which of the following is the product of the rational expressions still here?

Changing the exponent by 1/2 ( going from x to 1/2x)

This does not change the y-intercept.

It does sharpen the curve, which means the y value does not increase as quickly when x is increased.

THe 3rd choice is correct.

Proof: make x=2

Y = 3^2 = 9

Y = 3^1/2(2) = 3^1 = 3

You can see y is smaller with the 1/2 included.

Answer:

1. 38.3 x 10^5

2. 6.67 x 10^9

3. 4.48 x 10^4

Step-by-step explanation:

4.2 X 10 ^6 - 1.2 X 10^5 - 2.5 x 10^5

For the above question, we need to make the exponents equal

=> 42 x 10^5  -  1.2 x 10^5  -  2.5 x  10^5

SInce, all the exponents are equal, we can now add and subtract the normally.

=> (42 - 1.2 -2.5) x 10^5

=> (42 - 3.7) x 10^5

=> 38.3 x  10^5

So, the answer to the 1st question is 38.3 x 10^5

Next question:

=> 3.3 x 10^9 + 2.6 x 10^9 +7.7 x 10^8

=>  we need to make the exponents equal

=> 3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9

=> All the exponents are equal, we can now add and subtract the normally.

=> (3.3 + 2.6 + .77) x 10^9

=> 6.67 x 10^9

=> So the answer to the 2nd question is 6.67 x 10^9

Next question,

=> 8 X 10^4 - 3.4 x 10^4  - 1.2 x 10^3

=> we need to make the exponents equal

=> 8 x 10^4 - 3.4 x 10^4 - .12 x 10^4

=> All the exponents are equal, we can now add and subtract the normally.

=> (8 - 3.4 - .12) x 10^4

=> 4.48 x 10^4

=> So the answer to the 3rd question is 4.48 x 10^4

The solutions to the expressions are:

[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]=[tex]38.3\times 10^5[/tex]

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex] = [tex]6.67\times 10^9[/tex]

[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex] = [tex]4.48 \times 10^4[/tex]

[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]

Combine like terms:

[tex]4.2 \times 10^6 - (1.2+2.5) \times 10^5[/tex]

[tex]4.2 \times 10^6 - 3.7 \times 10^5[/tex]

[tex]42 \times 10^5 - 3.7 \times 10^5[/tex]

[tex](42-3.7)\times 10^5[/tex]

[tex]38.3\times 10^5[/tex]

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex]

Convert all terms with same power:

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 0.77 \times 10^9[/tex]

[tex](3.3+2.6+0.77) \times 10^9[/tex]

[tex]6.67\times 10^9[/tex]

[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex]

[tex]8.0 \times 10^4 - 3.4 \times 10^4 - 0.12 \times 10^4[/tex]

[tex](8.0-3.4-0.12) \times 10^4[/tex]

[tex]4.48 \times 10^4[/tex]

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Answer:

B

Step-by-step explanation:

f(x) = x+5 when x>0. f(5)=10

Answer:

C

Step-by-step explanation:

C is the set with whole numbers as it contains 0 and natural numbers

Answer:

Constant

Step-by-step explanation:

Whole numbers are numbers like 1,2,3 and 4.

1.1,2.3 and Pi arent't whole numbers. Fractions like 3/4 and 5/3 aren't whole numbers.

The whole numbers starting from 5 to 7 are:

● 5, 6 and 7

You can see that we have only one whole number between 5 and 7 wich is 6.

So m has only one value (m=6).

=> m is a constant

Answer:

the answer must be 7/4 because

Step-by-step explanation:

1 3/4 4×1+3=7

Answer:

Step-by-step explanation:

[tex]9^{-4}[/tex]

=[tex]\frac{1}{9^{4} }[/tex]                   ∴     [tex]x^{-n} = \frac{1}{x^{n} }[/tex]

=[tex]\frac{1}{9*9*9*9}[/tex]

=[tex]\frac{1}{6561}[/tex]

sin O = 1/2 = p/h

p=1, h = 2.

by pythagoras tgeorem,

b =

[tex] \sqrt{3} [/tex]

tan0= p/b

[tex]1 \div \sqrt{3} [/tex]

Answer:

3

Step-by-step explanation:

2 tangents of a circle drawn from an external point are said to be congruent, according to the two-tangents theorem. Thus:

MN = ML (both tangents from external point M)

ML = 6 - KL

KL = KJ (tangents from point K)

PQ = QJ = 1 (tangents from point Q)

Therefore, KJ = 4 - 1 = 3

Since kJ = KL = 3,

ML = 6 - KL = 6 - 3

ML = MN = 3

Answer:

# 28750

Step-by-step explanation:

Intrest = P. A. * Intrest Rate * Time

Intrest = 250000 * 11.5/100 = 28750

Answer: Infinitely many solutions

Step-by-step explanation:

The lines is on top of each other so this makes it many solution.

It can't be NO solution because the lines are not parallel  to each, which means  they will not intersect.

It  can't be one solution because the lines doesn't intersect.

It can't be two solutions because the lines never intersect and they never intersect twice either.

Answer:

[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]

Step-by-step explanation:

Given:

Focus of parabola: (-4, 6)

Directrix: y = 2

Required:

Equation for the parabola

Using the formula, [tex] y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) [/tex] , the equation for the parabola can be derived.

Where,

a = -4

b = 6

k = 2

Plug these values into the equation formula

[tex] y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) [/tex]

[tex]y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)[/tex]

[tex]y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}[/tex]

[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]

Answer:

uhfcytuyyytt ryffffffffgtgghhh

Answer:

Hey there!

4^2-2(3(5)+1)

16-2(15+1)

16-2(16)

-16

C is correct.

Let me know if this helps :)

Answer:

Step-by-step explanation:

[tex] \mathsf{ {4}^{2} - 2(3 \times 5 + 1)}[/tex]

Evaluate the power

⇒[tex] \mathsf{16 - 2(3 \times 5 + 1)}[/tex]

Multiply the numbers

⇒[tex] \mathsf{16 - 2(15 + 1)}[/tex]

Calculate the sum

⇒[tex] \mathsf{16 - 2 \times 16}[/tex]

Multiply the numbers

⇒[tex] \mathsf{16 - 32}[/tex]

Calculate

⇒[tex] \mathsf{ - 16}[/tex]

Hope I helped!

Best regards!

This are a few of Rational numbers are not whole numbers: 8,−3,32,7−5.

Step-by-step explanation: Hope this helps

Answer: 35%

Step-by-step explanation: It grows 3.5% every year. A decade is 10 years. 10 x 3.5% = 35% because you move the decimal one point to the right.

The population grows 41.1% per decade. Therefore, option B is the correct answer.

If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.

Given that, a population grows 3.5% per year.

Now, D(n)=P(1+R/100)ⁿ

Let P=1

So, D(1)=1(1+0.035)¹

D(1)=1.035

Similarly per 10 years with the same rate

D(10)=1(1+0.035)¹⁰

= (1.035)¹⁰

= 1.41059

= 1.411-1 (Initial population is 1)

= 0.411

= 0.411×100

= 41.1%

The population grows 41.1% per decade. Therefore, option B is the correct answer.

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Answer:

[tex]\huge\boxed{10.4\ units\²}[/tex]

Step-by-step explanation:

Area of circle:

=> [tex]\pi r^2[/tex]

Where r = 2.8

=> [tex](3.14)(2.8)^2[/tex]

=> (3.14)(7.84)

=> 24.6 units²

Area of Triangle:

=> 1/2 (Base)(Height)

=> 1/2 (10)(7)

=> 5 * 7

=> 35 units²

Area of the shaded region:

=> 35 - 24.6

=> 10.4 units²

Answer:

x=5

y=2

w= -5

Step-by-step explanation:

We have that the two matrix are equal, so all corresponding elements are equal.

X-Y=3

From the second row and second column, we have y=2

so x-2=3

x=5

From the third row and the first column, we have w= - 5

Step-by-step explanation:

[tex]3x + 3x + 1 + 3x + 2 = 39 \\ 9x + 3 = 39 \\ 9x = 39 - 3 \\ 9x = 36 \\ x = \frac{36}{9} \\ x = 4[/tex]

Answer:

x = 4

Step-by-step explanation:

combine all of the 3x first to get:

9x + 1 + 2 = 39

9x + 3 = 39

subtract 3 from both sides:

9x = 36

divide by 9

x = 4

Answer:

(0.5,3)

Hope this helps..Have a good day!!

Two lines are parallel if they are equidistant from one another. The following proves [tex]a || m[/tex]

[tex]Ratio = 1:3[/tex] means that:

[tex]BP=3PA[/tex]

[tex]BQ=3QC[/tex]

To prove that [tex]a || m[/tex] is to prove that side length SR and side length PQ are parallel because:

[tex]SR = a\\ PQ = m[/tex] --------- See attachment for quadrilateral

Considering [tex]\triangle ABC[/tex], we have: [tex]BP=3PA[/tex]

Divide both sides by PA

[tex]\frac{BP}{PA} = \frac{3PA}{PA}[/tex]

[tex]\frac{BP}{PA} = 3[/tex]

Similarly: [tex]BQ=3QC[/tex]

Divide both sides by QC

[tex]\frac{BQ}{QC} = \frac{3BQ}{QC}[/tex]

[tex]\frac{BQ}{QC} = 3[/tex]

So, we have:

[tex]\frac{BP}{PA} = \frac{BQ}{QC} = 3[/tex]

Express as ratios

[tex]BP:PA = BQ:QC = 3[/tex]

[tex]BP:PA \to[/tex] means point P divided side length BA into 3:1

[tex]BQ:QC \to[/tex] means point Q divided side length BC into 3:1

Thales Theorem states that: A line that divides any two sides of a triangle in the same ratio is parallel to the third side.

The third side of [tex]\triangle ABC[/tex] is [tex]AC[/tex].

This means that: [tex]PQ[/tex] is parallel to [tex]AC[/tex]

Since [tex]AC[/tex] is parallel to [tex]SR[/tex], then [tex]PQ[/tex] is parallel to [tex]SR[/tex]

i.e. [tex]SR || PQ[/tex]

Recall that:

[tex]SR = a\\ PQ = m[/tex]

Hence:

[tex]a || m[/tex] has been proved.

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10 more

The number of seventh-graders that must join the club in order to meet the president's wishes is 10.

Since there are 45 eighth graders and 20 seventh graders in a school club and the president of this club wants 40% of the club’s members to be seventh graders, we need to find the number of seventh graders that will be added to the school club to make their percentage 40 %.

Let the number of seventh-graders to be added be x.

So, the new number of seventh-graders is 20 + x and the new number of people in the club is 45 + 20 + x = 65 + x

Thus, the percentage of seventh graders in the club is thus

[tex]\frac{20 + x}{65 + x} X 100[/tex] %

Since this percentage equals 40 %, we have that

[tex]\frac{20 + x}{65 + x} X 100[/tex]% = 40 %

[tex]\frac{20 + x}{65 + x} = \frac{40}{100} \\\frac{20 + x}{65 + x} = 0.4[/tex]

Cross-multiplying we have

[tex]20 + x = 0.4(65 + x)[/tex]

Expanding the bracket, we have

[tex]20 + x = 26 + 0.4x[/tex]

Subtracting 20 from both sides we have

[tex]x = 26 - 20 + 0.4x\\x = 6 + 0.4x[/tex]

Subtracting 0.4x from both sides, we have

[tex]x - 0.4x = 6\\0.6x = 6[/tex]

dividing both sides by 0.6, we have

x = 6/0.6

x = 10

So, the number of seventh-graders that must join the club in order to meet the president's wishes is 10.

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Answer:

a) [tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]

b) (i) [tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]

   (ii) [tex]k=2[/tex]

Step-by-step explanation:

It is given that,

[tex]a=\begin{pmatrix}4\\-10\end{pmatrix},b=\begin{pmatrix}-2\\1\end{pmatrix},c=\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

a)

We need to find the value of a+b+c.

[tex]a+b+c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

[tex]a+b+c=\begin{pmatrix}4+(-2)+(-4)\\-10+1+6\end{pmatrix}[/tex]

[tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]

b)

(i) We need to find the value of a+2c.

[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+2\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-8\\12\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}4+(-8)\\-10+12\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]

(ii) It is given that a+2c=kb, where k is an integer. We need to find the value of k.

[tex]a+2c=k\begin{pmatrix}-2\\1\end{pmatrix}[/tex]

[tex]\begin{pmatrix}-4\\2\end{pmatrix}=\begin{pmatrix}-2k\\k\end{pmatrix}[/tex]

On comparing both sides, we get

[tex]k=2[/tex]

Answer:

142

Step-by-step explanation:

The exterior angle of a triangle is equal to sum of the opposite interior angles

x = 52+90

x = 142

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

[tex]\large\bf{{\purple{ \longrightarrow \:\large\rm \: x \: = \: 52 \degree \: + \: 90 \degree }}} \\ [/tex]

[tex]\large\bf{{\purple{ \longrightarrow \:\large\rm \: x \: = \: 142 \degree }}} \\ [/tex]

Answer:

47°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles

124° is an exterior angle , thus

77 + ? = 124 ( subtract 77 from both sides )

? = 47°

Answer:

The random variable [tex]\bar x[/tex] has approximately a normal distribution because of the central limit theorem.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n ≥ 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

Let the random variable X be defined as the age of cars owned by residents of a small city.

It is provided that:

μ = 6 years

σ = 2.2 years

n = 400

As the sample selected is too large, i.e. n = 400 > 30, according to the central limit theorem the sampling distribution of the sample mean ([tex]\bar x[/tex]) will be approximately normally distributed.  

Answer:

144 cm²

Step-by-step explanation:

This figure is formed by rectangles and triangles, so we need to find the surface area of they and add all to have the surface area of the figure:

area of the rectangles:

4×3 = 12, and there are two of these rectangles

6×3 = 18, and there are just one of that

4×6 = 24, and there are two of these

5×3 = 15, and there are two of these

Now the area of a triangle:

6×4/2 = 12, and there are two of these

12×2 + 18 + 24×2 + 15×2 + 12×2 = 144 cm²

Step-by-step explanation:

Hey, there!!!

Let me explain you very simply,

The equation is;

y= -2/3 x +1/3

Now, we know the equation of a st.line in slope intercept form is,

y= m.x + c

now, comparing the given equation with y= m.x + c. we get,

m= -2/3

and y-intercept = 1/3.

Hope it helps...

Answer:

The correct answer is

Step-by-step explanation:

Answer:

Red Team

Step-by-step explanation: