5x + y = 10
5y = 3x - 6
Solution: (0,0)
Solve for system of equations

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:

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

Answer:

X=-2

Step-by-step explanation:

PLUG IT IN HTE EQUATION BRAINLIEST PLZZZ

Answer:

x = - 2

Step-by-step explanation:

Given

2x - (4x - 4) = 16 - 8 = 8 ← distribute parenthesis and simplify left side

2x - 4x + 4 = 8

- 2x + 4 = 8 ( subtract 4 from both sides )

- 2x = 4 ( divide both sides by - 2 )

x = - 2

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.

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:

5,070

Step-by-step explanation:

Answer:

5069.0

Step-by-step explanation:

The tenth value is the value directly after the decimal point. In this case, the number given is a whole number, and so to find the tenth place value, add a decimal point and a 0 to the back.

~

Step-by-step explanation:

3B+b=_5+12+1

4Bb=8

4Bb/4=8/4

Bb=2

Answer:

B = 2

Step-by-step explanation:

To solve the linear equation;

- 12 + 3B -1 = -5 - B

we will first collect like-term that is; we will make all the B variables to be on the left-hand side of the equation and all the constant to be on the right-hand side of the equation

( when -B cross over to the left-hand side of the equation,  B becomes positive, when -12 and -1 cross over to the right-hand side of the equation, they become positive 12 and 1)

3B + B  =   -5  +  12 + 1

4B   =  8

Divide both-side of the equation by 4 to get the value of B

4B/4  =  8/4

(on the left-hand side of the equation ,4 will cancel out 4 leaving us with B and 8 will be divided by 4 to give us 2)

B =  2

Therefore the solution to the linear of the equation is B = 2

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:

bro in Ur pictures there is no 7-10

Step-by-step explanation:

10-7 is 3 right so 7-10 is -3 it simple . but show me questions again because there is no 7-10 . Thank for ur asking me !

The product of two square roots is equal to the square root of the product, so the product of √y3 and √y3 is y3.

The equation is asking you to multiply the square root of y cubed by itself.

Based on the properties of square roots, if you multiply the square root of a number by itself, you get the original number.

This is because multiplication is the inverse operation for square roots. Meaning, it undoes the square root.

So, in this scenario, you are multiplying [tex]\sqrt{y^{3} }[/tex] * [tex]\sqrt{y^{3} }[/tex]which results in y^3.

Thus, the product of [tex]\sqrt{y^{3} }[/tex] and  [tex]\sqrt{y^{3} }[/tex]is y^3, assuming y≥0.

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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!

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:

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:

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:

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.

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]

Keywords: Solving Fractions

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Answer:

[tex]a_n = 8n+8[/tex] represent the sequence 16,24,32,40...

Step-by-step explanation:

The sequence given is

16,24,32,40.

And the options given are

an=4n+1

an=8n+8

an=8n+16

We will check for all so as to find the correct expression.

In the given sequence the first term is 16,

i.e a1 = 16

1). We will check for an = 4n+1 whether the first term is 16 or not.

We will put the value of n as 1;

[tex]a_1= 4\times1+1= 4+1=5[/tex]

With this option we get the first term as 5 but in the given sequence first term is 16.

Hence this option is Incorrect.

2). We will check for an = 8n+8 whether the first term is 16 or not.

We will put the value of n as 1;

[tex]a_1= 8\times1+8= 8+8=16[/tex]

With this option we get the first term as 16 and in the given sequence also first term is 16.

Hence this option is correct.

3). We will check for an = 8n+16 whether the first term is 16 or not.

We will put the value of n as 1;

[tex]a_1= 8\times1+16= 8+16=24[/tex]

With this option we get the first term as 24 but in the given sequence first term is 16.

Hence this option is Incorrect.

Hence we can say that an = 8n+8 represent the sequence 16,24,32,40...

Answer:

The correct answer is C. 0.033/2

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Annual interest rate = 3.3% compounded semiannually

2. Let's find the exact value of the rate:

Number of periods (n) = n/2, given that periods are semesters and not years

Annual interest rate (r) = 3.3% = 3.3/ 100 = 0.033

For using the correct value in the present value annuity formula, we also have to divide the annual interest rate because the interest is compounded semiannually or every six months, what it means:

0.033/2

The correct answer is C. 0.033/2

c. [tex]\frac{0.033}{2}[/tex]

on edgen

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

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:

+1

Step-by-step explanation:

The y-intercept is +1.

Answer: x= -25

Step-by-step explanation:

Answer:

x=-25

Step-by-step explanation:

x/5 = 8 = 3 you would multiply both sides by 5

youd end up with x+40=15 then you would move the constan to the right

x=15-40 you would subtract 40 from 15

x=-25

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

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:

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:

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)