Answer:
D. 640 students
Step-by-step explanation:
hope this helps
Given the function f(x)= 7lx-4l, calculate the following values:F(0)=F(2)=F(-2)=F(x+1)=F(x^2+2)=
As given by the question
There is given that the function
[tex]f(x)=7\lvert x-4\rvert[/tex]Now,
First find the value of f(0):
Then, put the value of 0 for x into the given function.
Now,
[tex]\begin{gathered} f(x)=7\lvert x-4\rvert \\ f(0)=7\lvert0-4\rvert \\ f(0)=7\lvert-4\rvert \\ f(0)=7\cdot4 \\ f(0)=28 \end{gathered}[/tex]Then,
[tex]\begin{gathered} f(x)=7\lvert x-4\rvert \\ f(2)=7\lvert2-4\rvert \\ f(2)=7\lvert-2\rvert \\ f(2)=7\cdot2 \\ f(2)=14 \end{gathered}[/tex]Then,
[tex]\begin{gathered} f(x)=7\lvert x-4\rvert \\ f(-2)=7\lvert-2-4\rvert \\ f(-2)=7\lvert-6\rvert \\ f(-2)=7\cdot6 \\ f(-2)=42 \end{gathered}[/tex]Then,
[tex]\begin{gathered} f(x)=7\lvert x-4\rvert \\ f(x)=7\lvert x+1-4\rvert \\ f(x)=7\lvert x+1-4\rvert \\ f(x)=7\lvert x-3\rvert \end{gathered}[/tex]And,
[tex]\begin{gathered} f(x)=7\lvert x-4\rvert \\ f(x^2+2)=7\lvert x^2+2-4\rvert \\ f(x^2+2)=7\lvert x^2-2\rvert \end{gathered}[/tex]Gavin and Jim win some money and share it in the ratio 1:3. Gavin gets £15. How much did Jim get?
Using ratios we can conclude that Jim will get £45.
What are ratios?In mathematics, a ratio shows how frequently one number appears in another. For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons. Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.So, the money Jim gets will be:
The ratio, that they got money in is 1:3.
Gavin:JIM = 1:3Gavin gets £15.Then Jim will bet:
£15 × 3£45Therefore, using ratios we can conclude that Jim will get £45.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
"how long" is the question.
so, we will need an answer in seconds.
the other options do not define a time duration.
to fall from top to the ground it means the object fell 1503 ft, that means that s(t) = 1503.
16t² = 1503
t² = 1503/16
t = sqrt(1503/16) = sqrt(9×167/16) = 3/4 × sqrt(167) =
= 9.692135987... seconds
it took the object 9.692135987... seconds to fall from the top to the ground.
What is this expression in simplified form?
5√63-6√28
O A. 3√7
OB. 21√7
O C. 27√7
O D. 11√7
Answer:
23467788
Step-by-step explanation:
666789909 +75445899553235653889
I'm sure the
2x+1=2(x-2) solve for x
Answer:
There is no solution to this equation
Step-by-step explanation:
2x+1=2(x-2)=
2x+1=2x-4
0x = -5
Answer is no solution
this statement is false
2x+1=2(x-2)
2x+1=2x-4
cancel equal terms
1=-4
A babysitting job pays $4 per hourWhich table show the relationship between the number of hours worked and the total amount of money earned babysitting?
Given that the ratio is $4 per hour, we just have to find the table that shows this relation.
Observe that table C shows that the Total Money Earned is 4 times the Hours worked.
Hence, the answer is C.Michaels is very busy with work and her children so she decides to subscribe to. A monthly meal plan services. The company charges a flat monthly cost of $125 per month for their classic meals. Michelle wants to try a few of the family meals so she can have her babysitter over for dinner a few nights this month . One family meal costs $9.99 if Michelle cooks dinner for her babysitter three times this month using the family package and still purchases her classic meal package how much will Michelle pay for her subscription this month
Michelle will pay $154.97 if she cooks dinner for her babysitter three times this month using the family package and still purchases her classic meal package.
What is meant by cost?A cost function is a mathematical formula that shows how production costs change at different output levels. In other words, it calculates the total cost of production based on the quantity produced. The cost function can be used to calculate the average cost, which is the amount of money it costs to produce one unit on average.
The average cost function is A(x)=C(x)x A (x) = C (x) x A (x) = C (x) x, where x>0. The average cost per unit is calculated by dividing the total cost by the number of units produced.
Given,
Monthly cost of $125 per month for their classic meals
and one family meal costs $9.99
if Michelle cooks dinner for her babysitter three times this month using the family package, the the cost of 3 family meal cost will be
3 × $9.99 = $29.97 and still purchases her classic meal package
Hence, the total pay will be $125 + $29.97 = $154.97
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Raj completed his homework in 5/6 hour. His older brother took 1½ times as long as Raj did to
complete his homework.
How long did it take Raj's older brother to complete his homework?
Answer:
B
Step-by-step explanation:
Determine the equation of the line that passes through the point (1/−3,−9) and is perpendicular to the line 5y+x=1.
Given the following equation of a line:
[tex]5y+x=1[/tex]We will write the equation in the slope-intercept form: y = m x + b
[tex]\begin{gathered} 5y+x=1 \\ 5y=-x+1 \\ \\ y=-\frac{1}{5}x+\frac{1}{5} \end{gathered}[/tex]Now, we will find the equation of the line that is perpendicular to the given line.
Note: if the slope of the given line = m
So, the slope of the perpendicular line = -1/m
From the given line: slope = m = -1/5
So, the slope of the perpendicular line = -1/m = 5
The required line passes through the point (-1/3, -9)
We will use the point-slope form to write the equation of the required line:
[tex]\begin{gathered} (y-k)=m*(x-h) \\ \\ y-(-9)=5*(x-(-\frac{1}{3})) \\ \\ y+9=5x+\frac{5}{3} \end{gathered}[/tex]Simplify the equation to be like the standard equation:
[tex]\begin{gathered} y+9=5x+\frac{5}{3}\to\times3 \\ 3y+27=15x+5 \\ \\ 3y-15x=-22 \end{gathered}[/tex]So, the answer will be:
3y - 15x = -22
Pierre's unicycle wheel has a diameter of 80 cm.
O
80 cm
a)
1
Tarks
b)
a) How far does the unicycle move if the
wheel turns once?
Give your answer in metres, correct
to 2 decimal places.
b) Pierre enters a 100 m unicycle race.
How many times must the wheel rotate
completely in order for Pierre to
travel 100 m?
Give your answer to the nearest
whole number.
+
m
1+ times
Answer:
80 cm ×2 = 160 but it is not there in the option
find the area of the shape
We can decompose the shape into two triangles, one with a base of 4 yds and a height of 5 yds, and the other with a base of 4 yds and a height of 13 yds.
The area of a triangle is calculated as follows:
[tex]A=\text{base}\cdot\text{height}\cdot\frac{1}{2}[/tex]Then, the area of the triangles are:
[tex]\begin{gathered} A_1=4\cdot5\cdot\frac{1}{2} \\ A_1=10yd^2 \\ A_2=4\cdot13\cdot\frac{1}{2} \\ A_2=26yd^2 \end{gathered}[/tex]And the are of the shape is 10 + 26 = 36 yd²
Use long division or a calculator to write 1/6 as a decimal. Then tell whether the decimal is terminating or repeating
It can be seen that it is a repeating decimal because the division is continuous
Omar and Devin both leave the bookstore at the same time, but in opposite directions. If Devin travels 7 mph faster than Omar and after 3 hours they are 93 miles apart, how fast is each traveling?
Omar and Devin both leave the bookstore at the same time, but in opposite directions.
Let the speed of Omar = x
Speed of Devin = x + 7
They travel for 3 hours
Speed = Distance/Time
Distance = Speed x Time
Since, they are 93 miles apart
93 = (speed pf Omar + Speed of Devin) Time
93 = (x + x + 7)3
93 = (2x + 7)3
93 = 6x + 21
93 - 21 = 6x
6x = 72
x = 72/6
x = 12
Thus, Speed of Omar is 12 mph
Speed of Devin : x + 7
x + 7 = 12 + 7
= 19
Thus, speed of Devin is 19mph
An inlet pipe on a swimming pool can be used to fill the pool in 34 hours. the drain pipe can be used to empty the pool in 35 hours. if the pool is 1/2 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
595 hours is time it will take to fill the swimming pool .
What are fraction ?A fraction is a mathematical symbol representing any quantity of equal parts, and it also represents a portion of a whole. When employed in conversational English, a fraction—such as one-half, eight-fifths, and three-quarters—indicates the number of components of a particular size.
Calculationinlet pipe will fill the pool in 34 hours. Every hour, it fills 1/34 of the pool
Outlet pipe will empty the pool in 35 hours. Every hour, it empties 1/35 of the pool.
In x hours we want 1/2 the pool to fill, since half is already filled.
We want (x/34) - (x/35) = 1/2
multiply by 1190 both sides, the LCD.
35x-34x=595 (1190/2)
x=595 hours
in that time 595/34-595/35=0.5
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6) Endpoint: (5,0), midpoint: (1, -1)
hello
we're required to find the second end point from the given values
end point = (5, 0)
mid point = (1, -1)
to solve this problem, we'll need to use thw formula for mid-point
[tex]x,y=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}[/tex]now let's identify our variables
[tex]\begin{gathered} x=1,y=-1, \\ x_1=5,y_1=0 \\ x_2=\text{ ?} \\ y_2=\text{ ?} \end{gathered}[/tex]let's substitute in our values and solve respectively
[tex]\begin{gathered} x=\frac{x_2+x_1}{2} \\ 1=\frac{x_2+5}{2} \\ \text{cross multiply both sides} \\ 1\times2=x_2+5 \\ 2=x_2+5 \\ x_2=2-5 \\ x_2=-3 \end{gathered}[/tex]now let's do the same for y
[tex]\begin{gathered} y=\frac{y_2+y_1}{2} \\ -1=\frac{y_2+0}{2} \\ \text{cross multiply both sides} \\ 2\times-1=y_2+0_{} \\ -2=y_2 \\ y_2=-2 \end{gathered}[/tex]the values of the other end point are (-3, -2)
A line drawn on the coordinate plane passes through the points (1, 4) and (2, 7). What is the equation of the line?
Thus, the equation of the straight line passing through the point (1,4) and (2,7) is: y=3x+1
A line passing through the coordinate plane also passes through points (1,4) and (2,7)
Let point(1,4) be=P
let point(2,7) be=Q
The formula for the equation of a straight line when two points are given is given as:
y-y1=m X (x-x1) + c
where m=y2-y1/x2-x1
here y= Y axis
x= X axis
m= Slope of the line
c= constant
Here taking P as point 1 and Q as point 2 we get:
x1=1 y1=4
and
x2=2 y2=7
m=y2-y1/x2-x1
Now putting values
m=(7-4)/(2-1)
m=3/1
Thus m=3
now putting values in the equation
(y-4)=3(x-1) +c
y-4=3x- 3+c
y=3x-3+4+c
y=3x+1+c
Since Line passes through point Q(2,7) it satisfies the equation.
now putting the values of point Q in the equation to get the constant:
y=3x+1+c
(7)=3(2)+1+c
7=6+1+c
7=7+c
7-7=c
c=0
Thus, the constant is 0.
Thus, the equation of the straight line passing through the point (1,4) and (2,7) is: y=3x+1
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Find the sum of the interior angles of a 22-sided polygon. 1,980° 2,160° 3,360° 3,600°
The sum of the interior angles of a 22-sided polygon is (d) 3600 degrees
How to determine the sum of the interior angles?From the question, we have the following parameters that can be used in our computation:
Shape = 22-sided polygon
Parameter to calculate = the sum of the interior angles
The sum of the interior angles is calculated using the following angle formula
The sum of the interior angles = ( n − 2 ) × 180 ∘ where is the number of sides
In this case
n = 22
Substitute the known values in the above equation, so, we have the following representation
The sum of the interior angles = (22 − 2) × 180∘
Evaluate
The sum of the interior angles = 3600∘
Hence, the angle is (d) 3600 degrees
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Carolina needs a total of $6.50 in quarters for a coin-operated car wash. He already has $1.50. Which equation can be used to find g, the
additional quarters Carolina needs in order to have enough money for the car wash?
Answer: 20 quarters
Step-by-step explanation:
As we look at this problem we can convert $6.50 dollars into 26 quarters. Us already knowing that Carolina has $1.50 (6 quarters) we can take the two numbers and minus both of them. 26 quarters ($6.50) - 6 quarters ($1.50) = 20 quarters($5.00)
Step-by-step explanation:
every $ is equivalent to 4 quarters.
every half-$ is equivalent to 2 quarters.
after all, 1 quarter = $0.25.
so, the equation is
4×1.5 + g = 4×6.5
or simplified
6 + g = 26
and from there we get then immediately that
g = 20
what is the slope of a line perpendicular to the line whose equation is x+y=9
Answer:
perpendicular slope = 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x + y = 9 ( subtract x from both sides )
y = - x + 9 ← in slope- intercept form
with slope m = - 1
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1
Working in the health sciences, you will find that you will have to make different kinds of mathematical conversions. Start this activity by reading through the following story problems to familiarize yourself with the various conversions that you will need to perform. Use the information below to answer the questions.Submit your answer (rounded to 2 decimals) and all work.Conversion Formulas1 oz = 29.57mL1 ml = 0.20 teaspoonsQuestion 7: Dymelor 0.75 g is ordered. Scored tablets are labeled 500 mg. each. How many tablets will you give?
Since 1 g is equal to 1000 mg, multiply 0.75 g by 1000 mg / 1 g to convert the given value to mg.
[tex]0.75g\cdot\frac{1000mg}{1g}=750mg[/tex]Since one tablet is 500 mg, multiply the obtained product by 1 tablet / 500 mg.
[tex]750mg\cdot\frac{1\text{ tablet}}{500\text{ mg}}=1.5\text{ tablet}[/tex]Thus, there must be 1.5 or 1 1/2 tablet.
I need some help with math
if the perimeter is 28 and part of it is 5 what is the cm
The other side of the rectangle is 9 cm.
Given that:-
Perimeter of the rectangle = 28 cm
One side of the rectangle = 5 cm
We have to find the other side of the rectangle.
Let the length of the rectangle be 5 cm and,
The breadth of the rectangle be b cm.
We know that,
Perimeter of the rectangle = 2(l + b)
Hence, we can write,
2(5 + b) = 28
5 + b = 28/2
5 + b = 14
b = 14 - 5
b = 9 cm
Hence, the other side of the rectangle is 9 cm.
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-1/7 divided by-3/14
Evaluate 3x + 2y - 22when x = 5, y = 2 and z = 1.
3x + 2y - 2z = 17
when x = 5, y = 2, and z = 1
Explanation:Given
3x + 2y - 2z
For x = 5, y = 2 and z = 1, we have:
3(5) + 2(2) - 2(1)
= 15 + 4 - 2
= 17
The equation 2x = 50-3x can be solved by graphing y = 2x and y=50-3x,
Use the drop-down menu to complete the statement to explain why a graph can be
used to solve this equation. Answer
The solution of the equation is x = 10. The graph is attached below.
We are given an equation. The equation has one variable. The equation is given below.
2x = 50 - 3x
First of all, we will solve the equation directly to find the solution.
2x = 50 - 3x
5x = 50
x = 10
The above equation can be also be solved by graphing y = 2x and y = 50 - 3x. These are two linear equations. These equations represent two straight lines. The solution is found by locating the intersection point of these two straight lines on the graph. The graph of the two straight lines is attached below.
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Answer:
20 is the answer
Step-by-step explanation:
The area of a triangle is 15. Two of the side lengths are 5.5 and 7.5 and the includedangle is acute. Find the measure of the included angle, to the nearest tenth of adegree.
α =46º
1) Let's start by gathering the data:
S = 15 u²
a= 5.5
b= 7.5
Sketcing out:
2) One of the formulas to find out the area of a triangle is:
[tex]S=\frac{ab\cdot\sin (\alpha)}{2}[/tex]Plugging the given data into the formula we have:
[tex]\begin{gathered} 15=\frac{5.5\cdot7.5\sin (\alpha)}{2}\text{ }\times2 \\ 30\text{ =41.25}\cdot\sin (\alpha) \\ \frac{30}{41.25}=\frac{\text{41.25}\cdot\sin (\alpha)}{41.25} \\ 0.72=\sin (\alpha) \end{gathered}[/tex]2.2) Since we want to know the measure of that angle, then let's make use of the arcsine of (0.72)
[tex]\begin{gathered} \alpha=\sin ^{-1}(0.72) \\ \alpha=46.05\approx46 \end{gathered}[/tex]3) Hence, the missing acute angle is α =46º (rounded off to nearest whole number)
I need help with my geometry homework thank you.
Answer:
2.5
Step-by-step explanation:
point B
4K = 10
4/4 K = 10/4 K
K = 5/2 = 2.5
in larg cities, people often take taxi to get from one place to another. what is the cost per mile of taxi ride how much is 47-mile taxi ride
People in large cities use taxis to get from one location to another; the cost is $25.20 every 36 miles, and a 47-mile taxi ride will cost $32.9.
What is the multiplication and division rule?Multiplication Rule If events A and B occur in the same sample space, the probability of both A and B occurring is equal to the probability that A occurs multiplied by the probability that B occurs, given that A has occurred.
Returning to the previous example, the first response is correct because it follows the BODMAS principles, which state that division can be done before multiplication and must be done before addition. Multiplication happens before addition.
Given,
Cost every 36 miles = 25.20
Cost of one mile = Cost for 36 miles / 36
Cost of one mile = 25.20/36
Cost of one mile = 0.7
Cost of 47 miles = Cost of one mile × 47
Cost of 47 miles = 0.7 × 47
Cost of 47 miles = 32.9
47 miles taxi ride will cost 32.9
The complete question is:
In large cities people out and take taxis to get from one place to another the cost is $25.20 every 36 miles how much is a 47 mile taxi ride
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is two over nine a rational number
Two over nince is fraction formed by two integers which equal a repeting decimal, which means it's a rational number.
Hence, the answer is yes.7. A box contains bags of nails. Each
bag has 24 nails. There are 960 nails
in the box. How many bags are in
the box?
40 bags of 24 nails in the box
Answer:
Step-by-step explanation:
you divide 960 by 24 and you will have 40 so you will have 40 nails. :0