The formula for the general term of the sequence is Tn = 4n - 2
How to determine the formula?The sequence is given as:
{2, 6, 10, 14, 18, . . . }
The above sequence is an arithmetic sequence with the following features:
First term, a = 2Common difference, d = 4 i.e. 6 - 2The formula for the general term is calculated using:
Tn = a + (n - 1) * d
This gives
Tn= 2 + (n - 1) * 4
Expand
Tn = 2 + 4n - 4
Evaluate the like terms
Tn = 4n - 2
Hence, the formula for the general term of the sequence is Tn = 4n - 2
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If f(x) = 8- 10x and g(x) = 5x + 4, what is the value of (fg) (-2)?
O -196
O -168
O 22
O 78
One of the tables shows a proportional relationship.
Use the points from this table to graph the line representing the proportional
relationship.
Line
10-
9
8-
7
5
4
3
2
-2-
3 7 4
-3-
Undo
1 2
3
4
Redo
$
6
x Reset
7 8 9 10
X
y
x
y
X
y
X
y
2
1
2
1
0
2
1
3
2
4
3
2
2
2
4
5
6
3
4
6
4
5
3
7
27
6
4
8
4
5
8
9
6
Answer:
See attached
Step-by-step explanation:
The graph of a proportional linear relationship is a line that passes through the origin (0, 0).
From inspection of the given tables, the linear equations for each table of points is:
Table 1: y = x + 1Table 2: y = x/2Table 3: y = x + 2Table 4: y = 2x + 1The only equation for which y = 0 when x = 0 is y = x/2 → Table 2.
Given points from Table 2:
(2, 1)(4, 2)(6, 3)(8, 4)To graph the line, plot the given points and draw a line through them (see attached).
Evaluate the fraction for x = 0. (x-1)² (1-x)² 01 0-1 02
Evaluating the given algebra fraction (x - 1)²/(1 - x)² at x = 0 gives; 1
How to Evaluate Algebra Fractions?
We want to evaluate the algebra fraction;
(x - 1)²/(1 - x)² at x = 0.
Now, let us first break down the expression to get;
[(x - 1) * (x - 1)]/[(1 - x) * (1 - x)]
At x = 0, we have;
[(0 - 1) * (0 - 1)]/[(1 - 0) * (1 - 0)]
⇒ (-1 * -1)/(1 * 1)
⇒ 1
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Dont Really need explanation Simply answer Just I didn’t understand Maybe I can get help
Based on the calculations, Tart & Sweet's total profit from April to June is equal to -2 dollars.
What is a bar chart?A bar chart can be defined as a type of chart that is used for the graphical representation of a data set, especially by using rectangular bars or vertical columns.
In order to determine Tart & Sweet's total profit, we would simply add the amount of money (in dollars) generated from April to June as follows:
April = -8.May = 2.June = 4.Total profit = -8 + 2 + 4
Total profit = -$2.
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In isosceles ∆ABC, points M and N belong to base
BC
so that BM = CN. Prove:
∆BAM ≅ ∆CAN
∆AMN is an isosceles triangle.
From the statements and reasons given below as regards the Isosceles Triangle, we have been able to prove that; ∆BAM ≅ ∆CAN
How to prove an Isosceles Triangle?Isosceles Triangle means that two sides of the triangle are equal and also 2 angles are equal.
Now, we are told that triangle ABC is an Isosceles and as such, AB and AC are congruent.
We are given that BM and NC are congruent. Now, due to the fact that Triangle AMN is an isosceles triangle, it means that the sides AM and AN are congruent to each other.
Thus, from the proofs above and from the definition of the isosceles Triangle, we can say that triangles BAM and CAN are congruent.
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Answer & Step-by-step explanation:
To prove ∆BAM ≅ ∆CAN:
1. Given that ∆ABC is an isosceles triangle with base BC, and BM = CN, we know that AB = AC.
2. Using the Side-Angle-Side (SAS) congruence criterion, we can show that ∆ABM and ∆ACN are congruent.
3. Therefore, corresponding angles ∠BAM and ∠CAN are congruent.
4. Similarly, ∠BMA and ∠CNA are congruent.
5. By showing that corresponding angles in ∆ABM and ∆ACN are congruent, we can conclude that ∆BAM ≅ ∆CAN.
To prove ∆AMN is an isosceles triangle:
1. From the given information, we know that BM = CN.
2. By proving ∆BAM ≅ ∆CAN, we have shown that ∠BAM ≅ ∠CAN.
3. Since ∠BAM and ∠CAN are congruent, we can conclude that ∠BAN ≅ ∠CAM using the Transitive Property of Congruence.
4. By establishing that ∠BAN ≅ ∠CAM, we can conclude that ∆AMN is an isosceles triangle because it has two congruent angles.
Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths.
The answer to the question that is modeled here is one sixth plus four sixths.
How to solve for the expression
We have the following fractions
1/6 and 5/6
We are to find the fraction which when added to 1/6 would give us 5/6. Hence we have
1/6 + 4/6 = 5/6
Hence the correct answer to the question here is option a.
complete questionPLS HELP 1HOUR LEFT Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths one sixth plus five sixths
one sixth plus four sixths
five sixths minus one sixth
five sixths minus four sixths
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Identify the segments that are parallel, if any angle ABC equals angle HCB
Answer: A. DC||AB
Step-by-step explanation:
Line DC is parallel to AB so the correct answer is option B.
What is the similarity?
If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
In the given image we can see that the two angles ABC and HCB are congruent to each other. So the line DC is parallel to AB.
Therefore Line DC is parallel to AB so the correct answer is option B.
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What is the value of "y" that satisfies the expression below?
5 y + 14 = 9 ( 3 y + 1 )
Round your answer to 2 decimal points (i.e. #.##)
Answer:
0.23
Step-by-step explanation:
5y+14=27y+9
14-9=27y-5y
5=22y
dividing through by 22
y=0.23
Melissa's mother asked her to buy a gallon of milk at the store. The store only had quarts of milk. How many quarts of milk does Melissa need to buy?
Answer:
4 quarts of milk
Step-by-step explanation:
4 quarts = 1 gallon
so, melissa needs to buy 4 quarts
Solve for t in this equation and show steps please d = vt + 1/2(a)(t^2)
Desperately need help. pls
By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.
How to find the value of composition between two functions
Compositions are binary operators between two functions: f - Former function, g - Latter function.
f ° g (x)
Where the input of the former function is the output of the latter function. By a brief observation, we find the following relationships in accordance with the two tables:
Case I
f(x):
0 → 1
g(x):
1 → - 2
Case II
f(x):
1 → 0
g(x):
0 → 1
By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.
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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
ANSWER:
CORRECT (SELECTED)
Josiah's distance from the starting line at a time when he is behind Chana
Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance.
Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance. This is a distance-time graph problem.
What is the proof for the above?
Recall that Josiah had a head start of 10 meters and he skates at 2 meters per second.
Since Y is the function that represents the distance in meters from the finished line, by observation, it is clear to see that all the factors that are related to his race are adequately represented in:
y = 10 + 2x
Where 10 is the head start in meters
2 is the rate at which he skates per second; and
x is the unknown amount of time in seconds.
Given that the point F sits over 25 seconds,
that is F(y) = 10 + 2 * 25
= 60 meters.
Hence, Point F is on line a, so it does represent Josiah's distance at exactly 25 seconds.
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Find f(2) and f(a + h) when f(x) = 3x2 + 2x + 4.
Step-by-step explanation:
[tex]f(x) = 3 {x}^{2} + 2x + 4[/tex]
[tex] \: [/tex]
[tex]f(2) = 3. {2}^{2} + 2.2 + 4[/tex]
[tex]f(2) = 3.4 + 4 + 4[/tex]
[tex]f(2) = 12 + 8[/tex]
[tex]f(2) = 20 \\ [/tex]
[tex] \: [/tex]
[tex]f(a + h) = 3 {(a + h)}^{2} + 2.(a + h) + 4[/tex]
[tex]f(a + h) = 3( {a}^{2} + 2ah + {h}^{2} ) + 2a + 2h[/tex]
[tex]f(a + h) = 3 {a}^{2} + 6ah + 3 {h}^{2} + 2a + 2h + 4[/tex]
[tex]f(a + h) = 3 {a}^{2} + 3 {h}^{2} + 6ah + 2a + 2h + 4[/tex]
Which expression is a non-real complex number?
-4 +√7
3
1 + √²
5-√15
27
28
The expression that represents a complex number is the one in the second option.
[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} }= \frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]
Which expression is a non-real complex number?Remember that the complex number i is given by:
[tex]i = \sqrt{-1}[/tex]
So we have complex numbers when we have negative arguments inside of square roots.
In this particular case, the only option with a negative argument on a square root is on the second option:
[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{-1} *\sqrt{\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]
We conclude that the correct option is the second one.
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Answer:
(2)/(3)+\sqrt(-(27)/(28))
Step-by-step explanation:
Plato/Edmentum
Simplify the expression.
[tex]\huge\boxed{4x}[/tex]
Start by simplifying the power.
[tex](5x)^3=5^3x^3=125x^3[/tex]
[tex]\dfrac{500x^4}{125x^3}[/tex]
Cancel out the common factor of [tex]125[/tex].
[tex]\dfrac{4x^4}{x^3}[/tex]
Finally, cancel out the common factor of [tex]x^3[/tex].
[tex]\boxed{4x}[/tex]
Can anyone explain this answer, I'll give brainliest.
Where does the 0.693 and 2.303 come from?
The constants 0.693 is the natural log of 2 and the constant 2.303 is the multiplicative factor of converting log of a number to the natural log of that same number.
What are 0.693 and 2.303 used for?It follows from the task content that the calculation involves the use of the half-life of radioactive materials formula.
Hence, the constant 0.693 is the real number value of ln(2). Additionally, the constant 2.303 as used by convention is used to convert log value of a number x to its natural log value. Hence,. it follows that the relation which holds true is; ln(x) = 2.303 × log(x).
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For a normally distributed data set with a mean of 830 and a standard deviation of 96.7, calculate the z-score for a
data point of 915.
Round this however your teacher instructs.
=================================================
Work Shown:
mu = 830 = mean
sigma = 96.7 = standard deviation
x = 915 = given raw score we want to convert
z = (x - mu)/sigma
z = (915 - 830)/(96.7)
z = (85)/(96.7)
z = 0.8790072 approximately
Identify the type of sequence and write the recursive rule −1,−2,−4,−8,
6) Simplify the following:
axaxbxb
The simplified expression of axaxbxb is a^2b^2
How to simplify the expression?The expression is given as;
axaxbxb
Rewrite properly as:
a * a * b * b
Evaluate the product
a^2b^2
Hence, the simplified expression of axaxbxb is a^2b^2
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Find the non-extraneous solutions of the square root of the quantity x plus 6 minus 5 equals quantity x plus 1
The non-extraneous solutions are -6 and -5.
How to find non-extraneous solutions?By checking these solution values in the original equation.
[tex](x+6)^{1/2}-5=x+1\\(x+6)^{1/2}=x+6\\((x+6)^{1/2})^2=(x+6)^2\\x+6=x^2+12x+36\\0=x^2+11x+30\\(-11+(11^2-4(1)(30))^{1/2})/2\\(-11+((1)^{1/2})/2\\(-11+1)/2=-5\\(-11-1)/2=-6\\((-6)+6)^{1/2}-5=(-6)+1\\(0^{1/2})-5=-5[/tex]
Thus, -6 is non-extraneous.
[tex]((-5)+6)^{1/2}-5=(-5)+1\\(1^{1/2})-5=-4\\1-5=-4\\-4=-4[/tex]
Thus, -5 is non-extraneous.
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look at this system of exquations. y=2x-1 4x +y=2 which shows a correct step using substitution to solve the system of equations?
The solution to the system of equations is x = 0.5, y = 0
How to solve the system of equations?The system of equations is given as:
y = 2x-1
4x + y=2
Substitute y = 2x-1 in 4x + y=2
4x + 2x-1 =2
Evaluate the like terms
6x = 3
Divide by 6
x = 0.5
Substitute x = 0.5 in y = 2x-1
y = 2 * 0.5 - 1
Evaluate
y = 0
Hence, the solution to the system of equations is x = 0.5, y = 0
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In a recent year, 27.2% of all registered doctors were female. If there were 55,900 female registered doctors that year, what was the total number of registere doctors? Round your answer to the nearest whole number. In a recent year , 27.2 % of all registered doctors were female . If there were 55,900 female registered doctors that year , what was the total number of registere doctors ? Round your answer to the nearest whole number .
it's B why they need me to write something long the answer is ez B
Step-by-step explanation:
it f common sense
Solve the following equation for m.
F=mv^2 / r
Answer:
Step-by-step explanation:
F = [tex]\frac{mv^2}{r}[/tex]
mv² = Fr
m = [tex]\frac{Fr}{v^2}[/tex]
why is the derivative of a constant zero
A constant function is exactly that - constant - meaning it exhibits no change whatsoever with respect to any change in its input. If [tex]f(x) = 1[/tex], then it doesn't matter what value of [tex]x[/tex] I give you, the value of [tex]f(x)[/tex] will always be nothing other than 1.
That the derivative of such a function is zero follows immediately from the definition of the derivative. If [tex]c\in\Bbb R[/tex] and [tex]f(x) = c[/tex], then
[tex]f'(x) = \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0} \frac{1 - 1}h = \lim_{h\to0}\frac0h = 0[/tex]
Find the value of x.
x = 2
x = 3
x = 33
x = 52
Find the value of x and y using the diagram below.
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
x = 2 , y = 3Step-by-step explanation:
As the given figure is a rectangle, therefore the opposite sides should be equal. So -
3x + y = 12 – y...(eqn (i) )
and
y – x = x – 1...(eqn (ii) )
Solving eqn (ii) we get -
→ y – x = x – 1
→ y = x + x – 1
→ y = 2x – 1...eqn(iii)
Solving eqn (i) we get -
→ 3x + y = 12 – y
→ 3x = 12 – y – y
→ 3x = 12 – 2y
Substituting the value of eqn (iii)
→ 3x = 12 – 2(2x– 1)
→ 3x = 12 – 4x + 2
→ 3x + 4x = 14
→ 7x = 14
→ x = 14/7
→ x = 2
Hope it helps you!!Answer:
x = 2; y = 3
Step-by-step explanation:
Since the quadrilateral has 4 right angles, it is a rectangle.
In a rectangle, opposite sides are congruent.
3x + y = 12 - y
x - 1 = y - x
We have a system of two equation is 2 variables.
Let's simplify both equations.
3x + 2y = 12
2x - y = 1
Rewrite the first equation. Multiply both sides of the second equation by 2. Add the equations.
3x + 2y = 12
(+) 4x - 2y = 2
-------------------------
7x = 14
Divide both sides by 2.
x = 2
Substitute 2 for x in the second original equation and solve for y.
x - 1 = y - x
2 - 1 = y - 2
1 = y - 2
y = 3
Answer: x = 2; y = 3
A student's grade on the Fundamentals of Engineering exam has a z-score of 0.5. Make an observation about the student's grade.
The observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.
What is z score?It should be noted that the z score is a numerical measurement which describes the relationship of a value to the mean value of the group.
In this case, the observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.
This is illustrated as the z score is 0.5.
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The cost of 25 apples is $18.50. What is the cost of one apple
Answer:
0. 74$Step-by-step explanation:
$18. 50÷25=0. 74$
Please help me with this on the picture
Answer:
5, 7
Step-by-step explanation:
The mode of the numbers is 5, which means that 5 should be the most common card (highest frequency). Therefore the cards should have at least one more 5 among them.
Considering that 5 is one of the hidden cards and x is the other,
• Using the equation for the mean:
[tex]mean = \frac{sum \space\ \space\ of \space\ \space\ numbers}{number \space\ \space\ of \space\ \space\ numbers}[/tex]
[tex]6 = \frac{4+5+ 9 + 5 + x}{5}[/tex]
⇒ [tex]30=23 + x[/tex]
⇒ [tex]x = 7[/tex]
This means 5 and 7 are the hidden cards.
Question 5 3 pts A corral for cattle is in the shape of a circle with a radius of 17.8 m; find the total area of the corral. Round your answer to the nearest whole number. Do not type the units in the space below.
Step-by-step explanation:
the area of s circle is
pi×r²
r being the radius.
so, in our case
pi×17.8² = pi×316.84 = 995.3822164... ≈ 995 m²