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3 years ago

when a number is multiplied by -3, the result is atleast 15. What is the greatest value the number can have?

Mathematics

1 answer:

Diano4ka-milaya [45]3 years ago

7 0

Answer:-5

Step-by-step explanation:

-5•-3=15

The number can’t be any greater and still work. For example, if you used -4 instead of -5, you would get 12(which is less than 15)

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Type the missing numbers in this sequence:<br> -101, -105,<br> -109,<br> -117

PIT_PIT [208]

Answer:

The answer is - 113 that is the correct answer skipping in three's and the first one is - 97

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2 years ago

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Which of the following options is equivalent to 140%? Select all that apply.

bija089 [108]

There aren’t any options, use a picture?

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3 years ago

For an exponential regression equation in the form y=ab^x which of the following values of b will cause y to get smaller as x ge

sdas [7]

Answer:

d) 0.798

Step-by-step explanation:

Since we know that an exponential function is in form: $y=a*b^x$ , where,

a= Initial value,

b = For growth b is in form (1+r), where r is rate in decimal form.

b = For decay or regression b is less than 1 and in form (1-r), where r is rate in decimal form.

Upon looking at our given choices we can see that options a, b and c are in form 1+r, while choice provided in option d is less than 1 and in form 1-r, therefore, option d is the correct choice.

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3 years ago

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Leonardo is solving the equation 4 (x minus one-fifth) = 2 and two-thirds. His work is shown. Where is his error?

Brilliant_brown [7]

Answer:

Step 3

Step-by-step explanation:

Leonardo is solving the equation 4 (x minus one-fifth) = 2 and two-thirds. His work is shown. Where is his error?

Given :

4(x - 1/5) = 2 2/3

Open the bracket

4x - 4/5 = 2 2/3

Add 4/5 to both sides

4x - 4/5 + 4/5 = 8/3 + 4/5

Lcm of 3 and 5 = 15

4x = (40 + 12) / 15

4x = 40/15 + 12/15

4x = 52/15

Multiply by 1/4

4x * 1/4 = 52/15 * 1/4

x = 52 / 60

x = 13 / 15

Hence, the error is in step 3

15/5 * 3 = 12

Rather ; Leonardo wrote 16

5 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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