The roots of the polynomial are:
2, -9 (with a multiplicity of 4), and -14
What are the roots of the polynomial?Remember that for a polynomial of degree N with the roots:
{x₁, ..., xₙ}
Can be written as:
P(x)= (x - x₁)*(x - x₂)*...*(x - xₙ)
Here the polynomial given is:
P(x) =(x+2)(x-9)^4(x-14)
We can expand this as:
P(x) =(x + 2)*(x - 9)*(x - 9)*(x - 9)*(x - 9)*(x - 14)
Then the roots are:
2, -9, and -14
(where the -9 has a multiplicity of 4).
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The values of x for which the point (x,y) lies on both the line and the parabola satisfy the quadratic equation: 2 x 2 bx c
The value of x that makes the point (x,y) lies on both the line and the parabola is x = 0 and x=1.
The values of x for which the point (x,y) lies on both the line and the parabola, we set the equation of the line y = 4x equal to the equation of the parabola y^2 = 16x.
By substituting y = 4x into the equation of the parabola we get (4x)^2 = 16x and further simplifying it results in 16x^2 = 16x.
so x=1 and x=0
This means that x = 0 and x=1 is the solution that makes the point (x,y) lies on both the line and the parabola and any other value of x will not make the equation true.
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Complete question:
The values of x for which the point (x,y) lies on both the line and the parabola satisfy the quadratic equation:
The equation of line is y = 4x
equation of parabola is [tex]y^2[/tex] = 16x
The perimeter of a rectangle is 50 inches. Its length is 3 times its width. Write and solve an equation to determine the length and width of the rectangle
Answer:
Let the width equal x Let the length equal x + 3 Next, the formula for determining the perimeter of a rectangle is as follows: P = 2 (L + W) or P = 2 (L) + 2 (W) where P equals the perimeter, L equals the length, and W equals the width.
Step-by-step explanation:
The length of the rectangle is 18.75 inches and the breadth of the rectangle is 6.25 inches.
Let, the breadth of the rectangle (b)= x
then the length of the rectangle (l) = 3x
(since the length is 3 times its breadth)
We know that the perimeter of a rectangle (p) = 2 (l+b)
where, l = length of the rectangle
b = breadth of the rectangle
According to the question, P = 50
P = 2 (l+ b)
(Put all the values in the equation)
50 = 2(3x + x)
50 = 2(4x)
8x = 50
x = 50/8
= 6.25
if x =6.25, then 3x = 3* 6.25 = 18.75
Hence, the length of the rectangle is 18.75 inches and the breadth of the rectangle is 6.25 inches.
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For positive integers N and k, define N to be k-nice if there exists a positive integer a such that a k has exactly N positive divisors. Find the number of positive integers less than 1000 that are neither 7-nice nor 8-nice.
The number of positive integers less than 1000 that are neither 7-nice nor 8-nice is 749.
N = (ke1 + 1)(ke2 + 1)· · ·(kei + 1).
This means we must have N ≡ 1 (mod k).
Yes, choose a = 2^N−1/k so that
a^k = 2^N−1
, which has N divisors.
So, we need to find the number of integers that are neither 1 mod 7
nor 1 mod 8.
We can use the principle of inclusion and exclusion.
There are [999/7]= 143 integers that are 1 mod 7.
There are [999/8]= 125 integers that are 1 mod 8.
There are [999/56 ]= 18 integers that are 1 mod 56.
By PIE, the answer is 999 − 143 − 125 + 18 = 749.
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.
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Kin made a picture frame for a square picture with sides that are 5f - 4 inches long. Framing the picture adds 2 inches to the length of each side. Use the distributive property to write two expressions for the perimeter of the framed picture. Show your work.
The perimeter of the picture is 20f-8 inches.
Sides of the picture = 5f-4
Inches added to the picture = 2
The perimeter of a two-dimensional form, like a square or a rectangle, is the space surrounding its edge. It is frequently employed to gauge a parcel of land's dimensions or the width of a fence.
Since two inches are added, therefore after framing the side length becomes-
5f-4+2
= 5f-2
The perimeter of the square is given as
= side x 4 or 4s
Therefore, the perimeter of the framed picture will be given as -
= 4(5f-2)
= 20f - 8
The perimeter can also be found by adding the side length four times. This can be noted as -
5f-2 + 5f-2 + 5f-2 + 5f-2
= 20f - 8
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You need 3 sticks of butter for every 24cookies you bake.
