To achieve 204 gallons of 5% butterfat milk, one would need 136 gallons of 6% butterfat milk and 68 gallons of 3% butterfat milk by solving a system of linear equations.
How to Mix Butterfat Percentages for Milk
To solve the problem of mixing two different butterfat percentages of milk to achieve a certain amount of milk with a desired fat content, we will use a system of equations.
Let x represent the gallons of 6% butterfat milk, and y represent the gallons of 3% butterfat milk.
To achieve 204 gallons of 5% butterfat milk, we have the following equations:
Equation 1: x + y = 204 (total gallons of milk)
Equation 2: 0.06x + 0.03y = 0.05(204) (total butterfat content)
Solving these equations simultaneously, we find:
From equation 1, we can express y as y = 204 - x.
Substituting this into equation 2 gives us 0.06x + 0.03(204 - x) = 10.2.
Simplifying this, we get 0.06x + 6.12 - 0.03x = 10.2, which leads to 0.03x = 4.08.
Hence, x = 136 gallons of 6% butterfat milk and y = 68 gallons of 3% butterfat milk.
What value would be placed in the space shown to create a perfect square trinomial?
x^2 - 3x +___
1) 3/2
2) 9/4
3) - 9/4
4) -3/2
Answer:
9/4 (Answer 2)
Step-by-step explanation:
Take half the coefficient of x and square that result:
(1/2)(-3) = -3/2
Squaring this, we get 9/4 (Answer 2)
To create a perfect square trinomial [tex]\frac{9}{4}[/tex] should be placed in the space shown in x^2 - 3x +___
How to form a trinomial equation?The trinomial equation is of the form
[tex]x^{2}[/tex] - 2ax + [tex]a^{2}[/tex]
given equation is [tex]x^{2}[/tex] - 3x + _
comparing the two equation
2ax = 3x
a = [tex]\frac{3}{2}[/tex]
[tex]a^{2}[/tex] = [tex]\frac{9}{4}[/tex]
[tex]x^{2}[/tex] - 3x + [tex]\frac{9}{4}[/tex] = [tex]( x- \frac{3}{2} )^{2}[/tex]
Therefore, option 2) 9/4 is the correct answer
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How do I count by twelfths
12, x 1 = 12
12 x 2 =24
12 x 3 = 36
12 x 4 =48
12 x 5= 60
12 x 6 =72
12 x 7 = 84
12 x 8= 96
12 x 9= 108
12 x 10 = 120
12 x 11=132
12x 12= 144
hope this helps
Write a polynomial function in factored form with zeros at −2, 5, and 6.
Answer:
f(x) = (x + 2)(x - 5)(x - 6)
Step-by-step explanation:
given the zeros of f(x) are x = a, x= b and x = c, then the factors are
(x - a), (x - b) and (x - c)
The function is then the product of the factors
f(x) = (x - a)(x - b)(x - c)
Here zeros are x = - 2, x = 5 and x = 6, thus the factors are
(x + 2), (x - 5) and (x - 6), so
f(x) = (x + 2)(x - 5)(x - 6) ← in factored form
Final answer:
To create a polynomial with zeros at -2, 5, and 6, the factored form is (x + 2)(x - 5)(x - 6).
Explanation:
To write a polynomial function in factored form with zeros at −2, 5, and 6, we start by creating factors based on these zeros. Each zero corresponds to a factor of the polynomial where the variable x is set equal to the zero value. Therefore, the factors would be (x + 2), (x - 5), and (x - 6). We then multiply these factors together to get the polynomial.
The factored form of the polynomial is then (x + 2)(x - 5)(x - 6). If you wanted to write this polynomial in standard form, you would expand the factors to get x³ - 9x² + 4x + 60.
Solve x2 – 8x = 3 by completing the square. Which is the solution set of the equation?
