Solve for x -
[tex]\sf 6+4x+3=6x-21[/tex]

Answer: The decrease in price is $64, and the sale price is $192.

Step-by-step explanation:

0.25 * $256 = $64

$256 - $64 = $192

Answer:

[tex]x=\dfrac{-3+\sqrt{37}}{2}, \quad x=\dfrac{-3-\sqrt{37}}{2}[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]x^2+3x-7=0[/tex]

Step 1

When completing the square for a quadratic equation in the form [tex]ax^2+bx+c=0[/tex] the first step is to move the constant to the right side of the equation:

[tex]\implies x^2+3x-7+7=0+7[/tex]

[tex]\implies x^2+3x=7[/tex]

Step 2

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies x^2+3x+\left(\dfrac{3}{2}\right)^2=7+\left(\dfrac{3}{2}\right)^2[/tex]

Simplify:

[tex]\implies x^2+3x+\left(\dfrac{3^2}{2^2}\right)=7+\left(\dfrac{3^2}{2^2}\right)[/tex]

[tex]\implies x^2+3x+\dfrac{9}{4}=7+\dfrac{9}{4}[/tex]

[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{28}{4}+\dfrac{9}{4}[/tex]

[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{28+9}{4}[/tex]

[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{37}{4}[/tex]

Step 3

Factor the perfect square trinomial on the left side:

[tex]\implies \left(x+\dfrac{3}{2}\right)^2=\dfrac{37}{4}[/tex]

Step 4

Square root both sides:

[tex]\implies \sqrt{\left(x+\dfrac{3}{2}\right)^2}=\sqrt{\dfrac{37}{4}}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{37}}{\sqrt{4}}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{37}}{2}[/tex]

Step 5

Subtract ³/₂ from both sides:

[tex]\implies x+\dfrac{3}{2}-\dfrac{3}{2}=-\dfrac{3}{2}\pm\dfrac{\sqrt{37}}{2}[/tex]

[tex]\implies x=-\dfrac{3}{2}\pm\dfrac{\sqrt{37}}{2}[/tex]

[tex]\implies x=\dfrac{-3\pm\sqrt{37}}{2}[/tex]

Therefore, the solutions of the given quadratic equation are:

[tex]x=\dfrac{-3+\sqrt{37}}{2}, \quad x=\dfrac{-3-\sqrt{37}}{2}[/tex]

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Answer:

i d k

Step-by-step explanation:

The missing numbers in the third level can be 10, 6 and 18

On the first level of the number tower, we have

First level = 40

On the second level, we have

Second level = 16 and 24

The numbers on the third level of the number tower are missing.

However, these numbers must add up to the sum of 16, while the other must add up to 24

So, we can make use of

10, 6 and 18

This is because

10 + 6 + 6 + 18 = 40

Here, we have

2x + y = 14 and x + 2y = 16

Multiply 2x + y = 14 by 2

4x + 2y = 28

Subtract x + 2y = 16 from 4x + 2y = 28

4x - x + 2y - 2y = 28 - 16

Evaluate

3x = 12

Divide

x = 4

Also, we have 2x + y = 14

This gives

y = 14 - 2x

y = 14 - 2 x 4

y = 6

So, the values of x and y for 2x + y = 14 and x + 2y = 16 are 4 and 6, respectively

This has the same step as part (b)

In (b), we have

x = 4

Which gives

2x + y = 14

Make y the subject

y = 14 - 2x

Substitute 4 for x

y = 14 - 2 x 4

Evaluate

y = 6

Hence, the values of x and y for 2x + y = 14 and x + 2y = 16 are 4 and 6, respectively

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Answer:

a)Figure C

b) Figure A, B, and C

c)Figure B and C

Step-by-step explanation:

Note squares are rectangles

Answer:

1. acute angle (less than <90)

2. right angle (approximately <90)

3. obtuse angle (more than <90)

4. acute angle (less than <90)

According to the given function, which contains a square root, the domain must contain numbers that are greater than or equal to 5, otherwise, we would obtain the square root of a negative value, which is not real.

It means that the domain is

The range contains numbers greater than 0, this is because the minimum value of the domain is 5, when we evaluate the function at this value, the result is 0, which means that the range is:

The answer is the first option.

Answer: R(8,1)

Step-by-step explanation:

[tex]\displaystyle\\M(9,2)\ \ \ \ S(10,3)\ \ \ \ R(x,y)=?\\\\M_x=\frac{R_x+S_x}{2} \\\\\Rightarrow\ 9=\frac{x+10}{2\\\\}[/tex]

Multiply both parts of the equation by 2:

[tex]9(2)=x+10\\18=x+10\\18-10=x+10-10\\8=x[/tex]

[tex]\displaystyle\\M_y=\frac{R_y+S_y}{2} \\2=\frac{y+3}{2}[/tex]

Multiply both parts of the equation by 2:

[tex]2(2)=y+3\\4=y+3\\4-3=y+3-3\\1=y[/tex]

⇒   R(8,1)

The measure of ∡KJR is 69°.

What is the sum of two supplementary angles?
Two angles are referred to as supplementary angles if their combined value is 180°. A straight angle is created when supplementary angles are combined (180°).
In other words, ∡A and ∡B are supplementary if ∡A plus ∡B equals 180°. Angles A and B are described as "supplements" of one another in this context.
In math, A° + B° = 180°.

Given, m∡RJI = 12x - 3, m∡KJR = 6x - 5, m∡KJI = 172°
As seen from diagram, m∡RJI + m∡KJR = m∡KJI
⇒ (12x-3)+(6x-50) = 172° ⇒ 18x - 53 = 172° ⇒ x = ([172 + 53]/18)° = 12.5°
Therefore, the value of x = 12.5°
Thus, m∡KJR = 6x - 5 = (6*12.5) - 5 = 69°

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The ratio of the short leg to the hypotenuse in the right triangle is 1 : 2. the correct option is D. 1 : 2

From the question, we are to determine the ratio of the short leg to the hypotenuse in the given right triangle

Given an equilateral triangle with side lengths 2 units each and interior angle 60° each as shown in the diagram below. If the triangle is divided into 2 equal right triangles as shown in the given diagram, the length of the hypotenuse will be 2 units, the length of the short leg will be 1 unit, and the length of the long leg will be √3 units.

Thus,

The ratio of the short leg to the hypotenuse will be

1 unit / 2 units

= 1 : 2

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The equivalent expression for [tex](3.7)^{-5}*(3.7)^{9}[/tex] is [tex](3.7)^{4}[/tex].

This is a question of exponents and powers.

Exponents

The exponent of a number says how many times to use the number in a multiplication. In [tex]8^2[/tex] the "2" says to use 8 twice in a multiplication, so [tex]8^2[/tex] = 8 × 8 = 64.

Here, 2 is the exponent or power and 8 is the argument.

We can use exponents when we have to deal with very large numbers.

For example:-

The distance between the Earth and the Sun is measured to be 149,600,000 Km.

To write it in simple terms we will write,

[tex]1.496 * 10^8[/tex] km.

We know that:-

[tex]a^b*a^c=a^{b+c}[/tex]

Here,

a = 3.7,

b = -5 and,

c = 9

Hence, we can write,

[tex](3.7)^{-5}*(3.7)^{9}=(3.7)^{-5+9}=(3.7)^{4}[/tex].

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Answer: x = -9

Step-by-step explanation:1

Combine like terms

2 Add the numbers

3 Rearrange terms

4 Subtract 14 from both sides

5 Simplify

6 Add x to both sides

7 Simplify

8 Divide both sides by the same factor

9 Simplify

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Answer:

x= -9

Step-by-step explanation:

Simplify  3x+14 -6x to -3x +14

Simplify 25−x+7  to  32−x32−x.

Add 3x3x to both sides.

Simplify  32−x+3x32−x+3x  to  32+2x32+2x.

Divide both sides by 22.

Simplify  18/2 to  99.

x=−9 is your final answer

Using an exponential function, it is found that:

An exponential function is modeled according to the following rule:

[tex]y = ab^{\frac{x}{n}}[/tex]

In which:

Considering that the pool has 1500 gallons, and drains 3% every 5 minutes, the parameters of the function are given as follows:

a = 1500, b = 1 - 0.03 = 0.97, n = 5.

Hence the amount of water in the poll after x minutes is given by:

[tex]y = 1500(0.97)^{\frac{x}{5}}[/tex]

After 50 minutes, the amount of water in the pool is:

[tex]y = 1500(0.97)^{\frac{50}{5}} = 1500(0.97)^{10} = 1106[/tex]

1106 gallons.

The poll will have less than 1000 gallons when:

y = 1000 (we can use it because the function decreases continuously).

Hence:

[tex]1500(0.97)^{\frac{x}{5}} = 1000[/tex]

[tex](0.97)^{\frac{x}{5}} = \frac{1000}{1500}[/tex]

[tex](0.97)^{\frac{x}{5}} = \frac{2}{3}[/tex]

[tex]\log{(0.97)^{\frac{x}{5}}} = \log{\left(\frac{2}{3}\right)}[/tex]

[tex]\frac{x}{5}\log{0.97} = \log{\left(\frac{2}{3}\right)}[/tex]

[tex]x = 5\frac{\log{\left(\frac{2}{3}\right)}}{\log{(0.97)}}[/tex]

x = 66.6 minutes.

The capacity of the pool is missing, and it is of 1500 gallons.

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The multiplication of polynomials (3x² - 5x + 7) and (2x² - 5x + 7) is:

6x^4 - 25x³ + 60x² - 70x + 49

In this question, we have been given two polynomials 3x² - 5x + 7 and 2x² - 5x + 7

We need to multiply given polynomials.

(3x² - 5x + 7) × (2x² - 5x + 7)                          ............(Given polynomials)

= 3x²(2x² - 5x + 7) - 5x(2x² - 5x + 7) + 7(2x² - 5x + 7)      ..........(Distribute)

= 6x^4 - 15x³ + 21x² - 10x³ + 25x² - 35x + 14x² - 35x + 49     .....(Simplify)

= 6x^4 - 15x³ - 10x³ + 21x² + 25x² + 14x² - 35x -35x + 49

= 6x^4 - 25x³ + 60x² - 70x + 49

Therefore, the multiplication of polynomials (3x² - 5x + 7) and (2x² - 5x + 7) is 6x^4 - 25x³ + 60x² - 70x + 49

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Answer:

x = 12, y = 60

Step-by-step explanation:

We have parallel lines, so alternate interior angles are congruent.

6x + 3 = 75

6x = 72

x = 12

The interior angles of a triangle add up to 180 degrees.

45 + 75 + y = 180

120 + y = 180

y = 60

Answer: down here

Step-by-step explanation:

4−50

5−Y

6−150

​

Factor the expressions that are not already factored.

−46=−2×23

−144=−2

4

×3

2

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

3312(Y−5)

Expand the expression.

3312Y−16560

Answer: 3/2

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that Y'X'=3 and YX=2, so the scale factor is 3/2.

For the linear function y = 9 - 5x, it is found that:

A linear function, in slope-intercept format, is modeled according to the following rule below:

y = mx + b

In which:

In the context of this problem, the linear function is modeled as follows:

y = 9 - 5x.

In standard format, with the slope in front, we have that:

y = -5x + 9.

Meaning that the coefficients are given as follows:

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Answer:

Symmetric property of congruence

Answer:

No.

The square root of any number can never be negative/ -1

Solving for f

Adjacent angles of a parallelogram are supplementary, so (f+30)+72=180. It follows that f=78.

Solving for g

Opposite sides of a parallelogram are congruent, so 25=8g-3. It follows that g=3.5.

Option C correctly represents the function.

For the given question;

From the definition of the function, two values in the domain can not have the same image, thus option a and b are incorrect.

Only option c correctly described the function, as for every value of out put there is only one input.

Thus, option c correctly described the function.

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The length of the sides of equilateral triangles are as follows

5cm,  15m , 8cm , 300m , 12m , 90mm .  

The whole length of a shape's boundary is referred to in geometry as the perimeter of the shape. By multiplying the lengths of all the sides and edges that surround an object, the perimeter may be calculated. It is measured in measures of length that are linear, such as centimeters, meters, inches, or feet. A regular polygon's sides are all the same length, as far as we know.

Therefore,

A regular polygon's perimeter is equal to the product of all of its sides, which is equal to the number of sides divided by the length of a side.

The measurement of a shape's length along its outline is known as its perimeter. Simple addition of the lengths of the object's edges serves as the perimeter measurement method.

The perimeter of an equilateral triangle

= 3a      where a is each side

So,

(a) P = 15 cm

3a = 15

a = 5

each side = 5 cm

(b) 45 m

3a = 45

a = 15 m

each side = 15 m

(c) 24 m

3a = 24

a = 8 cm

each side =  8 cm

(d) 900 m

3a = 900

a = 300 m

each side = 300 m

(e) 36 cm

3a = 36

a = 12 cm

each side = 12 cm

(f) 270 mm

3a = 270

a = 90 mm

each side = 90 mm

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The domain and range of this function f(x) = 4(∛8)ˣ are: A. {x| x is a real number}; {y| y > 0}.

A function simply refers to a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable to an output variable.

In this scenario, the function f(x) = 4(∛8)ˣ represents an exponential function. Generally speaking, an exponential function is defined by the set of all real numbers on the x-axis.

Additionally, the value of four (4) is greater than zero (0) and as such the range defined by the set of all real numbers on the y-axis that are greater than zero (0).

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Answer:

A. {x| x is a real number}; {y| y > 0}

Step-by-step explanation:

on edge

Annual cost to operate farm B well with cost of natural gas $2.50 per 1,000 cubic feet and uses of 10000cubic feet of natural gas per year is $25.

As given,

Farm A:

Cost of natural gas per 1,000 cubic feet=$2.50

Farm B:

Uses of natural gas per year = 10000cubic feet

Cost of natural gas of farm B is same as farm A

Cost of natural gas per 1,000 cubic feet=$2.50

⇒1cubic feet=2.50/1000

Annual cost to operate 200ft well that uses 10000 cubic feet natural gas

10000 cubic feet=(2.50 ×10000)/1000

                             =$25

Therefore, annual cost to operate farm B well with cost of natural gas $2.50 per 1,000 cubic feet and uses of 10000cubic feet of natural gas per year is $25.

The complete question is:

Farm A has a 100 ft well that uses 7,000 cubic feet of natural gas per year. If the cost of natural gas for farm A is $2.50 per 1,000 cubic feet. And farm B has a 200 ft well that uses 10000 cubic feet of natural gas per year. if the cost of natural gas is the same a farm A, what is the annual cost to operate this well?

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120% is considered an enlargement since the scale factor is greater than one.

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

It is considered a reduction of the scale factor is less than one, and an enlargement if the scale factor is greater than one.

120% = 1.2 > 1, hence an enlargement.

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The Inverse Function Line Test

A given graph represents a function only if for every value of x there is only one corresponding value of y.

This can be checked by using a vertical line and moving it through the x-axis. If that line intersects the graph more than once, then the graph does not correspond to a function.

The image shows a graph and if we move our imaginary vertical line from x=-2 to x=7 that line would intersect the graph only once. This means that the graph corresponds to a function in the domain [-2,7].

For the inverse function to exist, the horizontal line test must be passed.

Imagine a horizontal line moving through the y-axis. It would intersect the graph only once from y=0 to y=6.

We can conclude this graph corresponds to a function and it has an inverse function because it passed the horizontal line test.

Answer: D.

Answer:

267 times 6

Step-by-step explanation:

Both methods are observational studies because both include students who do and do not play a musical instrument. So, this method describes an observational study.

Several various kinds of non-experimental studies in which behavior is routinely observed and documented are together referred to as observational research. A variable or combination of variables must be described in order to be the focus of observational research.

In a broader sense, the objective is to capture a moment in time of certain traits of a person, group, or environment. We cannot draw causal inferences from observational research since nothing is altered or controlled, as previously said, making it non-experimental. Although they may also be quantitative or both, the data that are gathered in observational research investigations are frequently qualitative in nature (mixed-methods).

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Answer:

IF ITS THIS QUESTION

An article in a psychology journal claims that young students who play a musical instrument tend to have higher test scores on state math exams. To assess the claim, a government official considers two methods to collect data.

Method 1: Contact many city schools and ask them to provide summary data on state math exam performance and students who participate in music lessons.

Method 2: Choose two city schools and provide free music lessons to students who register. At the end of the year, compare state math exam scores for students who participated in the music lessons with the scores for those who did not.

Step-by-step explanation:

THE AWNSER IS C

Method 2 is an observational study because students can choose to participate in the music lessons.

An observational study is a type of research in which researchers observe and record the behavior of a group of individuals, but do not manipulate or intervene in any way. In this case, Method 2 describes an observational study because the researchers are not manipulating the students' participation in music lessons. Instead, the students are free to choose whether or not to participate in the music lessons, and the researchers simply observe and record the state math exam scores for both groups of students. In contrast, Method 1 is not an observational study because it involves collecting summary data on state math exam performance and music lesson participation, rather than observing and recording the behavior of the students.

Answer:

Step-by-step explanation:

Find The Edge Of The Cube Whose Leteral Surface Area Is 36cm^2

LSA of cube = x^2 + x^2 + x^2 + x^2 = 4x^2

so

4x^2 = 36

x^2 = 9

x = 3

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

check

4 * 3^2 =

4 * 9 =

36

the answer is good

Answer: 3 cm

Step-by-step explanation: