Answers
The value of matrix multiplication is
a) [tex]C = \begin{pmatrix}14&20\\ 32&46\end{pmatrix}[/tex]
b) [tex]C = \begin{pmatrix}7&35\\ 8&42\end{pmatrix}[/tex]
c) [tex]C = \begin{pmatrix}22&32\\ 26&38\end{pmatrix}[/tex]
d) [tex]C =\begin{pmatrix}-3&-5\\ 34&52\end{pmatrix}[/tex]
What is multiplication of matrices?
The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix
Given data ,
a)
Let the first be A
[tex]A = \left[\begin{array}{ccc}1 &2 \\ 3 & 4 \\\end{array}\right][/tex]
Let the second matrix be B
[tex]B = \left[\begin{array}{ccc}4 &6 \\ 5 & 7 \\\end{array}\right][/tex]
Now , the product of matrices A and B is C
where the matrix C is A x B
[tex]C = \begin{pmatrix}1\cdot \:4+2\cdot \:5&1\cdot \:6+2\cdot \:7\\ 3\cdot \:4+4\cdot \:5&3\cdot \:6+4\cdot \:7\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}14&20\\ 32&46\end{pmatrix}[/tex]
Therefore , the value of matrix is [tex]C = \begin{pmatrix}14&20\\ 32&46\end{pmatrix}[/tex]
b)
Let the first matrix be A
[tex]A = \left[\begin{array}{ccc}3 &5 \\ 4 & 6 \\\end{array}\right][/tex]
Let the second matrix be B
[tex]B = \left[\begin{array}{ccc}-1 &0 \\ 2 & 7 \\\end{array}\right][/tex]
Now , the product of matrices A and B is C
where the matrix C is A x B
[tex]C = \begin{pmatrix}3\left(-1\right)+5\cdot \:2&3\cdot \:0+5\cdot \:7\\ 4\left(-1\right)+6\cdot \:2&4\cdot \:0+6\cdot \:7\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}7&35\\ 8&42\end{pmatrix}[/tex]
Therefore , the value of matrix is [tex]C = \begin{pmatrix}7&35\\ 8&42\end{pmatrix}[/tex]
c)
Let the first matrix be A
[tex]A = \left[\begin{array}{ccc}4 &6 \\ 5 & 7 \\\end{array}\right][/tex]
Let the second matrix be B
[tex]B = \left[\begin{array}{ccc}1 &2 \\ 3 & 4 \\\end{array}\right][/tex]
Now , the product of matrices A and B is C
where the matrix C is A x B
[tex]C = \begin{pmatrix}4\cdot \:1+6\cdot \:3&4\cdot \:2+6\cdot \:4\\ 5\cdot \:1+7\cdot \:3&5\cdot \:2+7\cdot \:4\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}22&32\\ 26&38\end{pmatrix}[/tex]
Therefore , the value of matrix is [tex]C = \begin{pmatrix}22&32\\ 26&38\end{pmatrix}[/tex]
d)
Let the first matrix be A
[tex]A = \left[\begin{array}{ccc}-1 &0 \\ 2 & 7 \\\end{array}\right][/tex]
Let the second matrix be B
[tex]B = \left[\begin{array}{ccc}3 &5 \\ 4 & 6 \\\end{array}\right][/tex]
Now , the product of matrices A and B is C
where the matrix C is A x B
[tex]C = \begin{pmatrix}\left(-1\right)\cdot \:3+0\cdot \:4&\left(-1\right)\cdot \:5+0\cdot \:6\\ 2\cdot \:3+7\cdot \:4&2\cdot \:5+7\cdot \:6\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C =\begin{pmatrix}-3&-5\\ 34&52\end{pmatrix}[/tex]
Therefore , the value of matrix is [tex]C =\begin{pmatrix}-3&-5\\ 34&52\end{pmatrix}[/tex]
Hence , the matrix multiplication is solved and the results are given
To learn more about matrix multiplication click :
https://brainly.com/question/13198061
#SPJ1
Related Questions
............. i need help past due
Answers
The unit rate in acres of land planned by the workers per day is found is 16/35 acres.
What is meant by rate of doing work?Power refers to the rate of work completion. It is a measure of how much energy is used up each unit of time. The joule per second (J/s) is the unit of power in the SI system.Force applied across a distance is called work. Examples such work include dragging down a confined helium balloon, driving a vehicle up a steep hill, and lifting an article against the gravitational attraction of the Earth. Energy manifests mechanically as work.For the mentioned question-
Total acres of land planted = 2/5 acres.
Total time taken = 7/8 days.
Thus, unit rate in acres per day = Total acres of land planted / Total time taken
unit rate in acres per day = (2/5) / (7/8)
unit rate in acres per day = (2*8)/(5*7)
unit rate in acres per day = 16/35
Thus, unit rate in acres of land planned by the workers per day is found is 16/35 acres.
To know more about the rate of doing work, here
https://brainly.com/question/25864308
#SPJ1
Determine if the triangles are similar by Angle-Angle similarity
Answers
The triangles are similar by Angle-Angle similarity since they are congruent.
What is Angle-Angle Similarity?According to the Angle-Angle Similarity Theorem, if two angles in one triangle are equal to two angles in another triangle, the triangles are similar. The triangles are similar if two pairs of corresponding angles in a pair of triangles are congruent. We know this because if two angle pairs are equal, then the third pair must be equal as well.
Two triangles with two angles, starting with Triangle 1, one measuring 47 degrees and the other measuring 53 degrees, are congruent to two angles in Triangle 2. Following the AA similarity theorem, it is assumed that Triangle 1 is similar to Triangle 2.
In this case, angle MNP = angle QPL (corresponding angles, //lines) (A)
angle QLP is common angle (A)
By AA, the 2 triangles are similar.
Learn more about triangles on:
https://brainly.com/question/17335144
#SPJ1
There were 234 roses growing in the back garden. If 50% of the roses were red. How many were not red?
Answers
Answer:117
Step-by-step explanation:
I’m good at math
Answer:
117 Roses
Step-by-step explanation:
234 *0.5 = 117
Draw and label a coordinate plane so that the x-axis extends from -9 to 9 and the y-axis
extends from -6 to 6. Represent each of these points with a dot, and label the point using
its letter name.
Answers
The required given Co-ordinates are plotted in graph below.
What are Co-ordinates?The numbers on a direction lattice are utilized to find focuses. Each point can be recognized by an arranged sets of numbers; that is, a number on the x-axis called a x-coordinate, and a number on the y-hub called a y-coordinate. Requested matches are written in enclosures (x-coordinate, y-coordinate).
Explain graph.Graph is characterized as to make an outline that shows a connection between at least two things. An illustration of diagram is to make a progression of bars on charting paper
According to question:coordinates plane so that the x-axis extends from -9 to 9 and the y-axis
extends from -6 to 6
Plotted points on the graph are shown in image below.
To know more about Graphs visit:
brainly.com/question/17267403
#SPJ1
What will the dividend income be on W number of shares of XYZ stock if XYZ distributes a $Y per share dividend?
Answers
Answer:
In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.
Step-by-step explanation:
The dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend. This is because the dividend income is calculated by multiplying the number of shares that an investor owns by the amount of the dividend per share.
For example, if an investor owns W = 100 shares of XYZ stock and XYZ distributes a $Y = 5 per share dividend, then the investor's dividend income will be 100 * 5 = 500 dollars.
In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.
Write an equation of the line that passes through the point (1, 4) and has a slope of -2
WIth point- intercept form
Answers
The equation of the line that passes through the point (1, 4) and has a slope of -2 is y = -2x + 6
What is slope-intercept form of a line?
The equation of the line in slope-intercept form is given by:
y = mx + c
Here,
(x, y) = Every point on the line
m = Slope of the line
c = y-intercept of the line
According to the given question:
The given line has slope m = -2 and point (1, 4) passes through the line.
By slope-intercept form general equation of line is y = mx + b where b is
y-intercept.
Substituting values of m and point (1, 4) in this equation to get value of b
y = mx + b
4 = -2(1) + b
b = 6
Hence equation of the line is y = -2x + 6
To know more about slope-intercept form visit
https://brainly.com/question/9682526
#SPJ1
(a) Write 7.97 x 10 ^-6 as an ordinary number.
Answers
Answer:
0.00000797
Step-by-step explanation:
In this diagram, the area of the large square is equal to the combined areas of the tilted square and the four right triangles.
(the picture)
When written as an equation, this relationship can be simplified algebraically, as shown in these 4 steps.
Step 1: (a + b) (a + b) = c2+ 2ab
Step 2: a2 + 2ab + b2 = c2 + 2ab
Step 3: a2 + 2ab ─ 2ab + b2 = c2 + 2ab ─ 2ab
Step 4:
What equation fits in the box in Step 4 to complete the proof
(part B)
Builders use the equation from Part A to determine the number, height, and depth of stairs necessary to extend from the first floor to the second floor of a building.
Given that the ceiling is 12 feet high, stairs are 8 inches high and the stairwell is 16 feet long, describe in detail how a builder could use the equation to determine the number, height, and depth of the stairs.
Answers
Answer:
Step-by-step explanation:
Find the measure of each acute angle in a right triangle where the measure of one acute angle is 8 times the measure of the other acute angle
Answers
The measure of the acute angles in the right triangle are 10 and 80 degrees.
How to find the angle of a right angle triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.
The sum of angles in a right angle triangle is 180 degrees.
The other measures of the right triangle are acute angles.
Any angle that measures greater than 0° and less than 90° is called an acute angle.
Hence, let's find the measure of the acute angles
let
x = measure of one acute angle
Hence,
x + 8x + 90 = 180
9x = 180 - 90
9x = 90
x = 90 / 9
x = 10
Therefore, the measure of the acute angles are 10 and 80 degrees.
learn more on right angle triangle here: brainly.com/question/13737075
#SPJ1
Damian was out at a restaurant for dinner when the bill came. His dinner came to $26. He wanted to leave a 31% tip. How much was his meal plus the tip, before tax, in dollars and cents?
Answers
Answer:
34 dollars and 6 cents
Step-by-step explanation:
1 percent = 0.26
0.26 x 31 = 8.06
26 + 8.06 = 34 dollars and 6 cents
I believe it is 34.06
Solve 3+8X+6 = 5(X+2) + 3X-1
Answers
Answer: x= (−∞,∞)
Step-by-step explanation:
3+8x+6 = 5(x+2) + 3x-1
9+ 8x = 5x +10 + 3x -1
9 + 8x = 8x +9
Subtract nine on both sides
8x= 8x
x = Any number!
Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 9x2 − 3xy + 5. The friends have already collected the following number of cans:
Jessa: 5xy + 2
Tyree: 6x2 − 5
Ben: x2
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work. (5 points)
Answers
Answer:
Part A
7x² + 5xy – 3
Part B
2x² – 8xy + 8
Step-by-step explanation:
Part A
the canned food collected so far is the sum of the canned food the three friends have by combining the expression
5xy + 2 + 6x² – 5 + x²
= 6x² + x² + 5xy + 2 – 5
= 7x² + 5xy – 3
Part B
The total of cans the friend need to collect to meet their goal is the canned food collected so far minus their targeted goal
= 9x² – 3xy + 5 – (7x² + 5xy – 3)
= 9x² – 3xy + 5 – 7x² – 5xy + 3
= 9x² – 7x² – 3xy – 5xy + 5 + 3
= 2x² – 8xy + 8
i hope this helps
The graph shows the results of a survey that asked people to choose their favorite
dinner foods. One of the persons surveyed is chosen at random.
What is the probability that she chose Potatoes?
Answers
Answer:
7.5%
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
the totally possible cases is everybody in the survey :
24+18+14+10+8+6 = 80
the desired cases are everybody having potatoes a favorite food : 6
the probability the picked person prefers potatoes is
6/80 = 3/40 = 0.075 = 7.5%
There is a dramatic change in desert temperatures from day to night because:
A: of the lack of nitrogen in the soil.
B: of the lack of water.
C: sand is such a poor insulator.
D: of the lack of vegetation
Answers
There is a dramatic change in desert temperatures from day to night because B. of the lack of water.
Why is there a change in temperature?It should be noted that because the air in the desert is so dry, heat escapes quickly at night, the temperature can vary dramatically from day to night. The temperature during the day averages 38°C, while at night it can drop to -4°C in some deserts. The temperature varies greatly depending on where you are in the desert.
During the day, the sand's radiation from the sun's energy superheats the air, causing temperatures to rise. And, because the desert air is so dry, heat escapes quickly at night, according to NASA. The desert biomes are the driest of all biomes.
Learn more about desert in:
https://brainly.com/question/24323334
#SPJ1
What is the correct prime factorization of 24? 2 ∙ 2 ∙ 6 2 ∙ 3 ∙ 3 2 ∙ 2 ∙ 3 ∙ 3 2 ∙ 2 ∙ 2 ∙ 3
Answers
Answer:
2x2x2x3
Step-by-step explanation:
Jane had 5 1/6 pecan pies. Marge had 4 3/6 pecan pies. How much pie do they had all together?
Answers
Answer:
9 4/6
Step-by-step explanation:
5 + 4 = 9
1/6 + 3/6 = 4/6
9 4/6
Hope this helps! :)
What is the answer i need answers now I'm am going to fail
pls explain to
Answers
Answer:
Step-by-step explanation:
It is not a prime factorization because the term 8 is common multiplied by 2 and the line has 2 elevated to 3 that itselt is 8.
A prime factorization should be stay equal without any commom multiples.
Select the correct answer. about 1,500,000 bacteria are found in 1 milliliter of water of coastal ocean. how many bacteria will be there in 100 milliliters of water? a. 1.5 × 104 b. 1.5 × 105 c. 1.5 × 106 d. 1.5 × 107 e. 1.5 × 108
Answers
The amount of bacteria that will be there in 100 milliliters of water will be: 1.5 × 10⁸.
What is standard notation?A standard notation is a method of writing a given number, equation, or expression in a specific format that adheres to certain rules. 4.5 billion years, for example, is written as 4,500,000,000 years.
The main reason for converting numbers to scientific notation is to make calculations involving unusually large or small numbers easier.
Even though zeros are no longer always seemed to set the decimal point, all digits in a scientific notation number are significant.
Here, it is given that,
The number of bacteria found in 1 milliliter of water = 1,500,000.
So,
The number of bacteria in 100 milliliters of water = 1,500,000 x 100
The number of bacteria in 100 milliliters of water = 15,00,00,000
The number of bacteria in 100 milliliters of water = 1.5 × 10⁸.
Correct option: e
To know more about standard notation refer to:
brainly.com/question/10253124
#SPJ4
Reflect TIY across y=x to map onto DOG.
(PLEASE HELP!)
Answers
The coordinates will be after applying the transformation, I(-5,0) --I'(0, -5), Y(0, 2) - -> Y'(2, 0) and T(4, 4) --> T'(4, 4).
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The graph is shown in the picture.
From the picture the coordinates are:
I(-5,0), Y(0, 2), and T(4, 4)
The transformation rule:
(x, y) --> (y, x)
I(-5,0) --I'(0, -5)
Y(0, 2) - -> Y'(2, 0) and
T(4, 4) --> T'(4, 4)
Thus, the coordinates will be after applying the transformation, I(-5,0) --I'(0, -5), Y(0, 2) - -> Y'(2, 0) and T(4, 4) --> T'(4, 4).
Learn more about the geometric transformation here:
brainly.com/question/16156895
#SPJ1
The number of students in attendance since 2000 at Lamar Community College can be represented by the equation below, where x equals the time in years after 2000. S(x) = (x - 50)² + 19 The college creates a graph to better view the decreases and increases in attendance. Which of the following describes the end behavior of their graph? O A. As x approaches positive infinity, S(x) remains constant. OB. As x approaches positive infinity, S(x) approaches positive infinity. OC. As x approaches positive infinity, S(x) approaches zero. OD. As x approaches positive infinity, S(x) approaches negative infinity.
Answers
As domain x approaches positive infinity, S(x) approaches positive infinity. Option B is correct.
What is a graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Given expression for the attendance of the student is,
S(x) = (x - 50)² + 19
The end behavior of their graph is given as after x = 50 the graph starts heigh increasing gradient and it keeps increasing, till x = infinity, as shown in the graph.
Thus, the curve of the given equation S(x) will increase from x = 50 to x = ∞ .
Learn more about graphs here:
brainly.com/question/16608196
#SPJ1
The volume of a cylinder having height one and half of the radius is 12,936 m3 what minimum square cm of paper is needed to cover the curved surface area of the cylinder? The answer should be 1848m2. please solve my question.
Answers
Answer:
Lateral Surface Area = 1848 m^2 (does not include the top and bottom)
Step-by-step explanation:
Vol Cylinder = pi*r^2 *h
h = (3/2)r
Vol = pi*r^2((3/2)r) [We are told that the volume is 12,936 m^3]
pi*r^2((3/2)r) = 12,936 m^3
pi*(3/2)*(r^3) = 12,936 m^3
pi*r^3 = (12,936 m^3)*(2/3)
pi*r^3 = 8,624 m
r^3 = (8,624 m)/(3.14)
r^3 = 2745.1
r = 14.0 m
Lateral Surface = 2*(pi)*r*h [Lateral is just the curved portion of the right cylinder.
Lateral Surface Area = 2*(3.14)*(14.0)(21.0)
Lateral Surface Area = 1848 m^2
The number of beads in a jar is 50 to the nearest ten.
(a) What is the minimum possible number of beads in the jar?
(b) What is the maximum possible number of beads in the iar?
Answers
b) the maximum possible number of beads in the jar is 54
Answer:
a) 45
b) 54
Step-by-step explanation:
a) To be able to round up to the nearest 10, the number in the "ones column" needs to be 5 at the minimum.
You could argue it could be a decimal point however, you shouldn't really have a decimal of a bead ( it's possible but it over complicates the answer ) and, it's to the nearest 10, not nearest one decimal point for example.
Therefore, the min is 45 beads
b) ( The above poster was correct oops, I made a silly mistake )
The max is 54 beads as if anything in the ones column is under 4, you can't round up to the nearest 10. Hence it remains as 50 when rounding
Therefore, the max is 54 beads
In \triangle EFG,△EFG, \angle E \cong \angle G,∠E≅∠G, GE = 17GE=17 and FG = 10FG=10. Find the length of EF. EF
Answers
In the triangle EFG, ∠E≅∠G, GE = 17 units and FG = 10 units, then the length of the side EF is 10 units
The given triangle EFG
The length of the side GE = 17 units
The length of the side FG = 10 units
The measure of angle E is equal to the measure of angle G
The equation will be
∠E≅∠G
Therefore the triangle is Isosceles triangle
The length of the side FG will be equal to the length of the side FE
The length of the side EF = The length of the side FG = 10 units
Therefore, the length of the side EF is 10 units
Learn more about isosceles triangle here
brainly.com/question/10147636
#SPJ4
what is (-4x² + 3x + 3)(x² - 2x + 2) as a polynomial
Answers
The given expression is in the form of the polynomial as -4x⁴+11x³-5x²+6 and the degree of the polynomial is 4.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that the polynomial expression is, (-4x² + 3x + 3)(x² - 2x + 2)
We have to simplify the expression by multiplying the expression as,
=-4x²(x² - 2x + 2)+3x(x² - 2x + 2)+3(x² - 2x + 2)
=-4x⁴+8x³-8x²+3x³-6x²+6x+3x²-6x+6
= -4x⁴+11x³-5x²+6
Thus, the given expression is in the form of the polynomial as -4x⁴+11x³-5x²+6 and the degree of the polynomial is 4.
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ1
how would your conclusion change if your sample mean had been 1.355 mg/l? what point does this make about statistical significance?
Answers
A small change in x can change the conclusion of our test.
Given :
how would your conclusion change if your sample mean had been 1.355 mg/l.
t - test :
A t-test is a statistical test that compares the means of two samples. It is used in hypothesis testing, with a null hypothesis that the difference in group means is zero and an alternate hypothesis that the difference in group means is different from zero.
if x = 1.355
t = 1.355 - 1.3 / 0.18 / [tex]\sqrt{30}[/tex]
= 0.055 / 0.18 / [tex]\sqrt{30}[/tex]
= 0.055 * [tex]\sqrt{30}[/tex] / 0.18
= 1.67
df = n - 1
= 30 - 1
= 29
P - value from t table :
p = 0.525
fail to reject [tex]H_0[/tex]
Learn more about the sample mean here:
https://brainly.com/question/14127076
#SPJ4
Full question :
The Environmental Protection Agency has determined that safe drinking water should contain no more than 1.3 mg/liter of copper. You are testing water from a new source, and take 30 water samples. The mean copper content in your samples is 1.36 mg/l and the standard deviation is 0.18 mg/l. There do not appear to be any outliers in your data .
how would your conclusion change if your sample mean had been 1.355 mg/l? what point does this make about statistical significance?
*URGENT* I need help with 5,6,7 please answer correctly and quickly
Answers
Answer:
Step-by-step explanation:
(5). ( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~~~~
( 4 , 8 )
y = [tex]\frac{1}{7}[/tex] x - 5 ; slope m = [tex]\frac{1}{7}[/tex]
Slope of line ⊥ to the given line is opposite reciprocal to [tex]\frac{1}{7}[/tex] and equal to ( - 7)
y - 8 = - 7( x - 4 )
(6).
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{ y_{2} -y_{1} }{ x_{2} -x_{1} }[/tex]
y = mx + b
~~~~~~~~~~~~
( 4 , 3 )
( 5 , 1 )
m = [tex]\frac{1-3}{5-4}[/tex] = - 2
y - 3 = - 2( x - 4 )
y = - 2x + 11
(7). y = - [tex]\frac{1}{2}[/tex] x + 2
which statement about the graph of y=3x+5 is correct?
Answers
The correct statement regarding the linear function y = 3x + 5 is given as follows:
The line passes through the ordered pair (0,5) and has a slope of 3.
What are the slope and the intercept of the linear function?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
The slope and the intercept are given as follows:
m is the slope, representing the rate of change of the linear function.The intercept is of b, representing the numeric value of the function when the input is of zero, hence the line passes through the ordered pair (0,b).In this problem, the function is defined as follows:
y = 3x + 5.
Hence the coefficients have the values given as follows:
m = 3, b = 5.
Missing InformationThe statements are given by the image shown at the end of the answer.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Is 38 / 53 and simplest form explain? Why t? Or or why not
Answers
yes 38/53 is the simplest form
Step-by-step explanation:
The fraction is already reduced.
3. The coordinate (4, 3) is the solution to which system of equations?
Answers
The coordinate (4, 3) is the solution of the following system of equations:
y = 1/2x + 1 and y = -x + 7
y = x - 1 and y = 1/4x + 2
The solution implies that the coordinate is the: point of intersection.
What is the Solution to a System of Equations?The solution to a system of equations are the coordinate of the point where the two lines that represent the equations of the system intersect each other. The coordinate of x and the coordinate of y, when plugged into any of the equations would be true.
The graph of the system of equations, y = x - 1 and y = 1/4x + 2 shows that both equations intersect at the point with the coordinate (4, 3) [see the graph in figure 1].
Also, the graph in figure two shows that y = 1/2x + 1 and y = -x + 7 also intersect at (4, 3).
Therefore, we can state that, the system of equations with (4, 3) as the solution are:
y = 1/2x + 1 and y = -x + 7
y = x - 1 and y = 1/4x + 2
The solution means point of intersection.
Learn more about the system of equations on:
https://brainly.com/question/13729904
#SPJ1
2. Fill in the blanks to factor the trinomial 3x² + 13x - 10 by grouping.
3x² + 13x - 10 = 3x² -
=
3x²-x+.
_X+X-10
(3x - 2) +(3x - 2)
+
)(3x - 2)
Answers
Answer:
-2 and 15x and 5x and 5Step-by-step explanation:
You want the steps involved in factoring 3x² +13x -10 by grouping.
FactorsTo fill in the blanks, you need to know the product of the first and last coefficients, and the factor pairs of that product that have a sum equal to the middle coefficient.
3(-10) = -30 = (-1)(30) = (-2)(15) = (-3)(10) = (-5)(6)
The sums of these factor pairs are 29, 13, 7, 1. The sum of interest is ...
-2 + 15 = 13
These are the values that go in the first pair of blanks.
= 3x² -2 x + 15 x -10
Factors of pairsWe want to identify the common factor for each pair of terms:
= x (3x -2) + 5 (3x -2)
Factored trinomialFinally, the common factor (3x -2) is removed and we have ...
= ( x + 5 )(3x -2)