Answer:
a + b = 12
Step-by-step explanation:
Given
Quadrilateral;
Vertices of (0,1), (3,4) (4,3) and (3,0)
[tex]Perimeter = a\sqrt{2} + b\sqrt{10}[/tex]
Required
[tex]a + b[/tex]
Let the vertices be represented with A,B,C,D such as
A = (0,1); B = (3,4); C = (4,3) and D = (3,0)
To calculate the actual perimeter, we need to first calculate the distance between the points;
Such that:
AB represents distance between point A and B
BC represents distance between point B and C
CD represents distance between point C and D
DA represents distance between point D and A
Calculating AB
Here, we consider A = (0,1); B = (3,4);
Distance is calculated as;
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex](x_1,y_1) = A(0,1)[/tex]
[tex](x_2,y_2) = B(3,4)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}[/tex]
[tex]AB = \sqrt{( - 3)^2 + (-3)^2}[/tex]
[tex]AB = \sqrt{9+ 9}[/tex]
[tex]AB = \sqrt{18}[/tex]
[tex]AB = \sqrt{9*2}[/tex]
[tex]AB = \sqrt{9}*\sqrt{2}[/tex]
[tex]AB = 3\sqrt{2}[/tex]
Calculating BC
Here, we consider B = (3,4); C = (4,3)
Here,
[tex](x_1,y_1) = B (3,4)[/tex]
[tex](x_2,y_2) = C(4,3)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}[/tex]
[tex]BC = \sqrt{(-1)^2 + (1)^2}[/tex]
[tex]BC = \sqrt{1 + 1}[/tex]
[tex]BC = \sqrt{2}[/tex]
Calculating CD
Here, we consider C = (4,3); D = (3,0)
Here,
[tex](x_1,y_1) = C(4,3)[/tex]
[tex](x_2,y_2) = D (3,0)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}[/tex]
[tex]CD = \sqrt{(1)^2 + (3)^2}[/tex]
[tex]CD = \sqrt{1 + 9}[/tex]
[tex]CD = \sqrt{10}[/tex]
Lastly;
Calculating DA
Here, we consider C = (4,3); D = (3,0)
Here,
[tex](x_1,y_1) = D (3,0)[/tex]
[tex](x_2,y_2) = A (0,1)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}[/tex]
[tex]DA = \sqrt{(3)^2 + (- 1)^2}[/tex]
[tex]DA = \sqrt{9 + 1}[/tex]
[tex]DA = \sqrt{10}[/tex]
The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral
[tex]Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}[/tex]
[tex]Perimeter = 4\sqrt{2} + 2\sqrt{10}[/tex]
Recall that
[tex]Perimeter = a\sqrt{2} + b\sqrt{10}[/tex]
This implies that
[tex]a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}[/tex]
By comparison
[tex]a\sqrt{2} = 4\sqrt{2}[/tex]
Divide both sides by [tex]\sqrt{2}[/tex]
[tex]a = 4[/tex]
By comparison
[tex]b\sqrt{10} = 2\sqrt{10}[/tex]
Divide both sides by [tex]\sqrt{10}[/tex]
[tex]b = 2[/tex]
Hence,
a + b = 2 + 10
a + b = 12
Answer:
a+b=6
Step-by-step explanation:
The tutor verified answer is mostly correct however, if you look under both by comperision sections you will see that it is:
[tex]4\sqrt{2}[/tex] and [tex]2\sqrt{10}[/tex] thus the answer is 4+2=6
ASAP PLZZZ Find the area of the shaded polygons:
Step-by-step explanation:
You can use the Pick's theorem:
[tex]A=i+\dfrac{b}{2}-1[/tex]
where
i - number of lattice points in the interior located in the polygon
b - number of lattice points on the boundary placed on the polygon's perimeter
[tex]1.\\i= 5;\ b=12\\\\A=5+\dfrac{12}{2}-1=5+6-1=10\\\\2.\\i=3;\ b=4\\\\A=3+\dfrac{4}{2}-1=3+2-1=4\\\\3.\\i=5;\ b=10\\\\A=5+\dfrac{10}{2}-1=5+5-1=9[/tex]
Answer:
Of course, the Pick's theorem is the way to solve this question, but consider:
Another approach is using topography:
Gauss's Area Calculation Formula:
[tex]$A=\frac{1}{2} \sum_{i=1}^{n} (x_{i} \cdot y_{i+1}-y_{i} \cdot x_{i+1})$[/tex]
Taking the purple one:
We have 6 points. I will name them:
[tex]A(0, 4);B(0, 0);C(1, 1);D(4, 0);E(4, 4);F(1, 2);[/tex]
[tex]$D=\begin{vmatrix}0& 0& 1 & 4& 4 & 1 & 0\\ 4& 0 & 1 & 0& 4 & 2 & 4 \end{vmatrix}$[/tex]
[tex]D=28-8=20[/tex]
[tex]$A=\frac{20}{2} =10$[/tex]
Write an ordered pair for each point graphed below.
Answer:
[tex]\boxed{(-1,4)}[/tex]
Step-by-step explanation:
The point is located in Quadrant II of the graph, where x-values are negative and y-values are positive.
Each marking on the graph represents one unit of distance. The two axes meet at the origin, where the coordinate point is equal to [tex](0,0)[/tex].
So, you can count backwards once from the origin to get your x-value ⇒ [tex]-1[/tex] and count up upwards four times from [tex]x=-1[/tex] to get your y-value ⇒ [tex]4[/tex].
Finally, place these in a coordinate point [tex](x,y)[/tex] ⇒ [tex]\boxed{(-1,4)}[/tex].
Answer:
(-1, 4)
Step-by-step explanation:
The point lies on the line x = -1.
The point lies on the line y = 4.
Where both lines intersect, that is the coordinate.
(x, y)
(-1, 4)
in 50 gram portion of cereal 8 grams of it are sugar which of the following represents the present of the 50 grams that is sugar
a)4
b)8
c)16
d)24
Answer:
C
Step-by-step explanation:
8/50= 0.16
Answer:
C = 8/50 = 0.16 * 100 = 16
Step-by-step explanation:
Write the equations after translating the graph of y = | 1 /2 x−2|+3 one unit down,
Answer:
[tex]y=|\frac{1}{2} x-2|+2[/tex]
Step-by-step explanation:
If your original function is:
[tex]y=|\frac{1}{2} x-2|+3[/tex]
the translation of its graph vertically down one unit, can be obtained by simply subtracting 1 from the whole functional expression:
[tex]y=|\frac{1}{2} x-2|+3-1=|\frac{1}{2} x-2|+2[/tex]
Use the De Morgan law that states: ~(p ∧ q) is equivalent to ~ p ∨ ~ q to write an equivalent English statement for the statement. It is not the case that a gun and a nose are both weapons. A gun is not a weapon or a nose is not a weapon. guns are not noses. A gun is a weapon but a nose is not. A gun is not a weapon and a nose is not a weapon.
Answer:
Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!
Step-by-step explanation:
Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!
Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!
The equivalent statement for the given statement - It is not the case that a gun and a nose are both weapons is A gun is not a weapon or a nose is not a weapon.
What is De Morgan's Law?The De Morgan's law states that → ~(p ∧ q) is same as (~ p ∨ ~ q). Theoretically, we can write it as → Not (A and B) is the same as Not A or Not B.
Given is the following statement - It is not the case that a gun and a nose are both weapons.
Now, we know that the De Morgan's law states that → Not (A and B) is the same as Not A or Not B. In the statement given -
A = gun
B = nose
~(p ∧ q) = Not(A ∧ B)
So, we can write it as -
~(p ∧ q) = Not(A ∧ B) = A gun is not a weapon or a nose is not a weapon.
where -
A gun is not a weapon → ~p
or → ∨
a nose is not a weapon → ~q
Therefore, the equivalent statement for the given statement - It is not the case that a gun and a nose are both weapons is A gun is not a weapon or a nose is not a weapon.
To solve more questions on De Morgan's Law, visit the link below-
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What is (12!) - (10!)?
Answer:
step 1
12! =479001600
step2
10!=3628800
step 3
479001600-3628800=
475372800
If Triangle Q S R is congruent to triangle Y X Z describes two triangles, which other statement is also true? A: Triangle Q R S is congruent to Triangle X Y Z // B: Triangle Q R S is congruent to Triangle Y Z X // C: Triangle Q R S is congruent to Triangle Z X Y // D: Triangle Q R S is congruent to Triangle X Z Y
Answer:
ANSER IS B FIRST IS INCORRECT
Step-by-step explanation:
The true statement:
ΔQRS ≅ ΔYZX.
