Find the value of x.

Answer:

Two solutions were found :

t =(16-√288)/-2=8+6√ 2 = 0.485

t =(16+√288)/-2=8-6√ 2 = -16.48

Step-by-step explanation:

Answer:

-IF THE EQUATION IS [tex]\frac{1}{t-2}=\frac{t}{8}[/tex], THEN:

[tex]t_1=4\\t_2=-2[/tex]

-IF THE EQUATION IS [tex]\frac{1}{t}-2=\frac{t}{8}[/tex], THEN:

[tex]t_1=-16.485\\t_2=0.485[/tex]

Step-by-step explanation:

-IF THE EQUATION IS [tex]\frac{1}{t-2}=\frac{t}{8}[/tex] THE PROCEDURE IS:

Multiply both sides of the equation by [tex]t-2[/tex] and by 8:

[tex](8)(t-2)(\frac{1}{t-2})=(\frac{t}{8})(8)(t-2)\\\\(8)(1)=(t)(t-2)\\\\8=t^2-2t[/tex]

Subtract 8 from both sides of the equation:

[tex]8-8=t^2-2t-8\\\\0=t^2-2t-8[/tex]

Factor the equation. Find two numbers whose sum be -2 and whose product be -8. These are -4 and 2:

[tex]0=(t-4)(t+2)[/tex]

Then:

[tex]t_1=4\\t_2=-2[/tex]

-IF THE EQUATION IS [tex]\frac{1}{t}-2=\frac{t}{8}[/tex] THE PROCEDURE IS:

Subtract [tex]\frac{1}{t}[/tex] and [tex]2[/tex]:

[tex]\frac{1}{t}-2=\frac{t}{8}\\\\\frac{1-2t}{t}=\frac{t}{8}[/tex]

Multiply both sides of the equation by [tex]t[/tex]:

[tex](t)(\frac{1-2t}{t})=(\frac{t}{8})(t)\\\\1-2t=\frac{t^2}{8}[/tex]

Multiply both sides of the equation by 8:

[tex](8)(1-2t)=(\frac{t^2}{8})(8)\\\\8-16t=t^2[/tex]

Move the [tex]16t[/tex] and 8 to the other side of the equation and apply the Quadratic formula. Then:

[tex]t^2+16t-8=0[/tex]

[tex]t=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\\\t=\frac{-16\±\sqrt{16^2-4(1)(-8)}}{2(1)}\\\\t_1=-16.485\\t_2=0.485[/tex]

Answer:

x = 4/9

C

Step-by-step explanation:

log_2(6x/) - log_2(x^(1/2) = 2         Given

log_2(6x/x^1/2) = 2                         Subtracting logs means division

log_2(6 x^(1 - 1/2)) = 2                     Subtract powers on the x s

log_2(6 x^(1/2) ) = 2                         Take the anti log of both sides

6 x^1/2 = 2^2                                    Combine the right

6 x^1/2 = 4                                        Divide by 6  

x^1/2 = 4/6 = 2/3                               which gives 2/3 now square both sides

x = (2/3)^2                                      

x = 4/9

Answer:

Option c

Step-by-step explanation:

The given logarithmic equation is

[tex]log_{2} (6x)-log_{2}(\sqrt{x})=2[/tex]

[tex]log_{2}[\frac{(6x)}{\sqrt{x}}]=2[/tex] [since log[tex](\frac{a}{b})[/tex]= log a - log b]

[tex]log_{2}[\frac{(6\sqrt{x})\times\sqrt{x}}{\sqrt{x}}]=2[/tex] [since x = [tex](\sqrt{x})(\sqrt{x})[/tex]]

[tex]log_{2}(6\sqrt{x} )=2[/tex]

[tex]6\sqrt{x} =2^2[/tex]  [logₐ b = c then [tex]a^{c}=b[/tex]

[tex]6\sqrt{x} =4[/tex]

[tex]\sqrt{x} =\frac{4}{6}[/tex]

[tex]\sqrt{x} =\frac{2}{3}[/tex]

[tex]x=(\frac{2}{3})^2[/tex]

        = [tex]\frac{4}{9}[/tex]

Option c is the answer.

Answer:16.66

Step-by-step explanation:

To convert 1/6 into a percent, multiply by 100 to get approximately 16.67 percent.

To convert a fraction to a percent, you can follow a standard way of expressing the fraction such that the denominator equals 100. For 1/6, you want to find what number over 100 is equivalent to it. To do so, you can set up a proportion where 1/6 equals x/100. Solving for x, you would cross-multiply and divide to get:

1 * 100 = 6 * x
[tex]\( x = \frac{100}{6} \)[/tex]
x ≈ 16.67

Therefore, 1/6 as a percent is approximately 16.67 percent.

Answer:

Option B. [tex]tan(2\theta)= -\frac{336}{527}[/tex]

Step-by-step explanation:

we know that

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

[tex]sin(2\theta)=2(sin(\theta))(cos(\theta))[/tex]

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

[tex]cos^{2}(\theta)+sin^{2}(\theta)=1[/tex]

we have

[tex]sin(\theta)=\frac{24}{25}[/tex]

step 1

Find the value of cosine of angle theta

[tex]cos^{2}(\theta)+sin^{2}(\theta)=1[/tex]

[tex]cos^{2}(\theta)+(\frac{24}{25})^=1[/tex]

[tex]cos^{2}(\theta)=1-\frac{576}{625}[/tex]

[tex]cos^{2}(\theta)=\frac{49}{625}[/tex]

[tex]cos(\theta)=\frac{7}{25}[/tex]

The value of cosine of angle theta is positive, because angle theta lie on the I Quadrant

step 2

Find [tex]sin(2\theta)[/tex]

[tex]sin(2\theta)=2(sin(\theta))(cos(\theta))[/tex]

we have

[tex]sin(\theta)=\frac{24}{25}[/tex]

[tex]cos(\theta)=\frac{7}{25}[/tex]

substitute

[tex]sin(2\theta)=2(\frac{24}{25})(\frac{7}{25})[/tex]

[tex]sin(2\theta)=\frac{336}{625}[/tex]

step 3

Find [tex]cos(2\theta)[/tex]

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

we have

[tex]sin(\theta)=\frac{24}{25}[/tex]

[tex]cos(\theta)=\frac{7}{25}[/tex]

substitute

[tex]cos(2\theta)=(\frac{7}{25})^{2}-(\frac{24}{25})^{2}[/tex]

[tex]cos(2\theta)=(\frac{49}{625})-(\frac{576}{625})[/tex]

[tex]cos(2\theta)=-\frac{527}{625}[/tex]

step 4

Find the value of [tex]tan(2\theta)[/tex]

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

we have

[tex]sin(2\theta)=\frac{336}{625}[/tex]

[tex]cos(2\theta)=-\frac{527}{625}[/tex]

substitute

[tex]tan(2\theta)= -\frac{336}{527}[/tex]

By using the Pythagorean identity and the double angle identity for tangent, it is found that the value of tan 2θ when sin θ =24/25 and 0 ≤ θ ≤ π/2 is -527/336.

In the field of Mathematics, particularly in trigonometric equations, the problem given is asking for the value of tan 2θ, given that sin θ=24/25 and 0 ≤ θ ≤ π/2.

Firstly, we can find cos θ by using the Pythagorean identity sin²θ + cos²θ = 1. This gives us cos θ = sqrt (1 - sin²θ) = sqrt (1 - (24/25)²) = 7/25.

Then, knowing that tan θ = sin θ/cos θ, we can plug in these values to get tan θ = (24/25) / (7/25) = 24/7. Finally, using the double angle identity for tan (tan 2θ = 2 tan θ / (1 - tan²θ)), we can find that tan 2θ = 2(24/7) / (1 - (24/7)²) = -527/336.

So, the exact value of tan 2θ when sin θ =24/25 and 0 ≤ θ ≤ π/2 is -527/336, which is answer option A.

https://brainly.com/question/11016599

#SPJ3

Answer:

[tex]\large\boxed{(-6b^3-362.6)+(2b^3-362)=-4b^3-724.5}[/tex]

Step-by-step explanation:

[tex](-6b^3-362.6)+(2b^3-362)\\\\=-6b^3-362.6+2b^3-362\qquad\text{combine like terms}\\\\=(-6b^3+2b^3)+(-362.5-362)\\\\=-4b^3-724.5[/tex]

Answer:

g and h

Step-by-step explanation:

both g and h have constant relationships while f's f(x) values aren't constant so it doesn't have a linear relationship

Answer:

Of the three functions g and h represent linear relationship.

Step-by-step explanation:

If a function has constant rate of change for all points, then the function is called a linear function.

If a lines passes through two points, then the slope of the line is

[tex]m=\frac{x_2-x_1}{y_2-y_1}[/tex]

The slope of function f(x) on [1,2] is

[tex]m_1=\frac{11-5}{2-1}=6[/tex]

The slope of function f(x) on [2,3] is

[tex]m_2=\frac{29-11}{3-2}=18\neq m_1[/tex]

Since f(x) has different slopes on different intervals, therefore f(x) does not represents a linear relationship.

From the given table of g(x) it is clear that the value of g(x) is increased by 8 units for every 2 units. So, the function g(x) has constant rate of change, i.e.,

[tex]m=\frac{8}{2}=4[/tex]

From the given table of h(x) it is clear that the value of h(x) is increased by 6.8 units for every 2 units. So, the function h(x) has constant rate of change, i.e.,

[tex]m=\frac{6.8}{2}=3.4[/tex]

Since the function g and h have constant rate of change, therefore g and h represent linear relationship.

Answer: 4b + 3r

Step-by-step explanation: The student correctly subtracted the 2b, but accidentally added the r instead of subtracting it, she likely misunderstood the parentheses.

The correct answer would be 4b + 3r

Answer:

Third option     ✔ 4b + 3r

Step-by-step explanation:

E D G E N U I T Y

Answer:

Step-by-step explanation:

0 = x2 + 3x - 10

10 = 2x+3x

10 = 5x

x = 2

0x = 5.2

0x = 10

x = 10.2 = 20

x = 20

0x = -5.-2

0x = -10

x = -10.2 = -20

x = -20

x = -5.2

x = -10

x = 5-2​

x = 3

GOOD LUCK ! ;)

Answer:

4x+6

Step-by-step explanation:

f(x)=8x-3

g(x)=4x-9

f(x)-g(x) = 8x-3-(4x-9)=8x-3-4x+9=4x+6

The value of f(x) - g(x) is 4x+6 and The domain is all real value of x.

A function can be defined as a mathematical expression which establishes relation between a dependent variable and an independent variable.

It always comes with a defined range and domain.

It is given in the question

functions f and g

f(x) = 8x - 3; g(x) = 4x - 9

f- g = ?

The value of f(x) - g(x) = 8x -3 - (4x -9)

f(x) - g(x) = 8x -3 - 4x +9

f(x) - g(x) = 4x +6

h(x) = 4x+6

The domain is all real value of x.

To know more about Function

https://brainly.com/question/12431044

#SPJ2

we know the center of the circle, and we also know a point on the circle, well, the distance from the center to a point is just the radius.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[4-(-6)]^2+[-2-7]^2}\implies r=\sqrt{(4+6)^2+(-2-7)^2} \\\\\\ r=\sqrt{10^2+(-9)^2}\implies r=\sqrt{100+81}\implies r=\sqrt{181} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{7}{ k})\qquad \qquad radius=\stackrel{\sqrt{181}}{ r}\\[2em] [x-(-6)]^2+[y-7]^2=(\sqrt{181})^2\implies (x+6)^2+(y-7)^2=181[/tex]

Answer:

the awncer would be x=0

Step-by-step explanation:

.

This is your answer:

if then number is $499.49 that would mean it rounds down to $499.00

but in your case $499.76 rounds to $500.00

(Remember .50 and up goes up!)

Therefor your answer is $500.00

Answer:

$499.76 rounded to the nearest dollar is $500 !!

Step-by-step explanation:

Why?

  A dollar ($1) would be in the ones column and it's asking for the nearest dollar! So you would round it by the number on the right of the dollar, the tenths.

[tex]y=3\cdot0 + 2\cdot0 - 13=-13[/tex]

The y-intercept is [tex](0,-13)[/tex]

Answer:

3 miles per hour

Step-by-step explanation:

Let x miles per hour be the current of the river.

1. The boat travels 2.4 miles downstream with the speed of (21+x) miles per hour. It takes him

[tex]\dfrac{2.4}{21+x}\ hours.[/tex]

2. The boat travels 1.8 miles upstream with the speed of (21-x) miles per hour. It takes him

[tex]\dfrac{1.8}{21-x}\ hours.[/tex]

3. The time is the same, so

[tex]\dfrac{2.4}{21+x}=\dfrac{1.8}{21-x}[/tex]

Cross multiply:

[tex]2.4(21-x)=1.8(21+x)[/tex]

Multiply it by 10:

[tex]24(21-x)=18(21+x)[/tex]

Divide it by 6:

[tex]4(21-x)=3(21+x)\\ \\84-4x=63+3x\\ \\84-63=3x+4x\\ \\7x=21\\ \\x=3\ mph[/tex]

Answer:

42 degrees

Step-by-step explanation:

So we are given that m<BOC+m<AOB=90

So we have (6x-6)+(5x+8)=90

11x+2=90

11x=88

x=8

We are asked to find m<BOC

m<BOC=6x-6=6(8)-6=48-6=42

Answer:

Choice number one:

[tex]\displaystyle \frac{5}{10}\cdot \frac{4}{9}[/tex].

Step-by-step explanation:

The question is asking for the possibility that event [tex]A[/tex] and [tex]B[/tex] happen at the same time. However, whether [tex]A[/tex] occurs or not will influence the probability of [tex]B[/tex]. In other words, [tex]A[/tex] and [tex]B[/tex] are not independent. The probability that both [tex]A[/tex] and [tex]B[/tex] occur needs to be found as the product of

5 out of the ten numbers are even. The probability that event [tex]A[/tex] occurs is:

[tex]\displaystyle P(A) = \frac{5}{10}[/tex].

In case A occurs, there will only be four cards with even numbers out of the nine cards that are still in the bag. The conditional probability of getting a second card with an even number on it, given that the first card is even, will be:

[tex]\displaystyle P(B|A) = \frac{4}{9}[/tex].

The probability that both [tex]A[/tex] and [tex]B[/tex] occurs will be:

[tex]\displaystyle P(A \cap B) = P(B\cap A) =  P(A) \cdot P(B|A) = \frac{5}{10}\cdot \frac{4}{9}[/tex].

Answer: 8 remainder 2

Step-by-step explanation:

3 • 8 = 24

26 - 24 = 2

Your answer is 8 with a remainder of 2

Answer:

8 r2

Step-by-step explanation:

Answer:

length of shortest piece = 13 in

length of middle piece =  19 in

length of longest piece =  22 in

Step-by-step explanation:

Total length of sandwich = 54 inch

Let shortest piece = x

Middle piece = x+6

Longest piece = x+9

Add this pieces will make complete sandwich

x+(x+6)+(x+9) = 54

Solving

x+x+6+x+9 = 54

Combining like terms

x+x+x+6+9 = 54

3x + 15 = 54

3x = 54 -15

3x = 39

x = 13

So, length of shortest piece = x = 13 in

length of middle piece = x+6 = 13+6 = 19 in

length of longest piece = x+9 = 13+9 = 22 in

Answer:

The three pieces should be 13 , 19 , 22 inches

Step-by-step explanation:

* Lets study the information to solve the problem

- The length of the sandwich is 54 in

- The sandwich will cut into three pieces

- The middle piece is 6 inches longer than the shortest piece

- The shortest piece is 9 inches shorter than the longest piece

* Lets change the above statements to equations

∵ The shortest piece is common in the two statements

∴ Let the length of the shortest piece is x ⇒ (1)

∵ The middle piece is 6 inches longer than the shortest piece

∴ The length of the middle piece = x + 6 ⇒ (2)

∵ The shortest piece is 9 inches shorter than the longest piece

∴ The longest piece is 9 inches longer than the shortest piece

∴ The longest piece = x + 9 ⇒ (3)

∵ the length of the three pieces = 54 inches

- Add the length of the three pieces and equate them by 54

∴ Add (1) , (2) , (3)

∴ x + (x + 6) + (x + 9) = 54 ⇒ add the like terms

∴ 3x + 15 = 54 ⇒ subtract 15 from both sides

∴ 3x = 39 ⇒ divide both sides by 3

∴ x = 13

* The length of the shortest piece is 13 inches

∵ The length of the middle piece = x + 6

∴ The length of the middle piece = 13 + 6 = 19 inches

* The length of the middle piece is 19 inches

∵ The length of the longest piece = x + 9

∴ The length of the longest piece = 13 + 9 = 22 inches

* The length of the longest piece is 22 inches

* The lengths of the three pieces are 13 , 19 , 22 inches

Answer:

15625

Step-by-step explanation:

Let us consider each dial individually.

We have 25 choices for the first dial.

We then have 25 choices for the second dial.

We then have 25 choices for the third dial.

Let us consider any particular combination, the probability that combination is right is (probability the first number is right) * (probability the second number is right) * (probability the third number is right) = 1/25 * 1/25 * 1/25 = 1/15625

Therefore there are 15625 combinations

Answer:

x =0 and x = 4

Step-by-step explanation:

It is a quadratic function and hence will have two roots. It cuts graph at 2 points( x - axis ). Hence has two roots.

Answer:

.05

Step-by-step explanation:

See The attachment for explanation

Hope it helps you...☺

Answer:

A

Step-by-step explanation:

Linear functions go into a straight line in order

Y in set b goes from 2 to 1250 so it is traveling much faster than set A

To do solve this you must isolate x. First subtract 16 to both sides (what you do on one side you must do to the other). Since 16 is being added to x, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

x + (16 - 16) = 24 - 16

x = 8

Check:

8 + 16 = 24

24 = 24

Hope this helped!

~Just a girl in love with Shawn Mendes

if you subtract 16 from both sides you would get x=8

Final answer:

To convert 720° to radians, multiply by π/180 to get 4π rad. This shows that 720° is equivalent to 4π radians.

Explanation:

To convert 720° to radians, we use the relationship that 1 revolution equals 360° or 2π radians. Therefore, to convert degrees to radians, you multiply the number of degrees by π/180. In this case:

720° × (π rad / 180°) = 4π rad

Thus, 720° is equal to 4π radians. The concept of angular velocity is related to radians as it is the rate of change of an angle with time, and using radians can be especially useful in calculations involving angular motion.

Answer: Last Option

[tex]H (m) = 25 + 3m\\H (m) = 10 + 8m[/tex]

Step-by-step explanation:

The initial height of the plant of species A is 25 cm and grows 3 centimeters per month.

If m represents the number of months elapsed then the equation for the height of the plant of species A is:

[tex]H (m) = 25 + 3m[/tex]

For species B the initial height is 10 cm and it grows 8 cm each month

If m represents the number of months elapsed then the equation for the height of the plant of species B is:

[tex]H (m) = 10 + 8m[/tex]

Finally, the system of equations is:

[tex]H (m) = 25 + 3m\\H (m) = 10 + 8m[/tex]

The answer is the last option

Answer: 0.67 (to 3 s.f)

Step-by-step explanation:

f(x)=g(x)

-3x + 4 = 2

-3x = -2

x = 2/3

x = 0.67

Hope it helped

Answer:

Answer 64*sqrt(2)

Step-by-step explanation:

Givens

c = 128 cm

a = b = ??

formula

a^2 + b^2 = c^2                            combine the two equal legs.

2a^2 = c^2                                    Substitute 128 for c

2a^2 = 128^2                                Square

2a^2 = 16384                               Divide by 2

a^2 = 16384/2                  

a^2 = 8192                                   Factor (8192)

8192 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2    count the 2s

8192 = 2^13                                 Break 13 into 2 equal values with 1 left over

sqrt(8192) = sqrt(2^6   *   2^6    *    2^1)

sqrt(8192) = 2^6 * sqrt(2)

The length of one leg is 64*sqrt(2)

Answer:

Length of one leg of the given triangle will be 64√2 cm.

Step-by-step explanation:

Length of the hypotenuse of a 45°- 45°- 90° triangle has been given as 128 cm.

Since two angles other than 90° are of same measure so other two sides of the triangle will be same in measure.

Therefore, by Pythagoras theorem,

Hypotenuse² = Leg(1)² + Leg(2)²

Let the measure of both the legs is x cm

(128)² = 2x²

16384 = 2x²

x² = [tex]\frac{16384}{2}[/tex]

x² = 8192

x = √8192

  = 64√2 cm

Therefore, length of one leg of the given triangle will be 64√2 cm.

Answer:

-44

Step-by-step explanation:

We have the expression

[tex]-2|6x - y|[/tex]

We need to find the value of the expression when x = -3 and y = 4

Then we must replace the variable with the number -3 and the variable y with the number 4

This is:

[tex]-2|6(-3) - (4)|[/tex]

[tex]-2|-18 - 4|[/tex]

[tex]-2|-22|[/tex]

Remember that the absolute value always results in a positive number.

So

[tex]-2|-22| = -2(22)=-44[/tex]

the answer is -44

Answer:

The correct answer is -44

Step-by-step explanation:

Points to remember

|x| = x

|-x| = x

To find the value of  –2|6x – y|

We have  –2|6x – y|  When x = -3 and y = 4

Substitute the value of x and y

–2|6x – y| =  –2|(6 * -3)  – 4|

 = -2|-18 - 4|

 = -2|-22|

 = -2 * 22

 = -44

Therefore the value of –2|6x – y|  when x = -3 and y = 4

–2|6x – y|

Answer:

Find the place value you want (the "rounding digit") and look at the digit just to the right of it.

If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.

If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.

Step-by-step explanation:

Step-by-step explanation: To round a decimal, you first need to know the indicated place value position you want to round to. This means that you want to first find the digit in the rounding place which will usually be underlined.

Once you locate the digit in the rounding place, look to the left of that digit. Now, the rules of rounding tell us that if a number is less than 4, we round down but if a number is greater than or equal to 5, we round up.

I'll show an example.

Round the following decimal to the indicated place value.

0.8005

To round 0.8005 to the indicated place value position, first find the digit in the rounding place which in this case is the 0 in the thousandths place.

Next, find the digit to the right of the rounding place which in this case is 5. Since 5 is greater than or equal to 5, we round up.

This means we add 1 to the digit in the rounding place so 0 becomes 1. So we have 0.801. Now, we change all digits to the right of the rounding place to 0 so 5 changes to 0.

Finally, we can drop of any zeroes to the right of our decimal as long as they're also to the right of the rounding position.

So we can write 0.8010 as 0.801.

Image provided.