Answer:
(a, b, c) = (-1/3, 2, 5)y = (-1/3)x^2 +2x +57.90 secondsStep-by-step explanation:
From your equations in Part A, we can write the matrix equation as ...
[tex]\left[\begin{array}{ccc}9&3&1\\25&5&1\\36&6&1\end{array}\right] \cdot\left[\begin{array}{c}a&b&c\end{array}\right] = \left[\begin{array}{c}8&\frac{20}{3}&5\end{array}\right][/tex]
For the purpose of finding the inverse matrix (which we don't really need to do to solve this), it is convenient to use an augmented matrix that will give both the matrix inverse and the solution.
[tex]\left[\begin{array}{ccc|ccc|c}9&3&1&1&0&0&8\\25&5&1&0&1&0&\frac{20}{3}\\36&6&1&0&0&1&5\end{array}\right][/tex]
For the first step in the solution, we'll divide the first row by 9, then subtract 25 times that from the second row, and 36 times that from the third row. The goal of this step is to make the first column be 1, 0, 0. The result is ...
[tex]\left[\begin{array}{ccc|ccc|c}1&\frac{1}{3}&\frac{1}{9}&\frac{1}{9}&0&0&\frac{8}{9}\\0&-\frac{10}{3}&-\frac{16}{9}&-\frac{25}{9}&1&0&-\frac{140}{9}\\0&-6&-3&-4&0&1&-27\end{array}\right][/tex]
For the second step in the solution, we'll multiply the second row by -3/10, then subtract 1/3 times that from the first row and add 6 times that to the third row. The goal of this step is to make the second column be 0, 1, 0. The result is ...
[tex]\left[\begin{array}{ccc|ccc|c}1&0&-\frac{1}{15}&-\frac{1}{6}&\frac{1}{10}&0&-\frac{2}{3}\\0&1&\frac{8}{15}&\frac{5}{6}&-\frac{3}{10}&0&\frac{14}{3}\\0&0&\frac{1}{5}&1&-\frac{9}{5}&1&1\end{array}\right][/tex]
For the third step in the solution, we'll multiply the third row by 5, then add 1/15 of that to the first row and -8/15 of that to the second row. The goal of this step is to make the third column be 0, 0, 1. The result is ...
[tex]\left[\begin{array}{ccc|ccc|c}1&0&0&\frac{1}{6}&-\frac{1}{2}&\frac{1}{3}&-\frac{1}{3}\\0&1&0&-\frac{11}{6}&\frac{9}{2}&-\frac{8}{3}&2\\0&0&1&5&-9&5&5\end{array}\right][/tex]
The middle section of this augmented matrix is the inverse of the coefficient matrix:
[tex]A^{-1}=\left[\begin{array}{ccc}\frac{1}{6}&-\frac{1}{2}&\frac{1}{3}\\-\frac{11}{6}&\frac{9}{2}&-\frac{8}{3}\\5&-9&5\end{array}\right][/tex]
The right section of the augmented matrix is the solution set:
[tex]X=\left[\begin{array}{c}a\\b\\c\end{array}\right]=\left[\begin{array}{c}-\frac{1}{3}\\2\\5\end{array}\right][/tex]
__
The equation of the parabola is ...
[tex]\boxed{y=-\dfrac{1}{3}x^2+2x+5}[/tex]
__
The ball will hit the ground when y=0. The values(s) of x can be found from the quadratic formula:
x = (-b±√(b²-4ac))/(2a) = (-2±√(2²-4(-1/3)(5)))/(2(-1/3))
x = (2 ± √(32/3))/(2/3) = 3±√24 = {-1.899, 7.899}
It will take about 7.90 seconds for the ball to hit the ground.
When solving this system of linear equations with the elimination method,
you can multiply the bottom equation by 3.
3x +6y - 38
3( 5x - 2y) = 3(-30)
This step works because of the
O A. commutative property
O B. multiplication property of equality
O C. distributive property
O D. addition property of equality
Answer:
B.
Step-by-step explanation:
Multiplication property of equality.
A simple example is
x = x Multiply by 3:
3x = 3x
This step works because of the distributive property - option C.
System of Linear EquationsSystem of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
Properties of MultiplicationThe properties of multiplication are:
Distributive: a(b±c)= ab±acComutative: a . b = b. aAssociative: a(b+c)= c(a+b)Identity: b.1=bFor the given system linear system was used the distributive property. Because it was used as a common factor to multiply an expression with a sum.
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*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.
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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
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
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
Find the magnitude of the vector.
