The system of equations:
\(\begin{gathered} 6x+7y=14 \\ 7x+8y=27 \end{gathered}\)can be written as:
\(\begin{bmatrix}6 & 7 \\ 7 & 8\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}=\begin{bmatrix}14 \\ 27\end{bmatrix}\)To find the solution we need to find the inverse matrix of the coefficients matrix. For a two by two matrix the inverse is given as:
\(\frac{1}{\mbox{det }A}\begin{bmatrix}d & -b \\ -c & a\end{bmatrix}\)Then in this case the inverse matrix is
\(undefined\)3. The West Rock School District ordered
118 cartons of math books. The books
were shipped in cartons that each held
36 books.
A. Estimate the total number of math
books in the shipment. Write an
equation to model your work.
Answer:
4000 or 4800
Step-by-step explanation:
118 turns into 120
and 36 turns into 40
120x40=4800
or 118 turns into 100
and 36 turns into 40 meaning the ansar would be 4000
Answer:
4000 for sure
I had this question before
Complete this puzzle using each of these numbers only once : 2, 4, 5, 7, 8, 11, 13, 14, 16 Put the even numbers in the squares and the odd nurmbers in the circles. Each row of three numbers must add up to 26.
Here is one solution to the puzzle:
Squares: 2, 8, 16
Circles: 5, 7, 14
Total: 26
You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.
What are even and odd numbers?An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.
Therefore, the correct answer is as given above
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A community center sells a total of 299 tickets for a basketball game. An adult ticket costs $4. A student ticket costs $1. The sponsors collect $587 in ticket sales. Find the number of each type of ticket sold.
Answer:
96 adult tickets203 student ticketsStep-by-step explanation:
The most expensive ticket is the adult ticket, so we'll use "a" to represent the number of those sold. Then (299-a) student tickets were sold, and total revenue was ...
4a +1(299-a) = 587
3a = 288
a = 96
96 adult tickets and 203 student tickets were sold.
What’s the correct answer for this?
Answer:
Answer is the first one :)
Step-by-step explanation:
√(-7-5)² + (-7-9)²
answer is 20
hope this helps
Answer:
A.
Step-by-step explanation:
In the attached file
please help. 10 points
Answer:
8 divided by 1/3 is 24 because you are dividing a fraction so it is basically 8*3 (inverse operations). As for 2/3 it does not have one as a numerator so it automatically is less that 1/3
Step-by-step explanation:
Sry If it doesn't make sense!
If you are confused let me know and I will explain in the comments.
what is the radical form 2 4/3
The radical form of the expression 2^(4/3) is given as follows:
\(2^{\frac{4}{3}} = \sqrt[3]{2^4} = 2\sqrt[3]{2}\)
How to obtain the radical form of each expression?The general format of the exponential expression is given as follow
\(a^{\frac{n}{m}}\)
To obtain the radical form, we have that:
a is the radicand.n is the exponent.m is the root.Hence the radical form of the exponential expression is given as follows:
\(a^{\frac{n}{m}} = \sqrt[m]{a^n}\)
The parameters for this problem are given as follows:
a = 2, n = 4, m = 3.
Hence the radical form of the expression is given as follows:
\(2^{\frac{4}{3}} = \sqrt[3]{2^4} = 2\sqrt[3]{2}\)
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6 ≤ -3x + 12
can somone solve this for me *correctly* ill give u brainlest only if ur right
Answer:
x ≤ 2
Step-by-step explanation:
-3x+12≥6
-3x≥6
3x≤6
x ≤ 2
Answer:
x ≤ 2 is the correct answer!
Step-by-step explanation:
Hope this helps!
What the meaning of "f is order-preserving if x < y implies f(x) < f(y)"?
An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.
In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.
Order-Preserving Function:
A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.
Increasing Function:
If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).
Isomorphism:
A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:
a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).
b. f is onto (surjective): Every element in Q has a pre-image in P.
When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.
Automorphism:
An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.
These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.
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1. A right triangle LMN is given where: side MN = 8 side NL (the hypotenuse) =
10 What is the length of side LM?*
Step-by-step explanation:
\( \underline{ \underline{ \text{Given}}} : \)
Length of MN ( Base ) = 8 Length of NL ( Hypotenuse ) = 10\( \underline{ \underline{ \text{To \: find}}} : \)
Length of LM ( Perpendicular )\( \underline{ \underline{ \text{Using \: pythagoras \: theorem}}} : \)
\( \boxed{ \sf{ {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2} }}\)
⤑ \( \sf{ Perpendicular = \sqrt{ {(Hypotenuse)}^{2} - {(Base)}^{2} } }\)
⤑ \( \sf{ \sqrt{ {(10)}^{2} - {(8)}^{2} } }\)
⤑ \( \sf{ \sqrt{100 - 64}} \)
⤑ \( \sf{ \sqrt{36}} \)
⤑ \( \boxed{ \sf{6\: units}}\)
\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline { \tt{6 \: units}}}}}}}\)
Hope I helped ! ツ
Have a wonderful day / night ! ♡
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
help me out please
Answer:
The one that does not a a decimal or fraction is the correct answer
Step-by-step explanation:
Vinnie drives his car 210 miles and has an average of a certain speed. If the average speed had been 3mph more, he could have traveled 228 miles in the same length of time. What was his average speed?
Answer:
35 mph
Step-by-step explanation:
time = distance / speed
210 miles and has an average of a certain speed
t = 210 / s
If the average speed had been 3mph more, he could have traveled 228 miles in the same length of time
t = 228 / (s + 3)
Set equal
210 / s = 228 / (s + 3)
Cross multiply
210s + 630 = 228s
Subtract 210s from both sides
630 = 18s
Divie both sides by 18
35 = s
35 mph
Sorry this took so long.....
Had to get some help from the internet
Have a great day!!!!!
Safiya needs to find a number that can be multiplied by 3√18
to result in a rational product.Which values could she use?
Safiya can use either ∛12 or ∛(1/6) to find a rational product when multiplied by ∛18. So, correct options are e and f.
The cube root of 18 is an irrational number because it cannot be expressed as a fraction of two integers. Safiya needs to find a rational number that, when multiplied by ∛18, results in a rational product. To do this, she needs to look for cube roots of numbers that are perfect cubes of integers.
Option a) ∛4 is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option b) ∛18 is the given number and is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option c) ∛3 is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option d) ∛(1/18) is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option e) ∛12 is a rational number and it can be expressed as ∛(2³ × 3). Therefore, it is a valid choice.
Option f) ∛(1/6) is a rational number and can be expressed as ∛(1/216). Therefore, it is a valid choice.
So, correct options are e and f.
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What is the difference between the sum of the measures of the interior angles in an octagon and the sum of the measures of the interior angles in a
hexagon?
540 degrees
180 degrees
360 degrees
720 degrees
PLS ANSWER IF YOU KNOW!!!
which number is composite? (9,5,11,2)
Answer: 9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
3 x 3 = 9 :)
Chandler decided to go cliff jumping into the lake at his cottage. He started on the cliff at 32 ft above sea level. He jumped for 40 feet! How far below sea level did Chandler end up?
Chandler ended up 8 feet below sea level. The negative sign indicates that his final position is below sea level. This means that he has descended further into the lake compared to the starting point on the cliff.
Chandler started on the cliff at 32 feet above sea level. When he jumped for 40 feet, we need to determine the final position in relation to sea level.
Since Chandler jumped down, the distance below sea level will be calculated as a negative value. To find how far below sea level Chandler ended up, we subtract the jump distance (40 feet) from the starting height (32 feet above sea level):
32 feet - 40 feet = -8 feet
It's important to note that negative values are used here to represent the direction and magnitude of Chandler's descent relative to sea level
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Answer:
-8 feet
Step-by-step explanation:
Please help :)
this is adding polynomials.
h(x)+g(x)
h(x)=6x^2+4x^4+7x
HELP!!!!!!!!!!!!!!!!
