What is the apparent solution to the system of equations?
y=12x+2y=2x−1

y=12x+2y=2x−1

Graph the system of equations using the Line tool. Plot a point at the apparent solution to the system using the Point tool.

Answer:

27 and 40

Step-by-step explanation:

Final answer:

The sum of two numbers is 67 and the difference is 13. The two numbers are 40 and 27.

Explanation:

Let's solve this problem step by step:

Therefore, the two numbers are 40 and 27.

Answer:

Two answers are given because the question is "unexpected." cos(θ) = √(3/4) is more commonly seen in such problems than is cos(θ) = (√3)/4, which is what you have written here. Choose the answer that matches your intent.

Step-by-step explanation:

The cosine function is an even function, so cos(θ) = cos(-θ).

The relationship between sin(θ) and cos(θ) is ...

... sin(θ) = ±√(1 -cos(θ)^2)

For sin(θ) < 0 and cos(θ) = (√3)/4, ...

... sin(θ) = -√(1 -3/16) = -√(13/16)

... sin(θ) = -(√13)/4

For sin(θ) < 0 and cos(0) = √(3/4), ...

... sin(θ) = -√(1 -3/4) = -√(1/4)

... sin(θ) = -1/2

Answer:

-√13/4 took the test.

Answer:

So, our rate of exponential growth is is 6.93 %

Step-by-step explanation:

The formula for exponential growth rate is

A = P[tex]e^{rt}[/tex] .... (1

Here

P = is the initial investment

A = amount after certain time

As we are given after 10 years (t = 10) the investment doubles

so plugging A=2P and t= 10 into equation (1)

2P = P[tex]e^{10r}[/tex]

cancelling P on both sides

2 = [tex]e^{10r}[/tex]

taking natural log on both sides

ln (2) = ln ([tex]e^{10r}[/tex]

ln(2) = 10r(lne)

as ln(e) = 1

ln (2) = 10r

r = [tex]\frac{ln(2)}{10}  [/tex]

solving the natural log

r = 0.0693

or

r =6.93 %

So, our rate is 6.93 %

Answer:

x = 1 and y = 5

Step-by-step explanation:

Use substitution because you know that x = y - 4, and plug this into the first equation to get -10(y - 4) + 3y = 5, or -10y + 40 + 3y = 5. This is -7y = -35 so y = 5. Plug this into the 2nd equation to get that x = 1 and y = 5.

We have the triangle 30° - 60° - 90°.

The sides are in proportion: 2 : √3 : 1

(look at the picture).

[tex]2a=14[/tex]       divide both sides by 2

[tex]a=7[/tex]

[tex]a\sqrt3=7\sqrt3[/tex]

The area of a trinagle AFD:

[tex]A_{\Delta}=\dfrac{1}{2}(7)(7\sqrt3)=\boxed{\dfrac{49\sqrt3}{2}}[/tex]

The area of a triangle ADF is 42.46 square units.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Given that, in ∆ADF, m∠F=90°, AD = 14 and m∠D=30°

We know that, sinθ= Perpendicular/Hypotenuse

Now, sin A=FD/AD

sin60°=FD/14

⇒ √3/2 = FD/14

⇒ FD=7√3

sin30°=FA/AD

⇒ 1/2 =FA/14

⇒ FA=7

We know that, area of a triangle is 1/2 ×Base×Height

Area of ∆ADF

= 1/2 ×FD×FA

= 1/2×7√3×7

= 42.46 square units

Therefore, the area of a triangle ADF is 42.46 square units.

Learn more about the trigonometric ratios here:

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Answer:

C) horizontal reflection over y-axis and horizontal stretch

Step-by-step explanation:

1a- A vertical reflection over the x-axis occurs when a function [tex]f(x)[/tex] is transformed into [tex]f(-x)[/tex]

1b- A horizontal reflection over the y-axis occurs when a function [tex]f(x)[/tex] is transformed into [tex]-f(x)[/tex]

2a- A function is being compressed if [tex]f(x)[/tex] is multiplied by a positive factor k: [tex]k f(x)[/tex] with [tex]k>1[/tex]

2b- A function is being stretched if [tex]f(x)[/tex] is multiplied by a positive factor k: [tex]k f(x)[/tex] with [tex]k<1[/tex]

In our problem, the original function [tex]f(x)[/tex] is:

- Multiplied by 1/2, so by a factor which is smaller than 1, so we are in case 2b

- Transformed from [tex]f(x)[/tex] into [tex]-f(x)[/tex] (due to the negative sign in front of it), so we are in case 1b

So, overall, we had a horizontal reflection over the y-axis and a stretch of the function.

Answer:

8x2 or (8)(2)

Step-by-step explanation:

The value of 1 hour is 2 widgets, in 8 hours simplified would lead to 8x2 which is 16 widgets.

This leaves you with 16 widgets made in 8 hours.

Frank can make 16 widgets by working 8 hours a day.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that at Frank's work he can produce 2 widgets every hour.

Thus if he produce 2 widgets in one hour, using Unitary method

In 1 hour Frank can make 2 widgets.

Thus in 8 hour work, Frank can make (2 * 8) widgets.

In 8 hour work, Frank can make 16 widgets.

To learn more about Unitary method, refer -

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Answer:

Step-by-step explanation:

This is a system of inequalities such that:

[tex]\left \{ {{2x+3y\geq 2} \atop {3x-4y\leq 3}} \right.[/tex]

Let's start by solving for y for both equations:

Equation 1:

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

Equation 2:

[tex]3x-4y\leq 3\\\\-4y\leq -3x+3\\\\y\geq -\frac{(-3x+3)}{4}[/tex]

Now if we substitute the 2nd y into the first equation we obtain:

[tex]2x+3(\frac{3x-3}{4}) \geq  2\\\\2x+\frac{9x-9}{4}\geq 2\\\\\frac{8x+9x-9}{4}\geq 2\\\\17x-9\geq 8\\\\17x\geq 17\\\\x\geq 1[/tex]

Now we will solve for the second equation using the first result of y and we obtain:

[tex]3x-4(\frac{-2x+2}{3}\leq 3\\\\3x+\frac{8x-8}{3}\leq 3\\\\\frac{9x+8x-8}{3}\leq 3\\\\17x-8\leq 9\\\\17x\leq 17\\\\x\leq 1[/tex]

And so our solution for the system of equations is:

[tex]x \leq 1\\and \\y\geq \frac{-2x+2}{3}[/tex]

As well as:

[tex]x>1\\and\\y\geq \frac{3x-3}{4}[/tex]

Answer:

1) By SAS theorem, ΔADE≅ΔCDF

2) By SSS theorem, ΔBDE≅ΔBDF

Step-by-step explanation:

Consider isosceles triangle ABC (see diagram).

1. In triangles ADE and CDF:

By SAS theorem, ΔADE≅ΔCDF.

2. In triangles BDE and BDF:

Be SSS theorem, ΔBDE≅ΔBDF.

96 necklaces

To find out how many necklaces Camilla can make, we need to see how many times the required number of beads "goes into" the available number of beads.

Silver: 8160/85 = 96

Black: 2880/30 = 96

Camilla has enough beads to make 96 necklaces.

_____

Comment on this answer

Obviously, if one of the quotients is smaller than the other, Camilla can only make as many necklaces as are supported by the constraining resource.

Even if she had 3000 black beads (way more than 2880), she could still only make 96 necklaces (for example) because she would run out of silver beads making that 96th necklace. (There would be 120 black beads left over in that scenario.)

Combine the left hand side, then write both sides as powers of 6:

[tex]\log_64x^2-\log_6x=\log_6\dfrac{4x^2}x=2\implies6^{\log_6\frac{4x^2}x}=6^2[/tex]

[tex]\implies\dfrac{4x^2}x=36[/tex]

[tex]\implies x^2=9x[/tex]

[tex]\implies x^2-9x=x(x-9)=0[/tex]

[tex]\implies x=0,x=9[/tex]

However, for any base [tex]b[/tex], [tex]\log_bx[/tex] is undefined if [tex]x=0[/tex], so the only solution is [tex]x=9[/tex].

Answer:

D. x=9

Step-by-step explanation:

D) 10.2 ft

The mnemonic SOH CAH TOA reminds you that

... Sin = Opposite/Hypotenuse

You want to find the length of the side Opposite the 50° angle, given the Hypotenuse is 12 ft. Then the relation is ...

... sin(50°) = height/(12 ft)

Multiplying by 12 ft gives

... height = (12 ft)·sin(50°) ≈ 9.2 ft

The height of the platform is 1 ft up from this value:

... 9.2 ft + 1 ft = 10.2 ft

Final answer:

Ramona rode rides at a rate of 2 rides per hour during her visit to the theme park.

Explanation:

Ramona's Rate of Riding Rides:

Rate = Number of rides ÷ Number of hours

Rate = 14 rides ÷ 7 hours

Rate = 2 rides per hour

Answer:

option 2

Step-by-step explanation:

in the given triangle,

tan45° = 8/x

=> 1 = 8/x

=>x = 8

for y,

cos45° = 8/y

=>1/√2 = 8/y

=>y = 8√2

Answer:

x=8, [tex]y=8 \sqrt2[/tex]

Step-by-step explanation:

Consider the given right triangle,

As, [tex]\tan \Theta = \frac{Perpendicular}{Base}[/tex]

Consider [tex]\tan 45^{\circ}=\frac{x}{8}[/tex]

[tex]1=\frac{x}{8}[/tex]

So, x=8

As, [tex]\sin \Theta = \frac{Perpendicular}{Hypotenuse}[/tex]

Consider [tex]\sin 45^{\circ}=\frac{8}{y}[/tex]

[tex]\frac{1}{\sqrt2}=\frac{8}{y}[/tex]

So, [tex]y=8 \sqrt2[/tex]

Therefore, x = 8 and [tex]y=8 \sqrt2[/tex]

Answer:

Jeff got 20 answers right.

Step-by-step explanation:

The maximum number of points Jeff can get is 100. (25 * 4) However, for each question he gets wrong, he's actually losing 6 points because he doesn't get the four points for getting right, and has the additional -2 points for getting it wrong. Since he only got a score of 70, that means he lost 30 points.

30/6 = 5. So he missed 5 question and got 20 question right.

As per the given values, Jeff got 20 questions right.

Total questions answered = 25

Total points for each correct answer = 4

Total points for each incorrect answer = 2

To find the number of questions Jeff got right, we can set up the equation:

4x - 2(25 - x) = 70,

where x represents the number of questions he got right.

Simplifying the equation, we get -

6x - 50 = 70.

Adding 50 to both sides, we have 6x = 120.

Dividing both sides by 6, we get x = 20.

Therefore, Jeff got 20 questions right.

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A. Yes, because both points are equidistant from the center of the circle.

The point (0, 5) is 5 units from the point (0, 0).

The point (0, -5) is 5 units from the point (0, 0).

The given points are equidistant from the circle center at (0, 0), so both will lie on the circle—along with any other points that are 5 units from (0, 0).

Answer:

10.8 units

Step-by-step explanation:

As the equation represents the area of a rectangle

i.e.

length * width = Area

Now area is 285.12 units square

while length is 26.4

and width is represented by w

now putting in the formula it will become

26.4 * w = 285.12

dividing both sides by 26.4

[tex]\frac{26.4w}{26.4}=\frac{285.12}{26.4}[/tex]

this will become

w = 10.8 units

Which is the required width of the Rectangle

so answer is 10.8 units

Answer:

p = 1/12 = p(o1) = p(o3) = p(o5)

3p = 1/4 = p(o2) = p(o4) = p(o6)

Step-by-step explanation:

p(o1) +p(o2) +... +p(o6) = 1 . . . . the condition on the sum of probabilities

... p +3p +p +3p +p +3p = 1 . . . . substitute values

... 12p = 1 . . . . simplify

... p = 1/12 . . . . divide by 12

Then ...

... 3p = 3/12 = 1/4

Final answer:

The probabilities of rolling each face of a loaded six-sided die, where even numbers are three times more likely than odd numbers, are 1/9 for odd numbers (1, 3, 5) and 1/3 for even numbers (2, 4, 6), satisfying the condition that the total probability sums to 1.

Explanation:

The student is dealing with a probability question involving a "loaded" die. To find the probabilities for each face of the die, we assign a variable p to represent the probability of rolling an odd-numbered face and 3p for an even-numbered face. The sum of all probabilities must equal 1 because one of the outcomes must occur when the die is rolled. We can set up the following equation: p + 3p + p + 3p + p + 3p = 1.

Combining like terms gives us 9p = 1, so p = 1/9. Thus, the probabilities of rolling each face are as follows:

This system satisfies the condition that all probabilities sum to 1, making it the correct distribution for this loaded die.

Answer:

C

Step-by-step explanation:

When x = 0, y = 9

When x = 11, y = 3

Find 11 on the horizontal line and go up to the crossing and the follow the line till the y-axis(going to the left direction(. Did you see the 3?

That is the (11 | 3) point

Multiplying 3 by a smaller number gives a smaller product.

1/10 is smaller than 10, so 3·(1/10) is smaller than 3·10.

The amount borrowed is $84,000. The annual interest rate is 6%. There are 12 payments per year for 21 years at a monthly payment amount of $587.

The question pertains to the fundamentals of loan calculation. Let us identify the components asked:

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In the loan scenario, the person borrowed $84,000 at an annual interest rate of 6%. They will make 12 payments of $587 each year for a term of 21 years.

In the provided loan scenario, the following key components can be identified:

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The midpoint between (-1+9i) and B=(5-3i) is (2+3i).

The midpoint between (-1+9i) and B=(5-3i) can be found by taking the average of the real and imaginary parts separately.

For the real part, we take the average of -1 and 5 which is 2. For the imaginary part, we take the average of 9i and -3i which is 3i.

Therefore, the midpoint between (-1+9i) and B=(5-3i) is (2+3i).

Answer:

24.5

Step-by-step explanation:

A calculator or spreadsheet is good for doing this sort of computation.

_____

You add up the magnitudes of the differences between the given y-value and the corresponding value you get from the equation. For the first couple of points, these values are ...

... |3 - (0.1·1 +2.9)| = 0

... |2.5 -(0.1·6 +2.9)| = |2.5 -3.5| = 1

The computation proceeds like this for the remaining 6 points, and the numbers added. The result is 24.5.

Answer:

(16 + 8√3) in²

Step-by-step explanation:

The ratio of side dimensions for a 30°-60°-90° triangle are 1 : √3 : 2. If we call the horizontal dimension of the triangle its base, then its height (vertical dimension) will be √3×4 in. Of course the area of the triangle is ...

... A = (1/2)bh = (1/2)(4 in)(4√3 in) = 8√3 in²

The total sod area is the sum of the square area (16 in²) and the triangle area, so is ...

... area to cover = (16 +8√3) in²

_____

Comment on problem dimensions

The area involved here is not much larger than the size of your hand. It would make more sense for the dimensions to be in feet or yards or meters, rather than inches.

Answer: 29.9 in.

Step-by-step explanation:

16+(8*√3)

You may solve this problem in two ways:

If you solve the inequality explicitly (divide both sides by 4), you get

[tex] \dfrac{4n}{4} < \dfrac{16}{4} \iff n < 4 [/tex]

So, if [tex] n [/tex] has to be stricktly less than 4, you can only choose 1, 2 and 3 as answers.

Alternatively, you can plug in all of the values you're proposed and check if the inequality holds:

If [tex] n=1 [/tex], you have [tex] 4<16 [/tex], which is true.

If [tex] n=2 [/tex], you have [tex] 8<16 [/tex], which is true.

If [tex] n=3 [/tex], you have [tex] 12<16 [/tex], which is true.

If [tex] n=4 [/tex], you have [tex] 16<16 [/tex], which is false.

So, again, only 1, 2 and 3 are solutions.

Answer:

y = 2 3/8

Step-by-step explanation:

Multiply by the denominator. This gives a linear equation that can be solved in the usual way.

... 3 = 8(y -2)

Divide by 8.

... 3/8 = y - 2

Add 2

... 2 3/8 = y

_____

In problems involving rational expressions, it often works well to multiply by the product of the denominators, or by their least common multiple, if that is easy to find. Doing this eliminates fractions. Here there is only one denominator (y-2), so we multiply by that.

Answer:

36 and 24

Step-by-step explanation

36 - 24 = 12

36 + 24 = 60

Answer:

z=-0.35 ( Depending on value given)

Step-by-step explanation:

Let the value be x. For calculation purposes, let us take x as 3.68. ( as mean is 4.68). We may assume a higher value as well. Depends on the given value.

The formula for z score is given as-

z=(value-mean)/Standard Deviation

z=(3.68-4.68)/2.83

z=-0.35

A graph is attached

The equation is in slope-intercept form:

...  y = mx + b

Here, the value of m (the slope) is 1/2, and the value of b (the y-intercept) is -3.

This means that point (0, -3) is a point on the graph. This point is on the y-axis, 3 units below the x-axis.

Slope is sometimes referred to as "rise over run." The slope of 1/2 means the line will rise 1 unit for each 2 units to the right. That is, for some point (x, y) on the ine, another point will be found at (x+2, y+1).

Given a point at (0, -3), another point will be (0, -3) +(2, 1) = (2, -2), and another point will be (2, -2) +(2, 1) = (4, -1).

You can plot as many points as you like, then draw the line through them.