None of the statements (1) to (6) are true about the equation [tex]x^2-6x+2=0[/tex].
What does a math quadratic equation mean?Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd polynomial formula in a variable. a 0. It has at least 1 solution since it is a 2nd polynomial equation, which is guaranteed by the algebraic theorem. The solution might be simple or difficult.
None of the statements (1) to (6) are true about the equation. [tex]x^2-6x+2=0[/tex].
Reason why:
(1) The coefficient of the [tex]x^2[/tex] term is positive, so the graph of the quadratic equation is a parabola that opens upward. Therefore, it does not have a minimum value, but instead has a minimum point.
(2) The coordinates of the minimum point can be found using the formula x = -b/2a, which gives x = 6/2 = 3. Substituting x = 3 into the equation gives y = 2, so the minimum point is (3, 2).
(3) The point (7,-3) is not on the graph of the equation.
(4) The solutions to the equation are given by the quadratic formula x = [tex][6\± \sqrt{(6^2 - 4(1)(2))]}/2 = [6\± \sqrt{(28)]}/2 = 3\± \sqrt{7}[/tex]. So, statement (4) is partially correct, but the value of -3 is incorrect.
(5) Statement (5) is correct, as the solutions to the equation are x = [tex]3\±\sqrt7}[/tex].
(6) The graph of the quadratic equation has a minimum value, not a maximum value.
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Complete question is: Which of the following statements are true about the equation below?
x^2-6x+2=0
( 1 ) The graph of the quadratic equation has a minimum value.
( 2 ) The extreme value is at the point (3,-7).
( 3 ) The extreme value is at the point (7,-3).
( 4 ) The solutions are x = -3 + or - the square root of 7 .
( 5 ) The solutions arex = 3 + or - the square root of 7.
( 6 ) The graph of the quadratic equation has a maximum value.
PART 2: TABLE 1: Mr. Flynn found that his car can drive 12,5km for every litre of petrol it consumes. This helps him to be sure that he has enough petrol when driving certain distances - due to the nature of his work. The table below represents the car's petrol consumption. The extreme petrol price per litre of R22,50 also impacts Mr. Flynn's travelling. Study the table and answer the questions that follow. 2.1 2.2 2.3 4 2.4 PETROL CONSUMPTION VERSUS TRAVEL DISTANCE (OBSERVABLE PATTERN) DISTANCE TRAVELLED PER LITRE PETROL CONSUMED Litres of Petrol 0 1 2 3 B 5 6 7 8 Distance to Travel (km) A 12,5 25,0 37,5 50,0 62,5 C 87,5 100 Describe the general relationship between distance travelled and litres
The proportional relationship between distance traveled and liters spent is given as follows:
y = 0.08x.
What is a proportional relationship?A proportional relationship is defined by a linear model with intercept of zero as follows:
y = kx.
In which k is the constant of proportionality.
Mr. Flynn found that his car can drive 12,5km for every litre of petrol it consumes, hence the constant is given as follows:
k = 1/12.5
k = 0.08.
Then the equation is given as follows:
y = 0.08x.
In which:
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Calc !
PLEASEE HELPP!
The size of a certain insect population is given by P(t) = 200e0.01t, where t is
measured in days. At what time will the population equal 1000?
Answer:
Your answer is about t = 621.5 days the population of insect will equal to 1000.
Step-by-step explanation:
Given:
[tex]P(t)=200e^{0.01t}[/tex] and population equal to 1000?
You are trying to find t in number of days when the insect population reaches equal to 1000 so.
[tex]1000=200e^{0.01t}\\\\\frac{1000}{200}=e^{0.01t} \\\\500=e^{0.01t}\\\\ln(500)=0.01t\\\\t=\frac{ln(500)}{0.01} \\\\t=621.4608098[/tex]
Answer
109.861 days
Step-by-step explanation:
a) initial population means when t=0, p(0)=500
b) dP/dt=5e^.01t
c)500e.01t =1000 (divide both sides of eq by 500)
e.01t =2 (take natural log of both sides)
ln( e.01t)=ln(2)
.01t= ln(2) (divide both sides of the eq by .01)
t= ln(2)/.01
t=69.315 days
d) 500e.01t=1500
(repeat steps in (c) above and you will get)
t=ln(3)/.01
t=109.861 days
a forest of 800 trees is exposed to a disease that kills 1/4 of the trees per year. how many trees will be left after after 11 years? round your answer to the nearest whole number
Answer:
34
Step-by-step explanation:
34 trees will be left after 11 years
The manager at Frydays sets a company goal to receive consistent, positive ratings by customers on social media over the next month.
