Examine the equation. 4(x – 3) = 4x – 12 Which of the following is true? (Check all that apply.) It is a true statement. Any input will result in an equivalent equation. It is equivalent to an equation of the form a = a. It has no solution. Only one input will result in a true statement.

Step-by-step explanation:

the horizontal Component of force =

14 × cos 30° = 14 × ½√3

= 7√3 or 12.12 Newtons

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

Answer:

The speed of George the Pigeon in still air = 21 miles/hr

The speed of air = 3 miles/hr

Step-by-step explanation:

Let the speed of George the Pigeon in still air = \(u\) miles/hr

Let the speed of air = \(v\) miles/hr

Distance traveled = 72 miles

Relative speed against the wind = \((u-v)\) miles/hr

Time taken against the wind = 4 hours

Relative speed with the wind = \((u+v)\) miles/hr

Time taken against the wind = 3 hours

Using the formula:

\(Speed = \dfrac{Distance}{Time}\)

\(u-v=\dfrac{72}{4}\\\Rightarrow u-v=18 ..... (1)\)

\(u+v=\dfrac{72}{3}\\\Rightarrow u+v=24 ..... (2)\)

Adding (1) and (2):

\(2u=42\\\Rightarrow u = 21\ miles/hr\)

By equation (1):

\(v = 21-18\\\Rightarrow v = 3\ miles/hr\)

Therefore, the answer is:

The speed of George the Pigeon in still air = 21 miles/hr

The speed of air = 3 miles/hr

Answer:

The minimum value of the function is 5.6.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

\(f(x) = ax^{2} + bx + c\)

It's vertex is the point \((x_{v}, y_{v})\)

In which

\(x_{v} = -\frac{b}{2a}\)

\(y_{v} = -\frac{\Delta}{4a}\)

Where

\(\Delta = b^2-4ac\)

If a<0, the vertex is a maximum point, that is, the maximum value happens at \(x_{v}\), and it's value is \(y_{v}\).

If a > 0, then \(y_{v}\) is the minimum value of the function.

In this question:

We are given the following function:

\(f(x) = 0.1x^2 - x + 8.1\)

Which is a quadratic function with \(a = 0.1, b = -1, c = 8.1\).

To find the minimum value, we have that:

\(\Delta = b^2-4ac = (-1)^2 - 4(0.1)(8.1) = -2.24\)

\(y_{v} = -\frac{-2.24}{4(0.1)} = 5.6\)

The minimum value of the function is 5.6.

Answer:

22 cakculator is write answer

Answer:

a i guess there isnt a queston here

Step-by-step explanation:

Answer: hello there! the answer is a. <A ≅ <A; reflexive property, hope this helps :)

Step-by-step explanation: i just completed the unit practice test and got 100%

Answer:

The slope is undefined.

Step-by-step explanation:

If the x value stay the same between a set of points, the slope of the line will be undefined.

Answer:

Step-by-step explanation:

Please give detailed question

Answer:

? what's the problem

Step-by-step explanation:

Answer:

length is 26 and width is 23

Step-by-step explanation:

let width be x

then length is 3+x since it is 3 more than the width

perimeter of a rectangle = 2l + 2w

98=2 [3+x] + 2x

98=6+2x+2x

98=6+4x

98-6=4x

92=4x

x=23

width is 23 and

breadth is 26

Answer:

Airplanes

Step-by-step explanation:

Aviation is the Airplanes and they need to take off on their flight on their way for Visit! Welcome Aboard!

Answer:

10h and 9 min

Step-by-step explanation:

Answer:

Your Answer is 3. Because 135÷45

Step-by-step explanation:

135÷45

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

there is not enough information because x and 55 are parrallel, not congruent.

Step-by-step explanation:

Answer: (0, 3)

Step-by-step explanation:

Find where 0 is on the x axis and correspond the coordinate to the y axis.

There are 29 degrees of freedom for this repeated-measures t-test.

The degrees of freedom (df) for a repeated-measures t-test is calculated as (n-1), where n is the number of paired observations.

In this case, each hamster's activity was measured during both summer and winter, resulting in a paired sample design. Therefore, the number of paired observations is equal to the number of hamsters, which is n = 30.

Hence, the degrees of freedom for this repeated-measures t-test is:

df = n - 1 = 30 - 1 = 29

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The value of the expressions 7^-2 x 7^5 x 7^-3 is 1.

Expressions that are equivalent do the same thing even though they have different appearances. When we enter the same values for the variable, two algebraic expressions that are equivalent have the same values. Using the equality (=) sign, equivalent expressions are represented.

Since the values of both expressions remain the same for any value of x, the expressions 3(x + 2) and 3x + 6 are equivalents. When values are substituted for the variable and both expressions yield the same result, you can also tell if two expressions are equivalent.

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 5³, 3 is the exponent and 5³ is called 5 raise to the power of 43.

The value of the expression will be:

= 7^-2 x 7^5 x 7^-3

= 7^(-2 + 5 - 3)

= 7^0

= 1

In conclusion, the value is 1.

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\(P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} \)

\(P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407\)

\(P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} \)≈0.999787

Answer:

The answer is 50.

Step-by-step explanation:

Use MDAS

Multiplication, Division, Addition and Subtraction

2 + 6 * 8 =

Multiply first then add

2 + 6*8 = ?

= 2 + 48

= 50

Answer:

15/7 or 2.142

Step-by-step explanation:

x=3/7×5

x=15/7

Answer:

No, the zeros of the function are at x = 3/4 and x = –2

Step-by-step explanation:

the equation

4x² + 5x – 6 = 0

(note: since there is a coefficient of x² we need to multiply it to the last term(6))

4x² + 5x – 24 = 0

the factors are :- 8x and – 3x

4x² + 8x – 3x – 6 = 0

4x( x + 2) –3( x + 2) = 0

( 4x – 3)( x + 2) = 0

the zeros will be

4x – 3 = 0

4x = 3

\(x = \frac{3}{4} \)

x + 2 = 0

x = – 2

the zeros are x= 3/4 or –2

i hope this helps

Correct option is D, The perimeter of the trapezoid J K L M is units 9 + StartRoot 2 EndRoot + StartRoot 5 EndRoot units (= 9 + √5 + √2 units. )

The length of a two-dimensional shape's boundary is its perimeter. It is frequently referred to as the sum of the lengths of the sides of the object. Such shape's perimeter is equal to the side lengths added together algebraically. We have formulas for the various geometric shapes.

The vertices of KLMN an isosceles trapezoid are (-7,4), (-4,4), (-2,3), (-8,3).

perimeter of trapezoid JKLM = sum of sides

Using distance formula \(\sqrt{(x2-x2)^2 + (y2 - y1)^2}\),

Distance between the sides of trapezoid is,

(-7,4), (-4,4) =

\(\sqrt{(-7 + 4)^2 + (4 - 4)^2}\\= \sqrt{9}\\= 3 units\)

(-4,4), (-2,3) =

\(\sqrt{(-2 + 4)^2 + (3 - 4)^2}\\= \sqrt{5} units\)

(-2,3), (-8,3) =  

\(\sqrt{(-8 + 2)^2 + (3-3)^2}\\= \sqrt{6}^2\\= 6 units\)

(-7,4), (-8,3)

\(\sqrt{(-8 +7)^2 + (3-4)^2}\\= \sqrt{-1^2 + -1^2}\\= \sqrt 2 $ units $\)

So, the sum of sides will be -

= 3 + √5 + 6 + √2

= 9 + √5 + √2 units.

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Answer:

its D

Step-by-step explanation:

i took the test on edg

Answer:

169

Step-by-step explanation:

Larger Number = 196

Smaller Number = 169

Step-by-step explanation:

larger sum = 196/

smaller sum = 169/

hope it helps. :)

Answer:

a, and b are your answers

explanation: plug them in

The solution to the equation -2(x + 3) = -6 is x = 0.

To simplify the expression 5t + 7 + 8b, we can combine like terms.

There are two like terms in the expression: 5t and 8b.

Combining the like terms gives us:

5t + 8b + 7

Therefore, the simplified form of the expression 5t + 7 + 8b is 5t + 8b + 7.

Regarding the equation -2(x + 3) = -6:

To solve this equation, we can follow these steps:

Distribute the -2 to the terms inside the parentheses:

-2 * x + (-2) * 3 = -6

This simplifies to:

-2x - 6 = -6

Move the constant term to the right side by adding 6 to both sides of the equation:

-2x = 0

Divide both sides of the equation by -2 to isolate the variable x:

x = 0 / -2

Simplifying the right side of the equation gives us:

x = 0

The solution to the equation -2(x + 3) = -6 is x = 0.

The simplified expression 5t + 7 + 8b remains as 5t + 8b + 7, and the solution to the equation -2(x + 3) = -6 is x = 0.

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All other things being equal, outliers tend to have a greater effect on the value of the mean, as compared to the value of the median. The given statement is true.

What is the mean and median?

Outliers are values that are significantly different from the other values in a data set, and their presence can greatly affect the value of measures of central tendency, such as the mean and the median.

The mean is a measure of central tendency that is calculated as the sum of all the values in a data set divided by the number of values. The presence of outliers can greatly affect the mean because outliers can have a large impact on the sum of the values in the data set. For example, if a data set has a few very large outliers, the mean will be pulled up to be much higher than the median, which represents the midpoint of the data set.

On the other hand, the median is a measure of central tendency that is calculated as the middle value of a data set when the values are arranged in order. The median is not as sensitive to outliers as the mean because outliers do not affect the median unless the number of outliers is so large that it changes the value of the middle value.

Hence, all other things being equal, outliers tend to have a greater effect on the value of the mean than on the value of the median.

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According to mathematics, a regular hexagon's area A is  288 sq units option -A is correct answer.

How to Locate a Hexagon's Area

A regular hexagon's side length can be determined in step 1.

Step 2: Calculate the area using the formula for the area of a hexagon (3√3 s²)/2, where s is the length of the hexagon's sides.

A regular hexagon whose side length is 8 in.

and the apothem is 12 in.

The equation for the area,

A=(3√3)/2 × a²

Therefore

A = 6×(0.5×8×12)

A = 288 sq units

In conclusion, a regular hexagon's surface area A is 288 square feet.

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Answer:

Your answer is A) \(288in^{2}\)

Step-by-step explanation:

Answer:

4.28%

Step-by-step explanation:

We Know

Last year you earned $72,400

This year you earned $75,500

What was the rate of change in your earnings since last year?

We Take

(75,500 ÷ 72,400) x 100 ≈ 104.28%

Then We Take

104.28 - 100 = 4.28%

So, the earning increased by about 4.28%.

Its a weird problem but I think u should use formula:

(a+b)^2=a^2+2ab+b^2

5(q+p+3)=5q+15+5p=(√5q+√5p)^2

it is only thing u can do.