Answer: a₁=31 a₁₁=-9
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{a_4=19} \atop {a_7=7}} \right. \\\\a_n=a_1+(n-1)d\\\\\left \{ {{a_1+(4-1)d=19} \atop {a_1+(7-1)d=7}} \right. \\\\\left \{ {{a_1+3d=19\ \ \ \ (1)} \atop {a_1+6d=7\ \ \ \ \ (2)}} \right.[/tex]
Subtract equation (2) from equation (1):
[tex]3d=-12[/tex]
Divide both parts of the equation by 3:
[tex]d=-4[/tex]
Thus,
[tex]a_1+(3)(-4)=19\\a_1-12=19\\a_1-12+12=19+12\\a_1=31\\a_{11}=a_1+(11-1)d\\a_{11}=31+(10)(-4)\\a_{11}=31-40\\a_{11}=-9[/tex]
Answer:
a = 43
d = -6
[tex]\sf a_{11} = -17[/tex]
Step-by-step explanation:
Arithmetic sequence:
Use the formula to find the nth term:
[tex]\sf \boxed{\bf a_n= a+(n-1)d}[/tex]
Here, a is the first term, n is the number of terms and d is the common difference.
[tex]\sf a_4 = 19\\\\a+(4-1)*d = 19\\\\a + 3d = 19 -------------------(i)[/tex]
[tex]\sf a_7 = 7\\\\a + 6d = 7 ------------------(ii)\\[/tex]
Subtract equation (i) from (ii) and thus 'a' will be eliminated and we can find the value of 'd'.
(ii) a + 6d = 7
(i) a + 4d = 19
- - = -
2d = -12
d = -12/2
[tex]\sf \boxed{\bf d = -6}[/tex]
Now, plugin d = -6 in any of the two equations. We are substituting the 'd' value in equation (i)
a + 4*(-6) = 19
a - 24 = 19
a = 19 + 24
[tex]\sf \boxed{\bf a = 43}[/tex]
[tex]\sf a_{11} = a + 10d[/tex]
= 43 + 10*(-6)
= 43 - 60
[tex]\sf \boxed{\bf a_{11} = -17 }[/tex]
Solve each absolute value equation.
(1/3)|5x-3|=6
1/3|5x-3|=6
Absolute value equality entered
(1/3) |5x-3| = 6
Clear the absolute-value bars by splitting the equation into two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is (1/3) |5x-3|
For the Negative case, we'll use -(1/3) (5x-3)
For the Positive case, we'll use (1/3) (5x-3)
-(1/3) (5x-3) = 6
Multiply
-5x/3+1 = 6
Rearrange and add up
-5x/3 = 5
Multiply both sides by 3
-5x = 15
Divide both sides by 5
-x = 3
Multiply both sides by (-1)
x = -3
Which is the solution for the Negative Case
(1/3)(5x-3) = 6
Multiply
5x/3-1 = 6
Rearrange and add up
5x/3 = 7
Multiply both sides by 3
5x = 21
Divide both sides by 5
x = (21/5)
Which is the solution for the Positive Case
x=-3
x=21/5
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is -2/3 a natural number
Answer:
no it is not because natural numbers are whole numbers :)
hope this was helpful!
Kahoe says he is thinking of a four-digit number in which all digits are the same. The value of the digit in the hundreds place is 600. what is the numnber?
Answer:
6,666
Step-by-step explanation:
A four-digit number: 1,234
All digits are the same: 1111, 2222, 3333...
Value in the hundreds place: 0,600
Answer: 6,666
Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of a pendulum has a length of 100 cm and the return swing is 99 cm .
b. What is the total distance traveled by the pendulum when it comes to rest?
The total distance traveled by the pendulum when it comes to rest is 10,000 cm.
Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of a pendulum has a length of 100 cm and the return swing is 99 cm .
Now,
Given,
On the first swing, the distance traveled is 100, and on the second swing, the distance is 99.
The first term of the geometric sequence is, a1 = 100
The second term of the sequence is, a2 = 99
The common ratio r = 99/100
Therefore, the expression for the n-t h term of the sequence is:
a_n = 100*(99/100)^(n-1)
Theoretically, using this formula, it would take an infinite number of trips to come to rest.
Hence we need to find the sum of the series a_n = 100*(99/100)^(n-1) from n=1 to n=infinity.
The sum of an infinite series is given by S = a/(1-r) where a=the first term and r=the common ratio.
Therefore,
the total distance traveled is S = 100/(1-(99/100) = 100/0.01 = 10,000 cm
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Explain why classifying an equiangular triangle as an acute equiangular triangle is unnecessary.
Classifying an equiangular triangle as an acute equiangular triangle is unnecessary because by definition, all angles are 60°
What is an equiangular triangle?An equiangular triangle is one with three equal sides and three equal angles, all of which are measured at 60 degrees. Given that the characteristics of both triangles are the same, an equiangular triangle can also be referred to as an equilateral triangle.
This triangle is regarded as a regular polygon because its sides and angles are both equal. Equiangular refers to angles that are all equal.
All triangles have 3 angles that together total 180 degrees. Because an equilateral triangle has equal sides, its angles can only be 60 degrees. This entails that all angles must be acute. It is not required to write that it is intense because of this.
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serve this for me
[tex]x + 3 > 19 = 3x[/tex]
For the given set of inequality, the value of x is 8.
What is an inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Given, the equation is -
x+ 3 > 19 = 3x
⇒ x + 3 > 19 - 3x
Subtracting 3 from bot sides
⇒ x > 16 - 3x
subtracting x from both sides
⇒ 16 - 2x > 0
⇒ x = 8
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whats the slope for (29, 11) and (-3, -7)
The slope of the given points are (29, 11) and (-3, -7):
= 0.5625.
What is slope?A line's slope indicates whether sharp it is.. The slope is defined mathematically as "climb overrun" (change in y divided by change in x).
What is the definition of slope in a straight line?In general, a line's slope indicates its steepness as well as direction. The slope of a straight line connecting two points (x1,y1) and (x2,y2) can be simply calculated by subtracting the coordinates of both the points. The slope is commonly denoted by the letter'm.'
According to the given data:X₁ = 29
Y₁ = 11
X₂ = -3
Y₂ = -7
The slope is the degree of tilt a line has and it may be positive, negative, zero, or undefined.
slope = (y₂ - y₁) / (x₂ - x₁)
Substituting the value in the given formula:
slope = [tex]\frac{(-7 - 11)}{(-3 - 29)}[/tex]
= -18 / -32
= -9 / -16
= 0.5625
The slope of the given points are (29, 11) and (-3, -7) = 0.5625.
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The formula I = √W/R gives the electric current I in amperes that flows through an appliance, where W is the power in watts and R is the resistance in ohms. Which set of numbers best describes the value of I for the given values of W and R ? W=500, R=100
For I = [tex]\sqrt{W/R}[/tex] gives electric current I , when W=500 , R=100 implies I = [tex]\sqrt{5}[/tex] , the set of numbers best describes the value of I are irrational numbers.
As given in the question,
Formula I = [tex]\sqrt{W/R}[/tex]
I = electric current in amperes
W = power in watts
R = Resistance in ohms
When W = 500 , R = 100
I = [tex]\sqrt{500/100}[/tex]
⇒ I = [tex]\sqrt{5}[/tex] amperes
Therefore, for I = [tex]\sqrt{W/R}[/tex] gives electric current I , when W=500 , R=100 implies I = [tex]\sqrt{5}[/tex] , the set of numbers best describes the value of I are irrational numbers.
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How are line symmetry and rotational symmetry related?
A symmetrical figure is one that is identical on both sides of a line. Rotational symmetry occurs when an object is rotated and retains the same appearance as the original figure.
Symmetry:
In common parlance, symmetry refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term "symmetry" has a more precise definition and is typically used to refer to an object that is invariant under certain transformations such as translation, reflection, rotation, or scaling.Rotational symmetry:
In geometry, rotational symmetry, also recognized as radial symmetry, is the property that a shape has when it looks the same after a partial turn rotation. The degree of rotational symmetry of an object is the number of distinct orientations in which it appears exactly the same for each rotation.Relation:
The relation between line symmetry and rotational symmetry is that s symmetrical figure is one that has the same appearance on both sides of a line. Rotational symmetry occurs when an object is rotated and retains its original appearance.Therefore, a symmetrical figure is one that is identical on both sides of a line. Rotational symmetry occurs when an object is rotated and retains the same appearance as the original figure.
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Use the graph shown to complete the following sentence.
If (4, y ) is an ordered pair of the function, then y =
.
Answer: If (4, y ) is an ordered pair of the function, then y = 1
Step-by-step explanation:
The known x coordinate for the position (4,y) is 4.
We'll just refer to it as y since we don't know the y coordinate just yet.
On the x axis, trace a vertical line through 4 (see related remark below).
Thus in red (see attached image).
The red line crosses the graph at the point (4,1)
so this tells us that,
y = 1
Although it's helpful to see how it turns out, you are not need to draw a vertical red line.
You will be able to visually perceive the solution without these extra lines after you become accustomed to these kinds of situations.
Therefore,
If (4, y ) is an ordered pair of the function, then y = 1
y = 1
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Figure DEF is an isosceles triangle. The measure of D is 55°. Select all the possible measures of
A. 55°
B. 60°
C. 70°
D. 110°
E. 125°
The correct answer is option (a) 70° is the possible measures of A.
Given that, the isoceles triangle's base angles are equal
let angle D be its vertical angle.
With angle E equal to angle F
angle D+ angle E+ angle F=180'
angle D+ 55'+55'=180',
angle D+ 110'=180'
angle D=180'-110'
angle D=70'.
Figure DEF is an isosceles triangle. The measure of A is 55°, while the measure of B is 70°. As there are two possible measures of D, it can be calculated that the base area equal to 426 square units and the height equals 232 square units.
Hence, 70° is the possible measures of A.
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This is my homework and i need help asap
Using the segment addition postulate, it is found that:
1. Point B is between the other two.
2. The measures are: RS = 5, RT = 10, PR = 10, PQ = 6.
3. The value of x is of x = 9.5.
4. The value of y is of y = ± 5.
What is the segment addition postulate?The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.
In item 1, we have that the largest segment is of AC, hence it represents the line, while point B splits the segment into two parts, that is, point B is between the other two.
In item 2, we have that:
S is the midpoint of RT, hence RS = ST = 5.For the same reason above, RT = RS + ST = 10.PR is congruent to RT, hence PR = 10.PR = PQ + QR -> PQ = PR - QR = 10 - 4 = 6.For item 3, applying the Postulate, we have that:
AB + BC + CD = AD
4 + 4 + 2x - 6 = 21
2x = 19
x = 9.5.
For item 4, due to the midpoint, we have that:
LM = MN
Hence:
y² + 4 = 29
y² = 25
y = ± sqrt(25)
y = ± 5.
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Evaluate each algebraic expression for x=3 and (y=-2).
5x+y
The result of the algebraic expression 5x+y for x=3 and y=-2 is 13
Given,
The algebraic expression =5x+y
x= 3
y= -2
Substitute the values in the expression
5x+y =5(3)+(-2)
=15-2
=13
Hence, the result of the algebraic expression 5x+y for x=3 and y=-2 is 13
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Given p(x)=−3(x−4)2+14, what is the value of p(2)?
PS you cant leave out exponents when typing questions without the attached photo. multiplying by 2 is not the dame as a exponent of 2. Use ^2 to show that a number is to the power of 2.
the value of p(2) in this equation is 2.
Answer:
p(2) = 2
Step-by-step explanation:
substitute x = 2 into p(x)
p(2) = - 3(2 - 4)² + 14
= - 3(- 2)² + 14
= - 3(4) + 14
= - 12 + 14
= 2
Angle A and B are supplementary. If m (is less than sign) A = 3y + 12 and m (is less than sign) B = 2y +48, find the value of y.
Answer: y=24
Step-by-step explanation:
Supplementary angles add up to 180 degrees.
A+B=180
3y + 12 + 2y +48=180
3y+2y+12+48=180
5y+60=180
5y=120
y=24
What is the value of the expression?
Answer:
13/6
Step-by-step explanation:
1 Simplify \sqrt{8}
8
to 2\sqrt{2}2
2
.
\frac{2}{6\times 2\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})
6×2
2
2
2
−(−
81
18
)
2 Simplify 6\times 2\sqrt{2}6×2
2
to 12\sqrt{2}12
2
.
\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})
12
2
2
2
−(−
81
18
)
3 Since 9\times 9=819×9=81, the square root of 8181 is 99.
\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{9})
12
2
2
2
−(−
9
18
)
4 Simplify \frac{18}{9}
9
18
to 22.
\frac{2}{12\sqrt{2}}\sqrt{2}-(-2)
12
2
2
2
−(−2)
5 Rationalize the denominator: \frac{2}{12\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{2\sqrt{2}}{12\times 2}
12
2
2
⋅
2
2
=
12×2
2
2
.
\frac{2\sqrt{2}}{12\times 2}\sqrt{2}-(-2)
12×2
2
2
2
−(−2)
6 Simplify 12\times 212×2 to 2424.
\frac{2\sqrt{2}}{24}\sqrt{2}-(-2)
24
2
2
2
−(−2)
7 Simplify \frac{2\sqrt{2}}{24}
24
2
2
to \frac{\sqrt{2}}{12}
12
2
.
\frac{\sqrt{2}}{12}\sqrt{2}-(-2)
12
2
2
−(−2)
8 Use this rule: \frac{a}{b} \times c=\frac{ac}{b}
b
a
×c=
b
ac
.
\frac{\sqrt{2}\sqrt{2}}{12}-(-2)
12
2
2
−(−2)
9 Simplify \sqrt{2}\sqrt{2}
2
2
to \sqrt{4}
4
.
\frac{\sqrt{4}}{12}-(-2)
12
4
−(−2)
10 Since 2\times 2=42×2=4, the square root of 44 is 22.
\frac{2}{12}-(-2)
12
2
−(−2)
11 Simplify \frac{2}{12}
12
2
to \frac{1}{6}
6
1
.
\frac{1}{6}-(-2)
6
1
−(−2)
12 Remove parentheses.
\frac{1}{6}+2
6
1
+2
13 Simplify.
\frac{13}{6}
6
13
Done
How many different signals can be made with 5 flags from 8 flags of different colors?
The total number of signals that can be made using 5 flags from 8 flags of different colors is 6720.
Permutations:
A permutation is an act of arranging the objects or numbers in order.
The formula for permutations is:
nPr = n!/(n-r)!
where
nPr = permutation
n = total number of objects
r = number of objects selected
Combinations:
Combinations are the way of selecting the objects or numbers from a group of objects or collection, and the order of the objects does not matter.
The formula for combinations is:
nCr = n!/[r! (n-r)!]
Where,
nCr = number of combinations
n = total number of objects in the set
r = number of choosing objects from the set
Given,
Here we need to find how many different signals can be made with 5 flags from 8 flags of different colors.
The number of ways that 5 flags can be selected is the combination of 8 flags taken 5 at a time.
After choosing 5 flags from 8, it can be arranged in
=> ₅P₅ ways = (5!)
Therefore, the total number of signals that can be made is
=> ₈C₅ x ₅P₅
=> (8!/(8-5)!5!) x 5!
=> (8! / 3!)
=> 40320 / 6
=> 6270
Therefore, the total number of signals that can be made is 6270.
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Will give brainlyist
30 - The amount he earns every week
12 - the fee for one hour of lawn service without the base fee
12h - the cost for h hours of lawn service without the base fee
Hope this helps you!! :3
Evaluate each logarithm. log₅ 25
A logarithm is a power that requires a number to be raised to another power. The bases of all the values involved must be identical. So, we must create equivalent expressions in the equation that all have equal bases. And the two expressions then formed can only be said equal if the exponents are also similar. Now we will move towards the solution to the problem.
Solution:
log (5,25)
log (5,25)
=log (25) log (5)
=log (52) log (5)
=2log (5) log (5)
=2
2nd Solution:
log (5,25) =2
Solution steps:
=log (5,25)
=log5(25)
=2
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A family with 4 adults and 3 children spends 47 for movie tickets at the theater. Another family with 2 adults and 4 children spends 36 . What is the price of a child's ticket in dollars?
Answer:
The price of a child ticket in dollars $8.00
Step-by-step explanation:
Which lines are parallel to the graph of 4x – y = 6? Check all that apply.
x – 4y = –12
y – 2 = –4(x + 1)
y + 1 = 4(x – 2)
y = 4x + 11
y = x – 3
8x – 2y = 6
Answer: Options 3, 4, 6
Step-by-step explanation:
[tex]4x-y=6 \\\\-4x+y=-6\\\\y=4x-6[/tex]
This means are looking for lines with a slope of 4 (since parallel lines have the same slope).
x – 4y = –12: This rearranges to y=0.25x+3, so the slope is 1/4.y – 2 = –4(x + 1): This has a slope of -4.y + 1 = 4(x – 2): This has a slope of 4.y = 4x + 11: This has a slope of 4.y = x – 3: This has a slope of 1.8x – 2y = 6: This rearranges to y=4x-3, so the slope is 4.Answer:
Which lines are parallel to the graph of 4x – y = 6? Check all that apply.x – 4y = –12y – 2 = –4(x + 1)y + 1 = 4(x – 2)y = 4x + 11y = x – 38x – 2y = 6
Step-by-step explanation:
Which lines are parallel to the graph of 4x – y = 6? Check all that apply.x – 4y = –12y – 2 = –4(x + 1)y + 1 = 4(x – 2)y = 4x + 11y = x – 38x – 2y = 6
What is the relationship of the angles?
Corresponding angles
Alternate interior angles
Consecutive interior angles
alternate Exterior angles
Answer:
Alternate Exterior ANgles
Step-by-step explanation:
Maths
m solving/reasoning
The length of each side of a regular hexagon is 4.7cm to 1 decimal place
Write the error interval for the perimeter, P
27.9 cm≤ perimeter ≤28.5cm
The length of the regular hexagon is 4.7cm to 1 decimal place, i.e.,
4.65≤ length≤4.75
As we know the number of sides of a regular hexagon is 6
So the perimeter for the upper bound of length = 6×4.65
= 27.9cm
The lower bound of length perimeter = 6× 4.75
= 28.5cm
Therefore the interval of the perimeter of a regular hexagon is:
27.9cm ≤ perimeter ≤ 28.5cm
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What is the equation of the line that passes through the point (6, 1) and has a slope
of
-5/6
Answer:
[tex]y=-\frac{5}{6} (x-6)+1[/tex]
Step-by-step explanation:
Using point slope form:
[tex]y=m (x-x_1)+y_1[/tex]
Put in the given parameters:
[tex]m=-\frac{5}{6}[/tex]
[tex]x_1=6[/tex]
[tex]y_1=1[/tex]
Now get the solution:
[tex]y=-\frac{5}{6} (x-6)+1\\[/tex]
Write a sentence to describe how an unethical recruiter could use statistics to mislead prospective employees
The mean of the salary is $120000.
By adding up a list of salaries and dividing by the total number of salaries on the list, mean salaries are derived. This means that exceptionally high and extremely low incomes have the same weight in the final average, which is crucial to bear in mind while investigating industry salaries.
By ranking the wages of a group of employees in descending order, you may determine the median base salary by finding the income that is in the middle of the distribution.
Mean=(5*440,00+2*100,000+1*540,000)/(5+2+1)
=(220,000+200,000+540,000)/8
=960,000/8
=120,000
Median is 100,000.
Hence, the mean salary is 120,000 but 7/8 members salary is lower than 120,000. Because the firm’s owner salary is too high. thus the firm’s owner is so unethical regarding employee salary.
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An architectural drawing has a scale of 2 in: 5 ft. If the living room is 15ft by 18ft in real life, what is the area in the drawing?
Answer: 7.5
Step-by-step explanation: 15 ft * 2 in/ft = 30 in18 ft * 2 in/ft = 36 inso area on plan = 30*36 = 1080 in^2on the real size area = 15*18 = 270 ft^2well to compare them change in^2 to ft^2there are 12 in /ftso 144 in^2 per ft^2so1080 in^2 *1 ft^2/144 in^2 = 7.5 ft^2or you could say30 in = 30/12 ft36 in = 3 ftarea = 90/12 ft^2 = 7.5 ft^2 luckily :)
Help me asap this is a quick one !
Eric has scores of 71, 80, and 83 on his history tests. the final exam counts as two tests, and a b is received if the final course average is greater than or equal to 80
Answer:
he doesnt get a b
Step-by-step explanation:
71+80+83+83=317
317/4= 79.25
79.25 !=< 80
9/10 divided by 4/5 pls help
A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 2 feet above the ground. The horizontal distance from the bottom of the ramp to the building is 15 feet. What is the angle of elevation of the ramp to the nearest degree?
The angle of elevation of the ramp to the nearest degree is 8°
How to determine the angle of elevationFrom the information given, we have the following deductions;
The end of the ramp connected to the doorway is 2 feet above the ground, this is the opposite side The horizontal distance from the bottom of the ramp to the building is 15 feet, this is the adjacent sideThe tangent identity is expressed as;
tan θ = opposite/ adjacent
substitute the values
tan θ = 2/ 15
find the ratio
tan θ = 0. 1333
Find the tangent inverse of the value
θ = [tex]tan^-^1(0. 1333)[/tex]
θ = 7. 79 °
θ = 8° in the nearest degree
Thus, the angle of elevation of the ramp to the nearest degree is 8°
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