Answer:
x = 4 ± [tex]\sqrt{19}[/tex]
Step-by-step explanation:
Given
x² - 8x = 3
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = 3 + 16
(x - 4)² = 19 ( take the square root of both sides )
x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )
x = 4 ± [tex]\sqrt{19}[/tex]
Final answer:
To solve the equation x^2 - 8x = 3 by completing the square, we first rearrange the equation, add 16 to both sides to form a perfect square, and then take the square root of both sides resulting in the solution set {4 + √19, 4 - √19}.
Explanation:
Completing the Square Method
To solve the equation x2 − 8x = 3 by completing the square, follow these steps:
Move the constant term to the right side of the equation: x2 − 8x = 3 becomes x2 − 8x − 3 = 0.Add ½ of the coefficient of x, squared, to both sides to complete the square: The coefficient of x is -8, so ½ of -8 is -4, and (-4)2 is 16. Thus, add 16 to both sides: x2 − 8x + 16 = 3 + 16.Now the equation is (x − 4)2 = 19, which shows a perfect square on the left.The solution set for the equation is {4 + √19, 4 − √19}.
5. Clarissa has 20 DVDs that she owns. She puts
them into different categories. She owns 16 comedy
movies. Which fraction is equivalent to the number
of DVDs that are comedy movies?
A. 4/8
B. 4/5
C. 1/4
D. 4/16
Answer
B. 4/5
Explanation
Since Clarissa has 20 DVDs, it is safe to assume that the denominator will be 20 since that is the complete total.
She also owns 16 comedy movies which is the numerator.
So far, the fraction we have is 16/20
Now reduce that number into simplest terms
16/4 = 4
20/4 = 5
4/5
Please help ASAP my grade is so dependent on this and I need help I’m so lost
Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{x}{4}[/tex] > - 16 ( multiply both sides by 4 )
x > - 64
To show the solution on a number line
Place an open circle ( indicating x ≠ - 64 ) at - 64
greater than - 64 is to the right of - 64 , hence the direction of the shaded line points to the right of - 64
Tell me if you have troubles understanding something!
If x= -3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?
A) The discriminant is negative.
B) The discriminant is -3.
C) The discriminant is 0.
D) The discriminant is positive.
Answer:
C) The discriminant is 0.
Step-by-step explanation:
Since the graph of the quadratic equation has only one x-intercept, we can conclude that the quadratic has only one real root.
If a quadratic equation has only one real root, then the discriminant is 0
1. Halla la circunferencia de un círculo cuyo diámetro es 18 cm.
Answer:
C ≈ 56.55
Step-by-step explanation:
First I translated this into English.
"Find the circumference of a circle whose diameter is 18 cm."
Formula:
C = 2πr
Translated in Spanish:
Primero tienes que dividir la circunferencia por dos. Luego lo enchufas en la fórmula para "R" y resuelves.
English Translation:
First you have to divide the circumference by two. Then you plug it into the formula for "R" and solve.
Help please on both please
On what I don’t see anything on here
how much interest is earned on a principal of $575 invested at an interest rate of 7% compounded annually for nine years?
Answer:
$482.11 in interest
Step-by-step explanation:
Use the compound amount formula. Calculate the compound amount and then subtract the principle to find the amount of interest earned.
A = P(1 + r)^t, where r is the interest rate as a decimal fraction
This becomes:
A = $575(1 + 0.07)^9, or A = $1057.11.
Subtracting the principal: A - P: $1057.11 - $575 = $402.11
The total interest earned is $482 on a principal of $575 invested at an interest rate of 7% compounded annually for nine years
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
Given, P = $575, n = 9 and r = 7%.
∴ A = 575(1 + 7/100)⁹.
A = 575(1.07)⁹.
A = 575(1.84).
A = 1057.
So, Interest earned is (A - P) = (1057 - 575) = $482.
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REALLY NEED THIS PLZZ ANSWER ESY I JUST DON'T KNOW PLZZZZZZZZZZZWhich quadratic rule represents the data in the table? 20PTS AND BRAINLIEST !!!!!!!!!!!!!!!
x –1 0 1 2 3
y –4 –5 –4 –1 4
A.)y = –2x² + 5
B.) = –x² + 5
C.) y = x² – 5
D.y = x² + 5
Answer:
It is answer C
Step-by-step explanation:
Answer:
C.) y = x^2 -5
Step-by-step explanation:
The table pair (x, y) = (0, -5) tells you that the constant will be -5. Only answer choice C has that value for the constant.
___
You can check other (x, y) values in the rule to see that they work.
what is the volume of a regular pyramid having a base area of 24 in.² and a height of 6 inches?
Answer:
48 in³
Step-by-step explanation:
The volume (V) of a pyramid is calculated as
V = [tex]\frac{1}{3}[/tex] × area of base × height
here area of base = 24 and height = 6, so
V = [tex]\frac{1}{3}[/tex] × 24 × 6 = 8 × 6 = 48 in³
Find the radius of a sphere with a surface area of 1024π square inches
Answer:
R = 16 inStep-by-step explanation:
The formula of a Surface Area of a sphere:
[tex]S.A.=4\pi R^2[/tex]
R - radius
We have
[tex]S.A.=1024\pi\ in^2[/tex]
Substitute:
[tex]4\pi R^2=1024\pi[/tex] divide both sides by π
[tex]4R^2=1024[/tex] divide both sides by 4
[tex]R^2=256\to R=\sqrt{256}\\\\R=16\ in[/tex]
To find the radius of a sphere when you are given the surface area, you can use the formula for the surface area of a sphere, which is:
\[ \text{Surface area of a sphere} = 4 \pi r^2 \]
where \( r \) is the radius of the sphere. Now, let's solve for \( r \) using the surface area provided:
We are given that the surface area is \( 1024 \pi \) square inches, so we set that equal to the formula for the surface area:
\[ 1024 \pi = 4 \pi r^2 \]
To solve for \( r^2 \), we first divide both sides of the equation by \( 4 \pi \):
\[ \frac{1024 \pi}{4 \pi} = \frac{4 \pi r^2}{4 \pi} \]
On simplifying the left-hand side and cancelling \( 4 \pi \) from the right-hand side, we get:
\[ 256 = r^2 \]
Now, to solve for \( r \), we take the square root of both sides:
\[ r = \sqrt{256} \]
This results in:
\[ r = 16 \]
So, the radius of the sphere is 16 inches.
Please Help Quickly!!
A box contains red, blue, green, purple, and yellow crayons such that the probability of drawing a purple crayon is 3/7.
Answer:
Option C.
Step-by-step explanation:
It is given that a box contains red, blue, green, purple, and yellow crayons such that the probability of drawing a purple crayon is 3/7.
We draw two crayons randomly such that both draws are independent.
Let X be a random variable that assigns the number of purple crayons to each outcome.
We need to find the range of X.
If no purple crayon is selected, then X=0
If 1 purple crayon is selected, then X=1
If 2 purple crayons are selected, then X=2
The range of X is {0,1,2}.
Therefore, the correct option is C.
Use the relation to answer the following questions. Graph the relation. State the domain of the relation. State the range of the relation. Is the relation a function? How do you know? Answer:
Answer:
All answers in the pic attached
Determine whether the two figures are similar if so give the similarity ratio of the smaller figure to the larger figure figures are not drawn to scale
[tex]\bf \cfrac{\textit{small prism}}{\textit{large prism}}\qquad \qquad \stackrel{~\hfill \textit{yes 1:4}}{\cfrac{18}{72}\implies \boxed{\cfrac{1}{4}}\qquad \cfrac{4}{16}\implies \boxed{\cfrac{1}{4}}\qquad \cfrac{3}{12}\implies \boxed{\cfrac{1}{4}}}[/tex]
The figures are same and the ratio of the adjacent sides of the small rectangular prism to big is 1:4 option first is correct.
What is a cuboid?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape.
As we can see in the figure two three-dimensional figures are given.
To know whether the two figures are similar or not we first find the ratio of the adjacent sides.
4/16 = 1/4
3/12 = 1/4
18/72 =1/4
The ratios are equal that's why the two figures are same, and the ratio is: 1:4
Thus, the figures are same and the ratio of the adjacent sides of the small rectangular prism to big is 1:4 option first is correct.
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what is the value of t=1
Answer:
B. 7
Step-by-step explanation:
When you solve the series for each term, you get 4 + 2 + 1 = 7
Answer:
A
Step-by-step explanation:
10 points which of the following describes the graph ? Help
Needed
ANSWER
First choice
EXPLANATION
The graph of f(x) and
[tex] {f}^{ - 1} (x)[/tex]
are symmetric about the line y=x.
This means that the graph of
[tex]{f}^{ - 1} (x)[/tex]
is the reflection of f(x) in the line y=x.
This explains why the composition of a function and its inverse yields x, as the result.
The first choice is correct.
(y 3 - 4y 2 + 7y - 6) divided by (y - 2)
Answer:
Quotient: y^2 -2y +3
Remainder = 0
Step-by-step explanation:
We need to solve he equation:
y^3-4y^2+7y-6 ÷ y -2
It is solved in the figure attached below:
After solving we get
Quotient: y^2 -2y +3
Remainder = 0
HELP! ASAP! Five friends ate in a restaurant together and split the cost, c, equally. Each person paid less than $10. Which statements represent the scenario? Check all that apply.
A. The situation can be represented using the inequality c ÷ 5 < 10.
B. The total cost of the food could be $40. The maximum total cost of the food could be determined by dividing 10 by 5.
C. When graphed, the number line would be shaded to the left of the maximum value.
D. The total cost of the food could be $50.
Answer:
I know that A is correct
B the first part is correct, But the second part isnt.
C I dont know, not a good grapher
D would be correct if there was tax.
Step-by-step explanation:
Answer:A,B,D are correct!
Step-by-step explanation:
12 _ (7 - 4) +5 _ 3 = 19
The first blank is "division" and the second blank is "multiplying"
12 / (3) = 4
5 x 3 = 15
15 + 4 = 19
The student's equation 12 _ (7 - 4) + 5 _ 3 = 19 is solved by inserting addition after 12 and subtraction after 5, resulting in 12 + (7 - 4) + 5 - 3. Following correct order of operations, we get the desired result of 19.
Explanation:The student has presented a mathematical equation with missing operations that needs to be solved to equal 19. To find the correct operations, we can see that 12 with an addition operation followed by 5 minus 3 gives us 14. Adding this to the original 12 gives us the desired result of 19. Hence, the missing operations are addition after the 12 and subtraction after the 5.
The equation now looks like 12 + (7 - 4) + 5 - 3 = 19. Here, we first perform the operation inside the parentheses, which is 7 - 4 = 3. Then, we substitute this result into the expression and proceed with the operations: 12 + 3 + 5 - 3. Next, we add the numbers together, which gives us 12 + 3 + 5 = 20, and finally deduct 3 to get 20 - 3 = 19.
This kind of problem teaches us the significance of operation placement within equations, as seen in different examples provided. Understanding the properties of arithmetic operations and the correct application of the order of operations (parentheses, exponents, multiplication and division, addition and subtraction) is crucial for solving such mathematical puzzles.
Use the order of operations to simplify the expression
23 + 5 × 10 ÷ 2 – 33 + (11 – 8)
A. 9
B. 41
C. 10
D. 55
For this case according to the order PEMDAS we have:
P: Perform the parenthesis calculations
E: Simplify exponential expressions
MD: Multiplications and divisions from left to right
AS: Addition and subtraction from left to right.
We have:
23 + 5 * 10÷2-33 + (11-8) =
23 + 5 * 10÷2-33 + 3 =
23 + 50÷2-33 + 3 =
23 + 25-33 + 3 =
48-33 + 3 =
15 + 3 =
18
Thus, the value of the expression is 18
ANswer:
18
can somebody help me..... Please
Answer:
[tex]\large\boxed{B.\ \dfrac{7}{8}}[/tex]
Step-by-step explanation:
[tex]\text{Put the values}\ x=\dfrac{15}{8}\ \text{and}\ y=-3\ \text{to the expression}\ \dfrac{3}{8}y^2-\dfrac{4}{3}x:\\\\\dfrac{3}{8}(-3)^2-\dfrac{4}{3\!\!\!\!\diagup_1}}\cdot\dfrac{15\!\!\!\!\!\diagup^5}{8}=\dfrac{(3)(9)}{8}-\dfrac{(4)(5)}{8}=\dfrac{27}{8}-\dfrac{20}{8}=\dfrac{27-20}{8}=\dfrac{7}{8}[/tex]
25 points. What is the value of x in the figure?
The inside angle next to the 70 degrees would be 180 - 70 = 110 degrees.
The measure of an outside angle is equal the the sum of the two opposite inside angles.
X is an exterior angle and it's 2 opposite inside angles are 40 and 110.
X = 40 + 110 = 150 degrees.
The answer is E.
What is the reflection of point P(−1, 6) across the line y = x?
ANSWER
P'(6,-1)
EXPLANATION
The mapping for a reflection in the line y=x is
The line y=x is the mirror line for a function and it's inverse.
[tex](x,y)\to (y,x)[/tex]
The x and y coordinates swap position.
The reflection of point P(−1, 6) across the line y = x is
P'(6,-1)
Please assist, thank you.
Answer:
392 ft²
Step-by-step explanation:
Break this area into two parts, that is, into two trapezoids. The first trapezoid, on the left, has length 8 ft and average length (30 ft + 27 ft)/2, so its area is (8 ft)(28.5 ft) = 228 ft ².
The second trapezoid has width 8 ft and average length (19 + 22)/2 ft, or 8 ft by 20.5 ft). The area of this part is 164 ft².
Thus, the total area is 164 ft² + 228 ft², or 392 ft²
1. Victoria is opening a pet store. She will start by making custom dog collars. If the collar cost her $3 each, the embellishments $2, and $0.15 per bag, what is her unit cost per collar?
Answer:
$5.15
Step-by-step explanation:
A dog collar usually consists of a base(collar), the embellishments and the bag in which it is packed.
As we are given,
Collar Price = c = $3
Embellishment price = e = $2
and
Bag price = b =$0.15
The cost of one collar will be the cost of all these combined.
So,
Cost of collar = c+e+b
=3+2+0.15
=5.15
So the price of one collar is $5.15 ..
Answer:
5.15
Step-by-step explanation:
cjvjfgxgxhzjxjcjgkfifjffifi
Answer:
∛x^4
Step-by-step explanation:
x^(4/3) = ∛x^4
Last option is the answer
Find Kara’s percent grade if she answered 94 questions correctly on the test that had 100 questions
Answer:
94%
Step-by-step explanation:
Since there are 100 questions, it's like 1% for each question. If she answers 94 questions right, then it is 94%.
Solve the equation x2 - 2x - 7= 0 by using
the quadratic formula.
B is the correct choice
We used the quadratic formula (-b ± √(b² - 4ac) / 2a) to solve the quadratic equation x² - 2x - 7 = 0. We identified a, b, and c from the equation, plugged them into the formula, and solved for x to find the roots of the equation.
Explanation:The subject of your question involves solving the equation
x2 - 2x - 7 = 0
using the
quadratic formula.
This is a task in Algebra, a branch of Mathematics. The quadratic formula is a tool for solving equations of the form
ax² + bx + c = 0
, also known as quadratic equations. If we apply the quadratic formula, which is -b ± √(b² - 4ac) / 2a, to solve for your equation, we start by identifying a = 1, b = -2, and c = -7 from your equation. Substituting these into the formula gives:
x = [2 ± √((-2)² - 4*1*(-7))] / 2*1
After simplifying the above, we will get the solutions for x which are the roots of the quadratic equation.
We used the quadratic formula to solve the algebraic equation x2 - 2x - 7 = 0.
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