Step 1
compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally.
Step 2
Math problem
455 + 229
Compatible numbers
455 + 225 = 680
680 is close to 455+229 = 684
Step 3:
Hence
By compatible numbers, 455 + 229 is more than 650.
Simplify and express in " a + bi " form.Show Detailed Step By Step Calculations
So, let's simplify
(8 - 10i) - (22 - 6i) =
8 -10i -22 +6i = (adding like terms)
-4i -14i
= The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 82. If state A has more counties than state B, how many counties does each state have? State A has counties.
State A have 42 counties and State B have 40 counties.
Define Linear equation
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant
Let,
x = The number of counties of state B
x + 2 = The number of counties of State A
It's given, The sum of counties of state A and state B is 82
so, the equation become is linear.
The linear equation will be,
x + (x + 2) = 82
solve for x,
2x + 2 = 82
2x = 82 - 2
2x = 80
x = 80/2
x = 40 (counties of State B)
put the value in x in x + 2,
40 + 2 = 42 (counties of State A)
Therefore, State A have 42 counties and State B have 40 counties.
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30. Landscaping Calculate the area (in square feet) of a flower garden shaped like a circular sector withradius 60 ft and central angle 33 degrees.31. In problem 30; if shrubs are planted every 2 ft along the outer border of the garden, how many shrubsare needed?
Explanation
the area of a circular sector is given by
[tex]\begin{gathered} \text{Area}_{sc}=\frac{\theta}{360}\pi r^2 \\ \text{where r is the radius and }\theta\text{ is the angle in degr}ees \end{gathered}[/tex]then
Step 1
Let
[tex]\begin{gathered} \text{radius}=\text{ 60 ft} \\ \text{angle}=33\text{ \degree} \end{gathered}[/tex]now, replace in the formula
[tex]\begin{gathered} \text{Area}_{sc}=\frac{\theta}{360}\pi r^2 \\ \text{Area}_{sc}=\frac{33}{360}\pi(60ft)^2 \\ \text{Area}_{sc}=1036.72ft^2 \\ \text{rounded} \\ \text{Area}_{sc}=1036.72ft^2 \end{gathered}[/tex]Step 2
if shrubs are planted every 2 ft along the outer border of the garden, how many shrubs
are needed?
to figure out this, we need to take the perimeter of the circular sector and divide by 2 ft, to get the total number of shrubs in the border
so,
[tex]\text{perimeter}=(2\cdot\text{radius)}+length\text{ of arc}[/tex]so, we need to find the length of the arc
the length of the arc is given by
[tex]l=\frac{2\pi r}{360}\cdot\theta[/tex]replace.
[tex]\begin{gathered} l=\frac{2\pi r}{360}\cdot\theta \\ l=\frac{2\pi\cdot60}{360}\cdot33 \\ l=34.55 \end{gathered}[/tex]finally, replace in the perimeter formula
[tex]\begin{gathered} \text{perimeter}=(2\cdot\text{radius)}+length\text{ of arc} \\ \text{perimeter}=(2\cdot60ft\text{)}+34.55 \\ \text{perimeter}=120\text{ ft+34.55 ft} \\ \text{Perimeter}=154.55\text{ ft} \end{gathered}[/tex]divde by 2 to know the numbers of shrubs
[tex]\begin{gathered} Numbver\text{ of shrubs=}\frac{\text{ perimeter}}{2})=\frac{154.55\text{ ft}}{2} \\ Numbver\text{ of shrubs=}77.275\text{ ft} \\ Numbver\text{ of shrubs=}78 \end{gathered}[/tex]
Two legs of a step ladder are each 4 metres long. The angle formed between the two legs is 30degrees.Make a labelled scale drawing of the ladder using the scale Icm=0.5 metres and fill in the blanksbelow.
assume the figure as two step ladder
3. The function f(x) has the coordinates below. State the changes made to f(x) which result in the function g(x). Write the (x,y) rule that would transform the coordinates of f(x) to the coordinates of g(x). g(x) = -2f(x + 1) - 4
Problem
The function f(x) has the coordinates below. State the changes made to f(x) which result in the function g(x). Write the (x,y) rule that would transform the coordinates of f(x) to the coordinates of g(x). g(x) = -2f(x + 1) - 4
Solution
From this table we know that
f(-1) = 5, f(2) = 1, f(6)=0
The rule for this case would be:
y= 13/84x^2 -125/84x +47/14
We also know that we have the following transformation
g(x) = -2f(x + 1) - 4
The corresponding coordinates of x on g(x) are:
0, 3, 7
So we have this:
f(0) = 47/14
f(3)= 2/7
f(7) = 11/21
And the corresponding y coordinates are:
-2(47/14) -4=-75/7
-2(2/7) -4=-3277
-2(11/21) -4=-106/21
Solve the system of equations below using any method you learned in this unit. Show all work (even if you are using your calculator).
Given the system of equations
[tex]\begin{gathered} x+4y-z=20-----1 \\ 3x+2y+z=8-----2 \\ 2x-3y+2z=-16-----3 \end{gathered}[/tex]We can solve for x, y and z below.
Explanation
Step 1: Find the value of z using the substitution method
[tex]\begin{gathered} \begin{bmatrix}x+4y-z=20\\ 3x+2y+z=8\\ 2x-3y+2z=-16\end{bmatrix} \\ Isolate\text{ for x in equation 1} \\ x=20-4y+z \\ \mathrm{Substitute\:}x=20-4y+z\text{ in equation 2 and 3} \\ \begin{bmatrix}3\left(20-4y+z\right)+2y+z=8\\ 2\left(20-4y+z\right)-3y+2z=-16\end{bmatrix} \\ sinplify \\ \begin{bmatrix}-10y+4z+60=8 \\ -11y+4z+40=-16\end{bmatrix} \\ Isolate\text{ for y in}-10y+4z+60=8 \\ -10y=8-4z-60 \\ y=\frac{8-4z-60}{-10} \\ y=\frac{-4z-52}{-10} \\ y=\frac{2\left(z+13\right)}{5} \\ \mathrm{Substitute\:}y=\frac{2\left(z+13\right)}{5}\text{ in }-11y+4z+40=-16 \\ \begin{bmatrix}-11\cdot \frac{2\left(z+13\right)}{5}+4z+40=-16\end{bmatrix} \\ simplify \\ \begin{bmatrix}\frac{-2z-286}{5}+40=-16\end{bmatrix} \\ multiply\text{ through by 5} \\ -2z-286+200=-80 \\ isolate\text{ for z} \\ -2z=-80-200+286 \\ -2z=6 \\ z=\frac{6}{-2} \\ z=-3 \end{gathered}[/tex]Step 2: Find y
[tex]\begin{gathered} \mathrm{Substitute\:}z=-3\text{ in}\mathrm{\:}y=\frac{2\left(z+13\right)}{5} \\ y=\frac{2(-3+13)}{5} \\ y=\frac{2(10)}{5} \\ y=4 \end{gathered}[/tex]Step 3: Find z
[tex]\begin{gathered} \mathrm{Substitute\:}z=-3,\:y=4\text{ in }x=20-4y+z \\ x=20-4\cdot \:4-3 \\ x=1 \end{gathered}[/tex]Answer: The solutions to the system of equations are
[tex]x=1,\:z=-3,\:y=4[/tex]#3b. Two bicyclists ride in the same direction. The first bicyclist rides at a speed of 8 mph.One hour later, the second bicyclist leaves and rides at a speed of 12 mph. How long will thesecond bicyclist have traveled when they catch up to the first bicyclist?I’m
Answer:
2 hours
Explanation:
[tex]\text{Speed}=\frac{Dis\tan ce}{Time}[/tex]The first bicyclist rides at a speed of 8 mph. Therefore:
[tex]\begin{gathered} 8=\frac{d}{t} \\ \implies d=8t \end{gathered}[/tex]One hour later, the second bicyclist leaves and rides at a speed of 12 mph.
Therefore, the time of the second bicyclist = (t-1) hours.
Therefore:
[tex]\begin{gathered} 12=\frac{d}{t-1} \\ \implies d=12(t-1) \end{gathered}[/tex]Since the second bicyclist will catch up to the first bicyclist, the distance traveled will be the same.
So:
[tex]\begin{gathered} 8t=12(t-1) \\ 8t=12t-12 \\ 8t-12t=-12 \\ -4t=-12 \\ \frac{-4t}{-4}=\frac{-12}{-4} \\ t=3\text{ hours} \end{gathered}[/tex]Therefore, the second bicyclist will have traveled for:
(t-1) = (3-1) =2 hours.
What is the equation in slope-intercept form of the line that passes through the point (1,5) and is parallel to the line represented by 3x-y=4?
Answer:
[tex]3x - 14[/tex]
Step-by-step explanation:
-y= -3x+4
-1 because de y no have a number in front
-1y÷-1= -3x÷-1 4÷-1
if the probability of drawing an A or B is 9/25, what is the probability of the complementary event?
If an event has a probability of "A", then the complementary event will have a probability of "1 - A".
Given, the probability of an event is 9/25, we can easily find the probability of the complementary event. Shown below:
[tex]\begin{gathered} 1-\frac{9}{25} \\ =\frac{25}{25}-\frac{9}{25} \\ =\frac{16}{25} \end{gathered}[/tex]The correct answer is:
[tex]\frac{16}{25}[/tex]The table to right gives the projections of the population of a country from 2000 to 2100.Answer parts (a) through (c).
c.
As found in part (a), the data in the table can be represented by the linear model as follows,
[tex]f(x)=2.928x+270.641[/tex]Here, 'x' is the number of years after year 2000.
To find: The population in 2080 as predicted by the model.
The value of 'x' corresponding to the year 2080 can be obtained as follows,
[tex]\begin{gathered} x=2080-2000 \\ x=80 \end{gathered}[/tex]Substitute the value of 'x' in the model for population,
[tex]\begin{gathered} f(80)=2.928\cdot(80)+270.641 \\ f(80)=234.24+270.641 \\ f(80)=504.881 \\ f(80)\approx504.9 \end{gathered}[/tex]Thus, the population in 2080 will be 504.9 million approximately, as predicted by the linear model.
You flip a coin 3 times. Let's fill out a tree diagram to see allof the possible outcomes.What is the probabilitythat you will flip a headsall 3 times?
Answer
Explanation
Given:
You flip a coin 3 times.
To determine the tree diagram to see all of the possible outcomes when you flip a coin 3 times, we first note that we can get either Heads or Tails. So the tree diagrams is shown below:
The possible outcomes would be:
HHH, HHT,HTH,HTT,THH,THT,TTH,TTT
We can notice that there are 8 possible outcomes. But, the number of cases to get exactly 3 heads is just 1.
Hence, the probability of getting 3 heads is:
Probability = 1/8 =0.125
Therefore, the probability that you flip a heads all 3 times is 0.125.
I need some help with this
The product is:
(7*10⁵)*(3*10²) = 2.1*10⁸
So the correct option is D
The quotient is:
(2*10⁵)/(4*10²) = 5*10²
So the correct option is B.
How to get the products?
Here we want to get the product between numbers in scientific notation, the first one is:
a) (7*10⁵)*(3*10²)
We can rewrite this as:
(7*10⁵)*(3*10²) = (7*3)*(10⁵*10²) = (21)*(10⁵⁺²) = 21*10⁷
In scientific notation we can have only one digit at the left of the decimal point, so we can rewrite:
21*10⁷ = 2.1*10⁸
So the correct option is D.
b) Now the quotient is:
(2*10⁵)/(4*10²) = (2/4)*(10⁵*10²) = 0.5*10⁵⁻² = 0.5*10³
Again, we need to have a single digit in the left of the decimal point:
0.5*10³ = 5*10²
The correct option is B.
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number serieswhat number comes next in the following series 27, 28, 32, 41, 57, 82, ?
Answer:
The number that comes next is;
[tex]118[/tex]Explanation:
Given the series;
[tex]27,28,32,41,57,82[/tex]From the series, if we observe the series closely we can see a relationship between the difference between consecutive terms.
[tex]\begin{gathered} 28-27=1=1^2 \\ 32-28=4=2^2 \\ 41-32=9=3^2 \\ 57-41=16=4^2 \\ 82-57=25=5^2 \end{gathered}[/tex]We can see that the difference follows the same pattern.
So, the next term would be the sum of the last term and the square of 6;
[tex]\begin{gathered} 82+6^2 \\ =82+36 \\ =118 \end{gathered}[/tex]Therefore, the number that comes next is;
[tex]118[/tex]Faith borrowed $2250 for home repairs. She paid back 24 payments of$132 each. How much did she pay in interest on the loan?a. $87.71b. $2,520c. $918d. $4.38
• We are given that Faith paid $132 for 24 months.
So; 132 * 24 = $3168
• Since we know that Faith initially borrowed $2250
Interest paid = $3168 - $2250
= $918
• Option C is the correct choice.
Mai is filling her fish tank water flows into the tank at a constant rate. 2.&- 0.5 1.6 time (minutes) water (gallons) 0.5 0.8 1 x1.6 1.6 x1.6 4.8 25 G 3 40 1) How many gallons of water will be in the fish tank after 3 minutes? Explain or show your reasoning. 2) How long will it take to fill the tank with 40 gallons of water? Explain or show your reasoning. 3) What is the constant of proportionality? What does it tell us about this situation?
Given
x = 0.5; y = 0.8
The constant of proportionality has to be calculated to estimate the other values.
