The solution of the given quadratic equation is x = 1/3 or -3.
The given quadratic equation is 3x^2 + 8x - 3 = 0.
Multiplying the coefficient of the first term and the last term, we get:
3 x 3 = 9
Factors of 9 are:
1 and 9
3 and 3
We choose 1 and 9 as these factors, when subtracted give us the middle term.
Hence, we can write 3x^2 + 9x - x - 3 = 0
3x (x+3) -1 (x+3) = 0
(3x -1) (x+3) = 0
x = 1/3 or -3
The question is incomplete, the complete question is:
Find the solution of the quadratic equation 3x^2 + 8x - 3 = 0.
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Determine all minors and cofactors of 2 -8 5 3 9 6 -1 -2 -3
The minors of the 2 x 3 matrix are -3, -2, -1, 9, -2, -3, 6, and 5. The cofactors are -18, 16, 5, -3, -18, 18, 3, -12, and -5.
Minor of 2: -3
Cofactor of 2: -18
Minor of -8: -2
Cofactor of -8: 16
Minor of 5: -1
Cofactor of 5: 5
Minor of 3: 9
Cofactor of 3: -3
Minor of 9: -2
Cofactor of 9: -18
Minor of 6: -3
Cofactor of 6: 18
Minor of -1: -3
Cofactor of -1: 3
Minor of -2: 6
Cofactor of -2: -12
Minor of -3: 5
Cofactor of -3: -5
The minors of the 2 x 3 matrix are -3, -2, -1, 9, -2, -3, 6, and 5. The cofactors are -18, 16, 5, -3, -18, 18, 3, -12, and -5.
The given 2 x 3 matrix is composed of the values 2, -8, 5, 3, 9, 6, -1, -2, and -3. The minors of the matrix can be found by using the Laplace expansion formula and removing the row and column of the element in question. This yields the minors -3, -2, -1, 9, -2, -3, 6, and 5. The cofactors of the matrix can be calculated by taking the determinant of the minor and multiplying it by the sign of the element in question. This results in the cofactors -18, 16, 5, -3, -18, 18, 3, -12, and -5.
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Miss Howard is baking cookies for her friends. She buys 5 pounds of flour and spends a total of $11. What is the cost for each pound of flour?
Answer:
[tex]\huge\boxed{\sf \$ 2.2}[/tex]
Step-by-step explanation:
From the question,5 pounds of flour = $11
Divide both sides by 55/5 pound of flour = $11 / 5
1 pound of flour = $2.2[tex]\rule[225]{225}{2}[/tex]
2) You go out to breakfast and order a meal that costs $7.24
and a coffee that costs $2.65. You want to leave a 15% tip.
How much will you leave for a tip?
Answer:
$1.48
Step-by-step explanation:
Meal cost: $7.24
Coffee cost: $2.65
Total cost: $9.89
Now we need to find 15% of 9.89.
This is a percentage question, we need to first multiply 9.89 with 15% then divide it by 100%:
9.89 × 15 ÷ 100 = 1.48 approximately.
Viola graphed the function f(x)=3x-12 on a coordinate plane. Which
statement about this graph is true of all functions?
It is a linear graph.
It has a positive correlation.
It assigns a specific input to each output.
It assigns a unique output to each input.
Answer: It assigns a unique output to each input.
This statement is true of all functions, including the function f(x) = 3x - 12.
A function assigns a unique output to each input, meaning that for each value of x that is input into the function, there is a corresponding and unique value of y that is output. This is also called the vertical line test, if for any vertical line cuts the graph of a function at most one time, it is a function.
It does not matter whether it is linear or nonlinear or whether the correlation is positive or negative, the statement that It assigns a unique output to each input is true for all functions.
Step-by-step explanation:
The head of a hammer is located 9 cm to the left of its
center of mass, while the bottom of the handle of the
hammer is 29 cm to the right of the center of mass. Determine the length of the hammer. Justify your
answer using an appropriate geometry principle (definition, theorem, etc.)
The length of this hammer is going to be 38cm
What is length?Length has the dimension of distance in the International System of Quantities. The majority of measuring systems choose a base unit for length from which all other units are derived.
The formula that we would use to get the length is
r₁ + r₂ = L
Where r₁ is the lenght 9 cm from the head
29 cm is the length from the bottom
When we add these two, we would have the length of the hammer
29 + 9 = 38cm'
Hence the length of the hammer is 38 cm
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select all the irrational numbers, pls ive been stuck for like 20 minutes
Answer: 15
Step-by-step explanation:
15 can't be divided by two and make a non-repeating decimal.
What is f1 and f2 in lens?
F1 and F2 refer to the two principal focal lengths of a lens.
The two main focal lengths of a lens are referred to as f1 and f2 in the field of optics. The first principal focal length, or f1, is the distance from the lens to the point where parallel light rays, which have already passed through the lens, condense into a single point known as the focal point.
The second principal focal length, or f2, is the distance from the lens to the point where light rays diverging from a single point will appear to converge after passing through the lens. The distance from the lens to the point at which the light rays converge or diverge is known as the focal length. The values of f1 and f2, respectively, depend on the shape and type of the lens.
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8 identically sized squares of paper have been placed on top of one another.which one is at the bottom?
Since 8 is at the bottom where 8 equally sized squares of paper have been stacked on top of one another, the sequence is 82543671, therefore 8.
What is sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important.
Similar to a set, it has members (also called elements, or terms).
The length of the series is the number of elements (potentially infinite). In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important.
A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions.
An indexed family, which is a function from any index set, can be thought of as a generalization of the idea of a sequence.
For instance, the letter combinations (M, A, R, and Y) have the.
According to our question-
It is evident from the figure that 1 is a top.
I must locate Bottom 1.
6 is less than 7
If 3 weren't below 6, then 6 wouldn't be visible.
In the absence of 4, half of 3 would have been covered.
Unless 5 is below 4, 4 would have been covered.
Unless 2 is less than 5, half of 5 would have been covered.
If 8 were above 2, 2 would have been covered.
The sequence is 82543671.
therefore 8 is at the bottom.
Hence, Since 8 is at the bottom where 8 equally sized squares of paper have been stacked on top of one another, the sequence is 82543671, therefore 8.
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In two or more complete sentences explain how to balance the chemical equation and classify its reaction type.
_P₁+0₂_P₂03
Answer:
A balanced chemical equation is defined as the equation in which total number of individual atoms on the reactant side is equal to the total number of individual atoms on the product side. These equations follow law of conservation of mass.
PLEASE ANSWER IN UNDER 5mins!!!!!!!!!!!!!!!! pls help i appreciate you!
Answer:
[tex]\textsf{B)} \quad \dfrac{x^2+3x-4}{2x-1}[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{\dfrac{x^2+2x-3}{x-4}}{\dfrac{2x^2+5x-3}{x^2-16}}[/tex]
[tex]\textsf{Factor}\;\;x^2+2x-3:[/tex]
[tex]\implies x^2+3x-x-3[/tex]
[tex]\implies x(x+3)-1(x+3)[/tex]
[tex]\implies (x-1)(x+3)[/tex]
[tex]\textsf{Factor}\;\;2x^2+5x-3:[/tex]
[tex]\implies 2x^2+6x-x-3[/tex]
[tex]\implies 2x(x+3)-1(x+3)[/tex]
[tex]\implies (2x-1)(x+3)[/tex]
[tex]\textsf{Factor}\;\;x^2-16:[/tex]
[tex]\implies x^2-4x+4x-16[/tex]
[tex]\implies x(x-4)+4(x-4)[/tex]
[tex]\implies (x+4)(x-4)[/tex]
Therefore:
[tex]\implies \dfrac{\dfrac{x^2+2x-3}{x-4}}{\dfrac{2x^2+5x-3}{x^2-16}}=\dfrac{\dfrac{(x-1)(x+3)}{x-4}}{\dfrac{(2x-1)(x+3)}{(x+4)(x-4)}}[/tex]
[tex]\textsf{Apply\:the\:fraction\:rule}:\quad \dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a\cdot \:d}{b\cdot \:c}[/tex]
[tex]\implies \dfrac{ (x-1)(x+3)(x+4)(x-4)}{(x-4)(2x-1)(x+3)}[/tex]
Cancel the common factors:
[tex]\implies \dfrac{ (x-1)(x+4)}{(2x-1)}[/tex]
Expand the numerator:
[tex]\implies \dfrac{x^2+3x-4}{2x-1}[/tex]
A triangle has sides with lengths of 3cm, 6cm and 9cm. Is the triangle right? Explain the process you used to determine if is a right triangle and show your math work.
A triangle that has sides with lengths of 3cm, 6cm and 9cm is not a right-angled triangle.
What is the Triangle Inequality Theorem?In Mathematics, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < a < b + c
Where:
a, b, and c represent the side lengths of this triangle.
By applying the Triangle Inequality Theorem to the side lengths of this triangle, the right-angled triangle that can be formed would be determined as follows:
6 + 3 > 9
9 > 9 (False and not a right-angled triangle).
In conclusion, we can logically deduce that the two (2) short side lengths does not exceed the long side lengths and as such it is not a right-angled triangle.
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can any one explain why you have to do Addition and Subtraction in Scientific Notation or how we will use it in the real world
We must remember to multiply each integer by a power of 10 while subtracting numbers in scientific notation.
what is significant figures ?A value's accuracy is influenced by the number of significant digits in the value, which is frequently a measurement. Count the significant digits starting with the first non-zero digit. All zeros are permitted in the decimal places to the right of the last non-zero place. Consider the five significant digits in the number 0.0079800. Any zeros to the right of the last non-zero digit, when they come from the measurement, are significant. rounding an integer to 3 significant digits and 3 decimal places is identical. Go up to three and begin counting at the first digit that is not zero. Remove the last digit after that. The final two digits to the right of the decimal point should be increased by zeros.
To make it simple to subtract these integers, they must all be in the same power, as demonstrated in the example below.
5×10^2−3×10^2=
5(100)−3(100)^2×10^2=
(500−300)^2×10^2
=200
However, before continuing, we must restate the numbers in similar powers of ten if the powers of ten for the numbers to be subtracted are not the same.
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y varies inversely with x. Write an equation relating x and y.
Then find the indicated value. Show your work.
y = 3 when x = 8. Find the value of y when
x = 6.
y = 9 when x = 6. Find the value of x when
y = 4.
y= 1.5 when x = 14. Find the value of y when
x = 9.
y = 20 when x = 10. Find the value of x when
y = 25.
The equation of variation is xy = k.
The required values are given below.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
y inversely varies as x.
That means, y ∝ 1/x.
So, y = kx, where k constant of variation.
Then, x × y = k
When y = 8, x = 3.
k = 3 × 8 = 24
So, the equation of variation is xy = 24.
When x = 6,
6y = 24
⇒ y = 4
When y = 9, x = 6.
k = 6 × 9 = 54
So, the equation of variation is xy = 54.
When y = 4,
4x = 54
⇒ x = 27/2
When y = 1.5, x = 14.
k = 1.5 × 14 = 21
So, the equation of variation is xy = 21.
When x = 9,
9y = 21
⇒ y = 7/3
When y = 20, x = 10.
k = 20 × 10 = 200
So, the equation of variation is xy = 200.
When y = 25,
25x = 200
⇒ x = 8
Therefore, the values are given above.
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could someone pls help
Answer:
the answer is y = -4x + 5
Step-by-step explanation:
Im dum i cant explain it :D
Help with geometry Similar triangles ABC ~ ___ by ___ with a scale factor of ___
Answer choices RST, TSR, SRT, STR, or None
Side Side Side, Side Angle Side, Angle Angle, or None
1:6, 1:3, 4:15, or N/A
Both the triangles are not similar.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
Two triangles are comparable if they have two pairs of sides that are in the same ratio and if the included angles are likewise equal.
The square of any ratio between any two matching sides of two comparable triangles is equal to the ratio of their areas. As an illustration, Area of ABC/Area of DEF equals (AB)2/(DE)2 = (BC)2/(EF)2 = (AC)2(DF)2 for any two comparable triangles ABC and DEF.
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33. What is the value of 0.41128 divided by 0.3 correct to two decimal places
Answer :
0.41128 ÷ 0.30.41128 × 100000 ÷ 0.3 × 10000041128 ÷ 3000041128 [tex]\sqrt{x}[/tex] 300001.370933333331.370931.37ANS- 1.37Find the area of the shaded region.
9.8 m13.25 m2.5 m2.5 m4.75 m
The area is ?
m2.
The shaded region composed of triangle and square has an area of 28 in²
What is an equation?An equation is an expression relating two or more numbers and variables.
The area of a rectangle is the amount of space occupied by the rectangle. It is given by:
Area = length * width
From the diagram:
Area of rectangle = length * width = 8 in * 5 in = 40 in²
Area of triangle = (1/2) * base * height = (1/2) * 8 in * 3 in = 12 in²
Area of shaded region = Area of rectangle - Area of triangle = 40 in² - 12 in² = 28 in²
The shaded region area is 28 in²
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a student estimated a mass to be 325g, but upon carefully measuring it, found the actual mass to be 342g.what is the percent error?
Answer:
4.97% is your answer
Step-by-step explanation:
In a random sample of 9 residents of the state of Montana, the mean waste recycled per person per day was 2.8 pounds with a standard deviation of 0.68 pounds. Determine the 90% confidence interval for the mean waste recycled per person per day for the population of Montana. Assume the population is approximately normal.
Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
The confidence interval is given as : 2.379 < u < 3.221
How to solve for the confidence intervalHow to solve for the confidence interval
we have the following details to solve the problem with
n = 9 residents
mean = x = 2.8
s = 0.68
significance level ∝ = 1 - c
= 1 - 0.9
= 0.1
the confidence interval is given as:
C.I = x ± t ∝/2 , n - 1 * s/√n
t ∝/2 , n - 1 is the critical value. This is = 1.859
C.I = 2.8 ± 1.859 * 0.68 / √9
C.I = 2.8 ± 0.421
C.I = 2.8 - 0.421, 2.8 + 0.421
C.I = 2.379 < u < 3.221
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What is the image of the point 2/3 in the line?
The image of the point (2, 3) in the line y=−x is (-3, -2).
Let there be a point P(2, 3) on the cartesian plane. The image of this point in the line y=−x will lie on a line that is perpendicular to this line and the distance of this point from y=−x will be equal to the distance of the image from this line.
Let Q be the image of p and let the co-ordinate of Q be (h, k)
The slope of line y=−x is −1
Line joining P, Q will be perpendicular to y=−x so, its slope =1.
Let the equation of the line be y=x+c since this passes through points (2,3)
3=2+c⇒c=1
and the equation y=x+1
The point of intersection R lies in the middle of P & Q. Point of the intersection of lines y=−x and y=x+1 is
2y =1 , y= [tex]\frac{1}{2}[/tex] and x = [tex]-\frac{1}{2}[/tex]
Hence, [tex]\frac{h+2}{2} = -\frac{1}{2}[/tex] and [tex]\frac{k+3}{2} = \frac{1}{2}[/tex]
⇒ h=−3 and k =−2
So, the image of the point (2, 3) in the line y=−x is (-3, -2).
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The correct question is:
What is the image of the point (2,3) in the line y= -x?
p) find a1 for the geometric sequence
Sn = 46560 r = 4 n = 4
The first term of the Geometric Sequence will be 9,312.
What is Geometric Sequence?It is a sequence in which every term (except the first term, a) is multiplied by a constant number (common ratio, r) to get its next term. i.e., To get the next term in the sequence, we have to multiply with the common ratio, and to find the preceding term, we just have to divide the term by the same common ratio.
[tex]Sum = \frac{a(r^{n} - 1) }{r - 1}[/tex]
where;
Sn = 46560
r = 4
n = 4
[tex]46560 = \frac{a(4^{4} - 1) }{4 - 1}\\46560 = \frac{a(16 - 1) }{3}\\\\46560 = \frac{a(15\\) }{3}\\\\\\46560 = \frac{a(15\\) }{3}\\\\\\[/tex]
46560 = 5a
a = 9,312
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Slope intercept form of this equation?
From linear equation of a line,
y=mx+c or y=mx+b
Slope of a line is m and y-intercept is c (or b).
So first we have to make y the subject in
→8x+y=9
→y= - 8x+9
y = mx + c
Hence slope is (-8) and y-intercept is 9.
for x-intercept, put y=0 and we get
0 = -8x+9
x=-8/-9
x= 8/9
therefore x intercept is 8/9.
a.
You made a critical assumption in problem 4-56 when you made a probability
area model and multiplied the probabilities.
Blood type is affected by genetic inheritance. What if Zack and Nick were
related to each other? What if they were brothers or father and son? How
could that affect the possible outcomes?
b. What has to be true in order to assume a probability area model will give
an accurate theoretical probability?
(a) They are no longer independent because they are related and will more than likely have related blood types. (b) A probability area model will give an accurate theoretical probability is they must be independent.
What is genetic inheritance?Genetic information is transmitted from parent to kid through inheritance. Members of the same family typically share traits in common because of this. The process of fertilizations occurs during sexual reproduction when the sperm and egg cells join forces to create the first cell of the new organism.
Genetic material from the two parents is present in each of the newborn's cells. If you look at the shared traits of family members, such as average height, nose and ear shape, eye and hair color, and hair and eye color, you can see how genetic material is passed down.
