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4 years ago

Kristen goes on a cave tour with her family. They climb down to 8 meters below ground level.

Mathematics

2 answers:

Serjik [45]4 years ago

5 0

Answer:

16 meters

Step-by-step explanation:

Since the question is asking you to find the meters they climbed in all, you can add the absolute values of -8 and +8 to get 16

aleksley [76]4 years ago

5 0

I think the answer is 16
When you get questions like these you would need to even them out by adding them
Hope this helps!!!:)

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The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Check all that apply.

Dominik [7]

<u>Answer-</u>

YZ = 9 cm
$XZ=9\sqrt2$
XZ is the longest segment in triangle XYZ.

<u>Solution-</u>

Triangle XYZ is a right angle triangle with ∠Y=90°

Triangle XYZ is also an isosceles triangle, as

∠X =45°= ∠Z

Therefore, triangle XYZ is a right angle isosceles triangle.

So,

XY = YZ = 9 cm

Applying Pythagoras theorem,

$\Rightarrow XZ^2=XY^2+YZ^2\\\\\Rightarrow XZ^2=9^2+9^2\\\\\Rightarrow XZ^2=2\times 9^2\\\\\Rightarrow XZ=\sqrt{2\times 9^2}=9\sqrt2$

In a right angle triangle, always the hypotenuse is the largest. So XZ is the longest segment in triangle XYZ.

6 0

3 years ago

Read 2 more answers

Hey can you please help me posted picture of question

ipn [44]

The number of roots of a quadratic function can be determined from its discriminant.

If Disc> 0, the function has two distinct roots
If Disc = 0, the function has a repeated root
If Disc < 0, the function has no real root.

The discriminant can be calculated as:

Disc = b² - 4ac

For the given equation:

Disc = 9 - 4(2)(1) =1

Since the value of discriminant is positive, the function will have two distinct roots.

So, the answer to this question is option B

7 0

3 years ago

X^+17x+72=12 factoring quadratic equation

Tom [10]

Answer:

The first term is, x2 its coefficient is 1 .

The middle term is, -17x its coefficient is -17 .

The last term, "the constant", is +60

Step-1 : Multiply the coefficient of the first term by the constant 1 • 60 = 60

Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -17 .

-60 + -1 = -61

-30 + -2 = -32

-20 + -3 = -23

-15 + -4 = -19

-12 + -5 = -17 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -5

x2 - 12x - 5x - 60

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-12)

Add up the last 2 terms, pulling out common factors :

5 • (x-12)

Step-5 : Add up the four terms of step 4 :

(x-5) • (x-12)

Which is the desired factorization

Equation at the end of step

(x - 5) • (x - 12) = 0

STEP

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x-5 = 0

Add 5 to both sides of the equation :

x = 5

Solving a Single Variable Equation:

2.3 Solve : x-12 = 0

Add 12 to both sides of the equation :

x = 12

Supplement : Solving Quadratic Equation Directly

Solving x2-17x+60 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-17x+60

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 8.5000

Plugging into the parabola formula 8.5000 for x we can calculate the y -coordinate :

y = 1.0 * 8.50 * 8.50 - 17.0 * 8.50 + 60.0

or y = -12.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-17x+60

Axis of Symmetry (dashed) {x}={ 8.50}

Vertex at {x,y} = { 8.50,-12.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 5.00, 0.00}

Root 2 at {x,y} = {12.00, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2-17x+60 = 0 by Completing The Square .

Subtract 60 from both side of the equation :

x2-17x = -60

Now the clever bit: Take the coefficient of x , which is 17 , divide by two, giving 17/2 , and finally square it giving 289/4

Add 289/4 to both sides of the equation :

On the right hand side we have :

-60 + 289/4 or, (-60/1)+(289/4)

The common denominator of the two fractions is 4 Adding (-240/4)+(289/4) gives 49/4

So adding to both sides we finally get :

x2-17x+(289/4) = 49/4

Adding 289/4 has completed the left hand side into a perfect square :

x2-17x+(289/4) =

(x-(17/2)) • (x-(17/2)) =

(x-(17/2))2

Things which are equal to the same thing are also equal to one another. Since

x2-17x+(289/4) = 49/4 and

x2-17x+(289/4) = (x-(17/2))2

then, according to the law of transitivity,

(x-(17/2))2 = 49/4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x-(17/2))2 is

(x-(17/2))2/2 =

(x-(17/2))1 =

x-(17/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x-(17/2) = √ 49/4

Add 17/2 to both sides to obtain:

x = 17/2 + √ 49/4

Since a square root has two values, one positive and the other negative

x2 - 17x + 60 = 0

has two solutions:

x = 17/2 + √ 49/4

x = 17/2 - √ 49/4

Note that √ 49/4 can be written as

√ 49 / √ 4 which is 7 / 2

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2-17x+60 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

In our case, A = 1

B = -17

C = 60

Accordingly, B2 - 4AC =

289 - 240 =

Applying the quadratic formula :

17 ± √ 49

x = —————

Can √ 49 be simplified ?

Yes! The prime factorization of 49 is

7•7

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 49 = √ 7•7 =

± 7 • √ 1 =

± 7

So now we are looking at:

x = ( 17 ± 7) / 2

Two real solutions:

x =(17+√49)/2=(17+7)/2= 12.000

or:

x =(17-√49)/2=(17-7)/2= 5.000

Two solutions were found :

x = 12

x = 5

Step-by-step explanation:

please mark my answer in brainlist

8 0

3 years ago

Brittany opened a savings account with an annual interest rate of 10% and an initial deposit of $7000. If her interest is compou

GenaCL600 [577]

Initial Deposit = $7000

It means P= $7000

rate of interest = 10%

So , r = 0.10

compounded quarterly , so n = 4

and we have to find the amount after 5 years , So t = 5

Now the formula we use here is

$A= P(1+\frac{r}{n} )^{nt}$

$A= 7000(1+\frac{0.10}{4} )^{(4)(5)}$

$A= 7000(1.025 )^{(20)}$

$A= 7000(1.63861644029)$

$A= 11470.315$

So amount after 5 years = $11470.315

5 0

4 years ago

Read 2 more answers

Imagine a world in which only decimals, not fractions, are used. How would your life be different?

nataly862011 [7]

I used to hate fractions. But in time, you learn to love them. This is because there's a big difference between fractions and decimals, even though when you divide the actual fraction it comes out to a decimal. Decimals go on and on sometimes, and it would be impossible to write out all those numbers, especially when taking a timed test, for example. Fractions, in this case, would be much more useful (as long as you know how to use them to your advantage). Fractions are basically all those decimal numbers wrapped up into a single, simple division. It makes the outcome of your answer much more accurate than if you estimate every decimal you get throughout a math problem. The more you estimate throughout the problem-solving process, the less accurate your final answer will be. Hence why teachers will usually tell you to estimate when you're putting down the final answer. Fractions are complex at times, so it may be easier to use them in decimal form for certain situations (especially if the decimal form is short and sweet). A world without fractions will result in many, many inaccurate situations involving mathematical knowledge.

3 0

3 years ago