The required equation of the polynomial is p(x) = 4(x - 2 )⁵(x+5).
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given the following properties: fifth degree, 2 is a zero of multiplicity 4, −5 is the only other zero, and the leading coefficient is 4.
The general form of the polynomial will be written as,
p(x) = 4(x - 2 )⁵(x+5).
Therefore, the required equation of the polynomial is p(x) = 4(x - 2 )⁵(x+5).
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Three times the quantity of a number c increased by 7 is equal to the same number, c, decreased by 15
After solving the given equation, we know that the value of c is -11.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
Let's learn more about math equations in this tutorial.
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
Sc, we have the equation:
3c + 7 = c - 15
Now, calculate this equation for c as follows:
3c + 7 = c - 15
3c - c = -15 - 7
2c = -22
c = -22/2
c = -11
Therefore, after solving the given equation, we know that the value of c is -11.
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Three times the quantity of a number c increased by 7 is equal to the same number, c, decreased by 15. What is c in this situation?
Describe the graph of the proportional relationship represented by the equation y = 7.5x.
The graph is a line that goes through points (0, 0) and (7.5, 7.5).
The graph is a line that goes through points (0, 0) and (15, 2).
The graph is a line that goes through points (0, 0) and (7.5, 1).
The graph is a line that goes through points (0, 0) and (1, 7.5).
The graph of the proportional relationship represented by the equation y = 7.5x is The graph is a line that goes through points (0, 0) and (1, 7.5)
What is a graph of linear function?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
considering the given equation y = 7.5x.
c = 0
hence the graph passed through (0, 0)
substituting x = 1 gives y = 7.5 hence (1, 7.5) is another point
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Evaluate the following:
Logc1 = ?
The given logarithmic expression can be evaluated as Logc1 = 0.
What is Logarithm?Logarithm function is defined as the inverse of the exponential function.
If a^(b) = c, then b = log(c) at the base of a.
Logarithm of any number is always positive.
For negative numbers, the logarithm are complex numbers.
The given expression is Logc1.
It implies that it is the logarithm of 1 with c as a base.
Sine, the logarithm of 1 to any base is equal to zero, the given expression can be evaluated as follows,
Logc1 = 0
Hence, the value of the given expression is 0.
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Please hurry please help me but correct answer
Answer:
increase of 100%
Step-by-step explanation:
50 cents to 1 dollar is an increase.
The percent increase can be calculated by dividing the increased amount by the original amount.
$1.00 - $0.50 = $0.50 increase
% increase = 100%
Liam works at a zoo. He was looking at some data showing the masses of their
5
55 African elephants. The mean mass of the elephants was
3
,
800
kg
3,800kg3, comma, 800, start text, k, g, end text, and the median mass was
3
,
600
kg
3,600kg3, comma, 600, start text, k, g, end text. The smallest elephant, named Lola, weighed
2
,
700
kg
2,700kg2, comma, 700, start text, k, g, end text.
Lola then got very sick and lost weight until her mass reached
1
,
800
kg
1,800kg1, comma, 800, start text, k, g, end text.
How will Lola's mass decreasing affect the mean and median?
Median won't change, however Mean will fall by 180.
What do mean and median?By summing all the numbers in a data collection and dividing by the total number of values in the set, one may get the mean (average) of the data set. When a data collection is sorted from least to largest, the median represents the midpoint value.
African elephants total 555 in number.
Elephants had a 3800 kg average mass.
Elephants had a 3600 kg median mass.
Lola, the elephant that was the smallest, weighed 2700 kg.
Later, Lola became really ill and lost a lot of weight, reaching a mass of 1800 kg.
What effect will Lola's weight loss have on the mean and median as well as Currently, the median is 3600 and the lowest is 2700.
now 2700 becomes 1800
so Median remains the same as 3600
No change in Median
The mean mass of the elephants was 3800 kg
=> total weight = 5 x 3800 = 19000 kg
2700 kg becomes 1800 kg
Hence new total mass = 19000 - 2700 + 1800 = 181000 kg
New Mean = 18100/5 = 3620 kg
Mean reduced by 3800 - 3620 = 180 kg
No change in Median weight
Mean reduced by 180 kg
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Carlos sells tickets for a concert. He earns $200 plus
$2.50 per ticket he sells. So far, Carlos has earned
$300. How many more tickets does Carlos need to sell
to earn $350?
A. 20
B. 50
C. 125
D. 150
Answer:
A. 20
Step-by-step explanation:
300 ÷ 2.5= 120
So
50÷2.5 = 20
Select the correct answer. Solve for x. x2 + 4x - 21 = 0 A. -3, -7 B. -3, 7 C. 3, -7 D. 3, 7
Answer:
Answer: the correct option is(C) 3, -7.
Step-by-step explanation:
If you sold 30% of a business for 500 dollars how much is the bussnis worth
it would be 1600 i hope this helps
26034 i hope this help man pls pls
Which of the following statements are true?
i. It is okay to use the median to estimate the mean since both are a measure of the center of a
distribution.
ii. It is okay to use the standard deviation to estimate the IQR since both are measures of variability.
iii. Point estimates based on a sample are sometimes far from a parameter's value.
Oi only
O ii only
O iii only
Oi and ii
Oi and iii
O i, ii, and iii
Check Answer
The correct answer is c) iii only as statement 1 and statement 2 are false.
What do mean and standard deviation tell us?
In statistics, the measurement of variability known as the standard deviation (SD) is frequently utilized. It demonstrates how different things are from the norm (mean). While a high SD shows that the data are dispersed throughout a wide range of values, a low SD suggests that the data points tend to be close to the mean.
What is relationship between mean and standard deviation?
The standard deviation is a measure that summarizes how far away from the mean each observation is. The positive would exactly balance the negative if the discrepancies themselves were totaled together, making their aggregate equal to zero. The squares of the discrepancies are then added as a result.
What is median?
The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.
Statement 1: False, it only works if distributiion is syummetric, for non- symmetric distribution, median is not unbiased estimator population in mean.
Statement 2: False standard deviation is not equal to IQR, and is heavily influenced by sample mean and outliers.
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Solve the system of equations by using the addition method.
5x+-7y=-2
10x+5y=15
Answer:
y=1, x=1
Step-by-step explanation:
no need for step by step cause i know
How do I take an antiderivative of the following equation?
[tex]dy/dx+ky-77k=0[/tex]
The required anti derivative of given function is -(ky^2)/2 + 77ky.
What is integration(anti-derivative)?Anti-differentiation or integration is the converse interaction to separation. For instance, if f (x) = 2x, we realize that this is the subordinate of f(x) = x^2.
According to question:We have,
dy/dx +ky - 77k = 0
dy/dx = -ky + 77k
Integrate with respect to x
∫dy/dx = ∫(-ky + 77k)
∫dy/dx = -∫ky +∫77k
y = -(ky^2)/2 + 77ky
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The required antiderivative is [tex]y=e^{-(kx+c)} +77[/tex]
What is antiderivative?
In calculus, a differentiable function F whose derivative is identical to the original function f is known as an antiderivative, inverse derivative, primitive function, primitive integral, or indefinite integral of a function f. F' = f can be used to represent this.
[tex]\frac{dy}{dx} = 77k - ky\\\\dx=\frac{dy}{77k-ky} \\\\dx = \frac{dy}{77-y} \times \frac{1}{k} \\\\kdx = \frac{dy}{77-y} \\\\-\frac{dy}{y-77} =kdx\\\\log(y-77)=-(kx+c)\\\\y=e^{-(kx+c)} +77[/tex]
Hence, The required antiderivative is [tex]y=e^{-(kx+c)} +77[/tex]
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ABCD is a rhombus and side AE Is congruent to EC prove triangle AEB is congruent to CEB
ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
Given that the side AE is congruent to EC of rhombus.
That means, AE ≅ EC.
And the diagonals of rhombus bisects each other.
Both the triangle AEB and triangle CEB share the same side which is BE.
That means BE ≅ BE, by the reflexive property.
And the sides AB and BC are the sides of rhombus.
So, AE ≅ BC.
Therefore, if ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.
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x^-3=1/343 what does x equals please show all work.
Answer:
Step-by-step explanation:
X^-3=1/343
X^-3=1/7^3
X^-3=7^-3
Since the powers are equal, the bases should also be equal.
Therefore, X=7
From question 28 -29
Help please
By using the concept of vector, it can be calculated that
28) First option is correct
29) Fourth option is correct
What is vector?
Anything that has both magnitude and direction and follow the vector addition law is called vector.
28) The vectors are
[tex]\vec{v} = -2i-5j,[/tex]
[tex]\vec{w} = -3i+j[/tex]
[tex]\vec{v}. \vec{w} = (-2i-5j).( -3i+j) = 6 - 5 = 1\\|\vec{w}|^2 = (-3)^2+(1)^2 = 9 + 1 = 10\\\vec{v_1} = \frac{1}{10}( -3i+j) = \frac{-3}{10}i+\frac{1}{10}j[/tex]
[tex]\vec{v_2} = (-2i-5j) - (-\frac{3}{10}i - \frac{1}{10}j)\\\vec{v_2}= (-2+\frac{3}{10})i+(-5 - \frac{1}{10}j)\\\vec{v_2}=-\frac{17}{10}i - \frac{51}{10}j\\[/tex]
First option is correct
29) P = (1, 2) and Q = (-6, -1)
Position vector = (-6-1)i + (-1-2)j = -7i - 3j
Fourth option is correct
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Divide. Give the quotient and remainder.
133 2
Answer:
Quotient: 66
Remainder: 1
Step-by-step explanation:
133/2 = 66.5
66.5 =
66 + 0.5 =
66 + 1/2 = 66 1/2
1/2 * 2 = 1 ==> Remainder: 1
Whole number : 66
Quotient: 66
Remainder: 1
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Find the intercept of the line 4x−3y=17
Answer:
see attachment
Step-by-step explanation:
(100 POINTS AND BRAINLYEST GURANTEE PLEASE I NEED HELP)
Answer everything in the image listed below please.
To prove parallelograms is a parallelograms we have show that, diagonals cut each other in half, and one angle adds to both following angles .
What is parallelograms ?One particular type of quadrilateral that is created by parallel lines is a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel.
The sum of all the sides' lengths determines a rhombus' perimeter. A rhombus's perimeter is equal to four times the length of each side because all of its sides are equal. A diamond's perimeter is given in 4x units, for instance, if one of its sides is x units.
P=4a
The two opposing side pairs must be parallel, the two opposite side pairings must coincide, the two opposite angle pairs must coincide, the diagonals must cut each other in half, the first angle must add to both the following angles, and one set of opposing sides must be both parallel AND congruent. These are the six basic properties of parallelograms.
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 18 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
The top 18 percent of scores fall within two standard deviations of the mean.
What is publicly recognized?Publicly recognized refers to something that is well-known or acknowledged by the public or by a large segment of the population. This could include a famous person, a popular business, or an important event or achievement. Public recognition is often seen as an indicator of success, as it shows that the person or thing being recognized has achieved something noteworthy or has had a positive influence on the public. Examples of publicly recognized things include awards, honors, and other achievements.
Assuming a normal distribution, a student needs to score at least two standard deviations above the mean to be publicly recognized. This is because the top 18 percent of scores fall within two standard deviations of the mean. This can be expressed mathematically as:
P(x > μ + 2σ) = 0.18
where μ is the mean and σ is the standard deviation.
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Find the equation of a line parallel to y=−7+4x that passes through the point (-2,-1)
To find the equation of a line that is parallel to y=−7+4x and passes through the point (-2,-1), we can use the point-slope form of the equation of a line. The point-slope form of the equation of a line is:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
Since the given line y=−7+4x is in slope-intercept form, we can find the slope by taking the coefficient of x, which is 4. This means that the slope of the line is 4.
We can then use the point-slope form to find the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1). Plugging in the values for the slope and the point, we get:
y - (-1) = 4(x - (-2))
Simplifying this expression gives us:
y + 1 = 4(x + 2)
Which simplifies to:
y = 4x + 5
So the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1) is y = 4x + 5.
If ABTS = AGHD, BS = 25, IS = 14, BT = 31, GD = 4x - 11, m2S = 56, mLB = 21°, and mLH = (7y + 5)°, find the values of x and y.
Answer:
x = 8
y = 2
Step-by-step explanation:
From the graph, estimate what numbers should go into the empty cells in the first two columns. Do not complete the columns on the right of the dividing line.
The first two columns of the table, considering logarithms, are completed as follows:
2 - 10^0.3.5 - 10^0.7.9 - 10^(0.95).4 - 10^(0.6).2.51 - 10^(0.4).How to complete the table?The table is completed in this problem applying the logarithms.
This is because on the first column we had that:
10^(0.3) = 2, which means that log10(2) = 0.3.
(log10(x) represents the logarithm of base 10 of x).
For the second row, the decimal approximation is found applying the power of 10^0.7, hence:
10^0.7 = 5.
For the third and fourth rows, to obtain the power of 10 expression, we need to calculate the logarithms of these numbers, as follows:
log10(9) = 0.95.log10(4) = 0.6.Hence the power of 10 expressions are given as follows:
9 = 10^(0.95).4 = 10^(0.6).For the fifth row, we just need to calculate the exponential expression, hence:
10^(0.4) = 2.51.
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A container is a hemisphere of radius 30cm.
Sand fills the container at a rate of 4000 cm³ per minute.
Does it take less than a quarter of an hour to fill the container?
You must show your working.
Since the time is 0.24 hour. Yes, it takes less than a quarter of an hour to fill the container
How to determine if it takes less than a quarter of an hour to fill the container?Given: A container is a hemisphere of radius 30cm
Sand fills the container at a rate of 4000 cm³ per minute
A hemisphere is half a sphere. Thus:
The volume of a hemisphere = 1/2 × 4/3 πr³ = 2/3 πr³
The volume of a hemisphere = 2/3 × π × 30 = 56548.67 cm³
Rate = Volume / Time
Time = Volume/Rate
Time = 56548.67 /4000 = 14.14 minutes
In hours: Time = 14.14/60 = 0.24 hour
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Cailen needs at least $150 to buy an X-box. She earns $15 for each lawn she mows and has $30 in savings. Write an inequality to determine how many lawns Cailen must mow to buy an x-box. How many lawns must she mow to buy the x-box?
total = 15x + 30
EDIT: She has to mow 8 lawns. I didn't read the question
there you go its that simple
Solve for x. 4 (x + 1 1/3) = 9 2/3 Enter your answer as a mixed number in simplest form in the box.
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.
The value of x is 6.
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,
4(x + 11/3) = 9(2/3)
Divide both sides by 4.
x + 11/3 = 29/3
Subtract 11/3 on both sides.
x = 29/3 - 11/3
x = (29 - 11) / 3
x = 18/3
x = 6
Thus,
The value of x is 6.
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Determine algebraically whether the given function is even, odd, or neither.
f(x) = -5x² + |2x|
well, as you already know, to check if a function is EVEN, we simply check what's f( -x ), if f( -x ) = f( x ), then voila!!. and if f( -x ) = -f( x ), then oddly enough, is an ODD function.
well, let's plug in " -x " to see what we get anyway
[tex]f(x)=-5x^2 + |2x|\implies \boxed{f(x)=-5x^2 + 2x} \\\\[-0.35em] ~\dotfill\\\\ f(-x)=-5(-x)^2 + |2(-x)|\implies f(-x)=-5(-x)(-x) + |-2x| \\\\\\ f(-x)=-5(+x^2) +2x\implies \boxed{f(-x)=-5x^2 + 2x}~\hfill \stackrel{\textit{\LARGE Even}}{f(-x)=f(x)}[/tex]
find the circumference of the circle use 3.14 r=6
The circumference of the circle with the dimensions radius = 6 and π = 3.14 is 37.68
What is the circumference of a circle?The circumference of a circle refers to the line that bounds a circle or other two-dimensional figure.
Circumference of a circle = 2πr
Where,
π = 3.14Radius, r = 6Circumference of a circle = 2πr
= 2 × 3.14 × 6
= 37.68
Therefore, the circumference of the circle is given by 37.68
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A table of 1,022 guests are attending a reception. If each table can seat exactly 12 people,what is the least number of tables needed to seat all guests?
Answer:
86
Step-by-step explanation:
If you did 1,022 divided by 12, you would get something crazy like 85.16666666666. So round up.
Gina puts $ 4500 into an account earning 7.5% interest compounded continuously. How long will it take for the amount in the account to grow to $ 5150?
Time in years =
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5150\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=years \end{cases}[/tex]
[tex]5150=4500e^{0.075\cdot t} \implies \cfrac{5150}{4500}=e^{0.075t}\implies \cfrac{103}{90}=e^{0.075t} \\\\\\ \log_e\left( \cfrac{103}{90} \right)=\log_e(e^{0.075t})\implies \log_e\left( \cfrac{103}{90} \right)=0.075t \\\\\\ \ln\left( \cfrac{103}{90} \right)=0.075t\implies \cfrac{\ln\left( \frac{103}{90} \right)}{0.075}=t\implies\stackrel{\textit{about 1 year and 291 days}}{ 1.8\approx t}[/tex]
Which of the following statements is correct based on the number line below?
-8
-6
A
B
C
D
-4 -2
P
200
808
Q
0 2 4
6
√68 is to the right of Point Q because it is less than 8.
√68 is between points P and Q because it is less than 0 and greater than 8.
√68 is between points P and Q because it is greater than 0 and less than 8.
68 is to the right of Point Q because it is greater than 8.
The perimeter of a playing field for a certain sport is 302 ft. The field is a rectangle, and the length is 47 ft longer than the width. Find the dimensions. What is the width?
Answer:
To find the dimensions of a rectangle
Step-by-step explanation:
perimeter=302
let width=x
length=x+47
p=2(L+W)
302=2(x+x+47)
302=2(2x+47)
302=4x+94
subtracting 94 from the other side we have
302-94=4x
208=4x
x=52
length=99
width=52