Solve. √2 x+3 -7=0

Given that Point T is on line segment SU, T is collinear with S and U, and the numerical length of SU is 24.

Since Point T is on line segment SU, then S, T, and U are collinear.

Collinear points refers to the points that lies on the same straight line.

IF S, T, and U are collinear, then the sum of the numerical length of ST and the numerical length of TU is equal to the numerical length of SU.

ST + TU = SU

Given:

ST = 3x + 2

TU = 3x + 4

SU = 5x + 9

Substitute the expressions in the equation and solve for x.

ST + TU = SU

3x + 2 + 3x + 4 = 5x + 9

3x + 3x - 5x = 9 - 2 - 4

x = 3

Substitute the value of x in the expression for SU.

SU = 5x + 9

SU = 5(3) + 9

SU = 24

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For the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).

We are given the system of equations as:

4 x+2 y = 4    … (1)

6 x+2 y = 8    … (2)

We need to solve it to find the value of x and y.

Subtracting equation (1) form equation (2), we get that:

6 x - 4 x + 2 y - 2 y = 8 - 4

Combining the like terms, we get that:

2 x = 4

x = 4 / 2

x = 2

Now put it in equation (1) to get the value of y

4 (2) + 2 y = 4

8 + 2 y = 4

2 y = - 4

y = - 2

(x, y) = (2, - 2)

Therefore, we get that, for the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).

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The answer would be 0.0078

The decimal number 0.00784 rounded off to 2 decimal places is 0.

We round off numbers to make them easier to remember and it also keeps its value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, 0.00784 and we have to round off to two significant figures means

the number will have 2 digits after the decimal place.

Now, 0.00784

= 0.00780.

= 0.0078.

= 0.0080.

= 0.008.

= 0.010.

= 0.01.

= 0.00.

= 0.

So, 0.00784 rounded off to 2 decimal places is 0.

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Answer:

Heya, your answer would be 52 horses, and 42 chickens.

Step-by-step explanation:

By doing the long, long and I mean long process of adding 2 + 2 or 4 + 4 (due to the fact chickens have 2 legs and horses have 4), we get to 52 horse legs, and 62 chicken legs.

Adieu

Answer:

There are 9 horses and 29 chickens.

Step-by-step explanation:

a = animals

a = 38

h = horses

c = chickens

l = legs

l = 94

Equation 1: h + c = 38

Horses have 4 legs. Chickens have 2 legs.

Equation 2: 4h + 2c = 94

Manipulate the equations so that one of the coefficients are the same.

We will multiple Equation 1 by 2 so that both equations have 2c.

Equation 1: 2h + 2c = 76

Equation 2: 4h + 2c = 94

Subtract Equation 1 from Equation 2.

Equation 2 - Equation 1

(4h + 2c) - (2h + 2c) = 94 - 76

(4h - 2h) + (2c - 2c) = 94 - 76

2h = 18

h = 9

Substitute h into either equation to solve for c.

Equation 1: 2h + 2c = 76

Equation 1: 2(9) + 2c = 76

Equation 1: 18 + 2c = 76

Equation 1: 2c = 76 - 18

Equation 1: 2c = 76 - 18

Equation 1: 2c = 58

Equation 1: c = 29

Equation 2: 4h + 2c = 94

Equation 2: 4(9) + 2c = 94

Equation 2: 36 + 2c = 94

Equation 2: 2c = 94 - 36

Equation 2: 2c = 58

Equation 2: c = 29

There are 9 horses and 29 chickens.

Answer:

Rate of change in y is -6

-3-6 = -9

-9-6=-15

-15-6=-21

Rate of change in x is 1

1+1=2

2+1= 3

3+1 = 4

4-1=5

........And so on

Answer:

The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.

Step-by-step explanation:

Given function:

[tex]\text{g}(x) = -2|x+3|[/tex]

Parent function:

[tex]\text{f}(x) = |x|[/tex]

A parent function is the simplest form of a family of functions.

