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What is the area of the triangle?
A)24 square units
B)32 square units
C)48 square units
D)96 square units

Answer:  x = 7

`Step-by-step explanation:

Because the figure shows two triangles that are similar. we can write and solve an equation of ratios:

 9 cm       72 cm

----------- = -----------

3x - 20      56 cm

Cross-multiplying, we get (3x - 20)(72 cm) = (9 cm)(56 cm) = 504 cm²

Dividing both sides by 72 cm, we get:

3x - 20 = (504 cm²) / (72 cm) = 7

Then 3x - 20 = 7, and 3x = 27.  Then x must be 9.

The value of x in the triangle with parallel lines is 9.

To find the value of x in the equation involving a triangle with parallel lines, we can start by simplifying the equation and then solve for x.

The given equation is:

9/72 = (3x - 20)/56

Let's first simplify the left-hand side of the equation:

9/72 = 1/8

Now, the equation becomes:

1/8 = (3x - 20)/56

To isolate x, we can cross-multiply:

1 * 56 = 8 * (3x - 20)

56 = 24x - 160

Next, add 160 to both sides of the equation:

56 + 160 = 24x

216 = 24x

Finally, divide both sides by 24 to solve for x:

x = 216/24

x = 9

So, the value of x in the given equation is 9.

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Answer:

-3.2

Step-by-step explanation:

Answer:

Complex numbers are numbers in which the real component and the imaginary part of the number are both represented. The numbers in standard form will be a + bi, where a is the real part and bi is the imaginary part. An example of a complex number would be 3 +5i. 3 is the real part, and 5i is the imaginary part.

Step-by-step explanation:

Hope this helps!

The complex number 3cis210 can be written in standard form as - (3√3/2)i - (3/2).

The complex number 3cis210 can be written in standard form as:

3cis210 = 3(cos(210°) + i sin(210°))
Using the trigonometric identities cos(210°) = -√3/2 and sin(210°) = -1/2, we can simplify:

3cis210 = 3(-√3/2 + i(-1/2))

Therefore, the complex number 3cis210 in standard form is - (3√3/2)i - (3/2).

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The complete Question is given below:

Write as a complex number in standard form 3cis210

Answer:

Simplifying the equation:

[tex]\frac{2}{3} x - \frac{5}{6} = -\frac{5}{12} x + \frac{1}{4}[/tex]

Grouping like terms:

[tex]\frac{2}{3} x + \frac{5}{12} x= \frac{1}{4} + \frac{5}{6}[/tex]

⇒ [tex]\frac{39}{36} x=\frac{26}{24}[/tex]

Solving for 'x', we have:

⇒ [tex]x=\frac{26}{24}\frac{36}{39}=1[/tex]

For this case we place the terms with "x" on the left side of the equation, and the terms without "x" on the right side:

[tex]\frac {2} {3} x + \frac {5} {12} x = \frac {1} {4} + \frac {5} {6}[/tex]

We add similar terms:

[tex]\frac {24 + 15} {36} x = \frac {6 + 20} {24}\\\frac {39} {36} x = \frac {26} {24}[/tex]

We simplify both sides:

[tex]\frac {13} {12} x = \frac {13} {12}[/tex]

Dividing by [tex]\frac {13} {12}[/tex] on both sides of the equation:[tex]x = 1[/tex]

Answer:

[tex]x = 1[/tex]

Answer:

[0,∞), {y|y≥0}

Step-by-step explanation:

The graph of y =|3x + 1| is attached.

By observation, we can see that the the least y-value that the graph can take is y =0 (i.e the x-axis) and the greatest y-value that the graph can take is positive infinity.

Hence the range is [0,∞), {y|y≥0}

Final answer:

The range of the function y = |3x + 1| is [0, infinity), as absolute value functions always yield non-negative values.

Explanation:

The range of the function y = |3x + 1| can be determined by understanding the behavior of absolute value functions. The absolute value function |x| always yields a non-negative value. Therefore, for any real number x, |3x + 1| will also be non-negative. Hence, the range of y = |3x + 1| is [0, ∞), meaning that y can be any real number greater than or equal to zero.

Answer: 4.24264069

Step-by-step explanation: I think you mean the square root?

[tex]x+y-3z=8\\x=-y+3z+8[/tex]

The range is given by: largest number in the data set - smallest number in the data set.

In our case, the largest value is 9 and the smallest value is 6.9. Therefor:

Range = 9 - 6.9 = 2.1

Thus, you have correctly identified the answer as the second choice (2.1). It is easy to get confused with much larger data sets but always keep in mind that the range is simply the largest value minus the smallest value. This makes sense since 'range' refers to the spread in something, for example if you were testing your vocal range you would find the highest note you could sing and the lowest note - this is the same here, we are just finding the range of a data set instead.

Answer:

The correct answer is second option

2.1

Step-by-step explanation:

Points to remember

Range of a data set

The range of a data set means that, the difference between the highest and lowest value of the data set.

To find the range of data set

It is given that, a data set

7.7, 8.4, 9, 8, 6.9

Highest value = 9 and lowest value = 6.9

Range = Highest value - lowest value

 = 9 - 6.9 = 2.1

Therefore the correct answer is second option

Answer:

14 inch

Step-by-step explanation:

formula for circumference:

2(pi)r @ (pi)d

*where: r = radius

d= diameter

pi used = 22/7

22/7 x d = 44

d= 44/ (22/7)

=14

Answer:

false

Step-by-step explanation:

In a mapping diagram, a relation that is a function can have two arrows coming from the same input value

false

Answer: False.

Step-by-step explanation:

By definition, a relation is a function if each input value has only one output value.

Knowing this, we can say that in a mapping diagram, a function will never have two arrows coming from the same input value.

 In other words, if in a mapping diagram a relation has two arrows coming from the same input value, this means that this input value has two output values, and according to the definition mentioned above, this relation cannot be a function.

Therefore, the statement "In a mapping diagram, a relation that is a function can have two arrows coming from the same input value", is FALSE.

Answer:

96

Step-by-step explanation:

If m - n = 2, then 4m - 4n = 4(m - n) = 4(2).

Then (4x + 2y)(4m - 4n) equals (4x + 2y)(8), or 8(4x + 2y).

But we are told that 2x + y = 6.  Multiplying all terms by 2, we get

4x + 2y = 12.  Substituting 12 for 4x + 2y, we get our final answer:

(4x + 2y)(4m - 4n) equals (4x + 2y)(8), or 8(4x + 2y), or 8(12) = 96

Answer:

96

Step-by-step explanation:

(4x + 2y)(4m - 4n) = ?

We have an equation

2x+y =6

Multiply it by 2

2(2x+y) = 2*6

Distribute

4x+2y = 12

Substitute 12 in for 4x+2y into the original problem

12(4m - 4n) = ?

We have an equation

m-n = 2

Multiply this by 4

4(m-n) = 4*2

Distribute

4m-4n = 8

Substitute 8 in for 4m -4n in 12(4m - 4n) = ?

12 * 8 = ?

96

For this case we have that if two lines are perpendicular, then the product of their slopes is -1.

If we have the following equation of the line:

[tex]y = -4x + 9[/tex]

The slope is [tex]m_ {1} = - 4[/tex]

Then yes:

[tex]m_ {1} * m_ {2} = - 1\\m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {- 4}\\m_ {2} = \frac {1} {4}[/tex]

The equation of the new line will be:

[tex]y = \frac {1} {4} x + b[/tex]

We substitute the point to find "b":

[tex]5 = \frac {1} {4} (4) + b\\5 = 1 + b\\b = 5-1\\b = 4[/tex]

Finally, the equation is:

[tex]y = \frac {1} {4} x + 4[/tex]

Answer:

[tex]y = \frac {1} {4} x + 4[/tex]

Answer:

-5x

Step-by-step explanation:

Answer:

-5x

Step-by-step explanation:

-4x-x --------------> factor out the x

= (-4-1) x

= -5x

Answer:

2/3

Step-by-step explanation:

We can find the slope of the line by using points

We have 2 points (-2,0) and (1,2)

Using the formula for slope

m = (y2-y1)/(x2-x1)

   = (2-0)/(1--2)

  = 2/(1+2)

  = 2/3

Answer:

Slope of JK = -4/5

Step-by-step explanation:

We know that GHJK is a parallelogram. If GHJK is a parallelogram then the sides of parallelogram will be:

GH, HJ, JK, GK

Hence the opposite sides will be:

GH and JK

HJ and GK

We know that opposite sides of parallelogram are parallel to each other and the slopes of parallel lines is equal.

So the slope of GH and JK will be equal.

And slopes of HJ and GK will be equal.

As we are given the slope of GH which is -4/5, the slope of JK will also be -4/5 because both lines are parallel.

Answer:

x = -1, 1, -5 , 5.

Step-by-step explanation:

x4 – 26x2 + 25 = 0

Factoring:

(x^2 - 25)(x^2 - 1) = 0

So x^2 - 25 = 0 gives x^2 = 25 and x = +/- 5.

x^2 - 1  gives  x^2 = 1 and x = +/- 1.

Follow below steps:

To solve the equation x4 − 26x2 + 25 = 0, we can use substitution to simplify the equation. Let's set u = x2, which turns our equation into a quadratic form: u2 − 26u + 25 = 0.

Now, we apply the quadratic formula where a = 1, b = -26, and c = 25 to find the values of u. The quadratic formula is u = (-b ± √(b2 - 4ac))/(2a). Substituting the values, we get the roots for u which are u = 25 and u = 1.

Now we substitute back for x by setting x2 = u, which gives us two separate equations to solve: x2 = 25 and x2 = 1. Solving these, we find the solutions for x to be x = 5, x = -5, x = 1, and x = -1.

the assumption being that the endpoints are two continuous points in the pentagon, Check picture below.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[2-(-1)]^2+[3-4]^2}\implies d=\sqrt{(2+1)^2+(3-4)^2} \\\\\\ d=\sqrt{9+1}\implies d=\sqrt{10}~\hfill \stackrel{\stackrel{~\hfill \stackrel{\textit{5 sides}}{}}{\textit{perimeter of the pentagon}}}{5\sqrt{10}}[/tex]

Answer:

The relationship between cell phone use and cancer is difficult to determine.

Step-by-step explanation:

Its pretty difficult to determine the relationship between using your phone and cancer, and how they correspond to each other.

Answer:

The relationship between cell phone use and cancer is difficult to determine.

Step-by-step explanation:

There has been always a conflicting conclusions whether there is a relationship between a cell phone and the cause of brain cancer. Many years of studies by the scientist and the neurologist on the relation on cellphones and cancer have resulted in controversial arguments.

Thus, the most significant weakness in this type of study is the relationship between cell phone use and cancer is difficult to determine.

Answer:

Z°= 88.36

Tan-1×35=88.36

Answer:

z = 38 degrees

Step-by-step explanation:

As we can see in the picture that the triangle is a right angle triangle and two of the angles are known.

We also know that the sum of internal angles of a triangle is 180 degrees.

We know that one angle is 90 degrees and second is 52 degrees.

So,

Sum of three angles = 180 degrees

90 + 52 + z = 180

z = 180 - 90 - 52

z = 38 degrees ..

Answer:

I would go with A. 3(4 + 7) acres

Step-by-step explanation:

Easy, the expression is equivalent to the sum of two areas... Beans and the Squash... you just add them all together and you get 33 acres. Add the parenthesis first and then multiply by 3 you get 33

Answer:

the answer is 3(4+7

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Given

a cos2x

b

2sinxcosx = sin2x

c

2cos²x - 1 = cos2x

d

1 - 2sin²x = cos2x

b is the expression not equal to the others

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

Note

cos2x = cos²x - sin²x = cos²x - (1 - cos²x) = 2cos²x - 1

cos2x = (1 - sin²x) - sin²x = 1 - 2sin²x

ANSWER

See explanation

EXPLANATION

If we can simplify the first fraction to obtain the second fraction, then the two fractions are equivalent pairs

EQUIVALENT PAIRS

[tex] \frac{32}{4} \: and \: \frac{8}{1} [/tex]

[tex]\frac{36}{6} \: and \: \frac{6}{1} [/tex]

[tex]\frac{35}{7} \: and \: \frac{5}{1} [/tex]

NOT EQUIVALENT PAIRS

[tex]\frac{18}{3} \: and \: \frac{9}{1} [/tex]

[tex]\frac{20}{5} \: and \: \frac{3}{1} [/tex]

[tex]\frac{100}{10} \: and \: \frac{5}{1} [/tex]

Answer:

Equivalent pairs

32/4 and 8/1

36/6 and 6/1

35/7 and 5/1

Not Equivalent pairs

18/3 and 9/1

20/5 and 3/1

100/10 and 5/1

Step-by-step explanation:

Equivalent pairs: Those pairs that are different fractions but represent the same number.

1. 18/3 and 9/1

18/3 can be simplified into 6/1

so, 18/3 and 9/1 are not equivalent pairs

2. 32/4 and 8/1

32/4 can be simplified into 8/1

so, 32/4 and 8/1 are equivalent pairs

3. 36/6 and 6/1

36/6 can be simplified into 6/1

so, 36/6 and 6/1 are equivalent pairs

4. 20/5 and 3/1

20/5 can be simplified into 4/1

so, 20/5 and 3/1 are not equivalent pairs

5. 35/7 and 5/1

35/7 can be simplified into 5/1

so, 35/7 and 5/1 are equivalent pairs

6. 100/10 and 5/1

100/10 can be simplified into 10/1

so, 100/10 and 5/1 are not equivalent pairs

Answer:

It is A

Step-by-step explanation:

2x + y = 5

y + 3 = 2x

From equation 2:

y = 2x - 3

Substituting in the first equation:

2x + 2x - 3 = 5.

Answer:

2x + 2x - 3 = 5.

Step-by-step explanation:

Answer:

   3a^2  +    2b^2

= ----------------------

          abc

Step-by-step explanation:

 3a           2b

------- +  ----------

 bc           ac

   3a^2  +    2b^2

= ----------------------

          abc

Answer:

(5, 8)

Step-by-step explanation:

f(x) + 4 is the graph of f(x) translated 4 units vertically up

given (5, 4) is a point on f(x), then the coordinates of the corresponding point

x- coordinate remains unchanged and add 4 to the y- coordinate

The corresponding point on f(x) + 4 is (5, 4 + 4) = (5, 8)

Answer:

(x+1)^2+(y+4)^2=9

Step-by-step explanation:

First equation in what I like to call center-radius form is (x-h)^2+(y-k)^2=r^2 where (h,k) is center and r is radius.

So we are given (h,k)=(-1,-4) so we have so far that

(x+1)^2+(y+4)^2=r^2

Passes through the point (-1,-1) means at some point (x,y) takes on the point (-1,-1) so guess what we are going to find r^2 by plugging in that point where x and y are.

(-1+1)^2+(-1+4)^2=r^2

(0)^2+(3)^2=r^2

9=r^2

so the equation of the circle is (x+1)^2+(y+4)^2=9

Answer:

(x + 1)² + (y + 4)² = 9

Step-by-step explanation:

The equation of a circle is:

(x - h)² + (y - k)² = r²

where (h, k) is the center and r is the radius.

The center is (h, k) = (-1, -4).  The radius is the distance from the center to any point on the circle.  (-1, -1) is 3 units above the center, so r = 3.

(x + 1)² + (y + 4)² = 9

Answer:

B.

Step-by-step explanation:

It is just common sense. The top numbers have to be smaller than the top numbers