Choose the set of equations that best represent the following information:

The sum of two numbers, a and b, is 12. The first number, a, is 8 more than the second number.

A. ab = 12, a + 8 > b
B. a + b = 12, a = b + 8
C. a + a = 12, b - 8 = a
D. a + b = 8, a > b + 12

Answer:

The total area of the five rooms = 3 × 13² + 2 × 15² ⇒ answer A

Step-by-step explanation:

* lets revise the area of the square

- The area of any square is (the length of its side)²

- We have five room

- Three of them have side length 13 feet each

- Two of them have side length 15 feet each

* lets find the total area of the five room

- The area of the three rooms of side length 13 feet

∵ The length of the side of each square is 13 feet

∴ The area of each room of the three = 13²

∴ The total area of the three rooms = 3 × 13² feet² ⇒ (1)

- The area of the two rooms of side length 15 feet

∵ The length of the side of each square is 15 feet

∴ The area of each room of the two = 15²

∴ The total area of the three rooms = 2 × 15² feet² ⇒ (2)

- To find the area of the five rooms and (1) and (2)

∴ The total area of the five rooms = 3 × 13² + 2 × 15²

Answer:

A. [tex](3*13^2)+(2*15^2)[/tex]

Step-by-step explanation:

The area of a square can be calculated with this formula:

[tex]A=s^2[/tex]

Where "s" is the lenght of any side of the square.

You know that any side of three square rooms measure 13 feet each and any side of two square rooms measure 15 feet each.

Let be [tex]s_1[/tex] the lenght of any side that measures 13 feet and and [tex]s_2[/tex]  the lenght of any side that measures 15 feet.

Then, the total area will be:

[tex]A_{total}=3(s_1)^2+2(s_2)^2\\\\A_{total}=(3*13^2)+(2*15^2)[/tex]

Therefore, the expression that shows the total area of these five rooms is the expression shown in the option A.

If I am correct the best option would be answer B

Answer:

[tex]\large\boxed{8n^{18}}[/tex]

Step-by-step explanation:

The formula of an area of a square:

[tex]A=s^2[/tex]

s - side length

We have

[tex]A=64n^{36}[/tex]

Method 1:

Substitute:

[tex]s^2=64n^{36}[/tex]

[tex]s^2=8^2n^{18\cdot2}[/tex]            use [tex](a^n)^m=a^{nm}[/tex]

[tex]s^2=8^2(n^{18})^2[/tex]         use [tex](ab)^n=a^nb^n[/tex]

[tex]s^2=(8n^{18})^2\to s=8n^{18}[/tex]

Method 2:

Substitute:

[tex]s^2=64n^{36}\to s=\sqrt{64n^{36}}[/tex]   use [tex]\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]

[tex]s=\sqrt{64}\cdot\sqrt{n^{36}}[/tex]

[tex]s=8\sqrt{n^{(18)(2)}[/tex]     use [tex](a^n)^m=a^{nm}[/tex]

[tex]s=8\sqrt{(n^{18})^2}[/tex]      use [tex]\sqrt{a^2}=a[/tex] for [tex]a\geq0[/tex]

[tex]s=8n^{18}[/tex]

Answer:

Step-by-step explanation:

1.

x= 18 y= 3

2.

x= -5 y=1

The answer is:

The rewritten expression is:

[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]

To solve this problem we need to use the trigonometric identity of the double angle for the cosine which states that:

[tex]cos(2\alpha)=cos^{2}(\alpha)-sin^{2}(\alpha)[/tex]

Also, if we want to rewrite only with terms of cos(x) and sin(x), we can apply the following property:

[tex](a^{2} -b^{2})=(a+b)(a-b)[/tex]

So, rewriting the trigonometric equation, we have:

[tex]cos^{2}(\alpha)-sin^{2}(\alpha)=(cos(x)+sin(x))*(cos(x)-sin(x))[/tex]

Then, we are given the expression:

[tex]cos(2x)+sin(x)[/tex]

Now, rewriting the given expression with only sin(x) and cos(x), we have:

[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]

Hence, the answer is:

[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]

Have a nice day!

Answer:

Function represents decay.

[tex]V(t)=3000(0.70)^t[/tex]

Step-by-step explanation:

Given that the value of a $3000 computer decreases about 30% each year. Now we need to write a function for the computers value V(t). then determine if the function represent growth or decay.

It clearly says that value decreases so that means function represents decay.

For decay we use formula:

[tex]A=P(1-r)^t[/tex]

where P=initial value = $3000,

r= rate of decrease =30% = 0.30

t= number of years

A=V(t) = future value

so the required function is [tex]V(t)=3000(1-0.30)^t[/tex]

or [tex]V(t)=3000(0.70)^t[/tex]

Answer:

second option

Step-by-step explanation:

The triangle pairs that can be mapped to each other using a reflection and a translation are option (b).

Hence, the correct answer is option (b).

Learn more about Reflection and Translation, refer to:

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Answer:

B

Step-by-step explanation:

It is a straight line that goes through the origin

Answer:

B

Step-by-step explanation:

Answer:

Option B.  g(x)=(1/4 x)^2

Step-by-step explanation:

Answer:

Option B.) $8,123.79

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=5\ years\\ P=\$7,000\\ r=0.03\\n=2[/tex]  

substitute in the formula above  

[tex]A=\$7,000(1+\frac{0.03}{2})^{2*5}[/tex]  

[tex]A=\$7,000(1.015)^{10}=\$8,123.79[/tex]  

The worth of the investment after 5 years at an interest of 3% is $8,123.79.

As the function for interest is already given to us, also,

The principal amount, P = $7,000

The rate of Interest, r = 3%

Time period, t =  5 years

Compounded semiannually, n = 2

Substitute the values,

[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]

   [tex]=7000(1+\dfrac{0.03}{2})^{2 \times 5}\\\\=\$ 8,123.79[/tex]

Hence, the worth of the investment after 5 years at an interest of 3% is $8,123.79.

Learn more about Compound Interest:

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Answer:

Part A:

( 1.8333, -0.08333)

Part B:

x = 2 or x = 5/3

Step-by-step explanation:

The quadratic equation

[tex]3x^{2}-11x+10=0[/tex] has been given.

Part A:

We are required to determine the vertex. The vertex is simply the turning point of the quadratic function. We shall differentiate the given quadratic function and set the result to 0 in order to obtain the co-ordinates of its vertex.

[tex]\frac{d}{dx}(3x^{2}-11x+10)=6x-11[/tex]

Setting the derivative to 0;

6x - 11 = 0

6x = 11

x = 11/6

The corresponding y value is determined by substituting x = 11/6 into the original equation;

y = 3(11/6)^2 - 11(11/6) + 10

y = -0.08333

The vertex is thus located at the point;

( 1.8333, -0.08333)

Find the attached

Part B:

We can use the quadratic formula to solve for x as follows;

The quadratic formula is given as,

[tex]x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]

From the quadratic equation given;

a = 3, b = -11, c = 10

We substitute these values into the above formula and simplify to determine the value of x;

[tex]x=\frac{11+/-\sqrt{11^{2}-4(3)(10) } }{2(3)}=\frac{11+/-\sqrt{1} }{6}\\\\x=\frac{11+/-1}{6}\\\\x=\frac{11+1}{6}=2\\\\x=\frac{11-1}{6}=\frac{5}{3}[/tex]

Answer:

You don't even have to graph it.

A) X + Y -6 = 0

B) X - Y = 0

We add the equations and get:

2x -6 = 0

x = 3 and therefore, y = 3

The correct answer is the third answer (3, 3)

Step-by-step explanation:

Answer: (3, 3)

Step-by-step explanation:

Add the equations to eliminate y:

   x + y = 6

   x - y  = 0

 2x      =  6

÷2         ÷2

   x      = 3

Substitute x = 3 into either of the equations to solve for y:

x - y = 0

3 - y = 0

3      = y

We need the graph to answer.

Answer: equal 1/4

A). 1/4

Answer:

C. is the answer

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 4, thus

y = 4x + c ← is the partial equation

To find c substitute (- 4, - 5) into the partial equation

- 5 = - 16 + c ⇒ c = - 5 + 16 = 11

y = 4x + 11 → C

Answer: [tex]A=2*10^{10}m^2[/tex]

Step-by-step explanation:

The area of a rectangle can be calculated with this formula:

[tex]A=lw[/tex]

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

You know that the dimensions of this rectangle are 5*10⁵meters and 4*10⁴ meters, then you need to multiply them to get the area:

[tex]A=(5*10^5m)(4*10^4m)[/tex]

Since 10⁵ and 10⁴ have equal base, you must add the exponents:

[tex]A=20*10^{(5+4)}m^2[/tex]

[tex]A=20*10^9m^2[/tex]

Scientific notation has the form:

[tex]a*10^n[/tex]

Where "a" is any number between 1 and 10 but less than 10, and "n" is an integer.

Since 20 is greater than 10, you must move the decimal point to the left:

[tex]A=2.0*10^{10}m^2[/tex]

Rewriting the result, you get:

[tex]A=2*10^{10}m^2[/tex]

The area of the rectangular section of wilderness that will be set aside as a new wildlife refuge is [tex]2 * 10^{10[/tex] square meters

The dimensions of the rectangular section of wilderness that will be set aside as a new wildlife refuge are given as:

5 x 10^5 meters by 4 x10^4 meters

The area is the product of the dimensions.

So, we have:

[tex]Area = 5 * 10^5 * 4 * 10^4[/tex]

Evaluate the product

[tex]Area = 20 * 10^9[/tex]

Rewrite as:

[tex]Area = 2 * 10^{10[/tex]

Hence, the area of the rectangular section of wilderness that will be set aside as a new wildlife refuge is [tex]2 * 10^{10[/tex] square meters

Read more about area at:

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Answer:

y+1 = 3/5(x+3)  (point slope form)

y = 3/5x +4/5 slope intercept form

Step-by-step explanation:

Since we have a point and a slope, we can use the point slope form of the equation

y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point

y--1 = 3/5(x--3)

y+1 = 3/5(x+3)  (point slope form)

We can distribute

y+1 = 3/5x +9/5

Subtract 1 from each side

y+1-1 = 3/5x +9/5 -1

y = 3/5x +9/5 -5/5

y = 3/5x +4/5 slope intercept form

Answer:

Equation:  y = 3/5 x + 4/5

Step-by-step explanation:

y = mx + b

so

b = y - mx

passes through (-3,-1) and has a slope of 3/5

So

b = -1 - (3/5) (-3)

b = -1 + 9/5

b = - 5/5 + 9/5

b = 4/5

So equation

y = 3/5 x + 4/5

Answer:

The distance formula is really just the Pythagorean Theorem in disguise.

Step-by-step explanation:

AB=√(x2−x1)2+(y2−y1)2

Step-by-step explanation:

[tex]\text{Let}\ A(x_1,\ y_1)\ \text{and}\ B(x_2,\ y_2).\ \text{Then the distance between}\ A\ \text{and}\ B\ \text{is:}\\\\|AB|=\sqrt{(x_2-x_1)^2+(y_2-y1)^2}\\\\Example:\\\\A(2,\ 5),\ B(-1,\ 1)\\\\|AB|=\sqrt{(-1-2)^2+(1-5)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

The probability of winning a bet with odds of 7 to 8 in favor is 7/15, or approximately 46.67%.

If you are given odds of 7 to 8 in favor of winning a bet, to find the probability of winning, you need to understand the relationship between odds and probability.

Odds of 7 to 8 means that for every 8 losses, there are 7 wins.

The total number of possibilities is 7 wins + 8 losses = 15 possible outcomes.

To convert odds to probability, you divide the number of ways to win by the total number of possible outcomes:

Probability of winning = 7 wins / 15 total outcomes = 7/15.

Therefore, the probability of winning the bet is 7/15, which can be approximated as 0.4667 or 46.67%.

Hello! :)

All angles in triangles must equal 180* degrees. So there is the 90 degrees at the meter Q and you add: 43+90=133* degrees. Remember, to make 180 so you do 180-133=47* degrees. I didn’t get any answer choices but if there are, choose the closest one to 47* degrees.

Hope this helped and I hope I answered in time!

Good luck!

~ Destiny ^_^

Answer:

The value of x = 47°

Step-by-step explanation:

From the figure we can see that a circle with center O.

PQ is a tangent to the circle fro point P.

m<P = 43°

Therefore <Q = 90°

To find the value of x

From the given triangle we can write,

x + m<Q + m<P = 180

x = 180 - (m<Q + m<P)

 = 180 - (90 + 43)

 = 180 - 133 = 47°

Therefore the value of x = 47°

Answer:

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":[1]

Step-by-step explanation:

Answer:

C.) 418 cm²

I hope this helped you : )

Step-by-step explanation:

First, you find the area of the square:

19 cm x 19 cm = 361 cm

Next, you find the area of the triangle:

(19 cm x 6 cm) ÷2 =57 cm

Last, you add the two:

361 cm + 57 cm = 418 cm²

Answer:

it is C i took a quiz on it

Step-by-step explanation:

the answer is the last one because sin =opposite/hypo.

Check the picture below.

Answer:

x = 51.1 degrees

Step-by-step explanation:

As this is a right triangle, we may use Sin, Cos, and Tan in order to find this answer. Sin is defined as the opposite over the hypotenuse, so that is what we can use. 7 is the opposite value and 9 is the hypotenuse of the triangle.

So we can set up an equation like this

[tex]sinx = \frac{7}{9}[/tex]

Then we can use the inverse of sin in order to solve for x

[tex]x = sin^{-1} (\frac{7}{9})[/tex]

When this is plugged into a calculator you get:

[tex]x= 51.057[/tex] degrees

This rounds to 51.1 degrees

The final answer is 3+9i

Answer:

3+9i

Step-by-step explanation:

The given expression is

(4 + 2i) - (1 - 7i)

Expand the parenthesis to obtain;

4 + 2i-1 + 7i

Group the imaginary parts and the real number parts separately to obtain;

4 -1+ 2i+ 7i

Combine the similar terms to get;

3+ 9i

For this case we must solve the following inequality, finding the values for the variable "t":

[tex]t + 18 <43[/tex]

We subtract 18 from both sides of the inequality:

[tex]t + 18-18 <43-18\\t <25[/tex]

Thus, the variable "t" is defined for all strict lower values than 25.

Answer:

[tex]t <25[/tex]

Option A

Answer: Figure one

Step-by-step explanation: this is a very very easy question and i will explaing it for you :) So basically all your doing is folding a peice of paper. If you look closley at figure two you can see that if you fold that it wont even turn into a shape. And if you look at figure three it has uneven sides when a square has all even sides. So your only valid option would be figure one because that would fold in to a square

I hope i helped you figure this out A thanks and a brainlist would be greatly appreciated :)

Answer:

[tex]14+3+c=14+8\quad :\quad c=5[/tex]

Hope this helps!!!

"The subject of this question is Mathematics." The student asked to solve two equations, one of which is already true and the other involves finding the value of a variable. By simplifying the equation, we can find that c is equal to 5.

The subject of this question is Mathematics.

In the equation 14 = 14, both sides are equal to each other, so the equation is true by the reflexive property of equality.

In the equation 14 + 3 + c = 14 + 8, we can simplify both sides of the equation. Starting with the left side, 14 + 3 + c becomes 17 + c. On the right side, 14 + 8 becomes 22. So, the equation can be rewritten as 17 + c = 22.

To solve for c, we subtract 17 from both sides of the equation. This gives us c = 22 - 17, which simplifies to c = 5.

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To translate a triangle by moving it 5 units to the right and 2 units up, you add 5 to the x-coordinates and 2 to the y-coordinates of all its vertices.

To translate  riangle ABC by moving it 5 units to the right and 2 units up, you would perform the following steps:

This transformation doesn't change the shape or size of  riangle ABC; it merely repositions it on the coordinate plane.

Answer:

8

Step-by-step explanation:

Find the point on the x-axis where x = 3 and look at the height of the line there.

Answer:

AC=BD

CAD=CBD

ACB=ADB

Step-by-step explanation:

You're essentially looking for anything of equal proportions. Obviously, your circle is split by several lines, and each side is symmetric. Since you know this, it's simply a matter of identifying one element then finding its symmetric match.

Follow the lines and trace the path with your finger for each question. If you do this, you'll see that AC=BD is an answer that involves a symmetric pair, because these two are equal distances and equal (but opposite) in placement.

Continuing with this method, keep track of the parts of the triangles you trace. With CAD=CBD, you trace across a hypotenuse, a leg, and a base in BOTH, making this true.

Continuing further with ACB=ADB, you trace across a hypotenuse, a leg, and a base with both AGAIN, making this true.

With AB=CD, this is obviously incorrect. You can't jump between points.

Answer:

only letter c is incorrect A, B, and D are correct

Step-by-step explanation: