The answer for the given polynomial by synthetic division is 3x+16+(30/(x-3)).
Step-by-step explanation:
The given polynomial is (3x^2 +7x -18) divided by (x - 3)
Take (x-3)=0, then x=3
3 | 3 7 -18
9 48
3 16 30
step 1: write the coefficients of x^2, x and constant in first row. The divisor 3 is written separately on outside.
step 2: Write down the coefficient of x^2= 3 in the answer row as it is without any change.
step 3: Multiply each number in the answer row with the divisor and fill the answers in the second row.
step 4: The final step is to add the first row and second row. After addition, the answers are written in answer row and the last number in the answer row is the Remainder.
step 5: The remainder is written by dividing it with the divisor (x-3). The answer in the descending powers of x is 3x + 16 + (30/(x-3)).
The result of the division (3x^2 + 7x - 18) by (x - 3) using synthetic division is obtained as (3x + 16 + 30/(x - 3)).
Explanation:To perform the synthetic division, the divisor (x - 3) is represented by its root '3'. Write down the coefficients from the dividend polynomial (3, 7, -18) at the top of your division setup. Write '3' to the left, leave some space, and then write down '3', '7', -18.
Then, perform the synthetic division: step one, bring the first coefficient (3) straight down. Step two, multiply this number by the root of the divisor (3), which is also 3. Write this product (9) underneath the next coefficient (7). Add these two numbers (7 + 9) to get 16. Write this number under the line. Now, repeat the previous step by multiplying 16 by the root, 3, to get 48. Write this under -18, add to get 30.
The quotient of the division is the polynomials received from the synthetic division which is 3x + 16 with a remainder of 30. So, the result of division (3x^2 + 7x - 18) by (x - 3) is (3x + 16 + 30/(x - 3)).
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what is the answer to the factor equation of 12 1/3 subtract 5 2/3
Answer:
The answer to the factor expression is [tex]\frac{20}{3}[/tex]
Therefore [tex]12\frac{1}{3}-5\frac{2}{3}=\frac{20}{3}[/tex]
Step-by-step explanation:
Given that the factor expression is [tex]12\frac{1}{3}-5\frac{2}{3}[/tex]
Now convert the mixed fraction into improper fraction as below :
[tex]12\frac{1}{3}-5\frac{2}{3}=\frac{37}{3}-\frac{17}{3}[/tex]
[tex]=\frac{37-17}{3}[/tex]
[tex]=\frac{20}{3}[/tex]
Therefore [tex]12\frac{1}{3}-5\frac{2}{3}=\frac{20}{3}[/tex]
The answer to the factor expression is [tex]\frac{20}{3}[/tex]
a/3 -7=15 im confused for my son
Answer: a = 22
Step-by-step explanation: First isolate a/3 by adding 7 to both sides of the equation. That gives you a/3 = 22.
From here since a is being divided by 3, multiply both sides of the equation by 3 so a = 66. We can check our answer by substituting a 66 back in for a in the original equation and we have [tex]\frac{66}{3} - 7 =15[/tex] or 22 - 7 = 15 or 15 = 15. Since this is a true statement, our answer checks.
3.) Write an equation of a line that has a negative slope and goes through the y-axis at -5.
Answer:
y = -x -5
Step-by-step explanation:
The -x (i.e., multiplication of x by -1) gives the line a slope of -1. The -5 translates the line down to cross the y-axis at -5.
A dean polled the sophomore class about their intended majors, then created this graph based on the data.
Which of the following statements is true about the students' intended majors?
A. Fewer students intend to major in Foreign Language than intend to major in Social Science.
B.More students intend to major in Foreign Language than intend to major in Math/Computer Science and Social Science combined.
C.Social Science and Math/Computer Science (CS) combined represent about
of the intended majors.
D.Science and Social Science combined represent half the intended majors.
Answer:
C & D
Step-by-step explanation:
Social Science and Math/CS do represent 1/4 of the total majors.
Furthermore, Science and Social Sciences represent half of the majors.
Therefore, C & D are true.
Combining Science and Social Science represent half the intend majors. Therefore, option D is the correct answer.
Given that, a dean polled the sophomore class about their intended majors, then created this graph based on the data.
What is pie chart?A pie chart is a type of a chart that visually displays data in a circular graph. It is one of the most commonly used graphs to represent data using the attributes of circles, spheres, and angular data to represent real-world information.
From the given pie chart,
More students intend to majors in science
Less students intend to majors in Maths/CS
1/4 of students intend to major in other subjects.
Combining Science and Social Science represent half the intend majors. Therefore, option D is the correct answer.
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Which expression is equivalent to –4.5 – 6.2y?
Answer:
-6.2y-4.5
Step-by-step explanation:
Answer:
The correct answer is A
Step-by-step explanation:
(Full question above)
The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.
A.60
B.300
C.540
D.780
The volume of the solid is 540 mm
Step-by-step explanation:
The volume a rectangular prism is calculated as the product of its length, width and height.
Mathematically, V=l*w*h where l is length of the prism, w is width and h is the height
Given that the dimensions of the rectangular prism as;
Length=15 mm
Width= 6 mm
Height = 6 mm
V=15*6*6= 540 mm
If this is the best answer please mark brainilest. Have a great day, hope this helps!What is 0.2(5x – 0.3) – 0.5(–1.1x + 4.2) simplified? 0.2 [5x + (–0.3)] + (–0.5)(–1.1x + 4.2) x – 2.16
The required simplified expression for 0.2(5x – 0.3) – 0.5(–1.1x + 4.2) is 1.55x - 2.16.
What is simplification ?
Simplification means reducing the expression in a simpler form using various operations. It eliminates unnecessary diversiry and variety.
The given expression is
0.2(5x – 0.3) – 0.5(–1.1x + 4.2)
or, 0.2 [5x + (–0.3)] + (–0.5)(–1.1x + 4.2) x – 2.16
Now,Let us expand the bracket-
0.2*5x - 0.2*0.3 - 0.5(-1.1x) - 0.5*4.2
Further,
x - 0.06 + 0.55x - 2.1
therefore,
x + 0.55x - 0.06 - 2.1
⇒ 1.55x - 2.16
Hence,the required simplified expression for 0.2(5x – 0.3) – 0.5(–1.1x + 4.2) is 1.55x - 2.16.
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Answer:
1.55 is the answer on edge
A charitable organization packed 72 bags of rice, 48 blankets, and 24 cases of water equally in the boxes. Find the greatest possible number of boxes that the items can be packed into so that there are no leftovers.
Answer:
The greatest possible number of boxes that is needed to pack the items with no leftovers is 24.
Step-by-step explanation:
Given:
Number of rice bags = 72
Number of blankets =48
Number of water cases = 24
To Find :
The greatest possible number of boxes that the items can be packed into so that there are no leftover = ?
Solution:
we can find the greatest possible number of boxes that is required by finding the HCF(Highest common factor) of(24,48,72)
Finding the HCF (Highest common factor):
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
24 is the greatest common factor
Hence 24 will the number boxes required
A horse walks around a circular track while its trainer stands in the center. The trainer is 14 feet from the horse at all times. About how far had the horse traveled after walking around the track 5 times? Explain
The horse traveled 439.6 feet after walking around the track 5 times
Solution:
Given that, horse walks around a circular track while its trainer stands in the center
The trainer is 14 feet from the horse at all times
Therefore, radius of circular track = 14 feet
The circumference of circle is the distance traveled by horse for 1 lap
The circumference of circle is given as:
[tex]C = 2 \pi r[/tex]
Where, "r" is the radius and [tex]\pi[/tex] is a constant equal to 3.14
[tex]C = 2 \times 3.14 \times 14\\\\C = 87.92[/tex]
Thus the distance traveled by horse for one time in circular track is 87.92 feet
About how far had the horse traveled after walking around the track 5 times?
Multiply the circumference by 5
[tex]distance = 5 \times 87.92\\\\distance = 439.6[/tex]
Thus the horse traveled 439.6 feet after walking around the track 5 times
3. Kurt's car gets 23 miles to a gallon of gasoline. He filled up his car's gas tank with g gallons. Write an expression that shows how far Kurt can drive on a tank of gasoline.
The expression D=23g shows the distance that Kurt can drive on a tank of gasoline.
Step-by-step explanation:
Given,
Distance covered by Kurt's car = 23 miles per gallon of gasoline
Kurt fills up tank of his car with g gallons.
Number of gallons in car's tank = g gallons
Distance covered by g gallons = D = Distance covered by one gallon * Number of gallons
D = 23*g
D = 23g
The expression D=23g shows the distance that Kurt can drive on a tank of gasoline.
Keywords: distance, multiplication
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13x + 8 = 5x
Whats the answer ?
Answer:
Answer:Let's solve your equation step-by-step.
Step 1:
13x+8−5x=5x−5x
8x+8=0
Step 2: Subtract 8 from both sides.
8x+8−8=0−8
8x=−8
Step 3: Divide both sides by 8.
8x
8
=
−8
8
x=−1
Answer:
x=−1
Answer:
the solution of given problem is x= -1
Step-by-step explanation:
step:-1
given equation is 13 x+8=5 x
subtracting 5 x on both sides we get
[tex]13 x +8-5 x = 5 x -5 x[/tex]
simplify [tex]8x +8 =0[/tex]
subtracting 8 on both sides , we get solution is
[tex]8 x = -8[/tex]
[tex]x=-1[/tex]
МАЗА
$50 is invested biweekly in an
ordinary simple annuity, earning
3.5% interest per annum,
compounded biweekly. What will the
value of the annuity be in 10 years?
Answer:
The value of the annuity in 10 years will be US$ 15,552.90
Step-by-step explanation:
Let's use the ordinary simple annuity formula to calculate the value of the annuity in 10 years, this way:
FV = Future value of an annuity stream
PMT = Dollar amount of each annuity payment = US% 50
r = Interest rate = 3.5% compounded biweekly = 0.035/26
n = Number of periods in which payments will be made = 26 * 10 = 260
FV = PMT * [(1 + r)ⁿ − 1]/r
Now, replacing with the real values, we have:
FV = 50 * [(1 + 0.035/26)²⁶⁰ − 1]/(0.035/26)
FV = 50 * [(1.001346154)²⁶⁰ − 1]/0.001346154
FV = 50 * 0.41873217/0.001346154
FV = 50 * 311.058148
FV = 15,552.90
We only rounded the last product to the next cent, in all the other cases we used all the decimals for the calculations.
This problem gives you the chance to:
• work with graphs and equations of linear and non-linear functions
On the grid are eight points from two different functions.
• four points fit a linear function
the other four points fit a non-linear function.
For the linear function:
1. Write the coordinate pairs of its four points.
4,5
S3
2
3
4
5
6
7
8
Draw the line on the grid.
2. Write an equation for the function.
Show your work
Answer: try this hi i am in four
Lola has 62 stamps in her collection,
Anita has 15 stamps fewer than Lola.
How many stamps does Anita have?
Answer:
47 stamps
Step-by-step explanation:
You just have to subtract 15 from 62 so it looks like this: 62-15=47
What math property is this 19(24)=19(20)+19(4)
Answer:
Distributive Property
Step-by-step explanation:
19(24)=19(20)+19(4)
456 = 380 + 76
456 = 456
Hope this helps
-Amelia
SOLVE THE EQUATION
j-5=3.4
j=?
LOOKING FOR BRAINLIEST !!Ashton surveyed some of the employees at his company about their cell phone habits. From the data, he concluded that most employees at his company use cell phones primarily for business. For which sample could this generalization be valid?
A.
all managers in the company
B.
some managers and some sales executives selected at random
C.
every fifth employee on the employee list
D.
every other sales executive on the employee list
what is the answer for the question 20.x+90
Answer:
20.x + 90 = 110.x
reply fast pls I only have 20 min to answer pls help in 20 min ill give brainlyest to the first one to reply and get it correct
Answer:
see the explanation
The solution's table in the attached figure
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
Let
y ----> the price
x ----> the weight
Find the value of the proportionality constant for each ordered pair in each table
[tex]k=\frac{y}{x}[/tex]
If all the values of k are equal, then the table represents a proportional relationship between the variable x and the variable y
Table 1
For x=1.5 lb, y=$4.50 ----> [tex]k=\frac{4.5}{1.50}=3[/tex]
For x=2 lb, y=$9.00 ----> [tex]k=\frac{9.00}{2}=4.5[/tex]
The values of k are different
therefore
The table not represent a proportional relationship
Table 2
For x=10 g, y=$0.50 ----> [tex]k=\frac{0.50}{10}=0.05[/tex]
For x=15 g, y=$0.55 ----> [tex]k=\frac{0.55}{15}=0.04[/tex]
The values of k are different
therefore
The table not represent a proportional relationship
Table 3
For x=0.5 Kg, y=$0.75 ----> [tex]k=\frac{0.75}{0.5}=1.5[/tex]
For x=5 g, y=$7.50 ----> [tex]k=\frac{7.50}{5}=1.5[/tex]
The values of k are equal
therefore
The table represent a proportional relationship
Table 4
For x=1 oz, y=$2.00 ----> [tex]k=\frac{2}{1}=2[/tex]
For x=2 lb, y=$4.00
Convert lb to oz
Remember that
1 lb=16 oz
so
2 lb=2(16)=32 oz
For x=32 lb, y=$4.00 ----> [tex]k=\frac{4}{32}=0.125[/tex]
The values of k are different
therefore
The table not represent a proportional relationship
(-6x3-4x2-8)+(x3-x2-9x+4) add together and simply
Answer:
-5x³ -5x² -9x - 4
Step-by-step explanation:
(-6x³-4x²-8)+(x³-x²-9x+4)
Add the like terms.
-6x³ and x³ are like terms. -6x³ + x³ = -5x³
-4x² and -x² are like terms. -4x² - x² = -5x²
-8 and 4 are like terms. -8 + 4 = -4
-6x³-4x²-8 +x³-x²-9x+4 = -5x³ -5x² -9x - 4
List the next four multiples of the unit fraction 1/8
Answer:2/16 4/32 8/64 16/4,096
Step-by-step explanation:what you do is multiply 2and4
What is the equivalent expression to 3(x-5)
Answer: x = 5
Step-by-step explanation:
multiply the outside number to both numbers in parenthesis
3x-15 divide
find out how many time 3 goes into 15 and divide
three divided by fifteen equals five
Final answer:
The equivalent expression to 3(x-5) is 3x - 15, which is found by applying the distributive property of multiplication over subtraction.
Explanation:
The question asks for an expression equivalent to 3(x-5). To find an equivalent expression, we need to apply the distributive property of multiplication over subtraction. This means we will multiply the number 3 by each term inside the parentheses.
Here's the step-by-step process:
Multiply 3 by x to get 3x.
Multiply 3 by -5 to get -15.
Combine these two products to get the equivalent expression, which is 3x - 15.
Therefore, the equivalent expression to 3(x-5) is 3x - 15.
From a standard deck of 52 cards, what is the probability of picking a 6 at random from the deck?
A) 1/13
B) 1/26
C) 1/4
D) 1/52
Answer:
1/13
Step-by-step explanation:
since there are four 6 in a deck ( 1 for each suite )
probability of picking up a 6 is 4/52 = 1/13
A: 1/13
Divide 52 by 4 because there are 4 copies of each card in the deck (Not counting joker) You should get 13 and if you are drawing only ONE card, then you will have a 1/13 chance to draw a 6
a construction company is building a wall. the company can build 30 cm of the wall per minute. after 40 minutes 3/4 if the wall is completed. how many meters is the wall?
Answer:
This is a lengthy answer
Step-by-step explanation:
So contact me. Message me and I can explain to the fill extent
Final answer:
To find the total length of the wall, calculate the length built in 40 minutes (1200 cm) and divide by 3/4 to get the full length of 1600 cm, which is equivalent to 16 meters.
Explanation:
The question is asking us to determine the total length of the wall that a construction company is building, given that 3/4 of the wall is built in 40 minutes at a rate of 30 cm per minute. First, let's calculate the length of the wall built in 40 minutes:
Length built in 40 minutes = 40 minutes × 30 cm/minute = 1200 cmSince 1200 cm represents 3/4 of the wall, the full wall is:Full length = 1200 cm ÷ (3/4) = 1200 cm ÷ 0.75 = 1600 cmTo convert centimeters to meters: 1600 cm × (1 meter / 100 cm) = 16 metersThe total length of the wall is 16 meters.
M and N are independent events. P(M | N) = 0.71. Find P(M)
Since M and N are independent events, [tex]P(M)=P(M|N)=0.71[/tex]
Step-by-step explanation:
Two events A and B are said to be independent when the probability of A happening does not depend on whether B has happened or not.
In other word, this condition can be rewrite as follows:
[tex]P(A|B)=P(A)[/tex]
where
[tex]P(A|B)[/tex] is the probability of A happening given that B has happened
[tex]P(A)[/tex] is the probability of A happening
In this problem, we have:
- M and N are independent events: so M does not depend on whether N occurs or not
Therefore,
[tex]P(M)=P(M|N)[/tex]
- Also, we know that
[tex]P(M|N)=0.71[/tex]
Therefore, it follows that
[tex]P(M)=0.71[/tex]
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PLEASE HELP, WILL MARK BRAINLIEST
SELECT ALL THAT APPLY.
Which of the following could you use to solve this problem?
What is 25% of 37?
a. x/37 = 25/100
b. p = (0.25)37
c. 37/0.25 = w
d. 25/100 x 37
SELECT ALL THAT APPLY.
Answer:
A, B, D
Step-by-step explanation:
25% of 37
= 25/100 × 37
= 1/4 × 37
= 0.25 × 37
= 9.25
To find 25% of 37, you can use the equations: 'x/37 = 25/100', 'p = (0.25)37', and '25/100 x 37'. Option '37/0.25 = w' is not appropriate for finding 25% of 37.
Explanation:To find 25% of 37, you can use the following methods: a), b), and d).
These three options essentially represent how percentages can be calculated:
a) This represents 25% as a fraction (25/100) with 37 as the total (x/37). Solving for x gives you the answer. b) This signifies that 25% is converted to a decimal (0.25), and then multiplied by 37 to get the answer. d) It's similar to option a, but this time the fraction is multiplied by the total amount (25/100 * 37) directly making it a single step process.
Option c) is not suitable here because by dividing 37 by 0.25, you are finding out how many times 25% can fit into 37, not 25% of 37.
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Choose Yes or No to tell if the fraction
3
5
will make each equation true.
7
20
+
□
=
19
20
□
+
3
10
=
3
15
1
2
+
2
3
=
□
1
10
+
1
2
=
□
can someone please answer this for me thank you
The fraction 3/5 makes only the fourth equation true when added with the existing fractions. The first three equations do not yield true results when 3/5 is added.
Explanation:In Mathematics, when dealing with fractions, we need to maintain the rules of basic arithmetic, meaning that equal sums must be identical on both sides of the equation. Let's check each of these equations with the fraction 3/5:
Equation 1: 7/20 + 3/5 = 14/20 + 12/20 = 26/20 ≠ 19/20. So, the answer is 'No'.
Equation 2: 3/5 + 3/10 = 12/20 + 6/20 = 18/20 ≠ 3/15. So the answer is 'No'.
Equation 3: 1/2 + 2/3 ≠ 3/5. So the answer is 'No'.
Equation 4: 1/10 + 1/2 = 2/20 + 10/20 = 12/20 = 3/5. So the answer is 'Yes'.
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What is 2(5)+3(4)+5^2? (The ^ means the exponent)
GEOMETRY-20 POINTS-ANSWER ASAP
i have zero clue what im doing (obviously by the wrong answer) can anyone explain how to do this?? |
|
Answer:
tan(F) = z/(2y)
Step-by-step explanation:
Make use of the similarity relationship to find the side necessary to compute the tangent. Then make use of the tangent definition.*
__
The two triangles are given as being similar. That means corresponding sides have the same ratios:
EF/AC = ED/AB
ED = AB·(EF/AC) = 4z(x/(8x)) = (4/8)z = z/2
The mnemonic SOH CAH TOA reminds you that the tangent relationship is ...
Tan = Opposite/Adjacent
tan(F) = ED/DF = (z/2)/y
tan(F) = z/(2y)
_____
* Actually, you need to do this in reverse order: first you need to determine if you have all the necessary information to answer the question. You don't.
You need to know the length of side ED in terms of z. You notice that the corresponding side in similar triangle ABC has its length marked as a function of z, so all you need to find ED is the scale factor between the two triangles.
Since both hypotenuses are marked in terms of x, the scale factor is easily found.
The current ratio (assets/liabilities) of company X is 2.9. Given that the current assets are $377000, find the current liabilities:
Current liabilities = 130000
The board of directors determines that the current ratio must never be below 2.6. What is the maximum amount that the company can borrow?
Answer:
The maximum amount that the company X can borrow is $ 145,000
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Current ratio of assets/liabilities = 2.9
Current assets = $ 377,000
Current liabilities = Currents assets/Ratio = 377,000/2.9 = $ 130,000
2. The board of directors determines that the current ratio must never be below 2.6. What is the maximum amount that the company can borrow?
Desired ratio of assets/liabilities = 2.6
Current assets = $ 377,000
Desired liabilities = $ Current assets/Ratio = 377,000/2.6 = $ 145,000
The maximum amount that the company X can borrow is $ 145,000