Find two positive numbers such that their sum is 60 and their product is a maximum. Select one: O a. 30 and 30 O b. 25 and 35 O c. 1 and 59 O d. 20 and 40​

Using the mean concept, the expression that gives the average of the low and high temperatures is:

(-3 + 8)/2.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

In this problem, the two observations are -3 and 8, hence their average is given by:

(-3 + 8)/2.

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Pauline has 371 stickers. Karl, Serene, and Pauline have 1281 stickers altogether.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Let Karl, Serene and Pauline have x, y, and z stickers.

Given condition;

Karl, Serene, and Pauline have 1281 stickers altogether;

x+y+z = 1281

Pauline had 3 times as many stickers as Serene.

z = 3 y

y=z/3

Karl had 175 stickers fewer than Pauline.

x=z -175

Substitute all the values in the terms of z;

x+y+z = 1281

z -175 + z/3 + z = 1281

8z/3 = 1281 +175

z=546

Pauline have;

x = z -175

x =546 -175

x = 371

Hence Pauline has 371 stickers.

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Answer:

16 and 34

Step-by-step explanation:

The general form = 3n+4

The 4th term = 3(4)+4 = 12+4 = 16

The 10th term = 3(10)+4= 30+4= 34

Answer:

20x + 8

Step-by-step explanation:

5*4x + 5*5 -17

20x +25 -17

20x + 8

Answer:

[tex]80\times3[/tex]

Step-by-step explanation:

Based on the given conditions, formulate:  [tex]80\times3[/tex]

Calculate the product or quotient: 240

get the result: 240

Answer: 240

To find this answer, we had to use the expression 80 * 3, therefore making it the answer.

Answer:

240

Step-by-step explanation:

80*3=240

so u multiply the equation

Answer:

(0, a)

Step-by-step explanation:

We can start by imagining this rectangle as a square.

(This is written as if it is a square:)

The distance that a square reaches on the x-axis (assuming it has its lower left point at the origin, like this one does) is the same distance that it reaches on the y-axis.

meaning that we will have (length, 0) along the x-axis and (0, length) along the y-axis

so, if we are to treat this as a square, the point (2a, 0) means that our opposite vertex is (0, 2a)

However, because this length is only half of the length that it would be (if it were a square), we must divide our length by 2

2a ÷ 2 = a

So, the coordinates of the top-left vertex of this rectangle:

(0, a)

Answer:

coordinates of top left vertex: (0, a)

Answer:

y = -5

Step-by-step explanation:

Isolate y:

-3x + 9y = -57

9y = -57 + 3x

y = (-57/9) + (3/9)x

Substitute for x:

y = (-57/9) + (3/9)(4)

y = (-57/9) + (12/9)

y = (-45/9)

y = -5

Answer:

[tex]\mathsf {y = -5}[/tex]

Step-by-step explanation:

[tex]\textsf {Given :}\\\textsf {-3x + 9y = -57}[/tex]

[tex]\textsf {Divide throughout by 3 :}[/tex]

[tex]\mathsf {\frac{1}{3} \times (-3x + 9y) = \frac{1}{3} \times -57}[/tex]

[tex]\mathsf {-x + 3y = -19}[/tex]

[tex]\textsf {Substitute x = 4 :}[/tex]

[tex]\mathsf {-(4) + 3y = -19}[/tex]

[tex]\mathsf {3y = -15}[/tex]

[tex]\textsf {Divide by 3 on both sides :}[/tex]

[tex]\mathsf {\frac{3y}{3} = \frac{-15}{3} }[/tex]

[tex]\mathsf {y = -5}[/tex]

Answer:

Step-by-step explanation:

Cost of 6 kg of rice is 540 what is the cost of 13 kg of rice. ​

we can solve with an equation

6 : 540 = 13 : x

x = 540 * 13 : 6

x = 7020 : 6

x = 1170

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

check

6 : 540 = 13 : 1170

0.01111111111 = 0.01111111111

the answer is good

If the radius of tree stump is 11 inches and volume is 13685 cubic inches then the height will be equal to 36 inches.

Given Radius of tree stump is 11 inches and volume is 13685 cubic inches.

We know that the volume of cylinder will be equal to π[tex]r^{2} h[/tex].

Volume which is given as 13685 cubic inches.

13685=π[tex]r^{2}h[/tex]

π=22/7

13685=π[tex](11)^{2}[/tex]h

h=13685*7/22*121

h=95795/2662

h=35.98

if we round it to nearest tenth then the value of h be 36 inches.

Hence if radius is 11 inches, volume is 13685 cubic inches then the height of tree stump will be 36 inches.

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Answer:36

Step-by-step explanation:

The attached graph represents the graph of the parallel lines

The equation of the lines are linear equation

A linear equation is represented as:

y = mx + b

Where b represents the y-intercept.

Using the above form of linear equation as a guide, the equations of the lines are

y = -x + 5

y = -x + 2

y = -x - 3

y = -x - 2

Where -5, 2, -3 and -2 are the given y-intercepts and y = -x is the base equation.

Next, we plot the equations on a coordinate grid

See attachment

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The normal distribution is also known as the Gaussian distribution. The correct option is B, while the approx z-score is 0.31.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Since the normal distribution is symmetrical about the mean. Therefore, the correct option is B, while the approx z-score is 0.31.

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Step-by-step explanation:

2and5 is 7

1and 5 is 6

4and 6 is 10

2and 6is 8

Answer:

m∠GLI = 2m∠GLH

Step-by-step explanation:

Angle GLI (red) is made of angles GLH (purple) and HLI (green).

m∠GLI = m∠GLH + m∠HLI

First option: ∠GLH ≅ ∠ILM (Angle GLH is congruent to angle ILM.)

This doesn't tell us anything about the relationship between angles GLI, GLH and HLI. So it can't be used.

Second option: m∠KLM = 5m∠ILM (Measure of angle KLM is 5 times the measure of angle ILM.)

This also cannot be used, because it doesn't include angles GLI, GLH or HLI.

Third option: m∠GLI = 2m∠GLH (Measure of angle GLI is two times the measure of angle GLH.)

Now this option is more interesting. It includes two angles of three that we are interested in.

If angle GLI is two times angle GLH, then that means that angle GLH is congruent to angle HLI!

Let's prove this with equations.

1) m∠GLI = m∠GLH + m∠HLI (from picture)

2) m∠GLI = 2m∠GLH (from third option)

Substitute m∠GLI in first equation with m∠GLI in second.

m∠GLI = m∠GLH + m∠HLI

2m∠GLH = m∠GLH + m∠HLI

m∠GLH = m∠HLI

So this proves that the angles GLH and HLI have the same measure, therefore ray LH is bisector of GLI.

Fourth option: m∠GLI = 1/2m∠GLH + 1/2m∠HLI​

There are all angles we are interested in, but there is a mistake. We can see in the picture that angle GLI is made of angle GLH and HLI and not of half of them. This just is not true. The correct equation would be m∠GLI = m∠GLH + m∠HLI.

Answer:

(2+6)/2= 4 (x-coordinate of midpoint)

(7+3)/2= 5(y=coordinate of midpoint)

Answer:

Hope it will help you:)

Step-by-step explanation:

Solution:

here,

A(2,7)-([tex]x_{1,}y_{1[/tex])

B(6,3)-([tex]x_{2},y_{2[/tex])

Now using midpoint formula,

midpoint of ab=(x1 + x2)/2, (y1 + y2)/2

                        =(2+6)/2,(7+3)/2

                         =(8/2,10/2)

                          =(4,5)

The midpoint of AB is(4,5).

Answer:

[tex]\fbox {5 times}[/tex]

Step-by-step explanation:

Days where both will be done :

⇒ 2nd day × 3rd day

⇒ 6th day

Number of times in September :

⇒ The month has 30 days

⇒ Number of times = 30/6

⇒ Number of times = 5

Answer:

5 times

Step-by-step explanation:

• Calculate the lowest common multiple (LCM) of 2 and 3 to find the first day of the month in which she will do both:

LCM (2 and 3) = 2 x 3

                       = 6

This means, she will do both every 6th day.

• There are 30 days in September. To find how many days she will do both in September, we have to calculate how many 6-day blocks there are in 30 days:

⇒ 30 ÷ 6

= 5 times

The value is 3 which represents the vertical translation from the graph of the parent function f(x)=x² option third 3 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = x²

The above function is a parent function.

The translation: vertical translation from the graph of the parent function.

F(x) → f(x) + 3

F(x) = x² + 3

The above function will shift vertical up by 3 units.

Thus, the value is 3 which represents the vertical translation from the graph of the parent function f(x)=x² option third 3 is correct.

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Answer:

Step-by-step explanation:

Solution

17 = a + b

b =  a + 1                    Substitute b into the top equation

17 = a + a+1                Combine

17 = 2a + 1                  Subtract 1 from both sides

17-1 = 2a+1-1               Combine

16 = 2a                       Divide both sides by 2

16/2 = 2a/2

a = 8

b = 8 + 1 = 9

Answer

a = 8

b = 9

The incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b = c\\log_ac =b[/tex]

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

2ln(x) = In(3x) - [In(9) - 2ln(3)]

In(x²) = In(3x) - [In(9) - In(9)]

ln(x²) = ln(3x) - 0

ln(x²) = ln(3x/0)   (incorrect step)

ln(x²) = ln(3x)

x² = 3x  (correct step)

x² - 3x =0

x(x - 3) = 0

x = 0, 3

Thus, the incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3

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Based on the required width and height of the tent, the length of the cloth would have to be 14.4 ft.

The opening of the tent would be an isosceles triangle but if it is divided in two from the top, a right-angled triangle will be formed and the hypotenuse will be the length of the cloth on one side.

That length - according to the Pythagoras theorem - would be:

= √(6² + (8 /2)²)

= √(36 + 16)

= 7.2 ft

As this is the length of one side of the cloth, the length of the entire cloth is:

= 7.2 x 2

= 14.4 ft

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The equation -2(5x+8) = 14+6x solved using step by step representation is x = -15/8.

The equation to be considered as given in the task content is; -2(5x+8)=14+6x.

It follows from the task content that the steps for solving the equation are as follows;

-2(5x+8) = 14+6x

-10x - 16 = 14 + 6x

-10x - 6x = 14 + 16

-16x = 30

x = 30/-16

x = -15/8

Hence, the value of x upon solving the equation is; -15/8.

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The answer choice which represents a relative frequency bar graph is; A bar graph titled social media preferences has platform on the x-axis. Upstart, 0.10; Aster, 0.25; Babble, 0.30; Techy, 0.35.

The statistical definition of relative frequency is simply the ratio of the frequency of an event in a statistical experiment with respect to the total frequency. Hence, since the frequencies in the social media bar chart as decimals (fractions of a whole), it follows that it is a relative frequency representation.

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Answer  Its B

Step-by-step explanation:Edge 2022 I guess

Answer:

3

Step-by-step explanation:

Slope of a line between any two points (x1,y1) and (x2,y2) is given by the equation:
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

let's take (x1,y1) as (4,4) and (x2,y2) as (5,7)

So slope = [tex]\frac{7-4}{5-4}[/tex] = 3

Answer:

y = 3x - 8

Step-by-step explanation:

y = Mx + c

m = 3 / 1

4 = 3(4) + c

4 - 12 = c

If we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.

The foreign exchange market works according to the principles of firms, households, and investors:

Therefore, if we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.

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By applying algebraic handling on the two equations, we find the following three solution pairs: x₁ ≈ 5.693 ,y₁ ≈ 10.693; x₂ ≈ 1.430, y₂ ≈ 6.430; x₃ ≈ - 0.737, y₃ ≈ 4.263.

In this question we have a system formed by a linear equation and a non-linear equation, both with no trascendent elements and whose solution can be found easily by algebraic handling:

x - y = 5      (1)

x² · y = 5 · x + 6       (2)

By (1):

y = x + 5

By substituting on (2):

x² · (x + 5) = 5 · x + 6

x³ + 5 · x² - 5 · x - 6 = 0

(x + 5.693) · (x - 1.430) · (x + 0.737) = 0

There are three solutions: x₁ ≈ 5.693, x₂ ≈ 1.430, x₃ ≈ - 0.737

And the y-values are found by evaluating on (1):

y = x + 5

x₁ ≈ 5.693

y₁ ≈ 10.693

x₂ ≈ 1.430

y₂ ≈ 6.430

x₃ ≈ - 0.737

y₃ ≈ 4.263

By applying algebraic handling on the two equations, we find the following three solution pairs: x₁ ≈ 5.693 ,y₁ ≈ 10.693; x₂ ≈ 1.430, y₂ ≈ 6.430; x₃ ≈ - 0.737, y₃ ≈ 4.263.

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The value(s) for which the rational expression −5u+12−2u+2 is undefined is u = 1.

The expression or an equation which can be undefined at some point is a celled the radial expression.

f(u) = -5u +12 / -2u +2

For the function to be undefined, denominator must be equal to zero.

-2u +2 =0

-2u =-2

u = 1

Thus, the value for which the given expression is undefined is 1.

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Answer:

9a + 18

Step-by-step explanation:

so the first step is to evaluate the value of f(2).

[tex]f(2) = 9(2)^2-7\\f(2)=9(4)-7\\f(2)=36-7\\f(2)=29[/tex]

Now that we have this value we can use the slope formula (y2 - y1) / (x2 - x1) where y2 is f(a), y1 is 29, x2 is a, and x1 is 2

[tex]\frac{f(a)-29}{a-2}\\\\\frac{(9a^2-7)-29}{a-2}\\\frac{9a^2-36}{a-2}[/tex]

Now from here we can use long division to simplify it further

[tex]9a^2/a = 9a\\9a(a-2)=9a^2-18a\\(9a^2-36)-(9a^2-18a)\\18a-36\\\\18a/a=18\\18(a-2)=18a-36\\(18a-36)-(18a-36)\\0\\\\9a+18[/tex]

Answer:

x-intercept: (1,0)

y-intercept: (0,1)

Step-by-step explanation:

Given: Find the x and y intercepts of 2x + 2y = 2

To solve for a x - intercept we have to substitue 0 in for y and solve for [tex]x[/tex]

Lets do it:

2x + 2(0) = 2

2x + 0 = 2

2x = 2

x = 1

Therefore, this means that when y = 0, x = 1 or (1,0)

To solve for a y - intercept we have to substitue 0 in for x and solve for [tex]y[/tex]

Lets do it:

2(0) + 2y = 2

0 + 2y = 2

2y = 2

y = 1

Therefore, this means that when x = 0, y = 1 or (0,1)

Answer:

27

Step-by-step explanation:

Answer:

19.51 units = x

Step-by-step explanation:

Here is one way :

Height = 18 cos 47 = 12.276

then     cos 51 = 12.276 /  x

                 x = 12.276 / cos 51 = 19.51