Milk and cream contain different percents of butterfat. How much 3% milk needs to be mixed with how much 15% cream go give 20 L if 6% cream?

Answer:

Equation: [tex]3(x-6)^2=12[/tex]

Solutions: [tex]x=4\text{ or }x=8[/tex]

Step-by-step explanation:

Unknown variable [tex]= x[/tex]

Difference of x and 6 [tex]= x - 6[/tex]

Square of the difference of x and 6 [tex]=(x-6)^2[/tex]

Three times the square of the difference of x and 6 [tex]=3(x-6)^2[/tex]

Three times the square of the difference of x and 6 is 12, then

[tex]3(x-6)^2=12[/tex]

Divide this equation by 3:

[tex](x-6)^2 =4[/tex]

Now

[tex]x-6=2\text{ or }x-6=-2\\ \\x=2+6\text{ or }x=-2+6\\ \\x=8\text{ or }x=4[/tex]

Answer:

The answer is x=4 or x=8

Step-by-step explanation:

The square with a side length of  [tex]2\frac{1}{2}[/tex] inches has a larger area of 6.25 square inches, compared to the area of the rectangle which is 5.25 square inches.

To determine which shape has a larger area, let's calculate the area of both the rectangle and the square. The rectangle measures 7 inches by 3/4 inch, so its area is calculated by multiplying these dimensions:

Area of the rectangle = length ×width = 7 inches × [tex]\frac{3}{4}[/tex] inch = [tex]\frac{21}{4}[/tex] square inches or 5.25 square inches.

The square has a side length of [tex]2\frac{1}{2}[/tex] inches, which is equivalent to 2.5 inches. Hence, the area of the square is:

Area of the square = side ×side = 2.5 inches × 2.5 inches = 6.25 square inches.

Comparing the two, we can see that the square with a side length of [tex]2\frac{1}{2}[/tex] inches has a larger area of 6.25 square inches compared to the rectangle's area of 5.25 square inches.

Step-by-step explanation:

Look at the picture

a. 5pk → 5

b. f = 1f → 1

c. -9t → -9

d. -j = -1j → -1

Answer:

A. $301

B. $721

Step-by-step explanation:

Let $x be the amount of money they raised.

Rowena tried to put the $1 bills into two equal piles and found one left over at the end, then

[tex]x=2q_1+1[/tex]

Polly tried to put the $1 bills into three equal piles and found one left over at the end, then

[tex]x=3q_2+1[/tex]

Frustrated, they tried 4, 5, and 6 equal piles and each time had $1 left over, then

[tex]x=4q_3+1\\ \\x=5q_4+1\\ \\x=6q_5+1[/tex]

Finally Rowena put all the bills evenly into 7 equal piles, and none were left over, then

[tex]x=7q_6[/tex]

This means [tex]x-1[/tex] is divisible by 2, 3, 4, 5 and 6 without remainder, so

[tex]x-1=2\cdot 3\cdot 2\cdot 5n=60n[/tex]

Hence,

[tex]x=60n+1, \ n\in N[/tex]

The smallest amount of money they could have raised is $301, because

[tex]x=60\cdot 5+1=301[/tex] is divisible by 7.

Now, the number [tex]x=60n+1[/tex] should be divisible by 7 and must be greater than 500.

So,

[tex]60n+1>500\\ \\60n>499\\ \\n>8[/tex]

When n = 9,

[tex]x=60\cdot 9+1=541[/tex] is not divisible by 7.

When n = 10,

[tex]x=60\cdot 10+1=601[/tex] is not divisible by 7.

When n = 11,

[tex]x=60\cdot 11+1=661[/tex] is not divisible by 7.

When n = 12,

[tex]x=60\cdot 12+1=721[/tex] is divisible by 7.

B. The least amount of money they could have raised is $721

Answer:

A:301 and b: 721

Answer:

Vertex of parabola (-1, -10)

Step-by-step explanation:

For a given quadratic y = ax² + bx + c, the vertex (h, k) is found by computing h = –b/2a, and then evaluating y at h to find k. If you've already learned the Quadratic Formula, you may find it easy to memorize the formula for k, since it is related to both the formula for h and the discriminant in the Quadratic Formula: k = (4ac – b2) / 4a.

Hey!

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Solution:

y² = 81

To solve just take the square root of 81.

√81 = 9

---------------------------------------------------------

Check:

(9)² = 81

81 = 81

---------------------------------------------------------

Answer:

x = 9

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Hope This Helped! Good Luck!

Good evening ,

______

Answer:

x=2ln2.

___________________

Step-by-step explanation:

Look at the photo below for the details.

:)

The price after Allie uses the coupon to buy two tubes of toothpaste is $1.93.

To find the price after Allie uses the coupon, you first need to calculate the total cost of two tubes of toothpaste without the coupon and then subtract the coupon value. The total cost of two tubes of toothpaste, which is $1.39 times 2. The result is $2.78.

So now, we need Allie's coupon by subtracting the discount, which is $0.85, from the total cost ($2.78 - $0.85).

Therefore, The final cost, or the price after using the coupon, is $1.93.

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The price of two tubes of toothpaste after Allie uses the coupon is $1.93.

To calculate the price of two tubes of toothpaste after Allie uses the coupon, we can use the following steps:

Calculate the price of two tubes of toothpaste without the coupon.

Subtract the value of the coupon from the price of two tubes of toothpaste without the coupon.

Step 1: Calculate the price of two tubes of toothpaste without the coupon.

The price of one tube of toothpaste is $1.39, so the price of two tubes of toothpaste is:

$1.39/tube * 2 tubes = $2.78

Step 2: Subtract the value of the coupon from the price of two tubes of toothpaste without the coupon.

The value of the coupon is $0.85, so the price of two tubes of toothpaste after Allie uses the coupon is

$2.78 - $0.85 = $1.93

Therefore, the price of two tubes of toothpaste after Allie uses the coupon is $1.93.

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Simplifying

64 + -12w = 6w

Solving

64 + -12w = 6w

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-6w' to each side of the equation.

64 + -12w + -6w = 6w + -6w

Combine like terms: -12w + -6w = -18w

64 + -18w = 6w + -6w

Combine like terms: 6w + -6w = 0

64 + -18w = 0

Add '-64' to each side of the equation.

64 + -64 + -18w = 0 + -64

Combine like terms: 64 + -64 = 0

0 + -18w = 0 + -64

-18w = 0 + -64

Combine like terms: 0 + -64 = -64

-18w = -64

Divide each side by '-18'.

w = 3.555555556

Simplifying

w = 3.555555556

Answer:

[tex]60[/tex]

Step-by-step explanation:

Suzzane can work 10 math problems in 15 minutes. We need to use proportion and raito.

One hour and a half is equal to 90 minutes. But to equal out the math problem, change it to 900.

So:

[tex]\frac{10}{15}[/tex]  [tex]= \frac{x}{900}[/tex]

[tex]= 60[/tex]

Final answer:

The question asks for the ratio of yellow eggs to colored eggs, which is 10 yellow eggs to 12 colored eggs. Simplifying the ratio, we get 5:6. This concept of ratios is also seen in Mendel's genetic experiments with plants, where traits are passed in specific ratios like 3:1.

Explanation:

In mathematical terms, a student's question regarding the ratio of yellow eggs to the total number of colored eggs can be answered using simple division to derive a fraction or ratio. Given that there are 10 yellow eggs out of 12 colored eggs, the ratio can be expressed as 10:12.

However, ratios should be simplified to their smallest form to be more understandable; therefore, this ratio simplifies to 5:6 since both numbers can be divided by 2.

When looking at historical experiments, such as the ones conducted by Mendel, we find that phenotypic ratios play a significant role in understanding genetics. Mendel observed that traits could manifest in a specific ratio, like a 3:1 ratio for dominant to recessive traits. The ratios observed in the experiments provided can serve as examples to understand how ratios represent the occurrence of certain outcomes over others.

In this case, the ratio of yellow to green seeds in Mendel's experiment can serve as an analogy to understand the ratio of yellow eggs: both ratios quantitatively describe the presence of a certain characteristic compared to another.

Answer:

C. [tex]x=\frac{5}{2}[/tex]

Step-by-step explanation:

The quadratic formula is:

[tex]x_{1,2}=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}[/tex]

Where [tex]a[/tex] is the coefficient of the quadratic team. [tex]b[/tex] is the coefficient of the linear term, and [tex]c[/tex] is the independent term.

So, the given equation is:

[tex]x^2 - 5x + \frac{25}{4}  = 0[/tex]

Where:

[tex]a=1\\b=-5\\c=\frac{25}{4}[/tex]

[tex]x_{1,2}=\frac{-(-5)\±\sqrt{(-5)^{2}-4(1)(\frac{25}{4} )}}{2(1)}\\x_{1,2}=\frac{5\±\sqrt{25-25}}{2}\\x_{1,2}=\frac{5\±\sqrt{0}}{2}\\x_{1,2}=\frac{5}{2}[/tex]

This means that the equation has a unique solution.

Therefore, the right answer is C.

Answer:

equilateral triangle

Step-by-step explanation:

all sides are equal

Hey!

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Answers:

Equilateral

Acute

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Explanation:

The lines on each side show that all the sides are the same length. Acute angles are angles that are less than 90 degrees. Each angle is less than 90 degrees.

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Hope This Helped! Good Luck!

Answer:

y=6

Step-by-step explanation:

8y-5y-2=16

8y-5y=16+2

3y=18

y=18/3

y=6

Hey!

------------------------------

Solution:

8y - (5y + 2) = 16

3y - 2 = 16

3y + (-2) + 2 = 16 + 2

3y = 18

3y/3 = 18/3

y = 6

------------------------------

Answer:

y = 6

------------------------------

Hope This Helped! Good Luck!

Answer: 2400

Step-by-step explanation:

for every pound there is 300 gallons, so

300 x 8 = 2400

Hope this helps!

Answer:

corresponding

Step-by-step explanation:

Answer:congruent because they are corresponding angles.

Step-by-step explanation:

Answer:

x represents Jane's initial amount of money in her bank account.

Step-by-step explanation:

x - 135 = 650

650 + 135 = x

x = 785

Answer:

950,000

Take the placement before the placement you need to round and round.

Answer:

U'(3, -6), V'(8, -1), W'(3, -1)

Step-by-step explanation:

According to the 180°-rotation rule, you take the OPPOSITE of both the y-coordinate and x-coordinate:

Extended Rotation Rules

270°-clockwise rotation [90°-counterclockwise rotation] >> (x, y) → (-y, x)

270°-counterclockwise rotation [90°-clockwise rotation] >> (x, y) → (y, -x)

180°-rotation >> (x, y) → (-x, -y)

I am joyous to assist you anytime.

Answer:

irrational

Step-by-step explanation:

Answer:

8a + 5 - 10a - 11 simplified equals -2a - 6

Step-by-step explanation:

1st group like terms: 8a - 10a + 5 - 11

2nd add similar elements: 8a - 10a = -2a,

-2a + 5 - 11

3rd add/subtract the numbers: 5 - 11 = -6

-2a - 6

I am joyous to assist :)

Answer:

a) false

b) false

c) true

d) true

e) false

f) false

Step-by-step explanation:

hope this helps :)

Answer:  The correct option is

(B)  g(x) has a greater slope.

Step-by-step explanation:  We are given the following two functions :

[tex]f(x)=2x-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

x                    2                      4                    6

g(x)                0                      5                     10

Comparing equation (i) of f(x) with the slope-intercept form y = mx+c, we get

[tex]\textup{slope, m}=2.[/tex]

Now, we know that if a linear function contains two points (a, b) and (c, d), then its slope is given by

[tex]m=\dfrac{d-b}{c-a}.[/tex]

Since (2, 0) and (4, 5) are two points on g(x), so its slope will be

[tex]m=\dfrac{5-0}{4-2}=\dfrac{5}{2}=2.5.[/tex]

Therefore, slope of f(x) = 2 and slope of g(x) = 2.5.

Thus, slope of g(x) is greater.

Option (B) is CORRECT.  

Answer:

if your asking for the difference between the temperatures then it would be

8, but if your asking for the sum it would be -4

Hope i helped :)

[tex]4^{2}[/tex] – 2(3 • 5 + 1) = -16

The 2 is a superscript which was the first person's mistake

Answer: She needs to walk 5 miles an hour

There's two numbers 2.5 miles and 0.5 hours, you divide that, and you get the number 5, so that means, 5 miles an hour

She needs to walk at a speed of 4 miles/hour to reach the destination in 45 minutes.

Speed is the ratio of the total distance covered by an object and the required time to cover that by that object. It is also called Velocity.

[tex]Velocity=\frac{Distance}{Time}[/tex]

Velocity is the measurement which shows an object is how fast.

In this given problem,

The total distance Danielle needs to cover by walking is 3 miles.

She needs to reach the destination in 45 minutes

We know that,

60 minutes = 1 hour

1 minute = [tex]\frac{1}{60}[/tex] hour

45 minutes [tex]=\frac{45}{60}=\frac{3}{4}[/tex] hours

So she has to have the velocity/speed of [tex]=\frac{3}{\frac{3}{4}}=3\times\frac{4}{3}=4[/tex] miles/hour

Hence she needs to walk 4 miles/hour.

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Answer:   b) 225.2 mg

Step-by-step explanation:

Convert 1 kg to 2.2 lbs.

[tex]\dfrac{3.3\ mg}{1\ kg}\times \dfrac{1\ kg}{2.2\ lbs}\times 150.1\ lbs\quad =\dfrac{3.3(150.1)\ mg}{2.2}\quad =\dfrac{495.33\ mg}{2.2}\\\\\\=\large\boxed{225.15\ mg}[/tex]

Answer:

84.9*64=5433.6

3900/2.6=1500

1080/15.9=67.9245283019

2.86*8.77*200=5016.44

1500/64=23.4375

6007/5.5=1092.1818....

Step-by-step explanation:

Answer:

no .8 9 10 are false statement

Step-by-step explanation:

8.angle 3 and angle 5 are not vertical angles because the two lines do not intersect

9 angle 3 and angle 4 are not complementary angle because their non common arms are two opposite rays.

10.angle 1 and angle 2 are not supplementary angles because their non common arms are not two opposite rays.

The answers for #8-10 involve finding the derivative of a function, solving a system of equations, and finding the slope of a line.

For question #8, you need to find the derivative of the given function. This involves using the power rule and the chain rule. For question #9, you are given a system of equations and you need to solve for the values of x and y. This can be done using substitution or elimination. Finally, for question #10, you are asked to find the slope of a line given two points. You can use the formula (y2 - y1) / (x2 - x1) to find the slope.

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