The question is below please answer quickly

1) [tex]7y=8x-14, y=6[/tex] [given]

2) [tex]7(6)=8x-14[/tex] [substitution]

3) [tex]56=8x[/tex] [addition property of equality]

4) [tex]7=x[/tex] [division property of equality]

5) [tex]x=7[/tex] [symmetric property of equality]

A two columns proof is given in the attached image below as per the concept of solving equations.

A two columns proof is given below:

Statement | Reasons

y = 6 | Given

7y = 8x - 14 | Given

7(6) = 8x - 14 | Substitution (Substitute y with 6 in statement 2)

42 = 8x - 14 | Simplification

42 + 14 = 8x | Addition Property of Equality (Add 14 to both sides)

56 = 8x | Simplification

56/8 = x | Division Property of Equality (Divide both sides by 8)

7 = x | Simplification (Simplify the fraction 56/8)

x = 7 | Symmetric Property of Equality (Rearrange statement 9)

In this two-column proof, we start with the given information that y is equal to 6 (statement 1).

Then, we substitute the value of y into the equation 7y = 8x - 14 (statement 2) to get 42 = 8x - 14 (statement 3).

We simplify the equation to isolate 8x and find that 56 = 8x (statement 6). Dividing both sides of this equation by 8 (statement 7) gives us x = 7 (statement 8).

Finally, we use the symmetric property of equality to rearrange the equation and conclude that x is indeed equal to 7 (statement 9).

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The determination of the money multiplier and the money supply for each reserve requirement listed in the following table are as follows:

Reserve Requirement    Simple Money     Money Supply

(percent)                             Multiplier             (Dollars)

  5                                          20                      $8,000

10                                           10                      $4,000

The money multiplier is the ratio of the reserve to the money supply.

The formula for determining the money multiplier is 1/r where r is the reserve ratio.

The money supply is the total amount of money circulating in the commercial banking system.

The quantity of the money supply is determined by multiplying the money multiplier by the total reserves.

Reserve Requirement    Simple Money     Money Supply

(percent)                             Multiplier             (Dollars)

  5                                    20 (1/0.05)               $8,000 ($400 x 20)

10                                     10 (1/0.1)                  $4,000 ($400 x 10)

Reserve Requirement    Simple Money     Money Supply

(percent)                             Multiplier             (Dollars)

  5

10

Thus, the money multiplier and money supply for the 5% reserve requirement are higher than for the 10% reserve requirement.

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the school purchased 742 items in total.

Just add 256+332+154

which equals...742. :)

Answer:

742 items

Step-by-step explanation:

Add up all the items that the cafeteria purchased. 256+332+154=742!

[tex]z=\dfrac{kx^3}{y^3}\\\\\\59=\dfrac{k\cdot 8^3}{8^3}\\k=59\\\\\\z=\dfrac{59x^3}{y^3}\\\\\\z=\dfrac{59\cdot 3^3}{4^3}=\dfrac{1593}{64}[/tex]

Answer: It’s a trinomial

Step-by-step explanation: It has three terms, so it’s classified as a trinomial. (Tri=three)

Answer:

x=23

Step-by-step explanation:

put it in desmos and was right

The required value for the sum is 9580.

[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]

Simplification in mathematics to solve the given condition on its operators.

[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]

= [tex]\frac{10000}{1.028^2} +68*\frac{1-\frac{1}{1.028^2} }{\frac{0.115}{4} } \\9451+68*\frac{1-0.94}{\frac{0.115}{4} } \\\\9451+68*\frac{0.054}{\frac{0.115}{4} } \\\\\\9451+3.72{\frac{4}{0.115} } \\\\\\9451+129\\[/tex]

= 9580

The required solution is given as 9580.

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Answer:

[tex]f(x) = a(x^2+4)(x-3)^2[/tex]

Step-by-step explanation:

So I'm assuming it means that one of the zeros is at x=3 with a multiplicity of 2 and it has an imaginary solution of 4i. Anyways, imaginary solutions come in conjugate pairs meaning if you have a complex solution of [tex]a-bi[/tex] there is another complex solution which is the conjugate of that which is [tex]a+bi[/tex] but since the imaginary solution is 4i, the complex number is just [tex]0+4i[/tex] so the conjugate is [tex]0-4i[/tex] or [tex]-4i[/tex]. So since you have x=3 as a zero that can be represented as [tex](x-3)^2[/tex] since 3 would make it 0 and it has a multiplicity of 2. As for the other factors, you won't just have ([tex](x-4i)(x+4i)[/tex], you'll have a factor that is set up in a way that the solutions are: [tex]x=\pm\sqrt{-4}[/tex]. That means it'll be a quadratic. So it'll be in the form [tex]x^2+b[/tex]. Since you're moving b to the other side and it's negative. that means it has to be positive and since the value is 4, you'll have the factor [tex](x^2+4)[/tex] which when set equal to zero has the solutions sqrt(-4). So this gives you the equation

[tex]f(x) = a(x^2+4)(x-3)^2[/tex]

Answer:

117 degrees

Step-by-step explanation:

Answer:

13 feet

Step-by-step explanation:

A^2 + B^2 = C^2

A=5 ^2 = 25

B=12 ^2 = 144

144 +25 = 169

C=13

Answer:

[tex]-\frac15[/tex]

Step-by-step explanation:

Hello!

We can utilize the slope formula to find the slope.

Slope Formula: [tex]S = \frac{y_2-y_1}{x_2-x_1}[/tex]

Remember that a coordinate is written in the form (x,y)

The slope of the line is [tex]-\frac15[/tex].

Answer:

-1/5

Step-by-step explanation:

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-4 - (-2)) / (5 - (-5))

Simplify the parentheses.

= (-4 + 2) / (5 + 5)

= -2 / 10

Simplify the fraction.

-2/10

= -1/5

This is your slope.

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The inverse function of [tex]f(x) = -\frac 12\sqrt{x + 3}[/tex] is[tex]f^{-1}(x) = 4x^2- 3[/tex]

The function is given as:

[tex]f(x) = -\frac 12\sqrt{x + 3}[/tex]

Rewrite as;

[tex]y = -\frac 12\sqrt{x + 3}[/tex]

Swap the positions of x and y

[tex]x = -\frac 12\sqrt{y + 3}[/tex]

Multiply through by -2

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

Square both sides

4x^2 = y + 3

Subtract 3 from both sides

y = 4x^2 - 3

Express as an inverse function

[tex]f^{-1}(x) = 4x^2- 3[/tex]

Hence, the inverse function of [tex]f(x) = -\frac 12\sqrt{x + 3}[/tex] is[tex]f^{-1}(x) = 4x^2- 3[/tex]

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Answer:

B

Step-by-step explanation:

1.(5x^3)(xy^4 -2x^3y)

2.5x^4y^4 -10x^6y

Answer:

S= 4

Step-by-step explanation:

add 9 to -5

= 4

s=4

The only statement that holds for the given operation is Statement II

Given the following operartions

a [] b = a+b - ab/2

We need to check the true statement

For the expression x [] (y+z) =  x [] y +  x [] z

x [] (y+z) = x+y+z - x(y+z)/2

x [] (y+z) = x+y+z - (xy+xz)/2

x [] y +x [] z =  x+y - xy/2 +[x+z - xz/2 ]

x [] y +x [] z = x+y+x+z -xy/2 - xz/2

x [] y +x [] z = 2x+y+z - (xy+xz)/2

This shows that the statement I is incorrect

For the second statement

y [] z =  y+z - yz/2

x [] (y [] z) = x + (y+z - yz/2) - x(y+z-yz/2)/2

x [] (y [] z) = x+y+z-yz/2 -xy/2 - xz/2+xyz/4

For the other expression

x [] y =  x+y - xy/2

(x [] y) [] z = x+y - xy/2 + z - z(x+y - xy/2)/2

(x [] y) [] z = x+y+z- xy/2 -zx/2 - zy/2 + xyz/4

This shows that x [] (y [] z) = (x [] y) [] z is correct (Statement II)

For the third statement

x [] z =  x+z - xz/2

y [] z =  y+z - yz/2

z [] 0 = z+0 - z(0)/2

z [] 0 = z

x[]z + y[]z - z[]0 = x+z - xz/2 + y+z - yz/2 - z

x[]z + y[]z - z[]0 = x+y+z - xz/2 - yz/2

For the expression (x+y)[] z

(x+y)[] z = (x+y)+z - (xyz)/2

Hence the statement III is not valid

Based on the explanations above, the only statement that holds for the given operation is Statement II

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Answer:

So, the vertex form of your function is  [tex]y(x)=2*(x+2)^2-7[/tex].

The vertex is at [tex](-2|-7)[/tex]

Step-by-step explanation:

Given function:

[tex]y(x)=2*x^2+8x+1[/tex]

Steps:

[tex]y(x)=2*x^2+8x+1\\[/tex]

[tex]y(x)=2(x^2+4x+\frac{1}{2} )[/tex]    (Factor out)

[tex]y(x)=2(x^2+4x+2^2-2^2+\frac{1}{2} )[/tex]  (Complete the square)

[tex]y(x)=2((x+2)^2-2^2+\frac{1}{2} )[/tex]  (Use the binomial formula)

[tex]y(x)=2((x+2)^2-\frac{7}{2} )[/tex]  (Simplify)

[tex]y(x)=2*(x+2)^2-7[/tex] (Expand)

49^2m-m : Not equivalent

7^2m-2m : Not equivalent

7^2m-m : Not equivalent

This is actually a trick question. All of the following are actually false statements. Want to know why? Let me show you.

For exponents, if you are dividing a number to some power (i.e 5^3) by the SAME number to a different power (i.e 5^2), then the expression is 5^3-2 or 5^1 = 5. This is true for any number a such that a^b ÷ a^c = a^b-c.

Since 7 and 49 are not the same number, this rule does not apply and thus cannot be simplified any further.

Let me prove why. 5^3 = 125, and 5^2 = 25, and 125 ÷ 25 = 5. This is also the same as 5^3-2 = 5^1 = 5. We just proved this as so.

But, what about 7 and 49, or 2 different numbers. Well it doesn't apply. 7^3 = 343, and 49^2 = 2401, and 343 ÷ 2401 ≈ 0.14. Thus, this is NOT equal to 7^3-2 which is 7. We just proved that a^y ÷ b^z ≠ a^y-z. Congratulations!

Hope this helped!

The expression a/b ÷ c/d = ad/bc is A. true.

Given to show that if a/b and c/d are rational expressions, then a/b ÷ c/d = ad/bc.

The ratio of two polynomials is an example of a rational expression. If an expression f is rational, it can be expressed in the form p/q, where p and q are polynomials.

Here we have a ,b ,c and d in the form of p/q form.

We take the reciprocal of the expression on the right side of the division sign when the rational expression a/b is to be divided by the rational expression c/d.

so, L.H.S = a/b ÷ c/d

= a/b × 1/(c/d)

= a/b × d/c

= ad/bc

= R.H.S

since L.H.S = R.H.S

a/b ÷c/d = ad/bc

Hence the expression a/b ÷ c/d = ad/bc is A.true.

Your question was incomplete. Please find the missing content here.

If A/B and C/D are rational expressions, then: A/B ÷C/D

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Answer:

5621 years

Step-by-step explanation:

Plug everything in first.

[tex]N=N_0e^{-kt}\\\\\implies 0.57 = e^{-0.0001t}\\\\\implies\ln \left(0.57\right)=-0.0001t\\\\t=-\frac{\ln \left(0.57\right)}{0.0001}[/tex]

Round to closest amount of years = 5621 years

Answer:

[tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]

Step-by-step explanation:

So when two lines are parallel there slopes are the same, but there y-intercepts are different, since if they had the same y-intercept, then they would be the same exact line. To convert an equation into slope-intercept form you simple isolate y by moving everything else to the other side, and then divide by the coefficient of y so the coefficient of y becomes 1. This will give you the equation in the form: y=mx+b where m is the slope and b is the y-intercept (because when the linear equation crosses the y-axis, the x is 0, thus mx will be 0, leaving only b, so the y-intercept is b).

Original Equation:

3x + 2y = 4

Subtract 3x from both sides

2y = -3x + 4

Divide both sides by 2

y = -3/2x + 2

Generally any parallel line will be in the form:

[tex]y=-\frac{3}{2}x + b\ \ \ \ \ b\ne2[/tex]. Since as stated before if two lines have the same slope and y-intercept, they're the same line, which is not the same as parallel, since parallel lines never intersect.

So since we're given a point in the parallel line (-1, 5) we can plug those values into the equation to find the value of b

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

Multiply and

[tex]5=\frac{3}{2}+ b[/tex]

Convert 5 into a fraction with a denominator of 2

[tex]\frac{5}{1} * \frac{2}{2} = \frac{10}{2}[/tex]

Write equation using this form of 5:

[tex]\frac{10}{2}=\frac{3}{2}+b[/tex]

Subtract 3/2 from both sides

[tex]\frac{7}{2}=b[/tex]

Now take this value and input it into the slope-intercept form to finish the equation: [tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]

sinA+sinB+sinC

=2sin(A+B)/2cos(A-B)/2+sin C

=2sin(pi-C)/2cos(A-B)/2+2sin C/2cosC/2

=2cosC/2(cos(A-B)/2+cos(A+B)/2)

=4 cos A/2 cos B/2 cos C/2

= RHS

Answer: 3 answers

Step-by-step explanation:

The lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

We have:

A survey of 504 citizens found that 378 of them favor a new bill introduced by the city.

Sample proportion = p = 378/504 = 0.75

q = 1 - p = 1 - 0.75 = 0.25

[tex]\rm SD = \sqrt{\dfrac{pq}{n}}[/tex]

[tex]\rm SD = \sqrt{\dfrac{0.75\times0.25}{504}}[/tex]

SD = 0.01928

For 95% confidence interval Z value = 1.96

Lower limit = 0.75 - 1.96(0.01928)

= 0.712

Thus, the lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.

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Answer:

just hey effect me II rieirjttjhg shewtha

The equation of function g is f(x) = 7^3x + 1

The function f(x) is given as:

f(x) = 7^x + 1

The rule of horizontal compression by a factor of 3 is represented as

g(x) = f(kx)

Where k = 3

So, we have:

f(x) = 7^3x + 1

Hence, the equation of function g is f(x) = 7^3x + 1

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Each number in the sum is even, so we can remove a factor of 2.

2 + 4 + 6 + 8 + ... + 78 + 80 = 2 (1 + 2 + 3 + 4 + ... + 39 + 40)

Use whatever technique you used in (a) and (b) to compute the sum

1 + 2 + 3 + 4 + ... + 39 + 40

With Gauss's method, for instance, we have

S = 1 + 2 + 3 + ... + 38 + 39 + 40

S = 40 + 39 + 38 + ... + 3 + 2 + 1

2S = (1 + 40) + (2 + 39) + ... + (39 + 2) + (40 + 1) = 40×41

S = 20×21 = 420

Then the sum you want is 2×420 = 840.

The number of red tiles in the box given the chance ratio of red to blue tiles is 18

= 12 + 2x

Number of red tiles = 3 / 8 × 12+2x

x = 3(12 + 2x) / 8

x = (36 + 6x) / 8

8x = 36 + 6x

8x - 6x = 36

2x = 36

x = 36/2

x = 18 tiles

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Answer: 28

Step-by-step explanation:

Answer:

cos4B =1-8sin^2(B)+8sin^4(B)

Step-by-step explanation:

cos4B =1-8sin^2(B)+8sin^4(B)

The liquid that will be the least dense liquid in the density column is; The  liquid floating on the top.

The formula for density is;

Density = Mass/Volume

Thus, the greater the mass, the more the density. Thus, it means that heavier objects will sink while lighter ones will float.

Thus, this means that the liquid that is most dense will be at the bottom of the liquid.

The liquid that is least dense will be at the top of the liquid.

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Applying the angles of intersecting chords theorem, m∠BEC = 109°.

According to the angles of intersecting chords theorem, the measure of angle BEC equals half the sum of the measures of arcs AD and BC.

arc mAD = 103°

arc mBC = 115°

Therefore, we would have:

m∠BEC = 1/2(103 + 115)

m∠BEC = 109°

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