Explanation:
Tommy calculated the area of the base by squaring the diameter, not the radius. If he's going to use the diameter in the area formula, he needs to divide the result by 4.
A = πr² = πd²/4
Answer:
Sample response: Tommy used the diameter instead of the radius in the formula to find the area of the base. The diameter needs to be divided by 2 to find the radius. The correct area of the base is 1 pi square inches. The correct total volume is 3 pi cubic inches.Step-by-step explanation:
Todd Foley is applying for a $98,000 mortgage. He can get a $651 monthly payment for principal and interest and no points, or a $541 monthly payment with 2.075 points. Approximately, how many months will it take Todd to cover the cost of the discount points if he takes the lower monthly payment? (Round your answer to the nearest whole month.)
Answer:
18 months
Step-by-step explanation:
The difference in payments is $651 -541 = $110 per month. The cost of the points is ...
$98,000 × 0.02075 = $2033.50
So, it will take $2033.50/($110/mo) ≈ 18.48 mo to make up the cost.
It will take Todd 18 months to cover the cost of the discount points.
_____
Comment on rounding
The question asks for the answer to be rounded to the nearest whole month. Since the quotient is about 18.486, this rounds to 18. After 18 months, the cost of the points is not quite covered. $53.50 remains to be covered. It isn't until Todd's 19th payment that the cost of points has been fully covered. For "break even" problems such as this one, I prefer to round to the next higher integer, rather than the nearest integer.
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 4 - 4 cos θ
Answer:
Symmetric about the y-axis only
Step-by-step explanation:
Graph the function using a calculator
alternatively,
Sketch the graph via the following steps
-sketch cosθ
- reflect about the x-axis to get (- cosθ)
- multiply vertex values by 4 to get -4cosθ
- shift the graph in the positive y direction by 4 units to get 4 - 4cosθ
you will end up with the attached graph:
By observation, we can see that the graph is
1) NOT symmetric about the x-axis
2) Symmetric about the y-axis
3) Not symmetric bout the origin
to run a symmetry test on a polar, we can simply do a few ( r , θ ) replacements, if the equation resulting from the replacements, resembles the original, then it has that symmetry type, now, let's recall the symmetry trigonometry identity, cos(-θ) = cos(θ).
[tex]\bf r=4-4cos(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{testing with respect to the y-axis, using }-r,-\theta ~\hfill }{(-r)=4-4cos(-\theta )\implies -r=4-4cos(\theta )}\implies r=-4+4cos(\theta )~\hfill \bigotimes \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{testing with respect to the x-axis, using }-\theta ~\hfill }{r=4-4cos(-\theta )\implies r=4-4cos(\theta )}~\hfill \stackrel{\textit{symmetry with respect}}{\textit{to x-axis}~\hfill }\textit{\Large\checkmark} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{testing with respect to the origin, using }-r~\hfill }{(-r)=4-4cos(\theta )\implies r=-4+4cos(\theta )}~\hfill \bigotimes[/tex]
Wayne needs to drive 470 miles to reach Milwaukee. Suppose he drives at a constant speed of 50 miles per hour. Which function represents Wayne's distance in miles from Milwaukee in terms of the number of hours he drives? A. y = 420x B. y = 470 + 50x C. y = 50 ? 470x D. y = 50 + 470x E. y = 470 ? 50x
Answer:
223
Step-by-step explanation:
i honestly dont even know
Answer:b y=470+50x
Step-by-step explanation:
Which of the following functions is graphed below?
Answer:
The function graphed is y = Ix - 5I - 4 ⇒ answer D
Step-by-step explanation:
* Lets explain how to solve this problem
- From the graph
# The graph intersects the x-axis at x = 1 and x = 9
∴ The x-intercepts are 1 and 9
- We can find x-intercept by equate y by 0
* Lets equate the answers by zero to find the x-intercept
# y = Ix + 5I - 4
∵ Ix + 5I - 4 = 0
- Add 4 to both sides
∴ Ix + 5I = 4
- Remember in Ia + bI = c, then we have two answers :
a + b = c OR a + b = -c
∵ Ix + 5I = 4
∴ x + 5 = 4 ⇒ subtract 5 from both sides
∴ x = -1
- OR
∴ x + 5 = -4 ⇒ subtract 5 from both sides
∴ x = -9
∴ The x-intercepts are -1 and -9 not the same with figure
# y = Ix - 5I + 4
∵ Ix - 5I + 4 = 0
- Subtract 4 from both sides
∴ Ix - 5I = -4
- Remember in Ia + bI = c , c can't be negative because the absolute
value is always positive
∴ We can't solve this equation
# y = Ix + 5I + 4
∵ Ix + 5I + 4 = 0
- Subtract 4 from both sides
∴ Ix + 5I = -4
- Remember in Ia + bI = c , c can't be negative because the absolute
value is always positive
∴ We can't solve this equation
# y = Ix - 5I - 4
∵ Ix - 5I - 4 = 0
- Add 4 to both sides
∴ Ix - 5I = 4
- Remember in Ia + bI = c, then we have two answers :
a + b = c OR a + b = -c
∵ Ix - 5I = 4
∴ x - 5 = 4 ⇒ add 5 to both sides
∴ x = 9
- OR
∴ x - 5 = -4 ⇒ add 5 to both sides
∴ x = 1
∴ The x-intercepts are 1 and 9 the same with figure
* The function graphed is y = Ix - 5I - 4
You select a card at random from the cards that make up the word "replacement". Without replacing the card, you choose a second card. Find the probability of choosing a vowel and then not a vowel. There is 1 letter for each card.
Answer:
The probability is 14/55
Step-by-step explanation:
The word replacement contains 11 letters.
In which 4 letters are vowel = e,a,e,e
And 7 letters are not vowel = r,p,l,c,m,n,t
The probability of getting the vowel in the first try = 4/11
The probability of getting something that is not a vowel = 7/10.
The denominator is one less because the vowel card is not replaced, meaning there is one less card to choose from.
Multiply the values:
=4/11 * 7/10
=28/110
=14/55
The probability is 14/55....
Geometry:
The vertices of triangle ABC are A(0, 0), B(8, 1), and C(5, 5). Find the coordinates of the image of triangle ABC after a rotation of 90 degrees counterclockwise about the origin, a reflection over the x-axis, and a translation using the rule (x, y) → (x + 6, y - 1).
Answer:
Step-by-step explanation:
The transformations you want are ...
90° CCW: (x, y) ⇒ (-y, x)reflection over x-axis: (x, y) ⇒ (x, -y)translation by your rule: (x, y) ⇒ (x+6, y-1)Taken together, these make the transformation ...
(x, y) ⇒ (-y+6, -x-1)
So, your points become ...
A(0, 0) ⇒ A'(6, -1)
B(8, 1) ⇒ B'(5, -9)
C(5, 5) ⇒ C'(1, -6)
___
The attachment shows the original triangle in red and the progression to the final triangle in blue.
A workbook contains 1,213 problems. If 837 of the problems have been solved, how many unsolved problems are left in the workbook?
Answer:
376
Step-by-step explanation:
This is a subtraction problem.
1,213 - 837 =
1,213
- 837
-----------
376
Answer: 376
Answer:376
Step-by-step explanation:1213-837=376
polygons BCDE & FGHI are similar
please help
Answer: [tex]\bold{a)\quad \dfrac{BC}{FG}=\dfrac{BE}{FI}}[/tex]
b) ∠H
c) ∠E
Step-by-step explanation:
I find it easiest to do these problems if I write one polygon on top of the other. That way I can easily see the angles and sides that match.
B C D E
F G H I
a) BC matches to FG and FI matches to BE
The proportion is: [tex]\dfrac{BC}{FG}=\dfrac{BE}{FI}}[/tex]
*****************************************************************************************
b) What matches with ∠D? Look at the letter below to see that it is ∠H
******************************************************************************************
c) What matches with ∠I? Look at the letter above to see that it is ∠E
Verify sin(360º - θ)= -sin θ
Show your work
Answer:
A nice way to show it is through the unit circle.
In the unit circle, the point at angle theta from the origin has a y value of sin theta.
If you rotate a point 360-theta degrees from the origin, that is like rotating it theta degrees "backwards", or downwards, which is going to yield the same exact point, reflected through the x-axis. In other words, the y value, or sin(360-theta), is exactly -sin(theta).
Answer:
The verification is in the explanation.
Step-by-step explanation:
To solve this I'm going to use the difference identity for sine:
[tex]\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)[/tex].
[tex]\sin(360^\circ-\theta)=\sin(360^\circ)\cos(\theta)-\sin(\theta)\cos(360^\circ)[/tex]
We are going to apply that [tex]\sin(360^\circ)=0 \text{ while } \cos(360^\circ)=1[/tex]
[tex]\sin(360^\circ-\theta)=0 \cdot \cos(\theta)-\sin(\theta)\cdot 1[/tex]
[tex]\sin(360^\circ-\theta)=-\sin(\theta)[/tex]
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Place the indicated product in the proper location on the grid.
-4x 3 y 2(7xy 4)
Answer:-28x^4y^2(-4x^3y^6)
Step-by-step explanation: Distribute and add exponents, put in parentheses to make it easier to understand but it's not necessary for the final answer.
Answer:
[tex]-28x^4y^6[/tex]
Step-by-step explanation:
The given expression is
[tex]-4x^3y^2(7xy^4)[/tex]
We need to place the indicated product in the proper location on the grid.
The given expression can be rewritten as
[tex](-4\times 7)(x^3x)(y^2y^4)[/tex]
[tex]-28(x^3x)(y^2y^4)[/tex]
Using the product property of exponent, we get
[tex]-28\times x^{3+1}\times y^{2+4}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]-28\times x^{4}\times y^{6}[/tex]
[tex]-28x^{4}y^{6}[/tex]
Therefore the answer of given product is [tex]-28x^{4}y^{6}[/tex].
In America, a person uses about 100 gallons of water each day, which is equal to 1,600 water-filled drinking glasses. How many water-filled drinking glasses would 281 Americans fill in a weeks time?
Your answer is 3,147,200 water-filled drinking glasses.
The first thing I would do is change the value of 1,600 water-filled drinking glasses to be equivalent to the total that would result from 281 Americans.
To do this, you just want to multiply 1,600 by 281, as the value of 1,600 is from one person, and for 281 people, the 1,600 would happen 281 times.
1,600 * 281 = 449600
Next, since the value of 449,600 is for 281 Americans in one day's time, multiply by 7 to make it equal to one week's time. This is because one week = 7 days, so the 449,600 total would happen 7 times in one week.
449,600 * 7 = 3,147,200
Therefore, your answer is 3,147,200.
Hope this helps!
In a week 281 Americans will use 3,147,200 water-filled drinking glasses.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Each day one person uses 1,600 water-filled drinking glasses.
∴ In a week the person will uses (1600×7) = 11200 water-filled drinking glasses.
∴ 281 will use (11200×281) = 3,147,200 water-filled drinking glasses.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ5
SOMEONE PLEASE HELP ME WITH THIS MATH QUESTION FILL ALL BLANKS
David is throwing a stone in the air at an angle from the ground with an initial velocity of 30 feet per second. The equation h=-10t2 + 40t +2 gives the height of the stone thrown. Find the maximum height of the stone
Answer:
42 feet
Step-by-step explanation:
The vertex of the quadratic function described by the equation is located at ...
t = -(40)/(2(-10)) = 2
The value of height at t=2 is ...
h = -10(2²) +40(2) +2 = -40 +80 +2 = 42 . . . . feet
The maximum height is 42 feet.
_____
The equation gives the vertical speed at t=0 as 40 ft/sec, which is in contradiction to the number given in the problem statement as the initial velocity. We have used the given equation to answer the question. Since we don't know the throwing direction, we cannot properly adjust the equation to match the description of the scenario.
A camera is placed in front of a hyperbolic mirror. The equation of the hyperbola that models the mirror is , where x and y are in inches. The camera is pointed toward the vertex of the hyperbolic mirror and is positioned such that the lens is at the nearest focus to that vertex.
