The solutions to the equation x³ - x² - 18 = 0 are given as follows:
x = 3, x = -1 ± 2.236i.
How to obtain the solutions to the equation?The equation for this problem is defined as follows:
x³ - x² - 18 = 0
x - 3 is a factor, hence one solution is given as follows:
x - 3 = 0
x = 3.
Also considering that x - 3 is a factor, and x - 3 is of the first degree while the equation is of the third degree, we have that:
(x - 3)(ax² + bx + c) = x³ - x² - 18
ax³ + (b - 3a)x² + (c - 3b)x - 3c = x³ - x² - 18
Hence the coefficients are given as follows:
a = 1.b - 3 = -1 -> b = 2.-3c = -18 -> c = 6.Hence the remaining solutions are given as follows:
x² + 2x + 6 = 0.
Using a quadratic function calculator:
x = -1 ± 2.236i.
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Jorge asked each of the 24 students in his class if they play a musical instrument. He also asked each student if they play a sport. He gathered the following results:
6 students play both a musical instrument and a sport.
3 students play neither a musical instrument nor a sport.
14 students in total play a sport.
Can you help Jorge organize the results into a two-way frequency table?
i need help with this for math class
The expression that shows an equivalent expression include the following:
1/4(14x - 8 + 6x) = 5x - 2.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we have the following mathematical expression:
1/4(14x - 8 + 6x)
By opening and expanding the bracket, we have the following mathematical expression:
1/4(14x - 8 + 6x) = 1/4(20x - 8)
1/4(20x - 8) = 5x - 2
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what is - 3x > 15 equal to
Answer:
x < -5
Step-by-step explanation:
- 3x > 15 is equal to x < -5
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Consider the function.
Match each transformation of f(x) with its description.
g(x) = 2x
g(x) = 8x
-
10
6
g(x)
f(x) = 2x - 6
= 2x - 2
g(x) = 8x 24
-
compresses f(x) by a factor
of toward the y-axis
shifts f(x) 4 units right
stretches f(x) by a factor
of 4 away from the x-axis
shifts f(x) 4 units down
g(x) = 2x - 14
g(x) = 82 - 4
The transformations are matched accordingly is given below.
What are the matching transformations?A function transformation takes whatever the underlying function f (x) is and "transforms" (or "equates") it, which is a fancy way of saying you alter the equation and shift the graph over.
Parent function is given as f(x) = 2x - 6
The transformations are shifts f(x) 4 units down
f(x) → f(x) - 4
⇒ g(x)= 2x - 6 - 4 = 2x - 10
Then stretches f(x) by a factor of 4 away from the x-axis
f(x) → 4*f(x)
⇒ g(x) = 4(2x - 6) = 8x - 24
Now shifts f(x) 4 units right
f(x) → f(x - 4)
⇒ g(x) = 2(x - 4) - 6 = 2x - 14
To compresses f(x) by a factor of toward the y-axis (must be 4)
f(x) → f(4x)
⇒ g(x) = 2*4x - 6 = 8x - 6.
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Use a 10-by-10 grid to solve.
What is 12% of 150?
At soccer practice last night, Leroy made 4 times as many penalty kicks as he missed.
Pick the diagram that models the ratio in the story.
If Leroy made 9 more penalty kicks than he missed, how many penalty kicks did he make?
Penalty kicks:
The model that would model the ratio is 4 : 1
the penalties made is given as 12
How to solve for the penaltiesTo get the penalty kicks that he made given that he made 9 more penalty kicks than he missed
let the penalty kicks be
= x
if he made more than 9 than missed we would have
x + 9 = 4
x = 1
cross multiply
1 (x + 9) = 4 * X
x + 9 = 4x
9 = 3x
x = 3
since x + 9 penalties made
3 + 9 = 12
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As Bin is driving her car, she notices that after 1 hour her gas tank has 7.25 gallons left and after 4 hours of
driving, it has 3,5 gallons of gas left in it.
(3) Represent this information as two coordinate
pairs in the form (1, g), Where A is the
number of hours driven and g is the gallons of Gas left
Bin had 7.25 gallons of gas to start with using the unitary method.
Unitary method is a problem-solving technique that involves finding the value of one unit and using it to calculate the value of other units. In this case, we will use unitary method to find the number of gallons Bin had to start with.
Firstly, we need to find the rate of gas consumption. The slope of the line, which is the change in the gas level over time, gives us this information. Since the slope is -1.25, this means Bin is losing 1.25 gallons of gas per hour.
Next, we need to find the total time Bin has been driving. From the problem, we know that after 1 hour, she had 7.25 gallons left, and after 4 hours, she had 3.5 gallons left. This means that she drove for 3 hours (4-1).
Using the unitary method, we can calculate the total amount of gas Bin had to start with. We know that she lost 1.25 gallons of gas per hour, and she drove for 3 hours. Therefore, she lost a total of 3.75 gallons of gas during the trip.
To find the initial gas level, we need to subtract the amount of gas she lost from the gas level she had at the end of the trip. This gives us:
Initial gas level = Gas level at end of trip + Gas lost during the trip
Initial gas level = 3.5 gallons + 3.75 gallons
Initial gas level = 7.25 gallons
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Complete question:
As Bin is driving her car, she notices that after 1 hour her gas tank has 7.25 gallons left and after 4 hours of driving, it has 3.5 gallons of gas left in it. The rate at which she is LOSING gas is 1.25 gallons....So, the slope is -1.25. How many gallons did she have to START?
volume of prism
25cm 40cm
Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.
Answer:
The volume of a rectangular prism with length 25 cm and width 40 cm can be calculated as follows:
Volume = Length * Width * Height
Since the height is not given, we cannot calculate the exact volume.
Step-by-step explanation:
g knowing the value of p tells one: select one: a. the size of the difference between two groups or means. b. whether there is statistical significance. c. the correlation between two groups or means. d. the t value.
Knowing the value of p tells one that option b. whether there is statistical significance.
The concept of probability, which is a measure of the likelihood of an event occurring. It is an essential tool in statistics, and it helps us make informed decisions based on data.
Now, let's dive into the answer to the question. Knowing the value of p tells us about the statistical significance of our results. In statistical analysis, we often conduct hypothesis tests to determine whether a particular effect is significant or just occurred by chance.
The p-value is the probability of observing the results we obtained under the null hypothesis, assuming that the null hypothesis is true. The null hypothesis is the default assumption that there is no significant difference between groups or means.
If the p-value is low, say less than 0.05, we reject the null hypothesis and conclude that there is a significant difference between groups or means. On the other hand, if the p-value is high, we fail to reject the null hypothesis, and we cannot claim that there is a significant difference between groups or means.
To give an example, suppose we conducted an experiment to test whether a new drug reduces blood pressure. We would have a control group that receives a placebo and a treatment group that receives the drug. We measure the blood pressure of both groups and compute the p-value. If the p-value is less than 0.05, we would conclude that the drug is effective in reducing blood pressure.
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8. the weights of cows offered at an auction in one region are normally distributed with a mean of 825.0 pounds and a standard deviation of 74.8 pounds. one cattleman only wants to bid on cows that are in the top 5% of weight. what is the lowest weight cow that the cattleman should bid on
The cattleman should bid on cows that weigh at least 944.0 pounds, which is the weight corresponding to the top 5% of the normally distributed weights of cows.
To determine the lowest weight cow that the cattleman should bid on, we need to find the weight that corresponds to the top 5% of the weight distribution.
Using the standard normal distribution, we can find the z-score that corresponds to the top 5% of the distribution as follows:
z = invNorm(0.95) ≈ 1.645
where invNorm is the inverse of the standard normal cumulative distribution function, which can be found using a statistical calculator or a standard normal distribution table.
Next, we can use the z-score formula to convert the z-score to a weight value:
z = (x - μ) / σ
Solving for x, we get:
x = z * σ + μ
Substituting the values given in the problem, we get:
x = 1.645 * 74.8 + 825.0
x ≈ 944.0 pounds
Therefore, the cattleman should bid on cows that weigh at least 944.0 pounds.
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You started a savings account by depositing $4,200. The savings account earns 2.1% APY, compounded monthly. What was the balance in the account after 2 months?
1=Prt
4214.7 is the balance in the account after 2 months .
What does compound and simple interest mean?
A fixed proportion of the principal amount borrowed or lent is what is known as simple interest and is paid or received over a given period of time.
Borrowers are required to pay interest on interest in addition to principal because compound interest accrues and is added to the total amount of interest from earlier periods.
P = $4200
R = 2.1% = 2.1/100 = 0.021 =
T = 2 month = 2/12 = 1/6
I = PRT
= 4200 * 0.021 * 1/6 = 14.7
Amount = P + I = 4200 + 14.7 = 4214.7
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The graph of g(x) = |x – h| + k is shown on the coordinate grid. What must be true about the signs of h and k?
Both h and k must be positive.
Both h and k must be negative.
h must be positive and k must be negative.
h must be negative and k must be positive.
On solving the provided question we can say that from the graphs,
y = f(x) = |x| and g(x) = |x-h| + k
What is graphs?Mathematicians use diagrams to logically bring facts or values using visual representations or charts. A graph point usually reflects a contact between two or more things. Nodes or vertices and corner form a graph, which is a nonlinear data construction. We often glue knots together called vertices. This graph has vertices V=1, 2, 3, 5 and edges E=1, 2, 1, 3, 2, 4 and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) are graphical representations of expanding growth. Logarithmic graph in the format of a triangle
from the graphs,
y = f(x) = |x|
y = f(x) + k
y = f(x+h)
g(x) = |x-h| + k
now, it will be
k>0 and h<0
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Use the law of sines to find each missing side or angle
15
12
128
X
The missing angle is approximately 108.5 degrees.
What is the law of sines?Law of sines is a trigonometric formula that relates the sides and angles of any triangle. Specifically, the law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.
Using the law of sines:
sin(128°)/15 = sin(x)/12
Multiplying both sides by 12:
sin(x) = 12sin(128°)/15
Taking the inverse sine of both sides:
x = sin^-1(12sin(128°)/15)
x ≈ 108.5°
Therefore, the missing angle is approximately 108.5 degrees.
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A grain silo has a cylindrical shape. Its diameter is 17 , and its height is 38. What is the volume of the silo?
The volume of the silo of cylinder shape containing grain is 8625.24 cubic units.
The volume of the cylindrical shaped grain silo will be calculated by the formula -
Volume = πr²h, where r represents radius and h represents height of the cylinder.
Now, as we know radius is half of the diameter. So, radius = 17/2
Performing division on Right Hand Side of the equation
Radius of the cylinder = 8.5
Keep the values in formula to find the value of volume of silo
Volume = π × 8.5² × 38
Taking square and performing multiplication on Right Hand Side of the equation
Volume = 8625.24 cubic units
Hence, the volume is 8625.24 cubic units.
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What is A ‘ C please help
Answer: 11.7 in.
Step-by-step explanation:
I don't really know this stuff myself since I'm in 8th grade, but I can say that AA is 12in. long. I measured the length of A'C, and it was a little shorter than AA. So therefore, I think the answer is 11.7 in. I just wanted to help you out.
Find each percent change. Use a calculator and round answer to the nearest tenth as needed. State if it is an increase or decrease. 88 to 20.
A.22.7% decrease
B.14.2% decrease
C.77.3% decrease
D.340% decrease
well, if a value goes from 88 to 20, it clearly decreased, hmmm 88 - 20 = 68, by 68 units.
so if we take 88(origin amount) to be the 100%, what's 68 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 88 & 100\\ 68& x \end{array} \implies \cfrac{88}{68}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 22 }{ 17 } ~~=~~ \cfrac{ 100 }{ x }\implies 22x=1700\implies x=\cfrac{1700}{22}\implies x\approx 77.3[/tex]
What is the area of the following composite figure? All angles are right angles. 22 m 2 29 m 2 24 m 2 27 m 2
The area of the composite figure is 24m², which is option C.
What is a composite figure?
A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. To get the area of a composite shape, first determine the individual areas of every component. The total of the individual regions will then represent the area of the composite shape.
From the figure, we can see that from a big rectangle, 4 small identical squares of side 1m are cut from each corner.
We are asked to find the area of the rest of the rectangle which makes the composite figure.
W first find the area of the original rectangle.
Its length = 5 + 1 + 1 = 7 m
Its breadth = 2 + 1 + 1 = 4 m
So the area of the rectangle = length * breadth = 7*4 = 28 m²
Now the side length of the square = 1 m
Area of one square = 1*1 = 1m²
So are of four identical squares = 4 * 1 = 4 m²
Therefore area of the composite figure = area of big rectangle - area of 4 squares = 28 - 4 = 24m²
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Answer:
24m^2 is ur answer
Step-by-step explanation:
Hope this helps
If 7 book cost rs 300 than 5 same books find the cost of a book
When the cost of 7 books is equal to Rs 300 more than the 5 same books then the cost of a single book is equal to Rs 150.
Let us consider Rs 'x' be the cost of a single book .
Equation to represents the given expression 7 books is equal to Rs 300 more than the 5 same books is :
⇒ 7x = 300 + 5x
Subtract 5x from both the side of the equation we get,
⇒ 7x -5x = 300 + 5x - 5x
⇒ 2x = 300
Divide both the side by 2 we get,
⇒ 2x / 2 = 300 / 2
⇒ x = Rs. 150
Therefore, the cost of a single book as per the given condition of 7 books is equal to Rs 300 more than the 5 same books is given by Rs 150.
The above question is incomplete, the complete question is:
If 7 books cost Rs. 300 more than 5 books, find the cost of a book.
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When you
make a stem-and-leaf plot for the data set
5.6, 5.4, 4.1, 3.2, 4.7, 3.9, which place value
will the stems represent? Which place
value will the leaves represent?
The values on the stem are {5, 5, 4, 3, 4, 3} and the leaf of the data set is represented by {6, 4, 1, 2, 7, 9}.
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.
A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf.
According to the stem leaf plot the first digit is the stem and the second digit is the leaf.
Hence, the values on the stem are {5, 5, 4, 3, 4, 3} and the leaf of the data set is represented by {6, 4, 1, 2, 7, 9}.
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Use the vertex ( h, k ) and a point on the graph ( x, y ) to find the standard form of the equation of the quadratic function:
Vertex = (1,-5)
Point = (5,-7)
G( x )= Answer field 1
(x- Answer field 2
)^2 +Answer field 3
The standard form of the equation of the quadratic function is y = -1/8x^2 + 1/4x - 41/8
How to find the standard form of the equation of the quadratic functionFrom the question, we have the following parameters that can be used in our computation:
(h, k) = (1, -5)
(x, y) = (5, -7)
A quadratic function is represented as
y = a(x - h)^2 + k
So, we have
y = a(x - 1)^2 - 5
Given that
(x, y) = (5, -7)
We have
-7 = a(5 - 1)^2 - 5
This gives
16a = -2
So, we have
a = -1/8
Recall that
y = a(x - 1)^2 - 5
So, we have
y = -1/8(x - 1)^2 - 5
Expand
y = -1/8(x^2 - 2x + 1) - 5
This gives
y = -1/8x^2 + 1/4x - 41/8
So, the required equation is y = -1/8x^2 + 1/4x - 41/8
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Joseph runs 212 miles on Monday. Each day after that, he runs the same 113 mile route every morning. His goal is to run at least 6 miles by the end of the week. Which inequality represents the least number of days after Monday that Joseph needs to run to reach his goal?
The inequality that represents the least number of days after Monday that Joseph needs to run to reach his goal is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
Number of miles that Joseph run on Monday = [tex]2\frac{1}{2}[/tex] miles
Number of miles that Joseph run each day after that = [tex]1\frac{1}{3}[/tex] miles
The inequality is the mathematical statement that shows the relationship between two expression using an inequality symbol. The inequality symbols are less than, greater than, less than or equal and greater than or equal.
Then the inequality will be
[tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
Where x is the number of days after Monday that Joseph needs to run to reach his goal
Therefore, the inequality is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
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y=x^2 6 units to the left 2 units up
The translation of the graph is represented by y = -6(x+2)² - 7.
What is translation ?A translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.
Given that the graph of y= x² translated left 2 units and up 8 units. The translated equation is:-
Start with y = x².
Shift 2 units left to get y = (x+2)².
Vertically stretch to get y = 6(x+2)².
Reflect across x-axis to get y = -6(x+2)².
Shift 7 units down to get y = -6(x+2)² - 7.
Hence, the translation of the graph is represented by y = -6(x+2)² - 7.
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The question is incomplete so solved for,
Suppose the graph of y= x^2 translated left 2 units, and up 8 units
There are cups in a gallon.
The equation gives the number of cups in terms of the number of gallons.
Write an equation for this situation that gives the number of gallons in terms of the number of cups.
Answer:
16c
Step-by-step explanation:
Answer:
g = 16c
Step-by-step explanation:
Let's use g (the number of gallons) and c (the number of cups).
Since there are 16 cups in one gallon, the equation can be represented by:
one gallon = 16 cups →
g = 16c.
We use the coefficient to represent the quantity of cups needed to make one gallon.
The staff at a company went from 40 to 29 employees. What is the percent decrease in staff
Answer:
27,5%
Step-by-step explanation:
To find the percent decrease, we need to calculate the difference between the original number and the new number and then divide it by the original number and multiply by 100%.
