The number of problems which Darren must correct each week according to the task content is; 900 corrections.
How many corrections must Darren provide?Since it follows from the task content that; the class contains 25 students, each who are each given 3 assignments per week consistent of 12 problems.
On this note, the number of problems he must correct since the homework is assigned distinctly to each student, the number of problems which he must correct is;
= 25 × 12 × 3
= 900 corrections.
However, if the assignment is same for all students; the number of corrections is;
= 12 × 3 = 36 corrections.
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The area of rectangle A is bigger than the area of rectangle B
Work out the lowest possible integer value of x.
A=
2x-3
5 cm
B
3 cm
X+2
The lowest possible integer value of x is 3 such that (x ≥ 3).
What is referred as the inequalities?An inequality depicts the relationship between two non-equal values in such an algebraic expression. Inequality symbols can indicate that one of the two variables is greater than, greater or equal to, equal to some other value.For the given question;
The area of rectangle A is bigger than the area of rectangle B.
The sides of the rectangle A are 2x-3 and 5 cm.
Area = length×breadth
Area A = (2x - 3)(5)
Area A = 10x - 15
The sides of the rectangle B are x = 2 and 3 cm.
Area = length×breadth
Area B = (x + 2)3
Area B = 3x + 6
As area B > area B
Then,
10x - 15 ≥ 3x + 6
Solving the inequality;
10x - 3x ≥ 6 + 15
7x ≥ 21
x ≥ 3
Thus, the minimum value of the x is 3 to make the area A bigger than Area B.
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What equation/inequality represents the following scenario? Product of two consecutive odd integers is less than 76, where b is the first odd integer
a) n(n+2)> with a line under 76
b) n(n+1)>76
c) n(n+1)<76
d) n(n+2)<76
The two consecutive odd integers are less than 76 is the numbers are 37 and 39.
Any integer's reverse and sum are both equal to zero.
A positive sum results from adding two positive numbers, whereas a negative sum results from adding two negative integers.
Take the absolute value of each integer, then subtraction, to obtain the total of a positive and a negative integer.
Let two consecutive odd numbers be x and x+2
According to question
⇒ x........... equation (1)
⇒ x+2........equation (2)
by adding equation 1 and 2
⇒ x+x+2=76
⇒ 2x+2=76
⇒ 2x=76-2
⇒ 2x=74
⇒ x=74/2
⇒ x=37
We apply the value of x=37 in equation (2)
⇒ x+2
⇒ 37+2
⇒ 39
so, the numbers are 37 and 39.
Therefore, the two consecutive odd integers are less than 76 is the numbers are 37 and 39
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MATH HELP
PART 2 since the first one was to blurry
Using a system of equations, it is found that there were a total of 825,000 Arabic speakers, and the diagram is completed as follows:
Larger part: 639,000.Smaller part: 825,000 - 639,000 = 186,000.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the variables are given as follows, considering the situation described:
Variable f: number of French Creole speakers.Variable a: number of Arabic speakers.There were 639,000 French Creole speakers, hence:
f = 639,000.
There were 186,000 more Arabic speakers than French Creole speakers, hence:
a = 186,000 + f = 186,000 + 639,000 = 825,000.
There were a total of 825,000 Arabic speakers, and the diagram is completed as follows:
Larger part: 639,000.Smaller part: 825,000 - 639,000 = 186,000.More can be learned about a system of equations at https://brainly.com/question/24342899
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Solve each equation. Check each solution. y/5 + y/2 = 7
The solution of the above equation y/5 + y/2 = 7 for y is 10.
According to the given question.
We have an equation y/5 + y/2 = 7.
Since, we have to solve the above equation y/5 + y/2 = 7 for y.
Therefore, the solution of the above equation for the above equation y/5 + y/2 = 7 is given by
y/5 + y/2 = 7
⇒ (2y + 5y)/10 = 7
⇒ 7y /10 = 7
⇒ 7y = 70
⇒ y = 70/7
⇒ y = 10
Hence, the solution of the above equation y/5 + y/2 = 7 for y is 10.
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Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
B(√3, 2,2√2) and C(-2√3, 4,4√2)
The midpoint is at ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])
In the given statement is
To find the midpoint of the line segment joining the pair of points
B(√3, 2,2√2) and C(-2√3, 4,4√2)
Midpoint:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
m = (A +B)/2
If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2} ,[/tex] )
where:
(x1 , y1 ,z1) are the coordinates of the first point:
(x2 , y2 , z2) are the coordinates of the second point:
Now, We are given the three points B(√3, 2,2√2) and C(-2√3, 4,4√2)
Solving for the midpoint , we have,
m = ([tex]\frac{\sqrt{3}+(-2\sqrt{3} ) }{2}, \ \frac{2+4}{2}, \frac{2\sqrt{2} +4\sqrt{2} }{2}[/tex])
m = [tex]\frac{-2\sqrt{3} }{2} ,\frac{6}{2},\frac{6\sqrt{2} }{2}[/tex]
m = ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])
Therefore, the midpoint is at( [tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])
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-3y + 2x = -7
8x - 3y = -1
Answer: If you're solving for the substitution method then your answer would be (1,3)
Step-by-step explanation:
Answer:
x = -4/5
y = 9/5
Step-by-step explanation:
-3y + 2x = -7
8x - 3y = -1
make one of the equations y=....
-3y + 2x = -7
-3y = -7 - 2x
y = (-7 - 2x)/3
now put (-7 - 2x)/3 where y is in the other equation
8x - 3y = -1
8x - 3((-7 - 2x)/3) = -1
8x - 1*(-7 - 2x) = -1
8x + 7 + 2x = -1
solve for x
8x + 7 + 2x = -1
8x+2x = -8
10x = -8
x = -8/10
x = -4/5
now put -8/10 in one of the equations to get what y is
-3y + 2x = -7
-3y + 2(-8/10) = -7
-3y - 16/10 = -7
-3y = -7 + 16/10
-3y = -70/10 + 16/10
-3y = -54/10
y = -54/10 * -1/3
y = 18/10
y = 9/5
Pre Algebra 1/10+x=1/5 view attachment for more
Answer:Your answer would be x=1/10
Step-by-step explanation:
Below are graphs of functions over the interval [-4, 4]. Find the following for each function:
The domain
Zeros of the function
Intervals where the function is positive and intervals where it is negative
The positive interval is (0,2) and the negative range is calculated as (-4,0) and (2,4).
A graph is used to show the relationship between variables on a coordinate plane.
The domain of the function is [-4,4].
The zeros are: -2,0 and 2.
The positive interval is between (0,2).
The range of negative values is (-4,0) to (2,4). This is the set of x values in the graph. The graph demonstrates that the x value is between -4 and 4.
Thus, the domain is [-4,4]. The zeros of the function: Where it crosses the x- axis. The graph touches the x-axis when it is at -2,0 and 2. As a result, the function has the following zeros:-2,0 and 2.
Positive interval:
On the graph, positive values range from x = 0 to x = 2.
Consequently, the positive interval is (0,2).
Negative duration:
This is the x values when the function gives a negative result.
The graph shows negative values from x = -4 to x = 0, then from x = 2 to x = 4.
The negative range is therefore (-4,0) and (2,4).
Hence, the positive interval is (0,2) and the negative range is (-4,0) and (2,4).
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a 12 pound can of lemonade cost 1.32 how much would a 16 ounce can of lemonade cost? please tell me the answer I need to get this right thx xo
Answer:
1.76.
Step-by-step explanation:
1.32 ÷ 12 = 0.11
16 x 0.11 = 1.76.
Hope this helped! ..・ヾ(。＞＜)シ xx
Use the Distance Formula to find the distance between the pair of points.
A(0,0), B(15,20)
Using the distance formula, the distance between the pair of points A(0,0) and B(15,20) is 25 units
Given,
The points = A(0,0) and B(15,20)
We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Substitute the values in the equation
The distance = [tex]\sqrt{(15-0)^{2}-(20-0)^{2} }[/tex]
[tex]=\sqrt{15^{2}+20^{2} } \\=\sqrt{225+400}\\ =\sqrt{625}[/tex]
=25 units
Hence, using the distance formula, the distance between the pair of points A(0,0) and B(15,20) is 25 units.
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Determine whether the sequence converges or diverges. if it converges, find the limit. if it diverges write none. a_n = (9 3 n**2)/(n 8 n**2)
According to the question, determine whether the given sequence converges or diverges.
The given sequence is: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} }[/tex]
Taking limits tends to infinity on both sides. And dividing numerator and denominator by [tex]n^{2}[/tex]
Therefore, the final term can be re-written as: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} } = \frac{3}{8}[/tex].
Hence, the given sequence converges and the limit is [tex]\frac{3}{8}[/tex].
What converges and diverges in limits?
When the limits of the sequence exist and have finite value that means the sequence is a convergent sequence. The calculated value is a real number. And the tem divergence means limits do not exist.
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can someone please help me
Answer:
It's B
Step-by-step explanation:
Step-by-step explanation:
[tex]\displaystyle\\12-15x > 22\\12-15x+15x > 22+15x\\12 > 22+15x\\12-22 > 22+15x-22\\-10 > 15x\\Divide\ both\ parts\ of \ the \ equation\ by\ 15:\\-\frac{10}{15} > x\\\\-\frac{5*2}{5*3} > x\\\\-\frac{2}{3} > x \\\\Thus,\\\\x < \frac{-2}{3}[/tex]
Answer: A
[tex]\displaystyle\\4\leq 3x+10 < 19\\\\4-10\leq 3x+10-10 < 19-10\\\\-6\leq 3x < 9\\\\Divide\ the\ inequality\ by \ 3:\\\\-2\leq x < 3\\\\Answer:\ -2\leq x < 3[/tex]
Determine whether each relation is a function. (3,9),(11,21),(121,34),(34,1),(23,45)
Domain - { 3, 11, 121, 34 , 23 , } is domain of each relation is a function.
What is domain and range ?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.How are the domain and range determined?
In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).Domain - { 3, 11, 121, 34 , 23 , }
Range - { 9, 21 , 34 , 1 , 45 }
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Use square roots to solve the equation x2 = –100 over the complex numbers. Select any solutions that apply.
The solution using the square root property for given complex numbers would be x = 10i where i is an imaginary number.
What is a complex number?A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib,
where a, and b are real numbers and i is an imaginary number.
We have been given the equation of complex numbers x² = -100
Using the square roots property to solve the above equation
⇒ x² = -100
⇒ x = √-100
⇒ x = √(-1×10×10)
∵ i² = - 1 or i = √-1
Here i is an imaginary number.
⇒ x = 10(√-1)
⇒ x = 10i
Therefore, the solution of given complex numbers would be x = 10i where i is an imaginary number.
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Help me I’m so confused
The number of apples Chee bought is 2, and the number of peaches she bought is 8
Solving System of Linear Equations GraphicallyFrom the question, we are to determine the number of apples, x, and the number of peaches, y, that Chee bought
From the given information,
She bought $6 worth of apples and peaches
and
Each apple costs $1 and each peach costs $0.50
Then, we can write that
$1 × x + $0.50 × y = $6
x + 0.50y = 6
Also,
She bought 4 times as many peaches as apples
That is,
y = 4x
Now, we will solve the system of equations graphically
x + 0.50y = 6
y = 4x
From the graph, the solution to the system of equations is x = 2, y = 8.
Hence, the number of apples Chee bought is 2, and the number of peaches she bought is 8
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Evaluate the function for f(x) = x + 3 and g(x) = x2 − 2. (f + g)(−8) (f + g)(−8) =
The value of the function (f + g)(−8) (f + g)(−8) for f (x) = x + 3 and g (x) = x² - 2 is 3249.
We are given the functions:
f(x) = x + 3
g(x) = x² − 2
Now,
(f + g) (−8) × (f + g)(−8)
= [ (f + g) (−8) ]²
Substituting the values of the functions, we get that:
=(x + 3 + x² - 2)² , where x = -8
= ( -8 + 3 + 64 - 2 )²
= ( -5 + 62)²
= (57) ²
= 3249
So, the value of the function (f + g)(−8) (f + g)(−8) for f (x) = x + 3 and g (x) = x² - 2 is 3249.
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A grocery store sells a bag of 6 oranges for $5.64. How much would it cost for 8
oranges?
The cost of 8 oranges is $7.52
How to find the cost of 8 oranges ?The first step is to find the cost of one orange
6 oranges cost 5.65
1 orange= 5.64/6
= 0.94
Therefore the cost of 8 oranges can be calculated as follows
= 0.94×8
= 7.52
Hence 8 oranges cost $7.52
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A craftsman wants to build this fiddle. He needs to know the area of the face of the fiddle. How could he use the measurements shown to find the area? Use your strategy to find the area of the face of
the fiddle.
Write an equation of each line.slope =0 ; through (4,-2)
The equation of the line, with slope equal to 0 and passing through the point located at (4 , -2), is y = -2.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values to set up the equation.
(y - y1) = m(x - x1)
where m = 0 and (x1 , y1) = (4 , -2)
(y - -2) = 0(x - 4)
(y + 2) = 0
y = -2
In slope-intercept form, the equation of the line is:
(y + 2) = 0
y = -2
In standard form, the equation of the line is:
y = -2
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What is the property of 10+(-10)=0
Write the equation for each line. Use slope-intercept form. m = - 3/8 and the y -intercept is (0,12) .
The equation of the line in slope-intercept form with a slope of -3/8 and y-intercept of (0 , 12) is y = (-3/8)x + 12.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
Given that the slope of the line is -3/8 and the y-intercept is (0 , 12), write the equation of the line by simply plugging in its values.
y = mx + b
y = (-3/8)x + 12
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Put the numbers in order from smallest to largest.
Answer:
3.24x10^-5, 5.48x10^-2, 1.2x10^1, 4.68x10^6, 8.34x10^6
Step-by-step explanation:
3.24 x 10^-5 = 0.0000324
5.48 x 10^-2 = 0.0548
1.2 x 10^1 = 12
4.68 x 10^6 = 4680000
8.34 x 10^6 = 8340000
Mr. Sowers wants to purchase expo markers for his classroom. He has a budget of $35. A four pack of markers costs $5.49, including tax. Write and solve an inequality to solve for the number of packs of markers Mr. Sowers can purchase
The number of packs of markers Mr. Sowers can purchase is 6.4 packs.
The number of packs of markers Mr. Sowers can purchaseAccording to the task content, it is required that an inequality should be written and solved for the number of packs of markers Mr. Sowers can purchase.
Mr sower's budget = $35Cost of four pack of markers including tax = $5.49Number of packs of markers = x5.49x ≤ 35
divide both sides by 5.49x ≤ 35 / 5.49
x ≤ 6.375227686703096
Approximately
x ≤ 6.4
Therefore, the number of packs of markers Mr. Sowers can purchase is 6.4 packs
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a. A circle contains the points (0,0),(6,8) , and (7,7) . Find its equation by solving a system of three equations.
Using system of three equations, the equation of the circle that contains the points (0 , 0), (6 , 8), and (7 , 7) is (x - 3)^2 + (y - 4)^2 = 25.
The standard form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Substituting the values of the x and y coordinates of each point to the standard form of the equation of a circle, the three system of equations are:
(x - h)^2 + (y - k)^2 = r^2
(0 , 0) : (0 - h)^2 + (0 - k)^2 = r^2
(6 , 8) : (6 - h)^2 + (8 - k)^2 = r^2
(7 , 7) : (7 - h)^2 + (7 - k)^2 = r^2
Expanding these equations,
(0 , 0) : h^2 + k^2 = r^2 (equation 1)
(6 , 8) : 36 - 12h + h^2 + 64 - 16k + k^2 = r^2 (equation 2)
(7 , 7) : 49 - 14h + h^2 + 49 - 14k + k^2 = r^2 (equation 3)
Subtracting equation 1 from equation 2 and 3.
