The value of the expression 8² + 3 × 78² + 3 × 7 will be 18337.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The expression is given below.
⇒ 8² + 3 × 78² + 3 × 7
Simplify the expression, then we have
⇒ 8² + 3 × 78² + 3 × 7
⇒ 64 + 3 × 6084 + 21
⇒ 85 + 18252
⇒ 18337
The value of the expression 8² + 3 × 78² + 3 × 7 will be 18337.
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What quartic polynomial equation has roots 2-3 i, 8,2 ?
The Quatric polynomial is x⁴ + 11x³ + 20x² - 44x - 96
Given,
Zeros are: x = 2, x = -3, x = 8, and x = 2
That is: x + 2 = 0, x - 3 = 0, x + 8 = 0, and x + 2 = 0
So the factors are: (x + 2) (x - 3) (x + 8) (x + 2) = 0
Multiply two at a time:
(x + 2)(x - 3) = x² - x - 6
(x + 8)(x + 2) = x² + 10x + 16
Now multiply those polynomials together using distributive method:
x² (x² + 10x + 16) - x(x² + 10x + 16) - 6(x² + 10x + 16)
= x⁴ + 10x³ + 16x² + x³ + 10x² + 16x - 6x² - 60x - 96
= x⁴ + 11x³ + 20x² - 44x - 96
The Quatric polynomial is x⁴ + 11x³ + 20x² - 44x - 96
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Use the graph to answer the following question.
The figure shown was transformed from Quadrant II to Quadrant IV .
Which of the following BEST represents this transformation?
reflection over the x-axis followed by a dilation of scale factor 2
rotation 90° clockwise followed by a reflection over the y-axis
reflection over the y-axis followed by a translation down 6 units
reflection over the x-axis followed by a translation right 5 units
The transformation is rotation 90° clockwise followed by a reflection over the y-axis
How to use the graph to answer the question?The question is given as
Which of the following BEST represents this transformation?
From the question, we have the figure shown to be
A transformation of a figure from Quadrant II to Quadrant IV
From the figure, we can see that the shapes in both quadrants have the same dimensions
This means that the shapes are not dilated
However, the orientation of the figures are difference
Because of the positioning of the shapes, we can conclude that the transformaton is rotation 90° clockwise followed by a reflection over the y-axis
Hence, the transformation is rotation 90° clockwise followed by a reflection over the y-axis
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14. The nth term of a quadratic sequence is n²+ 3n-2
(a) Find the fourth term of this sequence.
Here are the first five terms of a different quadratic sequence.
1, 7, 17, 31, 49
(b) Find, in terms of n, an expression for the nth term of this sequence.
Step-by-step explanation:
14a)
the 4th term = 4² + 3×4 - 2 = 16 + 12 - 2 = 26
b)
1, 7, 17, 31, 49
s1 = 1
s2 = s1 + 6
s3 = s2 + 10
s4 = s3 + 14
s5 = s4 + 18
the added term d grows with every step by 4. starting with a constant "+ 2" on top of -1 to create s1.
d1 = 2
d2 = d1 + 4
d3 = d2 + 4
dn = dn-1 + 4 = d1 + 4(n-1)
s1 = -1 + d1
s2 = s1 + d2 = -1 + d1 + d1 + 4
s3 = s2 + d3 = -1 + d1 + d1 + 4 + d1 + 4 + 4
s4 = s3 + d4 = -1 + d1 + d1 + 4 + d1 + 4 + 4 + d1 + 4 + 4 + 4
sn = -1 + n×d1 + sum(4(n - 1)) = -1 + 2n + 4n(n - 1)/2 =
= -1 + 2n + 2n(n - 1) = -1 + 2n(1 + n - 1) = -1 + 2n² =
= 2n² - 1
solve: 1/2 x 3.4/4. Why is this your answer? How do you know this is correct?
Answer: 3.4/8 or 0.425
Step-by-step explanation:
Use this Rule: a/b * c/d = ac/bd
Simplify numerator (top): 1 * 3.4 = 3.4
Than Simplify denominator (bottom): 2 * 4 = 8
Finally: 3.4/8 or 0.425 (decimal)
This is my answer and I know this is correct because of using the Rule which demostrates that you should multiply top and bottom
what is the equation 2(h+3.5)=-11
Answer:
h = -9
Step-by-step explanation:
Open the parentheses:
2(h+3.5) = -11
2h+7 = -11
Subtract 7 both sides
2h = -11 - 7
2h = -18
h = -9
Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn using the Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning.
Given: If a quadrilateral has diagonals that bisect each other, then it is a parallelogram.
The diagonals of quadrilateral PQRS bisect each other
No valid conclusion drawn from the statements.
You can "detach" the hypothesis from the conclusion using the law of detachment. More specifically, if p and p -q are known to be true, we can infer that q is true. On the other hand, we can cram conditional statements together using the law of syllogism. When p-q and q-r are known to be true, they can be combined to form p-r. After all, it would be silly-gism to go through q when we can just go from p to r.
P = quadrilateral has diagonals
Q = quadrilateral diagonals bisect each other
R= the quadrilateral is a parallelogram
Statement P is true because all quadrilaterals have 2 diagonals that runs from one edge to another eg square, rectangle, parallelogram, kite etc
Statement Q is False because not all quadrilateral's diagonals bisect each other as in the case of trapezium, likewise quadrilateral whose diagonals bisects each other are not only parallelogram, kite, square and rectangle diagonals bisect each other.
Statement R is False because a quadrilateral whose diagonals bisect each other is not only parallelogram. Square, rectangle and Kite diagonals also bisect each other, and they are also parallelogram.
Therefore, no valid conclusion made from the statements because parallelogram is not the only quadrilateral whose diagonals bisect each other and not all quadrilateral's diagonals bisect each other.
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if a bag contains 10 red 6 yellow 24 blue and 8 white balloons what si the part to whole ratio of blue balloons to all baloons
Answer: Part to whole is 1:2
Using the graph below which of the following is a gas
A: NaCI
B: KCI
C: NaNO3
D: Ce2(SO4)3
Using the graph of solubility, D. Ce₂(SO₄)₃ is a gas
What is a gas?A gas is a state of matter with no fixed shape or volume.
What is solubility?Solubility of a substance is the amount of solute that can dissolve in unit volume of solvent at a given temperature.
Which of the following compounds is a gas?Note that the solubility of a substance depends on the temperature
For gases, the solubility decreses with incresing temperatureFor liquids, temperature has no effect on solubility and For solids, the solubility increases with temperature if the reaction is endothermixc and dedreases with temperature if the reaction is exothermic.From the graph above, we see that the compound with the least solubility is Ce₂(SO₄)₃. Since the solubility of gases derease with increasing temperature, thus Ce₂(SO₄)₃ is a gas
So, using the graph of solubility, D. Ce₂(SO₄)₃ is a gas
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find the circumference and the area of a circle with diameter 8 cm.
Answer:
Step-by-step explanation:
If the diameter is 8 cm, and the formula is A=pie*radius^2, the radius is 4.
The area would be 16*pie
The formula for finding the circumference 2*pie*radius, so the circumference is 8*pie.
6. application jeremy has a job at the movie theater.
his hourly wage is $7.38. suppose 15% of his income
is withheld for taxes and social security
a. what percent does jeremy get to keep?
b. what is his hourly take home wage?
a) Jeremy get to keep 85%
b) $6.273 is Jeremy's hourly take home wage.
Given,
Jeremy has a job at the movie theatre.
Hourly wage of Jeremy = $7.38
The % of income withheld for taxes and social security = 15%
7.38 × (15/100) = 1.107
That is, $1.107 from Jeremy's income is withheld for taxes and social security.
a) Percentage of income Jeremy get to keep:
= 100% - Withheld percentage
= 100 - 15
= 85
So, Jeremy gets 85% of his income to keep with him.
b) Jeremy's hourly take home wage:
Total income - Withheld amount
7.38 - 1.107 = 6.273
That is, Jeremy's hourly take home wage is $6.273.
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Use the proportion d / 180° = r radians/πradians . Find the equivalent degree measure or radian measure 415°
Answer:
the answer is the 235⁰ ok that
The postal service charges $2 to ship packages up to 5 ounces in weight, and $0.20 for each additional ounce up to 20 ounces. After that, they charge $0.15 for each additional ounce.
Using it's concept, the domain of the relation is given as follows:
x ≥ 0.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input of the function.The range of a function is the set that contains all the values of the output of the function.In a graph, the domain and the range are found as follows:
The domain is given by the values of x, present in the horizontal axis of the graph.The range is given by the values of y, present in the vertical axis of the graph.From the graph, we have that the weights of the packages assume all values to the right of 0, hence the domain of the relation is given as follows:
x ≥ 0.
What is the missing information?The relation is incomplete, and is given by the graph at the end of the answer.
The question asked is the domain of the relation.
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2. Denesha is thinking of a number that is divisible by both 9 and 7. What is the smallest number Denesha could be thinking of?
Answer:
63
Step-by-step explanation:
Numbers divisible by 9:
18, 27, 36, 45, 63, 72, 81, 90 and 99.
Numbers divisible by 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.
Least common multiple=63
What is the
equation of the line through (-2, 5) and (0, 3)?
Answer:
y=-x+3
Step-by-step explanation:
the gradient of the equation is -1
and the y intercept is 3
Cody decreased the speed of his car by 3.5 miles per second over the period of 60 seconds. find the average change in speed each second
The average change in speed each second is 0.0583 miles per squared second
How to find the average change in speed each second?The given parameters are:
Speed = 3.5 miles per second
Time = 60 seconds
The average change in speed each second is calculated as
Average change = Speed/Time
This gives
Average change = (3.5 miles per second)/60 seconds
Evaluate the quotient
Average change = 0.0583 miles per squared second
Hence, the average change in speed each second is 0.0583 miles per squared second
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Which point is located at (5,-2)?
-7-8-54
+
point A
point B
point C
point D
revious Activity
0₂
8
7654
4
3-
2-
4
7 7 3 7 8 9
-2-
Mark this and return
1234567 x
16
C
D
Save and Exit
Next
Submit
Based on the attached graph, the point that is located at (5,-2) is point F
How to determine which point is located at (5,-2)?The graph that completes the question is added as an attachment
The point located at (5,-2) implies that the coordinates of the point are
x-coordinate = 5
y-coordinate = -2
From the attached graph, we can see that the point F has the following properties
x-coordinate = 5
y-coordinate = -2
This means that the point F is located at (5,-2)
Hence, the point that is located at (5,-2) is point F
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simplify the following expression. 7^5/6 x 7^7/6
A. 1/14
B. 14
C. 1/49
D. 49
The simplified form of the given expression [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex] is option d 49.
Given,
The expression = [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex]
We can simplify this expression by using Laws of Indices;
The first rule: [tex]a^{n}[/tex] × [tex]a^{m}[/tex] = [tex]a^{m+n}[/tex]
The second rule: [tex](a^{n}) ^{m}[/tex] = [tex]a^{mn}[/tex]
The third rule: [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]
The fourth rule: [tex]a^{0}[/tex] = 1
The fifth rule: [tex]a^{-1}[/tex] = [tex]\frac{1}{a}[/tex] ; [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
The sixth rule: [tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex] ; [tex]a^{\frac{1}{m} }[/tex] = [tex]\sqrt[m]{a}[/tex] ; [tex]a^{\frac{n}{m} }[/tex] = [tex](a^{\frac{1}{m} } )^{n}[/tex] = [tex](\sqrt[m]{a} )^{n}[/tex]
Here we can use First, Second, Fifth and Sixth rule:
[tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex]
= [tex](7^{5} )^{\frac{1}{6} }[/tex] ×[tex](7^{7} )^{\frac{1}{6} }[/tex]
= [tex]16807^{\frac{1}{6} }[/tex] × [tex]823543^{\frac{1}{6} }[/tex]
= 5.061140185 × 9.68161288
= 49
That is, the simplified form of the expression [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex] is 49.
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34. Samir can rent a moving truck
from Company A for $135 plus
$0.50 per mile or from Company B
for $125 plus $0.70 per mile. Which
statement is true?
® Renting from Company A will
always be cheaper.
® Renting from Company B will
always be cheaper.
Renting from both companies
will cost the same if Samir drives
the truck 50 miles.
Renting from Company B will be
cheaper if Samir drives the truck
100 miles.
According to linear equation, Renting from Company A will always be cheaper. Thus option A is correct option.
According to the statement
We have to find that the correct statement.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
Samir can rent a moving truck from Company A for $135 plus $0.50 per mile or from Company B for $125 plus $0.70 per mile.
Then
The equation is given as,
y = mx + c
Where m is that the slope of the road and c is that the y-intercept of the line.
Let y be the whole amount and x be the amount of miles.
Samir can rent a moving truck from Company A for $135 plus $0.50 per mile. Then the equation are going to be
y = 0.5x + 135 ....1
Company B for $125 plus $0.70 per mile. then the equation are going to be
y = 0.7x + 125 ....2
For the identical rent, the amount of miles are going to be
0.7x + 125 = 0.5x + 135
0.2x = 100
x = 500 miles
Renting from Company A are going to be cheaper if Samir drives the truck 500 miles. Then the right option is A .
So, According to linear equation, Renting from Company A will always be cheaper. Thus option A is correct option.
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Evaluate the expression. 1 4 + 1 2 ÷ 2 3 ÷ 3 5 Write your answer as a fraction or as a whole or mixed number.
The solution of the expression 1/4 + 1/2 ÷ 2/3 ÷ 3/5 is 1 1/2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution of the expression?The expression is given as
1/4 + 1/2 ÷ 2/3 ÷ 3/5
Express the quotient as a product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 1/2 x 3/2 ÷ 3/5
Evaluate the product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 3/4 ÷ 3/5
Express the quotient as a product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 3/4 x 5/3
Evaluate the product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 5/4
Evaluate the sum
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 6/4
Simplify
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1 1/2
Hence, the solution of the expression 1/4 + 1/2 ÷ 2/3 ÷ 3/5 is 1 1/2
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2x - 6y = 6
6x- 4y = 2
Answer:
3/7y= -8/7
Step-by-step explanation:
reduce the greatest common factor on both sides of th equation
Is it possible for a number to be both a whole number and an integer why and why not
A number system is defined as the representation of numbers by using digits or other symbols. It is possible for a number to be both a whole number and an integer.
What is a Number system?A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner.
The given question is Is it possible for a number to be both a whole number and an integer why and why not.
The answer is yes because every whole number is an integer but not every integer to be a whole number.
For example 5 is both a whole number and integer but -5 is a integer but ot a whole number because in whole numbers we do not have negative numbers.
Therefore it is possible for a number to be both whole number and integer.
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A cube has a side length of 3x^6 units. a smaller cube has a side length of x^2. how many smaller cubes will fit in the larger cube
[tex]27x^{12}[/tex] smaller cubes will fit in the larger cube.
Given,
Side length of the smaller cube = [tex]x^{2}[/tex] units.
Side length of the larger cube = [tex]3x^{6}[/tex] units.
We have to find the number of smaller cubes that can be fitted in the larger cube.
Volume of cube is given by the formula,
Volume = (side)³
Volume of the larger cube = [tex](3x^{6} )^{3}[/tex] = [tex]27x^{18}[/tex]units³
Volume of the smaller cube = [tex](x^{2} )^{3}[/tex] = [tex]x^{6}[/tex] units³
Let the number of smaller cube that can be fitted in the larger cube = n
Volume of n cubes = [tex]nx^{6}[/tex] units³
If space inside the larger cube will be occupied by 'n' smaller cubes,
volume of n smaller cubes = Volume of a larger cube
[tex]nx^{6}[/tex] = [tex]27x^{18}[/tex]
n = [tex]27x^{12}[/tex]
Therefore, [tex]27x^{12}[/tex] smaller cubes can be fitted in the larger cube.
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Identify if slope is negative or positive (please)
The slopes are:
the top graphs, we have (from left to right): Negative, positive, positive, positive.Now the bottom ones: Negative, positive, negative, positive.How to identify if the slope is positive or negative?A general linear equation in the slope-intercept form is written as:
y = m*x + k
Where m is the slope and k is the y-intercept.
Particularly, if the slope is positive, we will see that the line goes upwards when read from left to right, while if it is negative, it goes downwards.
First the top graphs, we have (from left to right)
Negative, positive, positive, positive.
Now the bottom ones:
Negative, positive, negative, positive.
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can someone help me really quick
Answer:
2.5£ =25tacos
1£ =?
=1*25/2.5
=10 tacos:
Use synthetic division to determine whether each binomial is a factor of 3x³+10 x²-x-12 x+3.
If the liquid continues to cool at the same rate , what will the temperature be at 3pm pls i need this answer
The temperature of the liquid at 3PM will be -7.5 °C
The initial temperature of the liquid at 9 AM = 0°C
Given that the temperature changes by -5/4 °C each hour.
That is the rate of change of temperature = -5/4 °C
We have to find the temperature of the liquid at 3 PM.
Let x denote the number of hours.
Then the temperature after x hours, t = 0 + ( -5/4)x = -(5/4)x is the linear equation modelling this set up.
So from 9 AM to 3PM, the number of hours = 6 hours
Put x = 6 .
Then, t = (-5/4) x 6
= -7.5
Therefore, the temperature of the liquid at 3 PM = -7.5°C
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Select the expression that matches the scenario correctly. On January 1, the high temperature was 81 F in Kona, Hawaii the low temperature was -29 F in Barrow, Alaska. What was the difference between the two temperatures?
A. -29 + 81
B. |89 - 21|
C. |81 - (-29)|
D. 36 divided 6
Answer: |81 - (-29)|==> C
Step-by-step explanation:
h=high temperature
h=81
l=low temperature
l=-29
d=difference in high and low temperature
h-l=d
81-(-29)=d
81+29=d
d=110 ==> |81 - (-29)|=|81 +29|=|110|=110
|81 - (-29)|==> C
|81 -29|=|52|=52
-29 + 81=81-29=52
SOMEONE TELL ME IF IM CORRECT AND TELL ME HOW MUCH TO COLOR IN!!!!
Answer:
Seems correct. I would never use pen for a math assignment though ;-;
Here’s the answer sheet lol.
Step-by-step explanation:
Which number is closest to 161 ?
positive square roots
in decimal form
The number that is closest to the square root of 161 is 13.
How to calculate the square root?In mathematics, the square root is a factor that, when multiplied by itself, equals the original integer.
A number y such that y² = x, or a number y whose square is x, is referred to as the square root of a number x in mathematics. For instance, -4 and 4 are the square roots of 16.
It should be noted that the square root of 161 is 12.689. Therefore, the number that is closest to the square root of 161 is 13.
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Which number is closest to the square root of 161 ?
The methods used to analyze data produced by scientific studies are called:_____.
a. experiments.
b. correlations.
c. statistics.
d. replications.
The methods used to analyze data produced by scientific studies are called statistics. Option (c) is correct.
What are experiments and how do we analyze them using statistics?
Experiments are procedures or methods carried out under controlled conditions to discover a new fact or to test or establish a hypothesis that already exists.
From experiments we generate certain scientific data but to analyze data we need statistics.
Statistics is a process of collecting and analyzing and interpreting data.
Therefore the methods used to analyze data produced by scientific studies will be done by statistics.
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Answer:
Step-by-step explanation: Hello,
the answer