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Oksi-84 [34.3K]
3 years ago
8

How many units up was the graph of f(x) =∛x shifted to form the translation?

Mathematics
2 answers:
kati45 [8]3 years ago
7 0

Answer:

2 units up was the graph of f(x) =∛x shifted to form the translation

Step-by-step explanation:

y-intercept:

A line crosses the y-axis of the graph.

i.e

Substitute x = 0 and solve for y.

Given the parent function:

f(x) = \sqrt[3]{x}

by definition of y-intercept

y-intercept of the parent function = 0

Since, the another graph cuts the y-axis at 2.

⇒y-intercept = 2

Then the new graph becomes:

f(x) = \sqrt[3]{x}+2

Therefore, 2 units up was the graph of f(x) =∛x shifted to form the translationf(x) = \sqrt[3]{x}+2

Alexus [3.1K]3 years ago
5 0
The <span>graph of f(x) =∛x was shifted 2 units up to form the translation.</span>
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Convert to slope form: 3x-4y=8 then graph the line on the grid.​
alexandr402 [8]

Answer: 3/4

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Graph the line using the slope and y-intercept, or two points.

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6 0
2 years ago
Two numbers have a sum of 18, and 4 times the first number minus the second number is equal to 17. What is the smallest number?
sammy [17]

Answer:

The smallest number is 7

Step-by-step explanation:

Using simultaneous equation;

x+y = 18.....(1)

4x-y = 17.....(2)

from equation (1)..

x+y = 18

y = 18-x...(3)

substitute y into equation (2)

4x-y = 17

4x-(18-x) = 17

4x-18+x = 17

4x+x = 17+18

5x = 35

x = 35÷5

x = 7

substitute x into equation (3)

y = 18-x

y = 18-7

y = 11

Therefore; x=7

y=11

11+7=18

(4×7)-11=17

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4 0
3 years ago
One of the vertices of an equilateral triangle is on the vertex of a square and two other vertices are on the not adjacent sides
Elina [12.6K]
<h2>Answer:</h2>

<em> The side of the triangle is either 38.63ft or 10.35ft</em>

<h2>Step-by-step explanation:</h2>

This problem can be translated as an image as shown in the Figure below. We know that:

  • The side of the square is 10 ft.
  • One of the vertices of an equilateral triangle is on the vertex of a square.
  • Two other vertices are on the not adjacent sides of the same square.

Let's call:

Since the given triangle is equilateral, each side measures the same length. So:

x: The side of the equilateral triangle (Triangle 1)

y: A side of another triangle called Triangle 2.

That length is the hypotenuse of other triangle called Triangle 2. Therefore, by Pythagorean theorem:

\mathbf{(1)} \ x^2=100+y^2

We have another triangle, called Triangle 3, and given that the side of the square is 10ft, then it is true that:

y+(10-y)=10

Therefore, for Triangle 3, we have that by Pythagorean theorem:

(10-y)^2+(10-y)^2=x^2 \\ \\ 2(10-y)^2=x^2 \\ \\ \\ \mathbf{(2)} \ x^2=2(10-y)^2

Matching equations (1) and (2):

2(10-y)^2=100+y^2 \\ \\ 2(100-20y+y^2)=100+y^2 \\ \\ 200-40y+2y^2=100+y^2 \\ \\ (2y^2-y^2)-40y+(200-100)=0 \\ \\ y^2-40y+100=0

Using quadratic formula:

y_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ y_{1,2}=\frac{-(-40) \pm \sqrt{(-40)^2-4(1)(100)}}{2(1)} \\ \\ \\ y_{1}=37.32 \\ \\ y_{2}=2.68

Finding x from (1):

x^2=100+y^2 \\ \\ x_{1}=\sqrt{100+37.32^2} \\ \\ x_{1}=38.63ft \\ \\ \\ x_{2}=\sqrt{100+2.68^2} \\ \\ x_{2}=10.35ft

<em>Finally, the side of the triangle is either 38.63ft or 10.35ft</em>

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3 years ago
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What is m∠5?
kolbaska11 [484]
The answer is 27 degrees i know i took the test
5 0
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