Let's begin by listing out the information given to us:
[tex]\begin{gathered} f(x)=x^2-4x+3 \\ f(x)=y \\ \Rightarrow y=x^2-4x+3 \\ y=x^2-4x+3 \end{gathered}[/tex]We will proceed to choose values for x (values of x lesser than 2); x = 1, 0, -1
[tex]\begin{gathered} y=x^2-4x+3 \\ x=1 \\ y=1^2-4(1)+3=1-4+3=4-4=0 \\ y=0 \\ (x,y)=(1,0) \\ \\ x=0 \\ y=0^2-4(0)+3=0-0+3=3 \\ y=3 \\ (x,y)=(0,3) \\ \\ x=-1 \\ y=(-1^2)-4(-1)+3=1+4+3=8 \\ y=8 \\ (x,y)=(-1,8) \end{gathered}[/tex]From the calculation, we see a trend that the y-values increase as the x-value decreases. Hence, it is true
8. Bobbie is self-employed and made a profit of $22, 150 last year. She mustpay $2572 in income tax. She also must pay social security tax of 13.3% ofher profit. What is Bobbie's total tax liability? Round to the nearestdollar,a $5912b. $4998c. $5518
income tax = $2572
social security tax = 13.3% of the profit
= 13.3% of $22,150
= 13.3/100 * 22,150 = $2,945.95
So, the total tax =
2572 + 2,945.95 = $5,517.95
Rounding to the nearest dollar
the total tax = $5,518
The answer is option C. $5,518
which costes more , a hamburger or a Chicken salad ? use. The vives princesa to write a n inequality that show your answer Hamburger $ 4.30, hot Dog $ 2.35, Chicken salad $ 4.49 pizza 2.49
Chicken salad costs more
Explanation:Cost of Hamburger = $ 4.30
Cost of hot Dog = $ 2.35
Cost of Chicken salad = $ 4.49
Cost of pizza = $2.49
$4.49 is greater than $4.30
Cost of of Chicken salad is greater than Cost of Hamburger
Hence, Chicken salad costs more
An inequality that shows the answer:
4.49 > 4.30
How to calculate the square foot
Solution:
To find square feet, multiply the length measurement in feet by the width measurement in feet.
Hence, the standard formula to calculate square foot is;
[tex]length\times width[/tex]A restaurant sells tea for $1.50 plus $0.50 per refill. the restaurant brews enough tea for 4 refills per customer. The linear function that represents the total cost of, r , tea refill is C(r)=0.5r+1.5.
C(r)=0.5r+1.5.
The domain of a function is the set of all input variables of the function. In this case "r"
The domain r is the number of tea refills.
Sam used his calculator to multiply two large numbers. His calculator gave the result 6E7. Which numbers are equal to the result his calculatorshowed? Select all that apply.0.00000066x 1076 x 1076,000,00060,000,000
The expression: 6E7, is a way of writing a number in scientific notation and it is equivalent to:
[tex]6\cdot10^7[/tex]Since 10^7=10,000,000, then:
[tex]6\cdot10^7=60,000,000[/tex]I need help simplifying this question (last answer that is cropped is 1 over 9 with exponent of 5
To simplify this expression we need to follow this procedure:
It means that the correct answer is:
[tex]\frac{1}{9^5}[/tex]What is 10 meters long by 7 meters wide in square meters?
1) Assuming this is a quadrilateral, then the area is width times length
So
A =10 x 7
A= 70 m²
It's an area of 70 m²
According to the United States Treasury Department, the U.S national debt was 1.815 x 10 to the 13th power dollars on September 30, 2015 . On September 29, 2005 , the national debt was 4.974 x 10 to the power of 12 dollars . Find the amount of Increase in the national debt from September of 2005 to september of 2015? Write a sentence describing the increase in the national debt from 2005 to 2015 using scientific notation and using standard form.
The U.S national debt on 2015 was 1.815 * 10^13
The U.S national debt on 2005 was 4.974 * 10^12
So, the amount of increase =
1.815 * 10^13 - 4.974 * 10^12 =
18.15 * 10^12 - 4.974 * 10^12 =
(18.15 - 4.974) * 10^12 = 13.176 * 10^12
= 1.3176 * 10 * 10^12 = 1.3176 * 10^13
Hi tutor,What is the connection between the slope of a tangent of a function at a given point, and it’s derivative evaluated at that point? If possible, can you please use a diagram and derivation steps to help explain?
Given:
Derivative and sope of tangent
Required:
We want to define relation
Explanation:
The derivative of a function gives us the slope of the line tangent to the function at any point on the graph. This can be used to find the equation of that tangent line for example
and the slope of that tangent is the derivative of function at point P
Now to find equation of a tangent line
1) Find the first derivative of f(x).
2) Plug x value of the indicated point into f '(x) to find the slope at x.
3) Plug x value into f(x) to find the y coordinate of the tangent point.
4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.
A standard die is rolled. Find the probability that the number rolled is less than 3. Express your answer as a fraction
Once a die has the numbers 1,2,3,4,5 and 6, it means the numbers that are less than 3 are just the numbers 1 and 2. Now the probability can be built as follows:
As we can see above, once there are just two possibilities of numbers that are less than 3, the probability that the number rolled is less than 3 is equal to 2/6.
Two of the angles in a triangle measure 56° and 6° what is the measure of the third angle
The sum of angle in a triangle is 180°
If two of the angles in a triangle is 56° and 6°
Let x be the third angle
56 + 6 + x = 180° (sum of angle in a triangle)
62° + x = 180°
subtract 62° from both-side of the equation
x = 180° - 62°
x = 118°
Hence, the third side is 118°
Determine The Domain for the relation below
Answer:
The domain would be all real numbers.
Step-by-step explanation:
For Interval notation, it would be written as (-∝, ∝)
(I don't know what signs those are, but they are supposed to be infinity signs)
Domain is what x can or can't be. In the function that is in the image, the function is y=a constant. So, no matter what x is, y will always be the constant. So, x can be all real numbers.
Hope this helps!
Determine the Coordinate represented in the Table of Values. ch on at 2 7 9 6 3 5 una) f(9) = 5b) f(5) = 9c) f(5, 9) = 14d) f(9, 5) = 14
Given the table:
x f(x)
2 6
7 3
9 5
To determine the coordinate given in the table, we have the following:
f(2) = 6
f(7) = 3
f(9) = 5
From the answer choices, the only coordinate given is:
f(5) = 9
ANSWER:
f(9) = 5
Which best describes what happens when the number of trials increases significantly
Solution:
Given:
[tex]\begin{gathered} Head,H=4 \\ Total=12 \\ P(H)=\frac{4}{12} \\ P(H)=\frac{1}{3} \end{gathered}[/tex]From the probability, it can be deduced that as the number of trials increases, the observed frequency will get closer to the expected frequency.
Therefore, if the number of trials increases significantly, then the observed frequency of landing heads up gets closer to the expected frequency based on the probability of the coin landing heads up.
find a slope of the line that passes through (6,8) and (95,86)
find a slope of the line that passes through (6,8) and (95,86)
Applying the formula to calculate the slope
we ahve
m=(86-8)/(95-6)
m=78/89
therefore
the slope is 78/89in 2 years steve wants to buy a bicycle that 800.00. if he opens a savings account that earns 3 % interest compounded monthly how much will he have to despoit as principal to have enough money in 2 years to buy the bike
Answer
393.55
Explanation
The amount that results after an amount P is invested at compound interest at rate r% and time period t is given as
A = P (1 + r)ᵗ
For this question,
A = 800
r = 3% = 0.03
t = 2 (12) = 24 (Since the interest is compounded monthly, over 2 years)
P = ?
800 = P (1 + 0.03)²⁴
800 = P (1.03)²⁴
800 = P (2.0328)
2.0328P = 800
Divide both sides by 2.0328
(2.0328P/2.0328) = (800/2.0328)
P = 393.55
Hope this Helps!!!
Luke opened a savings account 3 years ago. the account earns 6%interest compounded quarterly if the current balance is 300.00 how much did he deposit initially
Answer
This is similar to the first one too.
A = P (1 + r)ᵗ
For this question,
A = 300
r = 6% = 0.06
t = 3 (4) = 12 (Since the interest is compounded quarterly, over 3 years; there are 4 quarters per year)
300 = P (1 + 0.06)¹²
300 = P (1.06)¹²
300 = P (2.0122)
2.0122P = 300
Divide both sides by 2.0122
(2.0122P/2.0122) = (300/2.0122)
P = 149.09
Hope this Helps!!!
Hi, i need help with question 1 of my Precalculus homework.
The interval notation uses the form (x1,x2) and it depends on whether the interval includes or does not includes the limits. if the interval includes the limit then we use the notation [x1,x2].
a. Since neither of the endpoints is included in the inequality the interval notation should be
[tex]-1b. The inequality includes all numbers greater or equal to 5, the interval notation should be [tex]x\ge5=\lbrack5,\infty)[/tex]c. The inequality includes all numbers that are less to 4 but does not include number -4, the interval notation should be
[tex]-4>x=(-\infty,-4)[/tex]d. The solution for the inequality includes two solutions, then we write both separately and unite them together. The interval notation should be
[tex]-4\le x<-1or0e. The interval notation should be between numbers 5 and 100 [tex]\lbrack5,100\rbrack[/tex]f. The numbers should be all less than pi, but it does not include pi
[tex](-\infty,\pi)[/tex]g. all numbers greater or equal to 3
[tex]\lbrack3,\infty)[/tex]h. All numbers less or equal to -2
[tex](-\infty,-2\rbrack[/tex]i. All numbers greater than 0, but it does not include 0
[tex](0,\infty)[/tex]j. all numbers less than e but it does not include e
[tex](-\infty,e)[/tex]I was on vacation for this unit and having a hard time
1.a
We can rewrite the given information in an algebraic expression as follows:
[tex]\frac{3}{8}x=6[/tex]where x represents the number of 3/8-inch thick books. Solving for x:
[tex]x=\frac{6}{\frac{3}{8}}[/tex]We can rearrange the operation:
[tex]x=\frac{6}{3}\cdot8[/tex][tex]x=\frac{48}{3}[/tex][tex]x=16[/tex]Then, we need 16 3/8-inch books to make a stack 6 inches tall.
1.b
To solve this exercise, we can use the same procedure as in 1.a.
0. Writing the information in an algebraic expression.
[tex]\frac{1}{2}x=2\cdot\frac{3}{4}[/tex]where x represents the groups of 1/2 pound.
We can convert the mixed number into an improper fraction:
[tex]2\cdot\frac{3}{4}=\frac{2\cdot4+3}{4}=\frac{8+3}{4}=\frac{11}{4}[/tex]2. Rewriting the operation:
[tex]\frac{1}{2}x=\frac{11}{4}[/tex][tex]x=\frac{\frac{11}{4}}{\frac{1}{2}}[/tex][tex]x=\frac{11\cdot2}{4\cdot1}[/tex][tex]x=\frac{22}{4}[/tex][tex]x=5.5[/tex]We have 5.5 groups of 1/2 pounds in 2 (3/4) pounds.
Answer:
• 1.a 16
,• 2.b 5.5
In the parallelogram ABCD, MLA = 2x + 50 and m C = 3x + 40. The measure of LA is
The measure of angle m∠A will be 70°,for the parallelogram ABCD
Parallelogram and its Properties:
Parallelogram is a special kind of quadrilateral, in which opposite sides are equal and parallel to each other.
Properties:
1. Opposite sides are parallel to each other.
2. Length of opposite sides are equal.
3.Diagonally opposite angles are equal.
4. Diagonals bisects each other.
5. Sum of any two adjacent angle is 180°
From figure,
ABCD is a parallelogram
m∠A = 2x + 50
m∠ C = 3x + 40
In a parallelogram ABCD we know opposite angles are equal to each other,
m∠A = m∠C
2x + 50 = 3x + 40
3x - 2x = 50 - 40
x = 10
Hence,
m∠A = 2x + 50
put the value of x we get,
m∠A = 2 * 10 + 50
= 20 + 50
= 70°
m∠A = 70°
To learn more about Parallelogram Visit:
https://brainly.com/question/11220936
#SPJ9
A chemistry student needs 80.0 mL of ethanolamine for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers thatthe density of ethanolamine is 1.02 g.cm. Calculate the mass of ethanolamine the student should welgh out.Be sure your answer has the correct number of significant digits.
STEP 1: Identify and Set Up
We are given a question that requires us to find mass when given volume and density.
It is common knowledge that these parameters are related by the formulae:
[tex]\begin{gathered} \text{density = }\frac{\text{mass}}{\text{volume}} \\ \text{This gives mass = volume }\times\text{ density} \end{gathered}[/tex]We use this relation to find mass
STEP 2: Execute
Density = 1.02 g/cc
Volume = 80ml = 80 cc
Mass is therefore:
[tex]\text{mass = 1.02}\times80=81.6g[/tex]Mass = 81.6g
Pls helpppp I don't know what 2×2 IS plsss
we have
2*2=2+2=4
5*5=5+5+5+5+.5=25
5 times 5
example
2*3
its 2 times 3
3+3=6
4*3
4 times 3
3+3+3+3=12
Answer:
2 x 2 = 4.
two multiplied by two equals four.
In parallelogram ABCD, which angle is congruent to
In parallelogram ABCD, which angle is congruent to ?
Let us draw the parallelogram to better understand the problem.
As you can see from the above figure,
∠ABC and ∠CDA are congruent. (drawn in black color)
Also, ∠BCD and ∠DAB are congurent. (drawn in red color)
This means that the opposite angles are congruent in a parallelogram.
Therefore, the correct answer is option C
∠ABC and ∠CDA are congruent.
cost of iPhone $699 with a 15% discount what will be the total paid
cost = $699
Discount = 15% = 15/100 = 0.15 (decimal form)
Multiply the cost by the discount in decimal form
699 x 0.15 = 104.85
Subtract the discount amount
699-104.85 = $594.15
10.2 x 3.80
I am still confused on this question
Answer: 38.76
Step-by-step explanation:
All you have to do is move both decimals to the right and multiply, example, 10.2 = 102. & 3.80 = 380., then you multiply both numbers. In this case, 102 x 380 is 38760. After you multiply both numbers, you move the decimal to the left, so 38760. = 38.760 or 38.76.
These dot plots show the ages (in years) for a sample of sea turtles and a sample of sharks. Sea Turtles 00 000 to 0000 000 : 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Sharks 000000 : OO 00000 0000 000 OO o 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Age (in years) What are the differences between the centers and spreads of these distributions? Select two choices: one for the centers and one for the spreads. O A. Centers: The sea turtles have a lower median age than the sharks. B. Spreads: The ages of the sea turtles are more spread out. O C. Centers: The sea turtles have a greater median age than the sharks. O D. Spreads: The ages of the sharks are more spread out
Options C and D.
The median age of the Sea turtles is 55 while the median age of the sharks is 30, thus validating OPTION C
We can get the ranges of the two distributions to be:
Sea Turtles: 65 - 45 = 20
Sharks: 55 - 10 = 45
Sharks have a larger range, validating OPTION D
List the sale price of the item. Round to two decimal places when necessary. Original price: $25; Markdown: 12%.
Answer
Sale Price = $22
Explanation
Mark down percentage is given as
[tex]\text{Markdown percentage = }\frac{(Original\text{ Price) - (Sale Price)}}{(Original\text{ }Price)}\times100[/tex]For this question,
Markdown percentage = 12%
Original Price = $25
Sale Price = ?
[tex]\begin{gathered} \text{Markdown percentage = }\frac{(Original\text{ Price) - (Sale Price)}}{(Original\text{ }Price)}\times100 \\ 12=\frac{25-(\text{Sale Price)}}{25}\times100 \\ \text{Divide both sides by 100} \\ 0.12=\frac{25-(\text{Sale Price)}}{25} \\ \text{Cross multiply} \\ 25-(\text{Sale Price) = (0.12 }\times25) \end{gathered}[/tex]25 - (Sale Price) = 3
Sale Price = 25 - 3
Sale Price = $22
Hope this Helps!!!
Write the STANDARD FORM of the equation through the point (4,-4) witha slope of -2.
The general equation of line with the slope "m" and passing points (a,b) is :
y - b = m (x -a)
In the given question:
Slope m = -2, passing points (a,b) = (4,-4)
Substitute the value of a = 4, b = -4 in the general equation of line
[tex]\begin{gathered} y-b=m(x-a) \\ y-(-4)=(-2)(x-4) \\ y+4=-2(x-4) \\ y+4=-2x+8 \\ y+2x=8-4 \\ 2x+y=4 \end{gathered}[/tex]The equation with the slope -2 and passing points (4,-4) is 2x + y = 4
Answer : 2x + y = 4
I need help with the hidden message. Help me please. Thank You I really appreciate it if you have helped me.
We have symbols that represent a letter and a number.
With the equations or relations in the left we have to find the numeric value for each picture, and then use the letter to complete the hidden message.
First equation is:
[tex]\begin{gathered} \text{spyder web + spyder web =16} \\ 2\cdot\text{spyder web = 16} \\ \text{spyder web = }\frac{16}{2}=8 \end{gathered}[/tex]So, the value of a spyder web is 8 and the letter for that is i.
The second equation is:
[tex]\begin{gathered} \text{candy - spyder web = 9} \\ \text{candy - 8 =9} \\ candy\text{ = 9+8=17} \end{gathered}[/tex]The value of candy is 17 and the letter is T.
The Third equation is:
[tex]\begin{gathered} \text{spyder web }\cdot\text{ cat - candy = 7} \\ 8\cdot\text{cat - 17 =7} \\ 8\cdot\text{cat=7+17=24} \\ \text{cat}=\frac{24}{8}=3 \end{gathered}[/tex]The value of cat is 3 and the letter is S.
The fourth equation is:
[tex]\begin{gathered} ballons\text{ / cat =11} \\ \text{ballons /3 =11} \\ \text{ballons}=11\cdot3=33 \end{gathered}[/tex]The value of ballons is 33 and the letter is E.
The fifth equation is:
[tex]\begin{gathered} \text{bat + (ballons - candy) = 23} \\ \text{bat + (33-17) = 23} \\ bat+16=23 \\ \text{bat = 23 - 16 = 7} \end{gathered}[/tex]The value of bat is 7, but there is some mistake, it must be 6 and the letter C.
The sixth equation is:
[tex]\begin{gathered} \text{bat}+\text{cat}\cdot pumpkin\text{ = 27} \\ 6+3\cdot\text{pumpkin}=27 \\ 3\cdot\text{ pumpkin = 27-6=21} \\ \text{pumpkin =}\frac{21}{3}=7 \end{gathered}[/tex]The value of pumpkin is 7 and the letter is O.
The seventh equation is:
[tex]\begin{gathered} \text{spyder / spyder web }\cdot\text{ pumpkin = 21} \\ \frac{spyder}{8}\text{ }\cdot7=21 \\ \text{spyder = 21}\cdot\frac{8}{7}=3\cdot8=24 \end{gathered}[/tex]The value of spyder is 24 and the letter is B.
The last equation is:
[tex]\begin{gathered} tree\text{ +ghost}=0 \\ tree\text{ + 0=0} \\ \text{tre}e\text{ = 0} \end{gathered}[/tex]The only value for ghost is zero and the letter L and the value of tree is zero too and the letter is O.
The hidden message is:
BOIL IS IOOOCEOT
need help asappppppp
At first, we will find the volume of the cone and the volume of the sphere, then subtract them to find the answer
The rule of the volume of the cone is
[tex]V_c=\frac{1}{3}\times\pi\times r^2\times h[/tex]Since the height of the cone is 1 cm and its radius is 3 cm, then
h = 1 and r = 3
Substitute them in the rule above
[tex]\begin{gathered} V_c=\frac{1}{3}\times\pi\times(3)^2\times(1) \\ V_c=\frac{1}{3}\times\pi\times9\times1 \\ V_c=3\pi \end{gathered}[/tex]The formula of the volume of the sphere is
[tex]V_{sp}=\frac{4}{3}\times\pi\times r^3[/tex]Since the diameter of the sphere is 3 cm, then
[tex]\begin{gathered} r=\frac{1}{2}\times3 \\ r=\frac{3}{2} \\ r=1.5\operatorname{cm} \end{gathered}[/tex]Substitute it in the formula above
[tex]\begin{gathered} V_{sp}=\frac{4}{3}\times\pi\times(1.5)^3 \\ V_{sp}=4.5\pi \end{gathered}[/tex]Noe subtract them to find the answer
[tex]\begin{gathered} V=4.5\pi-3\pi \\ V=1.5\pi \end{gathered}[/tex]The amount of the extra soap is
[tex]1.5\pi cm^3[/tex]Find the equation of the line with Slope = 5 and passing through (-7,-34). Write your equation in the form y=mx+b .
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-34})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-34)}=\stackrel{m}{ 5}(x-\stackrel{x_1}{(-7)}) \implies y +34= 5 (x +7) \\\\\\ y+34=5x+35\implies {\Large \begin{array}{llll} y=5x+1 \end{array}}[/tex]