The first term of the given arithmetic sequence is 2.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.
Given that, the fourth term of an arithmetic sequence is 8 and the common difference is 2.
Here, a₄=a+(4-1)×2
8=a+6
a=2
Therefore, the first term of the sequence is 2.
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Which point is an x-intercept of the quadratic function
f(x) = (x – 8)(x + 9)?
What is the value of X
180 - 70 - 42 = 68
x = 68 degrees
What is the maximum length possible for her blanket?
Answer: c: 60
Step-by-step explanation:
i did the test
Which postulate or theorem proves that △ RNM and △ QNP are congruent?
A) HL congruence theorem
B) SAS congruence postulate
C) AAS congruence theorem
D) SSS congruence postulate
Answer:
B) SAS congruence postulate
Step-by-step explanation:
We have marked that RN and NQ are congruent. We also have marked that MN and NP are congruent.
∠MNR≅∠QNP because they are vertical angles. Vertical angles are opposite angles that share only a vertex; these are vertical angles so they are congruent.
This gives us two sides and an included angle; this is SAS.
B) SAS congruence postulate proves that △ RNM and △ QNP are congruent
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know two triangles are congruent when we have at least three respective sides or angles or both that are same as the other sides or angles of a triangle.
We also know that vertically opposite angles have the same measures.
here the vertically opposite angles are ∠RNM and ∠PNQ.
It is given that side RN is congruent to side NQ and side PN is congruent to side MN.
∴ It is proven by SAS congruence postulate.
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N a contest, a total of $12,000 was divided among the first, second, and third-place winners in the ratio of 3 to 2 to 1, respectively. how much did the first-place winner receive
The admission fee at an amusement park is $2.00 for children and $5.60 for adults. On a certain day, 352 people entered the park, and the admission fees collected totaled 1280 dollars. How many children and how many adults were admitted?
A bakery makes donuts at the rate of 225 per hour. How long will it take the bakery to fill an order of 500 donuts?
Vectors...
Let u = <-3, -5>, v = <-3, 1>. Find u + v.
Answer:
u + v = <-3 + -3, -5 + 1> = <-6 , -4>
u + v = <-6 , -4>
Step-by-step explanation:
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How to solve nonlinear equations using iteration method?
A triangle has three different integer side lengths and a perimeter of 20 units. What is the max length of any one side?
Final answer:
Using the Triangle Inequality Theorem and given a perimeter of 20 units for a triangle with integer side lengths, the maximum length of one side is found to be 15 units.
Explanation:
To determine the maximum length of one side of a triangle with integer side lengths and a perimeter of 20 units, we must apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given a perimeter of 20 units, if we denote the longest side as x, and the other two sides as y and z, we must satisfy two conditions:
x + y + z = 20 (perimeter condition)
x < y + z (Triangle Inequality Theorem)
Since the triangle has different integer side lengths, the largest x can be is when y and z are consecutive integers because this allows for the largest possible x. If we try the smallest integers, 1 and 2, for y and z, their sum is 3. To satisfy the triangle inequality, the largest possible integer for x would be 20 - 1 - 2 = 17. However, this does not satisfy the inequality x < y + z, because 17 is not less than 3.
Next, we increase y and z to 2 and 3, respectively, which sums up to 5. Thus, for x, we have 20 - 2 - 3 = 15. Since 15 is less than 2 + 3, it satisfies the condition required by the Triangle Inequality Theorem. Therefore, the maximum length of any one side of the triangle is 15 units.
Consider the equation below. log4 (x+3)=log2 (2x). Which system of equations can represent the equation?
What is the length of the hypotenuse of an isosceles right triangle with an area of 32?
Emma read the statement “the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5.” She translated it as shown below.
Emma should have used division to represent the quotient of six and x, and she should have used parentheses to show that -2 is multiplied by (4.5 - x). Hence the correct options are 1 and 5.
Emma made two errors in translating the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." First, instead of representing the quotient of six and x, she incorrectly wrote 6x, which implies multiplication rather than division. The correct representation should be 6/x.
Second, Emma failed to use parentheses to show that -2 is multiplied by the difference of x and 4.5. The correct expression should be -2(x - 4.5) to ensure proper order of operations. These errors impact the accuracy of the translated equation, and correcting them would yield a more faithful representation of the original statement. Hence the correct options are 1 and 5.
Complete question:
Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." She translated it as shown below 6x=-2x-4.5 What errors did Emma make? Select two options
She should have used division to represent the quotient of six and x.
She should not have included an equal sign.
She should have used parentheses to show that -2 is multiplied by (x-4.5).
She should have subtracted the difference (x-4.5) from -2.
She should have used parentheses to show that -2 is multiplied by (4.5-x).
Emma made the following errors in her translation:
E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation, 6x = -2x - 4.5, lacks parentheses around the expression (x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2, she should have written -2(x-4.5).
D. She should have subtracted the difference (x-4.5) from -2. Emma’s equation does not correctly account for the subtraction of the difference (x-4.5) from -2. The correct equation should be 6x = -2(x-4.5).
The other options are not relevant to Emma’s specific errors in translating the statement.
Emma made the following errors in her translation:
E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation,
6x = -2x - 4.5, lacks parentheses around the expression
(x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2
, she should have written
-2(x-4.5)
.D. She should have subtracted the difference(x-4.5) from -2
. Emma’s equation does not correctly account for the subtraction of the difference
(x-4.5)
from
-2
The correct equation should be
6x = -2(x-4.5)
Complete question:
Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." She translated it as shown below 6x=-2x-4.5 What errors did Emma make? Select two options
A. She should have used division to represent the quotient of six and x.
B. She should not have included an equal sign.
C. She should have used parentheses to show that -2 is multiplied by (x-4.5).
D. She should have subtracted the difference (x-4.5) from -2.
E. She should have used parentheses to show that -2 is multiplied by (4.5-x).
During the 2005 football season, Team Tackle beat Team Sack by 5 points. If their combined scores totaled 89, find the individual team scores.
Solve the equation the square root of the quantity x minus 6 plus 2 equals 6 for the variable. Show each step please. Remember the X - 6 is under a square root sign
factor the trinomial x^2 - 16x +63
After 6 years, what is the total amount of a compound interest investment of $35,000 at 4% interest, compound quarterly?
Round to the nearest cent.
If w= the weight of trout. Which algebraic expression represents the phrase below?
Product means multiplication.
Given w= weight of a trout.
So, we need to convert "product of 16 and weight of trout: w " into an algebraic expression.
So, product of 16 and w can be written as 16*w or simply 16w.
Hence, B is the correct choice.
Answer:
B
Step-by-step explanation:
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A pizza parlor sold 38mc005-1.jpg pizzas during a dinner hour. If each pizza contained 8 slices, how many slices of pizza were sold?
The options are
38 pizzas times 8 slices each =
38 *8 = 304 slices total
A rectangle has length x+9 and width 2x-1 what are the areas of the rectangle
What would '6 meters to 60 meters' be in a ratio
Which graph represents the inequality y<−1+2x?
Karen's penny bank is 1/3 full. After she removes 240 pennies, it is 1/9 full. How many pennies can Karen's bank hold?
The difference between the bank being 1/3 and 1/9 full equals 240 pennies, so 1/9 of the bank's capacity equals 120 pennies. So, Karen's bank can hold a total of 1080 pennies.
Explanation:This is a mathematics problem dealing with fractions and subtraction. From the problem, we understand that after Karen removes 240 pennies, the bank is 1/9 full from previously being 1/3 full. So, the difference between 1/3 and 1/9, which is 2/9, accounts for the 240 pennies that were removed.
To find out the total capacity of the penny bank, you need to consider that 1/9 (the fraction representing the bank's fill level after removal of the 240 pennies) is equivalent to 120 pennies (half of 240, as 2/9 of the capacity is 240 pennies). This means that the total capacity of the bank (comparable to 9/9 of the fraction) is 120 pennies times 9, which equals to 1080 pennies.
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Doris put $4000 in a 2-year CD paying 6% interest, compounded monthly. After 2 years, she withdrew all her money. What was the amount of the withdrawal?
a. 4000.00
B. $4214.41
C. $4508.64
D. $4448.13
The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the measure of the third angle of the triangle is 35° more than three times the measure of either of the other two angles, find the measure of each angle of the triangle. (Recall that the sum of the measures of the angles of a triangle is 180°.)
The function f(x) is graphed on the coordinate plane. What is f(−4) ?
Explain how to write and evaluate an algebraic expression that represents the situation. The blueberries were divided equally into six bowls. Evaluate when b = 210.
The variable is the number of blueberries, the operation is division, and the constant is 6. Write the division expression as the fraction, b/6 . To evaluate, substitute 210 in for the variable, b, and simplify. 210 divided by 6 is 35. So each bowl has 35 blueberries.
The algebraic expression can be written in terms of the variable b and and evaluated as b/6 = 210/6 = 35
According to the question;
The blueberries were divided equally into six bowls;Hence, the algebraic expressions is;
b/6where, b = total number of blueberries
Hence, when b= 210
The number of blueberries in each bowl is; 210/6 = 35
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Jasmine has $15 dollars and saves $2.50 every month. Radha has $0 and saves $3.50 every month. Jasmine’s savings after x months can be represented by the function f(x) = 2.5x + 15. Radha’s savings after x months can be represented by the function g(x) = 3.5x. a. After how many months will they both have the same amount in savings? Find the values of x for which f(x) = g(x). b. Explain how to check your work. c. Explain what the graph of the two functions would look like.
2.5x+15 = 3.5x
subtract 2.5x from both sides
15 =x
15 months
Which ordered pairs lie on the graph of the exponential function f(x)=4(5)2x?
Select each correct answer.
(−1,4/25)
(0,0)
(1,4)
(2,2500)
Complete the equation of the line through (4,-8) and (8,5).
Use exact numbers.
y=_______ Topic:
Slope-intercept from two points.
The equation of the line that passes through (4, -8) and (8, 5) in slope intercept form is y = 13 / 4 x - 21
Slope intercept form of a lineThe slope intercept form of a line is represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
(4, -8) and (8, 5)
m = 5 + 8 / 8 - 4
m = 13 / 4
Therefore, using (8, 5)
5 = 13 / 4(8) + b
5 = 26 + b
b = 5 - 26
b = -21
Hence, the equation is as follows:
y = 13 / 4 x - 21
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