Rewrite the equation in standard form of the line that passes through the given points (-1,-4); (1,6)

Answer:

6^ -24

Step-by-step explanation:

We know that a^b^c = a^ (b*c)

(6^-4)^6  = 6^ (-4*6) = 6^ -24

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:

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:

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:

1.609344 kilometers

Step-by-step explanation:

Answer:

The slope is 745 and the y-intercept is 500

The slope means The amount of money increases by $745 per month

The y-intercept means the business opened with initial amount $500

Step-by-step explanation:

* Lets explain how to solve the question

- The graph represents the relation between the number of months

  since the business opened and the total amount of money the

  business has earned

- The x-axis represents the number of month

- The y-axis represents the amount of money

- In the line the slopes from any two points on the line are equal

- The slope of the line whose end-points are (x1 , y1) and (x2 , y2)

  is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

- The equation of the line is y = mx + c ,where m is the slope of the line

 and c is the y-intercept

* Lets check is the relation between x and y is linear by calculating the

 slopes between each to points

∵ (2 , 1990) , (5 , 4225) , (9 , 7205) are points from the graph

- m1 is the slope of the points (2 , 1990) and (5 , 4225) , m2 is the slope

 of the points (5 , 42250) and (9 , 7205) , m3 is the slope of the points

 (2 , 1990) and (9 , 7205)

∵ [tex]m_{1}=\frac{4225-1990}{5-2}=745[/tex]

∵ [tex]m_{2}=\frac{7205-4225}{9-5}=745[/tex]

∵ [tex]m_{3=\frac{7205-1990}{9-2}}=745[/tex]

∴ m1 = m2 = m3 = 745

∴ The relation between the number of months and the amount of

   money is linear

* The slope is 745

∵ The form of the linear equation is y = mx + c

∵ m = 745

∴ y = 745 x + c

- The y-intercept means the line intersect the y-axis at point (0 , c),

  then to find c substitute x and y of the equation by the coordinates

  of any point on the line

∵ x = 2 , y = 1990

∴ 1990 = 745(2) + c

∴ 1990 = 1490 + c ⇒ subtract 1490 from both sides

∴ c = 500

∵ c is the y-intercept

* The y-intercept is 500

* The slope represents the rate of increasing of money per month

∴ The amount of money increases by $745 per month

* The y-intercept represents the initial amount of money when the

  business opened

∴ The business opened with initial amount $500

Answer:

The slope is 745 and the y-intercept is 500

The slope means The amount of money increases by $745 per month

The y-intercept means the business opened with initial amount $500

Step-by-step explanation:

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:

b

Step-by-step explanation:

I would use b.

Why?

[tex]2 \csc(2x)[/tex]

[tex]2 \frac{1}{\sin(2x)}[/tex]

[tex]\frac{2}{\sin(2x)}[/tex]

[tex]\frac{2}{2\sin(x)\cos(x)}[/tex]

[tex]\frac{1}{\sin(x)\cos(x)}{/tex]

[tex]\frac{1}{\sin(x)\frac{1}{\cos(x)}[/tex]

[tex]\csc(x) \sec(x)[/tex]

I applied the identity sin(2x)=2sin(x)cos(x) in line 3 to 4.

Answer: OPTION B.

Step-by-step explanation:

It is important to remember these identities:

[tex]csc(x)=\frac{1}{sin(x)}\\\\sec(x)=\frac{1}{cos(x)}[/tex]

Knowing this, we can say that:

[tex]csc(x) sec(x)=\frac{1}{sin(x)}*\frac{1}{cos(x)}=\frac{1}{sin(x)*cos(x)}[/tex]

Now we need to use the following Double angle identity :

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

And solve for [tex]sin(x)cos(x)[/tex]:

[tex]\frac{sin(2x)}{2}=sin(x)cos(x)[/tex]

The next step is to make the substitution into [tex]\frac{1}{sin(x)*cos(x)}[/tex] and finally simplify:

[tex]\frac{1}{\frac{sin(2x)}{2}}=\frac{\frac{1}{1}}{\frac{sin(2x)}{2}}=\frac{2}{sin(2x)}=2csc(2x)[/tex]

Answer:

D

Step-by-step explanation:

Given

9 - 7x = (4x - 3)² + 5 ← expand the squared factor

9 - 7x = 16x² - 24x + 9 + 5, that is

9 - 7x = 16x² - 24x + 14 ( subtract 9 - 7x from both sides )

0 = 16x² - 17x + 5, that is

16x² - 17x + 5 = 0 ← in standard form → D

Answer:

y-int:3

slope:-3

Step-by-step explanation:

6x-2y=-6

change to y=mx+b: -2y=-6x-6

divide by -2

y=3x+3

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:

√135

Step-by-step explanation:

3^2+b^2=12^2

9+b^2=144

9-9+b^2=144-9

b^2=135

√135=b

Answer:

Option A

Step-by-step explanation:

Given:

Center of circle = (h,k)= (3,8)

Radius = r = 5

The standard form of equation of circle with center and radius is:

[tex](x-h)^2+(y-k)^2=r^2\\Putting\ the\ values\\(x-3)^2+(y-8)^2=(5)^2\\Simplifying\\x^2+9-6x+y^2+64-16y=25\\x^2+y^2-6x-16y+9+64=25\\x^2+y^2-6x-16y+73=25\\x^2+y^2-6x-16y+73-25=0\\x^2+y^2-6x-16y+48=0[/tex]

Therefore, the general form of the equation of circle given is:

[tex]x^2+y^2-6x-16y+48=0[/tex]

Hence, option A is correct ..

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.

https://brainly.com/question/33989272

#SPJ11

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:

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:

1 3/4 t -7/2

Step-by-step explanation:

t + 3/4t - 7/2

Get a common denominator for the t terms, which is 4

4/4t + 3/4t - 7/2

7/4 t -7/2

This is an improper fraction so change it to a mixed number

1 3/4 t -7/2

Answer:

The distance is equal to [tex]3\sqrt{13}\ units[/tex]

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]R(-1,0)\\S(8,6)[/tex]  

substitute the values

[tex]d=\sqrt{(6-0)^{2}+(8+1)^{2}}[/tex]

[tex]d=\sqrt{(6)^{2}+(9)^{2}}[/tex]

[tex]d=\sqrt{36+81}[/tex]

[tex]d=\sqrt{117}\ units[/tex]

Simplify

[tex]d=3\sqrt{13}\ units[/tex]

Answer:

False.

Step-by-step explanation:

To see if these sides can form a right triangle, all we need to do is see if the following equation holds [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the larger measurement.  [tex]a \text{ and } b[/tex] it doesn't really matter which you assign as 5 or 8.

So I'm choosing the following [tex]a=5,b=8,c=12[/tex].

[tex]c[/tex] has to be 12 because 12 is the largest.

Now we got to see if [tex]a^2+b^2=c^2[/tex] holds.

That is, we need to see if [tex]5^2+8^2=12^2[/tex] holds.

[tex]5^2+8^2=12^2[/tex]

[tex]25+64=144[/tex]

[tex]89=144[/tex]

That's totally false.  89 is definitely not 144 so 5,8, and 12 cannot be put together to form a right triangle.

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:

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:

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:

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

(0, 1), (1, 3), (2, 9), (3, 27)

EXPLANATION

The first and third options are completely out because the y-value of an exponential function is never zero.

For the second option the y-values has no geometric pattern or common ratio.

For the last option, we can observe the following pattern

[tex]1 = {3}^{0} [/tex]

[tex] {3}^{1} = 3[/tex]

[tex] {3}^{2} = 9[/tex]

[tex] {3}^{3} = 27[/tex]

:

:

[tex] {3}^{x} = y [/tex]

The correct choice is the last option

Answer:

D

Step-by-step explanation:

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 , 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:

$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:

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:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=5x+2&(1)\\3x=-y+10&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\3x=-(5x+2)+10\\3x=-5x-2+10\qquad\text{add 5x to both sides}\\8x=8\qquad\text{divide both sides by 8}\\x=1\\\\\text{put the value of x to (1):}\\\\y=5(1)+2\\y=5+2\\y=7[/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 ^-^