The triangle below is equilateral. Find the length of side � x in simplest radical form with a rational denominator. x 6

PLEASE GIVE BRAINLIEST!

thank you and have a good day :)

Answer:

YES, x = 8

Step-by-step explanation:

plug in 8 for x and see if both sides are equal

3/4 times 8 = 24/4 or 6

Answer:

Step-by-step explanation:

If we solve it as....

[tex]\mathrm{\cfrac{3}{4}x=6}[/tex]

[tex]\mathrm{4\times\cfrac{3}{4}x=6\times\:4}[/tex]

[tex]\mathrm{3x=24}[/tex]

[tex]\mathrm{\cfrac{3x}{3}=\cfrac{24}{3}}[/tex]

[tex]\mathrm{x=8}[/tex]

Yes, 8 would be the solution!

___________________

Hope this helps!

Step-by-step explanation:

If we use direct substitution, we will get

[tex] \frac{0}{0} [/tex]

Which is intermediate from so we must use.algebraic manipulation

Let's divide everything by x

We would get

[tex] \frac{x + 1}{1} [/tex]

So the limit as x approaches 0 is

[tex]1[/tex]

Proof using a graph:

As x gets close and closer to 0, f(x) approaches 1. Limits does not care about discontinuity, only what the function gets closer to.

Answer:

Step-by-step explanation:

To find the total number of seats in the theater, we can use the formula for the sum of an arithmetic series, which is given by:

S = n/2 * (a_1 + a_n)

where n is the number of terms in the series, a_1 is the first term, and a_n is the last term.

In this case, the first term is 25 seats and the last term is 25 + (38-1) * 4 seats (since the number of seats in each row increases by 4 each time). So, we have:

n = 38 (the number of rows)

a_1 = 25

a_n = 25 + (38-1) * 4 = 25 + 37 * 4 = 25 + 148 = 173

Now, we can substitute these values into the formula:

S = n/2 * (a_1 + a_n) = 38/2 * (25 + 173) = 19 * 198 = 3,762

So, the total number of seats in the theater is 3,762, which corresponds to option O3,762.

Answer: 12.72 ft.

Step-by-step explanation:

[tex]\frac{6}{8.3} = \frac{x}{17.6} \\\\ 8.3x= 105.6\\\\x= 12.72[/tex]

Another form of representing the cost of the book is (75/100)×D.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

We know, Percentages and decimals are related.

10% in decimal form is equivalent to (10/100) - 0.1 in decimal.

An expression that represents the sale day book price is 0.75D.

Another expression that would represent the cost of the book priced 'D' would be,

= (75/100)×D.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ9

Answer: Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.

The accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.

Step-by-step explanation:

To calculate Victor's annual income after 12 years as a teacher, we need to find the future value of his starting salary of $40,000 after 12 years with an average 4 percent raise every year.

Using the formula for the future value of a single amount (FV = PV * (1 + r)^n), where PV is the present value, r is the interest rate, and n is the number of years, we can calculate the future value as follows:

FV = $40,000 * (1 + 0.04)^12 = $47,564

So, Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.

To calculate the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year, we need to use the formula for the future value of a series of equal amounts (FV = A * (1 + r)^n - 1 / r), where A is the annual payment and r is the interest rate.

Plugging in the values, we get:

FV = $3,000 * (1 + 0.05)^12 - 1 / 0.05 = $41,592

So, the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.

A graph of the equation under this condition {(x, y): x + y = 5)} is shown in the image attached below.

In Mathematics, an ordered pair simply refers to a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Next, we would determine the ordered pairs that satisfies the given linear function in standard form.

When the value of x = 1, the output value of this linear function is given by;

y = 5 - x

y = 5 - 1

y = 4 ⇒ (1, 4)

When the value of x = 0, the output value of this linear function is given by;

y = 5 - x

y = 5 - 0

y = 5 ⇒ (0, 5).

When the value of x = 2, the output value of this linear function is given by;

y = 5 - x

y = 5 - 2

y = 0 ⇒ (2, 3).

Read more on ordered pair here: https://brainly.com/question/16553312

#SPJ1

Selma needs to leave the money in the new account for at least one year, option A. 1 to recover the penalty paid.

Assuming Selma wants to recover the penalty paid using the extra interest earned in the new account, she needs to calculate the amount of time it will take for the new account's interest to make up for the penalty paid.

Let P be the initial amount of money in Selma's current account. The penalty for closing the account is 5% of P, which is 0.05P.

If Selma leaves the money in the current account for one year, she will earn simple interest of 5% of P, which is 0.05P. So at the end of the year, the balance in the current account will be P + 0.05P = 1.05P.

If Selma transfers the money to the new account, it will earn compound interest of 8% per year, compounded quarterly. The quarterly interest rate is 8%/4 = 2%.

After one quarter, the balance in the new account will be:

P*(1 + 2%/4) = P*1.02

After two quarters, the balance will be:

P1.02(1 + 2%/4) = P*1.02^2

After three quarters, the balance will be:

P1.02^2(1 + 2%/4) = P*1.02^3

After four quarters (i.e., one year), the balance will be:

P1.02^3(1 + 2%/4) = P*1.02^4

So at the end of one year, Selma will have 1.05P in the current account and P*1.02^4 in the new account.

To recover the penalty of 0.05P, Selma needs the balance in the new account to be at least 1.05P. That is,

P*1.02^4 >= 1.05P

Simplifying, we get:

1.02^4 >= 1.05

Taking the fourth root of both sides, we get:

1.02 >= 1.05^(1/4)

Using a calculator, we get:

1.02 >= 1.01298

So Selma needs to leave the money in the new account for at least one year to recover the penalty paid.

learn more about compound interest: https://brainly.com/question/24274034

#SPJ1

The required perimeter of the triangle with vertices (-9,-6), (-5, 0), and (10,-7) is 42.72 units.

The distance between two points (x₁, y₁) and (x₂, y₂) in the plane can be found using the distance formula,

d = √((x₂- x₁² + (y₂ - y₁)²)

Here

Using the above formula, we can find the length of each side of the triangle:

Length of the first side:

d = √((-5 - (-9))² + (0 - (-6))²)
   = √(4² + 6²)
   = √52 = 7.2

Similarly, the length of the second and third sides:

d =√274 = 16.5

Length of the third side:

d =  √362 = 19.02

Finally, the perimeter of the triangle is the sum of the lengths of its sides, P = 7.2 + 16.5 + 19.02
P = 42.72 units

So, the perimeter of the triangle is approximately 42.72 units.

Learn more about the distance formula here:
https://brainly.com/question/29754800
#SPJ1

The equation to represent the total cost, y, for x months is y = 12x + 30.

From the given table, we can observe that the total cost increases by $12 for each additional month of usage.

This means that the rate of change, or the slope of the equation, is $12 per month.

We can represent this relationship using the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope (rate of change) is $12, and the y-intercept can be determined by examining the table. When x = 0 months, the total cost is $30. Therefore, the y-intercept is $30.

Putting it all together, the equation to represent the total cost, y, for x months is:

y = 12x + 30

Learn more about the equations here:

brainly.com/question/10413253

#SPJ5

Answer:

54 and 47

Step-by-step explanation:

Lets first number be "x" and second number be "y"

x = y + 7

x + y = 101

(y + 7) + y = 101

2y + 7 = 101

2y = 94

y = 47

x = 47 + 7

x = 54

The value of sin(tetha/2) is ±√½(1-8/√113)

In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45°), and so on. If θ is an angle, then the half angle is represented by θ/2.

if tan(tetha) = 7/8

this means that 7 is the opposite and 8 is the adjacent

hyp² = opp² +adj²

hyp² = 49+64

hyp = √113

sin(tetha/2) = ±√1-cos(tetha))/2

= ±√1-(8/√113))/2

therefore the value is sin(tetha)/2

= ±√1-(8/√113))/2 or ±√½(1-8/√113)

learn more about half angles from

https://brainly.com/question/2254074

#SPJ1

1) Based on the percentage of the downpayment, the total payment made for the store item is $1,100, which includes a finance charge or interest of $100.

2) The monthly payment for 12 installments is $87.50.

The total cost of the item is based on the downpayment's equivalent percentage (proportion).

A proportion is the equation of two or more ratios.

Finance Charge (Interest) = $100

Downpayment = $50 or 5%

Installment period = 12 months

Cost of item = $1,000 ($50/5%)

Total payment = $1,100 ($1,000 + $100)

Monthly payment = $87.50 ($1,100 - $50)/12

Learn more about proportions and percentages at https://brainly.com/question/1496357.

#SPJ1

The downpayment is 5% of the total cost of the item.

Answer:  I can explain the steps for calculating descriptive statistics for the given data.

For the "number" column:

Mean: To find the mean, add up all the values and divide by the number of values.

Median: To find the median, arrange the values in numerical order and find the middle value. If there is an even number of values, take the average of the two middle values.

Mode: To find the mode, find the value that appears most frequently. If there is no value that appears more than once, then there is no mode.

Maximum: To find the maximum, find the largest value in the list.

Minimum: To find the minimum, find the smallest value in the list.

For the "percent" column:

Mean: To find the mean, add up all the values and divide by the number of values.

Median: To find the median, arrange the values in numerical order and find the middle value. If there is an even number of values, take the average of the two middle values.

Mode: To find the mode, find the value that appears most frequently. If there is no value that appears more than once, then there is no mode.

Maximum: To find the maximum, find the largest value in the list.

Minimum: To find the minimum, find the smallest value in the list.

Regarding the statistics on children whose parents do not have secure employment, it can be determined how each state compares to the surrounding states by comparing the mean, median, and mode of the "number" and "percent" columns. The state with the best or worst data can be determined by comparing the maximum and minimum values in each column. The value that gives a better comparison would depend on the purpose of the analysis. If the goal is to understand the overall number of children affected, then the "number" column would be more appropriate. If the goal is to understand the proportion of children affected in each state, then the "percent" column would be more appropriate.

Step-by-step explanation:

Answer:

4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.

Step-by-step explanation:

To find the weight of 4.4 cubic feet of water in pounds, we need to find the number of gallons it contains and then multiply it by the weight of one gallon of water.

1 cubic foot = 7.48 gallons

So, 4.4 cubic feet = 4.4 * 7.48 = 32.912 gallons

And the weight of 32.912 gallons of water in pounds is:

32.912 gallons * 8.33 pounds/gallon = 273.5016 pounds

To convert this weight to tons, we divide the weight in pounds by 2000:

273.5016 pounds / 2000 = 0.13676 tons

So, 4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.

Answer:

The sum of the series is 260.

------------------------

Each term of given series is expressed as:

This is an arithmetic progression with 13 terms and the first and last terms are:

Use the sum of the first terms of AP formula:

Answer:

The sum of the series is 260.

Step-by-step explanation:

[tex]\displaystyle \sum^{13}_{n=1}(3n-1)[/tex]

The given sigma notation means:

As (3n - 1) is linear, the series is arithmetic.

The first term (n = 1) is:

The second term (n = 2) is:

The third term (n = 3) is:

… and the last term (n = 13) is:

Therefore, we need to find 2 + 5 + 8 + ... + 38.

Since we know that the first term, a, is 2, the last term, l, is 38, and the common difference, d, is 3, we can use the sum of the first n terms formula to calculate the sum of the series of the first 13 terms.

[tex]\begin{aligned}\text{Using:} \quad S_{n}&=\dfrac{1}{2}n(a+l)\\\\\implies S_{13}&=\dfrac{1}{2}(13)(2+38)\\\\&=\dfrac{1}{2}(13)(40)\\\\ &=\dfrac{520}{2}\\\\&=260\end{aligned}[/tex]

Therefore, the sum of the series is 260.

Answer: |-16| =x

- (-16)= x

x = 16

Step-by-step explanation:

thank you

The amount invested in the account that earns 10% interest is $4,000 and the amount invested in the account that earns 11% interest is $3,000.

The system of equations that represent the information in the question is:

a + b = 7000 equation 1

0.1a + 0.11b = 730 equation 2

Where:

a = amount invested in the account that earns 10% interest

b = amount invested in the account that earns 11% interest

The elimination method would be used to solve the equations.

Multiply equation 1 by 0.1

0.1a + 0.1b = 700 equation 3

Subtract equation 3 from equation 2

0.01b = 30

Divide both sides of the equation by 0.01

b = 30 / 0.01

b = 3000

Substitute for b in equation 1:

a + 3000 = 7000

a = 7,000 - 3000

a = 4000

To learn more about system of  equations, please check: https://brainly.com/question/25875552

#SPJ1

The height of the tulip sculpture is 66 inches, which is twice the height of the sunflower sculpture.

From the question, we have the following parameters that can be used in our computation:

Sunflower = 33 inches

Tulip = Twice of sunflower

Using the above as a guide, we have the following:

Tulip = 2 * Sunflower

substitute the known values in the above equation, so, we have the following representation

Tulip = 2 * 33

Evaluate

Tulip = 66

Therefore, the height of the tulip sculpture is 66 inches.

Read more about scale factor at

https://brainly.com/question/15891755

#SPJ1

Answer:

  C.  Solve for the variable y.

Step-by-step explanation:

You want to know what needs to be done to an equation to find the slope and y-intercept.

The slope-intercept form of the equation for a line is ...

  y = mx + b

This is a polynomial equation written in standard form with the terms in decreasing order of the power of the variable. In this equation, the coefficient 'm' is the slope of the line, and the constant 'b' is the y-intercept on the graph.

This equation can be obtained from other forms of the equation for a line by solving for y and arranging the terms to match this form. That is, to find the slope and y-intercept, what needs to be done is ...

  C.  Solve for the variable y.

__

Additional comment

The description "standard form" as used above applies to polynomials in general. Specific polynomial equations, as for lines, circles, ellipses, hyperbolas, have their own "standard form."

The form called "standard form" for a linear equation is ...

  ax +by = c

where a, b, c are mutually prime integers with a > 0. In the case of a horizontal line, b > 0.

<95141404393>

Answer:

The circumference of one of the semicircles with a radius of 7 meters would be approximately 21.98 meters.

Step-by-step explanation:

The circumference of a circle can be calculated using the formula:

C = 2πr

where C is the circumference, π (pi) is approximately equal to 3.14, and r is the radius of the circle.

For a semicircle with a radius of 7 meters, the circumference can be calculated as follows: Because the semicircle is a half circle, then:

C = (2πr)/2= 3.14 × 7 = 21.98 meters

So, the circumference of one of the semicircles with a radius of 7 meters would be approximately 21.98 meters.

Answer:

The circumference of one of the semicircles is 21.98 m.

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.

A semicircle is half a circle, therefore the length of the curved part of the circumference of a semicircle is half the circumference of a circle: πr.

Given the radius of one of the semicircles is 7 m and π ≈ 3.14, the circumference of the semicircle is:

⇒ C = 3.14 · 7

⇒ C = 21.98 m

The measure of ∠B of the right angle is 152°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ABC

Now , the measure of ∠A = 2x - 8

The measure of ∠B = 3x + 5

And , angle A and angle B make a right angle

On simplifying the equation , we get

2x - 8 = 90

Adding 8 on both sides of the equation , we get

2x = 98

Divide by 2 on both sides of the equation , we get

x = 49

Substitute the value of x in equation , we get

∠B = 3 ( 49 ) + 5

The measure of ∠B = 152°

Hence , the angle is ∠B = 152°

To learn more about triangle click :

https://brainly.com/question/16739377

#SPJ1

On solving the provided question, we can say that by fraction, 4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

by fraction

4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.

16/12+9/12+8/12+9/12=42/12=3 and 1/2 cups.

20/3.5=5.7 or 6

To know more about fraction visit:

https://brainly.com/question/10354322

#SPJ1

Answer:

x = 50 tablets

Step-by-step explanation:

Ket's call the number of tablets taken in a week "x".

A typical dose for a 100-pound person is 22 mg every six hours, so in 24 hours, they would take 22 mg * 24 hours / 6 hours = 88 mg.

In one week, they would take 88 mg * 7 days = 616 mg.

And since each tablet is 12.3 mg, they would take 616 mg / 12.3 mg/tablet = 50 tablets in a week.

So the answer is x = 50 tablets.

Answer:

0.4850 knots.

Step-by-step explanation:

To convert the speed of the California Current from centimeters per second to knots, we can use the conversion factor of 1 knot = 0.514444444 cm/s.

So, 0.25 cm/s * 1 knot / 0.514444444 cm/s = 0.4850 knots.

Therefore, the California Current moves at a speed of approximately 0.4850 knots.

Answer:

The original number is 86.

Step-by-step explanation:

The only two-digit numbers whose digits sum to 14 are:

If we reverse and double the original number:

If we add the result of reversing and doubling the original number to the original number:

As the sum of adding the result of reversing and doubling the original number to the original number is 222, the original number must be 86.

Step-by-step explanation:

To plot the integer -7 on the number line, we can place it to the left of 0. The number line would look like this:

-10 -8 -7 -6 -4 -2 0 2 4 6 8 10

The distance between 0 and -7 is 7 units, since 0 is 7 units to the right of -7.

The absolute value of -7 is 7, since the absolute value of a number is its distance from 0 on the number line.

The magnitude of -7 is also 7, which is the same as its absolute value. The magnitude of a number refers to its size or absolute value, regardless of its sign. In this case, the magnitude of -7 is 7.