The solutions can be read off of the diagonal entries in the reduced matrix.
To solve a 3 x 3 system of equations using matrices, first we need to create the augmented matrix for the system of equations. The augmented matrix contains the coefficients of the variables and the constants for each equation on each row. Then we can use row operations to reduce the augmented matrix to reduced row-echelon form. This can be done by adding or subtracting rows to each other, multiplying or dividing a row by a non-zero number, and swapping two rows. After reducing the matrix to row-echelon form, we can back-substitute the solutions to the system of equations. The solutions can be read off of the diagonal entries in the reduced matrix. For example, if the matrix is reduced to the form [a b c d e f g h i] then the solution to the system of equations is x = d/a, y = e/b, and z = f/c.
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A box of cookies contains three chocolate chip cookies, two oatmeal raisins, and four
gingerbreads. What is the probability of picking a chocolate chip, and then a gingerbread?
Answer: [tex]\dfrac{1}{6}[/tex]
Step-by-step explanation:
Given
A box contains 3 chocolate chip cookies, 2 oatmeal raisins, and 4 gingerbreads
First Probability of selecting a chocolate chip is
[tex]\Rightarrow \dfrac{3}{9}[/tex]
After that there are 8 items left. So probability of selecting a gingerbread
[tex]\Rightarrow \dfrac{4}{8}[/tex]
On combining, the required probability is
[tex]\Rightarrow \dfrac{3}{9}\times \dfrac{4}{8}\\\\\Rightarrow \dfrac{1}{6}[/tex]
A reflection over a vertical line maps ΔJKL to ΔPQR. Which best compares the perimeters of ΔJKL and ΔPQR?
Answer:
The perimeters of ΔJKL and ΔPQR are equal
Step-by-step explanation:
Given
[tex]\triangle JKL[/tex] to [tex]\triangle PQR[/tex]
Reflection over a vertical line
Required
The perimeter of both triangles
When a shape is transformed to another through reflection, the side lengths and angle of both shapes will be the same.
Hence, the side lengths of ΔJKL and ΔPQR are the same
This means that the perimeter of both shapes will be the same
You borrowed $59,000 for 2 years at 11% which was compounded annually. What
total will you pay back?
Answer:
$72693.9
Step-by-step explanation:
To get this answer you need to use the compound interest formula, which will be A=P(1+r/n)^n(t). P=59,000 r=11%=0.11 n=1 (annually) t=2 years. From there you should be able to figure the rest out and get the answer. Hope this helps!
Solve Similar Triangles (advanced)
Solve for X.
Given:
[tex]m\angle B=90^\circ, m\angle D=90^\circ, AB=6, BD=4, BC=2, DE=x[/tex].
To find:
The value of x.
Solution:
In triangles ABC and ADE,
[tex]\angle B\cong \angle D[/tex] (Right angles)
[tex]\angle A\cong \angle A[/tex] (Common angles)
[tex]\Delta ABC\sim \Delta ADE[/tex] (AA property of similarity)
We know that the corresponding sides of similar triangles are proportional. So,
[tex]\dfrac{AB}{AD}=\dfrac{BC}{DE}[/tex]
[tex]\dfrac{6}{(6+4)}=\dfrac{2}{x}[/tex]
[tex]\dfrac{6}{10}=\dfrac{2}{x}[/tex]
[tex]\dfrac{3}{5}=\dfrac{2}{x}[/tex]
On cross multiplication, we get
[tex]3\times x=5\times 2[/tex]
[tex]3x=10[/tex]
[tex]x=\dfrac{10}{3}[/tex]
Therefore, the value of x is [tex]\dfrac{10}{3}[/tex] units.
Katy organised a wedding. Guests had to choose their meal from pasta , chicken or beef. 1/3 of the guests chose pasta. 5/12 of the guests chose chicken. 24 of the guests chose beef. How many guests were at the wedding ?
guys please help i’ll even give brainliest and give the correct answer not wrong ones
With the help of equations we can say that, the wedding had 96 attendees.
What is an equation ?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it.
According to our question-
x is the total number of wedding attendees.
1/3 of the attendees =1/3 who chose pasta=1/3x----1
Those who selected chicken =5/12x---2
24 people opted for meat.----3
adding 1,2,3
x = 96
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108% of 75.5 is what number
Answer:
81.54
Step-by-step explanation:
% of a # = (% * #)/100
% = 108
# = 75.5
(108 * 75.5)/100
8,154/100
81.54
OR
% of a # = (%/100) * #
% = 108
# = 75.5
(108/100) * 75.5 = 1.08 * 75.5
81.54
There is a line that includes the point (9,–8) and has a slope of –19. What is its equation in point-slope form?
Answer:
y +8 = -1/9(x -9)
Step-by-step explanation:
You want the point-slope form of the equation of the line through point (9, -8) with slope -1/9.
Point-slope formThe equation of the line through point (h, k) with slope m is ...
y -k = m(x -h)
You have (h, k) = (9, -8), and m = -1/9. Using these values, the equation is ...
y +8 = -1/9(x -9)
answer these question, please
A rectangular prism and its dimensions are shown in the diagram.
26
6.5 in.
5 in.
7.5 in.
What is the total surface area of this prism in square inches?
Record your answer and fill in the bubbles on your answer document. Be sure to use the
correct place value.
Answer: 21
Step-by-step explanation: you add and subtract
Answer:
21
Step-by-step explanation:
which system of equations has only one solution
4x+2y=8 -4x-2y=3
Jello someone please please help me
No links or files
Answer: question number 2 is A dot plot shows data with small sets of numbers and a histogram shows data with large sets of numbers
Step-by-step explanation:
The model represents an equation.
What is the solution for this equation?
PLEASE HELP ASAP! 55 POINTS Jackie wraps a sheet of paper tightly around a wax candle whose diameter is two inches, then cuts through them both with a sharp knife, making a 45° angle with the candle's axis. After unrolling the paper and laying it flat, Jackie sees the wavy curve formed by the cut edge, and wonders whether it can be described mathematically. Sketch this curve, then show that it is sinusoidal. It is very helpful to use radian measure to describe angles in this problem.
Gabe and Bridgette are preparing meals to serve at a local homeless shelter. The number of people they will be able to serve depends on the number of meals they prepare.
p = the number of people Gabe and Bridgette will be able to serve
m = the number of meals Gabe and Bridgette prepare
Which of the variables is independent and which is dependent?
Answer:
The independent variable in this scenario is the number of meals Gabe and Bridgette prepare (m), because this is the variable that they can control and manipulate. The dependent variable is the number of people they will be able to serve (p), because this is the variable that depends on the number of meals they prepare.
Step-by-step explanation:
In other words, the number of people they can serve is affected by the number of meals they prepare, but the number of meals they prepare is not affected by the number of people they can serve.
Answer:
independent variable = m
dependent variable = p
Step-by-step explanation:
The number of people they are able to serve depends on the number of meals they prepare.
What is the volume of a hemisphere with a radius of 3.8in, rounded to the nearest tenth of a cubic inch
Answer: [tex]114.9\ in.^3[/tex]
Step-by-step explanation:
Given
The radius of the hemisphere is [tex]r=3.8\ in.[/tex]
The volume of a hemisphere is given by
[tex]V=\dfrac{2}{3}\pi r^3[/tex]
Insert the value
[tex]V=\dfrac{2}{3}\pi \times (3.8)^3\\\\V=114.9\ in.^3[/tex]
the 10th term of the arithmetic 5x + 6, 11x + 2, 17x - 2,
Answer:
t10 = 59x - 30
Step-by-step explanation:
a = 5x + 6
d = 11x + 2 - 5x - 6
d = 6x - 4
n = 10
tn = a + (n - 1)*d
t10 = 5x + 6 + (10 - 1) ( 6x - 4)
t10 = 5x + 6 + 9(6x - 4)
t10 = 5x + 6 + 54x - 36
t10 = 59x - 30
Check by finding the 3rd term
d = 6x - 4
n = 3
a = 5x + 6
t3 = 5x + 6 + (3-1)*(6x - 4)
t3 = 5x + 6 + 2(6x - 4)
t3 = 5x + 6 + 12x - 8
t3 = 17x - 2 which is exactly what it should be.
Is Avogadro's number the same for all elements?
The Avogadro's number of every element remains is the same. The number of atoms of 1 mole in every element is Avogadro's number. One mole of an element is 6.02214076×10²³ atoms.
What is an atom?
Each atom is made up of a nucleus and one or more electrons that are linked to it. One or more protons and a significant number of neutrons make up the nucleus. Only the most prevalent type of hydrogen is neutron-free. Atoms that are neutral or ionized make up every solid, liquid, gas, and form of plasma.
The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of 6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.
The number of atoms of one mole substance is 6.02214076 × 10²³ which is Avogadro's number.
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I don’t know I just need the answer
6th grade math help me please and thank you
What should I do FIRST to solve this problem?
5f - 7 = 23
divide by 5 on each side
subtract 7 from each side
subtract 23 from each side
add 7 to each side
Answer:
add 7 to both sides
then you are left with 5f=30
divide by 5 on both sides
you get f=6
Step-by-step explanation:
Find f(-2) for f(x) = 2 x 3x
O A. -18
O B. 2/9
O c. 1/18
O D. -36
Step-by-step explanation:
f(x) = 2 x 3x
2 x 3x
2 (-2) 3(-2)
-4-6=-10
Step-by-step explanation:
f(x)=2 x 3x
2 x 3x
2(-2) 3 (-2)
-4 - 6 = -10
A machine makes 12 articles in half an hour.
How many articles will it make in 6 hours?
Answer:
144
I wish you luck in your assignments.
Answer: 144 articles
Step-by-step explanation:
If it makes 12 in half-hour, then 24 in an hour because 12*2 is 24.
then 24*6=144.
Given both, find (f-g)(x)
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Functions.
Here, we are given with,
f(x) = 4x + 4 and g(x) = 5x - 8
hence, now we have time get (f-g) (x)
so we get as,
==> (f-g) (x) ==> f(x) - g(x)
===> 4x + 4 - (5x - 8)
==> 4x + 4 -5x +8
==> -x + 12
==> hence, 12 - x
so we get as,
(f-g) (x) ==> 12 - x
which answer? (multiple choice).
Joseph has a standard deck of 52 playing cards. What is the probability that Joseph will draw a Jack then a Queen with replacement?
Answer: four out of 52 to pull a jack
Step-by-step explanation:
Rasheen and Eric went to Taco Express. Rasheen bought seven tacos and two fajitas and paid $12.65. Eric bought four tacos and one fajita and paid $6.95. Find the cost of one taco.
Question 8 options:
$1.35
$1.45
$1.25
$1.95
Which postulate proves the two
triangles are congruent?
A. SAS
B. SSS
C. HL
D. none
Answer:
D. none
Step-by-step explanation:
The figure shows two triangles. We see a right angle in each triangle. All right angles are congruent. One angle of one triangle is congruent to one angle of the other triangle. We are not given any other information about congruent sides or other congruent angles. Therefore, there is not enough information to prove the triangles are congruent.
Answer: none
Someone please help me with this algebra
Which number will have the same result, when rounded to the nearest hundred or thousand? (3-5) A 1,049 B 1,118 and 5 C 1,179 D 2,149
Answer:
The answer is "Option A".
Step-by-step explanation:
In this question except for choice "A", all the value is not nearest about the hundred or thousand, that why the correct answer is "1,049".
A bag contains 8 red marbles, 6 blue marbles and 7 green marbles. If two marbles are
drawn out of the bag, what is the probability, to the nearest 1000th, that both
marbles drawn will be red?
Answer:.029
Step-by-step explanation:
The probability of the first being blue is 6/17, the second is 5/16 and the third is 4/15. Multiply these together to get the total probability:
6/17 x 5/16 x 4/15 = .029
ps: have a nice day :)
7. The power of the expressions 2x is
Answer:
2x= 1
hope it is helpful to you