The correct answer is (b) Ratings with a high mean and a low mean absolute deviation.
What is the mean absolute deviation?
Mean absolute deviation (MAD) is a statistical measure of how much the data values in a set deviate from the mean of the set.
Given options are
a. Ratings with a high mean and a high mean absolute deviation
b. Ratings with a high mean and a low mean absolute deviation
c. Ratings with a low mean and a high mean absolute deviation
d. Ratings with a low mean and a low mean absolute deviation
The manager at Frydays wants to receive consistent, positive ratings by customers on social media over the next month. Consistency means that the ratings are close to each other, and positive ratings mean that they are higher than average. Therefore, the goal is to have ratings with a high mean and a low mean absolute deviation.
The mean is a measure of central tendency that represents the average rating of customers, and a high mean indicates that the ratings are positive. The mean absolute deviation (MAD) is a measure of dispersion that represents how spread out the ratings are from the mean. A low MAD indicates that the ratings are close to each other and consistent.
Hence, The correct answer is (b) Ratings with a high mean and a low mean absolute deviation.
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The area of AQRS is 14 square feet. What is the area, in square feet, of the image of AQRS after dilation with scale factor 2?
The area of the image of AQRS after dilation with scale factor 2 is 56 square feet.
What is the area, in square feet, of the image of AQRS after dilation with scale factor 2?Given the data in the question;
Area of AQRS = 14 square feetArea of image AQRS after dilation with scale factor 2 ?If we dilate a figure with a scale factor of 2, the area of the dilated figure will be 2² = 4 times the area of the original figure.
So, to find the area of the image of AQRS after dilation with scale factor 2, we just need to multiply the area of AQRS by 4:
Area of dilated image = 4 × Area of AQRS
Area of dilated image = 4 × 14
Area of dilated image = 56 square feet
Therefore, the area of the image of AQRS is 56 square feet.
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The area of AQRS is 14 square feet. What is the area, in square feet, of the image of AQRS after dilation with scale factor 2?
The area of the image is 56ft²
What is area scale factor?A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.
The area scale factor is the square of the linear scale factor.
Therefore area scale factor = 2² = 4
Therefore the area of the image of the triangle = 14× 4
= 56ft²
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b) On average, about 240 people visit a local food pantry every day in search of groceries. On an extremely cold day, visitors to the food pantry can be 175% of the average amount. About how many visitors might go to the food pantry on an extremely cold day?
About 420 visitors might go to the food pantry on an extremely cold day
What is the percentage?
Percentage refers to a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, if 30 out of 100 students in a class are girls, the percentage of girls in the class is 30%. Percentages are commonly used in many fields, such as finance, statistics, and science, to express proportions, rates, and changes over time.
The problem states that on average, about 240 people visit the food pantry every day in search of groceries. To find out how many visitors might go to the food pantry on an extremely cold day, we need to use the given percentage increase.
The phrase "175% of the average amount" means that we need to find 175% of 240, which is the same as multiplying 240 by 1.75 (since 175% is the same as 1.75 as a decimal). Using the multiplication, we get:
175% of 240 = (175/100) * 240 = 420
So, on an extremely cold day, the number of visitors to the food pantry might be around 420.
Therefore, about 420 visitors might go to the food pantry on an extremely cold day.
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2(4+62)-20divided by 4
Answer:
the answer is 28
4+62 = 66
66x2 = 132
132-20 = 112
112 divided by 4 = 28
hope this helps <3
Answer:
28
Step-by-step explanation:
i hope this helps
solve for x. 4(x+56.5)=30x-112
Answer:
x = 13
Step-by-step explanation:
Let's simplify and solve for x:
4(x+56.5) = 30x - 112
First, we distribute the 4:
4x + 4(56.5) = 30x - 112
Simplifying the expression:
4x + 226 = 30x - 112
Now we move all the x terms to one side and all the constants to the other:
226 + 112 = 30x - 4x
338 = 26x
Finally, we solve for x by dividing both sides by 26:
x = 13
Therefore, the solution to the equation 4(x+56.5)=30x-112 is x = 13.