Fourth answer
basically the points where y=0
hope this helped
Find the Measure of each angle.
Answer:
x = 10
Step-by-step explanation:
to find the measure of angles we first need to find the value of x
The sum of interior angles in a triangle is equal to 180
9x + 7x + 2x = 180 add like terms
18x = 180 divide both sides by 18
x = 10 to find angle measures replace x with 10 in each representative like:
m<L = 9x and 9*10 = 90 and so on
what is the slope of the line -3y=12x+6
Answer:
Step-by-step explanation:
uhh
Graph the solution to the inequality on the number line. w−0.9>−2.1 First select the correct ray. Then select the location of the endpoint to plot the inequality on the number line.
The solution to the inequality \(w - 0.9 >-2.1\) is \(w >-1.2\)
InequalityInequalities are used to represent expressions of unequal values
The inequality is given as:
\(w - 0.9 >-2.1\)
Add 0.9 to both sides of the inequality
\(w - 0.9+ 0.9 >-2.1 + 0.9\)
Simplify the inequality
\(w >-1.2\)
The above inequality means that:
The arrow on the number line points to the rightThe arrow begins at point -1.2 with an open circle or dotted linesSee attachment for the inequality that represents \(w >-1.2\)
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Find the midpoint of AB when A=(1,-2) B=(1,-1)
Answer:
Midpoint Of AB = ( 1+1/2 , -2-1/2)
= (2/2 , -3/2)
= ( 1 , -1.5)
Hope this helps
Please mark Branliest.
Answer:
-2,0
Step-by-step explanation:
PLEASE HELPPP!!!!!!!!!
If tanA= 40/9 and sin B = 45/53
and angles A and B are in
Quadrant I, find the value of tan (A-B).
The value of tan (A-B) is equal to 715/2052.
To find the value of tan(A - B), we can use the trigonometric identity:
tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))
Given that tan(A) = 40/9 and sin(B) = 45/53, we can determine the values of cos(B) and tan(B) using the Pythagorean identity:
sin^2(B) + cos^2(B) = 1
cos(B) = sqrt(1 - sin^2(B))
cos(B) = sqrt(1 - (45/53)^2)
cos(B) = sqrt(1 - 2025/2809)
cos(B) = sqrt(784/2809)
cos(B) = 28/53
tan(B) = sin(B)/cos(B)
tan(B) = (45/53)/(28/53)
tan(B) = 45/28
Now we can substitute the values into the formula for tan(A - B):
tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))
tan(A - B) = (40/9 - 45/28)/(1 + (40/9)(45/28))
tan(A - B) = [(1120/252 - 405/252)] / (1 + (1800/252))
tan(A - B) = (715/252) / (2052/252)
tan(A - B) = 715/2052
Therefore, tan(A - B) is equal to 715/2052.
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Use point-slope form to write the equation of a line that passes through the point (-13,15) with slope 1
The equation of a line that passes through the point (-13,15) with slope 1 using point slope form is y-x = 28
What is the point slope form of a line?The point slope form of line is given by y -y₁= m(x -x₁), where m is the slope of the line , x is x coordinate, y is y coordinate and (x₁, y₁) is given point on the line .
Given that the slope of a line is 1 and a point on the line is (-13,15), then using point slope form we can find the equation of the line
Take slope of the line , m = 1 and point on the line (x₁, y₁) = (-13,15)
then the equation of the line :
(y -15) = 1 (x-(-13))
y-15 = x+13
y-x = 28
Therefore the equation of the given line is y-x = 28
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how do I understand implicit function
Answer: An implicit function is a function, written in terms of both dependent and independent variables, like y-3x2+2x+5 = 0. Whereas an explicit function is a function which is represented in terms of an independent variable.
Step-by-step explanation: To find the implicit derivative,
Differentiate both sides of f(x, y) = 0 with respect to x.
Apply usual derivative formulas to differentiate the x terms.
Apply usual derivative formulas to differentiate the y terms along with multiplying the derivative by dy/dx.
Solve the resultant equation for dy/dx (by isolating dy/dx).
Using a number cube and this hat with 5 different-colored marbles, which simulation would help you answer this question? During the first 70 days of school, Becca’s science class does a lab experiment 23 of the time. The class meets Monday through Friday. If you choose a class at random, what are the chances that Becca did a lab experiment on a Friday?
The solution is, given below.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
We assume that the question is interested in the probability that a randomly chosen class is a Friday class with a lab experiment (2/15). That is somewhat different from the probability that a lab experiment is conducted on a Friday (2/3).
Based on our assumption, we want to create a simulation that includes a 1/5 chance of the day being a Friday, along with a 2/3 chance that the class has a lab experiment on whatever day it is.
That simulation can consist of choosing 1 of 5 differently-colored marbles, and rolling a 6-sided die with 2/3 of the numbers being designated as representing a lab-experiment day. (The marble must be replaced and the marbles stirred for the next trial.) For our purpose, we can designate the yellow marble as "Friday", and numbers greater than 2 as "lab-experiment".
The simulation of 70 different choices of a random class is shown in the attachment.
Comment on the question
IMO, the use of 70 trials is coincidentally the same number as the first 70 days of school. The calendar is deterministic, so there will be exactly 14 Fridays in that period. If, in 70 draws, you get 16 yellow marbles, you cannot say, "the probability of a Friday is 16/70." You need to be very careful to properly state the question you're trying to answer.
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9. A has some amount of money with him. He gave one half of one third from that amount One half of the amount received by B is 20. What is the amount that A originally had?
Using the expression 5x/12 = 20, the amount that A originally had was $48.
We have,
Let x be the amount of money that A originally had.
Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.
The amount received by B is 1/2 of the remaining amount,
which is (x - x/6)/2 = 5x/12.
We know that 5x/12 = 20,
Solving for x.
5x/12 = 20
5x = 240
x = 48
Therefore,
The amount that A originally had was $48.
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Determine if the following functions are bottom heavy, top heavy, or equal
Answer:
• (a)Bottom-Heavy, y=0
,• (b)Equal, y=1/3
,• (c)Top heavy, No horizontal asymptote
Explanation:
• A Rational function is bottom-heavy when ,the degree of the numerator is less than the degree of the denominator,.
,• A Rational function is top-heavy when ,the degree of the numerator is more than the degree of the denominator,.
,• It is balanced (or equal) when ,the degree of the numerator is equal to the degree of the denominator,.
Part A
\(\frac{x+2}{x^2+4x+11}\)The function is bottom-heavy.
Since the function is bottom-heavy, the horizontal asymptote is:
\(y=0\)Part B
\(\frac{x^2-5}{3x^2+4}\)The function is equal.
Since the function is equal, divide the leading coefficients to find the horizontal asymptote.
The horizontal asymptote is at y=1/3.
Part C
\(\frac{3x^4+x^2-2}{4x^2+3}\)The function is top-heavy.
Since it is top-heavy, it has no horizontal asymptote.
Find the measure of the arc or angle indicated
The unknown angle in the cyclic quadrilateral is as follows:
∠R = 86 degrees
How to find arc angle?The diagram above is cyclic quadrilateral. A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.
The sum of angles in a cyclic quadrilateral is 360 degrees. The opposite angles in a cyclic quadrilateral is supplementary.
Hence, let's find the unknown angle.
∠R = 1 / 2 (92 + 80)
∠R = 1 / 2 (172)
∠R = 86 degrees
Therefore, the unknown angle is 86 degrees.
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What is the length of ab
A (-7) b(8)
EXCUSE ME WHAT?! I hate my school. They haven’t even said anything about this yet.
Answer:
The first one is acute, the second is right, and the third is obtuse.
Step-by-step explanation:
Hope this helps :)
Have an excellent day!
~sunny~
Answer:
Angle 1 - acute angle
Angle 2 - right angle
Angle 3 - obtuse angle
Step-by-Step Explanation:
The acute angle is smaller than right angles, right angles are 90 degrees, and obtuse angles have larger degree angle than right angles.