At a sale this week, a desk is being sold for $561. This is 68% of the original price. What is the original price?​

Answer:

[tex]3^2=x+5[/tex]

Step-by-step explanation:

Given equation:

[tex]\log_3(x+5)=2[/tex]

Method 1

[tex]\textsf{Using the Log law:} \quad \log_ab=c \:\: \Longleftrightarrow \:\: a^c=b[/tex]

[tex]\implies \log_3(x+5)=2[/tex]

[tex]\implies 3^2=x+5[/tex]

Method 2

Make both sides of the equation the index to base 3:

[tex]\implies \log_3(x+5)=2[/tex]

[tex]\implies 3^{\log_3(x+5)}=3^2[/tex]

Apply the log law [tex]a^{\log_ax}=x[/tex] :

[tex]\implies x+5=3^2[/tex]

Swap sides:

[tex]\implies 3^2=x+5[/tex]

Solve for x

Although the question hasn't asked to solve for x, here is the solution:

[tex]\implies 3^2=x+5[/tex]

[tex]\implies 9=x+5[/tex]

[tex]\implies x=9-5[/tex]

[tex]\implies x=4[/tex]

Check

Substitute the found value of x into the original equation:

[tex]x=4 \implies \log_3(4+5)=\log_39=2 \quad \leftarrow\textsf{correct}[/tex]

[tex]\\ \rm\Rrightarrow log_3(x+5)=2[/tex]

[tex]\\ \rm\Rrightarrow x+5=3^2[/tex]

[tex]\\ \rm\Rrightarrow x+5=9[/tex]

[tex]\\ \rm\Rrightarrow x=9-5[/tex]

[tex]\\ \rm\Rrightarrow x=4[/tex]

Answer:

4/2 is the wrong answer

Step-by-step explanation:

because it is

Step-by-step explanation:

[tex] \frac{5 {}^{ - 4x + 7} }{125 {}^{x} } [/tex]

[tex] \frac{5 {}^{ - 4x + 7} }{5 {}^{3x} } [/tex]

[tex]5 {}^{ - 4x + 7 - 3x} [/tex]

[tex]5 {}^{ - 7x + 7} [/tex]

Answer:

1

Step-by-step explanation:

49 is divisible by 7, 1, 49. 25 is divisible by 5, 1, 25. they are exclusively prime so the highest factor is 1 and the only

Answer:

Step-by-step explanation:

[tex]25x^4-49y^2=(5x^2)^2-(7y)^2\\=(5x^2+7y)(5x^2-7y)\\=(5x^2+7y)[(\sqrt{5} x)^2-(\sqrt{7y} )^2]\\=(5x^2+7y)(\sqrt{5} x+\sqrt{7y} )(\sqrt{5} x-\sqrt{7y} )[/tex]

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The lines for the given statements can be plotted as shown below.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The lines for the given statements can be plotted as shown below.

The coordinate grid can be filled as,

1)

x        0         3         1

y        3         0         2

2.)

x        0         1         -1

y         1         0          2

3.)

x         0         4         -1

y         -2         0          2

4.)

x         0         1           1

y         -2         0         -2

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Answer:

Interpretation: A cube with sides of 4 units each has a volume of 64 units³.

Explanation:

As v(s) represents the volume of the cube, s represents the length of the sides.

∴ v(4) represents the volume of a cube with sides of  units, and the volume is 64 units³

By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.

All quadratic equations of the form a · x² + b · x + c = 0 have two roots that can be found by using the quadratic formula:

[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]     (1)

If we know that a = 2, b = - 4 and c = - 3, then the roots of the quadratic equations are:

[tex]x = \frac{4 \pm \sqrt{(-4)^{2}-4\cdot (2) \cdot (- 3)}}{2\cdot (2)}[/tex]

[tex]x = 1 \pm \frac{\sqrt{40}}{4}[/tex]

[tex]x = 1 \pm \frac{\sqrt{10}}{2}[/tex]

By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.

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Answer:

y=5x+13

Step-by-step explanation:

when x=-3, y=-2, and when x=-2,  y=3. we know that every time x increases by 1, y also increases by 5. This means that the slope is 5. to find the y-intercept, we need x to be 0. to find that, increase x by 2. if x increases by 2, then y would also increase by 10. add 10 to 3 and add 2 to -2 to get x=0 and y=13. the coordinates would be (0,13). the y-intercept is 13. now that we have enough information, we can conclude that y=5x+13. To check your answer, plug in the values for x.

The area of a circle to derive the formula for the area of a sector will be (θ/2π) x (area of the circle).

Let r be the radius of the circle. Then the area of the circle will be

Area = πr²

Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the area of the sector of the circle will be

Area = (θ/2π) πr²

Area = (θ/2π) x (area of the circle)

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Answer:

Step-by-step explanation:

Answer:

The domain is-3<x<3. It can also be (-∞,-3) U (-3,3) U (3, ∞).

Step-by-step explanation:

The U stands for Union. The second  answer usually used only for college algebra.

Answer:

that makes no sence at all i read it over 3 times and still font understand a word of it

sorry :(

Work Shown:

|x+2| + 7 > 10

|x+2| > 10-7

|x+2| > 3

x+2 > 3 or x+2 < -3

x > 3-2 or x < -3-2

x > 1 or x < -5

The graph for x > 1 has an open circle at 1 and shading to the right.

The graph for x < -5 has an open circle at -5 and shading to the left

Both of these facts combine to describe Choice C

In other words, we have open circles at -5 and 1, with nearly everything shaded except for the region between the open circles.

The open circles are used to exclude those x values mentioned.

Answer: It rounds to 28 km

Explanation:

The units or ones digit is "7". The next digit over (9) is five or larger. This means we bump the 27 up to 28. Everything after the 7 is ignored.

So we could have something like 27.999871212512 and we still follow the same idea of focusing on the 27, bumping it up to 28, and everything else gets ignored.

The reason for this is because 27.9 is much closer to 28 than it is to 27. Draw out a number line to help see this. Split the region from 27 to 28 into 10 equal pieces. The 9th little piece represents 27 & 9/10 aka 27.9

Refer to the number line diagram below.

The Graph B  best represents a parabola , Option D has the correct data points and so is the right answer.

A function is a mathematical way of representing relation between two variables.

The function given is

y = 2x²

For x = - 2, y = -2(- 2)² = -8

For x = - 1, y = -2(- 1)² = -2

For x = 0, y = -2(0)² = 0

For x = 1, y = -2(1)² = -2

For x = 2, y = -2(2)² = -8

the  table of x-y will be:

x  - 2    - 1    0    1    2

y    -8     -2   0  -2   -8

The graph is attached with the answer.

The parabola opens downward and has the data points as mentioned above .

Therefore Option D is the correct answer.

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Answer:

Step-by-step explanation:

Complete the following table using the equation: y = 2 x squared

x

-2

-1

0

1

2

y

Plot the points on a graph and determine which graph best represents the equation.

Graph A

On a coordinate plane, a parabola opens up and goes through (1, 3), has a vertex at (0, 0), and goes through (1, 3).

Graph B

On a coordinate plane, a parabola opens down and goes through (negative 1, negative 2), has a vertex at (0, 0), and goes through (1, negative 2).

a.

8, 2, 0, 2, 8; Graph A

b.

-8, -2, 0, -2, -8; Graph A

c.

8, 2, 0, 2, 8; Graph B

d.

-8, -2, 0, -2, -8; Graph B

Please select the best answer from the choices provided

A

B

C

D

   answer is '' a '  got it right

Answer:

p^2/r

Step-by-step explanation:

so I have shown every work in the picture attached

please let me know if this doesn't help

Answer:

  -5

Step-by-step explanation:

Substituting x=4 into the equation gives a 2-step linear equation in y. It is solved by isolating the variable and making its coefficient be 1.

__

When x=4, the equation becomes ...

  -3x +9y = -57

  -3(4) +9y = -57

  -12 +9y = -57

The first step is to "isolate" the variable term (9y) by adding the opposite of the constant that is on the same side of the equation. The result is that the variable term is by itself on one side of the equal sign.

  -12 +12 +9y = -57 +12 . . . . . add the opposite of -12

  9y = -45 . . . . . . . . . . . . . . simplify

The second step is to make the coefficient of y be 1. We do that by multiplying by its inverse, 1/9. Equivalently, we divide by 9.

  (1/9)(9y) = (1/9)(-45) . . . . multiply by the inverse of 9

  y = -5 . . . . . . simplify

Answer:

1)  x + 96 = 90°

2)  x + 89 = 80°

Step-by-step explanation:

Consecutive Interior Angles Theorem

When a transversal line intersects two parallel lines, it forms two pairs of consecutive angles on either side of the transversal line.  Each pair of consecutive interior angles are supplementary (sum to 180°).

To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 96)° + (x + 96)° = 180°

⇒ x + 96 + x + 96 = 180

⇒ 2x + 192 = 180

⇒ 2x + 192 - 192 = 180 - 192

⇒ 2x = -12

⇒ 2x ÷ 2 = -12 ÷ 2

⇒ x = -6

Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:

⇒ x + 96 = -6 + 96 = 90°

⇒ x + 96 = 90°

To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 109)° + (x + 89)° = 180°

⇒ x + 109 + x + 89 = 180

⇒ 2x + 198 = 180

⇒ 2x + 198 - 198 = 180 - 198

⇒ 2x = -18

⇒ 2x ÷ 2 = -18 ÷ 2

⇒ x = -9

Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:

⇒ x + 89 = -9 + 89

⇒ x + 89 = 80°

Answer:

[tex]\boxed {1) 90^{o}}\\\boxed {2) 80^{o}}[/tex]

Step-by-step explanation:

Part 1 :

Part 2 :

The area of the rectangular garden given the length and width is 16 1/2 square feet

Area of a rectangular garden = length × width

= 5 1/2 feet × 3 feet

= 11/2 × 3

= 33/2

= 16 1/2 square feet

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The function g(x) is derived by translating the function by the three units, according to the graph.The equation for the red graph will be,g(x) = x²+3

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

From the graph, it is obtained that the function g(x) is obtained by translating the function by the three units.

Hence,the equation for the red graph will be,g(x) = x²+3

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Step-by-step explanation:

Anything which has a decimal point is not a whole number

6830 is

66 is

717.59 is not

808 is

42.3 is not

1/10 = 0.1 ergo is not

The equivalent expression to ∑n(n+1) is ∑n²+∑n.

Equivalent expressions are defined as algebraic expressions which give the same resulting expression. An algebraic expression (or) a variable expression is defined as a combination of terms by the operations such as addition, subtraction, multiplication, division.

Here, given expression;

       ∑(n(n+1))

     = ∑ (n² + n)

     = ∑n²+∑n

Thus, the equivalent expression to ∑n(n+1) is ∑n²+∑n.

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Answer:

w (number)  = 2/3

Step-by-step explanation:

Variable w means use the letter w as the unknown number :

This is the equation made from the question :

2+(9w) = 8

Let's subtract 2 from both sides :

9w = 6

Divide both sides by 9 :

w = 6/9

Simplify fraction :

w = 2/3

Hope this helped and have a good day

Answer:

445

Step-by-step explanation:

I think it is 445 because each term is +1 and time is the number of terms you want to find.

So

(2+1) time 2 = 6

(6+1) time 3 = 7

(88+1)  time 5 = 445

Answer:

$21.25

Step-by-step explanation:

The cost of the 2 adult tickets before the discount is $8 * 2 = $16

The cost of the 2 child tickets before the discount is $5 * 2 = $10

The total cost before the discount is $16 + $10 = $26

The total cost after the discount is

$26 * (1 - 0.15) =

$26 * 0.85 =

$21.25

Answer: Yes.

Step-by-step explanation: However, charging your battery to high voltages except for the first time can significantly decrease your battery's lifespan. According to some studies charging a battery to only 85% to 90% can improve its discharge cycle from 300 to even an extra 1000 recharges.

Because in both graphs the shaded region is above the curve, the correct option is C.

On the graph we can see two parabolas, such that the y-intercepts of these are:

y = 6

y = -4

So we just need to find the pair of options with these y-intercepts, and noticing that for both cases, we must have:

y > parabola.

Because both shaded regions are above the parabolas.

The only option that meets these requirements is option C. Where there is a mistake, as you can see both curves have dashed lines, and always when we have dashed lines we should use the symbols > or <, while in that option we have a ≥ symbol

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We can rewrite the equation of the given line to be in slope-intercept form as follows.

[tex]x-y=7\\x=y+7\\y=x-7[/tex]

Thus, the slope of the given line is 1.

Since parallel lines have equivalent slopes, the slope of the line we want to find is also 1.

Substituting into point-slope form,

[tex]y-0=1(x-1)\\\\\boxed{y=x-1}[/tex]

Answer:

Its A

Step-by-step explanation:

I said so

Answer:

1000 pencils = $ 20.

10 pencils = ?

10 * 20 / 1000

200/1000

2/10

1/5

0.5.$

Answer:

$0.20

Step-by-step explanation:

If 1000 pencils cost $20, then we must first find the unit rate.

20/1000 = 0.02, so it costs $0.02 for each pencil. To find out what ten pencils cost, we multlipy 0.02 by 10.

0.02 * 10 = 0.2, or $0.20.

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