Find the slope of the line that passes through points (9,8) and (4,-2).

Dario could make 9 slices of lasagna with the provided amount of cheese, as each slice contains 1/4 pound of cheese and he has a total of roughly 2.33 pounds of cheese.

To answer this question, we first need to calculate the total weight of the cheese used in the lasagna. This consists of 2/3 pound of parmesan cheese, 5/4 pounds of ricotta cheese, and 4/3 pounds of mozzarella cheese. To total these up, we convert them into fractions with a common denominator. Doing this, we find that, in total, 28/12 or approximately 2.33 pounds of cheese are used. As each slice of lasagna contains 1/4 pound of cheese, we can determine the total number of slices by dividing the total weight of the cheese by the weight of the cheese in each slice. This gives us: 2.33 ÷ 0.25 = 9.32. As we can't have a fractional number of slices, we round down to get 9 slices, which would be the amount of lasagna slices Dario could make with the provided amount of cheese.

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Final answer:

The domain of the function h(x)=9x/x(x²-49) is all real numbers except for x = 0, x = -7, and x = 7, where the function is undefined due to division by zero. There are no additional nondifferentiable points within the domain, as the nondifferentiable points coincide with the excluded values.

Explanation:

To determine the domain of the function h(x)=9x/x(x^2-49), we need to identify all values of x for which the function is defined. Since this is a rational function, the function will be undefined where the denominator is zero. Thus, we set up the equation x(x² - 49) = 0 and solve for x.

First, factor the quadratic expression: x(x + 7)(x - 7) = 0. The solutions of this equation are x = 0, x = -7, and x = 7, which are the points where the function will be undefined.

Therefore, the domain of the function h(x) is all real numbers x except for x = 0, x = -7, and x = 7. These are the excluded values from the domain because they make the denominator equal to zero, which would result in division by zero.

Nondifferentiable Points

Aside from the excluded values, there may also be nondifferentiable points within the domain where the derivative does not exist or is not continuous. However, since all nondifferentiable points in this case coincide with the excluded values (the points where the denominator is zero), there will be no additional nondifferentiable points within the domain of the function.

Final answer:

A student's math problem involving an algebraic equation to find a number has been solved by isolating and solving variables, resulting in the number 12.

Explanation:

To solve the equation where ten times a number decreased by seven equals 101 plus that same number, we would set up the following equation:

10x - 7 = 101 + x

Now, we solve for x:

First, subtract x from both sides of the equation to get all the x terms on one side:

9x - 7 = 101

Next, add 7 to both sides of the equation to isolate the term with x:

9x = 108

Finally, divide both sides by 9 to solve for x:

x = 12

Hence, the number we are looking for is 12.

"Perimeter" is the distance all the way around the drawing.  If the drawing has sides, then the perimeter is the SUM of the lengths of all the sides.  It's exactly the distance an ant would have to walk along the line, to get all the way around to where he started from.

To get the perimeter of the triangle, you have to add up the lengths of the three sides.

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

2a - 3 + 2a + 3a + 1 .

Add up all the 'a's: 2a + 2a + 3a = 7a

Add up all the just plain numbers: -3 + 1 = -2

Write them together, as a binomial:  7a - 2

THAT's your expression for the perimeter.

The perimeter of a shape is the distance around it. For a rectangle, the perimeter can be represented by the expression '2(length + width)', which can also be written as '2(L + W)' when L is the length and W is the width.

Perimeter refers to the distance around a two-dimensional shape. Since the shape isn't specified in the question, let's assume a rectangle for our example. The perimeter of a rectangle is given by the formula '2(length + width)'. This means, you add the length and width of the rectangle together, and then multiply by 2. If we let L represent the length and W represent the width, then our expression for the perimeter of a rectangle would be '2(L + W)'.

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it is 79% hoped i helped

- 6x - 1

distribute parenthesis and collect like terms

- 2x - 3 - 4x + 2

= (- 2x - 4x) + (-3 + 2) = - 6x - 1

Answer:

k=2

Step-by-step explanation:

We have got a right triangle LNO with sides = m,4 and 8

By Pythagorean theorem

m^2=4^2 +8^2

Or m^2 = 80  ... i

IN triangle NOM, 4^2 +k^2 = l^2

i.e. 16+k^2 = l^2... i

In triangle LNM, m^2+l^2 = (8+k)^2

Substitute for m^2 as 80,

i.e. 80+l^2 = 64+k^2 +16k  ... iii

From i, l^2 = 16+k^2

Substitute in iii

80+16+k^2 = 64+k^2 +16k

16k = 32 or k =2

Given the function [tex]p(x)=x^2+4x-12.[/tex]

Part A.

To write the expression that defines [tex]p(x-6)+5,[/tex] you have to substitute x-6 instead of x into the function expression and then add 5 to the function:

[tex]p(x-6)+5=((x-6)^2+4(x-6)+12)+5,\\\\p(x-6)+5=x^2-12x+36+4x-24+12+5,\\\\p(x-6)+5=x^2-8x+29.[/tex]

Part B.

1 transformation is translation 6 units to the right (p(x-6) determines this transfromation).

2 transformation is translation 5 units up (+5 determines this transformation).

I think the answer you're looking for is $9.50.

513 / 54 = 9.5

Sue made $9.50 an hour.

The equivalent fraction for 40/100 is 2/5.

To find the equivalent fraction for 40/100, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20. When we divide 40 by 20, we get 2, and when we divide 100 by 20, we get 5. So, the equivalent fraction for 40/100 is 2/5.

The equivalent fraction for 40/100 is 2/5, which is obtained by dividing both the numerator and the denominator by their greatest common divisor, 20. In decimal form, 40/100 is 0.40, and as a percentage, it is 40%.

To find the equivalent fraction for 40/100, we look for a common factor that both the numerator (40) and the denominator (100) share. In this case, the number 20 is a common factor of both. Dividing the numerator and the denominator by 20, we reduce 40/100 to its simplest form:

40 ÷ 20 = 2
100 ÷ 20 = 5

Therefore, the equivalent fraction for 40/100 is 2/5.

Additionally, converting a fraction to a decimal involves dividing the numerator by the denominator, so 40/100 converted to a decimal is 0.40.

To convert this decimal to a percentage, we multiply by 100, yielding 40%.

3 hours because if u have 175 dollers and u spend 100 so now u have 75. 75 -20 is 55. then 55 - 20 is 35. then 35 - 20 is 15 so then you have 15 dollers to spare. so 3

You can represent this problem as a linear equation 100 + 20x = 175. Solving for x gives you 3.75, hence with $175, you can rent the jet ski for 3.75 hours.

To solve this problem, you need to set up a linear equation. Let's represent the number of hours of the jet ski rental as x. The jet ski rental company charges a $100 rental fee plus $20 per hour, so we can write this as a equation: 100 + 20x = 175.

Next, we need to solve for x. First, subtract 100 from each side of the equation, you obtain 20x = 75. Then, divide each side by 20 to solve for x. You'll find that x = 3.75. Therefore, with $175, you can rent the jet ski for 3.75 hours.

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the teacher has 2 1/4 pounds of clay so none of the students have enough

Answer:

In the picture

Step-by-step explanation:

simplify 9[3+4}

using bodmass

=9{7}

63

A. is this answer to this question.

The value of inequality is t ≤ -14  which means t will have all value less then and equals to -14 In number line.

What is number line ?

Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.

Here the given inequality is :

−5t ≥ 70

Now, to solve for t we divide both side by -5 :

−5t/-5 ≥ 70/-5

t ≤ -14  

It should be noted that negative -5 reverse the inequality sign.

Therefore, the value of inequality is t ≤ -14  which means t will have all value less then and equals to -14 In number line.

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40|2

20|2

10|2

5|5

1

[tex]40=2^3\cdot5[/tex]

Answer:

The answer is x ≤ 50.

Step-by-step explanation:

As, A -70 = -2 (P -40)

A = -2P + 80 + 70

A = -2P + 150

Y = -2x + 150.

When y = 0,

Putting in the values

-2x = -150

x = 75.

-2x + 150 ≥ 50

-2x ≥ -100

x ≤ 50.

Forty-nine percent of US teens have heard of a fax machine, then the probability that the teen has heard of a tax machine is p=0.49 and the probability that the tenn hasn't heard of a tax machine is q=1-p=1-0.49=0.51.

Use binomial distribution.

The probability that among 12 randomly selected teens exactly 6 have heard of a fax machine is

[tex]Pr(X=6)=C_{12}^6p^6q^{12-6}=\dfrac{12!}{6!(12-6)!}(0.49)^6(0.51)^6=\\\\\dfrac{6!\cdot 7\cdot 8\cdot 9\cdot 10\cdot 11\cdot 12}{6!\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6}(0.49\cdot 0.51)^6=924\cdot (0.2499)^6\approx 0.22505.[/tex]

The probability that among 12 randomly selected teens more than 8 have heard of a fax machine is

[tex]Pr(X>8)=C_{12}^9p^9q^{12-9}+C_{12}^{10}p^{10}q^{12-10}+C_{12}^{11}p^{11}q^{12-11}+C_{12}^{12}p^{12}q^{12-12}=\\\\\dfrac{12!}{9!(12-9)!}(0.49)^9(0.51)^3+\dfrac{12!}{10!(12-10)!}(0.49)^{10}(0.51)^2+\dfrac{12!}{11!(12-11)!}(0.49)^{11}(0.51)^1+\dfrac{12!}{12!(12-12)!}(0.49)^{12}(0.51)^0=220\cdot (0.49)^9(0.51)^3+66\cdot (0.49)^{10}(0.51)^2+12(0.49)^{11}(0.51)^1+(0.49)^{12}\approx 0.0638.[/tex]

Answer should be six. Hope this helps :)

6 is the number of which sum of a number and five more than the number is 17.

A numerical expression is in the form of numbers with their arithmetic operations the numbers can be variables and constants. We can form numerical expressions from statements, and from real-life situations also.

Assuming the number to be 'n' and the given statement the sum of a number and five more than the number is 17can be numerically expressed as,

n + (n + 5) = 17.

2n + 5 = 17.

2n = 12.

n = 6.

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So remember that the degree of the polynomial will indicate how many solutions there are, real or complex. Since the degree of the polynomial is 2, this means that there is a maximum of 2 real solutions in this equation.

Next, we are going to apply the difference of squares rule to this polynomial, which is [tex]x^2-y^2=(x+y)(x-y)[/tex] . In this case:

[tex]x^2-9=(x+3)(x-3)\\(x+3)(x-3)=0[/tex]

Now, we are going to apply the Zero Product Property, which states that if a × b = 0, this means that either a or b = 0 or a and b = 0. In this case, a = x + 3 and b = x - 3. Solve each as such:

[tex]x+3=0\\x=-3\\\\x-3=0\\x=3[/tex]

In short, there are 2 real solutions: x = 3 and x = -3.

The equation [tex]x^2-9=0[/tex] has two real solutions which are x=3 and x=-3. The solutions are obtained by applying the quadratic formula, which indicates that every equation containing an unknown squared will have two solutions.

The equation[tex]x^2-9=0[/tex] is a quadratic equation. For any quadratic equation in the form ax²+bx+c = 0, the solutions or roots can be calculated using the quadratic formula: -b ± √(b² - 4ac) / 2a.

In this specific equation, [tex]x^2-9=0[/tex]can be rewritten as x²-9+9 = 9, which simplifies to x² = 9. The solutions can then be obtained using the principal square root or the negative square root, resulting in x = ± √9. Therefore, the two real solutions are x = 3 and x = -3.

It's important to note that every equation containing an unknown squared will have two solutions, which can be both meaningful or only one of them can be reasonable depending on the context of the problem.

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You must perform a subtraction between the result of two multiplications. In fact, since multiplications have a higher priority than subtraction, you must perform them first. Also, remember that a positive times a negative is a negative.

So, you must perform the operations in this order:

[tex] [-6\cdot 7]-[6\cdot(-2)] = [-42]-[-12] = -42+12 = -30 [/tex]

First You do 30.75 x 12 This is because he said every month for a year and a year has 12 months The answer to 30.75 x 12 is 369 Now  all you have to do is 550 - 369 = 181.      

Hope this helps :D

Final answer:

To compare two numbers, understand that positive numbers are greater than negative ones, among positives or negatives, larger numerical values determine greatness, and among two negatives, those closer to zero are greater.

Explanation:

Comparing two numbers to decide which is greater involves understanding their signs and values. Here's how you can determine this:

Remember, the key to comparing numbers is understanding the role of positive and negative signs and the numerical value of the numbers.

4(x + 1) = 12(3 - x)

Distributive property on both sides.

4x + 4 = 36 - 12x

Add 12x to both sides.

16x + 4 = 36

Subtract both sides by 4.

16x = 32

Divide both sides by 16.

x = 2

the volume is 408

l times w times h

the length totals out to 12ft and the width totals out to 4ft.

To find the length and width of the rectangle, set up a system of equations using the given information. Solve for one variable in terms of the other using the equation for the area. Substitute the value of one variable into the equation for the perimeter. Solve the resulting quadratic equation to find the possible values for the width. Choose the appropriate positive value for width and find the corresponding length using the equation for the area.

To find the length and width of the rectangle, we need to set up a system of equations using the given information. Let's represent the length as 'l' and the width as 'w'. We know that the area of a rectangle is given by the formula A = lw, and the perimeter is given by the formula P = 2(l + w).

Given that the area is 48 square feet and the perimeter is 32 feet, we can set up the following equations:

From equation (1), we can solve for one variable in terms of the other. Let's solve for 'l':

l = 48/w

Now, substitute this value for 'l' in equation (2):

32 = 2(48/w + w)

Simplifying further:

16 = 48/w + w

Multiply both sides of the equation by 'w' to eliminate the fraction:

16w = 48 + w^2

Rearrange the equation:

w^2 + 16w - 48 = 0

Factoring the quadratic equation, we get:

(w + 8)(w - 6) = 0

Therefore, the possible values for 'w' are -8 and 6. Since width cannot be negative, we discard the -8 and conclude that the width is 6 feet.

To find the length, substitute the width value of 6 into equation (1):

l = 48/6 = 8 feet

Therefore, the length of the rectangle is 8 feet and the width is 6 feet.

Answer:

Its orientation may change and the measures of its angles stay the same.

Step-by-step explanation:

Answer:

When a figure is translated its orientation may change and the measures of its angles keeps the same measure.

Step-by-step explanation:

Whenever we translate a figure, we move a figure into some orientation given by this same vector. But the angles will remain the same since there is no distortion.

Just as the picture below

Answer:

The amount of minutes Grace has to use her cell phone this month is 59 minutes

Step-by-step explanation:

Let

x -----> amount of minutes Grace has to use her cell phone this month

we know that

The average usage during the four months is equal to the sum of the minutes used in the four months divided by four (the number of months)

so

[tex]55=\frac{42+62+57+x}{4}[/tex]

Solve for x

Multiply by 4 both sides to remove the fraction

[tex]55(4)=(42+62+57+x)[/tex]

[tex]220=(161+x)[/tex]

[tex]x=220-161[/tex]

[tex]x=59\ min[/tex]

therefore

The amount of minutes Grace has to use her cell phone this month is 59 minutes