MATHEMATICS HIGH SCHOOL

If ST = 3, TU = 1, and SU= 9, what is ST?

Answers

Answer 1

Answer:

Answer:

ST = 3

Step-by-step explanation:

it tells you that ST is 3

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Write the equivalent fraction of 3 /5 having denominator 35
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How to write 76.12 in words
A plane is heading 25° west of south. How many degrees south of west is this plane flying?
Kassy is traveling to Peru for her summer vacation. She looks at a map of the path of her flight. Her plane leaves from Texas, located at(5, 16) on the map’s coordinate grid, and then heads to its destination, Peru, located at(7, 8) on the map’s coordinate grid. Find the distance of Kassy's trip according to her map. Round your answer to the nearest hundredth.

Darien could swim 30 laps anhour last year. This year he can
swim 36 laps an hour. Determine the
percent change

Answers

Answer:

Step-by-step explanation:

If the percent change is 30 to 36 you can already see that it is an increase

here is the work

36 - 30

x 100% = 20%

Answer:

20% increase, which corresponds to the light

Step-by-step explanation:

(y - x)/x * 100

(36 - 30)/30 * 100

(6 * 100)/30

600/30

20% increase

In the diagram ce =12 and be=5 based on the given info ae =

Answers

the answer is ae=12 that what i got right on my test

12 - it is congruent to CE

Solve the equation the square root of the quantity x plus 3 plus 4 equals 5 for the variable.

Answers

Domain: expression under square root is greater or equal than zero.

x+3>0
x>-3

Then:

$√(x+3)}+4=5 \qquad |-4 \n \n √(x+3)=1 \qquad |(...)^2 \n \n x+3=1 \n \n x=-2 \in D$

So the answer is x=-2

Final answer:

By isolating the square root, squaring both sides to remove the square root, and then solving for x, the solution to the equation √(x + 3) + 4 = 5 is found to be x = -2.

Explanation:

To solve this equation, we start by isolating the square root. The equation given is √(x + 3) + 4 = 5. The first step is to subtract 4 from both sides of the equation to isolate the square root, resulting in √(x + 3) = 1.

Once the square root is isolated, we can square both sides of the equation to eliminate the square root, leading to x + 3 = 1² = 1.

Finally, subtract 3 from both sides, leaving us with the solution x = 1 - 3 = -2.

Learn more about Solving Equations here:

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What is the simplified base for the function f(x) = 2(3√27(2x)?2
3
9
18

Answers

Answer:

option C is correct i.e. 9

Step-by-step explanation:

We have given that : $f(x)=2 \sqrt[3]{27^(2x)}$

To find : The simplified base of the function f(x)

Solution:

Now, we solve the equation

$f(x)=2 \sqrt[3]{27^(2x)}$

$f(x)=2(27^x)^{(2)/(3)}$

$f(x)=2(3^(2x))$

$f(x)=2((3^2)^(x))$

$f(x)=2(9^(x))$

Therefore, the simplified base of the function f(x) is 9

Answer:

Option C is correct

9 the simplified base for the given function f(x)

Step-by-step explanation:

Using exponent rules:

$(x^m)^n = x^(mn)$

$\sqrt[n]{x^b} = x^{(b)/(n)}$

Given the function:

$f(x) = 2\sqrt[3]{27^(2x)}$

We can write 27 as:

$27 = 3 \cdot 3 \cdot 3 = 3^3$

then;

$f(x) = 2\sqrt[3]{(3^3)^(2x)}$

Apply the exponent rules:

$f(x) = 2\sqrt[3]{3^(6x)}$

Apply the exponent rules:

$f(x) =2 \cdot (3^(6x))^{(1)/(3)} = 2 \cdot 3^(2x)$

⇒ $f(x) = 2 \cdot (3^2)^x = 2 \cdot 9^x$

⇒ $f(x) =2 \cdot 9^x$

On comparing with exponential function $f(x) = ab^x$ where, b is base of the exponent function, then

b = 9

Therefore, the simplified base for the given function is, 9

If 160 is divided by x, then the remainder is 4. What is the remainder when 315 is divided by x?

Answers

Let us rewrite this equation as:
160/x = some number + 4/x
we can assume that some number of x's can fit into 160, but x is greater than 4 so we have a remainder.
We can figure out by using the remainder that x is completely divisible into (160-4) or 156. Knowing this we can assume that x is some factor of 156 that is greater than 4.
Let us list the factors of 156
1,2,3,4,6,12,13,26,39,52,78,156
Now let us refer back to the restrictions we put on x.
x must be > 4 as anything less than 4 would divide at least 1 more time into it. So now we are left with a bunch of other factors. And the cool thing is that all of the factors excluding anything that is = or < 4 all work for getting a remainder of 4. Thus we can use the largest factor and set it equal to x.
So x = 156
then if we divide 315 by x or 315/x = 315/156 = 2 and a remainder of 3
so the answer would be 3.

Suppose you know the base of a rectangle has a length of 4 inches and a diagonal has a length of 5 inches. Find the area of the rectangle.

Answers

The area of the rectangle is A = 12 inches²

What is the Area of a Rectangle?

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be A

Let's use the Pythagorean theorem to find the length of the other side of the rectangle.

Let's call the length of the other side "x".

Using the Pythagorean theorem, we have:

x^2 + 4^2 = 5^2

Simplifying and solving for x, we get:

x^2 + 16 = 25

x^2 = 9

x = 3

So the length of the other side of the rectangle is 3 inches.

To find the area of the rectangle, we multiply the length by the width:

Area of rectangle A = length x width = 4 x 3 = 12 inches²

Hence , the area of the rectangle is 12 square inches

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That diagonal will split the rectangle into two triangles, with 5 inches being the hypotenuse of each. If we know that one base is 4 inches, then we can use the Pythagorean theorem to find the length of the other side of the rectangle. Let's call that other side x for now. x^2+4^2=5^2, because of the pythagorean theorum.
$x^(2) +4^(2) = 5^(2)$
$x^(2) +16=25$
$x^(2) =9$
$x=3$
So 3 is the other side of the rectangle, take that times 4 and you'll get 12 in^2.

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