Answer:
The linear equation is 1.25x + 0.5x = y
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Price of ride ticket at country fair = US$ 1.25
Total spent by Tom for rides and admission= US$ 43.75
Number of ride tickets bought by Tom = 25
Price of admission is the same for everyone
Total cost = y
Number of tickets = x
2. Let's find out the cost of the admission:
Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission
Replacing with real values:
1.25 * 25 + Cost of admission * 25 = 43.75
31.25 + 25 * Cost of admission = 43.75
25 * Cost of admission = 43.75 - 31.25 (Subtracting 31.25 at both sides)
25 * Cost of admission = 12.50
Cost of admission = 12.50/25 (Dividing by 25 at both sides)
Cost of admission = 0.50
3. Let's write a linear equation to determine the cost for rides tickets and admission:
Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission
Total cost = y
Number of tickets = x
1.25x + 0.5x = y
20 POINTS AND WILL MARK BRAINLIEST PLZ HELP
Which is the equation of a line that has a slope of 1/2 and passes through point (2,–3)?
A. Y= 1/2x-4
B. Y= 1/2x-2
C. Y=1/2x +2
D. Y=1/2x +3
Answer:
The answer is A
Step-by-step explanation:
y = mx + c
m = 1/2
(2,-3)
y = (1/2)x + c
-3 = (1/2)(2) + c
c = -4
y = (1/2)x - 4
Which graph represents the function f(x)=x4+8x3+6x2−40x+25?
Answer:
Graphic A. (Upper left graphic)
Step-by-step explanation:
The roots of the fourth-order polynomial are, that is the values of x which make polynomial equal to zero:
[tex]x = 1[/tex] and [tex]x = -5[/tex]
By comparing the results with each graphic, it is evident that option A corresponds with the function. (Upper left graphic)
To graph the function f(x)=x4+8x3+6x2−40x+25, choose values of x, find corresponding y-values, and plot the points to form a curve.
To graph the function f(x) = x4 + 8x3 + 6x2 - 40x + 25, we need to plot points on a coordinate plane and connect them to form a graph. Here are the steps:
Choose a few values of x, such as -2, -1, 0, 1, and 2.Plug each value of x into the equation to find the corresponding y-values. For example, when x=-2, y=(-2)4+8(-2)3+6(-2)2-40(-2)+25.Plot the points on the coordinate plane (x,y) and connect them to form a smooth curve.The resulting graph should be a curve that goes through the plotted points.
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what is the answer if 2.4 x 5.8
Answer: 13.92
Step-by-step explanation: 8x4 then 8x2
zero the hero
5x4 then 5x2
lastly add
Answer:
13.92
Step-by-step explanation:
So the explanation is on the picture lol
What is the solution to the equation below? square root of 4-3x divided by square root of 3x equals 2
Possible answers: x=4/9 x=4/15 x= 7/9 x=7/15
Answer:
B.[tex]x=\frac{4}{15}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{4-3x}}{\sqrt{3x} } =2[/tex]can be simplify by doing some algebra.Particulary, in this case, [tex]\frac{\sqrt{4-3x}}{\sqrt{3x} } =\sqrt{\frac{4-3x}{3x} }[/tex], because of the distributive property with respect to division and multiplication.Then, by dividing numerator and denominator by 3x inside the power we get [tex]\sqrt{\frac{\frac{4}{3x}-1}{1}}=\sqrt{\frac{4}{3x}-1} =2[/tex].To dispose of the squared root, we raise to power 2 both sides of the equation, to obtain the following expression: [tex]\frac{4}{3x}-1=4[/tex].Finally, we just have to clear out the value of x from this expression, by addding 1 both sides of the equation: [tex]\frac{4}{3x}=5[/tex], and then by multiplying both sides by 3x, and then dividing the result by 15. This yields [tex]x=\frac{4}{15}[/tex]Answer:4/15
Step-by-step explanation:
what construction is illustrated above
Answer:
i believe it is the 2nd one
Step-by-step explanation:
I think the answer is B because the line is a congruent to the line segment.
Catskill is 15 miles from Saugerties. What would the
distance on the map be?
Answer:
6 inches
Step-by-step explanation:
the map is equal to
1/2.5 inch / miles
by proportion :
1/2.5 inch/miles = x inches / 15 miles
x = 15/2.5
x=6 inches!!
I hope this helped you!! :)
On a large map the distance from austin,texas,to milwaukee,wisconsin, is 13.7 inches. The actual distance is about 1000 miles.what is the distance on the same map from indianapolis,indiana,to louisville,kentucky, if the actual distance is about 100 miles?round your answer to the nearest tenth.
The distance from Indiana to Louisville is 1.37 inches on map.
Step-by-step explanation:
Distance from texas to milwaukee = 1000 miles
Distance on map = 13.7 inches
Distance from indiana to louisville = 100 miles
Distance on map = x
Using proportion;
Distance from texas to milwaukee: distance on map :: Distance from indiana to louisville : Distance on map
[tex]1000:13.7::100:x[/tex]
Product of mean = Product of extreme
[tex]100*13.7=1000*x\\1370=1000x\\1000x=1370[/tex]
Dividing both sides by 1000;
[tex]\frac{1000x}{1000}=\frac{1370}{1000}\\x=1.37\ inches[/tex]
The distance from Indiana to Louisville is 1.37 inches on map.
Keywords: Ratio, proportion, distance
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9. Wade has 126 inches of 1-inch wide bias tape for a border
on a rectangular banner. If the banner needs to be 48
inches long, what is the maximum width it could be?
Answer:
Let 'x' represent the width.
2*48 + 2x = 126
x = 15 in
The maximum width could be 15 inches.
Final answer:
To find the maximum width of the rectangular banner, calculate the total length of bias tape used, subtract it from the available bias tape, and divide the remaining inches by 2. The maximum width of the banner is 15 inches.
Explanation:
Maximum Width Calculation:
Calculate the total length of bias tape used: 48 inches x 2 sides = 96 inches.
Subtract the total length from the available bias tape: 126 - 96 = 30 inches.
Divide the remaining inches by 2 (since there are 2 widths): 30 / 2 = 15 inches.
!!!!!!!!!!!!!!!!!!!!
Option 3
The solution for given expression is [tex]\frac{(x - 4)(x - 4)}{(x + 3)(x + 1)}[/tex]
Solution:Given that we have to divide,
[tex]\frac{x^2 -16}{x^2 + 5x + 6} \div \frac{x^2 + 5x + 4}{x^2 -2x - 8}[/tex] ---- (A)
Let us first factorize each term and then solve the sum
Using [tex]a^2 - b^2 = (a + b)(a - b)[/tex]
[tex]x^2 -16 = x^2 - 4^2 = (x + 4)(x -4)[/tex] ----- (1)
[tex]x^2 + 5x + 6 = (x + 2)(x + 3)[/tex] ----- (2)
[tex]x^2 + 5x + 4 = (x+1)(x + 4)[/tex] ---- (3)
[tex]x^2 -2x - 8 = (x-4)(x + 2)[/tex] ---- (4)
Now substituting (1), (2), (3), (4) in (A) we get,
[tex]\frac{(x + 4)(x -4)}{(x +2)(x +3)} \div \frac{(x+1)(x+4)}{(x-4)(x +2)}[/tex]
To do division with fractions, we turn the second fraction upside down and change the division symbol to a multiplication symbol at the same time. Then we treat this as a multiplication problem, by multiplying the numerators and the denominators separately.
[tex]\frac{(x + 4)(x -4)}{(x +2)(x +3)} \times \frac{(x - 4)(x + 2)}{(x + 1)(x + 4)}[/tex]
On cancelling terms we get,
[tex]= \frac{(x -4)(x-4)}{(x + 3)(x + 1)}[/tex]
Thus option 3 is correct
f is a quadratic function whose graph is a parabola opening upward and has a vertex on the x-axis. The graph of the new function g defined by g(x) = 2 - f(x - 5) has a range defined by the interval
A. [ -5 , + infinity)
B. [ 2 , + infinity)
C. ( - infinity , 2]
D. ( - infinity , 0]
PLEASE MARK BRAINLIEST!
Answer:
Your answer is C. ( - infinity , 2]
Step-by-step explanation:
Because it is, and I found the answer right next to an image I was searching up. Coincidences, am I right?
PLEASE HELP I PUT 70 POINTS!!!!!
1. 8/64=1/8
2. 5/16
3. 33/84
4. 15/45=3/9=1/3
Answer:
1. 8/64=1/8
2. 5/16
3. 33/84
4. 15/45=3/9=1/3
Step-by-step explanation:
The functions from part A are f(x) = 2.5e-0.04x and g(x) = 1.2 + 0.2x. Enter the expression that results from f(x) − g(x). Give your answer in simplest form.
Answer: edmentum 100%
f(x) − g(x) = 2.5e-0.04x − (1.2 + 0.2x)
= 2.5e-0.04x − 1.2 − 0.2x
Step-by-step explanation:
The algebraic expression resulting from subtracting g(x) from f(x), required to subtract g(x) from f(x) term by term is [tex]2.5e^{(-0.04x)} - 1.2 - 0.2x.[/tex]
Given that the functions from part A are :
[tex]f(x) = 2.5e^{(-0.04x)}\\g(x) = 1.2 + 0.2x[/tex]
To find the expression resulting from subtracting g(x) from f(x), required to subtract g(x) from f(x) term by term.
Step 1: Given two functions
[tex]f(x) = 2.5e^{(-0.04x)}\\g(x) = 1.2 + 0.2x[/tex]
Step 2: find f(x) - g(x), subtract each term:
[tex]f(x) - g(x) = (2.5e^{(-0.04x)}) - (1.2 + 0.2x)[/tex]
Simplifying further, combine like terms:
[tex]f(x) - g(x) = 2.5e^{(-0.04x) }- 1.2 - 0.2x[/tex]
Therefore, the algebraic expression resulting from f(x) - g(x) is [tex]2.5e^{(-0.04x)} - 1.2 - 0.2x.[/tex]
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fire work a travels at the speed 300 ft/s firework b travels 240 ft/s. firework b is launched 0.25s before firework a. how many seconds after firework b launches will both fireworks explode?
Answer:
Both fireworks will explode after 1 seconds after firework b launches.
Step-by-step explanation:
Given:
Speed of fire work A= 300 ft/s
Speed of Firework B=240 ft/s
Time before which fire work b is launched =0.25s
To Find:
How many seconds after firework b launches will both fireworks explode=?
Solution:
Let t be the time(seconds) after which both the fireworks explode.
By the time the firework a has been launched, Firework B has been launch 0.25 s, So we can treat them as two separate equation
Firework A= 330(t)
Firework B=240(t)+240(0.25)
Since we need to know the same time after which they explode, we can equate both the equations
330(t) = 240(t)+240(0.25)
300(t)= 240(t)+60
300(t)-240(t)= 60
60(t)=60
[tex]t=\frac{60}{60}[/tex]
t=1
Final answer:
By setting the distance traveled by both fireworks equal, we find that both Firework A and B will explode 1.25 seconds after Firework B is launched.
Explanation:
To solve the problem of when both fireworks will explode, we can use the constant speed equation distance = speed × time. Firework A travels at 300 ft/s, and Firework B travels at 240 ft/s. Firework B is given a 0.25s head start. We need to find the time when they have traveled the same distance.
Let's call the time after Firework B launches when both explode as t. Since Firework A launches 0.25s after B, it will have traveled for t - 0.25s when they explode together. The equations for the distances traveled by both fireworks until that point will be:
Distance Firework A: 300 (t - 0.25)Distance Firework B: 240 tSetting these distances equal to each other:
300 (t - 0.25) = 240 t
Solving for t:
300t - 75 = 240t
60t = 75
t = 1.25s
Therefore, both fireworks will explode 1.25 seconds after Firework B launches.
Given ^MNO = ^PQR,
MN = 6 +2y, MO = 2x + 1,
PO = 3y + 4, and PR = 10 - X.
Find the lengths of PQ and PR.
Answer:
Part 1) [tex]PQ=10\ units[/tex]
Part 2) [tex]PR=7\ units[/tex]
Step-by-step explanation:
The correct question is
The triangles MNO and PQR are congruent. (MNO≅PQR)
Find the lengths of PQ and PR.
we know that
If two figures are congruent, then its corresponding sides are congruent
In this problem
MN and PQ are corresponding sides
MO and PR are corresponding sides
NO and QR are corresponding sides
therefore
MN≅PQ
MO≅PR
NO≅QR
step 1
Find the value of y
we have
[tex]MN = 6 +2y\\ PQ = 3y + 4[/tex]
equate the equations
[tex]3y + 4=6 +2y[/tex]
solve for y
[tex]3y-2y=6-4[/tex]
[tex]y=2[/tex]
step 2
Find the length of PQ
[tex]PQ = 3y + 4[/tex]
substitute the value of y
[tex]PQ = 3(2) + 4=10\ units[/tex]
step 3
Find the value of x
we have
[tex]MO = 2x + 1\\PR = 10 - x[/tex]
equate the equations
[tex]2x+1=10-x[/tex]
solve for x
[tex]2x+x=10-1[/tex]
[tex]3x=9[/tex]
[tex]x=3[/tex]
step 4
Find the length of PR
[tex]PR = 10 - x[/tex]
substitute the value of x
[tex]PR = 10-3=7\ units[/tex]
a line with a slope of 5/3 passes through the point (10, -5). what is its equation in point slope
The equation of line in point-slope form with slope 5/3 passing through the point (10-5) is:
[tex]y+5 = \frac{5}{3}(x-10)[/tex]
Step-by-step explanation:
Given
Slope = m = 5/3
Point = (x1,y1) = (10, -5)
Point-slope form is:
[tex]y-y_1 = m(x-x_1)[/tex]
As the slope and point is already given, we only have to put the values in the equation to get the equation of required line:
[tex]y-(-5) = \frac{5}{3}(x-10)\\y+5 = \frac{5}{3}(x-10)[/tex]
Hence,
The equation of line in point-slope form with slope 5/3 passing through the point (10-5) is:
[tex]y+5 = \frac{5}{3}(x-10)[/tex]
Keywords: equation of line, point-slope form
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The equation A = lw is an example of an
Answer:
A=lw is a formula for the area. L is length, W is width.
Diego has 48 chocolate chip cookies, 64 vanilla cookies, and 100 raisin cookies for a bake sale. He wants to make bags that have all three cookie flavors and the same number of each flavor per bag.
How many bags can he make without having any cookies left over?
The number of bags he can make without having any cookies left over is 4 bags.
Number of chocolate chips = 48Number of vanilla cookies = 64Number of raisin cookies = 100How to find highest common factor48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
64 = 1, 2, 4, 8, 16, 32 and 64
100 = 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The highest common factor of 48, 64 and 100 is 4
Therefore, the number of bags he can make without having any cookies left over is 4 bags
Each bag has:
chocolates cookies = 48/4
= 12 each
Vanilla cookies = 64/4
= 16 each
Raisin cookies = 100/4
= 25 each
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Diego can make 12 bags without having any cookies left over, ensuring each bag contains an equal number of each flavor.
To determine how many bags Diego can make without having any cookies left over, we need to find the greatest common divisor (GCD) of the quantities of each type of cookie.
Step 1:
Find the GCD of the quantities of each type of cookie:
GCD(48, 64, 100) = 4
Step 2:
Calculate the number of bags Diego can make:
Each bag will contain 4 cookies of each flavor, as determined by the GCD.
For chocolate chip cookies: 48 cookies ÷ 4 cookies/bag = 12 bags
For vanilla cookies: 64 cookies ÷ 4 cookies/bag = 16 bags
For raisin cookies: 100 cookies ÷ 4 cookies/bag = 25 bags
Step 3:
Determine the minimum number of bags Diego can make without any cookies left over:
The minimum number of bags is determined by the smallest number of bags he can make for any type of cookie, which is 12 bags for chocolate chip cookies.
Therefore, Diego can make 12 bags without having any cookies left over.
The length of the minute hand on a clock is 5 in....is it a dimeter, circumference, radius?
Answer: Radius
Step-by-step explanation: The radius of a circle is a segment that joins the center of the circle to a point on the circle.
The minute hand on a clock would start in the center and go outwards towards a certain number. However, the minute hand would not go the full length across the clock so it's not the diameter.
The circumference of a circle which is another way of saying the perimeter of the circle is the distance around the circle so it would not be the circumference.
This means that the minute hand would represent the radius of a clock.
The 5 inch length of the minute hand on the clock is actually a radius, not a diameter or circumference. This radius is the distance from the center of the clock face to the tip of the minute hand. The diameter, which would be twice the length of the radius, would be 10 inches, and the circumference of the circle formed by the minute hand's movement would be approximately 31.4 inches.
Explanation:In this case, the 5 inches refers to the radius of the circle that is created by the minute hand of the clock as it moves around the clock face. This radius is the distance from the center of the clock face to the tip of the minute hand. In general, in any circular motion, the length of the revolving component, like a clock hand, from the center to its tip is called the radius of the circle.
The diameter is simply twice the radius, and in this case if the radius is 5 inches, the diameter would be 10 inches. The circumference of a circle is calculated by the formula 2πr (2 times the value of pi times the radius), hence, in this instance, it would be 10π inches or approximately 31.4 inches.
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The volume of a cylinder, V(h), is given by the area of the base times the height, h. The base of the cylinder shown below has a diameter of 5 inches.
Part A: Write the function, V(h), that represents the volume of the cylinder
Part B: find V(3) and tell what it represents
Answer:
Part a) [tex]V(h)=6.25\pi h\ in^3[/tex]
Part b) [tex]V(3)=18.75\pi\ in^3[/tex] (see the explanation)
Step-by-step explanation:
we know that
The volume of a cylinder is equal to
[tex]V=Bh[/tex]
where
B is the area of the base of cylinder
h is the height of the cylinder
we have that
[tex]B=\pi r^{2}[/tex]
Part a) Write the function, V(h), that represents the volume of the cylinder
we have
[tex]r=5/2=2.5\ in[/tex] ----> the radius is half the diameter
substitute
[tex]B=\pi (2.5)^{2}[/tex]
[tex]B=6.25\pi\ in^2[/tex]
The volume is
[tex]V(h)=6.25\pi h\ in^3[/tex]
Part b) Find V(3) and tell what it represents
V(3) represent the volume of the cylinder with a height of 3 inches
so
For h=3 in
substitute
[tex]V(3)=6.25\pi(3)\ in^3[/tex]
[tex]V(3)=18.75\pi\ in^3[/tex]
Final answer:
The function for the volume of the cylinder with diameter 5 inches is V(h) = π * (2.5 inches)² * h. To find V(3), we calculate the volume with height 3 inches, which represents the physical volume of the cylinder at that height.
Explanation:
To find the volume of the cylinder, V(h), we must use the formula V = πr²h, where r is the radius of the base, and h is the height of the cylinder.
Part A: Given that the diameter is 5 inches, the radius is half of the diameter, so r = 5 / 2 = 2.5 inches. Thus, the function representing the volume is V(h) = π * (2.5 inches)² * h.
Part B: To find V(3), we substitute h with 3 inches into the function: V(3) = π * (2.5 inches)² * 3 inches. This gives us the volume of the cylinder when the height is 3 inches.
If y varies inversely as the square of x, and y=2 when x=4, find y when x=4
Answer:
y = 2
Step-by-step explanation:
Given that y varies inversely as the square of x then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
To find k use the condition y = 2 when x = 4
k = yx² = 2 × 4² = 2 × 16 = 32, thus
y = [tex]\frac{32}{x^2}[/tex] ← equation of variation
When x = 4, then
y = [tex]\frac{32}{4^2}[/tex] = [tex]\frac{32}{16}[/tex] = 2
the temperature is -2 if the temperature rises by 15 what is the new temperature
Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24? A. {2, 4, 9} B. {12, 4, -6} C. {-4, 4, 14} D. {-12, -4, 6}
The range is: B. {12, 4, -6}
Step-by-step explanation:
Given
12x + 6y = 24
Here x is the input and y is the output
So,
Replacing y with f(x)
[tex]12x +6f(x) = 24\\6f(x) = 24 - 12x\\\frac{6f(x)}{6} = \frac{24-12x}{6}\\f(x) = \frac{24-12x}{6}[/tex]
Domain = {-4, 0, 5},
We will put the elements of domain, one by one, to find range
[tex]f(-4) = \frac{24-12(-4)}{6}\\=\frac{24+48}{6}\\= \frac{72}{6}\\=12\\\\f(0) = \frac{24-12(0)}{6}\\=\frac{24}{6}\\= 4\\\\f(5) = \frac{24-12(5)}{6}\\=\frac{24-60}{6}\\=\frac{-36}{6}\\=-6[/tex]
Hence,
The range is: B. {12, 4, -6}
Keywords: Range, Domain, functions
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{12, 4, -6}
Step-by-step explanation:
The relation is given by the equation as 12x + 6y = 24 ........... (1)
Now, the domain of this function is {-4, 0, 5}
We have to find the range of this function corresponding to the given domain.
Now, for x = - 4,
12(-4) + 6y = 24 {From equation (1)}
⇒ 6y = 72
⇒ y = 12
Now, for x = 0,
12(0) + 6y = 24 {From equation (1)}
⇒ 6y = 24
⇒ y = 4
Now, for x = 5,
12(5) + 6y = 24 {From equation (1)}
⇒ 6y = -36
⇒ y = -6
Hence, the range for the relation is {12, 4, -6} (Answer)
Please help with steps:
converting a fraction to a termination decimal: basic
69
-----
20
Answer:
3.45
Step-by-step explanation:
if you look at the picture all the steps are provided
GOOD LUCK!!
what is 23,234+12,346?
For this case we must solve the following sum:
23,234
+ 12,346
---------------
35,580
We place the addends one below the other so that the units coincide in the same column. We add each digit, we get the expression:
[tex]35,580[/tex]
ANswer:
[tex]35,580[/tex]
What prevent is modeled below
It shows 100 squares and 35 are shaded
A 25%
B 35%
C 45%
D 65%
I think the answer is 35%
Answer:
B 35%
Step-by-step explanation:
35/100 reduces to .35. To turn this into a percent, multiply it by 100 and add a percent sign. .35 * 100 = 35. 35%
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
Total number of squares = 100
Number of shaded squares = 35
The percentage of shaded squares is 35%
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Total number of squares = 100
Number of shaded squares = 35
The percentage of shaded squares.
= 35/100 x 100
= 35%
Thus,
The percentage of shaded squares is 35%
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Stanley's mother owns a stationary shop. Stanley helped his mother pack 319 pencil cases into packets of 7. In the end, 25 packets of pencils cases were sold. How many pencils cases were not sold?
They sold 25 packets, containing 7 pencils each. So, they sold a total of
[tex]25\cdot 7=175[/tex]
pencils. This means that
[tex]319-175=144[/tex]
pencils were not sold.
A sphere with a radius of 6 cm has the same volume as a cone with a height of 6 cm. What is the radius of the cone?
A) 2 cm
B) 4 cm
C) 8 cm
D) 12 cm
D) 12 cm is the right answer
Step-by-step explanation:
Given
[tex]Radius\ of\ sphere = r_s = 6\ cm\\Height\ of\ cone = h = 6 cm\\[/tex]
As the volumes of cone and sphere are same
[tex]V_s = V_c\\\frac{4\pi {r_s}^3}{3} = \frac{\pi {r_c}^2h}{3}[/tex]
Putting the known values
[tex]\frac{4\pi {6}^3}{3} = \frac{\pi {r_c}^2*(6)}{3}[/tex]
Dividing both sides by pi
[tex]\frac{4\pi {(6)}^3}{3\pi } = \frac{\pi {r_c}^2*(6)}{3\pi }\\\frac{4*{(6)}^3}{3} = \frac{{r_c}^2*(6)}{3}[/tex]
Multiplying both sides by 3
[tex]4*(6)^3 = 6{r_c}^2\\{r_c}^2 = \frac{4*(6)^3}{6}\\{r_c}^2 = 4 * 6^2\\{r_c}^2 = 144[/tex]
Taking Square root on both sides
[tex]\sqrt{{r_c}^2}=\sqrt{144}\\r_c = 12\ cm[/tex]
Hence,
D) 12 cm is the right answer
Keywords: Volumes, areas
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A pizzeria sells pizza according to size:small pizzas cost 10$, medium pizzas 15$ and large pizzas cost 40$. They usually sell as many small pizzas as medium and large pizzas combined. The number of medium pizzas sold is usually twice as many as large ones. How many of each size pizza must they sell to get 600$.
Answer:
6 large, 12 medium and 18 small
Step-by-step explanation:
Lets call small pizzas s, medium pizzas m and large pizzas l, with its respective prices $10, $15 and $40.
As they sell as many small as medium and large combined we can say that:
s = m + l [eq 1]
Also, as the number of medium is twice the larges we can say that:
m = 2l [eq 2]
Finally, as the get $600 we know that every amount sold multiplied by its price, and summing all together must bring $600:
10s + 15m + 40l = 600 [eq 3]
Lets replace s by its value in eq 1:
10s + 15m + 40l = 10 (m+l) 15m + 40l = 10m +10l + 15m + 40l = 600
25m + 50l = 600
Now we can replace m by its value in eq 2:
25m + 50l = 25 (2l) + 50 l = 50l + 50l = 100l = 600
100l = 600
Now divide both sides by 100:
l = 6
So, 6 large pizzas were sold.
Replace l=6 in eq 2:
m = 6*2
m = 12
12 medium pizzas were sold.
Finally, replace l=6 and m=12 in eq 1
s = m + l = 12 + 6 = 18
And 18 small pizzas were sold.
Lets verify our results in eq. 3:
10*(18) + 15*(12) + 40*(6) = 600
180 + 180 + 240 = 600
360 + 240 = 600 ---> Verified!
How do you divide 3 1/4 and 3?
First we're going to change the 3 1/4 into an improper fraction.
3 1/4 is the same as 13/4
When dividing fractions, it's the same thing as multiplying by the reciprocal.
What this means is we're going to flip the second fraction.
So the original problem is this:
13/4 divided by 3/1
It now looks like this:
13/4 multiplied by 1/3
Then, simply multiply the top numbers together and then multiply the bottom numbers together.
13*1=13
4*3=12
your answer is 13/12
12ab = 4 solve for a
Two expressions connected with equal sign is called equation. a=1/3b is the value for equation 12ab=4.
What is an equation?Two expressions connected with equal sign is called equation.
Given 12ab=4
We need to solve for a
12ab=4
Divide both sides by 12b
a=4/12b
a=1/3b
So a=1/3b is the value of a for equation 12ab=4
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