Complete the table using equivalent ratios.
Sticks of butter Number of cookies
3 24
?
16 ?
5 ?
The table formed using equivalent ratios.
16 : 128
5 : 40.
Explain the term equivalent ratios?When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, 1:2 and 2:4 have the same ratio.3 sticks of butter -----> 24 cookies.
Let the number of cookies made for other stick of butter be 'y'.
Then, number cookies for the 16 sticks of butter
3/24 = 16/ y
y = 16*24 / 3
y = 128 cookies.
Again, number cookies for the 5 sticks of butter
3/24 = 5/ y
y = 5*24 / 3
y = 40 cookies.
Thus, number of cookies made by 5 sticks of buter are 40.
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Six points are equally spaced around a circle of radius 1. Three of these points are the vertices of a triangle that is neither equilateral nor isosceles. What is the area of this triangle
The area of the triangle with three points spaced equally around a circle of radius 1 is 8√3.
The area of the triangle can be calculated using Heron's formula:
Area = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle and a, b, c are the side lengths.
The semiperimeter can be calculated as follows:
s = (a + b + c)/2
For this triangle, the side lengths are:
2, 2√2, and 2
Therefore, the semiperimeter is
s = (2 + 2√2 + 2)/2 = 4√2
The area of the triangle is then:
Area = √(4√2(4√2-2)(4√2-2√2)(4√2-2))
= √(4√2*2√2*2*2)
= 8√3
The area of the triangle with three points spaced equally around a circle of radius 1 is 8√3.
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For each problem, find the equation of the line tangent to the function at the given point. Your answer should be in slope-intercept form.
the equation of the line tangent to the function at (3, 6) is y = 11x - 21.
1. f(x) = x^2 + 5x - 6, at (3, 6)
Answer: y = 8x - 21
f'(x) = 2x + 5
f'(3) = 2(3) + 5 = 11
The equation of the line tangent to the function at (3, 6) is y = 11x - b.
Substitute 6 for y and 3 for x to get 6 = 11(3) - b
Solve for b to get b = 21
Therefore, the equation of the line tangent to the function at (3, 6) is y = 11x - 21.
The equation of the line tangent to the function at (3, 6) is y = 8x - 21. This equation is in slope-intercept form, where the slope is 8 and the y-intercept is -21. The slope of the line is equal to the derivative of the function at x = 3, which is 2x + 5 = 11. Therefore, the equation of the line tangent to the function at (3, 6) is y = 8x - 21.
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Y=2/3x doe thi repreent a proportional relationhip? what i the contant of proportionality?
Yes, the equation Y = 2/3x represents a proportional relationship.
If one variable is always equal to a constant multiplied by the other variable(quantity), then we can say that those variables are in a proportional relationship.
In the direct relationship between two quantities, if one quantity increases, the other quantity also increases and vice-versa.
For example, if each square foot of carpet costs $1.50, then the cost of the carpet is proportional to the number of square feet. The direct proportion relationship is written as y ∝ x.
y = kx where k is the constant of proportionality.
The constant of proportionality is 2/3. It tells us that for every 1 unit increase in x, Y increases by 2/3 units.
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what is 1/13 of 18 as a proper fraction
Answer:
Step-by-step explanation:
1/13 x 18
of= multiply
18x1=18
13x1=13
18/13
As a PROPER FRACTION, it is 1 5/13
Answer: 18/13
Step-by-step explanation:
You have to multiply the fractions.
for women aged 18-24 systolic blood pressured are normally distributed with a mean of 114.8 and a standard deviation of 13.1 if 23 women aged 18-24 are randomly selected find the probability that their mean
The probability that the mean systolic blood pressure of 23 women is between 119 and 122 mm Hg is 0.0579.
The Central Limit Theorem states that the distribution of the mean of a large sample (n>30) taken from a population with a finite mean and standard deviation will be approximately normal.
Since we are given that systolic blood pressures are normally distributed and we have n = 23>30, we can assume that the mean systolic blood pressure of 23 women will be approximately normally distributed with a mean of 114.8 mm Hg and a standard deviation of 13.1/[tex]\sqrt{23}[/tex] = 2.731 mm Hg.
To find the probability that the mean systolic blood pressure of 23 women is between 119 and 122 mm Hg, we can standardize the problem and use the standard normal distribution table.
