What is the slope and y-intercept of the line 3x - 2y = 12?

Answer:

3 = x ÷ 4

Step-by-step explanation:

Given expressions:

8 = x - 2 ⇒ x = 8 + 2= 10

3 = x ÷ 4  ⇒ x = 3*4 = 12

x - 6 = 5  ⇒ x = 5 + 6 = 11

x - 3 = 9  ⇒ x = 9 + 3 = 12

3 of them involves addition, one of them - multiplication

The second expression doesn't belong

The correct answer for the given expression is 5.

Given,

evaluate the expression 4ˣ + 1

By putting x= 1,

we get 4¹ + 1

= 4+ 1

= 5

So, the the answer for the question, evaluate  4ˣ + 1 is 5.

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Using operations with functions, we have that:

a) w(t) = -3t + 5.

b) The pool will leak all the water in 1.67 hours.

c) 1.67 hours.

d) Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.

e) The domain of the function is 0 ≤ t ≤ 1.67.

The amount of water in the pool is determined by the subtraction of the amount flowing into the pool by the amount being drained out the pool.

For this problem, these following functions are given:

Hence the amount of water in the pool is given by:

w(t) = f(t) - d(t)

w(t) = t² + 8t + 9 - t² - 11t - 4

w(t) = -3t + 5.

Hence:

The function is: w(t) = -3t + 5.

The pool will have leaked all the water when:

w(t) = 0.

Hence:

-3t + 5 = 0.

3t = 5

t = 1.67.

The pool will leak all the water in 1.67 hours.

Equaling f(t) and d(t), we have that:

t² + 8t + 9 = t² + 11t + 4.

3t = 5.

t = 1.67.

Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.

The domain of a function is the set that contains all input values of the function. For this problem, the input is the time, hence:

Hence:

The domain of the function is 0 ≤ t ≤ 1.67.

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If two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, The speed (in mi/h) of the faster cyclist is: 5 mph and 10 mph.

Let r represent the speed of one

Let 2r represent thee speed of the other

Total distance traveled by both the sisters = 30 miles

Time ×rate = Distance

Hence,

2(2r+r) = 30

2(3r)=30

6r=30

r=30/6

r=5 mph

Speed=5 mph and (5 mph×2)

Speed=5 mph and 10 mph

Therefore If two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, The speed (in mi/h) of the faster cyclist is: 5 mph and 10 mph.

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Slant height of the conical frustum, l = 5 units.

Total surface area of the conical frustum, a = 329.87 square units.

Volume of the conical frustum, v = 1394.87 cubic units.

Given,

Radii of bases of a conical frustum,

r₁= 9

r₂ = 12

Height = 4

We have to find the total surface area of the frustum and volume of the frustum.

Formula for total surface area, a = [tex]\pi l(r_{1} +r_{2}[/tex][tex])[/tex]

Volume of the frustum, v = [tex]\frac{1}{3} \pi h(r_{1} ^{2} +r_{2} ^{2} +(r_{1} r_{2} )} )[/tex]

Here l is the slant height.

Slant height, l = [tex]\sqrt{(r_{1} -r_{2} )^{2} +h^{2} }[/tex]

First we have to find the slant height.

l = [tex]\sqrt{(r_{1} -r_{2} )^{2} +h^{2} }[/tex]

l = [tex]\sqrt{(9-12)^{2}+4^{2} }[/tex]

l = [tex]\sqrt{(-3)^{2} +16}[/tex]

l = [tex]\sqrt{9+16}[/tex]

l = [tex]\sqrt{25}[/tex]

Slant height, l = 5 units

Now,

Total surface area, a = [tex]\pi l(r_{1} +r_{2}[/tex][tex])[/tex]

a = [tex]\pi[/tex] × 5 × ( 9 + 12)

a = [tex]\pi[/tex] × 5 × 21

a = 329.87 square units.

Then,

Volume of the frustum, v = [tex]\frac{1}{3} \pi h(r_{1} ^{2} +r_{2} ^{2} +(r_{1} r_{2} )} )[/tex]

v = [tex]\frac{1}{3}[/tex] × π × 4 × (9² + 12² + ( 9×12))

v = [tex]\frac{1}{3}[/tex] × π × 4 × (81 + 144 + 108)

v = [tex]\frac{1}{3}[/tex] × π × 4 × 333

v = 1394.87 cubic units.

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The estimate for the side length of the square = the width of the rectangle (w) = √44.

Area of Rectangle = (length)(width)

Given the parameters below:

If this rectangle is divided to form two squares with equal areas, then the side length of each square would be equal to the length of the original rectangle = w.

(2w)(w) = 88

2w² = 88

w² = 88/2

w² = 44

√w² = √44

w = √44

Thus, an estimate of the side length of the square = the width of the rectangle (w) = √44.

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Answer:

10 hours

$352

Step-by-step explanation:

Given costs:

Define the variables:

Create a system of equations using the given costs and defined variables:

[tex]\begin{cases}y=132+22x\\y=152+20x \end{cases}[/tex]

To find how many hours Ryan would need to rent the boat in order for the cost of both companies to be the same, substitute equation 1 into equation 2 and solve for x:

[tex]\begin{aligned}132+22x & = 152+20x\\132+22x-20x & = 152+20x-20x\\132+2x & = 152\\132+2x-132 & = 152-132\\2x & = 20\\\dfrac{2x}{2} & = \dfrac{20}{2}\\x & = 10\end{aligned}[/tex]

Therefore, the number of hours Ryan would need to rent the boat in order for the cost of both companies to be the same is 10 hours.

Substitute x = 10 into one of the equations to find the cost at both companies if Ryan rented a boat for this many hours:

[tex]\begin{aligned}x=10 \implies y & = 132+22(10)\\& = 132+220\\& = 352\end{aligned}[/tex]

Therefore, the cost at both companies if Ryan rented a boat for 10 hours would be $352.

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Answer:

-1

Step-by-step explanation:

i just inserted it into an online graphing calculator called desmos.

The expression to represent the total amount of juice left in the jar is: (.25 + .30+  .75) -.20 and  the property used in each step is addition and extraction of Liquid from the mixture.

Expression:

(AJ+GP+PJ)-M

Where:

Apple juice=AJ

Grape juice=GP

Pineapple juice=PJ

Mixture=M

Hence,

(.25 + .30+  .75) -.20

b. Simplifying the expression

(.25 + .30+  .75) -.20

=1.3-.20

=1.10

Therefore the expression to represent the total amount of juice left in the jar is: (.25 + .30+  .75) -.20 and  the property used in each step is addition and extraction of Liquid from the mixture.

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Answer: E. The 20 plants in the two groups

Step-by-step explanation: experimental units are individuals on which the experiment is being performed. In this case the pepper plants are being used to test the effectiveness of the new fertilizer.

(12x^5 + x² + 4) /4.

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.

Given equation

x²/4+3x^5+1

Find common denominator

x²/4+3x^5 . 4/4+4/4

Combine fractions with common denominator

(x²+3x^5 . 4+4)/4

Multiply the numbers

(x²+12x^5 +4)/4

Rearrange terms

(x²+12x^5 +4)/4

(12x^5 + x² + 4) /4

Thus , solution of the given polynomial is (12x^5 + x² + 4) /4. we can also write it as -

3x^5 + x² / 4 + 1.

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Answer:

Smaller

Step-by-step explanation:

When you multiply something by 1/3, basically what you are doing is multiplying that thing by one and dividing it by 3.

To put it in a better perspective, let's say you have something that is 5 inches long and you multiply it by a scale factor of 1/3. The equation would be: (5*1)/3.

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The variance of the data sets is 77.7

Variance is the average of the squared differences from the Mean.

Therefore, to find the variance we have to find the mean, Then for each number: subtract the Mean and square the result.

Then work out the average of those squared differences.

Hence,

mean = 4 + 16 + 21 + 32 + 11 + 12 / 6 = 96 / 6 = 16

Therefore, lets find the difference and square it.

(4 - 16)² + (16 - 16)² + (21 - 16)² + (32 - 16)² + (11 - 16)²+ (12 - 16)²

144 + 0 + 25 + 256 + 25 + 16 = 466

Therefore,

variance = 466 / 6

variance = 77.6666666667

variance = 77.7

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The given function is a linear function because variable have first degree power.

The terms "linear function" in mathematics refer to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

A linear function is a function that represents a straight line on the coordinate plane. As an illustration, the equation y = 3x – 2 represents a linear function because it is a straight line in the coordinate plane.

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Answer:

B, 15 pencils

Step-by-step explanation:

Our equation: (5 x 42)/14

42 x 5 = 210

210/14= 15

The function which f(2) = 3 is the function with the equation f(x) = x + 1

The function value is given as

f(2) = 3

The above means that the value of the function is 3 when x = 2

i.e., f(x) = 3 when x = 2 or we substitute 2 for x in f(x)

Next, we test the above function in the list of given options

So, we have

f(x) = x^2 + 1

Substitute 2 for x in f(x)

f(2) = 2^2 + 1

Evaluate the exponent in the above equation

So, we have

f(2) = 4 + 1

Evaluate the sum in the above equation

So, we have

f(2) = 5

f(x) = 2x + 1

Substitute 2 for x in f(x)

f(2) = 2 x 2 + 1

Evaluate the product in the above equation

So, we have

f(2) = 4 + 1

Evaluate the sum in the above equation

So, we have

f(2) = 5

f(x) = x + 1

Substitute 2 for x in f(x)

f(2) = 1 x 2 + 1

Evaluate the product in the above equation

So, we have

f(2) = 2 + 1

Evaluate the sum in the above equation

So, we have

f(2) = 3

Hence, the function which f(2) = 3 is the function with the equation f(x) = x + 1

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Possible question

Identify each function for which f (2) = 3

f(x) = x^2 + 1

f(x) = 2x + 1

f(x) = x + 1

f(x) = 2x^3 + 1

The required zeros of the polynomial f(x) are 1 and ±√-1.

What are zeros of the polynomial?

All the possible values of x that will make the polynomial zero are called the zeros of the polynomial, p(x). Zeros of a polynomial can either be negative or positive.

Solving for the zeros of a polynomial

y = x³ - x² + x - 1

Let, f(x) = 0

x³ - x² + x - 1 = 0

Using heat and trial method, we get,

x =1 as one of the zero of the polynomial

It implies that (x-1) is the root of polynomial

Thus, dividing x³ - x² + x - 1 by x - 1, we get

x² + 1, which is then equated to 0 to obtain the zeros of the given polynomial

i.e. x² + 1 = 0

x = 1, ±√-1

Hence, the required zeros of the polynomial y are 1 and ±√-1.

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Answer:

n=-3

Step-by-step explanation:

2-2n=3n+17

-2n=3n+15

-5n=15

n=-3

The absolute value of the given modulus function are -1 and 7.

The given modulus function is;

|4x - 12| = 16

Removing modulus sign will provide two values;

4x - 12 = ±16

Solve for positive value of modulus function;

4x - 12 = 16

Add 12 on both side;

4x - 12 + 12 = 16 + 12

4x = 28

Dive both side by 4.

x = 7

Now, solve for negative value of modulus function.

4x - 12 = -16

Add 12 on both side;

4x - 12 + 12 = -16 + 12

4x = -4

Divide both side by 4;

x = -1

Thus, the two value of the given modulus function are -1 and 7.

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The magnitude of the Pennsylvania earthquake is 4.

An exponent is a logarithm. You may convert any exponential expression to logarithmic form. As an illustration, if 8 = 23, the base is 2, the exponent is 3, and the outcome is 8. This may be represented as 3 = log2 8 in logarithmic notation.

The equation y=logb(x+h)+k shifts the logarithmic function, y=logbx, by k units vertically and h units horizontally.

Using the formula,

log I₁ / I₂ = M₁ - M₂

M₁ = 7.7,     I₁ / I₂ = 4900

log 4900 = 7.7 - M₂

log 4900 ≈ 3.69

On calculating,

M₂ ≈ 4

The magnitude of the Pennsylvania earthquake is 4.

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The expression to illustrate the information when Toby's seventh grade class is going on a field trip to a history museum will be 0.2 (10x + 30y).

It should be noted that there are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each and the history museum gave the class 20% off as part of a group promotion.

Therefore, it should be noted that the expression to illustrate this will be:

= 20% × (10 × x) + (20 × y)

= 0.2 (10x + 30y)

Therefore, the expression to illustrate the information when Toby's seventh grade class is going on a field trip to a history museum will be 0.2 (10x + 30y).

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Toby's seventh grade class is going on a field trip to a history museum. There are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each. The history museum gave the class 20% off as part of a group promotion. What expression will illustrate this?

Answer:

Step-by-step explanation:

The most appropriate choice for modulus function is given by-

values of [tex]x[/tex] = [tex]\frac{48}{29}[/tex] and [tex]\frac{50}{27}[/tex]

What is modulus function?

Modulus function returns the absolute value of a function.

[tex]|x| = \left \{ {{x, x \geq 0} \atop {-x, x < 0}} \right.[/tex]

Here,

For [tex]14 - 8x \geq 0[/tex]

[tex]7(14-8x) = 2x + 2\\98 - 56x = 2x + 2\\56x + 2x =98 -2\\58 x = 96\\x = \frac{96}{58}\\ \\x = \frac{48}{29}[/tex]

For [tex]14 - 8x < 0[/tex],

[tex]7(8x - 14) = 2x + 2\\56x - 98 = 2x + 2\\56x - 2x =98 +2\\54 x = 100\\x = \frac{100}{54}\\ \\x = \frac{50}{27}[/tex]

So,  [tex]x = \frac{48}{29}[/tex] and [tex]x =\frac{50}{27}[/tex]

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The height of building is 0.2 miles.

The given points form a right angled triangle. Top of the building to base of building is the perpendicular, base of building to the angle of elevation is base and angle of elevation to top of the building is hypotenuse. So, considering this, tan of angle of elevation related the two sides of triangle as follows -

tan theta = perpendicular ÷ base

tan 6° = perpendicular ÷ 2

Perpendicular = 2 × tan 6°

Keep the value of tan 6°

Perpendicular = 2 × 0.1

Performing multiplication

Perpendicular = 0.2 miles

Hence, the height of the building is 0.2 miles.

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Answer:

A. 0

Step-by-step explanation:

Slope tells you steepness or flatness of your line.

If you know two points on a line find slope by subtracting the y's and put that on top of a fraction. And subtract the x's and put that on the bottom of the fraction.

Subtract y's: 3 - 3

Put it on top: 0/...

Subtract x's: 5 - -4

same as 5+4

Put that on the bottom: 0/9

slope, usually called m, is 0/9, which is 0.

Notice if you graph these two points its a hOrizOntal line. HOrizOntal lines have zerO slope.

  Solving the problem by multiplying and simplifying we have as a result 16x¹⁵

Simplification is a process of reducing terms to expressions, which do not generate changes or values.

  Multiplication is also known as product, and it is a mathematical operation of a successive sum, this operation consists of adding a number a certain number of times:

a x b the number "a" will be added "b" times.

  The algebraic expression that we must simplify to its minimum expression is:

4√16 x⁸ . 4√x¹⁴

4×4x⁸ × 4x¹⁴/²  

16x⁸× 4x⁷  ; multiply power of equal base

16x⁸⁺⁷

16x¹⁵

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Answer:

I believe it's 25% .............

Answer:

40%

Step-by-step explanation:

The cash price = $4,250

If Steve rents the computer for $595 for 10 months he would have to spend $595 x 10 = $5,950

The difference in money = 5950 - 4250 =$1700

As a percentage of the cash price this would be
1700/4250 x 100 =  40%

Answer:
Rent option is  40% more than the cash price 40%

We can verify this by noting that if there is an increase of r% in the price of an item then
Increased price = Old price + Increase

= Old price + Old price x r/100

In this case, Old price = 4250
r = 40%, r/100 = 0.04

New price = 4250 + 4250 x 0.04  = 4250(1 + 0.04) = 4250(1.04) = 5950 which tallies with given figures