Answer:
93 square units (the figure is not a rhombus)
Step-by-step explanation:
You want the area of the figure whose vertex coordinates are A(0,-5), B(9,2), C(12,13), and D(2,7).
Area from coordinatesThe formula for the area of a polygon based on its coordinates might be written ...
[tex]\displaystyle A=\frac{1}{2}\left|\sum_{k=1}^n{x_k(y_{k+1}-y_{k-1})}\right|[/tex]
where coordinate indices wrap around from the end to the beginning.
Using this formula, we find the area to be ...
A = 1/2|0(2-7) +9(13-(-5)) +12(7-2) +2(-5-13)|
A = (1/2)|0 +162 +60 -36| = 1/2(186) = 93
The area of the figure is 93 square units.
DiagonalsThe area of a rhombus could be calculated as half the product of the lengths of the diagonals. This is only true because the diagonals of a rhombus cross at right angles.
Here, the differences between diagonally opposite coordinates are ...
AC = (12, 18) . . . . slope = 18/12 = 3/2
BD = (-7, 5) . . . . slope = 5/-7 = -5/7
If the diagonals are perpendicular, their slopes have a product of -1. Here, the product is ...
(3/2)(-5/7) = (-15/14) ≠ -1
The given figure is not a rhombus.
If we assume the diagonals are perpendicular, then the area would be ...
A = 1/2√(12²+18²)√((-5)²+7²) = 1/2√34632 ≈ 93.048
Rounded to the nearest tenth, this area would be 93.0 square units.
The diagonals actually cross at an angle of about 88.152°, so the area is actually ...
93.048·sin(88.152°) = 93 square units (exactly)
(Development of this formula is beyond the scope of this answer.)
Sue has a 8 cups of flour and needs to fill it equally in containers that hold 3/4 of a cup each. How many containers can she fill?
Answer: Sue fills 32/3 (Decimal form = 10.6667 containers)
Step-by-step explanation: 8 divided by 3/4 equals 32/3. If you need it in decimal form it's 10.6667
Please heart this or rate it :)
Answer:
10 2/3 containers BUT can only fully fill 10 containers
Step-by-step explanation:
to solve this equation you need to divide 8 by 3/4
8 / 3/4
that is
8/1 / 3/4
when dividing fractions you must flip the second number and multiply both numbers together
8/1 * 4/3
32/3 is your answer
or
10 2/3
she can fully fill 10 containers
is 7 1/2 equal to 1/10, 1/5 or 4/5?
7y+2=3x-5 is the given equation. Finding the point that does not lie on the specified line, 7y+2=3x-5, is the next step.
To determine whether or not the point meets the provided equation, we will simply enter in the supplied point.
Check for (2,-1/7)
Connect it to 7y+2=3x–5.
7(-1/7)+2=3(2)-5
-1+2=6-5
1=1
Which is correct; as a result, this point is on the line 7y+2=3x-5.
Verify (3,-2/7)
Connect it to 7y+2=3x–5.
7(-2/7)+2=3(3)-5
-2+2=09-5
1=4
Which is False; as a result, the supplied line 7y+2=3x-5 does not include this point.
Connect it to 7y+2=3x–5.
7(-1)+2=3(0)-5
-7+2=0-5
-5=-5
Which is correct; as a result, this point is on the line 7y+2=3x-5.
Verify (1, -4, 7)
Connect it to 7y+2=3x–5.
7(-4/7)+2=3(1)-5
-4+2=3-5
-2=-2
This is why I'm making this point
lies on the line 7y+2=3x-5 that is presented.
Verify (-1, -10/7)
Connect it to 7y+2=3x–5.
7(-10/7)+2=3(-1)-5
-10+2=-3-5
-8=-8
Which is correct; as a result, this point is on the line 7y+2=3x-5.
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About one eighth of the population is left-handed. In what size school would you expect to find about 50 left-handed students?
Answer:
400 students, 1/8 are left handed
Step-by-step explanation:
graph the linear inequality 9x-y<9
The line has a slope of 9 and y-intercept of -9
Linear inequality graphA linear equation is a equation that has a linear degree of 1.
Given the inequality expression 9x-y<9
Write in slope-intercept form
-y < -9x + 9
y > 9x - 9
From the equation, we can see that the line has a slope of 9 and y-intercept of -9
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Determine if the following radical expression is a real number. If it is, you are to evaluate the expression.
3√-27
Answer
Selecting an option will display any text boxes needed to complete your answer.
Real Number
O Not a Real Number
When a constant force acts upon an object, the acceleration of the object varies Inversely with its mass. When a certain constant force acts upon an object with
mass 7 kg, the acceleration of the object is 10 m/s². If the same force acts upon another object whose mass is 5 kg, what is this object's acceleration?
The acceleration of the object is found as 14 m/s².
What is defined as the Newton's second law of motion?Newton's second law states that acceleration of an object is determined by two variables: the net force acting on it and its mass.
The acceleration of the body is proportional to the net force exerting on it and inversely proportional to its mass. This implies that as the force that acts on an object increases, so does the object's acceleration. Similarly, as an object's mass increases, the object's acceleration decreases.The formula for the Newton's second law is;
F = ma
F = acting force in Newton
m = mass of the body in Kg.
a is the acceleration in m/s².
The mass of 7 kg accelerates with 10m/s².
Force acting on it is;
F = ma
F = 7×10
F = 10 N.
The same force is acting on the body of mass 5 kg.
F = ma
a = F/m
a = 70/5
a = 14 m/s².
Therefore, the acceleration of the body is found as 14 m/s².
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A group of exchange students from Japan went to a convalescent home to sing songs for the seniors and to demonstrate origami. Groups of students and seniors sat together at tables so the students could teach the seniors to fold some origami figures. As it turned out, at each table there was either 1 student and 3 seniors, or 2 students and 4 seniors. There were 23 students and 61 seniors in all. How many tables were being used?
Answer:
19 tables
Step-by-step explanation:
Let X represent the number of tables that have 1 student and 3 seniors
Let Y represent the number of tables that have 2 student2 and 4 seniors
Therefore number students total
1X + 2Y =23 (1)
Number of seniors total
3X + 4Y = 61 (2)
Multiply equation (1) by 2 giving
2X + 4Y = 46 (3)
Subtract (3) from (2)
3X + 4Y - (2X+4y) = 61-46
3X + 4Y - 2X -4Y = 15
3X-2X = 15
X = 15
Plugging this value into equation (1) gives
1(15) + 2Y = 23
15 + 2Y = 23
Subtract 15 from both sides
2Y = 23 - 15
2Y = 8
Divide by 2 both sides
Y = 4
Thus total number of tables used = X +Y = 15+4 = 19
How many centimeters are in 2 miles?
Answer:
321,800 cm. (Rounded)
Step-by-step explanation:
2 × 160,900 = 321,800
There are 160,900 centimeters in one mile, so you must multiply that by 2 and round.
1 + 1 = 2
this is the answer to 1 plus 1
IT'S NOT 3???????????????
Answer:no it 11
Step-by-step explanation:
1+1 = 11
I’m kidding btw
The histogram shows the number of miles driven by a sample of automobiles in New York City. What is the class width
The class width of the histogram is 5000.
What is class width?It should be noted that the class width is the distance that can be found between the lower limits of consecutive classes.
The range is the difference between the maximum and minimum data entries.
class width of a histogram is given by the equation
Therefore, class width:
= maximum of a class - minimum of a class
In the given histogram, first-class start at 2500 and ends at 7500..Therefore considering first class,.minimum =2500 and maximum=7500.
Therefore, class width will be:
= 7500-2500
= 5000
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the endpoints of segment mn have coordinates (0, 0) and (5, 1). the endpoints of segment ab have coordinates (1 1 2 , 2 1 4 ) and (−2 1 4 , k ). for what value of k are these segments parallel?
Answer:
When k = 1.5 the given segments are parallel===============================
Parallel lines have equal slopes.
Find the slope of the first line, mn:
[tex]m = \cfrac{y_2-y_1}{x_2-x_1}= \cfrac{1-0}{5-0}=\cfrac{1}{5}[/tex]Find the slope of the second line, ab:
[tex]m= \cfrac{y_2-y_1}{x_2-x_1}= \cfrac{k-2.25}{-2.25-1.5}=\cfrac{k-2.25}{-3.75}[/tex]Compare the slopes and find the value of k:
[tex]\cfrac{k-2.25}{-3.75}=\cfrac{1}{5}[/tex][tex]k-2.25=-\cfrac{3.75}{5}[/tex][tex]k-2.25=-0.75[/tex][tex]k=2.25-0.75[/tex][tex]k=1.5[/tex]Answer:
[tex]k=\dfrac{3}{2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.3 cm}\underline{Slope formula}\\\\$m=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\ are points on the line.\end{minipage}}[/tex]
Segment MN
M = (0, 0)N = (5, 1)[tex]\implies \textsf{slope}=\dfrac{y_N-y_M}{x_N-x_M}=\dfrac{1-0}{5-0}=\dfrac{1}{5}[/tex]
Segment AB
A = (1 ¹/₂, 2 ¹/₄)B = (-2 ¹/₄, k)[tex]\implies \textsf{slope}=\dfrac{y_B-y_A}{x_B-x_A}=\dfrac{k-2 \frac{1}{4}}{-2\frac{1}{4}-1\frac{1}{2}}=\dfrac{k-2 \frac{1}{4}}{-2\frac{1}{4}-1\frac{2}{4}}=\dfrac{k-2 \frac{1}{4}}{-3\frac{3}{4}}[/tex]
Parallel lines have the same slope.
