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Korvikt [17]
3 years ago
13

Markus scared 85, 92, 82, and 94 on the first four tests of the semester. His teacher has not yet told him his score on his fift

h test, but did tell him that his score on the fifth test is five points lower than the average (arithmetic mean) of all five tests. Which equation could Markus use to determine the score of the fifth test, x?
Mathematics
2 answers:
vovikov84 [41]3 years ago
5 0

Answer:

5(x + 5) = 353 + x

Step-by-step explanation:

i got it right on edge

alexandr1967 [171]3 years ago
3 0

Answer:

y — x = 5

5y — x = 353

Step-by-step explanation:

Let the fifth score be x

Let the average of all the scores be y.

But the fifth score is 5 points lower than the average ie

y — x = 5 (1)

The average of the scores is the sum of all the scores divided the number of scores. This is written as

y = (85 + 92 + 82 + 94 + x) /5

y = (353 + x) /5

Multiply through by 5

5y = 353 + x

Rearrange the equation

5y — x = 353 (2)

The equation Markus will use to determine the x is given as

y — x = 5

5y — x = 353

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What are the focus and directrix of the parabola that is the graph of the function f(x)=x²?
Hitman42 [59]

Answer:

Step-by-step explanation:

Given

y=x^2

comparing it with standard equation x^2=4ay

so 4a=1

a=\frac{1}{4}

so Focus of parabola is (0,0)

directrix

y=-a

here a=\frac{1}{4}

y=-\frac{1}{4}      

5 0
3 years ago
A quadrilateral has vertices at $(0,1)$, $(3,4)$, $(4,3)$ and $(3,0)$. Its perimeter can be expressed in the form $a\sqrt2+b\sqr
seraphim [82]

Answer:

a + b = 12

Step-by-step explanation:

Given

Quadrilateral;

Vertices of (0,1), (3,4) (4,3) and (3,0)

Perimeter = a\sqrt{2} + b\sqrt{10}

Required

a + b

Let the vertices be represented with A,B,C,D such as

A = (0,1); B = (3,4); C = (4,3) and D = (3,0)

To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

Calculating AB

Here, we consider A = (0,1); B = (3,4);

Distance is calculated as;

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

(x_1,y_1) = A(0,1)

(x_2,y_2) = B(3,4)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}

AB = \sqrt{( - 3)^2 + (-3)^2}

AB = \sqrt{9+ 9}

AB = \sqrt{18}

AB = \sqrt{9*2}

AB = \sqrt{9}*\sqrt{2}

AB = 3\sqrt{2}

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

(x_1,y_1) = B (3,4)

(x_2,y_2) = C(4,3)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}

BC = \sqrt{(-1)^2 + (1)^2}

BC = \sqrt{1 + 1}

BC = \sqrt{2}

Calculating CD

Here, we consider C = (4,3); D = (3,0)

Here,

(x_1,y_1) = C(4,3)

(x_2,y_2) = D (3,0)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}

CD = \sqrt{(1)^2 + (3)^2}

CD = \sqrt{1 + 9}

CD = \sqrt{10}

Lastly;

Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

(x_1,y_1) = D (3,0)

(x_2,y_2) = A (0,1)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}

DA = \sqrt{(3)^2 + (- 1)^2}

DA = \sqrt{9 +  1}

DA = \sqrt{10}

The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral

Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}

Perimeter = 4\sqrt{2} + 2\sqrt{10}

Recall that

Perimeter = a\sqrt{2} + b\sqrt{10}

This implies that

a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}

By comparison

a\sqrt{2} = 4\sqrt{2}

Divide both sides by \sqrt{2}

a = 4

By comparison

b\sqrt{10} = 2\sqrt{10}

Divide both sides by \sqrt{10}

b = 2

Hence,

a + b = 2 + 10

a + b = 12

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8 0
2 years ago
I need help pleaseeeeeeee
Alekssandra [29.7K]

Answer:

T = 7M/N

Step-by-step explanation:

Cross multiply

NT = 7M

Divide by N

NT/N = 7M/N

T = 7M/N

3 0
3 years ago
How many times does she expect to draw a marble that isn’t red
otez555 [7]
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