(-2,-7)
Answer:
[tex]\sqrt{53}[/tex]
Step-by-step explanation:
[tex]\begin{pmatrix}-2&-7\end{pmatrix}\\=\sqrt{\left(-2\right)^2+\left(-7\right)^2}\\\\[/tex]
Then you need to simplify:
[tex]=\sqrt{2^2+\left(-7\right)^2}\\=\sqrt{2^2+7^2}\\=\sqrt{4+7^2}\\=\sqrt{4+49}\\=\sqrt{53}[/tex]
Answer:
53
Step-by-step explanation:
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.
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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
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
determine which function has the greatest rate of change as x approaches infinity
f(x)= 2^x- 10
g(x)=16x-4
h(x) = 3x^2-7x+8
there is not enough information to determine the answer
Answer:
f(x)= 2^x-10
Step-by-step explanation:
Exponential functions are ALWAYS greater in the long run!
Answer:
A) f(x) = 2^x − 10
Step-by-step explanation:
I graph all of these functions and f(x) = 2^x − 10 surpasses the other two functions. Exponential growth functions always exceed linear growth functions over time.
Match each solution to the equation it solves.
Hi there! Hopefully this helps!
---------------------------------------------------------------------------------------------------------------
Answer to the first equation: 3.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer to the second equation: 7
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer to the third equation: -2.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer to the fourth equation: -3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer:
3
7
-2
-3
Step-by-step explanation:
in that exact order
Find the value of x in the isosceles triangle shown below.
Answer:
x=10
Step-by-step explanation:
We can use the Pythagorean theorem to find x
The height meets the base at a right angle
The base is bisected ( cut in half) so the base is 6 the height is 8
a^2 + b^2 = c^2
6^2 + 8^2 = x^2
36+64 = x^2
100 = x^2
Taking the square root of each side
sqrt(100) = sqrt(x^2)
10 = x
Answer:
10
Step-by-step explanation:
This triangle is divided into 2 identical rigth triangles.
We will use the pythagorian theorem:
●8^2+ (12/2)^2 =x^2
● 64 + 36 = x^2
● x= 10
So x is 10
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
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.
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Which of the following equations have exactly one solution? Choose all answers that apply:
A -13x+12=13x+13
B -13x+12=13x-13
C 12x+12=13x+12
D 12x+12=13x-12
I need correct answer and description, so I can put Brainliest
Answer:
a
b
c
d
Step-by-step explanation:
Well lets look,
a)
If both slopes are different and have different y intercepts they have 1 solution.
So a has 1 solution
b)
Both slopes are different with different y intercepts.
1 solution
c)
Both slopes are different with different y intercepts
1 solution
d)
Different slopes different y intercepts
1 solution.
For proof look at the images below.
Thus,
the answer is a,b,c, and d.
Hope this helps :)
At Paul Bunyan’s tree farm they sell Fraser firs and blue spruce trees. They plant saplings of these two kinds of trees that are 8 inches in 5 inches tall, respectively. The Fraser firs grow at a constant rate of 12 inches per year, and a blue spruce trees grow at a constant rate of 14 inches per year. After how many years will these trees be at the same height? Express your answer as a common fraction.
Answer: 3/2
Step-by-step explanation:
Hi, to answer this question we have to write the next expressions::
Height 1= 8 +12 y
Height 2 =5 +14y
Where y = number of years
Since both heights must be the same
Height 1 = height 2
8+12y = 5+14y
solving for y:
8-5 =14y-12y
3 = 2y
3/2 =y
y = 3/2 years
Feel free to ask for more if needed or if you did not understand something.
8 + 12y = 5 + 14y
12y + 8 = 14y + 5
12y + 8 - 8 = 14y + 5 - 8
12y = 14y - 3
12y - 14y = 14y - 3 - 14y
-2y = -3
(-2y)/-2 = -3/-2
y = 3/2
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)
Pls help with this question thank u all
Answer:
4 cm (A)
Step-by-step explanation:
triangle BAC is just a larger version of triangle EAD. given that ED is 5cm, and BC is 10cm, triangle BAC must be twice the size of EAD. since the ratio of AD to ED is 4:5, and BC is twice the size, all we need to do is multiply both sides by 2 to find length AC. 4*2 = 8. now we can subtract length AD from AC to get CD. 8 - 4 = 4.
sorry if what i wrote is a little confusing
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).
Multiply 4/5 × 3/20. in simplest form
━━━━━━━☆☆━━━━━━━
▹ Answer
3/25
▹ Step-by-Step Explanation
[tex]\frac{4}{5} * \frac{3}{20} \\\\= \frac{12}{100} \\\\\frac{12}{100} divide each side by 4\\\\\frac{12}{100} \\\\= \frac{3}{25}[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
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.
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
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!
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!⭐️
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:
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
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]
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:
Please answer both questions
Answer:
which question......
What is (12!) - (10!)?
Answer:
step 1
12! =479001600
step2
10!=3628800
step 3
479001600-3628800=
475372800