The zeros of the polynomial p(x) = x³ + x² + 8x - 60 will be (- 2 + √4 i), (- 2 - √4 i) and 3.
Given that:
Polynomial, p(x) = x³ + x² + 8x - 60
A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
At x = 3, then we have
p(3) = 3³ + 3² + 8(3) - 60
p(3) = 60 - 60
p(3) = 0
The one zeros are 3. Then the other two zeros are given as,
(x³ + x² + 8x - 60) / (x - 3) = 0
[(x - 3)(x² + 4x + 20)] / (x - 3) = 0
x² + 4x + 20 = 0
x = [-4 ± √(4² - 4 × 1 × 20)] / (2 × 1)
x = - 2 ± √4 i
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Please help with this 8-9
Answer:
8) b. 15 m²
9) c. 63.5 ft²
Step-by-step explanation:
Area of composite figure:
8) To find the area of the composite figure, we have to add the area of rectangle, area of the top triangle and the area of the below triangle.
Rectangle:
length = 3m
width = 2.5 m
[tex]\boxed{\text{\bf Area of rectangle = length * width}}[/tex]
= 3 * 2.5
= 7.5 m²
Area of triangle:
[tex]\boxed{\text{\bf Area of triangle =$ \dfrac{1}{2}*base*height$}}[/tex]
Triangle1:
base = 3 m ; height = 1.5 m
[tex]\sf Area \ of \ triangle1 = \dfrac{1}{2}*3*1.5[/tex]
[tex]= 2.25 \ m^2[/tex]
Triangle2:
base = 3 m ; height = 2.5 + 1 = 3.5 m
[tex]\sf Area \ of \ triangle2 = \dfrac{1}{2}*3*3.5[/tex]
= 5.25 m²
Area of the figure = 7.5 + 2.25 + 5.25
= 15 m²
_______________________________________________________
9) To find area of the given area, add the area of rectangle1 and area of rectangle2.
length = 5 ft ; width = 5.5 ft
Rectangle1:
Area of rectangle1 = 5 * 5.5
= 27.5 ft²
Rectangle2:
length = 8ft
width = 10 - 5.5
= 4.5 ft²
Area of rectangle2 = 8 * 4.5
= 36 ft²
Area of the given figure = area of rectangle1 + area of rectangle2
= 27.5 + 36
= 63.5 ft²
rate of change between (-4,-12)and (2,4)
Answer: 2.667
Step-by-step explanation:
Answer:
Can you mark me brainiest.
Step-by-step explanation:
Instead of me telling you the answer I will make it easy for you go to M a th way its very easy.
Or 2.667
The density of milk is 1.03g/cm^3. What is the mass of 405 cm^3 of milk?
A 393.2
B 1016.2
C 206.23
D 417.15g
please help!!
The mass of 405 cm³ of milk is 417.15 g.
To solve this problem need to use the formula:
mass = volume x density
The volume of milk given in the problem is 405 cm³ and the density of milk is 1.03 g/cm³.
Substitute these values in the formula to calculate the mass of the milk.
mass = 405 cm³ x 1.03 g/cm³
mass = 417.15 g
The mass of 405 cm³ of milk is 417.15 g.
To understand the concept behind this formula we need to understand what density is.
Density is defined as the amount of mass per unit volume of a substance.
It is expressed in units of grams per cubic centimeter (g/cm³) for solids and liquids.
The formula for calculating the mass of a substance is the product of its volume and density.
In this problem we have been given the volume and density of milk so we can easily calculate its mass using this formula.
The density of a substance can vary with changes in temperature and pressure.
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Rewrite the expression as a single logarithm.
The expression [tex]3log_b(8) - log_b(7)[/tex] written as a single logarithm is [tex]log_b(\frac{512}{7})[/tex].
How to turn expressions into a single logarithm?Given the logarithmetic expression in the question:
[tex]3log_b(8) - log_b(7)[/tex]
To rewrite the expression [tex]3log_b(8) - log_b(7)[/tex] as a single logarithm, we can use the properties of logarithms.
Using the quotient rule property, which states that:
logₙ(a) - logₙ(b) = logₙ(a/b)
Applying the quotient rule:
First, rewrite [tex]3log_b(8) - log_b(7)[/tex] as:
[tex]log_b(8^3) - log_b(7)[/tex]
Now, since the base of the logarithm is the same (b), we can combine the two logarithms using the power rule, which states that logₙ(aᵇ) = b × logₙ(a).
[tex]log_b(\frac{8^3}{7})[/tex]
Simplify
[tex]log_b(\frac{512}{7})[/tex]
Therefore, the single logarithm is [tex]log_b(\frac{512}{7})[/tex].
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if a triangle has one side with a length of 20 meters and a second side with a length of 18 meters
Answer:
see attached
Step-by-step explanation:
You want the possible lengths of the third side of a triangle with side lengths 20 m and 18 m.
Triangle inequalityIf the third side is length c, the triangle inequality requires ...
18 +c > 20 ⇒ c > 2
20 +c > 18 ⇒ c > -2
18 +20 > c ⇒ c < 38
The possible lengths for the third side (c) are ...
2 < c < 38
That is, the third side must lie between the difference and the sum of the given sides.
The attachment shows the values on the list that are in this range.
The revenue generated by a company manufacturing lawn mowers is R= -0.5x^2+91x, where x represents the number of mowers produced. The cost to produce the mowers is C= 38x+300,where x is the number of mowers produced.
Find the profit polynomial (Hint: Profit = Revenue - Cost) that describes the total profit generated by the company manufacturing lawn mowers based on the number of mowers produced.
--------------------------.
Give the profit earned if 53 mowers are sold. ------------
add work please
The profit generated by the company manufacturing lawnmowers is given by the polynomial -0.5x²+ 53x - 300, where x is the number of mowers produced.
The profit generated by the company manufacturing lawn mowers is the difference between the revenue and the cost, so we can subtract the cost polynomial C= 38x+300 from the revenue polynomial R= -0.5x²+91x to obtain the profit polynomial:
P(x) = R(x) - C(x)
P(x) = (-0.5x²+91x) - (38x+300)
P(x) = -0.5x² + 53x - 300
Therefore, the profit generated by the company manufacturing lawnmowers is given by the polynomial -0.5x²+ 53x - 300, where x is the number of mowers produced.
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POLYGONS IN THE COORDINATE PLANE
Please help!
Worth a lot.
Note that from the coordinates of the above triangle, we can state that the triangle is an Isoceles triangle.
We can also state emphatically that it is NOT a right triangle.
What is the justification for the above?a) we now that the triangle is a scalene triangle because all three sides have unequal lengths.
This can be determined with the use of distance formula.
d = √((x2 - x1)² + (y2 - y1)²)
PQ = √((2-4)² + (7-1)²)
= 6.32455532034
PQ ≈ 6. 33
Using the same steps above,
QR = 6.33
Using the same steps
RP = 5.66
From the above as well as is show on the attached graph, we can see that the triangle has two equal sides hence an Isosceles triangle.
b) We know for a fact using the graphical method that the above triangle is NOT a right triangle.
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What is the solution to the equation Negative 3 (h + 5) + 2 = 4 (h + 6) minus 9?
Answer:
h = -10
Step-by-step explanation:
The solution to the equation is h = -10. To solve for h, we need to isolate h on one side of the equation. We do this by adding 9 to both sides, subtract 4h from both sides, and add 5 to both sides. This gives us:
Negative 3 (h + 5) + 2 + 9 = 4 (h + 6) - 9 + 9
Negative 3h + 14 = 4h + 15
Negative 3h - 4h = 15 - 14
-7h = 1
h = -1/7
h = -10
Please help asap !!! I will give points !!!
The value of p when q is 2 is 1
What is inverse variation?Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.
This means that has x increases y will decrease and vice versa.
If p is inversely proportional to q , then p = kq
when p = 2, q = 4
2 = k4
k = 2/4
k = 1/2
When q = 2
p = 1/2 × 2
p = 1
Therefore the value of p is 1
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Given that events A and B are independent with P(A) = 0.68 and
P(A and B) = 0.544, determine the value of P(B), rounding to the nearest
thousandth, if necessary.
The value of P (B) = 0.8
The probability of event A, P (A) = 0.68
The probability of events A and B, P (A ∩ B) = 0.544
The probability of event B, P (B) = ?
We know that Independent events are those where the probability of A event occurring doesn't affect the probability of B event. In other words, they don't depend upon each other and are independent.
By formula;
P (A ∩ B) = P (A) . P (B)
By substituting the values to the above equation, we get;
0.544= 0.68 * P (B)
P (B) = 0.8
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. Out of 250 randomly selected people who rode a jet 'ski, 90% wore life vests. Out of 275 randomly selected
boaters, 85% wore life vests. For a two proportion 95% confidence interval, find the margin of error. Use at least
two decimal places.
The margin of error for the two-proportion 95% confidence interval is 0.0662.
The margin of error for a two-proportion 95% confidence interval can be calculated using the following formula:
ME = z√(p₁(1-p₁)/n₁ + p₂(1-p₂)/n₂)
where ME is the margin of error, z is the z-score corresponding to the level of confidence (in this case 1.96 for a 95% confidence interval), p₁ and p₂ are the sample proportions, and n₁ and n₂ are the sample sizes.
Using the given information, we have:
Sample 1: n₁ = 250, p₁ = 0.90
Sample 2: n₂ = 275, p₂ = 0.85
Level of confidence: 95%
Substituting these values into the formula, we get:
ME = 1.96√[(0.90×0.10 / 250) + (0.85 × 0.15 / 275)]
ME = 0.0662
Therefore, the margin of error for the two-proportion 95% confidence interval is 0.0662.
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A coin-operated machine sells plastic rings. It contains 5 white rings, 6 orange rings, 7 purple rings, and 15 pink rings. Constance puts a coin into the machine. Find the theoretical probability she gets a orange ring. Express your answer as a decimal. If necessary, round your answer to the nearest thousandth.
The theoretical probability of Constance getting an orange ring from the coin-operated machine is 0.182. This means that out of all the possible outcomes, there is an 18.2% chance that Constance will get an orange ring.
To find the theoretical probability of Constance getting an orange ring from the coin-operated machine, we need to first understand what theoretical probability means. Theoretical probability is the likelihood or chance of an event happening based on the number of possible outcomes. In this case, the possible outcomes are the different colored rings that the machine contains.
We are given that the machine contains 5 white rings, 6 orange rings, 7 purple rings, and 15 pink rings.
Therefore, the total number of rings in the machine is 5 + 6 + 7 + 15 = 33.
The probability of Constance getting an orange ring can be calculated by dividing the number of orange rings by the total number of rings in the machine.
Therefore, the theoretical probability of Constance getting an orange ring is:
6 / 33 = 0.181818...
To express this as a decimal, we can round it to the nearest thousandth, which is 0.182.
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(h) Three meals per day are provided by the hotel. The hotel will charge a total of $9,240 for all meals for the entire group. What is the cost of meals for each person?
Answer:
$3,080 for each person
Step-by-step explanation:
9,240 / 3 = 3,080
asap 100 points step by step what is the value of x in x. in x/-9=0
Answer: x = 0
Step-by-step explanation:
Anything divided by 0 equals 0
Multiply -9 to the other side
x = 0 × -9
Anything Multiplied by 0 equals 0
x = 0
pls help!!!!!!!!!!!!!!!!!!!!!!!!!!
The area of the regular polygon, given the apothem and the side length, would be 52. 5 in².
How to find the area ?To find the area of a regular pentagon with a given apothem (a) and side length (s), we can use the formula:
Area = ( Perimeter × Apothem ) / 2
Perimeter would be :
= 5 x sides
= 5 x 6
= 30 inch
The area is therefore :
= ( Perimeter × Apothem ) / 2
= ( 30 in x 3. 5 in ) / 2
= 105 / 2
= 52. 5 in²
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I neeeeeeed help. Pleaseeee helpppp. I dont get the last question like what am i supposed to do?
Answer:
0.1429
Step-by-step explanation:
The formula for the average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]. a = 0, b = 7, f(a) = 2, and f(b) = 3, We plus the numbers into the formula and get 0.1429 as our answer.
The heights of a certain group of adult parrots was found to be normally distributed. The mean height is 34cm with a standard deviation of 8cm. IN a group of 400 of these birds, how many would be more than 18cm tall?
The required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.
Given that the heights of adult parrots are normally distributed with a mean height of 34 cm and standard deviation of 8 cm.
The formula used to calculate the z-score for the height of 18 cm is
z = (x - mean) / standard deviation
By substituting the value of mean and standard deviation gives,
z = (18 - 34) / 8.
On simplification of numerator gives,
z= -16 / 8 = -2.
To find the proportion of parrots more than 18 cm tall by calculating the area under the standard normal curve to the right of z = -2 by the standard normal distribution table.
That implies, proportion = area to right of z = -2 is approximately equal to 0.9772.
The formula used to calculate the number of parrots that is more than 18 cm tall is proportion × total number of parrots.
That implies, the number of parrots out of 400 birds which are more than 18 cm tall is 0.9772 × 400 = 390.88 ≈ 391.
Therefore, the required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.
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write a paragraph of 10 lines where you explain how human actions to the surrounding cause causes health problems
Human actions and behaviors towards our surroundings can have significant implications for human health, leading to the emergence of various health problems.
How can human actions cause health problems ?Our choices and activities encompassing lifestyle, pollution, and resource utilization exert direct impacts on our overall well-being. For instance, our exposure to environmental pollutants, encompassing air and water contaminants, toxic substances, and hazardous waste, can engender respiratory ailments, cancer, and an array of severe health conditions.
Similarly, the degradation of natural habitats, deforestation, and unsustainable practices contribute to the proliferation of infectious diseases, disrupt ecological balance, and undermine the stability of our food systems.
Moreover, unhealthy dietary patterns, sedentary behaviors, and limited access to healthcare services compound the complexities of prevailing health issues.
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Andrea tossed a fair number cube with faces numbered 1 through 6 a total of 30 times. The number 4 came up 8 times. How do Andrea’s results compare to the expected probability of getting the number 4 on 30 tosses?
a. The outcome of 4 occurred 3 more times than expected.
b. The outcome of 4 occurred 3 less times than expected.
c. The outcome of 4 occurred 2 more times than expected.
d. The outcome of 4 occurred 2 less times than expected.
The outcome of 4 occurred 3 more times than expected. This is the resulting probability. Therefore, the correct option is option A.
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which anything is probable to happen is basically what probability means. The outcome of 4 occurred 3 more times than expected.
Therefore, the correct option is option A.
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Suppose there is a regular polygon that can be decomposed into 46 triangles. The measure of one of it’s interior angles is (9.5x+26)
The value of x is equal to 15.1 units.
How to determine the value of x?In Mathematics and Geometry, the measure of each interior angle of a regular polygon can be calculated by using this mathematical equation:
Interior angle = [180 × (n - 2)]/n
Where:
n represents the number of sides of a regular polygon.
Since this regular polygon can be decomposed into 46 triangles, it ultimately implies that it has 46 x 3 = 138 sides.
Therefore, the value of each interior angle can be calculated as;
Interior angle = [180 × (n - 2)]/n
Interior angle = [180 × (138 - 2)]/138
Interior angle = 169.6⁰
For the value of x, we have:
9.5x + 26.2 = 169.6
9.5x = 143.4
x = 15.1 units.
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Complete Question:
Suppose there is a regular polygon that can be decomposed into 46 triangles. The measure of one of its interior angles is (9.5x+26.2).
What is the value of x?
Does the dollar belong inside the cash box or not? Explain your reasoning
We can see here that the dollar doesn't belong to the box.
How we arrived at the solution?We can see here that in order to known if the dollar belongs to the box or not, here is an explanation:
Let the single tickets = x
and the couples tickets = y
Note: $8 = 2 tickets (for couples),
Thus, 1 ticket = $4
5x + 4y = 200 -------(1)
x + y = 47 ----------- (2)
-4 × (2)
5x + 4y = 200 -------(1)
-4x - 4y = 188
x = 12
Substituting 12 in (2)
12 + y = 47
y = 47 - 12 = 35
y = 35
So, 5x + 4y = 200
5 (12) + 4 (35) = 200
60 + 140 = 200.
Thus, we see here that the dollar doesn't belong to the box.
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what value of X makes the model true?
The value of x is -1 which makes the model true
The equation from the given model will be 5x+6=1
We have to find the value of x
5x+6=1
Subtract 6 from both sides
5x=-5
Divide both sides by 5
x=-1
Hence, the value of x is -1 which makes the model true
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Seward Elementary School plans to sell friendship bracelets. The bracelets can be purchased from three
companies.
Company C charges $27 for 15 bracelets, plus a flat rate of $18 for shipping any number of bracelets.
Let n be a number of bracelets, and let t be the total cost in dollars.
For Company C, write an equation for the total cost in dollars t in terms of the number of friendship
bracelets n.
t=
In +
Answer:
Step-by-step explanation:
For Company C, the total cost in dollars, denoted as t, can be calculated using the following equation:
t = 27n + 18
In this equation, 27n represents the cost of the bracelets (charging $27 per bracelet), and 18 represents the flat rate for shipping any number of bracelets. By summing these two components, we obtain the total cost of the friendship bracelets from Company C in terms of the number of bracelets, n.
Determine the values of k for which the equation has no solutions:
|2x + 7|-k≤5
Ok> 5
Ok < 5
Ok < -5
Ok> -5
The expression has no solution when k < - 5.
Hence, option B is correct.
The given inequality is
|2x + 7|-k ≤ 5
We know that,
A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count.
A function with absolute values is another name for it.
No matter what input was provided to this function, the outcome is always favorable.
Now adding k both sides of inequality,
⇒ |2x + 7| ≤ 5 + k
When we take value of k less than -5
Then the expression |2x + 7| becomes negative.
Since it always gives absolute value,
Therefore,
There is no any solution when k < -5.
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Graph slope =-3 y-intercept=4
Answer:
Step-by-step explanation:
slope intercept: y = mx + b
where m is the slope and b is the y-intercept
Equation: y = -3x + 4
Since y-intercept is given, then we have the first point of the line as (0,4)
Let's find the value of x when y is 0
y = -3x + 4
0 = -3x + 4
3x = 4
x = 4/3
(4/3,0) ---second point
Since there are two points/coordinates already then we can now plot/graph.
De 2. A barbeque shop sells sausage and brisket by the pound. The first customer
orders 2 pounds of sausage and 3 pounds of brisket for $21. The second
customer orders 10 pounds of sausage and 14 pounds of brisket for $100.50.
Which two equations can be used to create a system of equations in order to
find the cost per pound of sausage, s, and brisket, b?
Select TWO correct answers.
< PREVIOUS
(02)
8
De
8
8
8
2b + 3s = 21
25+ 3b 100.5
10s+ 14b 100.5
10b+ 14s 100.5
2s + 3b = 21
NEXT >
The cost per pound of sausage, s, and brisket, b is 10s + 14b = 100.5
We are given that;
First customer order= $21
Second customer order= $100.50
Now,
The two equations that can be used to create a system of equations are:
2s + 3b = 21 10s + 14b = 100.5
These equations are obtained by multiplying the cost per pound of sausage and brisket by the number of pounds ordered by each customer and setting them equal to the total cost for each customer. The variables s and b represent the cost per pound of sausage and brisket, respectively.
Therefore, by the equation the answer will be 10s + 14b = 100.5
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What is the domain of the exponential function?
[tex]y=2^{x}+6[/tex]
The domain of the exponential function is all real numbers.
The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.
For the exponential function y = 2ˣ + 6, the domain includes all real numbers.
This is because there are no restrictions on the input values that can be plugged into the function.
We can take any real number x, substitute it into the expression 2ˣ, and then add 6 to get a corresponding output value y.
Hence, the domain of the exponential function is all real numbers.
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Need help on this!!!!!!!!
A. The greatest number of packages that can fit the truck is 24000
B. The volume of the part that is filled is 375 cubic feet
A. How to determine the greatest number of packagesGiven that
Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft
Also, we have
Package = 1/4 foot cube
So, we have
Number of packages = (8 * 6 1/4 * 7 1/2)/(1/4 * 1/4 * 1/4)
Evaluate
Number of packages = 24000
This means that the greatest number of packages is 24000
B. How to determine the volume of the part that is filledRecall that
Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft
So, we have
Volume = (8 * 6 1/4 * 7 1/2)
Evaluate
Volume = 375
Hence, the volume is 375 cubic feet
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How do I solve for this?
The first function in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]
Writing the trigonometry function in terms of the otherFrom the question, we have the following parameters that can be used in our computation:
First = tan(θ)
Second = cos(θ)
The basis trigonometry identity is
sin²(θ) + cos²(θ) = 1
Divide through the equation by cos²(θ)
So, we have
tan²(θ) + 1 = 1/cos²(θ)
Subtract 1 from both sides
tan²(θ) = - 1 + 1/cos²(θ)
Take the square root of both sides
tan(θ) = √[-1 + 1/cos²(θ)]
Hence, the first in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]
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an expression is given -2y+3/2x+7/4 which are equivelent to the given expression
The equivalent value of the expression is A = ( -16y + 12 + 7 ) / 8x
Given data ,
Let the equation be represented as A
Now , the value of A is
A = -2y+ 3/2x + 7/4
On simplifying , we get
A = ( -4y + 3 )/2x + 7/4
Taking LCM on both sides , we get
A = ( -16y + 12 + 7 ) / 8x
Hence , the expression is A = ( -16y + 12 + 7 ) / 8x
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