Are the ratios 2:1 and 14:6 equivalent?
yes
no

The function f(x) is vertically compressed to form g(x)

The functions are given as

f(x) =x^2

g(x) =3x^2

Substitute f(x) =x^2 in g(x) =3x^2

g(x) =3f(x)

This means that the function f(x) is vertically compressed to form g(x)

See attachment for the function g(x)

Also, both functions have the same domain and range

The complete table is:

x      -2    -1    0   1    2

g(x)  12    3    0    3   12

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Answer:

The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

Step-by-step explanation:

* Lets explain how to solve it

- Decreasing function means a function with a graph that moves

downward as it is followed from left to right.

- For example, any line with a negative slope is decreasing function

- Lets look to the attached graph to understand the meaning of the

decreasing function

∵ f(x) = IxI ⇒ green graph

∵ g(x) = Ix + 1I - 7 ⇒ purple graph

- From the graph f(x) translated 1 unit to the left and 7 units down to

form g(x)

- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}

- The range of f(x) is {y : y ≥ 0}

- The range of g(x) is {y : y ≥ -7}

# For f(x)

- The slope of the green line from (-∞ , 0) is negative

- The slope of the green line from (0 , ∞) is positive

# For g(x)

- The slope of the purple line from (-∞ , -1) is negative

- The slope of the purple line from (-1 , ∞) is positive

∵ The line with negative slope represent decreasing function

∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

The boat speeds of 15 km/h and 18 km/h, directions, and the time of travel of 45 minutes gives the angle between their paths as approximately 68°.

The given parameters are;

Direction of the first boat = Northeast

Speed of the first boat = 15 km/h

Direction of the second boat = Northwest

Speed of the second boat = 18 km/h

Distance between the boats after 45 minutes = 14.0 km.

45 minutes = 0.75 × 1 hour

Distance traveled by the first boat in 45 minutes, d1, is therefore;

d1 = 15 km/h × 0.75 hr = 11.25 km

For the second boat, we have;

d2 = 18 km/h × 0.75 hr = 13.5 km

Using cosine rule, we have;

14² = 11.25² + 13.5² - 2 × 11.25 × 13.5 × cos(A)

Where A is the angle between the paths of the two boats.

Which gives;

[tex]cos(A) = \frac{361}{972} [/tex]

[tex] A= \mathbf{ arccos\left(\frac{361}{972} \right) }\approx 68^\circ [/tex]

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Answer:

y = 4x^2 + 8x - 12

4(x^2 + 2x - 3) = 0

4(x - 1)(x + 3) = 0

x = 1, -3

Answer:

[tex]\fbox {x-intercepts : (1, 0) and (-3, 0)}[/tex]

[tex]\fbox {Roots : x = 1, x = -3}[/tex]

Step-by-step explanation:

Given :

4 cancels throughout.

Solving by quadratic formula :

∴ Hence, the x-intercepts are (1, 0) and (-3, 0). The roots of the equation are 1 and -3.

Answer:

x=1/3

Step-by-step explanation:

The next line after computing the sample standard deviation is to; determine the 2.5th and 97.5th percentiles of the values.

It follows from the task content that the 95% confidence interval for the population standard deviation using the bootstrap method in which case, after numerous sampling, the 2.5th and 97.5th percentiles of the standard deviations are determined.

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Answer:

C

Step-by-step explanation:

[tex]\frac{x+1}{x-4}[/tex] × [tex]\frac{5x}{x+1}[/tex] ← cancel x + 1 on numerator and denominator

= [tex]\frac{1}{x-4}[/tex] × [tex]\frac{5x}{1}[/tex]

= [tex]\frac{5x}{x-4}[/tex]

Answer:

5x/(x-4)

Step-by-step explanation:

To multiply fractions, all we have to do is multiply the numerators together and the denominators together. If we do that, we get the following:

[tex]\frac{x+1}{x-4}*\frac{5x}{x+1}=\frac{(x+1)(5x)}{(x-4)(x+1)}[/tex]

We notice that both the numerator and the denominator have an (x+1) term. Whenever you have something divided by itself, you get 1. In other words, they cancel out. As such, we can remove them from our answer to simplify it:

[tex]\frac{5x}{x-4}[/tex]

If we do that, we get the expression above. 5x/(x-4) is the reduced product of the rational expression given.

1) Quadrilateral PAST, TX=AX, [tex]\overline{TP} \parallel\overline{AS}[/tex] (given)

2) [tex]\angle XPT \cong \angle XSA[/tex] and [tex]\angle XTP \cong \angle XAS[/tex] (alternate interior angles theorem)

3) [tex]\triangle TXP \cong \triangle AXS[/tex] (AAS)

4) [tex]\overline{TP} \cong \overline{AS}[/tex] (CPCTC)

5) PAST is a parallelogram (a quadrilateral with two pairs of opposite congruent sides is a parallelogram)

(Adding to the other person's answer)

For the 5th step reason, put this: A quadrilateral is a parallelogram if a pair of opposite sides are parallel and congruent.