The graph of g(x) is related to the graph of f(x) by a series of transformations.  To determine the series of transformations, work out the steps of how to go from f(x) to g(x).

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]

Step 1

Translation left by 3 units:

[tex]\implies f(x+3) =|x+3|[/tex]

Step 2

Stretch in the direction of the y-axis (vertically) with scale factor 2:

[tex]\implies 2f(x+3) =2|x+3|[/tex]

Step 3

Reflection in the x-axis:

[tex]\implies -2f(x+3) =-2|x+3|[/tex]

Conclusion

The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.

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Given the values that we have here for the large sizes and the family size of cereal the one that has the lowest price per ounce is that of the Large size at $0.21 per ounce

For the family size

We would first have to divide 5.34 by 24

= 5.34 / 24

= 0.22 per dollar

For the large size we have

15 ounces for $3.14

= 3.14 / 15

= 0.21 dollars

Hence we can see that the size of the cereal that is the lowest price per ounce is given as Large size at $0.21 per ounce

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The total revenue the previous year is $20,000

This year the total revenue of the small  business is $14,200

This amount is 29% less than the total revenue in the previous year

Therefore the total revenue in the previous year can be calculated as follows

100 - 29

= 71

= 71/100

= 0.71

Total revenue= 14,200/0.71

= 20,000

Hence the total revenue the previous year is $20,000

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Answer: he was faster the second time

Step-by-step explanation:

1/15 is a smaller fraction and 1/12, 1/15 of an hour is 4 minutes and 1/12 of an hour is 5 minutes, so he took it in 4 minutes the second time which was quicker

Answer: - 2x³ - 5x² - 4x, trinomial

Step-by-step explanation:

    When writing a polynomial, the standard form is to have the terms ordered from highest power to lowest power. 3 > 2, so we will reorder them as so;

- 5x² - 2x³ - 4x ➜  - 2x³ - 5x² - 4x

    To identify the polynomial, we will look at the number of terms. This polynomial has three terms, so it is a trinomial.

- 2x³ - 5x² - 4x

[1] - 2x³

[2] - 5x²

[3] - 4x

Answer:15 spoonfuls

Step-by-step explanation:

Answer: x=0

Step by step explanation:

1/3 (9x+3) =3x+1

=3x+1=3x+1

=3x-3x=1-1

=0x=0

So x=0

I hope this helps you! Have a nice day!!!!

Answer: Using a property of operations, what can you say about the sum of two expressions, Then the temperature changed more on Day 2.

Step-by-step explanation:

Using a property of operations, what can you say about the sum of the two expressions.

Let us assume the table of values is : Sunrise (F) = -11.31 -7.69

                                                              Sunset (F) = 13.49 25.25

           Day 1 and Day 2

Sunrise Temperature (F) = -11.31 -7.69         (eq-1)

Sunset Temperature (F) = 13.49 25.25        (eq-2)

The sum of the two equations are:

Sunrise Temperature (F) = -11.31 -7.69

                                    (F) = -19

Sunset Temperature (F) = 13.49+  25.25

                                   (F) = 38.74

Which day saw the greatest variation in temperature? Describe your thinking. To do this, we only compute the absolute difference in daily temperatures between the times of sunrise and sunset.

So, we can write

Day 1 = |-11.31 - 13.49|

Day 1 = 24.8

Day 2 = |-7.69 - 25.25|

Day 2 = 32.94

 So,      32.94 is greater than 24.8

 Therefore,     Day 2 is greater than the Day 1

Hence, the temperature changed more on Day 2.

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Step-by-step explanation:

500.000 evvie was on the digit card

Answer:

73° & 107°

Step-by-step explanation:

1. Those angles are supplementary, so they add up to 180 degrees.

2. (8x - 20) + (8x + 8) = 180

3. You need to add both 8x's together to make 16x. Do the same with -20 & 8. That makes -18. This is binomial addition.

4. 16x - 18 = 180

5. Add 18 to both sides

6. 16x = 198

7. Divide both sides by 16

8. x = 12.375

9. Plug in your x for both angles.

Interest accrued at the end of the month is $1.41.

Credit cards impose interest on any sums that you don't pay by the due date each month. Interest accrues everyday when you hold a balance from month to month based on the so-called Daily Periodic Rate (DPR). DPR is only another term for your daily interest charge.

Step 1: Make the initial payment of $882 ($1,032 - $150).

Step 2: $882 times 1.00938 is $890.27

Step 3: Pay $1,032 multiplied by 1.00938 ($1,041.68) at the conclusion.

Step 4. $1,041.68 - $150= $891.68

The interest for the first month is $1.41.

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The fourth point of the parallelogram is (10, -3).

What is Parallelogram?

A Parallelogram is a quadrilateral with opposite sides parallel.

Given that;

Three points of a parallelogram are (4,3), (-4,3) and (2,-3).

Now, Take Two points at one diagonal of parallelogram are (4, 3) and

(2, -3).

Let fourth point of a parallelogram is (x, y).

Take (-4,3) and (x, y) on the another diagonal of a parallelogram.

Since, Midpoint of both diagonal is same.

Hence, Midpoint of (4, 3) and (2, -3) is calculated as;

(4+2/2, 3+(-3)/2) = (6/2, 0/2) = (3, 0)

So, Midpoint of (4, 3) and (2, -3) = (3, 0)

And, Midpoint of (-4,3) and (x, y)  = (-4+x/2, 3+y/2)

Since,  Midpoint of both diagonal is same.

Hence, (-4+x/2, 3+y/2) = (3, 0)

Equating coordinates we get;

⇒-4+x/2 = 3

⇒ -4 + x = 6

⇒ x = 6 + 4

⇒ x = 10

And, 3+y/2 = 0

    ⇒3 + y = 0

    ⇒y = -3

So, The fourth point of the parallelogram is (10, -3).

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The correct expansion of log₄√t/s is 1/2 log₄(t/s).

Logarithms is another way of writing exponents. Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only. Understanding logs is not so difficult. To understand logarithms, it is sufficient to know that a logarithmic equation is just another way of writing an exponential equation.

Logarithm and exponent are inverse forms of each other. One can understand this from the section below. Initially, a mathematician named John Napier introduced logarithms for making calculations in a simple way and this concept is quickly adopted by other scientists, engineers, etc.

Given that, log₄√t/s and we have to expand this logarithmic function having base 4 accordingly. So, let's proceed to solve this logarithmic expansion.

log₄√t/s = log₄((t/s)^(1/2))

= log₄((t/s)^(1/2))

Apply log rule, logₐ(xᵇ) = b.logₐ(x), assuming x ≥ 0

= 1/2 log₄(t/s)

Hence, log₄√t/s = 1/2 log₄(t/s) is the correct expansion.

Therefore, 1/2 log₄(t/s) is the required answer.

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Answer: Distance point is 8.

Step-by-step explanation:

You would do 2 by the power of 2 and double that (8)

The coordinate of point C from the given expression is (2, 4)

The formula for calculating the midpoint of coordinates is given by the equation shown below:

Midpoint = {(x₁+x₂)/2, (y₁+y₂)/2}

Given the following parameters

Midpoint = M(5, 2)

B(8, 0)

Required

Coordinate point C

Substitute the given parameters

5 = (8+x₂)/2

5(2) = 8+x₂

10 = 8+x₂

x₂ = 2

Similarly

2 = (0+y₂)/2

2(2) = 0+x₂

4 = 0 +y₂

y₂ = 4

Hence the coordinate of point C from the given expression is (2, 4)

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The required value of x using the properties of exponents and logarithm is 6.362.

What are the various properties of the logarithm?

Out of several properties of logarithms, some of the main properties are given below:

Product Rule

log (ab) = log a + log b

Change of base

log ₇ x = log x / log 7

Power Rule

log a² = 2 log a

Quotient Rule

log (a / b) = log a - log b

Solving the given equation for x

We are given a logarithmic expression: log (1 + 3x) = 3

On applying exponent both sides, we get,

e^[log (1 + 3x)] = e^3

Using the properties of exponents and logarithm, we get,

1 + 3x = 20.0855

3x = 19.0855

x = 6.362

Hence, the required value of x can be 6.362.

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Answer: Graph A represents the given inequality 3y−5x>−6. Option A is correct.

From the graphs, the graph is to choose which best describes the inequality 3y−5x>−6

Step-by-step explanation: hope this helps

Graph A represents the inequality 3y - 5x≤-6. Correct option is A. The inequality 3y - 5x ≤ -6 represents a linear inequality in two variables, y and x.

To graph this inequality, we can rearrange it into slope-intercept form (y = mx + b), where m is the slope, and b is the y-intercept.

Let's rearrange the given inequality:

3y - 5x ≤ -6

First, add 5x to both sides of the inequality:

3y ≤ 5x - 6

Now, divide both sides by 3 to isolate y:

y ≤ (5/3)x - 2

Now, you have the inequality in slope-intercept form:

y ≤ (5/3)x - 2

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The dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches

We are told that the dimensions of the rectangular plot of land is 120yd x 53yd.

Now, you want to draw this rectangular plot on a scale of 1 inch : 5 yards. This means that 1 inch will represent 5 yards.

Thus, for the side of 120 yards, using the scale gives us;

1/5 * 120 = 24 inches

For the side of 53 yards, using the scale gives us;

1/5 * 53 = 10.6 inches

Thus, the dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches

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[tex]21x + 4y = 300[/tex]

We have infinitely many numbers that make this equation hold. For example:

[tex](x,y)=(69,-287.25) \\ (x,y)=(1,69.75) \\ (x,y)=(7,38.25)[/tex]

This could go on forever, so your question does not have a right answer.

Answer: 5.94

Step-by-step explanation: In order to find the mean, you first add up all the values in the data set and then divide this number by the number of values!

Hope it helps ^^

Answer:

Step-by-step explanation:

Can somebody simplify this?

(−8) × (-6) − (−5)² =

48 - 25 =

23

Rollercoaster Car is at 4 m above the ground by using integer concept.

As per the question statement, Rollercoaster Car that goes above and below the ground.

Before solving the question, we need to know the concept of integer operations on a number line.

Here the car is [tex]1 meter[/tex] above the ground level and then goes 4 meter down.

So the position is [tex]1-4=-3 meter[/tex] or 3 meter below the ground level.

Now it rises 13 meter above the ground. So now the position is [tex]-3+13 = 10 meter[/tex] or 10 meter above the ground.

Now it again falls by 6 meter so position is [tex]10-6 = +4 meters[/tex] or 4 meters above the ground.

Therefore the final position is 4 meters above the ground level.

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0 is a counterexample to Kelvin's conjecture.

Firstly rewriting the expression -

x²>x + 1

Now, we will use hit and trial method to find the counterexample to Kelvin's conjecture.

We can not use first two options, because question mentions that x is not negative. So, starting our hit and trial method from 0.

We will keep the value in expression to find the result -

0²>0 + 1

0 > 1

This contradicts or opposes Kevin's statement, as 0 is not greater than 1.

Trying the second number -

5²>5 + 1

25 > 6

This is in accordance with Kevin's conjecture or conclusion, as 25 is greater than 6.

Hence, 0 is the value which is a counterexample to Kelvin's conjecture.

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The complete question is -

Given that x is a number that is not negative, Kelvin conjectured that x^2>x+1 .

Which value is a counterexample to Kelvin's conjecture?

−12

−2

0

5