This is really confusing for me pls help!

Answer:

The cost of an orange is 21.5

Step-by-step explanation:

let orange be O and lemon be L

it becomes simultaneous Equations

2O+3L=64----1. x3

3O+4L=89----2. x2

6O+12L=192

6O+8L=178

subtracting

4L=14

L=7

put 7 for L in equ 1

2O+3(7)=64

2O+21=64

2O=64-21

2O=43

O=21.5

For the right table , y/x = constant = k = 0.5

The coordinates of the intersection with the x-axis are

(8,0), and the coordinates of the point where x = -3, (-3 0).

What are the coordinates of the axis?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

We have,

The graph shows the sketch of y = f(x).

The graph crosses the y-axis at the point (0,-2), and the x-axis at the point (8,0).

The coordinates of the intersection with the x-axis are:

x = 8

y = 0

The coordinates of the point where x = -3,

y = 0.

Hence, the coordinates of the intersection with the x-axis are

(8,0), and the coordinates of the point where x = -3, (-3 0).

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Answer:

( x+10)-3= 2

x+10= 5

x= -5

3x+12= 3

3x= -9

x= -3

3( x+6 )= 5x

3x+ 18 = 5x

2x= 18

x =9

w= l-4 y= x-4

perimeter= 2l+ 2w

2(2x) + 2( x-4)

4x+2x-8 = 72

6x= 72+8

6x= 80

x= 13.3 width = 9.3 length = 13.3

4x=48

x = 12

each 2= 24

If Leila makes a dot plot of the heights of the girls in her class to the nearest ¹/₂ inch, the number of different heights that will include on the number line is 5.

A dot plot is a data visualization tool that consists of data points plotted as dots on a graph with an x- and y-axis.

The number of dots plotted on each number line shows the frequency of the data group.

Height    Frequency   Cumulative Frequency

56¹/₂             2                               2

57                 2                               4

57¹/₂             2                               6

58                2                               8

58¹/₂             1                               9

Thus, arranging the heights according to groups, the different heights on the number line can be classified into 5.

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Step-by-step explanation:

Subtract the envelope weight from the total weight....this will result in the weight of the paperclips alone:

49.5 g - 2.43 g = 47.07 g   of paper clips

Then:

47.07 g   / ( .83 g /clip)  = 56.7 = ~ 57 clips

From the given table, the following are observed:

No. of marbles that are not red and not small = No. of Big Green and Big Purple

= 14 + 9

= 23 Marbles

Total number of marbles = 9 + 14 + 9 + 9 + 9 + 6 + 10 = 66 Marbles

We get,

We can no longer simplify 23/66. Therefore, 23/66 is the answer.

Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours

This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.

Let's assume that Sarah worked x hours.

Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.

Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.

Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.

The total number of shirts ironed by both Sarah and Penelope is 475 shirts.

So, we can write the equation: 30x + (35/2)x = 475.

To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.

Now, we can solve for x: x = (475 * 2) / 95 = 10.

Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.

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The number of solutions that the system of equations has is given as follows:

The system of linear equations represented in the graph have

No solutions.

The first step in obtaining the number of solutions of the system of equations is obtaining the linear function that represents each line.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

m is the slope.

b is the y-intercept.

here, we have,

The first line goes through these following points:

(0,3) and (3,4).

The slope is given by change in y divided by change in x, hence:

slope = 3

When x = 0, y = 3,

hence the intercept is of b = 3

and the function is given as follows:

y = 3x - 3

The second line goes through these following points:

(0,-2) and (3,-1).

Hence the slope is of:

m = 3

The intercept is of b = -2,

and the equation is given as follows:

y = 3x-2.

Hence the solution is obtained as follows:

3x - 3=3x-2.

i.e.

The system of linear equations represented in the graph have

No solutions.

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The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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Answer:

(x,y) = (5/21, -50/21)

Step-by-step explanation:

The surface area of the prism include the following: C. two hundred seventy-five and one-eighth cm².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[(23/4 × 4) + (23/4 × 47/4) + (4× 47/4)]

Surface area of rectangular prism = 2[23 + 1081/16 + 47]

Surface area of rectangular prism = 275 1/8 cm².

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The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

From the question, we have the following parameters that can be used in our computation:

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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The point slope equation and slope of some lines are given below

1) For y - 6 = 3(x - 5), slope = 3

2) For  y - 4 = -9(x + 8), slope = -9

3) y - 2 = 5x, slope = 5

4) Point slope equation of line whose slope = -10 and passing through   (1, 4)

   y - 4 = -10(x - 1)

5) Point slope equation of line whose slope = 2 and passing through    (5, -3)

      y  + 3 = 2(x - 5)

6) Point slope equation of line whose slope = \(\frac{1}{2}\) and passing through    (-7, -7)

   \(y +7 = \frac{1}{2}(x +7)\\\)

What is equation of line in point slope form?

The most general form of equation of line in point slope form is given by \(y - y_1 = m(x - x_1)\) , \((x_1, y_1)\) is a point on the line

Where m is the slope of the line

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  \(\theta\) is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = \(tan\theta\)

1) y - 6 = 3(x - 5)

  y - 6 = 3x - 15

  y = 3x - 15 + 6

  y = 3x - 9

  Slope = 3

  If x = 0,

  \(y = 3 \times 0 -9\\y = -9\)

  (0, -9) is a point on the line

2) y - 4 = -9(x + 8)

   y - 4 = -9x - 72

   y = -9x - 72 + 4

   y = -9x - 68

   Slope  = -9

   If x = 0

   \(y = -9 \times 0 -68\\y = -68\)

   (0, -68) is a point on the line

3) y - 2 = 5x

   y = 5x + 2

  Slope = 5

    Putting x = 0

    \(y = 5 \times 0 + 2\\y = 2\)

    (0, 2) is a point on the line

4) Slope = - 10

    The line passes through (1, 4)

    Point slope equation

      y - 4 = -10(x - 1)

5) Slope = 2

    The line passes through (5, -3)

     Point slope equation

      y - (-3) = 2(x - 5)

      y + 3 = 2(x - 5)

6) Slope = \(\frac{1}{2}\)

      The line passes through (5, -3)

     Point slope equation

       \(y - (-7) = \frac{1}{2}(x - (-7))\\y +7 = \frac{1}{2}(x +7)\\\)

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Given statement solution is :- If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

If the expression 12x - 6x + 5 + 4x is set equal to 10x + 5, then there would be solution(s).

If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

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Answer:

1.5

Step-by-step explanation:

i am not certain but this is how I got it

First distribute which gives you the -3 with 2 I switched them around so I did -3(-5x+2) and you will get 15x-6

Then the opposite of subtraction is addition so you add 6 to both sides so you add six to 12 and to 6 leaving you with 15x=3x+18 you then will subtract 3x from 15x and 3 leaving you with 12x=18 the divide the numbers

After you divide you get 3/2 then put it has a decimal and you get 1.5

Answer:

Step-by-step explanation:

Answer:

B) 2

Step-by-step explanation:

Is BK bisecting CD?

x + 1 = 2x -1  Subtract x from both sides

1 = x -1  Add 1 to both sides

2 = x

(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.

(ii) The axioms of probability are:

the non-negativity (that the probability of an event is greater than or equal to zero), and

the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).

(iii) When two fair dice are thrown the probability of getting:

a) The sum of 9 = 1/9

b) Two odd numbers = 1/4

c) two prime numbers = 1/9

d)  two factors of 12 = 1/9

(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.

To find probability when two dice are thrown, we have:

(a) The sum of 9:

We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways

A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.

(b) Two odd numbers:

We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).

possible outcomes = 9,

So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.

(c) Two prime numbers

We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)

possible outcomes = 4,

So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.

(d) Two factors of 12:

We count the number of ways and divide by the total possible outcomes.

The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways

possible outcomes = 6

Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12

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Answer:

\(2\pi\)

Step-by-step explanation:

First, let's find the area of circle O.

The formula is \(\pi r^2\).

Plugging in the radius 3, we get the area is \(9\pi\).

To get the area of the sector, we have to find out what fraction of 360 degrees the POQ is.

\(\frac{80}{360} = \frac{2}{9}\).

We now multiply \(\frac{2}{9}\) by 9, getting 2.

The answer is \(2\pi\)

Problem 1

Reason: We start at 0 and move 4 units left. This is represented by 0+(-4) or 0-4. That simplifies to -4. Then add on 7 to move 7 units to the right to arrive at 3 as the final destination.

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

Problem 2

Reason: We start at 0 and move 8 units to the right. That is represented by +8 or simply 8. Then the +3 will move us 3 more units to the right to get to 11 on the number line. This is one visual way to see why 8+3 = 11.

Answer:

12 yards

Step-by-step explanation:

Robert's dimes are anywhere between 17 and 19.

Nickels

are worth 5 cents, and

dimes

are worth 10 cents. Since Robert has 10 nickels, he already has 50 cents. To reach a minimum of $2.20, or 220 cents, Robert needs at least 170 more cents. Because each dime is worth 10 cents, he needs a minimum of 17 dimes. If he has a maximum of 29 coins in total, subtracting the 10 nickels means that he can have up to 19 dimes. So, Robert could have anywhere between 17 and 19 dimes.

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The value of ∂x/∂s is  4s^2 * t^6.

To find ∂x/∂s, we need to differentiate x with respect to s while treating t as a constant. Let's begin by substituting the given expressions for x, y, and z into the function f(x, y, z):

f(x, y, z) = (x^2)(y^3) + z^3

Substituting x, y, and z:

f(s, t) = ((s^2)(t^3))^2 * (s*t)^3 + ((s^2)*t)^3

Expanding the expression:

f(s, t) = (s^4 * t^6) * (s^3 * t^3) + (s^6 * t^3)

Now, let's differentiate x with respect to s:

∂x/∂s = ∂/∂s [(s^2)(t^3)]^2

Using the chain rule, we can differentiate each term separately:

∂x/∂s = 2 * (s^2 * t^3)^1 * ∂/∂s [(s^2)(t^3)]

Differentiating (s^2)(t^3) with respect to s:

∂/∂s [(s^2)(t^3)] = 2s * t^3

Substituting back into the expression for ∂x/∂s:

∂x/∂s = 2 * (s^2 * t^3)^1 * 2s * t^3

Simplifying:

∂x/∂s = 4s^2 * t^6

Therefore, ∂x/∂s = 4s^2 * t^6.

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The possible coordinates for the fountain are (-11/4, -5/2) and (-11/4, 5/2),

To find the possible coordinates for the fountain that is 5 units away from both statues A and B, we can use the concept of distance formula.

The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁))

In this case, the coordinates for statue A are (-2, -1) and the coordinates for statue B are (4, -1).

Let's assume the coordinates for the fountain are (x, y). We want the distance between the fountain and both statues to be 5 units.

Using the distance formula for statue A:

5 = √((-2 - x)² + (-1 - y)²)

Simplifying:

25 = (-2 - x)² + (-1 - y)² (equation 1)

Using the distance formula for statue B:

5 = √((4 - x)² + (-1 - y)²)

Simplifying:

25 = (4 - x)²+ (-1 - y)² (equation 2)

We have a system of equations (equation 1 and equation 2) that represents the conditions for the fountain's coordinates.

By solving this system of equations, we can find the possible coordinates for the fountain.

Note: The solution to this system of equations will provide two sets of coordinates that satisfy the given conditions.

To solve the equations, we can expand and simplify:

From equation 1:

25 = 4 + 4x + x² + 1 + 2y + y²

x² + y² + 4x + 2y - 20 = 0 (equation 3)

From equation 2:

25 = 16 - 8x + x² + 1 + 2y + y²

x² + y² - 8x + 2y - 9 = 0 (equation 4)

Now, we can solve equations 3 and 4 simultaneously.

Subtracting equation 4 from equation 3 we get:

(8x - 4x) + (-9 + 20) = 0

4x + 11 = 0

4x = -11

x = -11/4

Substituting the value of x back into equation 3:

(-11/4)² + y² + 4(-11/4) + 2y - 20 = 0

y² + 2y - 25/4 = 0

Solving this quadratic equation, we can find the possible values of y. Factoring the equation:

(y + 5/2)(y - 5/2) = 0

This gives us two solutions:

y + 5/2 = 0 -> y = -5/2

y - 5/2 = 0 -> y = 5/2

Therefore, the two possible coordinates for the fountain are (-11/4, -5/2) and (-11/4, 5/2).

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Answer:

grrrr is 1)7

Step-by-step explanation:

The angles marked x in each of the polygons are 128° and 82° respectively.

Concave polygons are closed two dimensional figures whose at least one of the interior angle is more than 180 degrees.

The given polygons are named as ABCDEFGH and PQRSTU as shown below.

1) An interior angle and a corresponding exterior angles are supplementary.

Interior angle ∠B = 180° - 42° = 138°

Similarly,

Interior angle, ∠E = 180° - 34° = 146°

Also, angle around a point = 360°

Interior angle at G = 360° - 141° = 219°

Sum of the angles of a polygon = (n - 2) 180°, where n is the number of sides.

Here, number of sides, n = 8

x + 138° + 107° + 145° + 146° + 126° + 219° + 71° = (8 - 2) 180°

x + 952° = 1080

x = 1080 - 952

x = 128°

2) The dotted line implies that the shape is symmetrical.

∠Q = ∠U and ∠R = ∠T

∠Q = ∠U = 34°

Exterior angle at T = 87°

Interior angle at T = 360° - 87° = 273°

So ∠R = ∠T = 273°

Again number of sides, n = 6

x + 34 + 273 + 24 + 273 + 34 = (6 - 2) 180

x + 638 = 720

x = 720 - 638 = 82°

Hence the angle are 128° and 82°.

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Answer:

first angle of tht side is 90

n then the whole cirlcle is 360 so~

Step-by-step explanation:

Answer:

first angle of tht side is 90

n then the whole cirlcle is 360 so~

Step-by-step explanation:

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

Explanation:

Add 4 to both sides

a-4 < 10

a-4+4 < 10+4

a < 14

The reason why we add 4 to both sides is to undo the "minus 4" that's happening to the variable.