We can standardize the problem by finding the number of standard deviations away from the mean of the lower and upper bounds of the range.
z_lower = (119 - 114.8) / 2.731) = 1.537
z_upper = (122 - 114.8) / 2.731) = 2.636
Now we can use the standard normal distribution table to find the probability that a standard normal variable is between z_lower and z_upper.
P(z_lower < Z < z_upper) = P(Z ≤ 2.636) - P(Z < 1.537) = 0.9958 - 0.9379 = 0.0579
Therefore, the probability that the mean systolic blood pressure of 23 women is between 119 and 122 mm Hg is 0.0579.
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The complete question is -
For women aged 18-24, systolic blood pressures are normally distributed with a mean of 114.8 mm Hg and a standard deviation of 13.1 mm Hg. If 23 women aged 18-24 are randomly selected, find the probability that their mean systolic blood pressure is between 119 and 122 mm Hg. Round to four decimal places.
Simplify, 1.5:20 ratio
By means of ratio properties, the simplified form of ratio 1.5 : 20 is equivalent to ratio 3 : 40.
How to simplify a ratio with decimal numbers
Ratios are relationships between two real numbers of the form a : b, the simplification of ratios can be done by using the following ratio property:
Simplification property for ratios
a : b ← (a · c) : (b · c)
Where a, b, c are real numbers.
The purpose of ratio simplification is to eliminate any decimal number in a ratio. If we know that a = 1.5, b = 20 and c = 2, then the simplified form of the ratio is:
1.5 : 20 → (1.5 · 2) : (20 · 2)
(1.5 · 2) : (20 · 2) = 3 : 40
By ratio properties, ratio 3 : 40 is the simplified form of ratio 1.5 : 20.
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g we have 4 women and 5 men and want to create a committee with 2 women and 2 men. in how many ways we can do this?
The required number of ways in which we can create a committee with 2 women and 2 men is 60.
What are Combinations?Combinations are selections that are made by choosing some or all of a group of objects, regardless of how they are arranged.Utilizing the combinations formula, it is simple to determine how many distinct groups of r objects each may be created from the provided n unique objects. The factorial of n divided by the product of the factorial of r and the factorial of the difference between n and r, respectively, is the formula for combinations.Given:
We have 4 women and 5 men.
The required number of ways in which we can create a committee with 2 women and 2 men can be calculated as:
= 4C2 × 5C2
= 4!/(2!)(2!) × 5!/(2!)(3!)
= 6 × 10
= 60
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how to multiply matrices with different dimensions
The number of columns in the first matrix must equal the number of rows in the second matrix in order to multiply matrices with different dimensions.
First, jot down each matrix's dimensions. Let's imagine, for illustration, that we have a matrix A that is 2 by 3 and a matrix B that is 3 by 4. Create a new matrix C with the dimensions 2x4 in step 2. This is what the multiplication will ultimately produce.3. Determine the dot product of the corresponding row in matrix A and the corresponding column in matrix B for each element in matrix C.
4: The final response is matrix C, which is the union of the 2x3 matrix A and the 3x4 matrix B.
Therefore, the result is a 2x4 matrix, which is produced by taking the dot product of the rows and columns of matrix A and matrix B.
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What is the probability of Andre choosing a greater number than five?
Answer:
It is 1/2
Probability is (No of favourable outcomes/ No. of possible outcomes )
or 4/8 = 1/2
Answer:
1/2
Step-by-step explanation:
hope this helps.
solve 1000 divided by 39 in fraction
Answer:
1000/39
Step-by-step explanation:
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 45N acts on a certain object, the acceleration of the object is 9 m/s^2. If the acceleration of the object becomes 8 m/s^2, what is the force?
Answer:
Step-by-step explanation:
4 m/s squared
The area of a triangle is 2. Two of the side lengths are 6.6 and 1.1 and the
included angle is acute. Find the measure of the included angle, to the nearest
tenth of a degree.
Answer: 51.5 degrees
Step-by-step explanation:
The measure of the included angle is about 51.5 degrees. To find this, we can use the law of sines, which 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 three sides of the triangle. So, we can set up an equation using the information given: (area)/(0.5*(1.1)(6.6)) = (sin(x)) where x is the included angle. We know that area is 2, so we can put it in the equation: (2)/(0.5(1.1)(6.6)) = (sin(x)) .
Then using sin(x) = 2/(0.5(1.1)*(6.6)) , we can use a calculator to find the sin(x) = 0.094.
and then using a calculator, we can find that x = sin^-1 (0.094) ≈ 5.2 radians. To convert it to degrees, we can multiply it by 180/π ≈ 57.3. So the measure of the included angle is about 57.3 degrees. To the nearest tenth of a degree, it is 57.3, but it can also be rounded off to 51.5 degrees.
A line passes through points (3,14) and (9,20). Write a linear function rule in terms of x and y for this line.
Answer:
y = x + 11
Step-by-step explanation:
the equation of a straight line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 14 ) and (x₂, y₂ ) = (9, 20 )
m = [tex]\frac{20-14}{9-3}[/tex] = [tex]\frac{6}{6}[/tex] = 1 , then
y = x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, 14 )
14 = 3 + c ⇒ c = 14 - 3 = 11
y = x + 11 ← equation of line
A line passes through points (3,14) and (9,20), linear function rule in terms of x and y for this line is y = x + 11
A linear function in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the point values from the problem, we get:m = (20 - 14) / (9 - 3) = 6/6 = 1
The y-intercept be found by plugging in any one of the point values and the slope into the equation y = mx + b and solving for b. Using the point (3,14), we get:
14 = 1*3 + b
b = 11So the linear function in terms of x and y is:
y = x + 11
A linear function is a type of mathematical function that, when graphed, defines a straight line. It is defined by the equation y = mx + b, where x and y are variables, m is the line's slope, and b is the y-intercept (the point where the line crosses the y-axis). The slope (m) of the line represents its steepness, and the y-intercept (b) represents the point at which the line intersects the y-axis.
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please help me solve this
Answer:
i don't know br
Step-by-step explanation:
Sorry but this is like college stuff:(
The graph shows the solution to which systems of inequalities
Answer:
y ≤ x-2
y > -x + 5
y ≤ 3
y ≥ 0
Step-by-step explanation:
all answers have y ≥ 0 and y ≤ 3
next, we want to figure out if y < -x + 5 or y > -x + 5
plotting the line with a few points (e.g. (0,5), (5,0)), we can tell the red dotted line is y = -x + 5. the shaded area is above it, so we can say that y > -x + 5
similarly, we can tell the blue line is y = x-2. the shaded values are below it, so we can say that y ≤ x-2
the copeland family started out on a family vacation with plans to visit several states. first, mr. copeland drove 163 miles in 3 hours and 49 minutes. then, mrs. copeland took over, driving 411 miles in 6 hours and 27 minutes. what is the family's average speed so far?
The average speed so far is 226.4 miles per hour.
Time taken: 3 hours 49 minutes + 6 hours 27 minutes
= 10 hours 16 minutes
Total distance: 163 miles + 411 miles
= 574 miles
Average speed: 574 miles / (10 hours 16 minutes)
= 226.4 miles per hour
To calculate the average speed of the Copeland family's trip so far, we need to know the total distance they have traveled and the total time they have spent traveling. We can calculate this by adding the distance driven by Mr. Copeland (163 miles) and the distance driven by Mrs. Copeland (411 miles) to get a total distance of 574 miles. Then, we can add the time taken by Mr. Copeland (3 hours 49 minutes) and the time taken by Mrs. Copeland (6 hours 27 minutes) to get a total time of 10 hours 16 minutes. We can then divide the total distance (574 miles) by the total time (10 hours 16 minutes) to get an average speed of 226.4 miles per hour.
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postus has four 1-cent stamps, three 5-cent stamps, and three 25-cent stamps. how many different postage amount of at least one cent can postus make?
Portus has four 1-cent stamps, three 5-cent stamps, and three 25-cent stamps. 79 different postage amount of at least one cent can postbus make.
We can get the sums of 1 cent, 2 cents, 3 cents and 4 cents by combining one 1-cent coin, two 1-cent coins, three 1-cent coins and four 1-cent coins, respectively. i.e., 4 different sums.
We can get three sums of 5 cents, 10 cents, and 15 cents by combining mean five-cent coins., i.e. 3 different sums.
we can get three sums of 25 cents, 50 cents, and 75 cents by combining means twenty-five-cent coins. i.e,3 different sums.
Now,
4*3 = 12 different sums by combining 4 one-cent coins with 3 five-cent coins.
Again,
4*3 = 12 different sums by combining 4 one-cent coins with 3 twenty-five-cent coins. 3*3 = 9 different sums by combining 3 five-cent coins with 3 twenty-five-cent coins.4*3*3 = 36 different sums by combining 3 five-cent coins with 3 five-cent coins and 3 twenty-five-cent coins.Now,
add all these combinations:
4 + 3 + 3 + 12 + 12 + 9 + 36 = 79.
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I need explanation on these PLEASE
I'm struggling to understand how they got the answer!!!
Answer: The two problems aren't related
Step-by-step explanation:
The first problem has a 3 and a 9 but no 2, but the second problem does, which shows that these two problems are not related. Also, if you simplify the first one, you will get 27 [tex]\sqrt[4]{3}[/tex], which is not related to the second problem
17. Use Figure 5.5. On March 20, Paul deposited $1,000 into his savings account that pays 5.5% interest
compounded daily. How much interest will the money earn by April 20?
a. $3.77
b. $4.68
C.$4.83
d. $4.98
8. On February 24, Larissa deposited $5,000 in a savings account that pays 5.5% interest compounded daily.
What will be the amount in her account on March 17?
a. $5,015.80
b. $5,031.30
c.$5,037.33
d.$5,039.80
The interest generated in Pauls savings account is $4.68
The amount generated in Larissa's savings account is $5015.80
What is Compound Interest ?Compound interest is interest that builds up over a certain length of time on both principal and interest. The principle is also used to account for the interest that has accrued on a principal over time. Furthermore, the cumulative principal value is used to calculate interest for the subsequent time period. The new way of calculating interest now utilized in all international financial and commercial operations is known as compound interest. When we look at the compound interest values that have built over various time periods, the power of compounding is clearly apparent.
The interest that is paid on both principle and interest and is compounded on a regular basis is known as compound interest. The interest is calculated for the new principal at regular intervals when the accumulated interest and the current principal are combined. The initial principal plus the interest that has already accrued make up the new principal.
The initial principal(p) of Paul is $1000
rate(r) is 5.5%
Number of days(t) = 20th March to 20th April = 31 days = 31/365 years
So the Amount generated =[tex]p * (1 + \frac{r}{365})\x^{365*t}[/tex]
⇒ A = [tex]1000* (1 + \frac{5.5}{100*365})\x^{31} = 1000*1.00468 = 1004.68[/tex]
The interest generated = 1004.68 - 1000 = $4.68
Similarly for Larissa
time = 24th Feb to 17th March = 21 days = 21/365 years
So the Amount generated =[tex]p * (1 + \frac{r}{365})\x^{365*t}[/tex]
⇒ A = [tex]5000* (1 + \frac{5.5}{100*365})\x^{21} = 5000*1.00317 = 5015.80[/tex]
The amount generated is $5015.80
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how would i use math in my life ?
Answer:
money. you need to know how to count your money so nobody cheat you out of it
Jose wants to ride his bicycle 41.2 miles this week. He has already ridden 4 miles. If he rides for 6 more days, what is the average number of miles he would have to ride each day to meet his goal?
maybe try not
Step-by-step explanation:
Answer:
it would be 6 miles a day
Step-by-step explanation:
do to 41.2 miles in 1 week and a 4 mile start plus six more days it would be 6x6=36+4=40
What is the measure of angle x?
Answer: 112 degrees
Step-by-step explanation:
Since the two lines are parallel and the line that intersects them is a transversal, 180 - 68 = x
Solving 180 - 68,
you can find that x = 112 degrees :>
Answer: a measure of an x angle is the longest line on the graph so that how u know
Step-by-step explanation:
What does the graph of the function at each interval represent?
The graph of the function at each interval represent
(1) - increasing, (2) - decreasing, and (3) - decreasing.
What is graph of the function?
The set of ordered pairs where f(x) = y is displayed as the graph of a function in mathematics. These pairs are the Cartesian coordinates of points in two-dimensional space and, in the typical case where x and f(x) are real numbers, they form a subset of this plane.
Let the graph of the function is given.
We have to find What does the graph of the function at each interval represent.
As we can see that there are three intervals of the graph are shown (1), (2), and (3).
We can see that in the first interval (1) the graph is increasing.
And in the second (2) and third interval (3) the graph of the function is decreasing.
Hence, the graph of the function at each interval represent
(1) - increasing, (2) - decreasing, and (3) - decreasing.
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Which property would be used to isolate 2x on the left side of the inequality 2x+4≥6 ?
Answer:
Step-by-step explanation:
+1=2
State if the polygons are similar
Answer:
Yes, they are similar by SSS
