - 4 = 0
x = 4
x+ 1 = 0
x = - 1
What are the roots of x In-10x2 + 12x-9=0? OA. 61√6 -1 10 31√6 10 OB. O C. 31√24 10131/24 OD. ti√24 OE. 1, 2:√6 51 10 What are the roots of x In - 10x2 + 12x - 9 = 0 ? OA . 61√6 -1 10 31√6 10 OB . O C. 31√24 10131/24 OD . ti√24 OE . 1 , 2 : √6 51 10
Answer:
9=0
Step-by-step explanation:
9=0
The roots of x in the equation -10x² + 12x - 9 = 0 are:
x = (3/5) + (3/5)√(6)i
x = (3/5) - (3/5)√(6)i
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
To find the roots of x in the equation -10x² + 12x - 9 = 0, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation in standard form (ax² + bx + c).
In this case, a = -10, b = 12, and c = -9. Substituting these values into the quadratic formula, we get:
x = (-12 ± √(12² - 4(-10)(-9))) / 2(-10)
x = (-12 ± √(144 - 360)) / (-20)
x = (-12 ± √(-216)) / (-20)
Substituting this into the expression for x, we get:
x = (-12 ± 6√(6)i) / (-20)
Simplifying the expression further, we get:
x = (3/5) ± (3/5)√(6)i
Therefore, the roots of x in the equation -10x² + 12x - 9 = 0 are:
x = (3/5) + (3/5)√(6)i
x = (3/5) - (3/5)√(6)i
These roots are complex conjugates of each other.
To learn more about the quadratic equation;
https://brainly.com/question/17177510
#SPJ7
Simplify the expression -3z(1.8z-2.2).
-5.4z² + 6.6z
-5.4z²-6.6z
-1.2z²+5.2z
-1.2z²-5.2z
Mark this and return
Save and Exit
Next
Submit
Answer:
[tex] - 5.4z {}^{2} + 6.6z[/tex]
Step-by-step explanation:
Given:
[tex]-3z(1.8z-2.2)[/tex]
Solution:
Applying Distributive property,we obtain
[tex](−3z)(1.8z)+(−3z)(−2.2)[/tex]Simplifying using PEMDAS:
[tex] - 5.4z {}^{2} + 6.6z[/tex]Done!
Answer:A
Step-by-step explanation:
If I=$312.50 R=25% T=0.25 what is P
Step-by-step explanation:
please mark me as brainlest
Question 1(Multiple Choice Worth 4 points)
Which set of line segments could create a right triangle?
O24, 30, 35
O 12, 18, 30.
O 18, 24, 30
O 18, 24, 35
Answer: 18, 24, 30
Step-by-step explanation:
For the segments to create a right triangle, they must satisfy the Pythagorean theorem.
The only set which satisfies the Pythagorean theorem, is 18, 24, 30, since [tex]18^{2}+24^{2}=30^{2}[/tex]
25. (01.05)
Given the point (2, 3) and the slope of 4, find y when x = 22. (1 point)
I 78
O83
O88
091
Answer: 83
Step-by-step explanation:
The equation of the line in point-slope form is
[tex]y-3=4(x-2)[/tex]
Substituting in x = 22,
y - 3 = 4(22-2) [substitution]y -3 = 80 [simplify right hand side]y = 83 [add 3 to both sides]crash test results the insurance institute for highway safety crashed the 2010 ford fusion four times at 5 miles per hour. the costs of repair for each of the four crashes were $2529,$1889,$2610,$1073 $2529,$1889,$2610,$1073
compute the mean, median, and mode cost of repair.
Answer:
We know that
The costs of repair for each of the four crashes were
$2529, $1889, $2610, $1073
Here we have to compute the mean, median, and mode cost of repair.
Mean = total cost
the no of crashes
Mean = $2529 + $1889 +$2610 +$1073
4
Mean = $2025.25
Therefore the mean = 2025.25
Then we have to find median.
Now first we have to arrange the data in ascending order (smallest to highest).
$1073,$1889,$2529,$2610
Add the two middle numbers and then divide by two, to get the average:
$1889+$2529 = $4418
Median = $4418/2 = $2209
Therefore the median = $2209
Here there is no mode cost.
Help please asap I need help
Answer: 72
Step-by-step explanation:
[tex]\sum^{3}_{t=0} (6t^{2}-3)=(6(0)^{2}-3)+(6(1)^{2}-3)+(6(2)^{2}-3)+(6(3)^{2}-3)=\boxed{72}[/tex]
