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2 years ago

What is the remainder in the synthetic division problem below?

Mathematics

1 answer:

maks197457 [2]2 years ago

8 0

Answer:

im sure of my answer but three letter A C D

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The sum of three consecutive odd integers is − 87 . find the numbers.

DIA [1.3K]

Three consecutive odd integers are n, n+2 and n+4

n + n+2 + n+4 = -87
3n + 6 = -87
3n = -87 - 6
3n = -93
n = -93/3
n = -31

n+2 = -31 + 2 = -29
n+4 = -31 + 4 = -27

The numbers are -31, -29 and -27

5 0

4 years ago

What is the length of segment VS?<br> O 3 units<br> 11 units<br> 13 units<br> O 15 units

sergeinik [125]

Answer:

VS = 11

Step-by-step explanation:

If u could subscribe to penny_pg3d on YT, that would be great :)

5 0

3 years ago

There are 360 seals. Of them are 9/20 are pups. The rest are adult seals . How many pups are the beach .

k0ka [10]

Answer:

162 pups are on the beach

Step-by-step explanation:

9/20 of 360

The key word "of" tells us to multiply

Variable x = number of pups

9/20 × x/360

Cross multiply

9 × 360 = 20 × x

3,240 = 20x

Divide both sides by 20

162 = x

Check our work:

9/20 = 162/360

Cross multiply

9 × 360 = 20 × 162

3,240 = 3,240

Correct

3 0

3 years ago

A 10 ft ladder is being pulled away from a wall at a rate of 3 ft/sec. What is the rate of change in the area beneath the ladder

andriy [413]

Answer:

The rate of change in the area beneath the ladder is 5.25 ft²/s

Step-by-step explanation:

Area of triangle is given by;

$A = \frac{1}{2}bh\\\\2A = bh\\\\take \ derivative \ of \ both \ sides \ with \ respect \ to \ "t"\\\\2\frac{dA}{dt} = h\frac{db}{dt} + b\frac{dh}{dt}\\\\divide \ through \ by \ 2\\\\\frac{dA}{dt} = (\frac{h}{2} )\frac{db}{dt} + (\frac{b}{2}) \frac{dh}{dt}$

where;

b is the base of the triangle, given as 6 ft

h is the height of the triangle, determined by applying Pythagoras theorem.

h² = 10² - 6²

h² = 100 - 36

h² = 64

h = √64

h = 8 ft

Determine the rate of change of the height;

$h^2 + b^2 = 10^2\\\\h^2 + b^2 =100\\\\2h\frac{dh}{dt} + 2b\frac{db}{dt} =0\\\\h\frac{dh}{dt} + b\frac{db}{dt} =0\\\\h \frac{dh}{dt} = -b\frac{db}{dt} \\\\\frac{dh}{dt} = (\frac{-b}{h} )\frac{db}{dt}\\\\\frac{dh}{dt} =(\frac{-6}{8})(3)\\\\\frac{dh}{dt} = -\frac{9}{4} \ ft/s$

Finally, determine the rate of change of area beneath the ladder;

$\frac{dA}{dt} = (\frac{h}{2} )\frac{db}{dt} + (\frac{b}{2}) \frac{dh}{dt}\\\\\frac{dA}{dt} = (\frac{8}{2} )(3) + (\frac{6}{2}) (\frac{-9}{4})\\\\\frac{dA}{dt} = 12 - \frac{27}{4} \\\\\frac{dA}{dt} = \frac{48-27}{4}\\\\\frac{dA}{dt} = \frac{21}{4} \ ft^2/s\\\\\frac{dA}{dt} = 5.25 \ ft^2/s$

Therefore, the rate of change in the area beneath the ladder is 5.25 ft²/s

5 0

3 years ago

If angle 4 is 52.7, what are the measures of angles 1,2, and 3?

shusha [124]

Answer:

127.3
52.7
127.3
52.7

Step-by-step explanation:

Since we know the angle measure of angle 4, we already know that angle 2 will have the same measure according to do the vertical angle theorem. Now to find angles 1 and 3, we can make an equation and solve for x (supplementary angles).

52.7 + x = 180

x = 127.3

Best of Luck!

6 0

3 years ago