8.A recipe calls for 4 cups of dry ingredients. Of the 4 cups, 1 cup
is flour. What is the ratio of cups of flour to cups of
other dry ingredients used in the recipe? write as a fraction

Answer:

Graph represented by option D is the correct choice.

Step-by-step explanation:

We have been given that a parabola has a minimum value of 0, a y-intercept of 4, and an axis of symmetry at .

Since the minimum value of our given parabola is 0, so y-coordinate of vertex of parabola would be 0. This means that vertex of parabola will be at x-axis.

Since Since the minimum value of our given parabola is 0, so our parabola will be upward opening.

We are also told that parabola has an axis of symmetry at . This means that parabola will be symmetric about line .

The y-intercept of parabola is 4. This means that parabola will intersect y-axis at point .

Upon looking at our given choices, we can see that option D is the correct choice as it meets all the given conditions.

The answer is d. The y-intercept is at 4, the parabola is at 0 and the axis of symmetry is x=-2.

Answer:

d = 4√5

Step-by-step explanation:

d² = 8² + 4²

d² = 64 + 16

d² = 80

d =√80

d = √(16 * 5)

d = 4√5

Answer:

Step-by-step explanation:

hard to see graph ....

The sum of 10.6, 6, and 2.09 is 18.69. The question asks to add the following numbers: 10.6, 6, and 2.09. Adding them together, you simply line up the decimal points and add each column from right to left.

Step 1: Add the numbers in the hundredths place: there are no hundredths in 10.6 or in 6, and there are 9 hundredths in 2.09. So, we simply write down .09.

Step 2: Add the numbers in the tenths place: there are 6 tenths in 10.6, no tenths in 6, and no tenths in 2.09. Combined, we have .60.

Step 3: Add the numbers in the ones place: there are 0 ones in 10.6, 6 ones in 6, and 2 ones in 2.09. Combined, we have 8.0.

Step 4: Add the tens place: there is 1 ten in 10.6, no tens in 6, and no tens in 2.09. We write down 10.

Finally, adding these components together (0.09+,60+8.0+10) we get the total of 18.69.

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Answer:

18.69

Step-by-step explanation:

Final answer:

The charity needs to earn 55,000 dollars. Subtracting the donation of 10,000 they need to make 45,000 dollars from the race entries. They make 40 dollars per entry, so dividing 45,000 by 40 gives the number of race entries needed: 1125.

Explanation:

The charity makes $40 per race entry ($55 entry fee minus the $15 cost). It also receives an additional $10,000 in donations. To raise at least $55,000, the charity would need to make at least $45,000 from race entries because $55,000 - $10,000 = $45,000. This is the target earnings from the race entries.

The race entry is $40 so we divide the target by the amount earned per race to find out the number of race entries needed: $45,000 / $40 = 1125. Therefore, the charity would need to have at least 1125 race entries to raise at least $55,000.

So the inequality would be: 40x + 10,000 ≥ 55,000, where x is the number of race entries. Solving the inequality would give x ≥ 1125.

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Step-by-step explanation:

$55,000 - $10,000 = $45,000

$55 - $15 = $40

$45,000 : $40 = 1,125 race entries needed

The recursive formula for the given sequence as required in the task content is; f(n) = f (n - 1) - 50.

What is the recursive formula for the given sequence?

It follows from the task content that the recursive formula for the given sequence is to be determined.

By observation, the sequence is an arithmetic progression and the common difference, d can be evaluated as;

d = 750 - 800 = 800 - 850 = 850 - 900 = -50

Also, since the recursive formula for an arithmetic sequence takes the form;

f(n) = f (n - 1) + d.

Hence, since the recursive formula as required is;

f(n) = f (n - 1) - 50.

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Answer:

f(1)=900

f(n)=f(n-1)-50if n>1

Step-by-step explanation:

this is the correct

Answer:

L1 and L2 are skew

Step-by-step explanation:

Since the equation of the line is

L1:x=9+6t,y=12-3t,z=3+9t

L2:x=4+16s, y=12-8s, z=16+20s

then if they intersect each other , they will have both in that point P=(xp , yp ,zp) then

1)9+6t = 4+16s

2) 12-3t =2-8s

3) 3+9t = 16+20s

adding 2*2) to 1)

9+6*t + 24-6t  = 4+16*s + 4-16*s

33 = 8

since this is not possible , the error comes from our assumption that the lines intersect each other

then they are skew or parallel. They are parallel if their corresponding vectors are parallel , that is

L1 (x,y,z) = (9,12,3) + (6,-3,9)*t

L1 (x,y,z) = (4,2,16) + (16,-8,20)*t

then if they are parallel

(16,-8,20)= k*(6,-3,9)

16=6*k

-8 = -3*k

20= 9*k

since there is no k that satisfy for x , y and z simultaneously then L1 and L2 are not parallel

therefore L1 and L2 are skew

Final answer:

The lines L1 and L2 are neither parallel nor intersecting. Upon comparing their direction vectors and attempting to find a common solution, it is determined that they are skew.

Explanation:

In order to determine whether two lines in three dimensions are parallel, skew, or intersecting, we compare their direction vectors. The given lines L1 and L2 are in the form of parametric equations. The direction vectors for the lines are d1 = <6, -3, 9> for L1 and d2 = <16, -8, 20> for L2. To determine if they are parallel, we check if there is a constant ratio between the corresponding terms. This isn't the case here, so the lines are not parallel.

For skew lines, they neither intersect or are parallel. Since we have already confirmed the lines are not parallel, to confirm if they are skew we must try to find a common solution (point of intersection). If we cannot, then they are skew. However, solving the equations does not give a common solution, so they do not intersect either. Hence, the lines are skew.

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