Answer:
The lens is 1 inch from the mirror
Step-by-step explanation:
* Lets revise the equation of the hyperbola with center (0 , 0) and
transverse axis parallel to the y-axis is y²/a² - x²/b² = 1
- The coordinates of the vertices are (0 , ± a)
- The coordinates of the co-vertices are (± b , 0)
- The coordinates of the foci are (0 , ± c) where c² = a² + b²
* Lets solve the problem
∵ The equation of the hyperbola is y²/16 - x²/9 = 1
∵ The form of the equation is y²/a² - x²/b² = 1
∴ a² = 16
∴ a = √16 = 4
∵ The coordinates of the vertices are (0 , ± a)
∴ The coordinates of the vertices are (0 , 4) , (0 , -4)
∴ b² = 9
∴ b = √9 = 3
∵ c² = a² + b²
∴ c² = 16 + 9 = 25
∴ c = √25 = 5
∵ The coordinates of the foci are (0 , ± c)
∴ The coordinates of the foci are (0 , 5) , (0 , -5)
∵ The camera is pointed towards the vertex of the hyperbolic mirror
which is (0 , 4) and is positioned such that the lens is at the nearest
focus to that vertex which is (0 , 5)
∴ The distance between the lens and the mirror equal the distance
between the vertex and the focus
∵ The vertex is (0 , 4) and the nearest focus is (0 , 5)
∴ The distance = 5 - 4 = 1 inch
* The lens is 1 inch from the mirror
The Golden Braid Bookstore currently has $340,000 in cash, $280,000 in inventory, and $40,000 in accounts receivable. The company also has $65,000 in accounts payable, and $15,000 in other current liabilities. What is its quick ratio?
The quick ratio is a measure of a company's liquidity. It calculates a company's ability to pay off its current liabilities with its most liquid assets. The Golden Braid Bookstore has a quick ratio of 4.75.
Explanation:The quick ratio, also known as the acid-test ratio, is a measure of a company's liquidity. It calculates a company's ability to pay off its current liabilities with its most liquid assets. The formula for the quick ratio is:
Quick Ratio = (Cash + Accounts Receivable) / Current Liabilities
In this case, the Golden Braid Bookstore has $340,000 in cash and $40,000 in accounts receivable. Its current liabilities include $65,000 in accounts payable and $15,000 in other current liabilities. Plugging these values into the formula:
Quick Ratio = (340,000 + 40,000) / (65,000 + 15,000)
Quick Ratio = 380,000 / 80,000
Quick Ratio = 4.75
Therefore, the Golden Braid Bookstore has a quick ratio of 4.75.
If there are x teams in a sports league, and all the teams play each other twice, a total of n(x) games are played, where n(x)equalsxsquaredminusx. a football league has 7 teams, each of which play the others twice. if the league pays $45 per game, how much will it cost to play the entire schedule?
Answer:
$1,890
Step-by-step explanation:
Without including repeated instances of games (for instance, if I said that team 4 plays team 2 twice, then that would just be repeating when I already said that team 2 plays team 4 twice):
Team 1 plays:
teams 2, 3, 4, 5, 6, and 7 twice for a total of 12 games
Team 2 plays:
teams 3, 4, 5, 6, and 7 twice for a total of 10 games
Team 3 plays:
teams 4, 5, 6, and 7 twice for a total of 8 games
Team 4 plays:
teams 5, 6, and 7 twice for a total of 6 games
Team 5 plays:
teams 6 and 7 twice for a total of 4 games
Team 6 plays:
team 7 twice for a total of 2 games
--
Total it up:
[tex]12+10+8+6+4+2\\22+8+6+4+2\\30+6+4+2\\36+4+2\\40+2\\42[/tex]
Multiply by cost per game.
[tex]42*45=1890[/tex]
What is the value of x in the following equation: x - 2 = 9?
(please and thank you!!!)
AnswEr:
Add the two, to both sides. -2+2=0
So, the equation would like like this
x -2= 9
+2 +2
Then solve, the 2’s cancel out leaving you with x by itself. Finishing the equation to look like this-> x=11
PLEASE HELP!!!!!!!!!!!!!
Tasha used the pattern in the table to find the value of 4 to the power of -4
(refer to the graph)
She used these steps.
(refer to the picture of the steps)
In which step did Tasha make the first error?
Step 1
Step 2
Step 3
Step 4
Answer:
Tasha made her mistake in step 4.
Answer:
Step 4 is the incorrect.
Step-by-step explanation:
From the table attached,
Step 1. Find a pattern in the table.
Correct
Step 2. Find the value of [tex]4^{-3}=(\frac{1}{16})(\frac{1}{4})=\frac{1}{64}[/tex]
Correct
Step 3. Find the value of [tex]4^{-4}=(\frac{1}{64})(\frac{1}{4})=\frac{1}{256}[/tex]
Correct
Step 4. Rewrite the value of [tex]4^{-4}[/tex]
[tex](\frac{1}{256})=-\frac{1}{4^{-4} }[/tex]
Incorrect.
