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3 years ago

Find a real number between the square root of 70 and the square root of 75.

1 answer:

Alex3 years ago

3 0

Sqrt 70 < sqrt x < sqrt 75

sqrt of 64 = 8
sqrt of 81 = 9

8 < x < 9

8.4^2 = 70.56
8.5^2 = 72.25
8.6^2 = 73.96

sqrt 70 < sqrt (8.4^2 to 8.6^2) < sqrt 75

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I need help on this, please hurry and thank you!

inna [77]

Answer:

$A.\ a_n=n^2+1$

Step-by-step explanation:

$Check:$

$a_n=n^2+1\\\\a_1=1^2+1=1+1=2\qquad CORRECT\\\\a_2=2^2+1=4+1=5\qquad CORRECT\\\\a_3=3^2+1=9+1=10\qquad CORRECT\\\\a_4=4^2+1=16+1=17\qquad CORRECT\\\\a_5=5^2+1=25+1=26\qquad CORRECT$

Used PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

First Power, next Addition

4 0

3 years ago

Read 2 more answers

∆ABC is transformed with the center of dilation at the origin.

jonny [76]

Answer:

1/5

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−3, 4), B(−1, 12) and C(4, −2) to the image triangle A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4) and C' (0.8, −0.4).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A (−3, 4) ---> A' (−0.6, 0.8) = $\frac{-0.6}{-3} , \frac{0.8}{4}=(\frac{1}{5} , \frac{1}{5})$

B(−1, 12) ---> B' (−0.2, 2.4) = $\frac{-0.2}{-1} , \frac{2.4}{12} = (\frac{1}{5} , \frac{1}{5})$

C(4, −2) ---> C' (0.8, −0.4) = $\frac{0.8}{4} , \frac{-0.4}{-2} = (\frac{1}{5} , \frac{1}{5})$

Therefore, the scale factor of the dilation is 1/5.

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3 years ago

Kari's paper cup holds 6 fluid ounces. If one ounce is equivalent to 29.6 milliliters, how many milliliters does her paper cup h

Olegator [25]

Answer:

3245.8

Step-by-step explanation:

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3 years ago

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A box is to be constructed from a sheet of cardboard that is 20 cm by 50 cm by cutting out squares of length x by x from each co

Nezavi [6.7K]

We are given the dimensions of the box:

l = 50 cm

w = 20 cm

We know that the volume of a box is:

V = l w h

where h = x

However since x cuts is made on both all sides of the box, therefore the new dimensions would be:

V = (l – 2x) (w – 2x) x

V = (50 – 2x) (20 – 2x) x

V = 1000x – 100x^2 – 40x^2 + 4x^3

V = 4x^3 – 140x^2 + 1000x

To get the maxima value, we get the 1st derivative of the function then set dV/dx = 0 to solve for x:

dV / dx = 12x^2 – 280x + 1000

12x^2 – 280x + 1000 = 0

Transpose 1000 to the right side and divide everything by 12:

x^2 – (280/12)x = -(1000/12)

Completing the square:

x^2 – (280/12)x + (78400/576) = -(1000/12) + (78400/576)

[x – (280/24)]^2 = 52.78

x – (280/24) = ±7.26

x = (280/24) ± 7.26

x = 4.40, 18.93

x cannot be 18.93 since this would result in a negative value of 20 – 2x, therefore:

x = 4.40 cm

Calculating for the volume:

V = (50 – 2*4.4) (20 – 2*4.4) (4.4)

V = 2030.34 cm^3

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3 years ago

How can x + 3 = -2x + 5 be set up as a system of equations? (1 point)

Elena-2011 [213]

9514 1404 393

Answer:

4) y = x + 3

y = -2x + 5

Step-by-step explanation:

Set each side of the equal sign equal to y.

Left side:

y = x + 3

Right side:

y = -2x +5

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3 years ago