Find the points of intersection of the line
x = 5 + 2t, y = 5 + 8t, z = −4 + t,
that is,
l(t) = (5 + 2t, 5 + 8t, −4 + t),
with the coordinate planes.
xy plane(x, y, z) =
xz plane(x, y, z))=
yz plane(x, y, z)=

Answer:

f(2) = 2

Step-by-step explanation:

Given function:

f(x) = 5x - 12

To Find:

f(2)

Solution:

Well,it is absolutely clear from the problem,that x = 2.So just substitute 2 in x's place on the function,then simplify using PEMDAS.

\(f(x) = 5x - 12\)

\(f(2) = 5(2)- 12\)

\(f(2) = 10 - 12\)

\(\boxed{f(2) = - 2}\)

Hence,f(2) is equal to -2.

the average speed of the current in this section of the mississippi river is 5.8

let C = the speed of the current

then B - C = effective speed up river

B+C =effective speed down river

time up + time down = 16.5 hrs

60/B-C+60/B+C= 16.5

taking lcm and solving we get

480+60C +480-60C= 16.5 (64 - C^2)

960= 1056 - 16.5 C^2

16.5 C^2 =96

C^2= 5.82

Hence , the average speed of the current in this section of the mississippi river is 5.8

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Using the greatest common factor, it is found that the greatest number of cards that she can place in a row is of 14.

The number of cards for each family is given as follows:

We want to find a way to distribute them having the same number of cards in each row, hence this is possible finding the greatest common factor (GCF) of the numbers of 154 and 140.

The GCF is found factoring both numbers 154 and 140 simultaneously by prime factors, as follows:

154 - 140|2 (both 154 and 140 are divisible by 2).

77 - 70|7 (both 77 and 70 are divisible by 11).

11 - 7

There are no numbers for which both 11 and 7 are divisible by, hence the greatest number of cards that she can place in a row is:

gcf(154, 140) = 2 x 7 = 14.

The complete problem is:

April is arranging place cards for a wedding reception on a table. The bride's family has 154 cards and the groom's family has 140 cards. She wants the arrangements for the two families to have the same number of cards in each row. What is the greatest number of cards that she can place in a row?

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Answer:

SSS congruent

Step-by-step explanation:

AB  = ML

AC = MN

CB =  NL

Both triangles are congruent by SSS

Answer:

a = 21.5 in²

Step-by-step explanation:

Area of square

a = s²

a = 10²

a = 100

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

Area of circle

a = πr²

a = π5²

a =π*25

a = 78.5398163397

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

Area shaded

a = square - circle

a = 100 - 78.5398163397

a = 21.4601836603

Rounded

a = 21.5 in²

Answer:

59°

Step-by-step explanation:

The angles of a triangle equal 180°.

Also the angle of a straight line is 180°.

So you first find the missing bottom angle by taking 180-147 to equal 33.

Then you take 33+88+x=180

solve for x by subtracting 88 and 33 from 180 to equal 59.

Answer:

59°

Step-by-step explanation:

180 - 147 = 33

88 + 33 = 121

180 - 121 = 59

Step-by-step explanation:

you should give points to x and find y

and then you will have some points of x and y

Answer:

(4, 4)

Step-by-step explanation:

y = 7/4 x - 3       graph (0, -3) (2, .5), (4, 4) (8, 11).  Draw the line

y = x                        graph (0,0)  (2, 2), (4, 4) , ( -2, -2).  Draw the line

The two lines intersect at point (4, 4)

Answer:

2,712.96 yd³

Step-by-step explanation:

The formula for finding the volume of a cylinder:

πr²h

π (in this case) = 3.14

r = radius

h = height

In this picture, we are given all of the values we need to set up and solve this equation.

r = 12 yd

h = 6 yd

3.14(12)^2 · 6

3.14(144) · 6

452.16 · 6

2,712.96

The square root of 9 is 3, so the square root of 11 would be a little greater than 3

The answer would be C. 3.3

To calculate the total number of points for the ride based on the number of favorite votes (x), second favorite votes (y), and third favorite votes (z), we can assign point values to each category and sum them up.

Let's assume the point values are as follows:

Favorite vote: 3 points

Second favorite vote: 2 points

Third favorite vote: 1 point

To calculate the total points, we can use the following expression:

Total points = (3 * x) + (2 * y) + (1 * z)

This expression represents the sum of the points awarded for each category based on the number of votes received.

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Photic zone: seaweeds and corals live here

aphotic zone: mid-ocean level where no light reaches

deep ocean floor: animals that glow are found here

Hope this helped!

Answer:

deep ocean floor - animals that glow are found here

photic zone - seaweeds and coral live here

aphotic zone mid-ocean level where no light reaches

Step-by-step explanation:

I rly hope this helps!! :D

Answer:

112

Step-by-step explanation:

l : b = 8 : 7

b = 98m

so l / b = 8/7

l / 98 = 8 / 7

l = 98 * 8 / 7

= 112

Answer:

the answer is A

Step-by-step explanation:

no explanation

the PERT weighted average is 9 days

PERT can be defined as an estimating technique that uses a weighted average of three numbers to get a final estimate.

The formula for finding the PERT weighted average is given as;

PERT weighted average = (Optimistic + (4 X Most Likely) + Pessimistic)/6

We have;

Substitute the values into the formula

PERT weighted average  = \(\frac{6 + 4(8) + 16 }{6}\)

PERT weighted average  = \(\frac{54}{6}\)

PERT weighted average  = 9 days

Thus, the PERT weighted average is 9 days

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There are 3,060 ways to choose a dozen apples from a bushel containing 20 indistinguishable Delicious apples, 20 indistinguishable McIntosh apples, and 20 indistinguishable Granny Smith apples, if at least three of each kind must be chosen.

What is the concept of combinations?
In mathematics, combinations refer to the selection of items from a larger set without considering the order of selection. Combinations are a way to count the number of possible subsets or groups that can be formed from a given set, where the order of the elements within the subset does not matter.

To determine the number of ways to choose a dozen apples, we can use the concept of combinations. Since at least three of each kind must be chosen, we consider three cases: choosing exactly three of each kind, choosing four of one kind and three each of the other two kinds, and choosing five of one kind and three each of the other two kinds.

Case 1: Choosing exactly three of each kind:

We choose 3 Delicious apples, 3 McIntosh apples, and 3 Granny Smith apples, leaving 3 more apples to be chosen from any of the remaining varieties. The number of ways to choose these 3 apples is given by the combination formula: C(3, 3) = 1.

Case 2: Choosing four of one kind and three each of the other two kinds:

We choose 4 Delicious apples, 3 McIntosh apples, and 3 Granny Smith apples. The remaining 2 apples can be chosen from any of the three varieties. The number of ways to choose these apples is given by: C(3, 2) = 3.

Case 3: Choosing five of one kind and three each of the other two kinds:

We choose 5 Delicious apples, 3 McIntosh apples, and 3 Granny Smith apples. The remaining apple can be chosen from any of the three varieties. The number of ways to choose this apple is given by: C(3, 1) = 3.

Therefore, the total number of ways to choose a dozen apples is: 1 + 3 + 3 = 7.

However, since the apples of the same variety are indistinguishable, the order of selection does not matter. Hence, we need to divide the total by the number of permutations of the chosen apples. In this case, we have 12 indistinguishable apples, so the number of permutations is 12!.

Thus, the final number of ways to choose a dozen apples is: 7 / 12! ≈ 3,060.

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Answer:

$120

Step-by-step explanation:

Answer:

f(4) = 0

Step-by-step explanation:

If the value of x is between 0 and 5, then the f(x) will equal 0.

x = 4 is greater than 0 and less than 5, so f(4) = 0

Answer:

e

Step-by-step explanation:

a) When Lily's age is 20, and Raphael's age is divided by 3 then the expression of Lily's age in terms of h is h < 10.

b) Ethan's age is half of Raphael's age therefore, Ethan's age is half Raphael's age.

a) If Raphael is twice as old as his sister Lily, we can represent their ages as 2h and h, respectively, where h is Lily's age. The sum of their ages is less than 30, so we can write the equation:

2h + h < 30

Combining like terms, we get:

3h < 30

Dividing both sides by 3, we get:

h < 10

This is an expression of Lily's age in terms of h.

b) If Ethan's age is 16, and Raphael's age is twice Ethan's age, we can represent Raphael's age as 2 × 16 = 32.

Ethan's age is 16, which is half of Raphael's age of 32. Therefore, Ethan's age is half of Raphael's age.

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The question is -

Raphael is twice as old as his sister. The sum of their ages is less than 30.

a) Lily's age is 20, and Raphael's age is divided by 3. Write an expression in terms of h for Lily's age.

b) An expression for Ethan's age 16. Write a sentence to describe how Ethan's age compares with Raphael's age.

Let the given sides be,

x=7

y=11

z=6

To find:

Using the formula,

On substitution we get,

Hence, the ange of X is,

Next, we need to find the angle of y:

Using the formula,

On substitution we get,

Hence, the ange of Y is,

Next, we need to find the angle of Z:

Using the formula,

On substitution we get,

Hence, the ange of Z is,

Reflect \(\triangle ABC\) over the \(y\)-axis then translate along the vector \((6, -2)\).

The probability of a student being signed up for both Algebra 2 and Chemistry is approximately 0.2083, or about 20.83%.

To find the probability of the intersection of two events, we need to divide the number of outcomes in the intersection by the total number of outcomes.

In this case, we want to find P(Algebra 2 ∩ Chemistry), which represents the probability of a student being signed up for both Algebra 2 and Chemistry.

Looking at the table, we can see that the number of students in the intersection (Algebra 2 and Chemistry) is given as 100.

The total number of students is the sum of the values in the "Total" row, which is 480.

Therefore, to find the probability, we divide the number of students in the intersection by the total number of students:

P(Algebra 2 ∩ Chemistry) = Number of students in Algebra 2 and Chemistry / Total number of students

= 100 / 480

Simplifying the fraction, we get:

P(Algebra 2 ∩ Chemistry) ≈ 0.2083

So, the probability of a student being signed up for both Algebra 2 and Chemistry is approximately 0.2083, or about 20.83%.

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The value of Δz is approximately -0.0600.

To find f(5,3), we substitute x = 5 and y = 3 into the function:

f(5,3) = 5cos(3) ≈ -2.8019

To find f(5.1,3.05), we substitute x = 5.1 and y = 3.05 into the function:

f(5.1,3.05) = 5.1cos(3.05) ≈ -2.8619

To calculate Δz, we subtract the initial value of f from the final value:

Δz = f(5.1,3.05) - f(5,3)

≈ (-2.8619) - (-2.8019)

≈ -0.0600

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Answer:

what that person said

Step-by-step explanation:

The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.

The equation is √ 2x² − 5x+ √ 2 = 0

So the value of a, b, c are 2, -5, √2 respectively

Therefore, the discriminant is (-5)² - 4(2)(√2) = 25 - 8√2

So, The discriminant for √ 2x² − 5x+ √ 2 = 0 is -8√2

Answer:

The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula:

b² - 4ac

Given the equation √ 2x² − 5x + √ 2 = 0, we can find the discriminant by substituting the values of a, b, and c into the formula:

b² - 4ac = (-5)² - 4(√2)(√2) = 25 - 8 = 17

So, the discriminant of the equation √ 2x² − 5x + √ 2 = 0 is 17

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

3