The cost of one knife is £ 5.52.
Given, one knife is equal to three times spoon.
Let the cost of knife be x, and cost of spoon be y.
x=3y. ------(1)
9 spoons and 12 knives costs £82. 80, which can be written as
9(spoons)+12(knife)=£82. 80
9y+12x=£82. 80
9y+12(3y)=£82. 80
9y+36y=£82. 80
45y=£82. 80
y=£82. 80/45
y=£ 1.84
The cost of one spoon is £1.84.
We have to find the cost of one knife, we can substitute the value of y in equation 1 to get the cost of one knife.
x=3(1.84)
x=5.52.
Therefore, the cost of one knife is £5.52.
To learn more on cost here:
https://brainly.com/question/28367774#
#SPJ4
Corrected Question
A knife is three times the cost of a spoon. 9 spoon and 12 knives cost £82. 80 work out the cost of one knife.
Calculate this equation,3×y+(5/8)×y
what is the solution to
e^6x-11=104
The solution of the equation [tex]e^{6x}[/tex] - 11 = 104 is x = 0.79
The given equation is
[tex]e^{6x}[/tex] - 11 = 104
The equation is the mathematical statement that shows the relationship between two expression. The equation is consist of different variable, numbers and mathematical operators with the equal sign. The mathematical operators are addition, subtraction, division and multiplication. The inequality will not be the part of equation
The given equation is
[tex]e^{6x}[/tex] - 11 = 104
[tex]e^{6x}[/tex] = 104 + 11
Add the terms
[tex]e^{6x}[/tex] = 115
6x = ln (115)
x = ln (115) / 6
x = 0.79
Hence, the solution of the equation [tex]e^{6x}[/tex] - 11 = 104 is x = 0.79
Learn more about equation here
brainly.com/question/14603452
#SPJ1
Tonya deposited one check for $56.93, a second check for
$761.29, and a third check into a savings account for her daughter. She also
deposited $75.00 in currency and $25.00 in coin. If she withdrew $150.00 in
cash and their total deposit was $1,785.23, what was the amount of her
third check?
Help me please! So 2.35 + 0.25x = 1.75 + 0.40
Answer:
x = -0.8
Step-by-step explanation:
2.35+0.25x = 1.75+0.4
To find x, we must first isolate the value.
This is done by subtracting any values on the same side as the x.
Thus, we subtract 2.35 from both sides.
We are now left with the following:
0.25x=1.75+0.4-2.35
Now you should simplify the right side by finding the sum, which is -0.2, so:
0.25x=-0.2
Finally, solve by dividing each side by 0.25.
x = -0.8
Answer:
[tex]x = -\dfrac{4}{5} \ \ \textrm{or} \ \ x = -0.8[/tex]
Step-by-step explanation:
First, multiply both sides by 100 to make the numbers nicer to work with.
[tex](100)(2.35 + 0.25x) = (1.75 + 0.40)(100)[/tex]
[tex]235+25x=175+40[/tex]
Next, isolate x by moving all the constant terms to one side and then dividing by x's coefficient.
[tex]25x=175+40-235[/tex]
[tex]25x = -20\\\overline{\, \, 25 \, \,} \: \, \, \, \, \, \, \, \overline{ \,\, 25 \, \,}[/tex]
[tex]x = -\dfrac{20}{25}[/tex]
[tex]x = -\dfrac{4}{5}[/tex]
So, the value of x is -4/5 or 0.8.
What is the slope of a line perpendicular to the line whose equation is 5 x + y = − 4 5x+y=−4. Fully simplify your answer.
The slope of the perpendicular line is 1/5
How to determine the slope of the perpendicular line?The equation of the line is given as
5x + y = -4
The equation of a line can be represented as
y = mx + c
Where
Slope = m
So, the first step is to make the variable y the subject in 5x + y = -4
This gives
y = -5x - 4
By comparing the equations, we have the following
m = -5
This means that the slope of 5x + y = -4 is -5
So, we have
Slope 1 = -5
The slopes of perpendicular lines are opposite reciprocals
i.e.
Slope 2 = -1/Slope 1
This gives
Slope 2 = -1/-5
Evaluate
Slope 2 = 1/5
Hence, the perpendicular line has a slope of 1/5
Read more about linear equations at
brainly.com/question/4074386
#SPJ1
a(1)=-11
a(n)=a(n-1)x10
what is the 4th term?
The fourth term a₄ of the sequence aₙ is 15
How to determine the value of a₄?The definition of the function is given as
a(1)=-11
a(n)=a(n-1)x10
When this definition is rewritten properly, we have the following representation
a₁= 11
aₙ = aₙ₋₁ * 10
The above definitions imply that we simply multiply 10 and the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₂ = 11 * 10
Evaluate the products
So, we have
a₂ = 110
Also, we have
a₃ = 110 * 10
Evaluate the products
So, we have
a₃ = 1100
Lastly, we have
a₄ = 1100 * 10
Evaluate the products
So, we have
a₄ = 11000
This represents the 4th term of the sequence
Hence, the value of a₄ is 11000
Read more about sequence at
brainly.com/question/7882626
#SPJ1
Tommy was going to sell all of his Pokemon
cards to buy NBA 2K21. After selling half of
them he changed his mind and bought 17
more Pokemon cards. How many did he start
with if he now has 34?
Answer: [tex]x = 34[/tex]
Step-by-step explanation:
Let x be the original amount of Pokémon cards Tommy had, we know that he sold half of them; this can be express as:
[tex]\frac{x}{2}[/tex]
After this he changed his mind and bought 17 cards, then he has:
[tex]\frac{x}{2} + 17\\[/tex]
We know that he has 34, then we have the equation:
[tex]\frac{x}{2} + 17 = 34[/tex]
Solving for x we have:
[tex]\frac{x}{2} + 17 = 34[/tex]
[tex]\frac{x}{2} = 34 - 17[/tex]
[tex]\frac{x}{2} = 17[/tex]
[tex]x = (2)(17)[/tex]
[tex]x = 34[/tex]
(-6,4)
(-4,0)
(4,4)
(2,8)
what’s the perimeter
Answer:
Step-by-step explanation:
What is the image point of (0, -4) after the transformation T3,3 R270 ?
The image of the point (0, -4) after the transformation T3,3 R270 is (3, 1).
The image of the given point after transformation considers the given point is P(0, -4)
Rules of transformation R(27°,0)° T<3, 3> representing translation T<3, 3> after that rotate 270 degrees counter-clockwise If a figure translated by T<3, 3>
( x,y)= (( x + 3), ( y + 3))
p (0, -4) = p' (( 0 + 3), ( -4 + 3))
p (0, -4) = p'(3, -1)
When rotating a point 270 degrees counter-clockwise about the origin our point
p'(x,y) becomes p''(y,-x)
p'(3, -1) = p''(3, -(-1))
p'(-10,2) =p"(3, 1)
Therefore, the image of the point (0, -4) after the transformation T3,3 R270 is (3, 1).
To learn more about the transformations click here :
https://brainly.com/question/28029674
#SPJ1
An elevator goes from the 124th floor to the 8th floor of a sky scraper in 40 seconds. The elevator travels at constant speed. What is the elevator’s rate of change in floors per second?
The Elevator’s rate of change is found to be 3 floors per second using the given data.
What is the most basic definition of rate?Rate is the pace at which an object's location changes in any direction. Rate is defined as the ratio of distance traveled to time spent traveling. Speed is classified as a scalar quantity since it has just one direction and no magnitude.What is the speed calculation?Speed (or rate, r) is a scalar number that represents the distance traveled (d) divided by the change in time (t) by the equation r = d/t.
Given: In 40 seconds, an elevator travels from the 124 floor to the 8 floor of a skyscraper. The elevator maintains a constant speed.
We know that,
Rate = Distance/Time
Elevator’s rate of change = (124-8)/40
= 116/40
= 2.9 ≈ 3 floors per second
Therefore, the Elevator’s rate of change is found to be 3 floors per second using the given data.
Learn more about rate of change here:
https://brainly.com/question/25184007
#SPJ13
A student is 18 years old and is just starting to workout. Which of the following is their Target Heart Rate Zone?
Answer:
2.5
Step-by-step explanation:
simplify the following expression 9^-53·9^37
The simplification of the given expression would be = 9^-¹⁶
What is simplification?Simplification is defined as editing of a given mathematical expression in a more easy to under form or less complex form.
To simplify the given expression such as 9^-53·9^37 the law of exponents should be observed.
According to the law of exponents, a^m * a^n = a^m + n
9^-53·9^37
= 9^ -53+37
= 9^-16
Therefore, the simplification of the expression above would be = 9^-¹⁶.
Learn more about exponents here:
https://brainly.com/question/27385740
#SPJ1
A wheel of radius 14 inches is rotating 15degrees/s round answers to 2 decimal places
Krystal was able to drive her car 300 miles on 12 gallons of gasoline. At this rate, how many miles did she drive using 8 gallons of gasoline?
Answer:
523
Step-by-step explanation:
the game
Ann will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of 55$ and costs an additional per mile driven. The second plan has no initial fee but costs 0.8$ per mile driven.
The number of miles when they'll cost the same for Ann is 137.5 miles.
How to calculate the value?Ann can choose one of two plans. The first plan has an initial fee of 55$ and costs $0.4 an additional per mile driven and the second plan has no initial fee but costs 0.8$ per mile driven.
This will be illustrated as:
55 + 0.4m = 0.8m
Collect like terms
0.8m - 0.4m = 55
0.4m = 55
Divide
m = 55/0.4
m = 137.5m
The miles is 137.5 miles.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Complete question
Ann will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of 55$ and costs $0.4 an additional per mile driven. The second plan has no initial fee but costs 0.8$ per mile driven. How many miles will they cost the same?
What is the range of this relation?
Answer:
{-4,-2,4}
Step-by-step explanation:
range are y values so we just look at the y values of the coordinates plotted on the graph
Hopes this helps
The range of the relation that is graphed above is: {-4, -2, 4}.
What is Range of a Relation?All values of x that are plotted on a graph of a relation is the domain, while the corresponding y-values on the graph is the range of the relation.
Given the graph of the relation above, the x-values of each of the points make up the domain of the relation, while the corresponding y-values of each point make up the range of the relation.
The y-values of each of the points are: -4, -2, and 4
Therefore, the range is: {-4, -2, 4}.
Learn more about the range of the relation on:
https://brainly.com/question/1579288
#SPJ1
a piece of lumber which is 55 inches long is cut into two parts such that 2 times the larger part will be 12 more than 5 times the smaller part. how large are each of the pieces of lumber?
x=14 in is the smaller part of lumber
55-x=55-14=41 in is the larger part of lumber
What is linear equation ?Linear equations are described for strains withinside the coordinate system. If an equation has homogeneous variables of diploma 1 (that is, best one variable), the equation is stated to be a linear equation in a single variable. A linear equation may have more than one variables. When linear equations have variables, they may be known as bivariate linear equations.
Examples of linear equations are 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x - y + z = 3. This article gives definitions of linear equations, preferred types of linear equations in a single, , and 3 variables, and examples of them with complete explanations.
CalculationLet x=the smaller part
Then 55-x=the larger part
Now we are told the following:
2(55-x)=5x+12 simplify
110-2x=5x+12 add 2x to and subtract 12 from each side
110-2x+2x-12=5x+2x+12-12 collect like terms
98=7x
x=14 in--------------------smaller part
55-x=55-14=41 in-----------larger part
CK
2 times larger part=2*41=82 in
5 times smaller part=5*14=70 in
70+12=82
82=82
learn more about linear equation here :
brainly.com/question/11897796
#SPJ4
How could I simplify it, could someone show me step by step?
By simplifying the expression (-4-√7)² we get the value as 23+8√7 in decimals we get 44.12.
Given that,
The expression is (-4-√7)²
We need to find the value and simplify the expression.
Take the expression.
(-4-√7)²
We know that (a+b)²=a²+2ab+b²
The expression is in the form of (a+b)² substitute the formula.
(-4)²+2(-4)(-√7)+(-√7)²
Now do the square
16+2(-4)(-√7)+7
Now do the multiplication.
16+8√7+7
Now do the addition.
23+8√7
We can write the √7 value
23+8(2.64)
Multiply 8 and 2.64
23+ 21.12
Now adding
44.12
Therefore, By simplifying the expression (-4-√7)² we get the value as 23+8√7 in decimals we get 44.12.
To learn more about expression visit: https://brainly.com/question/14083225
#SPJ1
(03.03 MC)
Which of the following statements best describes the location of −(−2) on a number line?
Group of answer choices
A.) It is 2 units to the left of 2.
B.) It is 2 units to the right of 2.
C.) It is 2 units to the left of 0.
D.) It is 2 units to the right of 0.
Option (D) is the correct one and the number -(-2) is 2 units to the right of 0.
Given, a number -(-2),
we have to describe the location of the number -(-2) on a number line.
On simplifying, we get
-(-2) = +2
So, the number we have to plot is 2.
As, we know that the positive numbers are on the right side of the origin.
So, the number will be 2 units to the right of 0.
Hence, Option (D) is the correct one and the number is 2 units to the right of 0.
Learn more about Coordinate Geometry here https://brainly.com/question/18269861
#SPJ1
enter two pairs of values for x and y that make the equation x + 2y = 10
Answer:
x=1 y=4.5, x=2 y=4
Step-by-step explanation:
plug in random values of x and solve for y then you get your answer.
Consider the problem: Mai has $36 to spend on movie tickets. Each movie ticket costs $4.50. How many tickets can she buy?
Part 1:
Select BOTH a multiplication equation AND a division equation to represent this situation.
A. 36 ÷ 4.50 = ?
B. 4.50 ÷ 36 = ?
C. 4.50 · 36 = ?
D. ? · 4.50 = 36
Answer: A and D
Step-by-step explanation:
Chooe ALL anwer that decribe the quadrilateral VWXYVWXY if VW = 15VW=15, WX = 15WX=15, XY = 15XY=15, YV = 15YV=15, and diagonal have equal length: VX = WYVX=WY
The quadrilateral VWXY that has an equal length of diagonals and equal length of sides is the quadrilateral is a square
Since the information given to us about the quadrilateral VWXY is :
VW = 15, WX = 15, XY = 15, YV = 15
Since the side lengths of the quadrilateral VWXY and the diagonal lengths are equal. So, VX = WY = VX = WY. As we know The properties of a square are that their interior angles are congruent and are 90°, plus The four sides are of equal length, the Opposite sides are congruent and The length of the diagonals is equal.So it can be concluded that the equal length of the diagonals of a quadrilateral indicates that it can be a square
to know more about quadrilateral refer to the link https://brainly.com/question/13805601?referrer=searchResults.
#SPJ4
What is the difference of the polynomials?
(855³-9554 + 3^¹55)-(2^s5 - 5r³s^6-4r^5s^4
Answer: 5x^3 + 4x^2 – (6x^2 – 2x – 9) =
5x^3 + 4x^2 – 6x^2 + 2x + 9 =
5x^3 – 2x^2 + 2x + 9
Step-by-step explanation: We have to find the difference (5x^3 + 4x^2) - (6x^2 - 2x - 9)
On distributing the minus over the parenthesis, we get
5x^3 + 4x^2 - 6x^2 + 2x + 9
Now, we group the like terms and combine them
5x^3 + (4x^2 - 6x^2) + 2x + 9
=5x^3-2x^2 + 2x +9
Therefore, the last expression is the correct option.
The difference of the polynomial is 5x^3-2x^2 + 2x +9
722 divided by 68 =?
Answer:
Step-by-step explanation:
A man whose height is 1. 8 m casts a shadow that is 2. 9 m in length. What is the height of a building that casts a shadow of 11. 3 m?.
The height of a building is 7 m that casts a shadow of 11.3 m
The ratio between height to shadow length of man will be equal to the ratio of building. So, equating these two to find the height of building.
Height : Shadow length (man) = Height : shadow length (Building)
Keep the values as fraction
1.8/2.9 = Height/11.3
Height of building = (1.8 × 11.3) ÷ 2.9
Performing multiplication in numerator on Right Hand Side of the equation
Height of building = 20.34 ÷ 2.9
Performing division on Right Hand Side of the equation
Height of building = 7 m
Thus, the height of building is 7 m.
Learn more about shadow length -
https://brainly.com/question/14613383
#SPJ4
find the general term of the sequence
(0.2,0.22,0.222. . . )
Answer:
Step-by-step explanation:
LIBERTY
$1
10
FEDERAL RESERVE NOTE
THE UNITED STATES OF AMERICA
K
H88750416A
10 Catika kund
H88750416A
ONE
Zachen 7. Buy 10
10
2
Answer:
Step-by-step explanation:
$1.65
please help me with this math problem
[tex]\frac{1}{2} -\frac{3}{7} =\frac{7}{14} -\frac{6}{14} =\frac{1}{14}[/tex]
Answer:
[tex] \frac{1}{14} [/tex]
Step-by-step explanation:
[tex] \frac{1}{2} - \frac{3}{7} = \frac{7}{14} - \frac{6}{14} [/tex]
[tex] = \frac{1}{14} [/tex]
A student noticed that when she gets less than 8 hours of sleep at night, she scores lower on her test grades. Can one conclude that this positive correlation shows a casual relationship?
A. Yes, because it is well known that less sleep lowers test scores.
B. Yes, because it is not a negative correlation.
C. No, because all students get less than 8 hours of sleep at night.
D. No, because it is possible that the student gets lower test grades because of another factor, such as not studying.
D. No, because it is possible that the student gets lower test grades because of another factor, such as not studying.
What are positive and negative co-relations?When two variables behave in unison, rising or falling in lockstep with one another, there is a positive correlation.
When two variables move in opposition to one another—that is, when one rises, the other falls, this is known as a negative correlation.
Given, A student noticed that when she gets less than 8 hours of sleep at night, she scores lower on her test grades.
No, Because it is possible that the student gets lower test grades because of another factor, such as not studying.
learn more about correlations here :
https://brainly.com/question/13503439
#SPJ1
suppose x is a normally distributed random variable with a mean of 12 and a standard deviation of 3. the probability that x equals 19.62 is . a. 0 b. .0055 c. .4945 d. .9945
The probability of x being equal o 19.62 is d) 0.
It is given that x is normally distributed with a mean of 12 and a standard deviation of 3.
Now, Normal distribution is a continuous distribution.
This implies that the probability is measured over an interval, taking an infinite number of points in between.
If we plot a continuous distribution, the probability here at a point is not the value of the y coordinate at that point. Instead, it is seen as an area under the curve of the distribution, between the two intervals, say a and b.
Therefore, if we take up a single point say c, then the probability will be the area under the curve from c to c, which will obviously be 0.
Hence, the probability that x = 19.62 will be 0.
To learn more about normal distribution visit
https://brainly.com/question/13759327
#SPJ4
