The cost of 3 rackets and 2 squash balls is £26.57. The cost of 5 rackets and 7 squash balls is
The cost of 3 rackets and 2 squash balls is £26.57.
The cost of 5 rackets and 7 squash balls is £52.90.
Work out the cost of
a) a squash ball.
b) a racket
Answers
Taking into account the definition of a system of linear equations:
the cost of a squash ball and a racket are £2.35 and £7.29 respectively.the cost of 1 kg of radishes and 1 kg of carrots are £3.1 and £1.6 respectively.System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Cost of a squash ball and a racketIn this case, a system of linear equations must be proposed taking into account that:
"x" represents the cost of a squash ball."y" represents the cost of a racket.The cost of 3 rackets and 2 squash balls is £26.57.
The cost of 5 rackets and 7 squash balls is £52.90.
So, the system of equations to be solved is
[tex]\left \{ {{2x+3y=26.57} \atop {7x+5y=52.90}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable x from the first equation:
[tex]x=\frac{26.57 - 3y}{2}[/tex]
Substituting the expression in the second you get:
[tex]7\frac{26.57 - 3y}{2}+5y=52.90[/tex]
Solving:
[tex]\frac{7}{2}(26.57 - 3y)+5y=52.90[/tex]
[tex]\frac{7}{2}x26.57 - \frac{7}{2}x3y+5y=52.90[/tex]
92.995 - 10.5y +5y= 52.90
92.995 - 5.5y= 52.90
- 5.5y= 52.90 -92.995
- 5.5y= -40.095
y= (-40.095)÷ (-5.5)
y= 7.29
So: [tex]x=\frac{26.57 - 3y}{2}=\frac{26.57 - 3x7.29}{2}[/tex]
x= 2.35
Finally, the cost of a squash ball and a racket are £2.35 and £7.29 respectively.
Cost of 1 kg of radishes and 1 kg of carrotsIn this case, a system of linear equations must be proposed taking into account that:
"x" represents the cost of 1 kg of radishes."y" represents the cost of 1 kg of carrots.The cost of 4 kg of radishes and 1.5 kg of carrots is £14.80.
The cost of 3 kg of radishes and 2 kg of carrots is £12.50.
So, the system of equations to be solved is
[tex]\left \{ {{4x+1.5y=14.80} \atop {3x+2y=12.50}} \right.[/tex]
You can solve this system using the substitution method. Isolating the variable x from the first equation:
[tex]x=\frac{14.80 - 1.5y}{4}[/tex]
Substituting the expression in the second you get:
[tex]3\frac{14.80 - 1.5y}{4}+2y=12.50[/tex]
Solving:
[tex]\frac{3}{4}(14.80 - 1.5y)+2y=12.50[/tex]
[tex]\frac{3}{4}x14.80 - \frac{3}{4}x1.5y+2y=12.50[/tex]
11.1 - 1.125y +2y= 12.50
- 1.125y +2y= 12.50 - 11.1
0.875y= 1.4
y= 1.4 ÷0.875
y=1.6
So: [tex]x=\frac{14.80 - 1.5y}{4}=\frac{14.80 - 1.5x1.6}{4}[/tex]
x= 3.1
Finally, the cost of 1 kg of radishes and 1 kg of carrots are £3.1 and £1.6 respectively.
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Related Questions
Ted says that the triangle below cannot be classified because all sides are different lengths. Is Ted correct? Explain why or why not.
Answers
Answer:
Ted is wrong
The triangle is a right triangle because of the right 90° angle formed at the bottom.
Calculate the volume of the right rectangular prism shown.
Edulastic Question
Answers
since we have the area of the front side, to get its volume we can simple get the product of the area and the length, let's firstly change the mixed fractions to improper fractions.
[tex]\stackrel{mixed}{23\frac{2}{3}}\implies \cfrac{23\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{71}{3}} ~\hfill \stackrel{mixed}{4\frac{7}{8}}\implies \cfrac{4\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{39}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{71}{3}\cdot \cfrac{39}{8}\implies \cfrac{71}{8}\cdot \cfrac{39}{3}\implies \cfrac{71}{8}\cdot 13\implies \cfrac{923}{8}\implies 115\frac{3}{8}~in^3[/tex]
Determine if (6, 2) is a solution to the system of equations.
2x + y = 10
3x + 2y = 10
Answers
Answer:
no
Step-by-step explanation:
plug 6 in for x and 2 in for y, as (x, y) = (6, 2)
first equation:
y = 1 * y
2(6) + 1(2) = 10
12 + 2 = 10
14 = 10
this is false
second equation:
3(6) + 2(2) = 10
18 + 4 = 10
22 = 10
this is false
for this to be a solution, it must fit into both equations. as this fits into neither, this is not a solution
I need help on this assignment
Answers
Answer:
C
Step-by-step explanation:
the root can be a minnimum of 0 otherwise the function would be imaginary, sqrt(x-1)+2 has a minimum of 2. This means that g(x), or y is greater than or equal to two.
How many pieces 15/16 inch long can be cut from a strip of sheet metal 13 1/8 inches long?
Answers
Answer:
14 pieces
Step-by-step explanation:
Simplify 13 1/8 into fraction with denominator 16
13 1/8105/8210/16Number of pieces
(210/16)/(15/16)14 piecesIn a field of wildflowers, the number of flowers is decaying exponentially. One year there are 1,200 flowers, and the next year there are 900 flowers.
The percent of decrease is 33 25 30 20 and the decay factor is 0.75 1.25 0.67 0.70
Answers
Find the amount of decay:
1200 - 900 = 300
Divide amount of decay by original amount:
300/1200 = 0.25
The percent of decay is 25 %
The decay factor is 1.00 a 0.25 = 0.75
Given f (x)= x-4/x^2+13x+36, which of the following is true? f(x) is decreasing for all x > –9 f(x) is increasing for all x < –9 f(x) is increasing for all x > –4 f(x) is decreasing for all x > –4
Answers
The simplified expression of the function [tex]f (x)= \frac{x-4}{x^2+13x+36}[/tex] is
[tex]f (x)= \frac{x-4}{(x+9)(x+4)}[/tex]. f(x) is increasing for all x > –4
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
The function expression is given as:
[tex]f (x)= \frac{x-4}{x^2+13x+36}[/tex]
Expand the denominator
[tex]f (x)= \frac{x-4}{x^2+4x+9x+36}[/tex]
Factorize the denominator
[tex]f (x)= \frac{x-4}{x(x+4)+9(x+4)}[/tex]
Factor out x + 9
[tex]f (x)= \frac{x-4}{(x+9)(x+4)}[/tex]
Hence, the simplified expression of the function [tex]f (x)= \frac{x-4}{x^2+13x+36}[/tex] is
[tex]f (x)= \frac{x-4}{(x+9)(x+4)}[/tex]. f(x) is increasing for all x > –4
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Answer: f(x) is increasing for all x > -4
Proof of validity is shown below.
A deck of cards contains 52 different cards a card is drawn at random what is the probability that the card drawn is a queen
Answers
Answer: 4/52 = 1/13
Step-by-step explanation: We know that a full deck of cards is 52 and there are 4 suits in a deck. Which means that there are 4 queens in each deck. Now, we can add that up together which gives us 4/52, and can be simplified down to 1/13 because 4/52 isn't the smallest we can get our fraction.
Hope this helps :)
Answer:
0.077
Step-by-step explanation:
1/13 in decimal form is 0.07692307692 which rounds up to 0.077 which will be your answer.
A sporting goods store wants to know what products their customers most want. There were four different suggestions about how to survey the customers.
Which method of sampling customers is least biased?
A Survey every other adult who brings children along to shop.
B Survey only customers who enter the store's shoe section.
C Survey every person who enters the sporting goods store between 10:00 and 11:30 AM.
D Survey every 10th person or group who enters the sporting goods store throughout the entire day.
Answers
Answer:
I believe the answer is C
Step-by-step explanation:
if its wrong, im sorry an I will delete the answer
Evaluate the expression below x=5. 3x+2•|x-8|-12
Answers
Answer:
39
Step-by-step explanation:
3*5=15
15+2=17
|x-8|=3
3*17=51
51-12=39
Find the area of the circle
r = 6 ft
Answers
If the radius of the circle is 6 feet. Then the area of the circle will be 113.097 square feet.
What is a circle?It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.
The radius of the circle is 6 feet.
Then the area of the circle will be
Area = πr²
where r is the radius of the circle. Then we have
Area = π × 6²
Area = 36π
Area = 113.097 square feet
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find the surface area of this prism
3cm
7cm
5cm
Answers
Answer:
105cm
Step-by-step explanation:
please click crown below my answer.
1) Lorena is exercising on a treadmill that is moving a pace of 0.1 miles every
2 minutes. How many miles will she complete in 45 minutes?
Answers
Answer:
Step-by-step explanation:
0.1 * 45
= 4.5 miles
A circle with a centre 0, has an equation x2 + y2 = 25
The coordinate A (4,3) is on the circumference of the circle.
Find the equation of the tangent at point A.
Answers
The linear equation of the tangent at point A is given by:
[tex]y = \frac{-4x + 25}{3}[/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, to find the slope, we need to find the derivative at (4,3), using implicit differentiation. Hence:
[tex]2x\frac{dx}{dx} + 2y\frac{dy}{dx} = 0[/tex]
[tex]\frac{dy}{dx} = -\frac{x}{y}[/tex]
[tex]\frac{dy}{dx} = -\frac{4}{3}[/tex]
Then:
[tex]y = -\frac{4}{3}x + b[/tex]
We use point (4,3) to find b, hence:
[tex]y = -\frac{4}{3}x + b[/tex]
[tex]3 = -\frac{16}{3} + b[/tex]
[tex]b = \frac{25}{3}[/tex]
Hence, the equation is:
[tex]y = \frac{-4x + 25}{3}[/tex]
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There is a “family” of Z distributions?
Answers
Reason:
There is only one Z distribution, which is also known as the standard normal distribution. This distribution has a mean of mu = 0 and a standard deviation of sigma = 1. So unless you consider a family to only have one member, then I'd consider the statement your teacher gave you to be false.
On the other hand, if we were talking about the student T distribution, then this is a family of function curves. The reason being is that the degrees of freedom (df) will change the shape of said curve. The value of df will depend on the sample size n. Recall that df = n-1. As n gets larger, then the T distribution curves will slowly start to look like the Z distribution. For n > 30, the difference is so very minor that it's easier to swap over to the Z distribution even if you don't know sigma.
In other words, there is a family of T distribution curves in which slowly approach to mimicking the Z distribution curve when n is large (usually n > 30).
HELP NEEDED QUICK PLEASE
Answers
Answer:
49 degrees
Step-by-step explanation:
its the answer, trust
Marni has 24 ounces of walnuts. she needs 14 ounces for one recipe and 1/2 pounds for another. how many total ounces does she need to make her recipes?
Answers
The total ounces she needs to make her recipes is 22 ounces
Calculating quantityFrom the question, we are to determine how many total ounces Marni needs to make her recipe
From the given information,
Marni has 24 ounces of walnuts
Also,
She needs 14 ounces for one recipe
and
1/2 pounds for another
First, we will convert 1/2 pounds to ounces
NOTE: 1 pound = 16 ounces
∴ 1/2 pound = 8 ounces
Then, we can rewrite that
She needs 14 ounces for one recipe
and
8 ounces for another
The total ounces she needs to make her recipes = 14 ounces + 8 ounces
The total ounces she needs to make her recipes = 22 ounces
Hence, the total ounces she needs to make her recipes is 22 ounces
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Which triangle is possible?
3 ft, 4ft, and 5ft 4yd, 5ft, and 10yd
3 ft, 3 ft, and 7 ft.
4 in, 4 in, and 8 in
Answers
Answer:
(a) 3 ft, 4 ft, 5 ft
Step-by-step explanation:
The triangle inequality requires the sum of the two short sides exceed the long side.
__
a) 3 ft + 4 ft = 7 ft > 5 ft . . . . . triangle is possible
b) 4 yd + 1 2/3 yd = 5 2/3 yd < 10 yd . . . . not a possible triangle
c) 3 ft + 3 ft = 6 ft < 7 ft . . . . not a possible triangle
d) 4 in + 4 in = 8 in . . . . not a possible triangle (not greater than 8 in)
__
The first set of side lengths can form a triangle: 3 ft, 4 ft, 5 ft.
Triangle ABC is dilated by a scale factor of 1.5 to create triangle A'B'C'. Which of
the following it not a true statement?
A. The image is larger than the pre-image.
B. The orientation of triangle ABC is preserved.
C. Segment AB is congruent to segment A'B'.
D. The angle measures in triangle ABC are equal to the angle measures in triangle
A'B'C'.
Answers
Answer:
C. Segment AB is congruent to segment A'B'.
Step-by-step explanation:
Since ABC is being dilated by 1.5, it means that A'B'C will be bigger than ABC.
So, since A'B'C will be bigger than ABC, it sides will also be bigger than the sides in ABC.
And since the sides/segments are bigger than the original, they are not congruent (congruent means equal).
Jillian was asked to translate the expression 9 + n into words. She wrote “a number increased by nine.” Which best describes the accuracy of Jillian’s answer?
It is incorrect. The variable would come first in the expression “a number” (n) “increased by” (+) “nine” (9).
It is incorrect. The phrase “increased by” refers to the inequality symbol “greater than” (>), not addition.
It is correct. A number increased by nine (n + 9) is the same as nine increased by a number (9 + n).
It is incorrect. A number increased by nine refers to a multiplication expression (n times 9).
Answers
A number increased by nine (n + 9) is the same as nine increased by a number (9 + n), the correct option is C.
What is the pharse in mathematics?A mathematical phrase is a set of words or a combination of words and numbers that can be written as a mathematical expression.
Given
Jillian was asked to translate the expression 9 + n into words.
She wrote "a number increased by nine.
The expresion can be written into the two formate which is;
(n+9) and (9+n)
Hence, a number increased by nine (n + 9) is the same as nine increased by a number (9 + n), the correct option is C.
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Answer:
Step-by-step explanation:
It is correct. I don't know that getting rid of the other choices is helpful. The vocabulary (increases) in common usage means "add." I think I would accept it as it is and give her full credit. You can overthink an answer.
A recipe of chocolate chip cookies need 37 oz of oil for every 30 cups of flower. Approximately
how many ounces of oil do you need for 77 cups of flower?
Type your answer to the nearest whole ounce.
Answers
Answer:
95 oz
Step-by-step explanation:
37 oz / 30 c * 77 c = ~ 95 oz (see how the 'c' cancels and you are left with 'oz' ? )
A bottle of vanilla extract costs $1.28 & contains 48 teaspoons of extract. What is the cost per teaspoon?
Answers
Answer:
about 3 cents
Step-by-step explanation:
1.28 divided by 48 = 0.02667
whihc orunds to 0.03
The students in Class A and Class B were asked how many pets they each have. The dot plots below show the results.
Students in Class A
A dot plot titled Students in Class A. A number line going from 0 to 5 labeled Number of pets. There are 5 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.
Students in Class B
A dot plot titled Students in Class B. A number line going from 0 to 5 labeled Number of pets. There is 1 dot above 0, 2 above 1, 2 above 2, 4 above 3, 3 above 4, 3 above 5.
What is the difference between the ranges in the dot plots?
0
2
3
4
Answers
Answer:
The answer is 2
Step-by-step explanation:
the answer is 2
Combine like terms to create an equivalent expression.
Enter any coefficients as simplified proper or improper fractions or integers. LOOK AT PICTURE!
Answers
Answer:\frac{2p}{7}+\frac{1}{7}
Step-by-step explanation:you have to simplify these two number thats all can give u bro
The function g(x) is shown in the graph at right. The function g(x) is a transformation of the parent function f(x)=x^2. Based of the graph, which function represents g(x) in terms of f(x)
Answers
Answer: choice B
Step-by-step explanation:
If 1ml of water fills 1 cubic centimeter of space, how many ml of water are needed to fill each tank?
Answers
Answer:
Tank Volume/1 cubic centimeter.
Step-by-step explanation:
We dont know how big the tank is.
Pre-calc/Trig
Suppose that θ=arcsin(4/6). What is cos(2θ)? (round to 4 decimals)
Answers
Answer:
0.7453
Step-by-step explanation:
[tex]arcsin( \frac{4}{6} ) = 0.7297 \\ cos(0.7297) = 0.7453[/tex]
アhi can you please help me
Answers
Answer:
C) 1.
Step-by-step explanation:
Calculator
Find the distance between the points (6, -4) and (-7, -4)
Answers
Answer:
8
Step-by-step explanation:
Subtract 6 to 7 then add that to the 7.
someone please help me with this asap!
