a) The linear function used to find the equipment rental fee is of: y = 9x + 20.
b) The cost for 6 hours of training is of: $74.
How to define the linear function?The linear function is defined considering it's slope-intercept format, given as follows:
y = mx + b.
The coefficients of the function are given as follows:
m is the slope, representing the cost per hour.b is the intercept, representing the flat fee.A soccer training camp charges $9.50 per hour for training, hence the slope is of:
m = 9.
The total fee for 12 hours of training was $128, hence the intercept b is obtained as follows:
128 = 9(12) + b
b = 128 - 108
b = 20.
Hence the function is defined as follows:
y = 9x + 20.
The cost for six hours of training is obtained as follows:
y = 9(6) + 20 = $54.
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a summer soccer cam ordered a total of 84 soccer balls and t-shirts for the season. Soccer balls cost $25 each and t-shirts cost $9.50 each. if they paid $1,046 total for the purchase, how many of each item was ordered?
The Number of Soccer Balls is 16 and the Number of T-Shirts is 68
What is Linear Equation in Two Variables?
A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Solution:
Let,
Number of Soccer Balls = x
Number of T-Shirts = y
Equation 1:
x + y = 84 -----------(i)
Equation 2:
25x + 9.5y = 1046 ----------(ii)
Multiplying Equation 1 by 25
25x + 25y = 2100 ---------(iii)
Substracting Equation2 from Equation 1
15.5y = 1054
y = 68
So, x = 16
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The length of a rectangle is 3 m less than twice the width, and the area of the rectangle is 27 m. Find the dimensions of the rectangle.
Answer:
4.5 m and 6 m---------------------------
Let the length be l and width be w.
Given:
l = 2w - 3,A = lw = 27.Substitute l and solve for w:
lw = 27w(2w - 3) = 272w² - 3w = 272w² - 3w - 27 = 02w² - 9w + 6w - 27 = 0w(2w - 9) + 3(2w - 9) = 0(2w - 9)(w + 3) = 02w - 9 = 0 and w + 3 = 02w = 9 and w = - 3 (discarded as distance can't be negative)w = 4.5Find the value of l:
l = 2*4.5 - 3 = 9 - 3 = 6Write as a mixed number & simplify, if possible. 4 1/3 divided by 3 1/6
Answer:
1 7/19
Step-by-step explanation:
First, to solve this problem, you change the mixed fraction to improper fractions:
13/3 / 19/6
Now, you make it into a multiplication problem by multiplying the first number by the reciprocal of the second number.
13/3 x 6/19
Simplify :
13/1 x 2/19
Multiply the numerators by denominators to get the total:
26/19 or simplified: 1 7/19
The measure of one of the small angles of a right triangle is 6 more than 3 times the measure of the other small angle. Find the measure of both angles.
Input your answers into the following boxes.
The measures of the two angles in the order from the smallest to the greatest are
degrees and
degrees.
The measures of two angles in the order from the smallest to the greatest are 21° and 69°.
What is a right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Given the acute angle of a right triangle is 6 more than 3 times the measure of the other small angle.
Assume that the measurement of smaller angle is x.
Then the mathematical expression of 6 more than 3 times of x is 6 + 3x.
The measure of third angle is 90° since it a right triangle.
The sum of all interior angles of a right triangle is 180°.
The equation is
x + (6 + 3x) + 90 =180
x + 6 + 3x + 90 =180
Combine like terms:
(x + 3x) + (6 + 90) = 180
4x + 96 = 180
Subtract 96 from both sides:
4x = 180 - 96
4x = 84
Divide both sides by 4
x = 21
Putting x = 21 in the expression (6 + 3x) :
6 + 3x = 6 + 63 = 69.
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Turn 584/50 in improper fraction 
In the image below, is a leg of the 45-45-90 triangle.
Reason:
x and y are the legs.
[tex]5\sqrt{2}[/tex] is the hypotenuse.
The hypotenuse is always opposite the 90 degree angle.
The hypotenuse is always the longest side of any right triangle.
The cost of 2 kg of carrots is £7 Work out the cost of 5 kg of carrots.
Answer:
56
Step-by-step explanation:
Solve the systems and please show all work using substitution.
The value of x = -84/17, y= 24/17 and z = 9/17
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x -2y + z= -6
x- 5z= -12
-x+ 6y + 4z = 3
Put x= -12+ 5z in equation 1 and 3
-12+ 5z - 2y + z= -6
6z - 2y = 6
3z - y= 3............(a)
and, 12 - 5z + 6y + 4z = 3
6y - z = -9.......(b)
Solving a and b we get
6(3z- 3) - z = -9
18z - 18 - z= -9
17z = 9
z= 9/17
and, y= 3(9/17) - 3 = 24/17
and, x = -12 + 120/17= -84/17
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You have one type of chocolate that sells for $2.10/lb and another type of chocolate that sells for $9.90/lb. You would like to have 62.4 lbs of a chocolate mixture that sells for $2.40/lb. How much of each chocolate will you need to obtain the desired mixture?
You will need __ lbs of the cheaper chocolate and __ lbs of the expensive chocolate.
Answer:
This is a problem of weighted averages and can be solved with a system of equations.
Let's define:
- `x` as the amount (in lbs) of the cheaper chocolate,
- `y` as the amount (in lbs) of the expensive chocolate.
We can set up the following equations:
1. `x + y = 62.4` (the total amount of chocolate we want)
2. `$2.10x + $9.90y = $2.40 * 62.4` (the total cost of the chocolate mixture)
The second equation represents the total value of the chocolate, while the first represents the total weight.
We can solve this system of equations using substitution or elimination. In this case, it may be simpler to use elimination.
Let's first transform the second equation to get rid of the dollar signs:
2.10x + 9.90y = 2.40 * 62.4
2.10x + 9.90y = 149.76
Let's now multiply the first equation by 2.10 (the price per lb of the cheaper chocolate):
2.10x + 2.10y = 2.10 * 62.4
2.10x + 2.10y = 131.04
Subtracting the second equation (multiplied) from the original second equation, we get:
9.90y - 2.10y = 149.76 - 131.04
7.80y = 18.72
Solving for y, we get:
y = 18.72 / 7.80 = 2.4 lbs
Substituting y = 2.4 into the first equation:
x + 2.4 = 62.4
x = 62.4 - 2.4 = 60 lbs
So, you will need 60 lbs of the cheaper chocolate and 2.4 lbs of the expensive chocolate to obtain the desired mixture.
17/6 divided 5/3 what’s the answer
Answer:
17/6 divided by 5/3 is equal to 17/6 * 3/5, which simplifies to 51/30.
Help would be appreciated
The correct reason for the similarity of triangles ADC and CBA is given as follows:
SSA.
What are the similarity theorems?The similarity theorems are listed as follows:
SAS: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent by the SAS theorem.ASA: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent by the ASA theorem.SSS: If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are congruent by the SSS theorem.SSA: If two sides and an angle not include between them are respectively equal to two sides and an angle of the other then the two triangles are congruent by the SSA theorem.In this problem, we have that:
Sides AB and DC are equal.Angles BAC and DCA are equal.Sides AC are equal.Two sides and an angle not between them, hence they are congruent by the SSA theorem.
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A rectangle with a perimeter of 40 inches has a width that is 3 times the length. What is the length And the width
The Length is 5 inches and the Breadth is 15 inches
What is Perimeter?
A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.
Solution:
Perimeter of Rectangle = 2*(Length + Breadth)
According to the question
Breadth = 3*Length
Perimeter = 40
40 = 2*(Length + 3*Length)
20 = 4*Length
Length = 5 inch
Breadth = 15 inch
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If JK = 31, KI = 40, and NL = 12, find the length of MN. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale. 95⁰ 34° K N 34° M 950 51° L
please help i need this soon!!
The length of the MN is 9.4.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Triangle NML.
NL = 12
Sin 51 = NM / NL
0.78 = NM / NL
MN = 0.78 x NL
MN = 0.78 x 12
MN = 9.36
Rounding to the nearest tenth.
MN = 9.4
Thus,
MN is equal to 9.4.
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which of the following is not a characteristic of a binomial probability distribution?
Multiple choice
Each outcome is mutually exclusive
Each trial is Independent
The probability of sucess remains constant from trail to trail
The number of trails is limited to two
Answer: The number of trials is limited to two.
Given the equation cosx = x^2 prove that it has at least one root in the [0, pi] interval. Justify answer by indicating the theorem used.
1 is the root of the equation cosx = x² in the interval [0, pi]/
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given equation is cosx = x²
cosx-x²=0
y(x)=cosx-x²
y(0)=1
y(π)=-1-π²
y(π)<0<y(0) and y is continuous, there must be a value of x in [0, pi]
where
cosx−x²=0.
Hence, 1 is the root of the equation cosx = x² in the interval [0, pi].
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To simplify 8.3-4 1/5 (6.1+1/2) which operation must be performed first? Which is second and which is third?
the answer to the expression 8.3-4 1/5 (6.1+1/2)is -19.42
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
The given expression
8.3-4 1/5 (6.1+1/2)
=8.3-4 1/5 (6.6)
=8.3-(6.6*21/5)
=-19.42
Hence the answer is -19.42
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what is 2 4/5+ 4/6 equivalent to?
Answer:
To find the equivalent of 2 4/5 + 4/6, we first need to convert the mixed numbers to improper fractions. To do this, we multiply the whole number part of the mixed number by the denominator of the fraction part, and add the result to the numerator of the fraction part. So 2 4/5 becomes 2 * 5 + 4 = 14/5. Similarly, 4/6 becomes 4 * 1 + 6 = 10/6.
Next, we need to find a common denominator for the two fractions so that we can add them. A common denominator for 14/5 and 10/6 is 30, so we convert both fractions to have a denominator of 30. To convert 14/5 to have a denominator of 30, we multiply the numerator and denominator by 6, which gives us 14 * 6 / 5 * 6 = 84/30. Similarly, we multiply the numerator and denominator of 10/6 by 5 to get 10 * 5 / 6 * 5 = 50/30.
Now that both fractions have a denominator of 30, we can add them to get the equivalent of 2 4/5 + 4/6. This gives us 84/30 + 50/30 = 134/30. Finally, we simplify the fraction to get the final answer, which is 134/30 = 4 8/30 = 4 4/15. So, the equivalent of 2 4/5 + 4/6 is 4 4/15.
what table does not represent a function please help!!
Answer:
A,C
Step-by-step explanation:
A,C
Functions have only one output for every input
The graph of the line with equation Y equals 2/3 X is shown. What is the product of 2/3 and -3
Answer:
-2
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] * -3
= [tex]\frac{2}{3}[/tex] * [tex]-\frac{3}{1}[/tex]
= [tex]-\frac{6}{3}[/tex]
= [tex]-\frac{2}{1}[/tex]
= -2
Solve the equation. .35(x+4)=.25(X-6)
can someone please help
Step-by-step explanation: When you divide the 2 by 9, you get like 0.222222 (and it repeats forever), then since the 2 is less than 5, you round down, so it would be 0.22 after rounding. I hoped this helped!
From 2010 to 2012, the average selling price of tablets decreased by 20%. This percent
reduction amounted in a decrease of $140. Find the average selling price of tablets in 2010
and in 2012.
In 2010, the average selling price was $, and in 2012, the average selling price was $[
Answer:
In 2010, the average selling price was $700, and in 2012, the average selling price was $560.
Which statement is correct about the product of
3
2
3
and
10
9
?
Because
10
9
is greater than 1, the product of
3
2
3
and
10
9
is greater than
3
2
3
.
Because
10
9
is less than 1, the product of
3
2
3
and
10
9
is greater than
3
2
3
.
Because
10
9
is less than 1, the product of
3
2
3
and
10
9
is less than
3
2
3
.
Because
10
9
is greater than 1, the product of
3
2
3
and
10
9
is less than
3
2
3
.
option B is correct. 10/9 is greater than 1, the product of [tex]3\frac{2}{3}[/tex] and 10/9 is greater than 3 is the statement,
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
We need to find the product of [tex]3\frac{2}{3}[/tex] and 10/9.
Firstly let us convert the mixed fraction [tex]3\frac{2}{3}[/tex] to the improper fraction.
11/3 is the simplified form of [tex]3\frac{2}{3}[/tex]
11/3×10/9
110/27
4.1
As we observe the 10/9 is greater than 1, the product of [tex]3\frac{2}{3}[/tex] and 10/9 is greater than 3.
Hence, the statement 10/9 is greater than 1, the product of [tex]3\frac{2}{3}[/tex] and 10/9 is greater than 3.
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please have the right answers nothing wrong
The total distance walked in each case is given below;
15 feet4.5 feet6.75 feet1.5 feet1.5x feetWhat is the total distance?Jada's pet turtle walked 10 feet, and then half that length again
Total distance = 10 + (1/2 of 10)
= 10 + (1/2 × 10)
= 10 + 5
= 15 feet
Jada's pet baby brother walked 3 feet, and then half that length again
Total distance = 3 + (1/2 of 3)
= 3 + (1/2 × 3)
= 3 + 1.5
= 4.5 feet
Jada's pet hamster walked 4.5 feet, and then half that length again
Total distance = 4.5 + (1/2 × 4.5)
= 4.5 + 2.25
= 6.75 feet
Jada's pet robot walked 1 foot, and then half that length again
Total distance = 1 foot + (1/2 × 1)
= 1 + 0.5
= 1.5 feet
A person walked x feet, and then half that length again
Total distance = x + (1/2 × x)
= x + 1/2x
= 1.5x feet
In conclusion, the total distance is calculated by adding the initial distance and additional distance
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What is the constant of proportionality, k, for the data in the table above? Enter answer
Enter just the numeric answer.
Answer:
you really just click on peoples questions and just be like sorry im just here for the points so im doing it to you
Step-by-step explanation:
Points A(-6,10) and B(2,14) lie on circle O with its center at (2,4) what are the coordinates of point C, which is the midpoint of AB what is the relationship between chord AB and segment OC select the correct answer from drop down menu point C is located at chord Ab is segment OC
The coordinates of point C is (-2, 12)
The segment OC is perpendicular to the chord AB.
What is midpoint of a line segment?The midpoint of a line segment is given as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
Points A(-6,10) and B(2,14) lie on circle O with its center at (2,4).
C is the midpoint of the chord AB.
Now,
The coordinates of C = (x, y).
x = (-6 + 2) / 2 = -4/2 = -2
y = (10 + 14) / 2 = 24/2 = 12
(x, y ) = (-2, 12)
The relationship between chord AB and segment OC.
The segment OC is perpendicular to the chord AB.
Thus,
The coordinates of C is (-2, 12)
The relationship between segment OC and chord AB is that segment OC is perpendicular to chord AB.
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I’ll give BRAINLIEST if correct question is in the photo
Explain how to solve the question in the photo f(x)=5x+3
Chloe runs a farm stand that sells apples and peaches. Each pound of apples sells for
$3 and each pound of peaches sells for $4. Chloe sold 3 times as many pounds of
peaches as pounds of apples and she made $240 altogether. Graphically solve a
system of equations in order to determine the number of pounds of apples sold, x,
and the number of pounds of peaches sold, y.
pls help! plot on a line
Answer:
3x+4y=240; y=3x16 pounds of apples48 pounds of peachesStep-by-step explanation:
You want a system of equations and a graphical solution for the scenario that the weight of peaches sold (y) is 3 times the weight of apples sold (x), and the revenue from sales of apples at $3/lb and peaches at $4/lb was a total of $240.
EquationsThe revenue equation can be ...
3x +4y = 240
The relation between pounds of each fruit sold can be ...
y = 3x
GraphThe graph is attached. The solution is (x, y) = (16, 48).
16 pounds of apples and 48 pounds of peaches were sold.
__
Additional comment
We note that the 3x in the first equation can be substituted by y using the second equation. This gives 5y=240, or y = 48. Then 3x=48, so x=16. This agrees with the graphical solution, as it should.
50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!
Answer:
reflection over the y-axis
Step-by-step explanation:
Answer:
C?
Step-by-step explanation:
which relation is a function
Answer:
top right :)
Step-by-step explanation:
you can use the ruler trick! if you drag a ruler across the math problem and it crosses two lines at the same time then it's not a function. same goes for points. and as you can see if I were to drag a ruler across this one you won't pass two points at once!