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2 years ago

If A PQR = ASTU, which statement must be true?

Mathematics

1 answer:

Aleks [24]2 years ago

8 0

Answer:

O A. PQ = SU

Step-by-step explanation:

When two triangles are congruent then by CPCTC,

their corresponding parts ( angles and sides ) must be congruent.

In triangles PQR and STU,

Side PQ, QR and RP are corresponding to the sides ST, TU and US respectively,

Also, angles P, Q and R are corresponding to angles S, T and U respectively.

Here, Δ PQR ≅ Δ STU,

Thus, by the above property,

PQ ≅ ST, QR ≅ TU and RP ≅ US,

∠P ≅ ∠T, ∠Q ≅ ∠T and ∠R ≅ ∠U

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Given a function <img src="https://tex.z-dn.net/?f=f%28x%29%3D3x%5E4-5x%5E2%2B2x-3" id="TexFormula1" title="f(x)=3x^4-5x^2+2x-3"

Levart [38]

Answer:

$\huge\boxed{f(-1) = -7}$

Step-by-step explanation:

In order to solve for this function, we need to substitute in our value of x inside to find f(x). Since we are trying to evalue f(-1), we will substitute -1 in as x to our equation.

$f(-1) = 3(-1)^4 - 5(-1)^2 + 2(-1) - 3$

Now we can solve for the function by multiplying/subtracting/adding our known values.

Starting with the first term to the last term:

$3(-1)^4 = 3$

WAIT! How is this possible? $-1^4 = -1$ (according to my calculator), and $3 \cdot -1 = -3$ , not 3!

It's important to note that taking a power of a negative number and multiplying a negative number are two different things. Let's use $-2^2$ as an example.

What your calculator did was follow BEMDAS since it wasn't explicitly told not to.

BEMDAS:

- Brackets

- Exponents

- Multiplication/Division

- Addition/Subtraction

Examining the equation, your calculator used this rule properly. Note that exponents come over multiplication.

So rather than being "-2 squared" - it's "the negative of of 2 squared."

Tying this back into our problem, the squared method would only be true if it looks like $-1^4$ . However, since we're substituting in -1, it looks like $(-1)^4$ , so the expression reads out as "-1 to the fourth."

MULTIPLYING -1 by itself 4 times results in $-1\cdot-1\cdot-1\cdot-1=1$ .

Applying this logic to our original term, $3(-1)^4$ :

$3(-1\cdot-1\cdot-1\cdot-1)$
$3(1)$
$3$

Therefore, our first term is 3.

Let's move on to our second and third terms.

Second term: $-5x^2$

$-5(-1)^2$

Applying the same logic from our first term:

$-5(-1 \cdot -1)$
$-5(1)$
$-5$

Third term: $2x$

$2(-1) = -2$

-3 is just -3, no influence of x.

Combining our terms, we have $3-5-2-3$ .

This comes out to be -7, hence, the value of $f(-1)$ for our function $f(x)=3x^4-5x^2+2x-3$ is -7.

Hope this helped!

4 0

3 years ago

Read 2 more answers

Let x be normal distribution with mean 70 and standard deviation 2. given the following probability, p (x < a) = 0.9147, find

lapo4ka [179]

The value of a is 72.74.

<h3>What is Probability ?</h3>

Probability is the study of likeliness of an event to happen.

It is given that

The mean $\rm \mu$ of the distribution is 70

Standard deviation $\rm \sigma$ is 2

p( x<a) = 0.9147

a = ?

From Z table

For p ( p < 0.9147) , z = 1.37

$\rm Z = \dfrac { X - \mu}{ \sigma}$

$\rm \rm 1.37 = \dfrac { a - 70}{ 2}$

a = 70+ 2*1.37

a = 72.74

Therefore the value of a is 72.74.

To know more about Probability

brainly.com/question/11234923

#SPJ1

6 0

2 years ago

Two thirds of a number is 46, what is the number

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

If 46 is 2/3 then 1/3 should be 23 and 23 times 3 is 69.I hope this helps

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2 years ago

Write 34.996 to: i. 2 decimal places

Alinara [238K]

Answer:

34.996 to 2 dcp is 35.00

Step-by-step explanation:

6 rounds up 9 goes to 10 add the 1 left over to make the units number equal 5 but as it is decimal place remember to add the 0's

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3 years ago

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Mrs. Gomez is sewing a dress for each of her four daughters. Each dress uses 2.25 yards of fabric, and the fabric costs $4.15 pe

storchak [24]

If it is 2.25 yards per dress, and 4.15 a yard, multiply 2.25 by 4.15 and you get 9.3375 or just 9.34. if there are 4 girls, multiply 9.34 by 4 and you get $39.76

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3 years ago

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