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3 years ago

Help please much appreciated

Mathematics

2 answers:

leonid [27]3 years ago

7 0

The correct answer is A.

Explanation.....
Let h represent the temperature decreasing each hour.
60-3h<32
The answer must be below 32 degrees.

larisa [96]3 years ago

6 0

The answer is a.........

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Identify the lengths of sides m and n.

juin [17]

Answer:

m = 26

n = 13

Step-by-step explanation:

Use the sine rule

8 0

3 years ago

Find two consecutive integers such that one fifth of the first less one-ninth of the second is 3. Pls answer.

mart [117]

Answer:

35 and 36

Step-by-step explanation:

To solve this problem, we must interpret it line by line;

We are dealing with consecutive integers; these are integers with a difference of 1 between them.

let the first number = x

second number = x + 1

one - fifth of first;

$\frac{1}{5}$ x

one - ninth of the second;

$\frac{1}{9}$ (x + 1)

for the "less" ;

$\frac{1}{5}$ x - $\frac{1}{9}$ (x + 1) = 3

Multiply through by 45

45( $\frac{1}{5}$ x) - (45) $\frac{1}{9}$ (x + 1) = 3 x 45

9x - 5(x + 1) = 135

9x - 5x -5 = 135

4x = 135 + 5

4x = 140

x = 35

Now, x+1 = 35 + 1 = 36

The consecutive integers are 35 and 36

4 0

3 years ago

Which are sums of perfect cubes? Check all that apply.

vichka [17]

I think these are the sums of perfect cubes.

A = (2x²)³ + (3)³
B = (x³)³ + (1)³
D = (x²)³ + (x)³
E = (3x³)³ + (x^4)³

5 0

3 years ago

Type the correct answer in each box

Luba_88 [7]

Answer:

We know that the equation of the circle in standard form is equal to (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius of the circle.

We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :

1 - We first group terms with the same variable :

(x²+8x) + (y²+22y) + 37 = 0

2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)

(x²+8x) + (y²+22y) = - 37

3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process "completing the square".

x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²

y²+22y = (y²+22y+11²)-11² = (y+11)²-11²

4 - We plug the new values inside our equation :

(x+4)² - 4² + (y+22)² - 11² = -37

(x+4)² + (y+22)² = -37+4²+11²

(x+4)²+(y+22)² = 100

5 - We re-write in standard form :

(x-(-4)²)² + (y - (-22))² = 10²

And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)

5 0

3 years ago

A manufacturer cuts squares from the corners of a rectangular plece of sheet metal that measures 2 inches by 7 inches (see Figur

Vladimir79 [104]

Answer:

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the open-topped box is equal to

$V=LWH$

where

$L=(7-2x)\ in\\W=(2-2x)\ in\\H=x\ in$

substitute

$V=(7-2x)(2-2x)x$

Convert to expanded form

$V=(7-2x)(2-2x)x\\V=(14-14x-4x+4x^{2})x\\V=14x-14x^2-4x^2+4x^{3}\\V=4x^{3}-18x^{2} +14x$

using a graphing tool

Graph the cubic equation

Remember that

The domain for x is the interval -----> (0,1)

Because

If x>1

then

the width is negative (W=2-2x)

The maximum is the point (0.46,3.02)

see the attached figure

therefore

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

8 0

3 years ago