Answer:
x=9.94
Step-by-step explanation:
4x + 226 = 30x - 112
226+112 = 34x
338 = 34x
338/34=x
9.94=x
A retailer buys merchandise from a supplier with an invoice amount of $12,400. The terms of the sale are 6/20, n/30. What is the net amount due (in $) on the order if the bill is paid by the 20th day?
If the retailer pays the invoice within 20 days and takes the discount, the net amount due is $11,656.
The sale's "6/20, n/30" clause allows the retailer to choose between paying the invoice in full within 30 days or taking advantage of a 6% discount if they do it within 20 days. If the bill is paid by the 20th day, we can determine the net amount owed as follows:
Then, we multiply the invoice amount by the discount rate to determine the amount of the discount:
Discount: $744 ($12.400 x 0.06)
The amount owed if the discount is taken is then determined by deducting the discount from the invoice amount:
Discounted amount due: $12,400 - $744 = $11,656
The net amount owed is therefore $11,656 assuming the store pays the invoice within 20 days and applies the reduction.
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If 3 men can load a lorry of goods in 2 h, how long will it take (a) 6 men. (b) 5 men, and (e) 2 men, to load the lory of goods if they work at the same rate?
Answer:
Below
Step-by-step explanation:
A) this one is easy....twice the manpower would take 1/2 the time = 1 hr
B) this requires a bit of calculation find man-hrs required per lorry
(3 men x 2 hr )/1 lorry = 6 man hours per lorry
then: 5 men * x hr = 6 man hours
x = 6/5 hr ( 1 hr 12 min)
C) similar to B 2 men * x hr = 6 man hrs
x = 6/2 hrs = 3 hrs
Answer:
see below
Step-by-step explanation:
more men = more hands = more help = less hrs cos faster
so your ans must be..
more men = less hrs
less men = more hrs
if...
3 men = 2hrs
1 man = 2hrs x 3 = 6hrs
so...
6 men = 6hrs ÷ 6 = 1 hr
5 men = 6hrs ÷ 5 = 6/5hr = 1 1/5hrs
2 men = 6hrs ÷ 2 = 3hrs
The surface area of a right rectangular prism can be found by finding the sum of the area of each of the faces of the prism. What is the surface area of a right rectangular prism with length 4 centimeters (cm), width 9 cm, and height 3 cm? (Area of a rectangle is equal to length times width.)
The surface area of right rectangular prism is equal to 150 square centimeter
What is the surface area of a right rectangular prism?The surface area of a right rectangular prism can be found by finding the sum of the area of each of the faces of the prism.
A = 2(lw + hl + hw)
Where, "l" is the length and "h" is the height and "w" is the width
To determine the surface area of right rectangular prism.
Given the paramters as;
length = 4 cm
width = 9 cm
height = 3 cm
Substituting the given values, we get;
A = 2(lw + hl + hw)
A = 2 (36 + 27 + 12)
A = 150
Thus, surface area of right rectangular prism is 150 square centimeter
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Find an equation of the straight line passing through the points (4, 3) and (2, -5).
The equation of the straight line is 4x -y = 13. It is general form of equation of a line.
What is a line?
A line has length but no width, making it a one-dimensional figure. A line is made up of several points that are endlessly extended in opposite directions. Two points in a two-dimensional plane determine it. Collinear points are described as two points that are on the same line.
The equation of a line that passes through the points (x₁, y₁) and (x₂, y₂) is
y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).
The coordinates of the points are (4, 3) and (2, -5).
The slope of the line is (-5-3)/(2-4)
=-8/-2
= 4
The equation of line is
y - 3 = 4(x - 4)
→ y - 3 = 4x - 16
→ 4x -y = 13
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jack has 375in of sand to pour into a rectangular prism the base of the prism is 5 by 7 and the hight is 9 will the sand fit explain why or why not
Answer:
Yes, it will fit.
Step-by-step explanation:
To determine whether 375 cubic inches of sand will fit into the given rectangular prism, we need to calculate the volume of the prism and compare it to the amount of sand.
The formula for the volume of a rectangular prism is:
Volume = Base x Height x Width
In this case, the base of the prism is 5 by 7 inches, so the area of the base is:
Area of Base = 5 inches x 7 inches = 35 square inches
The height of the prism is 9 inches. Therefore, the volume of the prism is:
Volume = Base x Height = 35 square inches x 9 inches = 315 cubic inches
So, the volume of the prism is 315 cubic inches, which is less than the amount of sand Jack has (375 cubic inches). Therefore, all of the sand will fit inside the rectangular prism with room to spare.
In summary, the sand will fit inside the rectangular prism because the volume of the prism is greater than the amount of sand Jack has.
Find the slope of the line that passes through the points (-2,3) and (7.-4).
Answer:
Slope is [tex]\frac{7}{-9}[/tex]
Step-by-step explanation:
For this problem we must use the slope formula:
[tex]\frac{change* in *y}{change*in*x}[/tex]
Our 2 y coords are: 3, -4
To find the change in y, we must subtract.
3 - ( -4 ) = 7
Our 2 x coords are: -2, 7
-2 - 7 = -9
Therfore, our answer is
[tex]\frac{7}{-9}[/tex]
Maria and Connor are doing yard work for a neighbor. They make a total of $595.54. Since Connor works more hours than Maria, Connor gets 69% of the money. About how much (in whole
dollars) does Connor make?
Connor makes about
Answer: Since Connor gets 69% of the money, Maria gets the remaining 31%:
100% - 69% = 31%
Let's first find out how much money Maria makes:
Maria's share = 31% of $595.54
Maria's share = 0.31 x $595.54
Maria's share = $184.61
Now, to find out how much Connor makes, we can subtract Maria's share from the total:
Connor's share = Total - Maria's share
Connor's share = $595.54 - $184.61
Connor's share = $410.93
Therefore, Connor makes about $410.93 (rounded to the nearest dollar).
Step-by-step explanation:
Kara has 47 stickers.She buys 20 more stickers. How many stickers does she have now?Repeat for this problem.Tyrone has 30 stickers and buys 52 more stickers.How many stickers does he have now?
Answer:
Kara has 67 in total
Tyrone has 82 in total
and together they have 149
im not to sure what your asking but heres what i got...
pls help i will give 10 points to the first person to answer this question
The coordinates of the points on the number line are given as follows:
A = -2/3.B = -1/6.C = 1/2.D = 4/3.How to obtain the coordinates on the number line?Point C is exactly halfway between 0 and 1, hence it's coordinate is given as follows:
C = 0.5.
C is also the third dot between 0 and 0.5, hence the amount represented by each space is given as follows:
0.5/3 = 1/6.
Point B is one space to the left of 0, hence it's coordinate is given as follows:
B = -1/6.
Point A is three spaces to the left of point B, hence it's coordinate is given as follows:
A = -1/6 - 3 x 1/6 = -4/6 = -2/3.
Point D is two spaces to the right of 1, hence:
D = 1 + 2x 1/6 = 1 + 1/3 = 4/3.
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The following is data for the first and second Quiz scores for 8 students in a class.
First Quiz Second Quiz
14
16
29
42
43
44
47
48
11
17
31
35
37
37
38
43
Plot the points in the grid below, then sketch a line that best fits the data.
50+
45
40-
35
30
25
20
15
10-
5+
Clear All Draw:
5 10 15 20 25 30 35 40 45 SC
YAY
The equation of the line of best fit is ŷ = 0.8x + 3.3
How to determine the equation of the line of best fitFrom the question, we have the following parameters that can be used in our computation:
X- 14 16 29 42 43 44 47 48
Y- 11 17 31 35 37 37 38 43
When these values are entered in a graphing calculator, we have the following summary:
Sum of X = 283Sum of Y = 249Mean X = 35.375Mean Y = 31.125Sum of squares (SSX) = 1343.875Sum of products (SP) = 1055.625For the regression equation, we have
ŷ = bX + a
Where
b = SP/SSX = 1055.63/1343.88 = 0.78551
a = MY - bMX = 31.13 - (0.79*35.38) = 3.33764
So, we have
ŷ = 0.78551x + 3.33764
Approximate
ŷ = 0.8x + 3.3
Hence, the equation is ŷ = 0.8x + 3.3
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PLEASE HELP ASAP NOWS YOU CHANCE FOR BRANLIST AND POINTS Polygon JKLM is drawn with vertices J(-4,-4), K(-4, -6), L(-1, -6), M (-1, -4). Determine the image coordinates of L' if the preimage is reflected across y =
-2. OPTIONS ARE BELOW
L'(-3, 6)
OL'(-1,6)
OL'(-1, 2)
OL(1, 2)
The correct answer is (C) OL'(-1, 2) - This point is on the reflected line y=-2, but its y-coordinate is not consistent with the reflection of L. The correct y-coordinate is -4.
What is line?
A one-dimensional geometric figure that consists of infinitely many points arranged in a straight path or direction.
In this case, we are reflecting across the line y = -2, which is two units below the x-axis. Therefore, the y-coordinate of each point in the preimage will be changed by 2 units after reflection.
The coordinates of L are (-1, -6), and after reflecting across y = -2, the y-coordinate will become
-6 + 2 = -4
Therefore, the image of L, L', will have coordinates (-1, -4).
Looking at the given options:
A. L'(-3, 6) - This point is not on the reflected line y=-2, so it cannot be the reflection of L.
B. OL'(-1,6) - This point is above the reflected line y=-2, so it cannot be the reflection of L.
C. OL'(-1, 2) - This point is on the reflected line y=-2, but its y-coordinate is not consistent with the reflection of L. The correct y-coordinate is -4.
D. OL(1, 2) - This point is not on the reflected line y=-2, so it cannot be the reflection of L.
Therefore, the correct answer is option C: L'(-1, -4).
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need help with problem 8
Hence, a 93% confidence range for the actual proportional difference between the two populations equation (represented by the two samples) is between -0.086 and 0.142.
What is the equation?A mathematical equation connects two statements with the equals sign (=), which stands for equivalence. The equivalence of two mathematical propositions is established by a mathematical assertion that is utilized in algebraic equations. For instance, the equal sign separates the numbers 3x + 5 and 14 in equation 3x + 5 = 14. Use a mathematical formula to understand the relationship between the two sentences written on opposite sides of a letter. Usually, the program's particular logo matches it. A good example is 2x - 4 = 2.
For the initial example:
Sample proportion: 0.649 (p1 = 24/37)
Standard deviation SE1 is equal to
[tex]\sqrt{(p^1*(1-p^1))} /n1=\sqrt{(0.649*(1-0.649))/37)0.087}[/tex]
Regarding the second example:
P2 = 54/87 0.621 is the sample proportion.
The standard deviation SE2 is equal to
[tex]\sqrt{(p^2*(1-p^2))} /n2=\sqrt{(0.621*(1-0.621))/87)0.72}[/tex]
The crucial value for a 93% confidence interval has to be calculated next. We may use the conventional normal distribution and large sample size to obtain the z-value that represents the center 93% of the distribution:
[tex]1.812z=invNorm(\frac{1+0.93}{2} )[/tex]
We can finally determine the confidence interval:
CI is equal to (p1-p2) z*sqrt(SE12 + SE22)
CI is calculated as (0.649 - 0.621) 1.812*sqrt(0.0872 + 0.0722)
CI = 0.028 ± 0.114
CI = (−0.086, 0.142)
The real proportional difference between the two populations (represented by the two samples) thus lies between -0.086 and 0.142, with a 93% confidence interval.
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Here's a playground for a school of 360 children in Springfield.
1. The fence around the playground costs 90 dollars per 50-foot roll. Laying the grass across the area costs 400 dollars per 500 square feet. How much did the fencing and grass for this playground cost to build?
2. How many kids per square yard can Springfield's playground hold?
3. There's a new playground going up in nearby Wintermeadow. Wintermeadow has a budget about 3 times greater than Springfield's. Recommend a playground shape and size that would fit Wintermeadow's budget and hold at least 3 times as many kids as Springfield's playground at the same density of kids per square yard. How many kids can your playground hold?
1. The fencing and grass for this playground cost $16,360.
2. Springfield's playground can hold approximately 800 kids at a density of 25 square feet per child.
3. We can recommend a rectangular playground measuring approximately 166 yards by 40 yards, with a total area of 6,666.67 square yards. This playground should cost $49,200 for the fencing and grass.
