what is equivalent to (3+5i) - (7-2i)

Answer:

The correct answer option is f(x) = 3^(x+3).

Step-by-step explanation:

We are to determine whether which of the given answer options represent the given graph.

A graph which has a similar shape like that of the given graph here (big on the left and crawling along the x-axis on the right) represents the exponential growth or decay.

Therefore, the only correct option we have here is f(x) = 3^(x+3).

Answer:

Step-by-step explanation:

We know that the diagonals of the parallelogram intersect in half.

Therefore we hawe the equation:

x - 30 = -9 - 6x              add 30 to both sides

x = 21 - 6x              add 6x to both sides

7x = 21            divide both sides by 7

x = 3

X=3 hope this helps sorry if I’m wrong

Answer:

Final answer is 1/8.

Step-by-step explanation:

Total number cards in deck of cards = 52

Total number of cards with a letter = 16

Total number of cards with red King and letter both = 2

Then probability of getting card with letter P(L) = 16/52

Then probability of getting card with letter and king both  P(K and L) = 2/52

Then required compound probability P(K|L) is given by formula:

P(K and L)= P(L)*P(K|L)

2/52= 16/52*P(K|L)

(2/52)*(52/16)=P(K|L)

2/16=P(K|L)

1/8=P(K|L)

Hence final answer is 1/8.

The answer is:

The solution to the equation is:

[tex]x=6[/tex]

To solve the problem, we must remember how to operate with fractions.

So, adding fractions we have:

[tex]\frac{a}{b}+-\frac{c}{d}=\frac{(a*d)+-(b*c)}{b*d}[/tex]

Now, we are given the expression:

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

So, solving we have:

[tex]\frac{3}{x} +\frac{1}{3}=\frac{5}{6}\\\\\frac{3}{x}=\frac{5}{6}-\frac{1}{3}\\\\\frac{3}{x}=\frac{(5*3)-(6*1)}{6*3}\\\\\frac{3}{x}=\frac{15-6}{18}\\\\\frac{3}{x}=\frac{9}{18}\\\\\frac{3}{x}=\frac{1}{2} \\\\3*2=1*x\\\\x=6[/tex]

We have that the solution to the equation is:

[tex]x=6[/tex]

Answer with explanation:

Volume of a solid right pyramid with a square base = V (units)³

                            -------------------------------------(1)

The Solid right pyramid will be in the shape of Cube.

Length of edge of Right Pyramid = y units

So,Volume of Right Pyramid which is in the shape of Cube

= (Side)³

=y³ (Units)³

                           ---------------------------------(2)

   Equating (1) and (2)

[tex]\Rightarrow y^3=V[/tex]

Answer:

B) x + 1/y times h/g+1

Step-by-step explanation:

We need to divide [tex]\frac{x+1}{y}[/tex] by [tex]\frac{g+1}{h}[/tex] then match with given choices to find the correct equivalent result.

where given choices are:

A) x/y times h/g

B) x + 1/y times h/g+1

C) x+ 1/y divided h/g+1

D) y/x+1 divided g+1/h

So let's divide  [tex]\frac{x+1}{y}[/tex] by [tex]\frac{g+1}{h}[/tex]

[tex]\frac{\left(\frac{x+1}{y}\right)}{\left(\frac{g+1}{h}\right)}[/tex]

we are allowed to flip the bottom fraction and change division sign into multiplication. So we get:

[tex]=\left(\frac{x+1}{y}\right)\cdot\left(\frac{h}{g+1}\right)[/tex]

Hence correct choice is: B) x + 1/y times h/g+1

Let's start by simplifying the given expression step-by-step:
\[ \text{Given Expression:} \quad \frac{x + \frac{1}{y}}{g + \frac{1}{h}} \]
Firstly, we will find a common denominator for the numerator and denominator of the given fraction.
For the numerator, we already have a single term x and a fraction \( \frac{1}{y} \), which can be combined without altering the denominator.
For the denominator, we have term g and a fraction \( \frac{1}{h} \). To combine these, we need to multiply both terms by h to get a common denominator.
So, the expression becomes:
\[ \frac{x + \frac{1}{y}}{g + \frac{1}{h}} = \frac{xy + 1}{y} \cdot \frac{h}{gh + 1} \]
Next, we will multiply the separated fractions across the numerator and the denominator:
\[ \frac{xy + 1}{y} \cdot \frac{h}{gh + 1} = \frac{(xy + 1) \cdot h}{y \cdot (gh + 1)} \]
Now, let's consider the given options and check which one is equivalent to our simplified expression:
Option A) \( \frac{x}{y} \times \frac{h}{g} \)
This option simplifies to \( \frac{xh}{yg} \), which is not equivalent to the expression we have because we have \( xy + 1 \) in the numerator, not just \( xh \).
Option B) \( (x + \frac{1}{y}) \times \frac{h}{g+1} \)
For this option, if we simplify, we do not obtain a single fraction with the term \( xy + 1 \) in the numerator and \( y(gh + 1) \) in the denominator, instead, this option gives us \( xh + \frac{h}{y(g+1)} \), which is different from our simplified expression.
Option C) \( \frac{x + \frac{1}{y}}{h/(g + 1)} \)
To simplify this option, we take the reciprocal of the denominator and multiply it with the numerator:
\[ \frac{x + \frac{1}{y}}{h/(g + 1)} = (x + \frac{1}{y}) \times \frac{g + 1}{h} \]
\[ = \frac{(x + \frac{1}{y})(g + 1)}{h} \]
\[ = \frac{xg + x + \frac{g}{y} + \frac{1}{y}}{h} \]
\[ = \frac{xg + x + \frac{g + 1}{y}}{h} \]
This is not equivalent to our simplified expression either because it involves terms like \( xg \) and \( x \), which do not appear in our expression and does not fit the form \( \frac{(xy + 1) \cdot h}{y \cdot (gh + 1)} \).
Option D) \( \frac{y/(x+1)}{g + \frac{1}{h}} \)
To simplify this option, we multiply by the reciprocal of the denominator:
\[ \frac{y/(x+1)}{g + \frac{1}{h}} = \frac{y}{x+1} \times \frac{h}{gh + 1} \]
\[ = \frac{yh}{(x+1)(gh + 1)} \]
Again, this is not equivalent to our simplified expression, since the expressions \( y/(x+1) \) and \( (xy + 1)/y \) are different.
None of the options (A, B, C, or D) match the simplified form:
\[ \frac{(xy + 1) \cdot h}{y \cdot (gh + 1)} \]
Therefore, none of the given options are equivalent to the original expression \( \frac{x + \frac{1}{y}}{g + \frac{1}{h}} \).

Answer:yes that is the right answer

Step-by-step explanation:

Hello!

Answer:

x = 7

Step-by-step explanation:

Substitute y = 4 into the equation and solve for x

8x - (2 × 4) = 48

8x - 8 = 48 ( add 8 to both sides )

8x = 56 ( divide both sides by 8 )

x = 7

Answer:

Square root of 21 + 4 = w

Step-by-step explanation:

Answer: [tex]x^2+4x-21=0[/tex]

Step-by-step explanation:

You need to remember that formula for calculate the area of a rectangle:

[tex]A=lw[/tex]

Where "l" is the lenght and "w" is the width.

You know that "x" represents the width of the doghouse, its rectangular base has an area of 21 square feet ([tex]A=21[/tex]) and its length is 4 feet more than its width ([tex]l=x+4[/tex])

Then, substituting into the formula, you get:

[tex]21=(x+4)(x)[/tex]

Simplifying, you get the following  that can be used to determine the possible dimensions of the base of the doghouse:

[tex]21=x^2+4x[/tex]

[tex]x^2+4x-21=0[/tex]

the easiest to solve for is y in the first equation

Answer:

the easiest to  for y in the first equation

Step-by-step explanation: -3

[tex]\bf \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \\\\[-0.35em] \rule{34em}{0.25pt}\\[1em] [\log(3)-\log(4)]-\log(2)\implies \log\left( \cfrac{3}{4} \right)-\log(2)\implies \log\left( \cfrac{\frac{3}{4}}{~~2~~} \right) \\\\\\ \log\left( \cfrac{\frac{3}{4}}{~~\frac{2}{1}~~} \right)\implies \log\left( \cfrac{3}{4}\cdot \cfrac{1}{2} \right)\implies \log\left( \cfrac{3}{8} \right)[/tex]

To write the expression as a single logarithm, we'll use the properties of logarithms to combine them. The given expression is:
(log3 - log4) - log2
We start by combining the first two logarithms inside the parenthesis using the difference of logarithms property:
log(a) - log(b) = log(a/b)
Applying this property to (log3 - log4), we get:
log(3/4)
Now, our expression looks like this:
log(3/4) - log2
We can use the same property to combine this with the remaining logarithm:
log(a) - log(b) = log(a/b)
So we apply it with a = 3/4 and b = 2:
log((3/4)/2)
When dividing by 2, we are effectively multiplying by 1/2, so we have:
log(3/4 * 1/2)
Now we perform the multiplication inside the logarithm:
log(3/8)
And that is the expression written as a single logarithm:
log(3/8)

Answer:

B

Step-by-step explanation:

A translation of 3 units up, means adding 3 to the y- coordinate of the original points while the x- coordinates remain unchanged, that is

S(1, 1) → S'(1, 1 + 3) → S'(1, 4)

T(2, - 3) → T'(2, - 3 + 3) → T'(2, 0)

U(4, 0) → U'(4, 0 + 3) → U'(4, 3)

Esther should save $125 each month to reach her goal of $3,000 in 2 years.

Esther wants to save $3,000 in 2 years and is determining the fixed monthly amount she should contribute to her savings. To find the monthly savings amount, we must divide the total savings goal by the total number of months in 2 years.

Total amount to save: $3,000
Total number of months: 2 years x 12 months/year = 24 months

Fixed monthly saving amount = Total savings goal / Total number of months
Fixed monthly saving amount = $3,000 / 24
Fixed monthly saving amount = $125

Answer:

It is 2, 4, & 5.

Step-by-step explanation:

just got it right on edge.

Answer:

The length of the rectangular pen is [tex]40\ ft[/tex]

The width of the rectangular pen is [tex]20\ ft[/tex]

Step-by-step explanation:

Let

x-----> the length of the rectangular pen

y----> the width of the rectangular pen

we know that

The perimeter of the rectangular pen in this problem is equal to

[tex]P=x+2y[/tex] ---> remember that one side of the rectangle won’t need a fence

[tex]P=80\ ft[/tex]

so

[tex]80=x+2y[/tex]

[tex]y=(80-x)/2[/tex] -----> equation A

The area of the rectangular pen is equal to

[tex]A=xy[/tex] -----> equation B

Substitute equation A in equation B

[tex]A=x*(80-x)/2\\ \\A=-0.5x^{2}+40x[/tex]

The quadratic equation is a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex is the length of the rectangular pen that maximize the area of the pen

The y-coordinate of the vertex is the maximum area of the pen

using a graphing tool

The vertex is the point (40,800)

see the attached figure

so

[tex]x=40\ ft[/tex]

Find the value of y

[tex]y=(80-x)/2[/tex] ----> [tex]y=(80-40)/2=20\ ft[/tex]

therefore

The length of the rectangular pen is [tex]40\ ft[/tex]

The width of the rectangular pen is [tex]20\ ft[/tex]

Answer:

length is 40

Width is 20

Step-by-Step explanation:

Answer:

The length of NO is [tex]14\ ft[/tex]

Step-by-step explanation:

step 1

Find the value of x

we know that

The Kite  has two pairs of equal-length adjacent (next to each other) sides.

so

The perimeter is equal to

[tex]P=2[MN+NO][/tex]

[tex]P=80\ ft[/tex]

so

[tex]80=2[MN+NO][/tex]

[tex]40=[MN+NO][/tex]

substitute the values and solve for x

[tex]40=[(3x+5)+(x-7)][/tex]

[tex]40=[4x-2][/tex]

[tex]4x=42[/tex]

[tex]x=21\ ft[/tex]

step 2

Find the length of NO

[tex]NO=(21-7)=14\ ft[/tex]

the answer is 3.5987

Answer:

1. 1/4

2. 1/2

Step-by-step explanation:

If there are equal numbers of males and females, we can simplify that by saying there's one male and one female for each coat color.

1. What's the probability that both are males?

Well, there's a 1/2 chances the light-colored coat bear is a male and there's also a 1/2 chances the dark-colored coat bear is a male.  So, we can make this reference table:

Light             Dark

Male             Male

Male             Female

Female         Male

Female         Female

As you can see, the probability that both of the spotted bears are males is 1/4 (1/2 * 1/2).

2. If the light-colored bear, what are the odds both are males?

If we know for sure the light-one is male, then there's 1/2 chances the other is too, refer to the table above to verify.

For this case we have by definition, that the volume of a square base pyramid is given by:

[tex]V = \frac {1} {3} * L ^ 2 * h[/tex]

Where:

L: It's the side of the base (square side)

h: It's the height of the pyramid

Substituting:

[tex]L = 6 \ ft\\h = 10 \ ft[/tex]

[tex]V = \frac {1} {3} * (6) ^ 2 * 10\\V = \frac {1} {3} * 36 * 10\\V = 120 \ ft ^ 3[/tex]

Answer:

[tex]V = 120 \ ft ^ 3[/tex]

Answer:

[tex]\large\boxed{y-3=3(x+2)}\qquad\text{point-slope form}\\\boxed{y=3x+9}\qquad\text{slope-intercept form}\\\boxed{3x-y=-9}\qquad\text{standard form}\\\boxed{3x-y+9=0}\qquad\text{general form}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

We have the slope m = 3 and the point (-2, 3). Substitute:

[tex]y-3=3(x-(-2))\\\\y-3=3(x+2)[/tex]

the point-slope form

[tex]y-3=3(x+2)[/tex]        use the distributive property

[tex]y-3=3x+6[/tex]           add 3 to both sides

[tex]y=3x+9[/tex]

the slope-intercept form

[tex]y=3x+9[/tex]           subtract 3x from both sides

[tex]-3x+y=9[/tex]         change the signs

[tex]3x-y=-9[/tex]

the standard form

[tex]3x-y=-9[/tex]              add 9 to both sides

[tex]3x-y+9=0[/tex]

the general form

Answer:

[tex]\large\boxed{a=-\dfrac{1}{10}=0.1}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3=10a+b\\2=20a+b&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3=10a+b\\-2=-20a-b\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad1=-10a\qquad\text{divide both sides by (-10)}\\.\qquad-\dfrac{1}{10}=a\Rightarrow a=-\dfrac{1}{10}[/tex]

Answer:

this is in copy and paste form a = - 1/10 - 1.0

.140 I think it's that

Answer:

Step-by-step explanation:

Total number of marbles = 6 + 3 + 5 = 14

You want to draw out 3 marbles -- all of them red. In solving this, you have to assume that none are put back.

The answer is

P(Red) = 6/14 * 5/13 * 4/12

P(Red) = 3/7 + 5/13 + 1/3

numerator = 3*5*1 = 15

denominator = 7 * 13 * 3

denominator = 273

P(red) = 15 / 273

P(red) = 0.0549

Answer: [tex]x=11[/tex]

Step-by-step explanation:

Remembert that, by definition:

[tex]log_b(x)=y[/tex] → [tex]b^y=x[/tex]

Then, you can rewrite [tex]log_4(2x-6)=2[/tex] in exponential form:

[tex]4^2=2x-6[/tex]

Now you can solve for the variable "x":

Add 6 to both sides of the equation:

[tex]4^2+6=2x-6+6[/tex]

[tex]22=2x[/tex]

And finally you must divide both sides of the equation by 2, then:

[tex]\frac{22}{2}=\frac{2x}{2}\\\\x=11[/tex]

Answer:

Step-by-step explanation:

This shows step by step

Hope this helps <3

-1≤x≤3

i did that test

Good Luck

7.602 rounded to the nearest whole number would be 8.

Given is the number as -

7.602

We can round of the number to the nearest whole number as -

7.602

7.60

7.6

8

Therefore, 7.602 rounded to the nearest whole number would be 8.

To solve more questions on algebraic expressions, visit the link below-

brainly.com/question/1041084

#SPJ6

Answer:

Step-by-step explanation:

Put x = -3 to the equation of the function h(x) = x² - 2:

h(-3) = (-3)² - 2 = 9 - 2 = 7

Answer:

The measure of the central angle is 35° to the nearest degree

The area of the triangle formed is 28.7 inches²

Step-by-step explanation:

* Lets revise the cosine rule to solve the question

- In Δ ABC:

# AB² = BC² + AC² - 2(BC)(AC) cos∠C

- If you want to find m∠C, we can rearrange the rule

# cos∠C = BC² + AC² - AB²/2(BC)(AC)

* Now lets solve the problem

- The length of the radius of the circle is 10 inches

- The length of the chord is 6 inches

- The chord and the two radii drawn to the endpoints of the chord

 formed an isosceles triangle and the angle between the two radii

 is the central angle

- Lets use the cosine rule to find the measure of the central angle

- Let the name of the central angle is Ф

∵ cos Ф = r² + r² - (chord)²/2(r)(r)

∵ r = 10 inches and the chord = 6 inches

∴ cos Ф = (10)² + (10)² - (6)²/2(10)(10)

∴ cos Ф = (100+ 100 - 36)/200

∴ cos Ф = 164/200 = 41/50

- Find the measure of the Ф by using cos^-1 Ф

∴ m∠Ф = cos^-1 (41/50) ≅ 35°

* The measure of the central angle is 35° to the nearest degree

- To find the area of the triangle we will use the sine rule

# Area of any triangle by using the sine rule is

  A = 1/2 × (s1 × s2) × sin the included angle between them

∵ s1 = r , s2 = r and the angle between them is the central angle Ф

∴ Area of the triangle = 1/2 (r × r) × sin Ф

∵ r = 10 and Ф = 35°

∴ Area of the triangle = 1/2 × (10 × 10) × sin 35°

∴ Area of the triangle = 50(sin 35°) ≅ 28.7 inches²

* The area of the triangle formed is 28.7 inches²

Answer:

115°

Step-by-step explanation:

A triangle always has 3 angles, and thew sum of the angles is always 180°. Therefore,

38° + 27° + x° = 180°

65° + x° = 180°

x° = 115°

Answer:

0=0

Step-by-step explanation:

When you  combine both expressions  you multiply the first one  by -3

As result all the terms in the second expression are cancelled when both expressions are added

-3x -6y = -30

3x  + 6y =30

0   +  0  = 0

5(0)-5y=4

-5y=4

y=-4/5

the answer is 4/5

i hope this could help!!