The amount of rye seed and bluegrass seed used in the mixture is 109.8 and 70.2 pounds respective.
What exactly is the substitution method?The substitution method is an algebraic approach to solving simultaneous linear equations.As the name implies, the value with one variable from one equation is replaced in the other equation.In response to the given question;
Let's say the amount of rye seed is 'x.'
The cost of rye seed = $6.50 per pound
Let's say the amount of bluegrass seed is 'y.'
The cost of bluegrass seed = $3.50 per pound.
The total seeds are 180 pounds.
Thus,
x + y = 180
x = 180 - y .......eq 1.
The other equation for the total cost of $5.33 per pound is;
6.50x + 3.50y = 5.33×180
Put the value of x from eq 1.
6.50(180 - y) + 3.50y = 959.4
1170 - 6.50y + 3.50y = 959.4
3y = 210.6
y = 70.2
x = 180 - 70.2 = 109.8
Thus, the amount of rye seed and bluegrass seed used in the mixture is 109.8 and 70.2 pounds respectively.
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In a certain chemical, the ratio of zinc to copper is 3 to 16 A jar of the chemical contains 528 grams of copper. How many grams of zinc does it contain?
Answer:
99 grams of zinc
Step-by-step explanation:
Ser up a proportion
[tex]\frac{zinc}{copper}[/tex] = [tex]\frac{zinc}{copper}[/tex] Put in the ration and the actual amount of copper i and solve for the actual number of zinc
[tex]\frac{3}{16}[/tex] = [tex]\frac{z}{528}[/tex] cross multiply to solve for z
16z = 3(528)
16z = 1584 Divide both sides of the equation by 16
z = 99
In the circle,o is the centre and ab is the diameter
Answer:
centre =
diameter = ab
radius = (ab)/2
Step-by-step explanation: hope this helps
Tessa has a coin jar full of dimes and pennies. When she took the coin jar to the bank, she was told that it contained exactly $27.34. Give three different combinations of the number of dimes and pennies that could have been in the coin jar.
Answer:
Step-by-step explanation:
Note: In solving our problems below, we will use the value of the coins in dollars which are listed under the third column in the table above. As you can see, the penny has a value of 0.01, the nickel has a value of 0.05, the dime has a value of 0.10, and the quarter has a value of 0.25
solve 2x=1=7x+44
please try your best if you dont know
Answer: 2x-1=7x+44
2x-7x=44+1
-5x=45
x=-9
Step-by-step explanation:
Expand and simplify
(√15-√3)²
Give your answer in the form b-c√5
where b and c are integers.
[tex] = ( \sqrt{15} - \sqrt{3} )( \sqrt{15} - \sqrt{3} ) \\ = \sqrt{15} ( \sqrt{15} - \sqrt{3} ) - \sqrt{3} ( \sqrt{15} - \sqrt{3} ) \\ = 15 - \sqrt{45} - \sqrt{45} + 3 \\ = 15 + 3 - 2 \sqrt{45} \\ = 18 - 2( \sqrt{9 \times 5} ) \\ = 1 - 2(3 \sqrt{5} ) \\ = 1 - 6 \sqrt{5} [/tex]
ATTACHED IS THE SOLUTION
What Is the equation of a line that passes through the coordinates (4,1) and (1,4)
Equation of the line is x +y = -5.
What is equation?Equation is a declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
Given Data
coordinates (4,1) and (1,4)
A line is singular if you are aware that it goes through two specific coordinates (x₁ , y₁) and (x₂ , y₂) .The equation for the line is if the points are
[tex]\frac{x - x}{x_{1} - x}[/tex]¹₂ = [tex]\frac{y - y_{1} }{y_{1}- y_{2} }[/tex]
Equating coordinates:
[tex]\frac{x-4}{4-1}[/tex] = [tex]\frac{y-1}{1-4}[/tex]
[tex]\frac{x-4}{3}[/tex] = [tex]\frac{y-1}{-3}[/tex]
Cross multiplying,
-3(x-4) = 3(y-1)
-3x + 12 = 3y -3
3x + 3y = -15
x +y = -5
Equation of the line is x +y = -5.
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Here are two expressions whose sum is a new expression, A.
(2x²+5)+(6x0-7)=A
Select all the values that we can put in the box so that A is a polynomial.
All the values that we can put in the given box so that A is a polynomial,
[tex]A=(2x^{2} +5-7)\\A =2(x^{2} -1)\\A=2(x+1) (x-1)[/tex]
[tex]x[/tex] can take any value except ±1.
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Convert 98 pounds to kilograms. (1 pound = 0.454 kilogram) 444.92 kilograms 216 kilograms 44.492 kilograms 21.6 kilograms
The conversion of 98 pounds to kilograms is 44.5 pounds.
This is a question of conversion of weights.
Unitary method
The unitary method is used to find the value of a single unit from a given multiple. For example, the price of 40 pens is Rs. 400, then how to find the value of one pen here.
Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit.
We know that,
1 pound = 0.45359237 kilograms ≈ 0.454 kilograms
Hence, using unitary method, we can write,
98 pounds = 98*0.454 kilograms = 44.492 kilograms ≈ 44.5 pounds.
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If h(x)=x^2/f(x) and f(3) = 2 and f'(3) = 4, then h' (3) = -12.
true
false
Answer:
FALSE.
Step-by-step explanation:
Given:
h(x)=x^2/f(x) f(3) = 2 f'(3) = 4To Find:
Whether h'(3) = -12 or not.Formula used:
For a function y = f(x)/g(x), the differentiation of y is defined as y' = [f'(x)*g(x) - g'(x)*f(x)]/(g(x))^2. This is know as quotient rule of differentiation.Using the above formula, we have
h'(x) = [2x*f(x) - f'(x)*x^2]/(f(x))^2
So, h'(3) = [2*3*2 - 4*(3)^2]/(2)^2
h'(3) = (12-36)/4
h'(3) = -24/4 = -6
So, h'(3) = -6 and not -12.
So, the given value is FALSE.
Find the positive difference between 16 and -2
[tex] = 16 - ( - 2) \\ = 16 + 2 \\ = 18[/tex]
The positive difference is 18.
ATTENDING TO PRECISION Use the graph to write a function of the form y = a tan bx.
Y=?
Answer:.
Step-by-step explanation:
Help answering these please!!
Answer:
I will give you the formula and than it will be easy for you to solve this.
Which expression represents the perimeter
of this quadrilateral in units?
4r² - 1
²+3
2
5r²+2
A. 9² +8
B. 117² - 8
C.
11² + 8
D. 9r² + 2r-8
²+4
Answer: 11r² + 8 ==> C
Step-by-step explanation:
P=Sum of all sides
P=4r² - 1 + r² + 3 + r² + 4 + 5r² + 2
P=4r² + r² + r² + 5r² - 1 + 3 + 4 + 2
P=5r² + 6r² + 2 + 6
P=11r² + 8 ==> C
The temperature was 98 degrees last Friday. Wednesday it was 24 degrees
cooler. Which expression represents the relationship in the temperature
between Friday and Wednesday?
Answer:
98 + (-24)
Step-by-step explanation:
Under her cell phone plan, Sydney pays a flat cost of $35.50 per month and
$5 per gigabyte. She wants to keep her bill under $50 per month. Write and
solve an inequality which can be used to determine a, the number of
gigabytes Sydney can use while staying within her budget.
The number of gigabytes that Sydney can use while staying within her budget is less than 2.9 gigabytes.
What are gigabytes?gigabytes (GB) – pronounced with two hard Gs – is a unit of storage capacity equal to approximately 1 billion bytes. In decimal form (base 10), a gigabyte is exactly one billion bytes. In binary form, a gigabyte is 230 bytes or 1,073,71,82 bytes. Giga comes from the Greek word for giant. Werner Buchholz is credited with coining the term byte in 1956 and helped design IBM's 7030 Stretch, the first transistorized supercomputer.
gigabytes has been a common unit of measurement for data storage products since the mid-1980s. In recent years, terabytes (TB) have become a more common measure of storage capacity, especially for hard drives and solid-state drives.
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From the set {12, 22, 25}, use substitution to determine which value of x makes the inequality true 3x < 66
A difference between two values indicates whether one is smaller, larger, or simply not equal to other. From the set {12, 22, 25}, value of x makes the inequality true 3x < 66 is 12.
What do you mean by inequality?Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. a week ago.
A difference between two values indicates whether one is smaller, larger, or simply not equal to other.
A and B claim that they are not equal.A must be less than B if A = B.An is greater than b when a > b. These two constitute tight inequity.A must be smaller than or equal to b when dividing a by b.An is greater than b if a and b are equal.To know more about inequality visit: https://brainly.com/question/20383699
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Factor out the coefficient of the variable term 6s-3/4
The coefficient of the variable term in the equation 6s - 3/4 is 6. The variable term is s while the constant term is -3/4
How to find the coefficient of the variable termgiven data
6s-3/4
The coefficient of the variable term is the number multiplying the variable term. The variable term in the equation is "s"
The number in the given equation is 6
The equation could be written as
6 * s - 3/4
from the rewritten equation we can see that 6 is multiplying the variable and hence the coefficient.
The other term in the equation is constant term and this is - 3/4
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[tex]5sin^2x-3sinx=0[/tex]
solve in degrees
solve in the interval 0°[tex]\leq[/tex]x[tex]\leq[/tex]360°
[tex]5sin^2(x)-3sin(x)=0\implies sin(x)[5sin(x)-3]=0 \\\\[-0.35em] ~\dotfill\\\\ sin(x)=0\implies x=sin^{-1}(0)\implies x= \begin{cases} 0\\ 180^o\\ 360^o \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 5sin(x)-3=0\implies 5sin(x)=3\implies sin(x)=\cfrac{3}{5} \\\\\\ x=sin^{-1}\left( \cfrac{3}{5} \right)\implies x\approx \begin{cases} \stackrel{I~Quadrant}{36.87^o}\\\\ \stackrel{II~Quadrant}{143.13^o} \end{cases}[/tex]
Elisabeth has 10 princess movies, but can only take four of them to her sleepover.
How many different combinations of movies can she take?
Help again pleaseeee
Finding a grouping, ordering, or assignment of a discrete, finite set of things that complies with predetermined requirements is the goal of combinatorial issues.
She has 210 different combinations.
What is meant by combinatorial methods?A new wave of research methodology called the combinatorial approach to materials seeks to greatly speed up the discovery and development of novel substances.
The area of mathematics concerned with finding solutions to conundrums involving the selection and arrangement of parts of particular (often finite) sets in line with predetermined norms.
Finding a grouping, ordering, or assignment of a discrete, finite set of things that complies with predetermined requirements is the goal of combinatorial issues. Candidate solutions are combinations of solution elements that could be found while trying to find a solution, but they don't have to meet all the requirements.
So, she has [tex]$C_1^4=\frac{A H}{A \frac{A}{4}}=\frac{10 \times 2 \times 8 \times 7}{1 \times 2 \times 3 \times 4}=210$[/tex]
So she has 210 different combinations.
[tex]$c_{1=}^4=\frac{4 \%}{A f}$[/tex]
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Bunting has been hung in a straight line
between a wall and a house, as shown
below.
Calculate the height, p, of the house.
Give your answer in metres to 2 d.p.
36°
2.64 m
5.47 m
Not drawn accurately
Bunting has been hung in a straight line between a wall and a house, then the height, P, of the house P = 6.61 m.
Third angle in a triangle = 180 - (90+36)
= 180-126
= 54°
So,
Third angle in a triangle = 54°
We can use Sin rule,
Then, we get,
[tex]\frac{Sin A}{BC} =\frac{Sin B}{AC} =\frac{Sin C}{AB}[/tex]
Based on the given condition,
We can write,
Sin A = 54°
Sin B = 36°
BC = 5.47
Then,
Sin 54°/5.47 = Sin 36°/AB
Hence, Sin 54° = 0.8090
Sin 36° = 0.5877
[tex]\frac{0.8090}{5.47} =\frac{0.5877}{AB}[/tex]
AB = [tex]\frac{0.5877 * 5.47}{0.8090}[/tex]
AB = [tex]\frac{3.2147}{0.8090}[/tex]
AB = 3.97 m
So,
Height , P = 2.64 + 3.97
P = 6.61 m.
Therefore,
We can use triangle formula, then the height, P, of the house P = 6.61 m.
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PLSS HELP!!! When three times a number n is increased by 12, the result is at least 32. Solve, and then write your answer in set, interval, and graphical notation, if possible.
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
Which definition of inequality is the best?The meaning of inequality
A social discrepancy is one example of a characteristic that is unequal or uneven. b: unequal opportunity or distribution.
A disparity in size, quantity, quality, social standing, or another aspect is what is meant by the term "inequality." When you have ten of something and someone else has none, that is an instance of inequality.
A number = n 12
multiplied by a number = n+12
which is 32 less than the number = 3n-32
n+12 =3n-32
44 =2
The result is equal to 2n n=22.
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Find the Greatest Common Factor (GCF):
70x³z, 45y4z²
The greatest common factor for the given expression is 5z.
What is GCF?
The greatest common factor, which is the product of two or more numbers, is the largest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's factors have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF). The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers.
Given, the first expression is: y₁ = 70x³z = 5z.14x³ -(i)
Also, the second expression is: y₂ = 45y4z² = 5z.36yz -(ii)
Comparing (i) and (ii), the greatest common factor for y₁ and y₂ is 5z.
Thus, the greatest common factor for the given expression is 5z.
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3. Solve the compound inequality −2(x + 1) < 4 and
4x +1 -3. Graph the solution.
Part 2: Find the volume of the shipping box using the total number of fish food cubes. Step 1: Find the volume of the fish food cube. Remember to include units. Volume of the fish food cube = _____ × _____ × _____ = __________ Step 2: Find the volume of the shipping box using your answer from Part 1. Remember to include units. Volume of the shipping box = _____ × _____ = __________ Part 3: Find the volume of the shipping box using a volume formula. Remember to include units. V = l × w × h = _____ × _____ × _____ = __________ Are your answers for the volume of the shipping box in Parts 2 and 3 equal? Why or why not?
The volume of one fish food cubes is: 1/64 ft³
Using the volume formula, the volume of the shipping box is: 15/4 × 3 × 13/4 = 585/16 ft³
The number of fish food cubes that can be packed in the shipping box is: 2,340 fish food cubes.
What is the Volume of a Box and a Cube?The volume of a box = length × width × height
A cube has equal side lengths, therefore, the volume of a cube = (side length)³ = side length × side length × side length.
We are given that the fish food cubes have side lengths of 1/4 ft. Therefore:
Volume of fish food cubes = 1/4 × 1/4 × 1/4
Volume of fish food cubes = (1 × 1 × 1)/(4 × 4 × 4)
Volume of fish food cubes = 1/64 ft³
Using the volume formula, we are given the parameters of the box as:
Length (l) = 3¾ = 15/4 ft
Width (w) = 3 ft
Height (h) = 3¼ = 13/4 ft
Therefore,
Volume of shipping box = 15/4 × 3 × 13/4
Volume of shipping box = (15 × 3 × 13)/(4 × 4) = 585/16 ft³
The number of fish food cubes that can be packed in the shipping box = volume of shipping box/volume of one fish food cube
= 585/16 ÷ 1/64
= 585/16 × 64/1
= (585 × 64)/(16 × 1)
= 37,440/16
= 2,340 fish food cubes.
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please help me solve this
Answer:
400
Step-by-step explanation:
cheryl works 5 hours each day for 7 days a week she earns £490 each week how much does cheryl earn per hour
Answer:
14 pounds per hour
Step-by-step explanation:
[tex] \frac{490}{7\times 5} = \frac{490}{35} = 14[/tex]
pls solve I've attempted it loads of times and got the wrong answer
The cylinder below has a radius of 3cm and length if 14cm
work out the volume of the cylinder give your answer to the nearest integer
Answer:
396 cm³
Step-by-step explanation:
Volume= πr²*height
r=3
3² π *14
9*14*π= 396cm³
volume of a cylinder with radius as 3cm and height as 14cm is 396cm^3
Just need the bottom one answered
7th grade easy Math
NEED ANSWER ASAP DUE TODAY
Felicity put down $800 on a used car. She took out a loan to pay off the balance of the cost of the car. Her monthly payment will be $175. After 9 months how much will she have paid for the car?
Enter your answer in dollars.
John has two types of boxes. The smaller box can store 8 tins of coffee and the bigger box can store 12 tins of coffee. If the total number of boxes is 20 and he has 184 tins of coffee, by forming a pair of simultaneous equations, find the number of each kind of box.
He will need 14 boxes which can store can store 8 tins of coffee and 6 boxes that can store 12 tins of coffee.
let us assume:
Number of 8- tin boxes= x
Number of 12- tin boxes= y
we are given the condition that total number of boxes are 20, so-
x+y=20
⇒ x= 20-y
We are also given the condition that he has 184 tins of coffee, so-
8x+12y= 184
⇒ 8(20-y) + 12y = 184
⇒ 160 -8y +12y = 184
⇒ 4y= 24
⇒ y=6
⇒ x=20 -y
⇒ x= 20 - 6
⇒ x= 14
What do you mean by conditional linear equations?
A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer set is "all real numbers." An equation is conditional if there is only one solution to a linear equation, such as x = 3.
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