Dario cut 15 slices of lasagna containing 1/4 pounds of cheese.
Total amount of cheese in lasagna =
[tex] \frac{2}{3} [/tex] + [tex]1 \frac{3}{4} [/tex] + [tex]1 \frac{1}{3} [/tex]
Total amount of cheese = [tex] \frac{2}{3} [/tex] + [tex] \frac{7}{4} [/tex] + [tex] \frac{4}{3} [/tex]
Taking LCM we get 12
Total amount of cheese = (2×4) + (7×3) + (4×4)/12
Total amount of cheese = 8 + 21 + 16/12
Total amount of cheese = 45/12 pounds
Number of slices = total amount of cheese ÷ amount of cheese in each piece
Number of slices = 45/12 ÷ 1/4
Number of slices = (45×4) ÷ 12
Number of slices = 15
Thus, there are 15 slices of lasagna.
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Fill in the missing numbers
1/2 of 50 =
1/3 of 36 =
Answer:
25 and 12
Step-by-step explanation:
1/2 of 50 = can be rewritten as (1/2)*(50) = (50/2) = 25
1/3 of 36 = can be rewritten as (1/3)*(36) = (36/3) = 12
Answer:
1/2 of 50 could also be re-written as 1
___ × 50
2
So to solve this we need to multiply 1 by 50
like this 50×1
which is equal to 50 i.e 50 × 1 = 50
the next step is to then divide by 2
i.e 50
___ = 25
2
this is so because there are simply 2 25s in 50
So i guess you should be able to do the second one
Jaane
Which expression can be used to determine the slope of the linear function represented in the table?
0 5
4 9
9-5
4-0
4-0
9-5
5-0
9-4
9-4
5-0
The first expression (9 - 5) / (4 - 0) is used to determine the slope of the linear function represented in the table.
What is slope of the line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.
From the given table the points are, (0, 5) and (4, 9).
Since, for points [tex](x_1, y_1), (x_2, y_2)[/tex] the slope can be defined as,
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex](x_1, y_1)=(0, 5)\\(x_2, y_2)=(4, 9)[/tex]
So, the slope is
[tex]m = \frac{9-5}{4-0}[/tex]
This is the first expression.
Therefore, the first expression (9 - 5) / (4 - 0) is used to determine the slope of the linear function represented in the table.
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f(x) = 2x x = -3,5
The Value of f(x) for x = -3 is
Answer:
y = 2x we need to solve when x= -3. Using elimination, we can solve this system of equations like this:
y = 2x
x = -3
*2 *2
simplify
y = 2x
-6 = 2x
subtract
y+6=0
-6 -6
y=-6
So, when x=-3, y=-6
What is the midpoint of PQ
The density of copper is 9.86 g/cm3.
Work out the mass of the solid copper cuboid in kg.
10 cm
3 cm
5 cm
The mass of the solid copper is 1479 g.
According to the question,
We have the following information:
The density of copper is 9.86 g/[tex]cm^{3}[/tex].
Measurements of the solid copper cuboid = 10 cm, 3 cm and 5 cm
We know that the following formula is used to find the volume of cuboid:
Volume = length*breadth*height
Volume = 10*3*5
Volume = 150 [tex]cm^{3}[/tex]
Now, we know that the following formula is used to find the density of an object:
Density = mass/volume
9.86 = mass/150
Using the cross multiplication method:
Mass = 150*9.86
Mass = 1479 g
Hence, the mass of the solid copper is 1479 g.
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Math Learning task no.2
Ming Meding prepared 12 banna muffins
and 18 squid ball's find the ratio of the number of banna muffins to the number of squid balls. Write it in throw forms.
pls pa helg need ko na sagutan ^_^
Answer:
12:18
Step-by-step explanation:
Yan te ok na ata yan
Answer:
12:18
Step-by-step explanation:
You have 12 banana muffins, and 18 squid ball's.
Put it in ratio form. so it's B:S in name form, so the final answer will be 12:18.
If you put it in this form S:B, then the answer will be 18:12.
Goodluck!
A regular pentagon has side lengths of 14. 1 centimeters and an apothem with length 12 centimeters. What is the approximate area of the regular pentagon?.
The approximate area of the regular pentagon is 342cm²
Using the Pythagorean theorem, we can calculate the apothem of the pentagon.
We have then:
a = √(12² - (14.1/2)²)
a = 9.7
Then, the area of the pentagon is given by:
Area = 5 (1/2) x l x a
Where,
L: side of the pentagon
a: apotema
Substituting values:
area = 5(1/2) x 14.1 x 9.7
area = 341.925 cm²
Rounding the nearest whole we have: 342 cm²
Hence, the approximate area of the regular pentagon is 342cm²
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Write an equation in point-slope form of the line that passes through the given point and with the given slope m. (-7,1); m=6
Answer:
y - 1 = 6(x+7)
Step-by-step explanation:
point slope form is y-y₁=m(x-x₁)
given m = 6 and the point is (-7,1)
plug in your values
remember that an ordered pair is (x,y)
y-y₁=m(x-x₁) ----> y-1 = 6(x+7)...............just plug in values
2 in the coordinate plane, line p has slope 1 3 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin. What are the slope and y-intercept of line r?.
The slope of the line r is 3 and the y intercept is (0,15) .
We know that coordinates of the point (x,y) after dilation by factor k centered at (a,b) is (k(x-a) + a , k(y-b) + b) .
In the question ,
it is given that
the slope of the line p [tex]=[/tex] 3
and the intercept of the line p = (0,2)
So , the equation of the line p is y = 3x + 2 .
So , the coordinates of the point (0,2) after dilation by factor 3 centered at (0,0) is (3(0 - 0) + 0 , 3(5 - 0) + 0)
= (0 , 15)
Point (0,0) does not lie on the line, so the line r after dilation is parallel to the line p,
the slope of line r = 3 , the y intercept is 15 .
Therefore , The slope of the line r is 3 and the y intercept is (0,15) .
The given question is incomplete , the complete question is
In the coordinate plane, line p has slope 3 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin. What are the slope and y-intercept of line r ?
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a recipe for cookies says 2/3 of a cup of sugar will be enough to feed 3/4 of my class. how much sugar will i need to make enough cookies to feed my whole class?
Sugar will i need to make enough cookies to feed my whole class is 11 cups.
Given:
A recipe for cookies says 2/3 of a cup of sugar will be enough to feed 3/4 of my class.
2/3 cup of sugar = 3/4 of my class
Multiply by 12 on both sides
2*12/3 = 3*12/4
24/3 = 36/4
8 cups of sugar = 9 of my class.
if 3/4 = 9 whole class = 12.a
Add plus 3 on both sides
8 + 3 = 9 + 3
11 cups of sugar = 12 of my class.
Therefore Sugar will i need to make enough cookies to feed my whole class is 11 cups.
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Two lines L1 and L2 have equations 3y = 6x + 5 and y- 2x = 1 respectively. Show that two lines are parallel.
Answer:
see explanation
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 )
line 1
3y = 6x + 5 ( divide through by 3 )
y = 2x + [tex]\frac{5}{3}[/tex] ← in slope- intercept form
with slope m = 2
line 2
y - 2x = 1 ( add 2x to both sides )
y = 2x + 1 ← in slope- intercept form
with slope m = 2
• Parallel lines have equal slopes
then line 1 and line 2 are parallel
2. Taylor is about to go car shopping, and she has $5000 saved that she can use for a down
payment while still having extra cash in her emergency fund. She expects the exact model
car she's looking for to cost $35,000. If her top priority is having the lowest monthly
payments possible, which advice should she follow?wou tonte
a. Put in $0 for your down payment, and choose a loan with a short term length
b. Put in $2500 for your down payment, and choose a loan with a short term length
c. Put in $3500 for your down payment, and choose a loan with a long term length
d. Put in $5000 for your down payment, and choose a loan with a long term length
The best option for Taylor is d. Put in $5000 for your down payment, and choose a loan with a long term length
What is a loan?A loan is the lending of money by one or more individuals, organizations, or other entities to other individuals, organizations, or other entities in finance. The recipient (i.e., the borrower) incurs a debt and is typically required to pay interest on that debt until it is repaid, in addition to repaying the principal amount borrowed.
The document evidencing the debt (for example, a promissory note) will typically specify the principal amount borrowed, the interest rate charged by the lender, and the date of repayment.
In this case, choosing a long term repayment plan will make it easier to pay back.
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Which number produces an irrational number when multiplied by 1/2?
OA. -√49
OB. E
C. 0.555555...
O D.
2/3
Answer:
e
Step-by-step explanation:
e is already irrational so if multiplied by 1/2 it will stay irrational
What does Pascal's triangle represent?.
In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of every binomial formula, such as (x + y)ⁿ.
Explain the term Pascal's triangle?Although it is much older, it bears the name of the French scholar Blaise Pascal from the 17th century. In the eleventh century, the Chinese mathematician Jia Xian created a triangular form for the coefficients.
For instance, the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21), which was first discovered by the mediaeval Italian mathematician Leonardo Pisano ("Fibonacci") in his Liber abaci (1202; "Book of the Abacus"), is produced by drawing parallel "shallow diagonals" and adding the numbers on each line together. Another intriguing characteristic of the triangle is that it will form a fractal understood as the Sierpiski gasket, named for Polish mathematician Wacaw Sierpiski, who lived in the 20th century, if all the positions comprising odd numbers are shaded in black and every positions enclosing even numbers are shaded in white.To know more about the Pascal's triangle, here
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Michael has 12 cups of orange juice in a jar. he pours the juice into glasses that each hold 3/4 cup. How many glasses can he fill
Answer:
Step-by-step explanation:
. = 12\0.75
. = 16
Answer:
16
Step-by-step explanation:
12÷[tex]\frac{3}{4}[/tex] = [tex]\frac{12}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{48}{3}[/tex] = 16
I need this to be converted to a linear equation:
(-1, 3); slope = -3
After converting into a linear equation, we have the equation y = -3x
What is a linear equation?
A linear equation is one in which the variable's maximum power is consistently 1. A one-degree equation is another name for it. This indicates that there are no variables in a linear equation with exponents greater than 1. A linear equation's graph almost always takes the shape of a straight line.
Solution Explained:
From the question, we have
x = -1
y = 3
slope (m) = -3
Substituting these values in the equation,
y = mx + c
3 = (-3) x -1 + c
After simplyfing the equation, we get
c = 0
We again substitute the value of m and c in the equation,
y = mx + c
y = -3x + 0
y = -3x
Hence, the linear equation is y = -3x.
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You enter a bid. Your cost on the product you make is $112 per unit. If you bid at $138 per unit, what percent is the price you bid over your cost? (round to the nearest percent).
The price bid will be increased by 23% over the cost, according to the question.
What do you mean by percentage?
A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.
According to data in the given question,
We have given data:
Cost on the product you make is $112 per unit.
Bid amount $138 per unit,
Cost over the bid= $138-$112 = $26
Now, we need to determine the Percentage increase,
Percentage increase[tex]= \frac{26}{112}*100 \\[/tex]
= 23%
Therefore, the price bid will be increased by 23% over the cost.
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Solve b² +5b + 4 = 0 using completing the squares method
Answer:
b² +5b + 4 = 0
b² + 5b -41= 5.702
3
Step-by-step explanation:
1.1 Factoring b2+5b-4
The first term is, b2 its coefficient is 1 .
The middle term is, +5b its coefficient is 5 .
The last term, "the constant", is -4
Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4
Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is 5 .
-4 + 1 = -3 -2 + 2 = 0 -1 + 4 = 3
(s3-6s)+4t2 when s=5 and 3=t
Answer:
9
Step-by-step explanation:
(5)3-6(5)+4(3)2
(15-30)+4(3)2
-15+ 24
=9
An Olympic ized pool, which hold 660,000 gallon of water, i only 63% full. The pool Maintenance company add more water, filling the pill to 90% full. How many gallon of water did they add?
In linear equation, the amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable.It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.A linear equation in one variable would be 9x + 78 = 18, for instance.The amount of water an Olympic-sized pool can hold is, 660,000 gallons.
The pool is 63% full at the moment.
The of water in the pool now is
63% of 660,000 = 415,800 gallons
If the pool is 90% full then the amount of water in the pool is
90% of 660,000 = 594,000 gallons
The amount of water added by the pool maintenance is:
Amount of water added = 90% of 660,000 - 63% of 660,000
= 594000 - 415800
= 178200
Thus, the amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.
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david drives from his home to the airport to catch a flight. he drives miles in the first hour, but realizes that he will be hour late if he continues at this speed. he increases his speed by miles per hour for the rest of the way to the airport and arrives minutes early. how many miles is the airport from his home?
The distance between David's home and the airport is 210 miles.
Distance traveled after 1 hourlet the distance traveled after first 1 hour = y
distance/speed = time
after 1 hour his speed = (35 + 15) = 50 mph
total time after 1 hour and 30 mins = 1.5 hr
y/50 + 1.5 = y/35
multiply through by 350
7y + 525 = 10y
3y = 525
y = 525/3
y = 175 miles
In the first 1 hour, at 35 mph, distance covered = 35 miles
Distance from his home to airport = 175 miles + 35 miles = 210 miles
Thus, the distance between David's home and the airport is 210 miles.
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Suppose you are interested in learning about how much time seventh grade students at your school spend outdoors on a typical school day.
Select all the samples that are a part of the population you are interested in
Answer: how do you do the question what the
Step-by-step explanation:
y=sin^4(3x).find dy/dx
Keeping it short.
Differentiate each term with respect to [tex]x[/tex], then solve for [tex]y'.[/tex]
[tex]\frac{dy}{dx} =12\sin^3(3x)\text{cos}(3x)[/tex]
Thanks.
3.7x²+x2 combine like terms
Answer:
4.7x²
Step-by-step explanation:
3.7x² + x² = 3.7x² + 1x² = 4.7x²
If $10,000 is borrowed with an interest of 5. 0% compounded annually, what is the total amount of money needed to pay it back in 5 years? round your answer to the nearest cent and do not include the dollar sign. Do not round at any other point in the solving process; only round your answer.
The amount of money that is needed to pay after 5 years is 12762.9 .
In the question ,
it is given that ,
the amount borrowed(P) = $10000
the rate at which the amount is borrowed (r) = 5% = 0.05
the time for which the amount is borrowed (t) = 5 years
the number of times the interest is charge (n) = 1 .
The final amount for the compound interest is calculated using the formula .
Amount = [tex]P\times(1+\frac{r}{n})^{nt}[/tex]
Substituting the value of P , r , n and t , in the formula ,
we get
Amount = 10000 (1 + 0.05)⁵
= 10000*(1.05)⁵
= (10000)*(1.2762815625)
= 12,762.815625
≈ 12762.9
Therefore , The amount of money that is needed to pay after 5 years is 12762.9 .
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Provide an explanation please
Answer: 84m
Step-by-step explanation:
If one of the perimeters are 2m longer than the other that means on side can be expressed as x and the other expressed as x+2
So the equation for the area is [tex]x^{2} \\[/tex]+2x
Becasue the shaded area has an gap of in it we need to find the area of the gap to find the total area of the square
0.5x3x4=6
114+6
So the total area is 120
So we can use the area equation from before to figure out x
120=[tex]x^{2} \\[/tex]+2x
0=[tex]x^{2} \\[/tex]+2x-120
0=(x-10)(x+12)
Since its a measurement x must equal 10
Now we know that one side is 20m and the other is 22m
So the perimetre must be 84
Kevin is choosing between two cell phone plans. Plan A has a flat monthly charge of $32 for an unlimited number of minutes. Plan B has a monthly charge of $24 plus an additional charge of $0.05 per minute. For what number of minutes of monthly usage do both plans cost the same amount?
If Plan B has a monthly charge of $24 plus an additional charge of $0.05 per minute. The number of minutes of monthly usage that both plans cost the same amount is 160 minutes.
How to find the number of minutes?Let x represent the number of minutes of monthly usage
Hence,
Formulate an equation
0.05x + 24 = 32
Combine like terms
0.05x = 32 -24
0.05x = 8
Divide both side by 0.05x
x = 8/0.05
x = 160 minutes
Therefore 160 is the number of minutes.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The graph of the exponential function y = (3/4)^x is given by the following option:
Option A.
How to obtain the graph of the exponential function?The general format of an exponential function is defined as follows:
[tex]y = ab^x[/tex]
The meaning of the parameters a and b are given as follows:
a is the initial value of the function, which is the value of the function when it crosses the y-axis.b is the rate of change of the function, determining if the function increases or decreases, and how fast it decreases of increases.In this problem, the function is given by:
y = (3/4)^x.
Hence the values of the parameters are:
a = 1, b = 3/4.
The parameter a = 1 means that the function crosses the y-axis at y = 1, hence options B and C are removed.
From the table given in the problem, at x = -2 the function is very close to 2, while it decreases to a value close to 0.5 at x = 2, hence option A is the correct option for the graph of the exponential function.
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Let the graph of g be a vertical stretch by a factor of 2 and a
reflection in the x-axis, followed by a translation 3 units down of
the graph of f(x) = x². Write a rule for function g and identify the
vertex.
Vertex is slang for a corner or a place where two lines converge.The four corners of a square, for instance, are each referred to as a vertex.
Write a rule for function g and identify the vertex ?
The graph of g is a vertical stretch by a factor of 2 followed by a translation of 3 units down of the graph of f(x) = (x-1)²then the function g(x) = 2(x+4)²
f(x) =x²-2x+1 The graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of .f(x) =x²-2x+1
Rewrite the given function f(x).
f(x) = (x-1)²
Now, the graph is stretched vertically by a factor of 2.
= 2(-x-1)²
reflect the graph about the y-axis.
2(x+1)²
move to the left by 3 units.
= 2(x+3+1)²
=2(x+4)²
The function g(x) =2(x+4)²
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How do you find the table of values on a graph?.
The table of values on the given graph is for the polynomial y = -x+4.
The example we are using is a polynomial in one variable. It is to be represented graphically. The graph for it is given below.
From this graph, we can clearly see the coordinates of all points we have taken. In order to make the table of values, we need to find the x and y intercepts.
We see that the first point from the left is aligned to the -2 on the x-axis and to the 6 on the y-axis. Similarly, we can identify the following values from the given graph.
x = -2 and y = 6
x = -1 and y = 5
x = 0 and y = 4
x = 1 and y = 3
x = 2 and y = 2
This is the table of values that we found out through the graph.
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