pls help asap.........

The side of the edge of the cube is 9. 9cm

Given that the diagonal of a cube measures the square root of 294cm and the diagonal of a face measures 14cm

To find the edge of the face, we know that the face of the cube is a square

Formula for diagonal of a square = [tex]\sqrt{2a}[/tex]

Where is the side of the square

We then have,

[tex]\sqrt{2a} = 14[/tex]

Make 'a' the subject

a = [tex]\frac{14}{\sqrt{2} }[/tex]

Simplify the surd

a = [tex]\frac{14}{\sqrt{2} }[/tex] × [tex]\frac{14}{\sqrt{2} }[/tex]

a = [tex]\frac{14\sqrt{2} }{2}[/tex]

a = [tex]7\sqrt{2}[/tex]

a = 9. 9cm

Therefore, the side of the edge of the cube is 9. 9cm

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Answer: Its 9.8 cm

Step-by-step explanation: I said so

What the given proof is trying to show us is that; ∠3 = 126°

From the attached line, we see that angle 1 and angle 3 form a straight line. Now, since we know that angles on a straight line sum up to 180°, then it means that they are supplementary.

We are given;

1) ∠1 and ∠2 are supplementary

2) ∠1 = 36°

Thus from definition of complementary angles, we can say that;

36° + ∠2 = 90°

Subtraction property of equality when applied gives;

∠2 = 54°

We are told that ∠2 and ∠3 are linear pairs and as such;

∠2 + ∠3 = 180° from linear pairs theorem.

By substitution property of equality we have;

54° + ∠3 = 180°

Solving gives ∠3 = 126°

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the quadratic equation is:

y = 0.2*x*(x - 28)

If we know that the roots are J and K, and the leading coefficient is a, then the quadratic equation is:

y = a*(x - K)*(x - J)

Here we know that the roots are at x = 0 and x =28, then:

y = a*(x - 0)*(x - 28).

We also know that the vertex is a minimum, so a is positive, and we know that the vertex is (14, -40), then we have:

-40 = a*(14)*(14 - 24) = -a*196

a = 40/196 = 0.20

Then the quadratic equation is:

y = 0.2*x*(x - 28)

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Answer:

Hence the expression [tex]$$(4z-y)(z-6)=4z^2-yz-24z+6y$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{matrix}{} & {} & {} & {} & 4z & - & y \\ \times & {} & {} & {} & z & - & 6 \\ \end{matrix}$$[/tex]

_________________

[tex]$$\begin{matrix}{} & {} & {} & - & 24z & + & 6y \\ 4{{z}^2} & - & yz & {} & {} & {} & {} \\ \end{matrix}$$[/tex]

_________________

[tex]$$\begin{matrix}4{{z}^2} & - & yz & - & 24z & + & 6y \\ \end{matrix}$$[/tex]

Both climbers rested on the wall at a constant height for 2 minutes.

The illustrative graph that represents the climbers' movement is added as an attachment

From the attached graph, we have the following observation

The difference between the endpoints of both horizontal line is

Difference = 6- 4 = 2

Difference = 7 - 5 = 2

This means that both Brynn and Abby stopped for 2 minutes

Hence, the true statement about is that (d) Both climbers rested on the wall at a constant height for 2 minutes.

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[tex]m = \frac{ - 5 - 4}{3 - 0} = \frac{ - 9}{3} = - 3[/tex]

[tex]g(x) = - 3x + 4[/tex]

[tex]g(x) \: ha s \: a \: steeper \: slope[/tex]

The regression equation is y = 3.231x + 10.138

The regression model that fits the data is a linear model.

This is so because as x increases by 1, the y value increases by an almost constant rate

To determine the regression equation, we make use of a graphing calculator

From the graphing calculator, we have the following summary:

The regression equation is then calculated as;

y = bx + a

Where

b = SP/SSX = 56.55/17.5 = 3.23143

a = MY - bMX = 18.22 - (3.23*2.5) = 10.1381

So, we have:

y = 3.23143x + 10.1381

Approximate

y = 3.231x + 10.138

Hence, the regression equation is y = 3.231x + 10.138

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The y-intercept of the line is 0.75 or 3/4

The given parameters are:

Slope, m = 1/4

Point (x, y) = (0.2, 4/5)

A linear equation is represented as:

y = mx + b

This gives

4/5 = 1/4 * 0.2 + b

Evaluate the product

4/5 = 0.05 + b

Subtract 0.05 from both sides

b = 0.75

Hence, the y-intercept of the line is 0.75 or 3/4

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Answer:

For the function [tex]$f(x)=4 x-3$[/tex] the average rate change from x is equal 1 to x is equal 2 is 4 .

