Answers
Use AB, BC, CD, DA to make the triangles.
The left-overs make up a rectangle that has the area of 2x3, which is 6.
Triangle AB and CD are equivalent, they are both (1/2)(1)(3)=1.5 each, which add up to 3.
Triangle AD and BC are equivalent, they are both (1/2)(1)(4)=2 each, which add up to 4.
So, just add up the 6 from the rectangle and the 3 & 4 and you get 13.
The area of that parallelogram is 13.
13 square units
Further explanationConsider attachment for details.
We make a KLMN rectangle that touches all the vertices of the ABCD parallelogram. Consequently, the ABCD parallelogram is right inside the KLMN rectangle.
Let us take the following strategic steps:
Calculate the area of KLMN.Calculate the area of the triangles ABL, CDM, ADK, and BCN.Subtract the area of the KLMN rectangle with the area of all triangles.The difference in the area above is the area of the ABCD parallelogram.The Process:
The area of KLMN = 4 x 5 = [tex] \boxed{ \ 20 \ square \ units. \ }[/tex]The ADK triangle is congruent to the BCN triangle, and each area is [tex]\boxed{ \ \frac{1}{2} \times 4 \times 1 = 2 \ square \ units. \ }[/tex] Thus the total area of ADK and BCN is [tex]\boxed{ \ 2 + 2 = 4 \ square \ units. \ }[/tex]The ABL triangle is congruent to the CDM triangle, and each area is [tex]\boxed{ \ \frac{1}{2} \times 3 \times 1 = 1.5 \ square \ units \ }.[/tex] Thus, the combined area of ABL and CDM is [tex]\boxed{ \ 1.5 + 1.5 = 3 \ square \ units. \ }[/tex]Finally, the area of ABCD = 20 - 4 - 3 = 13.As a result, we get the area of the parallelogram ABCD is 13 square units.
Learn moreA triangle is rotated 90° about the origin https://brainly.com/question/2992432Find out the coordinates of the image of a vertex after the triangle is rotated 270° about the origin https://brainly.com/question/7437053 The midpoint https://brainly.com/question/3269852Keywords: what is the area of parallelogram ABCD, in square units, graph, cartesian coordinates, triangle, rectangular, congruent, touches all the vertices
Related Questions
There are five different colored cards in a hat (red, blue, green, yellow, and black). A card is randomly drawn and not replaced. Then a second card is drawn. What is the probability that the first card will be red and the second card will be blue?
Answers
The probability of drawing a red card first followed by a blue card from a hat with five different colored cards without replacement is 0.05 or 5%.
The question asks for the probability of drawing a red card first and a blue card second from a hat containing five different colored cards without replacement. To calculate this, we use the formula for conditional probability and the multiplication rule for independent events. Since the cards are drawn without replacement, the events are dependent.
The probability of drawing the red card first is 1/5, since there is one red card out of five. After drawing the red card, there are four cards left. The probability of drawing the blue card second is thus 1/4, as there is only one blue card left among the four remaining cards. The probability of both events occurring in sequence is the product of the probabilities of each event:
P(Red first and Blue second) = P(Red first) × P(Blue second | Red first) = (1/5) × (1/4) = 1/20 or 0.05.
Therefore, the probability that the first card is red and the second card is blue is 0.05 or 5%.
Can someone please solve this?
Answers
identity the two rational numbers
Answers
A rational number is a number that can be represented as a ratio fo two integers.
-7/3 is rational because both -7 and 3 are integers. 2.777... equals 25/9. 25 and 9 are both rational numbers.
We deal from a well-shuffled 52-card deck. calculate the probability that the 13th card is the first king to be dealt.
Answers
Final answer:
The probability that the 13th card is the first king to be dealt is 1/52.
Explanation:
To calculate the probability that the 13th card is the first king to be dealt from a well-shuffled 52-card deck, we need to consider the number of favorable outcomes and the total number of possible outcomes. There are 4 kings in the deck, so the probability of the first king being the 13th card is 1/52.
Final answer:
The probability that the 13th card is the first king to be dealt in a shuffled 52-card deck is 1/13.
