The polynomial long division of (5x^4 − 2x^3 − 7x^2 − 39) ÷ (x^2 + 2x − 4) gives a quotient of 5x^2 - 12x + 37
Dividing using polynomial long divisionFrom the question, we have the following parameters that can be used in our computation:
(5x^4 − 2x^3 − 7x^2 − 39) ÷ (x^2 + 2x − 4)
Using the polynomial long division setup, we have
x^2 + 2x − 4 | 5x^4 − 2x^3 − 7x^2 − 39
Evaluating the division, we have
5x^2 - 12x + 37
x^2 + 2x − 4 | 5x^4 − 2x^3 − 7x^2 − 39
5x^4 + 10x^3 - 20x^2
---------------------------------------
-12x^3 + 13x^2 - 39
-12x^3 - 24x^2 - 48
---------------------------------------
37x^2 + 9
37x^2 + 74x - 148
---------------------------------------
-74x + 157
Hence, the quotient is 5x^2 - 12x + 37
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Help me please! if a conditional statement is written in the form “If p then q”, how is the converse of the conditional statement is written?
A) If not q then p
B) If q then p
C) If not p then q
D) If not p then not q
The converse statement is of the conditional “If p then q” is the one in option B.
if q then p.
How can we identify the converse statement?For two given propositions p and q, a conditional statement is written as:
"if p, then q"
So, if the proposition p is true, also is the proposition q.
The converse statement just changes the order of the two propositions ( if the proposition q is true, also is the proposition p), then here start with q and end with p, so the converse statement is:
if q then p.
The correct option is B.
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You decide to make an investment in bonds. After much deliberation, you decide to purchase 10 State Farm bonds at a price of 99.40. These bonds have a 5% interest paid annually.
• How much did you pay for the 10 bonds (excluding commission)?
• How much interest will you receive each year from the bonds?
• What is your bond yield (to the nearest tenth percent)?
The bond yield is approximately 5.0% to the nearest tenth of a percent.
We have,
To find the total cost of the 10 State Farm bonds, we can multiply the price per bond by the number of bonds:
10 bonds x $99.40 per bond = $994.00
So, we paid $994.00 for the 10 State Farm bonds.
To calculate the amount of interest we will receive each year from the bonds, we can use the following formula:
Interest = Principal x Rate
where:
The principal is the amount invested in the bonds
Rate is the interest rate
In this case, our principal is $994.00 and our rate is 5%, or 0.05 as a decimal.
So, the annual interest we will receive from the bonds is:
Interest = $994.00 x 0.05 = $49.70
So,
We will receive $49.70 in interest each year from the bonds.
To calculate the bond yield, we need to use the following formula:
Bond yield = (Annual interest / Total cost) x 100%
In this case, the annual interest is $49.70 and the total cost is $994.00, so we can plug these values into the formula:
Bond yield = ($49.70 / $994.00) x 100% ≈ 5.0%
Therefore,
The bond yield is approximately 5.0% to the nearest tenth of a percent.
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Gary has 24 quarters, 16 dimes, and 32 pennies. Write a ratio that compares the combined number of dimes and pennies to the number of quarters
Wally wants to add a fence to the back of his house to make some room for his children to play safely (see diagram
below). He began measuring his yard but got distracted and forgot to finish measuring before he went to the store. If
he remembers that the back wall of his house is 15 yards long, how much fencing does he need to buy?
The fencing that Wally needs more in 81 feet
How to solve for the fencingA D = E F
A F = DE
AD = AB + BC + CD
Length of the back wall = 15 m
1 y ard = 3 ft
15 ya rds = 15 x 3 = 45
AD EF is a rectangle
5 + 45 + 3 feet
= 53 feet
Then the amount of the fencing that would be required is given as
5 feet + 3 feet + 10 feet + 10 feet + 53 feet
= 81 feet
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SOLVE the following equations (6x-50-7(3X+10)=0
Answer:
6x-50-7(3x+10)=0
Distribute the -7:
6x - 50 - 21x - 70 = 0
Combine like terms:
-15x - 120 = 0
Add 120 to both sides:
-15x = 120
Divide both sides by -15:
x = -8
BJ won the lottery and decided to invest some of his money in an account
that will be compounding continuously. The account he chose earned
5.2%. He invested $27,000. How much money will he have after 18 years,
when his newborn will graduate from high school?
