The quotient of the division (4d² + 2d - 3) ÷ (d - 7) is 4d + 30 and remainder is 207.
What is the Long Division?Dividing one polynomial by the other is very similar to dividing one number by the other.
The steps for dividing polynomials using long method are as follows:
Arrange the polynomial indices in descending order. Substitute 0 for the missing term(s).Divide the dividend's first term (the polynomial to also be divided) by the divisor's first term. This yields the quotient's first term.Multiply this same divisor by the quotient's first term.Subtract the dividend from the product, then reduce the next term. The difference between this term and the next is the new dividend. Keep in mind the rule of subtraction: "change the sign of a subtrahend before proceeding to addition."Steps 2–4 must be repeated to determine the second term of a quotient.Repeat the procedure till a remainder is acquired. This can be zero or a number with a lower index than that of the divisor.For the given question;
Dividend = 4d² + 2d - 3
Divisor = d - 7
Divide dividend by divisor.
= ( 4d² + 2d - 3)/(d -3)
The quotient will come as 4d + 30.
Remainder = 207.
Thus, 4d² + 2d - 3 is not completed divisible by d - 3.
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What is -10= -10 + 7m showing work?
Answer:
m = 0
Step-by-step explanation:
- 10 = - 10 + 7m ( add 10 to both sides )
0 = 7m ( divide both sides by 7 )
0 = m
ANSWER PLEASEEEEEEEEEEEEEEEEEE
Answer: x∈[-4,3) y∈(-5,5)
Step-by-step explanation:
[tex]Domain:x\in[-4,3)\\Range\ of\ y:\ y\in(-5,5)[/tex]
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Part 1 of 2
Shureka Washburn has scores of 61, 77, 65, and 81 on her algebra tests.
a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 72 or higher, given that the final exam counts as two tests
b. Explain the meaning of the answer to part (a).
a. The solution set is {x (Type an inequality.)
The value of x is 74
Surekha Washburn has scores of 61, 65, 77, and 81 on her algebra tests.
a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 72 or higher, given that the final exam
counts as two tests.
let score on final exam is x
two test are 2x
then we get the value of x
[tex]\frac{61 + 65 + 77 + 81 + 2x}{6}[/tex] = 72
[tex]\frac{284 + 2x}{6}[/tex] = 72
284 + 2x =432
2x = 432 - 284
x = [tex]\frac{148}{2}[/tex]
x = 74
The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Average Formula in Maths
The formula to find the average of given numbers or values is very easy. We just have to add all the numbers and then divide the result by the number of values given. Hence, the average formula in Maths is given as follows:
Average = Sum of Values/ Number of values
Suppose, we have given with n number of values such as x1, x2, x3 ,….., x n. The average or the mean of the given data will be equal to:
Average = (x1+x2+x3+…+x n)/n
How to Calculate Average?
We can easily calculate the average for a given set of values. We just have to add all the values and divide the outcome by the number of given values.
Average can be calculated using three simple steps. They are:
Step 1: Sum of Numbers:
The first step in finding the average of numbers is to find the sum of all the given numbers.
Step 2: Number of Observations:
Next, we have to count how many numbers are in the given dataset.
Step 3: Average Calculation:
The final step in calculating the average is to divide the sum by the number of observations.
Now, let us consider an example to calculate the average.
If there are a group of numbers say, 20, 21, 23, 22, 21, 20, 23. Then find the average of these values.
By average formula, we know,
Average = (Sum of values)/No. of values
= (20+21+23+22+21+20+23)/7
= 150/7
=21.42
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The following table contains the rate of commission, number of items sold,
and cost of each item for four different salespeople.
Using proportions, the person who earned the most commission is given by:
B. Bridget.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The commission is given by:
Rate(as a decimal) x Number of Items x Cost of Each Item.
Hence, for Bridget, the commission is given by:
B = 0.045 x 18 x 50 = $40.5.
For Curtis, the commission is given by:
C = 0.0375 x 11 x 80 = $33.
For Gloria, the commission is given by:
G = 0.0475 x 5 x 140 = $33.25.
For Hugo, the commission is given by:
H = 0.0425 x 13 x 60 = $33.15.
Hence Bridget earned the most commission and option B is correct.
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Trymaine is 7 years older than Sunny. In 3 years the sum of their ages will be 39. How old is Trymaine now?
Trymaine is 20 years old and Sunny is 13 years old.
GIven, Trymaine is 7 years older than Sunny.
In 3 years the sum of their ages will be 39.
Let the age of Trymaine be a and age of Sunny be b.
we have,
a = b ₊ 7
a ₊ 3 ₊ b ₊ 3 = 39
a ₊ b = 39 ₋ 6
a ₊ b = 33 .... eq(2)
therefore a = b ₊ 7
a ₋ b = 7 ....eq(1)
solve eq (1) and eq(2)
2a = 40
a = 20
and a ₋ b = 7
20 ₋ b = 7
₋b = 7 ₋ 20
₋b = ₋13
b = 13
hence Trymaine is 20 years old , whereas Sunny is 13 years old.
hence we get the ages of Trymaine and Sunny as 20 and 13 respectively.
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7.2 HELPPPPPPP
1.Find the missing length indicated. Leave your answer in simplest radical form.
2.Find the missing length indicated. Leave your answer in simplest radical form.
3.Find the missing length indicated. Leave your answer in simplest radical form.
4.Find the missing length indicated. Leave your answer in simplest radical form.
In simplest radical form, the values are,
(1) The missing length = 48
(2) The missing length = 48
(3) The missing length = 140
(4) The missing length = 25
(1) : In triangle,
ΔADB ≅ ΔABC
∠A = ∠A
∠ABC = ∠ABD
So, ΔADB ≅ ΔABC
AD/AB = AB/AC
AD = 64 AND AC = 100 substitute in this equation,
64/AB = AB/100
AB * AB = 64*100
[tex]AB^{2}[/tex] = 6400
AB = [tex]\sqrt{6400}[/tex]
AB = 80
Because,
∠ADB = 90°
So,
[tex]AD^{2} +BD^{2} =AB^{2}[/tex]
[tex]BD^{2} = AB^{2} -AD^{2}[/tex]
BD = [tex]\sqrt{BD^{2}-AD^{2} }[/tex]
BD = [tex]\sqrt{6400-4096}[/tex]
BD = [tex]\sqrt{2304}[/tex]
BD = 48
Therefore,
The missing length is BD = 48
(2) : In triangle,
ΔADB ≅ ΔABC
∠A = ∠A
∠ABC = ∠ABD
So, ΔADB ≅ ΔABC
AD/AB = AB/AC
AD = 64 AND AC = 100 substitute in this equation,
64/AB = AB/100
AB * AB = 64*100
[tex]AB^{2}[/tex] = 6400
AB = [tex]\sqrt{6400}[/tex]
AB = 80
Because,
∠ADB = 90°
So,
[tex]AD^{2} +BD^{2} =AB^{2}[/tex]
[tex]BD^{2} = AB^{2} -AD^{2}[/tex]
BD = [tex]\sqrt{BD^{2}-AD^{2} }[/tex]
BD = [tex]\sqrt{6400-4096}[/tex]
BD = [tex]\sqrt{2304}[/tex]
BD = 48
Therefore,
The missing length is BD = 48
(3): In triangle BDC
tanθ = BC/DC
tanθ = 60/36
θ = [tex]tan^{-1}[/tex](60/36)
θ = [tex]tan^{-1}[/tex](1.66)
θ = 53.16
And,
[tex]BD^{2} =BC^{2} +CD^{2}[/tex]
[tex](BD)^{2}[/tex] = 60*60 + 36*36
[tex](BD)^{2}[/tex] = 3600+1296
[tex](BD)^{2}[/tex] = 4896
BD = 69.97
In big triangle, ABC
cosθ = BC/AC
cosθ = 60/(36+u)
cos69.97 = 60/(36+u)
0.342 = 60/(36+u)
36+u = 60/0.342
36+u = 195.4
u = 195.4 - 36
u = 139.4
u = 140
Therefore,
The maximum length u = 140
(4) : In ΔABC and ΔDAB
∠B = ∠B (Common)
∠A = ∠D = 90°
Hence, ΔBAC ≅ ΔBDA
AB/BC = BD/AB
15/x = 9/15
x = (15*15)/9
x = 225/9
x = 25
Therefore,
The missing length x = 25
Hence,
(1) The missing length = 48
(2) The missing length = 48
(3) The missing length = 140
(4) The missing length = 25
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Babies are weighed at birth to monitor their progress. Martin weighs 0.6 kg less than Daniel who weighs 0.4 kg less than Kevin. Martin weighs x kilograms and the total weight of the three boys is 10.3 kg. Form an equation in x, solve it and state the weight of each baby
The weight of each baby based on the information will be:
Martin = 2.9 kg
Daniel = 3.5kg
Kevin = 3.9 kg
How to illustrate the information?Martin = x
Daniel = x + 0.6
Kevin = x + 1
Total weight = 10.3 kg
Therefore, this will be solved as:
x + x + 0.6 + x + 1 = 10.3
3x + 1.6 = 10.3
3x = 10.3 - 1.6
3x = 8.7
Divide
x = 8.7 / 4
x = 2.9
Therefore, the weights will be:
Martin = x = 2.9 kg
Daniel = x + 0.6 = 2.9 + 0.6 = 3.5kg
Kevin = x + 1 = 2.9 + 1 = 3.9 kg
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A baseball stadium has 45,000 seats. If tickets have been bought for 5/8 of the seats for the next game, how many seats are still available to buy?
A baseball stadium has 45,000 seats. If tickets have been bought for 5/8 of the seats for the next game, then 45000−(5/8⋅45000)=16875 seats left.
We will subtract (5/8⋅45000) from 45000.
To subtract in mathematics is to take something away from a group or a number of things. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction problem are the minuend, subtrahend, and difference.
Subtraction is therefore the antithesis of addition. Thus, addition and subtraction are the polar opposites of each other. We could say that subtraction is the opposite of addition.
A subtraction number sentence is an equation that displays the result of subtracting one number from another. The first number is the minuend, the second number is the subtrahend, and the answer is the difference in a subtraction number sentence.
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For Problem 5, explain why the triangles are similar
and find the stated length.
Help please
Answer: DG and EF are parallel. DE=13
Step-by-step explanation:
DG and EF are parallel. They are both right angled triangles.
EF/DG=DE/CD
5/1.25=DE/3.25
4=DE/3.25
4*3.25=DE
13=DE
Yossi used to have a square garage with 262 square feet of floor space. He recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
Increase in the length is 3.64 ft.
What is area of square?
The area of square is the product of side of the square.
i.e., Area of square = side * side
Given that;
Yossi has garage whose area =262 ft²
And, 50% area is incremented.
Now, the New Area is calculated as;
Area = 262 × 150%
= 393 ft²
As we know that;
Area of Square = (Length) × (Length)
Length = √393 = 19.82 ft
Also,
Length of garage = √262 = 16.18 ft
Hence, Increase in the length = 19.82 - 16.18 = 3.64 ft.
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Solve this quadratic equation using the quadratic formula.
x² + 8x - 5
Ox=-4± √21
Oz = -4 ± √11
Oz=5±2√2
Or = 8+2√/21
According to the given statement
Quadratic equation for x2+8x−5=0 is x=-4± √21
What is Quadratic equation?Second-degree algebraic expressions of the type ax2 + bx + c = 0 are known as quadratic equations.
There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are denoted as (, ) and are also known as the roots of the quadratic equations.
According to the given value;
For this equation: a=1, b=8, c=-5
1x2+8x+−5=0
Step 1: Use quadratic formula with a=1, b=8, c=-5.
x=
−b±√b2−4ac
2a
x=
−(8)±√(8)2−4(1)(−5)
2(1)
x=
−8±√84
2
x=−4+√21 or x=−4−√21
Hence,quadratic equation for x2+8x−5=0 is x=-4± √21
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Line perpendicular to 3y=4x+7 and goes through the point (6,-2)
Considering the definition of perpendicular line, the equation of of perpendicular line is y= -3/4x + 5/2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseIn this case, the line is 3y= 4x +7. Expressed in the form y = mx + b, you get:
y= (4x +7)÷ 3
y= 4/3x -+7/3
The line has a slope of 4/3. If you multiply the slopes of two perpendicular lines, you get –1, then:
4/3× slope perpendicular line= -1
slope perpendicular line= (-1)÷ 4/3
slope perpendicular line= -3/4
So, the perpendicular line has a form of: y= -3/4x + b
The line passes through the point (6, -2). Replacing in the expression for parallel line:
-2= (-3/4)×6 + b
-2= -9/2 + b
-2+ 9/2= b
5/2= b
Finally, the equation of of perpendicular line is y= -3/4x + 5/2.
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K
For the equation x² + y² - 6x-2y-26= 0, do the
following.
(a) Find the center (h,k) and radius r of the circle.
(b) Graph the circle.
(c) Find the intercepts, if any.
Answer:
Step-by-step explanation:
- Six inches more than 3 times the height, h
Answer:
3h+6 inches
Step-by-step explanation:
Multiply the polynomials (4a3-5a-3) and (2a2-7a+3). Simplify the answer.
Answer:
8a^5 - 28a^4 + 2a^3 +29a^2 + 6a - 9
Step-by-step explanation:
(4a3-5a-3) × (2a2-7a+3)
= 4a^3 × 2a^2 + 4a^3(-7a) + 4a^3 × 3 - 5a × 2a^2 - 5a(-7a) - 5a × 3 - 3 × 2a^2 - 3(-7a) - 3 × 3
= 8a^5 - 28a^4 + 2a^3 +29a^2 + 6a - 9
: The table below shows the cost of buying and shipping boxes of shirts. The variable, b, represents the number of boxes of shirts the client ordered. Which expression best represents the cost of the shirts plus shipping?
The expression that best represents the cost of shirts plus shipping is 20b + 5.
What is the expression that represents the cost of shirts plus shipping?An expression is a statement that is made up of at least two numbers or variables and at least one mathematical operation. An expression usually does not have an equal to sign.
The first step is to determine the cost of a shirt and the cost of shipping.
a + b = 25 equation 1
a + 2b = 45 equation 2
Where:
a = cost of shipping
Subtract equation 1 from equation 2
b = 20
a = 25 - 20
a = 5
Thus, the cost of one shirt is 20. The cost of shipping is 5. The cost of shirts increases with the number of shirts bought while the cost of shipping remains constant.
The expression is: 20b + 5
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For each function, find f(-2), f(0), and f(3)
The values of the functions are:
f(-2) = -6
f(0) = 0
f(3) = 9
How to Find the value of a Function?Given the function, f(x) = 3x, to find the values of f(-2), f(0), and f(3), solve as shown below.
Find f(-2) by substituting x = -2 into the function, f(x) = 3x:
f(-2) = 3(-2)
f(-2) = -6
The value of f(-2) for the given function is: -6
Find f(0) by substituting x = 0 into the function, f(x) = 3x:
f(0) = 3(0)
f(0) = 0
The value of f(0) for the given function is: 0
Find f(3) by substituting x = 3 into the function, f(x) = 3x:
f(3) = 3(3)
f(3) = 9
The value of f(3) for the given function is: 9
Thus, the values of the functions are:
f(-2) = -6
f(0) = 0
f(3) = 9
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7 cartons and 3 boxes of table balls did he order
Answer:
Step-by-step explanation: just mutiply 7x3 you get 21
State of the following Conjecture is true or false
Given X is not a negative number
Conjecture X is a positive number
True or false?
The given conjecture X is a positive number is not always correct. Therefore, the given conjecture is false.
Given X is not a negative number and conjecture X is a positive number.
What is a conjecture?A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases.
Given X is not a negative number
Conjecture X is a positive number
If X is 0, which is neither positive nor negative.
So, the statement is false.
The given conjecture X is a positive number is not always correct. Therefore, the given conjecture is false.
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The bills for the month of July have come in. The electric bill is $276.93, the water bill is $69.24, the cell phone bill is $102.56, and the cable bill is $73.69. Rounding each bill to the nearest dollar, estimate what the total household bills are for the month of July.
Answer:
Step-by-step explanation:
Round each number individually,
276.93 Rounded up -> 277
69.24 Rounded Down -> 69
102.56 Rounded up -> 103
73.69 Rounded up -> 74
Total = 523
Anything 0.50 to 0.99 gets rounded up
Anything 0.01 to 0.49 gets rounded down
When to the nearest dollar
15. Write a two-column proof.
GIVEN: m/GFI = 128°
PROVE: m/EFI = 40°
According to the given a two-column proof bellow the EFI = 40°
What is two-column proof?A two-column geometric proof is made up of a set of claims and the reasons why we know they are true. The statements are stated in the left column, while the reasons for making them are mentioned with in right column.
According to the given data:Given:
GFI = 128°where
9x - 2 = 128°
EFI = 40° And
4x = 40
So,
GFI = 128°where
9x - 2 + 4x = 128°
13x = 130
x = 10
putting the value x = 10 in EFI = 40° And 4x = 40:
So,
4x = 40
4(10) = 40
40 = 40
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Suppose a trucking company's costs for hauling consumer goods varies jointly with the number of trucks running and the hours each truck is used. When the company runs full fleet of 16 trucks at 8 hours each, the cost is $20,500. In an effort to cut costs, the owner of the trucking company wants to know what the cost would be when running only half of the fleet for 6 hours each?
The cost of running only half of the fleet for 6 hours each would be $7687.2 .
The company runs full fleet of 16 trucks at 8 hours each.
Which means total hours of running on full fleet = 128 Hours
So, The cost of running 128 hours = $20,500
Then, cost of running 1 hour = $20,500 ÷ 128
= $160.15
Now we will determine the cost of running trucks on half fleet for 6 hours each.
As we already know that
Full fleet = 16 Trucks
Then, Half fleet = 8 Trucks
Total hours of trucks running on half fleet = 8 × 6
= 48
The cost of running 48 hours = 48 × $160.15
= $7687.2
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Can I get help with this math problem lol
Answer:
m = 2
Step-by-step explanation:
Find LCM.
[tex]7,\:14\\14=7\cdot \:2\\=2\cdot \:7\\=7\cdot \:2\\=14\\[/tex]
Multiply
[tex]\frac{2m}{7}\cdot \:14+\frac{3m}{14}\cdot \:14=1\cdot \:14[/tex]
Simplify(AA)
[tex]\frac{2m}{7}\cdot \:14\\=\frac{2m\cdot \:14}{7}\\=\frac{28m}{7}\\=4m[/tex]
Simplify(AB)
[tex]\frac{3m}{14}\cdot \:14\\=\frac{3m\cdot \:14}{14}\\=3m[/tex]
Simplify(AC)
[tex]1\cdot \:14\\= 14[/tex]
Divide
[tex]=7m = 14\\\frac{7m}{7}=\boxed{\frac{14}{7}}\\= 2[/tex]
25. Communicate and Justify Charles says
that he can find the product of 12x6
by breaking apart 12 as 6 + 6 and then
multiply each 6 times 6. Is Charles
correct? Explain.
Charles is correct as the solution of the mathematical operation (6 + 6) × 6 is also 72 as 12 × 6 = 72.
What exactly are mathematical operations?In mathematics, an operation is a function that converts zero or more input data (also known as "operands" or "arguments") to the well output value.The number of operands determines the arity of the operation.So, 12 × 6 = 72
Now, let's do what Charles say as follows:
Break 12 as 6 + 6.
Therefore, Charles is correct as the solution of mathematical operation (6 + 6) × 6 is also 72 as 12 × 6 = 72.
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will mark brainliest 15 points
Based on the product rule of exponents, a^4 * a^6 = [tex]a^{10}[/tex]
What is the Product Rule of Exponents?The product rule of exponents says that if two quantities that are multiplied together have the same base, we will add their exponents together to get the product.
Given the following:
a^4 * a^6
Applying the product rule of exponents, we will have:
a^4 * a^6 = a[tex]^{(4 + 6)}[/tex]
a^4 * a^6 = [tex]a^{10}[/tex].
Therefore, based on the product rule of exponents, a^4 * a^6 = [tex]a^{10}[/tex].
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Find the constant of variation k for the direct variation. 4x = –6y
The constant of variation k for the direct variation in 4x = –6y will be 1.5.
What is direct variation?It should be noted that a direct variation simply means the mathematical relationship that exists between two variables which can be expressed by an equation such that a variable is equal to another one.
Therefore, the constant of variation k for the direct variation in 4x = –6y will be:
4x = –6y
Divide through by 4
4x / 4 = -6y / 4
x = -1.5y
Therefore, the constant of variation is 1.5.
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what is the aswer to -3/4 - -1/3
Answer:
[tex]\frac{-5}{12}[/tex]
Step-by-step explanation:
[tex]\frac{-3}{4}[/tex] - [tex]\frac{-1}{3}[/tex] Subtracting a negative number is the same as adding a positive
[tex]\frac{-3}{4}[/tex] + [tex]\frac{1}{3}[/tex] Rewrite each fraction with a common denominator. Let's use 12 as our new denominator.
[tex]\frac{-3}{4}[/tex] = [tex]\frac{-9}{12}[/tex] multiple the top and the bottom of the first fraction by 3 to get the equivalent fraction [tex]\frac{-9}{12}[/tex]
[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{12}[/tex] Multiple the top and bottom of the first fraction by 4 to get the equivalent fraction [tex]\frac{4}{12}[/tex].
Now, add the two fractions
[tex]\frac{-9}{12}[/tex] + [tex]\frac{4}{12}[/tex] = [tex]\frac{-5}{12}[/tex] The denominator stays the same and you add the numerators.
what is the quotation of -80 and -16
Based on the given task content, the quotient of - 80 and - 16 is 5
What is quotient?Quotient refers to the number resulting from the division of one number by another. Such as: the quotient of 12 divided by 4 is 3.
The divisor
The number or expression that another is to be divided by.
In "42 ÷ 3" the divisor is the 3.
The dividend
These refers to numbers or expressions that is to be divided by another.
In "42 ÷ 3" the dividend is the 42.
Quotient of -80 and -16= - 80 / - 16
= 5
Therefore, the quotient of -80 and -16 is 5
Complete question:
what is the quotient of -80 and -16
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What value of x is in the solution set of the inequality 2(3x – 1) ≥ 4x – 6? –10 –5 –3 –1
Answer:
-1
Step-by-step explanation:
Answer:
-1 is the answer
Step-by-step explanation:
What is the degree of the polynomial given below?
F(x) = 2x³-3x4 +5x-2
A. 2
OB. 5
O C. 3
OD. 4
Answer:
Choice C; degree is 3
Step-by-step explanation:
The degree of the polynomial is the greatest of the exponents (powers) of its various terms.
So the degree of this polynomial is 3 which is choice C