Therefore, equate the found slopes for the two segments and solve for k:
[tex]\implies \dfrac{k-2 \frac{1}{4}}{-3\frac{3}{4}}=\dfrac{1}{5}[/tex]
Cross multiply:
[tex]\implies 5 \left(k-2 \frac{1}{4}\right)=-3\frac{3}{4}[/tex]
[tex]\implies 5k-10 \frac{5}{4}=-3\frac{3}{4}[/tex]
[tex]\implies 5k-11 \frac{1}{4}=-3\frac{3}{4}[/tex]
Add 11 ¹/₄ to both sides:
[tex]\implies 5k-11 \frac{1}{4}+11 \frac{1}{4}=-3\frac{3}{4}+11 \frac{1}{4}[/tex]
[tex]\implies 5k=(-3+11)+\left(-\frac{3}{4}+\frac{1}{4}\right)[/tex]
[tex]\implies 5k=8-\frac{1}{2}[/tex]
[tex]\implies 5k=7\frac{1}{2}[/tex]
Divide both sides by 5:
[tex]\implies 5k \div 5=7\frac{1}{2} \div 5[/tex]
[tex]\implies 5k \div 5=\dfrac{15}{2} \div 5[/tex]
[tex]\implies k=\dfrac{3}{2}[/tex]
Therefore, the value of k for which the two segments are parallel is ³/₂.
A ball thrown horizontally at v₁ = 30.0 m/s travels a horizontal distance of d = 57.0 m before hitting the
ground. From what height h was the ball thrown?
Answer:
17.7 m
Step-by-step explanation:
57 m / 30 m/s = time in the air = 1.9 s
vertical drop for 1.9 s
vertical d = 1/2 a t^2 = 17. 7 m
amber has a 4/5 pound bag of colored sand she use 1/2 of the bag for an art project how much sand does she use for the project
The left over sand is a 3/10 bag of the colored sand.
According to the statement
We have to find that the how much sand does she use for the project.
So, For this purpose, we know that the
Left over is a something that remains unused or unconsumed
From the given information:
amber has a 4/5 pound bag of colored sand she use 1/2 of the bag for an art project
then it means
Total sand is = 4/5 pound bag of colored sand
Used sand is = 1/2 of the bag of colored sand
Then
Left over sand is = Total sand - Used sand
Left over sand is = 4/5 - 1/2
Left over sand is = 8 - 5/10
Left over sand is = 3/10.
So, The left over sand is a 3/10 bag of the colored sand.
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Determine the domain of the following graph
the domain of the following graph= [-5,10)
Domain :
The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.
For example, when we use the function notation f: R→R, we mean that f is a function from the real numbers to the real numbers. In other words, the domain of f is the set of real numbers R (and its set of possible outputs or codomain is also the set of real numbers R).
To, identify the domain and range of functions by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the
x-axis. The range is the set of possible output values, which are shown on the
y-axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values.
We can observe that the horizontal extent of the graph is -5 to 10, so the domain of f is [-5,10)
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Multiply the rational expressions
3(x-4)² 5(x + 4)5
8(x+4)³ 3(x-4)5
When the chef turned the new freezer on, the temperature on the internal thermometer was 2 °C.
After breakfast had been served, the temperature had gone down by 15 °C.
What was the new temperature?
Answer: -13 °C.
Step-by-step explanation:
7/5 fracción simplificada
Answer:
1,4
Step-by-step explanation:
7/5
Esto es una división, solo divide y ya
David and John own 37-1/2 acres of land. David owns 3/5 and John owns 2/5 of the land. They decide to section it off into ¾ acre lots to rent out as garden space for people who do not have garden space at their homes. The price for the entire summer for the rent of each lot is $50. Since there is no water supply to water the gardens, David and John have asked their renters if they would like a 100-gallon water tank or a 70-gallon water tank. 60% of the renters chose 100 gallons and 40% chose 70 gallons. David calculated that they would need to fill each tank 2 times and the cost of a gallon of water is $.05.
The total spent amount on water is $220
The total area is 37.5=75/2
The number of lots is 75/2/3/4=50 nos
Total rent is 50×50=2500
So 3/5 will go to david 2500×3/5=1500
2/5 will go to john 2500×2/5=1000
So 60% Renters choose 100 gallons
Total renters is 50
60% renters is 50×60%=30 nos
40% renters choose 70 gallons
40% of 50 is 20 nos
The tank fills twice
100×30+70×20=4400 to be filled
Per gallon cost is $0.05
So the total cost is 4400×0.5=$220
So they spent $220 on water
A fraction shows part of a whole. This entire may refer to a place or a group of places.A fraction can be a portion or section of any quantity out of a whole, where the whole can be number of any value.To learn more about fraction visit:
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73 term for the arithmetic sequence 18,30,42
The 73rd term of the arithmetic sequence 18,30,42 = 882.
What is arithmetic sequence ?An arithmetic sequence seems to be a series of numbers that are ordered and share a common difference amongst each succeeding term. There are arithmetic sequences 3, 9, 15, 21, and 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence.
What does not constitute an arithmetic sequence?The sequence is not arithmetic if the difference between subsequent terms is not constant. Subtracting two consecutive elements from the sequence yields a common difference.
According to the given data:Let us now look for the explicit rule for with this arithmetic sequence. We have the following:
aₙ = a₁ + (n - 1) * d
= 18 + 12 * (n - 1)
= 12n + 6.
The 73rd term is 12 (73) + 6 = 882.
The 73rd term of the arithmetic sequence 18,30,42 = 882.
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A triangle has side lengths of (26 +5c) centimeters, (10b + 7d) centimeters, and
(4d-3c) centimeters. Which expression represents the perimeter, in centimeters,
of the triangle?
The perimeter of the triangle will be 26 + 2c + 20b + 11d.
How to calculate the value?It should be noted that the perimeter of the triangle will be the addition of all the sides.
This will be:
26 + 5c + 10b + 7d + 4d - 3c
Collect like terms
26 + 5c - 3c + 10b + 11d
= 26 + 2c + 20b + 11d
Therefore, the perimeter of the triangle will be 26 + 2c + 20b + 11d.
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A triangle has side lengths of (26 +5c) centimeters, (10b + 7d) centimeters, and
(4d-3c) centimeters. Which expression represents the perimeter, in centimeters,
of the triangle?
4c + 26d
b + d + 26
26 + 2c + 20b + 11d.
HELP PLEASE I WILL GIVE BRAINLYEST! ALGEBRA 1 HW
describe a sequence of transformation that takes abcd to a'b'c'd'
The quadrilateral A'B'C'D' is the result of reflecting and translating the quadrilateral ABCD.
What kind of rigid transformations were done to transform ABCD to A'B'C'D'?
In this problem we find a representation of a quadrilateral and its image on a Cartesian plane. That image is the result of the following rigid transformations, that is, transformations applied on geometric loci such that Euclidean distance is conserved at every point of the locus.
After a careful inspection, we find that the following two rigid transformations were done:
Reflection about the x-axis.Translation 7 units in the + x direction.Now let is prove this steps:
Given: A(x, y) = (- 5, - 7), B(x, y) = (- 5, - 2), C(x, y) = (- 3, - 4), D(x, y) = (- 3, - 7)
Reflection:
A''(x, y) = (- 5, - 7) + (0, 14)
A''(x, y) = (- 5, 7)
B''(x, y) = (- 5, - 2) + (0, 4)
B''(x, y) = (- 5, 2)
C''(x, y) = (- 3, - 4) + (0, 8)
C''(x, y) = (- 3, 4)
D''(x, y) = (- 3, - 7) + (0, 14)
D''(x, y) = (- 3, 7)
Translation
A'(x, y) = (- 5, 7) + (7, 0)
A'(x, y) = (2, 7)
B'(x, y) = (- 5, 2) + (7, 0)
B'(x, y) = (2, 2)
C'(x, y) = (- 3, 4) + (7, 0)
C'(x, y) = (4, 4)
D'(x, y) = (- 3, 7) + (7, 0)
D'(x, y) = (4, 7)
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The average temperature in the mountains is 61° in April. The average temperature in that same spot is −2° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.
Answer: 59 degrees warmer and -2 is farther away form 0 than 61 degrees.
Step-by-step explanation: 59+2=61 so, that's how I got the answer. The rest is really easy.
The absolute value of 61°F is greater than the absolute value of 2°F. Therefore, the temperature of 61°F in April is the farthest away from 0°F.
To determine how much warmer the location is in April than in December, you can calculate the difference between the two temperatures:
Temperature difference = April temperature - December temperature
Temperature difference = 61°F - (-2°F)
Temperature difference = 61°F + 2°F
Temperature difference = 63°F
So, the location is 63 degrees Fahrenheit warmer in April than in December.
To determine which temperature is the farthest away from 0°F, you can calculate the absolute value of the difference between each temperature and 0°F and then compare them:
Absolute value of (61°F - 0°F) = 61°F
Absolute value of (-2°F - 0°F) = 2°F
The absolute value of 61°F is greater than the absolute value of 2°F. Therefore, the temperature of 61°F in April is the farthest away from 0°F.
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Which characteristics are appropriate for the Brand of camcorder? Choose all that apply
Question options:
O Nominal
O Scale
O String
O Numeric
Answer:
numeric
Step-by-step explanation:
what is 4.32 x 10^4 written in standard form
Answer:
43,200
Step-by-step explanation:
4.32 x 10∧4
10 x 10 x 10 x 10
4.32 x 10000
43,200
Find two numbers which differ by 4 and whose product is 45
Answer:
The two solutions are
5 and 9
-5 and -9
Step-by-step explanation:
Let x and y be the numbers
x-y = 4
x*y = 45
Using substitution
x = 4+y
(4+y)y =45
4y + y^2 = 45
Subtract 45 from each side
y^2 +4y -45 =0
Factor
(y - 5) ( y+9) = 0
Using the zero product property
y -5 =0 y+9 =0
y=5 y = -9
Now we can find x
y=5
x = 4+y
x =4+5
x=9
y = -9
x = 4+y
x = 4+-9
x = -5
The two solutions are
5 and 9
-5 and -9
Solve for x
7/8 of x is 14
Answer:
x =16Step-by-step explanation:
Solve for x
7/8 of x is 14
7/8x = 14
x = 14 : 7/8
x = 14 * 8/7
x =16
----------------
check
7/8 * 16 = 14
14 = 14
the answer is good
Please help show work pamdas
The solution by substitution of values to 4 ) is ( - 8 ) / 14 and 6 ) is - 213 .
4 ) Using substituition
By replacing values of c and d in given equation
( 5 [tex]c^{2}[/tex] - [tex]d^{2}[/tex] + 3 ) / ( 2 c - 4 d )
c = - 1 and d = - 4
( 5 [tex]( - 1 )^{2}[/tex] - [tex]( - 4 )^{2}[/tex] + 3 ) / ( 2 ( - 1 ) - 4 ( - 4 ) )
= ( 5 - 16 + 3 ) / ( - 2 + 16 )
= ( - 8 ) / 14
6 ) Using substituition
By replacing values of x and y in given equation
3 [tex]| x + y |^{2}[/tex] - [tex]( x y )^{2}[/tex]
x = 3 and y = - 5
3 [tex]| 3 + ( - 5 ) |^{2}[/tex] - [tex]( 3 * ( - 5 ) )^{2}[/tex]
( 3 * 4 ) - 225
= - 213
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Evaluate Log2 11 x Log6 2
The logarithmic expression is equal to:
Log₂(11)*log₆(2) = 1.34
How to evaluate the logarithmic expression?
Here we have the logarithmic expression:
Log₂(11)*log₆(2)
Now, remember that we can rewrite:
Logₐ(b) = Ln(b)/Ln(a)
Using that we can rewrite the expression:
Log₂(11)*log₆(2) = (Ln(11)/Ln(2))*(Ln(2)/Ln(6)) = Ln(11)/Ln(6)
Now using a calculator you can find these two natural logarithms:
Ln(11)/Ln(6) = 1.34
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Helpppppppppp
Urgenttttt
Pleaseeeee!
Answer:
The first set is a set of linear equations.
The way to figure this out is pretty easy. If you want to see it visually, go search up desmos graphing calculator and put in these equations.
A linear equation is a function that has a constant slope, meaning that the rate it increases or decreases will never change. The first one is a set of linear equations because it is 2 equations with constant slopes, meaning that the slopes will never change no matter what y and x are.
The second set is not, because while the first equation is linear, the second is an inequality. While it is a straight line, it doesn't count as a linear equation.
The third set, both equations have exponents on the x, which means that the slope will change depending on x. This means that both of these are not linear equations.
The only set that is a linear set is the one that has only linear equations.
