Upon solving using direct factoring, the value of k = 56i / 3, a = 4i.
What is the straightforward approach to the quadratic equation?The algebraic square and simplify method is used to finish the square in a quadratic equation in order to obtain the required equation roots. The answer to the quadratic equation ax2 + bx + c = 0 is a 0. To obtain the roots, we simplify this equation to read as ax2 + bx + c = 0.
What strategy is direct?It is referred to as the direct technique since it allows us to solve the given system of linear equations in a finite number of specified steps.
Given the equation are -
9k² + 8 = - 48
9k² = -48 - 8
9k² = - 56
k = -√56 / √9
k = -√56 / 3
5a² + 10 = - 70
5a² = -80
a² = -16
a = 4i
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I NEED HELP ASP WILL MARK BRAINLIEST IF CORRECT!!!
Based on the formula [tex]C (t) = 0.8 (1.2)^{t}[/tex] it is expected for the concentration of organisms to increase over time (third option).
How will the concentration of organisms change over time?To determine how the formula or function affects the number of organisms, let's use two different times in order to compare the results:
C (t) = 0.8 (1.2)^{t}
Let's find out the concentration of organisms with the times 2 and 5:
2:
C (t) = 0.8 (1.2)^{2}
C (t) = 0.8 x 1.44 = 1.152
5:
C (t) = 0.8 (1.2)^{5}
C (t) = 0.8 x 2.48 = 1.99
Based on this, it can be concluded that as time increases the concentration increases too.
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Determine which of the lines are parallel and which of the lines are perpendicular.
(1,6)
(-1,4)
6
(-1,1) 2
(3,-2)
The slope of Line a:
The slope of Line b:
TC
X
(3,-2) (3, 0)
The slope of Line c:
(5,6)
The slope of Line d:
(3, 2)
b
The slope of lines a, b, c, and d are 1/3, 1/4, 1/3, and -4 respectively. Line a is parallel to line c. Line b and line d are perpendicular to each other.
What is a line?
A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. The term "line" can also be used to describe a line segment in daily life that has two points that serve as its ends.
The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁).
Line a passes through points (-1,4) and (5,6).
The slope of line a is (6-4)/(5-(-1)) = 2/6 = 1/3
Line b passes through points (-1,1) and (3,2).
The slope of line b is (2-1)/(3-(-1)) = 1/4
Line c passes through points (-3,-2) and (3,0).
The slope of line c is (0-(-2))/(3-(-3)) = 2/6 = 1/3
Line d passes through points (1,6) and (3,-2).
The slope of line d is (-2-6)/(3-1) = -8/2 = -4.
The slopes of line a and line c are the same, thus line a is parallel to line c.
If two lines are perpendicular to each other, then the product of therir slope is -1.
The product of slopes of line b and line d is
1/4 × (-4) = -1
Thus line b and line d are perpendicular to each other.
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All people come very close to being able to float in water. What therefore is the volume (in cubic meters) of a 50-kg woman?
a. 0.007
b. 0.035
c. 0.050
d. 0.070
e. 0.085
All people come very close to being able to float in water. therefore, 0.007 is the volume (in cubic meters) of a 50-kg woman.
Correct answer will be a. 0.007
The volume of a person in water is determined by their body density and the amount of air in their lungs. The volume can be estimated using the principle of buoyancy, which states that a body floating in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.
In this case, we are given the weight of a 50-kg woman and asked to determine her volume in cubic meters. To do this, we can use the formula for buoyancy: Fb = ρf * V * g, where Fb is the buoyant force, ρf is the density of the fluid (water), V is the volume of the woman, and g is the acceleration due to gravity.
Since the woman is floating, the buoyant force is equal to her weight, so we can set these two equal to each other: ρf * V * g = 50 kg * 9.8 m/s^2. Solving for V, we find that V = 50 kg / (ρf * g) = 50 kg / (1000 kg/m^3 * 9.8 m/s^2) = 0.005 m^3.
Comparing this answer to the options given, we can see that the closest option is 0.007 m^3 (choice a), which is our final answer.
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i need help please
ill give 5 stars
The actual temperature after the freezer was on for five minutes could be 18ºF or 12ºF
What is a graph ?
Graph can be defined as visual representation of the data through the given ordered pairs .
First, you must find the y-value returned by the line in the graph for a time (x) of five minutes, and then use the deviation of 3º to conclude the range of the real temperature.
1. y- value at x = 5 min.
The trend line (blue line in the graph) passes through the point (5,15), which means that it predicts a temperature of 15ºF when the time (x) is 5 minutes, or five minutes after the freezer was turned on.
2. Actual temperature value
It is stated that the temperature was actually three degrees from what the trend line shows, that means that the actual temperature could be 3ºF more or 3ºF less than the predicted temperature of 15ºF.
Mathematically:
Temperature = 15ºF ± 3ºF
Temperature = 15ºF + 3ºF or 15ºF - 3ºF
Temperature = 18ºF or 12ºF
Therefore, The actual temperature after the freezer was on for five minutes could be 18ºF or 12ºF
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What are two ways to represent 4/5? Move numbers to the boxes two equation.
Answer: I don't know if this is what you wanted, but two ways to represent 4/5 are 0.8 and 4 divided by 5.
Step-by-step explanation:
4/5 = 8/10
8/10 = 0.8
fraction symbol means to divide.
I hope this helps!
The first term of an arithmetic sequence is 6. The common difference of sequence
is two-thirds the first term. Write the next three terms of the sequence.
this arithmetic sequence will be 10, 14, and 18.
What is arithmetic sequence?
There are two approaches to defining an arithmetic sequence. It is a "series where the differences between every two succeeding terms are identical" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term." The series where the common difference between any two next terms stays constant is known as the arithmetic sequence. Let's go through what a sequence is once again. A collection of numbers that follow a pattern is referred to as a sequence.
The first term of an arithmetic sequence is 6
common difference 2/3.
a2 = a+d = 6+4 =10
a3= a+8 =14
a4=a+12 =18
Hence this arithmetic sequence will be 10, 14, and 18.
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find the phase shift
y = -cos ( 1/2 x + pi/2 )
-pi is the phase shift of y = -cos ( 1/2 x + pi/2 )
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given function is y = -cos ( 1/2 x + pi/2 )
Standard form of the cosine function is y=acos(bx+c)+d
Phase shift is -c/b
b=1/2 and c is pi/2
Now phase shift=-(pi/2)/(1/2)
=-pi
Hence, -pi is the phase shift of y = -cos ( 1/2 x + pi/2 )
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There are 30 muffins in a tin. 14 of the muffins are iced, of which 6 contain raisins. 4 muffins are neither iced nor contain raisins. a) Draw a Venn diagram that shows the information above. b) Work out the probability that a muffin picked at random contains raisins. Give your answer as a fraction in its simplest form.
The probability that a muffin picked at random contains raisins is 3/5.
What is the probability that a muffin picked at random contains raisins?The probability that a muffin picked at random contains raisins is calculated as follows:
The number of muffins that are not frozen = 30 - 14
The number of muffins that are not frozen = 16
The number of muffins that are not frozen but contain raisins = 16 - 4
The number of muffins that are not frozen but contain raisins = 12
The total number of muffins that contain raisins = 12 + 6
The total number of muffins that contain raisins = 18
The probability that a muffin contains raisins, P(contain raisins) = 18/30
P(contain raisins) = 3/5
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Is 3
a factor of 81
? Use divisibility rules to explain.
Answer: Yes
Step-by-step explanation:
3 is a factor of 81 because on dividing 81 by 3, we get no remainder and 27, that is, the quotient in this division, which is also a factor of 81.
True or False?
15 + k is an equation
please and ty
False
If it doesn't have an equal sign ( = ), it's not an equation. It would be considered an expression.
Answer: False
Step-by-step explanation:
Police can estimate the speed of a vehicle before the brakes are applied using the formula 0.75d = [tex]\frac{s^2}{30.25}[/tex] where s is the speed in miles per hour and d is the length of the vehicle’s skid marks in feet. What was the approximate speed of a vehicle that left a skid mark measuring 100 feet?
The approximate speed of a vehicle that left a skid mark measuring 100 feet is 47.63 miles per hour
What was the approximate speed of a vehicle?Given the formula:
0.75d = s² / 30.25
Where,
d = length of the vehicle’s skid marks in feet = 100 feet
s = speed in miles per hour
Substitute d = 100 feet into the equation
0.75d = s² / 30.25
0.75(100) = s² / 30.25
75 = s² / 30.25
cross product
75 × 30.25 = s²
2,268.75 = s²
find the square root of both sides
s = √2,268.75
s = 47.63 miles per hour
Ultimately, 47.63 miles per hour is the approximate speed of the vehicle.
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determine whether the function f : r → r defined by f (x) = x2 4x 9 is (a) one-to-one, (b) onto
(a) The function f: r -> r is not one-to-one (injective) since there are two separate inputs (2 and -2) that have the same result. It is defined as f (x) = x2 - 4x + 9. (9).
(b) The element (-1) that occurs in the codomain of the function f: r -> r, which is defined by f (x) = x2 - 4x + 9, prevents the function from being onto (surjective).
As a result, neither one-to-one nor onto are applicable to the function
f: r -> r defined by f (x) = x2 - 4x + 9.
According to the Question
We must demonstrate that if a function f(x1) = f(x2), then x1 = x2 in order to establish whether the function is one-to-one (injective). To put it another way, no two unique inputs produce the same outcome.
We must demonstrate that there exists an x in the domain of f such that f(x) = y for every element y in the codomain of f in order to establish if a function f is onto (surjective). Alternatively expressed, each output in the codomain has an associated input in the domain.
For the function f: r → r defined by f (x) = x^2 - 4x + 9, we can easily see that it is not one-to-one since f(2) = f(-2) = 9.
It is also not onto, as the codomain of f is all real numbers and there is no real number x such that f(x) = -1.
So, we can conclude that the function f: r → r defined by f (x) = x^2 - 4x + 9 is neither one-to-one nor onto.
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For what value of c is the function f (x) = c x=-5; 4 x=1; x^2-25 / (x+5)(x-7) otherwise continous at x = -5?
The value of c at which the function is continuous is 5/6.
For a function to be continuous at a point, the left and right limit of the function must exist and be equal at that point. In this case, the point is x = -5.
The function f(x) = c for x = -5, f(x) = 4 for x = 1, and f(x) = (x^2 - 25) / (x + 5)(x - 7) for x ≠ -5 and x ≠ 7.
To determine the value of c, we need to find the limit of f(x) as x approaches -5 from the left and from the right.
From the left, we have:
lim x→−5− f(x) = lim x→−5− (x^2 - 25) / (x + 5)(x - 7) = 5/6
From the right, we have:
lim x→−5+ f(x) = 5/6
For the function to be continuous at x = -5, we must have:
lim x→−5− f(x) = lim x→−5+ f(x) = c
c = 5/6
--The question is not readable, answering to the question below--
"For what value of c is the function continuous at x = -5?
f (x) = c for x=-5; f(x)=4 for x=1; f(x) = x^2-25 / (x+5)(x-7) otherwise"
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what is 8/6 = 20/a
solve for a in the proportion
15
Step-by-step explanation:
20/8 =2.5
6x2.5=15
therefore, 15
if a student scored 92, 76, and 79 on the quizzes, exams, and final respectively, calculate the student's final grade. express your answer to three significant figures.
The student's final grade in three significant digits is 247.
Significant Figures refer to the number of important single digits from 0 to 9 in the coefficient of the expression that conveys the message accurately. These significant figures help engineers or scientists in asserting the quantity of any measurement, length, volume, or mass. For example, 453 has three significant figures.
The two main applications to understand significant figures are - Precision and Accuracy. Let's learn how these two terms play an important role in real-life situations when it comes to the concept of significant figures.
Precision - The closeness between two or more quantities to each other under the same condition is called precision. In precision, the level of measurement when repeated gives the same result and the individual measurement agrees to each other.
Accuracy - The closeness between the measurement and the accurate number is called accuracy. Accuracy helps in providing consistent results with no error along with accuracy in the result.
The final grade of the student would be equal to the sum of the grades obtained in the quizzes, exams, and final.
So, the total grades = 92 + 76+ 79 = 247
Calculating this to three significant digits, we get 247.
Thus, the student's final grade in three significant digits is 247.
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(Geometry Module 4 DBA review)
When a figure is dilated from the origin, each ordered pair of the image, maybe found according to the rule (x,y)->(kx, ky)
Yes, that's correct. When a figure is dilated from the origin, each ordered pair of the figure is transformed according to the rule
What is dilation in maths ?
A dilation is a function f from a metric space M into itself that fulfils the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real number.
Yes, that's correct!
When a figure is dilated from the origin, each ordered pair of the figure is transformed according to the rule (x, y) → (kx, ky), where k is the scale factor. The scale factor determines the size of the dilation; if k > 1, the dilation increases the size of the figure, while if 0 < k < 1, the dilation decreases the size of the figure. If k = 1, the figure remains unchanged.
It's important to note that dilations preserve the orientation of the figure and can be thought of as a non-uniform scaling of the figure.
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Find the length is segment of FB?
The length of segment FB is given as follows:
FB = 4 in.
How to obtain the length of segment FB?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately, as similar triangles are formed.
The parallel segments in this problem are given as follows:
DF, EF and AB.
Hence the proportional side lengths are given as follows:
3 in and 4 in.6 in and GF.3 in and FB.Meaning that the length of segment FB is obtained as follows:
3/4 = 3/FB
FB = 4 in.
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A circle has a radius of 3. An Arc in this circle has a central angle of 20 degrees. What is the length of the arc?
The arc length of the circle will be 0.35 units.
What is the length of the arc of the circle?Using the formula Length of an Arc = r x θ, where is in radians, one can determine the arc length of a circle given its radius and central angle. Arc length is equal to Arc = θ × (π/180) × r, where r is the radius in degrees.
Given that a circle has a radius of 3. An Arc in this circle has a central angle of 20 degrees.
The length of the arc of the circle will be calculated as:-
Arc = θ × (π/180) × r
Arc = 20 x (π/180) × 3
Arc = 0.35 units
Therefore, the arc length of the circle will be 0.35 units.
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Convert each of the following to a common fraction: in a sequence way.
According to the above, the fractions numbers would be: 0.8 = 4/5, 2.34 = 117/50, and 1.25 = 5/4.
How to write decimals as fractions?To convert a decimal to a fraction, we must write the decimal number as a numerator and its place value as the denominator. Also, if there is a number to the left of the decimal point, we leave that number as an integer. According to the above, the fractional numbers would be:
0,8 = 8/10 = 4/52,34 = 234/100 = 117/501,25 = 125/100 = 25/20 = 5/4Those fractions are simplified.
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Distribute to create an equivalent expression with the fewest symbols possible. 6(a+2b+3c)=
Answer:
6a + 12b + 18c
Step-by-step explanation:
Distribute 6 to all numbers in the parenthesis.
(6(a) + 6(2b) + 6(3c))
[6a + 12b + 18c]
Using the formula a(x+h)^2+k to solve 5x^2-3x-2=0 prove that the answer is 5(5x-3/10)^2-49/20
By Solving by factorization method of equation 5x² - 3x - 2 = 0
x = 1 , [tex]\frac{-2}{5}[/tex]
What is meant by Quadratic equations?The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).Square and quadrangle difficulties have a close relationship with quadratic equations (another name for rectangles). In actuality, the Latin word quadratus, which means square, is the root of the word quadratic.Quadratic equations include those that have the solutions 6x2 + 11x - 35 = 0, 2x2 - 4x - 2 = 0, 2x2 - 64 = 0, x2 - 16 = 0, x2 - 7x = 0, 2x2 + 8x = 0, etc. You can see from these examples that some quadratic equations don't contain the terms "c" and "bx."Given data :
Given equation is, 5x² - 3x - 2 = 0
Solving by factorization method,
5x² - 3x - 2 = 0
5x² - 5x + 2x - 2 = 0
( 5x + 2 ) ( x -*1 ) = 0
x = 1 , [tex]\frac{-2}{5}[/tex]
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if f(x) = x3, evaluate the difference quotient f(8 h) − f(8) h and simplify your answe
The difference quotient of f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h.
The difference quotient: what is it?When you hear the phrase "difference quotient formula," what comes to mind? Difference and quotient resemble the slope formula in appearance. Yes, the difference quotient formula does really provide the slope of a secant line drawn to a curve. What is a secant line? A line that joins any two points on a curve is known as the secant line.
Given that the function is f(x) = x³
The value of f(8 + h) = (x+ h)³ = x³ + 3x²h + 3xh³ + h³
The value of f(8) = (8)³ = 512
Substituting the value of f(8 + h) and f(8) we have:
f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h
Hence, the difference quotient of f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h.
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show that if a > √n and b > √n, then n ≠ ab, where a and b are positive integers. n = 25 a = 8 8 > 5 b = 9 9 > 5 25 ≠ (8 * 9) = 72 this is a valid proof.
The statement "if a > √n and b > √n, then n ≠ ab" is saying that if two positive integers, a and b, are both greater than the square root of another positive integer n, then the product of a and b is not equal to n. This statement can be proven by contradiction.
Suppose the opposite is true, and that n = ab, where a and b are positive integers such that a > √n and b > √n. Then, because n = ab, we have n/a = b and n/b = a. But because both a and b are greater than the square root of n, we have √n < a and √n < b. This leads to a contradiction, because it means that n/a = b > √n, but √n is the largest possible value of b such that b < n/a.
Thus, we have proven that if a > √n and b > √n, then n cannot equal ab, and our original statement is true.
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Consider functions f and g.
The graph shows a curve line g. Some major points on the curve are (3, 6), (1, 5), (0, 2), (0, 0), (0, minus 2), and (0, minus 4).
What is the value of ?
The value of g(f(-5)) is 5.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x)= |2x+ 9|
Now, g(f(-5))
f(-5) = |2(-5)+9|
= |-10 + 9|
= |-1|
= 1
and, g(f(-5)) = g(1)
So, from the graph we can see that the value of g(1) is 5.
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Mr. Mosquera sold 50 pieces of pillow case. He planned to add 10% to the original price which is Php 25. 00 each. How much should be his price for each pillow
The new price for each pillow case is Php 27.50.
The concept used in this problem is markup pricing, where a certain percentage is added to the cost price of a product to arrive at the selling price.
Markup is the difference between a product's selling price and cost as a percentage of the cost. For example, if a product sells for $125 and costs $100, the additional price increase is ($125 – $100) / $100) x 100 = 25%.
As given, Mr. Mosquera plans to add 10% to the original price which is Php 25. 00 each,
Php 25 * 10/100
= Php 2.50 for each pillow case.
So, the new price for each pillow case is
Php 25 + Php 2.50
= Php 27.50.
Therefore, the new price for each pillow case is Php 27.50.
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Mr. Mosquera ' price for each pillow is 27.50 php. His price for each pillow is 27.50 php.
Here, these values are given,
Total no. of pillows = 50
Original price of each pillow = 25.00 php
Original price of 50 pillows= 125000 php
After, planning to add 10% to the original price'
New price of pillow will increase after adding 10% to the previous price.
New price of each pillow became 25+ 25 of 10%
= 25+ 25 × 10/100
= 25+ 5/2
= 55/2
=27.50 php
New price of each pillow became 27.50 php.
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Please Help me with these questions!!!
The function f·g(x) for the functions f(x)=4x-5 and g(x)=2x+8 is 8x²+22x-40.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
7) The given functions are f(x)=2x+3 and g(x)=x²-3x-6.
Here, f·g(x) =f(x)×g(x)
f·g(x) = (2x+3)×(x²-3x-6)
f·g(x) = 2x(x²-3x-6)+3(x²-3x-6)
f·g(x) = 2x³-6x²-12x+3x²-9x-18
f·g(x) = 2x³-3x²-21x-18
8) The given functions are f(x)=4x-5 and g(x)=2x+8
f·g(x) =f(x)×g(x)
f·g(x) = (4x-5)×(2x+8)
f·g(x) = 4x(2x+8)-5(2x+8)
f·g(x) = 8x²+32x-10x-40
f·g(x) = 8x²+22x-40
Therefore, the function f·g(x) for the functions f(x)=4x-5 and g(x)=2x+8 is 8x²+22x-40.
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Calculate the approximate and exact doubling times for annual percentage increases of 5%, 10%, 15%, and 20%.
The exact doubling time calculation provides a more accurate estimate of how long it will take a given value to double.
Approximate Doubling Time:
5% - 14 Years
10% - 7 Years
15% - 5 Years
20% - 4 Years
Exact Doubling Time:
5% - 14.2 Years
10% - 6.93 Years
15% - 4.77 Years
20% - 3.58 Years
Approximate doubling times are calculated by dividing 72 by the percentage rate of growth. This method assumes a consistent rate of growth, which is not always the case. The exact doubling time can be calculated by using the formula T=ln(2)/ln(1+r) where r is the rate of growth. This formula accounts for the compounding effect of the growth rate, which is not taken into account in the approximate calculation. For example, for a 5% annual growth rate, the approximate doubling time is 14 years, but the exact doubling time is 14.2 years. The exact doubling time calculation provides a more accurate estimate of how long it will take a given value to double.
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3. The relation shown below
represents the
temperature, in degrees Celsius, of the air
a certain number of hours after noon on a
winter day. Is the temperature a function of
time? Explain.
(2, -1), (1, -6), (6, -3), (4, -7)
The temperature is a function of time, as there is a single temperature for each instant of time.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
For the set in this problem, we have that:
An input of 2 is mapped to an output of -1.An input of 1 is mapped to an output of -6.An input of 6 is mapped to an output of -3.An input of 4 is mapped to an output of -7.As there are no repeated inputs, the temperature is in fact a function of time.
More can be learned about relations and functions at brainly.com/question/10283950
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I NEED HELP ASAP, what is 4 2/3 divided by 2 1/6?! (Simplified)
Answer:
2 1/2
Step-by-step explanation:
f(t)=3-5t find the slope of the graph of the function at the given point.
The slope for the function f(t) = 3 - 3/5t at point (3/5, 2) is 5/3.
What is slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The given function is - f(t) = 3 - 3/5t.
The data points are - (3/5, 2)
Rewrite the function -
f(t) = 3 - 3/5 t^-1
Differentiate with respect to t. Use the difference rule.
d/dt (3) - d/dt (3/5 t^-1)
Use the constant rule and the constant multiple rule.
0 - 3/5 d/dt (t^-1)
Use the power rule.
-3/5(-1)t^(-1 - 1)
3/5t^-2
Now plug in 3/5 for t on the derivative in order to find the slope at point (3/5, 2).
3/5(3/5)^-2
3/5(5/3)^2
3/5 × 25/9
5/3
Therefore, the slope value is 5/3.
To learn more about slope from the given link
https://brainly.com/question/16949303
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Find the slope of the graph of the function at the given point.
Function Point f(t) = 3 - 3/5t (3/5, 2)