The function {(1,4), (2,5), (3, 6)} has the function rule y= 3x + 1.
True
False
Will mark brainliest
Answers
Answer:
true
Step-by-step explanation:
Related Questions
a certain type of flashlight requires two type-d batteries, and the flashlight will work only if both its batteries have acceptable voltages. suppose that 80% of all batteries from a certain supplier have acceptable voltages. among ten randomly selected flashlights, what is the probability that at least nine will work? (round your answer to three decimal places.)
Answers
The probability that at least nine of ten randomly selected flashlights will work, given that 80% of all batteries have acceptable voltages, is 0.2684.
This problem can be solved using the binomial distribution.
Let X be the number of flashlights out of 10 that will work. Then X is a binomial random variable with n = 10 and p = 0.8.
We want to find P(X ≥ 9). Using the binomial probability formula, we can compute
P(X ≥ 9) = P(X = 9) + P(X = 10)
= (10 choose 9)(0.8)^9(0.2)^1 + (10 choose 10)(0.8)^10(0.2)^0
= 0.2684
Therefore, the probability that at least nine out of ten flashlights will work is 0.2684 (rounded to three decimal places).
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Simplify a/2b times bc/a
Answers
Answer:
\(\dfrac{c}{2}\)
Step-by-step explanation:
We can simplify the given expression by canceling like terms.
Remember that anything divided by itself is 1.
ex:
\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)
Applying this logic to the given expression:
\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)
↓ simplify multiplication of fractions
\(\dfrac{a \cdot bc}{2b \cdot a}\)
↓ rewrite to align like variables
\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)
↓ separate out variables that are divided by each other
\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)
↓ represent them as 1
\(1 \cdot 1 \cdot \dfrac{c}{2}\)
↓ rewrite without unnecessary 1's
\(\dfrac{c}{2}\)
BOOKWORK Code: L82
allowed
Using Pythagoras' theorem, calculate the length of the hypotenuse in this right-
angled triangle.
Give your answer in centimetres (cm) to 1 d.p.
8 cm
3.9 cm
Not drawn accurately
Answers
The length of the hypotenuse in this right-angled triangle = 6.98 cm².
What exactly is the Pythagorean Theorem?The Pythagorean theorem states that the total of the squares on the legs of a right triangle equals the square upon that hypotenuse (the side opposite the right angle)—or, in popular algebraic notation, a2 + b2 = c2.
What is the triangle's formula?The basic formula for calculating the area of a triangle is the half square product of its base as well as height, i.e., A = 1/2 b h. This formula applies to all triangles, whether they are scalene triangles, isosceles triangles, or equilateral triangles.
According to the information:Hypotenuse (c) = 8 cm
Base (b) = 3.9 cm
Length =
C² = (a² + b³)
a² = C² - b²
a = √((8)² - (3.9)²)
= 6.98 cm²
The length of the hypotenuse in this right-angled triangle = 6.98 cm².
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PLEASE HELP IM CONFLICTED FOR TIME
3. A community is developing plans for a pool and hot tub. The community plans to
form a swim team, so the pool must be built to certain dimensions. Answer the
questions to identify possible dimensions of the deck around the pool and hot tub.
x+ 9 yds 9 yds
25 yds
x + 25 yds
6 ft
Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be
the same width on all sides of the pool. Including the deck, the total pool area has
11.8.4 Test (TST): Quadratic Equations and Functions
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a length of (x+25) yards, and a width of (x+9) yards.
a. Write an equation representing the total area of the pool and the pool deck. Use
y to represent the total area. Hint: The area of a rectangle is length times width.
(1 point)
Answers
Therefore, the equation representing the total area of the pool and pool deck is y = 25 * 9 + (x+25) (x+9).
What is length?Length is a measure of the size of an object, typically referring to the distance from one end to the other end in one dimension. It is commonly used to describe the size of objects such as lines, segments, curves, and shapes. Length is often measured in units such as meters, feet, inches, or centimeters, depending on the context and the system of measurement being used. In mathematics, length can also refer to the total number of elements in a sequence or the number of digits in a number.
The length of the pool deck is (x+25) yards and the width is (x+9) yards. The area of the pool deck can be found by multiplying the length and width:
Area of pool deck = (x+25) (x+9)
The area of the pool itself is 25 yards by 9 yards, or:
Area of pool = 25 * 9
To find the total area of the pool and pool deck, we need to add the area of the pool to the area of the pool deck:
Total area = Area of pool + Area of pool deck
y = 25 * 9 + (x+25) (x+9)
Therefore, the equation representing the total area of the pool and pool deck is y = 25 * 9 + (x+25) (x+9).
