Question 25: Use your calculator to calculate the following:
You need to prepare 50 portions of carrots, Jardinière cut. A prepared portion after peeling and trimming
weighs 0.070 kg. Peelings and trimmings account for 30% of the total weight. What quantity of carrots do
you need to order?

Answer:

\(3 {x}^{2} - 15x - 18 = 0\)

\( {x}^{2} - 5x - 6 = 0\)

\((x + 1)(x - 6) = 0\)

x = -1 or x = 6

The coordinates of the zeroes are (-1, 0) and (6, 0).

Answer:

58.6 miles / hour

Step-by-step explanation:

The formula is

d= rt  where d is the distance, r is the rate ( speed) and t is the time

205 miles = r * 3.5 hours

Divide each side by 3.5

205 miles/ 3.5 hours = r

58.57142857 miles / hour = r

To the nearest tenth

58.6 miles / hour

Answer:

58.6

Step-by-step explanation:

So the truck traveled 205 miles in 3.5 hours.

As given, the distance is the product of the rate and the time. In other words:

\(d\text{ mi}=r\cdot t\text{ hours}\)

Substitute 205 for d and 3.5 for t. Thus:

\(205\text{ mi} =r\cdot (3.5)\text{hours}\)

Divide both sides by 3.5 hours. Thus:

\(r=\frac{205\text{ mi}}{3.5\text{ hours}}\)

Divide 205 and 3.5:

\(r\approx58.6\text{ mi/hr}\)

The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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The quadratic function in vertex form is y = -1/2(x + 1)^2 - 2

The vertex is given as

(h, k) = (-1,-2)

The point is also given as

(x, y) = (3, -10)

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

Substitute (h, k) = (-1,-2)  in y = a(x - h)^2 + k

y = a(x + 1)^2 - 2

Substitute (x, y) = (3, -10)

-10 = a(3 + 1)^2 - 2

So, we have

-10 = a(4)^2 - 2

Add 2 to all sides

-8 = a(16)

Divide by 16

a = -1/2

Substitute a = -1/2 in y = a(x + 1)^2 - 2

y = -1/2(x + 1)^2 - 2

Hence, the equation is y = -1/2(x + 1)^2 - 2

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Answer:

$300 down payment

Step-by-step explanation:

John wants to purchase a boat that costs $1,500. He signs an installment agreement requiring a 20% down payment. How much will john need for the down payment

20% = 0.20

0.20 * 1,500 = $300 down payment

Answer: 103/15

Step-by-step explanation:

We can simplify the right-hand side to be \(2 \left(\frac{1}{3}+6 \right)=2 \left(\frac{19}{3} \right)=\frac{38}{3}\).

This means we need to solve:

\(\frac{1}{2}(5x-9)=\frac{38}{3}\\5x-9=\frac{76}{3}\\5x=\frac{103}{3}\\x=\boxed{\frac{103}{15}}\)

(f/g)(0) is an illustration of composite function.

The value of (f/g)(0) is -3/2

The given parameters are:

\(f(x) = x + 3\)

\(g(x) = x^2 - 2\)

First, we calculate (f/g)(x)

(f/g)(x) is represented as

\((f/g)(x) = \frac{f(x)}{g(x)}\)

Substitute values for f(x) and g(x)

\((f/g)(x) = \frac{x + 3}{x^2 -2}\)

Substitute 0 for x

\((f/g)(0) = \frac{0 + 3}{0^2 -2}\)

Evaluate the exponents

\((f/g)(0) = \frac{0 + 3}{0 -2}\)

Simplify the numerator and the denominator

\((f/g)(0) = \frac{3}{-2}\)

Rewrite as:

\((f/g)(0) = -\frac{3}{2}\)

Hence, the value of (f/g)(0) is -3/2

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Answer: Two can be factored from each term in the trinomial to generate 2( x 2 + 6 x + 9), and no.

Step-by-step explanation:

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Answer:

8

Step-by-step explanation:

bResponses

y = 8

y, = 8

y = 3

y, = 3

y=−3

Answer:

To find the expression that represents the height of the triangle, we need to use the formula for the area of a triangle:

Area = (1/2) * base * height

In this case, the trinomial x² + 4x + 4 represents the area of the triangle, and the binomial x + 2 represents the base.

Using the formula, we can rearrange it to solve for the height:

Area = (1/2) * base * height

x² + 4x + 4 = (1/2) * (x + 2) * height

Now, we can solve for the height by isolating it on one side of the equation:

2 * (x² + 4x + 4) = (x + 2) * height

2x² + 8x + 8 = (x + 2) * height

Divide both sides by (x + 2) to solve for height:

height = (2x² + 8x + 8) / (x + 2)

Therefore, the expression that represents the height of the triangle is (2x² + 8x + 8) / (x + 2).

