The absolute value equation used to solve this problem: | x - 82 | = 12, where x = grade.
What is an absolute value equation?A statement that contains an absolute value is known as an absolute value equation. The absolute value contains the variable of the equation.Now,
Given:
The average of grades = 82%Variation = 12%Let 'x' be the value that gives the value of grades.
The absolute value equation to find the grades will be given by: | x - 82 | = 12
=> x - 82 = ± 12
For maximum value of the grades, x - 82 = 12
=> x = 82 + 12
=> x = 94.
For minimum value of the grades, x - 82 = -12
=> x = 82 - 12
=> x = 70.
Hence, The absolute value equation used to solve this problem: | x - 82 | = 12, where x = grade.
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An octagon has all equal side lengths and angle measures. a point is at the center of the octagon. what is the smallest angle of rotational symmetry for the regular octagon? °
There is a regular octagon with n = 8 sides. The minimum rotational symmetry angle is,
= 360/n
= 360/8
= 45 degrees.
Rotating this amount does not change the regular octagon. The front and back look the same.
Suppose that we are given a regular polygon with N sides, the angles of rotational symmetry are:
A = n * 360° / N
where n can take values = 1, 2, N, and there are N different angles. It is the minimum rotational symmetry when n equals 1.
So, in this case,
A = 360 / N , R = 30°
And we want to find the number N.
30° = 360° / N
N = 360° / 30°
N = 12
This means that a regular polygon has 12 sides.
12 Upright Step by step:
360° ÷ 8 = 45°
8 because the octagon has 8 sides.
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Answer:
45 Degrees
Step-by-step explanation:
just answered <3
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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The inside of a flashlight surrounding the bulb is shaped like a parabola in which the base of the bulb represents the vertex and the top of the bulb represents the focus. Which of the following standard equations represents the parabola in which the base of the bulb is at (4, 6) and top of the bulb is at (4, 3)?
(x – 4)2 = –12(y – 6)
(x – 4)2 = –24(y – 6)
(x + 4)2 = 12(y + 6)
(x + 4)2 = 24(y + 6)
The standard equation which represents the parabola in which the base of the bulb is at (4, 6) and top of the bulb is at (4, 3) is: A. (x - 4)² = -12(y - 6).
How to determine the equation of a parabola?Mathematically, the standard equation with the vertex for any parabola that opens up and symmetric about the y-axis is given by:
(x - h)² = 4a(y - k)
where:
h and k represents the vertex.a is a point.In Geometry, the focus on the coordinate plane of a parabola is generally "n" units away from the vertex, and it's directly on the right side if it opens to the right or on the left side if it opens to the left.
Given the following data:
h = 4 and k = 6
a = 3 - 6 = -3
Substituting the given parameters into the formula, we have;
(x - h)² = 4a(y - k)
(x - 4)² = 4(-3)(y - 6)
(x - 4)² = -12(y - 6)
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Isaac deposits $2,500 into an account that pays 4.75% interest
compounding continuously. How long will it take to double his
initial investment? Show all work for full credit and round your
answer to two decimal places.
Answer:
14.59
Step-by-step explanation:
The key words in this problem is that you are compounding continuously, so that would be a equals p e to the r t power to show you that formula, and so when it says you have 2500 in the account e to the .4 excuse me, 0.0475 t Power is equal to, it says, doubling the investment, and so you just have to think about your doubling the investment you're going to take 2500 times to do it. The first thing i would do, then, is to divide the 2500 over which actually cancels out this 2500 point so you're. Looking at e to the .0475 t, power is equal to 2 right, 4.75 percent, so to solve for t want to natural log, both sides- i forgot my t in there so to solve for t natural log of 2 divided by 0475, so it takes about 14.593 Years or, however, you're supposed around it says: 2 decimals soul be 14.59
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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To pass a test in a water safety course, a student must get 80% of the questions
correct. There are 90 questions on the test. How many questions must a student
answer correctly to pass the test?
The student should answer 72 questions correctly to pass the test.
What is the percentage?Percentages are basically fractions with a denominator of 100. We use the percent symbol (%) besides a number to indicate that it is a percentage. For instance, if you answered 75 questions correctly out of 100 on a test (75/100), you would have received a 75%.So, a number of correct questions for 80%:
90/100 × 800.90 × 80= 72Therefore, 72 questions must a student answer correctly to pass the test
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Simplify each sum or difference. State any restrictions on the variables.
1 / x² - 4 + 6 / x+2
The simplification of difference of the given two rational expressions [tex]\frac{1}{x^{2} -4}+\frac{6}{x+2}[/tex] is equal to (6x-11)/ (x-2)(x+2).Restriction on the variables is given by x≠ -2, x≠ 2.
As given in the question,
Given expression is [tex]\frac{1}{x^{2} -4}+\frac{6}{x+2}[/tex]
Simplify the given two rational expressions by factorizing them,
[tex]\frac{1}{x^{2} -4}+\frac{6}{x+2}\\\\= \frac{1}{(x-2)(x+2)}+\frac{6}{x+2}\\\\= \frac{1+6(x-2)}{(x-2)(x+2)}\\\\= \frac{1+6x-12}{(x-2)(x+2)}\\\\= \frac{(6x-11)}{(x-2)(x+2)}[/tex]
Restriction on the variables is given by x≠ -2, x≠2.
Therefore, the simplification of difference of the given two rational expressions [tex]\frac{1}{x^{2} -4}+\frac{6}{x+2}[/tex] is equal to (6x-11)/ (x-2)(x+2). Restriction on the variables is given by x≠ -2, x≠ 2.
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Solve the following math problem I. Picture pls
Answer:
the answer is null in other words you cant
Step-by-step explanation:
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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Jerry has 4 2/3 cups of strawberries. He uses 2/12 cups of strawberries to make a breakfast smoothie. Jerry wants to use the remaining strawberries to make pancakes. If it takes 1 1/12 cups of strawberries to make one pancake, how many pancakes can he make?
Using simple fraction, Jerry can make 4 pancakes using the left strawberries.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.
Strawberries that Jerry has = 4 2/3 = 14/3cups
Strawberries used to make breakfast smoothies = 2/12cups
Left strawberries = 14/3 - 2/12
= 56 - 2 /12
= 54/12
Jerry uses cups to make pancake = 54/12 / 13 / 12
= 4 pancakes
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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:
The height of a golf ball hit into the air is modeled by the equation \large h=-16t^2+48t, where \large hrepresents the height, if feet, and \large t represents the number of seconds that have passed since the ball was hit.
What is the height of the ball after 2 seconds?
a
80 feet
b
16 feet
c
64 feet
d
32 feet
Answer:
32 feet.
Step-by-step explanation:
If t is the time in seconds and the problem asks us what the height is after 2 seconds, then that would mean t = 2.
So, now we can substitute 2 for t and solve.
-16 × 2² + 48 ×2
-16 × 4 + 96
-64 + 96
= 32 ft.
Hope this helps!
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 4 grams and the amount of gold in each necklace is 20 grams. The jeweler made a total of 14 bracelets and necklaces using 120 grams of gold. Graphically solve a system of equations in order to determine the number of bracelets made, x,x, and the number of necklaces made, y.
The number of bracelets will be 10 and the number of necklaces will be 4.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A predetermined quantity of gold was available to a jeweler to create bracelets and necklaces. Each bracelet has 4 grams of gold, and each necklace contains 20 grams of gold. The jeweler used 120 grams of gold to create a total of 14 bracelets and necklaces.
Let x be the number of bracelets and y be the number of necklaces. Then the equation will be
x + y = 14 ...1
4x + 20y = 120 ...2
From equations 1 and 2, then we have
4x + 20(14 - x) = 120
4x - 20x + 280 = 120
16x = 160
x = 10
Then the value of y will be
10 + y = 14
y = 14 - 10
y = 4
Thus, the number of bracelets will be 10 and the number of necklaces will be 4.
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I need to find the angle measure and am not sure how to
Answer: 13. m<TEA=58 degrees
14. m<TEF=37 degrees
Step-by-step explanation:
TEA=FEA+TEF ==> Angles FEA and TEF make up angle TEA
FEA=TEF ==> TEA was bisected to form FEA and TEF, so FEA and TEF are equal since the line EF has an equal distance from lines ET and EA.
13.
TEA=FEA+FEA
TEA=29+29
TEA=58
m<TEA=58 degrees
14. TEA=TEF+TEF
74=2 * TEF
74/2=TEF
TEF=37
m<TEF=37 degrees
How to graph of a piecewise function.
The required equations are y = -10, y = 3x / 2 + 21/ 2 and y = x /5 - 58/5.
The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.
Here,
For the line present at the left and third quarter is y = 3x / 2 + 21 / 2
For the horizontal curve, the equation is y = -10,
For the line in the fourth quadrant, the equation is y = x / 5 - 58/ 5.
Thus, the required equations are y = -10, y = 3x / 2 + 21/ 2 and y = x /5 - 58/5.
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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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find the volume of a sphere
Answer:
the volume of the sphere is 1436.76
HELP SSP SHOW UR WORK WILL BRAINLEST SND 10 points
Answer: number 1. 4 number2. 7
Step-by-step explanation:
I hope this helps!
Answer:
Step-by-step explanation:
1. Given
Jordan paid $550
from $550 $240 is for the parts
he paid $65 per hour
so 550-240
= 310
then if
1 hour = $65
? =$310
310*1/65
=4.76 hour
final answer for first question is 4.76 hour
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.
solve the expression
[tex]4( {3}^{3} - 7) \div 10[/tex]
The solution of the given expression is fraction 4/5.
What is square of a number?The result of multiplying an integer by the same integer is recognised as a square number.
A square number is essentially a number formed by the product of 2 identical numbers. The area of a square to 'n' as the length equal (in which n is an integer) is the clearest illustration of a square number in geometry.Square numbers always have the digits 0, 1, 4, 5, 6, and 9 at the end. For instance, 25, 49, 81, 100, and so on are perfect square numbers, whereas 37, 48, 22, and so on are not.A square number always has an even number of zeros just at end. This means that if a number ends with an odd number of zeros, it is not a square number.The given expression is;
= 4(3² - 7)/10
we know that 3² = 3x3 = 9, put the value;
= 4(9 - 7)/10
= 8/10
Divide both numerator and denominator by 2.
= 4/5
Thus, the obtained expression is 4/5.
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Derlene,vonzell,eric, and daimond went to the mall.Darlene spents $45,vozell spents $57 and eric spents $22.If altogether they spent $144,how much did diamond spent
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
How to solve with elimination
Solutions are different there 3 pictures click on one picture and there they will give a solution
Step-by-step explanation:
Good luck
Find each difference.
2(2/3) - 7(1/3)
The answer is - 14/3.
How to find the difference?The outcome of subtracting one number from another is difference.
The quantity difference between two numbers is what it alludes to.
Given,
2(2/3) - 7(1/3)
Solution:
2(2/3) - 7(1/3) = 8/3 - 22/3
= - 14/3
The answer is - 14/3.
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degree of monomial 2a^6b^3
Answer:
6th degree monomial
Step-by-step explanation:
The highest exponent is 6. Therefore, the monomial is a 6th degree monomial.
Hope this helps!
Please mark as brainliest if correct!
Have a great day!
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.
X intercept of y=10x+8
Answer:
this will look like
x= y + 4
__ __
10 5
the / are over so y on top of 10 and 4 over 5
Find the value of each variable
Answer:
x = 22, y = 12.
Step-by-step explanation:
5x + 4 = 114 (opposite angles).
5x + 4 + 3x - 24 + 2y = 180 (adjacent angles are supplementary)
From first equation:
5x = 110
x = 22.
Substituting for x in the second equation:
114 + 3(22) - 24 + 2y = 180
2y = 180 - 114 - 66 + 24
2y = 24
y = 12.
Find the ninth and tenth terms of each arithmetic sequence. 1,8,15,22, . . . .
The ninth and tenth term of the given arithmetic progression are: 57, 64.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.Given: 1, 8, 15, 22 (AP)
Here, a₁ = 1, d = 8-1 = 15 - 8 = 22 - 15 = 7
Thus, in the formula: [tex]a_n=a_1+(n-1)d[/tex],
For n = 9, a₉ = 1 + 8(7) = 57
For n =10, a₁₀ = 1 + 9(7) = 64.
Hence, The ninth and tenth term of the given arithmetic progression are: 57, 64.
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Michelle wants to buy a new 256 GB iPhone 11 that costs $849. She has $200 in savings and needs to earn the rest. If Michelle currently works at Subway and earns $12.50 per hour, which equation best represents this scenario?
