Solve for X
130, 40, ?

The scale factor of the enlargement will be 3. Then the center of enlargement is marked in the diagram.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

Shape A is enlarged to give shape B.

Then the scale factor of the enlargement will be

⇒ 3 / 1

Then the center of enlargement is marked in the diagram.

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Answer:

+ 10.53 % change

Step-by-step explanation:

Percent change is   4 more people added to 38

   4 / 38  * 100% = 10.53 %

Answer:

Step-by-step explanation:

there is no root in denominator so I think it is rationalised

Answer:

60

Step-by-step explanation:

2hrs = 120

120/30= 4

4×15=60

Answer:

60 pages :)

Step-by-step explanation:

First we turn the hours into minutes to make it easier :)

1 hr = 60 minutes

2 hrs = 120 minutes

Now that we have done that, we divide :)

120/30 =4

And now we multiply 1 more time :)

4 x 15 = 60

Have an amazing day!!

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Answer:

-3

Step-by-step explanation:

The points (3,-4) and (1,2) lie on the line.

m = (-4-2)/(3-1) = -3

True. We can probably expect that yacht sales will go down and the government will not collect lots of new tax revenues.

It is given that the US government has put a 20% luxury tax and the price elasticity for these yachts is elastic at 2.50.

Due to the new tax on luxury goods, it can be estimated that the sales of yachts go down as the maximum retail price of the yachts will become more expensive. This can mean that fewer people than before will be able to afford the yachts. Due to fewer sales, the government will not have enough tax revenues.

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Answer:

17.7 (2 dp)

Step-by-step explanation:

[tex] \sqrt{ {16}^{2} + {7.5}^{2} }[/tex]

Answer:

5.1% (nearest tenth)

Step-by-step explanation:

Annual Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for r:

[tex]\implies \sf 2209=2000\left(1+r\right)^{2}[/tex]

[tex]\implies \sf \dfrac{2209}{2000}=(1+r)^2[/tex]

[tex]\implies \sf 1.1045=(1+r)^2[/tex]

[tex]\implies \sf \sqrt{1.1045}=1+r[/tex]

[tex]\implies \sf r = \sqrt{1.1045}-1[/tex]

[tex]\implies \sf r = 0.05095194942...[/tex]

[tex]\implies \sf r = 5.095194942...\%[/tex]

Therefore, the annual interest rate is 5.1% (nearest tenth)

Answer:

putting the values of coordinates in equation to check for the solution.

For A

2x + y < 10

2(-5) + 4 < 10.

-10 - 4 < 10

-14 < 10 ( true)

2x - 4y > 8

2(-5) - 4(4) > 8

-10 - 16 > 8

-26 > 8

false..

it is not the solution of the equation.

similarly we can find for other coordinates.

E is the solution

The solution to the given quadratic expression is x = -1 and x = 5

Given the quadratic equation below

f(x) = x^2 - 4x - 5

Factorize

f(x) = x^2 - 5x + x - 5 = 0
f(x) = x(x - 5) + 1(x - 5) = 0
(x+1)(x-5) = 0
x = -1 and x = 5

Hence the solution to the given quadratic expression is x = -1 and x = 5

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Answer:

x = -1; x = 5

Step-by-step explanation:

Standard Form of a Quadratic Function: f(x) = ax² + bx + c, where a ≠ 0

Given function: f(x) = x² - 4x - 5

⇒ a = 1, b = -4, c = -5

We are asked to solve the following function by factoring. In order to do so, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = -5) and give us the sum of the middle term (b = -4).

Factors that give a product of a • c: 1 • -5 = -5

Factors that give a sum of b: 1 + (-5) = -4

Step 1: Substitute f(x) = 0.

⇒ 0 = x² - 4x - 5

Step 2: Rewrite the equation with the factors.

⇒ 0 = x² + x - 5x - 5

Step 3: Factor out x and -5.

⇒ 0 = (x² + x) + (-5x - 5)

⇒ 0 x(x + 1) - 5(x + 1) [ Factor out the common factor. ]

⇒ 0 = (x - 5)(x + 1)

Step 4: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0)

a) 0 = x - 5 ⇒ 0 + 5 = x - 5 + 5 ⇒ 5 = x

b) 0 = x + 1 ⇒ 0 - 1 = x + 1 - 1 ⇒ -1 = x

Therefore, the missing solution for this quadratic function is x = 5.

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The area of the octagon having an apothem of 6 meters and a side length of 7 meters is 168 meter square

Using the formula:

Area of an octagon = perimeter * apothem / 2

Note that perimeter of an octagon = 8 a

where a is the length of it's side

Perimeter = 8 * 7

Perimeter = 56 meters

Apothem = 6 meters

Substitute into the formula

Area = 56 * 6/ 2

Area = 336 / 2

Area = 168 meter square

Thus, the area of the octagon is 168 meter square

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Answer:

The mean will increase more than the median, but both will increase.

[third option listed]

Step-by-step explanation:

the median of a data set is the number in the middle [when listed from lowest to highest in value]

1 2 3 4 5 6 7 8 9 10 11 12 13

is the current median

let's consider what adding 12 would mean--it would mean that we move the median slightly higher [further along in the data set] because there are more numbers (but let's try this out to confirm:)

1 2 3 4 5 6 7 8 9 10 11 12 12 13

[if a median placement is shared between two numbers, the mean/average of those two numbers is taken, and that is considered to be the median]

so, 7.5 is the current median

(this is an increase of 0.5)

--

the mean of a data set is what we commonly refer to as the "average"

[you find this value by adding all of the numbers in the data set together and dividing by the number of terms in the data set]

1 2 3 4 5 6 7 8 9 10 11 12 13

mean of original data set:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 [= 91]

_______________________________________

                                    13

[91 ÷ 13 = 7]

because our number is greater than our original mean [12 > 7], we know that the mean must increase:

[91 + 12 = 103]

[103 ÷ 14 ≈ 9.36]

[we had an increase of 2.36]

so, median increased by 0.5, mean increased by 2.36

so, both values increased, whilst the mean increased by more than the median [as to be expected]

you could also express this as "The mean will increase more than the median, but both will increase." [third option listed]

hope this helps!! :)

AC is equal to BC by the corresponding side of a congruent triangle.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

The midpoint of a line segment means a point that lies in the mid of the given line segment.

If D is the midpoint of segment AB, then AD = BD.

So in a triangle ACD and BCD

AD = BD (by midpoint D)

angle ADC = angle BDC = 90

CD = CD (common)

Therefore, triangle ACD and BCD are congruent.

Hence, AC = BC by the corresponding side of a congruent triangle.

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Answer:

x is 48 and y is 100

Step-by-step explanation:

Angle y = 100 degree

Angle x = 48 degree

The correct option is k(x) = 5x - (5-x)

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, the given functions are;

g(x) = 5x                  h(x) = 5 - x

Now,

        k(x) = (g - h)(x)

        k(x) = g(x) - h(x)

        k(x) = 5x - (5 - x)

Thus, the correct option is k(x) = 5x - (5-x).

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negative number taken to an odd power gives a negative result (because, after cancelling, there will be one minus sign left over).

the answer is always. negative numbers raised to odd powers remain negative. negative numbers raised to even powers become positive.

Answer:

The sum of the polynomials is a 7th degree polynomial.

The difference of the polynomials is a 7th degree polynomial.

Step-by-step explanation:

Janie's polynomial is a 3rd degree with only x terms. Maybe she wrote:

f(x) = x^3

or maybe she was fancy and wrote:

f(x) =

x^3 + 2x^2 - 7x + 4

could be anything really, but the biggest exponent is 3.

Then Max does like:

g(x) = x^7

or

g(x) = x^7-x^4-3x+2

Whatever he made up, but the biggest exponent is 7.

So if they add or subtract their two polynomials, there's no x^7 in Janie's to add with the x^7 in Max's. MAYBE Max put some x^3 or x^2 or x or constants that might combine with the terms in Janie's.

Either way, anything that Max put in his polynomial that is a bigger power than 3 (4th, 5th, 6th, or 7th power) is just going to end up in the sum or difference.

Using it's concept, it is found that the probabilities are given as follows:

a) 0.0527 = 5.27%.

b) 0.0088 = 0.88%.

c) 0.0098 = 0.98%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Item a:

6 out of 16 songs are of the Beatles, hence the probability of a single music being from the Beatles is:

[tex]pB = \frac{6}{16} = \frac{3}{8}[/tex]

Of three musics, the probability is:

[tex]p = \left(\frac{3}{8}\right)^3 = 0.0527[/tex]

Item b:

For the Rolling stones, the probability is:

[tex]pR = \frac{4}{16} = \frac{1}{4}[/tex]

For the four musics, the probability is:

[tex]p = \left(\frac{1}{4}\right)^2 \times \left(\frac{3}{8}\right)^2 = 0.0088[/tex]

Item c:

For the doors, the probability is:

[tex]pD = \frac{2}{16} = \frac{1}{8}[/tex].

For Beatles or Rolling stones, the probability is:

[tex]pBR = \frac{10}{16} = \frac{5}{8}[/tex]

For the three musics, the probability is:

[tex]p = \left(\frac{1}{8}\right)^2 \times \frac{5}{8} = 0.0098[/tex]

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Answer:

equate two simultaneous equations for r and solve

Answer:

14a+2

Step-by-step explanation:

Perimeter of a rectangle: P=2(l+w) where l=length and w=width.

So P=2[(4a-1)+(3a+2)]=2(4a-1+3a+2)=2(4a+3a-1+2)=2(7a+1)=14a+2.

The expression to find the perimeter of the rectangle is 14a + 2.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

Given that,

Sides of a rectangle is represented as 4a - 1 and 3a + 2.

Perimeter of a rectangle is represented as,

Perimeter = 2 (l + w)

Here l is the length and w is the width.

Substituting,

Perimeter = 2 (4a - 1 + 3a + 2)

                = 2(7a + 1)

                = 14a + 2

Hence the expression to find the perimeter is 14a + 2.

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Answer:

2

Step-by-step explanation:

[tex]a+b=-5[/tex]

[tex]-(a+b)=-a-b=5[/tex]

[tex]\frac{|-5| + 5}{|5|}[/tex]

[tex]\frac{5+5}{5}[/tex]

[tex]2[/tex]

Answer:

2

Step-by-step explanation:

Given:

To find -a - b  

Factor out the common term -1:

⇒ -a - b = -(a + b)

Substitute a + b = -5:

⇒ -a - b = -(-5)

Apply rule -(-x) = x:

⇒ -a - b = 5

Therefore:

[tex]\begin{aligned}\implies \sf \dfrac{|a+b|+5}{|-a-b|} & = \sf \dfrac{|-5|+5}{|5|}\\\\& = \sf \dfrac{5+5}{5}\\\\& = \sf \dfrac{10}{5}\\\\& = \sf 2\end{aligned}[/tex]

Note:  |-x| = x

Answer: 10

Step-by-step explanation:

√( 7^2 + 7^2 ) = 10

Answer:

B.

Step-by-step explanation:

if x is 3 then you just substitue every instance of x as 3. 2(x-4) + 3x - x^2 =

2(3 - 4) + 3(3) - 3^2 =

6-8 + 9 - 9 =

-2

Answer: No answer

Step-by-step explanation:

You can calculate for x, because the equation isn't equal to anything.

[tex]\dfrac{6\sqrt 3~ \text{cis} \left( \dfrac{7 \pi} 6 \right)}{3 \sqrt 5 ~\text{cis} \left( \dfrac{\pi}{3}\right)}\\\\\\=\dfrac{2\sqrt 3 \cdot e^{i\tfrac{7\pi}{6}}}{\sqrt 5\cdot e^{i \tfrac{\pi}{3}}}\\\\\\=\dfrac{2 \sqrt 3}{\sqrt 5} \cdot \left(e^i \right)^{\tfrac{7\pi}{6} - \tfrac{\pi }{3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\text{cis}~ \theta = e^{i \theta}\right]\\\\\\=\dfrac{2 \sqrt{3}}{\sqrt 5} \cdot \left(e^i\right)^{\tfrac{5\pi}6}\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\cdot e^{i\tfrac{5 \pi}6}\\\\\\[/tex]

[tex]=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ \cos \left(\dfrac{5\pi}{6}\right) + i \sin \left(\dfrac{5\pi}{6}\right) \right]~~~~~~~~~~~~~~~~~~;\left[e^{i\theta} = \cos \theta + i \sin \theta} \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\left[ \cos \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) + i\sin \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ -\cos \left(\dfrac{\pi}{6}\right) + i \sin \left(\dfrac{\pi}{6}\right) \right]\\\\\\[/tex]

[tex]=\dfrac{2\sqrt{3}}{\sqrt 5}\left( -\dfrac {\sqrt{3}}{2} + i \cdot \dfrac 12 \right)\\\\\\=-\dfrac{3}{\sqrt 5} + i \dfrac{\sqrt 3}{\sqrt 5}[/tex]

Answer:

Step-by-step explanation:

Just took the test:

6sqrt3 cis (7pie/6)/ 3sqrt5 cis (pie/3)=

2sqrt15/5 cis (5pie/6)

When you acquire stock in a firm, you are acquiring a little portion of that company known as a share. The correct option is A.

When you acquire stock in a firm, you are acquiring a little portion of that company known as a share. Investors buy stocks in firms they believe will increase in value. If this occurs, the value of the company's shares rises as well.

For a 70-year-old investor, selling a weak stock at a loss may be a smart move to avoid potential additional future losses.

Hence, the correct option is A.

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Step-by-step explanation:

Answer:

d) 150%

Step-by-step explanation:

[tex]x=25*300\%=25*3=75\\[/tex]

[tex]y=25\%*40+40=50[/tex]

[tex]x/y*100\%=75\div50*100\%=150\%[/tex]

Answer:d

150%

Step-by-step explanation: