For what values of the variables are the following expressions defined? 1. 5y+2 2. 18/y 3. 1/x+7 4. 2b/10−b Example: X>7
PLEASE HELP

Answer:

x+10=1/2*(x+2)

2x+20=x+2

20-2= x-2x

x= -18

now,

LN= X+10

= -18+10

= -8

Answer:

2/5 =0.4

Step-by-step explanation:

Decimals are one of the method of representation of  fractions in which there is  power of 10 in the denominator of the fraction. They are  10,100,1000,10,000 ,100,0000 and so

Example = 1/10 = 0.1

1/100 = 0.01

1/1000 = 0.001

In 2/5 we have to make the denominator 10

since in denominator there is five , can be made 10 by multiplying it by 2

2/2 = 1 and 1* x = x , hence if we multiply numerator and denominator by 2 it won't change the fraction.

2/5×2/2=2×2/5×2=4/10=0.4

Thus, 2/5 =0.4 in decimal form.

Answer:

Option (2)

Step-by-step explanation:

Option (1)

In the interval [-1, 1] Or -1 ≤ x ≤ 1, value of the function will be represented by the y-values.

Since, the graph is below x-axis in the interval -1 ≤ x ≤ 0.5, function will be negative.

And in the interval 0.5 ≤ x ≤ 1, graph is above the x-axis, function will be positive.

Option (2)

In this option, graph is below the x-axis in the interval [-1, 1].

Therefore, the given graph is negative in this interval.

Option (3)

In this graph, function is negative and positive both in the interval -1 ≤ x ≤ 1.

Option (4)

In this graph function is completely above the x-axis in the interval -1 ≤ x ≤ 1.

So this function is positive in the interval [-1, 1].

Therefore, Option (2) will be the answer.

Answer:b since I got the others wrong

Answer:

c. (√3 + √5) - i

Step-by-step explanation:

(√3+i) + (√5-2i) =  √3+i + √5-2i = (√3 + √5) + (i - 2i) = (√3 + √5) - i

Answer: 585 miles

Step-by-step explanation: 60 x 7 for the first 7 hours = 420 miles, then 3 x 55 for the last 3 hours = 165 add them together, 420+265 you get= 585

60 miles per hour x 7 hours = 420 miles

55 miles per hour x 3 hours = 165 miles

Total miles = 420 + 165 = 585 miles

Answer:

D. 0° to 90°

Step-by-step explanation:

If we see curve of sin(o) on coordinate,  we will notice that value of sin curve increases from 0 to 90 degrees and then decreases from 90 to 180 degrees.

Hence option D is correct.

Alternatively

we see that

sin 0 = 0

sin 30 = 1/2

sin 45 = 1/[tex]\sqrt{2}[/tex]

sin 60 = [tex]\sqrt{3} /2[/tex]

sin 90 = 1

Thus, we see  that value of sin is increasing from 0 to 90

now lets see value of sin from 90 to 180

sin 90 = 1

sin 120 = [tex]\sqrt{3} /2[/tex]

sin 135 = 1/[tex]\sqrt{2}[/tex]

sin 150 = 1/2

sin 180 = 0

Thus, we see  that value of sin is decreasing from 90 to 180.

Answer:

Step-by-step explanation:

Hello,

[tex]x = (fof^{-1})(x)=f(f^{-1}(x))=\dfrac{-2}{f^{-1}(x)}-1\\\\<=>f^{-1}(x)(x+1)=-2\\\\<=> f^{-1}(x)=\dfrac{-2}{x+1}[/tex]

and this is g(x)

so they are inverses

Hope this helps

Answer:

$138

Step-by-step explanation:

Let the money with Raymond be $y

Let the cost of 1 tshirt be $x

then cost of 8 tshirt = cost of 1 t-shirt*8 = 8x

Raymond wanted to buy 8 t-shirt but he was short of $8.10

It means that 8x is equal to money he had plus $8.10

thus,

y + 8.10 = 8x

y = 8x - 8.10

Next situation

cost of 5 t-shirt = 5x

. instead he bought 5 T-shirt and had $12.60 left,

it means cost of 5 T-shirt plus $12.60 = total money Raymond had

y = 5x + 12.60

comparing y in both the equation

y = 8x - 8.10 and y = 8x - 8.10

5x + 12.60 =  8x - 8.10

=> 8x-5x = 12.60+8.10

=> 3x = 20.70

=> x = 20.70/3 = 6.9

Thus, cost of 1 T-shirt = $6.9

cost of 20 T-shirt = 20*$6.9 = $138  (Answer)

Answer:

Step-by-step explanation:

Let the cost of washer be ' x '

Let the cost of dryer be ' y '

According to Question,

x + y = 744 -----> equation (i)

x - y = 94 ------> equation (ii)

Adding equation (i) and (ii),

x + y = 744

+ x - y = 94

---------------------

2x = 838

Dividing both sides of the equation by 2

2x/2 = 838/2

Calculate

X = 419

Again,

Putting the value of X in equation (i)

X + y = 744

419 + y = 744

subtract 419 on both sides

y + 419 - 419 = 744 - 419

Calculate:

y = 325

The cost of dryer is $ 325.

Hope this helps...

Good luck on your assignment...

Answer:

1. what is a residual?

A. A residual is a value of y -y, which is the difference between an observed value of y and a predicted value of y.

2. The regression line has the property that the_sum of squares_of the residuals is the minimum possible sum.

Step-by-step explanation:

1. What is a​ residual?

A. A residual is a value of y -y, which is the difference between an observed value of y and a predicted value of y.

2. In what sense is the regression line the straight line that​ "best" fits the points in a​ scatterplot?

The regression line has the property that the_sum of squares_of the residuals is the minimum possible sum.

A residual is a value {Δy} that is a difference between an observed value of {y} and a predicted value of {y}.  

A regression line is an estimate of the line that describes the true, but unknown, linear relationship between the two variables. Mathematically -

[tex]$Y_i=f(X_i, \beta)+e_i[/tex]

Given is residual.

The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y. Mathematically -

[tex]r = x-x_{0}[/tex]

Therefore, a residual is a value {Δy} that is a difference between an observed value of {y} and a predicted value of {y}.  

To solve more questions on regression line, visit the link below -

https://brainly.com/question/7656407

#SPJ5

Answer:

when a number is divisible by 9, then the number is divisible by 3.

Step-by-step explanation:

They tell us "When a number is divisible by 9, the number is divisible by 3" we could change it by:

when a number is divisible by 9, then the number is divisible by 3.

Which makes sense because the number 9 is a multiple of the number 3, which means that the 9 can be divided by 3, therefore, if the number can be divided by 9, in the same way it can be divided by 3 .

Answer:

a

Step-by-step explanation:

Answer:

B. 17°.

Step-by-step explanation:

To solve the problem, we can use SOH CAH TOA.

SOH = Sine, Opposite divided by Hypotenuse

CAH = Cosine, Adjacent divided by Hypotenuse

TOA = Tangent, Opposite divided by Hypotenuse

In this case, we are given both the opposite and the hypotenuse, so we will use sine to solve it.

sine(N) = 4 / 14

sine(N) = 2 / 7

N = sec(2/7)

N = 16.6015496, which is about B. 17°.

Hope this helps!

Answer:      x<2   or   xϵ(-∞; 2)

Step-by-step explanation:

Add +3.2x to both sides of inequality:

2.5-1.2x+3.2x<6.5-3.2x+3.2x

2.5+2x<6.5

Deduct 2.5 from both sides of inequality:

2.5-2.5+2x<6.5-2.5

2x<4

Divide both sides of inequality by 2

2x/2<4/2

x<2   or   xϵ(-∞; 2) ( the answer can be written in 2 ways)

Answer:

2.5 - 1.2x < 6.5 - 3.2x

add 3.2x to both sides;

2.5 + 2x < 6.5

minus 2.5 from both sides;

2x < 4

 x < 2

Step-by-step explanation:

This is the exact same as doing a linear equation, so brush up on this skill.

Answer:

a) The sample space for this experiment includes

(Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (diamonds, tail), (hearts, head), (hearts, tail)

b) The two events are not mutually exclusive or disjoint as both events can occur at the same time and the set of A intersect B is not an empty set and P(A n B) ≠ 0.

c) P(A u B) = (3/4) = 0.75

d) P(A n B') = (1/4) = 0.25

Step-by-step explanation:

Let A be the event a club or spade is picked from a regular 52-card deck.

Let B the event a heads appears when the coin is tossed.

a) A sample space consists of all the possible outcomes of the whole process of picking a random suit and then tossing the coin for heads or tails.

There are 4 suits in a 52 deck card namely, clubs, spades, diamonds and hearts.

And in a toss of a coin, there are only 2 possible outcomes, a head or a tail.

The possible outcomes for the random pick of cards include

{clubs, spades, diamonds, hearts}

And for the second event

{Head, tail}

Combined, the sample space is

(Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (diamonds, tail), (hearts, head), (hearts, tail)

Noting that P(A) = probability of a club or a spade being picked = (26/52) = (1/2)

P(A') = Probability that a club or spade will not be picked, that is, a diamond or a heart will be picked = (26/52) = (1/2)

P(B) = Probability of a head turning up from the coin toss = (1/2)

P(B') = Probability of a head not turning up, that is, a tail turning up = (1/2)

b) Disjoint events are events that are mutually exclusive and cannot both occur at the same time. The set of the intersection of the two mutually exclusive/disjoint events is a null set.

Mathematically, mutually exclusive/disjoint events are proven through the relation that P(A n B) = 0.

But from the sample spaces obtained in (a) above, the event

(A n B) = (Clubs, head), (spades, head)

And it isn't a null set.

Since the probability of an event is the number of elements in the event divided by the total number of elements in the sample space.

n(A n B) = 2

n(total sample space) = 8

P(A n B) = (2/8) = (1/4) ≠ 0

Hence, the two events aren't disjoint.

c) P(A u B)

This represents the probability of obtaining a club or spade from the deck of card or getting head from the coin toss.

From the Total sample space, the set (A u B) includes (Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (hearts, head)

n(A u B) = 6

n(total sample space) = 8

P(A u B) = (6/8) = (3/4) = 0.75

d) P(A n B')

This represents the probability of obtaining a club or spade from the deck of card and NOT getting a head from the coin toss.

The set (A n B') includes (Clubs, tail), (spades, tail)

n(A n B') = 2

n(total sample space) = 8

P(A n B') = (2/8) = (1/4) = 0.25

Hope this Helps!!!

Answer:

6 ± i and 6 ± i

Step-by-step explanation:

Let x be the first number.

Let y be the second number.

x + y = 12

x × y = 37

Solve for x in the first equation.

x = 12 - y

Put x as 12-y in the second equation and solve for y.

(12- y)y = 37

12y - y² = 37

- y² + 12y - 37 = 0

y = 6 ± i

Put y as 6 ± i in the first equation and solve for x.

x + 6 ± i = 12

x = 12 - 6 ± i

x = 6 ± i

Answer:

$13.61

Step-by-step explanation:

$18 * 70% = $12.60

$12.60 * 1.08 = $13.61

Answer:

it's the step by step proceedure you use when solving an equation. Parentethese (do this first)

Exponents (take care of that after parentheses)  

Multiplication

Division

Addition

subtraction (always the last step in the problem)

Step-by-step explanation:

Answer:

PEMDAS = ( ), Exponents, Multiplication, Division, Addition, Subtraction

Step-by-step explanation:

essentially, PEMDAS are an order of a rule in which you have to follow.

1. P = Parenthesis/ ( )

2. E= Exponents/ ²

3. M= Multiplication/ x

4. D= Division/ ÷

5. A= Addition/+

6. S= Subtraction/-

Each goes in order, and if there isn't one of the steps included in the math problem you are given, then its better to move on to the next uwu

I hope this was helpful owo

Answer:

k = -21

Step-by-step explanation:

9/ (2k-3) = 4/(k+1)

Using cross products

9 * (k+1) = 4(2k-3)

Distribute

9k+9 = 8k -12

Subtract 8k from each side

9k-8k +9 = 8k-8k-12

k+9 = -12

Subtract 9 from each side

k+9-9 = -12-9

k = -21

Answer:

[tex]\huge\boxed{k=21}[/tex]

Step-by-step explanation:

[tex]\dfrac{9}{2k-3}=\dfrac{4}{k+1}[/tex]

First step:

Find domain.

We know: the denominator must be different than 0.

Therefore we have:

[tex]2k-3\neq0\ \wedge\ k+1[/tex]

[tex]2k-3\neq0\qquad\text{add 3 to both sides}\\2k\neq3\qquad\text{divide both sides by 2}\\\boxed{k\neq1.5}\\\\k+1\neq0\qquad\text{subtract 1 from both sides}\\\boxed{k\neq-1}\\\\\text{Domain:}\ x\in\mathbb{R}\backslash\{-1;\ 1.5\}[/tex]

Second step:

Solve for k.

[tex]\dfrac{9}{2k-3}=\dfrac{4}{k+1}\qquad\text{cross multiply}\\\\9(k+1)=4(2k-3)\qquad\text{use the distributive property}:\ a(b+c)=ab+ac\\\\(9)(k)+(9)(1)=(4)(2k)-(4)(3)\\\\9k+9=8k-12\qquad\text{subtract 9 from both sides}\\\\9k=8k-21\qquad\text{subtract}\ 8k\ \text{from both sides}\\\\\boxed{k=21}\in\text{Domain}[/tex]

Answer:

5,800 people

Step-by-step explanation:

We can find the enrollment for next semester by multiplying:

5,780(1.0035) = 5,800.23

We can round this to 5,800 people.

================================================

How to get this answer:

Midpoint formula: (A+B)/2 = C

A and B are the endpoints with C as the midpoint

A = 7/8

B = 6/7

A+B = 7/8 + 6/7

A+B = 49/56 + 48/56

A+B = (49+48)/56

A+B = 97/56

(A+B)/2 = (97/56) divided by 2

(A+B)/2 = (97/56) times (1/2)

(A+B)/2 = (97*1)/(56*2)

(A+B)/2 = 97/112

Answer:

[tex]-\frac{10}{3}ft/s[/tex]

Step-by-step explanation:

We are given that

Height of man=5 foot

[tex]\frac{dy}{dt}=-10ft/s[/tex]

Height of street light=20ft

We have to find the rate of change of the length of his shadow when he is 25 ft form the street light.

ABE and CDE are similar triangle because all right triangles are similar.

[tex]\frac{20}{5}=\frac{x+y}{x}[/tex]

[tex]4=\frac{x+y}{x}[/tex]

[tex]4x=x+y[/tex]

[tex]4x-x=y[/tex]

[tex]3x=y[/tex]

[tex]3\frac{dx}{dt}=\frac{dy}{dt}[/tex]

[tex]\frac{dx}{dt}=\frac{1}{3}(-10)=-\frac{10}{3}ft/s=-\frac{10}{3}ft/s[/tex]

Hence, the rate of change of the length of his shadow when he is 25 ft from the street light=[tex]-\frac{10}{3}ft/s[/tex]

Answer:

B: 8x^2+5x-6

Step-by-step explanation:

Answer:

y = 9x

Step-by-step explanation:

First find the slope

m = (y2-y1)/(x2-x1)

    = (0-9)/(0-1)

   -9/-1

   9

The y intercept is 0 since the y value is 0 when x=0

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = 9x +0

y = 9x

Answer:

top left

Step-by-step explanation:

Consider finding points on the graph using the equation.

x = 0 : f(0) = [tex]0.5^{0}[/tex] + 4 = 1 + 4 = 5 ← y- intercept

Since y- intercept is 5, this excludes the lower 2 graphs, which have y- intercepts of 1

x = 1 : f(1) = [tex]0.5^{1}[/tex] + 4 = 0.5 + 4 = 4.5 ⇒ (1, 4.5 )

x = - 1 : f(- 1) = [tex]0.5^{-1}[/tex] + 4 = [tex]\frac{1}{0.5}[/tex] + 4 = 2 + 4 = 6 ⇒ (1, 6 )

These points lie on the top left graph

Answer:

36 yd³

Step-by-step explanation:

The above solid shape given is a triangular prism.

The volume of triangular prism is given as ½ × base length of the triangle (b) × height of the triangle (h) × the length of the prism (l)

Base length of triangle (b) = 9 yd

Height of the triangle (h) = 2 yd

Length of the prism (l) = 4 yd

Volume = ½bhl

Volume = ½*9*2*4

Volume = 9*4

Volume of prism = 36 yd³

Answer:

a = first number

b = second number

"The sum of two numbers is 20."

a + b = 20

"[The difference of two numbers] is 118."

a - b = 118

Add the two equations together:

(a + b) + (a - b) = 20 + 118

Simply and solve:

2a = 138

a = 69

Use one of the above equations to solve for the second number.

a + b = 20

a = 69

69 + b = 20

b = -49

HOPE THIS HELPS AND PLSSS PLSSS MARK AS BRAINLIEST

THNXX :)

Answer:

Laura tiene 15 años mientras que su madre tiene 35 años.

Step-by-step explanation:

Deje que la edad de Laura sea L.

Deje que la edad de su madre sea m.

Tiene 3/7 de la edad de su madre:

L = 3 m / 7

En 5 años, la edad de su madre será el doble de su edad:

(m + 5) = 2 (L + 5)

m + 5 = 2L + 10

m - 2L = 5

Pon el valor de L:

m - 2 (3 m / 7) = 5

m - 6 m / 7 = 5

Multiplica por 7:

7m - 6m = 35

m = 35 años

=> L = 3 * 35/7 = 15 años

Laura tiene 15 años mientras que su madre tiene 35 años.

Step-by-step explanation:

firstly suppose f(X) as y and later interchange it with x and solve it to get inverse function of x.

The inverse of the given function is [tex]f^{-1}(x)=\dfrac{x+4}{2}[/tex].

Important information:

We need to find the inverse of the given function.

Substitute [tex]f(x)=y[/tex].

[tex]y=2x-4[/tex]

Interchange [tex]x[/tex] and [tex]y[/tex].

[tex]x=2y-4[/tex]

Isolate [tex]y[/tex].

[tex]x+4=2y[/tex]

[tex]\dfrac{x+4}{2}=y[/tex]

Substitute [tex]y=f^{-1}(x)[/tex].

[tex]\dfrac{x+4}{2}=f^{-1}(x)[/tex]

Thus, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{x+4}{2}[/tex].

Find out more about 'Inverse of a function' here:

https://brainly.com/question/11926240

Answer:

(B) {(2,1),(4,3),(5,7)}

Step-by-step explanation:

If the same x value goes to 2 different y values, it is not a function

(A) {(2,3),(2,5),(4,7)}   the x value 2 goes to 3 and 5

(B) {(2,1),(4,3),(5,7)}

(C) {(3,-2),(2,4),(3,6)}  3 goes to -2 and 6

(D) {(-1,4),(-1,5),(2,5)}​-1 goes to 4 and 5

Answer:  c) 88

Step-by-step explanation:

8, -16, 32, ...

We can see that each previous term is multiplied by -2

so the next two terms will be 32(-2) = -64 and -64(-2) = 128

So the first 5 terms of the sequence is:  8, -16, 32, -64, 128

Add the positive numbers and the negative numbers, then find their sum.

8 + 32 + 128 = 168

   -16 + (-64) = -80  

              Sum = 88