x=567
Step-by-step explanation:
Each side of an equilateral triangle is 4 m shorter than twice the length of each side of a square. Their perimeters. are the same. How long is each side of the triangle?
Answer: 8m
Step-by-step explanation:
Find the indicated term of each arithmetic sequence. a₁ =k+7, d=2 k-5 ; a₁₁
The value of term a11 is 21k - 43.
How to find the value of term a9?The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.
The formula of Arithmetic progression is
a(n) = a1 + (n - 1)d
given that the term of arithmetic sequence and common difference,
a1 = k+7 and d = 2k-5.
now find the value of term a11.
a(n) = a1 + (n - 1)d
now, substitute a(n) = a11, a1 = k+7, d = 2k-5.
a11 = k+7 + (11 - 1)(2k-5)
a11 = k + 7 + 10(2k-5)
a11 = k +7+ 20k - 50
a11 = 21k - 43
Hence,The value of term a11 is 21k - 43.
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The mean test score of 10 students is 50 marks.
A student joins the class.
The mean of all 11 students is now 55 marks.
Find the test score of the student who joined the class.
Answer:
105.
Step-by-step explanation:
Total score for 10 students = 50 * 10 = 500.
When 1 student joins:
mean score = (500 + x) / 11 = 55 where x is the test score of the new student.
500 + x = 55 * 11
x = 55*11 - 500
= 605 - 500
= 105.
In the given case , we can conclude The test score of the student who joined the class is 105 marks.
Let's solve this problem step by step:
The mean test score of the first 10 students is 50 marks. Therefore, the total marks scored by these 10 students is 10 x 50 = 500 marks.
When the new student joins, the mean score of all 11 students becomes 55 marks.
Therefore, the total marks scored by all 11 students is 11 x 55 = 605 marks.
To find the test score of the new student, we subtract the total marks of the first 10 students from the total marks of all 11 students: 605 - 500 = 105 marks.
Therefore, the test score of the student who joined the class is 105 marks.
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Find the coordinates of the midpoint of a segment with the given endpoints. A(-28,8), C(-10,2)
The coordinates of the midpoint of a segment with the given endpoints will be (-19, 5).
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoints are A(-28, 8) and C(-10, 2).
Then the coordinates of the midpoint of a segment with the given endpoints will be
(x, y) = [(-28 - 10) / 2, (8 + 2) / 2]
(x, y) = (-38/2, 10/2)
(x, y) = (-19, 5)
The coordinates of the midpoint of a segment with the given endpoints will be (-19, 5).
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At a football stadium, 5% of the fans in attendance were teenagers. If there were 260 teenagers at the football stadium, what was the total number of people at the stadium?
Answer:
5200 people
Step-by-step explanation:
1. Divide 100 by 5 (How many sets of 5 are there in 100)
100/5 = 20
2. Multiply 260 by 20 (To find the number of people, you need to find 100%)
260*20 = 5200
Answer:
5200
Step-by-step explanation:
URGENTTT ! PLEASE HELP :(((
1. 9miles
2. 6miles
3. 3miles
Prove that the expression x^2 +2x+2 can only have positive values
See below for the proof that the expression x^2 +2x+2 can only have positive values
How to prove that the expression x^2 +2x+2 can only have positive valuesThe expression is given as
x^2 + 2x + 2
The above expression is a quadratic expression
A quadratic expression is represented as
ax^2 + bx + c
Where the discriminant (d) is
d = b^2 - 4ac
So, we have
d = 2^2 - 4 * 1 * 2
Evaluate
d = -4
Because d is negative, it means that the expression has only complex roots
Quadratic expressions that have only complex roots can only have positive values
Hence, the expression x^2 +2x+2 can only have positive values
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What's total amount of rope that extends to the two stakes supporting tree in trigonometry?
According to the question, the total amount of rope needed to extend the two stakes supporting the tree in trigonometry can be determined by using the functions sine and cosine.
Explain trigonometric function with example.
If the rope can be tied with the tree trunk then the staked rope makes an angle with respect to the ground. And it can be calculated with the help of the trigonometric functions. And it states that the ratio of the length of the opposite sides and the hypotenuse of the right angle triangle. And the result of the ratio is sine function.
Therefore, the total amount of two ropes needed so that it extends to the two stakes of the supporting trees.
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SAT/ACT The sum of three consecutive integers is -48 . What is the least of the three integers?
A -15
B -16
C -17
D -18
E -19
The sum of three consecutive integers is -48 then the least of the three integers is -16.
What is meant by consecutive numbers?Consecutive numbers are numbers that follow each other in descending order from smallest to largest.
Consecutive numbers are those that come after each other in descending order from the smallest to the largest. The difference between consecutive numbers is always fixed and follows a predictable pattern.
The numbers are x-1, x, and x+1.
(x-1) + (x) + (x+1) = -48
simplifying the above equation, we get
x - 1 + x + x + 1 = -48
x + x + x + 1 - 1 = -48
3x + 1 - 1 = -48
3x = -48
Dividing throughout by 3, we get
x/3 = -48/3
x = -16
The value of x = -16.
The sum of three consecutive integers is -48 then the least of the three integers is -16.
Therefore, the correct answer is option B. -16.
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Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
==================================================
Explanation:
We need to divide both sides by -2 to fully isolate x.
Dividing both sides by a negative number will flip the inequality sign
We go from -6 < -2x to 3 > x
Then we flip 3 > x to x < 3 which is choice C
-----------------
A slightly longer approach:
-6 < -2x
-6+2x < 0 .... add 2x to both sides
2x < 6 .... add 6 to both sides
2x/2 < 6/2 .... divide both sides by 2
x < 3
We get the same answer as the previous section. It helps show why the sign flip happened when dividing both sides by a negative number.
HELP ITS URGENT! AND HAVE A GOOD DAY
PLEASE ANSWER CORRECTLY Finding the initial amount and rate of change given a table for a linear function
The initial amount and rate of change given a table for a linear function are $1160 and -$30, respectively
How to find the initial amount and rate of change given a table for a linear function?The table of linear function represents the given parameter
On the table, we have the following points
(x, y) = (6, 980) and (12, 800)
The rate of change is calculated as
Rate = (y2 - y1)/(x2 - x1)
So, we have
Rate = (980 - 800)/(6 - 12)
Evaluate
Rate = -30
This means that the rate of change is -$22.5
The initial amount is calculated as
y = m(x - x1) + y1
Where
m = -30
So, we have
y = -30(x - x1) + y1
Using one of the points, we have
y = -30(x - 6) + 980
Set x = 0
So, we have
y = -30(0 - 6) + 980
Evaluate
y = 1160
Hence, the initial amount and rate of change given a table for a linear function are $1160 and -$30, respectively
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For every $2 that Miguel saves his parents give him $4 if Miguel saves $60 how much money will his parents give him
Determine whether the polygons are always, sometimes, or never similar. Explain your reasoning. (Lesson 7-2)
A right triangle and an isosceles triangle
Given polygons a right triangle and an isosceles triangle sometimes be similar.
As given ,
Given polygons : A right triangle and isosceles triangle.
Polygon a right triangle and isosceles triangle never be similar.
Reason:
A right triangle is a triangle with one of the angle equals to 90 degree.A right triangle can be isosceles if and only if two acute angles are congruent to each other.If a right triangle is isosceles then they are similar.Through the transformation of dilation one can map one triangle onto others.Therefore, given polygons a right triangle and an isosceles triangle sometimes be similar.
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Select the correct answer.
The length of a rectangle is 3 meters more than the width. The perimeter of the rectangle is 26 meters. If the width is b, which equation represents the situation? How many solutions will this equation have?
Answer Choices:
A. (b + 3)(b) = 26, which has one solution
B. 2(b + 3) + 2b = 26, which has infinitely many solutions
C. 2[(b + 3) + b] = 26, which has one solution
D. 2[(b + 3) + b] = 26, which has no solution
The equation which represents the situation is 2[(b + 3) + b] = 26 and the equation has one solution.
The correct answer option from above is option C
What is meant by the perimeter of rectangle?The perimeter of a rectangle is the addition of all the sides of the rectangle, that is, the addition of the two length and two width.
Width of the rectangle = bLength of the rectangle = (b + 3)Perimeter of the rectangle = 26 metersPerimeter of the rectangle = 2(length + width)
26 = 2{(b + 3) + b}
26 = 2(b + 3 + b)
26 = 2(2b + 3)
open parenthesis26 = 4b + 6
Then substract 6 from both sides26 - 6 = 4b
20 = 4b
b = 20/4
b = 5
Width of the rectangle = b
= 5 meters
Length of the rectangle = (b + 3)
= (5 + 3)
= 8 meters
So therefore, length and width of the rectangle given the perimeter is 8 meters and 5 meters respectively.
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Evaluate each expression for the given values of the variables.
