Simplify 5^-4 over 5^3

Answer:

   3a^2  +    2b^2

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

          abc

Step-by-step explanation:

 3a           2b

------- +  ----------

 bc           ac

   3a^2  +    2b^2

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

          abc

Answer:

y = x³ + 2x² - 13x + 10

Step-by-step explanation:

Given

y = (x + 5)(x - 1)(x - 2) ← expand (x - 1)(x - 2)

  = (x + 5)(x² - 2x - x + 2)

  = (x + 5)(x² - 3x + 2)

Multiply each term in the second factor by each term in the first factor

= x(x² - 3x + 2) + 5(x² - 3x + 2) ← distribute both parenthesis

= x³ - 3x² + 2x + 5x² - 15x + 10 ← collect like terms

y = x³ + 2x² - 13x + 10

Answer:

1.25

Step-by-step explanation:

Calculate the scale factor as the ratio of corresponding sides of the image to the original.

here the corresponding sides are

image = 5 and original = 4

scale factor = [tex]\frac{5}{4}[/tex] = 1.25

Answer:

B

Step-by-step explanation:

A. (1, 2), (1,-2), (3, 2), (3, 4)

B. (1,6), (2, 7),(4,9), (0,5)

C. (0, 2), (2,3), (0, -2), (4,1)

D. (2, 4), (0, 2), (2, - 4), (5,3)

Theres no repeating x value.

B. (1,6), (2, 7),(4,9), (0,5) this ordered pairs is a function.

In mathematics, an expression, rule, or law defines the relationship between one variable (independent variable) and another (dependent variable). Functions are ubiquitous in mathematics and are essential for formulating the physical relationships of the natural sciences.

The types of functions can be broadly classified into four types. Based on elements: one-to-one function, many-to-one function, on-function, one-to-one and on-function, in-function. You can set the relationship as a table of ordered pairs. Then test that each element in the domain exactly matches one element in the range. If so, you have the feature!

Learn more about function here: https://brainly.com/question/2328150

#SPJ2

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).

https://brainly.com/question/20566728

#SPJ3

The complete Question is given below:

Write as a complex number in standard form 3cis210

Answer:

m = 12

Step-by-step explanation:

[tex]\frac{m+18}{m}[/tex]=[tex]\frac{5}{2}[/tex]

2(m+18) = 5(m)

2m + 36 = 5m

2m - 5m = -36

-3m = -36

m = 12

Answer:

Step-by-step explanation:

(m + 18) / m = 5/2

Do you know what cross multiplication is for a proportion? It means that you take the top of one fraction and multiply it by the bottom of the other fraction.

So for this question

5 (top right) * m (bottom left)

and put an equal sign

5*m =

Now take the top left and multiply by the bottom right.

2 * (m + 18)

Now equate the two results.

5m = 2*(m + 18)          Remove the brackets.

5*m = 2*m + 2*18       Combine the right.

5m = 2m + 36             Subtract 2m from both sides.

5m-2m=2m-2m+36    Combine

3m = 36                       Divide both sides by 3

3m/3 = 36/3

m = 12

Answer:

-2/3

Step-by-step explanation:

We need to put in slope intercept form..

Once we identify the slope of the line given, we can find the slope of the perpendicular line which is the opposite reciprocal of the slope for the given equation:

Let's do this:

2y-3x=86

add 3x on both sides to get 2y by itself

2y=3x+86

divide both sides by 2

y=3/2 x+43

So the slope is 3/2

The opposite reciprocal of 3/2 is -2/3 .

The answer is -2/3

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:

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: [tex]x=2[/tex]

Step-by-step explanation:

According to the Intersecting Secants Theorem, when two secants intersect each other outside a circle, then the products of their segments are equal.

Based on this, we can write this expression:

[tex](3)(3+5)=(4)(4+x)[/tex]

Knowing this, we can solve for "x". Therefore, this is:

[tex](3)(8)=(4)(4+x)\\\\24=16+4x\\\\24-16=4x\\\\8=4x\\\\\frac{8}{4}=x\\\\x=2[/tex]

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:

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:

Step-by-step explanation:

For a trinomial ax² + bx + c = 0, the discriminant is b² − 4ac.

If the discriminant is positive, there are 2 real solutions.

If the discriminant is 0, there is 1 real solution.

If the discriminant is negative, there are no real solutions.

a) x² − 4x − 7 = 0

Here, a = 1, b = -4, and c = -7.

b² − 4ac = (-4)² − 4(1)(-7) = 44

The discriminant is positive, so there are 2 real solutions.

b) 4r² + 11r − 3 = 0

Here, a = 4, b = 11, and c = -3.

b² − 4ac = (4)² − 4(11)(-3) = 148

The discriminant is positive, so there are 2 real solutions.

c) 3m² + 7 = 0

Here, a = 3, b = 0, and c = 7.

b² − 4ac = (0)² − 4(3)(7) = -84

The discriminant is negative, so there are no real solutions.

d) t² + 2t + 1 = 0

Here, a = 1, b = 2, and c = 1.

b² − 4ac = (2)² − 4(1)(1) = 0

The discriminant is zero, so there is 1 real solution.

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.

To know more about triangle click here :

https://brainly.com/question/30367378

#SPJ2

Answer:

L=130 while W=39

Step-by-step explanation:

Let's setup some equations.

W=.3L  from first sentence

2L+2W=338 from second sentence

I'm going to plug equation 1 into equation 2:

2L+2[.3L]=338

2L+.6L=338

2.6L=338

L=338/2.6

L=130

so W=.3L=.3(130)=39

Answer L=130 while W=39

Length of the rectangle = 130

Width of the rectangle = 39.

