When a figure is rotated, its angle measures( remain the same or may change), and its orientation (remains the same or may change).

Answer:

Step-by-step explanation:

2(9+4)

According to the BODMAS rule:

B = BRACKET

O = OPEN

D= DIVISION

M = MULTIPLICATION

A = ADDITION

S= SUBTRACTION

First we will solve the bracket:

=2(9+4)

=2(13)

=26....

Answer:

A, B, and C

Step-by-step explanation:

= 2 (9 +4)

= 2 (13)

= 26

A

= 2(9) + 2 (4)

= 18 + 8

= 26

B

= 2(13)

= 26

C

= 18 + 8

= 26

D

= 22

D does not apply because it does not equal 26

Answer:

f(x)=a(x-h)^2+k =f(x)=5(3-2)^(2)-4 and f(x)=1

Step-by-step explanation:

i really hope this helps im sorry if it doesnt

The answer is c $92,598

Answer:

$92,598

Step-by-step explanation:

The purchaser pays Ben $20,000 today and then $20,000 every year for the next 4 years.

The interest rate is 4% per annum.

So the net present value of all the payments is :

20000 + 20000/1.04 + 20000/(1.04^2) + 20000/(1.04^3) + 20000/(1.04^4)

= 20000 + 19230.77 + 18491.12 + 17779.73 + 17096.08

= 92597.7

= 92,598 (approx)

So the net present value of all the payments made to Ben is $92,598.

Answer:

3/5

Step-by-step explanation:

The word "Restaurant" contains a total of 10 letters, out of which 4 of the letters are vowels and 6 of the letters are consonants. The probability of selecting a vowel out of this word is:

P(selected letter is a vowel) = number of vowels/number of letters.

P(selected letter is a vowel) = 4/10 = 2/5.

Similarly, probability of selecting a non-vowel out of this word is:

P(selected letter is not a vowel) = number of non-vowels/number of letters.

P(selected letter is not a vowel) = 6/10 = 3/5.

Given that one of the letters randomly falls down, and assuming that the probabilities of each letter falling down is uniform and independent from each other, then:

P(a non-vowel falls down) = non-vowels/total = 6/10 = 3/5.

So the correct answer is 3/5!!!

Answer:

136

Step-by-step explanation:

The perimeter of the triangle is about 136

Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

There are several trigonometric identities that need to be recalled, i.e.

[tex]cosec ~ A = \frac{1}{sin ~ A}[/tex]

[tex]sec ~ A = \frac{1}{cos ~ A}[/tex]

[tex]cot ~ A = \frac{1}{tan ~ A}[/tex]

[tex]tan ~ A = \frac{sin ~ A}{cos ~ A}[/tex]

Let us now tackle the problem!

This problem is about Sine Rule.

First of all, we will calculate the ∠C :

∠A + ∠B + ∠C = 180°

72° + 16° + ∠C = 180°

∠C = 180° - 72° - 16°

∠C = 92°

Next, we will use the Sine Rule to find the length of the other side of the triangle.

[tex]\frac{c}{\sin \angle C} = \frac{b}{\sin \angle B}[/tex]

[tex]\frac{61}{\sin 92^o} = \frac{b}{\sin 16^o}[/tex]

[tex]b \approx \boxed {16.82}[/tex]

[tex]\frac{c}{\sin \angle C} = \frac{a}{\sin \angle A}[/tex]

[tex]\frac{61}{\sin 92^o} = \frac{a}{\sin 72^o}[/tex]

[tex]a \approx \boxed {58.05}[/tex]

Finally, we can find the perimeter of a triangle with the following formula

[tex]\text{Perimeter of the triangle} = a + b + c[/tex]

[tex]\text{Perimeter of the triangle} = 58.05 + 16.82 + 61[/tex]

[tex]\text{Perimeter of the triangle} \approx \boxed {136}[/tex]

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse  

Answer:

Step-by-step explanation:

Put a = -0.1 to the first an second equation and find velue of b:

3 = 10a + b

3 = 10(-0.1) + b

3 = -1 + b             add 1 to both sides

4 = b → b = 4

2 = 20a + b

2 = 20(-0.1) + b

2 = -2 + b       add 2 to both sides

4 = b → b = 4

CORRECT

Answer:

d) $130

Step-by-step explanation:

Average means you add up the numbers and divide by the number of numbers.

We want our average to be 131.

We have 128,135, and the next pay check amount.

So let's average the three numbers together.

[tex]\frac{128+135+x}{3}[/tex]

[tex]x[/tex] represent the amount on the next pay check.

We want this average to equal 131 so we have this equation to solve:

[tex]\frac{128+135+x}{3}=131[/tex]

First step: Add 128 and 135:

[tex]\frac{263+x}{3}=131[/tex]

Second step: Multiply both sides by 3:

[tex]263+x=3(131)[/tex]

Third step: Multiply 3 and 131:

[tex]263+x=393[/tex]

Fourth step: Subtract 263 on both sides:

[tex]x=393-263[/tex]

Fifth step: Subtract 393 and 263:

[tex]x=130[/tex]

d. 130

D). $130

In this question, we're trying to figure out what would be the lowest amount of money he earned on his next paycheck in order for his income to be an average of $131.

To do this, we would need to use some important information in the question.

Important information:

With the information above, we can use that to get the answer to the question.

We know that he made $128 and $135 on his recent paychecks, but we need to find on how much he needs to make on his next paycheck in order to reach his goal average.

We would be solving for x:

128, 135, x

131,  131,  131

We would add the numbers:

128, 135, x = 263 + x

131,  131,  131 = 393

We will now solve.

[tex]393 = 263+x\\\\\text{Subtract 263 on both sides}\\\\130=x[/tex]

When you're don solving, you should get 130. This means that Cal needs to make $130 on his next paycheck in order to have an average of $131.

We can check to see if it's right by adding up all of the numbers and divide by how many there are (3).

[tex]128+130+135=393\\\\393\div3=131[/tex]

Now, we can confirm that D). $130 would be the correct answer.

Answer:

The graphical is radical function sqrt(x) shifted 3 units left

Step-by-step explanation:

The argument of the radical function is x+3, this means, that if x=-3, then y=0 since sqrt(0)=0

The parent function y=sqrt(x), something simmilar ocurrs, y=0 when x=0

This is the key difference between the two given functions.

Answer:

B

Step-by-step explanation:

Given

x + 10 = 15 ( subtract 10 from both sides )

x = 5 → B

Answer:

727.29 − 248.50 + x ≥ 500; x ≥ $21.21

Step-by-step explanation:

Write down all the data given :

Beginning amount : $727.29

Balance to be maintained : $ 500

Check : $248.5

Current balance = 727.29 - 248.5 = $478.79

Tony must maintain a balance of $500 so he should have at least $21.21 more (500-478.79)

727.29 - 248.5 + 21.21 = 500

500=500

x can be 21.21 or greater than that which would maintain the balance of $500 or more.

Therefore the third statement is correct.

727.29 − 248.50 + x ≥ 500; x ≥ $21.21

!!

Answer:

A) -0.3 of an inch per second

Step-by-step explanation:

You'll have to put (2, 8.4) and (4, 7.8) into the slope formula.

It's represented as (∆y)/(∆x) = m

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

You subtract both y's in the numerator and subtract both x's in the denominator.

Like this:

(8.4-7.8)/(2-4) = m

(0.6)/(-2) = m

-0.3 = m

Answer:

y = (-0.3 in/sec)x + 9.0 in

Step-by-step explanation:

(2, 8.4) and (4, 7.8) are points on a linear graph.

As we go from  (2, 8.4)  to  (4, 7.8), x increases by 2 and y decreases by 0.6.

Thus, the slope of the line is m = rise / run = -0.6 / 2, or m = -0.3 inches/sec

Let's use the slope-intercept form of the equation of a straight line, with m = -0.3 in/sec and one point being (2, 8.4).

Then y = mx + b becomes 8.4 = (-0.3 in/sec)(2) + b, or

8.4 = -0.6 + b.  Thus, b = 9.0, and the desired equation is thus:

y = (-0.3 in/sec)x + 9.0 in

Answer:

So we have

[tex](fg)(x)=3x^3+x^2-18x-6[/tex]

[tex](f \circ g)(x)=3x^2-17[/tex]

Step-by-step explanation:

I'm going to do two problems just in case.

We are given [tex]f(x)=3x+1[/tex] and [tex]g(x)=x^2-6[/tex].

[tex](fg)(x)=f(x)g(x)=(3x+1)(x^2-6)[/tex]

Multiply out using foil!

First:  3x(x^2)=3x^3

Outer: 3x(-6)=-18x

Inner: 1(x^2)=x^2

Last: 1(-6)=-6

-------------------Add together:

[tex]3x^3+x^2-18x-6[/tex]

[tex](f \circ g)(x)=f(g(x))=f(x^2-6)=3(x^2-6)+1=3x^2-18+1=3x^2-17[/tex]

Answer:

It can be written as 825/1000. You can simplify this to get the simplest form which would be 33/40. All decimals are out of one, they are a part. When you first get a decimal, put the numbers such as 825 on top. The last number is in the thousandths place, so it is out of 1000. 1000 is your denominator. Your fraction is then 825/1000. From here you can simplify if possible.

Hope this helps ^-^

Answer:

x=(-3+-sqrt15)/2

Step-by-step explanation:

Without using calculatorsoup,

we can use the quadratic formula for x^2+3x-3=0

using it we find:

x=(-b+-sqrtb^2-4ac)/2a

x=(-3+-sqrt3-4*1*-3)/2

x=(-3+-sqrt15)/2

For this case we must resolve the following expression:

[tex]x ^ 2 + 3x-3 = 0[/tex]

The roots will be given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

We have to:

[tex]a = 1\\\b = 3\\c = -3[/tex]

So:

[tex]x = \frac {-3 \pm \sqrt {3 ^ 2-4 (1) (- 3)}} {2 (1)}\\x = \frac {-3 \pm \sqrt {9 + 12}} {2}\\x = \frac {-3 \pm \sqrt {21}} {2}[/tex]

We have two roots:

[tex]x_ {1} = \frac {-3+ \sqrt {21}} {2} = 0.7913\\x_ {2} = \frac {-3- \sqrt {21}} {2} = - 3.7913[/tex]

Answer:

[tex]x_ {1} = \frac {-3+ \sqrt {21}} {2} = 0.7913\\x_ {2} = \frac {-3- \sqrt {21}} {2} = - 3.7913[/tex]

To find the exact value of tan^-1(-sqrt(3)), we first rewrite the equation using the definition of the arctangent function. Next, we use the trigonometric identity sin^2(x) + cos^2(x) = 1 to simplify the equation and solve for sin(x). We find that sin(x) = sqrt(3)/2. By looking at the unit circle, we determine that the angle whose sine is sqrt(3)/2 is pi/3 radians. Therefore, the exact value of tan^-1(-sqrt(3)) in radians is -pi/3 + 2*pi*n, where n is an integer.

To find the exact value of tan^-1(-sqrt(3)), we need to recall the definition of the arctangent function. The arctangent function returns an angle whose tangent is equal to a given number. In this case, we are looking for an angle whose tangent is -sqrt(3). Since tan(x) = sin(x)/cos(x), we can rewrite the equation as -sqrt(3) = sin(x)/cos(x).

Next, we can use the fact that sin^2(x) + cos^2(x) = 1 to rewrite the equation as -sqrt(3) = sin(x)/sqrt(1 - sin^2(x)). Cross-multiplying and rearranging, we get -sqrt(3)*sqrt(1 - sin^2(x)) = sin(x).

Now, we can square both sides and simplify the equation to get -3*(1 - sin^2(x)) = sin^2(x). Expanding and rearranging, we have -3 + 3sin^2(x) = sin^2(x). Combining like terms and isolating sin^2(x), we get sin^2(x) = 3/4. Taking the square root of both sides, we find sin(x) = sqrt(3)/2.

Finally, we can find the angle whose sine is sqrt(3)/2 by looking at the unit circle. The angle is pi/3 in radians. Therefore, the exact value of tan^-1(-sqrt(3)) in radians is -pi/3 + 2*pi*n, where n is an integer.

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Answer: (5x-2)(3^2-5)

Step-by-step explanation:

So using the commutative property, we can change the equation 15x^3-6x^2-25x+10 into 15x^3-25x -6x^2+10

Let’s split that into two sections so it’s easier to see:

(15x^3-25x) - (6x^2+10)

Next let’s look at what 15x^3 and -25x have in common. They have 5x in common.

Factoring out 5x, we get this: 5x(3^2-5)

Next let’s look at what -6x^2and 10 have in common. They only have 2 in common, so we factor out 2.

2(-3^2+5) we can write this as -2(3^2-5)

So the end result will be : 5x(3^2-5)-2(3^2-5)

And the complete factorization will be (5x-2)(3^2-5)

Step-by-step explanation:

[tex]slope=\dfrac{rise}{run}=\dfrac{\Delta y}{\Delta x}\\\\\text{We have}\ m=0.5=\dfrac{1}{2}\to\Delta y=1,\ \Delta x=2\\\\\text{From given point (y-intercept: (0, 2), run 1 unit up and 2 units to the right.}\\(x+2,\ y+1)\to(0+2,\ 2+1)=(2,\ 3)\\\text{Mark new point.}\\\text{Plot the line passes throught given points.}\\\\======================\\\\\Delta x > 0-\text{run to the right}\\\Delta x<0-\text{run to the left}\\\Delta y>0-\text{run up}\\\Delta y<0-\text{run down}[/tex]

Answer:

D the last one

Answer:

-3 , 21

Step-by-step explanation:

RS = R + S = 12

S lies on 9

There are 12 spaces in between R & S, so you can add and subtract 12 from S:

9 - 12 = -3

9 + 12 = 21

R can be located on either -3 or 21.

~

Answer:

So angle G has measurement 127 degrees.

Step-by-step explanation:

     E                       F

H                     G

I had to write it out the parallelogram so I could have a better visual.

F and G are consecutive angles in a parallelogram (not on opposite sides).

This means they add to be 180 degrees.

F+G=180

(3x-10)+(5x+22)=180

(3x+5x)+(-10+22)=180

8x       +12=180

Subtract 12 on both sides:

8x           =180-12

Simplify:

8x           =168

Divide both sides by 8:

x              =168/8

x              =21

If x=21 and want the measurement of angle G, then

(5x+22)=(5*21+22)=127.

So angle G has measurement 127 degrees.

Answer: [tex]127^{\circ}[/tex]

Step-by-step explanation:

Given : In parallelogram EFGH, the measure of angle F is (3x − 10)° and the measure of angle G is (5x + 22)°.

We known that in a parallelogram , the sum of two adjacent angles is 180° .

Therefore , we have

[tex]3x -10+5x + 22=180\\\\\Rightarrow\ 8x+12=180\\\\\Rightarrow\ 8x=180-12\\\\\Rightarrow\8x=168\\\\\Rightarrow\ x=21[/tex]

Now, the measure of angle G =[tex](5x + 22)^{\circ}=(5(21)+22)^{\circ}=127^{\circ}[/tex]

Hence, the measure of angle G = [tex]127^{\circ}[/tex]

Answer:

(12, 3.2) would be the max amount of gas he could buy.  (11.25, 3) for an even gallon amount.

Step-by-step explanation:

Answer:

(3.2, 12)

Step-by-step explanation:

Total cost for gas = $12

Cost per gallon = $3.75

Letting total cost of gas be y and number of gallons be x, maximum number of gallons of gas he can buy would be ;

Total cost of gas/ cost per gallon = 12 / 3.75 = 3.2 gallons

Therefore , the coordinate pair (x, y) = (3.2, 12)

Answer:

B. 12ft

Step-by-step explanation:

Area of kite is 2 times the area of triangle

= 2[(1/2)(4)AC] = 48, ie., AC = 12 ft

Answer:

$225,000

Step-by-step explanation:

To calculate the percentage change we will apply the formula:

p= N-O/O *100

p is the increased percentage

N is the current value

O is the old value.

Substitute the values in the formula:

36 = 306,000 - O/O *100

Divide both the sides by 100

36/100 = 306,000 - O/O *100/100

36/100 = 306,000 - O/O

Now multiply O at both sides

36/100 * O = 306,000-O/O * O

At R.H.S O will be cancelled by O

At L.H.S 36/ 100 = 0.36

0.36 O= 306,000-O

Combine the like terms:

0.36 O+O =306,000

1.36 O = 306,000

Divide both the terms by 1.36

1.36 O/ 1.36 = 306,000/1.36

O= $225,000

Therefore  when the house was purchased its value was $225,000....

Answer:

x = 44 − y

Step-by-step explanation:

x is the number of glasses of iced tea, and y is the number of glasses of lemonade.  The sum is 44, so:

x + y = 44

Solving for x:

x = 44 − y

Answer: 44-y represents the number of glasses of ice tea she can serve.

Step-by-step explanation:

Since we have given that

Let x be the number of glasses of iced tea.

Let y be the number of glasses of lemonade.

Total number of glasses = 44

According to question,

[tex]x+y=44[/tex]

So, the number of glasses of ice tea she can serve is given by

[tex]x=44-y[/tex]

Hence, 44-y represents the number of glasses of ice tea she can serve.

Answer:

x = 1 - t and y = -2.5 - 2.5t.

Step-by-step explanation:

Parametric equations are the equations in which the all the variables of the equation are written in terms of a single variable. For example in 2-D plane, the equation of the line is given by y=mx+c, there x is the independent variable, y is the dependent variable, m is the slope, and c is the y-intercept. The equation of the given line is 10x - 4y = 20. The goal is to convert the variables x and y in terms of a single variable t. First of all, take two points which lie on the line. By taking x=1, y comes out to be -2.5 and by taking x=0, y comes out to be -5. The general form of the straight line is given by:

(x, y) = (x0, y0) + t(x1-x0, y1-y0), where (x, y) is the general point, (x0, y0) is the fixed point, t is the parametric variable, and (x1-x0, y1-y0) is the slope.

Let (x0, y0) = (1, -2.5) and (x1, y1) = (0, -5). Substituting in the general equation gives:

(x, y) = (1, -2.5) + t(-1, -2.5). This implies that x = 1 - t and y = -2.5 - 2.5t!!!

Answer:

C. x=2t, y=5t-5

Step-by-step explanation:

Answer:

x = 2 or x = -5

Step-by-step explanation:

It s given that,  (x – 2)(x + 5) = 0

To find the solution of given equation

Let  (x – 2)(x + 5) = 0

From this we get

either  (x – 2) = 0 or (x + 5) = 0

If (x - 2) = 0  then x = 2

If (x + 5) = 0 then x = -5

Therefore the solutions of given equation  (x – 2)(x + 5) = 0  are,

x = 2 or x = -5

Answer: X = 2 or X = -5

Step-by-step explanation:

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

X - 2 = 0 or X - 5 = 0

Therefore X=2 or X=5

Answer:

m=15

Step-by-step explanation:

-7 + m = 8

=>m=8+7

=>m=15

Answer:

A(1,1)

Step-by-step explanation:

the system is :

2x-y=1

x+2y=3

so :

y = 2x-1  .....the line color : red

y= (-1/2)x+3/2......the line color : blue

the pair solution is the intersection point for this line : A(1 ; 1)

Answer:

- 3, 9, 25

Step-by-step explanation:

To find the required terms of the sequence substitute n = 2, 5, 9 into the given rule, that is

[tex]a_{2}[/tex] = - 7 + (2 - 1)4  = - 7 + (1 × 4) = - 7 + 4 = - 3

[tex]a_{5}[/tex] = - 7 + (5 - 1)4 = - 7 + (4 × 4) = - 7 + 16 = 9

[tex]a_{9}[/tex] = - 7 + (9 - 1)4 = - 7 + (8 × 4) = - 7 + 32 = 25

The second, fifth, and ninth terms of the sequence are -3, 9, and 25, respectively.

The second, fifth, and ninth terms of the sequence defined by the formula an = -7 + (n - 1) * 4 are -3, 9, and 25, respectively.

To find the second, fifth, and ninth terms of the sequence given by the formula an = -7 + (n - 1) * 4, we can simply plug the corresponding values of n into the formula.

For the second term (a2), where n=2:

a2 = -7 + (2 - 1) * 4

a2 = -7 + 1 * 4

a2 = -7 + 4

a2 = -3

For the fifth term (a5), where n=5:

a5 = -7 + (5 - 1) * 4

a5 = -7 + 4 * 4

a5 = -7 + 16

a5 = 9

For the ninth term (a9), where n=9:

a9 = -7 + (9 - 1) * 4

a9 = -7 + 8 * 4

a9 = -7 + 32

a9 = 25

Therefore, the second, fifth, and ninth terms of the sequence are -3, 9, and 25, respectively.

Answer:

[tex]\large\boxed{D.\ \dfrac{-27w^{15}}{c^9}}[/tex]

Step-by-step explanation:

[tex](-3c^{-3}w^5)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=(-3)^3(c^{-3})^3(w^5)^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=-27c^{-3\cdot3}w^{5\cdot3}=-27c^{-9}w^{15}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=-27\left(\dfrac{1}{c^9}\right)w^{15}=\dfrac{-27w^{15}}{c^9}[/tex]

Final answer:

To simplify (-3c⁻³w⁵)³, you must distribute the power of 3 to each factor inside the parenthesis and apply the rule for negative exponents to end up with -27w¹⁵/c⁹, which is answer choice D.

Explanation:

The expression to simplify is  (-3c⁻³w⁵)³. We will apply the rule for exponents to simplify the expression. When applying this rule and the negative exponent rule which states that a⁻ⁿ = 1/aⁿ, we get:

The correct answer is D.  -27w¹⁵/c⁹.

Answer:

1.609344 kilometers

Step-by-step explanation: