The roots of the parabola are given as follows:
x = -2 and x = -4.
How to obtain the roots of the quadratic function?The quadratic function for this problem is defined as follows:
y = x² + 6x + 8.
Completing the squares, the quadratic function can be factored as follows:
y = (x + 4)(x + 2).
As:
The sum of the roots is of 6.The product of the roots is of 8.Then the roots are obtained as follows:
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a fishing boat accidentally spills 15 barrels of diesel oil into the ocean. each barrel contains 42 gallons. if the oil film on the ocean is 2.5 x 102 nm thick, how much area in square meters will the oil slick cover? assume 1 gal
The area in square meters will the oil slick cover is 9.5×10⁶ m².
15 barrels of diesel spilt into the ocean, where each barrel contains 42 gallons. Thereby the total volume of the oil spilt by 15 barrels is calculated as follows:
The total volume of the oil spilt by 15 barrels = 15× 42 gallons.
=630 gallons
1 gallon = 3.78541 liters
Volume in L = 630 gallons × 3.78541 liters/ 1 gallon
= 2384.8083 L
1 L = 10⁻³ m³
2384.8083 L = 2384.8083 × 10⁻³ m³
= 2.3848083 m³
The area covered by the oil spill has to be determined, where the thickness of the oil spill is given to be 2.5×10² nm.
1 nm = 10⁻⁹ m
Thereby, 2.5×10² nm = 2.5×10²×10⁻⁹ m
= 2.5×10⁻⁷ m
Area (m²) = volume (m³)/thickness (m)
= 2.3848083 m³/ 2.5×10⁻⁷ m
= 0.95392×10⁷ m²
= 9.5×10⁶ m²
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A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $91 and a standard deviation of $8. If the distribution can be considered mound-shaped and symmetric, what percentage of homes will have a monthly utility bill of more than $83?
Answer:
Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.
Step-by-step explanation:
If the distribution of the monthly utility bill for gas or electric energy can be considered mound-shaped and symmetric, we can use the standard normal distribution table to find the percentage of homes that have a monthly utility bill of more than $83.
To use the standard normal distribution table, we need to standardize the variable by subtracting the mean and dividing by the standard deviation:
(83 - 91) / 8 = -0.875
This means that a monthly utility bill of $83 is 0.875 standard deviations below the mean.
Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.
4% of what number is 77
Answer:
1935
Step-by-step explanation:
Step 1: If 4% of a number is 77, then what is 100% of that number? Setup the equation.
77
4% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
4Y = 77 x 100
4Y = 7700
Y = 7700
100 = 1,925
A rectangle has dimensions of x + 3 and x - 4. Find the area and the perimeter.
Step-by-step explanation:
The area of a rectangle is given by the formula:
Area = length * width
In this case, the length of the rectangle is given by x + 3 and the width is given by x - 4.
Therefore, the area of the rectangle is:
Area = (x + 3) * (x - 4)
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
In this case, the length of the rectangle is given by x + 3 and the width is given by x - 4.
Therefore, the perimeter of the rectangle is:
Perimeter = 2 * ((x + 3) + (x - 4)) = 2x - 2
So the area of the rectangle is (x + 3)(x - 4) and the perimeter is 2x - 2.
give me brainlist
Answer: Area= x^2-x-12 , Perimeter = 4x-2
Step-by-step explanation: According to the question,
Length = x+3
Breadth = x-4
Area of a rectangle = Length * breadth
Area = (x+3)(x-4)
Area = x^2-x-12
Perimeter of rectangle = 2*(length+ breadth)
Perimeter = 2* (x+3+x-4)
= 2*(2x-1)
= 4x-2
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the area of four walls of room is 90m if the rom is 7 m long and 2m wide , then find the height of the room
The height of the room is 5 m.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Length = 7 m
Width = 2 m
Height = x
Four walls of a room will have,
Two walls of length x height.
Two walls of Width x height.
Now,
Area four walls of the room = 90 m
2 (length x height) + 2 (Width x height) = 90
2 (7x) + 2 (2x) = 90
14x + 4x = 90
18x = 90
x = 5
Thus,
Height of the room = 5 m.
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Select one or more expressions that together represent all solutions to the equation. Your answer should be in degrees.
Assume
�
nn is any integer.
7
cos
(
9
�
)
−
1
=
1
7cos(9x)−1=17, cosine, left parenthesis, 9, x, right parenthesis, minus, 1, equals, 1
The trigonometric equation 7cos(9x) - 1 = 17 has an undefined solution.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
7cos(9x) - 1 = 17
Isolating the cosine, we have that:
7cos(9x) = 18
cos(9x) = 18/7
Now we isolate x applying the arc cosine, which is the inverse of the cosine, as follows:
9x = arccos(18/7)
9x = undefined.
The solution is undefined because the arccosine only exists for values between -1 and 1, as the cosine of an angle is always going to assume a value between -1 and 1.
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The non separable differential equation dy/dx=8x-2y has a linear particular solution of the form y = mx + b. Find m+b
The linear specific solution of the form [tex]y= mx + b[/tex] where [tex]m + b = 4- 2 = 2[/tex]
Differential equation that cannot be separated:
Non-separable differential equations are those that are incapable of being written as- [tex]\frac{dy}{dx} = f(x) g(y)[/tex]
In other words, the differential equations that cannot be separated are referred to as non-separable differential equations.Differential equations with non-separable variables are those in which the variables cannot be separated. These equations are difficult to solve and call for techniques that will be covered in upcoming courses, such as numerical or analytical approaches.
Given is the equation,
[tex]\frac{dy}{dx} = 8x - 2y[/tex]
[tex]y = 4x - 2 + ex^{-2x}[/tex]
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The width of a rectangle is 8.25t-6.5 feet and its length is 6.5t+10 feet. Find the perimeter of the rectangle.
The perimeter of the rectangle is (29.5t+7)feet
What is perimeter of a rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.
To find the perimeter of the rectangle we add a the sides together i.e
p = l+l+w+w
p = 2(l+w)
p =2 ( 8.25t - 6.5+ 6.5t + 10)
p = 2( 14.75t + 3.5)
p = (29.5t + 7) feet
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The population of alaska is approximently 6. 5 x 10^5 people. The population of illinois is about 1. 3 x 10^7 people. How many times greater is the population of illinois than alaska
After finding the ratio, the population of Illinois than Alaska is 20 times greater.
The population of Alaska is approximately 6.5 x [tex]10^5[/tex] people.
The population of Illinois is about 1.3 x [tex]10^7[/tex] people.
We have to find how many times greater is the population of Illinois than Alaska.
We will use their population ratio to determine how many times the population of Illinois is greater than the population of Alaska.
Ratio = Population of Illinois's /Population of Alaska
Ratio = 1.3 x [tex]10^7[/tex]/6.5 x [tex]10^5[/tex]
Now simplifying.
Ratio = 0.2 x [tex]10^2[/tex]
Ratio = 20
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3/4 + 1/3 what is it
Answer:
[tex] \frac{3}{4} + \frac{1}{3} \\ \frac{ \: \: 9 \: \: + \: \: 4 \: \: }{12} \\ \frac{13}{12} [/tex]
A persons blood has a pH of 7.371 and a carbonic acid concentration of 1.5, Approximate the concentration of bicarbonate in the persons blood.
Answer: The pH of blood is a measure of its acidity or basicity and is related to the concentration of hydrogen ions (H+) in the blood. The pH of 7.371 indicates that the blood is slightly basic. Carbonic acid (H2CO3) is a weak acid that dissociates into bicarbonate (HCO3-) and hydrogen ions (H+) in water. The carbonic acid concentration of 1.5 indicates the concentration of H2CO3 in the blood.
The concentration of bicarbonate (HCO3-) in the blood can be approximated by using the relationship between the pH, carbonic acid concentration and the bicarbonate concentration. The Henderson-Hasselbalch equation, which relates the pH and the pK of a buffer, to the ratio of the buffer's conjugate base to its acid form is:
pH = pK + log [HCO3-]/[H2CO3]
The pK of carbonic acid is 6.1 and the concentration of H2CO3 is given as 1.5.
Plugging these values into the Henderson-Hasselbalch equation,
7.371 = 6.1 + log [HCO3-]/1.5
Solving for [HCO3-],
[HCO3-] ≈ 25.8 mM
The approximate concentration of bicarbonate (HCO3-) in the person's blood is 25.8 mM.
Please note that this is an approximation, the actual value may vary depending on the person's health condition.
Step-by-step explanation:
Your cousin is building a new house. The layout of the first floor is shown in the diagram above. Using the
diagram and knowledge of polynomials find the following:
1. Write a polynomial that represents the length of the north side of the house. Then simplify the
expression.
2. Write a polynomial expression that represents the area of the kitchen. Then multiply to put the
polynomial in standard form.
3. Write a polynomial expression that represents the area of the bedroom. Then multiply to put the
polynomial in standard form.
4. Find the dimensions of the bathroom in terms of x. (Hint the west and east side of the house
should be equal.)
The polynomial for the north side of the house will be 2x^2+9x-32.
What are polynomials?
Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.
Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.
Now,
As the north side will be the sum of 5x-4,x^2-23 and 4x-5
so the polynomial for north will also be the sum of 5x-4,x^2-23 and 4x-5.
Hence,
Polynomial for north side= 5x-4 + x^2-23 + 4x-5
Polynomial for north side =2x^2+9x-32
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Consider the equations f(x)=1/x and g(x) = (x-1)^2-1. To the nearest tenth, what is the solution of f(x)=g(x)?
The solution of equation f(x)=g(x) is 2.
How do equations work?a formula that illustrates the relationship between the two expressions on either side of a sign. Usually, it has one variable and an equal sign. similar to 2. 2x - 4 = 2. The equals sign (=) in equations indicates that two expressions are equal. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.
The "left hand side" and "right hand side" of the equation refer to the expressions on each side of the equals sign. The right side of an equation is frequently thought of as zero.
Given : f(x)=g(x)
1/x = (x-1)^2-1
1 = x (x-1)² - 1
x (x-1)² = 2
x ( x² + 1 - 2x ) = 2
x³ + x - 2x² = 2
x³ + x - 2x² - 2 = 0
x³ - 2x² + x - 2= 0
x²(x-2) + 1(x-2) = 0
(x² +1) + (x-2) = 0
So, x = 2 .
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substitute 6x-5y=-1 and 6x+4y=-10
Answer:
x=-1 y=-1
Step-by-step explanation:
i am lazy to type
Answer:{x = -1}{y = -1}
Step-by-step explanation:
subtract the two equations
{6x - 5y = -1 ^
{6x + 4y = -10 ^
determine the sign
6x - 5y - (6x +4y) = -1 - (-10) ^
simplify
6x - 5y - 6x - 4y = -1 + 10 ^
substitute
y = -1 ^
solve the equation
6x + 4 x (-1) = -10 ^
write the solution
x = -1 ^
how do you prove an angle is a right angle when the other 2 angles are complementary in a triangle theorem
The two non-right angles in a right angled triangle balance each other out because the right angle already takes up 90 degrees of the triangle's 180 total angles. We refer to two angles as complementing each other when their sums equal 90 degrees.
The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The sum of the other two inner angles is 90 degrees. Base and perpendicular are the names of the other two sides that are close to the right angle. The Pythagorean Theorem is a triangle formula.
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which of the following describes an exact number? a. you ran two miles. b. the house has four bedrooms. c. there is one gram of salt in this beaker. d. you drank one liter of water. e. the little dog weighs 10 kilograms.
The choices that describe an exact number are option b, option c, option d, and option e because they show a definite countable quantity with 100% accuracy.
The following options describe an exact number:
b. The house has four bedrooms.
c. There is one gram of salt in this beaker.
d. You drank one liter of water.
e. The little dog weighs 10 kilograms.
These numbers are exact because they are specific measurements that are not subject to uncertainty. They are countable and defined. While "you ran two miles" or "you drank one liter of water" could be approximate measurements.
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−9(5 − 6x)
answers:
A 45 − 54x45 − 54x
B −45 − 54x−45 − 54x
C 45 + 54x45 + 54x
D −45 + 54x
Answer:
[D] -45 + 54x
Step-by-step explanation:
Base on the given we can use the distributive property to solve this:
Distributive property ⇒ Multiply outside numbers with each term inside the parenthesis.
-9 (5 - 6 x ) → {-9 × 5 = -45 } {-9 × -6x = 54x}
Now let's put it together;
-45 + 54x
Hence, [D] -45 + 54x is the correct answer.
RevyBreeze
Ali starts working on an annual salary of $20 000. His contract will give him an increase of $120 every 6 months. If he keeps working for 15 years, how much will Ali earn?
Answer: 23,600
Step-by-step explanation: 120x2 = 240, 240x15 = 3600. 20,000 + 3600 = 23,600
a college has 10 time slots for its courses, and blithely assigns courses to completely random time slots, independently. the college offers exactly 3 statistics courses. what is the probability that 2 or more of the statistics courses are in the same time slot?
Probability that 2 or more of the statistics courses are in same slot is 0.28.
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
probability that 2 or more of the statistics courses are in same slot
=1-P(all 3 are in different slots)
=1-P(select 3 from 10 slots and arrange them)
=1-(10*9*8)/10^3
=0.28
Therefore, probability that 2 or more of the statistics courses are in same slot is 0.28.
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The constant of the polynomial function f(x)=-(x+3(x+7)²(x-1)⁵(x+1)⁷(x-4) is
Answer:
The constant of a polynomial function is the coefficient of the term with the highest degree (the term with the highest power of x), which in this case is 0. Therefore, the constant of the polynomial function f(x)=-(x+3(x+7)²(x-1)⁵(x+1)⁷(x-4) is 0.
Look at the stem-and-leaf plot. What is the range of the numbers? Stem Leaf 1 0, 2, 2 2 2, 3, 4 3 0,5 Key 10-10 OA) 5 B) 21 OC) 25 OD) 35
For the given stem and leaf plot, the range of data is option C: 25.
What is stem and leaf plot?
A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
The stem and leaf plot for data is given.
The range of data is defined as a measure of the difference between the maximum value of data and the minimum value of data.
From the stem and leaf plot the maximum value obtained is = 35
From the stem and leaf plot the minimum value obtained is = 10
The range is then calculated as -
Range = Maximum value - Minimum value
Range = 35 - 10
Range = 25
Therefore, the range is 25.
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Please help
Gilligan sees a ship coming close to the shore he's standing on. He wants to
determine the distance (SD) from the ship to the shore. He walks 130 ft along the
shore from point D to point C and marks that spot. Then he walks 23 ft further and
marks point B. He turns 90° and walks until his location (point A), point C, and point
S are collinear
Answer the following questions making sure to show all your work.
(a) Can Gilligan conclude that triangle ABC and triangle SDC are similar? Why or why
not?
(b) Suppose AB = 90 ft. What can Gilligan conclude about the distance of the ship
from the shore? Explain.
As per the triangles ABC and SDC are similar triangles then Gilligan can conclude that triangles ABC and SDC are similar and Gilligan can conclude that the distance of the ship from the shore is 509 feet.
The term called triangle in math is defined as a three-sided polygon, which has three vertices
Here from the question we understand points S, C and A are collinear, here we have know that line AB and SD are vertical and parallel lines at the either sides of point C.
So we can conclude that triangles ABC and SDC are similar.
The distance from the ship is calculated as,
=> SD: 130 = AB: 23
Here we have to substitute 90 for AB, then we get,
=> SD: 130 = 90: 23
When write it as,
=>SD/130 = 90/23
When we simplify this then we get Gilligan can conclude that the distance of the ship from the shore is 509 ft
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Given that it takes an employee
about 14 seconds to lift, close, fill,and shelve a jar of peanut butter,calculate how many jars the employee can complete in 1 hour.
A. About 257 jars
C. About 300 jars
B. About 240 jars
D. About 840 jars
The solution is, A. About 257 jars, the employee can complete in 1 hour.
Here, we have,
given that,
Given that it takes an employee about 14 seconds to lift, close, fill, and shelve a jar of peanut butter,
To calculate this, you would take the number of seconds in an hour
(60 seconds/minute * 60 minutes/hour = 3600 seconds)
and divide it by the number of seconds it takes to complete one jar
(14 seconds/jar).
3600 seconds / 14 seconds/jar
= 257 jars/hour.
so, About 257 jars, the employee can complete in 1 hour.
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If f(x)=2x^3+6x^2+18x-26f(x)=2x
3
+6x
2
+18x−26 and x-1x−1 is a factor of f(x)f(x), then find all of the zeros of f(x)f(x) algebraically.
Upon factorization, The factors of the equation be x = 1, x = -2 + 3i, x = -2 - 3i and x = 1.
What does "factorizing method" mean?In mathematics, factorization or factoring is the process of breaking down one entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication produces the original number, matrix, etc.
Factorization is the process of shrinking the bracket of a quadratic equation, as opposed to widening the bracket and turning the equation into a product of factors that cannot be further reduced.
To solve a quadratic equation by factoring, factor the expression, set each factor equal to 0, and then solve each equation. To accomplish this, set up the terms in the equation so that the other side equals 0.
Let the given equation be f(x) = 2x³ + 6x² + 18 x - 26 and x - 1 then
2x³ + 6x² + 18x - 26 = 0
Factor 2x³ +6x² +18x-26: 2(x-1) (x²+4x+13)
2(x-1) (x²+4x+13) = 0
Using the Zero Factor Principle: If ab=0 then a=0 or b=0, x-1=0 or
Solve - 1=0:
x = 1
Solve x² + 4x + 13 = 0: x² + 3i, x = - 2 - 3i
The solutions are
x = 1, x = -2+31, x = -2 - 31
The given equation be x - 1,
x-1= 0 then x = 1.
Therefore, the factors of the equation be x = 1, x = -2 + 3i, x = -2 - 3i and x = 1.
The complete question is:
If f(x) = 2x²+6x²+18x-26 and x-1 is a factor of f(x), then find all of the zeros of f(x) algebraically.
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Factored form of 6+27 using GCF
The factored form of 6 + 27 is 3(2 + 9) using GCF.
What is GCF?The greatest common factor, which is the product of two or more numbers, is the biggest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's components have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF)
The given expression is:
6 + 27
Take the factors of the individual numbers:
6 = 1, 2, 3, 6
27 = 1, 3, 9, 17
Take the common factor from both the numbers, in this case it is 3.
Now, factor out the number from the given expression:
6 + 27
3(2 + 9)
Hence, the factored form of 6 + 27 is 3(2 + 9) using GCF.
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shota is a dangerous fellow who likes to go rock climbing in active volcanoes. one time, when he was 30 3030 meters below the edge of a volcano, he heard some rumbling, so he decided to climb up out of there as quickly as he could. he climbed up at a constant rate. after 4.5 4.54, point, 5 seconds, he was 7.5 7.57, point, 5 meters below the edge of the volcano. how fast did shota climb? meters per second in total, how long did it take shota to reach the edge of the volcano? seconds
The speed at which Shola climbed is 5 m/s and the time taken by Shola to reach the edge is 6 seconds.
According to the question
Given:
The total distance traveled by Shola = 30 meters
He covered a total distance of 22.5 meters (i.e. 30 meters - 7.5 meters) in 4.5 seconds.
His speed is thus 5 m/s since speed is equal to both distance and time.
Since he has 7.5 meters to cover, the remaining distance,
Therefore, the time it took him to travel the distance was 7.5/5, or 1.5 seconds.
Consequently, the total amount of time needed to go 30 meters,
T=4.5+1.5=6, or one second.
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Answer:
Step-by-step explanation:
Just use a calculator
Daniel mows lawns on the weekends. He graphed his earnings below.
What is the rate he charges to mow?
A.
$11.50 per lawn
B.
$13.00 per lawn
C.
$30.00 per lawn
D.
$7.50 per lawn
Answer:
where's the graph?
Step-by-step explanation:
Please help like ASAP find the value of X please ASAP
The value of x is 15 and the angles in the pentagon are 105,49,90,33,83
What is interior angles in a pentagon ?
The interior angles in a pentagon are the angles which are inside the pentagon and sum of the interior angles in a pentagon is 540 degrees.
Given ,
From the figure we can say that it is pentagon.
And the sum of exterior angles in a pentagon is always 360 degrees.
SO,
7x+49+6x+33+83 = 360
13x + 165 = 360
13x = 360 - 165
13x = 195
x = 195 / 13
x = 15
So, the angles could be 7x = 7*15 = 105 and 6x = 6*15 = 90
Therefore, The value of x is 15 and the angles in the pentagon are 105,49,90,33,83 .
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the weights (in pounds) of three adult males are 160, 215, and 195. what is the standard error of the mean for these data?
The standard error of the mean for these data is 13.14 pounds..
The standard error of the mean (SEM) is a measure of the variability of the sample mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size.
To find the SEM for the given data, we first need to calculate the sample mean:
(160 + 215 + 195) / 3 = 190
Then we need to calculate the deviation of each value from the mean:
160 - 190 = -30
215 - 190 = 25
195 - 190= 5
Next, we need to square these deviations:
(-30)² = 900
25² = 625
5² = 25
Next, we need to calculate the variance:
(900 + 625 + 25) / 3 = 516 2/3
Then we need to calculate the standard deviation:
√(516 2/3) = 22.73
Finally, we can calculate the standard error of the mean:
22.73 / √(3) = 13.14
So, the standard error of the mean for these data is 13.14 pounds.
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Given the scatter plot, choose the function that best fits the data.
f(x) = 2^x
f(x) = 2x
f(x) = −2x
f(x) = 2x^2
The given scatter plot depicts the exponential function. Therefore, option 1 f(x) = 2ˣ is the correct one.
A scatter plot is a particular kind of graphic diagram that uses Cartesian coordinates to show the values of two variables for a collection of data.
We write y as the function of x as y=f(x). Here, f is considered the name of the function and x is the value of the function. To check which function depicts the given scatter plot, we have to substitute the values for x and find the function. Then, plot the graph.
By doing we get, the plot for f(x) = 2ˣ is equivalent to the given scatter plot. Because this graph depicts the exponential function where the graph passes through the point (0,1). Therefore, option 1 correctly depicts the given plot. Option 2 depicts the identity function and 4 depicts squaring or quadratic function.
To know more about exponential function:
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