Step-by-step explanation:
[tex]4(12xy - 8x - 21xy ^{2} + 14xy + 15y - 10)[/tex]
[tex]4( - 21 {xy}^{2} + 26xy - 8x + 15y - 10)[/tex]
[tex] - 84 {xy}^{2} + 104xy - 32x + 60y - 40[/tex]
There are less than 30 students in Mr. Bartley’s math class. On a test, 1/3 of the class received a grade of B, 1/4 a C, 1/6 a D and 1/8 failed. How many more students received a B than received a grade of A?
6.25 more students received a B than that received a grade of A.
Total students = 30
No. of students received grade B = 1/3 of 30
= (1/3)*30
= 10
No. of students received grade C = 1/4 of 30
= (1/4)*30
= 7.5
No. of students received grade D = 1/6 of 30
= (1/6)*30
= 5
No. of students who failed = 1/8 of 30
= (1/8)*30
= 3.75
Total students with grade B,C,D or fail = 10 + 7.5 + 5 + 3.75
= 26.25
No. of students received grade A = 30 - 26.25
= 3.75
Difference between grade B and grade A = 10 - 3.75
= 6.25
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2/100 as a fraction a decimal or percent
Answer:
Step-by-step explanation:
Fraction=2/100
Decimal=0.02
Percent=2%
Answer: 0.02 as a decimal and 2%
Step-by-step explanation:
its correct!
nabil is saving 2.35 each day how much mony he will have by the second weekair
Answer:
2
Step-by-step explanation:
Equation in standard form using the given points
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
now, to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-6)}}} \implies \cfrac{-4}{-3 +6} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{4 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{4 }{ 3 }}(x-\stackrel{x_1}{(-6)}) \implies y -6 = - \cfrac{4 }{ 3 } ( x +6) \\\\\\ \stackrel{\textit{multiplying both sides by}\stackrel{LCD}{3}}{3(y-6)=3\left( - \cfrac{4 }{ 3 } ( x +6) \right)} \implies 3y-18=-4(x+6) \\\\\\ 3y-18=-4x-24\implies 3y=-4x-6\implies {\Large \begin{array}{llll} 4x+3y=-6 \end{array}}[/tex]
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
i) Angle 5 and 7 - Adjacent angles are supplementary
ii) Angle 3 and 5 - Same side interior angles are supplementary
iii) Angle 1 and 7 - Same side exterior angles are supplementary
Adjacent Supplementary Angles
If the total of two angles is 180 degrees, then those angles are said to be supplementary angles. Two additional angles are considered to be a linear pair if they are next to one another. Two neighboring additional angles added together equal 180.Same side interior angles are supplementary
According to the same-side interior angle theorem, the same-side interior angles that are created when two parallel lines are intersected by a transverse line are supplementary, or add up to 180 degrees.Same side exterior angles are supplementary
Same-side exterior angles are two external angles to the parallel lines that are on the same side of the transverse line. According to the theorem, same-side exterior angles are supplementary, which means they add up to 180 degrees.To know more about angles check the below link:
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Can somebody please solve this if you send picture please send good quality
Answer:
Step-by-step explanation:
Line p has an equation of y=5/3x-4 Line q includes the point
(-10,-3) and is perpendicular to line p. What is the equation of line q?
The equation of the line q that is perpendicular to line p is y = - 3 / 5 x - 9.
How to find equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, p has an equation of y = 5 / 3 x - 4 Line q includes the point (-10,-3) and is perpendicular to line p. The equation of line q can be found as follows:
The product of the slope of perpendicular lines is equals to negative one.
Therefore, let's find the slope of line q.
m₁m₂ = -1
5 / 3m₂ = - 1
m₂ = - 3 / 5
Hence, the equation of line q is y = - 3 / 5x + b.
Let's find the y-intercept using (-10, -3)
-3 = - 3 / 5(-10) + b
-3 = 6 + b
-3 - 6 = b
b = -9
Therefore, the equation of line q is y = - 3 / 5 x - 9
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19 In 2010, the population of Brazil was about 1.987 x 108 people. The population of Lithuania was about
3.555 x 106 people. What was the total population of Brazil and Lithuania? Write your answer in scientific
notation.
A.
C.
5.542 x 108 people
1.951 x 108 people
B. 2.02255 x 108 people
D.
5.542 x 1014 people
In the scientific notation, the total population of Brazil and Lithuania is 2.02255 x 10⁸
Scientific notation
A method of expressing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10 is known as Scientific notation.
Given,
In 2010, the population of Brazil was about 1.987 x 10⁸ people. The population of Lithuania was about 3.555 x 10⁶ people.
Here we need to find the total population of Brazil and Lithuania and expression the value in scientific terms.
Here we know that,
Population of Brazil = 1.987 x 10⁸
Population of Lithuania = 3.555 x 10⁶
In order to find the total population, first we have to make the exponent of the two value as equal,
For that we have to rewrite the population of Brazil as,
Population of Brazil = 198.7 x 10⁶
Now, we have to add the two population count in order to find the total population,
=> (198.7 x 10⁶) + (3.555 x 10⁶)
Take the exponent term as common,
=> (198.7 + 3.555) x 10⁶
=> 202.255 x 10⁶
Now, we have to move the two decimal point to simplify this one, then we get,
=> 2.02255 x 10⁸
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what's the answer?!!!
Answer:
6(y-2) would be 6y-12
Step-by-step explanation:
A formula 1 car travels at 50 m/s. What is this in km/h?
Answer:
50m/s = (50 ÷ 1000 × 60 × 60)km/h
= 180km/h
How many ounces of a 15% alcohol solution must be mixed with 16 ounces of a 20% alcohol solution to make a 17% alcohol solution?
24 ounces of a 15% alcohol solution must be mixed with 16 ounces of a 20% alcohol solution to make a 17% alcohol solution.
Let x ounces of 15% alcohol must be mixed with the 16 ounces of 20% alcohol.
The amount of alcohol in 16 ounces solution is = (20/100) * 16 ounces
= 3.2 ounces
The amount of alcohol in x ounces solution is = (15/100) * x
= 0.15x ounces
Total amount of alcohol is = (16 + x) ounces
According to the problem we get an equation,
(3.2 + 0.15x)/(16 + x) = 17/100
100(3.2 + 0.15x) = 17(16 + x)
320 + 15x = 272 + 17x
320 - 272 = 17x - 15x
48 = 2x
x = 48/2
x = 24
Therefore, 24 ounces of a 15% alcohol solution must be mixed with 16 ounces of a 20% alcohol solution to make a 17% alcohol solution.
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Find the range of values for which x^2-5x+6<0
Answer: 2 < x < 3
Step-by-step explanation:
Answer:
Step-by-step explanation:
the answer=x<6 and x>-11.
2.
3.
Two Truths & One Lie:
Which of the 3 statements below is a lie?
Explain how you made your decision.
x = 2
y = 3
Z=4
(m³)² = m7
(12)X = 126
(45)² = 420
LOL
00
2021
Answer:
1
Step-by-step explanation:
1) substitute z with 4 in the equation
(m^3)^4
2) multiply the index
m^3*4
=m^12
3) m^12≠ m^7
therefore, 1 is a lie
The statements above which is a lie is number 1
Statement 1 :
(m^3)^z = m^7
m^3z = m^7
3z = 7
z = 7/3 (False)
Statement 3 :
(4^5)^z = 4^20
4^5z = 4^20
5z = 20
z = 4 (True)
Statement 2 :
(12^3)^2 = 12^6
(12^y)^x = 12^6
12^6 = 12^6
(True)
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Suppose is Jeanine is building a tray for a floral table centerpiece in the shape of a pentagon.
The sum of interior angles of a tray that is of pentagon shape is 540°
Given,
There is a tray which is of pentagon shape.
We have to find the sum of interior angles of the tray.
We have to find the sum of interior angles of pentagon.
That is,
Sum of interior angle of polygon formula = (n - 2) × 180°
Where, n is the number of sides in a polygon.
Here,
Pentagon has 5 sides.
Then,
Sum of interior angles = (5 - 2) × 180° = 3 × 180° = 540°
That is,
The sum of interior angles of a tray that is of pentagon shape is 540°
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The question is incomplete. Completed question is given below;
Suppose is Jeanine is building a tray for a floral table centerpiece in the shape of a pentagon. The sum of the interior angles of the tray will be
The royal fruit company produces two types of fruit drinks. the first type is 30% pure fruit juice, and the second type is 80% pure fruit juice. the company is attempting to produce a fruit drink that contains 75% pure fruit juice. how many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 75% pure fruit juice?
5 and 45 pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 75% pure fruit juice.
Let x be the number of pints of the first fruit juice (i.e., 30%) and y be the number of pints of the second fruit juice (i.e., 80%).
Since the total number of pints to make the 75% pure fruit juice is 50, it can be represented using the equation:
x + y = 50 -----(1)
Also, x pints of the first juice = 0.30x, y pints of the second juice = 0.80y and 50 pints of the mixture to be produced = 50(0.75)= 37.5. Therefore:
This is represented as ;
30% × x + 80% × y = 50 of 75%
Make x in the subject x + y = 50
Substitute:
x = 50 - y in 30% × x + 80% × y = 50 of 75%
0.30 (50 - y) + 0.8 × y = 50 of 0.75
15 - 0.3y + 0.8y = 37.5
Collect like terms :
-0.3y + 0.8y = 37.5 - 15
0.5y = 22.5
y = 45
Recall that :
x = 50 - y
x = 50 - 45
x = 5
Hence, 5 and 45 pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 75% pure fruit juice.
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If two lines are exactly the same, then the system has infinite solutions.
False
True
Answer: true
Step-by-step explanation:
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of 6724 with a mean life of 645 minutes.
If the claim is true, in a sample of 152 batteries, what is the probability that the mean battery life would be greater than 636.4 minutes? Round your answer to four decimal places.
The probability that the mean battery life would be greater than 636.4 minutes if in a sample of 152 batteries having a variance of, 6724 and a mean life of 645 minutes is 0.0968.
What is probability?The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.
Given:
The variance = 6724,
The mean life of a battery, m = 645,
The total number of samples, n = 152
Calculate the probability of a mean battery life of lower than 636.4 minutes by the following formula,
z = m - x / (σ / √ n)
Here, x is the expected value, σ is the deviation, and z is the probability.
Substitute the values,
z = 645 - 636.4 / (82 / √ 152) [σ = √ variance = √6724 = 82]
z = 1.29
Consult the cumulative standard normal table
P (z < 636.4) = 0.9032,
But we know that
P (z > 636.4) = 1 - P (z < 636.4)
P (z > 636.4) = 1 - 0.9032 = 0.0968
Therefore, the probability that the mean battery life would be greater than 636.4 minutes if in a sample of 152 batteries having a variance of, 6724 and a mean life of 645 minutes is 0.0968.
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Grandma has 3 1 /4 pounds of flour. She uses 1 2 /3 pounds of flour to make rolls for Thanksgiving dinner. How much flour does Grandma have left over?
Step-by-step explanation:
[tex]1 - (\frac{1}{4} + \frac{2}{3}) \\ = 1 - ( \frac{3 + 8}{12}) \\ = 1 - ( \frac{11}{12} ) \\ = \frac{1}{12} [/tex]
Answer:
[tex]1 \frac{7}{12}\; \sf pounds[/tex]
Step-by-step explanation:
To find the amount of flour Grandma has left over, subtract the amount she used to make rolls from the original amount.
Given calculation:
[tex]3 \frac{1}{4}-1 \frac{2}{3}[/tex]
Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:
[tex]\implies \dfrac{3 \times 4+1}{4}-\dfrac{1 \times 3+2}{3}[/tex]
[tex]\implies \dfrac{13}{4}-\dfrac{5}{3}[/tex]
Change both fractions into equivalent fractions so both fractions have the same denominator:
[tex]\implies \dfrac{13 \times 3}{4\times 3}-\dfrac{5 \times 4}{3 \times 4}[/tex]
[tex]\implies \dfrac{39}{12}-\dfrac{20}{12}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]
[tex]\implies \dfrac{39}{12}-\dfrac{20}{12}=\dfrac{39-20}{12}=\dfrac{19}{12}[/tex]
Divide the numerator by the denominator:
[tex]\implies 19 \div 12 = 1 \; \sf remainder \; 7[/tex]
The solution as a mixed number is the whole number and the remainder divided by the denominator:
[tex]\implies 1 \frac{7}{12}[/tex]
Please help me answer this question
Step-by-step explanation:
We know rhat
[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{1 - \cos(x) }{2} } [/tex]
whenever x lies from 90 to 180.
If
[tex] \csc(x) = 9[/tex]
Using Reciprocal Identities
[tex] \sin(x) = \frac{1}{9} [/tex]
Using Pythagorean Identity,
[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]
[tex]( \frac{1}{9} ) {}^{2} + \cos {}^{2} (x) = 1[/tex]
[tex] \cos {}^{2} (x) = \frac{80}{81} [/tex]
[tex] \cos(x) = \frac{4 \sqrt{5} }{9} [/tex]
Cosine is negative in when x lies between 90 and 180 so
[tex] \cos(x) = - \frac{4 \sqrt{5} }{9} [/tex]
So
[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{1 + \frac{4 \sqrt{5} }{9} }{2} } [/tex]
[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{9 + 4 \sqrt{5} }{18} } [/tex]
For cosine remember
[tex] \cos( \frac{x}{2} ) = \sqrt{ \frac{1 + \cos(x) }{2} } [/tex]
Cosine is negative in second quadrant so
[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{1 + \cos(x) }{2} } [/tex]
[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{1 - \frac{4 \sqrt{5} }{9} }{2} } [/tex]
[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{9 - 4 \sqrt{5} }{18} } [/tex]
For tangent,
[tex] \tan( \frac{x}{2} ) = \frac{ \sin( \frac{x}{2} ) }{ \cos( \frac{x}{2} ) } [/tex]
[tex] \frac{ \sqrt{ \frac{1 - \cos(x) }{2} } }{ \sqrt{ \frac{1 + \cos(x) }{2} } } [/tex]
[tex] = \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } [/tex]
Tangent is negative over 90<x<180 so
[tex] - \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } [/tex]
[tex] - \sqrt{ \frac{1 + \frac{4 \sqrt{5} }{9} }{1 - \frac{4 \sqrt{5} }{9} } } [/tex]
[tex] - \sqrt{ \frac{ \frac{9 + 4 \sqrt{5} }{9} }{ \frac{9 - 4 \sqrt{5} }{9} } } [/tex]
[tex] - \sqrt{ \frac{9 + 4 \sqrt{5} }{9 - 4 \sqrt{5} } } [/tex]
[tex] - \sqrt{ \frac{1}{(9 - 4 \sqrt{5) {}^{2} } } } [/tex]
[tex] - \frac{1}{9 - 4 \sqrt{5} } [/tex]
so
[tex] \tan( \frac{x}{2} ) = - \frac{1}{ 9 + 4 \sqrt{5} } [/tex]
or
[tex] \tan( \frac{x}{2} ) = - 9 + 4 \sqrt{5} [/tex]
Janelle traveled 9.6 miles o her delivery route in 1.7 hours at the same rate what would be closest time it will take for janelle to travel 20 miles
If you invest $10,000 today at 10% interest how much will you have in 10 years
Answer:
$25940
Step-by-step explanation:
Future value of an Investment at r% for n years is given by:
Future Value = Initial Investment (1 + r/100)n
If r = 10% and n = 10 years
Future Value = 10000(1 + 10/100)10
= 10000(1.1)10
= 10000(2.594)
= $ 25940
Hence the required value is $ 25940.
[tex]\frac{2}{3} + \frac{4}{6}[/tex]
Answer:
[tex]\huge\boxed{\sf 1 \frac{1}{3}}[/tex]
Step-by-step explanation:
Given expression:[tex]\displaystyle =\frac{2}{3} + \frac{4}{6} \\\\Equalize \ the \ denominator \\\\= \frac{2 \times 2}{3 \times 2} + \frac{4}{6} \\\\= \frac{4}{6} + \frac{4}{6} \\\\Add \\\\=\frac{4+4}{6} \\\\= \frac{8}{6} \\\\Simplify\\\\= \frac{4}{3} \\\\Convert \ into \ mixed \ fraction\\\\= 1 \frac{1}{3} \\\\\rule[225]{225}{2}[/tex]
a seceret agent sent a messinger to deliver a package to a certain location. The messanger posed as a regular person out for a walk with a secret pacage tucked securely in a hidden pocket
Answer:
Don't be a secret agent. You never know what's going to happen.
Step-by-step explanation:
Until he slipped on a puddle of goose poop. His hat flew off, revealing a shiny, bald head, which he immediately grabbed his scarf to cover. In his rush, he failed to notice a goose prodding at the secret package in his pocket. With a flurry of wingbeats, the goose flew off with the secret package in its beak. The secret agent suddenly realized that the goose was a spy in disguise from a rival organization.
The functions f and g are shown below.
50 POINTS TO HELP ME!!
Which of the following statements is true?
A.
Over the interval [0, 2], the average rate of change of f is the same as that of g. The y-intercept of f is greater than the y-intercept of g.
B.
Over the interval [0, 2], the average rate of change of f is greater than that of g. The y-intercept of f is the same as the y-intercept of g.
C.
Over the interval [0, 2], the average rate of change of f is the same as that of g. The y-intercept of f is less than the y-intercept of g.
D.
Over the interval [0, 2], the average rate of change of f is less than that of g. The y-intercept of f is the same as the y-intercept of g.
Answer:
A ................................
A surveyor has taken measurements, a ft, b ft, and the angle y in degrees, as seen in the figure below.
If a = 217 ft, b = 347 ft, and y = 53°, find the distance across the lake.
a ft
Yo
The distance across the lake is how many ft?
The distance across the lake is 552.98 ft
Define Cosine Rule.
According to the Cosine Rule, the square of any side of a given triangle is equal to the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of the angle that separates them. Law of cosines and Cosine Formula are other names for the cosine rule.
a² = b² + c² – 2bc cos ∠x b² = a² + c² – 2ac cos ∠y c² = a² + b² – 2ab cos ∠zWe have,
a = 217 ft
b = 347 ft
y = 53°
We have cosine formula,
c² = a² + b² – 2ab cos ∠z
Here, ∠z = 53°
let, c = distance across the lake
Now, plug in the values like that
c² = (217)² + (347)² - 2 * 217 * 347 cos 53
= (217)² + (347)² - 2 * 217 * 347 * (-0.91828278621)
= (217)² + (347)² - (-138291.551037654)
= 47,089 + 120409 + 138291.551037654
= 167498 + 138291.551037654
c² = 305789.551037654
c = 552.982414763 or 552.98 ft
Therefore, the distance across the lake is 552.98 ft
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Can you please help me with this assignment
The longer diagonal is 4 more than the shorter diagonal of a kite.tje area is 5times the shorter diagonal.if the shorter side is 6cm find the longer diagonal and the area
Since the area of this kite is 5 times the shorter diagonal, the length of the longer diagonal is 10 cm and the area is equal to 30 cm².
How to calculate the area of a kite?In Mathematics, the area of a kite is equal to one-half the product of the length of its diagonals. Mathematically, the area of a kite can be calculated by using this formula:
A = ½ × d₁ × d₂
Where:
A is the area of a kite.d₁ and d₂ are the length of the diagonals of a kite.For the longer diagonal, we have:
d₁ = d₂ + 4
For the area of kite, we have:
Area = 5d₂ = 5(6) = 30 cm²
Substituting the given parameters into the formula, we have;
30 = ½ × d₁ × 6
60 = 6d₁
d₁ = 60/6
d₁ = 10 cm.
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Calculator What is the approximate volume of the sphere? Use 3.14 to approximate pi and round to the nearest hundredth if necessary. 36 in³ 84.78 in³ O 113.04 in³ O339.12 in 3 in
The volume of the sphere can be calculated using the formula V = 4/3πr³
What is a sphere?A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. It is a perfectly-round 3D shape with one continuous curved surface
We have a sphere.
Since the dimensions of a sphere are not given, we will assume it. Assume the radius of sphere be [r]. Then the approximate value of the volume of the sphere can be calculated using the formula -
V = 4/3πr³
Where -
[r] is the radius of sphere
Therefore, the volume of the sphere can be calculated using the formula V = 4/3πr³
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What is the nth term rule of the linear sequence below?
-5, -2, 1, 4, 7, ...
Tn
-
The nth term rule of linear sequence is aₙ = aₙ₋₁ + 3
Linear sequence is a sequence of number in order with same difference .or same ratio.
when fixed number is added to any term of a sequence to get next term . That Fixed number is known as common difference.
The sequence in the given question
-5 , -2 , 1 , 4 , 7, . . . .
The first term of sequence : a₁ = -5
The second term : a₂ = -2
Common difference : d = a₂ - a₁
=> d = -2 - (-5)
=> d = -2 + 5
=> d = 3
The nth rule of linear sequence is aₙ = aₙ₋₁ + d
replacing the value of d
aₙ = aₙ₋₁ + 3 is nth rule of the linear sequence.
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Find the surface area of a right square pyramid if the area of the base
is 16 cm² and the height of the pyramid is 8 cm.
The surface area of a square pyramid is 192 cm²
What is the surface area of a square pyramid?
The term "surface" refers to the "outer or exterior part of an object or body." As a result, the total surface area of a square pyramid is the sum of its lateral face and base areas.
To find the surface area of the square pyramid, we'll use the mathematical formula.
Mathematically, the formula for calculating the surface area A of a square pyramid is :
S.A. = s² + sl
where,
s is the pyramid height,
l is the base length.
S.A. = (8)² + 8 * 16
S.A. = 64 + 128
S.A. = 192 cm²
Hence, the surface area of a square pyramid is 192 cm².
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