36 - 12h + h^2 + 64 - 16k + k^2 = r^2
- (h^2 + k^2 = r^2)
36 - 12h + 64 - 16k = 0
100 - 12h - 16k = 0
12h + 16k = 100
Dividing both sides by 4,
3h + 4k = 25 (equation 4)
49 - 14h + h^2 + 49 - 14k + k^2 = r^2
- (h^2 + k^2 = r^2)
49 - 14h + 49 - 14k = 0
98 - 14h - 14k = 0
14h - 14k = 98
h + k = 4 (equation 5)
h = 7 - k
Substitute h = 7 - k to equation 4 and solve for k.
3h + 4k = 25 (equation 4)
3(7 - k) + 4k = 25
21 - 3k + 4k = 25
k = 25 - 21
k = 4
Substitute the value of k to equation 5 and solve for h.
h = 7 - k (equation 5)
h = 7 - 4
h = 3
Substitute the value of h and k to equation 1 and solve for r.
h^2 + k^2 = r^2 (equation 1)
3^2 + 4^2 = r^2
9 + 16 = r^2
r^2 = 25
r = 5
Hence, the equation of the circle that contains the points (0 , 0), (6 , 8), and (7 , 7) is (x - 3)^2 + (y - 4)^2 = 25.
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let f(x)=4x^2+5 and g(x)=2x-4. find f(x)+g(x)
Answer:
[tex]4x^2+2x+1[/tex]
Step-by-step explanation:
[tex]f(x)=4x^2+5\\g(x)=2x-4\\\\f(x)+g(x)=(4x^2+5)+(2x-4)\\\\4x^2+5+2x-4\\\\4x^2+2x+1[/tex]
The graph of function f is shown.
Function g is represented by the equation.
g(x) = 9(1/3)^x - 4
Which statement correctly compares the two functions?
OA. They have the same y-intercept but different end behavior.
OB. They have different y-intercepts but the same end behavior.
OC. They have different y-intercepts and different end behavior.
OD. They have the same y-intercept and the same end behavior.
Answer:
Step-by-step explanation:
B) is correct
Find the measures of the sides of ΔX Y Z and classify
triangle by its sides.
X(-4,-2), Y(-3,7), Z(4,-2)
The measures of the sides of ΔXYZ are XY = 9.1, YZ = 11.4, XZ = 8. and the triangle XYZ must be an acute triangle
In this questions we have been given the the coordinates of the triangle XYZ.
X(-4, -2), Y(-3, 7), Z(4, -2)
We need to find the measures of the sides of ΔXYZ .
We find the the measures of the sides using distance formula.
XY = √[(7 + 2)² + (-3 + 4)²]
XY = √[9² + 1²]
XY = √(81 + 1)
XY = √(82)
XY = 9.1
Now side YZ
YZ = √[(-2 - 7)² + (4 + 3)²]
YZ = √[(-9)² + (7)²]
YZ = √81 + 49
YZ = √130
YZ = 11.4
And the length of side XZ would be,
XZ = √[(-2 + 2)² + (4 + 4)²]
XZ = √0 + 8²
XZ = 8
We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.
the sum of the squares of the two smaller sides is,
= 8² + 9.1²
= 64 + 82.81
= 146.81
= 12.12²
And 11.4² = 129.96
Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.
Therefore, the measures of the sides of ΔXYZ are XY = 9.1, YZ = 11.4, XZ = 8. and the triangle XYZ must be an acute triangle
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Question 9 of 10
How many dimensions does a point have?
OA. Zero
B. Two
C. Three
D. One
SUB
Answer: A
Step-by-step explanation: took the quiz got it right
Find each measure if m ∠ D G F=53 and m∠ A G C=40 .
m ∠ 4
Answer:
a
Step-by-step explanation:
i ink
Five of seven kittens in a litter had black markings. Write a simplified ratio for each of the following:
Kittens without black markings to kittens with black markings: 2 to 5
s: 2 to 7
2 t
Kittens without black markings to total kittens:
Kittens with black markings to total kittens: 5 to 7
Kittens without black markings to kittens with black markings: 2:5
Kittens without black markings to total kittens: 2:7
Kittens with black markings to total kittens: 5:7
