Chocolate bars cost $2.50 each.
The more chocolate bars Terri buys, the more
money she will have to pay.
Identify the dependent variable.

The present ages of the father and his son are 50 and 30 years respectively.

An algebraic expression can be defined as an expression made up of constants, variables, terms, coefficients, and factors.

These expressions are also made up of mathematical or arithmetic operations, which includes;

From the information given;

Let the son's age be x

Let the father's age be x + y

x + x + y = 80

2x + y = 80

Then, 2x - y = 40

From equation (1), make 'y' the subject

y = 80 - 2x

Substitute the value

2x - (80 - 2x) = 40

2x - 80 + 2x = 40

collect like terms

4x = 120

x = 30

y = 80- 2(30)

y = 20

Hence, their ages are 30 years and 50 years

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Solid chance this is way above your knowledge level



A parabola is a curve in the shape of a U that is defined as the set of all points that are equidistant to a fixed point (called the focus) and a fixed line (called the directrix).

To write the equation of a parabola with a focus at (-2, 5) and a directrix at x = 3, we can use the standard form of the equation of a parabola, which is:

y = (1/(4f))x^2 + k

Where f is the distance between the focus and the vertex (the point where the parabola changes direction), and k is a constant that determines the position of the parabola along the y-axis.

To find the value of f, we can use the distance formula:

f = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) is the coordinate of the focus and (x2, y2) is the coordinate of the vertex.

Since the focus is at (-2, 5) and the directrix is at x = 3, we can use the y-coordinate of the focus as the y-coordinate of the vertex, and the x-coordinate of the directrix as the x-coordinate of the vertex. Therefore, the coordinate of the vertex is (3, 5).

Substituting these values into the distance formula, we get:

f = sqrt((3 - (-2))^2 + (5 - 5)^2)

= sqrt((5)^2 + (0)^2)

= sqrt(25)

= 5

Now that we have the value of f, we can substitute it into the standard form of the equation of a parabola to get:

y = (1/(4*5))x^2 + k

= (1/20)x^2 + k

This is the equation for a parabola with a focus at (-2, 5) and a directrix at x = 3. The constant k determines the position of the parabola along the y-axis.

Answer:  the area of the rectangle is 456 square millimeters.

Step-by-step explanation:

the perimeter is 88 mm, so if we let L be the length of the rectangle and W be the width, we can write the following equation to find the perimeter:

2L + 2W = 88 mm

Since the base of the rectangle is 38 mm, we know that the width of the rectangle is 38 mm, so we can substitute that value into the equation above to get:

2L + 2(38 mm) = 88 mm

Solving for L, we get:

2L = 88 mm - 2(38 mm)

2L = 88 mm - 76 mm

2L = 12 mm

Therefore, the length of the rectangle is 12 mm. Now that we know both the length and the width, we can find the area by multiplying the length and the width:

Area = L * W

Area = 12 mm * 38 mm

Area = 456 mm^2

Thus, the area of the rectangle is 456 square millimeters.

Answer:

A=228mm

Step-by-step explanation:

What formulas do we know?

Parameter= 2(length)+2(width)

Area= length x width

We can just substitute in values for parameters so,

88=2(length) + 2(38)

88=2L + 78 ------> 12=2L -------> L=6

Now we know width (which is just B) and Length (what we calculated)

Now we use area ----> Area= length x width

Area= (38)(6)-----> 228mm

The inequality or number of units produced per hour is 15.50<10+0.50x.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

According to the question the inequality can be

15.50<10+0.50x

15.50-10<0.50x

5.50<0.50x

5.50/0.50x

x> 11

For checking the Inequality

Let x=12.

15.50<10+.50*12

15.50+10+6

15.50<16

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the time it takes to preform a task has a continuous uniform distribution between 43 min and 57 min. 0.1875 is the the probability it takes between 54.7 and 56 min. round to 4 decimal places.

The probability of any event occurring is given by the formula P(x) = (x-a)/(b-a). In this case, the probability of the task taking between 54.7 and 56 minutes is (56-54.7)/(57-43) = 0.1875. This probability is equal to the area under the uniform distribution graph between 54.7 and 56 minutes. As the graph is a rectangle, the area is simply the width multiplied by the height, so 0.1875. Rounding to 4 decimal places, the probability is 0.1875.

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The Probability of getting less than 555 orders = x<555/ccc

Suppose we discuss about two events which can be occurred at any time but the occurrence of one event is not dependent on other event. In such case the probability of occurring each event is called independent probability.

The probability of two independent events is calculated by the formula

probability of one event × probability of another event

If A and B are two events occurred independently

    probability of happening two events = P(A)×P(B)

In our problem, order for cake over telephone is one event

         order for cake manually is another event

10 percent order get over telephone

So, percent of probability to get order from phone = 10/100 = 1/10

She got total ccc cake order in a month before getting order over phone

let. X is a number of orders she got before getting her first telephone order.

Therefore, the probability that it takes fewer than 555 orders for Lilyana to get her first telephone order = X<555/ccc

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Answer:

Use desmos to help with slopes and finished equations its a graphing calculator and its very helpful

Step-by-step explanation:

Answer:

y=3x-8

Step-by-step explanation:

slope, or m (3), is always next to an x. y-intercept (-8) goes always after the mx

Answer:

a) n less than or equal to 21

b) n greater than or equal to 5

c) n > 3/5

Step-by-step explanation:

i hope this helps!!

Answer:

A.) n ≤ 21

B.) n  ≥ 5

C.) n > 3/5

Step-by-step explanation:

For the first question it says that the number is no more than 21, so it could be equal to or less than 21

For the second question, it says that the number is at least 5, so it could be equal to or greater than 5

Finally, for the last question it says that the number is more than 3/5, so greater than would be the correct inequality symbol to use

The correction made by the student is incorrect simplification of 30ab√2a+20a√2a

The perimeter of a polygon is the sum of its, all the side lengths.

Given that, the dimension of a rectangle is given by, √50a³b² and √200a³

The perimeter of the rectangle is = 2(length + width)

Solving for the perimeter,

2(√50a³b²+√200a³)

= 2(5ab√2a+10a√2a)

= 10ab√2a+20a√2a

The student solved it as 30ab√2a,

Which is incorrect, because 'b' is not there in both the expressions, hence, we cannot add them.

Hence, The correction made by the student is incorrect simplification of 30ab√2a+20a√2a

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Answer:

Step-by-step explanation:

Answer is D on Edge,

The student incorrectly simplified 10ab sqrt 2a + 20a sqrt 2a

Answer:

Step-by-step explanation:

Formula for Circumference of a circle is 2* pi * radius

If r=16

C= 2*π*16

C=32π

Answer:

This is answer of 530.4 Q

Using proportions and constant of proportionality, the train always move the same distance and the cost is always the same

Proportion can defined as the comparison between two numbers or ratios. Using proportions, when two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The proportional relationship between two numbers can be represented as

y = kx

i)

In this question, let's determine if they have the same constant of proportionality.

y = kx

6 = k(2)

k = 3

12 = k(4)

k = 3

Since they have the same constant of proportionality, the train always go the same distance each minute.

ii)

The time travelled in 10 minutes

y = 3x

y = 3(10)

y = 30

The distance in 10 minutes is 30km

b)

Using constant of proportionality to determine if they have a proportional relationship;

y = kx

21 = k(3)

k = 7

42 = k(6)

k = 7

The equation is y = 7x and the constant of proportionality is 7.

The cost for each person is always the same

ii) From y = 7x

63 = 7x

x = 63 / 7

x = 9

The predicted number for a cost of $63 is 9

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Each type of coin marquis have is 18

The value of a dime is ten cents. The value of a quarter is 25 cents. Dimes are smaller than quarters. Fun fact: Copper and nickel, the metal used to create quarters and dimes, are the same. One dime is equal to ten cents. The value of a penny, often known as a one-cent coin, is one cent.

A dime coin is equivalent to 10 one-cent coins in value (pennies). The word "dime" derives from the Latin word "decimus," which means "one tenth." When they came up with the concept of money being split into ten parts in the 1500s, the French adopted the word "disme." The spelling was altered from "disme" to "dime" in America.

Here  d  =  number of dimes

Here  q  =  number of quarters and

Number equation:  d + q  =  26

Value equation:  0.10d + 0.25q  =  3.80

Here the value for the equation is multiplied by 100:  10d + 25q  = 380

the two equations:

d + q  +  26   --->   multipling by -10   --->    -10d - 10q  =  -260

10d + 25q  =  380                                --->   10d + 25q  = 380

Adding the columns:                                   15q  =  120

                                                                            q = 120/15

                                                                            q  =  8

                                                                             d + q  =  26

                                                                             d+8=26 ;        

                                                                             d=26-8    

                                                                              d  =  18

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Rabbit leaps two feet. Kangaroo leaps sixteen feet. sEight time as far as the rabbit, the kangaroo jumps.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

A bunny leaps two feet. The kangaroo leaps 16 feet. The kangaroo leaps eight times farther than the rabbit.

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This means that in order to make at least $790, the drama club must sell 47 number of student tickets. 47,48,49,50,51

The first equation is 5x + 7(73) = 790, where x is the number of student tickets. We can solve this equation to determine that x = 47. This means that in order to make at least $790, the drama club must sell 47 student tickets. Then, we can check the other possible values of x to see how many tickets they must sell. The other possible values are 48, 49, 50, and 51. Therefore, the answer is 47, 48, 49, 50, 51.

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The equation of line that would graph his salary over time will be;

⇒ y = 1/685x - 38.89

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

After 4 years, he makes $56,785; after 9 years, he makes $60,210.

Now,

Since, After 4 years, he makes $56,785; after 9 years, he makes $60,210.

Hence, The equation of line passes through the points (56,785, 4) and

(60,210, 9).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (9 - 4) / (60210 - 56785)

m = 5 / 3425

m = 1/685

Thus, The equation of line with slope 1/685 is,

⇒ y - 4 = 1/685 (x - 56,785)

⇒ y - 4 = 1/685x - 42.89

⇒ y = 1/685x - 42.89 + 4

⇒ y = 1/685x - 38.89

Therefore, The equation of line that would graph his salary over time will be;

⇒ y = 1/685x - 38.89

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The percentage represented is 72%, and the decimal is 0.72

First lets find the decimal, it will be equal to the quotient between the total number of shaded squares and the total number of squares.

There are 200 squares in total, and of these 200, there are 144 shaded ones, then the decimal is:

d = 144/200  = 0.72

To find the percentage, you only need to multiply the decimal by 100%, we will get:

p = 100%*0.72 = 72%

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Answer:

  A, C, E

Step-by-step explanation:

You want the values from the list that are included in the solution set of -6(1 + 2x) ≥ 6(2x - 1) + 2x.

Simplifying the inequality, we get ...

  -6 -12x ≥ 12x -6 +2x

  0 ≥ 26x . . . . . . . . . . . . . add 12x+6

  x ≤ 0 . . . . . . . . . . . . divide by 26

The solution set includes 0 (choice C) and all negative values (choices A and E).

Answer:

The dimensions of the right triangle are 9 meters by 7 meters.
or
The base of the triangle is 9 meters, and the height is 7 meters (since the height is 2 meters less than the base).

Step-by-step explanation:

To find the dimensions of the right triangle, we can use the formula for the area of a triangle, which is:

A = 1/2 * b * h

Where b is the base and h is the height of the triangle. In this case, we know that the area of the triangle is 40 square meters, and the height is 2 meters less than the base, so we can write the equation as:

40 = 1/2 * b * (b - 2)

To solve for b, we can rearrange the equation to get b by itself:

40 = 1/2 * b^2 - b

Then, we can move all the terms involving b to the left-hand side of the equation and all the constants to the right-hand side:

1/2 * b^2 - b - 40 = 0

Next, we can use the quadratic formula to solve for b:

b = (-(-1) +/- sqrt((-1)^2 - 4 * (1/2) * -40)) / (2 * (1/2))

Which simplifies to:

b = (1 +/- sqrt(1 + 80)) / 1

Since b must be a positive number, we take the positive solution:

b = (1 + sqrt(81)) / 1

Therefore, the base of the triangle is 9 meters, and the height is 7 meters (since the height is 2 meters less than the base). Thus, the dimensions of the right triangle are 9 meters by 7 meters.

Probability of Number of outcome is an even in likely situation is given as 512

Given that;

Number of time die roll = 1,000

Find:

Probability of Number of outcome is an even

Computation:

Probability of an even = 3 / 6

Probability of an even = 1 / 2

Probability of Number of outcome is an even = [Probability of an even]1000

Probability of Number of outcome is an even = [1/2]1000

Probability of Number of outcome is an even = 500

So most likely outcome is 512

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The area enclosed by the curve x = t2 − 3t, y = t and the y-axis is 9/2

In this question we have been given parametric equations x = t^2 − 3t, y = t

In this question we need to find the area enclosed by the curve x = t2 − 3t, y = t and the y-axis.

The curve has intersects with y-axis.

Consider x = 0

So, t^2 − 3t =  0

t(t - 3) = 0

t = 0   or  t = 3

Let f(t) =  t^2 − 3t and g(t) = t

Now we have to draw the graph,

Differentiate the curve f(t) with respect to t.

f'(t) = 2t - 3

Now, find the area under the curve using the above formula

A = ∫[a to b] g(t)f'(t) dt

so, A = ∫[0 to 3] t (2t - 3) dt

A = ∫[0 to 3] (2t^2 - 3t) dt

A = [2/3 t^3 - 3/2 t^2]_[t = 0, t = 3]

A = 2/3 3^3 - 3/2 3^2

A = 18 - (3^3)/2

A = 18 - 27/2

A = 9/2

Therefore,  the area of the curve is 9/2.

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Answer:

13 × 10 = 130 ( it's a rectangle)

5² π /2 ≈ 12.5 × 3.14 = 39.25 ( semicircle)

130 + 39.25 = 169.25 ≈ 170

Answer:8

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

y = - [tex]\frac{1}{2}[/tex] x - 7 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes

the slopes are not equal thus not parallel

• the product of the slopes of perpendicular lines is equal to - 1

2 × - [tex]\frac{1}{2}[/tex] = - 1

Thus the 2 lines are perpendicular to each other.

The explicit formula of the sequence is (b) a(n) = 8 - 2(n - 1)

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

a₁ = 8,

aₙ = aₙ₋₁ - 2

In the above sequence, we can see that the 2 is subtracted from the previous term to get the current term

This means that

first term, a = 8

common difference, d = -2

The nth term is then represented as

a(n) = a + (n - 1)d

Substitute the known values in the above equation, so, we have the following representation

a(n) = 8 + (n - 1) * -2

Evaluate

a(n) = 8 - 2(n - 1)

Hence, the explicit is (b) a(n) = 8 - 2(n - 1)

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For ∬∂WF⋅dS differentiable each of the following regions is 0, [tex]\frac{18 \sqrt{2}}{15}, -\frac{16 \sqrt{2}}{15}[/tex]

Let the f=[tex]\left(y^2+z^3, x^3+z^2, x z\right) \\[/tex],

Differentiability of Function: For a function to be differentiable at any point x=a in its domain, it must be continuous at that particular point but vice-versa is not always true. In complex analysis, complex-differentiability is defined using the same definition as single-variable real functions. This is allowed by the possibility of dividing complex numbers

Solution: For checking the continuity, we need to check the left hand and right-hand limits and the value of the function at a point x=a.

This means that f'(a) must exist, or equivalently:

[tex]$$\lim _{x \rightarrow a^{+}} f^{\prime}(x)=\lim _{x \rightarrow a^{-}} f^{\prime}(x)=\lim _{x \rightarrow a} f^{\prime}(x)=f^{\prime}(a)$$[/tex]

(A).

[tex]& x^{2 / t} y^2 \leq z \leq 2 \\\\& \int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}} \int_{z=\gamma^2}^2 \gamma \cos \theta d z d \gamma d \theta \\\\&=\int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}}[\gamma \cos \theta][z]_{\gamma^2}^2 d \gamma d \theta \\[/tex]

[tex]&=\int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}}\left(2-\gamma^2\right) \gamma \cos \theta d \gamma d \theta \\\\&=\int_{\theta=0}^{2 \pi}\left[\gamma^2-\frac{\gamma^4}{4}\right]_0^{\sqrt{2}} \cos \theta d \theta \\\\&=\int_{\theta=0}^{2 \pi} \cos \theta d \theta \\\\&=[\sin \theta]_0^{2 \pi} \\&=0[/tex]

(B).

[tex]& \ x^2+y^2 \leq 2 \leq 2 . \quad, x \geqslant 0 \\[/tex]

[tex]& \int_{0=-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_{\gamma=0}^{\sqrt{2}} \int_{z=\gamma^2}^2 \gamma^2 \cos \theta d z d \gamma d \theta . \\\\& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_0^{\sqrt{2}} \gamma^2 \cos \theta[z]^2 \gamma^2 \cdot d \gamma d \theta \text {. } \\[/tex]

[tex]& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_0^{\sqrt{2}} \cos \theta\left(2-\gamma^2\right) \gamma^2 d \gamma d \theta . \\\\& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos \theta\left[\frac{2}{3} \gamma^3-\frac{\gamma^5}{5}\right]_0^{\sqrt{2}} d \theta \text {. } \\[/tex]

[tex]& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos \theta\left[\frac{4}{3} \sqrt{2}-\frac{4 \sqrt{2}}{5}\right] d \theta . \\\\& =[\sin \theta]_{-\frac{\pi}{2}}^{\frac{\pi}{2}} d \theta\left[\frac{4}{4} \sqrt{2}-\frac{4 \sqrt{2}}{5}\right] \\\\& =\left[\frac{4 \sqrt{2}}{3}-\frac{4 \sqrt{2}}{5}\right] \\[/tex]

[tex]& =\left[\frac{4 \sqrt{2}}{3}-\frac{4 \sqrt{2}}{5}\right] \\\\& =\left[\frac{20 \sqrt{2}-12 \sqrt{2}}{15}\right]=2\left[\frac{8 \sqrt{2}}{15}\right] \\\\& =\frac{18 \sqrt{2}}{15}[/tex]

(C).

[tex]x^2+y^2 & \leqslant z \leqslant 2, x \leq 0 \\[/tex]

A+B+C

0=B+C

B=-C or C=-B

C=[tex]-\frac{16 \sqrt{2}}{15}[/tex]

Therefore, the differentiable of each function is 0, [tex]\frac{18 \sqrt{2}}{15}, -\frac{16 \sqrt{2}}{15}[/tex].

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Let F=[tex]\left(y^2+z^3, x^3+z^2, x z\right) \\[/tex]) . Evaluate ∬∂WF⋅dS for each of the following regions W:

A.[tex]& x^{2 / t} y^2 \leq z \leq 2 \\\\ \\[/tex]

B. [tex]& \ x^2+y^2 \leq 2 \leq 2 . \quad, x \geqslant 0 \\[/tex]

C. [tex]x^2+y^2 & \leqslant z \leqslant 2, x \leq 0 \\[/tex]

Answer:

The correct answer would be 5000 x ^108

Step-by-step