Step-by-step explanation:

A function is given f(x)=4x-3.

It is required to find the average rate change of the function from x is 1 to x is 2 . simplify.

Step 1 of 2

A function f(x)=4 x-3 is given.

Determine the function [tex]$f\left(x_{1}\right)$[/tex] by putting the value of x=1 in the given function.

[tex]$$\begin{aligned}&f(1)=4(1)-3 \\&f(1)=1\end{aligned}$$$$f(1)=1$$[/tex]

Determine the function [tex]$f\left(x_{1}\right)$[/tex] by putting the value of x is 2 in the given function.

[tex]$$\begin{aligned}&f(2)=4(2)-3 \\&f(2)=5\end{aligned}$$[/tex]

Step 2 of 2

According to the formula of average rate change of the equation [tex]$\frac{\Delta y}{\Delta x}=\frac{f\left(x_{2}\right)-f\left(x_{2}\right)}{x_{2}-x_{1}}$[/tex]

Substitute the value of [tex]$f\left(x_{1}\right)$[/tex] with, [tex]$f\left(x_{1}\right)$[/tex] with [tex]$3, x_{2}$[/tex] with 2 and [tex]$x_{1}$[/tex] with 1 .

[tex]$$\begin{aligned}&\frac{\Delta y}{\Delta x}=\frac{5-1}{1} \\&\frac{\Delta y}{\Delta x}=4\end{aligned}$$[/tex]

Answer:

b. The graph of g(x) is a translation 10 units right and 8 units up from the graph of f(x).

Step-by-step explanation:

See attached image.

Answer:

x = -3

y = 9

Step-by-step explanation:

6x + 3y = 9 ⇒ ( 1 )

Divide the whole equation by 3.

2x + y = 3 ⇒ ( 2 )

-9x - 2y = 9 ⇒ ( 3 )

Let us take equation (2) and make y the subject of the equation.

2x + y = 3

y = 3 - 2x ⇒ ( 4 )

Now let us take equation (3) and find the value of x.

For that, we can replace y with ( 3 - 2x ).

Let us solve it now.

-9x - 2y = 9

-9x - 2 ( 3 - 2x ) = 9

-9x -6 + 4x = 9

-5x - 6 = 9

-5x = 9 + 6

-5x = 15

Divide both sides by (-5).

x = -3

And now let us take equation (4) to find the value of y.

For that, we can replace x with -3.

Let us solve it now.

y = 3 - 2x

y = 3 - 2 × -3

y = 3 + 6

y = 9

Answer:

The table that has the y-value as 2 for each input

Step-by-step explanation:

The table that has the y-value as 2 for each input. This is because as x increases by 1, the y-value is increasing by 0, so the slope is 0/1 or 0. The vertical line doesn't have a zero slope, since it's undefined,  because if you take any two points the "run" is 0, thus you would be dividing by 0, the slope cannot be defined.

Answer:

[tex]5)\ \ \left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4=4x^{\frac{4}{5}}y^{\frac{2}{5}}[/tex]

[tex]6)\ \ \frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }=1[/tex]

Step-by-step explanation:

[tex]\left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4[/tex]

[tex]=x^{\frac{8}{10}}y^{\frac{4}{10}} +3x^{\frac{4}{5}}y^{\frac{4}{10} }[/tex]

[tex]=x^{\frac{4}{5}}y^{\frac{2}{5}} +3x^{\frac{4}{5}}y^{\frac{2}{5} }[/tex]

[tex]=x^{\frac{4}{5}}y^{\frac{2}{5}}\times(1+3)[/tex]

[tex]=4x^{\frac{4}{5}}y^{\frac{2}{5}}[/tex]

……………………………………

[tex]\frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }[/tex]

[tex]=\frac{(2+7) \times\sqrt{9^{5}} }{\sqrt{9^{2}} \times \sqrt{9^{5}} }[/tex]

[tex]=\frac{9 \times\sqrt{9^{5}} }{9 \times \sqrt{9^{5}} }[/tex]

[tex]=1[/tex]

4.59 g will be the amount of substance that will be present after 5 year.

Given: 16g of radioactive substance

            8g left after 8 year

Concept: In a chemical reaction, the half-life of a species is the time it takes for the concentration of that substance to drop to half its original value. In a first-order reaction, the half-life of the reactant is ln(2)/λ, where λ (also referred to as k) is the reaction rate constant.

The half-life is given as 5 years, so the amount remaining after 9 years will be found by using the steps done below:

Remaining amount of radioactive substance = initial × (1/2)^(t/(half-life))

Remaining substance = (16 g)×(1/2)^(9/5) ≈ 4.59 g

After 9 years i.e., after 8 years have passed

About 4.59 g of the substance remains.

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Current year's debt ratio is 2.50

Last year's debt ratio is 2.44

Compute Dan's Dependable Delivery debt ratio for two consecutive years?

The debt ratio is the total liabilities divided by the total assets

The debt ratio for the current year =  2.50

The debt ratio for last year =2.44(find attached excel file and formula sheet)

Debt ratio means the portion of the firm's total assets funded using borrowing(external funding), the lower the ratio, the better since having a higher debt means a higher interest would be paid, the higher the debt, the higher the chance of the firm defaulting on paying interest and repaying the principal borrowed.

The fact that the debt ratio has increased in the current year, means that the ratio has worsened because more debt has been taken.

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The probability that a randomly selected light bulb will last between 825 hours and 900 is 0.477.

From the information given, a standard deviation below the mean will be:

= 750 - 75 = 675

Two standard deviations below the mean will be:

= 750 - 75(2)

= 600

In this case, we ant to know the probability that make up the areas. This is illustrated in the graph.

In conclusion, the correct option is 0.477.

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Answer:

742 is 7.42x10^2

0.053 inches is 5.3x10-2 inches

Step-by-step explanation:

The goal is to convert he number into a format that has one digit to the left of the decimal point.  When moving the decimal point more to the left, each step reduces the number by a factor of 10/

742

74.2 is the original number reduced by 10.  To keep the number valid, we need to multiply by 10, which can be written as 74.2 x 10.

7.42 is reduced by another factor of 10:  7.42 x10x10  This is the same as 7.42x10^2

742 is 7.42x10^2

0.053

0.53 is the original number multiplied by 10.  To keep the number valid, we need to divide by 10, which can be written as 0.53x10^-1

5.3 is the original number divided by another factor of 10.  This can be written as 5.3x10^-2

0.053 inches is 5.3x10-2 inches

Hello!

d₁ = distance covered in Part 1

d₂ = distance covered in Part 2

d₃ = distance covered in Part 3

Distance in Part 2 :

⇒ d₃ = 15 x 300 = 4500 m

⇒ d₂ = 2/5d₃

⇒ d₂ = 2/5 x 4500

⇒ d₂ = 1800 meters

Speed in Part 2 :

⇒ v₂ = 1800 m / 12 min

⇒ v₂ = 150 meters per minute

Answer:

4 gifts

Step-by-step explanation:

4÷4=0

so you get each other a gift so there none to spare

Answer:

12 gifts

Step-by-step explanation:

If there are 4 people, and each person brings a gift for each of the other three people, that means that there are 12 gifts at the party. Let's say there are four people: A, B, C, and D. Person A would have to bring 3 gifts to give  B, C, and D. Similarly, B would bring a gift each for A, C, D. C would bring a gift for A, B, D. Lastly, D would bring a gift for A, B, and C. Each person brings three gifts to give to the other three people at the party, and 3*4 people is 12. I hope that makes sense.

Answer:

The number of ways in which the digits can be assigned in the color wheel can be determined by the permutation of 8 taken 4 since it is in circular formation and whichever comes first is not important.

number of ways = 9P4 = 3024 ways

The roots of a polynomial function tells us about the position of the equation on a graph and the roots also tells us about the complex and imaginary roots. So, Roots of chords are similar to the roots of polynomial functions.

A real root of a polynomial function is the point where the graph crosses the x-axis (also known as a zero or solution). For example, the root of y=x^2 is at x=0.

Roots can also be complex in the form a + bi (where a and b are real numbers and i is the square root of -1) and not cross the x-axis. Imaginary roots of a quadratic function can be found using the quadratic formula.

A root can tell you multiply things about a graph. For example, if a root is (3,0), then the graph crosses the x-axis at x=3. The complex conjugate root theorem states that if there is one complex root a + bi, then a - bi is also a complex root of the polynomial. So if you are given a quadratic function (must have 2 roots), and one of them is given as complex, then you know the other is also complex and therefore the graph does not cross the x-axis.

So, The roots of a polynomial function tells us about the position of the equation on a graph and the roots also tells us about the complex and imaginary roots. So, Roots of chords are similar to the roots of polynomial functions.

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Answer:

185 when we subtract 212-127 it gives 185 thanks for the seeing image

The measure of each interior angle of a regular polygon is [tex]\frac{180(n-2)}{n}[/tex] degrees, where n is the number of sides.

Question 1

[tex]144=\frac{180(n-2)}{n}\\\\144n=180(n-2)\\\\144n=180n-360\\\\-36n=-360\\\\n=10 \text{ sides}[/tex]

Question 2

[tex]\frac{180(n-2)}{n}=135\\\\180(n-2)=135n\\\\180n-360=135n\\\\-360=-45n\\\\n=8 \text{ sides}[/tex]

Answer:

probably c

Step-by-step explanation:

Answer:

11 and 19

Step-by-step explanation:

X + (X+8) = 30

Open bracket

X plus X + 8 = 30

2x + 8= 30

Collect like terms

2x = 30 - 8

2x = 22

X=11

And x + 8 = 11 + 8= 19

Answer:

∠ 3 = 105°

Step-by-step explanation:

∠ 3 and ∠ 6 are same- side interior angles and sum to 180° , that is

∠ 3 + ∠ 6 = 180°

∠ 3 + 75° = 180° ( subtract 75° from both sides )

∠ 3 = 105°

The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

When a linear equation is represented as:

Ax + By = C

The slope (m) is:

m = -A/B

When the linear equation is represented as:

y = mx + c

The slope is m

A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m

Using the above highlights, the equations of the lines are:

6. y = -2x + 5; (2, 7)

The slope is:

m = -2

The perpendicular slope is:

n = 1/2

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/2(x - 2) + 7

Evaluate

y = 1/2x - 1 + 7

This gives

y = 1/2x + 6

7. y = -5; (11, 15)

The slope is:

m = 0

The perpendicular slope is:

n = 1/0 = undefined

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 15

8. Graph ; (-12, 10)

The slope is:

m = (y2 - y1)/(x2 - x1)

Using the points on the graph, we have:

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

m = 1

The perpendicular slope is:

n = -1

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = -1(x + 12) + 10

y = -x - 12 + 10

Evaluate

y = -x - 2

9. y = -1/6x + 1; (-2, -9)

The slope is:

m = -1/6

The perpendicular slope is:

n = 6

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 6(x + 2) - 9

Evaluate

y = 6x + 12 - 9

This gives

y = 6x + 3

10. 6x + 2y = 14; (12, 0)

The slope is:

m = -6/2

m = -3

The perpendicular slope is:

n = 1/3

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/3(x - 12) + 0

Evaluate

y = 1/3x - 4

Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

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Rewriting the left hand side,

csc²t - cost sec t

= (1/sin²t)-(cost)(1/cost)

= 1/sin²t - 1

= 1/sin²t - sin²t/sin²t

= (1-sin²t)/sin²t

= cos²t/sin²t

= cot²t

Answer:

a=223.57

c=181.43

Step-by-step explanation:

a=405-c

substitute for a in the equation :

12a+5c=3590

12(405-c)+5c=3590

4860-12c+5c=3590

-7c=3590-4860

-7c=-1270

c=1270/7=181.43

a=405-1270/7

a=1565/7=223.57