Given: that the width of a rectangle exists 30% of the length.

Where Perimeter = 338 ft

Width of the rectangle = 0.3L

Perimeter = 2(Length + Width)

Substitute the value of perimeter in the above equation, we get

2L + 2W = 338

2L + 2[0.3L] = 338

2L + 0.6L=338

2.6L = 338

L = 338/2.6

L = 130

Length of the rectangle = 130

So, Width of the rectangle = 0.3L

= 0.3(130) = 39

The length of the rectangle is 130 and the width of the rectangle is 39.

To learn more about the length and width of the rectangle

https://brainly.com/question/2863975

#SPJ2

The term STR is not sufficiently defined in the question. It could represent a mathematical concept, an angle in geometry, or a term in physics or engineering. Without any context, it's not possible to give a precise answer.

It appears that there is some confusion in your question, as the term STR is not sufficiently defined. In general, STR could refer to a mathematical concept, a geometric angle, or a term in engineering. However, without context, it's challenging to provide a correct answer.

If STR represents 'Stress', 'Tensile Ratio', or 'Tensile Strength Ratio' in an engineering sense, it would refer to a measure of deformation due to tension. If STR stands for an angle in a triangle, it would need the triangle's full details to be calculated properly. It would be more beneficial if you could provide added context, so I could give you a more accurate response.

https://brainly.com/question/31942445

#SPJ3

Answer: 4.24264069

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

Answer:

9 cm

Step-by-step explanation:

Find the area of the 1st triangle

A=1/2 b*h

1/2 3*3

1/2 9

4.5

Find the area of the 2nd triangle

A=1/2 b*h

1/2 3*3

1/2 9

4.5

Both triangles have an area of 4.5

To find the area of the parallelogram you have to add the area of the triangles

4.5+4.5=9

A= 9 cm

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:

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:

10 hours.

Step-by-step explanation:

2 cartoon strips takes 5 hours

divide 5 by 2 to give us how much time is used for 1 strip

5/2 = 2.5 which is equal to 1 strip

Now the question is asking you how much will time for 4 strips?

Take 4 and multiply it by 2.5

4x2.5 = 10

Caroline sketches at a rate of 2 strips in 5 hours, so to sketch 4 strips, which is twice as many, it will take her twice the time, resulting in 10 hours.

To calculate how long it will take Caroline to sketch 4 cartoon strips, we first determine her rate of sketching, which is 2 strips in 5 hours. Therefore, her rate is 2/5 strips per hour. To find out how long it takes to sketch 4 strips, we can set up a proportion where the number of strips is directly proportional to the hours spent. Since she sketched 2 strips in 5 hours, sketching 4 strips will be twice the amount of strips, thus it should take her twice the time, hence 5 hours times 2. Therefore, Caroline will take 10 hours to sketch 4 strips.

https://brainly.com/question/14305692

#SPJ2

Answer:division property of equality

Step-by-step explanation: Because 0.36x divided by 0.36 is 1x. -1.8 divided by 0.36 is -5. Couuld you give me brainleist

Answer:

Division Property of Equality

Step-by-step explanation:

Addition Property of Equality :

a = b ⇒ a + c = b + c

Subtraction Property of Equality

a = b ⇒ a - c = b - c

Multiplication Property of Equality :

a = b ⇒ ca = cb,

Division Property of Equality :

[tex]a=b\implies \frac{a}{c}=\frac{b}{c}[/tex],

Here, the given equation is,

0.36x=-1.8,

For finding the value of x we need to isolate x,

For this we must divide both sides by 0.36,

That is, we were applied 'Division Property of Equality'.

Answer:

A

Step-by-step explanation:

Between 4 and 5 where the vertex is. The axis of symmetry is a line going through the vertex. For a while it will be of the form x = a

In this case, the axis of symmetry is x = 4.5

Answer:

-3.2

Step-by-step explanation:

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:

[tex]\large\boxed{V=3780\ in^3}\\\boxed{S.A.=1827\ in^2}[/tex]

Step-by-step explanation:

The formula of a volume of a prism:

[tex]V=BH[/tex]

B - base area

H - height

In the base we have the right triangle. The formula of an area of a right triangle:

[tex]A=\dfrac{(a)(b)}{2}[/tex]

a, b - legs

We have a = 14in and b = 22.5in. Substitute:

[tex]B=\dfrac{(14)(22.5)}{2}=157.5\ in^2[/tex]

H = 24in.

Calculate the volume:

[tex]V=(157.5)(24)=3780\ in^3[/tex]

The Surface Area:

We have

(1) two right triangles with area 157.5 in²

(2) three rectangles 24 in × 14 in, 24 in × 22.5 in, 24 in × 26.5 in.

Calculate the areas of the rectangles:

[tex]A_1=(24)(14)=336\ in^2\\\\A_2=(24)(22.5)=540\ in^2\\\\A_3=636\ in^2[/tex]

The Surface Area:

[tex]S.A.=2B+A_1+A_2+A_3\\\\S.A.=(2)(157.5)+336+540+636=1827\ in^2[/tex]

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x-3y=-1&\text{multiply both sides by (-3)}\\11x-9y=-13\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-6x+9y=3\\11x-9y=-13\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=-10\qquad\text{divide both sides by 5}\\.\qquad x=-2\\\\\text{put the value of x to the first equation:}\\\\2(-2)-3y=-1\\-4-3y=-1\qquad\text{add 4 to both sides}\\-3y=3\qquad\text{divide both sides by (-3)}\\y=-1[/tex]

Answer:

A on edge

Step-by-step explanation: