x-4y=-21
8y-x=45
Solve the system
(X,y)=

Answer: y=19

Step-by-step explanation:

The figure of the triangle is attached and we have the following data:

[tex]A=45\°[/tex]

[tex]s=18[/tex] is the length of arc

[tex]r=14[/tex] is the radius

This problem can be solved by the Law of Sines:

[tex]\frac{sin A}{r}=\frac{sin C}{y}=\frac{sin D}{r+x}[/tex]

In order to find [tex]C[/tex], we will use the formula of the length of arc:

[tex]s=\frac{2 \pi r C}{360\°}[/tex]

Then: [tex]C=\frac{360\° s}{2 \pi r}[/tex]

[tex]C=\frac{360\° (18)}{2 \pi (14)}=73.66\°[/tex]

Returning to the Law of Sines:

[tex]\frac{sin A}{r}=\frac{sin C}{y}[/tex]

Finding [tex]y[/tex]:

[tex]y=\frac{sin C r}{sin A}[/tex]

[tex]y=\frac{sin (73.66\°) 14}{sin (45\°)}[/tex]

Finally:

[tex]y=18.99 \approx 19[/tex]

The length of side y is approximately 19 units.

The problem can be approached using the Law of Sines, which relates the angles and sides of a triangle. Given the data:

Angle A (A) is 45°, the side opposite angle A (s) is 18 units, and the radius of the circumcircle (r) is 14 units.

This problem can be solved by the Law of Sines:

sinA / r = sinC / y= sin D/ r + x

To find the length of side y, we can first calculate the measure of angle C (C) by using the formula for the length of an arc:

s= 2πrC/ 360

Then:

C= 360 s/ 2πr

C= 360 (18) / 2π(14)

C= 73.66

Now, we can use the Law of Sines to find the length of side y. The Law of Sines states:

sinA / r = sinC / c

In this case, we want to find side y, which is opposite angle C:

sinA / r = sinC / y

Solving for y :

y = sinCr/ sinA

y= sin ( 73.66 )14/ sin 45

Finally:

y = 18.99 = 19

So, the length of side y is approximately 19 units.

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Answer:

{(-5, 7), (-4, -9), (–5, – 4), (2, -6)}

Step-by-step explanation:

In a function, no two points can have the same x-coordinates. In other words, all x-coordinates of the points must be different.

{(5, -6), (-1, - 2), (2, –9), (–8, -2)} : All x-coordinates are different: 5, -1, 2, -8. This is a function.

{(-5, 7), (-4, -9), (–5, – 4), (2, -6)} : Two x-coordinates are the same: -5, -5. This is not a function.

{(-4,2), (-2,8), (-1,6), (5,6)} : All x-coordinates are different: -4, -2, -1, 5. This is a function.

{(2,2), (-4,9), (9, -3), (-3, 2)}: All x-coordinates are different: 2, -4, 9, -3. This is a function.

Jeremy’s net income was $514.8

Step-by-step explanation:

The given is:

We need to find what Jeremy’s net income was

The net income = total income - taxes

∵ Jeremy’s pay is $8.25 per hour

∵ Jeremy worked 78 hours in a month

- Jeremy's income =  the pay for an hour × the worked hours

∴ Jeremy's income = 8.25 × 78

∴ Jeremy's income = $643.5 in a month

∵ There was $128.7 as taxes in his pay statement

∴ The taxes = $128.7

- Substitute the values of his income and the taxes in the

   formula of the net income

∵ The net income = total income - taxes

∴ The net income = 643.5 - 128.7

∴ The net income = $514.8

Jeremy’s net income was $514.8

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Answer:

They tagged 90 male deer s

Explanation:

Given a park ranger calculated 60% of male deer

Consider the deer they tagged to be x

According to question,

20% of deer were older than 4 years which equals 18

Then, 20% of x = 18

Solving for x,

x = 1800/20

x = 90

So, they tagged 90 male deer

2≤4 so you have to do that by seeing that 3 iss less that 7

Answer:

i) C; x=y= 80°, ii) B; x= 58°, iii) D; x= 62° and y= 56°, iv) D; none of these are correct.

Step-by-step explanation:

i) Full angle around is 360°

 As given one angle is 100°,which means vertically opposite angles are equal to 100°

Now, remaining angle is equal to [tex]360-200= 160°[/tex]

∵ x and y are vertically opposite angle, which means they are equal.