Answer:
$68,796.57
Step-by-step explanation:
approx $68,796.57 at 18 years
Complete the ratio table please help will mark the first answer brainliest answer
The proportional relationship is complete as follows:
Input of 57 for an output of 438.Output of 584 for an input of 76.What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
The constant for this problem is given as follows:
k = 146/19
k = 7.684.
Hence the equation is:
y = 7.684x.
The input for an output of 438 is given as follows:
7.684x = 438
x = 438/7.684
x = 57.
The output for an input of 76 is obtained as follows:
y = 7.684 x 76
y = 584.
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This question here. Thank you in advance
Answer:
Step-by-step explanation:
211
welcome hun
I just need the answer for the blank space, thank you.
At a drug research testing facility:
The population mean is 240 minutes.The population standard deviation is 40 minutes.The sample size is 10 people.Yes, it is given that the population distribution is normally distributed.The mean of the sample means will also be 240 minutes, which is the same as the population mean.The standard deviation of the sample means is (population standard deviation)/(sqrt(sample size)) = 40/(√(10)) = 12.65 minutes.What are the probabilities?To find the probability that the drug will wear off in less than 200 minutes:
The z-score is (200-240)/40 = -1.
Using a standard normal distribution table or calculator, P(z < -1) = 0.1587. Therefore, the requested probability is P(x < 200) = 0.1587.
To find the probability that the drug will wear off after 220 minutes:
The z-score is (220-240)/40 = -0.5.
Using a standard normal distribution table or calculator, P(z < -0.5) = 0.3085. Therefore, the requested probability is P(x > 220) = 0.3085.
To find the probability that the drug will wear off between 200 and 220 minutes:
Using the z-scores calculated above, find the area between them on the standard normal distribution. P(-1 < z < -0.5) = 0.1867.
Therefore, the requested probability is P(200 < x < 220) = 0.1867.
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Claude Monet's Impression: Sunrise (1872) is considered a(n) _____painting because it was completed out-of-doors.
plein-air
alfresco
alla prima
sfumato
Answer:
the answer
Step-by-step explanation:
plein-air painting
Enter the equation of the circle described below. Center (-1, 0), radius = sqrt 3
Answer:
(x + 1)² + y² = 3
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 1, 0 ) and r = [tex]\sqrt{3}[/tex] , then
(x - (- 1) )² + (y - 0)² = ([tex]\sqrt{3}[/tex] )² , that is
(x + 1)² + y² = 3
Find the volume of the cone in terms of pi.
15 cm
12 cm
9 cm
Answer: volume of the cone is 324pi cm^3
Step-by-step explanation:
the volume of the cone is derived by the formula
V= 1/3 pi r^2 h
v= volume of the cone
h= height of the cone
r= radius of the cone
V= 1/3 x pi x 9 x 9 x 12
V= 324pi cm^3
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Step-by-step explanation:
to find the volume use the formula (1/3)πr2h,
[tex]( \frac{1}{3})h\pi \: r {}^{2} \\ \frac{1}{ 3} \times \pi \times 9 \times 9 \times 12 \\ \frac{1}{3} \times 972\pi \: cm \\ = 324\pi \: cm {}^{3} [/tex]
Mrs. Wright is planning her best friend's baby shower. She calculates that the food will cost $9 per guest, and she has already spent $43 on decorations.
Write an equation showing how the cost of the baby shower, y, depends on the number of guests, x.
Do not include dollar signs in the equation.
Answer:
The equation that shows how the cost of the baby shower, y, depends on the number of guests, x is:
y = 9x + 43
In this equation, x represents the number of guests and y represents the cost of the baby shower. The term 9x represents the cost of food for each guest, multiplied by the number of guests. The term 43 represents the cost of decorations that has already been spent. Therefore, the total cost of the baby shower can be calculated by multiplying the number of guests by the cost of food per guest and adding the cost of decorations that have already been spent.
Answer: y = 9x + 43
Step-by-step explanation: y = cost of the baby shower
x = number of guests
$9 per guest would be 9x
Determine whether the ordered pair is a solution to the given equation.
(−4, 24); y = −6x
Answer: Yes, (-4, 24) is a solution to the given equation.
Step-by-step explanation:
24 = -6(-4)
24 = 24
given the expression (2^-3)(2^5)/2^7), select the three equivalent numerical expressions
The three equivalent numerical expressions are; Options M, R and S
How to determine the expressionsTo determine the expressions, we need to take note that index forms are described as forms that are used for the representation of numbers or variables that are too large or small to be written.
Some rules of index forms are;
Subtract the exponents when the same bases are dividedAdd the exponents when the same bases are multipliedFrom the information given, we have that;
(2^-3)(2^5)/2^7)
add the exponents of the numerator
2⁻³⁺⁵/2⁷
Add the values
2²/2⁷
Subtract the exponents
2⁻⁵
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Which expression is NOT equivalent to 24 + 12
Group of answer choices
3(8+4)
2(12+10)
2(12+6)
6(4+2)
Edouard Manet's Luncheon on the Grass was shown in the______after it was rejected for the annual salon.
World's Fair
Impressionist exhibition
O salon d'automne
Salon des Refusés
Answer:
Salon des Refusés. Is the correct answer
Edouard Manet's Luncheon on the Grass was shown in the Salon des Refusés after it was rejected for the annual salon.
Cual es el volumen, en cm cúbicos, de un prisma rectangular con una altura de 3 cm, un ancho de 2 cm y una longitud de 18 cm ?
Answer:
El volumen en cm cúbicos es 108 cm cúbicos (o a la tercera potencia). La fórmula utilizada para encontrar el volumen es largo por ancho por alto.
I NEED HELP FINDING THE ANNUAL INTEREST RATE!!
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$975\\ r=rate\to \text{\LARGE 5.7\%}\to \frac{5.7}{100}\dotfill &0.057\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years \end{cases} \\\\\\ A = 975\left(1+\frac{0.057}{1}\right)^{1\cdot t} \implies A = 975(1.057)^t[/tex]
Why is the following true?
rank(AB)
is less than or equal to
min {rank(A), rank(B)}.
Thank you in advance.
For any matrices A and B, where A is a m x n matrix and B is a n x p matrix, the inequality rank(AB) ≤ min rank(A), rank(B) holds.
To see why this is so, examine the rank of a matrix, which is defined as the matrix's greatest number of linearly independent rows or columns.
In other words, it is the dimension of the vector space covered by the matrix's rows or columns.
When we multiply matrices A and B to obtain AB, we get a matrix with m rows and p columns.
The dot product of a row from A and a column from B yields each element in the matrix.
Because the rows and columns of AB are linear combinations of the rows and columns of A and B, the rank of AB is at most the minimum of the rank of A and the rank of B.
If either A or B has a lower rank than the other, there will be some linear dependency between the rows or columns of one of the matrices, which will carry over to AB. This indicates that AB's rank will be strictly less than the bigger matrix's rank.
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The rim of a basketball hoop is 10 feet high. When Chase stretches his hand, it is 88 inches high. How many feet does Chase have to jump to be able to touch the rim?
Chase has to jump 2.67 feet to touch the rim.
The rim of the basketball hoop is 10 feet high, which is equal to 120 inches .
Chase's hand can reach 88 inches high.
To find out how many feet Chase has to jump to touch the rim, we need to subtract his reach from the height of the rim:
120 inches (height of rim) - 88 inches (Chase's reach) = 32 inches
So Chase has to jump 32 inches to touch the rim. To convert this to feet, we can divide by the number of inches in a foot:
32 inches ÷ 12 inches/foot = 2.67 feet
Therefore, Chase has to jump 2.67 feet to touch the rim.
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The data given represents the height of basketball players, in inches, on two different girls' teams.
Super Stars
66 66 66
63 63 63
65 65 65
64 64 64
58 58 58
Champs
62 69 65
68 60 70
70 58 67
66 75 70
69 67 60
Compare the data and use the correct measure of center to determine which team typically has the tallest players. Explain your answer.
The Champs, with a median of 67 inches
The Super Stars, with a mean of about 60.8 inches
The Champs, with a mean of about 66.4 inches
The Super Stars, with a median of 63 inches
Using the correct measure of center, the team that typically has the tallest players is C. The Champs, with a mean of about 66.4 inches.
What are the measures of center?The three typical measures of center are the mean, the median, and the mode.
The mean is the average value, obtained as the quotient of the total value of the data set divided by the number of items.
The median is the middle value of the data set arranged in descending or ascending order.
The mode refers to the value that occurs most in the data set.
Super Stars66 66 66 = 198
63 63 63 = 189
65 65 65 = 195
64 64 64 = 192
58 58 58 = 174
Total = 948
Mean = 63.2 (948 ÷ 15)
Median = 64 (58, 58, 58, 63, 63, 63, 64, 64, 64, 65, 65, 65, 66, 66, 66)
Champs62 69 65 = 196
68 60 70 = 198
70 58 67 = 195
66 75 70 = 211
69 67 60 = 196
Total = 996
Mean = 66.4 (996 ÷ 15)
Median = 67 (58, 60, 60, 62, 65, 66, 67, 67, 68, 69, 69, 70, 70, 70, 75)
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14. Sarah makes and sells candles. She spends $80 on supplies, and she sells
each candle for $6. Write an expression that represents her profit for
selling c candles.
Answer: hmm this question is based on 6-80 and if you calulate the sum and difference it is -74
suppose sin(A)=2/5 use the trig identity sin^2(A)+cos^2(A)=1 to find sin (A) in quadrant IV
The trigonometry identity value of sin(A) is -2/5
Solving the trigonometry identityFrom the question, we have the following parameters that can be used in our computation:
sin(A) = 2/5 sin^2(A) + cos^2(A) = 1 The angle A is in Quadrant IVThe value of sin(A) has already been given
However, because the angle A is in Quadrant IV, the value of the trigonometry identity would be negative (sine are negative in the 4th quadrants)
So, we have
sin(A) = -2/5
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To find the total number of people sitting in the full rows, Mandy multiplied 142 by 10 and 142 by 2 and then added the products. Does Mandy’s method make sense? Use what you know about multiplication to explain why or why not.
Mandy's solution makes sense since it entails multiplying the total number of persons in those entire rows (142) by the number of people in each row (ten).
How does multiplication apply?Similarly, multiplying the total number of people in the remaining seats (142) by the number of people in each row (2) yields the total number of people in the remaining seats. The total number of persons in the theater is calculated by adding these two components.
This is a viable use of multiplication's distributive property, in which we break down a multiplication issue into simpler products and then add them up. As a result, Mandy's approach is a viable method for determining the total number of people in the theater.
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If y= 2x +3, What is Y=(-5) + 3=
The value of the expression is -4
What is a function?
A function can simply be explained as an equation, law, rule or expression that tends to show the relationship between two distinct variables.
These variables are called the independent variables and dependent variables.
From the information given, we have the function as;
y= 2x +3
First, let's determine the function y(-5)
Substitute the values of x as -5 in the function;
y(-5) = 2(-5) + 3
expand the bracket
y(-5) = -10 + 3
Add the values
y(-5) = -7
Then, we get;
y(-5)+ 3
-7 + 3
-4
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Find the difference between 6c² +3c+9 and 3c-5.
Pls help
The shape below contains a rectangle and four semi circles.
The perimeter of the shape is 13π
The area of the shape is 48.125π square units
What are the perimeter and area of the shapes?The perimeter of the shape is calculated as follows:
The perimeter of shape = perimeter of the two semicircles of radius 2 + perimeter of the two semicircles of radius 4.5The perimeter of a semicircle = πr
The perimeter of shape = 2 * π * 2 + 2 * π * 4.5
The perimeter of shape = 13π
The area of the shape = area of the two semicircles of radius 2 + area of the two semicircles of radius 4.5 + area of the rectangle
Area of semicircle = πr²/2
The area of the shape = π * 2²/2 + π(4.5)²/2 + 4 * 9
The area of the shape = 48.125π square units
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The axis represents a students age in years and the y-axis represents the number of times the student cried each month on average. What type of data represented in this scatterplot? (Choose 2 )
Decreasing
Increasing
Bivariate
Univariate
Can someone help me with this maths questions
The solution is, the value of the angle & x is:
x = 43
43°, 51°, 86°
We have,
The sum of the angles is ...
x° + (x +8)° + 2x° = 180°
4x +8 = 180 . . . . . . . . . . . collect terms, divide by °
x +2 = 45 . . . . . . . . . . divide by 4
x = 43 . . . . . . . . . . subtract 2
x +8 = 51
2x = 86
The angles are 43°, 51°, 86°.
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complete question:
The sum of the angle measures of a triangle is 180°. Find the value of x. Then find the angle measures of the triangle.