Triangle QRS is congruent to Triangle YZX.
The correct option is C.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Given:
Triangle QSR is congruent to triangle YXZ.
ΔQSR ≅ ΔYXZ.
From the given choices:
The correct order of the congruent triangles.
ΔQRS ≅ ΔYZX.
Therefore, ΔQRS ≅ ΔYZX.
To learn more about the congruent;
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Which of the following graphs represents the equation below? y= 0.666667x + 3
Answer:
the last graph
Step-by-step explanation:
the y intercept is clearly shown as three and then using rise over run you can see that the slope is 2/3 or 0.667
Hiroto paid $4.28 in sales tax for the items that he purchased.
Percents
Total
100%
If the sales tax rate was 6.25 percent, what was the total cost of the items before tax was added?
$0.27
$0.68
$26.75
$68.48
Answer:
$68.48
Step-by-step explanation:
You want to find cost such that ...
6.25% × cost = $4.28
Dividing by the coefficient of cost, we get ...
cost = $4.28/0.0625 = $68.48
Answer:
the answer would be 68.48
Step-by-step explanation:
Determine the quotient. Write your answer in scientific notation.
(8.4 * 10%) + (1.2 x 102)
Answer:
0.84+122.4x is your answer. hope this helped
Step-by-step explanation:
Please solve for x and y. If you do, also write the steps you used.
Answer: a = 8, x = 56, y = 68
Step-by-step explanation:
Was there a description that stated this was a parallelogram?
Since that information was not provided....
I used the Law of Cosines to find x = 56°.
Congruent sides implies congruent angles so Center-Q-R = 56°.
Triangle Sum Theorem results in y = 68°
Vertical angles results in S-Center-P = 68°
Triangle sum Theorem results in S-P-Center = 68°
Now we can see that alternate interior angles are congruent, therefore PQRS is a parallelogram. Diagonals are bisected at the intersection so a = 8
Bert’s cab company charges $1.00 plus an additional $3.00 per mile for a ride. Madeline’s cab company charges $3.00 plus an additional $2.00 per mile for a ride. Write a system of linear equations that shows the cost in dollars, y, for a cab ride of x miles for each cab drive At what distance, in miles, will the cost be the same for both companies? Show your work
In your own words, what does it mean when something has an extrinsic value? What is an
example of an item having extrinsic value?
Answer using complete sentences.
Answer:
Extrinsic value means to have the motivation or desire to do something by yourself. To have the motivation to complete a task or goal without outside help.
Step-by-step explanation:
One way of having extrinsic value is that you go to school and you want to go to Germany. Your school fortunately has a student exchange program, so you apply hoping that you get in.
Now you go home, you get the best grades so people recognize you. You teach yourself German and you do all the things that you need to do in order to go.
What makes this extrinsic is that no one forced you to go, you did all this work by will. Your own motivation.
Using a System to Break Even
A company’s weekly revenue, in thousands, is modeled by the equation R = -p2 + 14p, where p is the price of the product it makes. The company is considering hiring an outside source to distribute its products, which will cost the company 4p + 24 thousand dollars per week.
Part B
Create a system of equations for the break-even point(s) of the company’s product to assist with the decision of hiring the distributor. Assume the distributor’s cost is the only cost that needs to be considered.
Answer: P^2 - 10p + 24 = 0
Step-by-step explanation:
Given that a company’s weekly revenue, in thousands, is modeled by the equation
R = -p2 + 14p,
where p is the price of the product it makes. The company is considering hiring an outside source to distribute its products, which will cost the company 4p + 24 thousand dollars per week.
If the company want to break even, the cost of hiring distributors will be equal to the revenue per week.
Therefore,
-P^2 + 14p = 4p + 24
Collect the like terms
-P^2 + 14p - 4p - 24 = 0
-P^2 + 10p - 24 = 0
Multiply all by minus sign
P^2 - 10p + 24 = 0
What is the Domain and Range *DON'T FORGET PARENTHESES AND BRACKETS*
Answer:
D= {-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6}
R={-6,-5,-4,-3,-2,-1,1,2,5)
Step-by-step explanation:
Please answer both questions
Answer:
which question......
In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answer: 16384
Step-by-step explanation:
Given: Total marbles = 7 (All are distinct)
Total jars = 4
Assume that, the jar is empty.
When we put marbles in the jar, we need to choose jar each time.
For each marble, total choices = Total jars = 4
Then, by using the fundamental counting principle,
The number of ways to put seven marbles in different colors into four jars =
[tex]4^7[/tex]
= 16384
Hence, the required number of ways =16384
Answer:
your answer is 16384
Step-by-step explanation:
have a nice day.
Rewrite the formula to determine the number of tickets they need to sell
Answer:
n = [tex]\frac{p}{(d-c)}[/tex]
Step-by-step explanation:
The goal is to solve for n meaning n needs to be by itself. In the current formula, n is multiplied by (d-c). Get n by itself by dividing both sides by (d-c).
*PLEASE ANSWER ASAP TY* Which of the following statements best describes a segment of a circle? a.) A segment is a portion of a sector that is bound by a chord and the major arc formed by that chord. b.) A segment is a portion of a sector that is bound by a radius and the minor arc formed by that radius. c.) A segment is a portion of a sector that is bound by a radius and the major arc formed by that radius. d.) A segment is a portion of a sector that is bound by a chord and the minor arc formed by that chord.
Answer: D
Step-by-step explanation:circle by a secant or a chord
A segment of a circle can best be described as: D. A segment is a portion of a sector that is bound by a chord and the minor arc formed by that chord.
What is a Segment of a Circle?The segment of a circle can be described as the region that is covered or surrounded by a chord and the corresponding arc that lies at both endpoints of the chord.
An example of a segment of a circle is shown in the picture attached below.
Therefore, the statement that best describes a segment of a circle is: D. A segment is a portion of a sector that is bound by a chord and the minor arc formed by that chord.
Learn more about segment of a circle on:
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Use the Venn diagram to list the elements of the set in the roster form
Answer:
Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!
Step-by-step explanation:
Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!
Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!
Can someone answer a-c please!
help me plz on this i just need the answer Use the given parent function f(x)=|x| to graph g(x)=|x|+5. Use the ray tool and select two points to graph each ray.
Answer:
no
Step-by-step explanation:
the answer is no because the quantum formula states that a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states.
PLEASE HELPPPPPPPPP!!! Graph the line that represents a proportional relationship between d and t with the property that an increase of 3 units in t corresponds to an increase of 4 units in d. What's the unit rate of change of d with respect to t? (That is, a change of 1 unit in t will correspond to a change of how many unites in d?) The unit rate is _____? Graph the relationship.
Answer:
Draw a straight line through these two points (0, 0) and (1, 3).
Step-by-step explanation:
"Proportional relationship" implies line or curve that goes through the origin; there is no "y-intercept" in this case.
Plot a dot at (0, 0). Next, move your pencil point 1 unit to the right (you'll end up at (1, 0), and then move it from there up to (1, 3). Draw a straight line through these two points (0, 0) and (1, 3).
Answer:
The unit rate of change of d with respect to t is 4/3.
The graph should be: (0,0) and (3/4).
Step-by-step explanation:
I got it wrong on khan academy :/
so i went over here and answer it
Plz help me with the hw I do not have points please help me please I will give you the questions and send it on the comment -4=-1/8e
Answer:
32
Step-by-step explanation:
-4=-1/8e
multiply both sides by -8
-8(-4)=-1/8(-8)e
32=e
Answer:
-32
Step-by-step explanation:
1/8 x8/1=1, so you would also multiply -4 by 8 and get -32
Claire is cycling at a speed of 12 miles per hour. Han is cycling at a speed of 8 miles per hour. If they start at the same position, chosen at zero, and bike in straight opposite directions, what will the distance between them be after 45 minutes?
Answer:
45 minutes is 3/4 of an hour, so find 3/4 of 12.
Divide 12 by 4 to get 1/4 of 12. That is 3.
3/4 is 3 of those, so multiply it by 3 to get 9.
So, she will have biked 9 miles.
Answer:
180 miles.