∴x=y= 80°

ii) As we know straight angle is equal 180°

  As given one of the angle is 32° and other says, it is a right angle which   is equal to 90°.

∴ ∠x= [tex]180-(90+32)= 58°[/tex]

∴∠x= 58°

iii) Full angle = 360°

2∠x = 124° (∵ Vertically opposite angle are equal )

⇒∠x= [tex]\frac{124}{2}[/tex]

∴∠x= 62°

∠x+∠x+∠y= 180° (∵ it is a straight angle)

2∠x+∠y= 180°

⇒[tex]124+ y= 180[/tex]

Subtracting both side by 124

⇒∠y= [tex]180-124= 56°[/tex]

∴∠y= 56°

iv) Full angle= 360°

∴ ∠x+22°+32°+51°= 360°

Subtracting both side by 105

∠x= [tex]360-105= 255°[/tex]

∴∠x= 255°

Which means none of the given option are correct.

Answer:

D

Step-by-step explanation:

multiply out the top to get 6x - 4 + 2x - 2 = 8x - 6

next look at the 4 choices.

when we multiply out and combine only for the x term, only the bottom two give us 8x.

3/4 * 4x + 5 * x = 8x

3/4 * 4x + 1/6 * 30x = 8x

next we look at the bottom two for which one will give us -6, in this case only D will.

3/4 * -8 + 5 * 15 = 69

3/4 * -12 + 1/6 * 18 = -6

Answer:

A) (x-1)^2+(y+4)^2=4

Step-by-step explanation:

Here's the equation of a circle with center and radius:

(x-h)^2+(y-k)^2=r^2 with the center being at the point (h, k)

and the radius being r.

(x-1)^2+(y-(-4))^2=2^2

(x-1)^2+(y+4)^2=4

The equation of a circle with center (1, -4) and radius 2 is (x-1)²+(y+4)²=4

The correct option is (A).

The equation of circle represents the locus of point whose distance from a fixed point is a constant value. This fixed point is called the center of the circle and the constant value is the radius of the circle.

The standard equation of circle with center at (x1,y1)  and radius r is (x−x1)²+(y−y1)²=r².

We know equation of circle,

(x-a)²+(y-b)²=r²

Here, a=1, b=-4 and r=2

So,

(x-1)²+(y-(-4))²= 2²

(x-1)²+(y+4)²=4

Hence, the equation of circle is: (x-1)²+(y+4)²=4

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Answer:

17 is the simplified answer.

Step-by-step answer:

Given that:

y = 4.

We have to evaluate:

=5 + y + 8

By putting value of y that is y =4 in above equation:

=5 +4 +8

=9 +8

=17

So 17 is simplified answer for this question.

I hope it will help you!

Answer:

[tex]\large\boxed{y>\dfrac{c-ax}{b}}\\\text{for}\ a>0,\ b>0,\ c>0[/tex]

Step-by-step explanation:

[tex]ax+by>c\qquad\text{subtract}\ ax\ \text{from both sides}\\\\ax-ax+by>c-ax\\\\by>c-ax\qquad\text{divide both sides by}\ b\ (\text{we can, because}\ b>0)\\\\\dfrac{by}{b}>\dfrac{c-ax}{b}\\\\y>\dfrac{c-ax}{b}[/tex]

To solve the inequality ax - by > c for y, you first subtract ax from both sides which gives -by > -ax + c. Then you divide both sides by -b, remembering to flip the inequality sign, which gives y < (ax - c) / b.

To solve the inequality ax - by > c for y, you need to isolate y on one side of the inequality.

This is the solution for the inequality in terms of y.

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Answer:

(3•5•2a3b4)

Step-by-step explanation:

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 -15ab • (0 -  (2a2 • b3))

Step  2  :

Multiplying exponential expressions :

2.1    a1 multiplied by a2 = a(1 + 2) = a3

Multiplying exponential expressions :

2.2    b1 multiplied by b3 = b(1 + 3) = b4

Answer:

Jayce's fee for his [tex]10^{th}[/tex] drive is equal to [tex]K[/tex] dollars.

Step-by-step explanation:

[tex]M(n)[/tex] models Jayce's fee (in dollars) for his [tex]n^{th}[/tex] drive on a certain day.

Substitute [tex]n=10,[/tex] then

[tex]M(10)[/tex] models Jayce's fee (in dollars) for his [tex]10^{th}[/tex] drive on a certain day.

This means Jayce's fee for his [tex]10^{th}[/tex] drive is equal to [tex]K[/tex] dollars.

Answer:

C

Step-by-step explanation:

Jayce's fee for his 10th drive is equal to K  dollars.

If the line is parallel to y=1/5x-4, the line must have the same slope.

So, the slope of your line is 1/5.

Now we need to find the y intercept. We should use the point given.

y=mx+b

1=1/5(5)+b

b=0

Equation: y=1/5x

Answer:

y = (1/5)x

Step-by-step explanation:

y = mx+b

m= slope would be the same i.e. 1/5 , since it's parallel to the given equation.

y= 1

x= 5

Hence, let's look for the equation of this line of which the coordinate is provided!

1 = (1/5)(5) + b

1 = 1 +b

1-1 = b

b = 0

Hence the equation of this line is:

y = 1/5(x)

Hope this helps!

Mark brainliest of you think I helped! Would really appreciate!

To solve 50 1/2 divided by 1/4, convert the mixed number 50 1/2 to an improper fraction (101/2), then multiply by the reciprocal of 1/4 (which is 4), resulting in 202. The numbers are related through these multiplication and division steps.

Step by Step Solution:

To understand how the numbers are related in the equation 50 1/2 divided by 1/4, follow these steps:

First, convert the mixed number 50 1/2 to an improper fraction. This is done by multiplying the whole number part by the denominator of the fractional part and adding the numerator. Therefore, 50 1/2 becomes:

50 × 2 + 1 = 101/2

Next, when dividing by a fraction, you multiply by its reciprocal. So, dividing by 1/4 is the same as multiplying by 4/1.

Now multiply the improper fraction 101/2 by 4/1:

(101/2) × (4/1) = 101 × 4 / 2 × 1 = 404/2

Simplify the result by dividing the numerator by the denominator:

404 / 2 = 202

Therefore, the numbers are related through these multiplication and division operations, confirming that 50 1/2 divided by 1/4 equals 202.

Answer:

6.67 feet

Step-by-step explanation:

The situation is as shown in the figure.

ON is the normal to the mirror at the point of incidence O

⇒ ∠BON = ∠DON = 90°

By the laws of reflection: angle of incidence = angle of reflection :

∠AON = ∠CON

⇒ ∠AOB = ∠COD

⇒tan(∠AOB) = tan(∠COD)

⇒[tex]\frac{AB}{OB}[/tex] = [tex]\frac{CD}{OD}[/tex]

⇒[tex]\frac{6}{4}[/tex] = [tex]\frac{10}{x}[/tex]

⇒x = [tex]\frac{40}{6}[/tex] = [tex]\frac{20}{3}[/tex] = 6.67 ft

∴ Distance of the mirror from basketball goal is 6.67 ft

Final answer:

Using the principles of similar triangles, we determine that the mirror is 6 feet from the basketball goal by setting up a proportion between the heights and distances of the triangles formed by the goal and Mumford's line of sight. The mirror is 6 feet from the basketball goal.

Explanation:

To determine how far the mirror is from the basketball goal, we can use the principles of similar triangles. Basketball star Mumford is a six-foot-tall senior forward, meaning he is 6 feet above the ground. The basketball goal is 10 feet tall. If he walks backward four feet, and then he is able to see the top of the basketball goal, we can set up a proportion because the angles of incidence and reflection are equal.

Let's let x be the distance from the base of the basketball goal to the mirror. We then have two similar triangles to work with:

The large triangle with the height of the goal (10 feet) and the base x + 4 feet (distance from the goal to Mumford's eyes).

The smaller triangle with the height from Mumford's eyes to the ground (which is 6 feet because he's a six-foot-tall person) and the base x (distance from the goal to the mirror).

The proportion we set up is:

(Height of basketball goal) / (Distance from goal to Mumford's eyes) = (Height of Mumford's eyes from the ground) / (Distance from goal to the mirror)
10 / (x + 4) = 6 / x

Solving for x gives us the distance from the mirror to the basketball goal:

10x = 6(x + 4)

10x = 6x + 24

4x =24

x = 6

Therefore, the mirror is 6 feet from the basketball goal.

Answer:

C

Step-by-step explanation:

The formula given is:

[tex]d=26t+32.5[/tex]

Where

d is the distance between two cars

and

t is the time it takes

We want the time it takes (so we need t) for the cars to be 117 miles apart (this is the distance). Thus, it means:

d = 117

t = ???

We plug in 117 into d and solve the equation for t. Shown below:

[tex]d=26t+32.5\\117=26t+32.5\\117-32.5=26t\\84.5=26t\\t=\frac{84.5}{26}\\t=3.25[/tex]

So, it takes 3.25 hours

Correct answer is C

Final answer:

Using the formula d = 26t + 32.5 and setting d to 117 miles, we solve for t to find that it takes approximately 3.25 hours for the two cars to be 117 miles apart. The correct answer is C: 3.25.

Explanation:

To find out how many hours it will take for two cars to be 117 miles apart if they travel in opposite directions using the formula d = 26t + 32.5, we need to set d equal to 117 miles and solve for t.

First, we substitute 117 for d in the equation:

117 = 26t + 32.5

Next, we subtract 32.5 from both sides to isolate the term with t:

117 - 32.5 = 26t => 84.5 = 26t

Then we divide both sides by 26 to solve for t:

t = 84.5 / 26 => t ≈ 3.25

Hence, it will take approximately 3.25 hours for the cars to be 117 miles apart.

Thus, the correct answer is C: 3.25.

Answer:

802,000

Step-by-step explanation:

The number in the thousands place is 1, and the number to the right of it is 5. And if the number to the right is greater than or equal to 5 the place value that you are rounding goes up by one.

There were 69 children, 83.5 students, and 34.5 adults in attendance at the movie theater.

To solve this problem, we can set up a system of equations.

Let's denote the number of children as 'c', the number of students as 's', and the number of adults as 'a'.

From the given information, we have the following equations:

c + s + a = 187 (equation 1)

5c + 7s + 12a = 1356 (equation 2)

We also know that there are half as many adults as children, so we have the equation:

a = (1/2)c (equation 3)

Substituting equation 3 into equations 1 and 2, we can solve for the variables.

Substituting (1/2)c for a in equation 1:

c + s + (1/2)c = 187

(3/2)c + s = 187 (equation 4)

Substituting (1/2)c for a in equation 2:

5c + 7s + 12((1/2)c) = 1356

5c + 7s + 6c = 1356

11c + 7s = 1356 (equation 5)

Now we can solve equations 4 and 5 simultaneously:

Multiplying equation 4 by 11:

(33/2)c + 11s = 2057/2

11c + 7s = 1356

Subtracting the second equation from the first:

(33/2)c - 11c = 2057/2 - 1356

(-1/2)c = -69/2

c = 69

Substituting c = 69 into equation 4:

(3/2)(69) + s = 187

103.5 + s = 187

s = 83.5

Finally, substituting c = 69 and s = 83.5 into equation 3:

a = (1/2)(69)

a = 34.5

Therefore, there were 69 children, 83.5 students (which is not a whole number, so it could be rounded to 84 students), and 34.5 adults (which could be rounded to 35 adults) in attendance at the movie theater.

Answer:

x + y = -5

Step-by-step explanation:

standard form is ax + by = c

equation is y - 2 = -x - 7

Add x to both sides.

x + y - 2 = -7

Now add 2 to both sides.

x + y = -5

Answer:

The numerical value of the trigonometric function is 30 °

Step-by-step explanation:

Given trigonometric function as :

[tex]\frac{1 + cos x}{sin x}[/tex] + [tex]\frac{sin x}{1 + cos x}[/tex] = 4

or, Taking LCM we get

[tex]\frac{(1+cosx)^{2}+sin^{2}x}{(sinx)\times (1+cosx)}[/tex] = 4

Or,  ( 1 + cos x )² + sin² x = 4 × ( sin x ) × ( 1 + cos x )

1 + cos² x + 2 cox + sin² x = 4 sin x + 4 sin x × cos x

or, (  cos² x + sin² x ) + ( 1 + 2 cos x ) = 4 sin x ( 1 + cos x )

 ∵  cos² x + sin² x = 1

or,  1 + 1 + 2 cos x  = 4 sin x ( 1 + cos x )

or, 2 + 2 cos x = 4 sin x ( 1 + cos x )

or, 2 ( 1 + cos x ) = 4 sin x ( 1 + cos x )

Or, [tex]\frac{2 ( 1+ cos x )}{4 ( 1 + cos x )}[/tex] = sin x

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

∴  x = [tex]sin^{-1}\frac{1}{2}[/tex]

 ∵ sin 30 ° = [tex]\frac{1}{2}[/tex]

I.e  x = 30 °

Hence The numerical value of the trigonometric function is 30 °  answer

Answer: D. sin x= 1/2

Step-by-step explanation:

Edg 2020

Answer:

$12.99

Step-by-step explanation:

you take $79.45 and subtract it by $14.59 that equals $64.95. Then you take 64.95 and divide it by 5 and your total of each DVD is 12.99

The price of each DVD from online retailer is, $12.99

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

There was a shipping charge of $14.50 for the complete order but no sales tax.

And, Mia’s total charge for her order was $79.45.

Now, The cost of 5 DVD = $79.45 - $14.50

                                      = $64.95

Hence, The price of each DVD from online retailer is,

⇒ $64.95 / 5

⇒ $12.99

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Answer:

y = 20x

m = 20 and b = 0

Step-by-step explanation:

For input values of x = 1, output value of y = 20 and for x = 4, y = 80.

Therefore, the equation of this relation can be written as  

[tex]\frac{y - 80}{80 - 20} = \frac{x - 4}{4 - 1}[/tex]

⇒ 3(y - 80) = 60(x - 4)

⇒ 3y - 240 = 60x - 240

⇒ y = 20x

Now, y = mx + b is the equation and hence, m = 20 and b = 0 and the actual equation is y = 20x. (Answer)

Answer:

C

Step-by-step explanation:

That is her final answer.

Answer:

Between step 4 and step 5

Step-by-step explanation:

The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.

That is, if a, b, and c are real numbers such that a = b and c ≠0, then  

[tex]\frac{a}{c} = \frac{b}{c}[/tex]

At step 4: The equation was -6x = 57

To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below

[tex]-6x = 57[/tex] ---- Divide both sides by -6 (Step 4)

[tex]\frac{-6x}{-6} = \frac{57}{-6}[/tex] ---- (Intermediary between step 4 and 5)

[tex]x = -9.5[/tex] ----- Step 5

Hence, we can conclude that the division property of equality was done between step 4 and step 5

q/18 = 5

q = 18×5

q = 90

Answer:

x=10

Step-by-step explanation:

3x-5=1/2x+2x

3x-5=1/2x+4/2x

3x-5=5/2x

3x-5/2x=5

6/2x-5/2x=5

1/2x=5

x=5/(1/2)

x=(5/1)(2/1)

x=10/1

x=10

28 men are needed to paint the room in 3 hours

Given that it takes 12 hours for 7 men to paint a room

We are asked to find number of men required to paint the room in 3 hours

Recognize, "paint the room" is 1 task. One job.

7 men -------- 12 hours ------ 1 job

(7/7) = 1 men ------- 12 x 7 (84)  ------- same 1 job

The one men is rate is 84 hours to do the job

We can express this as 1/84 jobs per hour, the one-person rate

Now lets find how many men needed to paint the room in 3 hours

Let the required number of men for 3 hours be "a"

The rates of each person is simply additive.

[tex]a \times \frac{1}{84} \times 3 = 1[/tex]

corresponds to rate x hours = jobs and "a" is a variable for how many men

[tex]a \times \frac{1}{28} = 28[/tex]

Thus 28 men are needed to paint the room in 3 hours

Solving the expression [tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex] we get [tex]-\frac{6(x-4)}{5(x-2)}[/tex]

Step-by-step explanation:

Solving the expression:

[tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex]

Solving the expression:

We will find factors of the quadratic terms:

[tex]x^2-12x+32\\=x^2-8x-4x+32\\=x(x-8)-4(x-8)\\=(x-4)(x-8)[/tex]

So, factors of [tex]x^2-12x+32[/tex] are [tex](x-4)(x-8)[/tex]

[tex]x^2-10x+16\\=x^2-8x-2x+16\\=x(x-8)-2(x-8)\\=(x-2)(x-8)[/tex]

So, factors of [tex]x^2-10x+16[/tex] are [tex](x-2)(x-8)[/tex]

Placing factors instead of quadratic equation and finding common terms:

[tex]\frac{(x-4)(x-8)}{(x-2)(x-8)}.\frac{6(x-5)}{-5(x-5)}[/tex]

Cancelling the common terms:

[tex]\frac{(x-4)}{(x-2)}.\frac{6}{-5}\\-\frac{6(x-4)}{5(x-2)}[/tex]

So, Solving the expression [tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex] we get [tex]-\frac{6(x-4)}{5(x-2)}[/tex]

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