The correct value of matrix by apply the row operation R₂ ↔ R₃ as;

\(\left[\begin{array}{ccc}-7&5&2\\-6&1&-8\\2&9&7\\2&-8&8\end{array}\right]\)

We have to given that;

The matrix is,

\(\left[\begin{array}{ccc}-6&1&-8\\-7&5&2\\2&9&7\\2&-8&8\end{array}\right]\)

Now, We can apply the row operation R₂ ↔ R₃ in above matrix as;

The matrix is,

\(\left[\begin{array}{ccc}-6&1&-8\\-7&5&2\\2&9&7\\2&-8&8\end{array}\right]\)

By changing row operation R₂ ↔ R₃ as,

\(\left[\begin{array}{ccc}-7&5&2\\-6&1&-8\\2&9&7\\2&-8&8\end{array}\right]\)

Thus, The correct value of matrix by apply the row operation R₂ ↔ R₃ as;

\(\left[\begin{array}{ccc}-7&5&2\\-6&1&-8\\2&9&7\\2&-8&8\end{array}\right]\)

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Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

11=1×2^1+1×2^0

101=1×2^2+0×2^1+1×2^0

Adding 2^0 's together gives 2×2^0. As two is not an allowed digit in binary, we must rewrite as 1×2^1 and carry over.

Combining 2^1 terms gives 2×2^1. We run into same problem. We will rewrite as 1×2^2 and carry.

Combining 2^2 terms gives 2×2^2. Same problem... we rewrite as 1×2^3 and carry.

No more 2^3 's other than the one we carried over from previous addition.

Answer is 1000.

Another way.

Covert fully to base 10 and then add. Then convert back.

11=1×2^1+1×2^0=2+1=3.

101=1×2^2+0×2^1+1×2^0=5.

3+5=8

2^3=8...which means there are no 2^2 's, 2^1 's, or 2^0 's.

It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

To multiply the square roots V7 and V2, we can combine the numbers inside the square roots and simplify the result.

V7 * V2 = V(7 * 2) = V14

Multiplying the numbers under the square roots, we get 7 * 2 = 14. Therefore, the product of V7 and V2 is V14.

This means that the square root of 14 is the result of multiplying V7 and V2. However, it is important to note that V14 cannot be further simplified because 14 does not have any perfect square factors.

In summary, the product of V7 and V2 is V14. It is worth mentioning that when multiplying square roots, we can multiply the numbers inside the square roots and keep the square root symbol intact, unless the numbers inside have perfect square factors that can be simplified further.

It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

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The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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Answer:

PEMDAS

Step-by-step explanation:

Answer:

\(=60\)

Step-by-step explanation:

\(\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\).

\(\left(18\div \:2+54\div \:9\right)\times \:2\)

\(=15\times \:2\)

\(=30\)

\(=30\times \:2\)

\(=60\)

Answer:

$0.10

Step-by-step explanation:

We know

A 3-foot piece of twine costs $3.60

3.60 / 3 = $1.20 per foot piece of twine

1 foot = 12 inches

What is the price per inch?

1.20 / 12 = $0.10

So, the price per inch is $0.10

Answer:

..........

Step-by-step explanation:

\(\pi\)

Answer:

(3) 48 meters in 3 seconds

Answer: E

Step-by-step explanation: Since this is a special right triangle(45,45,90), you know that the ratios of the leg to the hypotenuse is 1:1:sqrt2. 15 sort root two hold true to that rule and is the right answer.

We will have the following:

We are given the parabola:

And we can see that it follows:

Now, we will have that the vertex is given by:

From the equation we then have that the vertex is:

Now, we can see that p = 4 since 16 / 4 = 4. Now, we remember that the focus is located p units to the right since it is positive, thus the focus is given by:

So, the focus is at:

Finally we will have that the directrix of the parabola will be given by:

*First, we find the distance between the focus and the vertex, that is:

Now, since the x coordinate of the vertex is 3, then the directrix will pass at 4 units to its left, that is the directrix is given by:

That can be seing in the graph:

*** Summary***

Vertex: (3, -3)

Focus: (7, -3)

Directrix: x = -1

The statement correctly describes the perpendicular bisector construction below The construction of JK to bisect GH: Option D is the correct answer

The term perpendicular bisector refers to the line that divides another line into two equal parts, making an angle of 90 degrees. The term is made up of two words, perpendicular and bisector.

Perpendicular refers to angle 90 degrees, while the bisector refers to dividing into two equal parts.

In the picture, the main line is GH while JK is the line constructed to bisect the main line

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Answer: -9 and up

Step-by-step explanation: An integer is any whole number. An integer can be zero, greater than zero or less than zero. The integers greater than zero are the natural numbers.

Answer:

-7 through -1

Step-by-step explanation:

its more than -8 and less than 0 i had this question in 7th yr

The equation 6y + y = 5 can be written in a slope-intercept form as y = 5/7.

We have,

To write the equation 6y + y = 5 in slope-intercept form (y = mx + b), we need to simplify the equation and isolate the y variable on one side.

Starting with the equation 6y + y = 5:

Combining the like terms on the left side gives us:

7y = 5

To isolate the y variable, we divide both sides of the equation by 7:

y = 5/7

Now the equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, since the equation only contains the variable y and no x, the slope (m) is not present, and the y-intercept (b) is 5/7.

Therefore,

The equation 6y + y = 5 can be written in a slope-intercept form as y = 5/7.

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Answer:

Step-by-step explanation:

e

The range are all the possible values of "y". For this graph y can be all the possible real numbers.

So the answer is letter C y is all real numbers.

Answer:

\(5x+11\)

Step-by-step explanation:

Step 1: Distribute

\(3x+6+2x+5\)

Step 2: Add like terms

\(5x+11\) < your answer