Step-by-step explanation:
First, we have to find out how far Claire is after 45 minutes:
12 x 45 = 540
Now, we need to find out how far Han is after 45 minutes:
8 x 45 = 360
Lastly, we need to subtract how far Claire went by how far Han went:
540 - 360 = 180
Final answer:
The distance between Claire and Han after 45 minutes will be 180 miles.
Hope this helped! Have a nice day!
HELPPPP FIRST GET BRAINLLEST Measure the difference between the lower quartile of Data Set A and the lower quartile of Data Set B. Round to the nearest tenth when performing all operations.
Answer:
26
Step-by-step explanation:
Let's find first the lower quartile in both A and B
steps:
look for the smallest sum of two consecutive numbers divide by 2 to get the lower quartile A73 and 75 are the smallest consecutive numbers
73+75 = 148 148/2 =74The lower quartile in A is 74
B47 and 49 are the smallest consecutive numbers
47+49 = 9696/2 = 48The lower quartile in B is 48
74-48 = 26Answer:
29
Step-by-step explanation:
To find the lower quartile of each you need to find the median to split them into 2 groups (upper and lower quartile).
Lower quartile of Set A: 73, 75, 79, 81, 84, 85
Lower quartile of Set B: 47, 49, 51, 51, 55, 56
Now you find the median of the 2
Set A: 80
Set B: 51
Lastly you subtract A & B and get 29
If a store is selling packs of gum at 3 for $0.99, how much would 12 packs cost?
Answer:
$3.96.
Step-by-step explanation:
3 cost $0.99, so 12 packs would cost 12/3 = 4 times as much.
0.99 * 4 = 3.96.
12 packs would cost $3.96.
Hope this helps!
Hello! The answer will be below! :3
The answer to your question is 3.96.
Because we have to take the info that’s given like we first have to divide.
12 divided by 3 is 4
Now we multiply.
0.99 * 4 = 3.96
So the answer is 3.96
Hope this helps! :)
⭐️Have a wonderful day!⭐️
A cylinder has a volume of 675.1 cubic centimeters. The diameter of the cylinder is 10 cm. What is the height of the cylinder? (Assume = 3.14)
Answer:
8.6 cm
Step-by-step explanation:
V=pi r-squared h
diameter of 10 means radius of 5
675.1=3.14x5x5xh
675.1=78.5h
8.6
Find the table with unit rates greater than the unit range in the graph. Then arrange these tables in order from least to greatest unit rate?
Answer:
Except table 2, all tables have greater unit rate than the graph.
The required arrangements of tables is
Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < table 7 < Table 6
Step-by-step explanation:
Formula for unit rate :
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given graph it is clear that the line passes through the points (0,0) and (11,20). So, unit rat of graph is
[tex]m=\dfrac{20-0}{11-0}=1.8181...[/tex]
Similarly, we need to calculate the unit rate for each table.
[tex]m_1=\dfrac{26-13}{14-7}=\dfrac{13}{7}=1.85714[/tex]
[tex]m_2=\dfrac{18-9}{10-5}=\dfrac{9}{5}=1.8[/tex]
[tex]m_3=\dfrac{34-17}{18-9}=\dfrac{17}{9}=1.88..[/tex]
[tex]m_4=\dfrac{42-21}{22-11}=\dfrac{21}{11}=1.9090..[/tex]
[tex]m_5=\dfrac{38-19}{20-10}=\dfrac{19}{10}=1.9[/tex]
[tex]m_6=\dfrac{50-25}{26-13}=\dfrac{25}{13}=1.923[/tex]
[tex]m_7=\dfrac{46-23}{24-12}=\dfrac{23}{12}=1.9166..[/tex]
Except table 2, all tables have greater unit rate than the graph.
The required arrangement of tables is
Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < Table 7 < Table 6
Answer:
table 3 table 5 table 4 table 7 table 6
Step-by-step explanation:
I just took the test
Help help help help
Plz
Answer:
Step-by-step explanation:
Probability of getting any number less than 6 = 2/6 =1/3
So, It is unlikely
Answer:
2/6 or 1/3
Step-by-step explanation:
the two umbers less than 6 or 2 and 4. In total on the dice there is 6 numbers. so 2/6 is tha answer and then we spimlify