How did we arrive at these values?1. To calculate the cost of the fencing and grass, we first need to know the dimensions of the playground. Let's assume that the playground is a rectangular shape measuring 100 feet by 200 feet, for a total area of 20,000 square feet.
To determine the cost of the fence, we need to know how many rolls of fencing are required. Each roll is 50 feet long, so we need four rolls to fence the perimeter of the playground (100 + 100 + 200 + 200 = 600 feet / 50 = 12 rolls, but we can't buy half a roll, so we round up to four rolls). Therefore, the cost of the fence is:
4 rolls x $90/roll = $360
To determine the cost of the grass, we need to know how many square feet of grass we need to cover the playground. Since each roll of grass covers 500 square feet, we need:
20,000 sq ft / 500 sq ft per roll = 40 rolls of grass
Therefore, the cost of the grass is:
40 rolls x $400/roll = $16,000
Adding the cost of the fence and the grass, we get the total cost:
$360 + $16,000 = $16,360
So the fencing and grass for this playground cost $16,360.
2. To calculate how many kids per square yard the playground can hold, we need to know the area of the playground in square yards. There are 9 square feet in a square yard, so the playground measures:
20,000 sq ft / 9 sq ft per sq yd = 2,222.22 sq yds
Assuming that each child requires 25 square feet of space to play, we can calculate how many kids can fit on the playground:
2,222.22 sq yds x (9 sq ft per sq yd / 25 sq ft per child) = 800 kids
Therefore, Springfield's playground can hold approximately 800 kids at a density of 25 square feet per child.
3. To recommend a playground shape and size that would fit Wintermeadow's budget and hold at least 3 times as many kids as Springfield's playground at the same density of kids per square yard, we first need to know Wintermeadow's budget.
Let's assume that Springfield's budget is $50,000, so Wintermeadow's budget is $150,000.
To determine the size of the new playground, we can start by calculating the cost of the fencing and grass for Springfield's playground per square yard:
$16,360 / 2,222.22 sq yds = $7.38 per sq yd
We can then use this cost to estimate the size of the new playground. Let's assume that the new playground will also be rectangular, and that we want it to hold at least 3 times as many kids as Springfield's playground, or 2,400 kids. Using the same density of 25 square feet per child, we need:
2,400 kids x 25 sq ft per child = 60,000 sq ft
Since there are 9 square feet in a square yard, this is:
60,000 sq ft / 9 sq ft per sq yd = 6,666.67 sq yds
Multiplying this area by the cost per square yard, we get the cost of the fencing and grass for the new playground:
6,666.67 sq yds x $7.38 per sq yd = $49,200
Therefore, we can recommend a rectangular playground measuring approximately 166 yards by 40 yards, with a total area of 6,666.67 square yards. This playground should cost $49,200 for the fencing and grass.
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What percentage of votes did the last-place candidate receive?
The percentage of votes received by the last or fourth candidate in the example election is about 6.4%
What is a percentage?A percentage is a representation of a fraction of an b expressed using a denominator of 100.
A percentage is a representation of a part of whole as a fraction of 100
Therefore, the percentage of votes that a last place candidate in an election receives is the number of votes that the last candidate receives represented as a fraction of the total number of votes with the denominator of the fraction being 100.
An example of an election result is an election result in which the votes received by the four leading candidates can be presented as follows;
Party A = 8,794,726
Party B = 6,984,520
Party C = 6,101,533
Part D = 1,496,687
The percentage of votes received by the Party D is therefore;
% received by party D = ((1,496,687)/(8,794,726 + 6,984,520 + 6,101,533 + 1,496,687)) × 100 ≈ 6.4%The candidate of votes received by the fourth candidate, that received the least number of votes is 6.4%
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Solve:
|-6x|=30
no solution
x = 6 and x=10
x = -5 and x =5
x= -1 and x=-4
Answer:
x = -5 and x =5
Step-by-step explanation:
However, we notice that the solutions -5 and 5 satisfy the original equation in case 2, because |-6(-5)| = 30 and |-6(5)| = 30 is true. Therefore, the two solutions that satisfy the original equation in both cases are x = 5 and x = -5.
Hence, the solution to the equation |-6x| = 30 is x = 5 and x = -5.
Using matrix method solve the following simultaneous equations 1x + 4y = 9 2x-3y=7
Thus, using the matrix technique, the solutions to the simultaneous equations are x = -1 and y = 1.
what is matrix ?A rectangular array of numbers or even other mathematical objects that can perform actions like addition and multiplication is known as a matrix. Matrices are widely used to describe systems of equations, transformations, and data in mathematics, physics, engineering, computer science, and many other disciplines. The individual matrix components are frequently identified by their row and column positions, and matrices have a predetermined number of rows and columns. There are numerous actions that can be carried out on matrices, including addition, subtraction, and multiplication by other matrices.
given
We can write the equations in matrix form as follows to answer the simultaneous equations 1x + 4y = 9 and 2x - 3y = 7 using the matrix method:
Then, on the left side of the equation, we can locate the inverse of the coefficient matrix:
| 1 4 |^-1 = 1/(-11) | -3 -4 |
|-2 -1 |
When we multiply both sides of the equation by the coefficient matrix's inverse, we obtain:
| x | | 1 4 |^-1 | 9 |
| x | | -3/11 -4/11 | | 9 |
| y | = | -2/11 -1/11 | x | 7 |
If we simplify, we get:
x = (-3/11)*9 + (-4/11)*7 = -1
y = (-2/11)
*9 + (-1/11)
*7 = 1
Thus, using the matrix technique, the solutions to the simultaneous equations are x = -1 and y = 1.
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You create a masterpiece in your art studio and it is selected for an art exhibition. Your painting is 70 inches by 100 inches, and you choose framing that costs $4.95 per yard. Find the cost of framing.
The cost of framing for the masterpiece is $46.73.
How to calculate thisTo calculate the cost, we need to first determine the perimeter of the artwork.
Given the dimensions of the artwork, the perimeter is 100 + 100 + 70 + 70 = 340 inches.
The cost of framing is $4.95 per yard, so we need to convert the perimeter to yards.
To do this, we divide the perimeter by 36 inches since 1 yard equals 36 inches.
Thus, 340 inches divided by 36 inches equals 9.44 yards.
Therefore, the cost of framing the artwork will be 9.44 yards multiplied by $4.95 per yard, which equals $46.73.
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Cai and his children went into a movie theater and will buy bags of popcorn and pretzels. He must buy a maximum of 7 bags of popcorn and pretzels altogether. Write an inequality that would represent the possible values for the number of bags of popcorn purchased, � b, and the number of pretzels purchased, � . p.
Answer: b + p ≤ 7
Step-by-step explanation:
Let's use b to represent the number of bags of popcorn purchased and p to represent the number of bags of pretzels purchased.
Since Cai can buy a maximum of 7 bags of popcorn and pretzels altogether, we know that:
b + p ≤ 7
This is the inequality that represents the possible values for the number of bags of popcorn purchased (b) and the number of bags of pretzels purchased (p).
the width of a rectangle is 2 units less than the length. The area of the rectangle is 15 square units. What is the length of the rectangle
Answer: 5
Step-by-step explanation:
area = width x length
15 = w x w-2
15 = 5 x 3
3 is 2 less than 5, and if you multiply them together, you get the area, 15
Is this a planar graph? If so, draw a planar representation of the graph. If not,
explain why it is not planar.
Each of these vertices, which together make up a full graph with five equation vertices, can be seen to be linked to the other four vertices in the subgraph.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A formal statement that proves the equality of two calculations is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two phrases that are inscribed on opposite sides of a letter. Frequently, the logo and indeed the particular software are identical. like in 2x - 4 = 2, for example.
This graph is not planar because it has a subgraph that is isomorphic to the whole, non-planar graph with five vertices (K5).
K5 is a non-planar graph as it cannot be represented in a planar manner on a 2D plane without at least five crossing edges. This graph is also non-planar since K5 is a subgraph of it.
We may determine five vertices that make up a whole subgraph, for instance, vertices 1, 2, 3, 5, and 6, to demonstrate that this graph has K5 as a subgraph. Each of these vertices, which together make up a full graph with five vertices, can be seen to be linked to the other four vertices in the subgraph.
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need help please lol dont got much time. Simplify
Answer:
[tex]\frac{49}{45}[/tex] OR [tex]1\frac{4}{45}[/tex]
Step-by-step explanation: