There are total 77 students in the sixth grade.
Given, there are 28 students that have braces.
out of which there are 4 students with braces for every 7 students.
Therefore, 4 ₊ 7 = 11, which means every 11 member has 4 members with braces.
Therefore, based on the given conditions, formulate:
28 × (4 ₊ 7) ÷ 4
28 × 11 / 4
now cross out the common factors.
7 × ( 11)
multiply the above terms.
77
hence we get the answer as 77 students in total in the class.
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Which two tables represent the same function?
xy
48
6 7
xy
45
64
ху
28
85
xy
2 10
6 14
xy
29
8 6
1st and 5th tables represent the same function
To find the two equal functions we will formulate their equations, using the formula [tex]\frac{y-y1}{x-x1} = \frac{y2-y1}{x2-x1}[/tex] where (x1,y1) and (x2,y2) are the endpoints of the equation.
Now finding the equation for each table we get:
Table 1:
(x1,y1) = (4,8) and (x2, y2) = (6,7)
Putting this in the formula we get:
= [tex]\frac{y-8}{x-4} = \frac{7-8}{6-4}[/tex]
So, the equation will be x + 2y = 20
Table 2:
(x1,y1) = (4,5) and (x2, y2) = (6,4)
Putting this in the formula we get:
= [tex]\frac{y-5}{x-4} = \frac{4-5}{6-4}[/tex]
So, the equation will be x + 2y = 14
Table 3:
(x1,y1) = (2,8) and (x2, y2) = (8,5)
Putting this in the formula we get:
= [tex]\frac{y-8}{x-2}=\frac{5-8}{8-2}[/tex]
So, the equation will be x+2y=18
Table 4:
(x1,y1) = (2,10) and (x2, y2) = (6,14)
Putting this in the formula we get:
= [tex]\frac{y-10}{x-2} =\frac{14-10}{6-2}[/tex]
So, the equation will be x-y=-8
Table 5:
(x1,y1) = (2,9) and (x2, y2) = (8,6)
Putting this in the formula we get:
= [tex]\frac{y-9}{x-2}=\frac{6-9}{8-2}[/tex]
So, the equation will be x+2y=20
Hence, table 1 and table 5 represent the same function
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Evaluate (4X-4)(x+1) where X=3
pls help - find the measure of 6
The measure of the ∠6 which is interior to 144° measures 36°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An angle is formed at a point where two or more lines intersect. We have acute angles, right angle and obtuse angle depending on the angle measure.
From the diagram:
∠6 + 144 = 180° (interior angles are supplementary)
∠6 = 36°
The measure of the ∠6 which is interior to 144° measures 36°
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In a particular parking lot with 24 cars in it, 18 are blue. What fraction of the cars in the parking lot are blue?
Answer:
3/4
Step-by-step explanation:
If you do a ratio, 18 blue cars to 24 total cars, that would be 18:24. If you simplify that, then you would be left with 3:4. So for every 4 cars, 3 are blue. So 3/4 of the cars in the parking lot are blue.
Find the value of each follow expression use a title diagram or a number line to help you 3(4)
The value of the expression 3(4) can be expressed as 12 with the help of a title diagram or a number line and the explanation for this same can be done easily if we take into consideration a number line.
What does the math number line mean?A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It can also be assumed that every point present on a number line corresponds to a real number, and that every real number also corresponds to a point.
To solve this expression, we can deduce as follows:
As per the number line, for the expression 3(4).
Since it is absolutely positive, thus we will get the final answer in positive that means on the side of the number line lying right to zero.
To express this expression,
3 (4) means we have to move towards the right side of the number line from zero for 4 times and each time covering a total of 3 units each.
Thus, we start from zero, first time we reach 3 then 6, then 9 and then finally 12.
Thus, the value of the expression is received as 12.
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Tickets to a concert a Lake Sumter Community College cost $5 for general admission or $4
with a student ID. If 184 people paid to see the concert and $812 was collected, how many
of each type of ticket were sold?
On the basis of total cost per day for business travel to New York City and Washington DC
The required number of general admissions is 76 and the number of admission with student id is 108.
Here,
let the number of general admissions be x and the number of the admission with student id be y
Using arithmetic operations
According to the question,
x + y = 184
x = 184 - y - - - -(1)
5x + 4y = 812 - - - - (2)
From equation (1)
5 (184 - y) + 4y = 812
920 - 5y + 4y = 812
-y = 812 - 920
-y = 108
y = 108
Put y in equation 1
x = 184 - 108
x = 76
Thus, the required number of general admission is 76, and the number of admission with student id is 108.
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Helllllp
A construction crew has just built a new road. They worked for 6 weeks. They built the road at a rate of 7.68 kilometers per week. How many kilometers of road
did they build?
Answer:46.08
Step-by-step explanation the only thing you has to do was multiply your keyword was per I hope this helps
2. Gwen uses 3 teaspoons of sweetener for every 5 cups of iced tea. How many teaspoons of sweetener should she
add to 30 cups of iced tea if she wants the same flavor?
A. 9
B. 18
C. 28
D. 50
Answer:
B: 18
Step-by-step explanation:
3 t for every 5 c
30/5 = 6, 6 groups of 5
6 x 3 (3 for every 5 cups, but x by the 6 groups)
6 x 3 = 18.
what is the actual awnser to find the length x 14cm and 7 cm
Hi could u ask the question a bit clearer?
A cube-shaped shed has 6-foot high walls. If all the shed's walls are painted (not including the floor or ceiling), how much area will be painted?
The area that would be painted will be 144 square feet
Calculating surface areaFrom the question, we are to determine the area of the cube-shaped shed that was painted
From the given information,
The cube-shaped shed has 6-foot high walls
From the formula for the surface area of a cube,
Surface area = 6s²
Where s is the measurement of a side
A cube has six sides
Since, the floor and ceiling are not painted,
The area of the shed that was painted will be
Surface area painted = 4s²
s = 6 feet
Thus,
Surface area painted = 4 × 6²
Surface area painted = 4 × 36
Surface area painted = 144 square feet
Hence, the area that would be painted will be 144 square feet
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For a recent year, 34 more Democrats than Republicans represented a country. If the total number of representatives of the country from these two parties was 484, find the number of representatives from each party.
In linear equation the number of Republicans are 225 and the number of Democrats are 259 .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Let Republicans = x
then Democrats = x + 34
x + x + 34 = 484
2x + 34 = 484
2x = 484 - 34
2x = 450
x = 450/2
x = 225
x + 34 = 225 + 34 ⇒ 259
Therefore ,the number of Republicans are 225 and the number of Democrats are 259 .
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4. Stanley quilts a square rug that has an area of 400 square inches. What is the length of each side of the
rug?
A. 14 inches
B. 16 inches
C. 18 inches
D. 20 inches
Answer:
D. 20 inches
Step-by-step explanation:
Area = length * width
20 * 20 = 400 square inches
20 inches
Solve for Y
19= y/5 + 16
The solution to the given equation 19= y/5 + 16 is y = 15.
What is the solution to the given equation?Given the equation in the question;
19 = y/5 + 16y = ?First reorder the equation by moving all terms not containing y to the right side of the equation.
19 = y/5 + 16
19 - 16 = y/5
y/5 = 19 - 16
Subtract 16 from 19
y/5 = 19 - 16
y/5 = 3
Multiply both sides of the equation by 5
5( y/5 ) = 3 × 5
5y/5 = 15
y = 15
Therefore, the solution to the given equation 19= y/5 + 16 is y = 15.
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For the linear function f (x) = mx + b, f (-3) = 23 and f (2) = -7.
Find m and b.
Answer:
b = 8 , m = - 5
Step-by-step explanation:
For this question we can use simulteanous equations to solve for m and b.
We first come up with 2 equations.
Given the first condition:
23 = -3m + b
b - 3m = 23 (Equation 1)
Now the Second Condition:
-7 = 2m + b
b + 2m = -7 (Equation 2)
Now, we will use Equation 1 - Equation 2 to eliminate b to solve for m.
-3m - (+2m) = 23 - ( - 7)
- 5m = 30
m = 30 ÷ -6 = -5
Now we substitute m into Equation 1 to solve for b.
b - 3(- 5) = 23
b + 15 = 23
b = 23 - 15 = 8
Answer: m=-6 b=5
Step-by-step explanation:
f(x)=mx+b
f(-3)=23 f(2)=7
[tex]\displaystyle\\\left \{ {{23=(m)(-3)+b} \atop {-7=(m)(2)+b}} \right. \ \ \ \ \left \{ {{23=-3m+b\ \ \ \ (1)} \atop {-7=2m+b\ \ \ \ (2)}} \right.[/tex]
Subtract equation (2) from equation (1):
-30=5m
Divide both parts of the equation by 5:
-6=m
Thus, substitute m=-6 in (2):
-7=(-6)(2)+b
-7=-12+b
-7+12=-12+b+12
5=b
Hence,
y=-6x+5
What is the conjecture of pattern -3, 6, -9, 12
The conjecture of the pattern - 3, 6, - 9, 12 is all the set of series generated by the expression s = (- 1)ⁿ · 3 · n.
What is the conjecture behind a pattern of an arithmetic sequence?
In this problem we have a sequence with a pattern, which has to be translated into mathematical expressions. We notice two features of this sequence:
The elements of the sequence are multiples of 3.Two consecutive elements have signs opposite to each other.Then, the pattern can be generated by using the following expression:
s = (- 1)ⁿ · 3 · n
Now we check if the pattern is the same as the shown in the question:
n = 1
s = (- 1)¹ · 3 · 1
s = - 3
n = 2
s = (- 1)² · 3 · 2
s = 6
n = 3
s = (- 1)³ · 3 · 3
s = - 9
n = 4
s = (- 1)⁴ · 3 · 4
s = 12
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- 4/5w = -1 find w please
Answer:
The value of w = 4/5
Step-by-step explanation:
=> -4/5w = -1
=> -4 = -5w
=> 4 = 5w
=> w = 4/5
Answer:
5/4
Step-by-step explanation:
Match each number to a point on the number line.
Answer:
I dont understand it bc the pic is blurry
Step-by-step explanation:
Please mark Branliest
CALCULUS:
The position in feet of a race car along a straight track after t seconds is given by s(t) = t^2 − 4t + 4. Find its instantaneous velocity at t = 2 seconds.
The velocity of the car at t = 2 seconds is 0 ft/second.
How to find the instantaneous velocity at t = 2 seconds?We know that the position equation (in feet) of the race car is:
s(t) = t^2 - 4t + 4
To get the velocity equation we need to find the first derivative of the position equation, we will get:
v(t) = 2t - 4
Now we just need to evaluate this in t = 2 seconds, we will get:
v(2) = 2*2 - 4 = 4 - 4 = 0
The velocity of the car at t = 2 seconds is 0 ft/second.
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Rearrange the equation and solve for v, a, and t.
[tex]d=vt+\frac{1}{2}at^2[/tex]
Rearranging the equation to solve for the variables gives;
v = d - at^2/t
a = 2d - 2vt/t^2
How to solve for the variablesGiven the equation;
d = vt + 1/2 at^2
Let's solve for v
First, collect like terms
vt = d - 1/2 at^2
Now, divide both sides by the coefficient of v which is 't', we have;
vt/t = d - at^2/t
v =
[tex] \frac{d - a {t}^{2} }{t} [/tex]
Let's solve for a
d - vt = at^2/2
cross multiply
2( d - vt) = at^2
expand the bracket
2d - 2vt = at^2
divide both sides by the coefficient of a which is t^2, we have;
2d - 2vt /t^2 = a
a = 2d - 2vt/t^2
Thus, rearranging the equation to solve for the variables gives v = d - at^2/t and a = 2d - 2vt/t^2 respectively.
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what does 10x10x10+1-2+1 equal
Answer:
The answer is 1000
Step-by-step explanation:
10x10=100
100x10=1000
1000+1=1001
1001-2=999
999+1=1000
Answer:
1000
Step-by-step explanation:
10x10=100
100x10=1000
1000+1=1001
1001+1=1002
1002-2=1000.
therefore the answer is 1000
Which answer is equivalent to 5−2⋅924⋅4−3?
Answer:
-7390
Step-by-step explanation:
Parenthesis
Exponents
Multiply
Divide
Addition
Subtraction
5-2x924x4-3
First do multiplication or division what ever comes first and then addition or subtraction what ever comes first from left to right.
5-1848x4-3
5-7392-3
-7390
Can’t figure it out I need help on how to do this
Answer: 11
Step-by-step explanation:
the answer is 11 all it is asking for is finding the mode which simply means the highest group of repeated numbers
The mode of the frequency distribution based on the table is age 11 with 12 students.
What is the mode?Mode can be defined as the most occurring value in a statistical distribution. It is also the most repeated number.
According to the table given;
Age 9 = 3 students
Age 10 = 10 students
Age 11 = 12 students
Age 12 = 1 students
Based on this information, the age with the most number of students is age 11.
Therefore, the mode is 11
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Is −5 greater than, less than, or equal to |−5|?
Answer: Less than
Step-by-step explanation:
The symbols || indicate absolute value.
Absolute value changes a number into it's distance from 0 on the number line. As such, |27| = 27, but |-9| = 9.
Thus, |-5| = 5, and 5 > -5
|-5| > -5
Hope it helps
Answer:
Less than
Step-by-step explanation:
-5 is negetive 5 and |−5| means "positive 5", or just 5
How many solutions does this equation have? 6(x + 1) + 5 = 13 - 2 + 6x
Answer:
Step-by-step explanation:
So you start out with this equation
6(x+1)+5=13-2+6x
you simplify it down to get
6x+11=6x+11 if they are the same then there fore you answer is
Infinite solutions
What is 188.4÷60??? Thank you
Answer: 3.14
Step-by-step explanation:
Use the algorithm method.
3 . 1 4
6 0 | 1 8 8 . 4
1 8 0 .
8 . 4
6 . 0
2 . 4 0
2 . 4 0
2 Therefore, 188.4\div 60=3.14188.4÷60=3.14.
3.14
A water tank measures 5 in. by 6 in. by 6 in. If each dimension of the tank were doubled, approximately how many more gallons can the larger tank hold? (Hint : There are 231 cubic inches in 1 gallon.)
Answer:
6.23376623 gallons
Step-by-step explanation:
5×2 is 10
6×2 is 12
10x12x12 is 1440 inches
1440/231 is 6.23376623 gallons
round if you need to
Can someone help with this question?✨
The equation of the line perpendicular to y = 2x + 2 and passes through (4, 3) is y = - 1 / 2 x + 5
How to find the equation of a line perpendicular to another ?The equation of the line is perpendicular to y = 2x + 2 and passing through the points (4, 3).
Perpendicular lines follows the principle below:
m₁ m₂ = -1
where
m₁ and m₂ are the slopes.Therefore,
2m₂ = -1
m₂ = - 1 / 2
Let's find the y-intercept of the line using (4, 3).
y = - 1 / 2 x + b
3 = - 1 / 2 (4) + b
3 = - 2 + b
b = 3 + 2
b = 5
Therefore, the equation of the line perpendicular to y = 2x + 2 and passes through (4, 3) is y = - 1 / 2 x + 5
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Drag the numbers below to put them in order from least to greatest: 1.393 1.3 1.43 1.47 1.301 1.45
The order of the number from least to greatest is 1.30, 1.301, 1393, 1.43, 1.45, 1.47.
What is the order of the numbers?
Decimal is used to denote integers and non-integers. The integers are separated by non-integers using a decimal point. An example of a decimal is 1.393.
The place value of 1.393 is
1 - unit value 3 = tenth value 9 = hundredth value 3 = thousandth valueThe further away a number is from zero on the number line, the higher the value of the number.
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what is the surface area of a cylinder with a height of 8 feet and a base of 6 feet
The surface area of a cylinder = 527.52 feet
A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.
The total surface area of the cylinder formula is simply the sum of the base surface area and the lateral surface area:
total area = base area + lateral area ,
or
total area = 2πr² + (2πrh ),
or
total area = 2πr (r + h)
where h= Height
r= Radius
given that
height = 8 feet
base radius = 6 feet
Find the lateral surface area of a cylinder with a base radius of 6 feet and a height of 8 feet.
L.S.A.=2π(6)(8)=96π feet
for the total surface area of a cylinder is T.S.A.=2πrh+2πr².
T.S.A. = 96π + 2π (6²)
T.S.A. = 96π + 72π
T.S.A. =168π
where π= 3.14
T.S.A. = 168×3.14
T.S.A. = 527.52 feet
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At how many points does the graph of the function below intersect the x-
axis?
y = 4x²-9x+9
O A. 1
OB. 2
О с. о
SUBMIN
The points does the graph of the function below intersect the x-axis equation is= y = 4x²-9x+9 is C) - 0
because this equation does not have any x intercept
Y = 4x² -9x +9 is a quadratic equation
To know at what point this equation intersect x axis we have to put the value of y= 0
Y = 4x²2 -9x +9
0 = 4x² -9x + 9
4x²-9x+9=0
This equation can be solved using quadratic formula
We need to find the value of discriminant
D= √(b²-4ac)
D=√((-9)²-4(4)(9))
D= √(81-144)
D=√(-63)
As the value of discriminate is not a real number so reel roots does not exit and hence this equation does not have any x intercept
Hence, option c is correct because this equation does not have any x intercept
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