The graph to the right uses cylinders to
represent barrels of oil consumed by two
countries. Does the graph distort the data or
does it depict the data fairly? Why or why not?
If the graph distorts the data, construct a
graph that depicts the data fairly.


Does the graph distort the data? Why? Or Why not?

A. Yes, because 3D objects always distort the data in graphs.

B. Yes, because the graph incorrectly uses objects of volume to represent the data.

C. No, because the graph is technically correct.

D. No, because the proportions are accurate.

Answer:

angle b

Step-by-step explanation:

let's assume the triangle is a right angle triangle . either angle a or c can be equal to 60 degree

Answer:

\(\mathrm{B.}\) All real numbers except x = 2, x = 5

Step-by-step explanation:

If the denominator is equal to 0 then the function would be undefined.

Set the denominator equal to 0.

x² - 7x + 10 = 0

Factor the left side of the equation.

(x - 5)(x - 2) = 0

Set the factors equal to 0.

x - 5 = 0

x = 5

x - 2 = 0

x = 2

The domain is all real numbers except x = 2 and x = 5.

The length of x is 7.

In geometry, a triangle is a three-sided polygon made up of three line segments that join at three points called vertices. Triangles are one of the most basic and important shapes in geometry, and they are used in many areas of mathematics, science, and engineering.

Using the property of a median, we know that BD divides AC into two equal parts. Let's call the length of CD as y.

So, we have:

AC = AD + CD

x = 3 + y

Using the Pythagorean Theorem, we can find the length of BD:

BD² = AB² + AD² - 2(AB)(AD)(cos(B))

BD² = 4² + 3² - 2(4)(3)(cos(B))

BD² = 25 - 24cos(B)

BD = √(25 - 24cos(B))

Since BD is a median, we know that it divides BC into two equal parts. Let's call the length of BD as z.

So, we have:

BC = 2z

8 = 2z

z = 4

Now, using the property of medians again, we know that:

4² + y² = z²

16 + y² = 16

y² = 0

y = 0

Therefore, CD is also 4, and:

x = 3 + y

x = 3 + 4

x = 7

So, the length of AC is 7.

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Answer:

9.9

Step-by-step explanation:

remember your distribution rules.

x/3.3=3 make sure x is by itself. so take 3*3.3

When you have x divided by a number equaling a number take the number it equals to and multiply by the number that x is being divided by.

3=x/3.3

move 3.3 by multiplying it by 3 which gives you 9.9.

The solution of x in equation 3 = x / 3.3 is,

⇒ x = 9.9

We have to given that;

Expression is,

⇒3 = x / 3.3

Now, We can simplify the equation for x as;

⇒ 3 = x / 3.3

Multiply by 3.3 both side,

⇒ 3 × 3.3 = x

⇒ 9.9 = x

⇒ x = 9.9

Thus, Solution is,

⇒ x = 9.9

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Answer:

Step-by-step explanation:

The calculated value of x at g(x) = 2 is x = 2.5

from the question, we have the following parameters that can be used in our computation:

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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Answer:

8

Step-by-step explanation:

The cos of 30 is \(\sqrt{x}\) / 2.  Since the adjacent angle is 4 times that.  We would multiply 2 x 4 and get 8

Answer:

Your answer is A

Step-by-step explanation:

The triangles are not similar, because corresponding sides are not proportional.

Answer:

Step-by-step explanation:

We know that:

Let's use the triangle property to solve for x.

Work:

Hence, the value of x is 86°

Answer:

The answer to this question would depend on how many teachers are available in the day care center.

If every teacher is to have the same number of children then the number of teachers will be factors of 52 which are more than 1;

2, 4, 13, 26, 52

If there are 2 teachers, each teacher will have 26 children

If there are 4 teachers, each teacher will have 13 children

If there are 13 teachers, each teacher will have 4 children

If there are 26 teachers, each teacher will have 2 children

If there are 56 teachers, each teacher will have 1 child

Huda's error in evaluating (3) squared incorrectly led to the incorrect final result.

The correct answer should be -20, not 34.

Huda's error was that she evaluated (3) squared incorrectly.

Instead of calculating 3 squared as 9, she mistakenly considered it as 3. This error led to incorrect subsequent calculations and the final result of 34, which is not the correct answer.

To evaluate the expression correctly, let's go through the steps:

Negative 3 (8 minus 5) squared minus (negative 7) \(= -3(3)^2 - (-7)\)

First, we simplify the expression within the parentheses:

\(-3(3)^2 - (-7) = -3(9) - (-7)\)

Next, we evaluate the exponent:

-3(9) - (-7) = -3(9) + 7

Now, we perform the multiplication and addition/subtraction:

-3(9) + 7 = -27 + 7 = -20

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Answer: 16) Shifted LEFT 1 unit and DOWN 3 units

               17) Shifted LEFT 1 unit and DOWN 3 units

               18) Vertical stretch by a factor of 2

               19) Reflected over x-axis, shifted RIGHT 1 unit and UP 7 units

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k    where

f(x) = x²

16)  f(x) = (x - 1)² + 3

                    ↓      ↓

                  h= 1    k= 3

           Shifted RIGHT 1 unit and UP 3 units

17) f(x) = (x + 1)² - 3

                    ↓      ↓

                 h= -1   k= -3

           Shifted LEFT 1 unit and DOWN 3 units

18) f(x) = 2(x)²

              ↓    

             a= 2

           Vertical stretch by a factor of 2

19) f(x) = -(x - 1)² + 7

             ↓    ↓      ↓

           a= -1 h= 1  k= 7

           Reflected over x-axis, shifted RIGHT 1 unit and UP 7 units

Rules for the transformations of a parent function are given as,

 If the parent function f(x) = x² is transformed as,

        g(x) = (x + 1)²

        g(x) = (x - 1)²

        g(x) = x² + 1

        g(x) = x² - 1

        g(x) = kx²

        g(x) = -x²

With the help of these transformations, following transformed functions will be defined as,

 16). f(x) = (x - 1)² + 3

        Parent function is shifted 1 unit right and 3 units upwards.

  17). y = (x + 1)² - 3

        Parent function is shifted 1 unit left and 3 units left.

  18). g(x) = 2x²

        Parent function is vertically stretched by a factor of 2.

  19). f(x) = - (x - 1)² + 7

        Parent function is inverted about the x-axis, followed by 1 unit shift on the right and 7 units upwards.      

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The car will travel a distance of 52.08 seconds will the brakes applied before it stops

The acceleration of the car after t seconds that the brake was applied is given as:

\(a=-0.08t m/s^2\)

The speed of the car after  3 seconds that the brake was applied, u = 5 m/s

The speed of the car when it eventually stops, v = 0m/s

3 seconds after the brake was applied:

The time, t = 3 seconds

substitute t = 3 into the acceleration  \(a=-0.08t m/s^2\)

\(a=-0.08(3)m/s^2\\\\a = -0.24m/s^2\)

To calculate the distance traveled by the car after the brakes are applied, use the equation below

\(v^2=u^2+2as\)

Substitute u = 5, a = -0.24, and v = 0 into the equation above in order to calculate the distance

\(0^2=5^2+2(-0.24)s\\\\0=25-0.48s\\\\0.48s = 25\\\\s = \frac{25}{0.48}\\\\s = 52.08 m\)

The car will travel a distance of 52.08 seconds will the brakes applied before it stops

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Union of set A and set B' is A ∪ B' = {a, c, e, f, g}      

What is union of sets?

Union of two or more sets is the set containing all the elements of the given sets. Union of sets can be written using the symbol “⋃”

Given sets,

U = {a, b, c, d, e, f, g}

A = {a, c, e, g}

B = {a, b, c, d}

⇒ B' = {e, f, g}

A ∪ B' =  {a, c, e, g} ∪ {e, f, g}

A ∪ B' =  {a, c, e, f, g}          

Hence, A U B = {a, c, e, f, g} which union of both sets.

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Answer:

X= -1

Step-by-step explanation:

Step-by-step explanation:

that is really easy, when you have the function in such a factorial form already.

the zeros of the whole function are the x values that turn at least one factor to 0 (as when one factor is 0, then the whole expression is 0).

so, you get a zero, when x = 7, or x = 3, or x = 2.

because then either x-7 or x-3 or x-2 is 0.

therefore, C is the right answer.

Answer:

Step-by-step explanation:

The output voltage, in millivolts (mV), for the circuit would be = 1,350 millivolts.

An amplifier is defined as the electronic device that can be used to increase the electrical signal of a power source.

The output voltage of an amplifier= input voltage × gains.

Where;

input voltage = 45 mV

The gain = 30

Therefore the output voltage= 45×30 = 1350millivolts.

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The equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

The equation of a circle with center (a,b) and radius r is given by the equation:

(x - a)^2 + (y - b)^2 = r^2

Using the given values, the equation of the circle with center (1/2, 0) and radius 2 is:

(x - 1/2)^2 + (y - 0)^2 = 2^2

Expanding and simplifying, we get:

(x - 1/2)^2 + y^2 = 4 - 1/4

Therefore, the equation of the circle is:

(x - 1/2)^2 + y^2 = 15/4

So, the equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

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Answer

5-6/6-5

Step-by-step explanation:

The value of x, given that when it divides a number, there is a quotient and a remainder, is 400

To find the value of divisor, we can use a variant of the division algorithm formula :

Divisor = ( Dividend - Remainder ) / Quotient

x is the divisor

Dividend = 19, 432

Remainder = 232

Quotient = 48

This means that the value of x is:

x = ( 19, 432 - 232 ) / 48

x = 19, 200 / 48

x = 400

In conclusion, x is 400.

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It will take 7 days for Claire to sell as many candy bars as Ayden

Claire has sold 8 candy bars and sells 5 more each day

The first term = 8

Common difference = 5

nth term is = a+(n-1)d

= 8 +(n-1)5

= 8 + 5n - 5

= 3 +5n

Ayden has sold 20 candy bars and sells 3 more each day

The first term = 20

Common difference = 3

nth term = a+(n-1) d

= 20 +(n-1)3

= 20 + 3n -3

= 17 + 3n

Then,

3 + 5n = 17 + 3n

5n - 3n = 17 - 3

2n = 14

n = 14/2

n = 7

Hence, it will take 7 days for Claire to sell as many candy bars as Ayden

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The fraction in its lowest terms for 7 1/2 percent is 3/40.

To express the mixed number 7 1/2 percent as a fraction in its lowest terms, we need to convert it to a fraction and simplify.

First, we convert the mixed number to an improper fraction:

7 1/2 percent = 7 1/2 / 100

To simplify this fraction, we find the least common multiple (LCM) of the denominator (2) and the percent denominator (100), which is 200.

Now, we can rewrite the fraction with the common denominator:

7 1/2 / 100 = (7 * 2 + 1) / 200 = 15/200

To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 15 and 200 is 5.

15/200 = (15 ÷ 5) / (200 ÷ 5) = 3/40

Therefore, the fraction in its lowest terms for 7 1/2 percent is 3/40.

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The expression is factorized to give (x + 7) and (x + 7)

Factorization described a mathematical methods that consists of writing a number or mathematical object as a product of several other factors that are mostly simpler or smaller objects of the same kind.

Given the quadratic equation;

x² + 14x +49

Find the pair factors of 49 that sum up to 14, the numbers are 7 and 7

Now, substitute the numbers in the expression

x² + 7x + 7x + 49

Make into two expressions, we have;

(x² + 7x) + (7x + 49)

factor out the common terms, we get;

x(x + 7)+ 7(x + 7)

Then, we have;

(x + 7)

(x + 7)

Hence, the factorized form is (x + 7) and (x + 7)

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Given:-

To find:-

The required solution.

Now we simplify it. we get,

So the equation is,

Answer:

B only

Step-by-step explanation:

Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.

Therefore, only B is correct

The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.

The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.

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Answer:Umm you can do ratios if you learned it or you can times it

Step-by-step explanation:

Hope this helps

Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35