Answer:
£20 note, £5 note, 50p,50p,50p, 5p
Step-by-step explanation:
Liam buys some fruit for £26.55 by paying 2 notes of £20 and £5 and 3 coins of 50 cent and one coin of 5 cent.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
Liam buys some fruit for £26.55.
He pays the exact amount using two notes and four coins.
So, possible notes are £1, £5, £10 and £20.
And the possible coins are 1¢, 5¢, 10¢, 25¢, 50¢, and £1.
So, through trial and error,
we get notes of £20 and £5.
And the coins are three coins of 50 cent and 1 coin of 5 cent.
The total amount = adding the amount of notes and coins.
£26.55 = £20 + £5 + 3(50¢) + 5¢
Therefore, notes of £20 and £5 and the coins are three coins of 50 cent and 1 coin of 5 cent, Liam used.
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Need help finding the perimeter
13 + √85/3 is the perimeter of triangle .
Explain what a triangle is.
A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.The points P ( - 3 , -8 ) Q ( - 3, - 1) R ( -9,-8)
Distance between PQ = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]
= [tex]\sqrt{( - 1 + 8)^{2} + ( -3 + 3)^{2} }[/tex]
= [tex]\sqrt{( -7 )^{2} +0 }[/tex]
= √49 ⇒ 7
Distance between QR = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]
= [tex]\sqrt{( -9 + 3 )^{2} + ( -8 + 1)^{2} }[/tex]
= [tex]\sqrt{(- 6)^{2} + ( - 7)^{2} }[/tex]
= [tex]\sqrt{36 + 49}[/tex]
= √85
Distance between RP = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]
= [tex]\sqrt{( - 3 + 9)^{2} + ( -8 + 8)^{2} }[/tex]
= [tex]\sqrt{(6)^{2} }[/tex]
= √36
= 6
perimeter = PQ + QR+RP/3
= 7 + √85 + 6/3
= 13 + √85/3
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The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units.
A solid oblique pyramid has an equilateral triangle base with a base edge length of 14 units. The base triangle is triangle A C D. The apex is point B. The angles formed with the lateral sides are 45 degrees.
What is BC, the height of the pyramid?
7 units
7StartRoot 2 EndRoot units
14 units
14StartRoot 2 EndRoot units
The height of the pyramid = BC = 14 units
What is a pyramid?It is a three-dimensional shape that has a polygonal base and flat triangular faces which joins at the apex at the top of the pyramid.
We have,
Base edge length = 14 units
From the figure below,
The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units so,
We get,
AC = CD = AD = 14 units _____(1)
All sides in an equilateral triangle are equal.
In the right triangle ABC,
tan 45° = BC / AC
tan 45° = 1
1 = BC / AC _____(2)
From (1) and (2) we get,
1 = BC / 14
BC = 14 units
The height of the pyramid = BC = 14 units
Thus,
The height of the pyramid is 14 units.
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Answer: C 14 UNITS
Step-by-step explanation:
A (2,-4), B (3, 3) and C (-1,5) are the vertices of ΔABC . Find the equation of the altitude of the triangle through C.
Answer:
x + 7y = 34
Step-by-step explanation:
the altitude through C meets the opposite side AB at right angles
calculate the slope of AB using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A (2, - 4 ) and (x₂, y₂ ) = B (3, 3 )
[tex]m_{AB}[/tex] = [tex]\frac{3-(-4)}{3-2}[/tex] = [tex]\frac{3+4}{1}[/tex] = [tex]\frac{7}{1}[/tex] = 7
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}{7}[/tex] , then
y = - [tex]\frac{1}{7}[/tex] x + c ← partial equation of the altitude
to find c substitute C (- 1, 5 ) into the partial equation
5 = [tex]\frac{1}{7}[/tex] + c ⇒ c = 5 - [tex]\frac{1}{7}[/tex] = [tex]\frac{35}{7}[/tex] - [tex]\frac{1}{7}[/tex] = [tex]\frac{34}{7}[/tex]
y = - [tex]\frac{1}{7}[/tex] x + [tex]\frac{34}{7}[/tex] ( multiply through by 7 )
7y = - x + 34 ( add x to both sides )
x + 7y = 34 ← equation of altitude in standard form
If the breadth of a rectangle is reduced by 4cm it's are would be reduced by 240 cm². How long is the rectangle?
Answer:
Let the length be x. The breadth be y Area=xy. On reducing breadth by 4 new breadth will be (y-4). X(y-4)=xy-240. Xy-4x=xy-240. -4x=-240. X=60. Hence rectangle is 60cm long
Step-by-step explanation:
hope it will help
the population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. after 3 hours it is observed that 400 bacteria are present. after 10 hours 2000 bacteria are present. what was the initial number of bacteria?
The initial number of bacteria in a culture is found as 200.
What is defined as the population growth?When demographers try to forecast changes in population size, they generally focus on four factors: fertility rates, high mortality (life expectancy), and the population's initial age profile.Using the model P = P₀e^(kt),
Where:
P(t) = the amount of bacteria at time t = 2000.
P₀ = initial amount at time t = 0
r = growth rate
t = time (number of periods)
k is the growth constant.
For t = 3 hours.
400 =P₀e^(k*3) ......eq 1
2000 = P₀e^(k*10) ......eq 2
Re writing eq 1.
400 = P₀e^(k*3)
as (400/P₀) = [e^k]^3,
Solve for e^k,
∛(400/P₀) = e^k
For eq 2.
2000 = P₀e^(k*10)
Rewrite it as;
(2000/P) = [e^k]^10.
Substituting ∛(400/P₀) for e^k, we obtain:
(2000/P₀) = (400/P₀ )^(10/3)
Solved for P.
Raise sides by the power of 3, we get:
(2000/P₀)^3 = (400/P₀)^10.
Therefore,
2000^3/ P₀^3 = 400^10/P₀^10
Solve,
2000^3/ 1 = 400^10/P₀^7
Taking reciprocal.
Solving
P₀^7 = 400^10/2000^3
P₀^7 = 1.31 x 10¹⁶
Take the 7th root of both sides;
P₀ = 200.67
Thus, the initial number of bacteria in a culture is found as 200.
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Apply the Strategy Solve each problem by making a table. 5. 1. A page from Dana's album is shown. Dana puts the same number of stickers on each page. She has 30 pages of stickers. How many stickers does she have in all? Dana has stickers in all. MOPPOPPG-BUDG
Step 1:
First count the number of stickers on a page
There are 12 stickers in a page
Step 2
There are 30 pages,
Hence, the number of stickers in 30 pages = 30 x 12 = 360
Final answer
Dana has 360 stickers in all
Evaluate. −8+(6+4)÷(−2)
Answer:
-1
Step-by-step explanation:
-8+10÷(-2)
2÷(-2)
-1
Solve for y 10x -5y=30
Answer:
y=2(x−3)
Step-by-step explanation:
Round 2.629 to the nearest tenth.
Answer:
2.6
Step-by-step explanation:
cause it is 2.6299999999
2.629 to the nearest tenth is 2.6.
What is decimal?Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.
Given:
A decimal number,
2.629.
Here, 2 is the whole number component and 0.629 is the fractional component part.
To round the number to the nearest tenth:
The number in tenth place is 6.
And the value right next to 6 is 2.
6 > 2.
So, the number will stay the same.
2.629 = 2.63
Then 2.63 = 2.6 to the nearest tenth.
Therefore, 2.6 is the required decimal.
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with show work. trigonometry
Answer:
See below
Step-by-step explanation:
To find pole height
for a right triangle
sin 38 = opposite leg / hypotenuse = height /15 m
sin 38 = height / 15
15 sin 38 = height = 9.2 meters
To find rope DC
Use pythagorean theorem ( you have leg1 = height and leg 2 = 10.7)
DC ^2 = 9.2^2 + 10.7^2
DC = 14.1 m
The sum of three numbers is 23. The third number one more than the sum of the first and second numbers. The first number is ten less than the third number. Find the numbers.
Answer:
2, 9, 12
Step-by-step explanation:
We know that the first number is ten less than the third number and that the third number is one more than the first number and second number combined. Because of this, our third number has to be one away than the combination of the first two numbers. Now, we just have to see the numbers of the first two values and the first number is 10 less than the third number. You can mostly guess the numbers once you understand. I hope that this didn't confuse you more. Hope this helps!
If the point (2, – 3) lies on the graph of the equation 2y = ax – 7, then the value of a is
Answer:
a = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
since (2, - 3 ) lies on the graph then it makes the equation true.
substitute x = 2 and y = - 3 into the equation and solve for a
2(- 3) = a(2) - 7 , that is
- 6 = 2a - 7 ( add 7 to both sides )
1 = 2a ( divide both sides by 2 )
[tex]\frac{1}{2}[/tex] = a
Laura's Coffee Shop makes a blend that is mixture of two types of coffee. Type A coffee costs Laura $5.65 per pound, and type B coffee costs $4.35 per pound. This month, Laura made 158 pounds of the blend, for a total cost of $775.70. How many pounds of type A coffee did she use?
1) We can solve this problem by setting up a System of Linear Equations. So, based on this text, we can write out the following equations:
[tex]\begin{gathered} 5.65a+4.35b=775.70 \\ a+b=158 \end{gathered}[/tex]Note that the first equation relates itself to the total cost, and the second one to the amount of blend.
2) Now, we can solve this system of Linear Equations by the Elimination Method. Let's multiply the second equation by -5.65 so that we can add them both and eliminate "a"
[tex]\begin{gathered} 5.65a+4.35b=775.70 \\ -5.65a-5.65b=-892.7 \\ ---------------- \\ -1.3b=-117 \\ \frac{-1.3b}{-1.3}=\frac{-117}{-1.3} \\ b=90 \end{gathered}[/tex]Now, we can plug into the second equation b=90 and then solve it for a:
[tex]\begin{gathered} a+b=158 \\ a+90=158 \\ a+90-90=158-90 \\ a=68 \end{gathered}[/tex]Thus, the answer is:
[tex]a=68\: lbs,\: b=90\: lbs[/tex]1. Write a matrix to represent the following system.
[tex]\left \{ {{-9x+4y =1} \atop {7x-9=5}} \right.[/tex]
Complete the matrix below.
[ _ _ | _ ]
[ _ _ | _ ]
[ _ _ | _ ]
2. Write a matrix to represent the following system.
[tex]\left \{ {{-5x+6y=1} \atop {5x-2y=9}} \right.[/tex]
Complete the matrix below.
[ _ _ | _ ]
[ _ _ | _ ]
[ _ _ | _ ]
The augmented matrices for each system are given as follows:
1.
[ -9 4 | 1 ]
[ 7 0 | 14]
2.
[ -5 6 | 1 ]
[ 5 -2 | 9]
How to build the augmented matrix of a system of equations?For a system of n variables, the first n columns of the matrix are composed by the coefficients of the variable of the system.
The two systems in this problem have variables x and y, hence:
The first column is composed by the coefficients of x.The second column is composed by the coefficients of y.Then the last column is composed by the values on the right side of the equations, that is, the results of the operations.
The second equation of the first system is:
7x - 9 = 5 -> 7x + 0y = 14 (this format is needed to build the augment matrix.
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The area of a square is 150 square feet. What is the side length of the square?
Answer:37.5
Step-by-step explanation:
so basically a square has four sides so 150 divided by 4
(d^2+4)b=g
Solve for b
Answer:
b = [tex]\frac{g}{(d^{2}+4) }[/tex]
Step-by-step explanation:
([tex]d^{2}[/tex] + 4)b = g Divide both sides by ([tex]d^{2}[/tex] + 4)
b = [tex]\frac{g}{(d^{2}+4) }[/tex]
carly has a job that pays 35 a week plus 2 for each sale she makes. how many sales dose she need to make to earn more than 100 this week?
Carly needs to perform 33 additional sales to earn 100 this week.
Firstly forming the expression as per the weekly earning and individual payment on extra sale. Writing the expression -
Amount earned = 35 + 2×number of sales
Keep the value of amount earned in mentioned formula to find the number of sales.
100 = 35 + 2×number of sales
2×Number of sales = 100 - 35
Performing subtraction on Right Hand Side of the equation
2×Number of sales = 65
Shifting 2 to Right Hand Side of the equation
Number of sales = 65/2
Performing division on Right Hand Side of the equation
Number of sales = 32.5
Round off the number
Number of sales = 33
Therefore, she needs to make 33 additional sales.
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The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m, find the mass of one the bodies, if the mass of the other is 2050kg (G=6.7by 10^-11Nm^2kg^2
The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m, then the mass of one the bodies is
[tex]m_{1} = 1.88(10)^{-7}[/tex]
What is mass ?The amount of matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, a chair, your bed, a football, a glass, and even air. The mass of a thing determines whether it is light or heavy.
Given that : The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m
F=[tex]G\frac{m_{1} .m_{2} }{r^{2} }[/tex]
[tex]m_{1} =\frac{F.r^{2} }{Gm_{2} }\\ m_{1} =\frac{745.(70.3)^{2} }{6.7(10)^{-11}.2050 }\\\\[/tex]
[tex]m_{1} =\frac{26881.3(10^{7} )}{13735}[/tex]
[tex]m_{1} = 1.88(10)^{-7}[/tex]
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i need help with this
∠1 and ∠8 are supplementary angles, ∠5 and ∠6 are Congruent, ∠6 and ∠8 are Congruent .
Supplementary angles are those angles that sum up to 180 degrees. Two or more angles that are identical to each other are referred to as Congruent angles.
We are provided with the figure shown in the question. We need to name the angles provided or need to tell the relation between two angles.
∠1 and ∠8 are supplementary angles as there sum is 180°.
∠1 + ∠8 = 180°
So, angle ∠1 and ∠8 are supplementary.
∠5 and ∠6 are Congruent as they are identical to each other.
∠5 = ∠6
∠6 and ∠8 are Congruent as they are identical to each other.
∠6 = ∠8
Thus, we can conclude that ∠1 and ∠8 are supplementary angles, ∠6 and ∠8 are Congruent , ∠5 and ∠6 are Congruent.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
im lazzy thanks
Answer:
The answer is 18^4
Step-by-step explanation:
Its the answer
Anyone please help me this all and have solutions
Solutions are given below:
1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14
2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]
3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)
4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2
What is a solution?
A designation of values to that same unknown variables that establishes the equality inside this equation is referred to as a solution.To put it another way, a solution is a figure or set of values one for every unknown) that, when used to replace the unknowns, cause the equation to equal itself.Equations or networks of equations can have just one unique solution when they are solved mathematically.Solutions are given below:
1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14
2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]
3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)
4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2
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Miranda is making bracelets. She already has 15 and she can make 3
per day. Determine the slope and the y-intercept.
Answer:
y=3x+15
Step-by-step explanation:
she can make 3 a day so 3x and she already has 15 so the line crosses the y-axis at 15
Jamal is constructing the bisector of angle ABC. He has a list of steps for the construction, but they are not in
order.
What is the equation of the parabola with the vertex of (1,-8) that passes through (2,-6)
Hello!
What is the standard form of the parabola:
[tex]\hookrightarrow y=(x-h)^2+k[/tex]
(h,k): vertex's coordinate=> h: x-coordinate of vertex
=> k: y-coordinate of vertex
Since our vertex is (1,-8)
[tex]\hookrightarrow \text{Our equation is }y=(x-1)^2}-8[/tex] <== Answer
Hope that helps!
Please help. The problem is attatched!
The equation is 15 + 0.5x = 25 + 0.25x and number of miles is 40.
While writing the equation for green and blue cars, one time fee will be added with cost of driving for miles. Let us assume the number of miles to be x.
Firstly writing the equation for green car -
Cost = 15 + 0.5×x
Now writing the equation for blue car -
Cost = 25 + 0.25×x
The number of miles for same cost will be calculated by equating the expressions.
15 + 0.5x = 25 + 0.25x
0.5x - 0.25x = 25 - 15
Performing subtraction on Left Hand Side and Right Hand Side of the equation
0.25x = 10
Shifting 0.25 to Right Hand Side of the equation
x = 10 ÷ 0.25
Performing division on Right Hand Side of the equation
x = 40
So, if both the cars travel 40 miles, the rental cost will be same. The correct equation for calculation is 15 + 0.5x = 25 + 0.25x.
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help me please!!!!!!!!
If [tex]$f(x)=4^x$[/tex] and [tex]$g(x)=4^{x+1}-3$[/tex] be the two functions then Horizontal translation 1 units right.
What is meant by functions?An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Let [tex]$f(x)=4^x$[/tex] and [tex]$g(x)=4^{x+1}-3$[/tex]
We can see that in place x , we have x + 1
so, f(x) exists shifted right side by 1 unit
and we can see that 2 exists added to y-value
so, it exists shifted upside by 2 units
horizontal translation 1 unit right
vertical translation 2 units up
Therefore, the correct answer is option e) Horizontal translation 1 units right.
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The figures below are congruent. Name the corresponding sides.
Answer:
AC=KM
AB=KL
BC=LM
Step-by-step explanation:
Answer:
AC=MK
AB=KL
BC=LM
This are corresponding sides
The value of y varies directly with x. If y = 8, when x = 4, what is y when x = 48?
A function is defined as a relation between a set of inputs having one output each.
The value of y when x = 48 is 96.
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
We have,
The value of y varies directly with x.
y = 8, when x = 4.
Domain = input = 4
Range = output = 8
Now,
We can say that y is a function.
i.e y = 2x.
Where x = input = domain and y = range = output.
The value of y when x = 48:
y = 2x
y = 2 x 48
y = 96
Thus,
The value of y when x = 48 is 96.
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Solve for x and graph the solution on the number line below.
The solution is x ≤ -2 or x ≥ 10.
The inequalities are given in two parts which can be combined to form a single inequality as follows,
13 ≤ -5x + 3 or -47 ≥ -5x + 3
⇒ 13 ≤ -5x + 3 ≤ -47
Let's solve this.
First subtract 3 from all terms,
⇒ 10 ≤ -5x ≤ -50
Divide by 5 on all terms,
⇒ 2 ≤ -x ≤ -10
Multiply with (-1) on all terms, but then the inequality gets reversed as,
⇒ -2 ≥ x ≥ 10
We can now split the inequalities into two to make sense,
⇒ x ≤ -2 or x ≥ 10.
This solution can be graphed on a number line by darkening a line on the number line from 10, extended to the right of it. Then darken the line from -2, extend it to the left side.
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Sara hiked up a mountain on a steep 3-mile trail. Then she hiked downhill on a less
steep 5-mile trail. She hiked 0.5 mph faster downhill than uphill.
If Sara hiked uphill at a rate of r mph, how fast was she hiking downhill?
Answer:
wait, its r + 0.5
Step-by-step explanation: