The result by using long division method for the given polynomial equation is: 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]
What is long division method?
In mathematics, the long division method can be performed on the polynomial equations. Basically, in this big equation can be solved by making smaller group of equations to make the calculation simple. It divide the dividend with divisor.
According to the question, the given polynomial equation is 3x³ +19x² + 23x + 15. Using long division method, divide it by 25
Therefore, the expression can be written as:
Required expression: [tex]\frac{3x^{3} +19x^{2} + 23x + 15 }{25}[/tex]
Dividing it by 25, we get:
(25/3x³) +(25/19x²) + (25/23x) + (25/15)
⇒ 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]
Hence, the result by using long division method for the given polynomial equation is: 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]
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A piggy bank contains $2.65 in nickles and dimes. if the number of nickles is 7 less than three times the number of dimes. how many of each are there
In this question, we have been given a piggy bank contains 2.65$ in nickels and dimes. Then There are 29 nickels and 12 dimes in the piggy bank.
We need to find the number of nickels and dimes if the number of nickels is 7 less than three times the number of dimes.
Let x be the number of nickels and y be the number of dimes.
We know that, 1 dollar = 20 nickels
and 1 dollar = 10 dimes
So, we get an equation
0.05x + 0.1y = 2.65 ...........(1)
Also the number of nickels is 7 less than three times the number of dimes.
x = 3y - 7 .................(2)
Substitute above value of x in equation (1)
0.05(3y - 7) + (0.1)y = 2.65
0.15y - 0.35 + 0.1y = 2.65
0.25y = 2.65 + 0.35
0.25 y = 3
y = 12
Substitute above value of y in equation (2)
x = 3(12) - 7
x = 29
Therefore, there are 29 nickels and 12 dimes in the piggy bank.
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Write an equation in standard form for the line that passes through the given points
(3,0) and (0, -2)
Equation of a line in the standard form that passes through the points (3, 0) and (0, -2) will be [y = (2/3)x - 2].
As per the question statement, a straight line passes through the points (3, 0) and (0, -2).
We are required to determine the equation of the above mentioned line in it's standard form.
To solve this question, we need to know the formula to write the standard equation of a line passing through two points (x₁, y₁) and (x₂, y₂) which goes as [tex][(y-y_{1})=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}(x-x_{1})][/tex].
Here, let (x₁, y₁) be (3, 0) and (x₂, y₂) be (0, -2).
Therefore, equation of our concerned line passing through the two points (3, 0) and (0, -2), by substituting [(x₁, y₁) = (3, 0)] and [(x₂, y₂) = (0, -2)] in the above mentioned formula, will be [(y - 0) = {(-2 - 0)/0₂ - 3)}(x - 3)]
Or, [y = {(-2)/(-3)}(x -3)]
Or, [y = (2/3)(x - 3)]
Or, [y = (2/3)x - 2]
Equation: In mathematics, an equation is a statement that expresses the relation of equality between two expressions, by connecting them with the "equal to" sign (=).Line: In geometry, a line is an infinitely long one-dimensional object or shape with no width, depth, or curvature.To learn more about Equations and lines, click on the link below.
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HELP ASAP!!
Solve the inequality divided by negative 3. 2 is greater than or equal to 7. 6 for r.
A. ) r ≥ −24. 32
B. )r ≤ −24. 32
C. )r ≥ 2. 375
D. ) r ≤ −2. 375
Answer:
B. )r ≤ −24. 32
Step-by-step explanation:
1. Henry wants to go on a vacation. He knows it will cost $300 per
day that he's on vacation plus $650 for miscellaneous activities. He
has $2750 dollars in his savings account. How many days can he go
on vacation?
The number of days Henry can go on vacation is 7 days.
Given that, Henry knows it will cost $300 per day that he's on vacation plus $650 for miscellaneous activities.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of days be x.
Henry has $2750 dollars in his savings account.
So equation is 300x+650=2750
The obtained equation can be solved as follow
300x=2750-650
⇒ 300x = 2100
⇒ x = 2100/300
⇒ x = 7
Therefore, the number of days Henry can go on vacation is 7 days.
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Given the function:
g(x)=8-2.5x
Find the following values.
a) g(6)
b) g(0)
c) g(-6)
A) g(6)
g(6) = 8 -2.5*6
g(6) = 8 - 15
g(6) = -7
B) g(0)
g(0) = 8 -2.5*0
g(0) = 8 - 0
g(0) = 8
C) g(-6)
g(-6) = 8 -2.5*-6
g(-6) = 8 + 15
g(-6) = 23
standard form. (-3,0) and (0,8)
Answer:
8x−3y=−24
Step-by-step explanation:
7/3y = 21 solve for y simplify your answer as much as possible
Answer: y = 1/9
Step-by-step explanation:
7/3y=21
7= 21 x 3y
7/21 = 3y
1/3 = 3y
1/9 = y
The Jones family is having lasagna for dinner. Before dinner, 15/15 of the lasagna was in the pan. The family ate 10/15 of the lasagna.
What fraction of the lasagna was left in the pan after dinner? (PROVIDE SCREENSHOT TO SHOW HOW TO DO IT)
Answer:
5/15 of 1/3
Step-by-step explanation:
15/15-10/15=5/15
1-2p=-4p-9 solve equation
Answer: p= -5
Step-by-step explanation:
Answer:
-5
Step-by-step explanation:
carry the one over to the right side and subtract it to get an amount of -10.
then carry the -4p to the left and add it with -2p. which comes out to be 2p
now the equation reads as 2p=-10
continue to divide 2 to get p alone and divide -10 by 2 as well.
now p=-5 because a negative divided by a postive is a negative.
ou have three jars of gumballs. the first jar has 100 white gumballs and 25 green, the second jar has 50 white and 150 blue, and the third jar contains 500 white and 10 red. if you randomly draw one gumball from each jar, what is the probability for at least one white gumball?
The probability for at least one white gumball is 0.196
Consider the following:
First jar:100 whites, 25 green
Total=100+25
=125 gumball
P(White)=100/125=0.8
Second jar:50 whites, 150 blue
Total=50+150
=200 gumballs
P(White)=50/200=0.25
Third jar:500 whites, 10 red
Total=500+10
=510
P(White)=500/500=0.98
Now, probability for at least one white is
=P(white in jar 1)*P(white in jar 2)*P(white in jar 3)
=0.8*0.25*0.98
=0.196
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Find the area of ABCD with vertices A(-5,2), B(-3,2), C(-2,-5),
D(-4,-5).
Answer:
14 units²=============================
Given Vertices A(-5,2), B(-3,2), C(-2,-5), D(-4,-5)To find The area of ABCDSolutionWe can observe that:
1. AB and CD are horizontal segments, since both endpoints have same y-coordinates:
A and B have y = 2, C and D have y = - 52. AB and CD are of same length:
AB = - 3 - (-5) = 2,CD = - 2 - (-4) = 2.It means the ABCD is a parallelogram, since two opposite sides are parallel and of same length.
The area of parallelogram is:
A = bh, where b- base length, h - heightWe know the length of the base, it is found above, 2 units.
The height is the difference of y- coordinates:
h = 2 - (-5) = 7The area is:
A = 2*7 = 14 units²State the line of reflection
Based on the given figures, the line of reflection will be c. Reflection across x-axis.
How to find the line of reflection?If it looks like the line of reflection is a horizontal line as is the case here, the way to find the line of reflection is by finding the midway point between corresponding points on the graph.
For instance, use the coordinates of D and D' and C and C'.
The coordinates of D and D' are:
D = (-1, 1)
D' = (- 1, -1)
The Midpoint can be found to be:
= ( (x₁ + x₂) / 2, (y₁ + y₂) / 2)
= ( (-1 + (-1)) / 2), ( (1 + (-1)) / 2
= (-1, 0)
The coordinates of C and C' are:
C = (4, 1)
C' = (4, -1)
The Midpoint can be found to be:
= ( (x₁ + x₂) / 2, (y₁ + y₂) / 2)
= ( (4 + 4) / 2), ( (1 - (-1)) / 2
= (4, 0)
The line of reflection is therefore the x-axis because the value of y is 0 and the x = axis is the line that crosses y at 0.
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will give 30 points if its right need asap please
Answer:
2y + 1 maybe??????
Step-by-step explanation:
hope its correct if not please tell me
Why is the denominator of each fraction 12?
Pls help me
Answer: because it is out of 12
Step-by-step explanation:
Given a rectangle with the following dimensions: Area = 50 units Length = x + 10 units Width = x units Find the value of x.
Step-by-step explanation:
the area of a triangle is
length × width
in our case
(x + 10) × x = 50
x² + 10x = 50
x² + 10x - 50 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case that is
x = (-10 ± sqrt(10² - 4×1×-50))/(2×1) =
= (-10 ± sqrt(100 + 200))/2 =
= (-10 ± sqrt(300))/2 = (-10 ± sqrt(100×3))/2 =
= -5 ± sqrt(100×3/4) = -5 ± sqrt(25×3) =
= -5 ± 5×sqrt(3)
x1 = -5 + 5×sqrt(3) = 3.660254038...
x2 = -5 - 5×sqrt(3) = -13.66025404...
x2 gives us negative values for length and width. that does not make any sense for actual lengths of objects.
so,
x = 3.660254038...
a) Find the value of 8*1/3
b) Find the value of 8*2/3
c) Find the value of 164*3/4
1. 8/3
2. 16/3
3. 123
*some words for 20 symbols*
3. For items 3a-3d, choose Yes or No to
tell if the digit in the hundreds place
is to the value of the digit in the
thousands place.
3a. 8,556
3b. 6,855
3c. 5,568
3d. 5,656
Yes
Yes
Yes
Yes
No
No
No
O No
The Yes or No to for digit in the hundreds place is to the value of the digit in the thousands place are-
3a. 8,556 ; No , 3b. 6,855 ; No , 3c. 5,568 ; Yes , 3d. 5,656 ; No
What is termed as the place value system?Our a whole number system is built around place value. This is a system where the value of a number is determined by the position of its digits. The numbers 42,316 and 61,432 differ so because digits are in various positions.As per the place value system,
Thousand Hundred Tens Ones
3a. 8,556
Thousand value of number = 8000
Hundred value of number = 500
1/10 × 8000
800 ≠ 500
No, the digit at hundreds place is not 1/10 of the digit at thousand place.
3b. 6,855
Thousand value of number = 6000
Hundred value of number = 800
1/10 × 6000
600 ≠ 800
No, the digit at hundreds place is not 1/10 of the digit at thousand place.
3c. 5,568
Thousand value of number = 5000
Hundred value of number = 500
1/10 × 5000
500 = 500
Yes, the digit at hundreds place is 1/10 of the digit at thousand place.
3d. 5,656
Thousand value of number = 5000
Hundred value of number = 600
1/10 × 5000
500 ≠ 600
No, the digit at hundreds place is not 1/10 of the digit at thousand place.
Thus, the condition of yes and no for the given number are obtained.
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The complete question is-
3. For items 3a-3d,
Choose yes or no to tell if the digit in the hundreds place is 1/10 the value of the digit in the thousand place.
thousands place.
3a. 8,556
3b. 6,855
3c. 5,568
3d. 5,656
Brian is making bags of trail mix for hiking club. He will use 21 ounces of walnuts, 10.2 ounces of almonds, and 14.3 ounces of cashews. This amount makes 25 bags of trail mix. How many ounces are in each bag?
Answer:
See explanation
Step-by-step explanation:
First add all the weights, 21+10.2+14.3=45.5oz
Then you divide 45.5 by 25 which equals 1.82oz
Use I = PTR to solve
(time is in years)
I=$252
R=7% find T.
P=$900
The time period in years T = 4 years
The simple interest amount = $252
The rate of interest per year as percentage = 7%
The principal amount = $900
The simple interest I = PTR
Where I is the interest amount
P is the principal Amount
T is the time period involved in years
R is the rate of interest per year as a percent
Substitute the values in the equation
252 = 900 × T × (7 / 100)
252 = 900 × T × 0.07
252 = 63 × T
Move the 63 to other side
T = 252 / 63
T = 4 years
Hence, the time period in years T = 4 years
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No Spamming or will report! Will give Brainliest. Must have explanation
Find four consecutive even integers such that the least plus twice the greatest equals 264
The four consecutive integers in the question are; 51, 52, 53, 54
What is the Sum of the Integers?Let the four consecutive integers in the question be;
x, x + 1, x + 2 and 2(x + 4)
Now, we are told that the sum of these four consecutive integers is 264. Thus;
x + x + 1 + x + 2 + 2(x + 3) = 264
Expanding the bracket gives;
3x + 3 + 2x + 6 = 264
5x + 9 = 264
5x = 264 - 9
5x = 255
x = 255/5
x = 51
Thus;
Second integer = 51 + 1 = 52
Third integer = 51 + 2 = 53
Fourth Integer = 51 + 3 = 54
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WILL GIVE BRAINLIST IF ANSWERED CORRECTLY!!
Answer: 9 units to the right and 5 units down
Step-by-step explanation:
1) Measure the length.
You can find that you can match point C with point W. Next find how much it goes to the right and left.
Right from (C->W): 9 squares
Down from (C->W): 5
2) Fill in the blank
9 units to the right and 5 units down
Answer:
ΔABC ≅ ΔNKW because when ΔABC is translated 9 units right and 5 units down, it results in the other triangle.
Step-by-step explanation:
The triangles are congruent as the measures of their corresponding sides and angles are the same.
To determine the translation of ΔABC to ΔNKW, find the change in the x and y values from one of the points of ΔABC to its corresponding point of ΔNKW.
Point C = (0, 0)Point W = (9, -5)Therefore:
ΔABC ≅ ΔNKW because when ΔABC is translated 9 units right and 5 units down, it results in the other triangle.
Which postulate could we use to prove that the angles
Answer:
you can use the angle addition postulate I think that's what it's called
Tina's taco truck sold 3 times as many veggie tacos in August than in September. She sold twice as many in September than in October. She sold 927 veggie taco during the three months
The number of tacos sold in August, September and October is 103, 206, 618 respectively.
Let the number of veggie tacos sold by Tina in October be x
Then, number of veggie tacos sold in September is twice that of veggie tacos sold in october = 2x
Number of veggie tacos sold in August is thrice that of veggie tacos sold in September = 3 x 2x = 6x
Total veggie taco during the three months by Tina = 927
6x + 2x + x = 927
9x = 927
x = 927/9
x = 103
Tacos sold in August = 6x = 618
Tacos sold in September = 2x = 206
Tacos sold in October = x =103
Therefore, the number of tacos sold in August, September and October is 103, 206, 618 respectively.
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One teacher wants to give each student 4/9 of a slice of pizza. if the teacher has 4 slices of pizza, then how many students will she be able to hand out pizza to?
(2 x 47) / (6 + 9) =
(6 +17) / 3 = =
(42 - 3)/7 =
(6 +22) / (47 - 21) =
(932) / (827) =
Bloque 2
Bloque2
Redondea a 2 decimales
The length of the rectangle is 5 more than twice the width. If the perimeter is 10 times that of the width, what is the width, length, and perimeter of the rectangle?
Width of the rectangle is 2.5, Length is 10 and perimeter is 25
Given
Length of rectangle is 5 greater than double of width
let us say width = w
According to the question length L = 5 + 2w
Perimeter is 10 times the width
P= 10w
we know that perimeter of a rectangle is 2(L+W)
Substituting the values in the formula we get
10w = 2(5+2w + w)
10w = 10 + 6w
w= 2.5
From this length L = 5+2(2.5)
L = 10
Perimeter P = 10W
P= 10(2.5)
P= 25
Hence the length is 10, width is 2.5 and perimeter is 25
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Pls help ASAP
The question is in the picture
Answer:
1. x = 0 , x = 3
2. x = -2 , x = 2
3. (x - 1)²
ASAP!!
3x + 9x = 6x + 42
Solve the equation for X and include all steps for Branliest.
Answer:
x = 7
Step-by-step explanation:
3x + 9x = 6x +42
12x = 6x +42
12x - 6x = 6x -6x +42
6x = 42
[tex]\frac{6x}{6} = \frac{42}{6}[/tex]
x = 7
Ivan has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
Using combinations, there are a total of 20 distinct voting combinations.
We now have five bands. We'll refer to them as A, B, C, D, and E.
John will choose two bands from the available five if he is required to vote for his favorite and second-favorite.
We must pair bands and discover every possible combination in order to determine the TOTAL number of different possibilities.
The results/totals are as follows:
AB, AC, AD, AE
BA, BC, BD, BE
CA, CB, CD, CE
DA, DB, DC, DE
EA, EB, EC, ED
Thus, there are a total of 20 distinct voting combinations.
Since you already know that each of the five initial bands (A, B, C, D, and E) will result in a multiple of four, you may accomplish it more simply without listing by taking the five bands.
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The measure of a base angle of an isosceles triangle is 20 degrees. What is the measure of the vertex?
Answer:
140 degrees
Step-by-step explanation:
isosceles triangle so two angles are equal 20 and 20
ALL of the angles sum to 180 degrees
20+ 20 + vertex = 180
vertex = 140°