Because it should be [tex](\frac{1}{256})(\frac{1}{4})=\frac{1}{1024}[/tex]
Does the transformation of a vertical stretch to a parabola mean that the y coordinates of its points are shrunk or stretched the factor provided? Does the transformation of a horizontal stretch to a parabola mean that the x coordinates of its points are shrunk or stretched the factor provided?
Ex: Vertical stretch by a factor of 3 means the y coordinates are multiplied by three
Horizontal stretch by a factor 1/3 means the x coordinates are multiplied by three due to multiplying by the reciprocal.
PLS HELP
Answer:
Stretch in any direction (horizontal or vertical) means the corresponding coordinates are multiplied by the stretch factor: a horizontal stretch multiplies the x-coordinates by the stretch factor; a vertical stretch multiplies the y-coordinates by the stretch factor.
Step-by-step explanation:
If you know the coordinates, you can apply the stretch factor directly to the coordinates.
For example, consider the point (5, 25).
A horizontal stretch (only) by a factor of 3 will move this point to (15, 25).
A vertical stretch (only) by a factor of 3 will move the original point to (5, 75).
Note that only the corresponding coordinate is multiplied by 3.
___
The confusion can arise when this stretch concept is applied to the transformation of a function.
Consider the function f(x) = x^2. The point used in the example above is ...
(5, f(5))
Vertical Stretch Function Transformation
If we want to transform the function to one that is vertically stretched by a factor of 3, we can simply multiply the function value by 3:
g(x) = 3·f(x)
Then ...
(5, g(5)) = (5, 75) . . . . . . the location of the vertically stretched point in the above example.
Horizontal Stretch Function Transformation
If we want to stretch the above f(x) function horizontally by a factor of 3, we want a h(x) function that will produce the point (15, h(15)) = (15, 25). We can get that using f(x), but the argument to f(x) for that y-coordinate must be 5, not 15. This means the transformation must be ...
h(x) = f(x/3)
Dividing the function argument by the stretch factor means the argument must be larger by that factor in order to give the same function result.
(15, 25) = (15, h(15)) = (15, f(15/3)) = (15, f(5))
_____
Summary
Vertical stretch of a coordinate by the factor "a": (x, y) ⇒ (x, ay)
Vertical stretch of a function by the factor "a": g(x) = a·f(x)
__
Horizontal stretch of a coordinate by the factor "a": (x, y) ⇒ (ax, y)
Horizontal stretch of a function by the factor "a":
(x, y) ⇒ (ax, h(ax)), where h(x) = f(x/a), so h(ax) = f(ax/a) = f(x)
Use synthetic division to solve (x^3 + 1) ÷ (x – 1). What is the quotient?
Answer:
[tex](x^{2} +x+1)(x-1)+2[/tex]
Step-by-step explanation:
The synthetic division can be used to divide a polynomial function by a binomial of the form x-c, determining zeros in the polynomial.
step 1: Establish the synthetic division, placing the polynomial coefficients in the first row (if any term does not appear, assign a zero coefficient) and to the extreme left the value of c.
1 | 1 0 0 1
step 2: Lower the main coefficient to the third row.
1 | 1 0 0 1
1
Step 3: Multiply 1 by the main coefficient 1.
1 | 1 0 0 1
1
1
step 4: Add the elements of the second column.
1 | 1 0 0 1
1
1 1
step 5: Then repeat step 4 until the constant term 1 is reached.
1 | 1 0 0 1
1 1 1
1 1 1 2
step 6: Enter the quotient and remainder
quotient: [tex]x^{2} + x + 1[/tex]
remainder: 2
Solution: [tex]x^{2} + x + 1[/tex] [tex](x+1) + 2[/tex]
Answer:
x^2+x+1+[tex]\frac{2}{x-1}[/tex]
Step-by-step explanation:
TechWiz Electronics makes a profit of $35 for each MP3 player sold and $18 for each DVD player sold. Last week, TechWiz sold a combined total of 153 MP3 and DVD players. Let x be the number of MP3 players TechWiz sold last week. Write an expression for the combined total profit (in dollars) TechWiz made from MP3 and DVD players last week.
Final answer:
The expression for the combined total profit made by TechWiz Electronics from MP3 and DVD players last week is 17x + 2754.
Explanation:
The profit TechWiz Electronics made from selling MP3 players can be represented by the expression 35x, where x is the number of MP3 players sold.
The profit from selling DVD players can be represented by the expression 18(153-x), where 153 is the total number of players sold and x is the number of MP3 players sold.
To find the combined total profit, we can add these two expressions together:
Combined Total Profit = 35x + 18(153-x)
Using the distributive property, we can simplify as:
Combined Total Profit = 35x + 2754 - 18x
Combining like terms, we can simplify further:
Combined Total Profit = 17x + 2754
Therefore, the expression for the combined total profit TechWiz made from MP3 and DVD players last week is 17x + 2754.
The art club had a election to select to select a president 9 out of the 12 members of the art club voted in the election .What percentage of the members voted ?
75 percent of the art club members voted in the election.
To calculate the percentage of art club members who voted in the election, use the formula for percentage: part/whole *100. In this case, the part is the number of members who voted, and the whole is the total number of members in the art club.
Here's the step-by-step calculation:
Count the number of members who voted: 9.
Count the total number of members in the art club: 12.
Divide the number of voters by the total number of members: 9 / 12 = 0.75.
Multiply the result by 100 to get the percentage: 0.75 * 100 = 75%.
Therefore, 75 percent of the art club members voted in the election.
You bought a new television that has a 92 in. 76 in. screen. It has a feature that splits the screen to allow you to watch 4 channels at once. What is the scale factor and size for each channel when this feature is turned on?
Answer:
1/4
23in * 19 in.
Step-by-step explanation:
The scale factor is 1/4 and the channel size is 92*1/4 * 76 * 1/4
= 23 in * 19 in screen.
Answer:
Scale factor = 1/2, New screen 46 in by 38 in.
Step-by-step explanation:
The dimensions of screen is 92 in. by 76 in.
It has a feature that splits the screen to allow you to watch 4 channels at once as shown in the below figure.
All four parts are equal.
Let the dimensions of new screen be x in. by y in.
[tex]2x=92[/tex] and [tex]2y=76[/tex]
Divide both sides by 2.
[tex]x=46[/tex] and [tex]y=38[/tex]
Scale factor is
[tex]\text{Scale factor}=\frac{\text{New dimension}}{\text{Corresponding original dimension}}[/tex]
[tex]\text{Scale factor}=\frac{46}{92}[/tex]
[tex]\text{Scale factor}=\frac{1}{2}[/tex]
Therefore, the scale factor is 1/2.
What is the square footage for this property described by the metes-and-bounds method? Beginning at the point of the southerly side of Smith Street, 200 feet easterly from the corner formed by the intersection of the southerly side of Smith Street and the easterly side of Johnson Street; then east 200 feet; then south 100 feet; then west 200 feet; then north 100 feet to the POB.
A. 20,000 square feetB. 10,000 square feetC. 5,000 square feetD. 15,000 square feet
Answer:
A. 20,000 square feet
Step-by-step explanation:
The description is that of a rectangle 200 ft long and 100 ft wide. The area is the product of those dimensions:
area = (200 ft)(100 ft) = 20,000 ft²
The correct option is option A.
Area of a rectangle:The area of a rectangle is the region covered by the rectangle in a two-dimensional plane.
The formula to finding the area of the rectangle is,
[tex]A=l\times b[/tex]
It is given that,
Length=100 ft
Breadth=200 ft
[tex]A=l\times b[/tex]
Now, substituting the given values into the above formula we get,
[tex]A=200 \times 100\\A=20000[/tex]
The required area is 20,000 square feet.
Learn more about the topic area of the rectangle:
https://brainly.com/question/11202023
For a Saturday matinee, adult tickets cost $4.50 and kids under 12 pay only $2.00. If 100 tickets are sold for a total of $350, how many of the tickets were adult tickets and how many were sold to kids under 12?
Answer:
60 ADULT TICKETS
40 KIDS UNDER 12 TICKETS
Step-by-step explanation:
By playing around with numbers, you can figure out what makes this situation true. By multiplying 4.50 by 60, you get 270. Then, by multiplying 2 by 40, you get 80. Finally, add 270 and 80, which results in 350, which satisfies the problem.
Hope this helps!
By setting up a system of equations, we find that 60 adult tickets and 40 kids tickets were sold for the Saturday matinee when 100 tickets are sold for a total of $350.
Let x be the number of adult tickets sold and y be the number of kids tickets sold. We then have the following system of equations:
x + y = 100 (Total number of tickets)
$4.50x + $2.00y = $350 (Total revenue)
2x + 2y = 200
4.5x + 2y = 350
2.5x = 150
x = 60
y = 100 - 60 = 40
So, 40 kids tickets were sold.
f(x)=x^3−2x+6
g(x)=2x^3+3x^2−4x+2
Find (f−g)(x).
Select one:
a. x^3+3x^2−2x+4
b. x^3+3x^2−2x−4
c. 3x^3+3x^2−6x+8
d. −x^3−3x^2+2x+4
Answer:
d
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= x³ - 2x + 6 - (2x³ + 3x² - 4x + 2) ← distribute parenthesis by - 1
= x³ - 2x + 6 - 2x³ - 3x² + 4x - 2 ← collect like terms
= - x³ - 3x² + 2x + 4 → d
Which of the following equations uses the commutative property of addition to rewrite 1/3+2/5?
Select one:
a. 2/3+1/5=13/15
b. 1/3+2/5=5/15+6/15
c. 11/15−2/5=1/3
d. 2/5+1/3=11/15
Answer:
d. 2/5+1/3=11/15
Step-by-step explanation:
The commutative property of addition allows you to change the order of the operands in a sum. 2/5 is the second operand in the original sum; it is the first operand in selection D.
What is the average rate of change for the sequence shown below? coordinate plane showing the points 1, 4; 0.5, 3.5; 0, 3; and negative 0.5, 2.5
−2
−one half
1
2
Answer:
1
Step-by-step explanation:
Please use parentheses around the coordinates of your points:
(1, 4); (0.5, 3.5), etc.
If we go from (0.5, 3.5) to (1, 4), x increases by 0.5 and y increases by 0.5.
Thus the slope is m = rise / run = 1/1 = 1.
This is the average rate of change for the sequence shown.
The average rate of change for the sequence shown on the coordinate plane is calculated by finding the ratio of the differences in y-values to differences in x-values. For the given sequence, this average rate of change is 1.
Explanation:The average rate of change in a sequence given by a series of points on a coordinate plane can be calculated by finding the difference between the y-values divided by the difference in x-values. For the given points 1, 4; 0.5, 3.5; 0, 3; and negative 0.5, 2.5, we have:
Find the differences in y-values (4-3.5=0.5; 3.5-3=0.5; 3-2.5=0.5) Find the differences in x-values (1-0.5=0.5; 0.5-0=0.5; 0-(-0.5)=0.5) Find the ratio of difference in y-value to difference in x-value (0.5/0.5=1; 0.5/0.5=1; 0.5]/0.5=1)So, the average rate of change for the sequence shown is 1.
Learn more about Average Rate of Change here:
https://brainly.com/question/34745120
#SPJ3
What dividend is represented by the synthetic division below?
Answer:
2x³ + 10x² + x + 5
Step-by-step explanation:
The coefficients of the dividend are represented by the top row, that is
2 10 1 5 → 2x³ + 10x² + x + 5
The divisor is ( x + 5) and
the quotient is represented by the first 3 numbers on the bottom row
2 0 1 → 2x² + 1
The last zero on the same row is the remainder
Since zero this indicates that (x + 5) is a factor of 2x³ + 10x² + x + 5
Answer:
b
Step-by-step explanation:
A church rings its bells every 15 minutes, the school rings its bells every 20 minutes and the day care center rings its bells every 25 minutes. If they all ring their bells at noon on the same day, at what time will they next all ring their bells together? (Answer in the form AB:CD without am or pm such as 08:00)
Answer:
5 : 00 PM
Step-by-step explanation:
Given,
Church ring bells every 15 minutes,
School rings its bells every 20 minutes,
And, day care center rings its bells every 25 minutes,
Thus, the number of minutes after which they will ring together = LCM (15, 20, 25)
∵ 15 = 3 × 5,
20 = 2 × 2 × 5,
25 = 5 × 5,
Thus, LCM (15, 20, 25) = 300
Now, 1 minute = 1/60 hours ⇒ 300 minutes = 5 hours,
Hence, after 5 hours they will ring together,
If they rang at 12:00 PM,
Then they will ring after 5 hours that is 5:00 PM.