Write the solution set of the equation x2 – 4=0 in roster form

Answer:

Step-by-step explanation:

what is it that you don't understand about how to get this?  

2(4-3x) + 5(2x-3) = 20-5x

Answer:

B is the answer because the graph is translated 2 down. the translation cannot be included within the radical sign, so it can't be C

Step-by-step explanation:

here's the answer to your question

Answer:

4/9 of an hour (26.666 minutes)

Step-by-step explanation:

4 * x * 40/60 = 1

x * 160/60 = 1

x=60/160 = 6/16 = 3/8 (this is the rate for one worker)

~~~~~~~~~~~~~~~~

6 * (3/8) * x = 1

x = 4/9

The number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.

For the given situation,

Peter sold a cup of lemon juice = $1.25

Peter sold a cup of apple juice =  $2.50

Total number of cups sold = 155 cups

Total amount = $256

Let number of cup of lemon juice be x and

let number of cup of apple juice be y

The equations for the above statements are

[tex]x + y = 155 ------- (1)\\1.25x +2.50y = 256 ------- (2)[/tex]

From equation 1,

⇒ [tex]x=155-y[/tex]

Now substitute x in equation 2,

⇒ [tex]1.25(155-y)+2.50y=256[/tex]

⇒ [tex]193.75-1.25y+2.50y=256[/tex]

⇒ [tex]1.25y=256-193.75[/tex]

⇒ [tex]1.25y=62.25\\[/tex]

⇒ [tex]y=\frac{62.25}{1.25}[/tex]

⇒ [tex]y=49.8[/tex] ≈ [tex]50[/tex]

Now substitute y in equation 1,

⇒ [tex]x=155-50[/tex]

⇒ [tex]x=105[/tex]

Hence we can conclude that the number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

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Answer:

5:15 simplified as 1:3

Step-by-step explanation:

five I think I am not sure

Answer:

see explanation

Step-by-step explanation:

To verify cos²A + sin²A = 1 with A = 90° , then

cos²90° + sin²90°

= (0)² + (1)²

= 0 + 1

= 1

Answer:

A.

Step-by-step explanation:

A.-6r+6

Answer:

In order:

Distributive Property

Subtraction Property of Equality

Division Property of Equality or Reciprocal Property

Step-by-step explanation:

Answer:

Where are the ordered pairs?

Step-by-step explanation:

Hi there!

[tex]\large\boxed{77m^2}}[/tex]

We can divide the figure into 3 rectangles.

Area of top rectangle:

5 × 5 = 25m²

Long rectangle:

14 × 3 = 42m²

Bottom rectangle:

2 × 5 = 10m²

Add up the areas:

10 + 42 + 25 = 77m²

Answer:

b

Step-by-step explanation:

[tex]\frac{x^4}{x^7} =x^4 \times x^{-7} =x^{4-7} =x^{-3}[/tex]

Step-by-step explanation:

???????? what is easy??

Answer:

?=83 degrees

Step-by-step explanation:

74+120=194

360-194=166

166÷2=83

You divide by two because it is an inscribed angle, so it will always be half the measure of the arc it is inscribing or enclosing.

Answer:

HCF = 6

Step-by-step explanation:

Listing the factors of each number

18 is 1, 2, 3, 6, 9, 18

30 is 1, 2, 3, 5, 6, 10, 15, 30

36 is 1, 2, 3, 4, 6, 9, 12, 18, 36

common factors are 1, 2, 3, 6

the HCF is 6

9514 1404 393

Answer:

  (a) 6² +3² +1² +1² = 47

  (b) 5² +4² +2² +1² +1² = 47

  (c) 3³ +4² +2² = 47

Step-by-step explanation:

It can work reasonably well to start with the largest square less than the target number, repeating that approach for the remaining differences. When more squares than necessary are asked for, then the first square chosen may need to be the square of a number 1 less than the largest possible.

The approach where a cube is required can work the same way.

(a) floor(√47) = 6; floor(√(47 -6^2)) = 3; floor(√(47 -45)) = 1; floor(√(47-46)) = 1

__

(b) floor(√47 -1) = 5; floor(√(47-25)) = 4; ...

__

(c) floor(∛47) = 3; floor(√(47 -27)) = 4; floor(√(47 -43)) = 2

Answer:

[tex]\displaystyle y=\frac{1}{2}x+5[/tex]

Step-by-step explanation:

We want to find the slope in slope-intercept form of a line that is parallel to:

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

And passes through the point (-8, 1).

Recall that parallel lines have equivalent slopes.

Since the slope of our given line is 1/2, the slope of our new line must also be 1/2.

We are also given that it passes through the point (-8, 1). Since we are given a slope and a point, we can use the point-slope form:

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

Substitute 1/2 for m and (-8, 1) for (x₁, y₁). Hence:

[tex]\displaystyle y-(1)=\frac{1}{2}(x-(-8))[/tex]

Since we want the equation in slope-intercept form, we can isolate y. Distribute:

[tex]\displaystyle y-1=\frac{1}{2}x+4[/tex]

Therefore, our equation is:

[tex]\displaystyle y=\frac{1}{2}x+5[/tex]

Answer:

The two INTEGERS are :-

-3 and +4

-3 * (+4) gives us -12

-3 + (+4) gives us 1

hope it helps

have a nice day

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3.

Answer:

The lengths of the other sides would be 10, as well.

Step-by-step explanation:

Since we already know two of the three angles, we can subtract to find the other angle. The interior angles of a triangle will always add up to 180°. We have 60° and 60°, giving us 120°. 180 - 120 is equal to 60°, so that's the missing angle. Because all of the angles are the same, this is an equilateral triangle, which means the sides also have to be the same length. If one of the sides is 10, all of the sides are 10.

The triangle with sides 10 , 10 and 10 and all angles at 60° is an equilateral triangle

An equilateral triangle is a triangle in which all three sides have the same length.

Let the triangle be ΔABC , and

∠A = ∠B = ∠C = 60° and AB = BC = CA

Given data ,

Let the triangle be represented as ΔABC

Let the side length of the triangle be AB = 10

Now , the measure of ∠ABC = 60°

And , the measure of ∠BAC = 60°

So , the total sum of all the angles in a triangle = 180°

And , the measure of ∠ACB = 180° - ( 60° + 60° ) = 60°

Therefore , all the angles of the triangle are 60°

So , it is an equilateral triangle

And , the measure of side lengths of the triangle is 10

Therefore , AB = BC = CA = 10

Hence , it is an equilateral triangle

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Answer:

50.265

Step-by-step explanation:

Area is radius square times pi. Radius is half of diameter .Diameter is 8 inches. Radius is 4 inches. 4 squared is 16. 16 times pi is 50.265

Answer:

80°

Step-by-step explanation:

Triangle ABC and CYZ are similar so the angles would also be same

Answer:

A: The y-intercept of f(x) is equal to the x-intercept of g(x)

Step-by-step explanation:

From the equation of f(x) given, we have;

f(x) = -4(1.09)^(x)

Now,the y-Intercept will be the point where x = 0.

Thus;

f(0) = -4(1.09)^(0)

f(0) = -4

Now,from the table given for g(x), we can see that at x = 0,g(x) = -4.

Thus,it means that the y-intercept of f(x) is equal to the x-intercept of g(x)

Step-by-step explanation:

answer what ?

all we can see is a grid of coordinates with a functional graph drawn into it.

and we know this function is called y=h(x).

that is it.

what answer is needed ? there is no question visible.

Answer:

93600

Step-by-step explanation:

The divisibility rule of 24 is that the number has to be divisible by both 3 and 8. So we need to plug in numbers for x and y to find the greatest number. 93600 should be the answer.

Given:

30-hour review course average a score of 620 on that exam.

70-hour review course average a score of 749.

To find:

The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.

Solution:

Let x be the number of hours of review course and y be the average score on that exam.

30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).

70-hour review course average a score of 749. So, the linear function passes through the point (70,749).

The linear function passes through the points (30,620) and (70,749). So, the linear equation is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-620=\dfrac{749-620}{70-30}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}[/tex]

Adding 620 on both sides, we get

[tex]y=\dfrac{129}{40}x-\dfrac{387}{4}+620[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2480-387}{4}[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex]

We need to find the y-value for [tex]x=57[/tex].

[tex]y=\dfrac{129}{40}(57)+\dfrac{2093}{4}[/tex]

[tex]y=183.825+523.25[/tex]

[tex]y=707.075[/tex]

[tex]y\approx 707.1[/tex]

Therefore, the required linear equation for the given situation is [tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex] and the average score for persons taking a 57-hour review course is 707.1.