the volume of a triangular prism is 42 cubic centimeters. what is the volume of a similar prism that is twice as large as large as the first prism

Answer:

Final answer is approx x=1.27.

Step-by-step explanation:

Given equation is [tex]8^{-x+7}=3^{7x+2}[/tex].

Now we need to solve equation [tex]8^{-x+7}=3^{7x+2}[/tex] and round to the nearest hundredth.

[tex]8^{-x+7}=3^{7x+2}[/tex]

[tex]\log(8^{-x+7})=\log(3^{7x+2})[/tex]

[tex]\left(-x+7\right)\cdot\log\left(8\right)=\left(7x+2\right)\cdot\log\left(3\right)[/tex]

[tex]-x\cdot\log\left(8\right)+7\cdot\log\left(8\right)=7x\cdot\log\left(3\right)+2\cdot\log\left(3\right)[/tex]

[tex]-x\cdot\log\left(8\right)-7x\cdot\log\left(3\right)=2\cdot\log\left(3\right)-7\cdot\log\left(8\right)[/tex]

[tex]x\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)=\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)[/tex]

[tex]x=\frac{\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)}{\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)}[/tex]

Now use calculator to calculate log values, we get:

[tex]x=1.26501646392[/tex]

Round to the nearest hundredth.

Hence final answer is approx x=1.27.

Answer: Actually The Jacksonian Era was characterized by the thought that each individual also equally have right and he or she is important and that all should be able to have a say or participate in any government activities.

All in all i think its actually giving greater right to the common man.

Answer:

35 shelves

Step-by-step explanation:

If each shelf holds 36 books and there are a total of 1,260 books, divide 1,260 by 36 to get the number of shelves needed. 1,260/36 = 35 shelves. Think of it like 36 books per shelf and 35 shelves, 36*35 = 1,260.

Answer:

b. [tex]x\approx -2.426[/tex]

Step-by-step explanation:

The given equation is;

[tex]x^3+x^2+10x+15=0[/tex]

We solve by the x-intercept method. We need to graph the corresponding function using a graphing tool.

The corresponding function is

[tex]f(x)=x^3+x^2+10x+15[/tex]

The solution to [tex]x^3+x^2+10x+15=0[/tex] is where the graph touches the x-axis.

We can see from the graph  that; the x-intercept is;

(-2.426,0)

Therefore the real solution is:

[tex]x\approx -2.426[/tex]

Answer:

b. x ≈ -2.426

Step-by-step explanation:

Given that we have possible roots we can replace these values into the equation and check if it is satisfied.

option a: 2.426^3+4*2.426^2+10*2.426+15 = 77.08 ≠ 0

option b: (-2.426)^3+4*(-2.426)^2+10*(-2.426)+15 ≈ 0

option c: 5.128^3+4*5.128^2+10*5.128+15 = 306.31 ≠ 0

option d: (-5.128)^3+4*(-5.128)^2+10*(-5.128)+15 = -65.94 ≠ 0

Answer:

Yes

Step-by-step explanation:

Answer:

  y = csc(x) -1

Step-by-step explanation:

The vertical offset of -1 is your first clue. Your second clue is that the range does not include (-2, 0), typical of cosecant and secant functions (offset by -1).

_____

Comment on answer choices

Apparently the cosine choices are intended to be confused with the cosecant choice. The cosine function has a range of [-1, 1], so will not show any vertical asymptotes anywhere, regardless of scaling or translation.

Answer:

[tex]7;41[/tex]

Step-by-step explanation:

Let

x----> the time it take Ebru to walk to the school

we know that

[tex]x=2(13)=26\ min[/tex]

so

[tex]7;15 +26\ min=7;41[/tex]

Ebru takes 26 minutes to walk to school, twice as long as biking. Leaving at 7:15 AM means she would arrive at school by walking at 7:41 AM.

If Ebru bikes to school, it takes her 13 minutes. Walking takes her twice as long, which would be 26 minutes. If Ebru leaves her house at 7:15 AM, we can calculate the time she will get to school by walking by adding 26 minutes to the departure time.

Therefore, if Ebru walks to school, she will arrive at 7:41 AM.

64,781 --- 4,000

25,409 --- 400

4,000÷400=10

the answer should be C

Answer:

[tex]\large\boxed{B)\ 16x^2-25}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ (a-b)(a+b)=a^2-b^2[/tex]

[tex](4x-5)(4x+5)=(4x)^2-5^2=16x^2-25[/tex]

Answer:

C

Step-by-step explanation:

The equation is y = a(b(x-c))+d

So for it to move right three units, it would be x - 3.

For it to move up 4 unites, it would be x+4.

So the equation would be y = (x - 3)^2 + 4

The correct answer is C

First you would substitute the expression moving it to the left then you change the signs the power function with an even exponent is always a positive or 0 but there is no x intercept.

Answer:

112

Step-by-step explanation:

Answer:

1.33

Step-by-step explanation:

Solve for r in the first equation:

3(r+300) = 6

Use the distributive property:

3r + 900 = 6

Subtract 900 from both sides:

3r = -894

Divide both sides by 3:

r = -894 / 3

r = -298

Now you have r, replace r in the second equation and solve:

r +300 -2 =

-298 + 300 - 2 = 0

The answer is 0.

Answer:

0 is the value of r+300-2

Solve for r in the first equation:

3(r+300) = 6

Use the distributive property:

3r + 900 = 6

Subtract 900 from both sides:

3r = -894

Divide both sides by 3:

r = -894 / 3

r = -298

Now you have r, replace r in the second equation and solve:

r +300 -2 =

-298 + 300 - 2 = 0

The answer is 0.

Add the two numbers in the ratio: 7 +3 = 10

Divide total capacity by 10:

70,580 / 10 = 7,058

Multiply that by the ratio of filled seats:

7,058 x 7 = 49,406

49,406 seats were filled.

Answer:

probability is r/p+q+r

Step-by-step explanation:

to find the probability, you take the number of desired balls (blue in this case )

and divide it by the total number of balls in the problem (add them all up) to get your answer

I hope that answered your question!!

ANSWER

The distance is 10 units.

EXPLANATION

Let us use the distance formula to find the distance between,

[tex](x_1,y_1)=(1,4)[/tex]

and

[tex](x_2,y_2)=( - 5, - 4)[/tex]

The distance formula is given by,

[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} [/tex]

We plug in the values to get,

[tex]d = \sqrt{( - 5-1)^2 + ( - 4-4)^2} [/tex]

[tex]d = \sqrt{( -6)^2 + ( - 8)^2} [/tex]

[tex]d = \sqrt{36+ 64} [/tex]

[tex]d = \sqrt{100} [/tex]

[tex]d = 10[/tex]

Answer:

2:3.

Step-by-step explanation:

The number of children = 2+ 4 = 6.

So the required ratio is 4:6 which simplifies to 2:3.

Answer:

2.3

is yo sex answer

Answer:

8a - 48

Step-by-step explanation:

An equivalent expression is an expression which is equal to 8(a-6). You can expand or simplify an expression to make an equivalent expression. Apply the distributive property to form a new equivalent expression by multiplying 8 into each term. 8(a-6) = 8*a - 8*6 = 8a - 48. The options listed below do not connect to this problem since they do not use the same variable as the expression.

Square B Area = 144cm²

Square B = X

The dimensions of Square A are three times The dimensions of Square B

Square A = 3 * Square B

Square A = 3X

The area of Square A is 1,296 cm2.

Square A Area = (3X)² = 1296

Square B Area = X²

Solve to find X.

(3X)² = 1296

3X = 36

X = 36/3 = 12

Square B Area = 12² = 144

Square B Area = 144cm²

Final answer:

The area of Square B is 144 cm², calculated by dividing the area of Square A (1,296 cm²) by 9, because the area of a square scales with the square of its linear dimensions.

Explanation:

The area of Square A is given as 1,296 cm². Since the dimensions of Square A are three times the dimensions of Square B, we can find the area of Square B by understanding that area scales in proportion to the square of the linear dimensions. This means that if one dimension is three times another, the area will be nine times (3² = 9) larger.

To find the area of Square B, we simply divide the area of Square A by 9:

Area of Square B = Area of Square A / 9

Area of Square B = 1,296 cm² / 9

Area of Square B = 144 cm².

Therefore, the area of Square B is 144 cm².

the answer is B ln(0.0498)=-3

Answer:

 112 candles

Step-by-step explanation:

We can simply add up the 5 numbers of candles, or we can take advantage of the invention of multiplication to replace repeated addition. The number of candles altogether is the sum of the numbers of candles in each of the 5 boxes.

  16 + 4×24 = 16 +96 = 112

The total number of candles is 112.

Answer:

She needs 4 more gallons of blue paint than red paint

Step-by-step explanation:

Since the ratio is 3 to 2, 3 + 2 = 5.

The artist needs 20 gallons of purple paint, so 20/5 = 4

The amount of blue and red paint needed is 4x3 to 4x2, or 12 to 8.

She needs 12 gallons of blue paint and 8 gallons of red paint.

12 - 8 = 4

She needs 4 more gallons of blue paint than red paint.

Answer:

ok!

Step-by-step explanation:

blue = 8 gallons

red = 12 gallons

Answer:

Three solutions were found :

x = 5

x = 2

x = -1

Step-by-step explanation:

Answer:

d. [tex]x=-1,2,\:or\:5[/tex]

Step-by-step explanation:

The given equation is;

[tex]x^3-6x^2+3x+10=0[/tex]

To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator.

The corresponding function is

[tex]f(x)=x^3-6x^2+3x+10[/tex]

The solution to [tex]x^3-6x^2+3x+10=0[/tex] is where the graph touches the x-axis.

We can see from the graph  that; the x-intercepts are;

(-1,0),(2,0) and (5,0).

Therefore the real solutions are:

[tex]x=-1,2,\:or\:5[/tex]

Set [tex]f(x)=2x^3-3x^2+2[/tex]. Find the tangent line [tex]\ell_1(x)[/tex] to [tex]f(x)[/tex] at the point when [tex]x=x_1[/tex]:

[tex]f'(x)=6x^2-6x\implies f'(x_1)=12[/tex] (slope of [tex]\ell_1[/tex])

[tex]\implies\ell_1(x)=12(x-x_1)+f(x_1)=12(x+1)-3=12x+9[/tex]

Set [tex]x_2=-\dfrac9{12}[/tex], the root of [tex]\ell_1(x)[/tex]. The tangent line [tex]\ell_2(x)[/tex] to [tex]f(x)[/tex] at [tex]x=x_2[/tex] has slope and thus equation

[tex]f'(x_2)=\dfrac{63}8\implies\ell_2(x)=\dfrac{63}8\left(x+\dfrac9{12}\right)-\dfrac{17}{32}=7x+\dfrac{151}{32}[/tex]

which has its root at [tex]x_3=-\dfrac{151}{224}\approx-0.6741[/tex].

(The actual value of this root is about -0.6777)

Answer:

0.2312

Step-by-step explanation:

Using the formula given,

[tex]P(x) = p(1-p)^{x-1}[/tex],

we use 0.34 for p and 2 for x:

[tex]P(2) = 0.34(1-0.34)^{2-1}\\\\P(2) = 0.34(0.68)^1\\\\P(2) = 0.34(0.68) = 0.2312[/tex]

Answer:

217.01

Step-by-step explanation:

Answer:

Roughly $21.70

Step-by-step explanation:

1,205.62 times 0.018 (1.8% converted into decimal, to do so, move the decimal over to the right two places) equals 21.7

Answer:

C

Step-by-step explanation:

You are given that

Use the rule

[tex]\lim_{x\to x_0}(f(x)+g(x))=\lim_{x\to x_0} f(x)+\lim_{x \to x_0} g(x).[/tex]

In your case,

[tex]\lim_{x\to4}(f+g)(x)=\lim_{x\to4} (f(x)+g(x))= \lim_{x\to4} f(x)+ \lim_{x\to 4} g(x)=5+0=5.[/tex]

Lets say the number is ab. Its value is 10a + b  

When it is reversed it is 10b + a = 12a+1.2b (from the condition its value should increase 0.2 times).  

11 a = 8.8b  

a/b = 8.8/11 = 0.8/1 = 8/10 = 4/5 ( we do this because a and b should be natural numbers less than 10).  

answer is 45.

A two-digit number less than 100 that increases by one-fifth of its original value, when its digits are reversed, can be found by setting up an equation. By defining the tens digit as 'a' and the unit digit as 'b', the equation 6a = 9b is derived. Solving for the digits within their possible values, the number 12 is found.

To find a number less than 100 that increases by one-fifth of its value when its digits are reversed, we need to set up an equation. Let's call the tens digit a and the units digit b. The number can be written as 10a + b. When the digits are reversed, the number becomes 10b + a. The problem states that reversing the digits increases the number by one-fifth of its original value, which gives us the equation:

(10a + b) + \frac{1}{5}(10a + b) = 10b + a

Now solving the equation:

6a = 9b

As a and b are digits, their possible values range between 0 and 9. We find that a = 1 and b = 2 satisfy the equation. Hence, the number is:12

When we reverse the digits, we get 21, which is greater than 12 by \frac{1}{5} of 12, as required.

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3x+4=5x-50

54=2x

27=x

Answer:

x = 27

Step-by-step explanation:

The diagonals of a rectangle are congruent, hence

BD = AC ← substitute values

5x - 50 = 3x + 4 (subtract 3x from both sides )

2x - 50 = 4 ( add 50 to both sides )

2x = 54 ( divide both sides by 2 )

x = 27