Blood type is affected by genetic inheritance. if they were brothers or father and son then they are no longer independent because they are related and will more than likely have related blood types.
true in order to assume a probability area model will give an accurate theoretical probability is they must be independent.
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!!!40points!!!
It will take you t seconds to carry the water, which you will do y times a day. What is the total amount of
time you will be carrying water?
How many hours would you spend carrying water in a year?
Give me an expression, evaluation, and explanation and I will make you the brainliest.
Identify variables
T (time) seconds
Y amount of times per day
T * Y = amount of time you would spend carrying water in a day, 24 hrs
365 * t * y = 365 (amount of days per year, multiplied by the amount of time you carry water per day).
What is variables?In programming, a variable is a value that can change, depending on conditions or on information passed to the program. Typically, a program consists of instruction s that tell the computer what to do and data that the program uses when it is running. The data consists of constants or fixed values that never change and variable values (which are usually initialized to "0" or some default value because the actual values will be supplied by a program's user).Usually, both constants and variables are defined as certain data type s. Each data type prescribes and limits the form of the data. Examples of data types include: an integer expressed as a decimal number, or a string of text characters, usually limited in length.In object-oriented programming , each object contains the data variables of the class it is an instance of. The object's method s are designed to handle the actual values that are supplied to the object when the object is being used.To learn more about decimal number refer to:
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JK 12 and JN = 7
M
J
N
L
K
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10≤x≤15.
x f(x)
5 13
10 17
15 21
20 25
The average rate of change is 0.8
What is average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
Given:
x f(x)
5 13
10 17
15 21
20 25
As, The rate of change of the function is its gradient or slope.
So, the formula for calculating the gradient of a function is expressed as:
m = [tex](y_2 - y_1)/ (x_2 - x_1)[/tex]
Using the coordinate points from the table (5, 13) and (10, 17)
Substitute the coordinate into the expression:
m = (17- 13)/ (10 - 5)
m = 4 /5
m = 0.8
Hence, the average rate of change is 0.8.
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How many cm is 2 fingers dilation?
2 fingers dilation is normally 2 cm in measurement.
What is Dilation ?Dilation is the process of increasing an object's size without altering its form. Depending on the scale factor, the object's size may rise or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's form doesn't change.
A dilation is a function f from a metric space M into itself that, for any locations x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is a positive real integer. Such a dilatation is a resemblance of the space in Euclidean space.
Meaning of Dilation in Math. Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
Normally 1 finger dilation represents 1 cm so by unitary methord 2finger dilation is 2 cm
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The extension of two fingers is usually 2 cm.
What is dilation?Dilation is the process of enlarging an object without changing its shape. Depending on the magnification, the size of the object will increase or decrease. A 5 unit square can be expanded to a 1l5 unit square using dilation math, but the shape of the square remains the same. A dilation is a function f from the metric space M to itself, satisfying the identity d=rd for any position x,y in M. where d is the distance between x and y and r is a positive real number. Such an extension resembles the space of Euclidean space.
Stretching Used in Mathematics To change the size of an element, we use a transition called Stretch. Grow is used to enlarge or shrink an object. The result of this transformation is an image with the same shape as the original image. However, there is variation in the size of the shape.
Normally, one finger will stretch 1 cm, so in the unified method, two fingers will stretch 2 cm.
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Please help me with my class work
Answer:
3/2m^5n
Step-by-step explanation:
9m^8n^5÷6m^3n^4
(9/6)(m^8/m^3)(n^5/n^4)
3/2m^5n
Record each of the equations in slope intercept form ( y=Mx+b)
The equations are recorded in slope intercept form as below
equation slope intercept form
y + x = 3 y = -x + 3
2x + y = x + 4 y = -x + 4
x + y = -3 y = -x - 3
What is slope intercept form of linear equation?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the slope intercept form as shown below.
y = mx + b
definition of variable
y = output variable
m = slope
x = input variable
b = y intercept
The equation are written in the form y = mx + b as below
y + x = 3
rearranging the equation
y = -x + 3
2x + y = x + 4
rearranging the equation
y = -2x + x + 4
y = -x + 4
\
x + y = -3
rearranging the equation
y = -x - 3
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May I have help?
True or False: The graph represents a function.
Answer:
Step-by-step explanation:
It's gonna be true in just trust me when i say that im that guy
Answer:
true
Step-by-step explanation: