How is a system of equations created when each linear function is given as a set of two ordered pairs? Explain

Answer:

A = 47° and B = 43°

Step-by-step explanation:

Express angle A in terms of angle B, that is

A = B + 4

Complementary angles sum to 90°, hence

A + B = 90, that is

B + 4 + B = 90

2B + 4 = 90 ( subtract 4 from both sides )

2B = 86 ( divide both sides by 2 )

B = 43

Hence

∠B = 43° and ∠A = B + 4 = 43 + 4 = 47°

Answer:

A= 47°

B= 43°

Explanation:

A complementary angle is a 90° angle.

If A+B= 90 and B+4= A, we can rewrite it as...

B+4+B= 90

→ 2B+4= 90

→ 2B= 86

→ B= 43

Then we go back to the equation A+B= 90 and plug in B as 43...

A+43= 90

→ A= 47

Answer:

The firston one is a scale factor of two and the second one is a scale factor of three.

Step-by-step explanation:

You just look at the coordinates. (1,1):(2,2) and (4,0):(8,0) and then for the second one (-1,0):(-3,0) and (3,2):(9,6).

1x2=2

4x2=8

-1x3=-3

3x3=9

2x3=6

Answer:

Option C [tex]-7x-5y=-48[/tex]

Step-by-step explanation:

step 1

Find the slope of AB

we have

A(-3,-1) and B(4,4)

The slope m is equal to

[tex]m=(4+1)/(4+3)[/tex]

[tex]m=5/7[/tex]

step 2

Find the slope of BC

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

so

[tex]m1*m2=-1[/tex]

we have

[tex]m1=5/7[/tex]

substitute

[tex]5/7*m2=-1[/tex]

[tex]m2=-7/5[/tex]

step 3

Find the equation of the line into slope point form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-7/5[/tex]

[tex]B(4,4)[/tex]

substitute

[tex]y-4=-(7/5)(x-4)[/tex]

Multiply by 5 both sides

[tex]5y-20=-7x+28[/tex]

[tex]7x+5y=28+20[/tex]

[tex]7x+5y=48[/tex]

Multiply by -1 both sides

[tex]-7x-5y=-48[/tex]

The standard form of the equation for the specified line, we use the normal form equation, substitute the given values for the angle and the length of the normal segment, and simplify to obtain the equation as [tex]x - \(\sqrt{3}\) y = -16.[/tex]

To solve this, we'll use the concept of the normal form of the line equation, which is [tex]x cos(\(\theta\)) + y sin(\(\theta\)) = p, where \(\theta\)[/tex] is the angle the normal makes with the positive direction of the x-axis, and p is the length of the perpendicular from the origin to the line.

Given[tex]\(\theta = 120^\circ\) and \(p = 8\)[/tex], we substitute these values into the normal form to get [tex]x cos(120^\circ) + y sin(120^\circ) = 8.[/tex] Simplifying further using the values of [tex]cos(120^\circ) = -1/2 and sin(120^\circ) = \(\sqrt{3}/2\)[/tex], we obtain the standard form of the equation of the line as [tex]-1/2 x + \(\sqrt{3}/2\) y = 8[/tex], or multiplying through by -2 for a cleaner form: [tex]x - \(\sqrt{3}\) y = -16.[/tex]

Answer:

x ≥ - 8

Step-by-step explanation:

Given

[tex]\frac{x}{2}[/tex] ≥ - 4

Multiply both sides by 2 to eliminate the fraction

x ≥ - 8

Answer:

Step-by-step explanation:

x ≥ - 8

Answer:

X = 5

Step-by-step explanation

Add or subtract the like terms and take numbers in one side . Do the solution part and get your answer.

Answer:

x=5

Step-by-step explanation:

combine like terms: -2x + 6x = 4x

add eight to the other side 4x - 8 = 12 ----> 4x = 20

then divide 4x = 20 -----> x = 5

Answer:

444 (gets to 62,666)

Step-by-step explanation:

The closest you can think of first is 63,333. However, as long as there doesn't have to be the four numbers in a row, the "6" in the number can be one of the four same numbers.

This means that you need to get 3 other sixes in the number. There are many ways to do this, but the one requiring the least amount of driving is changing the last three digits (222). If you add 444 to the number, the amount of miles driven is 62,666, there being 4 sixes in the number. This is the least amount of driving needed before the odometer shows four of the five digits the same as each other.

444 is the least number that shows four out of the five digits same.

An odometer is an instrument for measuring the distance travelled by a wheeled vehicle.

Given that,

Total distance covered by Mr. Jackson = 62,222 miles,

The four digits of number 62,222 are same and are 2,

Again, odometer will show four out of 5 digit same, when there will be at least four times 6,

So add 444 in the 62,222

The number = 62,222 + 444 = 62,666

So the least number that can be added to make 4 digit same is 444.

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Final answer:

The equations are $25 + $0.80x for Express Movers and $35 + $0.60x for Smith & Smith Co.

Solving these equations shows that at 50 miles, both options cost the same.

Explanation:

The Brown family is trying to determine the breakeven point in miles for renting a moving truck from two different companies. Express Movers charges an initial fee of $25 plus $0.80 per mile, while Smith & Smith Co. charges $35 initially and $0.60 per mile. To find when these two options cost the same, we will set up equations and solve for the number of miles.

Let's define x as the number of miles driven. The totals cost from each company can be expressed as:

Express Movers: $25 + $0.80x

Smith & Smith Co.: $35 + $0.60x

To find the breakeven point, we equate the two expressions:

$25 + $0.80x = $35 + $0.60x

Now we solve for x by subtracting $0.60x from both sides and then subtracting $25 from both sides to isolate the variable:

$0.20x = $10

Dividing both sides by $0.20 gives us:

x = 50 miles

Therefore, at 50 miles, the cost of renting a truck from Express Movers or Smith & Smith Co. would be the same.

Answer:

21.99 units

164.93 units²

Step-by-step explanation:

given radius r = 15 units

angle of sector = 84°

Length of sector = [tex]\frac{84}{360}[/tex] x 2 x π x r

= [tex]\frac{84}{360}[/tex] x 2 x 3.14 x 15

= 21.99 units

Area of sector = [tex]\frac{84}{360}[/tex] x π x r²

= [tex]\frac{84}{360}[/tex] x 3.14 x 15²

= 164.93 units²

In a 30-60-90 triangle, the longer leg is sqrt(3) times the hypotenuse. Therefore, the correct ratios provided are A. sqrt(3) : 2 and D. 3sqrt(3) : 6, with the latter simplifying to the correct ratio when reduced.

The ratio of the length of the longer leg to the hypotenuse in a 30-60-90 triangle is determined by the properties of this special right triangle. In such a triangle, the sides are in a fixed ratio: the shorter leg is 1 times the length of the hypotenuse, the longer leg is sqrt(3) times the length of the hypotenuse, and the hypotenuse itself is 2 times the length of the shorter leg.

Using this knowledge, we can evaluate the options given:

Options B, C, E, and F do not represent the correct ratio of the longer leg to the hypotenuse of a 30-60-90 triangle. Therefore, options A and D are correct.

Answer: 8

Step-by-step explanation: We are dealing with a 30 60 90 triangle which has special side lengths that I will attach.

The short leg, in this case 4, is half of the hypotenuse in 30 60 90 triangles, therefore x = 8

Answer: Last option.

Step-by-step explanation:

You need to remember the following identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

In this case, we can observe that:

[tex]\alpha=30\°\\opposite=4\\hypotenuse=x[/tex]

Now you must substitute these values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for the hypotenuse. Then:

[tex]sin(30\°)=\frac{4}{x}\\\\(x)(sin(30\°))=4\\\\x=\frac{4}{sin(30\°)}\\\\x=8[/tex]

Final answer:

Dwight will make $1,575 per week by multiplying his hourly wage of $35 by the 45 hours he works each week.

Explanation:

To calculate how much Dwight will make per week, we need to multiply his hourly wage by the number of hours he works per week. According to the question, Dwight earns $35 per hour and works 45 hours per week.

The calculation is as follows: Hourly wage x Hours per week = Weekly earnings

$35/hour x 45 hours/week = $1,575/week

Therefore, Dwight will make $1,575 per week from his construction job.

The answer is:

The solutions to the system of equations are:

[tex]x=0\\y=1\\z=0[/tex]

To solve the system of equations by the easiest way, we need to use the reduction method. The reduction method consist of reducing the variables applying different math operations in order to be able to isolate the variables.

So, we are given the system:

[tex]4x+3y+6z=3\\5x+5y+6z=5\\6x+3y+6z=3[/tex]

Let's work with the first and the third equation:

[tex]4x+3y+6z=3\\6x+3y+6z=3[/tex]

Then, multiplying the first equation by -1, we have:

[tex]-4x-3y-6z=-3\\6x+3y+6z=3[/tex]

[tex]-4x+6x-3y+3y-6z+6z=-3+3[/tex]

[tex]2x=0[/tex]

[tex]x=0[/tex]

Now, working with the first and the second equation, we have:

[tex]4x+3y+6z=3\\5x+5y+6z=5[/tex]

Then, multiplying the first equation by -1, we have:

[tex]-4x-3y-6z=-3\\5x+5y+6z=5[/tex]

[tex]5x-4x+5y-3y-6z+6z=-3+5[/tex]

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

Then, substituting "x" into the equation, we have:

[tex]0+2y=2[/tex]

[tex]y=\frac{2}{2}=1[/tex]

Finally, working with the first equation and substituting "x" and "y", we have:

[tex]4x+3y+6z=3[/tex]

[tex]4*0+3*1+6z=3[/tex]

[tex]0+3+6z=3[/tex]

[tex]6z=3-3=0[/tex]

[tex]6z=0[/tex]

[tex]z=\frac{0}{6}=0[/tex]

Hence, we have that the solutions to the system of equations are:

[tex]x=0\\y=1\\z=0[/tex]

Have a nice day!

Answer:

[tex]x=0\\y=1\\z=0[/tex]

Step-by-step explanation:

Multiply the first equation by -1:

[tex](-1)(4x+3y+6z)=3(-1)\\\\-4x-3y-6z=-3[/tex]

Add the new equation and the third equation an solve for "x":

[tex]\left \{ {{-4x-3y-6z=-3\ \atop {6x+3y+6z=3} \right.\\...........................\\2x=0\\x=0[/tex]

Substitute the value of "x" into the first equation and solve for "y":

[tex]4(0)+3y+6z=3\\\\3y=3-6z\\\\y=\frac{3-6z}{3}\\\\y=1-2z[/tex]

Substitute the value of "x" and [tex]y=1-2z[/tex] into the second equation and solve for "z":

[tex]5(0)+5(1-2z)+6z=5\\\\5-10z+6z=5\\\\-4z=0\\\\z=0[/tex]

Knowing the values of "x" and "z", you can substitute them into any original equation and solve for "y". Then:

[tex]4(0)+3y+6(0)=3\\\\3y=3\\\\y=\frac{3}{3}\\\\y=1[/tex]

Answer:

[tex]x=\frac{1}{2}[/tex]

Step-by-step explanation:

When we have a point (a,b) on the unit circle, we can say that

[tex]a^2+b^2=1[/tex]

This is a property of the unit circle.

From the point given  [tex](x,\frac{\sqrt{3} }{2})[/tex] , now we can write the equation shown below and solve for x:

[tex]x^2+(\frac{\sqrt{3} }{2})^2=1\\x^2+\frac{3}{4}=1\\x^2=1-\frac{3}{4}\\x^2=\frac{1}{4}\\x=\frac{\sqrt{1}}{\sqrt{4} } \\x=\frac{1}{2}[/tex]

So, x = 1/2

Answer: x = 1/2

Step-by-step explanation:

We have that the point (x, (√3)/2)) is on the unit circle.

we can define a circle of radius R centered in the (0,0) as:

x^2 + y^2 = R^2

This means that:

x^2 + (√(3)/2)^2 = 1

x^2 + 3/4 = 1

x^2 = 1 - 3/4 = 1/4

x = √(1/4) = 1/2

So we have that x is equal to 1/2

[tex]\bf \cfrac{x}{4x+x^2}\implies \cfrac{\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(4+x)}\implies \cfrac{1}{4+x}\qquad \{x|x\in \mathbb{R}, x\ne -4\}[/tex]

if you're wondering about the restriction of x ≠ -4, is due to that would make the fraction with a denominator of 0 and thus undefined.

To simplify the expression x/4x + x^2, we combine like terms and factor out a common factor.and This simplified expression cannot be reduced further.

To simplify the expression x/4x + x^2, we need to combine like terms. First, let's simplify the fraction by finding a common denominator. The common denominator for 4x and x is 4x. Therefore, the fraction becomes x/(4x) + x^2. Next, let's combine the fractions by adding the numerators and keeping the same denominator. This gives us (x + 4x^2)/(4x). Finally, we factor out the common factor x from the numerator, resulting in x(1 + 4x)/(4x). This simplified expression cannot be reduced further.

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The coordinates of the roots of the given quadratic equation x^2 + 4x + 3 = 0 are -1 and -3.

The given equation is a quadratic equation in the form of ax² + bx + c = 0, where a = 1, b = 4, and c = 3. To find the coordinates of the roots, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the given values, we get:

x = (-4 ± √(4² - 4(1)(3))) / (2(1))

Simplifying further, we have:

x = (-4 ± √(16 - 12)) / 2

x = (-4 ± √4) / 2

x = (-4 ± 2) / 2

Therefore, the two roots of the equation are:

x₁ = (-4 + 2) / 2 = -1

x₂ = (-4 - 2) / 2 = -3

Answer:

Step-by-step explanation:

Assuming the problem is: 3/4  x +5/8=4x

Or .75 x+5/8=4x

Subtract .75 on both sides: 5/8=3.25x

Then divide both sides by 3.25:       (5/8)/3.25=x

So x=5/26

Hello!

The answer is 127,000%

Answer:

[tex]\large\boxed{x=0\ and\ x=\pi}[/tex]

Step-by-step explanation:

[tex]\tan^2x\sec^2x+2\sec^2x-\tan^2x=2\\\\\text{Use}\ \tan x=\dfrac{\sin x}{\cos x},\ \sec x=\dfrac{1}{\cos x}:\\\\\left(\dfrac{\sin x}{\cos x}\right)^2\left(\dfrac{1}{\cos x}\right)^2+2\left(\dfrac{1}{\cos x}\right)^2-\left(\dfrac{\sin x}{\cos x}\right)^2=2\\\\\left(\dfrac{\sin^2x}{\cos^2x}\right)\left(\dfrac{1}{\cos^2x}\right)+\dfrac{2}{\cos^2x}-\dfrac{\sin^2x}{\cos^2x}=2[/tex]

[tex]\dfrac{\sin^2x}{(\cos^2x)^2}+\dfrac{2-\sin^2x}{\cos^2x}=2\\\\\text{Use}\ \sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-(1-\cos^2x)}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-1+\cos^2x}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{1+\cos^2x}{\cos^2x}=2[/tex]

[tex]\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{(1+\cos^2x)(\cos^2x)}{(\cos^2x)^2}=2\qquad\text{Use the distributive property}\\\\\dfrac{1-\cos^2x+\cos^2x+\cos^4x}{\cos^4x}=2\\\\\dfrac{1+\cos^4x}{\cos^4x}=2\qquad\text{multiply both sides by}\ \cos^4x\neq0\\\\1+\cos^4x=2\cos^4x\qquad\text{subtract}\ \cos^4x\ \text{from both sides}\\\\1=\cos^4x\iff \cos x=\pm\sqrt1\to\cos x=\pm1\\\\ x=k\pi\ for\ k\in\mathbb{Z}\\\\\text{On the interval}\ 0\leq x<2\pi,\ \text{the solutions are}\ x=0\ \text{and}\ x=\pi.[/tex]

Remember that the slope intercept formula is:

y = mx + b

m is the slope ([tex]\frac{rise}{run}[/tex])

b is the y-intercept

In this case the slope is...

[tex]\frac{1}{2}[/tex]

The y-intercept is...

(0, 3)

so...

y = [tex]\frac{1}{2}[/tex]x + 3

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

(1,1);(11,1);(6,6);(6-4)

Step-by-step explanation:

The easiest way to do is add or subtract 5 to the x or y value.

The slope-intercept form of the equation for this line is y = 58x + 460.

Given:

Slope (m) = 58

Point [tex](x_1, y_1)[/tex] = (-8, -4)

Using the point-slope form of the equation, which is

[tex](y - y_1) = m(x - x_1)[/tex]

Substitute the values into the equation:

(y - (-4)) = 58(x - (-8))

(y + 4) = 58(x + 8)

To convert this equation into slope-intercept form

y + 4 = 58x + 464

y = 58x + 464 - 4

y = 58x + 460

Therefore, the slope-intercept form is y = 58x + 460.

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The length of the given rectangle is 3 yd and the width is 3.66 yd.

A rectangle is a type of parallelogram having equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

Given that,

The area of rectangle is 42 square yd.

Suppose the width of the rectangle is x yd.

Then its length is given by 3x - 11 yd.

As per the problem, the following equation can be formed,

x(3x - 11) = 42

Solve the above equation for x as,

x(3x - 11) = 42

=> 3x² - 11x = 42

=> 3x² - 11x - 42 = 0

=> x = -1, 4.66

Since, the width cannot be negative. The value of x is taken as 4.66.

Thus, the length is is given by 3 × 4.66 - 11 = 3.

Hence, the length and width of the rectangle are 3yd and 4.66yd respectively.

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She started with 45 and added 5 each month.

Find the table that has Y values that are increased by 5's for every 1 increase in x.

45 + 5 = 50

50+5 = 55

55 + 5 = 60

The correct table is the second one.

Hello There!

14 + 5x - 40 = -36

5x - 26 = -36

5x = -10

x = -2

Answer:

Step-by-step explanation:

14+4(x-8)=-36

19(x-8)=-36

x-8= -36-19

-8x=-55

6.875

Answer:

the second one, x+3y=18

Step-by-step explanation:

x+3y=18

3y=18-x

y=6-[tex]\frac{1}{3}[/tex]x

y=[tex]\frac{-1}{3}[/tex]x+6

Answer:

The height is 6.

Step-by-step explanation:

To find the answer, identify the dimensions you have and what you to find. We have the area (144) and base (24) and we need to find the height. To find the height, you must divide area by the base (it's really simple).

Ex.

[tex]144 / 24 = ?\\144 / 24 = 6[/tex]

The quotient you found is the height. Therefore, the answer is 6.

Final answer:

To find the height of a parallelogram with an area of 144 cm² and a base of 24 cm, divide the area by the base to obtain the height of 6 cm.

Explanation:

Mathematics:

To find the height of a parallelogram, you can use the formula Area = base * height. In this case, the area is given as 144 cm² and the base is 24 cm. Substituting these values into the formula, we get 144 = 24 * height. To find the height, divide both sides of the equation by 24: height = 144/24 = 6 cm. Therefore, the height of the parallelogram is 6 centimeters.

Answer:

Step-by-step explanation:

[tex]\dfrac{5}{2}=d-\dfrac{2}{4}\qquad\left/\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}\right/\\\\\dfrac{5}{2}=d-\dfrac{1}{2}\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\\dfrac{5}{2}+\dfrac{1}{2}=d-\dfrac{1}{2}+\dfrac{1}{2}\\\\\dfrac{5+1}{2}=d\\\\\dfrac{6}{2}=d\to d=3[/tex]