Answers
The common differences of arithmetic sequence are;
For a) -3
For b) - 20
For c) - 30
For d) - 10
What is Arithmetic sequence?
An arithmetic sequence is ordered set of numbers that have common difference between each consecutive term.
Given that;
The Arithmetic sequence are;
a) 35, 32, 29, 26 ...
b) - 3, -23, - 43, -63
c) -34, -64, -94, - 124
d) - 30, - 40, - 50, -60
Now, The common difference of an arithmetic sequence is calculated by the difference between each consecutive term.
For Arithmetic sequence a;
Common difference = 32 - 35 = -3
And, For Arithmetic sequence b;
Common difference = - 23 - (-3)
= - 23 + 3
= - 20
For Arithmetic sequence c;
Common difference = - 64 - (-34)
= - 64 + 34
= - 30
For Arithmetic sequence d;
Common difference = - 40 - (-30)
= - 40 + 30
= - 10
Thus, The common differences of arithmetic sequence are;
For a) -3
For b) - 20
For c) - 30
For d) - 10
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Related Questions
A(n)= 3+(n -1)(5)A(2) = 8A(4) = ?I understand how to do the steps however it's still hard for me to do.The example, I looked at was A(n)= A(1) + (n -1)dA(n)=15+(n-1)(4)A(4)=15+(4-1)(4)A(4)=15+(3)(4)A(4)=15+12A(4)=27Still a bit tough.
Answers
Step 1:
Write the equation
A(n) = 3 + (n - 1)5
Step 2:
To find A(2)
Compare A(2) with A(n)
You can see that n = 2 for A(2)
Next, substitute n = 2 in A(n) = 3 + (n-1)5 to find A(2)
[tex]\begin{gathered} A(n)\text{ = 3 + (n - 1)5} \\ A(2)\text{ = 3 + (2 - 1) }\times\text{ 5} \\ A(2)\text{ = 3 + 1}\times5 \\ A(2)\text{ = 3 + 5} \\ A(2)\text{ = 8} \end{gathered}[/tex]Step 3
Let find A(4)
[tex]\begin{gathered} A(n)\text{ = 3 + (n - 1)5} \\ \text{From A(4), n = 4} \\ A(4)\text{ = 3 + ( 4 - 1 ) }\times\text{ 5} \\ A(4)\text{ = 3 + 3}\times5 \\ A(4)\text{ = 3 + 15} \\ A(4)\text{ = 18} \end{gathered}[/tex]Final answer
A(4) = 18
Solve the system by the substitution method.
15x - y = 55
y = x² + 1
Answers
Answer:
Point Form: (8,65) , (7,50)
Equation Form:
x = 8, y = 65
x = 7, y = 50
Step-by-step explanation:
Evaluate (2 +40) : 2 when z = 8 answer A 8 B 5C 6D 48
Answers
1) Let's solve the equation given the condition
[tex]\frac{\mleft(x+40\mright)}{2^3}\Rightarrow\frac{(8+40)}{8}\Rightarrow\frac{48}{8}=6[/tex]After plugging into the equation, all that's left is to solve it with the PEMDA order of operation.
2) So the answer is C
Please help with this question pl
Answers
The missing reason 6 of the two column proof that m∠Z = 65° is; Substitution
How to carry out two column proof?The two column proof is as follows;
Statement 1: XYZ is a triangle
Reason 1; Given
Statement 2: m∠x + m∠y + m∠z = 180°
Reason 2: Postulate
Statement 3: m∠y = 50°
Reason 3: Given
Statement 4: ∠X ≅ ∠Z
Reason 4: Given
Statement 5: m∠X = m∠Z
Reason 5: Congruency
Statement 6: m∠Z + m∠Z = 180°
Reason6: Substitution
Statement 7: m∠Z + m∠Z = 130°
Reason 7: ?
Statement 8: 2(m∠Z) = 130°
Reason 8: Algebra
Statement 9: m∠Z = 65°
Reason 9: Division property of equality
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A pair of linear equations is shown:
y = −3x + 5
y = x + 2
Which of the following statements best explains the steps to solve the pair of equations graphically?
On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.
On a graph, find the point of intersection of two lines; the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2.
On a graph, find the point of intersection of two lines; the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1.
On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2.
Answers
The graph that shows the solution to the pair of linear equations is shown below. The best explanation for the step to take is: A. the first line is the red line while the second line is the blue line.
How to Solve a Pair of Linear Equations Graphically?To find the solution to a pair of linear equations using a graph, plot the given equations on a graph using their slopes and their y-intercepts.
The point where the two lines intersect is the solution to the pair of linear equations.
Given the linear equations:
y = −3x + 5
y = x + 2
The graph of y = -3x + 5 has a slope of -3 and a y-intercept of 5, while the graph of y = x + 2 has a slope of 1 and a y-intercept of 2.
The diagram that shows the graph where the two lines intersect at point (0.75, 2.75) is shown below.
The solution is: (0.75, 2.75)
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please write the value of x and the equation used.
Answers
Zachary pays $68 per month and $5 per months for gigabytes
X be the number of gifabytes
SO, price of x gigabytes = 5x
total budget = 5x + Amount paid :
So, y = 5x + 68
Answer: y = 5x + 68
One bag of rice that weighs 3.5 pounds will have enough rice if a recipe calls for 54 ounces of rice. (1 pound = 16 ounces) (3 points)
Answers
One bag of rice that weighs 3.5 pounds will have enough rice for the recipe if a recipe calls for 54 ounces of rice . the given statement is True .
In the question ,
it us given that
weight of one bag of rice = 3.5 pounds
given that ,
1 pound [tex]=[/tex] 16 ounces
So, we need to convert 3.5 pounds to ounces first .
we have 3.5 pounds = 16×3.5 ounces
= 56 ounces .
So , yes there will be enough rice for the recipe as only 54 ounces are needed and we have 56 ounces , that is 2 extra ounces of rice .
Therefore , "One bag of rice having weight 3.5 pounds ,will have enough rice for the recipe if a recipe calls for 54 ounces of rice" . the given statement is True .
The given question is incomplete , the complete question is
One bag of rice that weighs 3.5 pounds will have enough rice if a recipe calls for 54 ounces of rice. (1 pound = 16 ounces) . The given statement is TRUE or FALSE ?
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Find WZ if WX = 4a, XY = 28, YZ = 6a - 4 and XZ = 10a + 12
Answers
1) In this line segment, we can apply the the addition postulate to solve it and write:
WZ = WX +XY +YZ
10a +12 = (4a +28) +(6a - 4)
10a +12= 10a +24
0a = 12 No solution
2) Since this is a non-solution equation, then we can't solve for a and find the length of WZ
A kitten weighs 5 pounds what is the kilograms
Answers
Nelson, this is the solution:
Let's recall that 1 pound = 0.4536 kg, therefore:
• 5 pounds = 0.4536 * 5
,• 5 pounds = 2.268 kilograms
Find the area of the surface of a sphere of radius r, which is generated when rotating a semicircle centered at the origin, is rotated about its diameter.
Answers
The surface area of a sphere of radius r is
How to go from radians to degrees
Answers
Answer:
Recall that:
[tex]360^{\circ}=2\pi\text{ radians.}[/tex]Therefore:
[tex]1^{\circ}=\frac{2\pi}{360}radians,[/tex]or
[tex]1\text{ radian=}\frac{360^{\circ}}{2\pi}degrees.[/tex]Suppose that the relation T is defined as follows.T = {(0,6), (2, -8), (-8, 2), (-3, -3)}What is the domain and range?
Answers
Given the follwing relation T:
[tex]T=\mleft\lbrace(0,6\mright),(2,-8),(-8,2),(-3,-3)\}[/tex]to write the domain, we have to gather all the first components of each ordered pair. In this case, the domain is:
[tex]DomT=\mleft\lbrace0,2,-8,-3\mright\rbrace[/tex]the range will be the second component of each ordered pair:
[tex]Range(T)=\mleft\lbrace6,-8,2,-3\mright\rbrace[/tex]Simplify using exponent B-³
Answers
Answer:
B^-3
1/B³
Step-by-step explanation:
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when trying to find the probability of rolling a number four on a number cube with the number 1 through 6 how many desired outcomes are there
Answers
ANSWER
One desired outcome
EXPLANATION
We are trying to roll the number 4 on a number cube with numbers 1 through 6.
Since we are only trying to get one outcome/result from the experiment (4), there is only one desired outcome.
The answer is 1.
Determine the end (long run) behavior for: f(x)=−2(x−1)3(x+2)2
Answers
The end behavior of the function f(x) = −2(x−1) * 3(x+2) * 2 is
as x tends to ∞, f(x) tends to -∞as x tends to -∞, f(x) tends to -∞What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behaviorThe given function is:
f(x) = −2(x−1) * 3(x+2) * 2
The given function is first expanded
= −2(x−1) * 3(x+2) * 2
= (-2x + 2) * (3x + 6) * 2
= (-4x + 4) * (3x + 6)
= -12x² - 36x + 24
The end behavior is determined by the leading term = -12x²and it is described as
x ⇒ ∞ f(x) ⇒ -∞
x ⇒ -∞ f(x) ⇒ -∞
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Х m . In the segment shown point M is the mi M the midpoint of AB. Given AM = 3x+ 12 and MB = MB = 5x -4, find the length of AM. DP A M B M
Answers
From the information provided, M is the midpoint of line segment AB. This implies that the segments AM and MB are two equal halves of the entire length,
Therefore, we would have the following;
[tex]\begin{gathered} AM+MB=AB \\ \text{Also,} \\ AM=MB \\ \text{Where;} \\ AM=3x+12,MB=5x-4 \\ We\text{ now have;} \\ 3x+12=5x-4 \\ \text{Collect all like terms;} \\ 12+4=5x-3x \\ 16=2x \\ \text{Divide both sides by 2;} \\ \frac{16}{2}=\frac{2x}{2} \\ 8=x \end{gathered}[/tex]Where AM = 3x+12, we now have;
[tex]\begin{gathered} AM=3x+12 \\ AM=3(8)+12 \\ AM=24+12 \\ AM=36 \end{gathered}[/tex]ANSWER:
Segment AM = 36
Part 1: Factorial!2. Explain the steps that you took to calculate it on your calculator.
Answers
Given:
a factorial 14! is given
Find:
we have to evaluate the given factorial
Explanation:
we know, the factorial 14! is calculated as following
14! = 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
14! = 87178291200
or
14! = 8.71783E10
Wich is an example of multiplicative identityA. a×1=aB. a+0=aC. a+(-a)=0orD. a×1/a=1
Answers
Multiplicative Identity:
The multiplicative identity property states that if a number is multiplied by 1, the result is that number.
Examples:
[tex]\begin{gathered} a\times1=a \\ 5\times1=5 \\ 20\times1=20 \\ y\times1=y \end{gathered}[/tex]Therefore, the example of multiplicative identity is option A
[tex]a\times1=a[/tex]1233558844+12254788-1255+77777
Answers
1,233,558,844 + 12,254,788 − 1,255 + 77,777
= 1,245,890,154
Answer:
1245890154 easy, lol
I know this wasn't a real question but if it was good luck, lol
Dillon went out for dinner with four friends. All had the same meal and dessert, except for Dillon who did not order the $5 dessert. The total bill came to $45. Write an equation to determine how much each of his friends paid for their meal.
Answers
The equation to determine each of his friends paid for their meal would be; 4x + x - 5 = 45.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the Dillon and 4 friends went for dinner.
They all had the same meal except Dillion who did not order the 5 dollars dessert.