The difference is 40 - 29 = 11.
The percent decrease is (11/40) * 100% = 27.5%
So the percent decrease in staff is 27.5%
Determine the solution to the system of equations represented by the tables below.
-3 -2
-1 0
6
4
2 0
X
f(x)
X
g(x)
-2
7
-1
2
0 1
-3-8
Answer:
(-1, 2)
Step-by-step explanation:
The solution to a system of equation will always intersect on a graph, which means that at a certain point, they will have the same x and y coordinate.
As we can see from the table, for both f(x) and g(x) when x = -1, y = 2, which is the intersection point.
The points A B C D and E lie on the circle PAQ is a tangent to the circle at A and EC=EB Angle ECB=80° and angle ABE = 40° Find the values of v w x y and z
The values of v w x y and z are given below:
v= 40°w= 80°x= 40°y= 80°z= 80°How to solve these<EDA= <EBA= 40°
==> x= 40°
This is because the circumferential arc of the same arc is equal.
<PAE= <ADE= 40°
=>v= 40°
This is based on the alternate segment theorem.
Because EC= EB, <ECB= <EBC= 80°
=> w= 80°
This is based on the properties of an isosceles triangle.
<ECB = <EAB = 80°
=> y= 80°
This is because the circumferential angle of the same arc are equal
Because <EBC = <ECB= 80°
=> <BEC = 180° -(80 x2)
= 20°
This is because the sum of the interior angles of the triangle is 180°
<AEB = 180°-y - <ABE
= 60°.
<AEC = <AEB + <BEC= 60° + 20°
=80°.
So <ADC = <AEC = 80°
=> = 80°
This is because the circumferential angle of the same arc are equal
Therefore,
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four friends attended a school play and pay $6.25 per ticket. Each also buys a healthy snack bag sold by the theater club. If the friends spent a total of $37.00, how much did they each healthy snack beg cost, b? write and solve an equation.
Answer:
Since each ticket cost $6.25, then to find the total they spent on tickets you will multiply 6.25 by itself 4 times:
6.25 * 4 = 25
They spent $25 on movie tickets.
You can subtract that from the $37 to find the total they spent on the snacks:
37 - 25 = 12
Th spent $12 in total on movie snacks. Now to find how much they cost each, yo will divide that total by the 4 friends:
12/4 = 3
The movie snacks cost $3 each.
Step-by-step explanation:
Hope it helps! =D
A total of 709 tickets were sold for the school play. They were either adult tickets or student tickets. There were 59 more student
tickets sold than adult tickets. How many adult tickets were sold?
Solving the Question
First, assign variables to the given information:
Let the number of student tickets sold be x.Let the number of adult tickets sold be y.We're given:
[tex]x+y=709[/tex][tex]x=59+y[/tex]Plug the second equation into the first and solve using substitution:
[tex]x+y=709\\59+y+y=709\\59+2y=709\\2y=650\\y=325[/tex]
Therefore, 325 adult tickets were sold.
Answer325 adult tickets were sold.
robin is twice as old as earl and adam is 8 years younger than earl. in 6 years robin will be three times as old as adam. find their present ages
The present age of Earl is 12 years, Robin is 24 years and Adam is 4 years old.
Let us consider the present age of Earl to be x years.
According to the given question, the present age of Robin is twice that of Earl = 2x
And since it is given that Adam is 8 years younger than Earl, then his age
= x - 8
After 6 years, the age of Earl will be x + 6
Robin's age will be = 2x + 6
Adam's age will be = x - 8 + 6 = x - 2
According to the given question, Robin's age will be thrice the age of Adam.
Hence, 2x + 6 = 3 (x - 2)
⇒ 2x + 6 = 3x - 6 ⇒ 6 + 6 = 3x - 2x ⇒ 12 = x
Thus, the present age of Earl is 12 years,
Robin's age = 2x = 2 x 12 = 24 years
Adam's age = x - 8 = 12 - 8 = 4 years
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i need help guysss
schoology
Solving an equation we will see that the measure of angle a is 68°.
How to find the measure of the missing angle?We want to find the measure of angle a. On the image we can see that we have 3 angles, and the sum of these 3 angles should be equal to 180°, then we can write the equation:
28° + 90° + a = 180°
(the 90° angle is the one with the square).
Solving that equation for a, we will get:
a = 180° - 90° - 28°
a = 90° - 28°
a = 62°
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