The constant of proportionality "k" determines the relation of x and y, which can be represented as: y = kx.
So, in this exercise,
[tex]\begin{gathered} 0.8=k\cdot0.5 \\ \frac{0.8}{0.5}=k \\ k=1.6 \end{gathered}[/tex]y = 1.6y
(1) From this, we can estimate the value of y when x = 3.
[tex]\begin{gathered} y=1.6\cdot3 \\ y=4.8\text{gallons} \end{gathered}[/tex](2) If we want how long it will take to fill the tank with 40 gallons:
[tex]\begin{gathered} 40=1.6\cdot x \\ \frac{40}{1.6}=x \\ 25=x \end{gathered}[/tex]It will take 25 minutes.
(3) Finally, the constant of proportionality is 1.6 (as calculated above).
It tells us that the ratio between the gallons water of water and time. In other words, it tells us that for each 1 minute, 1.6 gallons are filled.
7. Principal = $39,300, Rate = 4.5%, Time = 6 months. What will that total principal + interest payment be rounded to the nearest dollar? o Lidhe total amount of
Given :
Principal = $39,300,
Rate = 4.5% = 0.045
Time = 6 months = 6/12 year = 0.5 year
Assume simple interest
So,
interest = Principal * rate * time = 39,300 * 0.045 * 0.5 = 884.25
So, the total = Principal + interest = 39,300 + 884.25 = 40,184.25
Rounding the answer to the nearest dollar
So, the total = $40,184
Solve the equation 3x - 4y = 16 for x.16 4OA. X-B. x1643C. X= 4y + 16O D. x= 3(16+47)
To solve for x, first, we add 4y to the equation:
[tex]\begin{gathered} 3x-4y+4y=16+4y, \\ 3x=16+4y\text{.} \end{gathered}[/tex]Now, we divide by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{16+4y}{3}, \\ x=\frac{16+4y}{3}\text{.} \end{gathered}[/tex]Answer:
[tex]x=\frac{16+4y}{3}\text{.}[/tex]In the diagram below , ^PQR = ^STR . Complete the statement
Given:
[tex]\Delta\text{PQR}\cong\Delta\text{STR}[/tex]Since it is given that triangles PQR and STR are congruent, the corresponding angles of the triangles are equal.
Hence,
Therefore, option D is correct.
The distance to your brother's house is 481 miles, and the distance to Disneyland is 518 miles. If it took 13 hours to drive to your brother's house, how long would you estimate the drive to Disneyland to take?
Answer:
364/7 = 260/d
Cross multiply.
364d = 1820
d = 5 hours
Miles per hour, mph = miles/hour
364 miles/7 hours = 52 mph
260 miles/52 mph = 5 hours
if a certain number is added to both the numerator and denominator of the fraction 8/9, the result is 6/7. Find the numer.
Sara is 33 years younger than Rolando. The sum of their ages is 105. Select the system of equations if Sara’s age is represented by S and Rolando’s age is represented by R.
Given:
Sara's age is represented by S and Ronaldo's age is represented by R.
Since,
Sara is 33 years younger than Ronaldo, then;
S= R - 33
Now, the sum of ages of Sara and Ronaldo is 105 then
[tex]R+S=105[/tex]Hence, from above,
[tex]\begin{gathered} S+R=105 \\ S=R-33 \end{gathered}[/tex]Therefore, second option is correct.
Henry has 3 3/5 metres of rope, and Sam has a piece of rope that is 1 1/2 metres
shorter. What is the total amount of rope that the boys have together?
A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. For instance, every integer and 3/7 are rational numbers.
The answer to the puzzle is 21 divided by ten.
What factors make a number rational?
It is possible to express rational numbers in the form pq, where p and q are integers and q0. Fractions cannot have a negative numerator or denominator, which is what distinguishes them from rational numbers.
Rates and ratios compare two different numbers. Simply put, a rate is a particular kind of ratio. The distinction is that a rate involves comparing two numbers.
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find the volume or missing value 3ft, 2.5ft, 6ft
The formula to find the volume of a rectangular prism is
[tex]\begin{gathered} V=l\cdot w\cdot h \\ \text{ Where V is the volume}, \\ l\text{ is the length,} \\ w\text{ is the width and} \\ \text{h is the height of the rectangular prism} \end{gathered}[/tex]Graphically,
So, in this case, you have
[tex]\begin{gathered} l=3ft \\ w=2.5ft \\ h=6ft \\ V=l\cdot w\cdot h \\ V=3ft\cdot2.5ft\cdot6ft \\ V=45ft^3 \end{gathered}[/tex]Therefore, the volume of the rectangular prism is 45 cubic feet.
ANSWER ASAP!! Raise the monomial to a power: -2m^3n^2t to the power of 4
"People who are generous help those in need however they can."
To which theory of ethics is the person who made this statement likely appealing?
Conventionalism
Virtue-based ethics
Kantian deontology
Egoism
Answer: Conventionalism
Step-by-step explanation:
The person who made the statement, "People who are generous help those in need however they can," is appealing to virtue-based ethics.
What is Virtue ethicsVirtue ethics is a way of thinking about what is right and wrong. It focuses on becoming a good person and practicing good qualities.
This focuses on helping people develop good qualities such as being generous, caring, and kind. In this situation, the statement means that being kind and helping people who need it is seen as doing the right thing.
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HelpWhich equation can be used to solve for x in the following diagram?
The sum of the angles is 90° because is a right angle because the square on the angle means it
then if we sum the angles 30° and 2x° we have 90°
[tex]30+2x=90[/tex]or
[tex]2x+30=90[/tex]then right option is A
if angle 2 = 106 degrees, what is the measurement of angle 6 ? ( better explanation in picture )
angle 2 and angle 6 are corresponding angles.
Since the lines crossed by the trnasversal are parallel, corresponding angles are congruent. (equal)
angle 6 = 106°
Sarah wants to take a vacation that will cost 2,562 if sarah plans to save for 9 months, then how much needs to be saved per month
Let:
x = Number of months
y = Total savings
a = Savings per month
so:
[tex]\begin{gathered} y=ax \\ where \\ y=2562 \\ x=9 \\ so\colon \\ 2562=9a \\ solve_{\text{ }}for_{\text{ }}a\colon \\ a=\frac{2562}{9} \\ a\approx284.67 \end{gathered}[/tex]She needs to save approximately $284.67 per month
Note:enter your answer and show all steps that you use to solve this problem3.jaoquin buys 3 dozen lightbulbs.after changing the lightbulbs in his house, he has 15 lightbulbs left how many lightbulbs did he use?*btw the not is the same thing to my question I have for number 6*6. the empire state building in new York City is 1,250 feet tall. it has 103 floors. rounded to the nearest whole, what is the height of each floor?
Answer: Number of lightbulbs that he used = 21 lightbulbs
1 dozen of light bulbs = 12 light bulbs
Jaoquin buys 3 dozens
3 dozens of lightbulbs = 3 * 12 lightbulbs
3 dozens of lightbulbs = 36 lightbulbs
This means that :
The number of light bulbs Jaoquin bought = 36
The number of lightbulbs that remain = 15
The number of lightbulbs that he used = (Number of lightbulbs that he buys) - (Number of lightbulbs that remains)
Number of lightbulbs that he used = 36 - 15
Number of lightbulbs that he used = 21 lightbulbs
Need help pleaseI was bad at math in school so lwant to learn
The probability of an event is expressed as
[tex]Pr(\text{event) =}\frac{Total\text{ number of favourable/desired outcome}}{Tota\text{l number of possible outcome}}[/tex]Given:
[tex]\begin{gathered} \text{Red}\Rightarrow2 \\ \text{Green}\Rightarrow3 \\ \text{Blue}\Rightarrow2 \\ \Rightarrow Total\text{ number of balls = 2+3+2=7 balls} \end{gathered}[/tex]The probability of drwing two blue balls one after the other is expressed as
[tex]Pr(\text{blue)}\times Pr(blue)[/tex]For the first draw:
[tex]\begin{gathered} Pr(\text{blue) = }\frac{number\text{ of blue balls}}{total\text{ number of balls}} \\ =\frac{2}{7} \end{gathered}[/tex]For the second draw, we have only 1 blue ball left out of a total of 6 balls (since a blue ball with drawn earlier).
Thus,
[tex]\begin{gathered} Pr(\text{blue)}=\frac{number\text{ of blue balls left}}{total\text{ number of balls left}} \\ =\frac{1}{6} \end{gathered}[/tex]The probability of drawing two blue balls one after the other is evaluted as
[tex]\begin{gathered} \frac{1}{6}\times\frac{2}{7} \\ =\frac{1}{21} \end{gathered}[/tex]The probablity that none of the balls drawn is blue is evaluted as
[tex]\begin{gathered} 1-\frac{1}{21} \\ =\frac{20}{21} \end{gathered}[/tex]Hence, the probablity that none of the balls drawn is blue is evaluted as
[tex]\frac{20}{21}[/tex]