Explanation:
In a well-shuffled 52-card deck, the probability that the 13th card is the first king to be dealt can be calculated as follows:
First, let's determine the number of favorable outcomes. Since there are 4 kings in the deck, there are 4 possible kings that can be the first king dealt.
Next, let's determine the number of possible outcomes. Since there are 52 cards in the deck, there are 52 possible cards to be the 13th card dealt.
Therefore, the probability is calculated as:
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 4 / 52
Probability = 1 / 13
So, the probability that the 13th card is the first king to be dealt is 1/13.
Sonya can walk 6 km in 3 hours. If she has to walk 10 km, how much time will it take her?
Answers
I don't understand what the question is asking?
Answers
bear in mind that 100/10 is 10, however, we have to include the very first post, which is not spaced away 10' from anywhere, is simply touching the barn wall. So the total is 10 spaced 10' from each other plus the starting post which is touching the barnwall. And you can start doing the counting from either side A or B and you'd get 11 total.
Notice the angle "tickmarks" btw, that means those two angles are equal, that means the triangle is an isosceles, and thus both of those sides are equal, so, if one is 50', the other is also 50'.
1. The function f(x) = –0.05(x2 – 26x – 120) represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent? (1 point)
2. What do the zeros of this function represent? Remember the zeros are where f(x) = 0. (1 point)
3. Will the zeros tell you where the net should be placed? Why or why not? (1 point)
4. To find the zeros, set the function equal to 0, and then factor the polynomial. Start by setting the function equal to 0. (1 point)
Factor the polynomial.
The polynomial (x2 – 26x – 120) is in the form x2 + bx + c which can be factored as (x + p)(x + q) .
5. Next factor the polynomial x2 – 26x – 120. To identify the factors, complete the table: Note: This table does not contain all the factors of –120, but it has enough to let you factor the polynomial. (2 points: 0.5 points for each row)
p q p + q
10 –12
–10 12
30 –4
4 –30
6. Which values of p and q give the correct factors? (1 point)
7. Factor the polynomial completely: (2 points: 1 point for each factor)
0 = –0.05(x2 – 26x – 120)
8. Find the roots of the equation by setting each factor equal to 0 and solving for x.
Hint: There are three factors, but the constant factor, –0.05, does not equal zero. Solve for x with the other two factors. (2 points: 1 point for each factor)
9. Identify the roots. (2 points: 1 point for each root)
10. What are the zeros of this function? Circle them on the graph. (1 point)
11. Are these zeros the same as the roots you found? (1 point)
12. What does a negative zero mean in terms of this problem? (1 point)
13. Following this trajectory, will Nik hit a net that is 30 feet from the cannon? How do you know? (1 point)
Answers
f(x) represents the distance of the cannon from the ground
Question 2
When f(x) = 0, there will two values of 'x'. The point on the positive x-axis where the graph crosses represent the point where the cannon hits the ground.
Question 3
Yes, it would. By knowing the spot where the cannon will hit the ground, we can set the net at the spot.
Question 4
f(x) = 0
-0.05 (x² - 26x -120) = 0
x² - 26x - 120 = 0
Question 5
Please refer to the table attached below
Question 6
The value of p and q that gives the correct factors are -30 and 4 since it gives p+q = -26
Question 7
Factorising the equation completely
-0.05 (x² - 26x - 120) = 0
-0.05 (x+4) (x-30) = 0
(x+4) (x-30) = 0
Question 8
Solving the equation
x+4 = 0 and x-30=0
x=-4 and x=30
Question 9
The roots of the equation is x = -4 and x = 30
Question 10
Please refer to the third graph
Question 11
Yes
Question 12
The negative zero means the initial distance of the cannon, where it was fired from
Question 13
The distance between x = -4 and x = 30 is 34 units. If the cannon was fired from the point when x = -4, the cannon will hit the ground again 34 units from the point it was fired from. If Nik put a net 30 units from the firing point, the cannon will fly pass it.
The motion of the projectile (cannonball), given by the (quadratic)
polynomial function is the path of a parabola.
Response:
Vertical heightThe point the projectile is at ground levelYes, because is it where the projectile will landx² - 26·x - 120 = 0(x - 30)·(x + 4) = x² - 26·x - 120 p = -30, and q = 4-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4) x - 30 = 0 and x + 4 = 0 Which gives; x = 30 or x = -4x = 30 or x = -4The zeros of the function are x = 30, and x = -4YesThe negative zero (x = -4) means that the ground level is a point before the location at which the cannonball is launched (x = 0). It also means that the cannonball was launched above ground level.Yes, because the projectile hits the ground 30 feet from the cannonWhich methods can be used to evaluate the polynomial?1. f(x) is the output of the projectile function, where;
x = The input which is the distance
Therefore;
f(x) = The vertical distance (height) of the cannonball at point x.2. The zeros are the points where the height, f(x) = 0
Therefore;
The zeros represent the points at which the cannonball is at ground level3. The net should be placed where the cannonball is expected to reach ground level.
Therefore;
The zeros indicates where the net should be placed4. The given polynomial can be equated to 0 as follows;
x² - 26·x - 120 = 0
5. x² - 26·x - 120 = x² - 30·x + 4·x- 120
Which gives;
x·(x - 30) + 4·(x- 30) = (x - 30)·(x + 4)
(x - 30)·(x + 4) = x² - 26·x - 1206. Where; (x + p)·(x + q) = a·x² + b·x + c
We have;
The values of p and q that give the correct factors are;
p = -30, and q = 47. The polynomial, -0.05·(x² - 26·x - 120) = 0 in factored form is therefore;
-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4)8. From the factors, we have;
-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4)
The roots of the equations, are given as follows;
x - 30 = 0 and x + 4 = 0
Which gives;
x = 30 or x = -49. The roots of the equation are therefore;
x = 30, and x = -410. The zeros for the function, are the values of x at which f(x) = 0
At x = 30 f(30) = -0.05 × (30² - 26 × 30 - 120) = 0
At x = -4, f(-4) = -0.05 × ((-4)² - 26 × (-4) - 120) = 0
The zeros of the function are x = 30, and x = -411. Yes. The zeros are the same as the roots found given that at the roots, f(x) = 0
12. The zeros of the function are x = 30 and x = -4, which are points at
which the projectile (cannonball) is at ground level. The negative zero, x
= -4, means that, apart from the point x = 30, the projectile can (also/only)
be at ground level at a point before the location where the projectile is
launched, (-4) which means that at the point at which the cannonball is
launched, which is at x = 0, the cannonball was not on the ground, but
at the lip of the barrel or at a more elevated position.
What the negative zero means are therefore;
It is a location before the point where the cannonball is launchedThe cannonball is launched from a height above ground level13. At 30 feet, x = 30, which is a zero of the function, and the cannonball
is at ground level, such that a net placed at 30 feet from the cannon
will be hit by the cannonball.
Therefore;
Yes Nik will hit a net that is 30 feet from the cannonLearn more about quadratic functions and projectiles here:
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Assume that the risk-free rate is 8 percent the required rate of return on the market is 13 percent and the required rate of return on acme healthcare stock is 15 percent what is the implied beta coefficient
Answers
f(x)=2× if x<0
|x| if x>0
Answers
The graph is in two parts: graph y = 2^x, but use only the part which is to the right of the y-axis (for x > 0), and the other part is the graph of y = |x| which lies to the left of the y-axis (for x < 0).
The open circles are to indicate that the function has no assigned value at x = 0.
If f(x) = x^2 - 4x + 1, find the range of f(x).
{y: y ≥ -3}
{y: y ≥ 13}
all reals
Answers
y= x² - 4x + 1
calculate : x
y = (x²-4x+4)-4+1
y+3 = (x-2)²
x exist : if y+3 ≥ 0
y ≥ -3
the range is : {y: y ≥ -3}
The range of the given function, f(x) = x^2 - 4x + 1, is {y: y ≥ -3}. This is determined by completing the square to find the vertex form of the parabola, which indicates that the minimum y-value is -3 (the y-coordinate of the vertex) and the function values extend to infinity.
Explanation:The question asks us to find the range of the function f(x) = x^2 - 4x + 1. In mathematics, the range of a function is the set of output values (the y-values) that the function produces when we substitute the domain (the x-values) into the function.
To determine the range of a quadratic function like this, we could complete the square for the function and adjust it to the vertex form of a parabola, which is f(x) = a(x - h)^2 + k, where k is the minimum or maximum y-value of the parabola.
For the function f(x) = x^2 - 4x + 1, the completed square form is f(x) = (x - 2)^2 - 3. So, the vertex of the parabola is (2, -3), and since the coefficient of (x - 2)^2 is positive, the parabola opens upwards. This means that the minimum y-value is -3 and the maximum y-value is infinity. So the range of the function is {y: y ≥ -3}.
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The RideEm Bicycles factory can produce 160 bicycles in a day at a total cost of $10,100. It can produce 180 bicycles in a day at a total cost of $11,000. What are the company's daily fixed costs
Answers
Answer:
$2,900
Step-by-step explanation:
The additional 180 - 160 = 20 bicycles cost an additional $11,000 - 10,100 = $900. That means the 180 bicycles cost 9·$900 = $8100, and the fixed costs are $11,000 - 8,100 = $2,900.
_____
Each group of 20 bikes costs $900, so 9 groups of 20 (180 bikes) cost 9×$900 = $8100.
To find the daily fixed costs of RideEm Bicycles factory, subtract the variable cost from the total cost.
Explanation:To find the daily fixed costs of RideEm Bicycles factory, we need to determine the fixed cost component of the total cost. We can do this by subtracting the variable cost from the total cost. The formula for calculating fixed cost is:
Fixed Cost = Total Cost - (Variable Cost per Unit x Number of Units)
Using the given information:
Number of bicycles produced when the total cost is $10,100: 160 bicycles
Number of bicycles produced when the total cost is $11,000: 180 bicycles
Variable cost per unit: (Total Cost - Fixed Cost) / Number of Units
By plugging in the values and solving the equations, we can find the daily fixed costs of the company.
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If a company has 5 employees with annual salaries of $30,000, $50,000, $30,000, $80,000, and $70,000, respectively, what is the mean annual salary at the company?
Answers
Answer:
Annual mean salary at the company is $52,000
Step-by-step explanation:
Given : If a company has 5 employees with annual salaries of $30,000, $50,000, $30,000, $80,000, and $70,000, respectively.
We have to determine the mean annual salary at the company.
Consider the given salaries of 5 employee of the company
$30,000, $50,000, $30,000, $80,000, and $70,000
The annual mean salary at the company is the sum of salary of the employees divided by the number of employees.
Annual mean salary =[tex]\dfrac{30,000+50,000+30,000+70,000+80,000}{5}=\frac{2,60,000}{5}[/tex]
Thus, Annual mean salary at the company is $52,000
If a cow has a mass of 9×1029×102 kilograms, and a blue whale has a mass of 1.8×1051.8×105 kilograms, which of these statements is true?
A.) The blue whale has about 200200 times more mass.
B.)The blue whale has about 500500 times more mass.
C.)The cow has about 200200 times more mass.
D.)There is no way to compare the masses.
Answers
whale : 1.8 x 10^5 = 1.8 * 100,000 = 180,000
180,000/900 = 200
The blue whale has about 200 times more mass <==
Answer:
The blue whale has about 200 times more mass.
How long will it take a $800 investment to be worth $900 if it is continuously compounded at 11% per year?
Answers
It takes approximately 1.083 years, or around 1 year and 1 month for an $800 investment to grow to $900 when continuously compounded with an 11% yearly interest rate.
Explanation:To calculate how long it will take for an $800 investment to grow to $900 with continuous compounding at an 11% yearly interest rate, we use the formula for continuously compounded interest, P = Pert, where P is the final amount, Pe is the original principal, r is the interest rate, and t is time in years.
Rearranging the equation to find t, we have, t = ln(P/Pe) / r.
Substitute P as $900, Pe as $800, and r as 0.11 into the formula.
Therefore, t = ln(900/800) / 0.11 = approximately 1.083 years or around 1 year and 1 month.
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Which input value produces the same output value for the two functions on the graph?
x = −3
x = −2
x = −1
x = 3
Answers
x = -2
Explanation:The line represents the output value (y) for a given input value (x). Where the lines cross, the output values are equal. These lines cross at x=-2.
Answer:x=-2
Step-by-step explanation:
got it right on edg
Which trinomial is a perfect square trinomial?
A) a^2 - 12a + 36
B) a^2 - 8a + 64
C) a^2 - 6a + 36
D) a^2 - 4a + 64
Answers
A) a^2 - 12a + 36
B) a^2 - 8a + 64
C) a^2 - 6a + 36
D) a^2 - 4a + 64
Answer:
d is the answer
Jessica and Franklin are volunteering to paint one of their community member’s fences for service hours. If Jessica could complete the job in 6 hours and Franklin could complete the job in 4.5 hours, how long would it take them to complete the job together, to the nearest minute?
Answers
t=18/7=2.57 hour =154 min
Reflecting the graph of y = sin x across the y-axis is the same as reflecting it across the x-axis. Is this statement true or false?
Answers
Answer:
The statement is true.
Step-by-step explanation:
Given : Reflecting the graph of y = sin x across the y-axis is the same as reflecting it across the x-axis.
To find : Is this statement true or false?
Solution:
Rules of reflection :
Along across y-axis if we have a point [tex](x,y)\rightarrow(-x,y)[/tex]
So, y=sinx
The reflection across y-axis→ [tex]y=sin(-x) \Rightarrow y = -sinx[/tex].......[1]
Along across x-axis if we have a point [tex](x,y)\rightarrow(x,-y)[/tex]
so, y=sinx
The reflection across x-axis → [tex]-y=sinx\Rightarrow y= -sinx[/tex] .....[2]
Hence, [1] and [2] both of them are equal
Therefore, the statement is true.
find the x-intercepts of the parabola with vertex (2,13) and y intercept (0,5)
round to the nearest hundredth
i have no idea how to do this problem please help!
Answers
the vertex form of the equation is given by:
y=a(x-h)^2+k
where:
(2,13) is the vertex:
Therefore;
y=a(x-2)^2+13
when x=0, y=5
Therefore the value of a will be:
5=a(0-2)^2+13
5-13=4a
4a=-8
a=-2
therefore the equation of the parabola will be:
y=-2(x-2)^2+13
y=-2x^2+8x+5
the x-intercept will be:
x=2-sqrt(7.5)
or
x=2+sqrt(7.5)
Answer:
What is the vertex of the parabola?
Round to the nearest hundredth.
✔ (8.33, 236.67)
Step-by-step explanation:
The figure has ____ lines of symmetry. A. 0 B. 4 C. 6 D. 8
Answers
Answer:
B. 4
Step-by-step explanation:
Vertical and horizontal lines through the vertices farthest from center are two of the lines of symmetry.
The other two lines of symmetry are the diagonal lines through the vertices closest to center.
There are a total of 4 lines of symmetry.
Answer:
4
Step-by-step explanation:
hope it helps
To be eligible for a basketball tournament, a basketball team must win at least 60% of its remaining games. If the team has 21 game remaining, how many games must the team win to qualify for the tournament?
Answers
The basketball team must win at least 13 out of their 21 remaining games to qualify for the tournament, as they need to win at least 60% of the games.
Explanation:To determine how many games a basketball team must win out of 21 to qualify for a tournament, given they must win at least 60%, we perform the following calculation:
First, multiply the total number of remaining games, which is 21, by 60% (or 0.60) to find the minimum number of games they need to win.Next, solve for the number: 21 games × 0.60 = 12.6.Since a team can't win a fraction of a game, they must win at least the next whole number of games, which is 13.Therefore, the team must win at least 13 games out of the remaining 21 to be eligible for the tournament.
How tall is a building that casts a 73 foot shadow when the angle of elevation of the sun is 29
Answers
For this problem, we are given the angle and the ADJACENT length (73). We want to find the OPPOSITE side's length.
TOA
We must use the tangent function.
TOA helps us remember this relationship:
tan( theta ) = opposite / adjacent.
Plug in our values:
tan(29 degrees) = opposite / 73
Multiply by 73 to isolate "opposite" and solve for it.
73 * tan(29) = opposite.
Using a calculator, the answer is approximately 40.46 ft.
The height of the building is approximately 40.39 feet.
Explanation:To find the height of the building, we can use the concept of similar triangles. The height of the building is proportional to the length of its shadow. We can set up a proportion using the angle of elevation of the sun and the length of the shadow.
Let x be the height of the building. The proportion can be set up as:
(x / 73) = tan(29°)
Using a calculator, we can find the value of tan(29°) to be approximately 0.5543. Solving for x, we get:
x = (73 * 0.5543)
Therefore, the height of the building is approximately 40.39 feet.
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In this assignment we will work on the creation of a poker game. at a minimum your game must deal 2 hands of cards, and print out what poker hand each has. it must also determine which hand has won the game – but breaking a tie will be for bonus points. for example, if both hands have 3 of a kind, that can be considered a tie. if you want the bonus points write some code that determines which 3 of a kind is higher. here is the output from dealing a hand of cards: ace of hearts ten of clubs ace of clubs eight of hearts seven of diamonds 2 2 1 0 <> 0 0 0 0 0 1 1 0 1 0 0 0 2 you have a pair!
Answers
public class Card //Name of your program
{
private short rank, suit;
private static String[] suits = { "hearts", "spades", "diamonds", "clubs" };
private static String[] ranks = { "Ace", "2", "3", "4", "5", "6", "7", "8", "9", "10", "Jack", "Queen", "King" };
public static String rankAsString( int __rank ) { return ranks[__rank];
}
Card(short suit, short rank)
{
this.rank=rank; this.suit=suit;
}
public @Override String toString()
{
return ranks[rank] + " of " + suits[suit];
}
public short getRank()
{
return rank;
}
public short getSuit()
{
return suit;
}
}//End of program
Tomas's grandfather is 100 years old.Tomas's grandfather is 10 times as old as Tomas.How old is Tomas? Can someonegive me the answer to this plz
Answers
If his grandfather is 100, then divide 100 by 10 and you will get Tomas's age.
Please correct me if I'm wrong.
100 years old ÷ 10 = 10 years old
Hope this helps : )
The number of chicken legs depends on how many chickens are in the coop. This is modeled by y=2x and is an example of _____ variation.
Answers
Answer:
y=2x is an example of direct variation.
Step-by-step explanation:
Direct variation is mathematical relationship in between two variables which can be expressed by an equation where one variable is equal to a constant multiplied by the other variable.
In the equation y=2x, x and y are the variables and 2 is a constant.
Here it is expressed as an equation where the variable y is equal to the constant 2 multiplied by the other variable x.
Thus we can say that it is an example of direct variation.
the directions for mixing water and powdered milk say that one should use 3 cups of water for each cup of powdered milk. how many cups of powdered milk are needed if 5 cups of water are used
Answers
5w(m/3w)=15m
So you will need 15 cups of milk if 5 cups of water are used.
A map scale has a scale of 1 inch equals 35 miles what is the actual distance if the distance on the map is 3.5 in
Answers
1 in/ 35 miles = 3.5 in/ x miles
1*3.5=3.5
35*3.5=122.5
x=122.5
Final answer: 122.5 miles
19 is 6% of what number?
The answer is 316 2/3
(but idk how they got it)
- please list the steps
Answers
which situation could be modeled by using a linear function
Answers
[tex]\bf \begin{array}{ccllll} \begin{array}{llll} price\ of\\ gallon \end{array}& \begin{array}{llll} pints\\ bought \end{array}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 10&1\\ 9&2\\ 7&3\\ 6&4 \end{array}\impliedby \begin{array}{llll} \textit{now if you graph that}\\ \textit{will give you a \underline{line}}\\ \textit{thus a \underline{line}ar function} \end{array}[/tex]
3(b-4)+5b=44
what number is b.
Answers
3b-12+5b=44
8b=44+12
8b=56
b=56/8
b=7
3b - 12 + 5b = 44
Then you can add the individual sides:
8b - 12 = 44
Then you can move the 12 over to the other side:
8b = 44 + 12
Sum the sides again:
8b = 56
Then you divide both sides by 8:
b = 7
Hope this helps! :)