Using a number line, find both the intersection and the union of the following
intervals:
[1, 5] and (0,8]

pls help !

A linear system has one solution if the slopes of the equation of lines are different.

The 3  possible solutions of a linear system are:

- Unique or one solution

- Infinite solutions

- No solution

A linear equation is equal to the equation of a line, which has the form:

y = mx +b

where m = slope

If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equation will have one solution.

Example:

2x + 5y = 34  .. .. (equation 1)

x + 5y = 32  .........(equation 2)

Change the equation 1 and equation 2 into slope-intercept form:

y = (-2/5) x + 34/5   ..... (equation 1a)

y =  (-1/5) x + 32/5   ..... (equation 2a)

The slope of equation is (-2/5) while equation 2 is (-1/5), which is different from equation 1.  Hence, the system of linear equation has one solution.

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Answer:

4f+9  or 4×f +9

Step-by-step explanation:

This is what the equation would look like. (: I hope that helps!

Answer:

Step-by-step explanation:

Answer: t = 0

Step-by-step explanation:

Expand 8950×0.7²: 4385.5t

8950(0.7) ²t

8950×0.49t = 4385.5t

N(t) = 4385.5t

N(t) - 4385.5t=0

Factor N(t) - 4385.5t: t (N - 4385.5)

t (N - 4385.5) =0

t=0

Answer: 25 + d

Step-by-step explanation:

Since there are 30 drummers competing in the Battle of the Bands this year and, 5 of the drummers will leave the following year, the number of drummers left will be gotten by the expression:

= 30 - 5

If If d is the number of drummers who will then join the competition, therefore, the expression that represent the number of drummers in the competition next year will be gotten as:

= 30 - 5 + d

= 25 + d

Therefore, the expression is 25+d.

Answer:

11

Step-by-step explanation:

Answer:

A) [tex]\sqrt21[/tex]

Step-by-step explanation:

First you have to plug in the numbers into the Pythagreom Theroum:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]\sqrt{5} ^{2} +4^{2} =c^{2}[/tex]

(C represents you hypotnuse)

Then you square the numbers:

5 + 16 = [tex]c^{2}[/tex]

(If your confused why [tex]\sqrt5^{2}[/tex] just came out to be 5, the square and the square root cancel each other out)

Then you add the numbers:

21 = [tex]c^{2}[/tex]

Then you sqaure root both sides to cancel out the [tex]c^{2}[/tex]:

c = [tex]\sqrt21[/tex]

Answer:

1) D =65

2) C = 52

3) D =18

4) B =10

5) A = 72 and 108

Step-by-step explanation:

1) D =65

2) C = 52

3) D =18

4) B =10

5) A = 72 and 108

The number of real solution varies according to the degree of the equation and the nature of the equation, The answer is dependent on degree and nature.

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

example:

A linear equation (degree 1) has one real solution.

A quadratic equation (degree 2) can have either two real solutions, one real solution or no real solutions, as it depends on the discriminant of the equation, as I explained in my previous answer.

A cubic equation (degree 3) can have one to three real solutions, depending on the coefficients of the equation.

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Answer:

its 6.11

6.11 ÷ 1 = 6.11

Calculated to 2 decimal places.

6. 1 1

1 6. 1 1

− 6

0 1

− 1

0 1

− 1

0

 The value of h'(2) = 50.

What do you mean by function?

A relation between a collection of inputs and outputs is known as a function. In other word, it is a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

here we are given a function h(x)

here h(x) = - 5f(g(x)) ------(i)

and we are given the value of

g(2) =3   ;   f(2) = 1     ;     g'(2) = -2

f(3) = 4   ;    f'(3) = 5    ;    f'(2) = 6.

and we need to find the value of h'(2).

here f(x), g(x) and h(x) are the function of x and f'(x), g'(x) and h'(x) denotes the derivative of f(x), g(x) and h(x) respectively.

so we are given ,

h(x) = - 5f(g(x))

differentiating with respect to x both side

h'(x) = -5 f'(g(x).g'(x).

at x =2,

h'(2) = [tex]-5*f'(g(2))*g'(2)[/tex]

and we know  g(2) = 3 and g'(2) = -2.

so,

h'(2) = [tex]-5*f'(3)*-2[/tex]

h'(2) = [tex]-5*5*-2\\[/tex]       ( as f'(3) = 5 )

h'(2) = 50

so Option C is correct, the value of h'(2) = 50.

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Step-by-step explanation:

the area of a triangle is base times height divided by 2.

A = (b × h) / 2

so, when b = 3 and h = 4, then

A = (3 × 4) / 2 = 12 / 2 = 6

correct.

now the other way around

we know the area (6).

=> 6 = (b × h) / 2

=> 12 = b × h

well, b=3, h=4 is one possible solution for this.

but so is e.g. b=2, h=6, or b=12, h=1, or ...

and that is just the natural numbers. then there are rational numbers and so on.

therefore there is an infinite set of possible (b, h) pairs that satisfy the equation 12 = b × h.

therefore the statement that we can conclude out of a given triangle area of 6 that b must be then 3 and h must be 4 is wrong.

simple - it is one equation with 2 variables and has therefore usually not just one solution.

Explanation:

The confidence interval spans from 440 to 472. This is a width of 472-440 = 32 units. It divides in half to get 32/2 = 16. We can think of this as the "radius" of the confidence interval, and it represents the margin of error. It's the distance from the center to either endpoint of the interval.

Side note: use the midpoint formula to determine the center.

Answer:

1/8

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

convert this to a decimal.

1/2 = 0.50

1/4 = 0.25

0.5 x 0.25 = 0.125

0.125 x 8 = 1

Answer:

c

Step-by-step explanation:

heres a trick it says whole number so 10 is th eonly answer that is rounded

Answer:

Oki! Mizuki here to help!

The answer you fill in the box is 6!

Step-by-step explanation:

3.5s + 5.75 [tex]\leq[/tex] 26.75

3.5s + 5.75 - 5.75 [tex]\leq[/tex] 26.75 - 5.75

3.5s [tex]\leq[/tex] 21

s [tex]\leq[/tex] 6

Answer:The cafeteria sold 2 Ham sandwiches and 10 Turkey sandwiches

Step-by-step explanation:

Let the number of Ham sandwiches be rep as x

and turkey sandwiches be x+8

such that the equation to solve the question since total amount of sandwiches sold is 12 becomes '

x + x+8=12

2x+8=12

2x=12-8=44

x=4/2=2

Therefore number of ham sandwiches sold is 2

and number of turkey sandwiches sold is x+8=2+8=10

Answer:

65

Step-by-step explanation:

260/4=65

65*4=260

Answer:

y=6x-23

Step-by-step explanation:

Step-by-step explanation:

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

m = (-5 -1)/(3-4) = -6/-1 = 6

y = 6x + b

then

slope point form

y - y1 = m (x - x1)

y - 1 = 6 (x - 4)

y - 1 = 6x - 24

y = 6x - 23

Answer:

1.12 < mn

xy - x + y

2/3x - x²

xy + x/y - 10

(x + 2)³

2(4b - 2x)

The probability that the first card is a heart and the second card is a 10 is 1/51.

Probability with Replacement is used for questions where the outcomes are returned to the sample space again. This means that once the item is selected, it is replaced in the sample space, so the number of elements of the sample space remains unchanged.

The following combinations are possible:

When we choose first card, total no. of card is 52 and card of heart is 13

so the probability of the first card to be heart is

P(1)= 13/52

= 1/4

When we choose second card, total no. of card is 51 and card of 10 is 4

so the probability of the first card to be 10 is

p(2)= 4/51

So the final probability is

= P(1)* P(2)

= 1/4 * 4/51

= 1/51

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Answer:

x=7/2

x=3/2

Step-by-step explanation:

Answer: ax^2+bx+c=0

(4x^2+20x+20=0)

Step-by-step explanation:

It may not make sense but...

Add -20 to both sides of the equation.

4x-20x=-20

Add -20 to both sides of the equation.

4x^2-20x+20=-20+20

Simplify the expression.

4x^2+20x+20=0

I hope this was what you were looking for. :) If not I'm still glad to help.

Answer:

Domain and Range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively

Step-by-step explanation:

We have the functions, f(x) = eˣ and g(x) = x+6

So, their composition will be g(f(x)).

Then, g(f(x)) = g(eˣ) = eˣ+6

Thus, g(f(x)) = eˣ+6.

Since the domain and range of f(x) = eˣ are all real numbers and positive real numbers respectively.

Moreover, the function g(f(x)) = eˣ+6 is the function f(x) translated up by 6 units.

Hence, the domain and range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.

Answer:

It is not D!!!! it is not all real numbers for both! I got it wrong!

Step-by-step explanation:

edge 2021

i had answered saying it was D but then I got it wrong, so I can't just delete my answer. But I can say it is absolutely not D.

The 30th term of the arithmetic sequence is 265

What is an arithmetic sequence in math?

This is an arithmetic sequence since there is a common difference between each term. In this case, adding 9 to the previous term in the sequence gives the next term. In other words,   [tex]a_{n}[/tex]= [tex]a_{1}[/tex]+ d ( n - 1 )

Arithmetic Sequence: d = 9

This is the formula of an arithmetic sequence.

[tex]a_{n}[/tex] =  [tex]a_{1}[/tex] + d ( n - 1 )

Substitute in the values of   [tex]a_{1}[/tex] = 4 and  d = 9

 [tex]a_{n}[/tex]= 4 + 9 ( n - 1 )

[tex]a_{n}[/tex]= 4 + 9n - 9

[tex]a_{n}[/tex] = 9n - 5

.30th term =   [tex]a_{n}[/tex] =   [tex]a_{1}[/tex]+ d ( n - 1 )

=  [tex]a_{30}[/tex]= 4 + 9 ( 30 -1 )

   [tex]a_{30}[/tex]=   4 + 9 x 29

  [tex]a_{30}[/tex]= 265

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The three equations for this problem are:

Let's call the number of chocolate cakes x, the number of fruit cakes y, and the number of sponge cakes z

so the

let's use the third equation to get the value of x,y and z:

If you get the values and substitute, then the answer would be:

4 chocolate cakes, 5 fruit cakes, 2 sponge cakes

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Answer:

29.5m because it is rectangular finger and one path is loss .loss Parth is triangle

Answer:

88cm^2

Step-by-step explanation:

Area of the rectangle: base x height

Area of parallelogram: base x height

Area of the shaded part: area of rectangle -area of parallelogram:

12x10-4x8=120-32=88

Answer:

g

Step-by-step explanation:  it is basically the same problem with the  opisate meaning

Answer:

D

Step-by-step explanation:

Answer:

D: because the factor, fraction, decimals wont be multiply hundreadths of it specially when you add 27 so D: is my answer

Step-by-step explanation:

Does this help?

Answer:

no sign (not positive or negative)

Step-by-step explanation:

The value of the expression

4.3 ⋅ (-3.2) ⋅ 0

is 0, as the value of any number multiplied by zero is 0.

The number zero is neither positive or negative; hence there is no sign.