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3 years ago

Could someone answer and explain these to me? That would be great, thanks!

Mathematics

2 answers:

Flura [38]3 years ago

6 0

Answer:

y=-x^2

Step-by-step explanation:

given that y = x^2 is the function.

For equivalent to -y, we can multiply this equation both the sides by -1

We get -y = -x^2

Hence option G is right.

Also y =x^2 is a parabola with vertex at origin open up.

Hence if F is selected we get -y =(-x)^2 = x^2, this will make the parabola open down and hence this option is wrong.

H: -y=-x is wrong because this represents a line but we had original equation as that of a parabola

J) -y = x^(-2) means x^2y =-1

This implies that rate of change of y = 2/x^3 but rate of change of y has to equal 2x since y = x^2 is original. Hence only option G is right.

pav-90 [236]3 years ago

6 0

These are two questions and two answers.

Question 1. When y = x², which of the following expressions is equivalent to - y?

Answer: the option G. -x².

Explanation:

The important thing is to be careful with the use of the negative sign before the function because a typical mistake is to incorporate the negative sign inside the parentheses, which yields to square it resulting, mistakenly, in a positive value.

The correct steps are:

Given y = x², find - y

Muliply both sides of the equation by - 1: - y = - (x²)

Delete the negative sign before the parentheses: - y = - x².

So, the answer is the option G.

Question 2. For the function h(x) = 4x² - 5x, what is the value of h(-3)?

Answer: option D. 51

Explanation:

Since, you have the explicit function h(x), to find h(-3), you just must subsititute the variable x with -3.

This is how you do it:

Given: h(x) = 4x² - 5x

Find h(-3) ⇒ substitute x = - 3

h(-3) = 4(-3)² - 5(-3) = 4(9) + 15 = 36 + 15 = 51 ← answer (option D.)

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HELP ASAP!!!

Umnica [9.8K]

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(a)/(a^2-16)+(2/(a-4))-(2/(a+4))=0

Simplify ————— a + 4 Equation at the end of step 1 : a 2 2 (—————————+—————)-——— = 0 ((a2)-16) (a-4) a+4 Step 2 : 2 Simplify ————— a - 4 Equation at the end of step 2 : a 2 2 (—————————+———)-——— = 0 ((a2)-16) a-4 a+4 Step 3 : a Simplify ——————— a2 - 16 Trying to factor as a Difference of Squares :

3.1 Factoring: a2 - 16

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
 A2 - AB + BA - B2 =
 A2 - AB + AB - B2 =
 A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 16 is the square of 4
Check : a2 is the square of a1 

Factorization is : (a + 4) • (a - 4)

Equation at the end of step 3 : a 2 2 (————————————————— + —————) - ————— = 0 (a + 4) • (a - 4) a - 4 a + 4 Step 4 :Calculating the Least Common Multiple :

4.1 Find the Least Common Multiple

 The left denominator is : (a+4) • (a-4)

 The right denominator is : a-4

Number of times each Algebraic Factor
 appears in the factorization of: Algebraic
 Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} a+4 101 a-4 111

Least Common Multiple:
(a+4) • (a-4)

Calculating Multipliers :

4.2 Calculate multipliers for the two fractions

 Denote the Least Common Multiple by L.C.M
 Denote the Left Multiplier by Left_M
 Denote the Right Multiplier by Right_M
 Denote the Left Deniminator by L_Deno
 Denote the Right Multiplier by R_Deno

 Left_M = L.C.M / L_Deno = 1

 Right_M = L.C.M / R_Deno = a+4

Making Equivalent Fractions :

4.3 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. a —————————————————— = ————————————— L.C.M (a+4) • (a-4) R. Mult. • R. Num. 2 • (a+4) —————————————————— = ————————————— L.C.M (a+4) • (a-4) Adding fractions that have a common denominator :

4.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

a + 2 • (a+4) 3a + 8 ————————————— = ————————————————— (a+4) • (a-4) (a + 4) • (a - 4) Equation at the end of step 4 : (3a + 8) 2 ————————————————— - ————— = 0 (a + 4) • (a - 4) a + 4 Step 5 :Calculating the Least Common Multiple :

5.1 Find the Least Common Multiple

 The left denominator is : (a+4) • (a-4)

 The right denominator is : a+4

Number of times each Algebraic Factor
 appears in the factorization of: Algebraic
 Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} a+4 111 a-4 101

Least Common Multiple:
(a+4) • (a-4)

Calculating Multipliers :

5.2 Calculate multipliers for the two fractions

 Denote the Least Common Multiple by L.C.M
 Denote the Left Multiplier by Left_M
 Denote the Right Multiplier by Right_M
 Denote the Left Deniminator by L_Deno
 Denote the Right Multiplier by R_Deno

 Left_M = L.C.M / L_Deno = 1

 Right_M = L.C.M / R_Deno = a-4

Making Equivalent Fractions :

5.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. (3a+8) —————————————————— = ————————————— L.C.M (a+4) • (a-4) R. Mult. • R. Num. 2 • (a-4) —————————————————— = ————————————— L.C.M (a+4) • (a-4) Adding fractions that have a common denominator :

5.4 Adding up the two equivalent fractions

(3a+8) - (2 • (a-4)) a + 16 ———————————————————— = ————————————————— (a+4) • (a-4) (a + 4) • (a - 4) Equation at the end of step 5 : a + 16 ————————————————— = 0 (a + 4) • (a - 4) Step 6 :When a fraction equals zero : 6.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

a+16 ——————————— • (a+4)•(a-4) = 0 • (a+4)•(a-4) (a+4)•(a-4)

Now, on the left hand side, the (a+4) • (a-4) cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
a+16 = 0

Solving a Single Variable Equation :

6.2 Solve : a+16 = 0

Subtract 16 from both sides of the equation :
 a = -16

One solution was found :

a = -16

4 0

3 years ago

What is the equation of the line that passes through the point (5,-2)and has a slope of the fraction 6/5?

Tju [1.3M]

Answer:

6x-5y-40 = 0

Step-by-step explanation:

y-(-2)=6/5(x-5)

5(y+2)= 6(x-5)

5y+10 =6x-30

6x-5y-40 = 0

6x-5y-40 = 0 is the answer

5 0

3 years ago

41,373 rounded to the nearest thousand is

KengaRu [80]

Answer:

Step-by-step explanation:

41,000

6 0

3 years ago

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Ganezh [65]

Answer:

(a) 0.20

(b) 31%

Step-by-step explanation:

The random variable Y models the amount of time the subject has to wait for the light to flash.

The density curve represents that of an Uniform distribution with parameters a = 1 and b = 5.

So, $Y\sim Unif(1,5)$

(a)

The area under the density curve is always 1.

The length is 5 units.

Compute the height as follows:

$\text{Area under the density curve}=\text{length}\times \text{height}$

$1=5\times\text{height}\\\\\text{height}=\frac{1}{5}\\\\\text{height}=0.20$

Thus, the height of the density curve is 0.20.

(b)

Compute the value of P (Y > 3.75) as follows:

$P(Y>3.75)=\int\limits^{5}_{3.75} {\frac{1}{b-a}} \, dy \\\\=\int\limits^{5}_{3.75} {\frac{1}{5-1}} \, dy\\\\=\frac{1}{4}\times [y]^{5}_{3.75}\\\\=\frac{5-3.75}{4}\\\\=0.3125\\\\\approx 0.31$

Thus, the light will flash more than 3.75 seconds after the subject clicks "Start" 31% of the times.

(c)

Compute the 38th percentile as follows:

$P(Y$

Thus, the 38th percentile is 2.52 seconds.

4 0

3 years ago

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Anni [7]

Since the person didn't write the answer choices they were:

A. On average, city A was warmer than city B.

B. The median and mode are different for city B.

C. The temperature range between the maximum and minimum values for city A is greater than the temperature range between the maximum and minimum values for city B.

D. The median is less for city A than for city B.

I believe it is A personally cause i took the test and got it right

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4 years ago

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