ok so I understand the first 2 steps of solving this but I dont entirely get it........
Answers
You have the following equation:
2x² - 12x + 16 = 0
in order to solve the previous equation, first divide by 2 both sides:
x² - 6x + 8 = 0
next, consider that the factors of the previous expression has the form:
(x - )(x - ) = 0
consider the first number inside the first factor is the result of the sum of two numbers, and the number of the second factor is the product of the same numbers. Such numbers are:
(2)·(4) = 8
2 + 4 = 6
hence, the factorized expression is:
(x - 8)(x - 2) = 0
the solutions of the equations are:
x = 8
x = 2
Related Questions
Is r = 3 + 3sin θ symmetrical along the y axis?
Answers
Answer:
Yes. r = 3 + 3sin θ is symmetrical along the y axis
Step-by-step explanation:
Original polar equation is
r = 3 + 3sinθ
If this plot is to be symmetrical about the y axis then replacing Θ with (π-θ) in the original equation should not change the equation and thereby should not change the plot
r = 3 + 3sinθ
Replace θ with π-θ:
==> 3 + 3sin(π-θ)
But sin(π-θ) = sinθ
So the equation is unchanged at 3 + 3sin(π-θ) from the original equation r = 3 + 3sinθ
Hence the equation is symmetrical along the y-axis
This can be also be clearly seen if you plot both the equations, you will see the plot does not change
Solve the inequality: 3x + 4 ≤ 5
Answer in interval notation.
Answers
(-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5 as it's definition states "a relationship between two expressions or values that are not equal to each other".
What is inequality?A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b. a ≤ b means that a is less than or equal to b. a ≥ b means that a is greater than or equal to b.
What is interval notation?When using interval notation, we first write the set's leftmost number, then a comma, and finally its rightmost number. Depending on whether those two numbers are a part of the set, we then enclose the pair in parentheses or square brackets (sometimes we use one parenthesis and one bracket!).
Here,
3x+4≤5
3x≤1
x≤1/3
(-∞,1/3]
As it's definition states "a relationship between two expressions or values that are not equal to each other" (-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5.
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What is the equation of the line that passes through the point (7,6) and has a slope of 0
Answers
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
Given,
The points which the line passes, (x₁, y₁) = (7, 6)
Slope of the line, m = 0
We have to find the equation of the line:
We know that,
y - y₁ = m(x - x₁)
So,
y - 6 = 0(x - 7)
y - 6 = 0
y = 6
That is,
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
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Given the following dataset, determine the mode 6056605570546055
Answers
Answer:
5
Step-by-step explanation:
put it in order
6056605570546055
and the one that appears the most is the mode
Solve the given equation:x = -8y + 9
Answers
We have to solve the equation.
[tex]x=-8y+9[/tex]We have 2 unknowns and one equation, so we can only express one in function of the other.
We already have x in function of y, so we will now express y in function of x:
[tex]\begin{gathered} x=-8y+9 \\ x-9=-8y+9-9 \\ \frac{x-9}{-8}=\frac{-8y}{-8} \\ \\ -\frac{x}{8}+\frac{9}{8}=y \\ \\ y=-\frac{x}{8}+\frac{9}{8} \end{gathered}[/tex]Answer:
y = -x/8 + 9/8
Annette Michaelson will need $11,000 in 8 years to help pay for her education. Determine the lump sum, deposited today at 4.5% compounded monthly, will produce the necessary amount.
Answers
Annette Michaelson will need $11,000 in 8 years to help pay for her education. Determine the lump sum, deposited today at 4.5% compounded monthly, will produce the necessary amount.
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
A=11,000
t=8 years
n=12
r=4.5%=0.045
substitute in the formula above
[tex]\begin{gathered} 11,000=P(1+\frac{0.045}{12})^{(12\cdot8)} \\ 11,000=P(\frac{12.045}{12})^{(96)} \\ \\ P=7,679.61 \end{gathered}[/tex]therefore
the answer is
$7,679.61thereforeDISREGARD THE LAST ONE
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
A company manufactures computer memory chips as circular silicon wafers with a diameter of 10 Inches. The wafers are cut into
different sized sectors. Match each wafer's central angle to the area of that sector.
48°
20°
62°
45°
55°
Answers
Answer:
25/18 - 20
155/36 - 62
25/8 - 45
Step-by-step explanation:
Make a segmented bar chart to show the relationship between age and behavior toward humans.
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1) Using the data from the table, we plot the following segmented bard chart for the relationship between age and behaviour toward humans.
2) From the graph we see that for each behaviour towards humans, we have approximately the same percentage of juveniles (around 10%) and adults (around 90%), that's because the blue and green portions are proportionally the same for each bar. Based on what we see from the graph, we conclude that there is no association between age and behaviour towards humans.
Find the volume round to the nearest 10th necessary. Use three. 144 pi and a calculator to get your answers.
Answers
The diameter of the cylinder is 24 mm.
Therefore, the radius is given by:
[tex]\frac{24}{2}=12mm[/tex]The height of the cylinder is given as 5 mm.
The formula for the volume V of a cylinder with radius r and height h is given by:
[tex]V=\pi r^2h[/tex]Substitute r = 12mm and h = 5 mm into the formula for volume:
[tex]V=\pi\left(12\right)^2\left(5\right)\approx2261.9[/tex]Therefore, the volume of the cylinder is approximately 2261.9 mm².
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a wall in marcus bedroom is 8 2/5 feet high and 16 2/3 feet long. of he paints 1/2 of the wall blue, how many square feet will be blue?140128 2/157064 2/15
Answers
Answer:
[tex]70[/tex]Explanation:
What we want to answer in this question is simply, the area of the room that will be painted blue if he decides he would paint exactly have the room blue
So, we need to simply get the area of the room and divide this by half
Mathematically, the area of a rectangle is the product of its two sides
Thus, we have it that the area of the room is:
[tex]\begin{gathered} 8\frac{2}{5}\times16\frac{2}{3} \\ \frac{42}{5}\times\frac{50}{3}\text{ = 14}\times10=140ft^2 \end{gathered}[/tex]Now, to get the area painted blue, we divide this by 2 as follows or multiply by 1/2
We have this as:
[tex]140\times\frac{1}{2}=70ft^2[/tex]
I need help please!!
Answers
f(x) = 3x² - 5x+20
Find f(-8)
Answers
Answer:
Substitute x = -8 into f(x).
f(-8) = 3(-8)² - 5(-8) + 20
= 3(64) + 40 + 20
= 192 + 60
= 252
Use Descartes Rules of signs to complete the chart with possibilities for the nature of the roots of the following equations:A) x^3 - x^2 + 4x - 6 = 0B) x^5 - x^3 + x + 1 = 0
Answers
Given:
[tex]\begin{gathered} x^3-x^2+4x-6=0 \\ x^5-x^3+x+1 \end{gathered}[/tex]Required:
To determine the possibilities for the nature of the roots of the given equation.
Explanation:
(A)
A company has net sales revenue of $175000 reporting period and $148000 in the next. using horizontal analysis, it has experienced a decrease of what percentage?A. 15%B. 18%C. 8%D. 12%
Answers
ANSWER:
A. 15%
STEP-BY-STEP EXPLANATION:
We can determine the percentage using the following formula:
[tex]\begin{gathered} r=\frac{\text{ fiinal value - initial value}}{\text{ initial value}}\cdot100 \\ \\ \text{ we replacing} \\ \\ r=\frac{148000-175000}{175000}\cdot100 \\ \\ r=-15.42\%=15\% \end{gathered}[/tex]Therefore, the correct answer is A. 15%
Find equation of line containing the given points (4,3) and (8,0) Write equation in slope-intercept form
Answers
SOLUTION
Write out the given point
[tex]\begin{gathered} (4,3) \\ \text{and } \\ (8,0) \end{gathered}[/tex]The equation of the line passing through the point above will be obtain by following the steps
Step1: Obtain the slope of the line
[tex]\begin{gathered} \text{slope,m}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Hence } \\ x_1=4,x_2=8 \\ y_1=3,y_2=0 \end{gathered}[/tex]Substituting the values we have
[tex]\begin{gathered} \text{slope,m}=\frac{0-3}{8-4}=-\frac{3}{4} \\ \text{Hence } \\ m=-\frac{3}{4} \end{gathered}[/tex]Step 2: Obtain the y- intercept
The y-intercept is the point where the graph touch the y, axis
[tex]\begin{gathered} \text{slope, m=-3/4} \\ y=6 \\ y-intercept=6 \end{gathered}[/tex]Steps 3; use the slope intercept rule
[tex]\begin{gathered} y=mx+b \\ \text{Where m=-3/4,b=y-intercept} \\ \text{Then } \\ y=-\frac{3}{4}x+6 \end{gathered}[/tex]Hence
The equation in slope intercept form is
y = - 3/4 x + 6
help me pleaseeeeeeeee
Answers
The value of the car after 5 years is $13,500 and the value of the car after 9 years is $10,500.
According to the question,
We have the following information:
The value of the car is given by V(x) where x is the number of years.
V(x) = -1500x + 21,000
(a) Now, to find the value of car after 5 years, we will put 5 in place of x in the given expression:
V(5) = -1500*5+21000
V(5) = -7500+21000
V(5) = $13,500
(b) Now, to find the value of car after 9 years, we will put 9 in place of x in the given expression:
V(9) = -1500*9+21000
V(9) = -10500+21000
V(9) = $10,500
(c) When V(12) = 3000 then it means that the value of the car after 12 years is $3000.
Hence, the value of car after 5 years and 9 years is $13,500 and $10,500 respectively.
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5/6+1/3×5/8 i need help
Answers
We will solve as follows:
[tex]\frac{5}{6}+\frac{1}{3}\cdot\frac{5}{8}=\frac{5}{6}+\frac{5}{24}=\frac{4}{4}\cdot\frac{5}{6}+\frac{5}{24}[/tex][tex]=\frac{20}{24}+\frac{5}{24}=\frac{25}{24}[/tex]
A one-day admission ticket to a park costs $43.85 for adults and $15.95 for children. Two families purchased nine tickets and spent $338.85 for the tickets. Fill in a chart that
summarizes the information in the problem. Do not solve the problem.
Answers
Using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, a number of adults and children who purchased the tickets:
Let, adults are 'a and children be 'c':Now, the equation can be:
a + c = 9a = 9 - cNow, the second equation will be:
43.85a + 15.95c = 338.85
Now, substitute a = 9 - c in equation (2) as follows:
43.85a + 15.95c = 338.8543.85(9 - c) + 15.95c = 338.85394.65 - 43.85c + 15.95c = 338.85- 27.9c = 338.85 - 394.65- 27.9c = - 55.8c = - 55.8/ - 27.9c = 55.8/27.9c = 2Hence:
a = 9 - ca = 9 - 2a = 7Then:
c = 2 ⇒ 15.95 × 2 = $31.9a = 7 ⇒ 43.85 × 7 = $306.95Sum = $338.85Therefore, using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.
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4x + 3x = 56. What is the value of x?
Answers
Given
The expression is given as
[tex]4x+3x=56[/tex]Explanation
To find x, add the expression.
[tex]\begin{gathered} 7x=56 \\ x=\frac{56}{7} \end{gathered}[/tex][tex]x=8[/tex]Answer
Hence the value of x is 8.
[tex]4x + 3x = 56\\7x = 56\\x = 56/7\\x = 8[/tex]
The answer is X=8
Find the equation of the line that is parallel to y= 3x -2 and contains the point (2,11) Y= ?x + ?
Answers
Solution:
Given:
[tex]\begin{gathered} y=3x-2 \\ \text{Through the point (2,11)} \end{gathered}[/tex]Two parallel lines have identical slopes.
[tex]m_1=m_2[/tex]Hence, the slope of line 1 is gotten by comparing the equation given to the equation of a line in the slope-intercept form.
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]
Thus,
[tex]\begin{gathered} y=mx+b \\ y=3x-2 \\ \\ \text{Comparing both equations,} \\ m_1=3 \\ \text{The slope of line 1 is 3.} \end{gathered}[/tex]Since both lines are parallel, then the slopes are equal.
[tex]\begin{gathered} m_1=m_2=3 \\ m_2=3 \\ \text{The slope of line 2 is 3} \end{gathered}[/tex]To get the equation of line 2 through the point (2,11), the formula below is used;
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=m \\ \\ \text{where;} \\ x_1=2 \\ y_1=11 \\ m=3 \\ \text{Hence,} \\ \frac{y-11}{x-2}=3 \\ \text{Cross multiplying,} \\ y-11=3(x-2) \\ y-11=3x-6 \\ y=3x-6+11 \\ y=3x+5 \end{gathered}[/tex]
Therefore, the equation of the line that is parallel to y = 3x - 2 passing through the point (2,11) is;
[tex]y=3x+5[/tex]zoe is 1.55 meters tall. at 2 pm she measure the lenght of a tree's shadow to be 17.35 meters . she stands 12.7 meters away from the tree so that the tip of her shadow meets the tip of tye tree's shadow. find the height of yhe tree to the nearest hundredth of a meter.
Answers
the figure below to better undesrtand the problem
Applying proportion
h/17.35=1.55/(17.35-12.70)
solve for h
h=17.35*1.55/4.65
h=5.78 mA restaurant offer 7 appetizers and 10 main courses.In how main ways can a person order a two-course meal
Answers
Take into account that there are 7 chices for the first course, and there are 10 choices for the entree.
The total number of choices is given bye:
total_choices = Choices_for_first_course x choices_fro_entree
Then, by replacing the values of the previous parameters you get:
total_choices = 7 x 10 = 70
There are 70 ways a person can order a two-course meal
Assume that when adults with smartphones are randomly selected , 52% use them in meetings or classes. If 7 adults smartphone users are randomly selected, find the probability that exactly 4 of them use their smartphones in meetings or classes.The probability is:
Answers
From the information available;
The population is 52% and the sample size is 7. The probability that exactly 4 of them use smartphones (if 7 adults are randomly selected) would be calculated by using the formula given;
[tex]\begin{gathered} p=52\text{ \%, OR 0.52} \\ n=7 \\ p(X=x) \\ We\text{ shall now apply;} \\ p(X=4)=\frac{n!}{x!(n-x)!}\times p^x\times(1-p)^{n-x} \end{gathered}[/tex]We shall insert the values as follows;
[tex]\begin{gathered} p(X=4)=\frac{7!}{4!(7-4)!}\times0.52^4\times(1-0.52)^{7-4} \\ =\frac{5040}{24(6)}\times0.07311616\times0.110592 \\ =35\times0.07311616\times0.110592 \\ =0.28301218 \end{gathered}[/tex]Rounded to four decimal places, this becomes;
[tex](\text{selecting exactly 4)}=0.2830[/tex]ANSWER:
The probability of selecting exactly 4 smartphone users is 0.2830
In the following diagram, we know that line AB is congruent to line BC and angle 1 is congruent to angle 2. Which of the three theorems (ASA, SAS, or SSS) would be used to justify that triangle ABC congruent triangle CDA?
Answers
The theorem that justifies why triangle ABC is congruent to triangle CDA is the: SAS.
What is the SAS Theorem?The SAS theorem states that if we can show that two triangles have a pair of corresponding congruent included angles, and two pairs of corresponding sides that are also congruent to each other, then we can prove that both triangles are congruent to each other.
The triangles, ABC and CDA have:
Two pair of corresponding sides that are congruent to each other, which are AB ≅ BC, and AC ≅ CA.
A pair of corresponding included angles, which is angle 1 ≅ angle 2.
Based on the above known information, we can conclude that triangle ABC is congruent to triangle CDA by SAS theorem.
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Mrs. Navarro has 36 students in her class, 16 boys and 20 girls.Select all ratios below that correctly describe the ratio of boys to girls in Mrs.Navarros's class.
Answers
First, we need to know the ratio of boys to girls in Mrs. Navarro's class. There are 16 boys and 20 girls. The ratio would be 16:20.
From this given, we can choose from the options which rations are equivalent to our given ratio.
8 to 10 is a ratio that is equivalent from our given. If we scale are ratio by 2, we can get 8:10.
5:4, 8:18, and 5 to 9, however, are NOT equivalent to 16:20.
4:5 is equivalent. We just need to scale 16:20 by 4, and we will get 4:5.
10:8 is another ratio that is NOT equivalent to 16:20.
*Scaling ratios are similar to finding the lowest terms of fractions.
For f(x) = 2x+1 and g(x) = x² − 7, find (f+ g)(x).
Answers
Given the functions:
[tex]\begin{gathered} f(x)=2x+1 \\ \\ g(x)=x^2-7 \end{gathered}[/tex]By definition, (f+g)(x) is equivalent to:
[tex](f+g)(x)=f(x)+g(x)[/tex]Finally, using the expressions for f and g:
[tex]\begin{gathered} f(x)+g(x)=2x+1+x^2-7 \\ \\ \therefore(f+g)(x)=x^2+2x-6 \end{gathered}[/tex]Hello I could really use help with this problem please!
Answers
Answer:
C
[tex]A=2\pi\text{ square units; }h=2\text{ units}[/tex]Explanation:
Given:
Volume of a cylinder (V) = 4pi cubic units
To find:
Base area(A) and height(h)
Recall that the volume of a cylinder(A) is usually given as;
[tex]\begin{gathered} V=A*h \\ \end{gathered}[/tex]So let's go ahead and try each of the options and see which gives us 4pi on the left-hand side as we have on the right-hand side for Volume.
For option A;
We have that A = 1 and h = 2, so we'll have;
[tex]\begin{gathered} V=A*h \\ 4\pi=1*2 \\ 4\pi\ne2 \end{gathered}[/tex]For option B;
We have A = 2pi and h = 1, so we'll have;
[tex]\begin{gathered} 4\pi=2\pi *1 \\ 4\pi\ne2\pi \end{gathered}[/tex]For option C;
We have A = 2pi and h = 2, so we'll have;
[tex]\begin{gathered} 4\pi=2\pi *2 \\ 4\pi=4\pi \end{gathered}[/tex]We can see from the above that option C is the right option.
NEED ASAP IF CORRECT ILL GOVE BRAINLIEST
Answers
Answer:
I believe the answer is g(x)=x+10
Step-by-step explanation:
it moves 4 units to the right making it positive, adding to the previous 6 units, making it move 10 units to the right
The table shows the amount of water used daily to water the fairways at Fairlawn Golf Course. To the nearest tenth,determine the mean absolute deviation of the data. A. 2.3 B. 7.7 C. 10 D. 12.3
Answers
Answer:
2.3
Explanation:
The formula for calulating mean deviation is expressed as:
[tex]\frac{1}{n}\sum ^n_{i\mathop=1}|x_i-m|[/tex]where;
m is the mean of the data set
Xi are individual values
n is the total sample space
Get the mean;
n = 7
mean = (10+12+11+15+9+8+5)/7
mean = 70/7
mean = 10
Get the mean deviation:
Mean deviation = (10-10)+(12-10)+(11-10)+(15-10)+(9-10)+(8-10)+(5-10)/7
Since the values is in modulus |xi - m| will give a positive value, hence;
Mean deviation = (0+2+1+5+1+2+5)/7
Mean deviation = 16/7
Mean deviation = 2.28
Mean deviation = 2.3 (to the nearest tenth)
Garret’s coin bank contains500 nickels dimes and quarters. He has the same number of nickels as dimes and the total value of the coins is &72.50. How many quarters does he have?
Answers
Since he has the same number of nickels as dimes.
x = nickels
x = dimes
500 - 2x = quarters
the total value of the coins is $72.50
5x + 10x + 25(500-2x) = 7250
Solve for x
15x + 25(500) + 25(-2x) = 7250
15x + 12,500 - 50x = 7250
Combine like terms
15x - 50x = 7250 - 12500
-35x = -5250
Divide both sides of the equation by -35
-35x/-35 = -5250/-35
x = 150
150 quarters