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how do your actual class data for genotypic and allelic frequencies compare with those of the random sampling of the usa population? would you expect them to match? what reasons can you think of to explain the differences or similarities?
Answers
The Genotype frequency is the percentage of the total number of individuals represented by a genotype.
The student population will most likely not match the US population figures. The data for the US population comes from a much larger sample and better represents the rates expected for a large heterogeneous population.
Since your class data represents a much smaller sample size, the allele frequencies will most likely be different. The frequency of the AA genotype is determined by the square of the frequency of the A allele.
The frequency of genotype Aa is obtained by multiplying the frequency of A times the frequency of A twice. The frequency of aa is the square of a. Try replacing p and q with other values, just making sure p and q are still 1.
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cherries cost $4/lb. Grapes cost $2.50/lb. You can spend no more than $15 on fruit, and you need at least 4lb in all, What is a graph showing the amount of each fruit you can buy?
Answers
The constraints are that you can spend no more than $15 on fruit and you need at least 4lb in all.
First, let's calculate the maximum amount of each fruit you can buy given the constraints:
Let x be the number of cherries in pounds, and y be the number of grapes in pounds.
The cost constraint can be written as 4x + 2.5y <= 15
The minimum amount constraint can be written as x + y >= 4
Solve for y in the cost constraint: y <= (15 - 4x) / 2.5
Plot these constraints on a graph:
Graph of cherry and grape purchase options
The shaded area represents the feasible region, or the combinations of cherries and grapes that satisfy the cost and minimum amount constraints. The red dots represent some possible points in the feasible region.
The dashed line represents the boundary of the feasible region, where the cost constraint or the minimum amount constraint is met exactly.
As you can see from the graph, there are several combinations of cherries and grapes that you can buy within the given constraints.
For example, you could buy 2 pounds of cherries and 2 pounds of grapes, or you could buy 3 pounds of cherries and 1 pound of grapes.
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The image point of A after a translation right 4 units and down 4 units is the point B(12, – 7). Determine the coordinates of the pre-image point A.
Answers
Answer:
(8, –3)Step-by-step explanation:
Translation right or left means change of the x-coordinate.
Translation up or down means change of the y-coordinate.
Translation right or up means adding.
Translation left or down means subtracting.
\(A=(x_A, y_A)\quad\rightarrow\quad B=(x_A+4,\,y_A-4)\\\\x_A+4=12\qquad\qquad y_A-4=-7\\\\x_A=12-4\qquad\qquad y_A=-7+4\\\\x_A=8\qquad\qquad\qquad y_A=-3\\\\A=(8,-3)\)
Create a histogram of the mass of geodes found at a volcanic site. Scientists measured 24 geodes in kilograms and got the following data: 0.8,0.9,1.1,1.1,1.2,1.5,1.5,1.6,1.7,1.7,1.7,1.9,2.0.2.3,5.3,6.8,7.5,9.6. 10.5,11.2,12.0,17.6,23.9, and 26.8.
Answers
The histogram displays the distribution of geode masses, with the x-axis representing the mass intervals and the y-axis representing the frequency of geodes within each interval.
To create a histogram of the mass of geodes found at a volcanic site, follow these steps:
Determine the range of the data. The minimum value is 0.8 kg, and the maximum value is 26.8 kg.
Decide on the number of bins or intervals for the histogram. Let's choose 8 bins for this example.
Calculate the bin width by dividing the range by the number of bins. In this case, the bin width is (26.8 - 0.8) / 8 = 3.375 kg.
Create the intervals for the bins by starting from the minimum value and incrementing by the bin width. The intervals are:
0.8 - 4.175 kg
4.175 - 7.95 kg
7.95 - 11.725 kg
11.725 - 15.5 kg
15.5 - 19.275 kg
19.275 - 23.05 kg
23.05 - 26.825 kg
Count the number of geodes that fall within each interval. From the given data, you can determine the frequencies for each interval.
Create the histogram by representing the intervals on the x-axis and the frequencies on the y-axis. Use bars of different lengths to represent the frequencies. Label the axes and provide a title for the histogram.
Here is the histogram-
Frequency
|
7 | *
6 |
5 |
4 |
3 | *
2 | **
1 | *
0 |____________________
0.8 7.95 15.5 23.05 26.825 (kg)
The histogram displays the distribution of geode masses, with the x-axis representing the mass intervals and the y-axis representing the frequency of geodes within each interval. The bars depict the frequencies for each interval, showing the pattern of the mass distribution.
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for what value of the variable is the value of the expression -3(2x+1) is 20 greater than the expression 8x+5
Answers
Answer:
- 3 ( 2x+1 ) 20
8x+5
_____________
8x+5×20 -3 ( 2×12.5+1 )
8×=100 -3 ( 25+1 )
100÷8= 12.5 -3 ( 26 )
×= 12.5
-3 ( 26 )
-3×2 + -3×6 = -6+ -18 = -24
-24
can someone answer page 3 question 3, page 5 question 3, all of page 6
Answers
The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7
What is trigonometrical ratios?Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle. There are three common trigonometric ratios: sine, cosine, and tangent
For page 3 question 3,
a) <A + <B = 90 since <C = right angle
b) SinA = BC/AB and CosB = BC/AB
The ratio of the two angles BC/AB ÷ BC/AB = 1
I notice that the ratio of sinA and cosB gives 1
b) The ratio of CosA and SinB will give
BC/AB ÷ BC/AB
= BC/AB * AB/BC = 1
For page 5 number 3
Tan28 = g/i
g/12.2 = tan28
cross multiplying to have
g = 12.2*tan28
g = 12.2 * 0.5317
g = 6.5
b) the angle I is given as 90-28 degrees
<I = 62 degrees
To find the side h we use the Pythagoras theorem
h² = (12.2)² + (6.5)²
h² = 148.84 +42.25
h²= 191.09
h=√191.09
h= 13.8
For page 6
1) Sin42 = x/18
x=18*sin42
x = 18*0.6691
x = 12.0
2) cos28 = 6/x
xcos28 = 6
x = 6/cos28
x [= 6/0.8829
x = 6.8
3) Tan63 = x/34
x = 34*tan63
x= 34*1.9526
x = 66.4
4) Sin50 123/x
xsin50 = 123
x = 123/sin50
x = 123/0.7660
x =160.6
5) Sin57 = P/8
Pole = 8sin57
the pole = 8*0.8387
The pole = 6.7
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whats the reciprocal
Answers
Reciprocal is defined as the inverse of a value or a number.
What is meant by reciprocal?
The reciprocal of any number in mathematics is one divided by that number.
If x is a real number, then \(\frac{1}{x}\) will be x's reciprocal. Hence, we must change the number to its upside-down form.
For instance, 1 divided by 4 is the reciprocal of 4. The result of multiplying a number by its reciprocal now equals one. Inverse multiplicative is another name for it.
The multiplicative inverse is another name for it. It can also be discovered by switching the numerator and denominator. A number's reciprocal and its product are equal to one.
Except for zero, every integer has a reciprocal.
Hence, reciprocal is defined as the inverse of a value or a number.
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Determine whether each number is an integer, a rational number that is not an integer, or an irrational number. pls help very urgent
Answers
Integer: 12
Irrational numbers: -2√10 and √20
Rational numbers: 17/4, 0.25, and -77/11.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
There are rational and irrational numbers in the image.
The numbers can be written in the form of p/q, where q is never zero is rational numbers.
And rest of the numbers are irrational numbers.
So, the solutions are given in the image below.
√144 = 12
0.25 = 25/100 = 1/4
Therefore, the solutions are given in the image below.
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Study the box below. Follow the directions and write the answer in the space provided.
Rule:
An exponent tells the number of times
a base is multiplied by itself.
-exponent
9.9.9.9= 94
-base
Examples:
43 = 4.4.4 Expanded form
2.4.2.4 = 22.42 Exponential form
52 = 25
Simplified
Write each problem in expanded form.
1. 78
3. x
5. 89.9
2. 45
4. al.ba
6. 22.35
Answers
The expressions in their expanded forms are:
\(7^8 = 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7\).\(4^5 = 4 \times 4 \times 4 \times 4 \times 4\).\(x^3 = x \times x \times x\).\(a^2 \cdot b^2 = a \times a \times b \times b\).\(8^9 \cdot 9 = 8 \times 8 \times 8 \times 8\times 8 \times 8 \times 8 \times 8 \times 8 \times 9\).\(2^2 \cdot 3^5 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3\).ExponentsThe exponent of a number or an expression is used to expand the expression.
Take for instance, the following expression in its exponential form
\(3^2\)
The above expression means that, the value of 3 multiplied twice
The problemsThe first expression is given as 7^8.
This represents the value of 7 multiplied by itself 8 times.
So, we have:
\(7^8 = 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7\)
Using the above as a guide, the expanded forms of the other expressions are:
\(4^5 = 4 \times 4 \times 4 \times 4 \times 4\).\(x^3 = x \times x \times x\).\(a^2 \cdot b^2 = a \times a \times b \times b\).\(8^9 \cdot 9 = 8 \times 8 \times 8 \times 8\times 8 \times 8 \times 8 \times 8 \times 8 \times 9\).\(2^2 \cdot 3^5 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3\).Read more about expansions at:
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What is the product of the polynomials below?
(6x²-3x-6) (4x² +5x+4)
Answers
Answer:
D
Step-by-step explanation:
every term of one expression gets multiplied with every term of the other expression.
(6x² - 3x - 6)(4x² + 5x + 4) =
= 6×4x²×x² + 6×5x²×x + 6×4x² - 3×4x×x² - 3×5x×x -
3×4x - 6×4x² - 6×5x - 6×4
3 terms × 3 terms = 9 terms.
now we combine similar factors for the 9 terms
24x⁴ + 30x³ + 24x² - 12x³ - 15x² - 12x - 24x² - 30x - 24
and now we combine similar terms
24x⁴ + 18x³ - 15x² - 42x - 24
the simple process of counting the number of observations (cases) that are classified into certain categories is known as .
Answers
The process of counting the number of observations is knowns as Tabulation.
What is tabulation?The logical representation of the numerical data written in rows and columns is known as tabulation. It helps in to facilitate the statistical analysis. The data that can be organized in the form of table is termed as tabulation. The data in the table can be represented in a systematic manner. The main objective of tabulation is to present the systematic data in a brief manner.
There are two types of tabulation. They are:
1.Simple tabulation
2.Complex tabulation
A simple example for the tabulation is, The population of the people is divided into religion, caste, gender, age etc.
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if 75% of all families spend > $75 weekly for food and the mean is $104, what is the standard deviation? (assume normal)
Answers
The standard deviation is $42.96.
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation. There are three ways to find the z-score that corresponds to a given area under a normal distribution curve 1. Use the z-table. 2. Use the Percentile to Z-Score Calculator.
Given : 75% of all families spend more than $75 weekly for food,
Mean = μ = $104
We have to find standard deviation σ.
75% of all families spend more than $75 weekly for food
For 100 - 75 = 25%, z = -0.675
Now, z = (x - μ) / σ
∴ σ = (x - μ) / z
σ = (75 - 104)/-0.675
= -29/-0.675
= 42.96
Thus, the standard deviation is $42.96.
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what is the equation of a line that passes through (-7, 3) and is perpendicular to -5/3x = 1/4y -8
Select all answers that apply
Y = 3/20x + 81/20
Y-3 = 3/20(x+7)
Y-3 = -20/3(x+7)
Y = -20/3x -32
3x -20y = -81
The answer can be anything thing that occurs during solving the problem or is the answer.
Answers
Answer:
The 1st, 2nd and 5th options are correct.
Step-by-step explanation:
The equation of a line can be written in the form of y=mx+c, where m is the gradient and c is the y-intercept.
①Rewrite the given equation into the form of y=mx+c to find the gradient.
\(- \frac{5}{3} x = \frac{1}{4} y - 8 \\ \frac{1}{4} y = - \frac{5}{3} x + 8 \\ y = - \frac{20}{3} x + 32\)
Thus, the gradient of the given equation is \( - \frac{20}{3} \).
② Find gradient of unknown line.
The product of the gradients of perpendicular lines is -1.
Let m be the gradient of the unknown line.
\(- \frac{20}{3} m = - 1 \\ m = - 1 \div ( - \frac{20}{3} ) \\ m = - 1 \times ( - \frac{3}{20} ) \\ m = \frac{3}{20} \)
③Substitute the value of m into the equation.
\(y = \frac{3}{20} x + c\)
④ Find the value of c by substituting a pair of coordinates.
When x= -7, y= 3,
\(3 = \frac{3}{20} ( - 7) + c \\ 3 = - \frac{21}{20} + c \\ c = 3 + \frac{21}{20} \\ c = 4 \frac{1}{20}\)
Thus, the equation of the line is \(y = \frac{3}{20} x + 4 \frac{1}{20} \).
Thus, the 4th option is incorrect.
Writing c as an improper fraction,
\(y = \frac{3}{20}x + \frac{81}{20} \)
Thus, the 1st option is correct.
-3 from both sides of the equation:
\(y - 3 = \frac{3}{20} x + \frac{21}{20} \)
Factorise 3/20 out of the right hand side:
\(y - 3 = \frac{3}{20} (x + 7)\)
Thus, the 2nd option is correct.
The 3rd option is incorrect as factorising -20/3 out would leave us with -0.0225 as the coefficient of x.
Let's look at the 5th option.
\(y = \frac{3}{20} x + 4 \frac{1}{20} \)
×20 on both sides:
\(20y = 3x + 81\)
-20y on both sides:
\(3x - 20y + 81 = 0\)
-81 on both sides:
\(3x - 20y = - 81\)
Thus, the 5th option is also correct.
27
Lalculate the projected balance or casn at the end or August. A. \( \$ 23000 \) B. \( \$ 29000 \) C. \( \$ 107000 \) D. \( \$ 38000 \)
Answers
The projected balance of cash at the end of August is $38,000. The correct option is D.
To calculate the projected balance of cash at the end of August, we need to consider the cash balance at the beginning of the month, cash collections, and cash payments for August.
Given that the cash balance on July 31 was $32,000.00, we start with this amount.
Cash collections for August are $52,000.00, which means this amount is added to the cash balance.
Next, we consider cash payments for August, which include purchases of direct materials and operating expenses. The total cash payments for August are $20,000 (purchases of direct materials) + $26,000 (operating expenses) = $46,000.00. This amount is subtracted from the cash balance.
Finally, we calculate the projected balance of cash at the end of August by adding the cash collections and subtracting the cash payments from the beginning cash balance:
Projected cash balance at the end of August = Beginning cash balance + Cash collections - Cash payments
= $32,000 + $52,000 - $46,000
= $38,000
Therefore, correct option is D.
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Complete question is:
Berman Company is preparing its budget for the third quarter. Cash balance on July 31 was $32,000.00. Assume there is no minimum balance of cash required and no borrowing is undertaken. Additional budgeted data are provided here:
July Aug Sep
Cash collections $51,000.00 $52,000.00 $50,000.00
Cash payments
Purchases of direct materials 23,000 20,000 24,000
Operating expenses 32,000 26,000 22,000
Capital expenditures 7,000 9,000 13,000
Calculate the projected balance of cash at the end of August.
A. $23000
B. $29000
C. $107000
OD. $38000
Suppose Y is a random variable with P{Y=−2}=2/10, P{Y=2}=5/10 and P{Y=3}=3/10. (a) Compute the mean of Y. (b) Compute E[Y 2
]. (c) Compute the variance of Y. (d) Compute E [Y +
]. (e) Compute E[|Y|]. (f) Compute E[Y∧2].
Answers
The mean of Y is 0.6, E[Y^2] is 5.7, the variance of Y is 7.24, E[Y+] is 3.6, E[|Y|] is 2.1, and E[Y^2] is 5.7.
(a) The mean of Y is calculated by multiplying each possible value of Y by its corresponding probability and summing the results. Therefore, E[Y] = (-2)*(2/10) + (2)*(5/10) + (3)*(3/10) = 0.6.
(b) E[Y^2] is calculated by squaring each possible value of Y, multiplying it by its corresponding probability, and summing the results. Therefore, E[Y^2] = (-2)^2*(2/10) + (2)^2*(5/10) + (3)^2*(3/10) = 5.7.
(c) The variance of Y is calculated by subtracting the mean of Y from each possible value of Y, squaring the difference, multiplying it by its corresponding probability, and summing the results. Therefore, Var(Y) = [(−2−0.6)^2*(2/10)] + [(2−0.6)^2*(5/10)] + [(3−0.6)^2*(3/10)] = 7.24.
(d) E[Y+] is calculated by taking the positive part of each possible value of Y, multiplying it by its corresponding probability, and summing the results. Therefore, E[Y+] = (0)*(2/10) + (2)*(5/10) + (3)*(3/10) = 3.6.
(e) E[|Y|] is calculated by taking the absolute value of each possible value of Y, multiplying it by its corresponding probability, and summing the results. Therefore, E[|Y|] = |-2|*(2/10) + |2|*(5/10) + |3|*(3/10) = 2.1.
(f) E[Y^2] is already calculated in part (b) and is equal to 5.7.
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a 15-inch candle burns down in 10 hours. at what rate does the candle burn in inches per hour
Answers
Answer:
5 inches per hour
Step-by-step explanation:
Answer:
1.5 inches per hour
Step-by-step explanation:
Find TV if TL = 5x + 3 and VL = 5x - 7
Answers
Answer:
10
Step-by-step explanation:
TV=TL-VL. TL=5x+3 and VL=5x-7. (5x+3)-(5x-7)=5x+3-5x+7=3+7=10. TV=10.
Answer: 10?
Step-by-step explanation:
Which is equivalent to
64 ^1/4?
O 24/4
O4
O 16
O 16/4
Answers
Answer: \(\sqrt[4]{64}\)
Step-by-step explanation:
\(64^{\frac{1}{4} }= \sqrt[4]{64}\)
20 tonnes of iron costs $60000. Find the cost of 560 kg of iron
Answers
Answer:
$200,583,320.
Step-by-step explanation:
welcome
1.
If you are trying to build a rectangular garden with 128 feet of fencing, what is the greatest
possible area you can create? Show your work.
Answers
Answer:
4096
Step-by-step explanation:
To get the highest answer, you must divide 128 by 2
128/2=64
Then you multiply it by each other.
64*64=4096
PROOF:We know this is the largest because 128*1 is not the largest number as it is unbalanced. We need the most balanced answer. What is more balanced then 128/2?
Sorry if formatting is weird, first time answering questions
what is the slope and y intercept of y = 1/3x
Answers
The slope and y-intercept of the given equation y = 1/3(x) are:
Slope = 1/3.
y-intercept = 0.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial number.Based on the information provided above, an equation that models the line is represented by this mathematical equation;
y = mx + c
y = 1/3(x)
By comparison, we have the following:
mx = 1/3(x)
Slope, m = 1/3.
Initial value or y-intercept, c = 0.
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Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in Rº that does not contain the origin. A=____ b =_____
Answers
this line does not pass through the origin (0, 0), since the vector x = [0, 0] does not satisfy the equation Ax = b.
One possible example is:
A = [[1, 2], [2, 4]]
b = [3, 6]
The solution set of Ax = b is the set of all vectors of the form x = [x1, x2] such that:
x1 + 2x2 = 3
2x1 + 4x2 = 6
Solving this system of equations, we get:
x1 = 3 - 2x2
x2 = x2
So the solution set is the set of all vectors of the form x = [3 - 2x2, x2]. This is a line in R² with slope -2 and y-intercept (3, 0)
Note that this line does not pass through the origin (0, 0), since the vector x = [0, 0] does not satisfy the equation Ax = b.
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The equation of the blue line is y = –x 5. manipulate the orange line by setting the sliders so its slope, m, is –1 and its y-intercept, b, is –3. does the system appear to have a solution after the changes?
Answers
The system does appear to have a solution after the changes.
The equation of the orange line after the changes is y = -x - 3. The system appears to have a solution after the changes because the equations for both lines are in the same form. The blue line has a slope of -5 and the orange line has a slope of -1. This means that the lines have the same slope and the same y-intercept. This means that the two lines are parallel and will intersect at the point (-3,3).
To calculate the point of intersection, we can plug in -3 for x in both equations and solve for y.
For the blue line: y = -(-3)^5 = 3
For the orange line: y = -(-3) - 3 = 3
This means that the point of intersection for these two lines is (-3,3). Therefore, the system does appear to have a solution after the changes.
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James buys 8 packages, each 20 mechanical pencils, and passes out 1/4 of then to his friends. Write and evaluate an expression to find out how many mechanical pencils James has left.
Answers
Answer:
the answer is 131 because if you multiply 20 by 8 is 190 then you divide 1/4 by 190 and you get 131
Step-by-step explanation:
The equation 4x2 8x 15 = 0 is being rewritten in vertex form. fill in the missing step. given 4x2 8x 15 = 0 step 1 4(x2 2x ___) 15 ___ = 0 step 2 ✔ step 3 4(x 1)2 11 = 0 4(x2 2x 1) 15 − 4 = 0 4(x2 2x 1) 15 − 1 = 0 4(x2 2x 2) 15 − 2 = 0 4(x2 2x 4) 15 − 4 = 0
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Answer:
a) is the correct answer
Given: f(x) = 2x4 +10 and g(x) = 4x – 15 What is the value of g f (x)?
Answers
Step-by-step explanation:
g (f(x)) = 4(2x⁴+10)-15
= 8x⁴+40-15
= 8x⁴+25