solve the algebraic equation 7 x - 2 equals to 2x + 13​

The excluded values are x = 4 and x - 1

The complete question is added as an attachment

The function is given as:

(2x^2 - 7x - 4)/(x^2 - 5x + 4)

Set the denominator to 0

x^2 - 5x + 4 = 0

Expand

x^2 - x - 4x + 4 = 0

Factorize the equation

x(x -1) - 4(x - 1) = 0

This gives

(x - 4)(x - 1) = 0

Solve for x

x = 4 and x - 1

Hence, the excluded values are x = 4 and x - 1

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Answer: Its D 1 and 4

Step-by-step explanation:

I took the assignment

The value of 8,590 − 4,586 is half the value of 2 x (8,590 − 4,586).

An equation is an expression that shows the relationship between two or more numbers and variables. The basic operations performed on an equation are addition, subtraction, multiplication and division.

The value of 8,590 − 4,586 = 4004

Half the value of 2 x (8,590 − 4,586) = (1/2) of 2 x (8,590 − 4,586) = 4004

The value of 8,590 − 4,586 is half the value of 2 x (8,590 − 4,586).

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Step-by-step explanation:

if I understand you correctly, then the 3 sides are

a = 20 m

b = 34 m

c = 42 m

under this assumption the best is to use Heron's Formula to get the area :

s = (a + b + c)/2

area = sqrt(s(s - a)(s - b)(s - c))

in our case

s = (20 + 34 + 42)/2 = 96/2 = 48

area = sqrt(48(48-20)(48-34)(48-42)) =

= sqrt(48×28×14×6) = sqrt(112,896) =

= 336 m²

Answer:

sorry i didnt know this D: <3

Step-by-step explanation:

By analyzing the end behavior of the graphed function, we conclude that the graphed function is an exponential one.

On the graph, we can see that as the independent variable (the one in the horizontal axis) tends to large negative values, the dependent variable (the one in the vertical axis) tends to zero.

And, as the independent variable increases in the positive domain, also does the dependent variable. So we have an increasing function

Finally, we can see that the range (set of the outputs) of the function is the set of values larger than zero.

These 3 are characteristics of exponential functions, so we conclude that the graphed function is an exponential one, thus the correct option is the first one.

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Answer:

Logarithmic

Step-by-step explanation:

HS Teacher

Answer:

2700 degrees

Step-by-step explanation:

The number of sides minus 2 times.

n = number of sides

(n-2)= 180

(17-2)(180)

(15)(180) = 2700

The distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone. This can be obtained by converting the conditions to equations.

A linear function containing one dependent and one independent variable.

It can be represented using the equation,

y = mx + c

where m is the slope

It is given in the question that,

Rachel is a stunt driver and one time during a gig where she escaped from a building about to explode she drove to get to the safe zone at 24 meters per second.

After 4 seconds of driving, she was 70 meters away from the safe zone.

Let, D(t) be the distance to the safe zone (measured in meters) and t be the  time (measured in seconds)

After 4 seconds of driving, she was 70 meters away from the safe zone.

⇒ This means that at t = 4 seconds, D(4) = 70 meters

Rachel's rate is the slope of the function D(t). Since the distance is decreasing when the time is increasing, the slope must be negative

⇒ m = - 24

y = mx + c

⇒ D(t) = (-24)t + c

Put t = 4,

D(4) = (-24)4 + c

70 = -96 + c ⇒ c = 166

⇒ D(t) = 166 - 24t

Hence the distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone.

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Answer: [tex]\Large\boxed{\dfrac{3}{8} }[/tex]

Step-by-step explanation:

Given information

[tex]b=2[/tex]

[tex]c=-\dfrac{7}{4}[/tex]

Given expression

[tex]b-(-\dfrac{1}{8}) +c[/tex]

Substitute values into the expression

[tex]=(2)-(-\dfrac{1}{8}) +(-\dfrac{7}{4} )[/tex]

Convert the fractions into the common denominator

Least Common Multiple (LCM) of 8 and 4 = 8

[tex]=(2)-(-\dfrac{1}{8}) +(-\dfrac{7\times2}{4\times2} )[/tex]

[tex]=(2)-(-\dfrac{1}{8}) +(-\dfrac{14}{8} )[/tex]

Simplify the parenthesis

[tex]=2+\dfrac{1}{8} -\dfrac{14}{8}[/tex]

Simplify by addition

[tex]=\dfrac{16}{8} +\dfrac{1}{8} -\dfrac{14}{8}[/tex]

[tex]=\dfrac{17}{8} -\dfrac{14}{8}[/tex]

Simplify by subtraction

[tex]\Large\boxed{=\dfrac{3}{8} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

100°

Step-by-step explanation:

basically, in this situation, whatever number or angle you're given, and the number diagonally across from it are supposed to add up to 180°.

(i think its called a cyclic quadrilateral, so do with that what you will.)

The area of the circle is 78.5 square yards and the circumference of the circle is 31.4  yards

The radius of the circle is given as:

r = 5 yard

The area is calculated using

A = pi r^2

Substitute the known values in the above equation

A =3.14 * 5^2

Evaluate the exponent

A =3.14 * 25

Evaluate the product

A =78.5

Hence, the area of the circle is 78.5 square yards

The radius of the circle is given as:

r = 5 yard

The circumference is calculated using

C = 2pi r

Substitute the known values in the above equation

C =2 * 3.14 * 5

Evaluate the product

C = 31.4

Hence, the circumference of the circle is 31.4  yards

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The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.

According to the statement

we have given that the some numbers of the songs which are added by the larrisa in her playlist.

And we have to tell the ways which are formed with the help of the combination and permutations.

So, For this purpose we know that the

The first condition we have given that the

"play no more than 4 blues songs" - indicates playlist can contain 0, 1, 2, 3, or 4 blues songs. You need to analyze five different cases and add them up together in the end. From 7 blues songs, you can either "pick" 0, 1, 2, 3, or 4. Since order matters, it's a permutation, not a combination.

Afterwards, it gets tricky. Consider the first case, where we have 0 blues songs. This means that there are 10 spaces for the remaining (3+5+7 = 15) songs, which means that they can be arranged in (7P0 ∙ 15P10) ways.

For the next case, where we have 1 blues songs, it means that there are 9 spaces for the remaining 15 songs, which means that they can be arranged in (7P1 ∙ 15P9) ways. Continue doing this for the cases of 2, 3, and 4 blues songs and add up all the cases together.

And from this way we get the all combinations which are formed.

So, For this purpose

n = (7P0 ∙ 15P10) + (7P1 ∙ 15P9) + (7P2 ∙ 15P8) + (7P3 ∙ 15P7) + (7P4 ∙ 15P6) = 4.43459016×1010,

which rounded to the hundredths place, is 4.43 x 10^10 possible playlists.

So, The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.

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Answer:

Step-by-step explanation:

Answer:

  34

Step-by-step explanation:

You want the value of |m² +n²| for m = -5 and n = 3.

Put the values where the variables are in the expression and do the arithmetic.

  |m² +n²| = |(-5)² +3²| = |25 +9| = |34| = 34

The value of the expression is 34.

__

Additional comment

Here, the absolute value bars don't do anything, because the value between them is positive. If it were negative, they would remove the minus sign.

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Part I: The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)

Part II: The midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)

From the question, we are to determine the formula for calculating the midpoint of a segment

The midpoint of a segment can be determined by using the formula,

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)

II. To determine the midpoint of the segment with endpoints (-2, -1) and (0, 9)

x₁ = -2

y₁ = -1

x₂ = 0

y₂ = 9

Putting the parameters into the formula,

Midpoint of the segment = ((-2 + 0)/2, (-1 + 9)/2)

Midpoint of the segment = (-2/2, 8/2)

Midpoint of the segment = (-1, 4)

Hence, the midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)

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Answer:

5

Step-by-step explanation:

Gradient (slope) of the curve can be found by deriving a curve function.

In this scenario, the given function is a polynomial function which we can use Power Rules to derive it.

Power Rules

[tex]\displaystyle{y=ax^n \to y' = nax^{n-1}}[/tex]

Thus, using the power rules, we will have:

[tex]\displaystyle{y'=3x^2-4x+5}[/tex]

Note that deriving a constant will always result in 0.

Then the problem gives us that we want to find the slope or gradient at where the curve crosses y-axis.

The curve crosses y-axis at x = 0 only. Therefore, we substitute x = 0 in a derived function.

[tex]\displaystyle{y'(0) = 3(0)^2-4(0)+5}\\\\\displaystyle{y'(0) = 5}[/tex]

Therefore, the slope at the point where a curve crosses y-axis will be 5.

The length of the transverse axis is 8.

Given the equation of hyperbola:[tex]\frac{(y-2)^{2} }{16}[/tex][tex]-\frac{(x+1)^{2} }{144 }[/tex][tex]=1[/tex]

Rewrite this equation as [tex]\frac{(y-2)^{2} }{4^{2} }[/tex][tex]-\frac{(x+1)^{2} }{12^{2} }[/tex][tex]=1[/tex]

When comparing this equation to the common hyperbola equation with a vertical transverse axis is [tex]\frac{(y-k)^{2} }{a^{2} }[/tex][tex]-\frac{(x+h)^{2} }{b^{2} }[/tex][tex]=1[/tex]

[tex]h = -1[/tex]

[tex]k= -2[/tex]

[tex]a = 4[/tex]

[tex]b = 12[/tex]

The length of the transverse axis is[tex]2a = 2*4[/tex]

                                                               [tex]=8.[/tex]

The length of the transverse axis is 8.

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$3,717.14

Compound interest is the interest on the principal funding as well as the interest itself.

Compound Interest Formula

Compound interest can be solved by plugging known values into a formula.

In this formula, the variables stand for different values.

So, for this question, we can plug in the values we are given and solve for P.

Identifying Known Values

First, let's find the exact numbers we are going to plug in.

Solving For P

Now we can plug all of these values in.

First, simplify the values within the parentheses and in the exponent through arithmetic.

Next, divide both sides by [tex]1.005^{96}[/tex]

*Note that the answer has been rounded to the nearest hundredth.

This means that you would need to deposit $3,717.14 into the account to have $6,000 in 8 years.

Answer: q = -2/3

Step-by-step explanation:

First, we need to apply the Distributive Law in order to proceed with the problem.

3(q + 4/3) = 2

3q + 3(4/3) = 2

We already know that 3(4/3) = 4, since the 3's cancel out. Or, 3(4/3) = 12/3 = 4.

Our new equation is,

3q + 4 = 2

Through transposition and isolation of variables, we get,

3q = -2

Dividing by 3 on both sides...

q = -2/3

A rigid motion is a type of motion in which all points on a given object move at the same time, in the same direction, and cover the same distance.

A rigid motion is a type of motion in which all points on a given object move at the same time, in the same direction, and cover the same distance. It is an essential type of motion used in geometry due to the rigid transformation of objects considered in the topic.

Rigid transformation is a method required to change the position, size, orientation, or dimensions of a given shape. This implies that the given shape (object) undergoes the appropriate transformation into its image. Types of rigid transformation are translation, rotation, dilation, and reflection.

Considering the given question, the quadrilateral performed a rigid motion. This was done by first reflecting it about the vertical axis, and now translating it 2 units downwards towards the horizontal axis.

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Answer:

L

Step-by-step explanation:

interior angle formula so

(number of sides - 2)*180

2*180 = 360

you can also just take an example from a square 4*90 = 360

360-121-58-70 = 111

Answer:

d - 7

Step-by-step explanation:

The word "difference" tells us that we will be using subtraction. Also, subtraction is not the same if you reverse the terms like, x - 2 and 2 - x are not the same. In your question it say "d and 7" so that's the order we use in the algebraic expression.

The preparation of the Cost of Goods Sold Budget for MingWare Ceramics Inc. in September is as follows:

Beginning inventory of finished goods $11,850

Cost of goods manufactured                485,310

Ending inventory of finished goods      (12,670)

Cost of Goods Sold                           $484,490

The cost of goods sold budget sums the costs of the beginning inventory of finished goods with the cost of goods manufactured and subtracts the ending inventory of finished goods.

The cost of goods sold budget is based on the cost of goods manufactured budget.

Direct materials:                            Enamel        Paint     Porcelain      Total    

Total direct materials purchases

budgeted for September            $35,870    $7,530    $139,890  $183,290

Estimated inventory, September 1   1,730        4,150          6,920      12,800 Desired inventory, September 30 (2,980)      (2,710)         (7,150)    (12,840)

Materials used in production                                                          $183,250

Direct labor cost:           Kiln Department    Decorating Department   Total

Total direct labor cost

budgeted for September    $51,550                   $149,500        $201,050

Finished goods inventories:             Dish       Bowl     Figurine             Total

Estimated inventory, September 1  $5,810   $3,310     $2,730        $11,850

Desired inventory, September 30    3,720    4,590       4,360         12,670

Work in process inventories:

Estimated inventory, September 1      $3,540

Direct materials used in production $183,250

Direct labor costs                              $201,050

Total factory overhead costs             $99,450

Desired inventory, September 30       (1,980)

Cost of goods manufactured           $485,310

Indirect factory wages $80,400

Depreciation of plant and equipment 10,550

Power and light 5,110

Indirect materials 3,390

Total 99,450

Thus, to prepare the cost of goods sold, as above, MingWare Ceramics, requires to determine the cost of goods manufactured for September.

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The true statements are;

-Both graphs are logarithmic functions

-Both graphs have been shifted and flipped (B and D).

A graph is a plot of information on the cartesian coordinates. The function is plotted on an x - y cartesian plane. Given the nature of function, we can understand the shape of the graph as shown.

In this case, the graph shows a flipped logarithmic function. As such, the following are true about the function;

-Both graphs are logarithmic functions

-Both graphs have been shifted and flipped

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Answer:

for normalian is a function of the form FX is equal to a and x n + a n - 1 x n - 1 + ax2 into X + A1 is equal to A2 is degree per normal highest power of X is

By the chain rule,

[tex]g(x) = f(4 - x^2) \\\\ \implies g'(x) = -2x f'(4 - x^2) \\\\ \implies g''(x) = -2 f'(4 - x^2) + 4x^2 f''(4 - x^2)[/tex]

Observe that

[tex]4 - x^2 = 1 \implies x^2 = 3 \implies x = \pm\sqrt3[/tex]

Then

[tex]g''(\sqrt3) = -2 f'(1) + 4\left(\sqrt3\right)^2 f''(1) = -2(-5) + 4(3)(-1) = \boxed{-2}[/tex]

Step-by-step explanation:

4W-8=3W+6

4W-3W=6+8

W=14°

lets find the value of W in this straight line

4W-8°=180°(angle on a straight line)

collect like terms

4W=180°+8°

4W=188°

divide both sides by the coefficient of W which is 4

W=47°

if i am correct pls rate it

The length of one of the remaining sides is 34.20 meters.

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Perimeter of an isosceles trapezoid =  sum of lengths of sides of a trapezoid

length of shorter base + length of longer base + (2 x legs)

108 = 11.5 + 28.1 + (2 x legs)

108 = 39.60 + (2 x legs)

108 - 39.60 =  (2 x legs)

68.40 =  (2 x legs)

leg = 68.40 / 2

= 34.20 meters

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Answer: 288

Step-by-step explanation:

(16x9)x2

Answer:

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

Find the cost, x:

Find the price to get 12% profit:

The option A is correct because the value of the statement is 6+3/n-8.

According to the statement

we have given that the statement and we have to write the statement in the numerical form.

So, For this purpose

we know that the given statement is

"Six more than the quotient of three and a number, decreased by eight".

In this statement "Six more than" indicates the sum between the quotient and 6.

And "The quotient of three and a number" indicates a fraction where the numerator is 3 and the denominator is , a number.

"Decreased by eight" indicates a subtraction between the quotient an 8 units".

If we unit all parts of the statements, we would have

6+3/n-8

So, From the given statement, The option A is correct because the value of the statement is 6+3/n-8.

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Step-by-step explanation:

The heaviest legal bowling ball weighs 16 pounds. The lightest weight you can usually find at most bowling alleys is six pounds.

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6.665 grams of the 13 grams remain after 8 hours.

The decay equation for the 13 grams of iron-52 is:

[tex]N(t) = 13g*e^{(-ln(2)/8.3h)*t}}[/tex]

Where N is the amount of iron-52, and t is the time in years.

Where we used the fact that the half-life is exactly 8.3 hours.

Now, the amount that is left is given by N(8h), so we just need to replace the variable t by by 8 hours, so we get:

[tex]N(8h) = 13g*e^{(-ln(2)/8.3h)*8h}} = 6.665g[/tex]

So 6.665 grams of the 13 grams remain after 8 hours.

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