The symmetry of a quadratic equation is given by the line that passes through its vertex, so in order to find the axis of symmetry we need to find the coordinate of the vertex, which is done below.
[tex]x_{\text{vertex}}=\frac{-b}{2a}[/tex]Where "a" is the number multiplying the square factor and "b" is the number multiplying the factor that isn't squared. To find these two constants we need to expand the equation given.
[tex]\begin{gathered} (x-3)\cdot(x+7) \\ x^2+7x-3x-21 \\ x^2+4x-21 \end{gathered}[/tex]We have that a = 1 and b = 4, therefore:
[tex]x_{\text{vertex}}=\frac{-4}{2\cdot1}=-2[/tex]The axis of symmetry for this quadratic equation is x=-2.
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.
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
$7,679.61thereforeIn 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?
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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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
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]
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.
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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Make a segmented bar chart to show the relationship between age and behavior toward humans.
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.
help me pleaseeeeeeeee
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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For f(x) = 2x+1 and g(x) = x² − 7, find (f+ g)(x).
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]f(x) = 3x² - 5x+20
Find f(-8)
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
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 restaurant offer 7 appetizers and 10 main courses.In how main ways can a person order a two-course meal
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
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%
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%
Use the law of detachment to determine what you can conclude from the given information
In mathematical logic, the Law of Detachment says that if the following two statements are true:
( 1 ) If p, then q.
( 2 ) p
Then we can derive a third true statement:
( 3 ) q.
In our question, we have
( 1 ) If 0º< A <90º, then A is an acute angle.
( 2 ) The measure of A is 58º.
Then, from the first statement, we can affirm
( 3 ) A is an acute angle.
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?
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
Hello I could really use help with this problem please!
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.
Solve the given equation:x = -8y + 9
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
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:
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
NEED ASAP IF CORRECT ILL GOVE BRAINLIEST
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
What is the equation of the line that passes through the point (7,6) and has a slope of 0
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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Is r = 3 + 3sin θ symmetrical along the y axis?
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
Find equation of line containing the given points (4,3) and (8,0) Write equation in slope-intercept form
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
I need help please!!
4x + 3x = 56. What is the value of x?
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 volume round to the nearest 10th necessary. Use three. 144 pi and a calculator to get your 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.
.
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.
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 mMrs. 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.
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.
Solve the inequality: 3x + 4 ≤ 5
Answer in interval notation.
(-∞,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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DISREGARD 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°
Answer:
25/18 - 20
155/36 - 62
25/8 - 45
Step-by-step explanation:
Given the following dataset, determine the mode 6056605570546055
Answer:
5
Step-by-step explanation:
put it in order
6056605570546055
and the one that appears the most is the mode
5/6+1/3×5/8 i need help
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]Find the equation of the line that is parallel to y= 3x -2 and contains the point (2,11) Y= ?x + ?
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]