4a+7b+3 a-2 b+2 a ; a=-5 and b=3
The result of the expression 4a+7b+3a-2b+2a for the variables a= -5 and b= 3 is -30
Given,
The algebraic expression = 4a+7b+3a-2b+2a
Rearrange the terms
=4a+3a+2a+7b-2b
Combine the like terms
=9a+5b
We know
a= -5
b= 3
Substitute the values in the expression
9(-5)+5(3)= -45+15
=-30
Hence, the result of the expression 4a+7b+3a-2b+2a for the variables a= -5 and b= 3 is -30
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a $5000
How much interest is earned an
depus it at 4.5% interest over 6 Years?
4.5
= 0.045
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (5000)(0.045)(6) \implies I = 1350[/tex]
can someone help to solve this question?
Using a system of equations, the prices are given as follows:
Reference: RM15.Exercise: RM9.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Cost of a reference book.Variable y: Cost of an exercise book.3 reference and 2 exercise cost RM63, hence:
3x + 2y = 63.
5 reference and 3 exercise cost RM102, hence:
5x + 3y = 102.
Multiplying the first equation by 3 and the second by -2, we have that:
9x + 6y = 189.-10x - 6y = -204.Adding them:
-x = -15 -> x = 15.
Hence:
3(15) + 2y = 63
2y = 18.
y = 9.
Hence the costs are:
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3. For the sequence
60, 90, 135, 202.5 ...
A. Find the next term (write your answer as a decimal):
B. Is the sequence arithmetic or geometric?
C. Write a recursive function for the sequence.
a. The next term in the sequence is 303.75.
b. The sequence is a geometric sequence.
c. The recursive function for the sequence is: aₙ = aₙ₋₁ (1.5) for n≥2.
Given the sequence is : 60,90,135,202.5,....
a. the next term in the sequence is:
Find the common ratio by dividing any term in the sequence by the term that comes before it:
a₂/a₁ = 90/60 = 1.5
a₃/a₂ = 135/90 = 1.5
a₄/a₃ = 202.5/135 = 1.5
The common ratio (r) of the sequence is constant and equals the quotient of two consecutive terms.
r = 1.5
find the sum:
To find the sum of the series, plug the first term: a = 60, the common ratio(r): 1.5 and the number of elements n = 4 into the geometric series sum formula:
Sₙ = a(1₋rⁿ/1₋r)
Sₙ = 60(1 ₋ 1.5⁴/1₋1.5)
Sₙ = 60(1 ₋ 5.0625/1₋1.5)
S₄ = 60(8.125)
S₄ = 478.5
To find the general form of the series, plug the first term:
aₙ = 60×1.5ⁿ⁻¹
use the general form to find the next term:
a₁ = 60
a₂ = a₁rⁿ⁻¹ = 60(1.5)¹ = 90
a₃ = a₁rⁿ⁻¹ = 60(1.5)² = 135
a₄ = a₁rⁿ⁻¹ = 60(1.5)³ = 202.5
a₄ = a₁rⁿ⁻¹ = 60(1.5)⁴ = 303.75
hence the required next term is 303.75
(b) The above sequence is geometric sequence.
(c) recursive function for the sequence : aₙ = aₙ₋₁ (1.5) for n≥2.
Hence we get the required answers.
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If K is the midpoint of JL, JK=8x+11 and KL=14x-1, find JL.
Given that K is the midpoint on segment JL, the numerical value of segment JL is 54.
What is the numerical value of segment JL?A midpoint is simply a point that divides a segment into two equal halves.
Given the data in the question;
K is the midpoint on segment JLSegment JK = 8x + 11 Segment KL= 14x - 1Numerical value of segment JL = ?Given that K is the midpoint on segment JL, this means segment JK is divided into two equal halves, Segment JK is equal to Segment KL.
Segment JK = Segment KL
8x + 11 = 14x - 1
Collect like terms
8x - 14x = -1 - 11
-6x = -12
x = -12/-6
x = 2
Hence, the numerical values of Segment JK and Segment KL will be;
Segment JK = 8x + 11 = 8(2) + 11 = 16 + 11 = 27
Segment KL = 14x - 1 = 14(2) - 1 = 28 - 1 = 27
Since Segment JK and Segment KL makes up segment JL, the numerical value of Segment JL is the sum of Segment JK and Segment KL.
Segment JL = 27 + 27 = 54
Given that K is the midpoint on segment JL, the numerical value of segment JL is 54.
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Help Please
A garden is in the shape of a square with a perimeter of 68 feet. The garden is surrounded by two fences. One fence is around the perimeter of the garden, whereas the second fence is 2 feet from the first fence on the outside. If the material used to build the two fences is $1.31per foot, what was the total cost of the fences? It costs $____ to build the fences.
Answer:
Step-by-step explanation:
68 / 4 = 17 = length or width (because it is a square both are the same)
19 + 2 = 19
4(19) = 76 (perimeter of outer fence)
68(1.31) + 76(1.31) = $188.64
Help Please
A 30-foot ladder is leaning against a building. The base of the ladder is 18feet from the side of the building. How high does the ladder reach along the side of the building? The ladder reaches _____ feet high on the building.
Answer:
Step-by-step explanation:
a² + b² = c²
18² + b² = 30²
324 + b² = 900
b² = 576
b = 24
Answer: 24
Step-by-step explanation: you use the formula: a^2 + b^2 = c^2. If you drew a picture, it would form a triangle with 30 as the length of the hypotonuse, and 18 as one of the legs. This given, we would have a^2 + 18^2 = 30^2 (hypotonuse = c) Then, solve.
Sophie spends a winter day recording the temperature once every three hours for
science class. At 9 am, the temperature was -1.7°F. Between 9am and noon, the
temperature increased by 18.1°F. Between noon and 3pm, the temperature increased
by 14.8°F. Between 3pm and 6pm, the temperature dropped 14.6°F. What was the
temperature at 6pm?
The temperature at 6pm based on the information will be 16.6°F.
How to illustrate the information?From the information, at 9 am, the temperature was -1.7°F, between 9am and noon, the.temperature increased by 18.1°F, between noon and 3pm, the temperature increased by 14.8°F and between 3pm and 6pm, the temperature dropped 14.6°F.
Therefore, the temperature at 6pm will be:
= -1.7°F + 18.1°F + 14.8°F - 14.6°F
= 16.6°F.
Therefore, the temperature at 6pm based on the information will be 16.6°F.
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Simplify each expression. 2x + 3y - 5x + 2y
Answer: −
3
x
+
5
y
Step-by-step explanation:
your bank gives you 50 points for monthly online bill pay, 50 points for monthly mobile deposits, 100 points per car payment, and 1.5 points per dollar credit card spent. You had monthly credit card charges of $1,400 last month. You earn $75 per 10,000 points. How much in dollars did you earn from points last month?
a) $17.25
b) $23.50
c) $75.00
d) $200.00
The amount that you earned last month would be the total of $17.25
How to solve for the earningWe have the following data
online pay bill per month = 50
The monthly online deposit = 50
The points that are made per car payment = 100
The point that is made per credit card = 1.5 points
The monthly credit card charges of $1,400
The monthly point would be 1400 * 1.5 = $2100
We have to solve for the total points
= 50 + 50 + 100 + 2100
= 2300
We have $75 per 10,000
For 2300 points, this would be 75/10000 * 2300
= $17.25
Hence the amount that is made in dollars from the points in the last month is $17.25
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Please answer best answer = brainliest
(a) A = 1/2 (bh)
(b) b = P/R
(c) 8?
Suppose you work for a packaging company and are designing a box that has a rectangular bottom with a perimeter of 36 cm . The box must be 4cm high. What dimensions give the maximum volume?
b. What information can you get from the function to find the maximum volume?
The dimension that give the maximum volume will be the sides.
The volume will be 324cm³.
How to calculate the value?It should be noted that the maximum value is when the rectangle is a square.
Let s be the side of the square.
The perimeter will be 4s.
Solving for s:
= 36/4
= 9cm
It should be noted that area = s²
where s = side
= 9² = 81cm
Therefore, the volume will be
= Area × Side
= 81 × 4
= 324cm³
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Write a two-column proof.
Given: MN ≅ PN, LM ≅ LP
Prove: ∠ L N M ≅ ∠ L N P
SSS postulate of congruence, to prove ∠ L N M ≅ ∠ L N P.
What do you mean by congruent?
Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.In triangles MLN and PLN,
MN ≅ PN,
LM ≅ LP
To prove :
Δ MLN ≅ Δ PLN
Statement Reason
1. LN ≅ LN 1. Common segment
2. MN ≅ PN; 2. Given
LM ≅ LP
3. Δ MLN ≅ Δ PLN 3. SSS postulate of congruence,
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2 3/4 divded by 5/6 , 1 1/3 divded by 1/4 , 2/5 divded by 1 2/5, 5/7 divded by 3 1/5 , 2 2/7 divded by 2 2/7 . PLEASEEE HELP ME IF ANYONE IS WILLING TO HELP ME COMPLETE ALL MY ASSINGMENTS PLS ADD AND MESSAGE ME THNX
Answer:
2 3/4 divided by 5/6 = 3 3/10
1 1/3 divided by 1/4 = 5 1/3
2/5 divided by 1 2/5 = 2/7
5/7 divided by 3 1/5 = 25/112
2 2/7 divided by 2 2/7 = 1
find the volume of a sphere
Answer:
the volume of the sphere is 1436.76