It won't work to just say something like the def. of parallelograms.

If the height of candle after 10 and 26 hours are 25 cm and 17 cm then the height of candle after 21 hours is 19.5 cm.

Given height of candle after 10 hours is 25 cm , height of candle after 26 hours is 17 cm.

We have to find the height of candle after 21 hours.

We have been given two points of linear function (10,25),(26,17).

We have to first form an equation which shows the height of candle after x hours.

let the hours be x and the height be y.

Equation from two points will be as under:

[tex](y-y_{1} )=(y_{2} -y_{1} )/(x_{2} -x_{1} )*(x- x_{1} )[/tex]

(y-25)=(17-25)/(26-10)* (x-10)

y-25=-8/16 *(x-10)

16(y-25)=-8(x-10)

16y-400=-8x+80

8x+16y=480

Now we have to put x=21 to find the height of candle after 21 years.

8*21+16y=480

168+16y=480

16y=480-168

16y=312

y=312/16

y=19.5

Hence the height of candle after 21 hours is 19.5 cm.

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The value of a is 6 and the value of b is 7

The function is given as:

h(x) = a . sin(x - π/2) + b

From the table of values, we have:

x = π/2 when y = 7

So, we have:

a . sin(π/2 - π/2) + b = 7

Evaluate the difference

a . sin(0) + b = 7

Evaluate the value of sin(0)

a . 0 + b = 7

Evaluate the product of a and 0

b = 7

Substitute b = 7 in h(x) = a . sin(x - π/2) + b

h(x) = a . sin(x - π/2) + 7

From the table of values, we have:

x = π when y = 13

So, we have:

a . sin(π - π/2) + 7 = 13

Evaluate the difference

a . sin(π/2) + 7 = 13

Subtract 7 from both sides

a . sin(π/2)  = 6

Evaluate sin(π/2)

a . 1 = 6

Divide both sides by 1

a = 6

Hence, the value of a is 6 and the value of b is 7

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Answer:

The roof does form a right triangle.

Step-by-step explanation:

If it is a right triangle then it will obey the Pythagoras Theorem.

Now  (√186)^2 = (√93)^2 + (√93)^2

              186 = 93 + 93 = 186

So it obeys the theorem and is therefore a right triangle.

The value of x in the triangle is 9.3

The side x of a triangle can be found as follows:

The triangle ABC is similar to triangle ADE.

Therefore, corresponding sides of similar triangles are in the same ratios.

Hence,

7  / 13 = x / x + 8

cross multiply

7(x + 8) = 13x

7x + 56 = 13x

subtract 7x from both sides of the equation

7x - 7x + 56 = 13x - 7x

56 = 6x

divide both sides by 6

x = 56 / 6

x = 9.33333333333

x = 9.3

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The least possible value of n is 27.

According to the statement

We have given that the set which is {2,4,6,8.....n} and and one set is removed from them the average of remaining integers is 28.

Then

Firstly set contain n numbers

But after that set contain n-1 numbers after removal of 1 digit from them.

and average value of remaining digit is 28 then 28th term become after removal is

28th term =28*2

28th term = 56.

then

we use the formula to calculate n

n-1 =28

then the value of n become 27.

the least possible value of n is 27.

So, The least possible value of n is 27.

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Answer: a

/////////////////

Answer:

The correct answer is  A.

Step-by-step explanation:

The absolute value of any number is always positive.

The amount of packing material is 1506 cubic inches

The given parameters are:

Can

Radius, r = 7 inches

Height, h = 18 inches

Box

Base dimension, l = 15 inches

Height, h = 19 inches

The volume of the can is:

[tex]V = \pi r^2h[/tex]

So, we have:

[tex]V_1 = 3.14 * 7^2 * 18[/tex]

[tex]V_1 = 2769[/tex]

The volume of the box is

[tex]V =l^2h[/tex]

So, we have:

[tex]V_2 =15^2 * 19[/tex]

[tex]V_2 =4275[/tex]

The amount of packing material is;

Amount = V2 - V1

This gives

Amount = 4275 - 2769

Evaluate

Amount = 1506

Hence, the amount of packing material is 1506 cubic inches

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The computation shows that the amount will be 44.70 Dollars.

The options are missing: Here are the missing options:

A. 44.70 US dollars

B. 73.06 US dollars

C. 136.87 US dollars

D. 140.41 US dollars

For solving this question first we will convert the USD to euros.

The conversion rate we have is:

1 euro = 1.3687 USD

250/1.3687 = 182.655 euros

Now we will subtract it from what he has spent:

= 182.655 - 150

= 32.655 euros

Now we will again convert it back to USD. This will be:

32.655 euros * 1.3687 = 44,695 us dollars

Therefore, the answer is 44.70.

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The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.

According to the statement

we have given Following are the pairs of the complex number:

(1+2i)(8i),

(1 + 2i)(2 – 5i)

(1+2i)(1-2i) and (1+2i)(4i)

We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".

So, For this purpose

we have to multiply these pairs with each other.

So,

(1+2i)(8i) = 8i +16(i)^2

And

(1 + 2i)(2 – 5i) = 2 +4i - 5i +10(i)^2

And

(1+2i)(1-2i) = 1 -4(i)^2 -2i +2i = 1+4 = 5

And

(1+2i)(4i) = 4i + 6(i)^2

From these multiplication we found that the third pair have a real number product.

So, The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.

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The equation in which b varies directly as the square root of c is b = 50 · √c. (Correct choice: B)

In this problem we have a case of direct variation between two variables, which is mathematically described by a direct proportionality model, whose form and characteristics are shown below:

b ∝ √c

b = k · √c      (1)

Where k is the proportionality constant.

First, we determine the value of the constant of proportionality by substituting on b and c and clearing the variable: (b = 100, c = 4)

k = b / √c

k = 100 / √4

k = 100 / 2

k = 50

Then, the equation in which b varies directly as the square root of c is b = 50 · √c. (Correct choice: B)

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Answer:

2y+6

Step-by-step explanation:

first, pull out the 2 from the top to separate the equation

second, factor out y

third, cancel out the common factor of y-1

fourth, remove the parenthesis from 2(y+3)

answer = 2y+6

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

There are two hemispheres in there with radius 3 cm, so we can consider it as a whole one. and the other shape in between is Cylinder with radius 3 cm and height 4 cm.

Volume of whole ahape = volume of Cylinder + volume of sphere ~

Volume of sphere :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{4}{3} \pi {r}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{4}{3} \sdot3.14 \sdot {(3)}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (4 )\sdot(3.14) \sdot(9)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 113.04 \: \: cm {}^{3} [/tex]

Volume of Cylinder :

[tex]\qquad \sf  \dashrightarrow \: \pi {r}^{2} h[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3.14 \cdot(3) {}^{2} \sdot4[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3.14 \sdot(9) \sdot(4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 113.04 \: \: cm {}^{3} [/tex]

Volume of whole shape :

[tex]\qquad \sf  \dashrightarrow \: 113.04 + 113.04 = 226.08 \: \: cm {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 226.08 \: \: cm {}^{3}[/tex]

The total surface area of the can of coke is 641.143 cm².

A can of coke has the shape of a cylinder. A cylinder is a three-dimensional object that is made up of a prism and two circular bases. The total surface area of a closed cylinder can be determined by adding the area of all its faces.

Total surface area of the closed cylinder = 2πr(r + h)

Where:

Total surface area of the closed cylinder = (2 x 22/7 x 6) x (6 + 11)

(264 / 7) x (17)

37.714 x 17 = 641.143 cm²

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Answer:

On a Sunday?

Step-by-step explanation:

Answer: 1

Step-by-step explanation: Any number raised to zero is always 1.

Answer:

298

Step-by-step explanation:

All perfect squares from 100-200 inclusive:

100, 121, 144, 169, 196

100+1=101, 101 is prime

121+2=123, 123=41*3 so its not prime

144+1=145 145=29*5 so its not prime

169+2=171 171=9*19 so its not prime

196+1=197, 197 is prime

101+197=298

Notice that I excluded all even numbers because they are obviously composite.

The best option that would be used to show the data would be the line graph.

The reason  I chose the line graph is that it would show us the trend in the data. This is in a way that we would see the periods there was a high bills.

Also the line graph is very simple to understand. The relationship and the changes in the data is easily seen.

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Step-by-step explanation:

1 ----> 22 times

2 ----> 16 times

3 ----> 26 times

4 ----> 29 times

5 ----> 1 times

6 ----> 6 times

so , total ----> 100 times

so , percentage of rolls 6 is :-

(6/100 ) × 100%

= 6%

Answer:

x = 2 or x = -1/4

Step-by-step explanation:

Let's solve your equation step-by-step.

4x2−7x−2=0

For this equation: a=4, b=-7, c=-2

4x^2+−7x+−2=0

Step 1: Use quadratic formula with a=4, b=-7, c=-2.

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(-2)} }{2(4)}[/tex]

[tex]x=\frac{7\pm\sqrt{81} }{8}[/tex]

x = 2 or x = -1/4

Answer:

x = 2 or x = -1/4

Answer:

discriminant = b^2 - 4ac

Step-by-step explanation:

discriminant = b^2 - 4ac

2^2 - 4x 3x2 = 4-24 = 20