3
\(3 + 4 = x - 1 \)
​

Answer:

Step-by-step explanation:

-1/4(-8x+12y)

-1*(-8x+12y)/4

8x-12y/4

4(2x-3y)/4(4 and 4 gets cancel)

2x-3y

Answer:

\(\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24\)

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of \(\triangle ACD\) and the hypotenuse of \(\triangle ADB\).

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

\(\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}\)

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is \(\angle CAD\). The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

\(\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}\)

Now use this value in the Law of Sines to find AD:

\(\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}\)

Recall that \(\sin 45^{\circ}=\frac{\sqrt{2}}{2}\) and \(\sin 60^{\circ}=\frac{\sqrt{3}}{2}\):

\(AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}\)

Now that we have the length of AD, we can find the length of AB. The right triangle \(\triangle ADB\) is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio \(x:x\sqrt{3}:2x\), where \(x\) is the side opposite to the 30 degree angle and \(2x\) is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent \(2x\) in this ratio and since AB is the side opposite to the 30 degree angle, it must represent \(x\) in this ratio (Derive from basic trig for a right triangle and \(\sin 30^{\circ}=\frac{1}{2}\)).

Therefore, AB must be exactly half of AD:

\(AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24\)

Answer:

\( \displaystyle 25 \sqrt{6} \)

Step-by-step explanation:

the triangle ∆ABD is a special right angle triangle of which we want to figure out length of its shorter leg (AB).

to do so we need to find the length of AD (the hypotenuse). With the help of ∆ADC it can be done. so recall law of sin

\( \boxed{ \displaystyle \frac{ \alpha }{ \sin( \alpha ) } = \frac{ \beta }{ \sin( \beta ) } = \frac{ c}{ \sin( \gamma ) } }\)

we'll ignore B/sinB as our work will be done using the first two

step-1: assign variables:

step-2: substitute

\( \displaystyle \frac{100}{ \sin( {45}^{ \circ} )} = \frac{AD }{ \sin( {60}^{ \circ} )} \)

recall unit circle therefore:

\( \displaystyle \frac{100}{ \dfrac{ \sqrt{2} }{2} } = \frac{AD }{ \dfrac{ \sqrt{3} }{2} } \)

simplify:

\(AD = 50 \sqrt{6} \)

since ∆ABD is a 30-60-90 right angle triangle of which the hypotenuse is twice as much as the shorter leg thus:

\( \displaystyle AB = \frac{50 \sqrt{6} }{2}\)

simplify division:

\( \displaystyle AB = \boxed{25 \sqrt{6} }\)

and we're done!

Answer:

93%

Step-by-step explanation:

divide 1395 by 1500

0.93

0.93=93%

Answer:

93%

Step-by-step explanation:

This problem can be best solved with a proportion! First, we can set up one side of the proportion with the two values that are given to us. It will look something like this:

\(\frac{1395}{1500}\)

Next, we need to set up the other side. Since we are solving for a percent, we know that our x will be out of 100. This side will look something like this:

\(\frac{x}{100}\)

Next, we need to set them equal to each other and solve for x.

\(\frac{1395}{1500} = \frac{x}{100}\)

To solve, just cross multiply and divide. Multiply 1395 by 100 to get 139,500. Next, divide 139,500 by 1500 to get a final answer of 93%! Hope this helps!

Answer:

Example of an equation with an undefined slope: x = 2

Step-by-step explanation:

The standard form of linear equations with an undefined slope is x = a, whose graph represents a vertical line. The value of a in the standard form is the x-intercept, (a, 0).  

The slope is the ratio of the vertical change in y-values to the horizontal change in x-values.

\(\displaystyle\mathsf{Slope(m) =\:\frac{\triangle y}{\triangle x}\:=\frac{y_2 - y_1}{x_2 - x_1}}\)

The slope of a vertical line is undefined because if we were to solve its slope, the denominator will be zero. As we know, division by zero is an undefined operation.  

For example, suppose that we have the following points (2, 5) (2, 10).

Let (x₁, y₁) = (2, 5)

     (x₂, y₂) = (2, 10)

Substitute these values into the slope formula:

\(\displaystyle\mathsf{Slope(m) =\:\frac{\triangle y}{\triangle x}\:=\frac{y_2 - y_1}{x_2 - x_1}\:=\:\frac{10\:-\:5}{2\:-\:2}\:=\frac{5}{0}}\)

Dividing the numerator, 5, by the denominator, 0, will have an undefined quotient.

Thus, the equation of the vertical line will be: x = 2, where a = 2.

Answer:

60/8 = 7.5 mins per mile

Step-by-step explanation:

To find the inverse of the function g: x → x, we need to determine which pairs of elements in x are mapped to each other by g.

From the definition of g, we have:

g(u) = v

g(v) = x

g(w) = w

g(x) = u

To find g^-1, we need to reverse the mapping in each of these pairs. So we have:

g^-1(v) = u

g^-1(x) = v

g^-1(w) = w

g^-1(u) = x

Therefore, the inverse of g is:

g^-1 = { (v, u), (x, v), (w, w), (u, x) }

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The relationship between the average rates is that ; The average rate of return trip is twice the average rate of front trip.

From the complete question seen online, we can say that;

Time taken on front trip = t

Time taken on return trip = 1/2 × t = t/2

Relationship between speed(Rate) and time is;

Rate ∝ 1/time

This means that Rate is inversely proportional to time.

Thus, for the front trip, the rate is; r = 1/t

For return trip, the rate is; R = 1/(t÷2)

R = 1 × 2/t

R = 2/t

Rate of front trip = 1/t

Rate of return trip = 2/t

Thus, we can say that the average rate of return trip is twice the average rate of front trip.

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Sanyo  option (b) would be chosen using the elimination-by-aspects decision rule.

In the elimination-by-aspects decision rule, you compare the options based on specific aspects and eliminate those that do not meet a certain cutoff point for each aspect.

Here's how the comparison unfolds based on the given information:

1. Performance: The cutoff point is ranked 1. Sanyo and Sony meet the cutoff, but Pioneer does not.

  Eliminated: Pioneer

2. Price: The cutoff point is ranked 4. Sanyo and Pioneer meet the cutoff, but Sony does not.

  Eliminated: Sony

3. Quality: The cutoff point is ranked 4. All three options (Sanyo, Sony, Pioneer) meet the cutoff.

4. Style: The cutoff point is ranked 3. Sanyo meets the cutoff, but Sony and Pioneer do not.

  Eliminated: Sony and Pioneer

Based on the elimination process, the remaining option is Sanyo. Therefore, (b) Sanyo would be chosen using the elimination-by-aspects decision rule.

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The surface area of the triangular prism is

To find the surface area of a prism, we use the formula SA=2B+ph, where SA stands for surface area, B stands for the area of the base of the prism, p stands for the perimeter of the base, and h stands for height of the prism. SA=2(lw)+2(l+w)h.

Area of the base 1 = ½bh

= ½ × 6× 4

= 12cm²

Area of base 2 = l×b

= 6×3 = 18 cm²

area of the front = 10×6 = 60cm²

area of the back = 60cm²

area of left = 3×10 = 30cm²

area of the right = 30cm²

total surface area = 60+60+30+30+18+12 = 210cm²

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Answer: -2(3x-5)

Step-by-step explanation: first you divide 72 and 8 then do the rest

Answer:

The signs of each monomial in the second polynomial are changed.

When subtracting two polynomials, the subtraction affects each monomial in the second polynomial by inverting the sign of each coefficient. That is, every coefficient in the second polynomial is multiplied by -1.

Polynomials are mathematical expressions that contain one or more terms. These terms are made up of coefficients and variables raised to powers, like x^2, y, or z^3.

When subtracting two polynomials, we need to keep in mind that each term within the polynomial is affected.

Example: Consider the following polynomial:

2x^2 + 3xy + 4y^2

When we subtract the polynomial 3x^2 - 2xy - 5y^2 from the above polynomial, we need to invert the sign of each coefficient in the second polynomial. That is, we have:

2x^2 + 3xy + 4y^2 - (3x^2 - 2xy - 5y^2)

Now, inverting the sign of each coefficient in the second polynomial, we get:

-3x^2 + 2xy + 5y^2

So the final result is:

2x^2 + 3xy + 4y^2 - (3x^2 - 2xy - 5y^2)

= 2x^2 + 3xy + 4y^2 - 3x^2 + 2xy + 5y^2

= -x^2 + 5xy + 9y^2

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The absolute maximum value of f(x,y) = x² - 2y + 1 on the set R={(x,y): x² + y²≤9} is (25/2). So, the correct option is OA.

We have the function,f(x,y) = x² - 2y + 1 and set R= {(x,y): x² + y²≤9}

Let's find the absolute maximum value of f(x,y) in R. Therefore, we have to check the values of f(x,y) on the boundary of R which is x² + y² = 9f(x,y) = x² - 2y + 1

Now, we need to convert the above function into a single variable function.f(x,y) = x² - 2y + 1 = x² - 2y + 9 - 8

Now, replace x² + y² = 9 in the above function to get a single variable function.

f(x) = x² - 8y + 9

Now, differentiate the above function to find the critical points. f'(x) = 2x = 0 => x = 0

Putting this value of x in x² + y² = 9 to get the value of y.y² = 9 => y = ±3

Hence, the critical points are (0,3) and (0,-3). Now, let's find the value of f(x,y) at the critical points and the boundary of R to find the absolute maximum and minimum values of f(x,y).f(0,3) = 10f(0,-3) = 10

Now, let's find the value of f(x,y) on the boundary of R. f(x,y) = x² - 2y + 1At (x,y) = (±3,0)f(±3,0) = 10 f(x,y) has a critical point (0,3), which is the absolute maximum value in the set R={(x,y): x² + y²≤9}.

The absolute maximum value is (25/2). Therefore, the correct option is OA.

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We can estimate it using the approximate value of the given points:

Therefore, the correct answer is:

0.872

Answer:

4

Step-by-step explanation:

10 / $2.50 = 4

You can buy 4 cans of Dr. Pepper for $10

Chow,...!

Answer:

\(6+ \sqrt{29},6-\sqrt{29}\)

Step-by-step explanation:

The given quadratic equation is \(x^2-12x+7=0\)

The general form of quadratic equation is given by :

\(ax^2+bx+c=0\)

Comparing both the equations,

a = 1, b = -12 and c = 1

The solution of a quadratic equation is given by :

\(x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\)

Put all the values,

\(a=\dfrac{-(-12)\pm \sqrt{(-12)^2-4\times 1\times 7} }{2(1)}\\\\=\dfrac{12\pm \sqrt{116}}{2}\\\\=\dfrac{12\pm 2\sqrt{29}}{2}\\\\=6\pm \sqrt{29}\)

So, the solutions of the given equation is \(6+ \sqrt{29},6-\sqrt{29}\). Hence, the correct option is (d).  

Answer:

17 people surveyed own a cat.

Step-by-step explanation:

Let d stand for dog, c stand for cat, and b stand for both. In total, d + c + b = 100 people. The number of people who own a dog is four times the number of people who own a cat, so d = 4c. In the problem, it's given that 15 people own both a dog and a cat. So, b can be replaced with 15. Now, d + c + 15 = 100. This system of equations can be solved by substitution.

d = 4c

d + c + 15 = 100

4c + c + 15 = 100

5c + 15 = 100

5c = 85

c = 17

Check:

The number of dog owners is 4 * 17, or 68.

68 + 17 + 15 = 100

Answer:

P' (- 3, 4 ) , Q' (2, 7 )

Step-by-step explanation:

the line passing through the origin and (4, 4 ) has equation

y = x

a point reflected in the line y = x

(x, y ) → (y, x ) , then

P (4, - 3 ) → P' (- 3, 4 )

Q (7, 2 ) → Q' (2, 7 )

Answer:

In asymptotic analysis we consider growth of algorithm in terms of input size. An algorithm X is said to be asymptotically better than Y if X takes smaller time than y for all input sizes n larger than a value n0 where n0 > 0.

Step-by-step explanation:

In asymptotic analysis, we consider growth of algorithm in terms of input size.

An algorithm X is said to be asymptotically better than Y if X takes smaller time than y for all input sizes n larger than a value n0 where n0 > 0.

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The range of the function f include the following: [-20, ∞].

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range and domain:

Range = [-20, ∞] or -20 ≤ y ≤ ∞.

Domain = [-∞, ∞] or -1 < x < ∞.

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Solve the system

Subtract the equations

Solve quadratic equation

Then, the solutions are:

And

Answer:

(2,0)

(6,16)

If you're looking for the lowest ratio for 70 to 210, it should be

1:3

70min=70×60=4200sec

ratio=4200/210

=210×20/210

=20/1

=20:1

Answer:

1.none of the above

2.x=50

Answer: its the 2nd one

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

66 students

Step-by-step explanation:

Percentage of students learning Spanish = 100% - 72% - 38% + 30%

                                                                     = 20%

No. of students learning Spanish = \(\frac{20}{100}\) × 330 students

                                                       = 66

The solution for  -1/3-(-5/12) is 3/4

Adding and subtraction:

In Mathematics, Addition and subtractions are two basic operations. Addition means putting together or adding together; subtraction means taking apart one number from another number.  

For adding or addition we use the symbol '+ '

For subtraction, we use the symbol ' - '

Here some are rules when addition (+) and subtraction (-) encounters with multiplicatin  

=>  (+) × (+) = (+)

=>  (-) × (+) = (-)  

=>  (-) × (-) = (-)

Here we have

=> -1/3-(-5/12)

As we learn (-) × (-) = (-)  

=> (1/3) + (5/12)

Here LCM of 3, 12 is 12

=> (4 + 5) / 12         [ 4 = 12/3 × 1 ]

=>  9/12 = 3/4

Therefore, the solution for  -1/3-(-5/12) is 3/4

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Answer:

The value of the cube root of 81 rounded to 6 decimal places is 4.326749. It is the real solution of the equation x3 = 81. The cube root of 81 is expressed as ∛81 or 3 ∛3 in the radical form and as (81)⅓ or (81)0.33 in the exponent form. The prime factorization of 81 is 3 × 3 × 3 × 3, hence, the cube root of 81 in its lowest radical form is expressed as 3 ∛3.

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer:

y=4x-3

Step-by-step explanation:

Parallel lines will always have the same slope (the number that comes before x in an equation). So, we can plug in 4 to the equation.

y=4x+?

Let's say the ? is b. If we plug in the point (1,1) into y=4x+b, we get

1=4(1)+b

reduce

1=4+b

subtract 4 from both sides

-3=b

and now we can add b=-3 into the original answer, and we get y=4x-3!