If a turtle can crawl 1/2 foot in 40 minutes, how many feet can he crawl in an hour and a half?

Answer:

Step-by-step explanation:

cos A = \(\frac{\sqrt{8} }{3}\)

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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Answer:

389 is the answer

Hope you like it!

The expression {P(x) + Q(x)} − {R(x) + S(x)} is a zero polynomial.

From the question, we have the following polynomial that can be used in our computation:

P(x) = 2x² (x + 3) − (7x − 10)

Q(x) = 8(x − 1) (x² + x + 1) − 3x² + 4

R(x) = (2x + 1)² - (2x² + 7)

S(x) = 2(5x³+6) + x(x - 11)

Add the expressions P(x) and Q(x)

So, we have

P(x)  + Q(x) = 2x² (x + 3) − (7x − 10) + 8(x − 1) (x² + x + 1) − 3x² + 4

Evaluate

P(x)  + Q(x) = 10x³ + 3x² - 7x + 6

Add the expressions R(x) and S(x)

So, we have

R(x) + S(x) = (2x + 1)² - (2x² + 7) + 2(5x³+6) + x(x - 11)

R(x) + S(x) = 10x³ + 3x² - 7x + 6

So, we have

P(x) + Q(x)} − {R(x) + S(x)} = 10x³ + 3x² - 7x + 6 - (10x³ + 3x² - 7x + 6)

Evaluate

P(x) + Q(x)} − {R(x) + S(x)} = 0

Hence, the expression {P(x) + Q(x)} − {R(x) + S(x)} is a zero polynomial.

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Answer:

39 3/8 ft ^2

Step-by-step explanation:

To find the area of a rectangle, multiply the length times the width.

A = l*w

  = 7 1/2  * 5 1/4

Change the mixed numbers to improper fractions.

A = 15/2 * 21/4

    =315/8

Change back to a mixed number.

8 goes into 315 39 times with 3 left over.

 = 39 3/8

Answer:

(you can round to 39.4)

Step-by-step explanation:

Find the area of the rectangle shown

7 1/2 ft

5 1/4ft

7 1/2 = 7.5 ft

5 1/4 = 5.25 ft

Area = L x W

Area = 7.5 x 5.25

Area = 39.375

Answer:

n^2 + 11 + (n - 15)

Step-by-step explanation:

eleven more than the square of a number n added to the difference between the number and fifteen

___ + 11

eleven more than the square of a number n added to the difference between the number and fifteen

n^2 + 11

eleven more than the square of a number n added to the difference between the number and fifteen

n^2 + 11 + (n - 15)

The expression that is equivalent to the given value would be = 18-i . That is option C.

An equivalent expression is defined as the type of expression that is similar to a given value when simplified.

The given expression = ( 3 + 4i) ( 2 - 3i)

Expand the given expression by removing the brackets as follows:

= =2(3+4i)−3i(3+4i)

=(6+8i)−(9i−12)

= (6+12)+i(8−9)

=18−i.

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The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

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The time that the ball traveled is given as follows:

1.5 seconds.

The quadratic function determining the ball's height after t seconds is given as follows:

H(t) = -16t² + 24t.

The roots of the quadratic function in this problem are given as follows:

-16t² + 24t = 0.

16t² - 24t = 0

8t(2t - 3) = 0.

Hence we apply the factor theorem as follows:

Hence the time is given as follows:

1.5 - 0 = 1.5 seconds.

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Answer:

24 and 27

Step-by-step explanation:

√600 = 24.4

√700 = 27.7

So, the numbers should be around 24 and 27

thus you have option 3

Answer:

\(\displaystyle F(v) = \frac{9}{5}(v-273)+32\)

Step-by-step explanation:

The temperature T(d) in degrees Fahrenheit in terms of Celsius d is given by:

\(\displaystyle T(d)=\frac{9}{5}d+32\)

And the temperature C(v) in degrees Celsius in terms of Kelvin v is given by:

\(C(v)=v-273\)

We want the formula for the temperature F(v) in degrees Fahrenheit in terms of the Kelvin temperature.

So, we can use a composition of functions. Since T(d) outputs the temperature in Fahrenheit and C(v) inputs the temperature in Kelvin, T(C(v)) will be the temperature in Fahrenheit given the temperature in Kelvin. So:

\(\displaystyle T(C(v))=\frac{9}{5}(C(v)))+32\)

Substitute:

\(\displaystyle T(C(v)) = F(v) = \frac{9}{5}(v-273)+32\)

Therefore:

\(\displaystyle F(v) = \frac{9}{5}(v-273)+32\)

Answer:

y = 8x + 38

Step-by-step explanation:

parallel to y=8x -3, that means the slope(m) = 8

points : -4 , 6

now put them in the formula y = mx + b

6 = 8(-4) + b

6 = -32 + b

6 + 32 = b

b = 38

y = 8x + 38

Answer:

The unit price of the book is 0.75.

Answer: x - y *2

Step-by-step explanation:

The man still owes R87,726 in taxes.

To calculate the tax amount the man still owes, we need to determine his taxable income first.

Gross income: R500,000

Less: PAYE deductions (17% of gross income): R500,000 * 0.17 = R85,000

Taxable income: R500,000 - R85,000 = R415,000

Next, we can use the tax table information provided to calculate the tax owed based on the taxable income.

Tax owed: R93,135 + 36% of (taxable income - R393,200)

Tax owed: R93,135 + 0.36 * (R415,000 - R393,200)

Tax owed: R93,135 + 0.36 * R21,800

Tax owed: R93,135 + R7,848

Tax owed: R100,983

Finally, we subtract the rebate amount of R13,257 from the tax owed to find the amount the man still owes.

Tax owed - Rebate: R100,983 - R13,257 = R87,726

Therefore, the man still owes R87,726 in taxes.

The correct option is not provided among the given answer choices.

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If f(x) = 3x and g(x)=x-2, then the value of f(g(4)) is 6.

What is a function?

A function is a mathematical object that assigns exactly one output to each input of a specified type. In other words, a function is a rule that takes in certain inputs (or "arguments") and produces a unique output. The inputs to a function are called the domain, while the set of possible outputs is called the range.

The given functions are f(x) = 3x and g(x)=x-2.

To find f(g(4)), we first need to evaluate g(4). The function g is defined as g(x) = x - 2, so g(4) = 4 - 2 = 2.

Next, we need to evaluate f(2), where f is defined as f(x) = 3x. So, f(2) = 3 * 2 = 6.

Therefore, f(g(4)) = f(2) = 6.

Hence, if f(x) = 3x and g(x)=x-2, then the value of f(g(4)) is 6.

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Answer:

22 meters

Step-by-step explanation:

Let x = width of the rectangle

Let y = length of the rectangle

Equation 1

If the length of the rectangle is 6 meters shorter than four times the width then:

⇒ y = 4x - 6

Equation 2

Perimeter of a rectangle = 2(width + length)

If the perimeter is 58 inches, then:

⇒ 58 = 2(x + y)

Solve by substitution

Substitute Equation 1 into Equation 2 and solve for x:

⇒ 58 = 2(x + 4x - 6)

⇒ 58 = 2(5x - 6)

⇒ 58 = 2 · 5x - 2 · 6

⇒ 58 = 10x - 12

⇒ 58 + 12 = 10x -12 + 12

⇒ 10x = 70

⇒ 10x ÷ 10 = 70 ÷ 10

⇒ x = 7

Substitute found value of x into Equation 1 and solve for y:

⇒ y = 4(7) - 6

⇒ y = 28 - 6

⇒ y = 22

Conclusion

The dimensions of the rectangle are:

Therefore, the length of the longer side is 22 meters

The length of the longer side is 22 meters.

Let, one side of the rectangle is x meters.

According to the problem, the other side is 6 meters shorter than four times this side, which means the length of the second side is (4x - 6) meters.

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

In this case, the perimeter is 58 meters:

58 = 2 * (x + 4x - 6)

Now, let's solve for x:

58 = 2 * (5x - 6)

58 = 10x - 12

Add 12 to both sides:

58 + 12 = 10x

70 = 10x

Now, divide both sides by 10 to isolate x:

x = 70 / 10

x = 7

So, one side of the rectangle is 7 meters.

Now, we can find the length of the longer side:

Length of the longer side = 4x - 6

Length of the longer side = 4 * 7 - 6

Length of the longer side = 28 - 6

Length of the longer side = 22 meters

Therefore, the length of the longer side is 22 meters.

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Answer:

48.7 I think

Step-by-step explanation:

hears the sender buddy

Answer:

48.5 the 7 is close to 10 so it rounds the 4 to 5

Answer:

\( \large \rm \frac{3}{4} + \frac{5}{6} + \frac{7}{8} \)

\( \large \rm \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24} \)

\( \large\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \)

\(\large \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} =\frac{59}{24}=2\frac{11}{24}\)

\( \dashrightarrow\dfrac{3}{4} + \dfrac{5}{6} + \dfrac{7}{8} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow \dfrac{\frac{3 \times 24}{4} + \frac{5 \times 24}{6} + \frac{7 \times24}{8}} {24} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow \dfrac{3 \times 6 +5 \times 4+ 7 \times 3} {24} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow \dfrac{18 +20+ 21} {24} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow \dfrac{18 +41} {24} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow \dfrac{59} {24} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow 2.4 \\ \\ \)

\( \\ \\ \)

The solutions to the problem of finding an answer to the given equation are:

\(x^2\) ≡ 2 (mod 11) are x = 5 and x = 6.

The given congruence is quadratic, so it has at most two solutions. We can solve this by checking each possible value for x in the range [0,10] since we're working modulo 11.

For congruence \(x ^2\)≡ 2 (mod 11), the solutions are x = 6 and x = 5. This is because \(6^2 = 36\) ≡ 2 (mod 11) and \(5^2 = 25\) ≡ 2 (mod 11).

The solutions to the problem of finding an answer to the given equation are:

\(x^2\) ≡ 2 (mod 11) are x = 5 and x = 6.

Only two numbers between 0 and 10 match the given rule.

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The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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Answer:

The last choice

Step-by-step explanation:

:)

Answer:

I believe the answer is C

Step-by-step explanation:

Answer:

A vertical line at a specific x-value of the domain will intersect the graph of a relation at each y-value in the range that

the x-value is mapped to by the relation. If even one such line has more than one intersection, then one input has two

or more outputs and the relation is not a function.

Happy to Help And brainliest please... I do this all the times sense I'm a honors student, let me know if you need help!

Step-by-step explanation:

The number of pork sliders sold is given as follows:

24 pork sliders.

The number of pork sliders sold is obtained applying the proportions in the context of the problem.

The total number of pork sliders is given as follows:

120 pork sliders.

The percentage of pork sliders sold is given as follows:

20%. (proportion of 0.2).

Hence the amount sold is given as follows:

0.2 x 120 = 24 pork sliders.

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Answer:

he has 8 classes 3 hours long, so 8×3 is how long he IS is class. subtract 24 from 63 and you get how long he is NOT in class. he is NOT in class for 39 hours.

Answer: 4 pounds is equal to 16 four-ounce (1/4 pound) increments.

To find the number of 3/4 pound bags Ann needs to buy, we can convert 16 four-ounce increments to three-fourth pound increments:

16 four-ounce increments = 16 x 4 = 64 ounces

64 ounces = 64/16 = 40 three-fourth pound increments

Therefore, Ann will need to buy 40 bags of walnuts, each weighing 3/4 of a pound.

Step-by-step explanation:

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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