The Total bill paid = $45
Let the amount paid by each friend = x
Then Amount paid by dillion = x - 5
4x + x - 5 = 45
5x - 5 = 45
5x = 45 + 5
5x = 50
x = 10
Thus, the Amount paid by each of the 4 friends = $10
Hence, Amoubt paid by Dillion is $10 - $5 = $5
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Did I correctly or incorrectly solve the equations below?From the information given, find the quadrant in which the terminal point determined by t lies. Input I, II, III, or IV.(a) sin(t)<0 and cos(t)<0 , quadrant_____III_____ ;(b) sin(t)>0 and cos(t)<0 , quadrant____II______ ;(c) sin(t)>0 and cos(t)>0, quadrant______I_____;(d) sin(t)<0 and cos(t)>0, quadrant____IV_______ ;
Answers
We know that the sine function is positive in the first and second quadrant; we also know that the cosine function is positive in the first and fourth quadrant.
What is the value of (-3)-4?
Answers
Answer:
-7
Step-by-step explanation:
-3-4=-7
:]
Answer:
-7
Step-by-step explanation:
Solve: x−6−−−−−√=x−6 . Enter the exact answers. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter.
Answers
ANSWER:
x = 6; 7
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\sqrt{x-6}=x-6[/tex]We solve for x:
[tex]\begin{gathered} \left(\sqrt{x-6}\right)^2=\left(x-6\right)^2 \\ \\ x-6=x^2-12x+36 \\ \\ x^2-12x-x+36+6=0 \\ \\ x^2-13x+42=0 \\ \\ -13x=-6x-7x \\ \\ x^2-6x-7x+42=0 \\ \\ \left(x^2-6x\right)+\left(-7x+42\right)=0 \\ \\ x\left(x-6\right)-7\left(x-6\right) \\ \\ \left(x-6\right)\left(x-7\right)=0 \\ \\ x-6=0\rightarrow x=6 \\ \\ x-7=0\operatorname{\rightarrow}x=7 \\ \\ \text{ We check each solution, as follows:} \\ \\ \sqrt{6-6}=6-6\rightarrow0=0\rightarrow\text{ True} \\ \\ \sqrt{7-6}=7-6\rightarrow1=1\rightarrow\text{ True} \\ \\ \text{ Both solutions are correct therefore:} \\ \\ x=6;7 \end{gathered}[/tex]Write an equation in standard form for the line that passes through the given points.
(1, 2) and (5, 7)
Answers
The equation of the line in standard form is represented by - (5 / 3) · x + (4 / 3) · y = 1.
What is the equation of the line that passes through two points?
In this problem we must derive the equation of the line in standard form that passes through the two points. The standard form is described below:
a · x + b · y = 1
Then, we must solve for a and b to determine the coefficients of the line equation:
a + 2 · b = 1
5 · a + 7 · b = 1
By numerical methods, the solution to the system is:
a = - 5 / 3, b = 4 / 3
The equation in standard form - (5 / 3) · x + (4 / 3) · y = 1.
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Please help with this word problem,Laurie, Moesha, and Carrie went to the mall. Laurie spent $20, Moesha spent $25, and Carrie spent $30. How many did they spend in all?
Answers
To determine how much they all spent we need to add the expenses of each person: Laurie, Moesha, and Carie. This is shown below:
[tex]\begin{gathered} \text{ total=Laurie+Moesha+Carrie} \\ \text{total}=20+25+30=75 \end{gathered}[/tex]They spent a total of $75.
A standard sheet of paper in Europe is `29.7` centimeters long and `21` centimeters wide.
Which standard sheet of paper has a greater area?
Answers
Standard sheet of paper in Europe has a greater area i.e. 29.7 cm. long and 21 cm wide.
1 in = 2.54 cm (in Europe)
In SI units standard-sized paper is 21.0 cm by 29.7 cm, which is equivalent to 8.268 in by 11.693 in.
In U.S.
U.S. sized standard paper is 8.0 in by 11.0 in therefore the SI (internationally) sized paper is longer.
Standard sheet of paper in Europe has a greater area than standard sheet of paper in U.S.
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a figure with a perimeter of 84 units is dilated by a factor of 3/4. the perimeter of the dilated figure is ___ units.
Answers
If the perimeter is 84 and it is dilated by a factor of 3/4 , then the perimeter of the dilated figure can be calculated by multiplying 84 by 3/4
That is;
Perimeter of dilated figure = 3/4 x 84
=63 units
PEOPLE WHO ARE GOOD AT MATH CAN YOU PLEASE HELP ME!!!
Answers
The cost of using 19 HCF of water is $32.49
Given in the question:
The monthly cost (in dollars) of the water use (in dollars) is a linear function of the amount of water used (in hundreds of cubic feet, HCF)
The cost for using 17 HCF of water is using $32.13
and, the cost of using 35 HCF is $61.83.
To find the cost of using 19 HCF of water.
Now, According to the question:
The cost for using 17 HCF of water is $32.13
and, the cost of using 35 HCF is $61.83.
To find the slope:
(17, 32.13) and (35, 61.83)
Slope = (61.83 - 32.13)/ (35 - 17) = 1.65
We know that:
Formula of slope :
y = mx + b
32.13 = 1.65 x 17 + b
b = 1.14
The equation will be :
C(x) = 1.65x + 1.14
Now, To find the cost of using 19 HCF of water.
C(19) = 1.65 × 19 + 1.14
C(19) = $32.49
Hence, the cost of using 19 HCF of water is $32.49.
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A police car traveling south toward Sioux Falls, Iowa, at 160 km/h pursues a truck traveling east away from Sioux Falls at
140 km/h.
At time t = 0, the police car is 60 km north and the truck is 50 km east of Sioux Falls.
Calculate the rate at which the distance between the vehicles is changing at t = 10 minutes.
(Use decimal notation. Give your answer to three decimal places.)
Answers
Using the Pythagorean Theorem, the rate at which the distance between the vehicles is changing at t = 10 minutes is of -20 km/hour.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the equation given below:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, the distances of the cars from Sioux Falls, considering the initial distances and the velocities, are given as follows:
Police: P(t) = 60 - 160t.Truck: T(t) = 50 + 140t.The distance after t hours is the hypotenuse of a right triangle in which the legs are the functions, hence:
D²(t) = P²(t) + T²(t).
Hence the rate of change of the distance after t hours is:
2D'(t) = 2P'(t) + 2T'(t)
Simplifying by 2:
D'(t) = P'(t) + T'(t).
Applying the exponent rules, the derivatives are given as follows:
P'(t) = -160.T'(t) = 140.Hence the constant rate is:
D'(t) = -160 + 140 = -20 km/hour.
Meaning that the police car is getting 20 km closer to the truck each hour.
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If angleA and angleB are supplementary, and angleA = (3x - 9)°, and angleB = (2x + 14)degree, find x.
Answers
The values of x in the supplementary angles is 35.
What are supplementary angles?Supplementary angles refer to the pair of angles that always sum up to 180°.
Two angles are Supplementary when they add up to 180 degrees.
Therefore, for angle A and angle B to be supplementary they must add up to 180 degrees.
Hence,
∠A + ∠B = 180°
∠A = 3x - 9
∠B = 2x + 14
Therefore,
3x - 9 + 2x + 14 = 180
5x - 9 + 14 = 180
5x + 5 = 180
5x = 180 - 5
5x = 175
x = 175 / 5
x = 35
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The required value of x would be 35 degrees which are supplementary angles
We have been given that angle A and angle B are supplementary angles
∠A = 3x - 9 and ∠B = 2x + 14
Whenever two angles are supplementary, their sum is 180 degrees.
As per the property of supplementary angles,
The given angles add up to 180 degrees.
Thus, ∠A + ∠B = 180°
Substitute the values of ∠A and ∠B in the above equation,
3x - 9 + 2x + 14 = 180
5x - 9 + 14 = 180
5x + 5 = 180
5x = 180 - 5
5x = 175
x = 35
Hence, the supplementary angles have a value of 35 for x.
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