Use the graph to answer the question.



Determine the translation used to create the image.


5 units down

5 units up

1 unit down

1 unit up

Answer:

Rewrite the equation using the logarithmic property loga(b) = loga(c) if and only if b = c:

x2 - 15 = 2x

Move all the terms to one side of the equation:

x2 - 2x - 15 = 0

Use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a = 1, b = -2, and c = -15

x = (-(-2) ± sqrt((-2)^2 - 4(1)(-15))) / 2(1)

x = (2 ± sqrt(64)) / 2

x = 1 ± 4

Potential solutions are x = 5 and x = -3.

Check each potential solution in the original equation to see if it is valid. The logarithm of a negative number is undefined, so x = -3 is an extraneous solution. Therefore, the only valid solution is x = 5.

Plug x = 5 into the original equation to check:

log(5^2 - 15) = log(2(5))

log(10) = log(10)

Both sides are equal, so x = 5 is the correct solution.

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

-4(3-1) + 2

=> -4(2) + 2

=> -8 + 2

=> -6

Answer:

x = -2

Step-by-step explanation:

5(−2x−1) −5x + 2 = 27

-10x - 5 - 5x + 2 = 27

-15x - 3 = 27

-15x = 30

x = -2

So, the answer is x = -2

Answer:

Let's solve for x:

5(-2x-1) - 5x + 2 = 27

Distribute the 5:

-10x - 5 - 5x + 2 = 27

Combine like terms:

-15x - 3 = 27

Add 3 to both sides:

-15x = 30

Divide by -15:

x = -2

Therefore, the solution is x = -2.

Step-by-step explanation:

the equation of the quartic polynomial in standard form is [tex]f(x) = x^4 + 12x^3 + 37x^2 + 29x - 60[/tex]

A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn in οne variable, which can be written in the standard fοrm: [tex]ax^2 + bx + c = 0[/tex], where x is the variable, and a, b, and c are cοnstants. The term "quadratic" cοmes frοm the fact that the highest degree οf the variable in this equatiοn is 2 (οr squared).

If the zerοs οf f(x) are -6, -5, -2, and 1, then the factοrs οf f(x) are:

(x + 6), (x + 5), (x + 2), and (x - 1)

Tο οbtain the standard fοrm οf the quartic pοlynοmial, we need tο expand the prοduct οf these factοrs:

f(x) = (x + 6)(x + 5)(x + 2)(x - 1)

We can expand this using the FOIL methοd οr by using the distributive prοperty repeatedly:

[tex]f(x) = (x^2 + 11x + 30)(x^2 + x - 2)[/tex]

Nοw we can multiply these factοrs using the distributive prοperty:

[tex]f(x) = x^4 + 12x^3 + 37x^2 + 29x - 60[/tex]

Since the leading cοefficient οf f(x) is 1 (as given in the prοblem statement), this is the standard fοrm οf the quartic pοlynοmial:

[tex]f(x) = x^4 + 12x^3 + 37x^2 + 29x - 60[/tex]

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Answer:

the lines are //

thales

15/45=x/(x+10)

15(x+10)=45x

15x+150=45x

15x-45x=-150

30x=150

x=150/30 = 5

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

Here the the line intersecting the two sides of the triangle is parallel to third side . So here we can use Thale's Theorem , according to which, If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio .

So , here ,

30/45 = 10/(10+x)

Simplify,

2/3 = 10/(10+x)

Cross multiply,

2(10+x) = 3*10

20 + 2x = 30

2x = 30 - 20

2x = 10

x = 5

Hence the value of x is 5 .

Answer:

y = 4(9)^x

Step-by-step explanation:

To find the equation of an exponential function in the form y = ab^x that passes through two given points, we need to use the following steps:

Step 1: Find the value of a by plugging in the coordinates of the first point (0,4).

y = ab^x

4 = ab^0

4 = a(1)

a = 4

Step 2: Find the value of b by plugging in the coordinates of the second point (3,2916) and using the value of a we found in Step 1.

y = ab^x

2916 = 4b^3

b^3 = 729

b = 9

Step 3: Write the equation in the form y = ab^x using the values of a and b we found in Steps 1 and 2.

y = 4(9)^x

Therefore, the exponential function in the form of y = ab^x that passes through the points (0,4) and (3,2916) is y = 4(9)^x.

Hope this helps, I'm sorry if it doesn't. If you need more help, ask me! :]

Angle BCD is equal to 65.5°.

What is the formula for the interior angle of a regular polygon?

The interior angle of a polygon = sum of interior angles and the number of sides is the formula for determining the amount of an interior angle.

It is given that B, A, and D are three consecutive vertices of a regular 8-gon.

The interior angle of a regular 8-gon (Octagon) is 135°.

It is given that C is a vertex of a regular heptagon(7-gon) whose one side is AB.

C, B, and D are at equal distances from A.

So A is the center and C, B, and D are points on the circle.

BD is the cord that is making an angle of 135° at A(center).

At the circumference, the cord makes half the angle.

So angle BCD is equal to 135/2 = 65.5°.

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Answer:

A = 3, B = 4

Step-by-step explanation:

To find A and B, we need to use the fact that the solution to the system of equations is (2,-4).

Substituting x=2 and y=-4 into the first equation, we get:

A(2) + 2(-4) = -2

Simplifying this equation, we get:

2A - 8 = -2

Adding 8 to both sides, we get:

2A = 6

Dividing both sides by 2, we get:

A = 3

So, we have found that A is equal to 3.

Now, substituting x=2 and y=-4 into the second equation, we get:

5(2) - B(-4) = 26

Simplifying this equation, we get:

10 + 4B = 26

Subtracting 10 from both sides, we get:

4B = 16

Dividing both sides by 4, we get:

B = 4

So, we have found that B is equal to 4.

Therefore, the values of A and B that satisfy the system of equations are A=3 and B=4.

The two solutions are: Cot x = [1 + √5] / 2, and Cot x = [1 - √5] / 2.

The relationships between the sides and angles of triangles, as well as the trigonometric functions that characterize those relationships, are the subject of the mathematical discipline of trigonometry. The Greek words "trigonon" (meaning triangle) and "metron" are the origins of the word "trigonometry" (meaning measurement).

Given: [tex]Cot x = Cosec^2 x / Cotx[/tex]

Multiplying both sides by [tex]Cot x,[/tex] we get:

[tex]Cot x * Cot x = Cosec^2 x[/tex]

Using the identity[tex]1 + Cot^2 x = Cosec^2 x[/tex], we can rewrite this as:

[tex]1 + Cot^2 x = Cot x * Cot x[/tex]

Rearranging terms, we get:

[tex]Cot^2 x - Cot x - 1 = 0[/tex]

Now we can solve for Cot x using the quadratic formula:

[tex]Cotx =[/tex] 1 ± [tex]\sqrt{(1 + 4*1*1)} ] / 2[/tex]

Cot x = [1 ± √5] / 2

Therefore, the two solutions are:

Cot x = [1 + √5] / 2, and Cot x = [1 - √5] / 2.

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Answer: The answer is 144 cm2

Step-by-step explanation:

The total mass of the books in Kelly's backpack is 2950 grams.

How many grammes are there in one kilogramme?

1000 grammes make up one kilogramme. The amount in kilogrammes must be multiplied by the conversion factor, which is 0.001.

We must add the masses of all 5 volumes to determine the overall weight of the books in Kelly's backpack.

The combined mass of the three books, each weighing 450 grammes, is: 3 x 450 = 1350 grammes.

The combined mass of the two volumes, each weighing 800 grammes, is 2 x 800 grammes.

We sum the weights of all the books to determine the overall mass:

1350 + 1600 = 2950 grammes

The combined weight of Kelly's backpack's books is 2950 grammes.

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Answer: B. 135

Step-by-step explanation: 180-45= 135 because all straight angles sum up to 180 (180 rule)

Answer:

5

Step-by-step explanation:

3 1/2 + 1 4/8=

7/2 +12/8=

28/8+12/8=

40/8=

5

The area under the curve between two values on the x-axis represents the probability that the random variable falls within that range, with the total area under the curve being equal to 1.

In the graph, the PDF is represented by the smooth curve. The highest point on the curve corresponds to the most likely value of the random variable. In this case, the most likely value appears to be around x = 2.5.

The area under the curve between any two values on the x-axis represents the probability that the random variable falls within that range. For example, the probability that the random variable falls between x = 1 and x = 3 is equal to the area under the curve between those two values.

It's important to note that the probability density function must satisfy the following two conditions:

The total area under the curve must be equal to 1.

The probability of the random variable taking on any specific value is equal to zero, since the function only describes the likelihood of the variable taking on a range of values.

PDFs are often used in statistics to describe continuous distributions, such as the normal distribution, and to make statistical inferences about populations based on samples.

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The two expressions can describe the area of the blue tiles are 4/9 , 44.4%, we have to learn about tiles.

Tiles are often thin, rectangle (rectangular) or square covers made of durable materials like ceramic, stone, metal, baked clay, or even glass.

Rectangle has the 4 sides and 4 angles and each of the angles are right angle. The opposite sides are parallel and equal.

Square has also 4 sides and 4 angles and each of the angles are also right angle as rectangle but its all side are equal.

16 tiles are blue out of 36.

So, blue tiles = 16/36 = 4/9

4/9 * 100 =  44.4 %.

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The two expressions can describe the area of the blue tiles are 4/9 , 44.4%, we have to learn about tiles.

Tiles are often thin, rectangle (rectangular) or square covers made of durable materials like ceramic, stone, metal, baked clay, or even glass.

Rectangle has the 4 sides and 4 angles and each of the angles are right angle. The opposite sides are parallel and equal.

Square has also 4 sides and 4 angles and each of the angles are also right angle as rectangle but its all side are equal.

16 tiles are blue out of 36.

So, blue tiles = 16/36 = 4/9

4/9 * 100 =  44.4 %.

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Answer:

168 = 18 * x + 12* 2x

Step-by-step explanation:

I answered this somewhere else

The area of the new triangle would be 9.9c * m², so the answer is C.

What is triangle ?

A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is one of the basic shapes in geometry, and it is widely used in mathematics, science, engineering, and other fields. Triangles can be classified based on the length of their sides and the size of their angles.

The area of a triangle is given by the formula A = (1/2) * b * h, where A is the area, b is the base, and h is the height.

Let the original base be b and the original height be h, so the original area is A = (1/2) * b * h = 10c * m²

If the base is increased by 10%, the new base is 1.1b, and if the height is decreased by 10%, the new height is 0.9h.

The new area can be calculated as follows:

new area = (1/2) * (1.1b) * (0.9h)

= 0.495bh

= 0.495 * 2A

= 0.99A

= 9.9c * m²

Therefore, the area of the new triangle would be 9.9c * m², so the answer is C.

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Answer:

y = -2x - 2

Step-by-step explanation:

To find a line which is perpendicular, the slope must be the opposite reciprocal.

We can rewrite the decimal as a fraction to clear up our equation, 0.5 is a half:

[tex]y=\frac{1}{2}x+2[/tex]

Flip the reciprocal and change the sign, making it [tex]-\frac{2}{1}[/tex]

[tex]y=-2x+2[/tex]

An equation parallel to this shown in the answer selection is:

[tex]y=-2x-2[/tex]

So  H is correct

Hence, in answering the stated question, we may say that side every probability time it is tossed five times is 1/16, which corresponds to option D.

Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.

When a fair coin is tossed five times, the probability of obtaining the same side every time is the same as getting all heads or all tails.

Because the chance of receiving heads or tails on one toss is 1/2, the chance of getting heads or tails on five independent tosses is (1/2)5 = 1/32.

The likelihood of receiving all heads or all tails is the sum of the probabilities of receiving all heads and all tails, which is:

P(all heads or all tails) = P(all heads Plus P(all tails) = (1/32 + 1/16)

As a result, the theoretical probability of the coin landing on the same side every time it is tossed five times is 1/16, which corresponds to option D.

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In 5.8 years, $1,000 will amοunt tο $1,700 at 12%.

Simple cοmpοund interest is a quick and easy way tο find οut hοw much mοney has accrued interest. Interest is always charged οn the principal and is calculated at the same rate each periοd.

Every bank we depοsit mοney with pays interest οn that amοunt. Simple interest is οne οf many fοrms οf interest charged by banks. Sο, befοre delving further intο the idea οf simple interest, let's first clarify what a lοan is.

A lοan is an amοunt οf mοney that sοmeοne bοrrοws frοm a bank οr οther financial institutiοn tο cοver expenses. Mοrtgages, autο lοans, student lοans, and persοnal lοans are examples οf lοans.

According to our question-

Principal amοunt = $1,000

Future value = $1,700

Interest rate = 12%

Time = ?

Interest earned = Future value - Principal amοunt

= 1,700-1,000

= $700

Time = Interest earned / ( Principal x interest rate)

= 700/(1,000 x 0.12)

= 700/120

= 5.8 years

Hence, in 5.8 years, $1,000 will amοunt tο $1,700 at 12%.

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Sin = 4/5, with the help of trigonometric ratios.

Triangle side length ratiοs are knοwn as trigοnοmetric ratiοs.

In trigοnοmetry, these ratiοs shοw hοw the ratiο οf a right triangle's sides tο each angle

Sine, cοsine, and tangent ratiοs are the three fundamental trigοnοmetric ratiοs.

The sin, cοs, and tan functiοns can be used tο οbtain the οther significant trig ratiοs, cοsec, sec, and cοt.

Trigοnοn, which means "triangle," and metrôn, which means "tο measure," are the rοοts οf the term "trigοnοmetry."

Triangle side length ratiοs are knοwn as trigοnοmetric ratiοs.

Here,

cot = cos/sin

sin= PERPENDICULAR/HYPOTENUSE

cot = BASE/HYPOTENUSE

sin = 4/5

Hence, Sin=4/5, with the help of trigonometric ratios.

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Answer:

Yup!

Step-by-step explanation:

Answer:

A) a fair six-sided number cube (by assigning one number to represent a win and the other five numbers to represent a loss)

D) a spinner with 6 equal sections (by assigning one section to represent a win and the other five sections to represent a loss)

Step-by-step explanation:

Answer:

80 miles per hour

Step-by-step explanation:

The unit rate in this problem is 1 hour.

To find the unit rate, we have to find a factor for 1 hour and 1 [tex]\frac{1}{4\\}[/tex] hours.

A common factor would be  [tex]\frac{1}{4\\}[/tex]  of an hour. Since  [tex]\frac{1}{4\\}[/tex]  is 1 [tex]\frac{1}{4\\}[/tex] divided by 5, we also have to divide 100 miles by 5, which is 20.

So now we have that Blake's car can travel 20 miles in [tex]\frac{1}{4\\}[/tex] of an hour.

We want to know how many miles it can travel in 1 hour. If we multiply [tex]\frac{1}{4\\}[/tex] by 4, we get one hour. Likewise, we multiply 20 miles by 4 to get 80 miles travel in one hour.

The linear regression equation's residuals are as follows: -1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18, and -0.7

A residual is the difference between the actual value and the expected value.

In a scatter plot with a line of best fit, the residual would be the vertical distance between the actual value and the line.

The residual's general shape can be described as predicted.

Remainder therefore has a value of -1.

This is the regression equation: y = 0.141x + 0.842

The projected values (y) at the matching x values are then calculated.

We thus have:

y = 0.141 × 13.8 + 0.842 = 2.78

y = 0.141 × 18 + 0.842 = 3.38

y = 0.141 × 16.7 + 0.842 = 3.20

y = 0.141 × 18 + 0.842 = 3.38

y = 0.141 × 0.7 + 0.842 = 0.94

y = 0.141 × 21.9 + 0.842 = 3.93

y = 0.141 × 15.5 + 0.842 = 3.03

y = 0.141 × 9.2 + 0.842 = 2.14

y = 0.141 × 19.5 + 0.842 = 3.59

y = 0.141 × 16.7 + 0.842 = 3.20

Next, the residuals are determined using:

Real value minus predicted value equals residual.

We thus have:

Residual = 1.42 - 2.78 = -1.36

Residual = 3.7 - 3.38 = 0.32

Residual = 3.21 - 3.20 = 0.01

Residual = 4 - 3.38 = 0.62

Residual = 1.11 - 0.94 = 0.17

Residual = 3.69 - 3.93 = -0.24

Residual = 3.92 - 3.03 = 0.89

Residual = 2.23 - 2.14 = 0.09

Residual = 3.77 - 3.59 = 0.18

Residual = 2.5 - 3.20 = -0.7

The linear regression equation's residuals are therefore 1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18, and -0.7.

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Therefore , the solution of the given problem of expressions comes out to be 6 is the simplified expression.

With constantly shifting variables, calculations that mix joining, deleting, and random division must be made. If they banded together, they could do the following: A software, some information, and a math issue. A statement of truth contains formulas, elements, and arithmetic procedures like additions, subtractions, errors, and groupings. It is possible to assess and analyse both words and phrases.

Here,

Remember that for any real integer a,

=> √a² = a. We can simplify the equation as follows by using this property:

=> √3² x √2² = 6.

Multiplying results in:

3 x 2 = 6

Consequently, √3² x √2² = 6.

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The value of x is 50°. Triangles are unquestionably similar but not necessarily congruent if two of their angles are equal.

In a planar construction, an angle is a shape made up of two intersecting rays or lines. The vertex and the two rays, which are frequently referred to as an angle's sides, are the same termini for two rays. Two rays that share a terminal are referred to as the angle's sides and vertices in Euclidean geometry, respectively. Two rays can combine to create angles in the plane in which they are positioned. Moreover, when two planes overlap, angles are created. Dihedral angles are what these are called.

This indicates that although not absolutely equal, the sides of the two triangles are obviously proportional.

The two triangles' respective sides must be equal on at least one side for the sides to be equal.

∠PTQ=∠PSQ

∠PTQ=50°

∠PSQ=50°

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The height of the building is approximately 28.85 feet.

What is trigonometric equations ?

Trigonometric equations are equations that involve trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant. These equations are typically solved for an unknown angle or variable using algebraic methods and trigonometric identities. Trigonometric equations are commonly used in various fields such as physics, engineering, and mathematics.

We can use the trigonometric function tangent (tan) to solve this problem. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, we can consider the opposite side to be the height of the building and the adjacent side to be the distance from you to the building. Therefore, we can set up the following equation:

tan(30 degrees) = height of building / 50 feet

To solve for the height of the building, we can multiply both sides by 50 feet:

50 feet * tan(30 degrees) = height of building

Using a calculator, we can find that tan(30 degrees) is approximately 0.577. Therefore:

50 feet * 0.577 = 28.85 feet

Therefore, the height of the building is approximately 28.85 feet.

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Answer:

  0.56 lb

Step-by-step explanation:

You want the weight of pretzels if they constitute 14% of the weight of 4 lb of snack mix.

Let p represent the weight of pretzels. The relation in the problem statement is written in equation form as ...

  pretzel weight = 14% of 4 lb

  p = 0.14 × 4 lb

  p = 0.56 lb . . . . . . . . . perform the multiplication

The weight of the pretzels in the trail mix is 0.56 lb.

__

Additional comment

In this context "of" usually means "times". That is "14% of 4 lb" means 14% × 4 lb".

The percent symbol (%) can be considered to be a shorthand way to write "/100". That is, you can replace the percent symbol with /100 and it doesn't change anything:

  14% × 4 lb = 14/100 × 4 lb

(Similarly, ‰ means /1000.)

You will notice that we wrote the weight as "4 lb", not just "4". The "lb" can be treated as though it were a variable, and "4 lb" is the product of "4" and "lb". Keeping units with the numbers can help guard against mistakes. As with other variables, you can only add (or subtract) "like" terms, ones with the same units.

In general, a percentage is a "pure number." It has no units, because it is the ratio of quantities having like units: (0.56 lb)/(4 lb) = 0.14 = 14%. The like units cancel the same way like variables would cancel.

The claim is incorrect because the car's odometer is not perfectly accurate. A 10-minute he can measure to an accuracy of 1 mile, but is prone to error due to wear, calibration, measurement error and other factors. Additionally, factors such as tire pressure and changes in road conditions can affect the accuracy of odometer readings.

An odometer is an in-vehicle device that measures the distance traveled by the vehicle. Displays the total number of miles or kilometers the car has traveled since the car was manufactured or the odometer was last reset. This measurement is important for several reasons. B. To track vehicle maintenance schedules, estimate fuel consumption, and determine vehicle resale value. Odometers typically use mechanical or electronic components to measure the distance traveled by a vehicle and display the information on the dashboard. However, as mentioned earlier, the accuracy of odometer readings depends on a number of factors. 

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