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4 years ago

Third-degree, with zeros of −5, −4, and 1, and a y-intercept of −15

Mathematics

1 answer:

VARVARA [1.3K]4 years ago

5 0

Answer:

y = 3/4( x+5)( x+4) ( x-1)

Step-by-step explanation:

The formula for the polynomial is

y = c( x- a1)( x- a2) ( x-a3) where c is a constant and a1,a2,a3 are the zeros

We have zeros -5,-4 and 1

y = c( x- -5)( x- -4) ( x-1)

y = c( x+5)( x+4) ( x-1)

We have a y intercept of -15

That means x=0 and y = -15

-15 = c ( 0+5)( 0+4) ( 0-1)

-15 = c( 5) ( 4) (-1)

-15 = c( -20)

Divide each side by -20

-15/-20 = c

3/4 =c

The equation is

y = 3/4( x+5)( x+4) ( x-1)

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Log22 rewrite as a quotient of two base 3 logarithms

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Log 22 = $(log 22/log 10)_{base=3}$

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3 years ago

The storage box shown has these dimensions.

Westkost [7]

Answer: D. 3/16 ft³

Step-by-step explanation:

The formula for finding volume is: V=hwl

v=volume
h=height
w=width
l=length

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

Given

h=3/4 ft

w=1/2 ft

l=1/2 ft

Substitute value into the formula

V=hwl

V=(3/4)(1/2)(1/2)

V=(3/8)(1/2)

V=3/16 ft³

Hope this helps!! :)

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7 0

3 years ago

Find the 76th term of the arithmetic sequence 17, 19, 21, ...

Dominik [7]

Answer: 167

Step-by-step explanation: To find the 76th term of this arithmetic sequence, we will be using our explicit formula which is shown below.

$^{a}n = ^{a}1 (n - 1)d$

Since we want to determine the 76th term, we are going

to substitute 76 in for n in our explicit formula.

Then, $^{a}1$ will be our first term in our sequence which is 17.

Lastly, d is our common difference or the difference between each of the terms in our arithmetic sequence which is 2.

So we have $^{a} 76 = 17 + (76 - 1)(2)$ .

Now we have all the information we need. Just simplify from here.

Make sure to apply order of operations because this is where many

students make mistakes. Inside the parentheses first!

(76 - 1) is going to be 75.

So we have $^{a} 76 = 17 + (75)(2)$ .

Then, we have to make sure we multiply before we add.

So (75)(2) is going to give us 150.

So we have $^{a} 76 = 17 + 150$ .

Now just add to find that $^{a} 76 = 167$ .

So the 76th term is 167.

5 0

4 years ago

Scientists on an oceanographic research vessel board a miniature submarine when it is at an elevation of 2 meters above the ocea

svetoff [14.1K]

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

The ocean floor directly beneath the boat is at a depth of = 180 meters

Submarine is at an elevation when it is above the ocean's surface = 2 meters

Total distance submarine needs to descends at a constant rate = 180+2=182 m

Rate of submarine descends = 0.4 meters per second.

Time taken by a scientist spend descending after boarding the submarine is given by

$Time=\frac{Distance}{Speed}\\\\Time=\frac{182}{0.4}\\\\Time=455\ seconds$

so, it must be less than 455 seconds.

therefore, it becomes x<455.

Hence, Option 'A' is correct.

5 0

3 years ago

Read 2 more answers

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Snowcat [4.5K]

Hi!

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Area of a triangle = $(base * height)/2$

Area of a square = $(side)^2$

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QUESTION 1: Determine the area of the triangular face.

$\frac{bh}{2}$

$32(20)/2$

$640/2$

$320$

The triangular face is 320 square feet.

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

QUESTION 2: Determine the surface area of the entire figure.

$a^2$

$32^2$

$1024$

Now, add the 4 triangular faces to the area of the square face.

$1024+320(4)$

$1024+1280$

$2304$

The total surface area is 1204 square feet.

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For more information, see:

brainly.com/question/4637102

brainly.com/question/22971514

5 0

3 years ago