How large an equilateral triangle can you fit inside a 2-by-2 square?

The choice which is equivalent is  [tex]6x^2\sqrt{3}[/tex] option B

We have that;

[tex]\sqrt{6x^2} * \sqrt{18x^2}[/tex] where [tex]x\geq 0[/tex]

First, we factorize the square root

= [tex]\sqrt{2 * 3 * x^2 } . \sqrt{3 * 3 * 2 * x^2}[/tex]

Find the common factors

= [tex]2 * 3 x^2\sqrt{3}[/tex]

= [tex]6x^2\sqrt{3}[/tex]

Thus, the choice which is equivalent is  [tex]6x^2\sqrt{3}[/tex] option B

The complete question is;

Which choice is equivalent to the product below for acceptable values of X? sqrt 6x² * sqrt 18x²

a. [tex]6\sqrt{3x}[/tex]

b. [tex]6x^2\sqrt{3}[/tex]

c. [tex]6\sqrt{18x}[/tex]

d. [tex]\sqrt{108x^2}[/tex]

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There does not appear to be a linear relationship between the high school girls' height and their IQ scores.

The complete question is added as an attachment

To plot the scatter plot, we make use of the following representations:

Next, we enter the values in a graphing calculator.

From the summary on the graphing calculator, we can conclude that the scatter plot is (c)

To determine the sample correlation coefficient, we make use of the following representations:

Next, we enter the values in a graphing calculator.

From the graphing calculator, we have the following summary:

X Values

Y Values

X and Y Combined

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -19.25 / √((107.875)(813.5))

r = -0.065

Hence, the sample correlation coefficient is -0.065

In (b), we have:

r = -0.065

This means that there is a negative correlation

i.e. There does not appear to be a linear relationship between the high school girls' height and their IQ scores.

To do this, we have:

Number of pairs, n = 8

Significance level =0.01

Using a graphing calculator;

At 0.01 significance level, the critical correlation coefficient is 0.7887

0.7887 is greater than 0.01

This means that we accept the null hypothesis.

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Answer: B

Step-by-step explanation: Since x is less than 7, the graph would be all real numbers that are less than 7, so the arrow would be on the left.

Also, since x is not 7 itself (not less than or equal to), the dot cannot be a full dot. Thus, the dot must be open (or curved in some textbooks) to indicate x is not apart of 7 but less than 7.

Hope this helped!

Answer:

(12 + n/3) = 2n + 1

Step-by-step explanation:

(12 + n/3) = 2n + 1

36 + n = 6n + 3

33 = 5n

n = 33/5

Approximately 5 number of trays must be sold to cover all costs including labor.

The profit on each tray that was sold excluding labor cost is;

Profit = $35-$14

Profit = $21

Total labor cost for making party tray for a day is;

Total Labor Cost = Total labor hours * wages per hour * No. of labors

Total Labor cost = $7 * $8*2

Total Labor Cost = $112

Number of trays that must be sold to cover cost  is;

Total labor cost/ Profit per tray

Number of trays = $112/$21

= 5.33

Approximately 5 trays must be sold to cover all costs including labor.

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The total interest on the mortgage loan  is $219,249.60

What is a mortgage loan?

It is a loan taken in order to purchase a property that requires periodic repayments such as monthly repayment since most mortgages are repaid monthly.

Our first task is to determine the monthly repayment using the present value formula of an ordinary annuity because the monthly payment becomes due at the end of each month.

PV=monthly repayment*(1-(1+r)^-N/r

PV=loan amount=$210,000

monthly repayment=unknown(assume it is X)

r=monthly interest rate=5.5%/12=0.00458333333333333

N=number of monthly payments in 30 years=30*12=360

$210,000=X*(1-(1+0.00458333333333333)^-360/0.00458333333333333

$210,000=X*(1-(1.00458333333333333)^-360/0.00458333333333333

$210,000=X*(1-0.19277525234572900)/0.00458333333333333

$210,000=X*0.80722474765427100/0.00458333333333333

$210,000=X*176.12176312456800000

X=$210,000/176.12176312456800000

X=monthly payment=$1,192.36

total repayments(360 months)=$1,192.36*360

total repayments(360 months)=$429,249.60

Total interest=total repayments(360 months)-loan amount

Total interest=$429,249.60-$210,000

Total interest=$219,249.60

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Answer:

x=30,y=165,z=5

Step-by-step explanation:

check it bro

Answer:

Exact form: 7/143

Decimal form: /0.048951

Answer:

[tex]x=\frac{7}{143}[/tex]

Step-by-step explanation:

Simplify the right side of the equation. [tex]3x+21=432x[/tex]. Subtract 21 from both sides of the equation. [tex]3x=432x-21[/tex]. Subtract 432x from both sides of the equation, [tex]-429x=-21[/tex]. The negative signs cancel out to get [tex]429x=21[/tex]. Divide both sides but 429 to get [tex]x=\frac{21}{429}[/tex].  Reduce to get [tex]x=\frac{7}{143}[/tex].

Answer:

2.92

Step-by-step explanation:

[tex]V=\frac{4}{3}\pi r^3 \\ \\ 105=\frac{4}{3}\pi r^3 \\ \\ r^3=\frac{105}{\frac{4}{3}\pi} \\ \\ r=\sqrt[3]{\frac{105}{\frac{4}{3}\pi}} \\ \\ r \approx 2.92[/tex]

The value of the sum of the angles x + y of the given triangle is; 220°

We know that the sum of angles in a straight line is equal to 180°. Thus;

∠CFE + ∠OFE = 180

140 + ∠OFE = 180

∠OFE = 180 - 140

∠OFE = 40°

Similarly, we can use the same principle to get;

∠OEF + ∠BEF = 180°

∠OEF + y = 180°

∠OEF = 180 - y

Similarly,

∠AOF + ∠EOF = 180°

x + ∠EOF = 180°

∠EOF = 180 - x

Sum of angles in a triangle is equal to 180°. Thus;

40 + 180 - y + 180 - x = 180

Rearranging gives;

x + y = 180 + 180 + 40 - 180

x + y = 220°

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4x - 10 = 7 - 2x (given)

6x - 10 = 7 (addition property of equality)

6x = 17 (addition property of equality)

x = 17/6 (division property of equality)

An equation is an expression that shows the relationship between two or more numbers and variables.

From the equation:

4x - 10 = 7 - 2x (given)

6x - 10 = 7 (addition property of equality)

6x = 17 (addition property of equality)

x = 17/6 (division property of equality)

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g(x) is just a translation of 10 units downwards, this means that the equation for g(x) is:

[tex]g(x) = f(x) - 10 = 5^x - 10[/tex]

Here we know that:

[tex]f(x) = 5^x[/tex]

And we want to find the equation for g(x), which is a translation of f(x).

If you look at the graph of f(x), you can see that it passes through:

(0, 1), (1, 5), (2, 25), etc.

And the graph of g(x) passes through:

(0, -9), (1, -5), (2, 15)

So in each point, the y-component is 10 units smaller than the correspondent for f(x).

Then g(x) is just a translation of 10 units downwards, this means that the equation for g(x) is:

[tex]g(x) = f(x) - 10 = 5^x - 10[/tex]

So the correct option is the last one.

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Answer:

x=20

Step-by-step explanation:

x-15=5

x=5+15

x=20

The graph whuch best represents the solution to the system of equations is; A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.

As an alternative, solving the system of equations algebraically, we have;

-2x +14 = 2x +2

x = 3 and by substitution;

y = 8.

On this note, the point (3,8) is a solution of the graph and hence, the answer choice with two lines intersecting at (3,8) is correct.

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The value of the text statistic. F  is given as : 0.742 See explanation below.

A test statistic is a numerical value determined by a statistical test.

It quantifies the distance between your observed data and the null hypothesis of no link between variables or no difference between sample groups.

Test Statistic F is given by:

= σ²₁/σ²₂

= 0.93²/1.08²

= (0.93/1.08)²

= 0.8611²

= 0.742

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Answer:

y = 40

Step-by-step explanation:

y/8 = 5

———————————————————

Multiply both sides by 8:

8y/8 = 5 * 8

———————————————————

Simplify:

y = 40

Hope that helps! :)

Answer:

Y = 40

Step-by-step explanation:

Step 1:

y/8 = 5

Bring 8 to the right side changing its arithmetic sign to multiply.

Step 2:

y = 5 x 8

Now multiply 5 by 8 to get the answer.

Step 3:

y = 40

Therefore, y is equal to 40.

Answer: -5

Step-by-step explanation:

[tex]h(4)=\frac{1}{2}(4)-5=-3\\\\f(4)=3h(4)+4=3(-3)+4=-5[/tex]

Answer:

(2,-3)

Step-by-step explanation:

I am not sure if you meant the first equation to be y or -y.  I solved it as y.

y = x-5                       -x -3y =7

I am going to take the second equation and write it as x =

-x - 3y = 7  Give equation

-x = 3y +7   Add 3y to both sides

x = -3y-7  Multiplied each term in the equation by -1 so that x could be positive

I am going to substitute -3y-7 for x in the first equation up above

y = x - 5

y = -3y -7 - 5  Substitute -3y-7 for x

y = -3y -12  Combined -7-5

4y = -12  Added 3y to both sides

y = -3  Divided both sides by 4.

I now know that y is -3, I will plug that into x = -3y-7 to solve for x

x = -3(-3) -7

x = 9-7   A negative times a negative is a positive

x = 2

Answer:

[tex]y=-2.5x+8[/tex]

Step-by-step explanation:

Parallel lines have the same slope but different y-intercepts. So, first, transform the given equation into the slope-intercept form, [tex]y=mx+b[/tex].

[tex]5x+2y=6[/tex]

[tex]2y=-5x+6[/tex]

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

Then, determine the equation of a line that has a slope of [tex]-\frac{5}{2}[/tex] and passes through (1, 5.5). Substitute all the known values and solve for b.

[tex]y=mx+b[/tex]

[tex]5.5 = -\frac{5}{2} *1+b[/tex]

[tex]5.5=-2.5+b[/tex]

[tex]b=8[/tex]

Therefore, the answer is [tex]y=-2.5x+8[/tex].

Linking each equation with its equivalent equation below:

Equivalent equation can be defined as an equation that has the same value with another equation.

Equivalent equation are not directly the same but can be transformed to look like each other.

In conclusion, The equivalent equations have been matched in the list above.

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Answer:

D. g(x) is a reflection of f(x) over the x-axis.

Step-by-step explanation:

So when you have the equation: [tex]-2x^2[/tex] it's just negating the value of f(x), which is [tex]2x^2[/tex] and since f(x) represents the y-value, you're negating the y-value and the x-value is unchanged. So each point on f(x) was originally: (x, f(x)) and now it's (x, -f(x)). Since the y-value is changing, it's going to be reflecting across the x-axis. So g(x) is a reflection of f(x) over the x-axis.

The volumes of the right prisms are listed below:

In this problem we have six cases of right prisms with rectangular bases, the volume of right prisms (V), in cubic length units, is equal to the product of the area of the base (A), in square length units, and the height (h), in length units. The equation of the volume of the right prism is shown below:

V = w · l · h     (1)

Where:

Now we proceed to calculate each volume:

Prism 1 (w = 2 / 3 ft, l = 1 / 3 ft, h = 1 / 2 ft)

V = (2 / 3 ft) · (1 / 3 ft) · (1 / 2 ft)

V = 1 / 9 ft³

Prism 2 (w = 1 / 8 in, l = 3 / 4 in, h = 13 / 16 in)

V = (1 / 8 in) · (3 / 4 in) · (13 / 16 in)

V = 39 / 512 in ³

Prism 3 (w = 7 / 8 cm, l = 1 / 4 cm, h = 1 / 12 cm)

V = (7 / 8 cm) · (1 / 4 cm) · (1 / 12 cm)

V = 7 / 384 cm³

Prism 4 (w = 1 / 7 cm, l = 7 / 8 cm, h = 2 / 3 cm)

V = (1 / 7 cm) · (7 / 8 cm) · (2 / 3 cm)

V = 1 / 12 cm³

Prism 5 (w = 9 / 10 m, l = 2 / 3 m, h = 1 / 5 m)

V = (9 / 10 m) · (2 / 3 m) · (1 / 5 m)

V = 3 / 25 m³

Prism 6 (w = 7 / 8 yd, l = 6 / 7 yd, h = 1 / 2 yd)

V = (7 / 8 yd) · (6 / 7 yd) · (1 / 2 yd)

V = 3 / 8 yd³

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Answer:

[tex]\boxed {(f-g)(x) = x^{2}+3}[/tex]

Step-by-step explanation:

Given :

Now, this problem can be used using a simple formula.

[tex]\fbox {(f - g)(x) = f(x) - g(x)}[/tex]

Let's solve.

∴ The answer will be x² + 3.

The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]

The derivative of a function f(x) is the ratio of the change in f(x) to the change in x

The given function is:

[tex]f(x)=5^{2x}[/tex]

Let u = 2x

Find the derivative of u. That is, du/dx

du/dx = 2

f(x) = 5^u

[tex]\frac{df}{du} =5^ulnu[/tex]

Using the chain rule of derivative

[tex]\frac{df}{dx}=\frac{df}{du} \times\frac{du}{dx}[/tex]

[tex]\frac{df}{dx} =5^uln5 \times 2\\\\\frac{df}{dx} =2ln5(5^{2x})[/tex]

The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]

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Answer:

Step-by-step explanation:

hello :

Solut i on :

1) A line that passes through A(0, -6 ) andB (8 ,- -8)

Hello : let A(0,-6) B(8,-8)

the slope is : (YB - YA)/(XB -XA)

(-8+6)/(8-0) = -2/8=-1/4

an equation is : y=ax+b a is a slope

y = (-1/4)x +b

the line through point A (0;-6) : -6 = (-1/4)(0)+b

b = -6            the equation is : y =(-1/)4x-6

The point has a real part of 0 and an imaginary part of 18, and thus corresponds to the point (0,18) in the complex plane.

Answer:

Inequality Form: x > 17

Interval Notation: (17, ∞)

Answer:

dependent

Step-by-step explanation:

because when x decreases y has to also decrease, so they are dependent on eachother

Answer:

24

Step-by-step explanation:

1) according to the additional (see the attached picture) f(6)= -6 and g(5)= -5. Then

2) the given experssion can be written:

f(6)-6*g(5)=-6-6*(-5)=-6+30=24.

Answer:

6

Step-by-step explanation:

Absolute value is a number's distance from 0, another way to think of it is that it makes any number positive, so |-6|, the absolute value of -6 would be 6.

Answer:

6

Step-by-step explanation:

The absolute value is always positive, since it's the number's distance from zero.

Thus, the absolute value of -6 is 6.

Done !!