Answers
Related Questions
Given conversion factor what is the above line segment's unit
1 ft
measure in inches? Round your answer to the nearest tenth.
Answer here
Please help
Answers
24
Step-by-step explanation:[tex]Convert\ the\ unit\ for\ \frac{12in}{1ft}:\\ \downarrow\\ 24[/tex]
I hope this helps you
:)
Find the area of the composite figure.
A: 96.75 units2
B: 112.5 units2
C: 139.5 units2
D: 192
Answers
The area of the composite figure from the image attached is 112.5 units²
What is the area of a composite figure?The area of a composite figure refers to the sum total of all the areas of the shapes in that composite figure. This can be done by first identifying the shapes in that composite figure, then finding each area, followed by the addition of all the areas to determine the area of the composite figure.
From the given figure; we can break it down into:
A parallelogramA rectangleA triangleThe area of a parallelogram = b × h
where;
b & h refers to the length of the two opposite diagonal lines.The area of a parallelogram = 9 × 6
The area of a parallelogram = 54 units²
The area of a rectangle = Length × breadth
The area of a rectangle = (9 × 3) units²
The area of a rectangle = 27 units²
The area of the triangle [tex]\mathbf{=\dfrac{1}{2}\times b \times h}[/tex]
where;
Base = b Height = hThe area of the triangle [tex]\mathbf{=\dfrac{1}{2}\times b \times h}[/tex]
The area of the triangle [tex]\mathbf{=\dfrac{1}{2}\times 9 \times 7}[/tex]
The area of the triangle [tex]\mathbf{= 31.5 units^2}[/tex]
Therefore, the area of the composite figure is:
= 54 + 27 + 31.5
= 112.5 units²
Learn more about composite figures here:
https://brainly.com/question/15981553
In a sequence of numbers, a5 = 30, a6 = 34, a7 = 38, a8 = 42, and a9 = 46.
Which equation can be used to find the nth term of the sequence?
A.) a,n = 4n + 10
B.) a,n = 4n + 30
C.) a,n = 6n + 30
D.) a,n = 6n
Answers
Answer:
A.)
Step-by-step explanation:
Try each choice to see which one works.
A.)
a_n = 4n + 10
a_5 = 4(5) + 10 = 30
a_6 = 4(6) + 10 = 34
a_7 = 4(7) + 10 = 38
Answer: A.)
Hello ! Here's a calculus question!
Find that value of
[tex]\\ \rm\Rrightarrow {\displaystyle{\int\limits_{\pi}^{2\pi}}}\dfrac{sin^6x+cos^6x}{sin^3xcos^3x}[/tex]
Note:-
Answer must include all steps properly .
Kindly don't waste time here if you don't know the answer .
All the best !
Answers
Answer:
Undefined.
Formula's used:
[tex]\longrightarrow \bold{sec(x) = \dfrac{1}{cos(x)} }[/tex]
[tex]\longrightarrow \bold{cosec(x) = \dfrac{1}{sin(x)} }[/tex]
[tex]\longrightarrow \bold{cot(x) = \dfrac{1}{tan(x)} }[/tex]
[tex]\longrightarrow \bold{tan(x) = \dfrac{sinx}{cos(x)} }[/tex]
[tex]\longrightarrow \bold{sin^2x + cos^2 x = 1 }[/tex]
[tex]\longrightarrow \sf \bold{Sum \ Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx}[/tex]
[tex]\longrightarrow \bold{ \int \:{sec^2(ax+b) = \dfrac{1}{a}tan(ax+b)+c }}[/tex]
[tex]\longrightarrow \bold{\int \:\dfrac{1}{ax+b} =\dfrac{1}{a} ln|ax+b|+c}[/tex]
Explanation:
[tex]\sf \Longrightarrow \int _{\pi }^{2\pi }\:\dfrac{sin^6(x)+cos^6(x)}{sin^3(x) \ * \ cos^3\left(x)}[/tex]
[tex]\sf \Longrightarrow \sf \int _{\pi }^{2\pi }\:\dfrac{sin^6\left(x\right)}{sin^3\left(x\right)\cdot \:cos^3\left(x\right)} +\dfrac{cos^6\left(x\right)}{sin^3\left(x\right)\cdot \:cos^3\left(x\right)}[/tex]
[tex]\Longrightarrow \sf \int _{\pi }^{2\pi }\:\dfrac{sin^3\left(x\right)}{\:cos^3\left(x\right)} +\dfrac{cos^3\left(x\right)}{sin^3\left(x\right)}[/tex]
[tex]\Longrightarrow \sf \int _{\pi }^{2\pi }\ tan^3(x)+ cot^3(x)[/tex]
[tex]\sf \Longrightarrow \sf \int _{\pi }^{2\pi } \tan ^3(x)dx+\int _{\pi }^{2\pi } \cot ^3 (x)dx[/tex]
[tex]\Longrightarrow \sf \bold{ [ }-\ln |\sec \left(x\right) |+\dfrac{\sec ^2(x)}{2}-\dfrac{\cot ^2 (x)}{2}-\ln |\sin(x)| \bold{ ] }^{2\pi }_\pi[/tex]
apply limits
[tex]\sf \Longrightarrow \sf -\ln \left|\sec \left(2\pi \right)\right|+\dfrac{\sec ^2\left(2\pi\right)}{2}-\dfrac{\cot ^2\left(2\pi\right)}{2}-\ln \left|\sin \left(2\pi\right)\right|-(-\ln \left|\sec \left(\pi \right)\right|+\dfrac{\sec ^2\left(\pi\right)}{2}-\dfrac{\cot ^2\left(\pi\right)}{2}-\ln \left|\sin \left(\pi\right)\right|)[/tex]
simplify using trigonometric basic functions
[tex]\Longrightarrow \sf -\ln \left|\dfrac{1}{\cos \left(2\pi \right)}\right|+\dfrac{\left(\dfrac{1}{\cos \left(2\pi \right)}\right)^2}{2}-\dfrac{\cot ^2\left(2\pi \right)}{2}-\ln \left|\sin \left(2\pi \right)\right|- ( -\ln \left|\dfrac{1}{\cos \left(\pi \right)}\right|+\dfrac{\left(\frac{1}{\cos \left(\pi \right)}\right)^2}{2}-\dfrac{\cot ^2\left(\pi \right)}{2}-\ln \left|\sin \left(\pi \right)\right|)[/tex]
The value of cot(2π) is not defined. [ cot(2π) = ∞ ]⇒ Undefined
Answer:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \boxed{\text{un} \text{de} \text{f}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationIntegration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Methods: U-Substitution + U-Solve
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integrand] Rewrite:[tex]\displaystyle \frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x} = \frac{\sin^6 x}{\sin^3 x \cos^3 x} + \frac{\cos^6 x}{\sin^3 x \cos^3 x}[/tex][Integrand] Simplify:
[tex]\displaystyle \frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x} = \tan^3 x + \cot^3 x[/tex][Integrand] Rewrite:
[tex]\displaystyle \frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x} = \tan x (\sec^2 x - 1) + \cot x (\csc^2 x - 1)[/tex]
Step 3: Integrate Pt. 2
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \int\limits^{2 \pi}_{\pi} {\tan x (\sec^2 x - 1) + \cot x (\csc^2 x - 1)} \, dx[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \int\limits^{2 \pi}_{\pi} {\tan x (\sec^2 x - 1)} \, dx + \int\limits^{2 \pi}_{\pi} {\cot x (\csc^2 x - 1)} \, dx[/tex]
Step 4: Integrate Pt. 3
Identify variables for u-solve.
1st Integral
Set u:[tex]\displaystyle u = \sec x[/tex][u] Apply Trigonometric Differentiation:
[tex]\displaystyle du = \sec x \tan x \, dx[/tex][du] Rewrite:
[tex]\displaystyle dx = \frac{1}{\sec x \tan x} \, du[/tex]
2nd Integral
Set v:[tex]\displaystyle v = \csc x[/tex][v] Apply Trigonometric Differentiation:
[tex]\displaystyle dv = - \cot x \csc x \, dx[/tex][dv] Rewrite:
[tex]\displaystyle dx = \frac{-1}{\cot x \csc x} \, dv[/tex]
Step 5: Integrate Pt. 4
[Integrals] Apply Integration Method [U-Solve]:[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \int\limits^{x = 2 \pi}_{x = \pi} {\frac{\tan x (\sec^2 x - 1)}{\sec x \tan x}} \, du + \int\limits^{x = 2 \pi}_{x = \pi} {\frac{- \cot x (\csc^2 x - 1)}{\cot x \csc x}} \, dv[/tex][Integrals] Simplify:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \int\limits^{x = 2 \pi}_{x = \pi} {\frac{u^2 - 1}{u}} \, du - \int\limits^{x = 2 \pi}_{x = \pi} {\frac{v^2 - 1}{v}} \, dv[/tex][Integrals] Apply Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \frac{u^2}{2} \bigg| \limits^{x = 2 \pi}_{x = \pi} - \int\limits^{x = 2 \pi}_{x = \pi} {\frac{1}{u}} \, du - \Bigg( \frac{v^2}{2} \bigg| \limits^{x = 2 \pi}_{x = \pi} - \int\limits^{x = 2 \pi}_{x = \pi} {\frac{1}{v}} \, dv \Bigg)[/tex][Integrals] Apply Logarithmic Integration:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \frac{u^2}{2} \bigg| \limits^{x = 2 \pi}_{x = \pi} - \ln | u | \bigg| \limits^{x = 2 \pi}_{x = \pi} - \Bigg( \frac{v^2}{2} \bigg| \limits^{x = 2 \pi}_{x = \pi} - \ln | v | \bigg| \limits^{x = 2 \pi}_{x = \pi} \Bigg)[/tex]Back-Substitute variables u and v:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \frac{\sec^2 x}{2} \bigg| \limits^{2 \pi}_{\pi} - \ln | \sec x | \bigg| \limits^{2 \pi}_{\pi} - \Bigg( \frac{\csc^2 x}{2} \bigg| \limits^{2 \pi}_{\pi} - \ln | \csc x | \bigg| \limits^{2 \pi}_{\pi} \Bigg)[/tex]Simplify:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \bigg( \ln | \csc x | - \ln | \sec x | + \frac{\sec^2 x - \csc^2 x}{2} \bigg) \bigg| \limits^{2 \pi}_{\pi}[/tex]Apply Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \boxed{\text{un} \text{de} \text{f}}[/tex]
∴ we have found the value of the given integral.
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Learn more about integration: https://brainly.com/question/14413972
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
what is 3 × 2/7 in lowest terms
Answers
Answer:
6/7
Step-by-step explanation:
3x2/7 in the same as 3/1x2/7, which is 6/7
(simply multiply the denominator and numerator of the fraction)
Answer: hii <3
Exact Form:
6/7
Decimal Form:
0.857142
Step-by-step explanation:
Simplify the expression.
Hopefully this helps you
- Matthew
Find the value of f(5) for the function.
F(x)=6+3x
Answers
Answer:
21
Explanation:
To solve this problem, you substitute in the 5 for the x creating this equation: f(5)=6+3(5).
f(5)=15+6
f(5)=21
pleaseee help (questions in photo) will mark brainliest
Answers
Answer:
270
Step-by-step explanation:
90, 180, 270, and 360 are standard position because they hold a part of a 90 angle
Answer:
Step-by-step explanation:
Standard position means that you will move clockwise about the origin to create the angle.
omg please help its due by 12 am! the sum of 2 numbers is 69. the larger number is 3 less than twice the smaller number .find the numbers. show your work!
Answers
Answer:
The smaller number is 24
The larger number is 45
Step-by-step explanation:
smaller number = x
Larger: 2x - 3
Smaller + larger = 69
x + 2x - 3 = 69 Combine left
3x - 3 = 69 add 3 to both sides
3x - 3+3 = 69+ 3 Combine
3x = 72 Divide by 3
3x/3 = 72/3
x = 24
Larger number = 2*24 - 3
Larger number = 45
Drew has a coin: one side shows heads and the other side shows tails. he also has a six-sided number cube with a number, 1 through 6, on each side. he flips the coin, rolls the number cube, and records his results. what is the probability, written as a fraction, that the coin shows tails and he rolls a 5?
Answers
Using it's concept, it is found that the probability that the coin shows tails and he rolls a 5 is of [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, the coin has two outcomes, one of which is tails, while the number cube has six outcomes, one of which is five. Since the coin and the number cube are independent, we just multiply the probabilities, hence:
[tex]p = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]
The probability that the coin shows tails and he rolls a 5 is of [tex]\frac{1}{12}[/tex].
More can be learned about probabilities at https://brainly.com/question/14398287
A certain brand of laundry detergent is manufactured for $4.40 and then marked up 25% by the local store before selling. The store offers a 30% discount with the purchase of three or more bottles of the detergent. Showing all work, determine the total cost, before tax, of three bottles of detergent. (10 points)
Answers
Using proportions, it is found that the total cost of three bottles of detergent is of $11.55.
What is a proportion?A proportion is a fraction of a total amount.
A certain brand of laundry detergent is manufactured for $4.40 and then marked up 25% by the local store before selling, hence the price of each bottle is given by:
P = 4.40 x 1.25 = $5.50.
The store offers a 30% discount with the purchase of three or more bottles of the detergent, hence the total cost is given by:
T = (3 x 5.50) x 0.7 = $11.55.
More can be learned about proportions at https://brainly.com/question/24372153
x/-6-8> -12
PLEASE HELP AND SOLVE
Answers
Answer:
24
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
x=24
PLEASE HELP I ILL MARK BRAINLIEST
Answers
Answer: 90 dergrees
Step-by-step explanation: 90 dergrees
For each pair of points, find the slope of the line that passes through the points.
(5, 4) and (0:1)
(3,7) and (-2,2)
Answers
Use the slope formula:-
[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]
[tex]\displaystyle\frac{1-4}{0-5}=\frac{-3}{-5} =\frac{3}{5}[/tex]
Second pair:-
[tex]\displaystyle\frac{2-7}{-2-3} =\frac{-5}{-5} =1[/tex]
notes:-If we multiply/divide a negative by a negative, we get a positive. :)
Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
(-4,9), (8,-7)
The endpoints of a diameter of a circle are given. Write the standard equation of the circle.
Answers
Answer:
(x-2)^2+(y-1)^2 = 10^2
(x-2)^2+(y-1)^2 = 100
Step-by-step explanation:
distance between points is diameter
x^2= (8--4)^2+(-7-9)^2
x^2=12^2+16^2
x^2=144+256
x^2=400
diameter x=20 so radius =10
center point =midpoint (-4+8)/2 and (-7+9)/2
center point =(2,1)
(x-2)^2+(y-1)^2 = 10^2
(x-2)^2+(y-1)^2 = 100
Suppose that you have a square pyramid like the one pictured. Which plane section will produce a trapezoid? Question 17 options: A) A cross section cut parallel with the bottom B) A cut parallel to the vertical axis, but off the vertical axis C) A cut parallel to the vertical axis, directly through the vertical axis D) Cutting off one of the bottom corners
Answers
Answer:
B
Step-by-step explanation:
Cut vertical but off vertcal axis.
A will produce a square and C and D will produce triangles.
1. Find the equation of a line passing through the points (1,-2) and (-3,10).
Answers
Answer:
Step-by-step explanation:
(1 , -2) x₁ =1 & y₁ = -2
(-3,10) x₂= -3 & y₂ = 10
First we need to find the slope.
[tex]\boxed{Slope = $\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$}[/tex][tex]\boxed{Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]
[tex]=\dfrac{10-[-2]}{-3-1}\\\\\\=\dfrac{10+2}{-4}\\\\\\=\dfrac{12}{-4}\\\\\\= - 3[/tex]
m = -3
Equation of the line: y = mx + b
y = -3x + b
To find the value of b, take one of the point and substitue in the above equaiton.
(1 , -2)
-2 = -3*1 + b
-2 = -3 + b
-2 + 3 = b
b = 1
Equation of the line:
y = -3x + 1
What is the area of this figure?
Answers
Answer:
through lengthy mafs, your answer should be 307 mi (wrong somehow)
Step-by-step explanation:
if you want an explanation, please, dont be afraid to comment ;)
(to other people who look this up the answer is actually 318 i dont know, but i got it wrong
Use the picture I provided to help me answer the math problem.
Answers
Part A
25%/100%1/4Part B
1 → 20 pieces 4 → (20*4) pieces 4 → 80 pieces of yellow paperAnswer:
See below ↓↓
Step-by-step explanation:
Part A
We have to write 25% as a rate per 100⇒ We know percentages are given to be the fraction of a number out of 100⇒ Therefore, 25% as rate per 100 = 25/100⇒ 1/4 [simplified]Part B
Let's take the total number of pieces of colored paper to be TThen 25% of T is 20Therefore our equation will be :⇒ T x 25/100 = 20Bring 100 to the other side⇒ 25T = 200025 is a factor of both 25 and 2000, so it cancels out, and we are left with :⇒ T = 80There are 80 pieces of paperJoel borrowed $18,000 for 6 years at simple interest to purchase a vehicle. If Joel repaid a total of $20,953.80, at what rate did he borrow the money?
Enter the percent with the percent symbol. If the percent is not a whole value, enter it as a decimal where the last digit is not zero and there is a zero before the decimal point for values less than 1. For example, if the answer is .35%, 0.35% should be entered. Round the percent to the nearest thousandth of a percent if needed.
Answers
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$20953.80\\ P=\textit{original amount deposited}\dotfill & \$18000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &6 \end{cases} \\\\\\ 20953.80=18000[1+(\frac{r}{100})(6)]\implies \cfrac{20953.80}{18000}=1+\cfrac{6r}{100}[/tex]
[tex]\cfrac{20953.80}{18000}=\cfrac{100+6r}{100}\implies \cfrac{2095380}{18000}=100+6r\implies \cfrac{11641}{100}=100+6r \\\\\\ \cfrac{11641}{100}-100=6r\implies \cfrac{1641}{100}=6r\implies \cfrac{1641}{600}=r \\\\\\ \cfrac{547}{200}=r\implies \stackrel{\%}{2.735} = r[/tex]
-3y (y⁴ + 2y³ - 5y²- y + 4)
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's expand the given expression ~
[tex]\qquad \sf \dashrightarrow \: - 3y( {y}^{4} + 2 {y}^{3} - 5 {y}^{2} - y + 4)[/tex]
[tex]\qquad \sf \dashrightarrow \: ( - 3y \cdot {y}^{4} ) + ( - 3y \cdot2 {y}^{3} ) + ( - 3y \cdot - 5 {y}^{2} ) + ( - 3y \cdot - y) + ( - 3y \cdot4)[/tex]
[tex]\qquad \sf \dashrightarrow \: - 3{y}^{5} - 6{y}^{4} + 1 5 {y}^{3} + 3{y}^{2} - 12y[/tex]
PLEASE HELP
Select the statements that are true.
O Correlation coefficients must be between 0 and 1.
Correlation coefficients must be between - 1 and 1
A correlation coefficient of r = 0.92 indicates a strong, positive correlation.
A correlation coefficient of r = 0.01 means there is no significant correlation.
A correlation coefficient of r = 0.17 indicates a strong, negative correlation.
Correlation coefficient is a numeric measure of the strength and the direction between two quantative variables.
Answers
Correlation measures the relationship between variables
The true statements are:
Correlation coefficients must be between - 1 and 1A correlation coefficient of r = 0.92 indicates a strong, positive correlation.Correlation coefficient is a numeric measure of the strength and the direction between two quantative variables.How to determine the true statements?For a correlation coefficient to be valid, the following, must be true:
The value of the correlation coefficient must be between -1 and 1Correlation greater than 0 are positive correlationCorrelation closer to 1 and -1 are strong correlationUsing the above highlights, the true statements are: (b) (c) and (e)
Read more about correlation coefficients at:
https://brainly.com/question/18054482
Expand & simplify
4
(
2
g
+
3
)
−
5
(
4
g
−
4
)
Answers
Answer:
-12g+32
Simplify and combine like terms.
If f(x)= 2x^3-12x^2+20x-16 and f(4)= 0, then find all the zeros of f(x) algebraically
Answers
Answer:
x = 4 is the only real zeroStep-by-step explanation:
Find the zero's of f(x)
2x³ - 12x² + 20x - 16 = 0x³ - 6x² + 10x - 8 = 0x³ - 4x² - 2x² + 8x + 2x - 8 = 0x²(x - 4) - 2x(x - 4) + 2(x - 4) = 0(x - 4)(x² - 2x + 2) = 0(x - 4)(x² - 2x + 1 + 1) = 0(x - 4)[(x - 1)² + 1] = 0x - 4 = 0 ⇒ x = 4, we already know this(x - 1)² + 1 = 0 ⇒ (x - 1)² = - 1, no real solution as the square is never negativeAnswer:
[tex]x=4, \quad x=1+i,\quad x=1-i[/tex]
(one real zero and 2 complex zeros)
Step-by-step explanation:
Given polynomial:
[tex]f(x)= 2x^3-12x^2+20x-16[/tex]
According to the Factor Theorem, if f(4) = 0 then (x - 4) is a factor of the given polynomial.
[tex]\implies f(x)=(x-4)(ax^2+bx+c)[/tex]
Expand the brackets:
[tex]\implies f(x)=ax^3+bx^2+cx-4ax^2-4bx-4c[/tex]
[tex]\implies f(x)=ax^3+(b-4a)x^2+(c-4b)x-4c[/tex]
Compare coefficients with the given polynomial:
[tex]\implies a=2[/tex]
[tex]\implies -4c=-16 \implies c=4[/tex]
[tex]\implies (b-4a)=-12 \implies b-8=-12 \implies b=-4[/tex]
Substitute the found values of a, b and c:
[tex]\implies f(x)=(x-4)(2x^2-4x+4)[/tex]
To find the zeros of f(x), set the function to zero and solve for x:
[tex]\implies (x-4)(2x^2-4x+4)=0[/tex]
[tex]\textsf{Therefore},\: (x - 4) = 0\: \textsf{ and }\: (2x^2-4x+4)=0[/tex]
[tex]\textsf{To solve}\: (2x^2-4x+4)=0\: \textsf{ use the quadratic formula}[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]\implies x=\dfrac{-(-4) \pm \sqrt{(-4)^2-4(2)(4)} }{2(2)}[/tex]
[tex]\implies x=\dfrac{4 \pm \sqrt{-16}}{4}[/tex]
[tex]\implies x=\dfrac{4 \pm \sqrt{16 \cdot -1}}{4}[/tex]
[tex]\implies x=\dfrac{4 \pm \sqrt{16}\sqrt{-1}}{4}[/tex]
[tex]\implies x=\dfrac{4 \pm 4i}{4}[/tex]
[tex]\implies x=1 \pm i[/tex]
Therefore, the zeros of the function are:
[tex]x=4, \quad x=1+i,\quad x=1-i[/tex]
(one real zero and 2 complex zeros)
B. Study the figure on the right.
1. Name the points on it
2 Name any three segments from the figure,
3. Which segments have B as one endpoint?
4. Which points are endpoints of only two segments?
5. Which points are endpoints of three segments?
6. Which point is the endpoint of six segments?
7. Name the lines with A as one of the points on them.
8. Name any three rays from the figure, 9. How many segments are there in the figure?
10. How many rays can be named from the figure?
Answers
Answer:
can you clear more I don't understand
Question 7 of 10
One spring, a group of students measured rainfall totals at their school. This
chart shows how many inches of rain the students measured each month.
How many more inches did it rain in May than in April?
RAINFALL
MONTH
March
April
May
5.7
3.2
7.3
Help me god
Answers
Answer:
9
Step-by-step explanation:
10
Help me
Question
Find mHK⌢.
Answers
Answer:
62
Step-by-step explanation:
(x+8)=(2x-15)
8=x-15
+15 +15
23=x
so
23 +8 = 31
23x2-15 = 46-15 =31
Both are the same always since one side is equal to the other
Therefore
62 is the answer!
Carly and Carter are comparing bedrooms. They are each getting new carpet and are trying to figure out which room will be the most expensive to cover with carpet. (The rooms are both rectangular) Carly's bedroom is 15.3 ft. long and 8.7 ft. wide. Carter's bedroom is 14.4 ft. long and 9.6 ft. wide. Which bedroom will be the most expensive to cover with carpet? Explain your steps for figuring out the area of the floor for each bedroom and determining your answer. Make sure to Show your math steps as well. ~ 100 POINTS AND ILL GIVE YOU BRAINLIEST IF YOU ANSWER CORRECTLY AND 5 SENTENCES NEEDED
Answers
If Carly's bedroom is 15.3ft long and 8.7 ft long then it is necessary to multiply them because you need to find the area of the room so 15.3*8.7= 133.11. We have to do the same for Carter's room so we multiply 14.4 and 9.6 to find the area of the room which is 138.24.
Now that we have both the areas we can compare which room is bigger. Carly's room is 133.11 ft in total and Carter's room is 138.24 ft in total. So it is clear that Carter's room is going to be more expensive to cover with carpet since Carter's room is bigger than Carly's.
Carly:-
L=15.3B=8.7Area:-
LB15.3(8.7)133.11ft^2#Carter
L=14.4B=9.6Area:-
14.4(9.6)138.24ft^2Carter's room is expensive
A box of chocolates contains five milk chocolates, five dark chocolates, and three white chocolates. You randomly select and eat three chocolates. The first piece is milk chocolate, the second is white chocolate, and the third is milk chocolate.
Answers
Answer:
2/7
Step-by-step explanation:
Total no. of chocolates in the box =14
No. of dark Chocolates=4
No. of white chocolates=5
No. of milk chocolates=5
Probability of getting a white chocolate
= No. of possible outcomes /Total No. of outcomes
=5/14
Probability of getting a dark chocolate =4/14=2/7
I need help please, Its for today
Answers
Answer:
a) 1,2; 3.4
b) <1=<6, <6+<6+72=180, 2<6=108, <6=54.
<1=54
You can tell this by "these are parallel lines"
Solve this Distributed property 2(3x+5)
Answers
Answer: x = -.6
Step-by-step explanation:
2(3x+5) = 6x + 10
10 = -6x
x = -.6
